ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 09:07:15 AM UTC 2026

% Result   : Theorem 32.68s 33.14s
% Output   : Proof 32.92s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
    ! [V_g_2,V_f_2] :
      ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
     => V_f_2 = V_g_2 ),
    file('theBenchmark.p',fact_ext) ).

fof(fact_triple__valid__Suc,axiom,
    ! [V_t,V_n,T_a] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
     => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ),
    file('theBenchmark.p',fact_triple__valid__Suc) ).

fof(fact_evaln_OBody,axiom,
    ! [V_s1,V_n,V_s0,V_pn] :
      ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
     => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ),
    file('theBenchmark.p',fact_evaln_OBody) ).

fof(fact_evaln_Oequations_I9_J,axiom,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
    <=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2)),V_a2_2,V_a3_2,V_a4_2) ),
    file('theBenchmark.p',fact_evaln_Oequations_I9_J) ).

fof(fact_evaln_OCall,axiom,
    ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2)
     => c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes))) ),
    file('theBenchmark.p',fact_evaln_OCall) ).

fof(fact_evaln_Oequations_I10_J,axiom,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2),V_a2_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)))
    <=> ? [B_s1] :
          ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2)),V_a4_2,B_s1)
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I10_J) ).

fof(fact_evaln__Suc,axiom,
    ! [V_s_H,V_n,V_s,V_c] :
      ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
     => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ),
    file('theBenchmark.p',fact_evaln__Suc) ).

fof(fact_Body__triple__valid__Suc,axiom,
    ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_b] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
    <=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ),
    file('theBenchmark.p',fact_Body__triple__valid__Suc) ).

fof(fact_evaln__elim__cases_I7_J,axiom,
    ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2),V_s_2,V_n_2,V_s1_2)
     => ~ ! [B_s1] :
            ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
           => ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1) ) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I7_J) ).

fof(fact_evaln__elim__cases_I6_J,axiom,
    ! [V_s1,V_n,V_s,V_P] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
     => ~ ! [B_n] :
            ( V_n = hAPP(c_Nat_OSuc,B_n)
           => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I6_J) ).

fof(fact_evalc_OCall,axiom,
    ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_s1_2))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ),
    file('theBenchmark.p',fact_evalc_OCall) ).

fof(fact_evalc_Oequations_I10_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes))))
    <=> ? [B_s1] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I10_J) ).

fof(fact_evaln_OLocal,axiom,
    ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
      ( c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2)
     => c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2))) ),
    file('theBenchmark.p',fact_evaln_OLocal) ).

fof(fact_evalc_OBody,axiom,
    ! [V_s1,V_s0,V_pn] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ),
    file('theBenchmark.p',fact_evalc_OBody) ).

fof(fact_evalc__elim__cases_I6_J,axiom,
    ! [V_s1,V_s,V_P] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I6_J) ).

fof(fact_evalc_OLocal,axiom,
    ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ),
    file('theBenchmark.p',fact_evalc_OLocal) ).

fof(fact_triple_Oinject,axiom,
    ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
      ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
    <=> ( V_fun2_2 = V_fun2_H_2
        & V_com_2 = V_com_H_2
        & V_fun1_2 = V_fun1_H_2 ) ),
    file('theBenchmark.p',fact_triple_Oinject) ).

fof(fact_com__det,axiom,
    ! [V_u,V_t,V_s,V_c] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
       => V_u = V_t ) ),
    file('theBenchmark.p',fact_com__det) ).

fof(fact_evaln__evalc,axiom,
    ! [V_t,V_n,V_s,V_c] :
      ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ),
    file('theBenchmark.p',fact_evaln__evalc) ).

fof(fact_eval__eq,axiom,
    ! [V_t_2,V_s_2,V_c_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
    <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ),
    file('theBenchmark.p',fact_eval__eq) ).

fof(fact_evalc_Oequations_I3_J,axiom,
    ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))))
    <=> ? [B_s1] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I3_J) ).

fof(fact_triple__valid__def2,axiom,
    ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_b] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2))
    <=> ! [B_Z,B_s] :
          ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
         => ! [B_s_H] :
              ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
             => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ),
    file('theBenchmark.p',fact_triple__valid__def2) ).

fof(fact_evalc_Oequations_I9_J,axiom,
    ! [V_a3_2,V_a2_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
    <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ),
    file('theBenchmark.p',fact_evalc_Oequations_I9_J) ).

fof(fact_evaln_Oequations_I3_J,axiom,
    ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2),V_a2_2,V_a5_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))
    <=> ? [B_s1] :
          ( c_Natural_Oevaln(V_a1_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2)),V_a5_2,B_s1)
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I3_J) ).

fof(fact_evalc__elim__cases_I7_J,axiom,
    ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_s1_2))
     => ~ ! [B_s1] :
            ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),B_s1)) ) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I7_J) ).

fof(fact_evalc__elim__cases_I3_J,axiom,
    ! [V_t_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s_2),V_t_2))
     => ~ ! [B_s1] :
            ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1)) ) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I3_J) ).

fof(fact_evaln__elim__cases_I3_J,axiom,
    ! [V_t_2,V_n_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s_2,V_n_2,V_t_2)
     => ~ ! [B_s1] :
            ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
           => ~ c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1) ) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I3_J) ).

fof(fact_com_Osimps_I43_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I43_J) ).

fof(fact_com_Osimps_I42_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I42_J) ).

fof(fact_com_Osimps_I40_J,axiom,
    ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    file('theBenchmark.p',fact_com_Osimps_I40_J) ).

fof(fact_com_Osimps_I63_J,axiom,
    ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2),
    file('theBenchmark.p',fact_com_Osimps_I63_J) ).

fof(fact_com_Osimps_I41_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I41_J) ).

fof(fact_com_Osimps_I62_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I62_J) ).

fof(fact_triple_Orecs,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    file('theBenchmark.p',fact_triple_Orecs) ).

fof(fact_triple_Osimps_I2_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    file('theBenchmark.p',fact_triple_Osimps_I2_J) ).

fof(fact_com_Osimps_I7_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
      ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2)
    <=> ( V_fun_2 = V_fun_H_2
        & V_pname_2 = V_pname_H_2
        & V_vname_2 = V_vname_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I7_J) ).

fof(fact_com_Osimps_I6_J,axiom,
    ! [V_pname_H_2,V_pname_2] :
      ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
    <=> V_pname_2 = V_pname_H_2 ),
    file('theBenchmark.p',fact_com_Osimps_I6_J) ).

fof(fact_vname_Osimps_I2_J,axiom,
    ! [V_loc_H_2,V_loc_2] :
      ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
    <=> V_loc_2 = V_loc_H_2 ),
    file('theBenchmark.p',fact_vname_Osimps_I2_J) ).

fof(fact_com_Osimps_I2_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
      ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
    <=> ( V_com_2 = V_com_H_2
        & V_fun_2 = V_fun_H_2
        & V_loc_2 = V_loc_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I2_J) ).

fof(fact_vname_Orecs_I2_J,axiom,
    ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2),
    file('theBenchmark.p',fact_vname_Orecs_I2_J) ).

fof(fact_vname_Osimps_I6_J,axiom,
    ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2),
    file('theBenchmark.p',fact_vname_Osimps_I6_J) ).

fof(fact_Body__triple__valid__0,axiom,
    ! [V_Q_2,V_pn_2,V_P_2,T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),
    file('theBenchmark.p',fact_Body__triple__valid__0) ).

fof(fact_evalc_OAssign,axiom,
    ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))),
    file('theBenchmark.p',fact_evalc_OAssign) ).

fof(fact_evalc__elim__cases_I2_J,axiom,
    ! [V_t_2,V_s_2,V_a_2,V_X_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
     => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I2_J) ).

fof(fact_evaln_OAssign,axiom,
    ! [V_n_2,V_s_2,V_a_2,V_X_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2))),
    file('theBenchmark.p',fact_evaln_OAssign) ).

fof(fact_evaln__elim__cases_I2_J,axiom,
    ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
     => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I2_J) ).

fof(fact_n__not__Suc__n,axiom,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    file('theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_Suc__n__not__n,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    file('theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_nat_Oinject,axiom,
    ! [V_nat_H_2,V_nat_2] :
      ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
    <=> V_nat_2 = V_nat_H_2 ),
    file('theBenchmark.p',fact_nat_Oinject) ).

fof(fact_Suc__inject,axiom,
    ! [V_y,V_x] :
      ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
     => V_x = V_y ),
    file('theBenchmark.p',fact_Suc__inject) ).

fof(fact_WTs__elim__cases_I8_J,axiom,
    ! [V_a_2,V_P_2,V_X_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
     => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I8_J) ).

fof(fact_WTs__elim__cases_I3_J,axiom,
    ! [V_c_2,V_a_2,V_Y_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
     => hBOOL(hAPP(c_Com_OWT,V_c_2)) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I3_J) ).

fof(fact_com_Osimps_I1_J,axiom,
    ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
      ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
    <=> ( V_fun_2 = V_fun_H_2
        & V_vname_2 = V_vname_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I1_J) ).

fof(fact_WT_Oequations_I2_J,axiom,
    ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))),
    file('theBenchmark.p',fact_WT_Oequations_I2_J) ).

fof(fact_WT_OAssign,axiom,
    ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))),
    file('theBenchmark.p',fact_WT_OAssign) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    file('theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
    file('theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__not__Suc,axiom,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    file('theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_WT_Oequations_I3_J,axiom,
    ! [V_a1_2,V_a3_2,V_a2_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
    <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ),
    file('theBenchmark.p',fact_WT_Oequations_I3_J) ).

fof(fact_WT_OLocal,axiom,
    ! [V_a_2,V_Y_2,V_c_2] :
      ( hBOOL(hAPP(c_Com_OWT,V_c_2))
     => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ),
    file('theBenchmark.p',fact_WT_OLocal) ).

fof(fact_com_Osimps_I30_J,axiom,
    ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    file('theBenchmark.p',fact_com_Osimps_I30_J) ).

fof(fact_com_Osimps_I31_J,axiom,
    ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I31_J) ).

fof(fact_com_Osimps_I32_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I32_J) ).

fof(fact_com_Osimps_I22_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I22_J) ).

fof(fact_com_Osimps_I33_J,axiom,
    ! [V_fun_2,V_vname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I33_J) ).

fof(fact_com_Osimps_I23_J,axiom,
    ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I23_J) ).

fof(fact_WT_Oequations_I8_J,axiom,
    ! [V_a3_2,V_a1_2,V_a2_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
    <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ),
    file('theBenchmark.p',fact_WT_Oequations_I8_J) ).

fof(fact_WT_OCall,axiom,
    ! [V_a_2,V_X_2,V_pn_2] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
     => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ),
    file('theBenchmark.p',fact_WT_OCall) ).

fof(fact_evaln_Oequations_I2_J,axiom,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_a1_2,V_a2_2),V_a3_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2))),
    file('theBenchmark.p',fact_evaln_Oequations_I2_J) ).

fof(fact_evalc_Oequations_I2_J,axiom,
    ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))),
    file('theBenchmark.p',fact_evalc_Oequations_I2_J) ).

fof(fact_triple_Osize_I1_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_triple_Osize_I1_J) ).

fof(fact_vname_Osize_I2_J,axiom,
    ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_vname_Osize_I2_J) ).

fof(fact_triple_Osize_I2_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_triple_Osize_I2_J) ).

fof(fact_vname_Osize_I4_J,axiom,
    ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_vname_Osize_I4_J) ).

fof(fact_vname_Osimps_I5_J,axiom,
    ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2),
    file('theBenchmark.p',fact_vname_Osimps_I5_J) ).

fof(fact_vname_Orecs_I1_J,axiom,
    ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2),
    file('theBenchmark.p',fact_vname_Orecs_I1_J) ).

fof(fact_com_Osize_I8_J,axiom,
    ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I8_J) ).

fof(fact_com_Osize_I2_J,axiom,
    ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I2_J) ).

fof(fact_com_Osize_I7_J,axiom,
    ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I7_J) ).

fof(fact_com_Osize_I16_J,axiom,
    ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I16_J) ).

fof(fact_com_Osize_I10_J,axiom,
    ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I10_J) ).

fof(fact_com_Osize_I15_J,axiom,
    ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I15_J) ).

fof(fact_vname_Osimps_I1_J,axiom,
    ! [V_glb_H_2,V_glb_2] :
      ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
    <=> V_glb_2 = V_glb_H_2 ),
    file('theBenchmark.p',fact_vname_Osimps_I1_J) ).

fof(fact_vname_Osize_I3_J,axiom,
    ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_vname_Osize_I3_J) ).

fof(fact_vname_Osize_I1_J,axiom,
    ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_vname_Osize_I1_J) ).

fof(fact_vname_Osimps_I3_J,axiom,
    ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H),
    file('theBenchmark.p',fact_vname_Osimps_I3_J) ).

fof(fact_vname_Osimps_I4_J,axiom,
    ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb),
    file('theBenchmark.p',fact_vname_Osimps_I4_J) ).

fof(fact_com_Osize_I11_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I11_J) ).

fof(fact_com_Osize_I3_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I3_J) ).

fof(fact_WT_OBody,axiom,
    ! [V_pn] :
      ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
     => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ),
    file('theBenchmark.p',fact_WT_OBody) ).

fof(fact_WT_Oequations_I7_J,axiom,
    ! [V_a_2] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
    <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ),
    file('theBenchmark.p',fact_WT_Oequations_I7_J) ).

fof(fact_zero__reorient,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Ozero(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
      <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__reorient) ).

fof(fact_of__nat__aux_Osimps_I2_J,axiom,
    ! [V_i_2,V_n_2,V_inc_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ),
    file('theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

fof(fact_com_Osize_I9_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I9_J) ).

fof(fact_com_Osize_I1_J,axiom,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I1_J) ).

fof(fact_of__nat__aux_Osimps_I1_J,axiom,
    ! [V_i_2,V_inc_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ),
    file('theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(fact_evalc__evaln,axiom,
    ! [V_t,V_s,V_c] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
     => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ),
    file('theBenchmark.p',fact_evalc__evaln) ).

fof(fact_zero__less__Suc,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))),
    file('theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__zeroE,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_less__zeroE) ).

fof(fact_Suc__mono,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_Suc__mono) ).

fof(fact_lessI,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))),
    file('theBenchmark.p',fact_lessI) ).

fof(fact_evaln__elim__cases_I1_J,axiom,
    ! [V_t,V_n,V_s] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
     => V_t = V_s ),
    file('theBenchmark.p',fact_evaln__elim__cases_I1_J) ).

fof(fact_evaln_OSkip,axiom,
    ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s),
    file('theBenchmark.p',fact_evaln_OSkip) ).

fof(fact_evalc_OSkip,axiom,
    ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
    file('theBenchmark.p',fact_evalc_OSkip) ).

fof(fact_evalc__elim__cases_I1_J,axiom,
    ! [V_t,V_s] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
     => V_t = V_s ),
    file('theBenchmark.p',fact_evalc__elim__cases_I1_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_add__left__cancel,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Ocancel__semigroup__add(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
      <=> V_b_2 = V_c_2 ) ),
    file('theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__right__cancel,axiom,
    ! [V_c_2,V_a_2,V_b_2,T_b] :
      ( class_Groups_Ocancel__semigroup__add(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
      <=> V_b_2 = V_c_2 ) ),
    file('theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__less__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
    file('theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__strict__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__left__imp__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Ocancel__ab__semigroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__right__imp__eq,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_nat__less__cases,axiom,
    ! [V_P_2,V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
       => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
     => ( ( V_m_2 = V_n_2
         => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
           => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
         => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_nat__less__cases) ).

fof(fact_add__lessD1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ),
    file('theBenchmark.p',fact_add__lessD1) ).

fof(fact_less__add__eq__less,axiom,
    ! [V_n,V_m,V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_add__less__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
    file('theBenchmark.p',fact_add__less__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_add__less__mono1) ).

fof(fact_trans__less__add2,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
    file('theBenchmark.p',fact_trans__less__add2) ).

fof(fact_trans__less__add1,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
    file('theBenchmark.p',fact_trans__less__add1) ).

fof(fact_less__not__refl3,axiom,
    ! [V_t,V_s] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
     => V_s != V_t ),
    file('theBenchmark.p',fact_less__not__refl3) ).

fof(fact_less__not__refl2,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
     => V_m != V_n ),
    file('theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__irrefl__nat,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    file('theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_add__neg__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__neg__neg) ).

fof(fact_add__pos__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__pos__pos) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [V_y,V_x] :
      ( V_x != V_y
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_nat__add__assoc,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_nat__add__left__commute,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)),
    file('theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__add__commute) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_nat__neq__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( V_m_2 != V_n_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_not__add__less2,axiom,
    ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
    file('theBenchmark.p',fact_not__add__less2) ).

fof(fact_not__add__less1,axiom,
    ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
    file('theBenchmark.p',fact_not__add__less1) ).

fof(fact_less__not__refl,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    file('theBenchmark.p',fact_less__not__refl) ).

fof(fact_add__gr__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
    file('theBenchmark.p',fact_add__gr__0) ).

fof(fact_less__add__Suc1,axiom,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))),
    file('theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))),
    file('theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ),
    file('theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_add__0__left,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__0__left) ).

fof(fact_add__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__0) ).

fof(fact_double__zero__sym,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_double__zero__sym) ).

fof(fact_add__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add__0__right) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_add__is__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_add__is__0) ).

fof(fact_add__eq__self__zero,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
     => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_add__Suc__shift,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_add__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_add__Suc) ).

fof(fact_add__Suc__right,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_add__Suc__right) ).

fof(fact_not__less0,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_not__less0) ).

fof(fact_neq0__conv,axiom,
    ! [V_n_2] :
      ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
    file('theBenchmark.p',fact_neq0__conv) ).

fof(fact_less__nat__zero__code,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_gr__implies__not0,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_gr0I,axiom,
    ! [V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    file('theBenchmark.p',fact_gr0I) ).

fof(fact_Suc__less__SucD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_Suc__lessD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__lessD) ).

fof(fact_less__SucE,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_less__SucE) ).

fof(fact_less__trans__Suc,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ),
    file('theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_Suc__lessI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => ( hAPP(c_Nat_OSuc,V_m) != V_n
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ),
    file('theBenchmark.p',fact_Suc__lessI) ).

fof(fact_less__SucI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_less__SucI) ).

fof(fact_less__antisym,axiom,
    ! [V_m,V_n] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_less__antisym) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [V_m_2,V_n_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
      <=> V_n_2 = V_m_2 ) ),
    file('theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_Suc__less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_less__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_not__less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ),
    file('theBenchmark.p',fact_not__less__eq) ).

fof(fact_evaln_Oequations_I1_J,axiom,
    ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1),
    file('theBenchmark.p',fact_evaln_Oequations_I1_J) ).

fof(fact_evalc_Oequations_I1_J,axiom,
    ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)),
    file('theBenchmark.p',fact_evalc_Oequations_I1_J) ).

fof(fact_WT_Oequations_I1_J,axiom,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    file('theBenchmark.p',fact_WT_Oequations_I1_J) ).

fof(fact_WT_OSkip,axiom,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    file('theBenchmark.p',fact_WT_OSkip) ).

fof(fact_com_Osimps_I19_J,axiom,
    ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I19_J) ).

fof(fact_com_Osimps_I18_J,axiom,
    ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H),
    file('theBenchmark.p',fact_com_Osimps_I18_J) ).

fof(fact_com_Osimps_I9_J,axiom,
    ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I9_J) ).

fof(fact_com_Osimps_I8_J,axiom,
    ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I8_J) ).

fof(fact_com_Osimps_I20_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I20_J) ).

fof(fact_com_Osimps_I10_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I10_J) ).

fof(fact_com_Osimps_I21_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I21_J) ).

fof(fact_com_Osimps_I11_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I11_J) ).

fof(fact_one__is__add,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
    <=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_one__is__add) ).

fof(fact_add__is__1,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_add__is__1) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
    <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ),
    file('theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_less__Suc0,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_less__Suc0) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( ? [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
            & V_m_2 = hAPP(c_Nat_OSuc,B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_WT__bodiesD,axiom,
    ! [V_b,V_pn] :
      ( c_Com_OWT__bodies
     => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
       => hBOOL(hAPP(c_Com_OWT,V_b)) ) ),
    file('theBenchmark.p',fact_WT__bodiesD) ).

fof(fact_pos__add__strict,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_pos__add__strict) ).

fof(fact_even__less__0__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_WTs__elim__cases_I7_J,axiom,
    ! [V_P] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
     => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I7_J) ).

fof(fact_the_Osimps,axiom,
    ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x,
    file('theBenchmark.p',fact_the_Osimps) ).

fof(fact_option_Osimps_I2_J,axiom,
    ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H),
    file('theBenchmark.p',fact_option_Osimps_I2_J) ).

fof(fact_option_Osimps_I3_J,axiom,
    ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_option_Osimps_I3_J) ).

fof(fact_not__Some__eq,axiom,
    ! [T_b,V_x_2] :
      ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
    <=> V_x_2 = c_Option_Ooption_ONone(T_b) ),
    file('theBenchmark.p',fact_not__Some__eq) ).

fof(fact_not__None__eq,axiom,
    ! [T_b,V_x_2] :
      ( V_x_2 != c_Option_Ooption_ONone(T_b)
    <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ),
    file('theBenchmark.p',fact_not__None__eq) ).

fof(fact_option_Osize_I2_J,axiom,
    ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_option_Osize_I2_J) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( V_x != V_y
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
    file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_option_Osize_I1_J,axiom,
    ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_option_Osize_I1_J) ).

fof(fact_option_Oinject,axiom,
    ! [V_a_H_2,V_a_2,T_b] :
      ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
    <=> V_a_2 = V_a_H_2 ),
    file('theBenchmark.p',fact_option_Oinject) ).

fof(fact_double__eq__0__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_nat_Osize_I2_J,axiom,
    ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat_Osize_I4_J) ).

fof(fact_option_Osize_I4_J,axiom,
    ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_option_Osize_I4_J) ).

fof(fact_option_Osize_I3_J,axiom,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_option_Osize_I3_J) ).

fof(fact_add__0__iff,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_add__0__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_com_Osize_I12_J,axiom,
    ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I12_J) ).

fof(fact_com_Osize_I4_J,axiom,
    ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I4_J) ).

fof(fact_com_Osize_I13_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I13_J) ).

fof(fact_com_Osize_I5_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I5_J) ).

fof(fact_evaln__elim__cases_I5_J,axiom,
    ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2)
     => ( ( hBOOL(hAPP(V_b_2,V_s_2))
         => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
       => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
           => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I5_J) ).

fof(fact_evaln_OIfTrue,axiom,
    ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(V_b_2,V_s_2))
     => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
       => c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ),
    file('theBenchmark.p',fact_evaln_OIfTrue) ).

fof(fact_evaln_OIfFalse,axiom,
    ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
       => c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ),
    file('theBenchmark.p',fact_evaln_OIfFalse) ).

fof(fact_evalc_OIfFalse,axiom,
    ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ),
    file('theBenchmark.p',fact_evalc_OIfFalse) ).

fof(fact_evalc_OIfTrue,axiom,
    ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(V_b_2,V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ),
    file('theBenchmark.p',fact_evalc_OIfTrue) ).

fof(fact_evalc__elim__cases_I5_J,axiom,
    ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
     => ( ( hBOOL(hAPP(V_b_2,V_s_2))
         => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
       => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I5_J) ).

fof(fact_evaln_OSemi,axiom,
    ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
      ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
     => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
       => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ),
    file('theBenchmark.p',fact_evaln_OSemi) ).

fof(fact_evalc_OSemi,axiom,
    ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ),
    file('theBenchmark.p',fact_evalc_OSemi) ).

fof(fact_WTs__elim__cases_I5_J,axiom,
    ! [V_c2_2,V_c1_2,V_b_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
     => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
         => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I5_J) ).

fof(fact_WTs__elim__cases_I4_J,axiom,
    ! [V_c2,V_c1] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
     => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
         => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I4_J) ).

fof(fact_com_Osimps_I4_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
      ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
    <=> ( V_com2_2 = V_com2_H_2
        & V_com1_2 = V_com1_H_2
        & V_fun_2 = V_fun_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I4_J) ).

fof(fact_com_Osimps_I3_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
      ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
    <=> ( V_com2_2 = V_com2_H_2
        & V_com1_2 = V_com1_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I3_J) ).

fof(fact_com_Osimps_I45_J,axiom,
    ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I45_J) ).

fof(fact_com_Osimps_I44_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I44_J) ).

fof(fact_nat__size,axiom,
    ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
    file('theBenchmark.p',fact_nat__size) ).

fof(fact_evaln_Oequations_I6_J,axiom,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2),V_a2_2,V_a4_2,V_a5_2)
    <=> ( ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2)
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2)
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I6_J) ).

fof(fact_evaln_Oequations_I5_J,axiom,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2),V_a2_2,V_a4_2,V_a5_2)
    <=> ( ( c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2)
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2)
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I5_J) ).

fof(fact_evalc_Oequations_I5_J,axiom,
    ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
    <=> ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I5_J) ).

fof(fact_evalc_Oequations_I6_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
    <=> ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I6_J) ).

fof(fact_WT_OIf,axiom,
    ! [V_b_2,V_c1_2,V_c0_2] :
      ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
     => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
       => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ),
    file('theBenchmark.p',fact_WT_OIf) ).

fof(fact_WT_Oequations_I5_J,axiom,
    ! [V_a2_2,V_a1_2,V_a3_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
    <=> ( hBOOL(hAPP(c_Com_OWT,V_a2_2))
        & hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ),
    file('theBenchmark.p',fact_WT_Oequations_I5_J) ).

fof(fact_com_Osimps_I54_J,axiom,
    ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    file('theBenchmark.p',fact_com_Osimps_I54_J) ).

fof(fact_com_Osimps_I55_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I55_J) ).

fof(fact_evaln_Oequations_I4_J,axiom,
    ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
    <=> ? [B_s1] :
          ( c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2)
          & c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I4_J) ).

fof(fact_evalc_Oequations_I4_J,axiom,
    ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
    <=> ? [B_s1] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I4_J) ).

fof(fact_WT_OSemi,axiom,
    ! [V_c1,V_c0] :
      ( hBOOL(hAPP(c_Com_OWT,V_c0))
     => ( hBOOL(hAPP(c_Com_OWT,V_c1))
       => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ),
    file('theBenchmark.p',fact_WT_OSemi) ).

fof(fact_WT_Oequations_I4_J,axiom,
    ! [V_a2_2,V_a1_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
    <=> ( hBOOL(hAPP(c_Com_OWT,V_a2_2))
        & hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ),
    file('theBenchmark.p',fact_WT_Oequations_I4_J) ).

fof(fact_com_Osimps_I48_J,axiom,
    ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
    file('theBenchmark.p',fact_com_Osimps_I48_J) ).

fof(fact_com_Osimps_I49_J,axiom,
    ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
    file('theBenchmark.p',fact_com_Osimps_I49_J) ).

fof(fact_com_Osimps_I27_J,axiom,
    ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I27_J) ).

fof(fact_com_Osimps_I26_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I26_J) ).

fof(fact_com_Osimps_I57_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I57_J) ).

fof(fact_com_Osimps_I56_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I56_J) ).

fof(fact_com_Osimps_I37_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I37_J) ).

fof(fact_com_Osimps_I36_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I36_J) ).

fof(fact_com_Osimps_I15_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I15_J) ).

fof(fact_com_Osimps_I14_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I14_J) ).

fof(fact_com_Osimps_I25_J,axiom,
    ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I25_J) ).

fof(fact_com_Osimps_I24_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I24_J) ).

fof(fact_com_Osimps_I50_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I50_J) ).

fof(fact_com_Osimps_I35_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I35_J) ).

fof(fact_com_Osimps_I51_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I51_J) ).

fof(fact_com_Osimps_I34_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I34_J) ).

fof(fact_com_Osimps_I13_J,axiom,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I13_J) ).

fof(fact_com_Osimps_I12_J,axiom,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
    file('theBenchmark.p',fact_com_Osimps_I12_J) ).

fof(fact_nat_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osize_I3_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [V_d,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [V_d,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_nat_Osize_I1_J,axiom,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osize_I1_J) ).

fof(fact_option_Orecs_I2_J,axiom,
    ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2),
    file('theBenchmark.p',fact_option_Orecs_I2_J) ).

fof(fact_option_Osimps_I5_J,axiom,
    ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2),
    file('theBenchmark.p',fact_option_Osimps_I5_J) ).

fof(fact_option_Orecs_I1_J,axiom,
    ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2,
    file('theBenchmark.p',fact_option_Orecs_I1_J) ).

fof(fact_option_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2,
    file('theBenchmark.p',fact_option_Osimps_I4_J) ).

fof(fact_bool_Osize_I1_J,axiom,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I1_J) ).

fof(fact_bool_Osize_I2_J,axiom,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I2_J) ).

fof(fact_com_Osize_I6_J,axiom,
    ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I6_J) ).

fof(fact_com_Osize_I14_J,axiom,
    ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I14_J) ).

fof(fact_is__none__code_I2_J,axiom,
    ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)),
    file('theBenchmark.p',fact_is__none__code_I2_J) ).

fof(fact_is__none__code_I1_J,axiom,
    ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)),
    file('theBenchmark.p',fact_is__none__code_I1_J) ).

fof(fact_is__none__def,axiom,
    ! [V_x_2,T_b] :
      ( c_Option_Ois__none(T_b,V_x_2)
    <=> V_x_2 = c_Option_Ooption_ONone(T_b) ),
    file('theBenchmark.p',fact_is__none__def) ).

fof(fact_evaln_OWhileFalse,axiom,
    ! [V_n_2,V_c_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ),
    file('theBenchmark.p',fact_evaln_OWhileFalse) ).

fof(fact_evaln_OWhileTrue,axiom,
    ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
      ( hBOOL(hAPP(V_b_2,V_s0_2))
     => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
       => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
         => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ),
    file('theBenchmark.p',fact_evaln_OWhileTrue) ).

fof(fact_evalc_OWhileTrue,axiom,
    ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
      ( hBOOL(hAPP(V_b_2,V_s0_2))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
       => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
         => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ),
    file('theBenchmark.p',fact_evalc_OWhileTrue) ).

fof(fact_evalc_OWhileFalse,axiom,
    ! [V_c_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ),
    file('theBenchmark.p',fact_evalc_OWhileFalse) ).

fof(fact_WTs__elim__cases_I6_J,axiom,
    ! [V_c_2,V_b_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
     => hBOOL(hAPP(c_Com_OWT,V_c_2)) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I6_J) ).

fof(fact_com_Osimps_I5_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
      ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
    <=> ( V_com_2 = V_com_H_2
        & V_fun_2 = V_fun_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I5_J) ).

fof(fact_evaln_Oequations_I7_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
    <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
       => ? [B_s1] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2)
            & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) ) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I7_J) ).

fof(fact_evaln_Oequations_I8_J,axiom,
    ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
    <=> ( ( ? [B_s1] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2)
              & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
          & V_a6_2 = V_a2_2 ) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I8_J) ).

fof(fact_evalc_Oequations_I8_J,axiom,
    ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
    <=> ( ( ? [B_s1] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
          & V_a5_2 = V_a2_2 ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I8_J) ).

fof(fact_evalc_Oequations_I7_J,axiom,
    ! [V_a2_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
    <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
       => ? [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I7_J) ).

fof(fact_WT_Oequations_I6_J,axiom,
    ! [V_a1_2,V_a2_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
    <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ),
    file('theBenchmark.p',fact_WT_Oequations_I6_J) ).

fof(fact_While,axiom,
    ! [V_b_2,V_c_2] :
      ( hBOOL(hAPP(c_Com_OWT,V_c_2))
     => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ),
    file('theBenchmark.p',fact_While) ).

fof(fact_com_Osimps_I59_J,axiom,
    ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I59_J) ).

fof(fact_com_Osimps_I58_J,axiom,
    ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    file('theBenchmark.p',fact_com_Osimps_I58_J) ).

fof(fact_com_Osimps_I53_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I53_J) ).

fof(fact_com_Osimps_I52_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I52_J) ).

fof(fact_com_Osimps_I28_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I28_J) ).

fof(fact_com_Osimps_I29_J,axiom,
    ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I29_J) ).

fof(fact_com_Osimps_I38_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I38_J) ).

fof(fact_com_Osimps_I61_J,axiom,
    ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I61_J) ).

fof(fact_com_Osimps_I39_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I39_J) ).

fof(fact_com_Osimps_I60_J,axiom,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    file('theBenchmark.p',fact_com_Osimps_I60_J) ).

fof(fact_com_Osimps_I46_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I46_J) ).

fof(fact_com_Osimps_I47_J,axiom,
    ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I47_J) ).

fof(fact_com_Osimps_I16_J,axiom,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I16_J) ).

fof(fact_com_Osimps_I17_J,axiom,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I17_J) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__0__less__iff) ).

fof(fact_bool_Osize_I4_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I4_J) ).

fof(fact_bool_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I3_J) ).

fof(fact_less__imp__Suc__add,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ),
    file('theBenchmark.p',fact_less__imp__Suc__add) ).

fof(fact_less__imp__add__positive,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ? [B_k] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k)) ) ),
    file('theBenchmark.p',fact_less__imp__add__positive) ).

fof(fact_gr0__implies__Suc,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ),
    file('theBenchmark.p',fact_gr0__implies__Suc) ).

fof(fact_evalc__elim__cases_I4_J,axiom,
    ! [V_t,V_s,V_c2,V_c1] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
     => ~ ! [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I4_J) ).

fof(fact_lift__Suc__mono__less__iff,axiom,
    ! [V_m_2,V_n_2,V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_lift__Suc__mono__less__iff) ).

fof(fact_lift__Suc__mono__less,axiom,
    ! [V_n_H_2,V_n_2,V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ),
    file('theBenchmark.p',fact_lift__Suc__mono__less) ).

fof(fact_evaln__elim__cases_I4_J,axiom,
    ! [V_t,V_n,V_s,V_c2,V_c1] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t)
     => ~ ! [B_s1] :
            ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1)
           => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I4_J) ).

fof(fact_of__nat__eq__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Nat_Osemiring__char__0(T_b)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
      <=> V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_int__eq__0__conv,axiom,
    ! [V_n_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__eq__0__conv) ).

fof(fact_int__0,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_int__0) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
    <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ),
    file('theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_zless__int,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_zless__int) ).

fof(fact_zadd__int__left,axiom,
    ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z),
    file('theBenchmark.p',fact_zadd__int__left) ).

fof(fact_zadd__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zadd__int) ).

fof(fact_zero__less__int__conv,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
    file('theBenchmark.p',fact_zero__less__int__conv) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_of__nat__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_of__nat__0) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_less__imp__of__nat__less,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ),
    file('theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_of__nat__less__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_of__nat__add,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__add) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_transfer__int__nat__relations_I2_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).

fof(fact_transfer__int__nat__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).

fof(fact_order__less__irrefl,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ),
    file('theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_linorder__neq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( V_x_2 != V_y_2
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_linorder__less__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
        | V_x = V_y
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [V_x_2,V_y_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__neqE,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_x != V_y
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
    file('theBenchmark.p',fact_linorder__neqE) ).

fof(fact_less__imp__neq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => V_x != V_y ) ),
    file('theBenchmark.p',fact_less__imp__neq) ).

fof(fact_int__less__0__conv,axiom,
    ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_int__less__0__conv) ).

fof(fact_int__int__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_int__int__eq) ).

fof(fact_transfer__int__nat__relations_I1_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_zadd__0,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
    file('theBenchmark.p',fact_zadd__0) ).

fof(fact_zadd__0__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
    file('theBenchmark.p',fact_zadd__0__right) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ),
    file('theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_zadd__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
    file('theBenchmark.p',fact_zadd__assoc) ).

fof(fact_zadd__left__commute,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
    file('theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_zless__linear,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
    file('theBenchmark.p',fact_zless__linear) ).

fof(fact_zadd__commute,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
    file('theBenchmark.p',fact_zadd__commute) ).

fof(fact_linorder__cases,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ( V_x != V_y
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
    file('theBenchmark.p',fact_linorder__cases) ).

fof(fact_order__less__asym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_order__less__asym) ).

fof(fact_xt1_I10_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_order__less__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I2_J,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I2_J) ).

fof(fact_ord__less__eq__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__less__eq__trans) ).

fof(fact_xt1_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I1_J) ).

fof(fact_ord__eq__less__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__eq__less__trans) ).

fof(fact_xt1_I9_J,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_order__less__asym_H,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ),
    file('theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => V_y != V_x ) ),
    file('theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => V_x != V_y ) ),
    file('theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
     => ? [B_n] :
          ( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
    file('theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(fact_of__int__0__less__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__0__less__iff) ).

fof(fact_of__int__less__0__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_of__int__less__0__iff) ).

fof(fact_zmult__zless__mono2__lemma,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ),
    file('theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

fof(fact_negative__zless__0,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_negative__zless__0) ).

fof(fact_split__nat,axiom,
    ! [V_i_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [B_n] :
            ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
           => hBOOL(hAPP(V_P_2,B_n)) ) ) ),
    file('theBenchmark.p',fact_split__nat) ).

fof(fact_zero__less__nat__eq,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    file('theBenchmark.p',fact_zero__less__nat__eq) ).

fof(fact_negative__zless,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    file('theBenchmark.p',fact_negative__zless) ).

fof(fact_int__Suc,axiom,
    ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
    file('theBenchmark.p',fact_int__Suc) ).

fof(fact_odd__less__0,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_odd__less__0) ).

fof(fact_less__1__mult,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ),
    file('theBenchmark.p',fact_less__1__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [V_a,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_square__eq__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oidom(T_b)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_square__eq__iff) ).

fof(fact_zmult__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
    file('theBenchmark.p',fact_zmult__assoc) ).

fof(fact_square__eq__1__iff,axiom,
    ! [V_x_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
      <=> ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
    file('theBenchmark.p',fact_square__eq__1__iff) ).

fof(fact_minus__mult__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_of__int__eq__iff,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
      <=> V_w_2 = V_z_2 ) ),
    file('theBenchmark.p',fact_of__int__eq__iff) ).

fof(fact_minus__mult__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_zmult__zminus,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
    file('theBenchmark.p',fact_zmult__zminus) ).

fof(fact_zmult__commute,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
    file('theBenchmark.p',fact_zmult__commute) ).

fof(fact_zmult__1__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
    file('theBenchmark.p',fact_zmult__1__right) ).

fof(fact_zmult__1,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
    file('theBenchmark.p',fact_zmult__1) ).

fof(fact_of__int__mult,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__mult) ).

fof(fact_minus__mult__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ),
    file('theBenchmark.p',fact_minus__mult__left) ).

fof(fact_minus__mult__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__mult__right) ).

fof(fact_of__int__minus,axiom,
    ! [V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__minus) ).

fof(fact_zminus__zminus,axiom,
    ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z,
    file('theBenchmark.p',fact_zminus__zminus) ).

fof(fact_of__int__1,axiom,
    ! [T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_of__int__1) ).

fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_minus__equation__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
      <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ),
    file('theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
      <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ),
    file('theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_mult__1__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_mult__1__right) ).

fof(fact_one__reorient,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oone(T_b)
     => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
      <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ),
    file('theBenchmark.p',fact_one__reorient) ).

fof(fact_mult__1,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__1) ).

fof(fact_mult__1__left,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__1__left) ).

fof(fact_minus__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ),
    file('theBenchmark.p',fact_minus__minus) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_of__nat__mult,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__mult) ).

fof(fact_of__nat__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_of__nat__1) ).

fof(fact_of__int__of__nat,axiom,
    ! [V_k,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) ) ),
    file('theBenchmark.p',fact_of__int__of__nat) ).

fof(fact_nat__zminus__int,axiom,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__zminus__int) ).

fof(fact_nat__1,axiom,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_nat__1) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(fact_minus__zero,axiom,
    ! [T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_minus__zero) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
      <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ),
    file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_equal__neg__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_neg__equal__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_less__minus__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
    file('theBenchmark.p',fact_less__minus__iff) ).

fof(fact_minus__less__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
    file('theBenchmark.p',fact_minus__less__iff) ).

fof(fact_neg__less__iff__less,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_minus__add__distrib,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ),
    file('theBenchmark.p',fact_minus__add) ).

fof(fact_add__minus__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ),
    file('theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_minus__add__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ),
    file('theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_mult__zero__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Omult__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__zero__left) ).

fof(fact_mult__zero__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Omult__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__zero__right) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_no__zero__divisors,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ono__zero__divisors(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_divisors__zero,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ono__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b = c_Groups_Ozero__class_Ozero(T_a)
          | V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_divisors__zero) ).

fof(fact_one__neq__zero,axiom,
    ! [T_a] :
      ( class_Rings_Ozero__neq__one(T_a)
     => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_one__neq__zero) ).

fof(fact_zero__neq__one,axiom,
    ! [T_a] :
      ( class_Rings_Ozero__neq__one(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_zero__neq__one) ).

fof(fact_zminus__0,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zminus__0) ).

fof(fact_nat__int,axiom,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
    file('theBenchmark.p',fact_nat__int) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_crossproduct__noteq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( ( V_c_2 != V_d_2
          & V_a_2 != V_b_2 )
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [V_b,V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_crossproduct__eq,axiom,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
      <=> ( V_y_2 = V_z_2
          | V_w_2 = V_x_2 ) ) ),
    file('theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_combine__common__factor,axiom,
    ! [V_c,V_b,V_e,V_a,T_a] :
      ( class_Rings_Osemiring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ),
    file('theBenchmark.p',fact_combine__common__factor) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    file('theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    file('theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_int__0__neq__1,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__0__neq__1) ).

fof(fact_of__int__int__eq,axiom,
    ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),
    file('theBenchmark.p',fact_of__int__int__eq) ).

fof(fact_one__less__nat__eq,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ),
    file('theBenchmark.p',fact_one__less__nat__eq) ).

fof(fact_neg__less__nonneg,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_less__minus__self__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_minus__unique,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ),
    file('theBenchmark.p',fact_minus__unique) ).

fof(fact_ab__left__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_ab__left__minus) ).

fof(fact_left__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_left__minus) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_right__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_right__minus) ).

fof(fact_nat__0,axiom,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__0) ).

fof(fact_transfer__nat__int__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__comm__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__neg__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
    file('theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
    file('theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_mult__pos__neg2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_mult__pos__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_not__square__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_zero__less__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_zero__less__one) ).

fof(fact_not__one__less__zero,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [V_d,V_c,V_b,V_a,V_r,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
       => ( ( V_c != V_d
            & V_a = V_b )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ),
    file('theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_less__add__one,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ),
    file('theBenchmark.p',fact_less__add__one) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_negative__eq__positive,axiom,
    ! [V_m_2,V_n_2] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
    <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_negative__eq__positive) ).

fof(fact_not__int__zless__negative,axiom,
    ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))),
    file('theBenchmark.p',fact_not__int__zless__negative) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ),
    file('theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_int__0__less__1,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_int__0__less__1) ).

fof(fact_odd__nonzero,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_odd__nonzero) ).

fof(fact_zless__add1__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> ( V_w_2 = V_z_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_of__int__0,axiom,
    ! [T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_of__int__0) ).

fof(fact_of__int__0__eq__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_of__int__0__eq__iff) ).

fof(fact_of__int__eq__0__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_of__int__eq__0__iff) ).

fof(fact_of__int__less__iff,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__less__iff) ).

fof(fact_of__int__add,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__add) ).

fof(fact_of__int__of__nat__eq,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
    file('theBenchmark.p',fact_of__int__of__nat__eq) ).

fof(fact_zless__nat__conj,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_zless__nat__conj) ).

fof(fact_nat__mono__iff,axiom,
    ! [V_w_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_nat__mono__iff) ).

fof(fact_zless__nat__eq__int__zless,axiom,
    ! [V_z_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ),
    file('theBenchmark.p',fact_zless__nat__eq__int__zless) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
      <=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_zero__less__two,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ),
    file('theBenchmark.p',fact_zero__less__two) ).

fof(fact_of__nat__Suc,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ),
    file('theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_int__Suc0__eq__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__Suc0__eq__1) ).

fof(fact_nat__aux__def,axiom,
    ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n),
    file('theBenchmark.p',fact_nat__aux__def) ).

fof(fact_negD,axiom,
    ! [V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ),
    file('theBenchmark.p',fact_negD) ).

fof(fact_sgn__if,axiom,
    ! [V_x,T_a] :
      ( class_Groups_Osgn__if(T_a)
     => ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
         => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
             => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
             => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) ) )
        & ( V_x = c_Groups_Ozero__class_Ozero(T_a)
         => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sgn__if) ).

fof(fact_sgn__neg,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_sgn__neg) ).

fof(fact_sgn__1__neg,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_zsgn__def,axiom,
    ! [V_i] :
      ( ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zsgn__def) ).

fof(fact_Suc__nat__eq__nat__zadd1,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ),
    file('theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).

fof(fact_nat__less__iff,axiom,
    ! [V_m_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ),
    file('theBenchmark.p',fact_nat__less__iff) ).

fof(fact_convex__bound__lt,axiom,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( class_Rings_Olinordered__semiring__1__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_sgn__pos,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_sgn__pos) ).

fof(fact_order__refl,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ),
    file('theBenchmark.p',fact_order__refl) ).

fof(fact_le0,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    file('theBenchmark.p',fact_le0) ).

fof(fact_negative__zle,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    file('theBenchmark.p',fact_negative__zle) ).

fof(fact_mult__le__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ),
    file('theBenchmark.p',fact_mult__le__mono) ).

fof(fact_mult__le__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ),
    file('theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_mult__le__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_nat__mult__assoc,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_nat__mult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(fact_nat__mult__commute,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_nat__mult__1__right,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_nat__1__eq__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
    <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(fact_nat__mult__1,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_nat__mult__1) ).

fof(fact_le__cube,axiom,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
    file('theBenchmark.p',fact_le__cube) ).

fof(fact_le__square,axiom,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
    file('theBenchmark.p',fact_le__square) ).

fof(fact_mult__eq__self__implies__10,axiom,
    ! [V_n,V_m] :
      ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
     => ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(fact_zle__refl,axiom,
    ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
    file('theBenchmark.p',fact_zle__refl) ).

fof(fact_sgn__sgn,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ),
    file('theBenchmark.p',fact_sgn__sgn) ).

fof(fact_zle__linear,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
    file('theBenchmark.p',fact_zle__linear) ).

fof(fact_zle__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ),
    file('theBenchmark.p',fact_zle__trans) ).

fof(fact_zle__antisym,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
       => V_z = V_w ) ),
    file('theBenchmark.p',fact_zle__antisym) ).

fof(fact_le__fun__def,axiom,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ),
    file('theBenchmark.p',fact_le__fun__def) ).

fof(fact_linorder__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_linorder__linear) ).

fof(fact_order__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( V_x_2 = V_y_2
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_order__eq__iff) ).

fof(fact_order__eq__refl,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( V_x = V_y
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_order__eq__refl) ).

fof(fact_le__funD,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
    file('theBenchmark.p',fact_le__funD) ).

fof(fact_order__antisym__conv,axiom,
    ! [V_x_2,V_y_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_ord__eq__le__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__eq__le__trans) ).

fof(fact_xt1_I3_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I3_J) ).

fof(fact_ord__le__eq__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__le__eq__trans) ).

fof(fact_xt1_I4_J,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I4_J) ).

fof(fact_order__antisym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
         => V_x = V_y ) ) ),
    file('theBenchmark.p',fact_order__antisym) ).

fof(fact_order__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I5_J,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
         => V_x = V_y ) ) ),
    file('theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_xt1_I6_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_le__funE,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
    file('theBenchmark.p',fact_le__funE) ).

fof(fact_linorder__le__cases,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_of__nat__le__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_zle__int,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_zle__int) ).

fof(fact_transfer__int__nat__relations_I3_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).

fof(fact_of__int__le__iff,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__le__iff) ).

fof(fact_one__le__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) ) ),
    file('theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_transfer__nat__int__relations_I3_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_order__le__less__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_xt1_I7_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__less__le__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I11_J,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( V_a != V_b
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( V_a != V_b
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( V_x = V_y
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_order__less__imp__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_leD,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_leD) ).

fof(fact_xt1_I12_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a != V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_order__neq__le__trans,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a != V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_not__leE,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_leI) ).

fof(fact_order__le__less,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_order__le__less) ).

fof(fact_less__le__not__le,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Opreorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_less__le__not__le) ).

fof(fact_order__less__le,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> ( V_x_2 != V_y_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_order__less__le) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__not__le,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_linorder__not__le) ).

fof(fact_linorder__not__less,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_linorder__not__less) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__mono) ).

fof(fact_add__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
    file('theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__le__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__le__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_mult__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
    <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_mult__cancel2) ).

fof(fact_mult__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
    <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_mult__cancel1) ).

fof(fact_mult__is__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__is__0) ).

fof(fact_mult__0__right,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mult__0__right) ).

fof(fact_mult__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mult__0) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_le__0__eq,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_le__0__eq) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le__minus__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
    file('theBenchmark.p',fact_le__minus__iff) ).

fof(fact_minus__le__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
    file('theBenchmark.p',fact_minus__le__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_le__imp__neg__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ),
    file('theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_add__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_add__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
    file('theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_not__less__eq__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
    file('theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_le__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_Suc__le__mono,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
    file('theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_le__SucI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_le__SucI) ).

fof(fact_le__SucE,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => V_m = hAPP(c_Nat_OSuc,V_n) ) ),
    file('theBenchmark.p',fact_le__SucE) ).

fof(fact_Suc__leD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__leD) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ),
    file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_nat__less__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ( V_m_2 != V_n_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_less__imp__le__nat,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_le__neq__implies__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => ( V_m != V_n
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [V_n,V_m] :
      ( ( V_m = V_n
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_le__add2,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
    file('theBenchmark.p',fact_le__add2) ).

fof(fact_le__add1,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
    file('theBenchmark.p',fact_le__add1) ).

fof(fact_le__iff__add,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ),
    file('theBenchmark.p',fact_le__iff__add) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_trans__le__add1,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
    file('theBenchmark.p',fact_trans__le__add1) ).

fof(fact_trans__le__add2,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
    file('theBenchmark.p',fact_trans__le__add2) ).

fof(fact_add__le__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_add__le__mono1) ).

fof(fact_add__le__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
    file('theBenchmark.p',fact_add__le__mono) ).

fof(fact_add__leD2,axiom,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ),
    file('theBenchmark.p',fact_add__leD2) ).

fof(fact_add__leD1,axiom,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leE,axiom,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ),
    file('theBenchmark.p',fact_add__leE) ).

fof(fact_zless__le,axiom,
    ! [V_w_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
    <=> ( V_z_2 != V_w_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) ) ),
    file('theBenchmark.p',fact_zless__le) ).

fof(fact_zadd__left__mono,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ),
    file('theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_evaln__nonstrict,axiom,
    ! [V_m,V_t,V_n,V_s,V_c] :
      ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ),
    file('theBenchmark.p',fact_evaln__nonstrict) ).

fof(fact_nat__le__eq__zle,axiom,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_nat__le__eq__zle) ).

fof(fact_nat__mult__distrib,axiom,
    ! [V_z_H,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ),
    file('theBenchmark.p',fact_nat__mult__distrib) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).

fof(fact_of__int__0__le__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__0__le__iff) ).

fof(fact_of__int__le__0__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_of__int__le__0__iff) ).

fof(fact_sgn__0__0,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_sgn__0__0) ).

fof(fact_sgn0,axiom,
    ! [T_a] :
      ( class_Groups_Osgn__if(T_a)
     => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_sgn0) ).

fof(fact_sgn__times,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ),
    file('theBenchmark.p',fact_sgn__times) ).

fof(fact_nat__mult__distrib__neg,axiom,
    ! [V_z_H,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ),
    file('theBenchmark.p',fact_nat__mult__distrib__neg) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__comm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
          <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
              & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_add__increasing,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__increasing2) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_split__mult__neg__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_split__mult__pos__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__mono) ).

fof(fact_mult__mono_H,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__comm__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__left__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__right__mono) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_mult__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_zero__le__square,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ),
    file('theBenchmark.p',fact_zero__le__square) ).

fof(fact_add__le__less__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_zero__le__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_zero__le__one) ).

fof(fact_not__one__le__zero,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_le__minus__self__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_minus__le__self__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_mult__eq__1__iff) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ),
    file('theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ),
    file('theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_mult__less__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ),
    file('theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_mult__less__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ),
    file('theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
    file('theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
    file('theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
    file('theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_mult__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_mult__Suc) ).

fof(fact_mult__Suc__right,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_One__nat__def) ).

fof(fact_Suc__le__lessD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
      <=> V_n_2 = V_m_2 ) ),
    file('theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_Suc__leI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    file('theBenchmark.p',fact_Suc__leI) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_Suc__le__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
    file('theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    file('theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_zero__zle__int,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    file('theBenchmark.p',fact_zero__zle__int) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [V_P_2] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
    <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_eq__nat__nat__iff,axiom,
    ! [V_z_H_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
       => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
        <=> V_z_2 = V_z_H_2 ) ) ),
    file('theBenchmark.p',fact_eq__nat__nat__iff) ).

fof(fact_ex__nat,axiom,
    ! [V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    file('theBenchmark.p',fact_ex__nat) ).

fof(fact_all__nat,axiom,
    ! [V_P_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ),
    file('theBenchmark.p',fact_all__nat) ).

fof(fact_transfer__nat__int__relations_I1_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).

fof(fact_zadd__zless__mono,axiom,
    ! [V_z,V_z_H,V_w,V_w_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ),
    file('theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_zmult__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zmult__int) ).

fof(fact_int__mult,axiom,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    file('theBenchmark.p',fact_int__mult) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zle__iff__zadd,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
    <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ),
    file('theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_int__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__1) ).

fof(fact_transfer__int__nat__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).

fof(fact_transfer__nat__int__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).

fof(fact_add__pos__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_add__nonneg__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__strict__increasing,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__strict__increasing2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__neg__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__nonpos__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_mult__strict__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ),
    file('theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ),
    file('theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ),
    file('theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_sgn__greater,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_sgn__greater) ).

fof(fact_sgn__less,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_sgn__less) ).

fof(fact_one__less__mult,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_one__less__mult) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ),
    file('theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_int__le__0__conv,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__le__0__conv) ).

fof(fact_nat__0__iff,axiom,
    ! [V_i_2] :
      ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_nat__0__iff) ).

fof(fact_nat__le__0,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_nat__le__0) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_nat__0__le,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
    file('theBenchmark.p',fact_nat__0__le) ).

fof(fact_int__eq__iff,axiom,
    ! [V_z_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        & V_m_2 = hAPP(c_Int_Onat,V_z_2) ) ),
    file('theBenchmark.p',fact_int__eq__iff) ).

fof(fact_int__nat__eq,axiom,
    ! [V_z] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ),
    file('theBenchmark.p',fact_int__nat__eq) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [V_z,V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ),
    file('theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_add1__zle__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
    file('theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ),
    file('theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_int__zle__neg,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
    <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_int__zle__neg) ).

fof(fact_negative__zle__0,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_negative__zle__0) ).

fof(fact_convex__bound__le,axiom,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( class_Rings_Olinordered__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_convex__bound__le) ).

fof(fact_transfer__nat__int__relations_I2_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

fof(fact_nat__less__eq__zless,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_nat__less__eq__zless) ).

fof(fact_nat__eq__iff,axiom,
    ! [V_m_2,V_w_2] :
      ( hAPP(c_Int_Onat,V_w_2) = V_m_2
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ) ),
    file('theBenchmark.p',fact_nat__eq__iff) ).

fof(fact_nat__eq__iff2,axiom,
    ! [V_w_2,V_m_2] :
      ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ) ),
    file('theBenchmark.p',fact_nat__eq__iff2) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).

fof(fact_nat__add__distrib,axiom,
    ! [V_z_H,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ),
    file('theBenchmark.p',fact_nat__add__distrib) ).

fof(fact_le__imp__0__less,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ),
    file('theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_not__zle__0__negative,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    file('theBenchmark.p',fact_not__zle__0__negative) ).

fof(fact_of__nat__nat,axiom,
    ! [V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ),
    file('theBenchmark.p',fact_of__nat__nat) ).

fof(fact_sgn__1__pos,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_self__quotient__aux2,axiom,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux2) ).

fof(fact_self__quotient__aux1,axiom,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_q__pos__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ),
    file('theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_q__neg__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ),
    file('theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ),
    file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_le__refl,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)),
    file('theBenchmark.p',fact_le__refl) ).

fof(fact_nat__le__linear,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_nat__le__linear) ).

fof(fact_eq__imp__le,axiom,
    ! [V_n,V_m] :
      ( V_m = V_n
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_eq__imp__le) ).

fof(fact_le__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ),
    file('theBenchmark.p',fact_le__trans) ).

fof(fact_le__antisym,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_le__antisym) ).

fof(fact_less__fun__def,axiom,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_less__fun__def) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
    <=> ( V_m_2 = V_n_2
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
    file('theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
      <=> V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_transfer__morphism__nat__int,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_transfer__morphism__nat__int) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Oboolean__algebra(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_compl__mono,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ),
    file('theBenchmark.p',fact_compl__mono) ).

fof(fact_ex__least__nat__less,axiom,
    ! [V_n_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(V_P_2,V_n_2))
       => ? [B_k] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
            & ! [B_i] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
               => ~ hBOOL(hAPP(V_P_2,B_i)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [V_y,V_q_1,V_b_1,V_a_1] :
      ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_zmult2__lemma__aux1,axiom,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_mod__mod__trivial,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mod__trivial) ).

fof(fact_mod__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__0) ).

fof(fact_mod__by__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_mod__by__0) ).

fof(fact_mod__self,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__self) ).

fof(fact_mod__add__self2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__add__self2) ).

fof(fact_mod__add__self1,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__add__self1) ).

fof(fact_mod__add__right__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__add__right__eq) ).

fof(fact_mod__add__left__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
    file('theBenchmark.p',fact_mod__add__left__eq) ).

fof(fact_mod__add__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__add__eq) ).

fof(fact_zmod__simps_I2_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ),
    file('theBenchmark.p',fact_zmod__simps_I2_J) ).

fof(fact_zmod__simps_I1_J,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ),
    file('theBenchmark.p',fact_zmod__simps_I1_J) ).

fof(fact_mod__add__cong,axiom,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
       => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
         => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ),
    file('theBenchmark.p',fact_mod__add__cong) ).

fof(fact_mod__mult__right__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__mult__right__eq) ).

fof(fact_mod__mult__left__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
    file('theBenchmark.p',fact_mod__mult__left__eq) ).

fof(fact_mod__mult__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__mult__eq) ).

fof(fact_mod__mult__mult1,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ),
    file('theBenchmark.p',fact_mod__mult__mult1) ).

fof(fact_mod__mult__mult2,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ),
    file('theBenchmark.p',fact_mod__mult__mult2) ).

fof(fact_zmod__simps_I4_J,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ),
    file('theBenchmark.p',fact_zmod__simps_I4_J) ).

fof(fact_mod__mult__cong,axiom,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
       => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
         => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ),
    file('theBenchmark.p',fact_mod__mult__cong) ).

fof(fact_mod__minus__eq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ),
    file('theBenchmark.p',fact_mod__minus__eq) ).

fof(fact_mod__minus__cong,axiom,
    ! [V_a_H,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
       => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ),
    file('theBenchmark.p',fact_mod__minus__cong) ).

fof(fact_zmod__self,axiom,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__self) ).

fof(fact_zmod__zero,axiom,
    ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__zero) ).

fof(fact_zmod__simps_I3_J,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),
    file('theBenchmark.p',fact_zmod__simps_I3_J) ).

fof(fact_zmod__zmult1__eq,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c),
    file('theBenchmark.p',fact_zmod__zmult1__eq) ).

fof(fact_zminus__zmod,axiom,
    ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m),
    file('theBenchmark.p',fact_zminus__zmod) ).

fof(fact_zmod__zminus__zminus,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    file('theBenchmark.p',fact_zmod__zminus__zminus) ).

fof(fact_zmod__zminus2,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)),
    file('theBenchmark.p',fact_zmod__zminus2) ).

fof(fact_mod__mult__self2__is__0,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__mult__self1,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_mod__by__1,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__by__1) ).

fof(fact_zmod__le__nonneg__dividend,axiom,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ),
    file('theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_pos__mod__bound,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ),
    file('theBenchmark.p',fact_pos__mod__bound) ).

fof(fact_neg__mod__bound,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
    file('theBenchmark.p',fact_neg__mod__bound) ).

fof(fact_zmod__eq__0__iff,axiom,
    ! [V_d_2,V_m_2] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ),
    file('theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_zmod__zminus2__not__zero,axiom,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zmod__zminus2__not__zero) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zmod__zminus1__not__zero) ).

fof(fact_pos__mod__sign,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
    file('theBenchmark.p',fact_pos__mod__sign) ).

fof(fact_pos__mod__conj,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ),
    file('theBenchmark.p',fact_pos__mod__conj) ).

fof(fact_mod__pos__pos__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
    file('theBenchmark.p',fact_mod__pos__pos__trivial) ).

fof(fact_neg__mod__sign,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_neg__mod__sign) ).

fof(fact_neg__mod__conj,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_neg__mod__conj) ).

fof(fact_mod__neg__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
    file('theBenchmark.p',fact_mod__neg__neg__trivial) ).

fof(fact_mult__left__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_mult__left__idem) ).

fof(fact_mult__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_mult__idem) ).

fof(fact_times_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_times_Oidem) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Oboolean__algebra(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_uminus__apply,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ouminus(T_b)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_uminus__apply) ).

fof(fact_double__compl,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ),
    file('theBenchmark.p',fact_double__compl) ).

fof(fact_mod__pos__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_split__zmod,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [B_i,B_j] :
              ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
             => hBOOL(hAPP(V_P_2,B_j)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_i,B_j] :
              ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
             => hBOOL(hAPP(V_P_2,B_j)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__zmod) ).

fof(fact_zmult2__lemma__aux3,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux3) ).

fof(fact_z3mod__def,axiom,
    ! [V_k,V_l] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) ),
    file('theBenchmark.p',fact_z3mod__def) ).

fof(fact_split__pos__lemma,axiom,
    ! [V_n_2,V_P_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
     => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
      <=> ! [B_i,B_j] :
            ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
           => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_split__neg__lemma,axiom,
    ! [V_n_2,V_P_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
      <=> ! [B_i,B_j] :
            ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
           => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [V_b,V_a,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ),
    file('theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_split__zdiv,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_split__zdiv) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_split__div_H,axiom,
    ! [V_n_2,V_m_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_split__div_H) ).

fof(fact_div__add1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_div__add1__eq) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zdiv__int,axiom,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    file('theBenchmark.p',fact_zdiv__int) ).

fof(fact_mod__mult2__eq,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)),
    file('theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_div__le__mono,axiom,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ),
    file('theBenchmark.p',fact_div__le__mono) ).

fof(fact_div__le__dividend,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)),
    file('theBenchmark.p',fact_div__le__dividend) ).

fof(fact_zdiv__zero,axiom,
    ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zdiv__zero) ).

fof(fact_mod__Suc__eq__Suc__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n),
    file('theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).

fof(fact_div__mult2__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c),
    file('theBenchmark.p',fact_div__mult2__eq) ).

fof(fact_mod__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ),
    file('theBenchmark.p',fact_mod__less) ).

fof(fact_mod__less__eq__dividend,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)),
    file('theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(fact_mod__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_mod__mult__distrib) ).

fof(fact_mod__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_mod__mult__distrib2) ).

fof(fact_zdiv__zminus2,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b),
    file('theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),
    file('theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_div__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_div__0) ).

fof(fact_div__by__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_div__by__0) ).

fof(fact_div__by__1,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_div__by__1) ).

fof(fact_nat__div__distrib,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ),
    file('theBenchmark.p',fact_nat__div__distrib) ).

fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).

fof(fact_div__1,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
    file('theBenchmark.p',fact_div__1) ).

fof(fact_div__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_div__less) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [V_n,V_m,V_k] :
      ( ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) )
      & ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_mod__1,axiom,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mod__1) ).

fof(fact_mod__Suc,axiom,
    ! [V_n,V_m] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mod__Suc) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_mod__less__divisor,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ),
    file('theBenchmark.p',fact_mod__less__divisor) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__neg__pos__less0) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).

fof(fact_zdiv__self,axiom,
    ! [V_a] :
      ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zdiv__self) ).

fof(fact_mod__eq__0__iff,axiom,
    ! [V_d_2,V_m_2] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ),
    file('theBenchmark.p',fact_mod__eq__0__iff) ).

fof(fact_DIVISION__BY__ZERO,axiom,
    ! [V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_DIVISION__BY__ZERO) ).

fof(fact_zmod__zdiv__trivial,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__zdiv__trivial) ).

fof(fact_mod__mult__self3,axiom,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),
    file('theBenchmark.p',fact_mod__mult__self3) ).

fof(fact_zdiv__zadd1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_zdiv__zadd1__eq) ).

fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
    ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmod__int,axiom,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    file('theBenchmark.p',fact_zmod__int) ).

fof(fact_div__mult__mult1,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_div__mult__self1__is__id,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ),
    file('theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ),
    file('theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_div__mult__mult1__if,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( ( V_c != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) )
        & ( V_c = c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_div__self,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_div__self) ).

fof(fact_mod__div__trivial,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__div__trivial) ).

fof(fact_div__le__mono2,axiom,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ),
    file('theBenchmark.p',fact_div__le__mono2) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ),
    file('theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__mult__self__is__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
    file('theBenchmark.p',fact_div__mult__self__is__m) ).

fof(fact_div__less__dividend,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
    file('theBenchmark.p',fact_div__less__dividend) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_zdiv__mono1,axiom,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ),
    file('theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_zdiv__mono2,axiom,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [V_i_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_mod__le__divisor,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ),
    file('theBenchmark.p',fact_mod__le__divisor) ).

fof(fact_int__div__less__self,axiom,
    ! [V_k,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ),
    file('theBenchmark.p',fact_int__div__less__self) ).

fof(fact_zdiv__zmult2__eq,axiom,
    ! [V_b,V_a,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ),
    file('theBenchmark.p',fact_zdiv__zmult2__eq) ).

fof(fact_mod__mult__self4,axiom,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n),
    file('theBenchmark.p',fact_mod__mult__self4) ).

fof(fact_zdiv__zmod__equality2,axiom,
    ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    file('theBenchmark.p',fact_zdiv__zmod__equality2) ).

fof(fact_zdiv__zmod__equality,axiom,
    ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    file('theBenchmark.p',fact_zdiv__zmod__equality) ).

fof(fact_zdiv__zmult1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_zdiv__zmult1__eq) ).

fof(fact_zmod__zdiv__equality,axiom,
    ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    file('theBenchmark.p',fact_zmod__zdiv__equality) ).

fof(fact_div__mult__self1,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_div__mult__self1) ).

fof(fact_div__mult__self2,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__add__self1,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self1) ).

fof(fact_div__add__self2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self2) ).

fof(fact_div__mod__equality,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ),
    file('theBenchmark.p',fact_div__mod__equality) ).

fof(fact_div__mod__equality2,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ),
    file('theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_mod__div__equality,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
    file('theBenchmark.p',fact_mod__div__equality) ).

fof(fact_mod__div__equality2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
    file('theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ),
    file('theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

fof(fact_split__div,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
             => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
               => hBOOL(hAPP(V_P_2,B_i)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_split__div) ).

fof(fact_mod__lemma,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_mod__lemma) ).

fof(fact_split__mod,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
             => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
               => hBOOL(hAPP(V_P_2,B_j)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__mod) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_Suc__times__mod__eq) ).

fof(fact_nat__mod__distrib,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ),
    file('theBenchmark.p',fact_nat__mod__distrib) ).

fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).

fof(fact_split__div__lemma,axiom,
    ! [V_m_2,V_q_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) )
      <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    file('theBenchmark.p',fact_split__div__lemma) ).

fof(fact_z3div__def,axiom,
    ! [V_k,V_l] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) ),
    file('theBenchmark.p',fact_z3div__def) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus1__eq__if) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus2__eq__if) ).

fof(fact_le__div__geq,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ),
    file('theBenchmark.p',fact_le__div__geq) ).

fof(fact_mod__div__decomp,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ),
    file('theBenchmark.p',fact_mod__div__decomp) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).

fof(fact_incr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
    file('theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( ! [B_z] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
       => ( V_a_2 = V_b_2
        <=> V_c_2 = V_d_2 ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_diff__commute,axiom,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j),
    file('theBenchmark.p',fact_diff__commute) ).

fof(fact_of__int__diff,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__diff) ).

fof(fact_minus__apply,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ominus(T_b)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_minus__apply) ).

fof(fact_of__nat__diff,axiom,
    ! [V_m,V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ),
    file('theBenchmark.p',fact_of__nat__diff) ).

fof(fact_zdiff__int,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_zdiff__int) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_right__minus__eq,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( V_a_2 = V_b_2
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_diff__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_diff__self) ).

fof(fact_diff__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_diff__0__right) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_add__diff__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ),
    file('theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_diff__add__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ),
    file('theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_minus__diff__eq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_mod__diff__right__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__diff__right__eq) ).

fof(fact_mod__diff__left__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
    file('theBenchmark.p',fact_mod__diff__left__eq) ).

fof(fact_mod__diff__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__diff__eq) ).

fof(fact_mod__diff__cong,axiom,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
       => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
         => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ),
    file('theBenchmark.p',fact_mod__diff__cong) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_diff__self__eq__0,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_diff__0__eq__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__0__eq__0) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    file('theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_Suc__diff__diff,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k),
    file('theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_less__imp__diff__less,axiom,
    ! [V_n,V_k,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ),
    file('theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_diff__less__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ),
    file('theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_mod__if,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ),
    file('theBenchmark.p',fact_mod__if) ).

fof(fact_mod__geq,axiom,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ),
    file('theBenchmark.p',fact_mod__geq) ).

fof(fact_diff__add__inverse2,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m,
    file('theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_diff__add__inverse,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m,
    file('theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__diff__left,axiom,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
    file('theBenchmark.p',fact_diff__diff__left) ).

fof(fact_diff__cancel,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    file('theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    file('theBenchmark.p',fact_diff__cancel2) ).

fof(fact_le__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_le__diff__iff) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ),
    file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_eq__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_diff__diff__cancel,axiom,
    ! [V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ),
    file('theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_diff__le__mono,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ),
    file('theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__le__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ),
    file('theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_diff__le__self,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)),
    file('theBenchmark.p',fact_diff__le__self) ).

fof(fact_le__mod__geq,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ),
    file('theBenchmark.p',fact_le__mod__geq) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    file('theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    file('theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_diff__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_zdiff__zmod__right,axiom,
    ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    file('theBenchmark.p',fact_zdiff__zmod__right) ).

fof(fact_zdiff__zmod__left,axiom,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    file('theBenchmark.p',fact_zdiff__zmod__left) ).

fof(fact_nat__diff__distrib,axiom,
    ! [V_z,V_z_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ),
    file('theBenchmark.p',fact_nat__diff__distrib) ).

fof(fact_zdiff__int__split,axiom,
    ! [V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) ) ),
    file('theBenchmark.p',fact_zdiff__int__split) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_eq__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oring(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
      <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ),
    file('theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_eq__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oring(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ),
    file('theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_diff__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ),
    file('theBenchmark.p',fact_diff__0) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_ab__diff__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_diff__def,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_diff__def) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_less__bin__lemma,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_diff__less,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
    file('theBenchmark.p',fact_diff__less) ).

fof(fact_zero__less__diff,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_zero__less__diff) ).

fof(fact_diff__less__Suc,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))),
    file('theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_diff__add__0,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__add__0) ).

fof(fact_diff__is__0__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_less__diff__conv,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ),
    file('theBenchmark.p',fact_less__diff__conv) ).

fof(fact_add__diff__inverse,axiom,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
    file('theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_Suc__diff__le,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_less__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_less__diff__iff) ).

fof(fact_diff__less__mono,axiom,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_diff__less__mono) ).

fof(fact_diff__add__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ),
    file('theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_add__diff__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ),
    file('theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
      <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
    file('theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_le__diff__conv2,axiom,
    ! [V_i_2,V_j_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ),
    file('theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_add__diff__assoc,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_le__add__diff,axiom,
    ! [V_m,V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ),
    file('theBenchmark.p',fact_le__add__diff) ).

fof(fact_le__diff__conv,axiom,
    ! [V_i_2,V_k_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ),
    file('theBenchmark.p',fact_le__diff__conv) ).

fof(fact_diff__diff__right,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ),
    file('theBenchmark.p',fact_diff__diff__right) ).

fof(fact_diff__int__def,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_diff__int__def) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w),
    file('theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__Suc__1,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n),
    file('theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_div__mod__equality_H,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_div__mod__equality_H) ).

fof(fact_mult__div__cancel,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_mult__div__cancel) ).

fof(fact_Divides_Omod__div__equality_H,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)),
    file('theBenchmark.p',fact_Divides_Omod__div__equality_H) ).

fof(fact_tsub__eq,axiom,
    ! [V_x,V_y] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
     => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ),
    file('theBenchmark.p',fact_tsub__eq) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_le__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
    file('theBenchmark.p',fact_le__add__iff2) ).

fof(fact_le__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

fof(fact_less__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_less__add__iff1) ).

fof(fact_less__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
    file('theBenchmark.p',fact_less__add__iff2) ).

fof(fact_diff__Suc__less,axiom,
    ! [V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ),
    file('theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_Suc__pred,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
    file('theBenchmark.p',fact_Suc__pred) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_P_2,B_d))
              & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_nat__diff__split,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ( ! [B_d] :
            ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
           => hBOOL(hAPP(V_P_2,B_d)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split) ).

fof(fact_zle__diff1__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
    file('theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [V_m,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [V_m,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_nat__diff__add__eq1,axiom,
    ! [V_n,V_m,V_u,V_i,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ),
    file('theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [V_n,V_m,V_u,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ),
    file('theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
      <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ),
    file('theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_zmod__zminus2__eq__if,axiom,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zmod__zminus2__eq__if) ).

fof(fact_zmod__zminus1__eq__if,axiom,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zmod__zminus1__eq__if) ).

fof(fact_zmod__zdiv__equality_H,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)),
    file('theBenchmark.p',fact_zmod__zdiv__equality_H) ).

fof(fact_zmult__div__cancel,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)),
    file('theBenchmark.p',fact_zmult__div__cancel) ).

fof(fact_tsub__def,axiom,
    ! [V_x,V_y] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
       => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
       => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ),
    file('theBenchmark.p',fact_tsub__def) ).

fof(fact_Suc__pred_H,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_Suc__diff__1,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ),
    file('theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_add__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) ),
    file('theBenchmark.p',fact_add__eq__if) ).

fof(fact_div__if,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ),
    file('theBenchmark.p',fact_div__geq) ).

fof(fact_mult__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__eq__if) ).

fof(fact_int__power__div__base,axiom,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    file('theBenchmark.p',fact_int__power__div__base) ).

fof(fact_decr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
    file('theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_incr__lemma,axiom,
    ! [V_x,V_z,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ),
    file('theBenchmark.p',fact_incr__lemma) ).

fof(fact_decr__lemma,axiom,
    ! [V_z,V_x,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ),
    file('theBenchmark.p',fact_decr__lemma) ).

fof(fact_nat__mod__eq__lemma,axiom,
    ! [V_y,V_n,V_x] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
       => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ),
    file('theBenchmark.p',fact_nat__mod__eq__lemma) ).

fof(fact_mod__induct__0,axiom,
    ! [V_i_2,V_P_2,V_p_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
         => ( hBOOL(hAPP(V_P_2,B_i))
           => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
     => ( hBOOL(hAPP(V_P_2,V_i_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_mod__induct__0) ).

fof(fact_expand__Suc,axiom,
    ! [V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_expand__Suc) ).

fof(fact_field__le__epsilon,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( ! [B_e] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_of__int__power,axiom,
    ! [V_n,V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ),
    file('theBenchmark.p',fact_of__int__power) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ),
    file('theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_eq__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Int_Oring__char__0(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_eq__number__of) ).

fof(fact_number__of__reorient,axiom,
    ! [V_x_2,V_w_2,T_b] :
      ( class_Int_Onumber(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
      <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ),
    file('theBenchmark.p',fact_number__of__reorient) ).

fof(fact_abs__idempotent,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ),
    file('theBenchmark.p',fact_abs__idempotent) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))),
    file('theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_abs__le__D1,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_abs__le__D1) ).

fof(fact_abs__ge__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
    file('theBenchmark.p',fact_abs__ge__self) ).

fof(fact_abs__zero,axiom,
    ! [T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_abs__zero) ).

fof(fact_abs__eq__0,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_abs__eq__0) ).

fof(fact_abs__add__abs,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
    file('theBenchmark.p',fact_abs__add__abs) ).

fof(fact_abs__mult__self,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
    file('theBenchmark.p',fact_abs__mult__self) ).

fof(fact_abs__mult,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
    file('theBenchmark.p',fact_abs__mult) ).

fof(fact_abs__minus__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ),
    file('theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_abs__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__one) ).

fof(fact_abs__minus__cancel,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ),
    file('theBenchmark.p',fact_abs__minus__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [V_q,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_abs__of__nat,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
    file('theBenchmark.p',fact_abs__of__nat) ).

fof(fact_abs__int__eq,axiom,
    ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),
    file('theBenchmark.p',fact_abs__int__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_zpower__zpower,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
    file('theBenchmark.p',fact_zpower__zpower) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_zpower__zmod,axiom,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m),
    file('theBenchmark.p',fact_zpower__zmod) ).

fof(fact_of__nat__number__of__lemma,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ),
    file('theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_number__of__eq,axiom,
    ! [V_k,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ),
    file('theBenchmark.p',fact_number__of__eq) ).

fof(fact_abs__number__of,axiom,
    ! [V_x,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) ) ),
    file('theBenchmark.p',fact_abs__number__of) ).

fof(fact_zero__less__zpower__abs__iff,axiom,
    ! [V_n_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).

fof(fact_abs__of__nonneg,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_abs__ge__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
    file('theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_abs__of__pos,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__pos) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_abs__not__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__mult__less,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_abs__mult__less) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
    file('theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_abs__le__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_abs__le__iff) ).

fof(fact_abs__leI,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ),
    file('theBenchmark.p',fact_abs__leI) ).

fof(fact_abs__le__D2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ),
    file('theBenchmark.p',fact_abs__le__D2) ).

fof(fact_abs__less__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_abs__less__iff) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [V_w_2,V_v_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Int_Onumber(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ),
    file('theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_left__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ),
    file('theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_right__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Oring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ),
    file('theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Oring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_le__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__number__of) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_less__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__number__of) ).

fof(fact_number__of__add,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__add) ).

fof(fact_add__number__of__eq,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ),
    file('theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_add__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ),
    file('theBenchmark.p',fact_add__number__of__left) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_mult__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ),
    file('theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_number__of__mult,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__mult) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [V_n,V_m] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_abs__zmult__eq__1) ).

fof(fact_number__of__diff,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__diff) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
    file('theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_number__of__minus,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_mult__sgn__abs,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ),
    file('theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_abs__sgn,axiom,
    ! [V_k,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ),
    file('theBenchmark.p',fact_abs__sgn) ).

fof(fact_abs__mult__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_abs__eq__mult,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring__abs(T_a)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ),
    file('theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ),
    file('theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_abs__of__nonpos,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ),
    file('theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_abs__of__neg,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ),
    file('theBenchmark.p',fact_abs__of__neg) ).

fof(fact_abs__if,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oabs__if(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ),
    file('theBenchmark.p',fact_abs__if) ).

fof(fact_zabs__less__one__iff,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zabs__less__one__iff) ).

fof(fact_add__number__of__diff1,axiom,
    ! [V_c,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ),
    file('theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_zabs__def,axiom,
    ! [V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) ),
    file('theBenchmark.p',fact_zabs__def) ).

fof(fact_minus__number__of__mult,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ),
    file('theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_nat__abs__mult__distrib,axiom,
    ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))),
    file('theBenchmark.p',fact_nat__abs__mult__distrib) ).

fof(fact_diff__number__of__eq,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_add__number__of__diff2,axiom,
    ! [V_w,V_c,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ),
    file('theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_power__strict__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ),
    file('theBenchmark.p',fact_power__strict__mono) ).

fof(fact_one__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
    file('theBenchmark.p',fact_one__less__power) ).

fof(fact_power__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_power__decreasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
    file('theBenchmark.p',fact_power__decreasing) ).

fof(fact_power__strict__decreasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
    file('theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_power__Suc__less__one,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ),
    file('theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_number__of__is__id,axiom,
    ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
    file('theBenchmark.p',fact_number__of__is__id) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_less__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [V_m_2,V_x_2] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(fact_power__Suc__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_power__Suc__0) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [V_n_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ),
    file('theBenchmark.p',fact_nat__zero__less__power__iff) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_int__number__of__def,axiom,
    ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w),
    file('theBenchmark.p',fact_int__number__of__def) ).

fof(fact_nat__one__le__power,axiom,
    ! [V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ),
    file('theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_nat__number__of,axiom,
    ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w),
    file('theBenchmark.p',fact_nat__number__of) ).

fof(fact_nat__number__of__def,axiom,
    ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),
    file('theBenchmark.p',fact_nat__number__of__def) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(fact_int__power,axiom,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
    file('theBenchmark.p',fact_int__power) ).

fof(fact_zpower__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zpower__int) ).

fof(fact_minus__numeral__code_I6_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),
    file('theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_power__eq__if,axiom,
    ! [V_p,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_power__eq__if) ).

fof(fact_int__eq__iff__number__of,axiom,
    ! [V_v_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
        & V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) ) ),
    file('theBenchmark.p',fact_int__eq__iff__number__of) ).

fof(fact_nat__power__eq,axiom,
    ! [V_n,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ),
    file('theBenchmark.p',fact_nat__power__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).

fof(fact_field__power__not__zero,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_power__commutes,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__commutes) ).

fof(fact_power__mult__distrib,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
    file('theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_power__one,axiom,
    ! [V_n,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__one) ).

fof(fact_of__nat__power,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ),
    file('theBenchmark.p',fact_of__nat__power) ).

fof(fact_power__mult,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ),
    file('theBenchmark.p',fact_power__mult) ).

fof(fact_one__div__nat__number__of,axiom,
    ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))),
    file('theBenchmark.p',fact_one__div__nat__number__of) ).

fof(fact_power__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ),
    file('theBenchmark.p',fact_power__abs) ).

fof(fact_power__one__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
    file('theBenchmark.p',fact_power__one__right) ).

fof(fact_zero__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_zero__le__power) ).

fof(fact_power__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ),
    file('theBenchmark.p',fact_power__mono) ).

fof(fact_zero__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_zero__less__power) ).

fof(fact_power__eq__0__iff,axiom,
    ! [V_n_2,V_a_2,T_b] :
      ( ( class_Rings_Ozero__neq__one(T_b)
        & class_Rings_Ono__zero__divisors(T_b)
        & class_Rings_Omult__zero(T_b)
        & class_Power_Opower(T_b) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_one__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_one__le__power) ).

fof(fact_power__0__Suc,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_power__0__Suc) ).

fof(fact_power__inject__exp,axiom,
    ! [V_n_2,V_m_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_power__inject__exp) ).

fof(fact_power__Suc2,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ),
    file('theBenchmark.p',fact_power__Suc2) ).

fof(fact_power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__Suc) ).

fof(fact_power__0,axiom,
    ! [V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__0) ).

fof(fact_power__add,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__add) ).

fof(fact_abs__power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_abs__power__minus) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_power__inject__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => V_a = V_b ) ) ) ),
    file('theBenchmark.p',fact_power__inject__base) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_power__gt1__lemma,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
    file('theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_power__less__power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
    file('theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_power__0__left,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_power__0__left) ).

fof(fact_power__gt1,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ),
    file('theBenchmark.p',fact_power__gt1) ).

fof(fact_power__strict__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_zero__le__power__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ),
    file('theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_power__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
    file('theBenchmark.p',fact_power__increasing) ).

fof(fact_power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__minus) ).

fof(fact_power__Suc__less,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
    file('theBenchmark.p',fact_power__Suc__less) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
             => V_a = V_b ) ) ) ) ),
    file('theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_one__mod__nat__number__of,axiom,
    ! [V_v_H] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_one__mod__nat__number__of) ).

fof(fact_power__power__power,axiom,
    ! [T_b] :
      ( class_Power_Opower(T_b)
     => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_power__power__power) ).

fof(fact_div__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_div__nat__number__of) ).

fof(fact_mod__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
          & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) ) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mod__nat__number__of) ).

fof(fact_power__nat__number__of,axiom,
    ! [V_n,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) ),
    file('theBenchmark.p',fact_power__nat__number__of) ).

fof(fact_power__nat__number__of__number__of,axiom,
    ! [V_w,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) ),
    file('theBenchmark.p',fact_power__nat__number__of__number__of) ).

fof(fact_zmod__minus1,axiom,
    ! [V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_zmod__minus1) ).

fof(fact_neg__number__of__Min,axiom,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    file('theBenchmark.p',fact_neg__number__of__Min) ).

fof(fact_rel__simps_I24_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I24_J) ).

fof(fact_rel__simps_I7_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I7_J) ).

fof(fact_not__neg__0,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_not__neg__0) ).

fof(fact_not__neg__int,axiom,
    ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    file('theBenchmark.p',fact_not__neg__int) ).

fof(fact_not__neg__1,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_not__neg__1) ).

fof(fact_bin__less__0__simps_I2_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_bin__less__0__simps_I2_J) ).

fof(fact_Int_OMin__def,axiom,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_Int_OMin__def) ).

fof(fact_mult__Min,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),
    file('theBenchmark.p',fact_mult__Min) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [V_x_2] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    file('theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_neg__def,axiom,
    ! [V_Z_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_neg__def) ).

fof(fact_neg__nat,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
     => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__nat) ).

fof(fact_not__neg__nat,axiom,
    ! [V_z] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
    file('theBenchmark.p',fact_not__neg__nat) ).

fof(fact_mult__minus1,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ),
    file('theBenchmark.p',fact_mult__minus1) ).

fof(fact_mult__minus1__right,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ),
    file('theBenchmark.p',fact_mult__minus1__right) ).

fof(fact_number__of__Min,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_number__of__Min) ).

fof(fact_arith__simps_I31_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
    file('theBenchmark.p',fact_arith__simps_I31_J) ).

fof(fact_abs__minus__one,axiom,
    ! [T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__minus__one) ).

fof(fact_zmod__minus1__right,axiom,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__minus1__right) ).

fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).

fof(fact_zmult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_zmult__eq__1__iff) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    file('theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)),
    file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_of__int__m1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
    file('theBenchmark.p',fact_of__int__m1) ).

fof(fact_zdiv__minus1__right,axiom,
    ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),
    file('theBenchmark.p',fact_zdiv__minus1__right) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [V_v] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__imp__number__of__eq__0) ).

fof(fact_neg__zminus__int,axiom,
    ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    file('theBenchmark.p',fact_neg__zminus__int) ).

fof(fact_abs__power__minus__one,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__power__minus__one) ).

fof(fact_div__eq__minus1,axiom,
    ! [V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    file('theBenchmark.p',fact_div__eq__minus1) ).

fof(fact_eq__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
    <=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
         => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
             => V_v_2 = V_v_H_2 )
            & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) )
          & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) ) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__left) ).

fof(fact_int__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_int__nat__number__of) ).

fof(fact_of__nat__number__of__eq,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
        & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_of__nat__number__of__eq) ).

fof(fact_div__pos__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
    file('theBenchmark.p',fact_div__pos__neg__trivial) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [V_n,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) ),
    file('theBenchmark.p',fact_Suc__nat__number__of__add) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_Suc__nat__number__of) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
         => ? [B_i] :
              ( hAPP(V_f_2,B_i) = V_k_2
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
    file('theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_int__val__lemma,axiom,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
         => ? [B_i] :
              ( hAPP(V_f_2,B_i) = V_k_2
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
    file('theBenchmark.p',fact_int__val__lemma) ).

fof(fact_eq__number__of__eq,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [V_v_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
    <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__number__of__pred__iff__0) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_succ__Min,axiom,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    file('theBenchmark.p',fact_succ__Min) ).

fof(fact_pred__Pls,axiom,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    file('theBenchmark.p',fact_pred__Pls) ).

fof(fact_succ__pred,axiom,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    file('theBenchmark.p',fact_succ__pred) ).

fof(fact_iszero__Numeral0,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ),
    file('theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_Pls__def) ).

fof(fact_rel__simps_I19_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_add__Pls__right,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_add__Pls__right) ).

fof(fact_add__Pls,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
    file('theBenchmark.p',fact_add__Pls) ).

fof(fact_mult__Pls,axiom,
    ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
    file('theBenchmark.p',fact_mult__Pls) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_minus__Pls,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_minus__Pls) ).

fof(fact_rel__simps_I40_J,axiom,
    c_Int_OMin != c_Int_OPls,
    file('theBenchmark.p',fact_rel__simps_I40_J) ).

fof(fact_rel__simps_I37_J,axiom,
    c_Int_OPls != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I37_J) ).

fof(fact_iszero__def,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( c_Int_Oiszero(T_b,V_z_2)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_iszero__def) ).

fof(fact_iszero__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_iszero__0) ).

fof(fact_not__iszero__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_not__iszero__1) ).

fof(fact_number__of__Pls,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ),
    file('theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_add__numeral__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_add__numeral__0,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0) ).

fof(fact_bin__less__0__simps_I1_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_nat__number__of__Pls,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__number__of__Pls) ).

fof(fact_semiring__norm_I113_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    file('theBenchmark.p',fact_semiring__norm_I113_J) ).

fof(fact_zero__is__num__zero,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    file('theBenchmark.p',fact_zero__is__num__zero) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [V_m,V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ),
    file('theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_rel__simps_I23_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I23_J) ).

fof(fact_rel__simps_I20_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I20_J) ).

fof(fact_rel__simps_I3_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I3_J) ).

fof(fact_rel__simps_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I6_J) ).

fof(fact_eq__number__of__Pls__Min,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    file('theBenchmark.p',fact_eq__number__of__Pls__Min) ).

fof(fact_not__neg__number__of__Pls,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('theBenchmark.p',fact_not__neg__number__of__Pls) ).

fof(fact_eq__special_I3_J,axiom,
    ! [V_x_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
    file('theBenchmark.p',fact_eq__special_I3_J) ).

fof(fact_eq__special_I1_J,axiom,
    ! [V_y_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_le__iff__pred__less,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ),
    file('theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_pred__def,axiom,
    ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_pred__def) ).

fof(fact_add__Min,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
    file('theBenchmark.p',fact_add__Min) ).

fof(fact_add__Min__right,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
    file('theBenchmark.p',fact_add__Min__right) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_eq__number__of__0,axiom,
    ! [V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [V_v_2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_number__of2,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('theBenchmark.p',fact_number__of2) ).

fof(fact_less__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) ) ),
    file('theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_le__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_succ__def,axiom,
    ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_succ__def) ).

fof(fact_diff__bin__simps_I2_J,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k),
    file('theBenchmark.p',fact_diff__bin__simps_I2_J) ).

fof(fact_nonzero__number__of__Min,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ),
    file('theBenchmark.p',fact_nonzero__number__of__Min) ).

fof(fact_le__special_I3_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_less__0__number__of,axiom,
    ! [V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ),
    file('theBenchmark.p',fact_less__0__number__of) ).

fof(fact_add__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) ),
    file('theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_number__of__succ,axiom,
    ! [V_k,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ),
    file('theBenchmark.p',fact_number__of__succ) ).

fof(fact_number__of__pred,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__pred) ).

fof(fact_mult__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_eq__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_eq__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
    file('theBenchmark.p',fact_eq__special_I4_J) ).

fof(fact_diff__special_I1_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_diff__special_I2_J,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_diff__special_I2_J) ).

fof(fact_Suc__div__eq__add3__div__number__of,axiom,
    ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    file('theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n),
    file('theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    file('theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    file('theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    file('theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OMin
    <=> V_k_2 = c_Int_OMin ),
    file('theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I43_J,axiom,
    ! [V_l_2] :
      ( c_Int_OMin = c_Int_OBit1(V_l_2)
    <=> c_Int_OMin = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I43_J) ).

fof(fact_Bit1__Min,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('theBenchmark.p',fact_Bit1__Min) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_Bit1__def,axiom,
    ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k),
    file('theBenchmark.p',fact_Bit1__def) ).

fof(fact_rel__simps_I30_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I30_J) ).

fof(fact_rel__simps_I26_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I26_J) ).

fof(fact_rel__simps_I9_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I9_J) ).

fof(fact_rel__simps_I13_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I13_J) ).

fof(fact_neg__number__of__Bit1,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
    file('theBenchmark.p',fact_neg__number__of__Bit1) ).

fof(fact_minus__Bit1,axiom,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))),
    file('theBenchmark.p',fact_minus__Bit1) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [V_w,T_a] :
      ( ( class_Int_Oring__char__0(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ),
    file('theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_succ__Pls,axiom,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_succ__Pls) ).

fof(fact_number__of__Bit1,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_mult__numeral__1,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ),
    file('theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_numeral__1__eq__1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ),
    file('theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_one__is__num__one,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_one__is__num__one) ).

fof(fact_nat__numeral__1__eq__1,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).

fof(fact_Numeral1__eq1__nat,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_Numeral1__eq1__nat) ).

fof(fact_diff__bin__simps_I4_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).

fof(fact_minus__Min,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_minus__Min) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_numeral__1__eq__Suc__0,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

fof(fact_numeral__3__eq__3,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_numeral__3__eq__3) ).

fof(fact_power3__eq__cube,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ),
    file('theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n),
    file('theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_transfer__int__nat__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).

fof(fact_transfer__nat__int__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_le__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
    file('theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_less__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
    file('theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_less__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_add__special_I3_J,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_add__special_I3_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ),
    file('theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

fof(fact_mod__Suc__eq__mod__add3,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    file('theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n),
    file('theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    file('theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_neg__zmod__mult__2) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [V_v,V_w] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_zmod__number__of__Bit1) ).

fof(fact_neg__zdiv__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ),
    file('theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ),
    file('theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ),
    file('theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_of__nat__double,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ),
    file('theBenchmark.p',fact_of__nat__double) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_Bit0__Pls) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [V_l_2] :
      ( c_Int_OPls = c_Int_OBit0(V_l_2)
    <=> c_Int_OPls = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit0(V_k_2) = c_Int_OPls
    <=> V_k_2 = c_Int_OPls ),
    file('theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
    file('theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
    file('theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
    file('theBenchmark.p',fact_Bit0__def) ).

fof(fact_mult__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_mult__Bit0) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_minus__Bit0,axiom,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)),
    file('theBenchmark.p',fact_minus__Bit0) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    file('theBenchmark.p',fact_rel__simps_I42_J) ).

fof(fact_rel__simps_I45_J,axiom,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I45_J) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_rel__simps_I28_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I28_J) ).

fof(fact_rel__simps_I8_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I8_J) ).

fof(fact_zdiv__number__of__Bit0,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_neg__number__of__Bit0,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
    file('theBenchmark.p',fact_neg__number__of__Bit0) ).

fof(fact_pred__Bit0,axiom,
    ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
    file('theBenchmark.p',fact_pred__Bit0) ).

fof(fact_pred__Bit1,axiom,
    ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
    file('theBenchmark.p',fact_pred__Bit1) ).

fof(fact_pred__Min,axiom,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    file('theBenchmark.p',fact_pred__Min) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [V_w_2,T_b] :
      ( ( class_Int_Oring__char__0(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ),
    file('theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_succ__Bit1,axiom,
    ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
    file('theBenchmark.p',fact_succ__Bit1) ).

fof(fact_succ__Bit0,axiom,
    ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
    file('theBenchmark.p',fact_succ__Bit0) ).

fof(fact_number__of__Bit0,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_mult__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l),
    file('theBenchmark.p',fact_mult__Bit1) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_diff__bin__simps_I5_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I5_J) ).

fof(fact_diff__bin__simps_I6_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I6_J) ).

fof(fact_diff__bin__simps_I8_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I8_J) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))),
    file('theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ),
    file('theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_number__of1,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) ) ),
    file('theBenchmark.p',fact_number__of1) ).

fof(fact_mult__2__right,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ),
    file('theBenchmark.p',fact_mult__2__right) ).

fof(fact_mult__2,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ),
    file('theBenchmark.p',fact_mult__2) ).

fof(fact_one__add__one__is__two,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_zero__eq__power2,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__eq__power2) ).

fof(fact_zero__power2,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_zero__power2) ).

fof(fact_numeral__2__eq__2,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_numeral__2__eq__2) ).

fof(fact_semiring__norm_I115_J,axiom,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_semiring__norm_I115_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_power2__eq__square,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
    file('theBenchmark.p',fact_power2__eq__square) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_one__power2,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_one__power2) ).

fof(fact_power2__minus,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power2__minus) ).

fof(fact_nat__mult__2,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    file('theBenchmark.p',fact_nat__mult__2) ).

fof(fact_nat__mult__2__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    file('theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_power__even__eq,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power__even__eq) ).

fof(fact_transfer__int__nat__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).

fof(fact_transfer__nat__int__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).

fof(fact_abs__power2,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_abs__power2) ).

fof(fact_power2__abs,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power2__abs) ).

fof(fact_nat__1__add__1,axiom,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_mod2__Suc__Suc,axiom,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_mod2__Suc__Suc) ).

fof(fact_div2__Suc__Suc,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_div2__Suc__Suc) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))),
    file('theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_add__self__div__2,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m,
    file('theBenchmark.p',fact_add__self__div__2) ).

fof(fact_power2__eq__imp__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
           => V_x = V_y ) ) ) ),
    file('theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_power2__le__imp__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_zero__le__power2,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_zero__le__power2) ).

fof(fact_zero__less__power2,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__less__power2) ).

fof(fact_power2__less__0,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_power2__less__0) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [V_w,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Groups_Omonoid__mult(T_b) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ),
    file('theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_less__2__cases,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__2__cases) ).

fof(fact_nat__2,axiom,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat__2) ).

fof(fact_power2__eq__1__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_a_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
    file('theBenchmark.p',fact_power2__eq__1__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
    ! [V_n,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_power__minus__even,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ),
    file('theBenchmark.p',fact_power__minus__even) ).

fof(fact_power2__less__imp__less,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_sum__power2__ge__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
    file('theBenchmark.p',fact_sum__power2__ge__zero) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).

fof(fact_not__sum__power2__lt__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      <=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_power2__sum,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
    file('theBenchmark.p',fact_power2__sum) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ),
    file('theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [V_n,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(fact_power__odd__eq,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('theBenchmark.p',fact_power__odd__eq) ).

fof(fact_power__minus1__even,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__minus1__even) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [V_v,V_w] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ),
    file('theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_mod2__gr__0,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_mod2__gr__0) ).

fof(fact_div__2__gt__zero,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_div__2__gt__zero) ).

fof(fact_power2__diff,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
    file('theBenchmark.p',fact_power2__diff) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ),
    file('theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

fof(fact_odd__power__less__zero,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_odd__power__less__zero) ).

fof(fact_power__minus1__odd,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_power__m1__even,axiom,
    ! [V_n,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__m1__even) ).

fof(fact_power__m1__odd,axiom,
    ! [V_n,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
    file('theBenchmark.p',fact_power__m1__odd) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).

fof(fact_int__of__code,axiom,
    ! [V_k] :
      ( ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
           => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
           => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
      & ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_int__of__code) ).

fof(fact_one__code__numeral__code,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_one__code__numeral__code) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [V_r_2,T_b] :
      ( ( class_Int_Onumber__ring(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ),
    file('theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_half__gt__zero,axiom,
    ! [V_r,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    file('theBenchmark.p',fact_half__gt__zero) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).

fof(fact_nat__intermed__int__val,axiom,
    ! [V_k_2,V_f_2,V_n_2,V_m_2] :
      ( ! [B_i] :
          ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
           => ? [B_i] :
                ( hAPP(V_f_2,B_i) = V_k_2
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ) ) ) ),
    file('theBenchmark.p',fact_nat__intermed__int__val) ).

fof(fact_code__numeral__zero__minus__one,axiom,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_code__numeral__zero__minus__one) ).

fof(fact_divide__zero__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__zero__left) ).

fof(fact_divide__zero,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__zero) ).

fof(fact_add__divide__distrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_times__divide__eq__right,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ),
    file('theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_times__divide__times__eq,axiom,
    ! [V_w,V_z,V_y,V_x,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ),
    file('theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_diff__divide__distrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_divide__1,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_divide__1) ).

fof(fact_minus__divide__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ),
    file('theBenchmark.p',fact_minus__divide__left) ).

fof(fact_minus__divide__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__divide__right) ).

fof(fact_minus__divide__divide,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_power__divide,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
    file('theBenchmark.p',fact_power__divide) ).

fof(fact_abs__divide,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
    file('theBenchmark.p',fact_abs__divide) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
    ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
    ! [V_n,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_divide__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__right__mono) ).

fof(fact_divide__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_divide__neg__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_divide__neg__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_divide__pos__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_divide__less__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ),
    file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
        <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ),
    file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_divide__eq__imp,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ),
    file('theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_eq__divide__imp,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
         => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ),
    file('theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_frac__eq__eq,axiom,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ),
    file('theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_divide__eq__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_divide__self__if,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring__inverse__zero(T_a)
     => ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) )
        & ( V_a = c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_divide__self__if) ).

fof(fact_divide__self,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_divide__self) ).

fof(fact_right__inverse__eq,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
        <=> V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ),
    file('theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_nonzero__minus__divide__divide) ).

fof(fact_nonzero__power__divide,axiom,
    ! [V_n,V_a,V_b,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
    file('theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ),
    file('theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_power__one__over,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ),
    file('theBenchmark.p',fact_power__one__over) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_frac__le,axiom,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ),
    file('theBenchmark.p',fact_frac__le) ).

fof(fact_frac__less,axiom,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ),
    file('theBenchmark.p',fact_frac__less) ).

fof(fact_frac__less2,axiom,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ),
    file('theBenchmark.p',fact_frac__less2) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_divide__strict__left__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_divide__strict__left__mono,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
    file('theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_divide__less__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq) ).

fof(fact_less__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq) ).

fof(fact_is__nat__def,axiom,
    ! [V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    file('theBenchmark.p',fact_is__nat__def) ).

fof(fact_add__frac__eq,axiom,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_add__frac__eq) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
    file('theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
    file('theBenchmark.p',fact_add__frac__num) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
    file('theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_add__num__frac,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
    file('theBenchmark.p',fact_add__num__frac) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
    file('theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
    file('theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_diff__frac__eq,axiom,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).

fof(fact_eq__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq__number__of) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq__number__of) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).

fof(fact_less__half__sum,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ),
    file('theBenchmark.p',fact_less__half__sum) ).

fof(fact_gt__half__sum,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ),
    file('theBenchmark.p',fact_gt__half__sum) ).

fof(fact_divide__Numeral0,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_abs__div__pos,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_abs__div__pos) ).

fof(fact_divide__Numeral1,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ),
    file('theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_divide__numeral__1,axiom,
    ! [V_a,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ),
    file('theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_divide__minus1,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ),
    file('theBenchmark.p',fact_divide__minus1) ).

fof(fact_zero__code__numeral__code,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    file('theBenchmark.p',fact_zero__code__numeral__code) ).

fof(fact_le__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq) ).

fof(fact_divide__le__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
    file('theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_divide__left__mono,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__left__mono) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_divide__less__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of1) ).

fof(fact_power__diff,axiom,
    ! [V_m,V_n,V_a,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__diff) ).

fof(fact_minus1__divide,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ),
    file('theBenchmark.p',fact_minus1__divide) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of1) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_divide__le__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_nat__of__aux__code,axiom,
    ! [V_n,V_i] :
      ( ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) )
      & ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) ),
    file('theBenchmark.p',fact_nat__of__aux__code) ).

fof(fact_code__numeral_Osize_I1_J,axiom,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_code__numeral_Osize_I1_J) ).

fof(fact_code__numeral_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_code__numeral_Osize_I3_J) ).

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    file('theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).

fof(fact_log_Osimps,axiom,
    ! [V_i,V_b] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
       => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
       => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
    file('theBenchmark.p',fact_log_Osimps) ).

fof(fact_negDivAlg__eqn__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_negDivAlg__div__mod,axiom,
    ! [V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
    file('theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_negDivAlg__minus1) ).

fof(fact_negDivAlg_Osimps,axiom,
    ! [V_b,V_a] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
       => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
       => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Osimps) ).

fof(fact_negDivAlg__eqn__number__of,axiom,
    ! [V_w,V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn__number__of) ).

fof(fact_negDivAlg__eqn,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
         => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
         => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn) ).

fof(fact_minus__shift__def,axiom,
    ! [V_r,V_l,V_k] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) ) ),
    file('theBenchmark.p',fact_minus__shift__def) ).

fof(fact_inc__shift__def,axiom,
    ! [V_k,V_v] :
      ( ( V_v != V_k
       => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
      & ( V_v = V_k
       => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
    file('theBenchmark.p',fact_inc__shift__def) ).

fof(fact_posDivAlg__eqn__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [V_b,V_a] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
       => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
       => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ),
    file('theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_posDivAlg__eqn__number__of,axiom,
    ! [V_w,V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn__number__of) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
         => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
         => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_posDivAlg__0,axiom,
    ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_posDivAlg__0) ).

fof(fact_posDivAlg__div__mod,axiom,
    ! [V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
    file('theBenchmark.p',fact_posDivAlg__div__mod) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
         => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
         => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opsimps) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [V_k,V_l] :
      ( ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) )
      & ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) ),
    file('theBenchmark.p',fact_pdivmod__posDivAlg) ).

fof(fact_pdivmod__def,axiom,
    ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),
    file('theBenchmark.p',fact_pdivmod__def) ).

fof(fact_zmult2__lemma,axiom,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
         => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
         => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_zmult1__lemma,axiom,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ),
    file('theBenchmark.p',fact_zmult1__lemma) ).

fof(fact_accp_Osimps,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Osimps) ).

fof(fact_accp_Oequations,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Oequations) ).

fof(fact_accp__downward,axiom,
    ! [V_a_2,V_b_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    file('theBenchmark.p',fact_accp__downward) ).

fof(fact_accp__subset,axiom,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ),
    file('theBenchmark.p',fact_accp__subset) ).

fof(fact_divmod__int__rel__0,axiom,
    ! [V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
    file('theBenchmark.p',fact_divmod__int__rel__0) ).

fof(fact_self__remainder,axiom,
    ! [V_r,V_q,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_self__remainder) ).

fof(fact_unique__quotient,axiom,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
       => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => V_q = V_q_H ) ) ),
    file('theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
       => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => V_r = V_r_H ) ) ),
    file('theBenchmark.p',fact_unique__remainder) ).

fof(fact_self__quotient,axiom,
    ! [V_r,V_q,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_self__quotient) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ),
    file('theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_negDivAlg__correct,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ),
    file('theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_divmod__int__rel__div__mod,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ),
    file('theBenchmark.p',fact_divmod__int__rel__div__mod) ).

fof(fact_posDivAlg__correct,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ),
    file('theBenchmark.p',fact_posDivAlg__correct) ).

fof(fact_zadd1__lemma,axiom,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
       => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ),
    file('theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_zminus1__lemma,axiom,
    ! [V_r_2,V_q_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ),
    file('theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_divmod__int__relI,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ),
    file('theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
               => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
               => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_code__numeral_Osize_I4_J,axiom,
    ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_code__numeral_Osize_I4_J) ).

fof(fact_code__numeral_Osize_I2_J,axiom,
    ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_code__numeral_Osize_I2_J) ).

fof(fact_divmod__int__def,axiom,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) )
              & ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) ) ) ),
    file('theBenchmark.p',fact_divmod__int__def) ).

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_code__numeral_Oinject,axiom,
    ! [V_code__numeral_H_2,V_code__numeral_2] :
      ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
    <=> V_code__numeral_2 = V_code__numeral_H_2 ),
    file('theBenchmark.p',fact_code__numeral_Oinject) ).

fof(fact_mod__int__def,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    file('theBenchmark.p',fact_mod__int__def) ).

fof(fact_code__numeral_Osimps_I3_J,axiom,
    ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).

fof(fact_code__numeral_Osimps_I2_J,axiom,
    ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
    file('theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).

fof(fact_mod__pos__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_mod__pos__neg) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2),
    file('theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).

fof(fact_negateSnd__eq,axiom,
    ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)),
    file('theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_mod__neg__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [V_qr,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ),
    file('theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_Suc__code__numeral__minus__one,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n,
    file('theBenchmark.p',fact_Suc__code__numeral__minus__one) ).

fof(fact_mod__neg__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_mod__neg__pos) ).

fof(fact_divmod__int__correct,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ),
    file('theBenchmark.p',fact_divmod__int__correct) ).

fof(fact_mod__pos__neg__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ),
    file('theBenchmark.p',fact_mod__pos__neg__1__number__of) ).

fof(fact_mod__pos__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_mod__pos__pos) ).

fof(fact_divmod__int__mod__div,axiom,
    ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)),
    file('theBenchmark.p',fact_divmod__int__mod__div) ).

fof(fact_equalityI,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_equalityI) ).

fof(fact_div__pos__neg__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ),
    file('theBenchmark.p',fact_div__pos__neg__1__number__of) ).

fof(fact_div__neg__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_div__neg__neg) ).

fof(fact_snd__eqD,axiom,
    ! [V_a,V_y,V_x,T_a,T_b] :
      ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
     => V_y = V_a ),
    file('theBenchmark.p',fact_snd__eqD) ).

fof(fact_snd__conv,axiom,
    ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b,
    file('theBenchmark.p',fact_snd__conv) ).

fof(fact_div__pos__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_div__pos__neg) ).

fof(fact_Pair__fst__snd__eq,axiom,
    ! [T_c,T_b,V_t_2,V_s_2] :
      ( V_s_2 = V_t_2
    <=> ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
        & hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) ) ),
    file('theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_prod__eqI,axiom,
    ! [V_q,V_p,T_b,T_a] :
      ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
     => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
       => V_p = V_q ) ),
    file('theBenchmark.p',fact_prod__eqI) ).

fof(fact_fst__conv,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
    file('theBenchmark.p',fact_fst__conv) ).

fof(fact_fst__eqD,axiom,
    ! [V_a,V_y,V_x,T_b,T_a] :
      ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
     => V_x = V_a ),
    file('theBenchmark.p',fact_fst__eqD) ).

fof(fact_surjective__pairing,axiom,
    ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
    file('theBenchmark.p',fact_surjective__pairing) ).

fof(fact_pair__collapse,axiom,
    ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
    file('theBenchmark.p',fact_pair__collapse) ).

fof(fact_div__int__def,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    file('theBenchmark.p',fact_div__int__def) ).

fof(fact_Pair__inject,axiom,
    ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
      ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
     => ~ ( V_a = V_a_H
         => V_b != V_b_H ) ),
    file('theBenchmark.p',fact_Pair__inject) ).

fof(fact_Pair__eq,axiom,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
    <=> ( V_b_2 = V_b_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_Pair__eq) ).

fof(fact_split__paired__All,axiom,
    ! [T_c,T_b,V_P_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ),
    file('theBenchmark.p',fact_split__paired__All) ).

fof(fact_psubset__eq,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> ( V_A_2 != V_B_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubset__eq) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> ( V_A_2 = V_B_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_psubset__imp__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_psubset__subset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_subset__psubset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_subset__refl,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
    file('theBenchmark.p',fact_subset__refl) ).

fof(fact_set__eq__subset,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityD1,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    file('theBenchmark.p',fact_equalityD2) ).

fof(fact_subset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_subset__trans) ).

fof(fact_equalityE,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_equalityE) ).

fof(fact_Compl__subset__Compl__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__subset__Compl__iff) ).

fof(fact_Compl__anti__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    file('theBenchmark.p',fact_Compl__anti__mono) ).

fof(fact_Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Diff__subset) ).

fof(fact_Diff__mono,axiom,
    ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Diff__mono) ).

fof(fact_double__diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_double__diff) ).

fof(fact_div__neg__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__neg__pos) ).

fof(fact_div__pos__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__pos__pos) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_prod__size__simp,axiom,
    ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_prod__size__simp) ).

fof(fact_div__mod__code__numeral__def,axiom,
    ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)),
    file('theBenchmark.p',fact_div__mod__code__numeral__def) ).

fof(fact_divmod__nat__step,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ),
    file('theBenchmark.p',fact_divmod__nat__step) ).

fof(fact_conjI__realizer,axiom,
    ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_p_2))
     => ( hBOOL(hAPP(V_Q_2,V_q_2))
       => ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
          & hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ),
    file('theBenchmark.p',fact_conjI__realizer) ).

fof(fact_exI__realizer,axiom,
    ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
     => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ),
    file('theBenchmark.p',fact_exI__realizer) ).

fof(fact_div__nat__def,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    file('theBenchmark.p',fact_div__nat__def) ).

fof(fact_double__complement,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_double__complement) ).

fof(fact_Compl__eq__Compl__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
    <=> V_A_2 = V_B_2 ),
    file('theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_psubset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_psubset__trans) ).

fof(fact_Diff__idemp,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Diff__idemp) ).

fof(fact_divmod__nat__zero,axiom,
    ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m),
    file('theBenchmark.p',fact_divmod__nat__zero) ).

fof(fact_mod__nat__def,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    file('theBenchmark.p',fact_mod__nat__def) ).

fof(fact_divmod__nat__base,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ),
    file('theBenchmark.p',fact_divmod__nat__base) ).

fof(fact_divmod__nat__div__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_divmod__nat__div__mod) ).

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_range,axiom,
    ! [V_s,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ),
    file('theBenchmark.p',fact_range) ).

fof(fact_divmod__nat__rel__def,axiom,
    ! [V_qr_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
    <=> ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) ) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) ) ) ) )
        & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__def) ).

fof(fact_divmod__nat__rel__unique,axiom,
    ! [V_qr_H,V_qr,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
       => V_qr = V_qr_H ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
    file('theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

fof(fact_divmod__nat__eq,axiom,
    ! [V_qr,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
     => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ),
    file('theBenchmark.p',fact_divmod__nat__eq) ).

fof(fact_mod__eq,axiom,
    ! [V_r,V_q,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ),
    file('theBenchmark.p',fact_mod__eq) ).

fof(fact_div__eq,axiom,
    ! [V_r,V_q,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ),
    file('theBenchmark.p',fact_div__eq) ).

fof(fact_divmod__nat__rel,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))),
    file('theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_prod_Orecs,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_prod_Orecs) ).

fof(fact_adjust__eq,axiom,
    ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))),
    file('theBenchmark.p',fact_adjust__eq) ).

fof(fact_iterate_Osimps,axiom,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) ),
    file('theBenchmark.p',fact_iterate_Osimps) ).

fof(fact_subtract__code__numeral__def,axiom,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_subtract__code__numeral__def) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m),
    file('theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_scomp__unfold,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
    file('theBenchmark.p',fact_scomp__unfold) ).

fof(fact_scomp__scomp,axiom,
    ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)),
    file('theBenchmark.p',fact_scomp__scomp) ).

fof(fact_fun__Compl__def,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ouminus(T_b)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__Compl__def) ).

fof(fact_fun__diff__def,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ominus(T_b)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__diff__def) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),
    file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat__number__of__Bit0) ).

fof(fact_scomp__Pair,axiom,
    ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2,
    file('theBenchmark.p',fact_scomp__Pair) ).

fof(fact_power__number__of__even,axiom,
    ! [V_w_2,V_z_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_power__number__of__even) ).

fof(fact_zpower__number__of__even,axiom,
    ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    file('theBenchmark.p',fact_zpower__number__of__even) ).

fof(fact_Pair__scomp,axiom,
    ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
    file('theBenchmark.p',fact_Pair__scomp) ).

fof(fact_power__number__of__even__number__of,axiom,
    ! [V_w_2,V_v_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_power__number__of__even__number__of) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [V_z_2,V_z_H_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) ),
    file('theBenchmark.p',fact_diff__nat__eq__if) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).

fof(fact_eq__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
    file('theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
    file('theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_nat__number__of__Bit1,axiom,
    ! [V_w_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__Bit1) ).

fof(fact_less__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ),
    file('theBenchmark.p',fact_less__number__of__Suc) ).

fof(fact_less__Suc__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ),
    file('theBenchmark.p',fact_less__Suc__number__of) ).

fof(fact_le__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ),
    file('theBenchmark.p',fact_le__number__of__Suc) ).

fof(fact_le__Suc__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ),
    file('theBenchmark.p',fact_le__Suc__number__of) ).

fof(fact_power__number__of__odd,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) ) ),
    file('theBenchmark.p',fact_power__number__of__odd) ).

fof(fact_zpower__number__of__odd,axiom,
    ! [V_z_2,V_w_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_zpower__number__of__odd) ).

fof(fact_power__number__of__odd__number__of,axiom,
    ! [V_v_2,V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) ) ),
    file('theBenchmark.p',fact_power__number__of__odd__number__of) ).

fof(fact_diff__nat__number__of,axiom,
    ! [V_v_2,V_v_H_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
    file('theBenchmark.p',fact_diff__nat__number__of) ).

fof(fact_of__int__num,axiom,
    ! [V_k_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_of__int__num) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_adjust__def,axiom,
    ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('theBenchmark.p',fact_adjust__def) ).

fof(fact_nat__case__number__of,axiom,
    ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))),
    file('theBenchmark.p',fact_nat__case__number__of) ).

fof(fact_nat__rec__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))),
    file('theBenchmark.p',fact_nat__rec__add__eq__if) ).

fof(fact_split__twice,axiom,
    ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
    file('theBenchmark.p',fact_split__twice) ).

fof(fact_split__weak__cong,axiom,
    ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
      ( V_p_2 = V_q_2
     => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ),
    file('theBenchmark.p',fact_split__weak__cong) ).

fof(fact_split__conv,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_split__conv) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_prod_Osimps_I2_J) ).

fof(fact_scomp__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_scomp__apply) ).

fof(fact_split__eta,axiom,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
    file('theBenchmark.p',fact_split__eta) ).

fof(fact_fst__def,axiom,
    ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
    file('theBenchmark.p',fact_fst__def) ).

fof(fact_snd__def,axiom,
    ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
    file('theBenchmark.p',fact_snd__def) ).

fof(fact_scomp__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_scomp__def) ).

fof(fact_nat__rec__0,axiom,
    ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    file('theBenchmark.p',fact_nat__rec__0) ).

fof(fact_nat__rec__Suc,axiom,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
    file('theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_nat__case__0,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    file('theBenchmark.p',fact_nat__case__0) ).

fof(fact_nat__case__Suc,axiom,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
    file('theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_prod__case__beta,axiom,
    ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    file('theBenchmark.p',fact_prod__case__beta) ).

fof(fact_split__beta,axiom,
    ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
    file('theBenchmark.p',fact_split__beta) ).

fof(fact_split__comp__eq,axiom,
    ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_split__comp__eq) ).

fof(fact_split__def,axiom,
    ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    file('theBenchmark.p',fact_split__def) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_diff__Suc,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)),
    file('theBenchmark.p',fact_diff__Suc) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    file('theBenchmark.p',fact_divmod__int__rel__def) ).

fof(fact_nat__rec__number__of,axiom,
    ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_nat__rec__number__of) ).

fof(fact_divmod__int__pdivmod,axiom,
    ! [V_l_2,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
          & ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_divmod__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
          & ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_divmod__int__code) ).

fof(fact_MGT__def,axiom,
    ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)),
    file('theBenchmark.p',fact_MGT__def) ).

fof(fact_min__Suc__number__of,axiom,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_min__Suc__number__of) ).

fof(fact_min__number__of__Suc,axiom,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_min__number__of__Suc) ).

fof(fact_prod__caseI,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
      ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_prod__caseI) ).

fof(fact_splitI,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_splitI) ).

fof(fact_splitD,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_splitD) ).

fof(fact_min__0R,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_min__0R) ).

fof(fact_min__0L,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_min__0L) ).

fof(fact_min__Suc__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_min__Suc__Suc) ).

fof(fact_min__diff__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__diff__distrib__left) ).

fof(fact_min__max_Ole__infE,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infE) ).

fof(fact_min__max_Oinf__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__mono) ).

fof(fact_min__max_Oinf__greatest,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__greatest) ).

fof(fact_min__max_Ole__infI,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI) ).

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__max_Ole__inf__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__inf__iff) ).

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_min__le__iff__disj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__le__iff__disj) ).

fof(fact_min__max_Oinf__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__assoc) ).

fof(fact_min__max_Oinf_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Oinf_Oassoc) ).

fof(fact_min__max_Oinf__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__left__commute) ).

fof(fact_min__max_Oinf_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).

fof(fact_min__max_Oinf__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_min__max_Oinf__left__idem) ).

fof(fact_min__max_Oinf_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).

fof(fact_min__max_Oinf__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_min__max_Oinf__commute) ).

fof(fact_min__max_Oinf_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_min__max_Oinf_Ocommute) ).

fof(fact_min__max_Oinf_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_min__max_Oinf_Oidem) ).

fof(fact_min__add__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_min__max_Oless__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_min__less__iff__disj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_min__less__iff__conj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_min__less__iff__conj) ).

fof(fact_min__diff,axiom,
    ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i),
    file('theBenchmark.p',fact_min__diff) ).

fof(fact_splitD_H,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
     => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ),
    file('theBenchmark.p',fact_splitD_H) ).

fof(fact_apsnd__conv,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_apsnd__conv) ).

fof(fact_fst__apsnd,axiom,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
    file('theBenchmark.p',fact_fst__apsnd) ).

fof(fact_apsnd__eq__conv,axiom,
    ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
      ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
    <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ),
    file('theBenchmark.p',fact_apsnd__eq__conv) ).

fof(fact_snd__apsnd,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    file('theBenchmark.p',fact_snd__apsnd) ).

fof(fact_min__number__of,axiom,
    ! [V_v,V_u,T_b] :
      ( ( class_Orderings_Oord(T_b)
        & class_Int_Onumber(T_b) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ),
    file('theBenchmark.p',fact_min__number__of) ).

fof(fact_min__Suc1,axiom,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_min__Suc1) ).

fof(fact_min__Suc2,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_min__Suc2) ).

fof(fact_negateSnd__def,axiom,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    file('theBenchmark.p',fact_negateSnd__def) ).

fof(fact_divmod__nat__if,axiom,
    ! [V_m_2,V_n_2] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
            | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) ),
    file('theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_min__ord__min,axiom,
    ! [T_b] :
      ( class_Orderings_Oord(T_b)
     => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
    file('theBenchmark.p',fact_min__ord__min) ).

fof(fact_max__number__of__Suc,axiom,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_max__number__of__Suc) ).

fof(fact_max__Suc__number__of,axiom,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_max__Suc__number__of) ).

fof(fact_apfst__apsnd,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
    file('theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_apsnd__apfst,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
    file('theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_min__max_Oless__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_max__less__iff__conj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_max__less__iff__conj) ).

fof(fact_less__max__iff__disj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_less__max__iff__disj) ).

fof(fact_max__add__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_max__add__distrib__left) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_min__max_Osup_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_Osup_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_le__max__iff__disj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_le__max__iff__disj) ).

fof(fact_le__maxI1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_le__maxI2) ).

fof(fact_min__max_Ole__iff__sup,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_min__max_Ole__iff__sup) ).

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI) ).

fof(fact_min__max_Osup__least,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__least) ).

fof(fact_min__max_Osup__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__mono) ).

fof(fact_min__max_Ole__supE,axiom,
    ! [V_x,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_max__diff__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_max__diff__distrib__left) ).

fof(fact_max__Suc__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_max__Suc__Suc) ).

fof(fact_max__0L,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_max__0L) ).

fof(fact_max__0R,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_max__0R) ).

fof(fact_min__max_Osup__inf__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_min__max_Osup__inf__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).

fof(fact_min__max_Osup__inf__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_apfst__conv,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2),
    file('theBenchmark.p',fact_apfst__conv) ).

fof(fact_apfst__eq__conv,axiom,
    ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
    <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ),
    file('theBenchmark.p',fact_apfst__eq__conv) ).

fof(fact_fst__apfst,axiom,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
    file('theBenchmark.p',fact_fst__apfst) ).

fof(fact_snd__apfst,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2),
    file('theBenchmark.p',fact_snd__apfst) ).

fof(fact_max__number__of,axiom,
    ! [V_v,V_u,T_b] :
      ( ( class_Orderings_Oord(T_b)
        & class_Int_Onumber(T_b) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ),
    file('theBenchmark.p',fact_max__number__of) ).

fof(fact_min__max_Odistrib__sup__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ),
    file('theBenchmark.p',fact_min__max_Odistrib__sup__le) ).

fof(fact_min__max_Odistrib__inf__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ),
    file('theBenchmark.p',fact_min__max_Odistrib__inf__le) ).

fof(fact_minus__max__eq__min,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_minus__max__eq__min) ).

fof(fact_minus__min__eq__max,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_minus__min__eq__max) ).

fof(fact_nat__minus__add__max,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__minus__add__max) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
    file('theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_max__Suc1,axiom,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_max__Suc1) ).

fof(fact_max__Suc2,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_max__Suc2) ).

fof(fact_dual__min,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ),
    file('theBenchmark.p',fact_dual__min) ).

fof(fact_max__ord__max,axiom,
    ! [T_b] :
      ( class_Orderings_Oord(T_b)
     => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
    file('theBenchmark.p',fact_max__ord__max) ).

fof(fact_Nitpick_OFrac__def,axiom,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_Nitpick_OFrac__def) ).

fof(fact_norm__frac_Osimps,axiom,
    ! [V_a_2,V_b_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
          & ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Osimps) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
            & ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_Min_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Min_Oidem) ).

fof(fact_Max_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Max_Oidem) ).

fof(fact_dual__max,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ),
    file('theBenchmark.p',fact_dual__max) ).

fof(fact_Nitpick_Oint__gcd__def,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    file('theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Opinduct) ).

fof(fact_Nitpick_Oint__lcm__def,axiom,
    ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    file('theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_Nitpick_Ozero__frac__def,axiom,
    ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Ozero__frac__def) ).

fof(fact_nat__gcd_Osimps,axiom,
    ! [V_x,V_y] :
      ( ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) )
      & ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) ),
    file('theBenchmark.p',fact_nat__gcd_Osimps) ).

fof(fact_Nitpick_Onat__lcm__def,axiom,
    ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)),
    file('theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).

fof(fact_Nitpick_Oone__frac__def,axiom,
    ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Oone__frac__def) ).

fof(fact_Nitpick_Onumber__of__frac__def,axiom,
    ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Onumber__of__frac__def) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
     => ( ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) )
        & ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)),
    file('theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_internal__split__def,axiom,
    ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
    file('theBenchmark.p',fact_internal__split__def) ).

fof(fact_internal__split__conv,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_internal__split__conv) ).

fof(fact_nat__gcd_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
           => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).

fof(fact_transfer__morphism__int__nat,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    file('theBenchmark.p',fact_transfer__morphism__int__nat) ).

fof(fact_pair__box_Osize_I1_J,axiom,
    ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_pair__box_Osize_I1_J) ).

fof(fact_rev__predicate2D,axiom,
    ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
       => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_pair__box_Oinject,axiom,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
    <=> ( V_b_2 = V_b_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_pair__box_Oinject) ).

fof(fact_rev__predicate1D,axiom,
    ! [V_Q_2,T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
       => hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_predicate1D,axiom,
    ! [V_x_2,V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
     => ( hBOOL(hAPP(V_P_2,V_x_2))
       => hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_predicate1D) ).

fof(fact_predicate2D,axiom,
    ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
     => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_predicate2D) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
    file('theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_Nitpick_Oof__frac__def,axiom,
    ! [V_q,T_a,T_b] :
      ( ( class_Rings_Oring__1(T_b)
        & class_Rings_Oinverse(T_b) )
     => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ),
    file('theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_Nitpick_Oinverse__frac__def,axiom,
    ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
    file('theBenchmark.p',fact_Nitpick_Oinverse__frac__def) ).

fof(fact_Nitpick_Ouminus__frac__def,axiom,
    ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
    file('theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_Nitpick_Oless__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] :
      ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_Nitpick_Oless__frac__def) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] :
      ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).

fof(fact_pair__box_Osize_I2_J,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_pair__box_Osize_I2_J) ).

fof(fact_pair__box_Osimps_I2_J,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_pair__box_Osimps_I2_J) ).

fof(fact_pair__box_Orecs,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_pair__box_Orecs) ).

fof(fact_The__split,axiom,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    file('theBenchmark.p',fact_The__split) ).

fof(fact_split__paired__The,axiom,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_split__paired__The) ).

fof(fact_The__split__eq,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    file('theBenchmark.p',fact_The__split__eq) ).

fof(fact_divmod__nat__def,axiom,
    ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)),
    file('theBenchmark.p',fact_divmod__nat__def) ).

fof(fact_the__eq__trivial,axiom,
    ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
    file('theBenchmark.p',fact_the__eq__trivial) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_code__numeral_Orecs_I2_J,axiom,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
    file('theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Random_Osimps,axiom,
    ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) ),
    file('theBenchmark.p',fact_Random_Osimps) ).

fof(fact_exE__realizer,axiom,
    ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
           => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
       => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ),
    file('theBenchmark.p',fact_exE__realizer) ).

fof(fact_code__numeral_Orecs_I1_J,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    file('theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
    file('theBenchmark.p',fact_Random__Sequence_Oempty__def) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
    file('theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_New__DSequence_Opos__not__seq__def,axiom,
    ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))),
    file('theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [V_i_2] :
      ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ),
    file('theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_beyond__def,axiom,
    ! [V_l,V_k] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) ),
    file('theBenchmark.p',fact_beyond__def) ).

fof(fact_Code__Numeral_Oof__nat__code,axiom,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).

fof(fact_Code__Numeral_Oof__nat__inject,axiom,
    ! [V_m_2,V_n_2] :
      ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
    <=> V_n_2 = V_m_2 ),
    file('theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

fof(fact_times__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_beyond__zero,axiom,
    ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_beyond__zero) ).

fof(fact_zero__code__numeral__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_zero__code__numeral__def) ).

fof(fact_one__code__numeral__def,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_one__code__numeral__def) ).

fof(fact_less__code__numeral__code,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
    file('theBenchmark.p',fact_less__code__numeral__code) ).

fof(fact_plus__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_plus__code__numeral__code) ).

fof(fact_less__eq__code__numeral__code,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
    file('theBenchmark.p',fact_less__eq__code__numeral__code) ).

fof(fact_subtract__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_code__numeral__decr,axiom,
    ! [V_k] :
      ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ),
    file('theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_pos__not__random__dseq__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)),
    file('theBenchmark.p',fact_pos__not__random__dseq__def) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_mod__code__numeral__def) ).

fof(fact_times__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_times__code__numeral__def) ).

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) )
      & ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) ),
    file('theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

fof(fact_code__numeral_Onat__of__inject,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [V_l_2,V_k_2] :
      ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_nat__of__inverse,axiom,
    ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
    file('theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_of__nat__nat__of,axiom,
    ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
    file('theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_nat__of__of__nat,axiom,
    ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
    file('theBenchmark.p',fact_nat__of__of__nat) ).

fof(fact_less__code__numeral__def,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
    file('theBenchmark.p',fact_less__code__numeral__def) ).

fof(fact_nat__of__number,axiom,
    ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k),
    file('theBenchmark.p',fact_nat__of__number) ).

fof(fact_less__eq__code__numeral__def,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
    file('theBenchmark.p',fact_less__eq__code__numeral__def) ).

fof(fact_nat__of__code,axiom,
    ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_nat__of__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n),
    file('theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))),
    file('theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_minus__code__numeral__def) ).

fof(fact_plus__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_plus__code__numeral__def) ).

fof(fact_div__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
    file('theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) )
      & ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) ),
    file('theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_curry__def,axiom,
    ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
    file('theBenchmark.p',fact_curry__def) ).

fof(fact_curryI,axiom,
    ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
      ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_curryI) ).

fof(fact_curryD,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
     => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_curryD) ).

fof(fact_curryE,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
     => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_curryE) ).

fof(fact_curry__conv,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),
    file('theBenchmark.p',fact_curry__conv) ).

fof(fact_curry__split,axiom,
    ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
    file('theBenchmark.p',fact_curry__split) ).

fof(fact_split__curry,axiom,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
    file('theBenchmark.p',fact_split__curry) ).

fof(fact_pos__empty__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
    file('theBenchmark.p',fact_pos__empty__def) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_pos__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_pos__bind__def) ).

fof(fact_New__DSequence_Oneg__bind__def,axiom,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_power__dvd__imp__le,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_power__dvd__imp__le) ).

fof(fact_dvd_Oorder__refl,axiom,
    ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
    file('theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(fact_dvd__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_dvd__0__right) ).

fof(fact_dvd__1__left,axiom,
    ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
    file('theBenchmark.p',fact_dvd__1__left) ).

fof(fact_dvd__mult__right,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ),
    file('theBenchmark.p',fact_dvd__mult__right) ).

fof(fact_dvd__mult__left,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ),
    file('theBenchmark.p',fact_dvd__mult__left) ).

fof(fact_dvdI,axiom,
    ! [V_k,V_b,V_a,T_a] :
      ( class_Rings_Odvd(T_a)
     => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ),
    file('theBenchmark.p',fact_dvdI) ).

fof(fact_mult__dvd__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_mult__dvd__mono) ).

fof(fact_dvd__mult,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_dvd__mult) ).

fof(fact_dvd__mult2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_dvd__mult2) ).

fof(fact_dvd__triv__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ),
    file('theBenchmark.p',fact_dvd__triv__right) ).

fof(fact_dvd__triv__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ),
    file('theBenchmark.p',fact_dvd__triv__left) ).

fof(fact_dvd__power__same,axiom,
    ! [V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__power__same) ).

fof(fact_div__dvd__div,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ),
    file('theBenchmark.p',fact_div__dvd__div) ).

fof(fact_one__dvd,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ),
    file('theBenchmark.p',fact_one__dvd) ).

fof(fact_dvd__0__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_dvd__0__left) ).

fof(fact_dvd__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd__trans) ).

fof(fact_dvd__refl,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ),
    file('theBenchmark.p',fact_dvd__refl) ).

fof(fact_dvd_Oless__asym,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__asym) ).

fof(fact_dvd_Oless__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oless__trans) ).

fof(fact_dvd_Oless__asym_H,axiom,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__asym_H) ).

fof(fact_dvd_Oless__le__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oless__le__trans) ).

fof(fact_dvd_Oord__less__eq__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
     => ( V_b = V_c
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).

fof(fact_dvd_Oless__imp__not__eq2,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => V_y != V_x ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).

fof(fact_dvd_Oless__imp__not__eq,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => V_x != V_y ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).

fof(fact_dvd_Oless__imp__not__less,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__less) ).

fof(fact_dvd_Oless__imp__le,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    file('theBenchmark.p',fact_dvd_Oless__imp__le) ).

fof(fact_dvd_Oless__not__sym,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__not__sym) ).

fof(fact_dvd_Oless__imp__neq,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => V_x != V_y ),
    file('theBenchmark.p',fact_dvd_Oless__imp__neq) ).

fof(fact_dvd_Ole__less__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__less__trans) ).

fof(fact_dvd_Oord__eq__less__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( V_a = V_b
     => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) )
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).

fof(fact_dvd_Oorder__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ),
    file('theBenchmark.p',fact_dvd_Oorder__trans) ).

fof(fact_dvd_Oantisym,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
       => V_x = V_y ) ),
    file('theBenchmark.p',fact_dvd_Oantisym) ).

fof(fact_dvd__antisym,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_dvd__antisym) ).

fof(fact_dvd_Oord__le__eq__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
     => ( V_b = V_c
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
    file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).

fof(fact_dvd_Oord__eq__le__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( V_a = V_b
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
    file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).

fof(fact_dvd_Ole__neq__trans,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
     => ( V_a != V_b
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).

fof(fact_dvd_Ole__imp__less__or__eq,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( V_x = V_y
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).

fof(fact_dvd_Oantisym__conv,axiom,
    ! [V_x_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_dvd_Oantisym__conv) ).

fof(fact_dvd_Oeq__refl,axiom,
    ! [V_y,V_x] :
      ( V_x = V_y
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    file('theBenchmark.p',fact_dvd_Oeq__refl) ).

fof(fact_dvd_Oneq__le__trans,axiom,
    ! [V_b,V_a] :
      ( V_a != V_b
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).

fof(fact_dvd_Oless__le,axiom,
    ! [V_y_2,V_x_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
    <=> ( V_x_2 != V_y_2
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__le) ).

fof(fact_dvd_Ole__less,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
    <=> ( V_x_2 = V_y_2
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__less) ).

fof(fact_dvd_Oeq__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_dvd_Oeq__iff) ).

fof(fact_dvd__add,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_dvd__add) ).

fof(fact_dvd__mod__iff,axiom,
    ! [V_m_2,V_n_2,V_k_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
        <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_dvd__mod__iff) ).

fof(fact_mod__mod__cancel,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
       => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ),
    file('theBenchmark.p',fact_mod__mod__cancel) ).

fof(fact_dvd__mod,axiom,
    ! [V_n,V_m,V_k,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ),
    file('theBenchmark.p',fact_dvd__mod) ).

fof(fact_dvd__mod__imp__dvd,axiom,
    ! [V_n,V_m,V_k,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ),
    file('theBenchmark.p',fact_dvd__mod__imp__dvd) ).

fof(fact_dvd__minus__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Ocomm__ring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_dvd__minus__iff) ).

fof(fact_minus__dvd__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Ocomm__ring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_minus__dvd__iff) ).

fof(fact_dvd__diff,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ),
    file('theBenchmark.p',fact_dvd__diff) ).

fof(fact_dvd__abs__iff,axiom,
    ! [V_k_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_dvd__abs__iff) ).

fof(fact_abs__dvd__iff,axiom,
    ! [V_k_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_abs__dvd__iff) ).

fof(fact_dvd__if__abs__eq,axiom,
    ! [V_k,V_l,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ),
    file('theBenchmark.p',fact_dvd__if__abs__eq) ).

fof(fact_dvd__diff__nat,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__diff__nat) ).

fof(fact_dvd__reduce,axiom,
    ! [V_n_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ),
    file('theBenchmark.p',fact_dvd__reduce) ).

fof(fact_nat__dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).

fof(fact_dvd__mult__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Rings_Oidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
          | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel__right) ).

fof(fact_dvd__mult__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Oidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
          | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel__left) ).

fof(fact_dvd__eq__mod__eq__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
      <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_dvd__eq__mod__eq__0) ).

fof(fact_dvd__imp__mod__0,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_dvd__imp__mod__0) ).

fof(fact_div__add,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_div__add) ).

fof(fact_div__mult__div__if__dvd,axiom,
    ! [V_w,V_z,V_x,V_y,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_div__mult__div__if__dvd) ).

fof(fact_dvd__div__mult,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ),
    file('theBenchmark.p',fact_dvd__div__mult) ).

fof(fact_dvd__div__mult__self,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ),
    file('theBenchmark.p',fact_dvd__div__mult__self) ).

fof(fact_div__mult__swap,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ),
    file('theBenchmark.p',fact_div__mult__swap) ).

fof(fact_dvd__mult__div__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ),
    file('theBenchmark.p',fact_dvd__mult__div__cancel) ).

fof(fact_dvd__neg__div,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_dvd__neg__div) ).

fof(fact_dvd__div__neg,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_dvd__div__neg) ).

fof(fact_le__imp__power__dvd,axiom,
    ! [V_a,V_n,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_le__imp__power__dvd) ).

fof(fact_dvd__power__le,axiom,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ),
    file('theBenchmark.p',fact_dvd__power__le) ).

fof(fact_power__le__dvd,axiom,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__le__dvd) ).

fof(fact_div__power,axiom,
    ! [V_n,V_x,V_y,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
    file('theBenchmark.p',fact_div__power) ).

fof(fact_dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_dvd__1__iff__1) ).

fof(fact_nat__dvd__not__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ),
    file('theBenchmark.p',fact_nat__dvd__not__less) ).

fof(fact_nat__mult__dvd__cancel__disj,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

fof(fact_dvd__diffD,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD) ).

fof(fact_dvd__diffD1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD1) ).

fof(fact_unity__coeff__ex,axiom,
    ! [V_l_2,V_P_2,T_b] :
      ( ( class_Rings_Osemiring__0(T_b)
        & class_Rings_Odvd(T_b) )
     => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) ) ) ),
    file('theBenchmark.p',fact_unity__coeff__ex) ).

fof(fact_inf__period_I4_J,axiom,
    ! [V_t_2,V_D_2,V_d_2,T_b] :
      ( ( class_Rings_Odvd(T_b)
        & class_Rings_Ocomm__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
       => ! [B_x,B_k] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_inf__period_I4_J) ).

fof(fact_inf__period_I3_J,axiom,
    ! [V_t_2,V_D_2,V_d_2,T_b] :
      ( ( class_Rings_Odvd(T_b)
        & class_Rings_Ocomm__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
       => ! [B_x,B_k] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_inf__period_I3_J) ).

fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Divides_Osemiring__div(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).

fof(fact_dvd__div__eq__mult,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
         => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
          <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_dvd__div__eq__mult) ).

fof(fact_dvd__div__div__eq__mult,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
           => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
             => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
              <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ),
    file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).

fof(fact_dvd__imp__le,axiom,
    ! [V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ),
    file('theBenchmark.p',fact_dvd__imp__le) ).

fof(fact_nat__mult__dvd__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

fof(fact_dvd__mult__cancel,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel) ).

fof(fact_dvd__power,axiom,
    ! [V_x,V_n,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( ( V_x = c_Groups_Oone__class_Oone(T_a)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) )
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__power) ).

fof(fact_dvd__mult__cancel2,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))
      <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel2) ).

fof(fact_dvd__mult__cancel1,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))
      <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel1) ).

fof(fact_neg__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_neg__bind__def) ).

fof(fact_dvd_Ostrict__monoD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
       => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
    file('theBenchmark.p',fact_dvd_Ostrict__monoD) ).

fof(fact_dvd_OmonoD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
    file('theBenchmark.p',fact_dvd_OmonoD) ).

fof(fact_nat__dvd__iff,axiom,
    ! [V_m_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
         => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ),
    file('theBenchmark.p',fact_nat__dvd__iff) ).

fof(fact_hoare__derivs_OCall,axiom,
    ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,V_s_H_2)))),V_X_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),V_a_2)))),c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_hoare__derivs_OCall) ).

fof(fact_empty__subsetI,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_empty__subsetI) ).

fof(fact_zdvd__zmod,axiom,
    ! [V_n,V_m,V_f] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ) ),
    file('theBenchmark.p',fact_zdvd__zmod) ).

fof(fact_zdvd__zmod__imp__zdvd,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ),
    file('theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).

fof(fact_uminus__dvd__conv_I1_J,axiom,
    ! [V_t_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ),
    file('theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

fof(fact_uminus__dvd__conv_I2_J,axiom,
    ! [V_t_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ),
    file('theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

fof(fact_zdvd__zdiffD,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ),
    file('theBenchmark.p',fact_zdvd__zdiffD) ).

fof(fact_subset__insertI,axiom,
    ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_subset__insertI) ).

fof(fact_subset__insertI2,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_subset__insertI2) ).

fof(fact_insert__mono,axiom,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
    file('theBenchmark.p',fact_insert__mono) ).

fof(fact_LoopF,axiom,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_LoopF) ).

fof(fact_Comp,axiom,
    ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_Comp) ).

fof(fact_hoare__derivs_OSkip,axiom,
    ! [V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_OSkip) ).

fof(fact_hoare__derivs_Oequations_I7_J,axiom,
    ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).

fof(fact_Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Diff__insert) ).

fof(fact_Diff__insert2,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
    file('theBenchmark.p',fact_Diff__insert2) ).

fof(fact_insert__Diff__single,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    file('theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_thin,axiom,
    ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ),
    file('theBenchmark.p',fact_thin) ).

fof(fact_weaken,axiom,
    ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ),
    file('theBenchmark.p',fact_weaken) ).

fof(fact_asm,axiom,
    ! [V_Ga_2,V_tsa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ),
    file('theBenchmark.p',fact_asm) ).

fof(fact_derivs__insertD,axiom,
    ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
        & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_derivs__insertD) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ),
    file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_cut,axiom,
    ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ),
    file('theBenchmark.p',fact_cut) ).

fof(fact_hoare__derivs_Oequations_I1_J,axiom,
    ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).

fof(fact_empty,axiom,
    ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_empty) ).

fof(fact_bot__apply,axiom,
    ! [V_x_2,T_c,T_b] :
      ( class_Orderings_Obot(T_b)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_bot__apply) ).

fof(fact_empty__not__insert,axiom,
    ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    file('theBenchmark.p',fact_empty__not__insert) ).

fof(fact_insert__not__empty,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_insert__not__empty) ).

fof(fact_insert__absorb2,axiom,
    ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
    file('theBenchmark.p',fact_insert__absorb2) ).

fof(fact_insert__commute,axiom,
    ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),
    file('theBenchmark.p',fact_insert__commute) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
    <=> ( ( V_b_2 = V_c_2
          & V_a_2 = V_d_2 )
        | ( V_b_2 = V_d_2
          & V_a_2 = V_c_2 ) ) ),
    file('theBenchmark.p',fact_doubleton__eq__iff) ).

fof(fact_insert__code,axiom,
    ! [V_x_2,V_A_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
    <=> ( hBOOL(hAPP(V_A_2,V_x_2))
        | V_y_2 = V_x_2 ) ),
    file('theBenchmark.p',fact_insert__code) ).

fof(fact_singleton__inject,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
     => V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_singleton__inject) ).

fof(fact_subset__singletonD,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
     => ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_subset__singletonD) ).

fof(fact_bot__fun__def,axiom,
    ! [V_x_2,T_c,T_b] :
      ( class_Orderings_Obot(T_b)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_bot__fun__def) ).

fof(fact_hoare__derivs_Oequations_I8_J,axiom,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I8_J) ).

fof(fact_Ass,axiom,
    ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Ass) ).

fof(fact_zdvd__antisym__abs,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ),
    file('theBenchmark.p',fact_zdvd__antisym__abs) ).

fof(fact_subset__empty,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_subset__empty) ).

fof(fact_Diff__cancel,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__cancel) ).

fof(fact_Diff__empty,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Diff__empty) ).

fof(fact_empty__Diff,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_empty__Diff) ).

fof(fact_not__psubset__empty,axiom,
    ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_weak__Body,axiom,
    ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_weak__Body) ).

fof(fact_BodyN,axiom,
    ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_BodyN) ).

fof(fact_bot__least,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Obot(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ),
    file('theBenchmark.p',fact_bot__least) ).

fof(fact_zdvd__antisym__nonneg,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
           => V_m = V_n ) ) ) ),
    file('theBenchmark.p',fact_zdvd__antisym__nonneg) ).

fof(fact_zdvd__not__zless,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
       => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ),
    file('theBenchmark.p',fact_zdvd__not__zless) ).

fof(fact_hoare__derivs_OLocal,axiom,
    ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),hAPP(hAPP(c_Natural_Ogetlocs,V_s_H_2),V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_c_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_hoare__derivs_OLocal) ).

fof(fact_zdvd__mono,axiom,
    ! [V_t_2,V_m_2,V_k_2] :
      ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ),
    file('theBenchmark.p',fact_zdvd__mono) ).

fof(fact_zdvd__mult__cancel,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
     => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_zdvd__mult__cancel) ).

fof(fact_zdvd__reduce,axiom,
    ! [V_m_2,V_n_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ),
    file('theBenchmark.p',fact_zdvd__reduce) ).

fof(fact_zdvd__period,axiom,
    ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ),
    file('theBenchmark.p',fact_zdvd__period) ).

fof(fact_zdvd__int,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ),
    file('theBenchmark.p',fact_zdvd__int) ).

fof(fact_transfer__int__nat__relations_I4_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I4_J) ).

fof(fact_zdvd__mult__div__cancel,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = V_m ),
    file('theBenchmark.p',fact_zdvd__mult__div__cancel) ).

fof(fact_zmod__eq__dvd__iff,axiom,
    ! [V_y_2,V_n_2,V_x_2] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) ),
    file('theBenchmark.p',fact_zmod__eq__dvd__iff) ).

fof(fact_zdvd1__eq,axiom,
    ! [V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zdvd1__eq) ).

fof(fact_abs__div,axiom,
    ! [V_x,V_y] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)) ),
    file('theBenchmark.p',fact_abs__div) ).

fof(fact_dvd_Ostrict__mono__mono,axiom,
    ! [V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
       => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ),
    file('theBenchmark.p',fact_dvd_Ostrict__mono__mono) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_subset__Compl__self__eq) ).

fof(fact_zdvd__imp__le,axiom,
    ! [V_n,V_z] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ),
    file('theBenchmark.p',fact_zdvd__imp__le) ).

fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).

fof(fact_dvd__imp__le__int,axiom,
    ! [V_d,V_i] :
      ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i))) ) ),
    file('theBenchmark.p',fact_dvd__imp__le__int) ).

fof(fact_transfer__nat__int__relations_I4_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I4_J) ).

fof(fact_zdvd__mult__cancel1,axiom,
    ! [V_n_2,V_m_2] :
      ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2))
      <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zdvd__mult__cancel1) ).

fof(fact_int__dvd__iff,axiom,
    ! [V_z_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ),
    file('theBenchmark.p',fact_int__dvd__iff) ).

fof(fact_dvd__int__iff,axiom,
    ! [V_m_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) ),
    file('theBenchmark.p',fact_dvd__int__iff) ).

fof(fact_the__elem__def,axiom,
    ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_the__elem__def) ).

fof(fact_the__elem__eq,axiom,
    ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2,
    file('theBenchmark.p',fact_the__elem__eq) ).

fof(fact_Option_Oset_Osimps_I2_J,axiom,
    ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Option_Oset_Osimps_I2_J) ).

fof(fact_escape,axiom,
    ! [V_Q_2,V_c_2,V_Ga_2,T_b,V_P_2] :
      ( ! [B_Z,B_s] :
          ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
         => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_escape) ).

fof(fact_conseq1,axiom,
    ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => ( ! [B_Z,B_s] :
            ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
           => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_conseq1) ).

fof(fact_bot__nat__def,axiom,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bot__nat__def) ).

fof(fact_set__empty__eq,axiom,
    ! [V_xo_2,T_b] :
      ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ),
    file('theBenchmark.p',fact_set__empty__eq) ).

fof(fact_Option_Oset_Osimps_I1_J,axiom,
    ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Option_Oset_Osimps_I1_J) ).

fof(fact_conseq2,axiom,
    ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => ( ! [B_Z,B_s] :
            ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
           => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_conseq2) ).

fof(fact_psubset__insert__iff,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
         => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
            & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_dvd_Ostrict__monoI,axiom,
    ! [V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( ! [B_x,B_y] :
            ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
       => c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ),
    file('theBenchmark.p',fact_dvd_Ostrict__monoI) ).

fof(fact_dvd_OmonoI,axiom,
    ! [V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
       => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ),
    file('theBenchmark.p',fact_dvd_OmonoI) ).

fof(fact_equalityCE,axiom,
    ! [V_c_2,T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
       => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_equalityCE) ).

fof(fact_emptyE,axiom,
    ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_emptyE) ).

fof(fact_insertE,axiom,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
     => ( V_a_2 != V_b_2
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_insertE) ).

fof(fact_insertCI,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
       => V_a_2 = V_b_2 )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_insertCI) ).

fof(fact_subsetD,axiom,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subsetD) ).

fof(fact_DiffE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_DiffE) ).

fof(fact_DiffI,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_DiffI) ).

fof(fact_ComplI,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    file('theBenchmark.p',fact_ComplI) ).

fof(fact_mem__splitI,axiom,
    ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ),
    file('theBenchmark.p',fact_mem__splitI) ).

fof(fact_insertI1,axiom,
    ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_insertI1) ).

fof(fact_all__not__in__conv,axiom,
    ! [V_A_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_all__not__in__conv) ).

fof(fact_ex__in__conv,axiom,
    ! [V_A_2,T_b] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
    <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ex__in__conv) ).

fof(fact_empty__iff,axiom,
    ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_empty__iff) ).

fof(fact_insert__iff,axiom,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
        | V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_insert__iff) ).

fof(fact_insert__ident,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
       => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
        <=> V_A_2 = V_B_2 ) ) ),
    file('theBenchmark.p',fact_insert__ident) ).

fof(fact_equals0D,axiom,
    ! [V_a_2,T_b,V_A_2] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    file('theBenchmark.p',fact_equals0D) ).

fof(fact_insertI2,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_insertI2) ).

fof(fact_insert__absorb,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
    file('theBenchmark.p',fact_insert__absorb) ).

fof(fact_set__mp,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__mp) ).

fof(fact_set__rev__mp,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__rev__mp) ).

fof(fact_in__mono,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_in__mono) ).

fof(fact_Compl__iff,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__iff) ).

fof(fact_ComplD,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplD) ).

fof(fact_ComplE,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplE) ).

fof(fact_Diff__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Diff__iff) ).

fof(fact_DiffD1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_DiffD1) ).

fof(fact_DiffD2,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
    file('theBenchmark.p',fact_DiffD2) ).

fof(fact_mem__def,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
    <=> hBOOL(hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_mem__def) ).

fof(fact_eqset__imp__iff,axiom,
    ! [V_x_2,T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_eqset__imp__iff) ).

fof(fact_eqelem__imp__iff,axiom,
    ! [V_A_2,T_b,V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_eqelem__imp__iff) ).

fof(fact_eq__mem__trans,axiom,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_eq__mem__trans) ).

fof(fact_pred__equals__eq,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
    <=> V_R_2 = V_S_2 ),
    file('theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_eq__mem,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_eq__mem) ).

fof(fact_psubsetD,axiom,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubsetD) ).

fof(fact_bot__empty__eq,axiom,
    ! [V_x_2,T_b] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bot__empty__eq) ).

fof(fact_pred__equals__eq2,axiom,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
    <=> V_R_2 = V_S_2 ),
    file('theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_bot__empty__eq2,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_pred__subset__eq,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ),
    file('theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_singleton__iff,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
    <=> V_b_2 = V_a_2 ),
    file('theBenchmark.p',fact_singleton__iff) ).

fof(fact_singletonE,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
     => V_b_2 = V_a_2 ),
    file('theBenchmark.p',fact_singletonE) ).

fof(fact_insert__subset,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_insert__subset) ).

fof(fact_subset__insert,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subset__insert) ).

fof(fact_insert__Diff__if,axiom,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    file('theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_insert__Diff1,axiom,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
    file('theBenchmark.p',fact_insert__Diff1) ).

fof(fact_elem__set,axiom,
    ! [V_xo_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
    <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ),
    file('theBenchmark.p',fact_elem__set) ).

fof(fact_pred__subset__eq2,axiom,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ),
    file('theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_Diff__insert__absorb,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ),
    file('theBenchmark.p',fact_Diff__insert__absorb) ).

fof(fact_insert__Diff,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ),
    file('theBenchmark.p',fact_insert__Diff) ).

fof(fact_diff__single__insert,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_diff__single__insert) ).

fof(fact_subset__insert__iff,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_in__rel__def,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ),
    file('theBenchmark.p',fact_in__rel__def) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
       => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).

fof(fact_Nitpick_Orefl_H__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Nitpick_Orefl_H(T_b,V_r_2)
    <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
    file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

fof(fact_flat__lub__def,axiom,
    ! [V_b_2,V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) ),
    file('theBenchmark.p',fact_flat__lub__def) ).

fof(fact_bot2E,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)),
    file('theBenchmark.p',fact_bot2E) ).

fof(fact_less__by__empty,axiom,
    ! [V_B_2,T_b,V_A_2] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_less__by__empty) ).

fof(fact_fold__graph_H_Ointros_I1_J,axiom,
    ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2),
    file('theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),
    file('theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

fof(fact_in__measure,axiom,
    ! [V_f_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    file('theBenchmark.p',fact_in__measure) ).

fof(fact_mlex__leq,axiom,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_mlex__leq) ).

fof(fact_mlex__less,axiom,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ),
    file('theBenchmark.p',fact_mlex__less) ).

fof(fact_Nats__number__of,axiom,
    ! [V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ),
    file('theBenchmark.p',fact_Nats__number__of) ).

fof(fact_Nats__0,axiom,
    ! [T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
    file('theBenchmark.p',fact_Nats__0) ).

fof(fact_Nats__add,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
    file('theBenchmark.p',fact_Nats__add) ).

fof(fact_Nats__mult,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
    file('theBenchmark.p',fact_Nats__mult) ).

fof(fact_Nats__1,axiom,
    ! [T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
    file('theBenchmark.p',fact_Nats__1) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
    file('theBenchmark.p',fact_of__nat__in__Nats) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_fold__graph_H_Oequations_I2_J,axiom,
    ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
      ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
    <=> ( ? [B_x,B_y] :
            ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
            & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
        | ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
          & V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ),
    file('theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

fof(fact_in__lex__prod,axiom,
    ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
          & V_a_2 = V_a_H_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_in__lex__prod) ).

fof(fact_pair__lessI2,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ),
    file('theBenchmark.p',fact_pair__lessI2) ).

fof(fact_Ints__0,axiom,
    ! [T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__0) ).

fof(fact_Ints__add,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__add) ).

fof(fact_Ints__mult,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__mult) ).

fof(fact_Ints__diff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__diff) ).

fof(fact_Ints__number__of,axiom,
    ! [V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__number__of) ).

fof(fact_Ints__1,axiom,
    ! [T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__1) ).

fof(fact_Ints__minus,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
    file('theBenchmark.p',fact_Ints__minus) ).

fof(fact_Ints__power,axiom,
    ! [V_n_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
    file('theBenchmark.p',fact_Ints__power) ).

fof(fact_Ints__of__nat,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__of__nat) ).

fof(fact_Ints__of__int,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__of__int) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
        <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_pair__lessI1,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ),
    file('theBenchmark.p',fact_pair__lessI1) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [V_a_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_same__fstI,axiom,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_same__fstI) ).

fof(fact_pair__leqI2,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ),
    file('theBenchmark.p',fact_pair__leqI2) ).

fof(fact_smax__insertI,axiom,
    ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ),
    file('theBenchmark.p',fact_smax__insertI) ).

fof(fact_smin__insertI,axiom,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ),
    file('theBenchmark.p',fact_smin__insertI) ).

fof(fact_smin__emptyI,axiom,
    ! [V_X_2] :
      ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
    file('theBenchmark.p',fact_smin__emptyI) ).

fof(fact_pair__leqI1,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ),
    file('theBenchmark.p',fact_pair__leqI1) ).

fof(fact_wmin__insertI,axiom,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ),
    file('theBenchmark.p',fact_wmin__insertI) ).

fof(fact_wmax__insertI,axiom,
    ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ),
    file('theBenchmark.p',fact_wmax__insertI) ).

fof(fact_wmin__emptyI,axiom,
    ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    file('theBenchmark.p',fact_wmin__emptyI) ).

fof(fact_min__strict__def,axiom,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('theBenchmark.p',fact_min__strict__def) ).

fof(fact_min__weak__def,axiom,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_min__weak__def) ).

fof(fact_max__rpair__set,axiom,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    file('theBenchmark.p',fact_max__rpair__set) ).

fof(fact_min__rpair__set,axiom,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    file('theBenchmark.p',fact_min__rpair__set) ).

fof(fact_less__than__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_less__than__iff) ).

fof(fact_sup1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
       => hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_sup1E) ).

fof(fact_sup1CI,axiom,
    ! [T_b,V_A_2,V_x_2,V_B_2] :
      ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
       => hBOOL(hAPP(V_A_2,V_x_2)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1CI) ).

fof(fact_UnCI,axiom,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnCI) ).

fof(fact_UnE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_UnE) ).

fof(fact_Un__empty,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Un__empty) ).

fof(fact_Un__empty__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Un__empty__right) ).

fof(fact_Un__empty__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    file('theBenchmark.p',fact_Un__empty__left) ).

fof(fact_sup__eq__bot__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Obounded__lattice__bot(T_b)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
      <=> ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
          & V_x_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ),
    file('theBenchmark.p',fact_sup__eq__bot__iff) ).

fof(fact_sup__bot__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ),
    file('theBenchmark.p',fact_sup__bot__right) ).

fof(fact_sup__bot__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ),
    file('theBenchmark.p',fact_sup__bot__left) ).

fof(fact_Un__upper1,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    file('theBenchmark.p',fact_Un__upper1) ).

fof(fact_Un__upper2,axiom,
    ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    file('theBenchmark.p',fact_Un__upper2) ).

fof(fact_subset__Un__eq,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('theBenchmark.p',fact_subset__Un__eq) ).

fof(fact_Un__absorb1,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('theBenchmark.p',fact_Un__absorb1) ).

fof(fact_Un__absorb2,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Un__absorb2) ).

fof(fact_Un__least,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
    file('theBenchmark.p',fact_Un__least) ).

fof(fact_Un__mono,axiom,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Un__mono) ).

fof(fact_inf__sup__ord_I3_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_sup__ge2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_sup__ge2) ).

fof(fact_le__iff__sup,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_le__iff__sup) ).

fof(fact_le__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_le__sup__iff) ).

fof(fact_le__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__supI2) ).

fof(fact_sup__absorb2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_sup__absorb2) ).

fof(fact_sup__absorb1,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_sup__absorb1) ).

fof(fact_le__supI,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ),
    file('theBenchmark.p',fact_le__supI) ).

fof(fact_sup__least,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ),
    file('theBenchmark.p',fact_sup__least) ).

fof(fact_sup__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_sup__mono) ).

fof(fact_le__supE,axiom,
    ! [V_x,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
    file('theBenchmark.p',fact_le__supE) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Un__Diff__cancel) ).

fof(fact_Un__Diff__cancel2,axiom,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Un__Diff__cancel2) ).

fof(fact_Un__Diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__Diff) ).

fof(fact_sup__max,axiom,
    ! [T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__sup(T_b) )
     => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ),
    file('theBenchmark.p',fact_sup__max) ).

fof(fact_Sup__fin_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Sup__fin_Oidem) ).

fof(fact_less__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_less__supI1) ).

fof(fact_less__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_less__supI2) ).

fof(fact_sup_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_sup_Oidem) ).

fof(fact_sup__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_sup__idem) ).

fof(fact_sup_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_sup__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_sup__commute) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_sup__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_sup__left__idem) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_sup__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_sup__left__commute) ).

fof(fact_sup_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_sup__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_sup__assoc) ).

fof(fact_sup__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_sup__apply) ).

fof(fact_Un__absorb,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Un__absorb) ).

fof(fact_Un__commute,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Un__commute) ).

fof(fact_Un__left__absorb,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_Un__left__commute,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Un__assoc,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__assoc) ).

fof(fact_bex__Un,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
    <=> ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_bex__Un) ).

fof(fact_ball__Un,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
           => hBOOL(hAPP(V_P_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_ball__Un) ).

fof(fact_sup__fun__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_sup__fun__def) ).

fof(fact_sup1I1,axiom,
    ! [V_B_2,T_b,V_x_2,V_A_2] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1I1) ).

fof(fact_sup1I2,axiom,
    ! [V_A_2,T_b,V_x_2,V_B_2] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1I2) ).

fof(fact_Un__insert__left,axiom,
    ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__insert__left) ).

fof(fact_Un__insert__right,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_Un__insert__right) ).

fof(fact_Un__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Un__iff) ).

fof(fact_UnI1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnI1) ).

fof(fact_UnI2,axiom,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnI2) ).

fof(fact_sup__Un__eq,axiom,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_insert__is__Un,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
    file('theBenchmark.p',fact_insert__is__Un) ).

fof(fact_Diff__partition,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ),
    file('theBenchmark.p',fact_Diff__partition) ).

fof(fact_Diff__subset__conv,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ),
    file('theBenchmark.p',fact_Diff__subset__conv) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_pair__less__def,axiom,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_pair__less__def) ).

fof(fact_max__weak__def,axiom,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_max__weak__def) ).

fof(fact_mlex__prod__def,axiom,
    ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
    file('theBenchmark.p',fact_mlex__prod__def) ).

fof(fact_intrel__iff,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
    <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ),
    file('theBenchmark.p',fact_intrel__iff) ).

fof(fact_rp__inv__image__rp,axiom,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_P_2)
     => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ),
    file('theBenchmark.p',fact_rp__inv__image__rp) ).

fof(fact_sup__nat__def,axiom,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    file('theBenchmark.p',fact_sup__nat__def) ).

fof(fact_rp__inv__image__def,axiom,
    ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
    file('theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_sup__Un__eq2,axiom,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_max__strict__def,axiom,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('theBenchmark.p',fact_max__strict__def) ).

fof(fact_max__ext__additive,axiom,
    ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_max__ext__additive) ).

fof(fact_max__extp__max__ext__eq,axiom,
    ! [V_xa_2,V_x_2,V_R_2,T_b] :
      ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_max__extp__max__ext__eq) ).

fof(fact_in__inv__image,axiom,
    ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ),
    file('theBenchmark.p',fact_in__inv__image) ).

fof(fact_Body1,axiom,
    ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_Body1) ).

fof(fact_equiv__intrel__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ),
    file('theBenchmark.p',fact_equiv__intrel__iff) ).

fof(fact_sup2E,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_sup2E) ).

fof(fact_sup2CI,axiom,
    ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
      ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2CI) ).

fof(fact_image__eqI,axiom,
    ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
      ( V_b_2 = hAPP(V_f_2,V_x_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_image__eqI) ).

fof(fact_Image__Un,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
    file('theBenchmark.p',fact_Image__Un) ).

fof(fact_image__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_image__Un) ).

fof(fact_sup2I1,axiom,
    ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2I1) ).

fof(fact_sup2I2,axiom,
    ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2I2) ).

fof(fact_subset__image__iff,axiom,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
    <=> ? [B_AA] :
          ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
    file('theBenchmark.p',fact_subset__image__iff) ).

fof(fact_image__mono,axiom,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ),
    file('theBenchmark.p',fact_image__mono) ).

fof(fact_image__image,axiom,
    ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
    file('theBenchmark.p',fact_image__image) ).

fof(fact_image__iff,axiom,
    ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
    <=> ? [B_x] :
          ( V_z_2 = hAPP(V_f_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_image__iff) ).

fof(fact_imageI,axiom,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ),
    file('theBenchmark.p',fact_imageI) ).

fof(fact_rev__image__eqI,axiom,
    ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( V_b_2 = hAPP(V_f_2,V_x_2)
       => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_image__insert,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_image__insert) ).

fof(fact_Image__empty,axiom,
    ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Image__empty) ).

fof(fact_empty__is__image,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_empty__is__image) ).

fof(fact_image__empty,axiom,
    ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_image__empty) ).

fof(fact_image__is__empty,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_image__is__empty) ).

fof(fact_Image__mono,axiom,
    ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_Image__mono) ).

fof(fact_Un__Image,axiom,
    ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Image) ).

fof(fact_insert__image,axiom,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ),
    file('theBenchmark.p',fact_insert__image) ).

fof(fact_image__diff__subset,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_image__diff__subset) ).

fof(fact_Image__iff,axiom,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_Image__iff) ).

fof(fact_rev__ImageI,axiom,
    ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_rev__ImageI) ).

fof(fact_image__constant__conv,axiom,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_image__constant__conv) ).

fof(fact_image__constant,axiom,
    ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_image__constant) ).

fof(fact_Image__singleton__iff,axiom,
    ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ),
    file('theBenchmark.p',fact_Image__singleton__iff) ).

fof(fact_measure__def,axiom,
    ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_measure__def) ).

fof(fact_hoare__derivs_OBody,axiom,
    ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ),
    file('theBenchmark.p',fact_hoare__derivs_OBody) ).

fof(fact_Body__sound__lemma,axiom,
    ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
     => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ),
    file('theBenchmark.p',fact_Body__sound__lemma) ).

fof(fact_of__int,axiom,
    ! [V_j_2,V_i_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ),
    file('theBenchmark.p',fact_of__int) ).

fof(fact_One__int__def,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_One__int__def) ).

fof(fact_mult,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_mult) ).

fof(fact_pair__imageI,axiom,
    ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_pair__imageI) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).

fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
    ! [V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).

fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
    <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).

fof(fact_transfer__int__nat__set__return__embed,axiom,
    ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).

fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
    ! [V_A_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_minus,axiom,
    ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_minus) ).

fof(fact_Zero__int__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Zero__int__def) ).

fof(fact_int__def,axiom,
    ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_int__def) ).

fof(fact_add,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_add) ).

fof(fact_nat,axiom,
    ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
    file('theBenchmark.p',fact_nat) ).

fof(fact_less,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
    file('theBenchmark.p',fact_less) ).

fof(fact_le,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
    file('theBenchmark.p',fact_le) ).

fof(fact_irrefl__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Oirrefl(T_b,V_r_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
    file('theBenchmark.p',fact_irrefl__def) ).

fof(fact_eq__Abs__Integ,axiom,
    ! [V_z_2] :
      ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_eq__Abs__Integ) ).

fof(fact_Field__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
    file('theBenchmark.p',fact_Field__insert) ).

fof(fact_ImageE,axiom,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
           => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_ImageE) ).

fof(fact_Field__empty,axiom,
    ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Field__empty) ).

fof(fact_mono__Field,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ),
    file('theBenchmark.p',fact_mono__Field) ).

fof(fact_Field__Un,axiom,
    ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
    file('theBenchmark.p',fact_Field__Un) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).

fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).

fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [V_A_2,V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_nat__set__def,axiom,
    ! [V_S_2] :
      ( c_Nat__Transfer_Onat__set(V_S_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    file('theBenchmark.p',fact_nat__set__def) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
    ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( V_A_2 = V_B_2
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
       => c_Nat__Transfer_Ois__nat(V_x_2) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_subset__equiv__class,axiom,
    ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_accp__acc__eq,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_wmax__emptyI,axiom,
    ! [V_X_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ),
    file('theBenchmark.p',fact_wmax__emptyI) ).

fof(fact_smax__emptyI,axiom,
    ! [V_Y_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
     => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ),
    file('theBenchmark.p',fact_smax__emptyI) ).

fof(fact_finite__Field,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Field) ).

fof(fact_acc__subset,axiom,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ),
    file('theBenchmark.p',fact_acc__subset) ).

fof(fact_equiv__class__self,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_equiv__class__self) ).

fof(fact_acc_Osimps,axiom,
    ! [V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc_Osimps) ).

fof(fact_acc__downward,axiom,
    ! [V_a_2,V_r_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downward) ).

fof(fact_equiv__class__eq,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_eq__equiv__class,axiom,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          & hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_equiv__class__subset,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_equiv__class__subset) ).

fof(fact_finite__Diff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_finite__Diff) ).

fof(fact_finite__imageI,axiom,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ),
    file('theBenchmark.p',fact_finite__imageI) ).

fof(fact_finite_OinsertI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ),
    file('theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_finite_OemptyI,axiom,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_OemptyI) ).

fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
    ! [V_A_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).

fof(fact_finite,axiom,
    ! [V_A_2,T_b] :
      ( class_Finite__Set_Ofinite(T_b)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite) ).

fof(fact_finite__code,axiom,
    ! [V_A_2,T_b] :
      ( class_Finite__Set_Ofinite(T_b)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__code) ).

fof(fact_finite_Oequations_I1_J,axiom,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_finite__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__insert) ).

fof(fact_finite__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_finite__Un,axiom,
    ! [V_Ga_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__Un) ).

fof(fact_finite__UnI,axiom,
    ! [V_Ga_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ),
    file('theBenchmark.p',fact_finite__UnI) ).

fof(fact_finite__Diff2,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Diff2) ).

fof(fact_finite__surj,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_finite__surj) ).

fof(fact_finite__Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_in__finite__psubset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_finite__pointwise,axiom,
    ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
     => ( ! [B_p] :
            ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
           => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
       => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
         => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ),
    file('theBenchmark.p',fact_finite__pointwise) ).

fof(fact_folding__one_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oremove) ).

fof(fact_folding__image__simple_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
         => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oremove) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ),
    file('theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_folding__one_Osingleton,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oinsert) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).

fof(fact_folding__image__simple_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [V_N_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
    <=> ? [B_m] :
        ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ),
    file('theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [V_N_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
    <=> ? [B_m] :
        ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ),
    file('theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_eq__equiv__class__iff2,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_equiv__class__nondisjoint) ).

fof(fact_inf1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
         => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_inf1E) ).

fof(fact_inf1I,axiom,
    ! [T_b,V_B_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
     => ( hBOOL(hAPP(V_B_2,V_x_2))
       => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_inf1I) ).

fof(fact_IntI,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_IntI) ).

fof(fact_IntE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_IntE) ).

fof(fact_finite__Int,axiom,
    ! [V_Ga_2,V_F_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ),
    file('theBenchmark.p',fact_finite__Int) ).

fof(fact_quotient__disj,axiom,
    ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | V_X_2 = V_Y_2 ) ) ) ),
    file('theBenchmark.p',fact_quotient__disj) ).

fof(fact_quotient__empty,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_quotient__empty) ).

fof(fact_quotient__is__empty2,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_quotient__is__empty2) ).

fof(fact_quotient__is__empty,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_quotient__is__empty) ).

fof(fact_inf__Int__eq,axiom,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_Int__lower1,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__lower1) ).

fof(fact_Int__lower2,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
    file('theBenchmark.p',fact_Int__lower2) ).

fof(fact_Int__absorb2,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Int__absorb2) ).

fof(fact_Int__absorb1,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('theBenchmark.p',fact_Int__absorb1) ).

fof(fact_Int__greatest,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_Int__greatest) ).

fof(fact_Int__mono,axiom,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Int__mono) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_inf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__le2) ).

fof(fact_le__iff__inf,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_le__iff__inf) ).

fof(fact_le__inf__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_le__inf__iff) ).

fof(fact_le__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI2) ).

fof(fact_inf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_inf__absorb1) ).

fof(fact_inf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_inf__absorb2) ).

fof(fact_le__infI,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_le__infI) ).

fof(fact_inf__greatest,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ),
    file('theBenchmark.p',fact_inf__greatest) ).

fof(fact_inf__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_inf__mono) ).

fof(fact_le__infE,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
    file('theBenchmark.p',fact_le__infE) ).

fof(fact_less__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_less__infI1) ).

fof(fact_less__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_less__infI2) ).

fof(fact_insert__inter__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_inf__bot__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_inf__bot__left) ).

fof(fact_inf__bot__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_inf__bot__right) ).

fof(fact_Int__empty__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Int__empty__left) ).

fof(fact_Int__empty__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Int__empty__right) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
             => B_x != B_xa ) ) ),
    file('theBenchmark.p',fact_disjoint__iff__not__equal) ).

fof(fact_IntD2,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
    file('theBenchmark.p',fact_IntD2) ).

fof(fact_IntD1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_IntD1) ).

fof(fact_Int__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__iff) ).

fof(fact_Un__Int__crazy,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Int__crazy) ).

fof(fact_Un__Int__distrib2,axiom,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Int__Un__distrib2) ).

fof(fact_Un__Int__distrib,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Un__Int__distrib) ).

fof(fact_Int__Un__distrib,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Int__Un__distrib) ).

fof(fact_sup__inf__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__distrib1) ).

fof(fact_sup__inf__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_sup__inf__absorb) ).

fof(fact_inf__sup__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_inf__sup__absorb) ).

fof(fact_inf1D2,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => hBOOL(hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf1D2) ).

fof(fact_inf1D1,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => hBOOL(hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf1D1) ).

fof(fact_Diff__Int2,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
    file('theBenchmark.p',fact_Diff__Int2) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Int__Diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Int__Diff) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_inf__min,axiom,
    ! [T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__inf(T_b) )
     => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ),
    file('theBenchmark.p',fact_inf__min) ).

fof(fact_inf__fun__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf__fun__def) ).

fof(fact_Int__assoc,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Int__assoc) ).

fof(fact_Int__left__commute,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Int__left__commute) ).

fof(fact_Int__left__absorb,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_Int__commute,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Int__commute) ).

fof(fact_Int__absorb,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Int__absorb) ).

fof(fact_inf__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf__apply) ).

fof(fact_inf__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_inf_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_inf__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_inf__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_inf__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__commute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_inf_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_inf__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_inf__idem) ).

fof(fact_inf_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_inf_Oidem) ).

fof(fact_Inf__fin_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Inf__fin_Oidem) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).

fof(fact_distrib__inf__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ),
    file('theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_distrib__sup__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ),
    file('theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_compl__inf__bot,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_compl__inf__bot) ).

fof(fact_inf__compl__bot,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_inf__compl__bot) ).

fof(fact_diff__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_diff__eq) ).

fof(fact_compl__sup,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_compl__sup) ).

fof(fact_compl__inf,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_compl__inf) ).

fof(fact_Int__insert__left__if1,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ),
    file('theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ),
    file('theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
    file('theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_Int__insert__left,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_Int__insert__left) ).

fof(fact_Int__insert__right,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Int__insert__right) ).

fof(fact_image__Int__subset,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))),
    file('theBenchmark.p',fact_image__Int__subset) ).

fof(fact_Diff__triv,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Diff__triv) ).

fof(fact_Diff__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__disjoint) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
    file('theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_Un__Diff__Int,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
    file('theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Un) ).

fof(fact_Diff__Int,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Int) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) ).

fof(fact_Compl__disjoint2,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__disjoint2) ).

fof(fact_Compl__disjoint,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__disjoint) ).

fof(fact_Image__Int__subset,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))),
    file('theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_Compl__Un,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Compl__Un) ).

fof(fact_Compl__Int,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Compl__Int) ).

fof(fact_Diff__Compl,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Diff__Compl) ).

fof(fact_Diff__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Diff__eq) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ),
    file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_folding__image__simple_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).

fof(fact_singleton__quotient,axiom,
    ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__quotient) ).

fof(fact_folding__one_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Ounion__inter) ).

fof(fact_folding__one_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Ounion__disjoint) ).

fof(fact_folding__image__simple_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).

fof(fact_quotientI,axiom,
    ! [V_r_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
    file('theBenchmark.p',fact_quotientI) ).

fof(fact_quotient__eq__iff,axiom,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
             => ( V_X_2 = V_Y_2
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_quotient__eqI,axiom,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
               => V_X_2 = V_Y_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_quotient__eqI) ).

fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
    ! [V_k_2,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
     => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).

fof(fact_dvd_OlessThan__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_dvd_OlessThan__iff) ).

fof(fact_dvd_OgreaterThan__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThan__iff) ).

fof(fact_dvd_OatMost__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ),
    file('theBenchmark.p',fact_dvd_OatMost__iff) ).

fof(fact_inf__nat__def,axiom,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    file('theBenchmark.p',fact_inf__nat__def) ).

fof(fact_inf__Int__eq2,axiom,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_ord_OgreaterThanLessThan__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).

fof(fact_ord_OgreaterThan__iff,axiom,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ),
    file('theBenchmark.p',fact_ord_OgreaterThan__iff) ).

fof(fact_ord_OlessThan__iff,axiom,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ),
    file('theBenchmark.p',fact_ord_OlessThan__iff) ).

fof(fact_ord_OatMost__iff,axiom,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ),
    file('theBenchmark.p',fact_ord_OatMost__iff) ).

fof(fact_dvd_OatLeast__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ),
    file('theBenchmark.p',fact_dvd_OatLeast__iff) ).

fof(fact_quotientE,axiom,
    ! [V_r_2,V_A_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
     => ~ ! [B_x] :
            ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_quotientE) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).

fof(fact_ord_OatLeastLessThan__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).

fof(fact_inf2E,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
         => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_inf2E) ).

fof(fact_inf2I,axiom,
    ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
     => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_inf2I) ).

fof(fact_inf2D2,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_inf2D2) ).

fof(fact_inf2D1,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_inf2D1) ).

fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).

fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
    ! [V_l_2,V_k_2] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).

fof(fact_dvd_OatLeastLessThan__empty,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
     => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).

fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
     => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).

fof(fact_ord_OatLeast__iff,axiom,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ),
    file('theBenchmark.p',fact_ord_OatLeast__iff) ).

fof(fact_ord_OatLeastAtMost__iff,axiom,
    ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_Max_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oremove) ).

fof(fact_Inf__le__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ),
    file('theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_Max_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_Sup__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_Max__ge,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ),
    file('theBenchmark.p',fact_Max__ge) ).

fof(fact_Max__in,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Max__in) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_sup__Inf__absorb) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oin__idem) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_inf__Sup__absorb) ).

fof(fact_Max_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
    ! [V_b_2,V_a_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).

fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).

fof(fact_dvd_OatLeastatMost__empty,axiom,
    ! [V_a_2,V_b_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) )
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).

fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
    ! [V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).

fof(fact_dvd_OatLeastAtMost__singleton,axiom,
    ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).

fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
    ! [V_c_2,V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    <=> ( V_b_2 = V_c_2
        & V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).

fof(fact_Max__mono,axiom,
    ! [V_N_2,V_M_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
       => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ),
    file('theBenchmark.p',fact_Max__mono) ).

fof(fact_Sup__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Max__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Max__insert) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

fof(fact_Max__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Max__Un) ).

fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).

fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2))
        & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2))
                & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) )
              | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2))
                & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) ) )
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__psubset__iff) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert) ).

fof(fact_Max_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_Sup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).

fof(fact_Inf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).

fof(fact_Sup__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).

fof(fact_Sup__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__inter) ).

fof(fact_Max_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_Inf__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).

fof(fact_Max_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_Max_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oclosed) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_Min_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oremove) ).

fof(fact_Min_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_Min__le,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_Min__le) ).

fof(fact_Min__in,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Min__in) ).

fof(fact_Min_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Min__antimono,axiom,
    ! [V_N_2,V_M_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
       => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ),
    file('theBenchmark.p',fact_Min__antimono) ).

fof(fact_Min__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Min__insert) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_Min__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Min__Un) ).

fof(fact_Min_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Min_Oinsert__remove) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [V_S_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [V_S_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_Min_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).

fof(fact_min__max_OInf__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oclosed) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_card__Diff__singleton,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_card_Oempty,axiom,
    ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_card_Oempty) ).

fof(fact_card__infinite,axiom,
    ! [V_A_2,T_b] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_card__infinite) ).

fof(fact_card__eq__0__iff,axiom,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__eq__0__iff) ).

fof(fact_card__ge__0__finite,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_card__insert__le,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ),
    file('theBenchmark.p',fact_card__insert__le) ).

fof(fact_card__seteq,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
         => V_A_2 = V_B_2 ) ) ),
    file('theBenchmark.p',fact_card__seteq) ).

fof(fact_card__mono,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
    file('theBenchmark.p',fact_card__mono) ).

fof(fact_card__image__le,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    file('theBenchmark.p',fact_card__image__le) ).

fof(fact_psubset__card__mono,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
    file('theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_card__insert__disjoint,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_card__insert__if,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_card__insert__if) ).

fof(fact_card__gt__0__iff,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_card_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_card__Un__Int) ).

fof(fact_card__Diff__subset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_card__Diff__subset__Int,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_card__Diff__subset__Int) ).

fof(fact_diff__card__le__card__Diff,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
    file('theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_card__psubset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card__psubset) ).

fof(fact_card__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ),
    file('theBenchmark.p',fact_card__insert) ).

fof(fact_card__Un__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_card__Diff1__le,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    file('theBenchmark.p',fact_card__Diff1__le) ).

fof(fact_card_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_card_Oinsert) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_card__Suc__Diff1) ).

fof(fact_card__Diff1__less,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
    file('theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_card__Diff2__less,axiom,
    ! [V_y_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_card__Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_card__Diff__insert) ).

fof(fact_card_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ),
    file('theBenchmark.p',fact_card_Oinsert__remove) ).

fof(fact_card_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_card_Oremove) ).

fof(fact_card_Ounion__inter__neutral,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
           => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter__neutral) ).

fof(fact_card__Suc__eq,axiom,
    ! [V_k_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
    <=> ? [B_b,B_B] :
          ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
          & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
          & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) ),
    file('theBenchmark.p',fact_card__Suc__eq) ).

fof(fact_equiv__imp__dvd__card,axiom,
    ! [V_k_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
             => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_equiv__imp__dvd__card) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_finite__Plus__iff,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__Plus,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__Plus) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_card__Plus,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_card__greaterThanLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_card__greaterThanLessThan__int) ).

fof(fact_setprod__gen__delta,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__gen__delta) ).

fof(fact_finite__greaterThanLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanLessThan__int) ).

fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
    ! [V_A_2,V_f_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).

fof(fact_of__int__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( class_Rings_Oring__1(T_b)
        & class_Groups_Ocomm__monoid__mult(T_b) )
     => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__int__setprod) ).

fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_of__nat__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( class_Rings_Osemiring__1(T_b)
        & class_Groups_Ocomm__monoid__mult(T_b) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_int__setprod,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setprod) ).

fof(fact_setprod__timesf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setprod__timesf) ).

fof(fact_setprod__1,axiom,
    ! [V_A_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod__1) ).

fof(fact_abs__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setprod) ).

fof(fact_setprod__zero,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Rings_Ocomm__semiring__1(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
    file('theBenchmark.p',fact_setprod__zero) ).

fof(fact_setprod__zero__iff,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Rings_Ono__zero__divisors(T_c)
        & class_Rings_Ocomm__semiring__1(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
        <=> ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_setprod__empty,axiom,
    ! [V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod__empty) ).

fof(fact_setprod_Oempty,axiom,
    ! [V_g_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_setprod__infinite,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
    file('theBenchmark.p',fact_setprod__infinite) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
    file('theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__eq__1__iff,axiom,
    ! [V_f_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
           => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_setprod__eq__1__iff) ).

fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).

fof(fact_setprod_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_setprod__dividef,axiom,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Fields_Ofield__inverse__zero(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod__dividef) ).

fof(fact_dvd__setprod,axiom,
    ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
      ( class_Rings_Ocomm__semiring__1(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_dvd__setprod) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [V_f_2,V_S_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_setprod__pos__nat__iff) ).

fof(fact_setprod__dvd__setprod__subset,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( ( class_Rings_Odvd(T_c)
        & class_Groups_Ocomm__monoid__mult(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_setprod__dvd__setprod__subset) ).

fof(fact_greaterThanLessThan__empty,axiom,
    ! [V_k_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanLessThan__empty) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_setprod__delta_H,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_setprod__delta,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__delta) ).

fof(fact_setprod__constant,axiom,
    ! [V_y_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod__constant) ).

fof(fact_setprod__insert,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__insert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setprod_Ounion__inter,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_setprod__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__Int) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_setprod_Ounion__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__disjoint) ).

fof(fact_setprod_Oremove,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_setprod__diff1,axiom,
    ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Fields_Ofield(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
         => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) )
            & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_setprod__diff1) ).

fof(fact_setprod__Un,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Fields_Ofield(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).

fof(fact_setprod__Un__one,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_finite__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanLessThan) ).

fof(fact_card__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)),
    file('theBenchmark.p',fact_card__greaterThanLessThan) ).

fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_quotient__def,axiom,
    ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_quotient__def) ).

fof(fact_finite__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_SUP1__I,axiom,
    ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
       => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_SUP1__I) ).

fof(fact_SUP1__iff,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP1__iff) ).

fof(fact_Image__UN,axiom,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)),
    file('theBenchmark.p',fact_Image__UN) ).

fof(fact_finite__UN,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_finite__UN) ).

fof(fact_greaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [V_l_2,V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__int_I14_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I14_J) ).

fof(fact_card__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    file('theBenchmark.p',fact_card__greaterThanAtMost) ).

fof(fact_Image__eq__UN,axiom,
    ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_ivl__disj__int_I10_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I10_J) ).

fof(fact_card__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    file('theBenchmark.p',fact_card__greaterThanAtMost__int) ).

fof(fact_ivl__disj__un_I16_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_UN__I,axiom,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_UN__I) ).

fof(fact_image__eq__UN,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_image__eq__UN) ).

fof(fact_UN__equiv__class2,axiom,
    ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class2) ).

fof(fact_ball__UN,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
             => hBOOL(hAPP(V_P_2,B_xa)) ) ) ),
    file('theBenchmark.p',fact_ball__UN) ).

fof(fact_SUP__commute,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
    file('theBenchmark.p',fact_SUP__commute) ).

fof(fact_UN__UN__flatten,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_UN__simps_I9_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    file('theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_congruent2D,axiom,
    ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
         => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ),
    file('theBenchmark.p',fact_congruent2D) ).

fof(fact_SUP__le__iff,axiom,
    ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ),
    file('theBenchmark.p',fact_SUP__le__iff) ).

fof(fact_less__SUP__iff,axiom,
    ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_less__SUP__iff) ).

fof(fact_UN__iff,axiom,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_UN__iff) ).

fof(fact_SUP__const,axiom,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ),
    file('theBenchmark.p',fact_SUP__const) ).

fof(fact_UNION__empty__conv_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UNION__empty__conv_I1_J) ).

fof(fact_UN__empty2,axiom,
    ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__empty2) ).

fof(fact_UN__constant,axiom,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__constant) ).

fof(fact_UNION__empty__conv_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UNION__empty__conv_I2_J) ).

fof(fact_UN__subset__iff,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ),
    file('theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    file('theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_image__UN,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_image__UN) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_UN__Un,axiom,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    file('theBenchmark.p',fact_UN__Un) ).

fof(fact_UN__Un__distrib,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    file('theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_SUPR__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_SUPR__apply) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_SUP__subset,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ),
    file('theBenchmark.p',fact_SUP__subset) ).

fof(fact_le__SUPI,axiom,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ),
    file('theBenchmark.p',fact_le__SUPI) ).

fof(fact_UN__insert__distrib,axiom,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_UN__upper,axiom,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UN__upper) ).

fof(fact_UN__absorb,axiom,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ),
    file('theBenchmark.p',fact_UN__absorb) ).

fof(fact_UN__extend__simps_I1_J,axiom,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I1_J) ).

fof(fact_UN__singleton,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
    file('theBenchmark.p',fact_UN__singleton) ).

fof(fact_UN__simps_I1_J,axiom,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_UN__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_UN__insert) ).

fof(fact_congruent2__implies__congruent__UN,axiom,
    ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
           => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ),
    file('theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_minus__int__def,axiom,
    ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    file('theBenchmark.p',fact_minus__int__def) ).

fof(fact_UN__equiv__class,axiom,
    ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_SUP2__I,axiom,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_SUP2__I) ).

fof(fact_Rep__Integ__inject,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_Rep__Integ__inject) ).

fof(fact_Rep__Integ__inverse,axiom,
    ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_congruentD,axiom,
    ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
       => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ),
    file('theBenchmark.p',fact_congruentD) ).

fof(fact_nat__def,axiom,
    ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    file('theBenchmark.p',fact_nat__def) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
     => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ),
    file('theBenchmark.p',fact_congruent2__implies__congruent) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
             => ( ! [B_x] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
                   => ! [B_y] :
                        ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
                       => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
                         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
               => V_X_2 = V_Y_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__inject) ).

fof(fact_UN__equiv__class__type2,axiom,
    ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
             => ( ! [B_x1] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
                   => ! [B_x2] :
                        ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
               => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__type2) ).

fof(fact_UN__equiv__class__type,axiom,
    ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_SUP2__iff,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP2__iff) ).

fof(fact_Id__on__def,axiom,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Id__on__def) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).

fof(fact_fold__image__empty,axiom,
    ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    file('theBenchmark.p',fact_fold__image__empty) ).

fof(fact_Id__on__def_H,axiom,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
    file('theBenchmark.p',fact_Id__on__def_H) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_Id__on__empty,axiom,
    ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Id__on__empty) ).

fof(fact_Image__Id__on,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Image__Id__on) ).

fof(fact_fold__image__distrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_fold__image__insert,axiom,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__semigroup__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__insert) ).

fof(fact_setprod_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_setprod_Oeq__fold) ).

fof(fact_Id__on__eqI,axiom,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Id__on__iff,axiom,
    ! [V_A_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        & V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_Id__on__iff) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_image__eq__fold__image,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ),
    file('theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_card__def,axiom,
    ! [V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ),
    file('theBenchmark.p',fact_card__def) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ),
    file('theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_fold__image__Un__one,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_Id__onE,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ),
    file('theBenchmark.p',fact_Id__onE) ).

fof(fact_comm__monoid__big_Oinfinite,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ),
    file('theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).

fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).

fof(fact_Max_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ohom__commute) ).

fof(fact_Min_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ohom__commute) ).

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_Sup__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_setprod__mono__one__right,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__mono__one__right) ).

fof(fact_setprod__mono__one__left,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__mono__one__left) ).

fof(fact_card__Pow,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_card__Pow) ).

fof(fact_finite__empty__induct,axiom,
    ! [V_P_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(V_P_2,V_A_2))
       => ( ! [B_a,B_A] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
             => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
               => ( hBOOL(hAPP(V_P_2,B_A))
                 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_finite__empty__induct) ).

fof(fact_PowI,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    file('theBenchmark.p',fact_PowI) ).

fof(fact_Pow__top,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
    file('theBenchmark.p',fact_Pow__top) ).

fof(fact_image__Pow__surj,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
     => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ),
    file('theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_Pow__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    file('theBenchmark.p',fact_Pow__mono) ).

fof(fact_Un__Pow__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_Pow__Int__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)),
    file('theBenchmark.p',fact_Pow__Int__eq) ).

fof(fact_Pow__insert,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))),
    file('theBenchmark.p',fact_Pow__insert) ).

fof(fact_finite__Pow__iff,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_Pow__not__empty,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Pow__bottom,axiom,
    ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
    file('theBenchmark.p',fact_Pow__bottom) ).

fof(fact_image__Pow__mono,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    file('theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_PowD,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_PowD) ).

fof(fact_Pow__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_Pow__iff) ).

fof(fact_UN__Pow__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_Pow__empty,axiom,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    file('theBenchmark.p',fact_Pow__empty) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ),
    file('theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
       => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I19_J) ).

fof(fact_finite__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastAtMost) ).

fof(fact_finite__atLeastAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastAtMost__int) ).

fof(fact_image__Suc__atLeastAtMost,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)),
    file('theBenchmark.p',fact_image__Suc__atLeastAtMost) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    file('theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_finite__imageD,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
     => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__imageD) ).

fof(fact_card__image,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ),
    file('theBenchmark.p',fact_card__image) ).

fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Nat__Transfer_Ois__nat(V_m_2)
     => ( c_Nat__Transfer_Ois__nat(V_n_2)
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).

fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).

fof(fact_atLeastatMost__empty__iff2,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastatMost__empty__iff2) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastatMost__empty__iff) ).

fof(fact_atLeastatMost__empty,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_atLeastatMost__empty) ).

fof(fact_atLeastatMost__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_atLeastAtMost__singleton_H,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( V_a_2 = V_b_2
       => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton_H) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      <=> ( V_b_2 = V_c_2
          & V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

fof(fact_atLeastAtMost__singleton,axiom,
    ! [V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton) ).

fof(fact_image__uminus__atLeastAtMost,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_finite__surj__inj,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
       => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_endo__inj__surj,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
         => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_pigeonhole,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
     => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ),
    file('theBenchmark.p',fact_pigeonhole) ).

fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2),
    file('theBenchmark.p',fact_card__atLeastAtMost) ).

fof(fact_atLeastAtMostSuc__conv,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
     => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ),
    file('theBenchmark.p',fact_atLeastAtMostSuc__conv) ).

fof(fact_Powp__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_Powp__mono) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_card__bij__eq,axiom,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
       => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
               => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ),
    file('theBenchmark.p',fact_card__bij__eq) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_ivl__disj__un_I22_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I13_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_simp__from__to,axiom,
    ! [V_i_2,V_j_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_simp__from__to) ).

fof(fact_card__inj__on__le,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
              & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_quotient__diff1,axiom,
    ! [V_a_2,V_A_2,V_r_2,T_b] :
      ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ),
    file('theBenchmark.p',fact_quotient__diff1) ).

fof(fact_card__atLeastAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_card__atLeastAtMost__int) ).

fof(fact_ivl__disj__un_I5_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_inj__on__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__Un) ).

fof(fact_inj__on__insert,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__insert) ).

fof(fact_inj__uminus,axiom,
    ! [V_A_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ),
    file('theBenchmark.p',fact_inj__uminus) ).

fof(fact_inj__on__empty,axiom,
    ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__on__empty) ).

fof(fact_inj__Suc,axiom,
    ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
    file('theBenchmark.p',fact_inj__Suc) ).

fof(fact_inj__Some,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__Some) ).

fof(fact_inj__on__add__nat,axiom,
    ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2),
    file('theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_swap__inj__on,axiom,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
    file('theBenchmark.p',fact_swap__inj__on) ).

fof(fact_inj__on__def,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
             => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
               => B_x = B_xa ) ) ) ),
    file('theBenchmark.p',fact_inj__on__def) ).

fof(fact_image__ident,axiom,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_image__ident) ).

fof(fact_inj__on__id2,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__id2) ).

fof(fact_inj__onD,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
           => V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_inj__onD) ).

fof(fact_inj__on__iff,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          <=> V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__on__contraD,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( V_x_2 != V_y_2
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
           => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ),
    file('theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_subset__inj__on,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_subset__inj__on) ).

fof(fact_inj__on__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_inj__on__Int) ).

fof(fact_inj__on__diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_inj__on__diff) ).

fof(fact_Cantors__paradox,axiom,
    ! [V_A_2,T_b] :
      ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2),
    file('theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_inj__on__image__Int,axiom,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
         => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
         => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_inj__on__iff__surj,axiom,
    ! [V_A_H_2,T_c,T_b,V_A_2] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ( ? [B_f] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
            & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
      <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ),
    file('theBenchmark.p',fact_inj__on__iff__surj) ).

fof(fact_all__nat__less,axiom,
    ! [V_P_2,V_n_2] :
      ( ! [B_m] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
         => hBOOL(hAPP(V_P_2,B_m)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less) ).

fof(fact_ex__nat__less,axiom,
    ! [V_P_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_P_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less) ).

fof(fact_aset_I6_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_aset_I6_J) ).

fof(fact_bset_I8_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ),
    file('theBenchmark.p',fact_bset_I8_J) ).

fof(fact_bset_I3_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
                 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
    file('theBenchmark.p',fact_bset_I3_J) ).

fof(fact_aset_I4_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( B_x != V_t_2
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
    file('theBenchmark.p',fact_aset_I4_J) ).

fof(fact_bset_I4_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( B_x != V_t_2
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
    file('theBenchmark.p',fact_bset_I4_J) ).

fof(fact_bset_I7_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ),
    file('theBenchmark.p',fact_bset_I7_J) ).

fof(fact_aset_I3_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
                 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
    file('theBenchmark.p',fact_aset_I3_J) ).

fof(fact_aset_I5_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_aset_I5_J) ).

fof(fact_bset_I6_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I6_J) ).

fof(fact_aset_I8_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I8_J) ).

fof(fact_periodic__finite__ex,axiom,
    ! [V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x,B_k] :
            ( hBOOL(hAPP(V_P_2,B_x))
          <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
       => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        <=> ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) ) ) ),
    file('theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_bset_I5_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I5_J) ).

fof(fact_aset_I7_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I7_J) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [V_x_2,V_y_2,V_c_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).

fof(fact_bset_I9_J,axiom,
    ! [V_t_2,V_B_2,V_D_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
           => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_bset_I9_J) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
          <=> ( V_b_2 = V_d_2
              & V_a_2 = V_c_2 ) ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
           => V_a_2 = V_c_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
           => V_b_2 = V_d_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_all__nat__less__eq,axiom,
    ! [V_P_2,V_n_2] :
      ( ! [B_m] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
         => hBOOL(hAPP(V_P_2,B_m)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [V_P_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_P_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_atLeastLessThan0,axiom,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_atLeastLessThan0) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    file('theBenchmark.p',fact_card__atLeastLessThan) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)),
    file('theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_ivl__diff,axiom,
    ! [V_m_2,V_n_2,V_i_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ),
    file('theBenchmark.p',fact_ivl__diff) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I11_J) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    file('theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_atLeastLessThan__singleton) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ),
    file('theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [V_k_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
     => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ),
    file('theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_atLeastLessThanSuc,axiom,
    ! [V_n_2,V_m_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThanSuc) ).

fof(fact_ivl__disj__un_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_ivl__disj__un_I3_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I3_J) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_aset_I10_J,axiom,
    ! [V_t_2,V_A_2,V_D_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
           => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I10_J) ).

fof(fact_bset_I10_J,axiom,
    ! [V_t_2,V_B_2,V_D_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
           => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_bset_I10_J) ).

fof(fact_aset_I9_J,axiom,
    ! [V_t_2,V_A_2,V_D_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
           => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I9_J) ).

fof(fact_finite__atLeastLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__atLeastZeroLessThan__int,axiom,
    ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).

fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).

fof(fact_image__add__int__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2),
    file('theBenchmark.p',fact_image__add__int__atLeastLessThan) ).

fof(fact_card__atLeastZeroLessThan__int,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2),
    file('theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).

fof(fact_card__atLeastLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    file('theBenchmark.p',fact_card__atLeastLessThan__int) ).

fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_fun__upd__image,axiom,
    ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__upd__image) ).

fof(fact_the__inv__into__into,axiom,
    ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__into) ).

fof(fact_fun__upd__triv,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2,
    file('theBenchmark.p',fact_fun__upd__triv) ).

fof(fact_finite__atMost,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
    file('theBenchmark.p',fact_finite__atMost) ).

fof(fact_atMost__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_atMost__eq__iff) ).

fof(fact_fun__upd__idem,axiom,
    ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = V_y_2
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ),
    file('theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_fun__upd__other,axiom,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( V_z_2 != V_x_2
     => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ),
    file('theBenchmark.p',fact_fun__upd__other) ).

fof(fact_fun__upd__twist,axiom,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
      ( V_a_2 != V_c_2
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_fun__upd__apply,axiom,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( ( V_z_2 != V_x_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) )
      & ( V_z_2 = V_x_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_fun__upd__same,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2,
    file('theBenchmark.p',fact_fun__upd__same) ).

fof(fact_fun__upd__upd,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2),
    file('theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
    <=> hAPP(V_f_2,V_x_2) = V_y_2 ),
    file('theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_fun__upd__def,axiom,
    ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
      ( ( V_x_2 != V_a_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) )
      & ( V_x_2 = V_a_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) ),
    file('theBenchmark.p',fact_fun__upd__def) ).

fof(fact_atLeast0AtMost,axiom,
    ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2),
    file('theBenchmark.p',fact_atLeast0AtMost) ).

fof(fact_card__atMost,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2),
    file('theBenchmark.p',fact_card__atMost) ).

fof(fact_atMost__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)),
    file('theBenchmark.p',fact_atMost__Suc) ).

fof(fact_atMost__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_atMost__iff) ).

fof(fact_atMost__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_UN__le__add__shift,axiom,
    ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2),
    file('theBenchmark.p',fact_UN__le__add__shift) ).

fof(fact_the__inv__into__f__eq,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hAPP(V_f_2,V_x_2) = V_y_2
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_the__inv__into__f__f,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ),
    file('theBenchmark.p',fact_the__inv__into__f__f) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_inj__on__the__inv__into) ).

fof(fact_the__inv__into__onto,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_inj__on__fun__updI,axiom,
    ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_the__inv__into__def,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
    file('theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_atMost__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_atMost__0) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [V_d_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [V_d_2,V_c_2,V_b_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_ivl__disj__un_I9_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_ivl__disj__int_I3_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I3_J) ).

fof(fact_ivl__disj__int_I1_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ),
    file('theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_UN__le__eq__Un0) ).

fof(fact_map__upd__nonempty,axiom,
    ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),
    file('theBenchmark.p',fact_map__upd__nonempty) ).

fof(fact_image__atLeastZeroLessThan__int,axiom,
    ! [V_u_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ),
    file('theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).

fof(fact_image__map__upd,axiom,
    ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ),
    file('theBenchmark.p',fact_image__map__upd) ).

fof(fact_finite__lessThan,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
    file('theBenchmark.p',fact_finite__lessThan) ).

fof(fact_card__lessThan,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2,
    file('theBenchmark.p',fact_card__lessThan) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_atLeast0LessThan,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2),
    file('theBenchmark.p',fact_atLeast0LessThan) ).

fof(fact_lessThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_lessThan__0) ).

fof(fact_lessThan__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)),
    file('theBenchmark.p',fact_lessThan__Suc) ).

fof(fact_lessThan__Suc__atMost,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2),
    file('theBenchmark.p',fact_lessThan__Suc__atMost) ).

fof(fact_lessThan__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_lessThan__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_lessThan__subset__iff) ).

fof(fact_lessThan__strict__subset__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_map__upd__Some__unfold,axiom,
    ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
    <=> ( ( hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
          & V_x_2 != V_a_2 )
        | ( V_b_2 = V_y_2
          & V_x_2 = V_a_2 ) ) ),
    file('theBenchmark.p',fact_map__upd__Some__unfold) ).

fof(fact_map__upd__triv,axiom,
    ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
      ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ),
    file('theBenchmark.p',fact_map__upd__triv) ).

fof(fact_map__upd__eqD1,axiom,
    ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
     => V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_map__upd__eqD1) ).

fof(fact_single__Diff__lessThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_single__Diff__lessThan) ).

fof(fact_ivl__disj__un_I8_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_ivl__disj__int_I4_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I4_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).

fof(fact_empty__upd__none,axiom,
    ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_empty__upd__none) ).

fof(fact_lessThan__Suc__eq__insert__0,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),
    file('theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).

fof(fact_ivl__disj__un_I2_J,axiom,
    ! [V_u_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ),
    file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I7_J) ).

fof(fact_arith__series__int,axiom,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
    file('theBenchmark.p',fact_arith__series__int) ).

fof(fact_ran__map__upd,axiom,
    ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
      ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
     => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ),
    file('theBenchmark.p',fact_ran__map__upd) ).

fof(fact_fun__upd__None__restrict,axiom,
    ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
    file('theBenchmark.p',fact_fun__upd__None__restrict) ).

fof(fact_setsum__abs,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_setsum__abs) ).

fof(fact_setsum__abs__ge__zero,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_restrict__in,axiom,
    ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ),
    file('theBenchmark.p',fact_restrict__in) ).

fof(fact_restrict__restrict,axiom,
    ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_restrict__restrict) ).

fof(fact_setsum__empty,axiom,
    ! [V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum__empty) ).

fof(fact_setsum_Oempty,axiom,
    ! [V_g_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setsum__infinite,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
    file('theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
    file('theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setsum__negf,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__negf) ).

fof(fact_of__int__setsum,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__int__setsum) ).

fof(fact_setsum__commute,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ),
    file('theBenchmark.p',fact_setsum__commute) ).

fof(fact_of__nat__setsum,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_setsum__product,axiom,
    ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__product) ).

fof(fact_setsum__left__distrib,axiom,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_setsum__right__distrib,axiom,
    ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_setsum__addf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__addf) ).

fof(fact_setsum__0,axiom,
    ! [V_A_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum__0) ).

fof(fact_abs__setsum__abs,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setsum__abs) ).

fof(fact_setsum__divide__distrib,axiom,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( class_Fields_Ofield(T_b)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_setsum__subtractf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_restrict__map__empty,axiom,
    ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_restrict__map__empty) ).

fof(fact_setsum_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).

fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_restrict__out,axiom,
    ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ),
    file('theBenchmark.p',fact_restrict__out) ).

fof(fact_restrict__map__insert,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)),
    file('theBenchmark.p',fact_restrict__map__insert) ).

fof(fact_setsum__add__nat__ivl,axiom,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__add__nat__ivl) ).

fof(fact_setsum__diff__nat__ivl,axiom,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff__nat__ivl) ).

fof(fact_setsum__delta,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__delta) ).

fof(fact_setsum__delta_H,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_restrict__map__def,axiom,
    ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ),
    file('theBenchmark.p',fact_restrict__map__def) ).

fof(fact_restrict__map__to__empty,axiom,
    ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_restrict__map__to__empty) ).

fof(fact_setsum__constant,axiom,
    ! [V_A_2,V_y_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ),
    file('theBenchmark.p',fact_setsum__constant) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [V_n_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [V_n_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_setsum_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_setsum__insert,axiom,
    ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__insert) ).

fof(fact_setsum__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_setsum__diff,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_setsum_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [V_k_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
    file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_setsum__head__upt__Suc,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head__upt__Suc) ).

fof(fact_setsum__head__Suc,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head__Suc) ).

fof(fact_setsum__restrict__set,axiom,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_ranI,axiom,
    ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
      ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ),
    file('theBenchmark.p',fact_ranI) ).

fof(fact_setsum_Oinsert__remove,axiom,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_setsum_Oinsert__remove) ).

fof(fact_setsum__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_setsum__Un,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_setsum__Un) ).

fof(fact_setsum__op__ivl__Suc,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_setsum__op__ivl__Suc) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_setsum__head,axiom,
    ! [V_P_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ),
    file('theBenchmark.p',fact_setsum__ub__add__nat) ).

fof(fact_fun__upd__restrict,axiom,
    ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2),
    file('theBenchmark.p',fact_fun__upd__restrict) ).

fof(fact_ran__empty,axiom,
    ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_ran__empty) ).

fof(fact_setsum__diff1_H,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1_H) ).

fof(fact_setsum_Oremove,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_setsum__diff1__ring,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Rings_Oring(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_setsum__diff1,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1) ).

fof(fact_geometric__sum,axiom,
    ! [V_n_2,V_x_2,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ),
    file('theBenchmark.p',fact_geometric__sum) ).

fof(fact_gauss__sum,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Ocomm__semiring__1(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ),
    file('theBenchmark.p',fact_gauss__sum) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('theBenchmark.p',fact_setsum__natinterval__difff) ).

fof(fact_fun__upd__restrict__conv,axiom,
    ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ),
    file('theBenchmark.p',fact_fun__upd__restrict__conv) ).

fof(fact_restrict__fun__upd,axiom,
    ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
       => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
       => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ),
    file('theBenchmark.p',fact_restrict__fun__upd) ).

fof(fact_restrict__complement__singleton__eq,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)),
    file('theBenchmark.p',fact_restrict__complement__singleton__eq) ).

fof(fact_restrict__upd__same,axiom,
    ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_restrict__upd__same) ).

fof(fact_arith__series__general,axiom,
    ! [V_n_2,V_d_2,V_a_2,T_b] :
      ( class_Rings_Ocomm__semiring__1(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ),
    file('theBenchmark.p',fact_arith__series__general) ).

fof(fact_setsum__mono2,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( class_Groups_Oordered__comm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_b] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono2) ).

fof(fact_setsum__bounded,axiom,
    ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Rings_Osemiring__1(T_c)
        & class_Groups_Oordered__ab__semigroup__add(T_c) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ),
    file('theBenchmark.p',fact_setsum__bounded) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setsum__eq__0__iff,axiom,
    ! [V_f_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
           => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__0__iff) ).

fof(fact_card__eq__setsum,axiom,
    ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
    file('theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_int__setsum,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setsum) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      <=> ? [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
               => ( B_x != B_xa
                 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
            & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__Suc0__iff) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ? [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
               => ( B_x != B_xa
                 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
            & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_setsum__shift__lb__Suc0__0,axiom,
    ! [V_k_2,V_f_2] :
      ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ),
    file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).

fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).

fof(fact_setsum__diff__nat,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [V_A_2,V_f_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).

fof(fact_setsum__diff1__nat,axiom,
    ! [V_f_2,V_A_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_setsum__diff1__nat) ).

fof(fact_setsum__Un__nat,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).

fof(fact_arith__series__nat,axiom,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
    file('theBenchmark.p',fact_arith__series__nat) ).

fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).

fof(fact_setsum__Un__zero,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_setsum__mono3,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono3) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
      ( class_Groups_Oordered__ab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
             => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ),
    file('theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_setsum__nonneg__leq__bound,axiom,
    ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
      ( class_Groups_Oordered__ab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

fof(fact_sum__diff__distrib,axiom,
    ! [V_n_2,V_P_2,V_Q_2] :
      ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ),
    file('theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_setsum__mono__zero__right,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
    file('theBenchmark.p',fact_folding__one__idem_Oidem) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oin__idem) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).

fof(fact_finite__subset__induct,axiom,
    ! [V_P_2,V_A_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
       => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
         => ( ! [B_a,B_F] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
               => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
                   => ( hBOOL(hAPP(V_P_2,B_F))
                     => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
           => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ),
    file('theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_setsum__strict__mono,axiom,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__strict__mono) ).

fof(fact_atMost__Int__atLeast,axiom,
    ! [V_n_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_atMost__Int__atLeast) ).

fof(fact_atLeast__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_atLeast__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_atLeast__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_atLeast__subset__iff) ).

fof(fact_Compl__atLeast,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_Compl__lessThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__lessThan) ).

fof(fact_ivl__disj__un_I14_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I14_J) ).

fof(fact_ivl__disj__int_I8_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [V_d_2,V_c_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_image__uminus__atMost,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_atLeast__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_atLeast__Suc) ).

fof(fact_ivl__disj__un_I12_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_ivl__disj__un_I13_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ),
    file('theBenchmark.p',fact_ivl__disj__un_I1_J) ).

fof(fact_atLeast__Suc__greaterThan,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2),
    file('theBenchmark.p',fact_atLeast__Suc__greaterThan) ).

fof(fact_greaterThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_Compl__greaterThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atMost,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atMost) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I7_J) ).

fof(fact_ivl__disj__un_I11_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_ivl__disj__int_I5_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I5_J) ).

fof(fact_greaterThan__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_greaterThan__Suc) ).

fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( V_A_2 = V_B_2
       => ( c_Nat__Transfer_Onat__set(V_B_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
               => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_dom__eq__singleton__conv,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Map_Odom(T_b,T_c,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
    <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ),
    file('theBenchmark.p',fact_dom__eq__singleton__conv) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_empty__fold__graphE,axiom,
    ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
     => V_x_2 = V_z_2 ),
    file('theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_fold__graph_OemptyI,axiom,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    file('theBenchmark.p',fact_fold__graph_OemptyI) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    file('theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).

fof(fact_finite__dom__body,axiom,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
    file('theBenchmark.p',fact_finite__dom__body) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_domIff,axiom,
    ! [V_m_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
    <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ),
    file('theBenchmark.p',fact_domIff) ).

fof(fact_domI,axiom,
    ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
      ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
     => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ),
    file('theBenchmark.p',fact_domI) ).

fof(fact_insert__dom,axiom,
    ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
     => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ),
    file('theBenchmark.p',fact_insert__dom) ).

fof(fact_dom__restrict,axiom,
    ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2),
    file('theBenchmark.p',fact_dom__restrict) ).

fof(fact_fold__graph_OinsertI,axiom,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
    file('theBenchmark.p',fact_fold__graph_OinsertI) ).

fof(fact_dom__empty,axiom,
    ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_dom__empty) ).

fof(fact_dom__eq__empty__conv,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ),
    file('theBenchmark.p',fact_dom__eq__empty__conv) ).

fof(fact_dom__minus,axiom,
    ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_dom__minus) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ),
    file('theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
    file('theBenchmark.p',fact_Diff1__fold__graph) ).

fof(fact_dom__fun__upd,axiom,
    ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
      ( ( V_y_2 != c_Option_Ooption_ONone(T_b)
       => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) )
      & ( V_y_2 = c_Option_Ooption_ONone(T_b)
       => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_dom__fun__upd) ).

fof(fact_fold1Set_Ointros,axiom,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_fold1Set_Ointros) ).

fof(fact_ran__restrictD,axiom,
    ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2))))
     => ? [B_x] :
          ( hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_ran__restrictD) ).

fof(fact_compl__unique,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ),
    file('theBenchmark.p',fact_compl__unique) ).

fof(fact_UNIV__I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_UNIV__I) ).

fof(fact_UNIV__option__conv,axiom,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_UNIV__option__conv) ).

fof(fact_range__composition,axiom,
    ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_range__composition) ).

fof(fact_UN__atMost__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__atMost__UNIV) ).

fof(fact_inj__int,axiom,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__int) ).

fof(fact_injD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
       => V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_injD) ).

fof(fact_inj__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_inj__eq) ).

fof(fact_inf__eq__top__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Obounded__lattice__top(T_b)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
      <=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
          & V_x_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ),
    file('theBenchmark.p',fact_inf__eq__top__iff) ).

fof(fact_inf__top__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ),
    file('theBenchmark.p',fact_inf__top__right) ).

fof(fact_inf__top__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ),
    file('theBenchmark.p',fact_inf__top__left) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__option__UNIV,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__nat) ).

fof(fact_finite__UNIV,axiom,
    ! [T_b] :
      ( class_Finite__Set_Ofinite(T_b)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__UNIV) ).

fof(fact_infinite__UNIV__int,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__int) ).

fof(fact_Int__UNIV__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_Int__UNIV__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    file('theBenchmark.p',fact_Int__UNIV__left) ).

fof(fact_Un__UNIV__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Un__UNIV__left) ).

fof(fact_Un__UNIV__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Un__UNIV__right) ).

fof(fact_subset__UNIV,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_subset__UNIV) ).

fof(fact_top__greatest,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Otop(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ),
    file('theBenchmark.p',fact_top__greatest) ).

fof(fact_sup__top__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__top__right) ).

fof(fact_sup__top__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__top__left) ).

fof(fact_equiv__intrel,axiom,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    file('theBenchmark.p',fact_equiv__intrel) ).

fof(fact_top__apply,axiom,
    ! [V_x_2,T_c,T_b] :
      ( class_Orderings_Otop(T_b)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ),
    file('theBenchmark.p',fact_top__apply) ).

fof(fact_UNIV__not__empty,axiom,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__not__empty) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_Pow__UNIV,axiom,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__UNIV) ).

fof(fact_card__UNIV__unit,axiom,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_card__UNIV__unit) ).

fof(fact_UN__lessThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__lessThan__UNIV) ).

fof(fact_fold1Set__nonempty,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
     => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_empty__fold1SetE,axiom,
    ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
    file('theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_range__eqI,axiom,
    ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
      ( V_b_2 = hAPP(V_f_2,V_x_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_range__eqI) ).

fof(fact_rangeI,axiom,
    ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_rangeI) ).

fof(fact_UN__atLeast__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__atLeast__UNIV) ).

fof(fact_Diff__UNIV,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__UNIV) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_finite__compl,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__compl) ).

fof(fact_Compl__partition2,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition2) ).

fof(fact_Compl__partition,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
    file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_code__numeral_Oof__nat__inject,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
       => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).

fof(fact_SUP__UN__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_finite__range__imageI,axiom,
    ! [V_f_2,T_d,V_g_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_nat__of,axiom,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_nat__of) ).

fof(fact_the__inv__f__f,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_inj__of__nat,axiom,
    ! [T_b] :
      ( class_Nat_Osemiring__char__0(T_b)
     => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__of__nat) ).

fof(fact_dom__const,axiom,
    ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_dom__const) ).

fof(fact_atLeast__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_atLeast__0) ).

fof(fact_inj__fun,axiom,
    ! [T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__fun) ).

fof(fact_compl__bot__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__bot__eq) ).

fof(fact_compl__top__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_compl__top__eq) ).

fof(fact_compl__sup__top,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__sup__top) ).

fof(fact_sup__compl__top,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__compl__top) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_range__ex1__eq,axiom,
    ! [V_b_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      <=> ? [B_x] :
            ( ! [B_y] :
                ( V_b_2 = hAPP(V_f_2,B_y)
               => B_y = B_x )
            & V_b_2 = hAPP(V_f_2,B_x) ) ) ),
    file('theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
       => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_image__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ),
    file('theBenchmark.p',fact_image__Int) ).

fof(fact_image__set__diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ),
    file('theBenchmark.p',fact_image__set__diff) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ),
    file('theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_of__nat__inverse,axiom,
    ! [V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ),
    file('theBenchmark.p',fact_of__nat__inverse) ).

fof(fact_fold1Set__sing,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
    <=> V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_finite__range__updI,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__updI) ).

fof(fact_UN__UN__finite__eq,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2),
    file('theBenchmark.p',fact_UN__UN__finite__eq) ).

fof(fact_inj__singleton,axiom,
    ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__singleton) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact_card__UNIV__bool,axiom,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_card__UNIV__bool) ).

fof(fact_inj__image__Compl__subset,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ),
    file('theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_greaterThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_greaterThan__0) ).

fof(fact_SUP__UN__eq2,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_UN__finite2__subset,axiom,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ),
    file('theBenchmark.p',fact_UN__finite2__subset) ).

fof(fact_UN__finite2__eq,axiom,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ),
    file('theBenchmark.p',fact_UN__finite2__eq) ).

fof(fact_UN__finite__subset,axiom,
    ! [V_C_2,V_A_2,T_b] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ),
    file('theBenchmark.p',fact_UN__finite__subset) ).

fof(fact_top1I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
    file('theBenchmark.p',fact_top1I) ).

fof(fact_Integ__def,axiom,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    file('theBenchmark.p',fact_Integ__def) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_equivp__equiv,axiom,
    ! [V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
    <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ),
    file('theBenchmark.p',fact_equivp__equiv) ).

fof(fact_equivp__transp,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
         => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_equivp__transp) ).

fof(fact_equivp__symp,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_equivp__symp) ).

fof(fact_equivp__reflp,axiom,
    ! [V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_equivp__reflp) ).

fof(fact_equivp__def,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
        <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ),
    file('theBenchmark.p',fact_equivp__def) ).

fof(fact_identity__equivp,axiom,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    file('theBenchmark.p',fact_identity__equivp) ).

fof(fact_Rep__Integ,axiom,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)),
    file('theBenchmark.p',fact_Rep__Integ) ).

fof(fact_type__definition__Integ,axiom,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    file('theBenchmark.p',fact_type__definition__Integ) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [V_a_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_inj__vimage__singleton) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( V_A_2 = V_B_2
       => ( c_Nat__Transfer_Onat__set(V_B_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
               => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).

fof(fact_vimageI,axiom,
    ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
      ( hAPP(V_f_2,V_a_2) = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_vimageI) ).

fof(fact_vimage__Diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Diff) ).

fof(fact_vimage__ident,axiom,
    ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_vimage__ident) ).

fof(fact_vimage__empty,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__empty) ).

fof(fact_vimage__code,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
    <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ),
    file('theBenchmark.p',fact_vimage__code) ).

fof(fact_vimage__Compl,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),
    file('theBenchmark.p',fact_vimage__Compl) ).

fof(fact_vimageI2,axiom,
    ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ),
    file('theBenchmark.p',fact_vimageI2) ).

fof(fact_vimageD,axiom,
    ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ),
    file('theBenchmark.p',fact_vimageD) ).

fof(fact_vimage__eq,axiom,
    ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ),
    file('theBenchmark.p',fact_vimage__eq) ).

fof(fact_vimage__mono,axiom,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ),
    file('theBenchmark.p',fact_vimage__mono) ).

fof(fact_vimage__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Un) ).

fof(fact_vimage__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__UN,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__UN) ).

fof(fact_vimage__UNIV,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__UNIV) ).

fof(fact_image__vimage__subset,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)),
    file('theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_surj__image__vimage__eq) ).

fof(fact_vimage__singleton__eq,axiom,
    ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
    <=> hAPP(V_f_2,V_a_2) = V_b_2 ),
    file('theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_vimage__insert,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__insert) ).

fof(fact_finite__vimageD,axiom,
    ! [V_F_2,V_h_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__vimageD) ).

fof(fact_vimage__subsetD,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_vimage__subsetD) ).

fof(fact_image__vimage__eq,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_finite__vimageI,axiom,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ),
    file('theBenchmark.p',fact_finite__vimageI) ).

fof(fact_inj__vimage__image__eq,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_inj__vimage__image__eq) ).

fof(fact_vimage__const,axiom,
    ! [T_c,V_A_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_vimage__const) ).

fof(fact_vimage__eq__UN,axiom,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_vimage__subsetI,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ),
    file('theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_vimage__if,axiom,
    ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ),
    file('theBenchmark.p',fact_vimage__if) ).

fof(fact_type__definition_ORep__range,axiom,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ),
    file('theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_type__definition_OAbs__image,axiom,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_type__definition_OAbs__image) ).

fof(fact_type__definition_ORep,axiom,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ),
    file('theBenchmark.p',fact_type__definition_ORep) ).

fof(fact_type__definition_ORep__inverse,axiom,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_type__definition_ORep__inject) ).

fof(fact_type__definition__code__numeral,axiom,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_type__definition__code__numeral) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
         => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
          <=> V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_type__definition_OAbs__inverse,axiom,
    ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
       => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ),
    file('theBenchmark.p',fact_type__definition_OAbs__inverse) ).

fof(fact_max__extp_Oequations,axiom,
    ! [V_a2_2,V_a1_2,V_R_2,T_b] :
      ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
    file('theBenchmark.p',fact_max__extp_Oequations) ).

fof(fact_max__ext_Ointros,axiom,
    ! [V_R_2,V_Y_2,V_X_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
       => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
               => ? [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                    & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
           => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_insert__fold1SetE,axiom,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
     => ~ ! [B_a,B_A] :
            ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
             => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ),
    file('theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
    <=> ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
          & hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) ),
    file('theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
    file('theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_fold1__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un) ).

fof(fact_SigmaI,axiom,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_SigmaI) ).

fof(fact_Times__eq__cancel2,axiom,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
     => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_Sigma__empty1,axiom,
    ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_Sigma__Diff__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_Times__Diff__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Diff__distrib1) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Diff__distrib1) ).

fof(fact_card__cartesian__product,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),
    file('theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
    file('theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_Times__empty,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Times__empty) ).

fof(fact_Sigma__empty2,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty2) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
    file('theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
    file('theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_swap__product,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
    file('theBenchmark.p',fact_swap__product) ).

fof(fact_fold1__singleton__def,axiom,
    ! [V_a_2,V_f_2,T_b,V_g_2] :
      ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
     => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_fold1__singleton__def) ).

fof(fact_fold1__singleton,axiom,
    ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2,
    file('theBenchmark.p',fact_fold1__singleton) ).

fof(fact_finite__cartesian__product,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ),
    file('theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_equiv__type,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    file('theBenchmark.p',fact_equiv__type) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
    file('theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_mem__Sigma__iff,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_SigmaD1,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    file('theBenchmark.p',fact_SigmaD1) ).

fof(fact_SigmaD2,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_SigmaD2) ).

fof(fact_SigmaE2,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
    file('theBenchmark.p',fact_SigmaE2) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__one_Oeq__fold) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
    file('theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_Times__subset__cancel2,axiom,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Times__subset__cancel2) ).

fof(fact_Image__subset,axiom,
    ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ),
    file('theBenchmark.p',fact_Image__subset) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_finite__cartesian__productD2,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_fst__image__times,axiom,
    ! [V_A_2,T_c,T_b,V_B_2] :
      ( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 )
      & ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_fst__image__times) ).

fof(fact_snd__image__times,axiom,
    ! [V_B_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_snd__image__times) ).

fof(fact_fold1__def,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
    file('theBenchmark.p',fact_fold1__def) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_Min_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_insert__times__insert,axiom,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
    file('theBenchmark.p',fact_insert__times__insert) ).

fof(fact_finite__equiv__class,axiom,
    ! [V_X_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ),
    file('theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_UN__Times__distrib,axiom,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
    file('theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_Sigma__def,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Sigma__def) ).

fof(fact_fold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__belowI) ).

fof(fact_finite__quotient,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ),
    file('theBenchmark.p',fact_finite__quotient) ).

fof(fact_below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_fold1__insert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_fold1__below__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_fold1__Un2,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un2) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_fold1__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
           => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold1__insert) ).

fof(fact_fold1__antimono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ),
    file('theBenchmark.p',fact_fold1__antimono) ).

fof(fact_semilattice__big_OF__eq,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [V_A_2,V_I_2,T_c,T_b] :
    ? [B_f] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
      & c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
    file('theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_fold__image__Sigma,axiom,
    ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_setprod__Sigma,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__Sigma,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Sigma) ).

fof(fact_card__SigmaI,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_card__SigmaI) ).

fof(fact_fold1__in,axiom,
    ! [V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold1__in) ).

fof(fact_finite__SigmaI,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ! [B_a] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_hom__fold1__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_SigmaE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
               => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ),
    file('theBenchmark.p',fact_SigmaE) ).

fof(fact_map__pair__surj,axiom,
    ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_map__pair__surj) ).

fof(fact_map__pair__inj__on,axiom,
    ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
       => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ),
    file('theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_map__pair__imageI,axiom,
    ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ),
    file('theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_snd__prod__fun,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
    file('theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_fst__map__pair,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)),
    file('theBenchmark.p',fact_fst__map__pair) ).

fof(fact_map__pair__simp,axiom,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
    file('theBenchmark.p',fact_map__pair__simp) ).

fof(fact_map__pair__ident,axiom,
    ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
    file('theBenchmark.p',fact_map__pair__ident) ).

fof(fact_map__pair__def,axiom,
    ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)),
    file('theBenchmark.p',fact_map__pair__def) ).

fof(fact_map__pair__surj__on,axiom,
    ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
     => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ),
    file('theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_prod__fun__imageE,axiom,
    ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
     => ~ ! [B_x,B_y] :
            ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_refl__on__def,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ),
    file('theBenchmark.p',fact_refl__on__def) ).

fof(fact_setprod__pos__nat,axiom,
    ! [V_f_2,V_S_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ),
    file('theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_refl__on__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_refl__on__empty,axiom,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_refl__on__empty) ).

fof(fact_refl__on__Un,axiom,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Un) ).

fof(fact_refl__on__Int,axiom,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__onD2,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_refl__onD2) ).

fof(fact_refl__onD1,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_refl__onD) ).

fof(fact_refl__onI,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
       => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_refl__onI) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
     => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
       => hBOOL(hAPP(V_P_2,V_y_2)) ) ),
    file('theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
     => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ),
    file('theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = V_z_2 )
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).

fof(fact_fun__left__comm__idem__remove,axiom,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_fun__left__comm__idem__remove) ).

fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ),
    file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).

fof(fact_fun__left__comm__idem__sup,axiom,
    ! [T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem__sup) ).

fof(fact_fun__left__comm__idem__inf,axiom,
    ! [T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).

fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
    ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).

fof(fact_fun__left__comm__idem,axiom,
    ! [T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem) ).

fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ),
    file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem__insert,axiom,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
    file('theBenchmark.p',fact_fun__left__comm__idem__insert) ).

fof(fact_card__less__Suc2,axiom,
    ! [V_i_2,V_M_2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ),
    file('theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_card__less,axiom,
    ! [V_i_2,V_M_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_card__less) ).

fof(fact_card__less__Suc,axiom,
    ! [V_i_2,V_M_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ),
    file('theBenchmark.p',fact_card__less__Suc) ).

fof(fact_CollectI,axiom,
    ! [T_b,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    file('theBenchmark.p',fact_CollectI) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [V_Q_2,V_P_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))),
    file('theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))),
    file('theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_Collect__split,axiom,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
    file('theBenchmark.p',fact_Collect__split) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
    file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_Collect__neg__eq,axiom,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
    file('theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
    file('theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_Collect__mem__eq,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_mem__Collect__eq,axiom,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
    <=> hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_CollectD,axiom,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectD) ).

fof(fact_CollectE,axiom,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectE) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
    file('theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_UNIV__def,axiom,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)),
    file('theBenchmark.p',fact_UNIV__def) ).

fof(fact_insert__Collect,axiom,
    ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
    file('theBenchmark.p',fact_insert__Collect) ).

fof(fact_Collect__conj__eq,axiom,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    file('theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_Collect__disj__eq,axiom,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    file('theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_Collect__def,axiom,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
    file('theBenchmark.p',fact_Collect__def) ).

fof(fact_empty__def,axiom,
    ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)),
    file('theBenchmark.p',fact_empty__def) ).

fof(fact_empty__Collect__eq,axiom,
    ! [V_P_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [V_P_2,T_b] :
      ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_Collect__empty__eq) ).

fof(fact_insert__compr__raw,axiom,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_insert__compr,axiom,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_insert__compr) ).

fof(fact_Un__def,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_Un__def) ).

fof(fact_Int__Collect,axiom,
    ! [V_P_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
    <=> ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__Collect) ).

fof(fact_Int__def,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_Int__def) ).

fof(fact_Collect__conv__if,axiom,
    ! [T_b,V_a_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_Collect__conv__if) ).

fof(fact_Collect__conv__if2,axiom,
    ! [T_b,V_a_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_Collect__conv__if2) ).

fof(fact_singleton__conv,axiom,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__conv) ).

fof(fact_singleton__conv2,axiom,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__conv2) ).

fof(fact_set__diff__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
    file('theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__not,axiom,
    ! [V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Collect__not) ).

fof(fact_insert__def,axiom,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
    file('theBenchmark.p',fact_insert__def) ).

fof(fact_Compl__eq,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
    file('theBenchmark.p',fact_Compl__eq) ).

fof(fact_vimage__def,axiom,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__def) ).

fof(fact_Collect__imp__eq,axiom,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    file('theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_dom__def,axiom,
    ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))),
    file('theBenchmark.p',fact_dom__def) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
    file('theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ),
    file('theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_if__image__distrib,axiom,
    ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
    file('theBenchmark.p',fact_if__image__distrib) ).

fof(fact_dom__if,axiom,
    ! [V_g_2,V_f_2,V_P_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))),
    file('theBenchmark.p',fact_dom__if) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [V_n_2,V_f_2,T_b,V_A_2] :
      ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_setsum__image__gen,axiom,
    ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ),
    file('theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_Image__singleton,axiom,
    ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
    file('theBenchmark.p',fact_Image__singleton) ).

fof(fact_setsum__cases,axiom,
    ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ),
    file('theBenchmark.p',fact_setsum__cases) ).

fof(fact_dom__override__on,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))),
    file('theBenchmark.p',fact_dom__override__on) ).

fof(fact_setsum__multicount,axiom,
    ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
             => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__multicount) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_Pow__Compl,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))),
    file('theBenchmark.p',fact_Pow__Compl) ).

fof(fact_Pow__def,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Pow__def) ).

fof(fact_finite__image__set,axiom,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ),
    file('theBenchmark.p',fact_finite__image__set) ).

fof(fact_finite__Collect__bounded__ex,axiom,
    ! [V_Q_2,T_c,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
      <=> ! [B_y] :
            ( hBOOL(hAPP(V_P_2,B_y))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_override__on__apply__notin,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ),
    file('theBenchmark.p',fact_override__on__apply__notin) ).

fof(fact_override__on__apply__in,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ),
    file('theBenchmark.p',fact_override__on__apply__in) ).

fof(fact_override__on__emptyset,axiom,
    ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2,
    file('theBenchmark.p',fact_override__on__emptyset) ).

fof(fact_inj__graph,axiom,
    ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__graph) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_override__on__def,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ),
    file('theBenchmark.p',fact_override__on__def) ).

fof(fact_finite__psubset__def,axiom,
    ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
    file('theBenchmark.p',fact_finite__psubset__def) ).

fof(fact_ran__def,axiom,
    ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))),
    file('theBenchmark.p',fact_ran__def) ).

fof(fact_inv__image__def,axiom,
    ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
    file('theBenchmark.p',fact_inv__image__def) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).

fof(fact_add__Max__commute,axiom,
    ! [V_k_2,V_N_2,T_b] :
      ( class_Groups_Olinordered__ab__semigroup__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
       => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ),
    file('theBenchmark.p',fact_add__Max__commute) ).

fof(fact_add__Min__commute,axiom,
    ! [V_k_2,V_N_2,T_b] :
      ( class_Groups_Olinordered__ab__semigroup__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
       => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ),
    file('theBenchmark.p',fact_add__Min__commute) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_min__max_Osup__Inf1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
    file('theBenchmark.p',fact_Nitpick_Oprod__def) ).

fof(fact_int__ge__less__than2__def,axiom,
    ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('theBenchmark.p',fact_int__ge__less__than2__def) ).

fof(fact_int__ge__less__than__def,axiom,
    ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('theBenchmark.p',fact_int__ge__less__than__def) ).

fof(fact_reflp__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Predicate_Oreflp(T_b,V_r_2)
    <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_reflp__def) ).

fof(fact_reflpE,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Predicate_Oreflp(T_b,V_r_2)
     => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_reflpE) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
      ( class_Rings_Osemiring__0(T_d)
     => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ),
    file('theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
             => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ),
    file('theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_image__id,axiom,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_image__id) ).

fof(fact_vimage__id,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_vimage__id) ).

fof(fact_of__int__eq__id,axiom,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    file('theBenchmark.p',fact_of__int__eq__id) ).

fof(fact_apsnd__id,axiom,
    ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_apsnd__id) ).

fof(fact_apfst__id,axiom,
    ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_apfst__id) ).

fof(fact_id__apply,axiom,
    ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
    file('theBenchmark.p',fact_id__apply) ).

fof(fact_id__def,axiom,
    ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
    file('theBenchmark.p',fact_id__def) ).

fof(fact_map__pair_Oid,axiom,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_inj__on__id,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__id) ).

fof(fact_surj__id,axiom,
    ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_surj__id) ).

fof(fact_apsnd__def,axiom,
    ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2),
    file('theBenchmark.p',fact_apsnd__def) ).

fof(fact_apfst__def,axiom,
    ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)),
    file('theBenchmark.p',fact_apfst__def) ).

fof(fact_split__Pair,axiom,
    ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_split__Pair) ).

fof(fact_setsum__reindex__id,axiom,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setsum__reindex__id) ).

fof(fact_setprod__reindex__id,axiom,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
    <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ),
    file('theBenchmark.p',fact_finite__conv__nat__seg__image) ).

fof(fact_rel__comp__def,axiom,
    ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
    file('theBenchmark.p',fact_rel__comp__def) ).

fof(fact_rel__compI,axiom,
    ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
    file('theBenchmark.p',fact_rel__compI) ).

fof(fact_rel__comp__empty2,axiom,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_rel__comp__empty1,axiom,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_O__assoc,axiom,
    ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)),
    file('theBenchmark.p',fact_O__assoc) ).

fof(fact_rel__comp__mono,axiom,
    ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
    file('theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_rel__comp__distrib,axiom,
    ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
    file('theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
    file('theBenchmark.p',fact_rel__comp__distrib2) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
    file('theBenchmark.p',fact_rel__comp__UNION__distrib) ).

fof(fact_rel__comp__UNION__distrib2,axiom,
    ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
    file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_union__comp__emptyL,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_union__comp__emptyL) ).

fof(fact_union__comp__emptyR,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_union__comp__emptyR) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ),
    file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_max__ext__compat,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_max__ext__compat) ).

fof(fact_min__ext__compat,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_min__ext__compat) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2),V_x_2,V_y_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ),
    file('theBenchmark.p',fact_pred__comp__rel__comp__eq) ).

fof(fact_reduction__pairI,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
       => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
    file('theBenchmark.p',fact_reduction__pairI) ).

fof(fact_wf__less__than,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_wf__less__than) ).

fof(fact_pred__comp_Ointros,axiom,
    ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
       => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2) ) ),
    file('theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_wf__empty,axiom,
    ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_wf__empty) ).

fof(fact_wf__inv__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
    file('theBenchmark.p',fact_wf__inv__image) ).

fof(fact_wf__lex__prod,axiom,
    ! [V_rb_2,T_c,V_ra_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_ra_2)
     => ( c_Wellfounded_Owf(T_c,V_rb_2)
       => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ),
    file('theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_wf__measure,axiom,
    ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
    file('theBenchmark.p',fact_wf__measure) ).

fof(fact_wf__comp__self,axiom,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
    <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ),
    file('theBenchmark.p',fact_wf__comp__self) ).

fof(fact_wf__int__ge__less__than,axiom,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
    file('theBenchmark.p',fact_wf__int__ge__less__than) ).

fof(fact_wf__not__refl,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__not__refl) ).

fof(fact_wf__not__sym,axiom,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__asym,axiom,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__asym) ).

fof(fact_wf__irrefl,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__irrefl) ).

fof(fact_wf__mlex,axiom,
    ! [V_f_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__mlex) ).

fof(fact_wf__Int2,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    file('theBenchmark.p',fact_wf__Int2) ).

fof(fact_wf__Int1,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
    file('theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__subset,axiom,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
       => c_Wellfounded_Owf(T_b,V_p_2) ) ),
    file('theBenchmark.p',fact_wf__subset) ).

fof(fact_wf__pair__less,axiom,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('theBenchmark.p',fact_wf__pair__less) ).

fof(fact_max__ext__wf,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_max__ext__wf) ).

fof(fact_pred__comp_Oequations,axiom,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
    <=> ? [B_b] :
          ( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
          & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) ),
    file('theBenchmark.p',fact_pred__comp_Oequations) ).

fof(fact_min__ext__wf,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_min__ext__wf) ).

fof(fact_wf__finite__psubset,axiom,
    ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
    file('theBenchmark.p',fact_wf__finite__psubset) ).

fof(fact_wf__acc__iff,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_acc__wfD,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acc__wfD) ).

fof(fact_wf__int__ge__less__than2,axiom,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
    file('theBenchmark.p',fact_wf__int__ge__less__than2) ).

fof(fact_wf__less,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_wf__less) ).

fof(fact_wf__no__loop,axiom,
    ! [V_R_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => c_Wellfounded_Owf(T_b,V_R_2) ),
    file('theBenchmark.p',fact_wf__no__loop) ).

fof(fact_wf__union__merge,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
    <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ),
    file('theBenchmark.p',fact_wf__union__merge) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ~ ? [B_f] :
          ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ),
    file('theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_wfE__pf,axiom,
    ! [V_A_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
       => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_wfE__pf) ).

fof(fact_wf__union__compatible,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => ( c_Wellfounded_Owf(T_b,V_S_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
         => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_wf,axiom,
    ! [T_b] :
      ( class_Orderings_Owellorder(T_b)
     => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ),
    file('theBenchmark.p',fact_wf) ).

fof(fact_reduction__pair__def,axiom,
    ! [V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_P_2)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
        & c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) ) ),
    file('theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [V_S_2,V_R_2,V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_P_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
         => ( c_Wellfounded_Owf(T_b,V_S_2)
           => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ),
    file('theBenchmark.p',fact_reduction__pair__lemma) ).

fof(fact_wf__map__pair__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_wf__lenlex,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_wf__lenlex) ).

fof(fact_wf__if__measure,axiom,
    ! [T_b,V_g_2,V_f_2,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
     => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ),
    file('theBenchmark.p',fact_wf__if__measure) ).

fof(fact_pred__nat__def,axiom,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    file('theBenchmark.p',fact_pred__nat__def) ).

fof(fact_wf__lex,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__pred__nat,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('theBenchmark.p',fact_wf__pred__nat) ).

fof(fact_lex__def,axiom,
    ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
    file('theBenchmark.p',fact_lex__def) ).

fof(fact_wf__lexn,axiom,
    ! [V_n_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ),
    file('theBenchmark.p',fact_wf__lexn) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lexn_Osimps_I1_J) ).

fof(fact_wf__same__fst,axiom,
    ! [T_b,V_R_2,T_c,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
         => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
     => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__same__fst) ).

fof(fact_Range__Collect__split,axiom,
    ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_RangeI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_RangeI) ).

fof(fact_Range__Id__on,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Range__Id__on) ).

fof(fact_Range__empty__iff,axiom,
    ! [V_r_2,T_b,T_c] :
      ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_Range__empty,axiom,
    ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__empty) ).

fof(fact_Range__Un__eq,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
    file('theBenchmark.p',fact_Range__Un__eq) ).

fof(fact_finite__Range,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Range) ).

fof(fact_snd__eq__Range,axiom,
    ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
    file('theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_Range__iff,axiom,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
    <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_Range__iff) ).

fof(fact_Range__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
    file('theBenchmark.p',fact_Range__insert) ).

fof(fact_Range__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
    file('theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_Range__Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Range__Diff__subset) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_RangeE,axiom,
    ! [V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
     => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ),
    file('theBenchmark.p',fact_RangeE) ).

fof(fact_RangeP_Ointros,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ),
    file('theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_RangeP_Oequations,axiom,
    ! [V_a2_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
    <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ),
    file('theBenchmark.p',fact_RangeP_Oequations) ).

fof(fact_wf__Un,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( c_Wellfounded_Owf(T_b,V_s_2)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ),
    file('theBenchmark.p',fact_wf__Un) ).

fof(fact_wfP__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
    <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_wfP__def) ).

fof(fact_wfP__empty,axiom,
    ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
    file('theBenchmark.p',fact_wfP__empty) ).

fof(fact_DomainI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_DomainI) ).

fof(fact_wfP__accp__iff,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
    <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ),
    file('theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_accp__wfPD,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ),
    file('theBenchmark.p',fact_accp__wfPD) ).

fof(fact_Domain__Id__on,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_wfP__subset,axiom,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
       => c_Wellfounded_OwfP(T_b,V_p_2) ) ),
    file('theBenchmark.p',fact_wfP__subset) ).

fof(fact_Domain__empty__iff,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Domain__empty,axiom,
    ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__empty) ).

fof(fact_Domain__mono,axiom,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ),
    file('theBenchmark.p',fact_Domain__mono) ).

fof(fact_Domain__Un__eq,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
    file('theBenchmark.p',fact_Domain__Un__eq) ).

fof(fact_finite__Domain,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Domain) ).

fof(fact_fst__eq__Domain,axiom,
    ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
    file('theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_Domain__iff,axiom,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
    <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
    file('theBenchmark.p',fact_Domain__iff) ).

fof(fact_Domain__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
    file('theBenchmark.p',fact_Domain__insert) ).

fof(fact_Domain__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
    file('theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Field__def,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
    file('theBenchmark.p',fact_Field__def) ).

fof(fact_wf__in__rel,axiom,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ),
    file('theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wfP__wf__eq,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
    <=> c_Wellfounded_Owf(T_b,V_r_2) ),
    file('theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_Domain__Collect__split,axiom,
    ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
    file('theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_DomainE,axiom,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
     => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
    file('theBenchmark.p',fact_DomainE) ).

fof(fact_DomainP_Ointros,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ),
    file('theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_DomainP_Oequations,axiom,
    ! [V_a1_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
    <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ),
    file('theBenchmark.p',fact_DomainP_Oequations) ).

fof(fact_wfP__acyclicP,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
     => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_pigeonhole__infinite,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => ? [B_x] :
            ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_pigeonhole__infinite) ).

fof(fact_wf__acyclic,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    file('theBenchmark.p',fact_wf__acyclic) ).

fof(fact_acyclic__subset,axiom,
    ! [V_r_2,V_s_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_s_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
       => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_acyclic__subset) ).

fof(fact_wf__iff__acyclic__if__finite,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => ( c_Wellfounded_Owf(T_b,V_r_2)
      <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
       => c_Wellfounded_Owf(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Nitpick_Owf_H(T_b,V_r_2)
    <=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
        & c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).

fof(fact_refl__on__def_H,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) ) ) ),
    file('theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_ball__empty,axiom,
    ! [V_P_2,T_b,B_x] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
     => hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_ball__empty) ).

fof(fact_Powp__def,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
         => hBOOL(hAPP(V_A_2,B_x)) ) ),
    file('theBenchmark.p',fact_Powp__def) ).

fof(fact_congruent__def,axiom,
    ! [V_f_2,V_r_2,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ),
    file('theBenchmark.p',fact_congruent__def) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [V_x_2] :
      ~ ! [B_y] :
          ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ),
    file('theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [V_x_2,V_P_2] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
         => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
     => hBOOL(hAPP(V_P_2,V_x_2)) ),
    file('theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_triples__valid__Suc,axiom,
    ! [V_n_2,V_tsa_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
         => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
     => ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
         => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ),
    file('theBenchmark.p',fact_triples__valid__Suc) ).

fof(fact_hoare__valids__def,axiom,
    ! [V_tsa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
    <=> ! [B_n] :
          ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
             => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
         => ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
             => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ),
    file('theBenchmark.p',fact_hoare__valids__def) ).

fof(fact_finite__UN__I,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ! [B_a] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__UN__I) ).

fof(fact_inj__on__diff__nat,axiom,
    ! [V_k_2,V_N_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
     => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ),
    file('theBenchmark.p',fact_inj__on__diff__nat) ).

fof(fact_wfP__SUP,axiom,
    ! [T_b,V_r_2,T_c] :
      ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
     => ( ! [B_i,B_j] :
            ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ),
    file('theBenchmark.p',fact_wfP__SUP) ).

fof(fact_finite__map__freshness,axiom,
    ! [V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
       => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ),
    file('theBenchmark.p',fact_finite__map__freshness) ).

fof(fact_mem__splitE,axiom,
    ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
     => ~ ! [B_x,B_y] :
            ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
           => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ),
    file('theBenchmark.p',fact_mem__splitE) ).

fof(fact_mem__splitI2,axiom,
    ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
      ( ! [B_a,B_b] :
          ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
         => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
     => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ),
    file('theBenchmark.p',fact_mem__splitI2) ).

fof(fact_vimage__Times,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__Times) ).

fof(fact_setsum__SucD,axiom,
    ! [V_n_2,V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
     => ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum__SucD) ).

fof(fact_o__id,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
    file('theBenchmark.p',fact_o__id) ).

fof(fact_id__o,axiom,
    ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
    file('theBenchmark.p',fact_id__o) ).

fof(fact_o__eq__id__dest,axiom,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
    file('theBenchmark.p',fact_o__eq__id__dest) ).

fof(fact_image__compose,axiom,
    ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)),
    file('theBenchmark.p',fact_image__compose) ).

fof(fact_comp__surj,axiom,
    ! [V_g_2,T_d,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_comp__surj) ).

fof(fact_vimage__compose,axiom,
    ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)),
    file('theBenchmark.p',fact_vimage__compose) ).

fof(fact_fun__upd__comp,axiom,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_fun__upd__comp) ).

fof(fact_apfst__compose,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apfst__compose) ).

fof(fact_apsnd__compose,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apsnd__compose) ).

fof(fact_comp__cong,axiom,
    ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
      ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
     => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ),
    file('theBenchmark.p',fact_comp__cong) ).

fof(fact_o__eq__elim,axiom,
    ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
     => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ),
    file('theBenchmark.p',fact_o__eq__elim) ).

fof(fact_o__eq__dest,axiom,
    ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ),
    file('theBenchmark.p',fact_o__eq__dest) ).

fof(fact_o__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    file('theBenchmark.p',fact_o__apply) ).

fof(fact_o__assoc,axiom,
    ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2),
    file('theBenchmark.p',fact_o__assoc) ).

fof(fact_o__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    file('theBenchmark.p',fact_o__def) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
    file('theBenchmark.p',fact_o__eq__dest__lhs) ).

fof(fact_K__record__comp,axiom,
    ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
    file('theBenchmark.p',fact_K__record__comp) ).

fof(fact_map__pair_Ocomp,axiom,
    ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
    file('theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_map__pair__compose,axiom,
    ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
    file('theBenchmark.p',fact_map__pair__compose) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
    file('theBenchmark.p',fact_map__pair_Ocompositionality) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__inj__on,axiom,
    ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
       => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_comp__inj__on) ).

fof(fact_inj__on__imageI,axiom,
    ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
     => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_inj__on__imageI2,axiom,
    ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
     => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ),
    file('theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_inj__comp,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
       => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_inj__comp) ).

fof(fact_setsum__reindex,axiom,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
    file('theBenchmark.p',fact_setsum__reindex) ).

fof(fact_setprod__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__reindex__cong) ).

fof(fact_setprod__reindex,axiom,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
    file('theBenchmark.p',fact_setprod__reindex) ).

fof(fact_setsum_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_setprod_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_the__inv__into__comp,axiom,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
     => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
         => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_fold__image__reindex,axiom,
    ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Oab__semigroup__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_Nitpick_Odenom__def,axiom,
    ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    file('theBenchmark.p',fact_Nitpick_Odenom__def) ).

fof(fact_Nitpick_Onum__def,axiom,
    ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    file('theBenchmark.p',fact_Nitpick_Onum__def) ).

fof(fact_UN__o,axiom,
    ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
    file('theBenchmark.p',fact_UN__o) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
    file('theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
    file('theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_split__comp,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    file('theBenchmark.p',fact_split__comp) ).

fof(fact_number__of__code__numeral__def,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    file('theBenchmark.p',fact_number__of__code__numeral__def) ).

fof(fact_int__of__def,axiom,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    file('theBenchmark.p',fact_int__of__def) ).

fof(fact_Loop__sound__lemma,axiom,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop__sound__lemma) ).

fof(fact_hoare__derivs_OIf,axiom,
    ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_hoare__derivs_OIf) ).

fof(fact_peek__and__def,axiom,
    ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2))
    <=> ( hBOOL(hAPP(V_p_2,V_s_2))
        & hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_peek__and__def) ).

fof(fact_Loop,axiom,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop) ).

fof(fact_folding_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oremove) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
         => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ),
    file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_folding__image_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_folding_Oempty,axiom,
    ! [V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ),
    file('theBenchmark.p',fact_folding_Oempty) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_folding_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_folding_Ounion,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
             => ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
                 => ( B_x != B_y
                   => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
                     => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
    file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_folding__idem_Oidem__comp,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ),
    file('theBenchmark.p',fact_folding__idem_Oidem__comp) ).

fof(fact_folding__idem_Oidem__left__comp,axiom,
    ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ),
    file('theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_neg__map__def,axiom,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
    file('theBenchmark.p',fact_neg__map__def) ).

fof(fact_neg__single__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
    file('theBenchmark.p',fact_neg__single__def) ).

fof(fact_pos__map__def,axiom,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
    file('theBenchmark.p',fact_pos__map__def) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x),
    file('theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_pos__single__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
    file('theBenchmark.p',fact_pos__single__def) ).

fof(fact_New__DSequence_Opos__single__def,axiom,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Osingle(T_a,V_x),
    file('theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_Eps__split,axiom,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    file('theBenchmark.p',fact_Eps__split) ).

fof(fact_exE__some,axiom,
    ! [T_b,V_c_2,V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
     => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
       => hBOOL(hAPP(V_P_2,V_c_2)) ) ),
    file('theBenchmark.p',fact_exE__some) ).

fof(fact_some__sym__eq__trivial,axiom,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_some__eq__trivial,axiom,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_some__eq__trivial) ).

fof(fact_some__eq__ex,axiom,
    ! [T_b,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
    <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
    file('theBenchmark.p',fact_some__eq__ex) ).

fof(fact_someI__ex,axiom,
    ! [T_b,V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
    file('theBenchmark.p',fact_someI__ex) ).

fof(fact_tfl__some,axiom,
    ! [T_b,B_P] :
      ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
     => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ),
    file('theBenchmark.p',fact_tfl__some) ).

fof(fact_someI,axiom,
    ! [T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
    file('theBenchmark.p',fact_someI) ).

fof(fact_split__paired__Eps,axiom,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_Eps__split__eq,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    file('theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_wfI__pf,axiom,
    ! [V_R_2,T_b] :
      ( ! [B_A] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
         => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(T_b,V_R_2) ),
    file('theBenchmark.p',fact_wfI__pf) ).

fof(fact_Sigma__mono,axiom,
    ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Sigma__mono) ).

fof(fact_acc_OaccI,axiom,
    ! [V_r_2,V_x_2,T_b] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acc_OaccI) ).

fof(fact_not__acc__down,axiom,
    ! [V_R_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
     => ~ ! [B_z] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
           => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_not__acc__down) ).

fof(fact_fold__image__1,axiom,
    ! [V_f_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
             => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ),
    file('theBenchmark.p',fact_fold__image__1) ).

fof(fact_card_Oneutral,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_card_Oneutral) ).

fof(fact_max__ext_Osimps,axiom,
    ! [V_R_2,V_a2_2,V_a1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
    file('theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_fold__image__cong,axiom,
    ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__semigroup__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__cong) ).

fof(fact_setprod__dvd__setprod__subset2,axiom,
    ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( class_Rings_Ocomm__semiring__1(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__dvd__setprod__subset2) ).

fof(fact_Max__eqI,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_y] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
           => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Max__eqI) ).

fof(fact_Min__eqI,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_y] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
           => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Min__eqI) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [V_f_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ),
    file('theBenchmark.p',fact_wf__no__infinite__down__chainE) ).

fof(fact_setsum__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( ! [B_a] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
               => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_setsum__ivl__cong,axiom,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
      ( ( class_Orderings_Oord(T_b)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( V_a_2 = V_c_2
       => ( V_b_2 = V_d_2
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
                 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__ivl__cong) ).

fof(fact_less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__eq) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).

fof(fact_fold__empty,axiom,
    ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    file('theBenchmark.p',fact_fold__empty) ).

fof(fact_fold__image__def,axiom,
    ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_fold__image__def) ).

fof(fact_wf__trancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_wf__trancl) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_fold__def,axiom,
    ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
    file('theBenchmark.p',fact_fold__def) ).

fof(fact_union__fold__insert,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ),
    file('theBenchmark.p',fact_union__fold__insert) ).

fof(fact_fold__sup__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__sup__insert) ).

fof(fact_fold__inf__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_less__than__def,axiom,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('theBenchmark.p',fact_less__than__def) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_acyclic__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acyclic__def) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_sup__le__fold__sup) ).

fof(fact_fold__inf__le__inf,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ),
    file('theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_min__max_Osup__le__fold__sup,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_fold1__eq__fold__idem,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_fold1__eq__fold__idem) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).

fof(fact_minus__fold__remove,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ),
    file('theBenchmark.p',fact_minus__fold__remove) ).

fof(fact_folding__one_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_fold1__eq__fold,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_Sup__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_trancl_Or__into__trancl,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_trancl_Or__into__trancl) ).

fof(fact_trancl__subset__Field2,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
    file('theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_r__into__trancl_H,axiom,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_trancl__empty,axiom,
    ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_trancl__empty) ).

fof(fact_trancl__domain,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
    file('theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
    file('theBenchmark.p',fact_trancl__range) ).

fof(fact_finite__trancl,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    file('theBenchmark.p',fact_finite__trancl) ).

fof(fact_r__r__into__trancl,axiom,
    ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_trancl__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__trans) ).

fof(fact_trancl__mono,axiom,
    ! [V_s_2,V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ),
    file('theBenchmark.p',fact_trancl__mono) ).

fof(fact_trancl__unfold,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_trancl__unfold) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    file('theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_trancl__Int__subset,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ),
    file('theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
         => V_y_2 = V_x_2 ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_fun__left__comm,axiom,
    ! [T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_fun__left__comm_Ofold__equality,axiom,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_fun__left__comm_Ofold__insert,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ? [B_y_H] :
              ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
              & V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) ) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_trancl__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
    file('theBenchmark.p',fact_trancl__insert) ).

fof(fact_r__into__rtrancl,axiom,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
    file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_trancl__into__rtrancl,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_trancl__into__rtrancl) ).

fof(fact_Domain__rtrancl,axiom,
    ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__rtrancl) ).

fof(fact_Range__rtrancl,axiom,
    ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__rtrancl) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_r__comp__rtrancl__eq,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    file('theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [V_S_2,V_R_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ),
    file('theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
    file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_rtrancl__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_rtrancl__subset,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
       => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ),
    file('theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
    file('theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_Image__closed__trancl,axiom,
    ! [V_X_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
     => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ),
    file('theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_rtrancl__idemp,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_rtrancl__idemp) ).

fof(fact_rtrancl__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_refl__rtrancl,axiom,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_trancl__unfold__left,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_trancl__unfold__right,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    file('theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).

fof(fact_trancl__rtrancl__trancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_rtranclD,axiom,
    ! [V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
     => ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
          & V_a_2 != V_b_2 )
        | V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_rtranclD) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
          & V_x_2 != V_y_2 )
        | V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_rtrancl__eq__or__trancl) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [V_y_2,V_R_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_Not__Domain__rtrancl) ).

fof(fact_acc__downwards,axiom,
    ! [V_b_2,V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downwards) ).

fof(fact_acc__downwards__aux,axiom,
    ! [V_r_2,V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downwards__aux) ).

fof(fact_wf__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        & c_Wellfounded_Owf(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_wf__insert) ).

fof(fact_acyclic__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        & c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_acyclic__insert) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
          | V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_irrefl__tranclI,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_INFI__fold__inf,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_INF2__E,axiom,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
       => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF2__E) ).

fof(fact_INF2__D,axiom,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_INF2__D) ).

fof(fact_INT__D,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
    file('theBenchmark.p',fact_INT__D) ).

fof(fact_INT__E,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
       => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INT__E) ).

fof(fact_INF1__D,axiom,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_INF1__D) ).

fof(fact_INF1__E,axiom,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
     => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
       => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF1__E) ).

fof(fact_finite__INT,axiom,
    ! [V_A_2,T_c,V_I_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ),
    file('theBenchmark.p',fact_finite__INT) ).

fof(fact_rtrancl__converse,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_trancl__converse,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_trancl__converse) ).

fof(fact_wf__converse__trancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
     => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_Range__converse,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
    file('theBenchmark.p',fact_Range__converse) ).

fof(fact_Domain__converse,axiom,
    ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
    file('theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__def,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
    file('theBenchmark.p',fact_Range__def) ).

fof(fact_vimage__INT,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__INT) ).

fof(fact_acyclic__converse,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    file('theBenchmark.p',fact_acyclic__converse) ).

fof(fact_INT__constant,axiom,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__constant) ).

fof(fact_INT__empty,axiom,
    ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_INT__empty) ).

fof(fact_INF__const,axiom,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ),
    file('theBenchmark.p',fact_INF__const) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_converse__rel__comp,axiom,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
    file('theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_INT__Un,axiom,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    file('theBenchmark.p',fact_INT__Un) ).

fof(fact_INT__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_INT__insert) ).

fof(fact_le__INF__iff,axiom,
    ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_le__INF__iff) ).

fof(fact_INT__insert__distrib,axiom,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_INT__lower,axiom,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_INT__lower) ).

fof(fact_INT__simps_I5_J,axiom,
    ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
    file('theBenchmark.p',fact_INT__extend__simps_I5_J) ).

fof(fact_converse__Un,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    file('theBenchmark.p',fact_converse__Un) ).

fof(fact_INT__subset__iff,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_INT__simps_I7_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_INT__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__simps_I6_J) ).

fof(fact_INT__extend__simps_I7_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_INT__extend__simps_I7_J) ).

fof(fact_Un__INT__distrib,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Un__INT__distrib) ).

fof(fact_INT__extend__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_INT__extend__simps_I6_J) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    file('theBenchmark.p',fact_Un__INT__distrib2) ).

fof(fact_Image__INT__subset,axiom,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
    file('theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_Pow__INT__eq,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
    file('theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_converse__Id__on,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2),
    file('theBenchmark.p',fact_converse__Id__on) ).

fof(fact_Field__converse,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2),
    file('theBenchmark.p',fact_Field__converse) ).

fof(fact_converse__INTER,axiom,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    file('theBenchmark.p',fact_converse__INTER) ).

fof(fact_converse__converse,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_converse__converse) ).

fof(fact_converse__inv__image,axiom,
    ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
    file('theBenchmark.p',fact_converse__inv__image) ).

fof(fact_INF__commute,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
    file('theBenchmark.p',fact_INF__commute) ).

fof(fact_INFI__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_INFI__apply) ).

fof(fact_INT__Int__distrib,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_converse__Int,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    file('theBenchmark.p',fact_converse__Int) ).

fof(fact_INTER__UNIV__conv_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).

fof(fact_INTER__UNIV__conv_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).

fof(fact_finite__converse,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ),
    file('theBenchmark.p',fact_finite__converse) ).

fof(fact_INF__INT__eq2,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_INF__INT__eq2) ).

fof(fact_INT__iff,axiom,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__iff) ).

fof(fact_INT__absorb,axiom,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ),
    file('theBenchmark.p',fact_INT__absorb) ).

fof(fact_INF__INT__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_INF__less__iff,axiom,
    ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_INF__less__iff) ).

fof(fact_converse__iff,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_converse__iff) ).

fof(fact_converseI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_converseI) ).

fof(fact_converseD,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_converseD) ).

fof(fact_refl__on__converse,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_refl__on__converse) ).

fof(fact_INT__extend__simps_I10_J,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    file('theBenchmark.p',fact_INT__simps_I10_J) ).

fof(fact_Compl__INT,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_Compl__UN) ).

fof(fact_converse__UNION,axiom,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    file('theBenchmark.p',fact_converse__UNION) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__simps_I7_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I7_J) ).

fof(fact_Collect__ball__eq,axiom,
    ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_INFI__bool__eq,axiom,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
    file('theBenchmark.p',fact_INFI__bool__eq) ).

fof(fact_equiv__comp__eq,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ),
    file('theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_INF__subset,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ),
    file('theBenchmark.p',fact_INF__subset) ).

fof(fact_INTER__def,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))),
    file('theBenchmark.p',fact_INTER__def) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_rtrancl__converseI,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_trancl__converseI,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    file('theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_trancl__converseD) ).

fof(fact_Image__subset__eq,axiom,
    ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ),
    file('theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_INF__leI,axiom,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ),
    file('theBenchmark.p',fact_INF__leI) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ),
    file('theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_comp__equivI,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
     => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
       => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_comp__equivI) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
       => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_INT__greaterThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_INT__greaterThan__UNIV) ).

fof(fact_INT__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_converse__def,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
    file('theBenchmark.p',fact_converse__def) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_sequence__trans,axiom,
    ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
      ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_sequence__trans) ).

fof(fact_reflcl__set__eq,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ),
    file('theBenchmark.p',fact_reflcl__set__eq) ).

fof(fact_IdI,axiom,
    ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
    file('theBenchmark.p',fact_IdI) ).

fof(fact_INF1__iff,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
    file('theBenchmark.p',fact_INF1__iff) ).

fof(fact_INF2__iff,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_INF2__iff) ).

fof(fact_converse__Id,axiom,
    ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
    file('theBenchmark.p',fact_converse__Id) ).

fof(fact_Image__Id,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Image__Id) ).

fof(fact_R__O__Id,axiom,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
    file('theBenchmark.p',fact_R__O__Id) ).

fof(fact_Id__O__R,axiom,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
    file('theBenchmark.p',fact_Id__O__R) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
    <=> V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_Domain__Id,axiom,
    ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__Id) ).

fof(fact_rtrancl__empty,axiom,
    ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
    file('theBenchmark.p',fact_rtrancl__empty) ).

fof(fact_Range__Id,axiom,
    ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__Id) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_refl__Id,axiom,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_refl__Id) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_pair__leq__def,axiom,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    file('theBenchmark.p',fact_pair__leq__def) ).

fof(fact_trancl__reflcl,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_reflcl__trancl,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_refl__reflcl,axiom,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    file('theBenchmark.p',fact_refl__reflcl) ).

fof(fact_Id__def,axiom,
    ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
    file('theBenchmark.p',fact_Id__def) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    file('theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [V_r_2,V_s_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ),
    file('theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_Image__INT__eq,axiom,
    ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ),
    file('theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_image__INT,axiom,
    ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
       => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
         => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_image__INT) ).

fof(fact_single__valued__Id,axiom,
    ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_single__valued__Id) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [V_s_2,T_d,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
     => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
       => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_single__valued__subset,axiom,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
       => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
    file('theBenchmark.p',fact_single__valued__subset) ).

fof(fact_single__valued__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_single__valued__def,axiom,
    ! [V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
         => ! [B_z] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
             => B_y = B_z ) ) ),
    file('theBenchmark.p',fact_single__valued__def) ).

fof(fact_single__valuedD,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
         => V_y_2 = V_z_2 ) ) ),
    file('theBenchmark.p',fact_single__valuedD) ).

fof(fact_single__valued__confluent,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ),
    file('theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_Image__Int__eq,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
     => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ),
    file('theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_total__on__diff__Id,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
    <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ),
    file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_relpow_Osimps_I1_J,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
    file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [V_n_2,V_R_2,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
     => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ),
    file('theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_rel__pow__imp__rtrancl,axiom,
    ! [V_R_2,V_n_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_rtrancl__power,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
    <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ),
    file('theBenchmark.p',fact_rtrancl__power) ).

fof(fact_comp__funpow,axiom,
    ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_comp__funpow) ).

fof(fact_wf__exp,axiom,
    ! [V_R_2,V_n_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
     => c_Wellfounded_Owf(T_b,V_R_2) ),
    file('theBenchmark.p',fact_wf__exp) ).

fof(fact_funpow__mult,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2),
    file('theBenchmark.p',fact_funpow__mult) ).

fof(fact_funpow__swap1,axiom,
    ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_funpow__swap1) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    file('theBenchmark.p',fact_relpow_Osimps_I2_J) ).

fof(fact_rel__pow__commute,axiom,
    ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    file('theBenchmark.p',fact_rel__pow__commute) ).

fof(fact_rel__pow__add,axiom,
    ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),
    file('theBenchmark.p',fact_rel__pow__add) ).

fof(fact_rel__pow__1,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
    file('theBenchmark.p',fact_rel__pow__1) ).

fof(fact_total__on__empty,axiom,
    ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
    file('theBenchmark.p',fact_total__on__empty) ).

fof(fact_total__on__converse,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_total__on__converse) ).

fof(fact_rel__pow__0__E,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
     => V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_rel__pow__0__E) ).

fof(fact_rel__pow__0__I,axiom,
    ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
    file('theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_funpow__add,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_funpow__add) ).

fof(fact_funpow_Osimps_I1_J,axiom,
    ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
    file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).

fof(fact_trancl__power,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
    <=> ? [B_n] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
    file('theBenchmark.p',fact_trancl__power) ).

fof(fact_total__on__def,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
             => ( B_x != B_xa
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_total__on__def) ).

fof(fact_rtrancl__is__UN__rel__pow,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
    file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_funpow__code__def,axiom,
    ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
    file('theBenchmark.p',fact_funpow__code__def) ).

fof(fact_rel__pow__E2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => V_x_2 != V_z_2 )
       => ~ ! [B_y,B_m] :
              ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_rel__pow__E,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => V_x_2 != V_z_2 )
       => ~ ! [B_y,B_m] :
              ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ),
    file('theBenchmark.p',fact_rel__pow__E) ).

fof(fact_Inf__fold__inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_finite__Inter,axiom,
    ! [V_M_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ),
    file('theBenchmark.p',fact_finite__Inter) ).

fof(fact_InterE,axiom,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
    file('theBenchmark.p',fact_InterE) ).

fof(fact_InterD,axiom,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
    file('theBenchmark.p',fact_InterD) ).

fof(fact_Un__Inter,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    file('theBenchmark.p',fact_Un__Inter) ).

fof(fact_Inter__insert,axiom,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Inter__insert) ).

fof(fact_Inter__lower,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ),
    file('theBenchmark.p',fact_Inter__lower) ).

fof(fact_Inf__less__iff,axiom,
    ! [V_a_2,V_S_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_le__Inf__iff,axiom,
    ! [V_A_2,V_b_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ),
    file('theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_Inter__eq,axiom,
    ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
    file('theBenchmark.p',fact_Inter__eq) ).

fof(fact_Inter__empty,axiom,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Inter__empty) ).

fof(fact_Inter__anti__mono,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_Inter__UNIV,axiom,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Inter__UNIV) ).

fof(fact_Inf__lower,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_Inf__lower) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_Inf__singleton,axiom,
    ! [V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_Inf__singleton) ).

fof(fact_Inf__empty,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ),
    file('theBenchmark.p',fact_Inf__empty) ).

fof(fact_Inf__UNIV,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_Inf__UNIV) ).

fof(fact_Inf__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ),
    file('theBenchmark.p',fact_Inf__insert) ).

fof(fact_Inter__image__eq,axiom,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    file('theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_Int__eq__Inter,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Int__eq__Inter) ).

fof(fact_Int__Inter__image,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    file('theBenchmark.p',fact_Int__Inter__image) ).

fof(fact_Inter__Un__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Inter__Un__subset) ).

fof(fact_Inf__binary,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_Inf__binary) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_Sup__Inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ),
    file('theBenchmark.p',fact_Sup__Inf) ).

fof(fact_Inf__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ),
    file('theBenchmark.p',fact_Inf__Sup) ).

fof(fact_UnionI,axiom,
    ! [V_A_2,V_C_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ),
    file('theBenchmark.p',fact_UnionI) ).

fof(fact_Inter__def,axiom,
    ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Inter__def) ).

fof(fact_Int__Union2,axiom,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Int__Union2) ).

fof(fact_Int__Union,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    file('theBenchmark.p',fact_Int__Union) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_Sigma__Union,axiom,
    ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Union) ).

fof(fact_image__Union,axiom,
    ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
    file('theBenchmark.p',fact_image__Union) ).

fof(fact_Range__Union,axiom,
    ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
    file('theBenchmark.p',fact_Range__Union) ).

fof(fact_Domain__Union,axiom,
    ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
    file('theBenchmark.p',fact_Domain__Union) ).

fof(fact_vimage__Union,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)),
    file('theBenchmark.p',fact_vimage__Union) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_subset__Pow__Union,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))),
    file('theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_finite__UnionD,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
    file('theBenchmark.p',fact_finite__UnionD) ).

fof(fact_Union__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Union__mono) ).

fof(fact_Union__disjoint,axiom,
    ! [V_A_2,V_C_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Union__disjoint) ).

fof(fact_Sup__le__iff,axiom,
    ! [V_b_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_Union__upper,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
    file('theBenchmark.p',fact_Union__upper) ).

fof(fact_Union__Pow__eq,axiom,
    ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_less__Sup__iff,axiom,
    ! [V_S_2,V_a_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_less__Sup__iff) ).

fof(fact_Field__Union,axiom,
    ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
    file('theBenchmark.p',fact_Field__Union) ).

fof(fact_Union__empty,axiom,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__empty) ).

fof(fact_Union__quotient,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ),
    file('theBenchmark.p',fact_Union__quotient) ).

fof(fact_Union__Un__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Union__Un__distrib) ).

fof(fact_Union__UNIV,axiom,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__UNIV) ).

fof(fact_Union__insert,axiom,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Union__insert) ).

fof(fact_Union__image__eq,axiom,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Union__image__eq) ).

fof(fact_UNION__eq__Union__image,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    file('theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_Sup__upper,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_Sup__upper) ).

fof(fact_Sup__empty,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_Sup__empty) ).

fof(fact_Sup__singleton,axiom,
    ! [V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_Sup__singleton) ).

fof(fact_Sup__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ),
    file('theBenchmark.p',fact_Sup__insert) ).

fof(fact_Sup__UNIV,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ),
    file('theBenchmark.p',fact_Sup__UNIV) ).

fof(fact_Un__eq__Union,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Un__eq__Union) ).

fof(fact_Un__Union__image,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    file('theBenchmark.p',fact_Un__Union__image) ).

fof(fact_Union__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))),
    file('theBenchmark.p',fact_Union__Int__subset) ).

fof(fact_Sup__binary,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_Sup__binary) ).

fof(fact_sup__Sup__fold__sup,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_sup__Sup__fold__sup) ).

fof(fact_Sup__fin__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_Sup__fold__sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_inj__on__Inter,axiom,
    ! [V_f_2,T_c,T_b,V_S_2] :
      ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [B_A] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
           => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ),
    file('theBenchmark.p',fact_inj__on__Inter) ).

fof(fact_Inter__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( ! [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ),
    file('theBenchmark.p',fact_Inter__subset) ).

fof(fact_Union__def,axiom,
    ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Union__def) ).

fof(fact_finite__Union,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
     => ( ! [B_M] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ),
    file('theBenchmark.p',fact_finite__Union) ).

fof(fact_insert__partition,axiom,
    ! [V_F_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
           => ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
               => ( B_x != B_xa
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_insert__partition) ).

fof(fact_card__partition,axiom,
    ! [V_k_2,V_C_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
       => ( ! [B_c] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
             => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
         => ( ! [B_c1] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
               => ! [B_c2] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
                   => ( B_c1 != B_c2
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ),
    file('theBenchmark.p',fact_card__partition) ).

fof(fact_inj__on__INTER,axiom,
    ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
      ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
           => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
       => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_inj__on__INTER) ).

fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
    ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ~ ! [B_y] :
                ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

fof(fact_acyclicI,axiom,
    ! [V_r_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    file('theBenchmark.p',fact_acyclicI) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
               => B_x = B_y ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
               => B_y = B_x ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_tranclD2,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_tranclD2) ).

fof(fact_tranclD,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) ) ),
    file('theBenchmark.p',fact_tranclD) ).

fof(fact_min__max_Ofold__sup__le__sup,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

fof(fact_min__max_Oinf__le__fold__inf,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_InterI,axiom,
    ! [V_A_2,V_C_2,T_b] :
      ( ! [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    file('theBenchmark.p',fact_InterI) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_inf__le__fold__inf) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_IdE,axiom,
    ! [V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
     => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ),
    file('theBenchmark.p',fact_IdE) ).

fof(fact_wf__eq__minimal,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ! [B_Q] :
          ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
         => ? [B_x] :
              ( ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
                 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) )
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) ) ),
    file('theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [V_P_H_2,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => ( hBOOL(hAPP(V_P_2,B_x))
          <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
     => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
         => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_Int__Collect__mono,axiom,
    ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_Q_2,B_x)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ),
    file('theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_UnionE,axiom,
    ! [V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
     => ~ ! [B_X] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
    file('theBenchmark.p',fact_UnionE) ).

fof(fact_map__add__upd__left,axiom,
    ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
     => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ),
    file('theBenchmark.p',fact_map__add__upd__left) ).

fof(fact_rel__compE,axiom,
    ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
     => ~ ! [B_x,B_y,B_z] :
            ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ),
    file('theBenchmark.p',fact_rel__compE) ).

fof(fact_map__add__SomeD,axiom,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
     => ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) )
        | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ),
    file('theBenchmark.p',fact_map__add__SomeD) ).

fof(fact_map__add__Some__iff,axiom,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
    <=> ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) )
        | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ),
    file('theBenchmark.p',fact_map__add__Some__iff) ).

fof(fact_map__add__def,axiom,
    ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)),
    file('theBenchmark.p',fact_map__add__def) ).

fof(fact_map__add__empty,axiom,
    ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2,
    file('theBenchmark.p',fact_map__add__empty) ).

fof(fact_empty__map__add,axiom,
    ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2,
    file('theBenchmark.p',fact_empty__map__add) ).

fof(fact_map__add__None,axiom,
    ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
    <=> ( hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b)
        & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ),
    file('theBenchmark.p',fact_map__add__None) ).

fof(fact_map__add__assoc,axiom,
    ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2),
    file('theBenchmark.p',fact_map__add__assoc) ).

fof(fact_map__add__find__right,axiom,
    ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
      ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
     => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ),
    file('theBenchmark.p',fact_map__add__find__right) ).

fof(fact_map__add__dom__app__simps_I2_J,axiom,
    ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
     => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I2_J) ).

fof(fact_map__add__dom__app__simps_I3_J,axiom,
    ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
     => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).

fof(fact_map__add__dom__app__simps_I1_J,axiom,
    ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
     => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).

fof(fact_map__add__upd,axiom,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),
    file('theBenchmark.p',fact_map__add__upd) ).

fof(fact_dom__map__add,axiom,
    ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)),
    file('theBenchmark.p',fact_dom__map__add) ).

fof(fact_inj__on__map__add__dom,axiom,
    ! [V_m_H_2,V_m_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2))
    <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ),
    file('theBenchmark.p',fact_inj__on__map__add__dom) ).

fof(fact_map__add__comm,axiom,
    ! [V_m2_2,V_m1_2,T_c,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ),
    file('theBenchmark.p',fact_map__add__comm) ).

fof(fact_finite__range__map__of__map__add,axiom,
    ! [V_l_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,c_Map_Omap__of(T_c,T_b,V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__map__of__map__add) ).

fof(fact_converseE,axiom,
    ! [V_r_2,V_yx_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
     => ~ ! [B_x,B_y] :
            ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_converseE) ).

fof(fact_finite__dom__map__of,axiom,
    ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_l_2)))),
    file('theBenchmark.p',fact_finite__dom__map__of) ).

fof(fact_finite__range__map__of,axiom,
    ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__of(T_c,T_b,V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_finite__range__map__of) ).

fof(fact_map__add__map__of__foldr,axiom,
    ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2),
    file('theBenchmark.p',fact_map__add__map__of__foldr) ).

fof(fact_,axiom,
    ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2),
    file('theBenchmark.p',fact_) ).

fof(fact_full__small__int__def,axiom,
    ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))),
    file('theBenchmark.p',fact_full__small__int__def) ).

fof(fact_small_H_Osimps,axiom,
    ! [V_f_2,V_i_2,V_d_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
       => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
       => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) ),
    file('theBenchmark.p',fact_small_H_Osimps) ).

fof(fact_small_H_Opsimps,axiom,
    ! [V_i_2,V_d_2,V_f_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
         => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
         => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) ) ),
    file('theBenchmark.p',fact_small_H_Opsimps) ).

fof(fact_small__int__def,axiom,
    ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))),
    file('theBenchmark.p',fact_small__int__def) ).

fof(fact_small__prod__def,axiom,
    ! [V_d_2,V_f_2,T_b,T_c] :
      ( ( class_Smallcheck_Osmall(T_b)
        & class_Smallcheck_Osmall(T_c) )
     => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ),
    file('theBenchmark.p',fact_small__prod__def) ).

fof(fact_small_H_Opinduct,axiom,
    ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2))))
     => ( ! [B_f,B_d,B_i] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
               => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
                 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
             => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
       => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ),
    file('theBenchmark.p',fact_small_H_Opinduct) ).

fof(fact_body__def,axiom,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    file('theBenchmark.p',fact_body__def) ).

fof(fact_map__of__mapk__SomeI,axiom,
    ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(c_Map_Omap__of(T_b,T_d,V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
       => hAPP(c_Map_Omap__of(T_c,T_d,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ),
    file('theBenchmark.p',fact_map__of__mapk__SomeI) ).

fof(fact_map__comp__def,axiom,
    ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)),
    file('theBenchmark.p',fact_map__comp__def) ).

fof(fact_inj__mapI,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__mapI) ).

fof(fact_map__comp__simps_I1_J,axiom,
    ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
      ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
     => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ),
    file('theBenchmark.p',fact_map__comp__simps_I1_J) ).

fof(fact_map__comp__Some__iff,axiom,
    ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
      ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
    <=> ? [B_k_H] :
          ( hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
          & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) ) ),
    file('theBenchmark.p',fact_map__comp__Some__iff) ).

fof(fact_map__comp__simps_I2_J,axiom,
    ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
      ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
     => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ),
    file('theBenchmark.p',fact_map__comp__simps_I2_J) ).

fof(fact_map__injective,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
     => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
       => V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_map__injective) ).

fof(fact_inj__mapD,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__mapD) ).

fof(fact_inj__map__eq__map,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
      <=> V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_inj__map,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__map) ).

fof(fact_map__ident,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
    file('theBenchmark.p',fact_map__ident) ).

fof(fact_List_Omap_Oidentity,axiom,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_List_Omap_Oidentity) ).

fof(fact_List_Omap_Oid,axiom,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_List_Omap_Oid) ).

fof(fact_map__map,axiom,
    ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2),
    file('theBenchmark.p',fact_map__map) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2),
    file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_map__comp__map,axiom,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_map__comp__map) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_foldr__map,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2),
    file('theBenchmark.p',fact_foldr__map) ).

fof(fact_map__comp__empty_I1_J,axiom,
    ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_map__comp__empty_I1_J) ).

fof(fact_map__comp__empty_I2_J,axiom,
    ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_map__comp__empty_I2_J) ).

fof(fact_map__comp__None__iff,axiom,
    ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
      ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
    <=> ( ? [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b)
            & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) )
        | hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ),
    file('theBenchmark.p',fact_map__comp__None__iff) ).

fof(fact_map__of__map,axiom,
    ! [V_xs_2,V_f_2,T_d,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),c_Map_Omap__of(T_b,T_d,V_xs_2)),
    file('theBenchmark.p',fact_map__of__map) ).

fof(fact_map__of__map__keys,axiom,
    ! [V_m_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
     => c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ),
    file('theBenchmark.p',fact_map__of__map__keys) ).

fof(fact_finite__set,axiom,
    ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_finite__set) ).

fof(fact_set__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)),
    file('theBenchmark.p',fact_set__map) ).

fof(fact_map__eq__conv,axiom,
    ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
         => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ),
    file('theBenchmark.p',fact_map__eq__conv) ).

fof(fact_Option_Omap_Ocomp,axiom,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_Option_Omap_Ocomp) ).

fof(fact_Option_Omap_Ocompositionality,axiom,
    ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2),
    file('theBenchmark.p',fact_Option_Omap_Ocompositionality) ).

fof(fact_option__map__comp,axiom,
    ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2),
    file('theBenchmark.p',fact_option__map__comp) ).

fof(fact_Option_Omap_Oidentity,axiom,
    ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)),
    file('theBenchmark.p',fact_Option_Omap_Oidentity) ).

fof(fact_Option_Omap_Oid,axiom,
    ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)),
    file('theBenchmark.p',fact_Option_Omap_Oid) ).

fof(fact_infinite__UNIV__listI,axiom,
    ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__listI) ).

fof(fact_dom__option__map,axiom,
    ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2),
    file('theBenchmark.p',fact_dom__option__map) ).

fof(fact_option__map__Some,axiom,
    ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_option__map__Some) ).

fof(fact_option__map__eq__Some,axiom,
    ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
    <=> ? [B_z] :
          ( hAPP(V_f_2,B_z) = V_y_2
          & V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z) ) ),
    file('theBenchmark.p',fact_option__map__eq__Some) ).

fof(fact_option__map__None,axiom,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_option__map__None) ).

fof(fact_option__map__is__None,axiom,
    ! [V_opt_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
    <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ),
    file('theBenchmark.p',fact_option__map__is__None) ).

fof(fact_option__map__o__empty,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_option__map__o__empty) ).

fof(fact_option__map__o__map__upd,axiom,
    ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))),
    file('theBenchmark.p',fact_option__map__o__map__upd) ).

fof(fact_map__inj__on,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
     => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
       => V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_map__inj__on) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
     => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
      <=> V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_map__fun__upd,axiom,
    ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ),
    file('theBenchmark.p',fact_map__fun__upd) ).

fof(fact_inj__on__mapI,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
     => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ),
    file('theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_map__of__eq__dom,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] :
      ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
     => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ),
    file('theBenchmark.p',fact_map__of__eq__dom) ).

fof(fact_map__of__is__SomeD,axiom,
    ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ),
    file('theBenchmark.p',fact_map__of__is__SomeD) ).

fof(fact_map__of__SomeD,axiom,
    ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ),
    file('theBenchmark.p',fact_map__of__SomeD) ).

fof(fact_dom__map__of__conv__image__fst,axiom,
    ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)),
    file('theBenchmark.p',fact_dom__map__of__conv__image__fst) ).

fof(fact_map__of__eq__None__iff,axiom,
    ! [V_x_2,V_xys_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
    <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ),
    file('theBenchmark.p',fact_map__of__eq__None__iff) ).

fof(fact_Option_Omap__def,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)),
    file('theBenchmark.p',fact_Option_Omap__def) ).

fof(fact_WT__bodies__def,axiom,
    ( c_Com_OWT__bodies
  <=> ! [B_x] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
       => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ),
    file('theBenchmark.p',fact_WT__bodies__def) ).

fof(fact_map__of__map__restrict,axiom,
    ! [V_ks_2,V_f_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)),
    file('theBenchmark.p',fact_map__of__map__restrict) ).

fof(fact_ran__distinct,axiom,
    ! [V_al_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2)))
     => c_Map_Oran(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ),
    file('theBenchmark.p',fact_ran__distinct) ).

fof(fact_set__map__of__compr,axiom,
    ! [V_xs_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
     => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),c_Map_Omap__of(T_b,T_c,V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ),
    file('theBenchmark.p',fact_set__map__of__compr) ).

fof(fact_distinct__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
    <=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
        & hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__map) ).

fof(fact_map__of__inject__set,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)))
       => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
        <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ),
    file('theBenchmark.p',fact_map__of__inject__set) ).

fof(fact_Some__eq__map__of__iff,axiom,
    ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
     => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2)
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ),
    file('theBenchmark.p',fact_Some__eq__map__of__iff) ).

fof(fact_map__of__eq__Some__iff,axiom,
    ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
     => ( hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ),
    file('theBenchmark.p',fact_map__of__eq__Some__iff) ).

fof(fact_map__of__is__SomeI,axiom,
    ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
       => hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ),
    file('theBenchmark.p',fact_map__of__is__SomeI) ).

fof(fact_greaterThanLessThan__upto,axiom,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_greaterThanLessThan__upto) ).

fof(fact_weak__map__of__SomeI,axiom,
    ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2)))
     => ? [B_x] : hAPP(c_Map_Omap__of(T_b,T_c,V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ),
    file('theBenchmark.p',fact_weak__map__of__SomeI) ).

fof(fact_atLeastAtMost__upto,axiom,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)),
    file('theBenchmark.p',fact_atLeastAtMost__upto) ).

fof(fact_set__upto,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),
    file('theBenchmark.p',fact_set__upto) ).

fof(fact_distinct__upto,axiom,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))),
    file('theBenchmark.p',fact_distinct__upto) ).

fof(fact_atLeastLessThan__upto,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_atLeastLessThan__upto) ).

fof(fact_greaterThanAtMost__upto,axiom,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)),
    file('theBenchmark.p',fact_greaterThanAtMost__upto) ).

fof(fact_nat__list__def,axiom,
    ! [V_l_2] :
      ( c_List_Onat__list(V_l_2)
    <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ),
    file('theBenchmark.p',fact_nat__list__def) ).

fof(fact_set__remove1__eq,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_set__remove1__eq) ).

fof(fact_remove1__idem,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__idem) ).

fof(fact_notin__set__remove1,axiom,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_in__set__remove1,axiom,
    ! [V_xs_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 != V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__remove1) ).

fof(fact_set__remove1__subset,axiom,
    ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_remove1__commute,axiom,
    ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)),
    file('theBenchmark.p',fact_remove1__commute) ).

fof(fact_distinct__remove1,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ),
    file('theBenchmark.p',fact_distinct__remove1) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_map__of__zip__map,axiom,
    ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_map__of__zip__map) ).

fof(fact_distinct__zipI2,axiom,
    ! [V_xs,T_b,V_ys,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ),
    file('theBenchmark.p',fact_distinct__zipI2) ).

fof(fact_distinct__zipI1,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ),
    file('theBenchmark.p',fact_distinct__zipI1) ).

fof(fact_zip__same__conv__map,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2),
    file('theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2,
    file('theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_map__zip__map,axiom,
    ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_map__zip__map) ).

fof(fact_map__zip__map2,axiom,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_map__zip__map2) ).

fof(fact_zip__same,axiom,
    ! [V_xs_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
    <=> ( V_a_2 = V_b_2
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ),
    file('theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_in__set__zipE,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
         => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ),
    file('theBenchmark.p',fact_in__set__zipE) ).

fof(fact_zip__map__map,axiom,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map__map) ).

fof(fact_zip__map1,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map1) ).

fof(fact_zip__map2,axiom,
    ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map2) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set__insert) ).

fof(fact_map__of__zip__upd,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
         => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2))
           => c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ),
    file('theBenchmark.p',fact_map__of__zip__upd) ).

fof(fact_length__zip,axiom,
    ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),
    file('theBenchmark.p',fact_length__zip) ).

fof(fact_set__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort) ).

fof(fact_neq__if__length__neq,axiom,
    ! [V_ys,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
     => V_xs != V_ys ),
    file('theBenchmark.p',fact_neq__if__length__neq) ).

fof(fact_length__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ),
    file('theBenchmark.p',fact_length__insort) ).

fof(fact_insort__left__comm,axiom,
    ! [V_xs_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ),
    file('theBenchmark.p',fact_insort__left__comm) ).

fof(fact_insort__key__left__comm,axiom,
    ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_insort__key__left__comm) ).

fof(fact_fun__left__comm__insort,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_fun__left__comm__insort) ).

fof(fact_lexn__length,axiom,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_lexn__length) ).

fof(fact_length__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
    file('theBenchmark.p',fact_length__map) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ),
    file('theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_remove1__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__insort) ).

fof(fact_card__length,axiom,
    ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_card__length) ).

fof(fact_card__distinct,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
     => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_card__distinct) ).

fof(fact_distinct__card,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_distinct__card) ).

fof(fact_map__of__zip__inject,axiom,
    ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
       => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
         => ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
           => V_ys_2 = V_zs_2 ) ) ) ),
    file('theBenchmark.p',fact_map__of__zip__inject) ).

fof(fact_map__fst__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ),
    file('theBenchmark.p',fact_map__snd__zip) ).

fof(fact_distinct__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
      <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    file('theBenchmark.p',fact_distinct__insort) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    file('theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
          & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_lenlex__conv,axiom,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
    file('theBenchmark.p',fact_lenlex__conv) ).

fof(fact_lenlex__def,axiom,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
    file('theBenchmark.p',fact_lenlex__def) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [T_b,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).

fof(fact_map__of__zip__is__None,axiom,
    ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
      <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_map__of__zip__is__None) ).

fof(fact_map__of__zip__is__Some,axiom,
    ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      <=> ? [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ),
    file('theBenchmark.p',fact_map__of__zip__is__Some) ).

fof(fact_length__remove1,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_length__remove1) ).

fof(fact_dom__map__of__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ),
    file('theBenchmark.p',fact_dom__map__of__zip) ).

fof(fact_finite__lists__length__le,axiom,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) ),
    file('theBenchmark.p',fact_Nitpick_Ocard_H__def) ).

fof(fact_listrel__iff__zip,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_listrel__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_listrel__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [V_xa_2,V_x_2,V_r_2,T_b] :
      ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))),
    file('theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_impossible__Cons,axiom,
    ! [V_x,V_ys,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
     => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ),
    file('theBenchmark.p',fact_impossible__Cons) ).

fof(fact_set__ConsD,axiom,
    ! [V_xs_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | V_y_2 = V_x_2 ) ),
    file('theBenchmark.p',fact_set__ConsD) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
    file('theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_set__subset__Cons,axiom,
    ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))),
    file('theBenchmark.p',fact_set__subset__Cons) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
    file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_not__Cons__self,axiom,
    ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
    file('theBenchmark.p',fact_not__Cons__self) ).

fof(fact_not__Cons__self2,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
    file('theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_list_Oinject,axiom,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
    <=> ( V_list_2 = V_list_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_list_Oinject) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
      ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
    <=> ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
        & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
    file('theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_listrelp_OCons,axiom,
    ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
     => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
       => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_map_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( V_x != V_y
       => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) )
      & ( V_x = V_y
       => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) ),
    file('theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_map__of__Cons__code_I2_J,axiom,
    ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
      ( ( V_l != V_k
       => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Map_Omap__of(T_b,T_c,V_ps),V_k) )
      & ( V_l = V_k
       => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) ),
    file('theBenchmark.p',fact_map__of__Cons__code_I2_J) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_list_Osize_I4_J) ).

fof(fact_listrel_OCons,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_listrel_OCons) ).

fof(fact_map__of_Osimps_I2_J,axiom,
    ! [V_ps_2,V_p_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__of(T_b,T_c,V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))),
    file('theBenchmark.p',fact_map__of_Osimps_I2_J) ).

fof(fact_Cons__in__lex,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_listrel__Cons,axiom,
    ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_listrel__Cons) ).

fof(fact_set__Cons__def,axiom,
    ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
    file('theBenchmark.p',fact_set__Cons__def) ).

fof(fact_listrel__Cons2,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
     => ~ ! [B_x,B_xs] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_listrel__Cons1,axiom,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
     => ~ ! [B_y,B_ys] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_length__sublist,axiom,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
    file('theBenchmark.p',fact_length__sublist) ).

fof(fact_pick_Osimps,axiom,
    ! [V_xs,V_x,T_a,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
       => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
       => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) ),
    file('theBenchmark.p',fact_pick_Osimps) ).

fof(fact_distinct__sublistI,axiom,
    ! [V_I_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ),
    file('theBenchmark.p',fact_distinct__sublistI) ).

fof(fact_in__set__sublistD,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_notin__set__sublistI,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ),
    file('theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_set__sublist__subset,axiom,
    ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    file('theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_pick__member,axiom,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_pick__member) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [V_xs,V_x,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ),
    file('theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_listsum__subtractf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_listsum__addf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__addf) ).

fof(fact_listsum__const__mult,axiom,
    ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_listsum__mult__const,axiom,
    ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ),
    file('theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_listsum__0,axiom,
    ! [V_xs_2,T_c,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_listsum__0) ).

fof(fact_listsum__abs,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_listsum__abs) ).

fof(fact_uminus__listsum__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ),
    file('theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_select__weight__def,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))),
    file('theBenchmark.p',fact_select__weight__def) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [V_f_2,V_xs_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [V_j_2,V_i_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ),
    file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [V_l_2,V_k_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_listsum__triv,axiom,
    ! [V_xs_2,V_r_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ),
    file('theBenchmark.p',fact_listsum__triv) ).

fof(fact_listsum__map__remove1,axiom,
    ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_select__weight__member,axiom,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_select__weight__member) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) ) ),
    file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [V_ns_2] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
         => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).

fof(fact_distinct__insort__insert,axiom,
    ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_insort__insert__triv,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort__insert) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_insort__insert__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_lexord__cons__cons,axiom,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_set__zip,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
    file('theBenchmark.p',fact_set__zip) ).

fof(fact_nth__zip,axiom,
    ! [V_ys,T_b,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
       => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ),
    file('theBenchmark.p',fact_nth__zip) ).

fof(fact_nth__map,axiom,
    ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ),
    file('theBenchmark.p',fact_nth__map) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ),
    file('theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_nth_Osimps,axiom,
    ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_nth_Osimps) ).

fof(fact_nth__Cons__0,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x,
    file('theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n),
    file('theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ),
    file('theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [T_b,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_distinct__conv__nth,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
    <=> ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => ! [B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
             => ( B_i != B_j
               => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ),
    file('theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
          <=> V_i_2 = V_j_2 ) ) ) ),
    file('theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_nth__mem,axiom,
    ! [V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_nth__mem) ).

fof(fact_in__set__conv__nth,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
    <=> ? [B_i] :
          ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_nth__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) ),
    file('theBenchmark.p',fact_nth__Cons_H) ).

fof(fact_set__conv__nth,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_set__conv__nth) ).

fof(fact_nth__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x ) ),
    file('theBenchmark.p',fact_nth__Cons__number__of) ).

fof(fact_listsum__setsum__nth,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__setsum__nth) ).

fof(fact_set__sublist,axiom,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))),
    file('theBenchmark.p',fact_set__sublist) ).

fof(fact_lexord__lex,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__lex) ).

fof(fact_listrel__iff__nth,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
    <=> ( ! [B_n] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_pick__same,axiom,
    ! [V_xs_2,T_b,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ),
    file('theBenchmark.p',fact_pick__same) ).

fof(fact_select__def,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))),
    file('theBenchmark.p',fact_select__def) ).

fof(fact_lexord__take__index__conv,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
    <=> ( ? [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
            & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
        | ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) ) ) ),
    file('theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_set__take__subset__set__take,axiom,
    ! [V_xs_2,T_b,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_in__set__takeD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__takeD) ).

fof(fact_nth__take,axiom,
    ! [V_xs,T_a,V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ),
    file('theBenchmark.p',fact_nth__take) ).

fof(fact_set__take__subset,axiom,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__take__subset) ).

fof(fact_take__all,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
     => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_take__all) ).

fof(fact_distinct__take,axiom,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_distinct__take) ).

fof(fact_take__take,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs),
    file('theBenchmark.p',fact_take__take) ).

fof(fact_take__zip,axiom,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)),
    file('theBenchmark.p',fact_take__zip) ).

fof(fact_length__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__take) ).

fof(fact_take__Suc__Cons,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_take__Suc__Cons) ).

fof(fact_sublist__upt__eq__take,axiom,
    ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2),
    file('theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_take__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_take__map) ).

fof(fact_listsum__update__nat,axiom,
    ! [V_n,V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ),
    file('theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_select__weigth__select,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ),
    file('theBenchmark.p',fact_select__weigth__select) ).

fof(fact_listrel__Nil2,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_listrel__Nil1,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_list__update__id,axiom,
    ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs,
    file('theBenchmark.p',fact_list__update__id) ).

fof(fact_nth__list__update__neq,axiom,
    ! [V_x,V_xs,T_a,V_j,V_i] :
      ( V_i != V_j
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ),
    file('theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_list__update__beyond,axiom,
    ! [V_x,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
     => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ),
    file('theBenchmark.p',fact_list__update__beyond) ).

fof(fact_take__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_take__eq__Nil) ).

fof(fact_take__0,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_take__0) ).

fof(fact_take__Nil,axiom,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_take__Nil) ).

fof(fact_list_Osize_I3_J,axiom,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_list_Osize_I3_J) ).

fof(fact_length__0__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_length__0__conv) ).

fof(fact_length__list__update,axiom,
    ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__list__update) ).

fof(fact_take__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2),
    file('theBenchmark.p',fact_take__Cons) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_map__update,axiom,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_map__update) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_zip__update,axiom,
    ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    file('theBenchmark.p',fact_zip__update) ).

fof(fact_update__zip,axiom,
    ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))),
    file('theBenchmark.p',fact_update__zip) ).

fof(fact_sublist__nil,axiom,
    ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_sublist__nil) ).

fof(fact_sublist__empty,axiom,
    ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_sublist__empty) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
    file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs),
    file('theBenchmark.p',fact_list__update__code_I2_J) ).

fof(fact_list__update__code_I3_J,axiom,
    ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)),
    file('theBenchmark.p',fact_list__update__code_I3_J) ).

fof(fact_list_Osimps_I3_J,axiom,
    ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list_Osimps_I3_J) ).

fof(fact_list_Osimps_I2_J,axiom,
    ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H),
    file('theBenchmark.p',fact_list_Osimps_I2_J) ).

fof(fact_sorted__list__of__set__empty,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_sorted__list__of__set__empty) ).

fof(fact_zip_Osimps_I1_J,axiom,
    ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_zip_Osimps_I1_J) ).

fof(fact_zip__Nil,axiom,
    ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_zip__Nil) ).

fof(fact_upto__empty,axiom,
    ! [V_i,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
     => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ),
    file('theBenchmark.p',fact_upto__empty) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2,
    file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_map__of__Cons__code_I1_J,axiom,
    ! [V_k,T_a,T_b] : hAPP(c_Map_Omap__of(T_b,T_a,c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_map__of__Cons__code_I1_J) ).

fof(fact_map__of_Osimps_I1_J,axiom,
    ! [V_x_1,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b,c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b),
    file('theBenchmark.p',fact_map__of_Osimps_I1_J) ).

fof(fact_list__update__nonempty,axiom,
    ! [V_x_2,V_k_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_list__update__overwrite,axiom,
    ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y),
    file('theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_list__update__swap,axiom,
    ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
      ( V_i != V_i_H
     => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ),
    file('theBenchmark.p',fact_list__update__swap) ).

fof(fact_remove1_Osimps_I1_J,axiom,
    ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_distinct_Osimps_I1_J,axiom,
    ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_insort__not__Nil,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_listrelp_ONil,axiom,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_listrelp_Oequations_I1_J,axiom,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_set__empty2,axiom,
    ! [V_xs_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_set__empty) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_length__greater__0__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
    <=> V_xs_2 != c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_length__greater__0__conv) ).

fof(fact_set__update__subsetI,axiom,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ),
    file('theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_take__1__Cons,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_take__1__Cons) ).

fof(fact_set__update__subset__insert,axiom,
    ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))),
    file('theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_nth__list__update,axiom,
    ! [V_x,V_j,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( ( V_i != V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) )
        & ( V_i = V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) ) ),
    file('theBenchmark.p',fact_nth__list__update) ).

fof(fact_list__update__same__conv,axiom,
    ! [V_x_2,V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
      <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_nth__list__update__eq,axiom,
    ! [V_x,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ),
    file('theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_listrel_ONil,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
    file('theBenchmark.p',fact_listrel_ONil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
    file('theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil__notin__lex,axiom,
    ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
    file('theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
    file('theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_set__update__memI,axiom,
    ! [V_x_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ),
    file('theBenchmark.p',fact_set__update__memI) ).

fof(fact_upto_Osimps,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
       => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
       => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) ),
    file('theBenchmark.p',fact_upto_Osimps) ).

fof(fact_sublist__singleton,axiom,
    ! [V_x_2,T_b,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
    file('theBenchmark.p',fact_sublist__singleton) ).

fof(fact_take__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_take__Cons_H) ).

fof(fact_upto__rec__number__of,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) ),
    file('theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_select,axiom,
    ! [V_s_2,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_select) ).

fof(fact_listrel__Nil,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listrel__Nil) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
    file('theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_take__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_distinct__list__update,axiom,
    ! [V_i_2,V_a_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ),
    file('theBenchmark.p',fact_distinct__list__update) ).

fof(fact_upto_Opsimps,axiom,
    ! [V_j_2,V_i_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
         => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
         => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ),
    file('theBenchmark.p',fact_upto_Opsimps) ).

fof(fact_anamorph_Osimps,axiom,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) ),
    file('theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_zip__Cons,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_zip__Cons) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2),
    file('theBenchmark.p',fact_list_Osimps_I5_J) ).

fof(fact_list_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2,
    file('theBenchmark.p',fact_list_Osimps_I4_J) ).

fof(fact_listset_Osimps_I2_J,axiom,
    ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)),
    file('theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_zip__Cons1,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2),
    file('theBenchmark.p',fact_zip__Cons1) ).

fof(fact_upto_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_i,B_j] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
             => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_map__upd__upds__conv__if,axiom,
    ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
       => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
       => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_map__upd__upds__conv__if) ).

fof(fact_map__upds__Nil1,axiom,
    ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2,
    file('theBenchmark.p',fact_map__upds__Nil1) ).

fof(fact_map__upds__Nil2,axiom,
    ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2,
    file('theBenchmark.p',fact_map__upds__Nil2) ).

fof(fact_map__upds__apply__nontin,axiom,
    ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ),
    file('theBenchmark.p',fact_map__upds__apply__nontin) ).

fof(fact_map__add__upds,axiom,
    ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2),
    file('theBenchmark.p',fact_map__add__upds) ).

fof(fact_map__upds__Cons,axiom,
    ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2),
    file('theBenchmark.p',fact_map__upds__Cons) ).

fof(fact_map__upds__list__update2__drop,axiom,
    ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
       => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_map__upds__list__update2__drop) ).

fof(fact_map__upds__twist,axiom,
    ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
     => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ),
    file('theBenchmark.p',fact_map__upds__twist) ).

fof(fact_restrict__map__upds,axiom,
    ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2))
       => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_restrict__map__upds) ).

fof(fact_dom__map__upds,axiom,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)),
    file('theBenchmark.p',fact_dom__map__upds) ).

fof(fact_map__upds__append1,axiom,
    ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
     => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_map__upds__append1) ).

fof(fact_sublist__Cons,axiom,
    ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
    file('theBenchmark.p',fact_sublist__Cons) ).

fof(fact_append1__eq__conv,axiom,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
    <=> ( V_x_2 = V_y_2
        & V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
    <=> ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
    <=> ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_fun__upds__append__drop,axiom,
    ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_fun__upds__append__drop) ).

fof(fact_fun__upds__append2__drop,axiom,
    ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_fun__upds__append2__drop) ).

fof(fact_list__update__length,axiom,
    ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)),
    file('theBenchmark.p',fact_list__update__length) ).

fof(fact_nth__append__length,axiom,
    ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x,
    file('theBenchmark.p',fact_nth__append__length) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
     => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
       => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ),
    file('theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_append__Cons,axiom,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),
    file('theBenchmark.p',fact_append__Cons) ).

fof(fact_take__append,axiom,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    file('theBenchmark.p',fact_take__append) ).

fof(fact_list__update__append1,axiom,
    ! [V_x,V_ys,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ),
    file('theBenchmark.p',fact_list__update__append1) ).

fof(fact_remove1__append,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) ),
    file('theBenchmark.p',fact_remove1__append) ).

fof(fact_length__append,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    file('theBenchmark.p',fact_length__append) ).

fof(fact_zip__append,axiom,
    ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
       => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ),
    file('theBenchmark.p',fact_zip__append) ).

fof(fact_map__append,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
    file('theBenchmark.p',fact_map__append) ).

fof(fact_nth__append__length__plus,axiom,
    ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n),
    file('theBenchmark.p',fact_nth__append__length__plus) ).

fof(fact_foldr__append,axiom,
    ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)),
    file('theBenchmark.p',fact_foldr__append) ).

fof(fact_map__of__append,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_ys_2),c_Map_Omap__of(T_b,T_c,V_xs_2)),
    file('theBenchmark.p',fact_map__of__append) ).

fof(fact_append__assoc,axiom,
    ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)),
    file('theBenchmark.p',fact_append__assoc) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
    <=> ? [B_us] :
          ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
            & hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
          | ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
            & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) ),
    file('theBenchmark.p',fact_append__eq__append__conv2) ).

fof(fact_same__append__eq,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
    <=> V_ys_2 = V_zs_2 ),
    file('theBenchmark.p',fact_same__append__eq) ).

fof(fact_append__same__eq,axiom,
    ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
    <=> V_ys_2 = V_zs_2 ),
    file('theBenchmark.p',fact_append__same__eq) ).

fof(fact_append__eq__appendI,axiom,
    ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
     => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
       => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ),
    file('theBenchmark.p',fact_append__eq__appendI) ).

fof(fact_set__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)),
    file('theBenchmark.p',fact_set__append) ).

fof(fact_listsum__append,axiom,
    ! [V_ys,V_xs,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ),
    file('theBenchmark.p',fact_listsum__append) ).

fof(fact_eq__Nil__appendI,axiom,
    ! [T_a,V_ys,V_xs] :
      ( V_xs = V_ys
     => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ),
    file('theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_append__self__conv2,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_append__self__conv) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_b)
        & V_xs_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [V_xs_2,T_b,V_ys_2] :
      ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_self__append__conv2) ).

fof(fact_self__append__conv,axiom,
    ! [V_ys_2,T_b,V_xs_2] :
      ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_self__append__conv) ).

fof(fact_append__Nil2,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
    file('theBenchmark.p',fact_append__Nil2) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_b)
        & V_xs_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_append__Nil,axiom,
    ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
    file('theBenchmark.p',fact_append__Nil) ).

fof(fact_lexord__append__leftI,axiom,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_distinct__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
    <=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__append) ).

fof(fact_nth__append,axiom,
    ! [V_ys,V_xs,T_a,V_n] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
    file('theBenchmark.p',fact_nth__append) ).

fof(fact_list__update__append,axiom,
    ! [V_x,V_ys,V_xs,T_a,V_n] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) ),
    file('theBenchmark.p',fact_list__update__append) ).

fof(fact_sublist__append,axiom,
    ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
    file('theBenchmark.p',fact_sublist__append) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          & V_xs_2 = V_ys_2 )
        | ( V_x_2 = V_y_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_lexord__append__leftD,axiom,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
     => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [V_xs_2,V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_listrel1__converse,axiom,
    ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
    file('theBenchmark.p',fact_listrel1__converse) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
    file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_listrel1__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_listrel1__mono) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_listrel1I2,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrel1I2) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
    file('theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
    file('theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_append__listrel1I,axiom,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_xs_2 = V_ys_2 )
        | ( V_us_2 = V_vs_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_append__listrel1I) ).

fof(fact_in__listrel1__converse,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_listrel__reflcl__if__listrel1,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_listrel1I1,axiom,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrel1I1) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
     => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ),
    file('theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_listrel1I,axiom,
    ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
       => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel1I) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_listrel1__iff__update,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
    <=> ? [B_y,B_n] :
          ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_listrel1E,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => ~ ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
           => ! [B_us,B_vs] :
                ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
               => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ),
    file('theBenchmark.p',fact_listrel1E) ).

fof(fact_rotate1__def,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
    file('theBenchmark.p',fact_rotate1__def) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [V_a,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
    file('theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_drop__append,axiom,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    file('theBenchmark.p',fact_drop__append) ).

fof(fact_drop__Nil,axiom,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_drop__Nil) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_drop__take,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__take) ).

fof(fact_take__drop,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
    file('theBenchmark.p',fact_take__drop) ).

fof(fact_in__set__dropD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__dropD) ).

fof(fact_set__rotate1,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rotate1) ).

fof(fact_set__drop__subset,axiom,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__drop__subset) ).

fof(fact_distinct1__rotate,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_distinct__drop,axiom,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_distinct__drop) ).

fof(fact_drop__0,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs,
    file('theBenchmark.p',fact_drop__0) ).

fof(fact_drop__drop,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs),
    file('theBenchmark.p',fact_drop__drop) ).

fof(fact_drop__zip,axiom,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)),
    file('theBenchmark.p',fact_drop__zip) ).

fof(fact_drop__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_drop__map) ).

fof(fact_length__rotate1,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rotate1) ).

fof(fact_length__drop,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__drop) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs),
    file('theBenchmark.p',fact_drop__Suc__Cons) ).

fof(fact_drop__1__Cons,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    file('theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_nth__via__drop,axiom,
    ! [V_ys,V_y,V_xs,V_n,T_a] :
      ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
     => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ),
    file('theBenchmark.p',fact_nth__via__drop) ).

fof(fact_drop__all,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
     => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_drop__all) ).

fof(fact_drop__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ),
    file('theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [V_xs_2,T_b,V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_append__take__drop__id,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs,
    file('theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
    <=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
        & V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ),
    file('theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_drop__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_drop__Cons) ).

fof(fact_drop__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
    file('theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_nth__drop,axiom,
    ! [V_xs,T_a,V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ),
    file('theBenchmark.p',fact_nth__drop) ).

fof(fact_append__eq__append__conv__if,axiom,
    ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
         => ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
            & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
         => ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
            & V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) ) ) ) ),
    file('theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_nth__drop_H,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ),
    file('theBenchmark.p',fact_nth__drop_H) ).

fof(fact_rotate__simps,axiom,
    ! [V_xs,V_x,T_b,T_a] :
      ( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
      & hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_rotate__simps) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
    file('theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_take__add,axiom,
    ! [V_xs,T_a,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_take__add) ).

fof(fact_rotate1__length01,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate1__length01) ).

fof(fact_zip__append1,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
    file('theBenchmark.p',fact_zip__append1) ).

fof(fact_zip__append2,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
    file('theBenchmark.p',fact_zip__append2) ).

fof(fact_id__take__nth__drop,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
    file('theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_take__hd__drop,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ),
    file('theBenchmark.p',fact_take__hd__drop) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
    file('theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_hd__append2,axiom,
    ! [V_ys,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ),
    file('theBenchmark.p',fact_hd__append2) ).

fof(fact_hd__append,axiom,
    ! [V_ys,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) ),
    file('theBenchmark.p',fact_hd__append) ).

fof(fact_hd_Osimps,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
    file('theBenchmark.p',fact_hd_Osimps) ).

fof(fact_hd__map,axiom,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_hd__map) ).

fof(fact_hd__in__set,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_hd__in__set) ).

fof(fact_hd__conv__nth,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_hd__conv__nth) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_hd__rotate__conv__nth,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    file('theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_drop__Suc,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_drop__Suc) ).

fof(fact_drop__tl,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__tl) ).

fof(fact_tl__drop,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_tl__drop) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_take__tl,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
    file('theBenchmark.p',fact_take__tl) ).

fof(fact_set__rotate,axiom,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rotate) ).

fof(fact_distinct__rotate,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rotate) ).

fof(fact_distinct__tl,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ),
    file('theBenchmark.p',fact_distinct__tl) ).

fof(fact_rotate__rotate,axiom,
    ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs),
    file('theBenchmark.p',fact_rotate__rotate) ).

fof(fact_rotate__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_rotate__map) ).

fof(fact_map__tl,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__tl) ).

fof(fact_length__rotate,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rotate) ).

fof(fact_rotate__conv__mod,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs),
    file('theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    file('theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_tl__append2,axiom,
    ! [V_ys,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ),
    file('theBenchmark.p',fact_tl__append2) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)),
    file('theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_rotate__Suc,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)),
    file('theBenchmark.p',fact_rotate__Suc) ).

fof(fact_rotate__def,axiom,
    ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)),
    file('theBenchmark.p',fact_rotate__def) ).

fof(fact_tl__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_tl__append) ).

fof(fact_rotate0,axiom,
    ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_rotate0) ).

fof(fact_rotate__add,axiom,
    ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)),
    file('theBenchmark.p',fact_rotate__add) ).

fof(fact_rotate__id,axiom,
    ! [V_xs,T_a,V_n] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__length01,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate__length01) ).

fof(fact_length__tl,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__tl) ).

fof(fact_tl__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_tl__take) ).

fof(fact_take__Suc,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ),
    file('theBenchmark.p',fact_take__Suc) ).

fof(fact_rotate__drop__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),
    file('theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_fold1__set,axiom,
    ! [V_xs_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( V_xs_2 != c_List_Olist_ONil(T_b)
       => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_fold1__set) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_list_Osize_I2_J) ).

fof(fact_foldl__append,axiom,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
    file('theBenchmark.p',fact_foldl__append) ).

fof(fact_foldl__Cons,axiom,
    ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
    file('theBenchmark.p',fact_foldl__Cons) ).

fof(fact_foldl__map,axiom,
    ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2),
    file('theBenchmark.p',fact_foldl__map) ).

fof(fact_list__size__map,axiom,
    ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2),
    file('theBenchmark.p',fact_list__size__map) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [V_a_2,V_xs_2,T_b] :
      ( class_Groups_Oab__semigroup__add(T_b)
     => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ),
    file('theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_foldl__assoc,axiom,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( class_Groups_Osemigroup__add(T_b)
     => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ),
    file('theBenchmark.p',fact_foldl__assoc) ).

fof(fact_foldl__absorb0,axiom,
    ! [V_zs_2,V_x_2,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ),
    file('theBenchmark.p',fact_foldl__absorb0) ).

fof(fact_start__le__sum,axiom,
    ! [V_ns_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ),
    file('theBenchmark.p',fact_start__le__sum) ).

fof(fact_foldl__Nil,axiom,
    ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2,
    file('theBenchmark.p',fact_foldl__Nil) ).

fof(fact_listsum__foldl,axiom,
    ! [T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_listsum__foldl) ).

fof(fact_foldl__foldr1,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [V_xs_2,V_a_2,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ),
    file('theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_sum__eq__0__conv,axiom,
    ! [V_ns_2,V_m_2] :
      ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
           => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_sum__eq__0__conv) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_list_Osize_I1_J) ).

fof(fact_fun__left__comm__idem_Ofold__set,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).

fof(fact_Sup__set__fold,axiom,
    ! [V_xs_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_Inf__set__fold,axiom,
    ! [V_xs_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Sup__fin__set__fold) ).

fof(fact_Inf__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Inf__fin__set__fold) ).

fof(fact_Min__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Min__fin__set__fold) ).

fof(fact_Max__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Max__fin__set__fold) ).

fof(fact_min__max_OInf__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).

fof(fact_min__max_OSup__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).

fof(fact_SUPR__set__fold,axiom,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_INFI__set__fold,axiom,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_list__size__estimation,axiom,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__size__estimation) ).

fof(fact_list__size__estimation_H,axiom,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_map__upds__fold__map__upd,axiom,
    ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)),
    file('theBenchmark.p',fact_map__upds__fold__map__upd) ).

fof(fact_elem__le__sum,axiom,
    ! [V_ns_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ),
    file('theBenchmark.p',fact_elem__le__sum) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),
    file('theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_listrel__subset,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ),
    file('theBenchmark.p',fact_listrel__subset) ).

fof(fact_lists__accI,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accI) ).

fof(fact_lists_ONil,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))),
    file('theBenchmark.p',fact_lists_ONil) ).

fof(fact_listrel__refl__on,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_lists__UNIV,axiom,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lists__UNIV) ).

fof(fact_equiv__listrel,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_equiv__listrel) ).

fof(fact_lists__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_lists__mono) ).

fof(fact_append__in__lists__conv,axiom,
    ! [V_A_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [V_A_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_in__lists__conv__set,axiom,
    ! [V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_lists__eq__set,axiom,
    ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
    file('theBenchmark.p',fact_lists__eq__set) ).

fof(fact_lists__empty,axiom,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_lists__empty) ).

fof(fact_lists__accD,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accD) ).

fof(fact_lexord__append__rightI,axiom,
    ! [V_r_2,V_x_2,T_b,V_y_2] :
      ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_lexord__Nil__left,axiom,
    ! [V_r_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
    <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ),
    file('theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_last__list__update,axiom,
    ! [V_x,V_k,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) )
        & ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) ) ),
    file('theBenchmark.p',fact_last__list__update) ).

fof(fact_listsum__mono,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
        & class_Groups_Omonoid__add(T_c) )
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__mono) ).

fof(fact_last_Osimps,axiom,
    ! [V_x,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ),
    file('theBenchmark.p',fact_last_Osimps) ).

fof(fact_last__ConsR,axiom,
    ! [V_x,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__ConsR) ).

fof(fact_last__ConsL,axiom,
    ! [V_x,T_a,V_xs] :
      ( V_xs = c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ),
    file('theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__append,axiom,
    ! [V_xs,T_a,V_ys] :
      ( ( V_ys != c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) )
      & ( V_ys = c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_last__append) ).

fof(fact_last__appendR,axiom,
    ! [V_xs,T_a,V_ys] :
      ( V_ys != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ),
    file('theBenchmark.p',fact_last__appendR) ).

fof(fact_last__appendL,axiom,
    ! [V_xs,T_a,V_ys] :
      ( V_ys = c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__appendL) ).

fof(fact_last__map,axiom,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_last__map) ).

fof(fact_last__in__set,axiom,
    ! [T_b,V_as_2] :
      ( V_as_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ),
    file('theBenchmark.p',fact_last__in__set) ).

fof(fact_last__snoc,axiom,
    ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
    file('theBenchmark.p',fact_last__snoc) ).

fof(fact_last__drop,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__drop) ).

fof(fact_last__conv__nth,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_last__conv__nth) ).

fof(fact_lexord__linear,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( ! [B_a,B_b] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
          | B_a = B_b
          | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
        | V_x_2 = V_y_2
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__linear) ).

fof(fact_lexord__irreflexive,axiom,
    ! [V_y_2,V_r_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_lists_Osimps,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
    <=> ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_lists_Osimps) ).

fof(fact_list__size__pointwise,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ),
    file('theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_butlast__take,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ),
    file('theBenchmark.p',fact_butlast__take) ).

fof(fact_nth__take__lemma,axiom,
    ! [V_ys,V_xs,T_a,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
             => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
         => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ),
    file('theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_map__butlast,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__butlast) ).

fof(fact_butlast__append,axiom,
    ! [V_xs,T_a,V_ys] :
      ( ( V_ys != c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) )
      & ( V_ys = c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_butlast__append) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [V_x,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_in__set__butlastD,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_distinct__butlast,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
       => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ),
    file('theBenchmark.p',fact_distinct__butlast) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_butlast__drop,axiom,
    ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)),
    file('theBenchmark.p',fact_butlast__drop) ).

fof(fact_drop__butlast,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__butlast) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ),
    file('theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_butlast__snoc,axiom,
    ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
    file('theBenchmark.p',fact_butlast__snoc) ).

fof(fact_take__butlast,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ),
    file('theBenchmark.p',fact_take__butlast) ).

fof(fact_length__butlast,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__butlast) ).

fof(fact_butlast__conv__take,axiom,
    ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs),
    file('theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_butlast__list__update,axiom,
    ! [V_x,V_xs,T_a,V_k] :
      ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) )
      & ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_butlast__list__update) ).

fof(fact_append__butlast__last__id,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ),
    file('theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
    <=> ( c_List_Olast(T_b,V_ys_2) = V_x_2
        & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
        & V_ys_2 != c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_transpose__aux__max,axiom,
    ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_partition__set,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
    file('theBenchmark.p',fact_partition__set) ).

fof(fact_length__filter__le,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__filter__le) ).

fof(fact_filter__is__subset,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_filter__is__subset) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_filter_Osimps_I1_J) ).

fof(fact_filter__empty__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => ~ hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_filter__id__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__id__conv) ).

fof(fact_filter__insort__triv,axiom,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_distinct__filter,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__filter) ).

fof(fact_filter__remove1,axiom,
    ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)),
    file('theBenchmark.p',fact_filter__remove1) ).

fof(fact_remove1__filter__not,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_filter__filter,axiom,
    ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
    file('theBenchmark.p',fact_filter__filter) ).

fof(fact_partition__filter1,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2),
    file('theBenchmark.p',fact_partition__filter1) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
    file('theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_filter__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)),
    file('theBenchmark.p',fact_filter__append) ).

fof(fact_partition__filter__conv,axiom,
    ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__map) ).

fof(fact_partition__filter2,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2),
    file('theBenchmark.p',fact_partition__filter2) ).

fof(fact_set__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)),
    file('theBenchmark.p',fact_set__filter) ).

fof(fact_length__filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_length__filter__map) ).

fof(fact_length__filter__less,axiom,
    ! [V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_length__filter__less) ).

fof(fact_set__minus__filter__out,axiom,
    ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
    file('theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_partition__P,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
           => ~ hBOOL(hAPP(V_P_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_partition__P) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_partition_Osimps_I1_J) ).

fof(fact_filter__in__sublist,axiom,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ),
    file('theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)),
    file('theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_length__filter__conv__card,axiom,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))),
    file('theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_map__filter__def,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)),
    file('theBenchmark.p',fact_map__filter__def) ).

fof(fact_transpose__max__length,axiom,
    ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)),
    file('theBenchmark.p',fact_transpose__max__length) ).

fof(fact_map__of__filter__in,axiom,
    ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
     => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
       => hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ),
    file('theBenchmark.p',fact_map__of__filter__in) ).

fof(fact_transpose__map__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)),
    file('theBenchmark.p',fact_transpose__map__map) ).

fof(fact_transpose_Osimps_I2_J,axiom,
    ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss),
    file('theBenchmark.p',fact_transpose_Osimps_I2_J) ).

fof(fact_transpose__empty,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
         => B_x = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_transpose__empty) ).

fof(fact_map__filter__simps_I2_J,axiom,
    ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_map__filter__simps_I2_J) ).

fof(fact_transpose_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)),
    file('theBenchmark.p',fact_transpose_Osimps_I1_J) ).

fof(fact_map__filter__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_map__filter__simps_I1_J) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))),
    file('theBenchmark.p',fact_sublist__shift__lemma__Suc) ).

fof(fact_select__weigth__drop__zero,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    file('theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2),
    file('theBenchmark.p',fact_pick__drop__zero) ).

fof(fact_nth__transpose,axiom,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ),
    file('theBenchmark.p',fact_nth__transpose) ).

fof(fact_length__transpose,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__transpose) ).

fof(fact_map__filter__map__filter,axiom,
    ! [V_xs_2,V_P_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_P_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2),
    file('theBenchmark.p',fact_map__filter__map__filter) ).

fof(fact_insort__key__remove1,axiom,
    ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
         => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
           => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ),
    file('theBenchmark.p',fact_insort__key__remove1) ).

fof(fact_sublist__def,axiom,
    ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__def) ).

fof(fact_sorted_ONil,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_sorted_ONil) ).

fof(fact_sorted__single,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_sorted__single) ).

fof(fact_sorted__same,axiom,
    ! [V_xs_2,V_g_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__same) ).

fof(fact_sorted__map__same,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ),
    file('theBenchmark.p',fact_sorted__map__same) ).

fof(fact_sorted__filter,axiom,
    ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__filter) ).

fof(fact_length__upt,axiom,
    ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i),
    file('theBenchmark.p',fact_length__upt) ).

fof(fact_upt__eq__Cons__conv,axiom,
    ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
      ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
    <=> ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2
        & V_i_2 = V_x_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) ) ),
    file('theBenchmark.p',fact_upt__eq__Cons__conv) ).

fof(fact_sorted__butlast,axiom,
    ! [V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_xs != c_List_Olist_ONil(T_a)
       => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
         => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ),
    file('theBenchmark.p',fact_sorted__butlast) ).

fof(fact_upt__rec__number__of,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) ),
    file('theBenchmark.p',fact_upt__rec__number__of) ).

fof(fact_sorted__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
      <=> ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
          & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
          & c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
    file('theBenchmark.p',fact_sorted__append) ).

fof(fact_sorted__Cons,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
      <=> ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
          & c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
    file('theBenchmark.p',fact_sorted__Cons) ).

fof(fact_upt__Suc,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ),
    file('theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__Suc__append,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_upt__add__eq__append,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_upt__add__eq__append) ).

fof(fact_sorted__many__eq,axiom,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
      <=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_sorted__many,axiom,
    ! [V_zs,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
         => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ),
    file('theBenchmark.p',fact_sorted__many) ).

fof(fact_take__upt,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ),
    file('theBenchmark.p',fact_take__upt) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [V_j_2,V_i_2] :
      ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
        | V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_upt__eq__Nil__conv) ).

fof(fact_upt__conv__Nil,axiom,
    ! [V_i,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
     => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_upt__conv__Nil) ).

fof(fact_sorted__drop,axiom,
    ! [V_n,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__drop) ).

fof(fact_drop__upt,axiom,
    ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j),
    file('theBenchmark.p',fact_drop__upt) ).

fof(fact_hd__upt,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ),
    file('theBenchmark.p',fact_hd__upt) ).

fof(fact_sorted_Oequations_I1_J,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_sorted_Oequations_I1_J) ).

fof(fact_upt__0,axiom,
    ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    file('theBenchmark.p',fact_upt__0) ).

fof(fact_sorted__take,axiom,
    ! [V_n,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__take) ).

fof(fact_set__upt,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2),
    file('theBenchmark.p',fact_set__upt) ).

fof(fact_atLeastLessThan__upt,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)),
    file('theBenchmark.p',fact_atLeastLessThan__upt) ).

fof(fact_sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
         => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
           => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
             => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
               => V_xs_2 = V_ys_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_sorted__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
      <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_sorted__insort) ).

fof(fact_distinct__upt,axiom,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))),
    file('theBenchmark.p',fact_distinct__upt) ).

fof(fact_sorted__remove1,axiom,
    ! [V_a,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__remove1) ).

fof(fact_sorted__upt,axiom,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)),
    file('theBenchmark.p',fact_sorted__upt) ).

fof(fact_sorted__upto,axiom,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)),
    file('theBenchmark.p',fact_sorted__upto) ).

fof(fact_sorted__list__of__set__range,axiom,
    ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2),
    file('theBenchmark.p',fact_sorted__list__of__set__range) ).

fof(fact_sorted__insort__insert,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert) ).

fof(fact_upt__conv__Cons,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ),
    file('theBenchmark.p',fact_upt__conv__Cons) ).

fof(fact_upt__rec,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ),
    file('theBenchmark.p',fact_upt__rec) ).

fof(fact_sorted__tl,axiom,
    ! [V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__tl) ).

fof(fact_sorted__insort__key,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
      <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_sorted__map__remove1,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_map__Suc__upt,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)),
    file('theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_last__upt,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_last__upt) ).

fof(fact_filter__insort,axiom,
    ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => ( hBOOL(hAPP(V_P_2,V_x_2))
         => hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ),
    file('theBenchmark.p',fact_filter__insort) ).

fof(fact_map__nth,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
    file('theBenchmark.p',fact_map__nth) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))),
    file('theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeast__upt,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)),
    file('theBenchmark.p',fact_atLeast__upt) ).

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_nth__upt,axiom,
    ! [V_j,V_k,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
     => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ),
    file('theBenchmark.p',fact_nth__upt) ).

fof(fact_greaterThanAtMost__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))),
    file('theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [V_a1_2,V_a2_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
      <=> ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) ) ) ),
    file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)),
    file('theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_nth__map__upt,axiom,
    ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
     => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ),
    file('theBenchmark.p',fact_nth__map__upt) ).

fof(fact_sorted__list__of__set,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
          & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
          & hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_atMost__upto,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))),
    file('theBenchmark.p',fact_atMost__upto) ).

fof(fact_insort__remove1,axiom,
    ! [V_xs_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_insort__remove1) ).

fof(fact_sorted__nth__mono,axiom,
    ! [V_j,V_i,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      <=> ! [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => ! [B_i] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
       => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
         => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
           => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
             => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
               => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
                 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_transpose__rectangle,axiom,
    ! [V_n_2,T_b,V_xs_2] :
      ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
       => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
       => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ),
    file('theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [V_xss_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
     => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
     => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).

fof(fact_transpose__column,axiom,
    ! [V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ),
    file('theBenchmark.p',fact_transpose__column) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_inj__on__rev,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__rev) ).

fof(fact_filter__concat,axiom,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__concat) ).

fof(fact_length__concat,axiom,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
    file('theBenchmark.p',fact_length__concat) ).

fof(fact_rev__eq__Cons__iff,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
    <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ),
    file('theBenchmark.p',fact_rev__eq__Cons__iff) ).

fof(fact_rev_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_rev_Osimps_I2_J) ).

fof(fact_rev_Osimps_I1_J,axiom,
    ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_rev_Osimps_I1_J) ).

fof(fact_concat_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_concat_Osimps_I1_J) ).

fof(fact_Nil__is__rev__conv,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_Nil__eq__concat__conv,axiom,
    ! [V_xss_2,T_b] :
      ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
         => B_x = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_Nil__eq__concat__conv) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [V_xss_2,T_b] :
      ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
         => B_x = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_concat__eq__Nil__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
    <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_rev__singleton__conv) ).

fof(fact_singleton__rev__conv,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
    <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_concat_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)),
    file('theBenchmark.p',fact_concat_Osimps_I2_J) ).

fof(fact_rev__concat,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_rev__concat) ).

fof(fact_rev__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    file('theBenchmark.p',fact_rev__map) ).

fof(fact_map__concat,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_map__concat) ).

fof(fact_rev__foldl__cons,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
    file('theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_concat__conv__foldl,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
    file('theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_foldl__conv__concat,axiom,
    ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
    file('theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_rev__append,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__append) ).

fof(fact_concat__append,axiom,
    ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
    file('theBenchmark.p',fact_concat__append) ).

fof(fact_distinct__rev,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rev) ).

fof(fact_set__concat,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
    file('theBenchmark.p',fact_set__concat) ).

fof(fact_length__rev,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rev) ).

fof(fact_listsum__rev,axiom,
    ! [V_xs,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ),
    file('theBenchmark.p',fact_listsum__rev) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
    <=> V_xs_2 = V_ys_2 ),
    file('theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_rev__swap,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
    <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ),
    file('theBenchmark.p',fact_rev__swap) ).

fof(fact_rev__rev__ident,axiom,
    ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
    file('theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_foldr__foldl,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    file('theBenchmark.p',fact_foldr__foldl) ).

fof(fact_foldl__foldr,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
    file('theBenchmark.p',fact_foldl__foldr) ).

fof(fact_set__rev,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rev) ).

fof(fact_zip__rev,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
     => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ),
    file('theBenchmark.p',fact_zip__rev) ).

fof(fact_rev__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    file('theBenchmark.p',fact_rev__filter) ).

fof(fact_last__rev,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ),
    file('theBenchmark.p',fact_last__rev) ).

fof(fact_hd__rev,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_hd__rev) ).

fof(fact_sorted__transpose,axiom,
    ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))),
    file('theBenchmark.p',fact_sorted__transpose) ).

fof(fact_rev__drop,axiom,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__take) ).

fof(fact_rotate__rev,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)),
    file('theBenchmark.p',fact_rotate__rev) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))),
    file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_rev__nth,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_rev__nth) ).

fof(fact_concat__injective,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
             => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
         => V_xs_2 = V_ys_2 ) ) ),
    file('theBenchmark.p',fact_concat__injective) ).

fof(fact_concat__eq__concat__iff,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
       => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
        <=> V_xs_2 = V_ys_2 ) ) ),
    file('theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_rev__update,axiom,
    ! [V_y,V_xs,T_a,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ),
    file('theBenchmark.p',fact_rev__update) ).

fof(fact_concat__map__singleton,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),
    file('theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_sorted__rev__nth__mono,axiom,
    ! [V_j,V_i,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__rev__nth__mono) ).

fof(fact_foldr__max__sorted,axiom,
    ! [V_y_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
       => ( ( V_xs_2 != c_List_Olist_ONil(T_b)
           => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) )
          & ( V_xs_2 = c_List_Olist_ONil(T_b)
           => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_transpose_Opsimps_I3_J,axiom,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
     => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_length__transpose__sorted,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_length__transpose__sorted) ).

fof(fact_transpose__column__length,axiom,
    ! [V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_transpose__column__length) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
         => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ),
    file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_transpose__transpose,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ),
    file('theBenchmark.p',fact_transpose__transpose) ).

fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).

fof(fact_takeWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_takeWhile__map) ).

fof(fact_return__list__def,axiom,
    ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
    file('theBenchmark.p',fact_return__list__def) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_set__takeWhileD,axiom,
    ! [V_xs_2,V_P_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
     => ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_length__takeWhile__le,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_distinct__takeWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_takeWhile__tail,axiom,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_sorted__takeWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_takeWhile__append1,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ),
    file('theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_takeWhile__nth,axiom,
    ! [V_xs_2,V_P_2,T_b,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ),
    file('theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_map__upds__def,axiom,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))),
    file('theBenchmark.p',fact_map__upds__def) ).

fof(fact_takeWhile__not__last,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
       => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [V_l] :
      ( c_List_Onat__list(V_l)
     => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ),
    file('theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_length__remdups__concat,axiom,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
    file('theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_distinct__remdups,axiom,
    ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
    file('theBenchmark.p',fact_distinct__remdups) ).

fof(fact_length__remdups__leq,axiom,
    ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
    file('theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_remdups__map__remdups,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_embed__list__def,axiom,
    ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
    file('theBenchmark.p',fact_embed__list__def) ).

fof(fact_set__remdups,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__remdups) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_remdups__eq__nil__right__iff,axiom,
    ! [V_x_2,T_b] :
      ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
    <=> V_x_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [V_x_2,T_b] :
      ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_x_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_sorted__remdups,axiom,
    ! [V_l,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_l)
       => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ),
    file('theBenchmark.p',fact_sorted__remdups) ).

fof(fact_remove1__remdups,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ),
    file('theBenchmark.p',fact_remove1__remdups) ).

fof(fact_distinct__remdups__id,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremdups(T_a,V_xs) = V_xs ),
    file('theBenchmark.p',fact_distinct__remdups__id) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_length__remdups__eq,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
    <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_remdups__remdups,axiom,
    ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
    file('theBenchmark.p',fact_remdups__remdups) ).

fof(fact_remdups__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)),
    file('theBenchmark.p',fact_remdups__filter) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
    file('theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_takeWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_dropWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_dropWhile__map) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2,
    file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_length__dropWhile__le,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_distinct__dropWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_sorted__dropWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_hd__dropWhile,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
     => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_hd__dropWhile) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(T_1)
     => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ! [T_2,T_1] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_1)
     => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(T_1)
     => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).

fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(T_1)
     => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).

fof(arity_fun__Lattices_Osemilattice__sup,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(T_1)
     => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).

fof(arity_fun__Lattices_Osemilattice__inf,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(T_1)
     => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).

fof(arity_fun__Lattices_Odistrib__lattice,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Odistrib__lattice(T_1)
     => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Oboolean__algebra(T_1)
     => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Opreorder(T_1)
     => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [T_1,T_2] :
      ( ( class_Finite__Set_Ofinite(T_1)
        & class_Finite__Set_Ofinite(T_2) )
     => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(arity_fun__Lattices_Olattice,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(T_1)
     => class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Olattice) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Oorder(T_1)
     => class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Otop(T_1)
     => class_Orderings_Otop(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Oord(T_1)
     => class_Orderings_Oord(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Obot,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Obot(T_1)
     => class_Orderings_Obot(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Obot) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [T_2,T_1] :
      ( class_Groups_Ouminus(T_1)
     => class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [T_2,T_1] :
      ( class_Groups_Ominus(T_1)
     => class_Groups_Ominus(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).

fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).

fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).

fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(arity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(arity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
    class_Smallcheck_Osmall(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Smallcheck_Osmall) ).

fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_Int__Oint__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).

fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(arity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(arity_Int__Oint__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(arity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(arity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(arity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

fof(arity_Int__Oint__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(arity_Int__Oint__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(arity_Int__Oint__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(arity_Int__Oint__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(arity_Int__Oint__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

fof(arity_Int__Oint__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(arity_Int__Oint__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(arity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(arity_Int__Oint__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(arity_Int__Oint__Rings_Oring,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(arity_Int__Oint__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(arity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

fof(arity_Int__Oint__Groups_Oone,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(arity_Int__Oint__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).

fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).

fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).

fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
    class_Orderings_Owellorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).

fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).

fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).

fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(arity_Nat__Onat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(arity_Nat__Onat__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(arity_Nat__Onat__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(arity_Nat__Onat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).

fof(arity_Nat__Onat__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(arity_Nat__Onat__Power_Opower,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(arity_Nat__Onat__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(arity_Nat__Onat__Int_Onumber,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

fof(arity_Nat__Onat__Groups_Oone,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(arity_Nat__Onat__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).

fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).

fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).

fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).

fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(arity_HOL__Obool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).

fof(arity_HOL__Obool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(arity_HOL__Obool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).

fof(arity_HOL__Obool__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(arity_HOL__Obool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).

fof(arity_HOL__Obool__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(arity_HOL__Obool__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [T_1,T_2] :
      ( ( class_Finite__Set_Ofinite(T_1)
        & class_Finite__Set_Ofinite(T_2) )
     => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ),
    file('theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [T_1] :
      ( class_Finite__Set_Ofinite(T_1)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ),
    file('theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [T_1,T_2] :
      ( ( class_Finite__Set_Ofinite(T_1)
        & class_Finite__Set_Ofinite(T_2) )
     => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(arity_prod__Smallcheck_Osmall,axiom,
    ! [T_1,T_2] :
      ( ( class_Smallcheck_Osmall(T_1)
        & class_Smallcheck_Osmall(T_2) )
     => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod__Smallcheck_Osmall) ).

fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).

fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Smallcheck_Osmall) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).

fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).

fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).

fof(help_c__COMBI__1,axiom,
    ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
    file('theBenchmark.p',help_c__COMBI__1) ).

fof(help_c__COMBK__1,axiom,
    ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
    file('theBenchmark.p',help_c__COMBK__1) ).

fof(help_c__COMBB__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBB__1) ).

fof(help_c__COMBC__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
    file('theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBS__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBS__1) ).

fof(help_c__fequal__1,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
    file('theBenchmark.p',help_c__fequal__1) ).

fof(help_c__fequal__2,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
      | V_x_2 != V_y_2 ),
    file('theBenchmark.p',help_c__fequal__2) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('theBenchmark.p',help_c__fFalse__1) ).

fof(help_c__fTrue__1,axiom,
    hBOOL(c_fTrue),
    file('theBenchmark.p',help_c__fTrue__1) ).

fof(help_c__fNot__1,axiom,
    ! [V_P_2] :
      ( ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
    file('theBenchmark.p',help_c__fNot__1) ).

fof(help_c__fNot__2,axiom,
    ! [V_P_2] :
      ( hBOOL(hAPP(c_fNot,V_P_2))
      | ~ ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fNot__2) ).

fof(help_c__fconj__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fconj__1) ).

fof(help_c__fconj__2,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fconj__3) ).

fof(help_c__fdisj__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    file('theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fdisj__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fimplies__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fimplies__1) ).

fof(help_c__fimplies__2,axiom,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    file('theBenchmark.p',help_c__fimplies__2) ).

fof(help_c__fimplies__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fimplies__3) ).

fof(conj_0,hypothesis,
    ! [B_x] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
     => c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),B_x) ),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,hypothesis,
    ! [B_Z,B_s] :
      ( v_P(B_Z,B_s)
     => ! [B_s_H] :
          ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,hAPP(c_Nat_OSuc,v_na),B_s_H)
         => v_Q(B_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s_H),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,B_s_H),c_Com_ORes))) ) ),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,hypothesis,
    v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
    file('theBenchmark.p',conj_2) ).

fof(conj_3,hypothesis,
    c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1),
    file('theBenchmark.p',conj_3) ).

fof(conj_4,conjecture,
    v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
    file('theBenchmark.p',conj_4) ).

fof(f_1_1,plain,
    ! [V_g_2,V_f_2] :
      ( V_f_2 = V_g_2
      | ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
    inference(fof_nnf,[status(thm)],[fact_ext]) ).

fof(f_1_2,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).

fof(f_1_4,plain,
    ! [U_1,U_2] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(definitional_conversion,[status(esa)],[f_1_3]) ).

cnf(f_1_5,plain,
    ( U_1 = U_2
    | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(clausify,[status(thm)],[f_1_4]) ).

fof(f_2_1,plain,
    ! [V_t,V_n,T_a] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t)
      | ~ c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) ),
    inference(fof_nnf,[status(thm)],[fact_triple__valid__Suc]) ).

fof(f_2_2,plain,
    ! [U_5,U_4,U_3] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,U_5)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),U_5) ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

fof(f_2_3,plain,
    ! [U_4,U_3,U_5] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,U_5)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),U_5) ),
    inference(definitional_conversion,[status(esa)],[f_2_2]) ).

cnf(f_2_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,U_5)
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),U_5) ),
    inference(clausify,[status(thm)],[f_2_3]) ).

fof(f_3_1,plain,
    ! [V_s1,V_n,V_s0,V_pn] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OBody]) ).

fof(f_3_2,plain,
    ! [U_9,U_8,U_7,U_6] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_6),U_7,hAPP(c_Nat_OSuc,U_8),U_9)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_6)),U_7,U_8,U_9) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ! [U_6,U_7,U_8,U_9] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_6),U_7,hAPP(c_Nat_OSuc,U_8),U_9)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_6)),U_7,U_8,U_9) ),
    inference(definitional_conversion,[status(esa)],[f_3_2]) ).

cnf(f_3_4,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_6),U_7,hAPP(c_Nat_OSuc,U_8),U_9)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_6)),U_7,U_8,U_9) ),
    inference(clausify,[status(thm)],[f_3_3]) ).

fof(f_4_1,plain,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
      ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2)),V_a2_2,V_a3_2,V_a4_2) )
      & ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2)),V_a2_2,V_a3_2,V_a4_2)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I9_J]) ).

fof(f_4_2,plain,
    ! [U_13,U_12,U_11,U_10] :
      ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_10),U_11,hAPP(c_Nat_OSuc,U_12),U_13)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_10)),U_11,U_12,U_13) )
      & ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_10)),U_11,U_12,U_13)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_10),U_11,hAPP(c_Nat_OSuc,U_12),U_13) ) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ( ! [U_21,U_19,U_17,U_15] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_15),U_17,hAPP(c_Nat_OSuc,U_19),U_21)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_15)),U_17,U_19,U_21) )
    & ! [U_20,U_18,U_16,U_14] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_14)),U_16,U_18,U_20)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_14),U_16,hAPP(c_Nat_OSuc,U_18),U_20) ) ),
    inference(miniscope,[status(thm)],[f_4_2]) ).

fof(f_4_4,plain,
    ( ! [U_17,U_19,U_15,U_21] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_15),U_17,hAPP(c_Nat_OSuc,U_19),U_21)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_15)),U_17,U_19,U_21) )
    & ! [U_18,U_20,U_14,U_16] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_14)),U_16,U_18,U_20)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_14),U_16,hAPP(c_Nat_OSuc,U_18),U_20) ) ),
    inference(definitional_conversion,[status(esa)],[f_4_3]) ).

cnf(f_4_5,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_14)),U_16,U_18,U_20)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_14),U_16,hAPP(c_Nat_OSuc,U_18),U_20) ),
    inference(clausify,[status(thm)],[f_4_4]) ).

cnf(f_4_6,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_15),U_17,hAPP(c_Nat_OSuc,U_19),U_21)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_15)),U_17,U_19,U_21) ),
    inference(clausify,[status(thm)],[f_4_4]) ).

fof(f_5_1,plain,
    ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OCall]) ).

fof(f_5_2,plain,
    ! [U_27,U_26,U_25,U_24,U_23,U_22] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_27,U_22,U_24),U_23,U_25,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_26),hAPP(c_Natural_Ogetlocs,U_23))),U_27),hAPP(hAPP(c_Natural_Ogetlocs,U_26),c_Com_ORes)))
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_22),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_23),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_24,U_23)),U_25,U_26) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ! [U_24,U_23,U_22,U_25,U_26,U_27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_27,U_22,U_24),U_23,U_25,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_26),hAPP(c_Natural_Ogetlocs,U_23))),U_27),hAPP(hAPP(c_Natural_Ogetlocs,U_26),c_Com_ORes)))
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_22),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_23),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_24,U_23)),U_25,U_26) ),
    inference(definitional_conversion,[status(esa)],[f_5_2]) ).

cnf(f_5_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_27,U_22,U_24),U_23,U_25,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_26),hAPP(c_Natural_Ogetlocs,U_23))),U_27),hAPP(hAPP(c_Natural_Ogetlocs,U_26),c_Com_ORes)))
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_22),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_23),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_24,U_23)),U_25,U_26) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_1,plain,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2),V_a2_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)))
        | ! [B_s1] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2)),V_a4_2,B_s1)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) ) )
      & ( ? [B_s1] :
            ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2)),V_a4_2,B_s1)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2),V_a2_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes))) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I10_J]) ).

fof(f_6_2,plain,
    ! [U_35,U_34,U_33,U_32,U_31,U_30] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_30,U_31,U_32),U_33,U_34,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_35),hAPP(c_Natural_Ogetlocs,U_33))),U_30),hAPP(hAPP(c_Natural_Ogetlocs,U_35),c_Com_ORes)))
        | ! [U_29] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_31),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_33),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_32,U_33)),U_34,U_29)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_35),hAPP(c_Natural_Ogetlocs,U_33))),U_30),hAPP(hAPP(c_Natural_Ogetlocs,U_35),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_29),hAPP(c_Natural_Ogetlocs,U_33))),U_30),hAPP(hAPP(c_Natural_Ogetlocs,U_29),c_Com_ORes)) ) )
      & ( ? [U_28] :
            ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_31),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_33),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_32,U_33)),U_34,U_28)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_35),hAPP(c_Natural_Ogetlocs,U_33))),U_30),hAPP(hAPP(c_Natural_Ogetlocs,U_35),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_28),hAPP(c_Natural_Ogetlocs,U_33))),U_30),hAPP(hAPP(c_Natural_Ogetlocs,U_28),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_30,U_31,U_32),U_33,U_34,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_35),hAPP(c_Natural_Ogetlocs,U_33))),U_30),hAPP(hAPP(c_Natural_Ogetlocs,U_35),c_Com_ORes))) ) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ( ! [U_47,U_45,U_43,U_41,U_39,U_37] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_37,U_39,U_41),U_43,U_45,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)))
        | ! [U_29] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_39),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_43),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_41,U_43)),U_45,U_29)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_29),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_29),c_Com_ORes)) ) )
    & ! [U_46,U_44,U_42,U_40,U_38,U_36] :
        ( ? [U_28] :
            ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_38),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_42),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_40,U_42)),U_44,U_28)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_28),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_28),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_36,U_38,U_40),U_42,U_44,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes))) ) ),
    inference(miniscope,[status(thm)],[f_6_2]) ).

fof(f_6_4,plain,
    ( ! [U_47,U_45,U_43,U_41,U_39,U_37] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_37,U_39,U_41),U_43,U_45,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)))
        | ! [U_29] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_39),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_43),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_41,U_43)),U_45,U_29)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_29),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_29),c_Com_ORes)) ) )
    & ! [U_46,U_44,U_42,U_40,U_38,U_36] :
        ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_38),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_42),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_40,U_42)),U_44,sK2(U_46,U_44,U_42,U_40,U_38,U_36))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK2(U_46,U_44,U_42,U_40,U_38,U_36)),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,sK2(U_46,U_44,U_42,U_40,U_38,U_36)),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_36,U_38,U_40),U_42,U_44,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_28,sK2(U_46,U_44,U_42,U_40,U_38,U_36))],[f_6_3]) ).

fof(f_6_5,plain,
    ( ! [U_38,U_42,U_36,U_40,U_44,U_46] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_38),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_42),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_40,U_42)),U_44,sK2(U_46,U_44,U_42,U_40,U_38,U_36))
        | ~ sP0(U_38,U_42,U_36,U_40,U_44,U_46) )
    & ! [U_38,U_42,U_36,U_40,U_44,U_46] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK2(U_46,U_44,U_42,U_40,U_38,U_36)),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,sK2(U_46,U_44,U_42,U_40,U_38,U_36)),c_Com_ORes))
        | ~ sP0(U_38,U_42,U_36,U_40,U_44,U_46) )
    & ! [U_29,U_41,U_39,U_37,U_47,U_43,U_45] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_37,U_39,U_41),U_43,U_45,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)))
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_39),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_43),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_41,U_43)),U_45,U_29)
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_29),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_29),c_Com_ORes)) )
    & ! [U_38,U_42,U_36,U_40,U_44,U_46] :
        ( sP0(U_38,U_42,U_36,U_40,U_44,U_46)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_36,U_38,U_40),U_42,U_44,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_6_4]) ).

cnf(f_6_6,plain,
    ( sP0(U_38,U_42,U_36,U_40,U_44,U_46)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_36,U_38,U_40),U_42,U_44,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes))) ),
    inference(clausify,[status(thm)],[f_6_5]) ).

cnf(f_6_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_37,U_39,U_41),U_43,U_45,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)))
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_39),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_43),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_41,U_43)),U_45,U_29)
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_47),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_47),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_29),hAPP(c_Natural_Ogetlocs,U_43))),U_37),hAPP(hAPP(c_Natural_Ogetlocs,U_29),c_Com_ORes)) ),
    inference(clausify,[status(thm)],[f_6_5]) ).

cnf(f_6_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_46),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,U_46),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK2(U_46,U_44,U_42,U_40,U_38,U_36)),hAPP(c_Natural_Ogetlocs,U_42))),U_36),hAPP(hAPP(c_Natural_Ogetlocs,sK2(U_46,U_44,U_42,U_40,U_38,U_36)),c_Com_ORes))
    | ~ sP0(U_38,U_42,U_36,U_40,U_44,U_46) ),
    inference(clausify,[status(thm)],[f_6_5]) ).

cnf(f_6_9,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_38),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_42),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_40,U_42)),U_44,sK2(U_46,U_44,U_42,U_40,U_38,U_36))
    | ~ sP0(U_38,U_42,U_36,U_40,U_44,U_46) ),
    inference(clausify,[status(thm)],[f_6_5]) ).

fof(f_7_1,plain,
    ! [V_s_H,V_n,V_s,V_c] :
      ( c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H)
      | ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__Suc]) ).

fof(f_7_2,plain,
    ! [U_51,U_50,U_49,U_48] :
      ( c_Natural_Oevaln(U_48,U_49,hAPP(c_Nat_OSuc,U_50),U_51)
      | ~ c_Natural_Oevaln(U_48,U_49,U_50,U_51) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_48,U_51,U_50,U_49] :
      ( c_Natural_Oevaln(U_48,U_49,hAPP(c_Nat_OSuc,U_50),U_51)
      | ~ c_Natural_Oevaln(U_48,U_49,U_50,U_51) ),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( c_Natural_Oevaln(U_48,U_49,hAPP(c_Nat_OSuc,U_50),U_51)
    | ~ c_Natural_Oevaln(U_48,U_49,U_50,U_51) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_b] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) )
      & ( c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2))
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__Suc]) ).

fof(f_8_2,plain,
    ! [U_56,U_55,U_54,U_53,U_52] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_52,U_53,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_54),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_55))),U_56))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_52,hAPP(c_Nat_OSuc,U_53),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_54),hAPP(c_Com_Ocom_OBODY,U_55)),U_56)) )
      & ( c_Hoare__Mirabelle_Otriple__valid(U_52,hAPP(c_Nat_OSuc,U_53),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_54),hAPP(c_Com_Ocom_OBODY,U_55)),U_56))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_52,U_53,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_54),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_55))),U_56)) ) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ( ! [U_66,U_64,U_62,U_60,U_58] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_58,U_60,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_62),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_64))),U_66))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_58,hAPP(c_Nat_OSuc,U_60),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_62),hAPP(c_Com_Ocom_OBODY,U_64)),U_66)) )
    & ! [U_65,U_63,U_61,U_59,U_57] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_57,hAPP(c_Nat_OSuc,U_59),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_57),U_61),hAPP(c_Com_Ocom_OBODY,U_63)),U_65))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_57,U_59,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_57),U_61),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_63))),U_65)) ) ),
    inference(miniscope,[status(thm)],[f_8_2]) ).

fof(f_8_4,plain,
    ( ! [U_60,U_58,U_62,U_64,U_66] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_58,U_60,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_62),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_64))),U_66))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_58,hAPP(c_Nat_OSuc,U_60),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_62),hAPP(c_Com_Ocom_OBODY,U_64)),U_66)) )
    & ! [U_59,U_65,U_61,U_63,U_57] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_57,hAPP(c_Nat_OSuc,U_59),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_57),U_61),hAPP(c_Com_Ocom_OBODY,U_63)),U_65))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_57,U_59,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_57),U_61),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_63))),U_65)) ) ),
    inference(definitional_conversion,[status(esa)],[f_8_3]) ).

cnf(f_8_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_57,hAPP(c_Nat_OSuc,U_59),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_57),U_61),hAPP(c_Com_Ocom_OBODY,U_63)),U_65))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_57,U_59,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_57),U_61),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_63))),U_65)) ),
    inference(clausify,[status(thm)],[f_8_4]) ).

cnf(f_8_6,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_58,U_60,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_62),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_64))),U_66))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_58,hAPP(c_Nat_OSuc,U_60),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_62),hAPP(c_Com_Ocom_OBODY,U_64)),U_66)) ),
    inference(clausify,[status(thm)],[f_8_4]) ).

fof(f_9_1,plain,
    ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] :
      ( ? [B_s1] :
          ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1)
          & V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2),V_s_2,V_n_2,V_s1_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I7_J]) ).

fof(f_9_2,plain,
    ! [U_73,U_72,U_71,U_70,U_69,U_68] :
      ( ? [U_67] :
          ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_69),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_71),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_70,U_71)),U_72,U_67)
          & U_73 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_67),hAPP(c_Natural_Ogetlocs,U_71))),U_68),hAPP(hAPP(c_Natural_Ogetlocs,U_67),c_Com_ORes)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_68,U_69,U_70),U_71,U_72,U_73) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ! [U_73,U_72,U_71,U_70,U_69,U_68] :
      ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_69),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_71),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_70,U_71)),U_72,sK3(U_73,U_72,U_71,U_70,U_69,U_68))
        & U_73 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK3(U_73,U_72,U_71,U_70,U_69,U_68)),hAPP(c_Natural_Ogetlocs,U_71))),U_68),hAPP(hAPP(c_Natural_Ogetlocs,sK3(U_73,U_72,U_71,U_70,U_69,U_68)),c_Com_ORes)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_68,U_69,U_70),U_71,U_72,U_73) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_67,sK3(U_73,U_72,U_71,U_70,U_69,U_68))],[f_9_2]) ).

fof(f_9_4,plain,
    ( ! [U_68,U_69,U_70,U_71,U_72,U_73] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_69),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_71),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_70,U_71)),U_72,sK3(U_73,U_72,U_71,U_70,U_69,U_68))
        | ~ sP1(U_68,U_69,U_70,U_71,U_72,U_73) )
    & ! [U_68,U_69,U_70,U_71,U_72,U_73] :
        ( U_73 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK3(U_73,U_72,U_71,U_70,U_69,U_68)),hAPP(c_Natural_Ogetlocs,U_71))),U_68),hAPP(hAPP(c_Natural_Ogetlocs,sK3(U_73,U_72,U_71,U_70,U_69,U_68)),c_Com_ORes))
        | ~ sP1(U_68,U_69,U_70,U_71,U_72,U_73) )
    & ! [U_68,U_69,U_70,U_71,U_72,U_73] :
        ( sP1(U_68,U_69,U_70,U_71,U_72,U_73)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_68,U_69,U_70),U_71,U_72,U_73) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_9_3]) ).

cnf(f_9_5,plain,
    ( sP1(U_68,U_69,U_70,U_71,U_72,U_73)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_68,U_69,U_70),U_71,U_72,U_73) ),
    inference(clausify,[status(thm)],[f_9_4]) ).

cnf(f_9_6,plain,
    ( U_73 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK3(U_73,U_72,U_71,U_70,U_69,U_68)),hAPP(c_Natural_Ogetlocs,U_71))),U_68),hAPP(hAPP(c_Natural_Ogetlocs,sK3(U_73,U_72,U_71,U_70,U_69,U_68)),c_Com_ORes))
    | ~ sP1(U_68,U_69,U_70,U_71,U_72,U_73) ),
    inference(clausify,[status(thm)],[f_9_4]) ).

cnf(f_9_7,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_69),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_71),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_70,U_71)),U_72,sK3(U_73,U_72,U_71,U_70,U_69,U_68))
    | ~ sP1(U_68,U_69,U_70,U_71,U_72,U_73) ),
    inference(clausify,[status(thm)],[f_9_4]) ).

fof(f_10_1,plain,
    ! [V_s1,V_n,V_s,V_P] :
      ( ? [B_n] :
          ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1)
          & V_n = hAPP(c_Nat_OSuc,B_n) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I6_J]) ).

fof(f_10_2,plain,
    ! [U_78,U_77,U_76,U_75] :
      ( ? [U_74] :
          ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_75)),U_76,U_74,U_78)
          & U_77 = hAPP(c_Nat_OSuc,U_74) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_75),U_76,U_77,U_78) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_78,U_77,U_76,U_75] :
      ( ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_75)),U_76,sK4(U_78,U_77,U_76,U_75),U_78)
        & U_77 = hAPP(c_Nat_OSuc,sK4(U_78,U_77,U_76,U_75)) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_75),U_76,U_77,U_78) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_74,sK4(U_78,U_77,U_76,U_75))],[f_10_2]) ).

fof(f_10_4,plain,
    ( ! [U_75,U_76,U_77,U_78] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_75)),U_76,sK4(U_78,U_77,U_76,U_75),U_78)
        | ~ sP2(U_75,U_76,U_77,U_78) )
    & ! [U_75,U_76,U_77,U_78] :
        ( U_77 = hAPP(c_Nat_OSuc,sK4(U_78,U_77,U_76,U_75))
        | ~ sP2(U_75,U_76,U_77,U_78) )
    & ! [U_75,U_76,U_77,U_78] :
        ( sP2(U_75,U_76,U_77,U_78)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_75),U_76,U_77,U_78) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_10_3]) ).

cnf(f_10_5,plain,
    ( sP2(U_75,U_76,U_77,U_78)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_75),U_76,U_77,U_78) ),
    inference(clausify,[status(thm)],[f_10_4]) ).

cnf(f_10_6,plain,
    ( U_77 = hAPP(c_Nat_OSuc,sK4(U_78,U_77,U_76,U_75))
    | ~ sP2(U_75,U_76,U_77,U_78) ),
    inference(clausify,[status(thm)],[f_10_4]) ).

cnf(f_10_7,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_75)),U_76,sK4(U_78,U_77,U_76,U_75),U_78)
    | ~ sP2(U_75,U_76,U_77,U_78) ),
    inference(clausify,[status(thm)],[f_10_4]) ).

fof(f_11_1,plain,
    ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_s1_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OCall]) ).

fof(f_11_2,plain,
    ! [U_83,U_82,U_81,U_80,U_79] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_83,U_79,U_81)),U_80),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_82),hAPP(c_Natural_Ogetlocs,U_80))),U_83),hAPP(hAPP(c_Natural_Ogetlocs,U_82),c_Com_ORes))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_79)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_80),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_81,U_80))),U_82)) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_79,U_80,U_81,U_82,U_83] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_83,U_79,U_81)),U_80),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_82),hAPP(c_Natural_Ogetlocs,U_80))),U_83),hAPP(hAPP(c_Natural_Ogetlocs,U_82),c_Com_ORes))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_79)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_80),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_81,U_80))),U_82)) ),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_83,U_79,U_81)),U_80),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_82),hAPP(c_Natural_Ogetlocs,U_80))),U_83),hAPP(hAPP(c_Natural_Ogetlocs,U_82),c_Com_ORes))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_79)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_80),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_81,U_80))),U_82)) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes))))
        | ! [B_s1] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I10_J]) ).

fof(f_12_2,plain,
    ! [U_90,U_89,U_88,U_87,U_86] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_86,U_87,U_88)),U_89),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_90),hAPP(c_Natural_Ogetlocs,U_89))),U_86),hAPP(hAPP(c_Natural_Ogetlocs,U_90),c_Com_ORes))))
        | ! [U_85] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_87)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_89),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_88,U_89))),U_85))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_90),hAPP(c_Natural_Ogetlocs,U_89))),U_86),hAPP(hAPP(c_Natural_Ogetlocs,U_90),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_85),hAPP(c_Natural_Ogetlocs,U_89))),U_86),hAPP(hAPP(c_Natural_Ogetlocs,U_85),c_Com_ORes)) ) )
      & ( ? [U_84] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_87)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_89),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_88,U_89))),U_84))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_90),hAPP(c_Natural_Ogetlocs,U_89))),U_86),hAPP(hAPP(c_Natural_Ogetlocs,U_90),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_84),hAPP(c_Natural_Ogetlocs,U_89))),U_86),hAPP(hAPP(c_Natural_Ogetlocs,U_84),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_86,U_87,U_88)),U_89),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_90),hAPP(c_Natural_Ogetlocs,U_89))),U_86),hAPP(hAPP(c_Natural_Ogetlocs,U_90),c_Com_ORes)))) ) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ( ! [U_100,U_98,U_96,U_94,U_92] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_92,U_94,U_96)),U_98),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes))))
        | ! [U_85] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_94)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_98),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_96,U_98))),U_85))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_85),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_85),c_Com_ORes)) ) )
    & ! [U_99,U_97,U_95,U_93,U_91] :
        ( ? [U_84] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_93)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_97),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_95,U_97))),U_84))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_84),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_84),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_91,U_93,U_95)),U_97),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)))) ) ),
    inference(miniscope,[status(thm)],[f_12_2]) ).

fof(f_12_4,plain,
    ( ! [U_100,U_98,U_96,U_94,U_92] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_92,U_94,U_96)),U_98),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes))))
        | ! [U_85] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_94)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_98),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_96,U_98))),U_85))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_85),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_85),c_Com_ORes)) ) )
    & ! [U_99,U_97,U_95,U_93,U_91] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_93)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_97),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_95,U_97))),sK5(U_99,U_97,U_95,U_93,U_91)))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK5(U_99,U_97,U_95,U_93,U_91)),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,sK5(U_99,U_97,U_95,U_93,U_91)),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_91,U_93,U_95)),U_97),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_84,sK5(U_99,U_97,U_95,U_93,U_91))],[f_12_3]) ).

fof(f_12_5,plain,
    ( ! [U_93,U_97,U_91,U_95,U_99] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_93)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_97),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_95,U_97))),sK5(U_99,U_97,U_95,U_93,U_91)))
        | ~ sP3(U_93,U_97,U_91,U_95,U_99) )
    & ! [U_93,U_97,U_91,U_95,U_99] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK5(U_99,U_97,U_95,U_93,U_91)),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,sK5(U_99,U_97,U_95,U_93,U_91)),c_Com_ORes))
        | ~ sP3(U_93,U_97,U_91,U_95,U_99) )
    & ! [U_85,U_92,U_94,U_96,U_98,U_100] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_92,U_94,U_96)),U_98),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes))))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_94)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_98),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_96,U_98))),U_85))
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_85),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_85),c_Com_ORes)) )
    & ! [U_93,U_97,U_91,U_95,U_99] :
        ( sP3(U_93,U_97,U_91,U_95,U_99)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_91,U_93,U_95)),U_97),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_12_4]) ).

cnf(f_12_6,plain,
    ( sP3(U_93,U_97,U_91,U_95,U_99)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_91,U_93,U_95)),U_97),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)))) ),
    inference(clausify,[status(thm)],[f_12_5]) ).

cnf(f_12_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_92,U_94,U_96)),U_98),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_94)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_98),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_96,U_98))),U_85))
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_100),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_100),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_85),hAPP(c_Natural_Ogetlocs,U_98))),U_92),hAPP(hAPP(c_Natural_Ogetlocs,U_85),c_Com_ORes)) ),
    inference(clausify,[status(thm)],[f_12_5]) ).

cnf(f_12_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_99),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,U_99),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK5(U_99,U_97,U_95,U_93,U_91)),hAPP(c_Natural_Ogetlocs,U_97))),U_91),hAPP(hAPP(c_Natural_Ogetlocs,sK5(U_99,U_97,U_95,U_93,U_91)),c_Com_ORes))
    | ~ sP3(U_93,U_97,U_91,U_95,U_99) ),
    inference(clausify,[status(thm)],[f_12_5]) ).

cnf(f_12_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_93)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_97),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_95,U_97))),sK5(U_99,U_97,U_95,U_93,U_91)))
    | ~ sP3(U_93,U_97,U_91,U_95,U_99) ),
    inference(clausify,[status(thm)],[f_12_5]) ).

fof(f_13_1,plain,
    ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))
      | ~ c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OLocal]) ).

fof(f_13_2,plain,
    ! [U_106,U_105,U_104,U_103,U_102,U_101] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_103,U_104,U_101),U_102,U_105,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_106),c_Com_Ovname_OLoc(U_103)),hAPP(hAPP(c_Natural_Ogetlocs,U_102),U_103)))
      | ~ c_Natural_Oevaln(U_101,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_102),c_Com_Ovname_OLoc(U_103)),hAPP(U_104,U_102)),U_105,U_106) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_105,U_106,U_104,U_102,U_101,U_103] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_103,U_104,U_101),U_102,U_105,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_106),c_Com_Ovname_OLoc(U_103)),hAPP(hAPP(c_Natural_Ogetlocs,U_102),U_103)))
      | ~ c_Natural_Oevaln(U_101,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_102),c_Com_Ovname_OLoc(U_103)),hAPP(U_104,U_102)),U_105,U_106) ),
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_103,U_104,U_101),U_102,U_105,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_106),c_Com_Ovname_OLoc(U_103)),hAPP(hAPP(c_Natural_Ogetlocs,U_102),U_103)))
    | ~ c_Natural_Oevaln(U_101,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_102),c_Com_Ovname_OLoc(U_103)),hAPP(U_104,U_102)),U_105,U_106) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_1,plain,
    ! [V_s1,V_s0,V_pn] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OBody]) ).

fof(f_14_2,plain,
    ! [U_109,U_108,U_107] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_107)),U_108),U_109))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_107))),U_108),U_109)) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_108,U_107,U_109] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_107)),U_108),U_109))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_107))),U_108),U_109)) ),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_107)),U_108),U_109))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_107))),U_108),U_109)) ),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [V_s1,V_s,V_P] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I6_J]) ).

fof(f_15_2,plain,
    ! [U_112,U_111,U_110] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_110))),U_111),U_112))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_110)),U_111),U_112)) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_110,U_111,U_112] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_110))),U_111),U_112))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_110)),U_111),U_112)) ),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_110))),U_111),U_112))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_110)),U_111),U_112)) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_1,plain,
    ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OLocal]) ).

fof(f_16_2,plain,
    ! [U_117,U_116,U_115,U_114,U_113] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_115,U_116,U_113)),U_114),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_117),c_Com_Ovname_OLoc(U_115)),hAPP(hAPP(c_Natural_Ogetlocs,U_114),U_115))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_113),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_114),c_Com_Ovname_OLoc(U_115)),hAPP(U_116,U_114))),U_117)) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_113,U_114,U_115,U_116,U_117] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_115,U_116,U_113)),U_114),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_117),c_Com_Ovname_OLoc(U_115)),hAPP(hAPP(c_Natural_Ogetlocs,U_114),U_115))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_113),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_114),c_Com_Ovname_OLoc(U_115)),hAPP(U_116,U_114))),U_117)) ),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_115,U_116,U_113)),U_114),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_117),c_Com_Ovname_OLoc(U_115)),hAPP(hAPP(c_Natural_Ogetlocs,U_114),U_115))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_113),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_114),c_Com_Ovname_OLoc(U_115)),hAPP(U_116,U_114))),U_117)) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_1,plain,
    ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
      ( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
        | V_fun2_2 != V_fun2_H_2
        | V_com_2 != V_com_H_2
        | V_fun1_2 != V_fun1_H_2 )
      & ( ( V_fun2_2 = V_fun2_H_2
          & V_com_2 = V_com_H_2
          & V_fun1_2 = V_fun1_H_2 )
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple_Oinject]) ).

fof(f_17_2,plain,
    ! [U_124,U_123,U_122,U_121,U_120,U_119,U_118] :
      ( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_118),U_119),U_120),U_121) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_118),U_122),U_123),U_124)
        | U_121 != U_124
        | U_120 != U_123
        | U_119 != U_122 )
      & ( ( U_121 = U_124
          & U_120 = U_123
          & U_119 = U_122 )
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_118),U_119),U_120),U_121) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_118),U_122),U_123),U_124) ) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ( ! [U_138,U_136,U_134,U_132,U_130,U_128] :
        ( ! [U_126] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_126),U_128),U_130),U_132) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_126),U_134),U_136),U_138)
        | U_132 != U_138
        | U_130 != U_136
        | U_128 != U_134 )
    & ! [U_137,U_135,U_133,U_131,U_129,U_127] :
        ( ! [U_125] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_125),U_127),U_129),U_131) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_125),U_133),U_135),U_137)
        | ( U_131 = U_137
          & U_129 = U_135
          & U_127 = U_133 ) ) ),
    inference(miniscope,[status(thm)],[f_17_2]) ).

fof(f_17_4,plain,
    ( ! [U_127,U_131,U_129,U_133,U_135,U_137] :
        ( U_131 = U_137
        | ~ sP4(U_127,U_131,U_129,U_133,U_135,U_137) )
    & ! [U_127,U_131,U_129,U_133,U_135,U_137] :
        ( U_129 = U_135
        | ~ sP4(U_127,U_131,U_129,U_133,U_135,U_137) )
    & ! [U_127,U_131,U_129,U_133,U_135,U_137] :
        ( U_127 = U_133
        | ~ sP4(U_127,U_131,U_129,U_133,U_135,U_137) )
    & ! [U_126,U_132,U_128,U_138,U_130,U_134,U_136] :
        ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_126),U_128),U_130),U_132) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_126),U_134),U_136),U_138)
        | U_132 != U_138
        | U_130 != U_136
        | U_128 != U_134 )
    & ! [U_127,U_131,U_125,U_129,U_133,U_135,U_137] :
        ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_125),U_127),U_129),U_131) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_125),U_133),U_135),U_137)
        | sP4(U_127,U_131,U_129,U_133,U_135,U_137) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_17_3]) ).

cnf(f_17_5,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_125),U_127),U_129),U_131) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_125),U_133),U_135),U_137)
    | sP4(U_127,U_131,U_129,U_133,U_135,U_137) ),
    inference(clausify,[status(thm)],[f_17_4]) ).

cnf(f_17_6,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_126),U_128),U_130),U_132) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_126),U_134),U_136),U_138)
    | U_132 != U_138
    | U_130 != U_136
    | U_128 != U_134 ),
    inference(clausify,[status(thm)],[f_17_4]) ).

cnf(f_17_7,plain,
    ( U_127 = U_133
    | ~ sP4(U_127,U_131,U_129,U_133,U_135,U_137) ),
    inference(clausify,[status(thm)],[f_17_4]) ).

cnf(f_17_8,plain,
    ( U_129 = U_135
    | ~ sP4(U_127,U_131,U_129,U_133,U_135,U_137) ),
    inference(clausify,[status(thm)],[f_17_4]) ).

cnf(f_17_9,plain,
    ( U_131 = U_137
    | ~ sP4(U_127,U_131,U_129,U_133,U_135,U_137) ),
    inference(clausify,[status(thm)],[f_17_4]) ).

fof(f_18_1,plain,
    ! [V_u,V_t,V_s,V_c] :
      ( V_u = V_t
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_com__det]) ).

fof(f_18_2,plain,
    ! [U_142,U_141,U_140,U_139] :
      ( U_142 = U_141
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_139),U_140),U_142))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_139),U_140),U_141)) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_141,U_140,U_139,U_142] :
      ( U_142 = U_141
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_139),U_140),U_142))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_139),U_140),U_141)) ),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    ( U_142 = U_141
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_139),U_140),U_142))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_139),U_140),U_141)) ),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_1,plain,
    ! [V_t,V_n,V_s,V_c] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
      | ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__evalc]) ).

fof(f_19_2,plain,
    ! [U_146,U_145,U_144,U_143] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_143),U_144),U_146))
      | ~ c_Natural_Oevaln(U_143,U_144,U_145,U_146) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_143,U_144,U_145,U_146] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_143),U_144),U_146))
      | ~ c_Natural_Oevaln(U_143,U_144,U_145,U_146) ),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_143),U_144),U_146))
    | ~ c_Natural_Oevaln(U_143,U_144,U_145,U_146) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_1,plain,
    ! [V_t_2,V_s_2,V_c_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
        | ! [B_n] : ~ c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) )
      & ( ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_eval__eq]) ).

fof(f_20_2,plain,
    ! [U_151,U_150,U_149] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_149),U_150),U_151))
        | ! [U_148] : ~ c_Natural_Oevaln(U_149,U_150,U_148,U_151) )
      & ( ? [U_147] : c_Natural_Oevaln(U_149,U_150,U_147,U_151)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_149),U_150),U_151)) ) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ( ! [U_157,U_155,U_153] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_153),U_155),U_157))
        | ! [U_148] : ~ c_Natural_Oevaln(U_153,U_155,U_148,U_157) )
    & ! [U_156,U_154,U_152] :
        ( ? [U_147] : c_Natural_Oevaln(U_152,U_154,U_147,U_156)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_152),U_154),U_156)) ) ),
    inference(miniscope,[status(thm)],[f_20_2]) ).

fof(f_20_4,plain,
    ( ! [U_157,U_155,U_153] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_153),U_155),U_157))
        | ! [U_148] : ~ c_Natural_Oevaln(U_153,U_155,U_148,U_157) )
    & ! [U_156,U_154,U_152] :
        ( c_Natural_Oevaln(U_152,U_154,sK6(U_156,U_154,U_152),U_156)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_152),U_154),U_156)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_147,sK6(U_156,U_154,U_152))],[f_20_3]) ).

fof(f_20_5,plain,
    ( ! [U_148,U_155,U_153,U_157] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_153),U_155),U_157))
        | ~ c_Natural_Oevaln(U_153,U_155,U_148,U_157) )
    & ! [U_156,U_154,U_152] :
        ( c_Natural_Oevaln(U_152,U_154,sK6(U_156,U_154,U_152),U_156)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_152),U_154),U_156)) ) ),
    inference(definitional_conversion,[status(esa)],[f_20_4]) ).

cnf(f_20_6,plain,
    ( c_Natural_Oevaln(U_152,U_154,sK6(U_156,U_154,U_152),U_156)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_152),U_154),U_156)) ),
    inference(clausify,[status(thm)],[f_20_5]) ).

cnf(f_20_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_153),U_155),U_157))
    | ~ c_Natural_Oevaln(U_153,U_155,U_148,U_157) ),
    inference(clausify,[status(thm)],[f_20_5]) ).

fof(f_21_1,plain,
    ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))))
        | ! [B_s1] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I3_J]) ).

fof(f_21_2,plain,
    ! [U_164,U_163,U_162,U_161,U_160] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_160,U_161,U_162)),U_163),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_164),c_Com_Ovname_OLoc(U_160)),hAPP(hAPP(c_Natural_Ogetlocs,U_163),U_160))))
        | ! [U_159] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_162),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_163),c_Com_Ovname_OLoc(U_160)),hAPP(U_161,U_163))),U_159))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_164),c_Com_Ovname_OLoc(U_160)),hAPP(hAPP(c_Natural_Ogetlocs,U_163),U_160)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_159),c_Com_Ovname_OLoc(U_160)),hAPP(hAPP(c_Natural_Ogetlocs,U_163),U_160)) ) )
      & ( ? [U_158] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_162),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_163),c_Com_Ovname_OLoc(U_160)),hAPP(U_161,U_163))),U_158))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_164),c_Com_Ovname_OLoc(U_160)),hAPP(hAPP(c_Natural_Ogetlocs,U_163),U_160)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_158),c_Com_Ovname_OLoc(U_160)),hAPP(hAPP(c_Natural_Ogetlocs,U_163),U_160)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_160,U_161,U_162)),U_163),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_164),c_Com_Ovname_OLoc(U_160)),hAPP(hAPP(c_Natural_Ogetlocs,U_163),U_160)))) ) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ( ! [U_174,U_172,U_170,U_168,U_166] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_166,U_168,U_170)),U_172),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166))))
        | ! [U_159] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_170),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_172),c_Com_Ovname_OLoc(U_166)),hAPP(U_168,U_172))),U_159))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_159),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) ) )
    & ! [U_173,U_171,U_169,U_167,U_165] :
        ( ? [U_158] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_169),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_171),c_Com_Ovname_OLoc(U_165)),hAPP(U_167,U_171))),U_158))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_158),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_165,U_167,U_169)),U_171),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)))) ) ),
    inference(miniscope,[status(thm)],[f_21_2]) ).

fof(f_21_4,plain,
    ( ! [U_174,U_172,U_170,U_168,U_166] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_166,U_168,U_170)),U_172),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166))))
        | ! [U_159] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_170),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_172),c_Com_Ovname_OLoc(U_166)),hAPP(U_168,U_172))),U_159))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_159),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) ) )
    & ! [U_173,U_171,U_169,U_167,U_165] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_169),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_171),c_Com_Ovname_OLoc(U_165)),hAPP(U_167,U_171))),sK7(U_173,U_171,U_169,U_167,U_165)))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK7(U_173,U_171,U_169,U_167,U_165)),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_165,U_167,U_169)),U_171),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_158,sK7(U_173,U_171,U_169,U_167,U_165))],[f_21_3]) ).

fof(f_21_5,plain,
    ( ! [U_167,U_165,U_169,U_171,U_173] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_169),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_171),c_Com_Ovname_OLoc(U_165)),hAPP(U_167,U_171))),sK7(U_173,U_171,U_169,U_167,U_165)))
        | ~ sP5(U_167,U_165,U_169,U_171,U_173) )
    & ! [U_167,U_165,U_169,U_171,U_173] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK7(U_173,U_171,U_169,U_167,U_165)),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165))
        | ~ sP5(U_167,U_165,U_169,U_171,U_173) )
    & ! [U_159,U_166,U_168,U_174,U_170,U_172] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_166,U_168,U_170)),U_172),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166))))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_170),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_172),c_Com_Ovname_OLoc(U_166)),hAPP(U_168,U_172))),U_159))
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_159),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) )
    & ! [U_167,U_165,U_169,U_171,U_173] :
        ( sP5(U_167,U_165,U_169,U_171,U_173)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_165,U_167,U_169)),U_171),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_21_4]) ).

cnf(f_21_6,plain,
    ( sP5(U_167,U_165,U_169,U_171,U_173)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_165,U_167,U_169)),U_171),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)))) ),
    inference(clausify,[status(thm)],[f_21_5]) ).

cnf(f_21_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_166,U_168,U_170)),U_172),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_170),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_172),c_Com_Ovname_OLoc(U_166)),hAPP(U_168,U_172))),U_159))
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_174),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_159),c_Com_Ovname_OLoc(U_166)),hAPP(hAPP(c_Natural_Ogetlocs,U_172),U_166)) ),
    inference(clausify,[status(thm)],[f_21_5]) ).

cnf(f_21_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_173),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK7(U_173,U_171,U_169,U_167,U_165)),c_Com_Ovname_OLoc(U_165)),hAPP(hAPP(c_Natural_Ogetlocs,U_171),U_165))
    | ~ sP5(U_167,U_165,U_169,U_171,U_173) ),
    inference(clausify,[status(thm)],[f_21_5]) ).

cnf(f_21_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_169),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_171),c_Com_Ovname_OLoc(U_165)),hAPP(U_167,U_171))),sK7(U_173,U_171,U_169,U_167,U_165)))
    | ~ sP5(U_167,U_165,U_169,U_171,U_173) ),
    inference(clausify,[status(thm)],[f_21_5]) ).

fof(f_22_1,plain,
    ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_b] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2))
        | ? [B_Z,B_s] :
            ( ? [B_s_H] :
                ( ~ hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H))
                & c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
            & hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) ) )
      & ( ! [B_Z,B_s] :
            ( ! [B_s_H] :
                ( hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H))
                | ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
            | ~ hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) )
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple__valid__def2]) ).

fof(f_22_2,plain,
    ! [U_185,U_184,U_183,U_182,U_181] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_181,U_182,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_181),U_183),U_184),U_185))
        | ? [U_180,U_179] :
            ( ? [U_178] :
                ( ~ hBOOL(hAPP(hAPP(U_185,U_180),U_178))
                & c_Natural_Oevaln(U_184,U_179,U_182,U_178) )
            & hBOOL(hAPP(hAPP(U_183,U_180),U_179)) ) )
      & ( ! [U_177,U_176] :
            ( ! [U_175] :
                ( hBOOL(hAPP(hAPP(U_185,U_177),U_175))
                | ~ c_Natural_Oevaln(U_184,U_176,U_182,U_175) )
            | ~ hBOOL(hAPP(hAPP(U_183,U_177),U_176)) )
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_181,U_182,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_181),U_183),U_184),U_185)) ) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ( ! [U_195,U_193,U_191,U_189] :
        ( ! [U_187] : c_Hoare__Mirabelle_Otriple__valid(U_187,U_189,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_187),U_191),U_193),U_195))
        | ? [U_180,U_179] :
            ( ? [U_178] :
                ( ~ hBOOL(hAPP(hAPP(U_195,U_180),U_178))
                & c_Natural_Oevaln(U_193,U_179,U_189,U_178) )
            & hBOOL(hAPP(hAPP(U_191,U_180),U_179)) ) )
    & ! [U_194,U_192,U_190,U_188] :
        ( ! [U_186] : ~ c_Hoare__Mirabelle_Otriple__valid(U_186,U_188,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_186),U_190),U_192),U_194))
        | ! [U_177,U_176] :
            ( ! [U_175] :
                ( hBOOL(hAPP(hAPP(U_194,U_177),U_175))
                | ~ c_Natural_Oevaln(U_192,U_176,U_188,U_175) )
            | ~ hBOOL(hAPP(hAPP(U_190,U_177),U_176)) ) ) ),
    inference(miniscope,[status(thm)],[f_22_2]) ).

fof(f_22_4,plain,
    ( ! [U_195,U_193,U_191,U_189] :
        ( ! [U_187] : c_Hoare__Mirabelle_Otriple__valid(U_187,U_189,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_187),U_191),U_193),U_195))
        | ? [U_179] :
            ( ? [U_178] :
                ( ~ hBOOL(hAPP(hAPP(U_195,sK8(U_195,U_193,U_191,U_189)),U_178))
                & c_Natural_Oevaln(U_193,U_179,U_189,U_178) )
            & hBOOL(hAPP(hAPP(U_191,sK8(U_195,U_193,U_191,U_189)),U_179)) ) )
    & ! [U_194,U_192,U_190,U_188] :
        ( ! [U_186] : ~ c_Hoare__Mirabelle_Otriple__valid(U_186,U_188,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_186),U_190),U_192),U_194))
        | ! [U_177,U_176] :
            ( ! [U_175] :
                ( hBOOL(hAPP(hAPP(U_194,U_177),U_175))
                | ~ c_Natural_Oevaln(U_192,U_176,U_188,U_175) )
            | ~ hBOOL(hAPP(hAPP(U_190,U_177),U_176)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_180,sK8(U_195,U_193,U_191,U_189))],[f_22_3]) ).

fof(f_22_5,plain,
    ( ! [U_195,U_193,U_191,U_189] :
        ( ! [U_187] : c_Hoare__Mirabelle_Otriple__valid(U_187,U_189,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_187),U_191),U_193),U_195))
        | ( ? [U_178] :
              ( ~ hBOOL(hAPP(hAPP(U_195,sK8(U_195,U_193,U_191,U_189)),U_178))
              & c_Natural_Oevaln(U_193,sK9(U_195,U_193,U_191,U_189),U_189,U_178) )
          & hBOOL(hAPP(hAPP(U_191,sK8(U_195,U_193,U_191,U_189)),sK9(U_195,U_193,U_191,U_189))) ) )
    & ! [U_194,U_192,U_190,U_188] :
        ( ! [U_186] : ~ c_Hoare__Mirabelle_Otriple__valid(U_186,U_188,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_186),U_190),U_192),U_194))
        | ! [U_177,U_176] :
            ( ! [U_175] :
                ( hBOOL(hAPP(hAPP(U_194,U_177),U_175))
                | ~ c_Natural_Oevaln(U_192,U_176,U_188,U_175) )
            | ~ hBOOL(hAPP(hAPP(U_190,U_177),U_176)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_179,sK9(U_195,U_193,U_191,U_189))],[f_22_4]) ).

fof(f_22_6,plain,
    ( ! [U_195,U_193,U_191,U_189] :
        ( ! [U_187] : c_Hoare__Mirabelle_Otriple__valid(U_187,U_189,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_187),U_191),U_193),U_195))
        | ( ~ hBOOL(hAPP(hAPP(U_195,sK8(U_195,U_193,U_191,U_189)),sK10(U_195,U_193,U_191,U_189)))
          & c_Natural_Oevaln(U_193,sK9(U_195,U_193,U_191,U_189),U_189,sK10(U_195,U_193,U_191,U_189))
          & hBOOL(hAPP(hAPP(U_191,sK8(U_195,U_193,U_191,U_189)),sK9(U_195,U_193,U_191,U_189))) ) )
    & ! [U_194,U_192,U_190,U_188] :
        ( ! [U_186] : ~ c_Hoare__Mirabelle_Otriple__valid(U_186,U_188,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_186),U_190),U_192),U_194))
        | ! [U_177,U_176] :
            ( ! [U_175] :
                ( hBOOL(hAPP(hAPP(U_194,U_177),U_175))
                | ~ c_Natural_Oevaln(U_192,U_176,U_188,U_175) )
            | ~ hBOOL(hAPP(hAPP(U_190,U_177),U_176)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_178,sK10(U_195,U_193,U_191,U_189))],[f_22_5]) ).

fof(f_22_7,plain,
    ( ! [U_191,U_195,U_189,U_193] :
        ( ~ hBOOL(hAPP(hAPP(U_195,sK8(U_195,U_193,U_191,U_189)),sK10(U_195,U_193,U_191,U_189)))
        | ~ sP6(U_191,U_195,U_189,U_193) )
    & ! [U_191,U_195,U_189,U_193] :
        ( c_Natural_Oevaln(U_193,sK9(U_195,U_193,U_191,U_189),U_189,sK10(U_195,U_193,U_191,U_189))
        | ~ sP6(U_191,U_195,U_189,U_193) )
    & ! [U_191,U_195,U_189,U_193] :
        ( hBOOL(hAPP(hAPP(U_191,sK8(U_195,U_193,U_191,U_189)),sK9(U_195,U_193,U_191,U_189)))
        | ~ sP6(U_191,U_195,U_189,U_193) )
    & ! [U_191,U_195,U_189,U_187,U_193] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_187,U_189,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_187),U_191),U_193),U_195))
        | sP6(U_191,U_195,U_189,U_193) )
    & ! [U_190,U_177,U_194,U_175,U_176,U_192,U_188,U_186] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_186,U_188,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_186),U_190),U_192),U_194))
        | hBOOL(hAPP(hAPP(U_194,U_177),U_175))
        | ~ c_Natural_Oevaln(U_192,U_176,U_188,U_175)
        | ~ hBOOL(hAPP(hAPP(U_190,U_177),U_176)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_22_6]) ).

cnf(f_22_8,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_186,U_188,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_186),U_190),U_192),U_194))
    | hBOOL(hAPP(hAPP(U_194,U_177),U_175))
    | ~ c_Natural_Oevaln(U_192,U_176,U_188,U_175)
    | ~ hBOOL(hAPP(hAPP(U_190,U_177),U_176)) ),
    inference(clausify,[status(thm)],[f_22_7]) ).

cnf(f_22_9,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_187,U_189,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_187),U_191),U_193),U_195))
    | sP6(U_191,U_195,U_189,U_193) ),
    inference(clausify,[status(thm)],[f_22_7]) ).

cnf(f_22_10,plain,
    ( hBOOL(hAPP(hAPP(U_191,sK8(U_195,U_193,U_191,U_189)),sK9(U_195,U_193,U_191,U_189)))
    | ~ sP6(U_191,U_195,U_189,U_193) ),
    inference(clausify,[status(thm)],[f_22_7]) ).

cnf(f_22_11,plain,
    ( c_Natural_Oevaln(U_193,sK9(U_195,U_193,U_191,U_189),U_189,sK10(U_195,U_193,U_191,U_189))
    | ~ sP6(U_191,U_195,U_189,U_193) ),
    inference(clausify,[status(thm)],[f_22_7]) ).

cnf(f_22_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_195,sK8(U_195,U_193,U_191,U_189)),sK10(U_195,U_193,U_191,U_189)))
    | ~ sP6(U_191,U_195,U_189,U_193) ),
    inference(clausify,[status(thm)],[f_22_7]) ).

fof(f_23_1,plain,
    ! [V_a3_2,V_a2_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I9_J]) ).

fof(f_23_2,plain,
    ! [U_198,U_197,U_196] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_196)),U_197),U_198))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_196))),U_197),U_198)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_196))),U_197),U_198))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_196)),U_197),U_198)) ) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ( ! [U_204,U_202,U_200] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_200)),U_202),U_204))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_200))),U_202),U_204)) )
    & ! [U_203,U_201,U_199] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_199))),U_201),U_203))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_199)),U_201),U_203)) ) ),
    inference(miniscope,[status(thm)],[f_23_2]) ).

fof(f_23_4,plain,
    ( ! [U_200,U_202,U_204] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_200)),U_202),U_204))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_200))),U_202),U_204)) )
    & ! [U_201,U_199,U_203] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_199))),U_201),U_203))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_199)),U_201),U_203)) ) ),
    inference(definitional_conversion,[status(esa)],[f_23_3]) ).

cnf(f_23_5,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_199))),U_201),U_203))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_199)),U_201),U_203)) ),
    inference(clausify,[status(thm)],[f_23_4]) ).

cnf(f_23_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_200)),U_202),U_204))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_200))),U_202),U_204)) ),
    inference(clausify,[status(thm)],[f_23_4]) ).

fof(f_24_1,plain,
    ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2),V_a2_2,V_a5_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))
        | ! [B_s1] :
            ( ~ c_Natural_Oevaln(V_a1_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2)),V_a5_2,B_s1)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) ) )
      & ( ? [B_s1] :
            ( c_Natural_Oevaln(V_a1_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2)),V_a5_2,B_s1)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2),V_a2_2,V_a5_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I3_J]) ).

fof(f_24_2,plain,
    ! [U_212,U_211,U_210,U_209,U_208,U_207] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_207,U_208,U_209),U_210,U_211,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_212),c_Com_Ovname_OLoc(U_207)),hAPP(hAPP(c_Natural_Ogetlocs,U_210),U_207)))
        | ! [U_206] :
            ( ~ c_Natural_Oevaln(U_209,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_210),c_Com_Ovname_OLoc(U_207)),hAPP(U_208,U_210)),U_211,U_206)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_212),c_Com_Ovname_OLoc(U_207)),hAPP(hAPP(c_Natural_Ogetlocs,U_210),U_207)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_206),c_Com_Ovname_OLoc(U_207)),hAPP(hAPP(c_Natural_Ogetlocs,U_210),U_207)) ) )
      & ( ? [U_205] :
            ( c_Natural_Oevaln(U_209,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_210),c_Com_Ovname_OLoc(U_207)),hAPP(U_208,U_210)),U_211,U_205)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_212),c_Com_Ovname_OLoc(U_207)),hAPP(hAPP(c_Natural_Ogetlocs,U_210),U_207)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_205),c_Com_Ovname_OLoc(U_207)),hAPP(hAPP(c_Natural_Ogetlocs,U_210),U_207)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_207,U_208,U_209),U_210,U_211,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_212),c_Com_Ovname_OLoc(U_207)),hAPP(hAPP(c_Natural_Ogetlocs,U_210),U_207))) ) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ( ! [U_224,U_222,U_220,U_218,U_216,U_214] :
        ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_214,U_216,U_218),U_220,U_222,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)))
        | ! [U_206] :
            ( ~ c_Natural_Oevaln(U_218,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_220),c_Com_Ovname_OLoc(U_214)),hAPP(U_216,U_220)),U_222,U_206)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_206),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) ) )
    & ! [U_223,U_221,U_219,U_217,U_215,U_213] :
        ( ? [U_205] :
            ( c_Natural_Oevaln(U_217,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_219),c_Com_Ovname_OLoc(U_213)),hAPP(U_215,U_219)),U_221,U_205)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_205),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_213,U_215,U_217),U_219,U_221,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213))) ) ),
    inference(miniscope,[status(thm)],[f_24_2]) ).

fof(f_24_4,plain,
    ( ! [U_224,U_222,U_220,U_218,U_216,U_214] :
        ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_214,U_216,U_218),U_220,U_222,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)))
        | ! [U_206] :
            ( ~ c_Natural_Oevaln(U_218,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_220),c_Com_Ovname_OLoc(U_214)),hAPP(U_216,U_220)),U_222,U_206)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_206),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) ) )
    & ! [U_223,U_221,U_219,U_217,U_215,U_213] :
        ( ( c_Natural_Oevaln(U_217,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_219),c_Com_Ovname_OLoc(U_213)),hAPP(U_215,U_219)),U_221,sK11(U_223,U_221,U_219,U_217,U_215,U_213))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK11(U_223,U_221,U_219,U_217,U_215,U_213)),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_213,U_215,U_217),U_219,U_221,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_205,sK11(U_223,U_221,U_219,U_217,U_215,U_213))],[f_24_3]) ).

fof(f_24_5,plain,
    ( ! [U_215,U_221,U_219,U_213,U_217,U_223] :
        ( c_Natural_Oevaln(U_217,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_219),c_Com_Ovname_OLoc(U_213)),hAPP(U_215,U_219)),U_221,sK11(U_223,U_221,U_219,U_217,U_215,U_213))
        | ~ sP7(U_215,U_221,U_219,U_213,U_217,U_223) )
    & ! [U_215,U_221,U_219,U_213,U_217,U_223] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK11(U_223,U_221,U_219,U_217,U_215,U_213)),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213))
        | ~ sP7(U_215,U_221,U_219,U_213,U_217,U_223) )
    & ! [U_224,U_218,U_206,U_216,U_214,U_220,U_222] :
        ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_214,U_216,U_218),U_220,U_222,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)))
        | ~ c_Natural_Oevaln(U_218,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_220),c_Com_Ovname_OLoc(U_214)),hAPP(U_216,U_220)),U_222,U_206)
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_206),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) )
    & ! [U_215,U_221,U_219,U_213,U_217,U_223] :
        ( sP7(U_215,U_221,U_219,U_213,U_217,U_223)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_213,U_215,U_217),U_219,U_221,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_24_4]) ).

cnf(f_24_6,plain,
    ( sP7(U_215,U_221,U_219,U_213,U_217,U_223)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_213,U_215,U_217),U_219,U_221,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213))) ),
    inference(clausify,[status(thm)],[f_24_5]) ).

cnf(f_24_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_214,U_216,U_218),U_220,U_222,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)))
    | ~ c_Natural_Oevaln(U_218,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_220),c_Com_Ovname_OLoc(U_214)),hAPP(U_216,U_220)),U_222,U_206)
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_224),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_206),c_Com_Ovname_OLoc(U_214)),hAPP(hAPP(c_Natural_Ogetlocs,U_220),U_214)) ),
    inference(clausify,[status(thm)],[f_24_5]) ).

cnf(f_24_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_223),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK11(U_223,U_221,U_219,U_217,U_215,U_213)),c_Com_Ovname_OLoc(U_213)),hAPP(hAPP(c_Natural_Ogetlocs,U_219),U_213))
    | ~ sP7(U_215,U_221,U_219,U_213,U_217,U_223) ),
    inference(clausify,[status(thm)],[f_24_5]) ).

cnf(f_24_9,plain,
    ( c_Natural_Oevaln(U_217,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_219),c_Com_Ovname_OLoc(U_213)),hAPP(U_215,U_219)),U_221,sK11(U_223,U_221,U_219,U_217,U_215,U_213))
    | ~ sP7(U_215,U_221,U_219,U_213,U_217,U_223) ),
    inference(clausify,[status(thm)],[f_24_5]) ).

fof(f_25_1,plain,
    ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] :
      ( ? [B_s1] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),B_s1))
          & V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_s1_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I7_J]) ).

fof(f_25_2,plain,
    ! [U_230,U_229,U_228,U_227,U_226] :
      ( ? [U_225] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_227)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_229),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_228,U_229))),U_225))
          & U_230 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_225),hAPP(c_Natural_Ogetlocs,U_229))),U_226),hAPP(hAPP(c_Natural_Ogetlocs,U_225),c_Com_ORes)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_226,U_227,U_228)),U_229),U_230)) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_230,U_229,U_228,U_227,U_226] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_227)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_229),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_228,U_229))),sK12(U_230,U_229,U_228,U_227,U_226)))
        & U_230 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK12(U_230,U_229,U_228,U_227,U_226)),hAPP(c_Natural_Ogetlocs,U_229))),U_226),hAPP(hAPP(c_Natural_Ogetlocs,sK12(U_230,U_229,U_228,U_227,U_226)),c_Com_ORes)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_226,U_227,U_228)),U_229),U_230)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_225,sK12(U_230,U_229,U_228,U_227,U_226))],[f_25_2]) ).

fof(f_25_4,plain,
    ( ! [U_227,U_226,U_228,U_229,U_230] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_227)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_229),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_228,U_229))),sK12(U_230,U_229,U_228,U_227,U_226)))
        | ~ sP8(U_227,U_226,U_228,U_229,U_230) )
    & ! [U_227,U_226,U_228,U_229,U_230] :
        ( U_230 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK12(U_230,U_229,U_228,U_227,U_226)),hAPP(c_Natural_Ogetlocs,U_229))),U_226),hAPP(hAPP(c_Natural_Ogetlocs,sK12(U_230,U_229,U_228,U_227,U_226)),c_Com_ORes))
        | ~ sP8(U_227,U_226,U_228,U_229,U_230) )
    & ! [U_227,U_226,U_228,U_229,U_230] :
        ( sP8(U_227,U_226,U_228,U_229,U_230)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_226,U_227,U_228)),U_229),U_230)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_25_3]) ).

cnf(f_25_5,plain,
    ( sP8(U_227,U_226,U_228,U_229,U_230)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_226,U_227,U_228)),U_229),U_230)) ),
    inference(clausify,[status(thm)],[f_25_4]) ).

cnf(f_25_6,plain,
    ( U_230 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK12(U_230,U_229,U_228,U_227,U_226)),hAPP(c_Natural_Ogetlocs,U_229))),U_226),hAPP(hAPP(c_Natural_Ogetlocs,sK12(U_230,U_229,U_228,U_227,U_226)),c_Com_ORes))
    | ~ sP8(U_227,U_226,U_228,U_229,U_230) ),
    inference(clausify,[status(thm)],[f_25_4]) ).

cnf(f_25_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_227)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_229),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_228,U_229))),sK12(U_230,U_229,U_228,U_227,U_226)))
    | ~ sP8(U_227,U_226,U_228,U_229,U_230) ),
    inference(clausify,[status(thm)],[f_25_4]) ).

fof(f_26_1,plain,
    ! [V_t_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
      ( ? [B_s1] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1))
          & V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s_2),V_t_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I3_J]) ).

fof(f_26_2,plain,
    ! [U_236,U_235,U_234,U_233,U_232] :
      ( ? [U_231] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_234),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_235),c_Com_Ovname_OLoc(U_232)),hAPP(U_233,U_235))),U_231))
          & U_236 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_231),c_Com_Ovname_OLoc(U_232)),hAPP(hAPP(c_Natural_Ogetlocs,U_235),U_232)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_232,U_233,U_234)),U_235),U_236)) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_236,U_235,U_234,U_233,U_232] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_234),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_235),c_Com_Ovname_OLoc(U_232)),hAPP(U_233,U_235))),sK13(U_236,U_235,U_234,U_233,U_232)))
        & U_236 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK13(U_236,U_235,U_234,U_233,U_232)),c_Com_Ovname_OLoc(U_232)),hAPP(hAPP(c_Natural_Ogetlocs,U_235),U_232)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_232,U_233,U_234)),U_235),U_236)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_231,sK13(U_236,U_235,U_234,U_233,U_232))],[f_26_2]) ).

fof(f_26_4,plain,
    ( ! [U_232,U_233,U_234,U_235,U_236] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_234),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_235),c_Com_Ovname_OLoc(U_232)),hAPP(U_233,U_235))),sK13(U_236,U_235,U_234,U_233,U_232)))
        | ~ sP9(U_232,U_233,U_234,U_235,U_236) )
    & ! [U_232,U_233,U_234,U_235,U_236] :
        ( U_236 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK13(U_236,U_235,U_234,U_233,U_232)),c_Com_Ovname_OLoc(U_232)),hAPP(hAPP(c_Natural_Ogetlocs,U_235),U_232))
        | ~ sP9(U_232,U_233,U_234,U_235,U_236) )
    & ! [U_232,U_233,U_234,U_235,U_236] :
        ( sP9(U_232,U_233,U_234,U_235,U_236)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_232,U_233,U_234)),U_235),U_236)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_26_3]) ).

cnf(f_26_5,plain,
    ( sP9(U_232,U_233,U_234,U_235,U_236)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_232,U_233,U_234)),U_235),U_236)) ),
    inference(clausify,[status(thm)],[f_26_4]) ).

cnf(f_26_6,plain,
    ( U_236 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK13(U_236,U_235,U_234,U_233,U_232)),c_Com_Ovname_OLoc(U_232)),hAPP(hAPP(c_Natural_Ogetlocs,U_235),U_232))
    | ~ sP9(U_232,U_233,U_234,U_235,U_236) ),
    inference(clausify,[status(thm)],[f_26_4]) ).

cnf(f_26_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_234),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_235),c_Com_Ovname_OLoc(U_232)),hAPP(U_233,U_235))),sK13(U_236,U_235,U_234,U_233,U_232)))
    | ~ sP9(U_232,U_233,U_234,U_235,U_236) ),
    inference(clausify,[status(thm)],[f_26_4]) ).

fof(f_27_1,plain,
    ! [V_t_2,V_n_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
      ( ? [B_s1] :
          ( c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1)
          & V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s_2,V_n_2,V_t_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I3_J]) ).

fof(f_27_2,plain,
    ! [U_243,U_242,U_241,U_240,U_239,U_238] :
      ( ? [U_237] :
          ( c_Natural_Oevaln(U_240,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_241),c_Com_Ovname_OLoc(U_238)),hAPP(U_239,U_241)),U_242,U_237)
          & U_243 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_237),c_Com_Ovname_OLoc(U_238)),hAPP(hAPP(c_Natural_Ogetlocs,U_241),U_238)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_238,U_239,U_240),U_241,U_242,U_243) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_243,U_242,U_241,U_240,U_239,U_238] :
      ( ( c_Natural_Oevaln(U_240,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_241),c_Com_Ovname_OLoc(U_238)),hAPP(U_239,U_241)),U_242,sK14(U_243,U_242,U_241,U_240,U_239,U_238))
        & U_243 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK14(U_243,U_242,U_241,U_240,U_239,U_238)),c_Com_Ovname_OLoc(U_238)),hAPP(hAPP(c_Natural_Ogetlocs,U_241),U_238)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_238,U_239,U_240),U_241,U_242,U_243) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_237,sK14(U_243,U_242,U_241,U_240,U_239,U_238))],[f_27_2]) ).

fof(f_27_4,plain,
    ( ! [U_238,U_239,U_240,U_241,U_242,U_243] :
        ( c_Natural_Oevaln(U_240,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_241),c_Com_Ovname_OLoc(U_238)),hAPP(U_239,U_241)),U_242,sK14(U_243,U_242,U_241,U_240,U_239,U_238))
        | ~ sP10(U_238,U_239,U_240,U_241,U_242,U_243) )
    & ! [U_238,U_239,U_240,U_241,U_242,U_243] :
        ( U_243 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK14(U_243,U_242,U_241,U_240,U_239,U_238)),c_Com_Ovname_OLoc(U_238)),hAPP(hAPP(c_Natural_Ogetlocs,U_241),U_238))
        | ~ sP10(U_238,U_239,U_240,U_241,U_242,U_243) )
    & ! [U_238,U_239,U_240,U_241,U_242,U_243] :
        ( sP10(U_238,U_239,U_240,U_241,U_242,U_243)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_238,U_239,U_240),U_241,U_242,U_243) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_27_3]) ).

cnf(f_27_5,plain,
    ( sP10(U_238,U_239,U_240,U_241,U_242,U_243)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_238,U_239,U_240),U_241,U_242,U_243) ),
    inference(clausify,[status(thm)],[f_27_4]) ).

cnf(f_27_6,plain,
    ( U_243 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK14(U_243,U_242,U_241,U_240,U_239,U_238)),c_Com_Ovname_OLoc(U_238)),hAPP(hAPP(c_Natural_Ogetlocs,U_241),U_238))
    | ~ sP10(U_238,U_239,U_240,U_241,U_242,U_243) ),
    inference(clausify,[status(thm)],[f_27_4]) ).

cnf(f_27_7,plain,
    ( c_Natural_Oevaln(U_240,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_241),c_Com_Ovname_OLoc(U_238)),hAPP(U_239,U_241)),U_242,sK14(U_243,U_242,U_241,U_240,U_239,U_238))
    | ~ sP10(U_238,U_239,U_240,U_241,U_242,U_243) ),
    inference(clausify,[status(thm)],[f_27_4]) ).

fof(f_28_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I43_J]) ).

fof(f_28_2,plain,
    ! [U_249,U_248,U_247,U_246,U_245,U_244] : c_Com_Ocom_OCall(U_244,U_245,U_246) != c_Com_Ocom_OLocal(U_247,U_248,U_249),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_247,U_245,U_248,U_246,U_244,U_249] : c_Com_Ocom_OCall(U_244,U_245,U_246) != c_Com_Ocom_OLocal(U_247,U_248,U_249),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    c_Com_Ocom_OCall(U_244,U_245,U_246) != c_Com_Ocom_OLocal(U_247,U_248,U_249),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I42_J]) ).

fof(f_29_2,plain,
    ! [U_255,U_254,U_253,U_252,U_251,U_250] : c_Com_Ocom_OLocal(U_250,U_251,U_252) != c_Com_Ocom_OCall(U_253,U_254,U_255),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_251,U_254,U_253,U_252,U_250,U_255] : c_Com_Ocom_OLocal(U_250,U_251,U_252) != c_Com_Ocom_OCall(U_253,U_254,U_255),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    c_Com_Ocom_OLocal(U_250,U_251,U_252) != c_Com_Ocom_OCall(U_253,U_254,U_255),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_1,plain,
    ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I40_J]) ).

fof(f_30_2,plain,
    ! [U_259,U_258,U_257,U_256] : c_Com_Ocom_OLocal(U_256,U_257,U_258) != hAPP(c_Com_Ocom_OBODY,U_259),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_256,U_258,U_257,U_259] : c_Com_Ocom_OLocal(U_256,U_257,U_258) != hAPP(c_Com_Ocom_OBODY,U_259),
    inference(definitional_conversion,[status(esa)],[f_30_2]) ).

cnf(f_30_4,plain,
    c_Com_Ocom_OLocal(U_256,U_257,U_258) != hAPP(c_Com_Ocom_OBODY,U_259),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_1,plain,
    ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I63_J]) ).

fof(f_31_2,plain,
    ! [U_263,U_262,U_261,U_260] : c_Com_Ocom_OCall(U_260,U_261,U_262) != hAPP(c_Com_Ocom_OBODY,U_263),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_261,U_260,U_262,U_263] : c_Com_Ocom_OCall(U_260,U_261,U_262) != hAPP(c_Com_Ocom_OBODY,U_263),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    c_Com_Ocom_OCall(U_260,U_261,U_262) != hAPP(c_Com_Ocom_OBODY,U_263),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I41_J]) ).

fof(f_32_2,plain,
    ! [U_267,U_266,U_265,U_264] : hAPP(c_Com_Ocom_OBODY,U_264) != c_Com_Ocom_OLocal(U_265,U_266,U_267),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_264,U_265,U_266,U_267] : hAPP(c_Com_Ocom_OBODY,U_264) != c_Com_Ocom_OLocal(U_265,U_266,U_267),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_264) != c_Com_Ocom_OLocal(U_265,U_266,U_267),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I62_J]) ).

fof(f_33_2,plain,
    ! [U_271,U_270,U_269,U_268] : hAPP(c_Com_Ocom_OBODY,U_268) != c_Com_Ocom_OCall(U_269,U_270,U_271),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_268,U_269,U_270,U_271] : hAPP(c_Com_Ocom_OBODY,U_268) != c_Com_Ocom_OCall(U_269,U_270,U_271),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_268) != c_Com_Ocom_OCall(U_269,U_270,U_271),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    inference(fof_nnf,[status(thm)],[fact_triple_Orecs]) ).

fof(f_34_2,plain,
    ! [U_277,U_276,U_275,U_274,U_273,U_272] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_272,U_273,U_274,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_272),U_275),U_276),U_277)) = hAPP(hAPP(hAPP(U_274,U_275),U_276),U_277),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ! [U_272,U_273,U_274,U_275,U_276,U_277] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_272,U_273,U_274,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_272),U_275),U_276),U_277)) = hAPP(hAPP(hAPP(U_274,U_275),U_276),U_277),
    inference(definitional_conversion,[status(esa)],[f_34_2]) ).

cnf(f_34_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(U_272,U_273,U_274,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_272),U_275),U_276),U_277)) = hAPP(hAPP(hAPP(U_274,U_275),U_276),U_277),
    inference(clausify,[status(thm)],[f_34_3]) ).

fof(f_35_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    inference(fof_nnf,[status(thm)],[fact_triple_Osimps_I2_J]) ).

fof(f_35_2,plain,
    ! [U_283,U_282,U_281,U_280,U_279,U_278] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_278,U_279,U_280,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_278),U_281),U_282),U_283)) = hAPP(hAPP(hAPP(U_280,U_281),U_282),U_283),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ! [U_279,U_278,U_280,U_281,U_282,U_283] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_278,U_279,U_280,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_278),U_281),U_282),U_283)) = hAPP(hAPP(hAPP(U_280,U_281),U_282),U_283),
    inference(definitional_conversion,[status(esa)],[f_35_2]) ).

cnf(f_35_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(U_278,U_279,U_280,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_278),U_281),U_282),U_283)) = hAPP(hAPP(hAPP(U_280,U_281),U_282),U_283),
    inference(clausify,[status(thm)],[f_35_3]) ).

fof(f_36_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
      ( ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2)
        | V_fun_2 != V_fun_H_2
        | V_pname_2 != V_pname_H_2
        | V_vname_2 != V_vname_H_2 )
      & ( ( V_fun_2 = V_fun_H_2
          & V_pname_2 = V_pname_H_2
          & V_vname_2 = V_vname_H_2 )
        | c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I7_J]) ).

fof(f_36_2,plain,
    ! [U_289,U_288,U_287,U_286,U_285,U_284] :
      ( ( c_Com_Ocom_OCall(U_284,U_285,U_286) = c_Com_Ocom_OCall(U_287,U_288,U_289)
        | U_286 != U_289
        | U_285 != U_288
        | U_284 != U_287 )
      & ( ( U_286 = U_289
          & U_285 = U_288
          & U_284 = U_287 )
        | c_Com_Ocom_OCall(U_284,U_285,U_286) != c_Com_Ocom_OCall(U_287,U_288,U_289) ) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ( ! [U_301,U_299,U_297,U_295,U_293,U_291] :
        ( c_Com_Ocom_OCall(U_291,U_293,U_295) = c_Com_Ocom_OCall(U_297,U_299,U_301)
        | U_295 != U_301
        | U_293 != U_299
        | U_291 != U_297 )
    & ! [U_300,U_298,U_296,U_294,U_292,U_290] :
        ( ( U_294 = U_300
          & U_292 = U_298
          & U_290 = U_296 )
        | c_Com_Ocom_OCall(U_290,U_292,U_294) != c_Com_Ocom_OCall(U_296,U_298,U_300) ) ),
    inference(miniscope,[status(thm)],[f_36_2]) ).

fof(f_36_4,plain,
    ( ! [U_294,U_300,U_290,U_296,U_292,U_298] :
        ( U_294 = U_300
        | ~ sP11(U_294,U_300,U_290,U_296,U_292,U_298) )
    & ! [U_294,U_300,U_290,U_296,U_292,U_298] :
        ( U_292 = U_298
        | ~ sP11(U_294,U_300,U_290,U_296,U_292,U_298) )
    & ! [U_294,U_300,U_290,U_296,U_292,U_298] :
        ( U_290 = U_296
        | ~ sP11(U_294,U_300,U_290,U_296,U_292,U_298) )
    & ! [U_295,U_297,U_293,U_291,U_299,U_301] :
        ( c_Com_Ocom_OCall(U_291,U_293,U_295) = c_Com_Ocom_OCall(U_297,U_299,U_301)
        | U_295 != U_301
        | U_293 != U_299
        | U_291 != U_297 )
    & ! [U_294,U_300,U_290,U_296,U_292,U_298] :
        ( sP11(U_294,U_300,U_290,U_296,U_292,U_298)
        | c_Com_Ocom_OCall(U_290,U_292,U_294) != c_Com_Ocom_OCall(U_296,U_298,U_300) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_36_3]) ).

cnf(f_36_5,plain,
    ( sP11(U_294,U_300,U_290,U_296,U_292,U_298)
    | c_Com_Ocom_OCall(U_290,U_292,U_294) != c_Com_Ocom_OCall(U_296,U_298,U_300) ),
    inference(clausify,[status(thm)],[f_36_4]) ).

cnf(f_36_6,plain,
    ( c_Com_Ocom_OCall(U_291,U_293,U_295) = c_Com_Ocom_OCall(U_297,U_299,U_301)
    | U_295 != U_301
    | U_293 != U_299
    | U_291 != U_297 ),
    inference(clausify,[status(thm)],[f_36_4]) ).

cnf(f_36_7,plain,
    ( U_290 = U_296
    | ~ sP11(U_294,U_300,U_290,U_296,U_292,U_298) ),
    inference(clausify,[status(thm)],[f_36_4]) ).

cnf(f_36_8,plain,
    ( U_292 = U_298
    | ~ sP11(U_294,U_300,U_290,U_296,U_292,U_298) ),
    inference(clausify,[status(thm)],[f_36_4]) ).

cnf(f_36_9,plain,
    ( U_294 = U_300
    | ~ sP11(U_294,U_300,U_290,U_296,U_292,U_298) ),
    inference(clausify,[status(thm)],[f_36_4]) ).

fof(f_37_1,plain,
    ! [V_pname_H_2,V_pname_2] :
      ( ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
        | V_pname_2 != V_pname_H_2 )
      & ( V_pname_2 = V_pname_H_2
        | hAPP(c_Com_Ocom_OBODY,V_pname_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J]) ).

fof(f_37_2,plain,
    ! [U_303,U_302] :
      ( ( hAPP(c_Com_Ocom_OBODY,U_302) = hAPP(c_Com_Ocom_OBODY,U_303)
        | U_302 != U_303 )
      & ( U_302 = U_303
        | hAPP(c_Com_Ocom_OBODY,U_302) != hAPP(c_Com_Ocom_OBODY,U_303) ) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ( ! [U_307,U_305] :
        ( hAPP(c_Com_Ocom_OBODY,U_305) = hAPP(c_Com_Ocom_OBODY,U_307)
        | U_305 != U_307 )
    & ! [U_306,U_304] :
        ( U_304 = U_306
        | hAPP(c_Com_Ocom_OBODY,U_304) != hAPP(c_Com_Ocom_OBODY,U_306) ) ),
    inference(miniscope,[status(thm)],[f_37_2]) ).

fof(f_37_4,plain,
    ( ! [U_307,U_305] :
        ( hAPP(c_Com_Ocom_OBODY,U_305) = hAPP(c_Com_Ocom_OBODY,U_307)
        | U_305 != U_307 )
    & ! [U_306,U_304] :
        ( U_304 = U_306
        | hAPP(c_Com_Ocom_OBODY,U_304) != hAPP(c_Com_Ocom_OBODY,U_306) ) ),
    inference(definitional_conversion,[status(esa)],[f_37_3]) ).

cnf(f_37_5,plain,
    ( U_304 = U_306
    | hAPP(c_Com_Ocom_OBODY,U_304) != hAPP(c_Com_Ocom_OBODY,U_306) ),
    inference(clausify,[status(thm)],[f_37_4]) ).

cnf(f_37_6,plain,
    ( hAPP(c_Com_Ocom_OBODY,U_305) = hAPP(c_Com_Ocom_OBODY,U_307)
    | U_305 != U_307 ),
    inference(clausify,[status(thm)],[f_37_4]) ).

fof(f_38_1,plain,
    ! [V_loc_H_2,V_loc_2] :
      ( ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
        | V_loc_2 != V_loc_H_2 )
      & ( V_loc_2 = V_loc_H_2
        | c_Com_Ovname_OLoc(V_loc_2) != c_Com_Ovname_OLoc(V_loc_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I2_J]) ).

fof(f_38_2,plain,
    ! [U_309,U_308] :
      ( ( c_Com_Ovname_OLoc(U_308) = c_Com_Ovname_OLoc(U_309)
        | U_308 != U_309 )
      & ( U_308 = U_309
        | c_Com_Ovname_OLoc(U_308) != c_Com_Ovname_OLoc(U_309) ) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ( ! [U_313,U_311] :
        ( c_Com_Ovname_OLoc(U_311) = c_Com_Ovname_OLoc(U_313)
        | U_311 != U_313 )
    & ! [U_312,U_310] :
        ( U_310 = U_312
        | c_Com_Ovname_OLoc(U_310) != c_Com_Ovname_OLoc(U_312) ) ),
    inference(miniscope,[status(thm)],[f_38_2]) ).

fof(f_38_4,plain,
    ( ! [U_311,U_313] :
        ( c_Com_Ovname_OLoc(U_311) = c_Com_Ovname_OLoc(U_313)
        | U_311 != U_313 )
    & ! [U_310,U_312] :
        ( U_310 = U_312
        | c_Com_Ovname_OLoc(U_310) != c_Com_Ovname_OLoc(U_312) ) ),
    inference(definitional_conversion,[status(esa)],[f_38_3]) ).

cnf(f_38_5,plain,
    ( U_310 = U_312
    | c_Com_Ovname_OLoc(U_310) != c_Com_Ovname_OLoc(U_312) ),
    inference(clausify,[status(thm)],[f_38_4]) ).

cnf(f_38_6,plain,
    ( c_Com_Ovname_OLoc(U_311) = c_Com_Ovname_OLoc(U_313)
    | U_311 != U_313 ),
    inference(clausify,[status(thm)],[f_38_4]) ).

fof(f_39_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
      ( ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
        | V_com_2 != V_com_H_2
        | V_fun_2 != V_fun_H_2
        | V_loc_2 != V_loc_H_2 )
      & ( ( V_com_2 = V_com_H_2
          & V_fun_2 = V_fun_H_2
          & V_loc_2 = V_loc_H_2 )
        | c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J]) ).

fof(f_39_2,plain,
    ! [U_319,U_318,U_317,U_316,U_315,U_314] :
      ( ( c_Com_Ocom_OLocal(U_314,U_315,U_316) = c_Com_Ocom_OLocal(U_317,U_318,U_319)
        | U_316 != U_319
        | U_315 != U_318
        | U_314 != U_317 )
      & ( ( U_316 = U_319
          & U_315 = U_318
          & U_314 = U_317 )
        | c_Com_Ocom_OLocal(U_314,U_315,U_316) != c_Com_Ocom_OLocal(U_317,U_318,U_319) ) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ( ! [U_331,U_329,U_327,U_325,U_323,U_321] :
        ( c_Com_Ocom_OLocal(U_321,U_323,U_325) = c_Com_Ocom_OLocal(U_327,U_329,U_331)
        | U_325 != U_331
        | U_323 != U_329
        | U_321 != U_327 )
    & ! [U_330,U_328,U_326,U_324,U_322,U_320] :
        ( ( U_324 = U_330
          & U_322 = U_328
          & U_320 = U_326 )
        | c_Com_Ocom_OLocal(U_320,U_322,U_324) != c_Com_Ocom_OLocal(U_326,U_328,U_330) ) ),
    inference(miniscope,[status(thm)],[f_39_2]) ).

fof(f_39_4,plain,
    ( ! [U_324,U_330,U_326,U_320,U_322,U_328] :
        ( U_324 = U_330
        | ~ sP12(U_324,U_330,U_326,U_320,U_322,U_328) )
    & ! [U_324,U_330,U_326,U_320,U_322,U_328] :
        ( U_322 = U_328
        | ~ sP12(U_324,U_330,U_326,U_320,U_322,U_328) )
    & ! [U_324,U_330,U_326,U_320,U_322,U_328] :
        ( U_320 = U_326
        | ~ sP12(U_324,U_330,U_326,U_320,U_322,U_328) )
    & ! [U_323,U_327,U_321,U_325,U_329,U_331] :
        ( c_Com_Ocom_OLocal(U_321,U_323,U_325) = c_Com_Ocom_OLocal(U_327,U_329,U_331)
        | U_325 != U_331
        | U_323 != U_329
        | U_321 != U_327 )
    & ! [U_324,U_330,U_326,U_320,U_322,U_328] :
        ( sP12(U_324,U_330,U_326,U_320,U_322,U_328)
        | c_Com_Ocom_OLocal(U_320,U_322,U_324) != c_Com_Ocom_OLocal(U_326,U_328,U_330) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_39_3]) ).

cnf(f_39_5,plain,
    ( sP12(U_324,U_330,U_326,U_320,U_322,U_328)
    | c_Com_Ocom_OLocal(U_320,U_322,U_324) != c_Com_Ocom_OLocal(U_326,U_328,U_330) ),
    inference(clausify,[status(thm)],[f_39_4]) ).

cnf(f_39_6,plain,
    ( c_Com_Ocom_OLocal(U_321,U_323,U_325) = c_Com_Ocom_OLocal(U_327,U_329,U_331)
    | U_325 != U_331
    | U_323 != U_329
    | U_321 != U_327 ),
    inference(clausify,[status(thm)],[f_39_4]) ).

cnf(f_39_7,plain,
    ( U_320 = U_326
    | ~ sP12(U_324,U_330,U_326,U_320,U_322,U_328) ),
    inference(clausify,[status(thm)],[f_39_4]) ).

cnf(f_39_8,plain,
    ( U_322 = U_328
    | ~ sP12(U_324,U_330,U_326,U_320,U_322,U_328) ),
    inference(clausify,[status(thm)],[f_39_4]) ).

cnf(f_39_9,plain,
    ( U_324 = U_330
    | ~ sP12(U_324,U_330,U_326,U_320,U_322,U_328) ),
    inference(clausify,[status(thm)],[f_39_4]) ).

fof(f_40_1,plain,
    ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2),
    inference(fof_nnf,[status(thm)],[fact_vname_Orecs_I2_J]) ).

fof(f_40_2,plain,
    ! [U_335,U_334,U_333,U_332] : c_Com_Ovname_Ovname__rec(U_332,U_333,U_334,c_Com_Ovname_OLoc(U_335)) = hAPP(U_334,U_335),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_335,U_332,U_334,U_333] : c_Com_Ovname_Ovname__rec(U_332,U_333,U_334,c_Com_Ovname_OLoc(U_335)) = hAPP(U_334,U_335),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    c_Com_Ovname_Ovname__rec(U_332,U_333,U_334,c_Com_Ovname_OLoc(U_335)) = hAPP(U_334,U_335),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_1,plain,
    ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2),
    inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I6_J]) ).

fof(f_41_2,plain,
    ! [U_339,U_338,U_337,U_336] : c_Com_Ovname_Ovname__case(U_336,U_337,U_338,c_Com_Ovname_OLoc(U_339)) = hAPP(U_338,U_339),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_336,U_338,U_337,U_339] : c_Com_Ovname_Ovname__case(U_336,U_337,U_338,c_Com_Ovname_OLoc(U_339)) = hAPP(U_338,U_339),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    c_Com_Ovname_Ovname__case(U_336,U_337,U_338,c_Com_Ovname_OLoc(U_339)) = hAPP(U_338,U_339),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_1,plain,
    ! [V_Q_2,V_pn_2,V_P_2,T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__0]) ).

fof(f_42_2,plain,
    ! [U_343,U_342,U_341,U_340] : c_Hoare__Mirabelle_Otriple__valid(U_340,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_340),U_341),hAPP(c_Com_Ocom_OBODY,U_342)),U_343)),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_340,U_341,U_342,U_343] : c_Hoare__Mirabelle_Otriple__valid(U_340,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_340),U_341),hAPP(c_Com_Ocom_OBODY,U_342)),U_343)),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    c_Hoare__Mirabelle_Otriple__valid(U_340,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_340),U_341),hAPP(c_Com_Ocom_OBODY,U_342)),U_343)),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_1,plain,
    ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))),
    inference(fof_nnf,[status(thm)],[fact_evalc_OAssign]) ).

fof(f_43_2,plain,
    ! [U_346,U_345,U_344] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_344,U_345)),U_346),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_346),U_344),hAPP(U_345,U_346)))),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_344,U_345,U_346] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_344,U_345)),U_346),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_346),U_344),hAPP(U_345,U_346)))),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_344,U_345)),U_346),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_346),U_344),hAPP(U_345,U_346)))),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [V_t_2,V_s_2,V_a_2,V_X_2] :
      ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I2_J]) ).

fof(f_44_2,plain,
    ! [U_350,U_349,U_348,U_347] :
      ( U_350 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_349),U_347),hAPP(U_348,U_349))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_347,U_348)),U_349),U_350)) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_347,U_348,U_349,U_350] :
      ( U_350 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_349),U_347),hAPP(U_348,U_349))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_347,U_348)),U_349),U_350)) ),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    ( U_350 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_349),U_347),hAPP(U_348,U_349))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_347,U_348)),U_349),U_350)) ),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_1,plain,
    ! [V_n_2,V_s_2,V_a_2,V_X_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2))),
    inference(fof_nnf,[status(thm)],[fact_evaln_OAssign]) ).

fof(f_45_2,plain,
    ! [U_354,U_353,U_352,U_351] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_351,U_352),U_353,U_354,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_353),U_351),hAPP(U_352,U_353))),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_351,U_352,U_353,U_354] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_351,U_352),U_353,U_354,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_353),U_351),hAPP(U_352,U_353))),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(U_351,U_352),U_353,U_354,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_353),U_351),hAPP(U_352,U_353))),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_1,plain,
    ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
      ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I2_J]) ).

fof(f_46_2,plain,
    ! [U_359,U_358,U_357,U_356,U_355] :
      ( U_359 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_357),U_355),hAPP(U_356,U_357))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_355,U_356),U_357,U_358,U_359) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_355,U_356,U_357,U_358,U_359] :
      ( U_359 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_357),U_355),hAPP(U_356,U_357))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_355,U_356),U_357,U_358,U_359) ),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    ( U_359 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_357),U_355),hAPP(U_356,U_357))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_355,U_356),U_357,U_358,U_359) ),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_1,plain,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_47_2,plain,
    ! [U_360] : U_360 != hAPP(c_Nat_OSuc,U_360),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_360] : U_360 != hAPP(c_Nat_OSuc,U_360),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    U_360 != hAPP(c_Nat_OSuc,U_360),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_48_2,plain,
    ! [U_361] : hAPP(c_Nat_OSuc,U_361) != U_361,
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_361] : hAPP(c_Nat_OSuc,U_361) != U_361,
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    hAPP(c_Nat_OSuc,U_361) != U_361,
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_1,plain,
    ! [V_nat_H_2,V_nat_2] :
      ( ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
        | V_nat_2 != V_nat_H_2 )
      & ( V_nat_2 = V_nat_H_2
        | hAPP(c_Nat_OSuc,V_nat_2) != hAPP(c_Nat_OSuc,V_nat_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat_Oinject]) ).

fof(f_49_2,plain,
    ! [U_363,U_362] :
      ( ( hAPP(c_Nat_OSuc,U_362) = hAPP(c_Nat_OSuc,U_363)
        | U_362 != U_363 )
      & ( U_362 = U_363
        | hAPP(c_Nat_OSuc,U_362) != hAPP(c_Nat_OSuc,U_363) ) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ( ! [U_367,U_365] :
        ( hAPP(c_Nat_OSuc,U_365) = hAPP(c_Nat_OSuc,U_367)
        | U_365 != U_367 )
    & ! [U_366,U_364] :
        ( U_364 = U_366
        | hAPP(c_Nat_OSuc,U_364) != hAPP(c_Nat_OSuc,U_366) ) ),
    inference(miniscope,[status(thm)],[f_49_2]) ).

fof(f_49_4,plain,
    ( ! [U_365,U_367] :
        ( hAPP(c_Nat_OSuc,U_365) = hAPP(c_Nat_OSuc,U_367)
        | U_365 != U_367 )
    & ! [U_366,U_364] :
        ( U_364 = U_366
        | hAPP(c_Nat_OSuc,U_364) != hAPP(c_Nat_OSuc,U_366) ) ),
    inference(definitional_conversion,[status(esa)],[f_49_3]) ).

cnf(f_49_5,plain,
    ( U_364 = U_366
    | hAPP(c_Nat_OSuc,U_364) != hAPP(c_Nat_OSuc,U_366) ),
    inference(clausify,[status(thm)],[f_49_4]) ).

cnf(f_49_6,plain,
    ( hAPP(c_Nat_OSuc,U_365) = hAPP(c_Nat_OSuc,U_367)
    | U_365 != U_367 ),
    inference(clausify,[status(thm)],[f_49_4]) ).

fof(f_50_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | hAPP(c_Nat_OSuc,V_x) != hAPP(c_Nat_OSuc,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__inject]) ).

fof(f_50_2,plain,
    ! [U_369,U_368] :
      ( U_368 = U_369
      | hAPP(c_Nat_OSuc,U_368) != hAPP(c_Nat_OSuc,U_369) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_369,U_368] :
      ( U_368 = U_369
      | hAPP(c_Nat_OSuc,U_368) != hAPP(c_Nat_OSuc,U_369) ),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( U_368 = U_369
    | hAPP(c_Nat_OSuc,U_368) != hAPP(c_Nat_OSuc,U_369) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ! [V_a_2,V_P_2,V_X_2] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2)))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I8_J]) ).

fof(f_51_2,plain,
    ! [U_372,U_371,U_370] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_371)))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_370,U_371,U_372))) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_372,U_371] :
      ( ! [U_370] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_370,U_371,U_372)))
      | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_371))) ),
    inference(miniscope,[status(thm)],[f_51_2]) ).

fof(f_51_4,plain,
    ! [U_370,U_371,U_372] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_370,U_371,U_372)))
      | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_371))) ),
    inference(definitional_conversion,[status(esa)],[f_51_3]) ).

cnf(f_51_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_370,U_371,U_372)))
    | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_371))) ),
    inference(clausify,[status(thm)],[f_51_4]) ).

fof(f_52_1,plain,
    ! [V_c_2,V_a_2,V_Y_2] :
      ( hBOOL(hAPP(c_Com_OWT,V_c_2))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I3_J]) ).

fof(f_52_2,plain,
    ! [U_375,U_374,U_373] :
      ( hBOOL(hAPP(c_Com_OWT,U_375))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_373,U_374,U_375))) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_375] :
      ( ! [U_374,U_373] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_373,U_374,U_375)))
      | hBOOL(hAPP(c_Com_OWT,U_375)) ),
    inference(miniscope,[status(thm)],[f_52_2]) ).

fof(f_52_4,plain,
    ! [U_373,U_374,U_375] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_373,U_374,U_375)))
      | hBOOL(hAPP(c_Com_OWT,U_375)) ),
    inference(definitional_conversion,[status(esa)],[f_52_3]) ).

cnf(f_52_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_373,U_374,U_375)))
    | hBOOL(hAPP(c_Com_OWT,U_375)) ),
    inference(clausify,[status(thm)],[f_52_4]) ).

fof(f_53_1,plain,
    ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
      ( ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
        | V_fun_2 != V_fun_H_2
        | V_vname_2 != V_vname_H_2 )
      & ( ( V_fun_2 = V_fun_H_2
          & V_vname_2 = V_vname_H_2 )
        | c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I1_J]) ).

fof(f_53_2,plain,
    ! [U_379,U_378,U_377,U_376] :
      ( ( c_Com_Ocom_OAss(U_376,U_377) = c_Com_Ocom_OAss(U_378,U_379)
        | U_377 != U_379
        | U_376 != U_378 )
      & ( ( U_377 = U_379
          & U_376 = U_378 )
        | c_Com_Ocom_OAss(U_376,U_377) != c_Com_Ocom_OAss(U_378,U_379) ) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ( ! [U_387,U_385,U_383,U_381] :
        ( c_Com_Ocom_OAss(U_381,U_383) = c_Com_Ocom_OAss(U_385,U_387)
        | U_383 != U_387
        | U_381 != U_385 )
    & ! [U_386,U_384,U_382,U_380] :
        ( ( U_382 = U_386
          & U_380 = U_384 )
        | c_Com_Ocom_OAss(U_380,U_382) != c_Com_Ocom_OAss(U_384,U_386) ) ),
    inference(miniscope,[status(thm)],[f_53_2]) ).

fof(f_53_4,plain,
    ( ! [U_386,U_382,U_380,U_384] :
        ( U_382 = U_386
        | ~ sP13(U_386,U_382,U_380,U_384) )
    & ! [U_386,U_382,U_380,U_384] :
        ( U_380 = U_384
        | ~ sP13(U_386,U_382,U_380,U_384) )
    & ! [U_387,U_385,U_381,U_383] :
        ( c_Com_Ocom_OAss(U_381,U_383) = c_Com_Ocom_OAss(U_385,U_387)
        | U_383 != U_387
        | U_381 != U_385 )
    & ! [U_386,U_382,U_380,U_384] :
        ( sP13(U_386,U_382,U_380,U_384)
        | c_Com_Ocom_OAss(U_380,U_382) != c_Com_Ocom_OAss(U_384,U_386) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_53_3]) ).

cnf(f_53_5,plain,
    ( sP13(U_386,U_382,U_380,U_384)
    | c_Com_Ocom_OAss(U_380,U_382) != c_Com_Ocom_OAss(U_384,U_386) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_6,plain,
    ( c_Com_Ocom_OAss(U_381,U_383) = c_Com_Ocom_OAss(U_385,U_387)
    | U_383 != U_387
    | U_381 != U_385 ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_7,plain,
    ( U_380 = U_384
    | ~ sP13(U_386,U_382,U_380,U_384) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_8,plain,
    ( U_382 = U_386
    | ~ sP13(U_386,U_382,U_380,U_384) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

fof(f_54_1,plain,
    ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I2_J]) ).

fof(f_54_2,plain,
    ! [U_389,U_388] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_388,U_389))),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_389,U_388] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_388,U_389))),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_388,U_389))),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))),
    inference(fof_nnf,[status(thm)],[fact_WT_OAssign]) ).

fof(f_55_2,plain,
    ! [U_391,U_390] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_390,U_391))),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_390,U_391] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_390,U_391))),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_390,U_391))),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_1,plain,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(f_56_2,plain,
    ! [U_392] : hAPP(c_Nat_OSuc,U_392) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_392] : hAPP(c_Nat_OSuc,U_392) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    hAPP(c_Nat_OSuc,U_392) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    inference(fof_nnf,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(f_57_2,plain,
    ! [U_393] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_393),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ! [U_393] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_393),
    inference(definitional_conversion,[status(esa)],[f_57_2]) ).

cnf(f_57_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_393),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_1,plain,
    ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(f_58_2,plain,
    ! [U_394] : hAPP(c_Nat_OSuc,U_394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_394] : hAPP(c_Nat_OSuc,U_394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    hAPP(c_Nat_OSuc,U_394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_1,plain,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_Suc__not__Zero]) ).

fof(f_59_2,plain,
    ! [U_395] : hAPP(c_Nat_OSuc,U_395) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_395] : hAPP(c_Nat_OSuc,U_395) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    hAPP(c_Nat_OSuc,U_395) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_1,plain,
    ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
    inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(f_60_2,plain,
    ! [U_396] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_396),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_396] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_396),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_396),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    inference(fof_nnf,[status(thm)],[fact_Zero__not__Suc]) ).

fof(f_61_2,plain,
    ! [U_397] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_397),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ! [U_397] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_397),
    inference(definitional_conversion,[status(esa)],[f_61_2]) ).

cnf(f_61_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_397),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_1,plain,
    ! [V_a1_2,V_a3_2,V_a2_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
        | ~ hBOOL(hAPP(c_Com_OWT,V_a1_2)) )
      & ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I3_J]) ).

fof(f_62_2,plain,
    ! [U_400,U_399,U_398] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_398,U_399,U_400)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_400)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_400))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_398,U_399,U_400))) ) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ( ! [U_406] :
        ( ! [U_404,U_402] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_402,U_404,U_406)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_406)) )
    & ! [U_405] :
        ( ! [U_403,U_401] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_401,U_403,U_405)))
        | hBOOL(hAPP(c_Com_OWT,U_405)) ) ),
    inference(miniscope,[status(thm)],[f_62_2]) ).

fof(f_62_4,plain,
    ( ! [U_402,U_406,U_404] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_402,U_404,U_406)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_406)) )
    & ! [U_405,U_403,U_401] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_401,U_403,U_405)))
        | hBOOL(hAPP(c_Com_OWT,U_405)) ) ),
    inference(definitional_conversion,[status(esa)],[f_62_3]) ).

cnf(f_62_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_401,U_403,U_405)))
    | hBOOL(hAPP(c_Com_OWT,U_405)) ),
    inference(clausify,[status(thm)],[f_62_4]) ).

cnf(f_62_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_402,U_404,U_406)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_406)) ),
    inference(clausify,[status(thm)],[f_62_4]) ).

fof(f_63_1,plain,
    ! [V_a_2,V_Y_2,V_c_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_WT_OLocal]) ).

fof(f_63_2,plain,
    ! [U_409,U_408,U_407] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_408,U_409,U_407)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_407)) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_407,U_408,U_409] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_408,U_409,U_407)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_407)) ),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_408,U_409,U_407)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_407)) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_1,plain,
    ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I30_J]) ).

fof(f_64_2,plain,
    ! [U_412,U_411,U_410] : c_Com_Ocom_OAss(U_410,U_411) != hAPP(c_Com_Ocom_OBODY,U_412),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_410,U_411,U_412] : c_Com_Ocom_OAss(U_410,U_411) != hAPP(c_Com_Ocom_OBODY,U_412),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    c_Com_Ocom_OAss(U_410,U_411) != hAPP(c_Com_Ocom_OBODY,U_412),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I31_J]) ).

fof(f_65_2,plain,
    ! [U_415,U_414,U_413] : hAPP(c_Com_Ocom_OBODY,U_413) != c_Com_Ocom_OAss(U_414,U_415),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_413,U_414,U_415] : hAPP(c_Com_Ocom_OBODY,U_413) != c_Com_Ocom_OAss(U_414,U_415),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_413) != c_Com_Ocom_OAss(U_414,U_415),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I32_J]) ).

fof(f_66_2,plain,
    ! [U_420,U_419,U_418,U_417,U_416] : c_Com_Ocom_OAss(U_416,U_417) != c_Com_Ocom_OCall(U_418,U_419,U_420),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_418,U_419,U_417,U_420,U_416] : c_Com_Ocom_OAss(U_416,U_417) != c_Com_Ocom_OCall(U_418,U_419,U_420),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    c_Com_Ocom_OAss(U_416,U_417) != c_Com_Ocom_OCall(U_418,U_419,U_420),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I22_J]) ).

fof(f_67_2,plain,
    ! [U_425,U_424,U_423,U_422,U_421] : c_Com_Ocom_OAss(U_421,U_422) != c_Com_Ocom_OLocal(U_423,U_424,U_425),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_421,U_422,U_423,U_424,U_425] : c_Com_Ocom_OAss(U_421,U_422) != c_Com_Ocom_OLocal(U_423,U_424,U_425),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    c_Com_Ocom_OAss(U_421,U_422) != c_Com_Ocom_OLocal(U_423,U_424,U_425),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_1,plain,
    ! [V_fun_2,V_vname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I33_J]) ).

fof(f_68_2,plain,
    ! [U_430,U_429,U_428,U_427,U_426] : c_Com_Ocom_OCall(U_426,U_427,U_428) != c_Com_Ocom_OAss(U_429,U_430),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_426,U_427,U_428,U_429,U_430] : c_Com_Ocom_OCall(U_426,U_427,U_428) != c_Com_Ocom_OAss(U_429,U_430),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    c_Com_Ocom_OCall(U_426,U_427,U_428) != c_Com_Ocom_OAss(U_429,U_430),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I23_J]) ).

fof(f_69_2,plain,
    ! [U_435,U_434,U_433,U_432,U_431] : c_Com_Ocom_OLocal(U_431,U_432,U_433) != c_Com_Ocom_OAss(U_434,U_435),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_432,U_431,U_433,U_434,U_435] : c_Com_Ocom_OLocal(U_431,U_432,U_433) != c_Com_Ocom_OAss(U_434,U_435),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    c_Com_Ocom_OLocal(U_431,U_432,U_433) != c_Com_Ocom_OAss(U_434,U_435),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_1,plain,
    ! [V_a3_2,V_a1_2,V_a2_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) )
      & ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2)))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I8_J]) ).

fof(f_70_2,plain,
    ! [U_438,U_437,U_436] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_436,U_437,U_438)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_437))) )
      & ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_437)))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_436,U_437,U_438))) ) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ( ! [U_444,U_442] :
        ( ! [U_440] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_440,U_442,U_444)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_442))) )
    & ! [U_443,U_441] :
        ( ! [U_439] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_439,U_441,U_443)))
        | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_441))) ) ),
    inference(miniscope,[status(thm)],[f_70_2]) ).

fof(f_70_4,plain,
    ( ! [U_444,U_440,U_442] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_440,U_442,U_444)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_442))) )
    & ! [U_439,U_441,U_443] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_439,U_441,U_443)))
        | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_441))) ) ),
    inference(definitional_conversion,[status(esa)],[f_70_3]) ).

cnf(f_70_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_439,U_441,U_443)))
    | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_441))) ),
    inference(clausify,[status(thm)],[f_70_4]) ).

cnf(f_70_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_440,U_442,U_444)))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_442))) ),
    inference(clausify,[status(thm)],[f_70_4]) ).

fof(f_71_1,plain,
    ! [V_a_2,V_X_2,V_pn_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) ),
    inference(fof_nnf,[status(thm)],[fact_WT_OCall]) ).

fof(f_71_2,plain,
    ! [U_447,U_446,U_445] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_446,U_445,U_447)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_445))) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_445,U_446,U_447] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_446,U_445,U_447)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_445))) ),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_446,U_445,U_447)))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_445))) ),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_1,plain,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_a1_2,V_a2_2),V_a3_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2))),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I2_J]) ).

fof(f_72_2,plain,
    ! [U_451,U_450,U_449,U_448] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_448,U_449),U_450,U_451,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_450),U_448),hAPP(U_449,U_450))),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_448,U_449,U_450,U_451] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_448,U_449),U_450,U_451,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_450),U_448),hAPP(U_449,U_450))),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(U_448,U_449),U_450,U_451,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_450),U_448),hAPP(U_449,U_450))),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_1,plain,
    ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I2_J]) ).

fof(f_73_2,plain,
    ! [U_454,U_453,U_452] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_452,U_453)),U_454),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_454),U_452),hAPP(U_453,U_454)))),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_452,U_453,U_454] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_452,U_453)),U_454),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_454),U_452),hAPP(U_453,U_454)))),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_452,U_453)),U_454),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_454),U_452),hAPP(U_453,U_454)))),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_triple_Osize_I1_J]) ).

fof(f_74_2,plain,
    ! [U_459,U_458,U_457,U_456,U_455] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_455,U_456,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_455),U_457),U_458),U_459)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_455,U_456,U_457,U_458,U_459] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_455,U_456,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_455),U_457),U_458),U_459)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(U_455,U_456,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_455),U_457),U_458),U_459)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_1,plain,
    ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_vname_Osize_I2_J]) ).

fof(f_75_2,plain,
    ! [U_460] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(U_460)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_460] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(U_460)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(U_460)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_triple_Osize_I2_J]) ).

fof(f_76_2,plain,
    ! [U_464,U_463,U_462,U_461] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_461)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_461),U_462),U_463),U_464)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_461,U_462,U_463,U_464] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_461)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_461),U_462),U_463),U_464)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_461)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_461),U_462),U_463),U_464)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_1,plain,
    ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_vname_Osize_I4_J]) ).

fof(f_77_2,plain,
    ! [U_465] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(U_465)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_465] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(U_465)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(U_465)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2),
    inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I5_J]) ).

fof(f_78_2,plain,
    ! [U_469,U_468,U_467,U_466] : c_Com_Ovname_Ovname__case(U_466,U_467,U_468,c_Com_Ovname_OGlb(U_469)) = hAPP(U_467,U_469),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_466,U_467,U_468,U_469] : c_Com_Ovname_Ovname__case(U_466,U_467,U_468,c_Com_Ovname_OGlb(U_469)) = hAPP(U_467,U_469),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    c_Com_Ovname_Ovname__case(U_466,U_467,U_468,c_Com_Ovname_OGlb(U_469)) = hAPP(U_467,U_469),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2),
    inference(fof_nnf,[status(thm)],[fact_vname_Orecs_I1_J]) ).

fof(f_79_2,plain,
    ! [U_473,U_472,U_471,U_470] : c_Com_Ovname_Ovname__rec(U_470,U_471,U_472,c_Com_Ovname_OGlb(U_473)) = hAPP(U_471,U_473),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_470,U_471,U_472,U_473] : c_Com_Ovname_Ovname__rec(U_470,U_471,U_472,c_Com_Ovname_OGlb(U_473)) = hAPP(U_471,U_473),
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    c_Com_Ovname_Ovname__rec(U_470,U_471,U_472,c_Com_Ovname_OGlb(U_473)) = hAPP(U_471,U_473),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_1,plain,
    ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I8_J]) ).

fof(f_80_2,plain,
    ! [U_476,U_475,U_474] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_474,U_475,U_476)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_474,U_475,U_476] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_474,U_475,U_476)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_474,U_475,U_476)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I2_J]) ).

fof(f_81_2,plain,
    ! [U_478,U_477] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_477,U_478)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_477,U_478] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_477,U_478)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_477,U_478)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I7_J]) ).

fof(f_82_2,plain,
    ! [U_479] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_479)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_479] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_479)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_479)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I16_J]) ).

fof(f_83_2,plain,
    ! [U_482,U_481,U_480] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_480,U_481,U_482)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_480,U_481,U_482] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_480,U_481,U_482)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_480,U_481,U_482)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I10_J]) ).

fof(f_84_2,plain,
    ! [U_484,U_483] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_483,U_484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_483,U_484] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_483,U_484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_483,U_484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_1,plain,
    ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I15_J]) ).

fof(f_85_2,plain,
    ! [U_485] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_485)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_485] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_485)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_485)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_1,plain,
    ! [V_glb_H_2,V_glb_2] :
      ( ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
        | V_glb_2 != V_glb_H_2 )
      & ( V_glb_2 = V_glb_H_2
        | c_Com_Ovname_OGlb(V_glb_2) != c_Com_Ovname_OGlb(V_glb_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I1_J]) ).

fof(f_86_2,plain,
    ! [U_487,U_486] :
      ( ( c_Com_Ovname_OGlb(U_486) = c_Com_Ovname_OGlb(U_487)
        | U_486 != U_487 )
      & ( U_486 = U_487
        | c_Com_Ovname_OGlb(U_486) != c_Com_Ovname_OGlb(U_487) ) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ( ! [U_491,U_489] :
        ( c_Com_Ovname_OGlb(U_489) = c_Com_Ovname_OGlb(U_491)
        | U_489 != U_491 )
    & ! [U_490,U_488] :
        ( U_488 = U_490
        | c_Com_Ovname_OGlb(U_488) != c_Com_Ovname_OGlb(U_490) ) ),
    inference(miniscope,[status(thm)],[f_86_2]) ).

fof(f_86_4,plain,
    ( ! [U_489,U_491] :
        ( c_Com_Ovname_OGlb(U_489) = c_Com_Ovname_OGlb(U_491)
        | U_489 != U_491 )
    & ! [U_490,U_488] :
        ( U_488 = U_490
        | c_Com_Ovname_OGlb(U_488) != c_Com_Ovname_OGlb(U_490) ) ),
    inference(definitional_conversion,[status(esa)],[f_86_3]) ).

cnf(f_86_5,plain,
    ( U_488 = U_490
    | c_Com_Ovname_OGlb(U_488) != c_Com_Ovname_OGlb(U_490) ),
    inference(clausify,[status(thm)],[f_86_4]) ).

cnf(f_86_6,plain,
    ( c_Com_Ovname_OGlb(U_489) = c_Com_Ovname_OGlb(U_491)
    | U_489 != U_491 ),
    inference(clausify,[status(thm)],[f_86_4]) ).

fof(f_87_1,plain,
    ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_vname_Osize_I3_J]) ).

fof(f_87_2,plain,
    ! [U_492] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(U_492)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_492] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(U_492)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(U_492)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_1,plain,
    ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_vname_Osize_I1_J]) ).

fof(f_88_2,plain,
    ! [U_493] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(U_493)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_493] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(U_493)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(U_493)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_1,plain,
    ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H),
    inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I3_J]) ).

fof(f_89_2,plain,
    ! [U_495,U_494] : c_Com_Ovname_OGlb(U_494) != c_Com_Ovname_OLoc(U_495),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_494,U_495] : c_Com_Ovname_OGlb(U_494) != c_Com_Ovname_OLoc(U_495),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    c_Com_Ovname_OGlb(U_494) != c_Com_Ovname_OLoc(U_495),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb),
    inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I4_J]) ).

fof(f_90_2,plain,
    ! [U_497,U_496] : c_Com_Ovname_OLoc(U_496) != c_Com_Ovname_OGlb(U_497),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_496,U_497] : c_Com_Ovname_OLoc(U_496) != c_Com_Ovname_OGlb(U_497),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    c_Com_Ovname_OLoc(U_496) != c_Com_Ovname_OGlb(U_497),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I11_J]) ).

fof(f_91_2,plain,
    ! [U_500,U_499,U_498] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_498,U_499,U_500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_500)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_498,U_499,U_500] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_498,U_499,U_500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_500)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_498,U_499,U_500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_500)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I3_J]) ).

fof(f_92_2,plain,
    ! [U_503,U_502,U_501] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_501,U_502,U_503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_503)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_501,U_502,U_503] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_501,U_502,U_503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_503)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_501,U_502,U_503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_503)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [V_pn] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
      | hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(fof_nnf,[status(thm)],[fact_WT_OBody]) ).

fof(f_93_2,plain,
    ! [U_504] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_504)))
      | hAPP(c_Com_Obody,U_504) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_504] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_504)))
      | hAPP(c_Com_Obody,U_504) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_504)))
    | hAPP(c_Com_Obody,U_504) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_1,plain,
    ! [V_a_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
        | ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) )
      & ( ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I7_J]) ).

fof(f_94_2,plain,
    ! [U_507] :
      ( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_507)))
        | ! [U_506] : hAPP(c_Com_Obody,U_507) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_506) )
      & ( ? [U_505] : hAPP(c_Com_Obody,U_507) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_505)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_507))) ) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ( ! [U_509] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_509)))
        | ! [U_506] : hAPP(c_Com_Obody,U_509) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_506) )
    & ! [U_508] :
        ( ? [U_505] : hAPP(c_Com_Obody,U_508) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_505)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_508))) ) ),
    inference(miniscope,[status(thm)],[f_94_2]) ).

fof(f_94_4,plain,
    ( ! [U_509] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_509)))
        | ! [U_506] : hAPP(c_Com_Obody,U_509) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_506) )
    & ! [U_508] :
        ( hAPP(c_Com_Obody,U_508) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK15(U_508))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_508))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_505,sK15(U_508))],[f_94_3]) ).

fof(f_94_5,plain,
    ( ! [U_506,U_509] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_509)))
        | hAPP(c_Com_Obody,U_509) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_506) )
    & ! [U_508] :
        ( hAPP(c_Com_Obody,U_508) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK15(U_508))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_508))) ) ),
    inference(definitional_conversion,[status(esa)],[f_94_4]) ).

cnf(f_94_6,plain,
    ( hAPP(c_Com_Obody,U_508) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK15(U_508))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_508))) ),
    inference(clausify,[status(thm)],[f_94_5]) ).

cnf(f_94_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_509)))
    | hAPP(c_Com_Obody,U_509) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_506) ),
    inference(clausify,[status(thm)],[f_94_5]) ).

fof(f_95_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
          | c_Groups_Ozero__class_Ozero(T_b) != V_x_2 ) )
      | ~ class_Groups_Ozero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).

fof(f_95_2,plain,
    ! [U_511,U_510] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_510) = U_511
          | U_511 != c_Groups_Ozero__class_Ozero(U_510) )
        & ( U_511 = c_Groups_Ozero__class_Ozero(U_510)
          | c_Groups_Ozero__class_Ozero(U_510) != U_511 ) )
      | ~ class_Groups_Ozero(U_510) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ( ! [U_510,U_511] :
        ( c_Groups_Ozero__class_Ozero(U_510) = U_511
        | U_511 != c_Groups_Ozero__class_Ozero(U_510)
        | ~ sP14(U_510,U_511) )
    & ! [U_510,U_511] :
        ( U_511 = c_Groups_Ozero__class_Ozero(U_510)
        | c_Groups_Ozero__class_Ozero(U_510) != U_511
        | ~ sP14(U_510,U_511) )
    & ! [U_510,U_511] :
        ( sP14(U_510,U_511)
        | ~ class_Groups_Ozero(U_510) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_95_2]) ).

cnf(f_95_4,plain,
    ( sP14(U_510,U_511)
    | ~ class_Groups_Ozero(U_510) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_5,plain,
    ( U_511 = c_Groups_Ozero__class_Ozero(U_510)
    | c_Groups_Ozero__class_Ozero(U_510) != U_511
    | ~ sP14(U_510,U_511) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_510) = U_511
    | U_511 != c_Groups_Ozero__class_Ozero(U_510)
    | ~ sP14(U_510,U_511) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [V_i_2,V_n_2,V_inc_2,T_b] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).

fof(f_96_2,plain,
    ! [U_515,U_514,U_513,U_512] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_512,U_513,hAPP(c_Nat_OSuc,U_514),U_515) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_512,U_513,U_514,hAPP(U_513,U_515))
      | ~ class_Rings_Osemiring__1(U_512) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_514,U_512,U_513,U_515] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_512,U_513,hAPP(c_Nat_OSuc,U_514),U_515) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_512,U_513,U_514,hAPP(U_513,U_515))
      | ~ class_Rings_Osemiring__1(U_512) ),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_512,U_513,hAPP(c_Nat_OSuc,U_514),U_515) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_512,U_513,U_514,hAPP(U_513,U_515))
    | ~ class_Rings_Osemiring__1(U_512) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I9_J]) ).

fof(f_97_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_97_1]) ).

cnf(f_97_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I1_J]) ).

fof(f_98_2,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_98_1]) ).

cnf(f_98_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    ! [V_i_2,V_inc_2,T_b] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).

fof(f_99_2,plain,
    ! [U_518,U_517,U_516] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_516,U_517,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_518) = U_518
      | ~ class_Rings_Osemiring__1(U_516) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_516,U_517,U_518] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_516,U_517,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_518) = U_518
      | ~ class_Rings_Osemiring__1(U_516) ),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_516,U_517,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_518) = U_518
    | ~ class_Rings_Osemiring__1(U_516) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    ! [V_t,V_s,V_c] :
      ( ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__evaln]) ).

fof(f_100_2,plain,
    ! [U_522,U_521,U_520] :
      ( ? [U_519] : c_Natural_Oevaln(U_520,U_521,U_519,U_522)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_520),U_521),U_522)) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_522,U_521,U_520] :
      ( c_Natural_Oevaln(U_520,U_521,sK16(U_522,U_521,U_520),U_522)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_520),U_521),U_522)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_519,sK16(U_522,U_521,U_520))],[f_100_2]) ).

fof(f_100_4,plain,
    ! [U_520,U_521,U_522] :
      ( c_Natural_Oevaln(U_520,U_521,sK16(U_522,U_521,U_520),U_522)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_520),U_521),U_522)) ),
    inference(definitional_conversion,[status(esa)],[f_100_3]) ).

cnf(f_100_5,plain,
    ( c_Natural_Oevaln(U_520,U_521,sK16(U_522,U_521,U_520),U_522)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_520),U_521),U_522)) ),
    inference(clausify,[status(thm)],[f_100_4]) ).

fof(f_101_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))),
    inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).

fof(f_101_2,plain,
    ! [U_523] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_523))),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_523] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_523))),
    inference(definitional_conversion,[status(esa)],[f_101_2]) ).

cnf(f_101_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_523))),
    inference(clausify,[status(thm)],[f_101_3]) ).

fof(f_102_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).

fof(f_102_2,plain,
    ! [U_524] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_524),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ! [U_524] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_524),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_102_2]) ).

cnf(f_102_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_524),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_102_3]) ).

fof(f_103_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).

fof(f_103_2,plain,
    ! [U_526,U_525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_525)),hAPP(c_Nat_OSuc,U_526)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_525),U_526)) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ! [U_525,U_526] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_525)),hAPP(c_Nat_OSuc,U_526)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_525),U_526)) ),
    inference(definitional_conversion,[status(esa)],[f_103_2]) ).

cnf(f_103_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_525)),hAPP(c_Nat_OSuc,U_526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_525),U_526)) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))),
    inference(fof_nnf,[status(thm)],[fact_lessI]) ).

fof(f_104_2,plain,
    ! [U_527] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_527),hAPP(c_Nat_OSuc,U_527))),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_527] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_527),hAPP(c_Nat_OSuc,U_527))),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_527),hAPP(c_Nat_OSuc,U_527))),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    ! [V_t,V_n,V_s] :
      ( V_t = V_s
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I1_J]) ).

fof(f_105_2,plain,
    ! [U_530,U_529,U_528] :
      ( U_530 = U_528
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_528,U_529,U_530) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_528,U_530,U_529] :
      ( U_530 = U_528
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_528,U_529,U_530) ),
    inference(definitional_conversion,[status(esa)],[f_105_2]) ).

cnf(f_105_4,plain,
    ( U_530 = U_528
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_528,U_529,U_530) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_1,plain,
    ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s),
    inference(fof_nnf,[status(thm)],[fact_evaln_OSkip]) ).

fof(f_106_2,plain,
    ! [U_532,U_531] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_531,U_532,U_531),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_532,U_531] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_531,U_532,U_531),
    inference(definitional_conversion,[status(esa)],[f_106_2]) ).

cnf(f_106_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_531,U_532,U_531),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_1,plain,
    ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
    inference(fof_nnf,[status(thm)],[fact_evalc_OSkip]) ).

fof(f_107_2,plain,
    ! [U_533] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_533),U_533)),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_533] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_533),U_533)),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_533),U_533)),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_1,plain,
    ! [V_t,V_s] :
      ( V_t = V_s
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I1_J]) ).

fof(f_108_2,plain,
    ! [U_535,U_534] :
      ( U_535 = U_534
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_534),U_535)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_534,U_535] :
      ( U_535 = U_534
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_534),U_535)) ),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_4,plain,
    ( U_535 = U_534
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_534),U_535)) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
      | ~ class_Groups_Oab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_109_2,plain,
    ! [U_539,U_538,U_537,U_536] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_537),U_538)),U_539) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_537),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_538),U_539))
      | ~ class_Groups_Oab__semigroup__add(U_536) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_536,U_537,U_538,U_539] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_537),U_538)),U_539) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_537),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_538),U_539))
      | ~ class_Groups_Oab__semigroup__add(U_536) ),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_537),U_538)),U_539) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_537),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_536),U_538),U_539))
    | ~ class_Groups_Oab__semigroup__add(U_536) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
          | V_b_2 != V_c_2 )
        & ( V_b_2 = V_c_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).

fof(f_110_2,plain,
    ! [U_543,U_542,U_541,U_540] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_542) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_543)
          | U_542 != U_543 )
        & ( U_542 = U_543
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_542) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_543) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_540) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ( ! [U_540,U_541,U_542,U_543] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_542) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_543)
        | U_542 != U_543
        | ~ sP15(U_540,U_541,U_542,U_543) )
    & ! [U_540,U_541,U_542,U_543] :
        ( U_542 = U_543
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_542) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_543)
        | ~ sP15(U_540,U_541,U_542,U_543) )
    & ! [U_540,U_541,U_542,U_543] :
        ( sP15(U_540,U_541,U_542,U_543)
        | ~ class_Groups_Ocancel__semigroup__add(U_540) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_110_2]) ).

cnf(f_110_4,plain,
    ( sP15(U_540,U_541,U_542,U_543)
    | ~ class_Groups_Ocancel__semigroup__add(U_540) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

cnf(f_110_5,plain,
    ( U_542 = U_543
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_542) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_543)
    | ~ sP15(U_540,U_541,U_542,U_543) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

cnf(f_110_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_542) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_540),U_541),U_543)
    | U_542 != U_543
    | ~ sP15(U_540,U_541,U_542,U_543) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_1,plain,
    ! [V_c_2,V_a_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
          | V_b_2 != V_c_2 )
        & ( V_b_2 = V_c_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).

fof(f_111_2,plain,
    ! [U_547,U_546,U_545,U_544] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_545),U_546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_547),U_546)
          | U_545 != U_547 )
        & ( U_545 = U_547
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_545),U_546) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_547),U_546) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_544) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ( ! [U_547,U_546,U_544,U_545] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_545),U_546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_547),U_546)
        | U_545 != U_547
        | ~ sP16(U_547,U_546,U_544,U_545) )
    & ! [U_547,U_546,U_544,U_545] :
        ( U_545 = U_547
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_545),U_546) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_547),U_546)
        | ~ sP16(U_547,U_546,U_544,U_545) )
    & ! [U_547,U_546,U_544,U_545] :
        ( sP16(U_547,U_546,U_544,U_545)
        | ~ class_Groups_Ocancel__semigroup__add(U_544) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_111_2]) ).

cnf(f_111_4,plain,
    ( sP16(U_547,U_546,U_544,U_545)
    | ~ class_Groups_Ocancel__semigroup__add(U_544) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

cnf(f_111_5,plain,
    ( U_545 = U_547
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_545),U_546) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_547),U_546)
    | ~ sP16(U_547,U_546,U_544,U_545) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

cnf(f_111_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_545),U_546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_544),U_547),U_546)
    | U_545 != U_547
    | ~ sP16(U_547,U_546,U_544,U_545) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).

fof(f_112_2,plain,
    ! [U_551,U_550,U_549,U_548] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_549),U_550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_551),U_550)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),U_549),U_551)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),U_549),U_551))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_549),U_550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_551),U_550))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_548) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ( ! [U_549,U_548,U_550,U_551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_549),U_550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_551),U_550)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),U_549),U_551))
        | ~ sP17(U_549,U_548,U_550,U_551) )
    & ! [U_549,U_548,U_550,U_551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),U_549),U_551))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_549),U_550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_551),U_550)))
        | ~ sP17(U_549,U_548,U_550,U_551) )
    & ! [U_549,U_548,U_550,U_551] :
        ( sP17(U_549,U_548,U_550,U_551)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_548) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_112_2]) ).

cnf(f_112_4,plain,
    ( sP17(U_549,U_548,U_550,U_551)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_548) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

cnf(f_112_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),U_549),U_551))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_549),U_550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_551),U_550)))
    | ~ sP17(U_549,U_548,U_550,U_551) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

cnf(f_112_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_549),U_550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_548),U_551),U_550)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_548),U_549),U_551))
    | ~ sP17(U_549,U_548,U_550,U_551) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).

fof(f_113_2,plain,
    ! [U_555,U_554,U_553,U_552] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_555)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),U_554),U_555)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),U_554),U_555))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_555))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_552) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ( ! [U_553,U_554,U_555,U_552] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_555)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),U_554),U_555))
        | ~ sP18(U_553,U_554,U_555,U_552) )
    & ! [U_553,U_554,U_555,U_552] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),U_554),U_555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_555)))
        | ~ sP18(U_553,U_554,U_555,U_552) )
    & ! [U_553,U_554,U_555,U_552] :
        ( sP18(U_553,U_554,U_555,U_552)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_552) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_113_2]) ).

cnf(f_113_4,plain,
    ( sP18(U_553,U_554,U_555,U_552)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_552) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),U_554),U_555))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_555)))
    | ~ sP18(U_553,U_554,U_555,U_552) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_552),U_553),U_555)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_552),U_554),U_555))
    | ~ sP18(U_553,U_554,U_555,U_552) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono]) ).

fof(f_114_2,plain,
    ! [U_559,U_558,U_557,U_556] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_556),U_557),U_559)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_556),U_558),U_559)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_556),U_557),U_558))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_556) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_558,U_557,U_559,U_556] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_556),U_557),U_559)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_556),U_558),U_559)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_556),U_557),U_558))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_556) ),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_556),U_557),U_559)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_556),U_558),U_559)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_556),U_557),U_558))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_556) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono]) ).

fof(f_115_2,plain,
    ! [U_563,U_562,U_561,U_560] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_560),U_563),U_561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_560),U_563),U_562)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_560),U_561),U_562))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_560) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_560,U_561,U_562,U_563] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_560),U_563),U_561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_560),U_563),U_562)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_560),U_561),U_562))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_560) ),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_560),U_563),U_561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_560),U_563),U_562)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_560),U_561),U_562))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_560) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).

fof(f_116_2,plain,
    ! [U_568,U_567,U_566,U_565,U_564] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_564),U_565),U_567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_564),U_566),U_568)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),U_567),U_568))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),U_565),U_566))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_564) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_564,U_565,U_566,U_567,U_568] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_564),U_565),U_567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_564),U_566),U_568)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),U_567),U_568))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),U_565),U_566))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_564) ),
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_564),U_565),U_567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_564),U_566),U_568)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),U_567),U_568))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_564),U_565),U_566))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_564) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( V_b = V_c
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).

fof(f_117_2,plain,
    ! [U_572,U_571,U_570,U_569] :
      ( U_571 = U_572
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_569),U_570),U_571) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_569),U_570),U_572)
      | ~ class_Groups_Ocancel__semigroup__add(U_569) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_571,U_569,U_570,U_572] :
      ( U_571 = U_572
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_569),U_570),U_571) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_569),U_570),U_572)
      | ~ class_Groups_Ocancel__semigroup__add(U_569) ),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( U_571 = U_572
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_569),U_570),U_571) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_569),U_570),U_572)
    | ~ class_Groups_Ocancel__semigroup__add(U_569) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( V_b = V_c
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).

fof(f_118_2,plain,
    ! [U_576,U_575,U_574,U_573] :
      ( U_575 = U_576
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_573),U_574),U_575) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_573),U_574),U_576)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_573) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_573,U_574,U_575,U_576] :
      ( U_575 = U_576
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_573),U_574),U_575) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_573),U_574),U_576)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_573) ),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    ( U_575 = U_576
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_573),U_574),U_575) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_573),U_574),U_576)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_573) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( V_b = V_c
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).

fof(f_119_2,plain,
    ! [U_580,U_579,U_578,U_577] :
      ( U_578 = U_580
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_577),U_578),U_579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_577),U_580),U_579)
      | ~ class_Groups_Ocancel__semigroup__add(U_577) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_577,U_578,U_579,U_580] :
      ( U_578 = U_580
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_577),U_578),U_579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_577),U_580),U_579)
      | ~ class_Groups_Ocancel__semigroup__add(U_577) ),
    inference(definitional_conversion,[status(esa)],[f_119_2]) ).

cnf(f_119_4,plain,
    ( U_578 = U_580
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_577),U_578),U_579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_577),U_580),U_579)
    | ~ class_Groups_Ocancel__semigroup__add(U_577) ),
    inference(clausify,[status(thm)],[f_119_3]) ).

fof(f_120_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).

fof(f_120_2,plain,
    ! [U_584,U_583,U_582,U_581] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_581),U_582),U_584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_581),U_582),U_583)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_581),U_584),U_583)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_581) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_581,U_582,U_583,U_584] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_581),U_582),U_584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_581),U_582),U_583)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_581),U_584),U_583)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_581) ),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_581),U_582),U_584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_581),U_582),U_583)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_581),U_584),U_583)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_581) ),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).

fof(f_121_2,plain,
    ! [U_588,U_587,U_586,U_585] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_585),U_587),U_588))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_585),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_585),U_586),U_587)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_585),U_586),U_588)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_585) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_585,U_586,U_587,U_588] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_585),U_587),U_588))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_585),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_585),U_586),U_587)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_585),U_586),U_588)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_585) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_585),U_587),U_588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_585),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_585),U_586),U_587)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_585),U_586),U_588)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_585) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_1,plain,
    ! [V_P_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & V_m_2 = V_n_2 )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).

fof(f_122_2,plain,
    ! [U_591,U_590,U_589] :
      ( hBOOL(hAPP(hAPP(U_591,U_590),U_589))
      | ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_590),U_589)) )
      | ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        & U_589 = U_590 )
      | ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_589),U_590)) ) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ( ! [U_589,U_590,U_591] :
        ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        | ~ sP21(U_589,U_590,U_591) )
    & ! [U_589,U_590,U_591] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_590),U_589))
        | ~ sP21(U_589,U_590,U_591) )
    & ! [U_589,U_590,U_591] :
        ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        | ~ sP20(U_589,U_590,U_591) )
    & ! [U_589,U_590,U_591] :
        ( U_589 = U_590
        | ~ sP20(U_589,U_590,U_591) )
    & ! [U_589,U_590,U_591] :
        ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        | ~ sP19(U_589,U_590,U_591) )
    & ! [U_589,U_590,U_591] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_589),U_590))
        | ~ sP19(U_589,U_590,U_591) )
    & ! [U_589,U_590,U_591] :
        ( hBOOL(hAPP(hAPP(U_591,U_590),U_589))
        | sP21(U_589,U_590,U_591)
        | sP20(U_589,U_590,U_591)
        | sP19(U_589,U_590,U_591) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20,sP21])],[f_122_2]) ).

cnf(f_122_4,plain,
    ( hBOOL(hAPP(hAPP(U_591,U_590),U_589))
    | sP21(U_589,U_590,U_591)
    | sP20(U_589,U_590,U_591)
    | sP19(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_589),U_590))
    | ~ sP19(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
    | ~ sP19(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_7,plain,
    ( U_589 = U_590
    | ~ sP20(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
    | ~ sP20(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_590),U_589))
    | ~ sP21(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

cnf(f_122_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_591,U_590),U_589))
    | ~ sP21(U_589,U_590,U_591) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).

fof(f_123_2,plain,
    ! [U_594,U_593,U_592] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_592),U_594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_592),U_593)),U_594)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_594,U_592,U_593] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_592),U_594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_592),U_593)),U_594)) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_592),U_594))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_592),U_593)),U_594)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_1,plain,
    ! [V_n,V_m,V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).

fof(f_124_2,plain,
    ! [U_598,U_597,U_596,U_595] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_597),U_598))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_597),U_596) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_595),U_598)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_595),U_596)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_596,U_597,U_595,U_598] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_597),U_598))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_597),U_596) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_595),U_598)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_595),U_596)) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_597),U_598))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_597),U_596) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_595),U_598)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_595),U_596)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).

fof(f_125_2,plain,
    ! [U_602,U_601,U_600,U_599] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_599),U_601)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_600),U_602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_601),U_602))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_599),U_600)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_599,U_600,U_601,U_602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_599),U_601)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_600),U_602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_601),U_602))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_599),U_600)) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_599),U_601)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_600),U_602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_601),U_602))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_599),U_600)) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).

fof(f_126_2,plain,
    ! [U_605,U_604,U_603] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_603),U_605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_604),U_605)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_603),U_604)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_604,U_603,U_605] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_603),U_605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_604),U_605)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_603),U_604)) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_603),U_605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_604),U_605)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_603),U_604)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).

fof(f_127_2,plain,
    ! [U_608,U_607,U_606] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_608),U_607)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_606),U_607)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_606,U_607,U_608] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_608),U_607)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_606),U_607)) ),
    inference(definitional_conversion,[status(esa)],[f_127_2]) ).

cnf(f_127_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_608),U_607)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_606),U_607)) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).

fof(f_128_2,plain,
    ! [U_611,U_610,U_609] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_610),U_611)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_609),U_610)) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_609,U_610,U_611] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_610),U_611)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_609),U_610)) ),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_610),U_611)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_609),U_610)) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_1,plain,
    ! [V_t,V_s] :
      ( V_s != V_t
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).

fof(f_129_2,plain,
    ! [U_613,U_612] :
      ( U_612 != U_613
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_612),U_613)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_612,U_613] :
      ( U_612 != U_613
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_612),U_613)) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( U_612 != U_613
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_612),U_613)) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [V_m,V_n] :
      ( V_m != V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).

fof(f_130_2,plain,
    ! [U_615,U_614] :
      ( U_615 != U_614
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_614),U_615)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_615,U_614] :
      ( U_615 != U_614
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_614),U_615)) ),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( U_615 != U_614
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_614),U_615)) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).

fof(f_131_2,plain,
    ! [U_616] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_616),U_616)),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_616] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_616),U_616)),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_616),U_616)),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).

fof(f_132_2,plain,
    ! [U_619,U_618,U_617] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_617),U_618),U_619)),c_Groups_Ozero__class_Ozero(U_617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),U_619),c_Groups_Ozero__class_Ozero(U_617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),U_618),c_Groups_Ozero__class_Ozero(U_617)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_617) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_617,U_618,U_619] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_617),U_618),U_619)),c_Groups_Ozero__class_Ozero(U_617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),U_619),c_Groups_Ozero__class_Ozero(U_617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),U_618),c_Groups_Ozero__class_Ozero(U_617)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_617) ),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_617),U_618),U_619)),c_Groups_Ozero__class_Ozero(U_617)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),U_619),c_Groups_Ozero__class_Ozero(U_617)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_617),U_618),c_Groups_Ozero__class_Ozero(U_617)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_617) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).

fof(f_133_2,plain,
    ! [U_622,U_621,U_620] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_620),U_621),U_622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),U_622))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),U_621))
      | ~ class_Groups_Oordered__comm__monoid__add(U_620) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_621,U_620,U_622] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_620),U_621),U_622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),U_622))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),U_621))
      | ~ class_Groups_Oordered__comm__monoid__add(U_620) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_620),U_621),U_622)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),U_622))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),c_Groups_Ozero__class_Ozero(U_620)),U_621))
    | ~ class_Groups_Oordered__comm__monoid__add(U_620) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
      | V_x = V_y ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(f_134_2,plain,
    ! [U_624,U_623] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_624),U_623))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_623),U_624))
      | U_623 = U_624 ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_623,U_624] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_624),U_623))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_623),U_624))
      | U_623 = U_624 ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_624),U_623))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_623),U_624))
    | U_623 = U_624 ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).

fof(f_135_2,plain,
    ! [U_627,U_626,U_625] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_625),U_626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_625),U_627)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_626),U_627)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_626),U_627))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_625),U_626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_625),U_627))) ) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ( ! [U_633,U_631] :
        ( ! [U_629] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_629),U_631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_629),U_633)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_631),U_633)) )
    & ! [U_632,U_630] :
        ( ! [U_628] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_628),U_630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_628),U_632)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_630),U_632)) ) ),
    inference(miniscope,[status(thm)],[f_135_2]) ).

fof(f_135_4,plain,
    ( ! [U_633,U_629,U_631] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_629),U_631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_629),U_633)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_631),U_633)) )
    & ! [U_630,U_628,U_632] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_628),U_630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_628),U_632)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_630),U_632)) ) ),
    inference(definitional_conversion,[status(esa)],[f_135_3]) ).

cnf(f_135_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_628),U_630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_628),U_632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_630),U_632)) ),
    inference(clausify,[status(thm)],[f_135_4]) ).

cnf(f_135_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_629),U_631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_629),U_633)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_631),U_633)) ),
    inference(clausify,[status(thm)],[f_135_4]) ).

fof(f_136_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).

fof(f_136_2,plain,
    ! [U_636,U_635,U_634] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_634),U_635) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_636),U_635)
        | U_634 != U_636 )
      & ( U_634 = U_636
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_634),U_635) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_636),U_635) ) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ( ! [U_642,U_640,U_638] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_638),U_640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_642),U_640)
        | U_638 != U_642 )
    & ! [U_641,U_639,U_637] :
        ( U_637 = U_641
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_637),U_639) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_641),U_639) ) ),
    inference(miniscope,[status(thm)],[f_136_2]) ).

fof(f_136_4,plain,
    ( ! [U_638,U_640,U_642] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_638),U_640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_642),U_640)
        | U_638 != U_642 )
    & ! [U_639,U_641,U_637] :
        ( U_637 = U_641
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_637),U_639) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_641),U_639) ) ),
    inference(definitional_conversion,[status(esa)],[f_136_3]) ).

cnf(f_136_5,plain,
    ( U_637 = U_641
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_637),U_639) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_641),U_639) ),
    inference(clausify,[status(thm)],[f_136_4]) ).

cnf(f_136_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_638),U_640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_642),U_640)
    | U_638 != U_642 ),
    inference(clausify,[status(thm)],[f_136_4]) ).

fof(f_137_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).

fof(f_137_2,plain,
    ! [U_645,U_644,U_643] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_643),U_644) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_643),U_645)
        | U_644 != U_645 )
      & ( U_644 = U_645
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_643),U_644) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_643),U_645) ) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ( ! [U_651,U_649] :
        ( ! [U_647] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_647),U_649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_647),U_651)
        | U_649 != U_651 )
    & ! [U_650,U_648] :
        ( ! [U_646] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_646),U_648) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_646),U_650)
        | U_648 = U_650 ) ),
    inference(miniscope,[status(thm)],[f_137_2]) ).

fof(f_137_4,plain,
    ( ! [U_651,U_647,U_649] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_647),U_649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_647),U_651)
        | U_649 != U_651 )
    & ! [U_648,U_650,U_646] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_646),U_648) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_646),U_650)
        | U_648 = U_650 ) ),
    inference(definitional_conversion,[status(esa)],[f_137_3]) ).

cnf(f_137_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_646),U_648) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_646),U_650)
    | U_648 = U_650 ),
    inference(clausify,[status(thm)],[f_137_4]) ).

cnf(f_137_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_647),U_649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_647),U_651)
    | U_649 != U_651 ),
    inference(clausify,[status(thm)],[f_137_4]) ).

fof(f_138_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).

fof(f_138_2,plain,
    ! [U_654,U_653,U_652] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_652),U_653)),U_654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_652),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_653),U_654)),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_652,U_653,U_654] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_652),U_653)),U_654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_652),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_653),U_654)),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_652),U_653)),U_654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_652),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_653),U_654)),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).

fof(f_139_2,plain,
    ! [U_656,U_655] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_655),U_656),U_656)),c_Groups_Ozero__class_Ozero(U_655)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),U_656),c_Groups_Ozero__class_Ozero(U_655))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),U_656),c_Groups_Ozero__class_Ozero(U_655)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_655),U_656),U_656)),c_Groups_Ozero__class_Ozero(U_655))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_655) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ( ! [U_656,U_655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_655),U_656),U_656)),c_Groups_Ozero__class_Ozero(U_655)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),U_656),c_Groups_Ozero__class_Ozero(U_655)))
        | ~ sP22(U_656,U_655) )
    & ! [U_656,U_655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),U_656),c_Groups_Ozero__class_Ozero(U_655)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_655),U_656),U_656)),c_Groups_Ozero__class_Ozero(U_655)))
        | ~ sP22(U_656,U_655) )
    & ! [U_656,U_655] :
        ( sP22(U_656,U_655)
        | ~ class_Groups_Olinordered__ab__group__add(U_655) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_139_2]) ).

cnf(f_139_4,plain,
    ( sP22(U_656,U_655)
    | ~ class_Groups_Olinordered__ab__group__add(U_655) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),U_656),c_Groups_Ozero__class_Ozero(U_655)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_655),U_656),U_656)),c_Groups_Ozero__class_Ozero(U_655)))
    | ~ sP22(U_656,U_655) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_655),U_656),U_656)),c_Groups_Ozero__class_Ozero(U_655)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_655),U_656),c_Groups_Ozero__class_Ozero(U_655)))
    | ~ sP22(U_656,U_655) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).

fof(f_140_2,plain,
    ! [U_659,U_658,U_657] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_658),U_659)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_658),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_657),U_659)),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_659,U_658,U_657] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_658),U_659)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_658),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_657),U_659)),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_658),U_659)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_658),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_657),U_659)),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).

fof(f_141_2,plain,
    ! [U_661,U_660] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_660),U_661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_661),U_660),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_660,U_661] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_660),U_661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_661),U_660),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_660),U_661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_661),U_660),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).

fof(f_142_2,plain,
    ! [U_663,U_662] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_662),U_663),U_663)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),U_663)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),U_663))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_662),U_663),U_663))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_662) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ( ! [U_663,U_662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_662),U_663),U_663)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),U_663))
        | ~ sP23(U_663,U_662) )
    & ! [U_663,U_662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),U_663))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_662),U_663),U_663)))
        | ~ sP23(U_663,U_662) )
    & ! [U_663,U_662] :
        ( sP23(U_663,U_662)
        | ~ class_Groups_Olinordered__ab__group__add(U_662) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_142_2]) ).

cnf(f_142_4,plain,
    ( sP23(U_663,U_662)
    | ~ class_Groups_Olinordered__ab__group__add(U_662) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

cnf(f_142_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),U_663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_662),U_663),U_663)))
    | ~ sP23(U_663,U_662) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

cnf(f_142_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_662),U_663),U_663)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_662),c_Groups_Ozero__class_Ozero(U_662)),U_663))
    | ~ sP23(U_663,U_662) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( V_m_2 != V_n_2
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | V_m_2 = V_n_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).

fof(f_143_2,plain,
    ! [U_665,U_664] :
      ( ( U_664 != U_665
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_665),U_664))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_664),U_665)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_665),U_664))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_664),U_665))
        | U_664 = U_665 ) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ( ! [U_669,U_667] :
        ( U_667 != U_669
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_669),U_667))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_667),U_669)) ) )
    & ! [U_668,U_666] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_668),U_666))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_666),U_668))
        | U_666 = U_668 ) ),
    inference(miniscope,[status(thm)],[f_143_2]) ).

fof(f_143_4,plain,
    ( ! [U_669,U_667] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_669),U_667))
        | ~ sP24(U_669,U_667) )
    & ! [U_669,U_667] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_667),U_669))
        | ~ sP24(U_669,U_667) )
    & ! [U_669,U_667] :
        ( U_667 != U_669
        | sP24(U_669,U_667) )
    & ! [U_666,U_668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_668),U_666))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_666),U_668))
        | U_666 = U_668 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_143_3]) ).

cnf(f_143_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_668),U_666))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_666),U_668))
    | U_666 = U_668 ),
    inference(clausify,[status(thm)],[f_143_4]) ).

cnf(f_143_6,plain,
    ( U_667 != U_669
    | sP24(U_669,U_667) ),
    inference(clausify,[status(thm)],[f_143_4]) ).

cnf(f_143_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_667),U_669))
    | ~ sP24(U_669,U_667) ),
    inference(clausify,[status(thm)],[f_143_4]) ).

cnf(f_143_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_669),U_667))
    | ~ sP24(U_669,U_667) ),
    inference(clausify,[status(thm)],[f_143_4]) ).

fof(f_144_1,plain,
    ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
    inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).

fof(f_144_2,plain,
    ! [U_671,U_670] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_670),U_671)),U_671)),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_670,U_671] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_670),U_671)),U_671)),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_670),U_671)),U_671)),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
    inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).

fof(f_145_2,plain,
    ! [U_673,U_672] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_672),U_673)),U_672)),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_672,U_673] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_672),U_673)),U_672)),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_672),U_673)),U_672)),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).

fof(f_146_2,plain,
    ! [U_674] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_674),U_674)),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_674] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_674),U_674)),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_674),U_674)),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).

fof(f_147_2,plain,
    ! [U_676,U_675] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_675),U_676)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_676))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_675)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_676))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_675))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_675),U_676))) ) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ( ! [U_680,U_678] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_678),U_680)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_680))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_678)) ) )
    & ! [U_679,U_677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_679))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_677))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_677),U_679))) ) ),
    inference(miniscope,[status(thm)],[f_147_2]) ).

fof(f_147_4,plain,
    ( ! [U_680,U_678] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_680))
        | ~ sP25(U_680,U_678) )
    & ! [U_680,U_678] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_678))
        | ~ sP25(U_680,U_678) )
    & ! [U_680,U_678] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_678),U_680)))
        | sP25(U_680,U_678) )
    & ! [U_677,U_679] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_679))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_677))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_677),U_679))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_147_3]) ).

cnf(f_147_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_679))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_677),U_679))) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

cnf(f_147_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_678),U_680)))
    | sP25(U_680,U_678) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

cnf(f_147_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_678))
    | ~ sP25(U_680,U_678) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

cnf(f_147_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_680))
    | ~ sP25(U_680,U_678) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

fof(f_148_1,plain,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))),
    inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).

fof(f_148_2,plain,
    ! [U_682,U_681] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_681),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_681),U_682)))),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_681,U_682] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_681),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_681),U_682)))),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_681),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_681),U_682)))),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))),
    inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).

fof(f_149_2,plain,
    ! [U_684,U_683] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_683),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_684),U_683)))),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_683,U_684] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_683),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_684),U_683)))),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_683),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_684),U_683)))),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ! [B_k] : V_n_2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) )
      & ( ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).

fof(f_150_2,plain,
    ! [U_688,U_687] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_687),U_688))
        | ! [U_686] : U_688 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_687),U_686)) )
      & ( ? [U_685] : U_688 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_687),U_685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_687),U_688)) ) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ( ! [U_692,U_690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_690),U_692))
        | ! [U_686] : U_692 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_690),U_686)) )
    & ! [U_691,U_689] :
        ( ? [U_685] : U_691 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_689),U_685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_689),U_691)) ) ),
    inference(miniscope,[status(thm)],[f_150_2]) ).

fof(f_150_4,plain,
    ( ! [U_692,U_690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_690),U_692))
        | ! [U_686] : U_692 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_690),U_686)) )
    & ! [U_691,U_689] :
        ( U_691 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_689),sK17(U_691,U_689)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_689),U_691)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_685,sK17(U_691,U_689))],[f_150_3]) ).

fof(f_150_5,plain,
    ( ! [U_686,U_690,U_692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_690),U_692))
        | U_692 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_690),U_686)) )
    & ! [U_691,U_689] :
        ( U_691 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_689),sK17(U_691,U_689)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_689),U_691)) ) ),
    inference(definitional_conversion,[status(esa)],[f_150_4]) ).

cnf(f_150_6,plain,
    ( U_691 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_689),sK17(U_691,U_689)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_689),U_691)) ),
    inference(clausify,[status(thm)],[f_150_5]) ).

cnf(f_150_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_690),U_692))
    | U_692 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_690),U_686)) ),
    inference(clausify,[status(thm)],[f_150_5]) ).

fof(f_151_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).

fof(f_151_2,plain,
    ! [U_694,U_693] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694) = U_694
      | ~ class_Groups_Omonoid__add(U_693) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_693,U_694] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694) = U_694
      | ~ class_Groups_Omonoid__add(U_693) ),
    inference(definitional_conversion,[status(esa)],[f_151_2]) ).

cnf(f_151_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694) = U_694
    | ~ class_Groups_Omonoid__add(U_693) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0]) ).

fof(f_152_2,plain,
    ! [U_696,U_695] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_695),c_Groups_Ozero__class_Ozero(U_695)),U_696) = U_696
      | ~ class_Groups_Ocomm__monoid__add(U_695) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_695,U_696] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_695),c_Groups_Ozero__class_Ozero(U_695)),U_696) = U_696
      | ~ class_Groups_Ocomm__monoid__add(U_695) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_695),c_Groups_Ozero__class_Ozero(U_695)),U_696) = U_696
    | ~ class_Groups_Ocomm__monoid__add(U_695) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).

fof(f_153_2,plain,
    ! [U_698,U_697] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_697),U_698),U_698)
          | U_698 != c_Groups_Ozero__class_Ozero(U_697) )
        & ( U_698 = c_Groups_Ozero__class_Ozero(U_697)
          | c_Groups_Ozero__class_Ozero(U_697) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_697),U_698),U_698) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_697) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ( ! [U_697,U_698] :
        ( c_Groups_Ozero__class_Ozero(U_697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_697),U_698),U_698)
        | U_698 != c_Groups_Ozero__class_Ozero(U_697)
        | ~ sP26(U_697,U_698) )
    & ! [U_697,U_698] :
        ( U_698 = c_Groups_Ozero__class_Ozero(U_697)
        | c_Groups_Ozero__class_Ozero(U_697) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_697),U_698),U_698)
        | ~ sP26(U_697,U_698) )
    & ! [U_697,U_698] :
        ( sP26(U_697,U_698)
        | ~ class_Groups_Olinordered__ab__group__add(U_697) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_153_2]) ).

cnf(f_153_4,plain,
    ( sP26(U_697,U_698)
    | ~ class_Groups_Olinordered__ab__group__add(U_697) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

cnf(f_153_5,plain,
    ( U_698 = c_Groups_Ozero__class_Ozero(U_697)
    | c_Groups_Ozero__class_Ozero(U_697) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_697),U_698),U_698)
    | ~ sP26(U_697,U_698) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

cnf(f_153_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_697),U_698),U_698)
    | U_698 != c_Groups_Ozero__class_Ozero(U_697)
    | ~ sP26(U_697,U_698) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).

fof(f_154_2,plain,
    ! [U_700,U_699] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_699),U_700),c_Groups_Ozero__class_Ozero(U_699)) = U_700
      | ~ class_Groups_Omonoid__add(U_699) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_699,U_700] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_699),U_700),c_Groups_Ozero__class_Ozero(U_699)) = U_700
      | ~ class_Groups_Omonoid__add(U_699) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_699),U_700),c_Groups_Ozero__class_Ozero(U_699)) = U_700
    | ~ class_Groups_Omonoid__add(U_699) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).

fof(f_155_2,plain,
    ! [U_702,U_701] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_701),U_702),c_Groups_Ozero__class_Ozero(U_701)) = U_702
      | ~ class_Groups_Ocomm__monoid__add(U_701) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_701,U_702] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_701),U_702),c_Groups_Ozero__class_Ozero(U_701)) = U_702
      | ~ class_Groups_Ocomm__monoid__add(U_701) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_701),U_702),c_Groups_Ozero__class_Ozero(U_701)) = U_702
    | ~ class_Groups_Ocomm__monoid__add(U_701) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(f_156_2,plain,
    ! [U_703] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_703) = U_703,
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_703] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_703) = U_703,
    inference(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_703) = U_703,
    inference(clausify,[status(thm)],[f_156_3]) ).

fof(f_157_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(f_157_2,plain,
    ! [U_704] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_704),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_704,
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_704] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_704),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_704,
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_704),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_704,
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).

fof(f_158_2,plain,
    ! [U_706,U_705] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_705),U_706) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_706 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_705 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_706 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_705),U_706) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ( ! [U_710,U_708] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_708),U_710) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_710 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_709,U_707] :
        ( ( U_709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_707),U_709) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_158_2]) ).

fof(f_158_4,plain,
    ( ! [U_707,U_709] :
        ( U_709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP27(U_707,U_709) )
    & ! [U_707,U_709] :
        ( U_707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP27(U_707,U_709) )
    & ! [U_710,U_708] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_708),U_710) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_710 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_707,U_709] :
        ( sP27(U_707,U_709)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_707),U_709) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_158_3]) ).

cnf(f_158_5,plain,
    ( sP27(U_707,U_709)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_707),U_709) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_158_4]) ).

cnf(f_158_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_708),U_710) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_710 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_158_4]) ).

cnf(f_158_7,plain,
    ( U_707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP27(U_707,U_709) ),
    inference(clausify,[status(thm)],[f_158_4]) ).

cnf(f_158_8,plain,
    ( U_709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP27(U_707,U_709) ),
    inference(clausify,[status(thm)],[f_158_4]) ).

fof(f_159_1,plain,
    ! [V_n,V_m] :
      ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) != V_m ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).

fof(f_159_2,plain,
    ! [U_712,U_711] :
      ( U_712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_711),U_712) != U_711 ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_712] :
      ( ! [U_711] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_711),U_712) != U_711
      | U_712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_159_2]) ).

fof(f_159_4,plain,
    ! [U_711,U_712] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_711),U_712) != U_711
      | U_712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_159_3]) ).

cnf(f_159_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_711),U_712) != U_711
    | U_712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_159_4]) ).

fof(f_160_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).

fof(f_160_2,plain,
    ! [U_714,U_713] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_713)),U_714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_713),hAPP(c_Nat_OSuc,U_714)),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_713,U_714] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_713)),U_714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_713),hAPP(c_Nat_OSuc,U_714)),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_713)),U_714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_713),hAPP(c_Nat_OSuc,U_714)),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).

fof(f_161_2,plain,
    ! [U_716,U_715] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_715)),U_716) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_715),U_716)),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_715,U_716] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_715)),U_716) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_715),U_716)),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_715)),U_716) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_715),U_716)),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).

fof(f_162_2,plain,
    ! [U_718,U_717] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_717),hAPP(c_Nat_OSuc,U_718)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_717),U_718)),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_717,U_718] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_717),hAPP(c_Nat_OSuc,U_718)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_717),U_718)),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_717),hAPP(c_Nat_OSuc,U_718)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_717),U_718)),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_not__less0]) ).

fof(f_163_2,plain,
    ! [U_719] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_719),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_719] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_719),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_163_2]) ).

cnf(f_163_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_719),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_1,plain,
    ! [V_n_2] :
      ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).

fof(f_164_2,plain,
    ! [U_720] :
      ( ( U_720 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_720)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_720))
        | U_720 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ( ! [U_722] :
        ( U_722 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_722)) )
    & ! [U_721] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_721))
        | U_721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_164_2]) ).

fof(f_164_4,plain,
    ( ! [U_722] :
        ( U_722 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_722)) )
    & ! [U_721] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_721))
        | U_721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_164_3]) ).

cnf(f_164_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_721))
    | U_721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_164_4]) ).

cnf(f_164_6,plain,
    ( U_722 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_722)) ),
    inference(clausify,[status(thm)],[f_164_4]) ).

fof(f_165_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).

fof(f_165_2,plain,
    ! [U_723] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_723),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_723] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_723),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_165_2]) ).

cnf(f_165_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_723),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [V_n,V_m] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).

fof(f_166_2,plain,
    ! [U_725,U_724] :
      ( U_725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_724),U_725)) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_725] :
      ( ! [U_724] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_724),U_725))
      | U_725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_166_2]) ).

fof(f_166_4,plain,
    ! [U_724,U_725] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_724),U_725))
      | U_725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_166_3]) ).

cnf(f_166_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_724),U_725))
    | U_725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_166_4]) ).

fof(f_167_1,plain,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_gr0I]) ).

fof(f_167_2,plain,
    ! [U_726] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_726))
      | U_726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_726] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_726))
      | U_726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_726))
    | U_726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).

fof(f_168_2,plain,
    ! [U_728,U_727] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_727),U_728))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_727)),hAPP(c_Nat_OSuc,U_728))) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_727,U_728] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_727),U_728))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_727)),hAPP(c_Nat_OSuc,U_728))) ),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_727),U_728))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_727)),hAPP(c_Nat_OSuc,U_728))) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).

fof(f_169_2,plain,
    ! [U_730,U_729] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_729),U_730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_729)),U_730)) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_729,U_730] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_729),U_730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_729)),U_730)) ),
    inference(definitional_conversion,[status(esa)],[f_169_2]) ).

cnf(f_169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_729),U_730))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_729)),U_730)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).

fof(f_170_2,plain,
    ! [U_732,U_731] :
      ( U_731 = U_732
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_731),U_732))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_731),hAPP(c_Nat_OSuc,U_732))) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_731,U_732] :
      ( U_731 = U_732
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_731),U_732))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_731),hAPP(c_Nat_OSuc,U_732))) ),
    inference(definitional_conversion,[status(esa)],[f_170_2]) ).

cnf(f_170_4,plain,
    ( U_731 = U_732
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_731),U_732))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_731),hAPP(c_Nat_OSuc,U_732))) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).

fof(f_171_2,plain,
    ! [U_735,U_734,U_733] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_733)),U_735))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_734),U_735))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_733),U_734)) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_733,U_734,U_735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_733)),U_735))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_734),U_735))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_733),U_734)) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_733)),U_735))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_734),U_735))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_733),U_734)) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
      | hAPP(c_Nat_OSuc,V_m) = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).

fof(f_172_2,plain,
    ! [U_737,U_736] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_736)),U_737))
      | hAPP(c_Nat_OSuc,U_736) = U_737
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_736),U_737)) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_736,U_737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_736)),U_737))
      | hAPP(c_Nat_OSuc,U_736) = U_737
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_736),U_737)) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_736)),U_737))
    | hAPP(c_Nat_OSuc,U_736) = U_737
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_736),U_737)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).

fof(f_173_2,plain,
    ! [U_739,U_738] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_738),hAPP(c_Nat_OSuc,U_739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_738),U_739)) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_739,U_738] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_738),hAPP(c_Nat_OSuc,U_739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_738),U_739)) ),
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_738),hAPP(c_Nat_OSuc,U_739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_738),U_739)) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_1,plain,
    ! [V_m,V_n] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).

fof(f_174_2,plain,
    ! [U_741,U_740] :
      ( U_741 = U_740
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_740),hAPP(c_Nat_OSuc,U_741)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_740),U_741)) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_740,U_741] :
      ( U_741 = U_740
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_740),hAPP(c_Nat_OSuc,U_741)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_740),U_741)) ),
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( U_741 = U_740
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_740),hAPP(c_Nat_OSuc,U_741)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_740),U_741)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
          | V_n_2 != V_m_2 )
        & ( V_n_2 = V_m_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(f_175_2,plain,
    ! [U_743,U_742] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),hAPP(c_Nat_OSuc,U_743)))
          | U_742 != U_743 )
        & ( U_742 = U_743
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),hAPP(c_Nat_OSuc,U_743))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),U_743)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ( ! [U_743,U_742] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),hAPP(c_Nat_OSuc,U_743)))
        | U_742 != U_743
        | ~ sP28(U_743,U_742) )
    & ! [U_743,U_742] :
        ( U_742 = U_743
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),hAPP(c_Nat_OSuc,U_743)))
        | ~ sP28(U_743,U_742) )
    & ! [U_743,U_742] :
        ( sP28(U_743,U_742)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),U_743)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_175_2]) ).

cnf(f_175_4,plain,
    ( sP28(U_743,U_742)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),U_743)) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

cnf(f_175_5,plain,
    ( U_742 = U_743
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),hAPP(c_Nat_OSuc,U_743)))
    | ~ sP28(U_743,U_742) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

cnf(f_175_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_742),hAPP(c_Nat_OSuc,U_743)))
    | U_742 != U_743
    | ~ sP28(U_743,U_742) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).

fof(f_176_2,plain,
    ! [U_745,U_744] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_744)),hAPP(c_Nat_OSuc,U_745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_744),U_745)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_744),U_745))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_744)),hAPP(c_Nat_OSuc,U_745))) ) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ( ! [U_749,U_747] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_747)),hAPP(c_Nat_OSuc,U_749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_747),U_749)) )
    & ! [U_748,U_746] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_746),U_748))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_746)),hAPP(c_Nat_OSuc,U_748))) ) ),
    inference(miniscope,[status(thm)],[f_176_2]) ).

fof(f_176_4,plain,
    ( ! [U_747,U_749] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_747)),hAPP(c_Nat_OSuc,U_749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_747),U_749)) )
    & ! [U_746,U_748] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_746),U_748))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_746)),hAPP(c_Nat_OSuc,U_748))) ) ),
    inference(definitional_conversion,[status(esa)],[f_176_3]) ).

cnf(f_176_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_746),U_748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_746)),hAPP(c_Nat_OSuc,U_748))) ),
    inference(clausify,[status(thm)],[f_176_4]) ).

cnf(f_176_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_747)),hAPP(c_Nat_OSuc,U_749)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_747),U_749)) ),
    inference(clausify,[status(thm)],[f_176_4]) ).

fof(f_177_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ( V_m_2 != V_n_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).

fof(f_177_2,plain,
    ! [U_751,U_750] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_750),hAPP(c_Nat_OSuc,U_751)))
        | ( U_750 != U_751
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_750),U_751)) ) )
      & ( U_750 = U_751
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_750),U_751))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_750),hAPP(c_Nat_OSuc,U_751))) ) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ( ! [U_755,U_753] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_753),hAPP(c_Nat_OSuc,U_755)))
        | ( U_753 != U_755
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_753),U_755)) ) )
    & ! [U_754,U_752] :
        ( U_752 = U_754
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_752),U_754))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_752),hAPP(c_Nat_OSuc,U_754))) ) ),
    inference(miniscope,[status(thm)],[f_177_2]) ).

fof(f_177_4,plain,
    ( ! [U_755,U_753] :
        ( U_753 != U_755
        | ~ sP29(U_755,U_753) )
    & ! [U_755,U_753] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_753),U_755))
        | ~ sP29(U_755,U_753) )
    & ! [U_755,U_753] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_753),hAPP(c_Nat_OSuc,U_755)))
        | sP29(U_755,U_753) )
    & ! [U_754,U_752] :
        ( U_752 = U_754
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_752),U_754))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_752),hAPP(c_Nat_OSuc,U_754))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_177_3]) ).

cnf(f_177_5,plain,
    ( U_752 = U_754
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_752),U_754))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_752),hAPP(c_Nat_OSuc,U_754))) ),
    inference(clausify,[status(thm)],[f_177_4]) ).

cnf(f_177_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_753),hAPP(c_Nat_OSuc,U_755)))
    | sP29(U_755,U_753) ),
    inference(clausify,[status(thm)],[f_177_4]) ).

cnf(f_177_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_753),U_755))
    | ~ sP29(U_755,U_753) ),
    inference(clausify,[status(thm)],[f_177_4]) ).

cnf(f_177_8,plain,
    ( U_753 != U_755
    | ~ sP29(U_755,U_753) ),
    inference(clausify,[status(thm)],[f_177_4]) ).

fof(f_178_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).

fof(f_178_2,plain,
    ! [U_757,U_756] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_756),U_757))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_757),hAPP(c_Nat_OSuc,U_756))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_757),hAPP(c_Nat_OSuc,U_756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_756),U_757)) ) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ! [U_761,U_759] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_759),U_761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_761),hAPP(c_Nat_OSuc,U_759))) )
    & ! [U_760,U_758] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_760),hAPP(c_Nat_OSuc,U_758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_758),U_760)) ) ),
    inference(miniscope,[status(thm)],[f_178_2]) ).

fof(f_178_4,plain,
    ( ! [U_759,U_761] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_759),U_761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_761),hAPP(c_Nat_OSuc,U_759))) )
    & ! [U_760,U_758] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_760),hAPP(c_Nat_OSuc,U_758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_758),U_760)) ) ),
    inference(definitional_conversion,[status(esa)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_760),hAPP(c_Nat_OSuc,U_758)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_758),U_760)) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

cnf(f_178_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_759),U_761))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_761),hAPP(c_Nat_OSuc,U_759))) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

fof(f_179_1,plain,
    ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I1_J]) ).

fof(f_179_2,plain,
    ! [U_763,U_762] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_762,U_763,U_762),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_763,U_762] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_762,U_763,U_762),
    inference(definitional_conversion,[status(esa)],[f_179_2]) ).

cnf(f_179_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_762,U_763,U_762),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I1_J]) ).

fof(f_180_2,plain,
    ! [U_764] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_764),U_764)),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ! [U_764] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_764),U_764)),
    inference(definitional_conversion,[status(esa)],[f_180_2]) ).

cnf(f_180_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_764),U_764)),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I1_J]) ).

fof(f_181_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(definitional_conversion,[status(esa)],[f_181_1]) ).

cnf(f_181_3,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_OSkip]) ).

fof(f_182_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(definitional_conversion,[status(esa)],[f_182_1]) ).

cnf(f_182_3,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_1,plain,
    ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I19_J]) ).

fof(f_183_2,plain,
    ! [U_765] : hAPP(c_Com_Ocom_OBODY,U_765) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_765] : hAPP(c_Com_Ocom_OBODY,U_765) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_765) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_1,plain,
    ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I18_J]) ).

fof(f_184_2,plain,
    ! [U_766] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_766),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_766] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_766),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_766),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I9_J]) ).

fof(f_185_2,plain,
    ! [U_768,U_767] : c_Com_Ocom_OAss(U_767,U_768) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_767,U_768] : c_Com_Ocom_OAss(U_767,U_768) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    c_Com_Ocom_OAss(U_767,U_768) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I8_J]) ).

fof(f_186_2,plain,
    ! [U_770,U_769] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_769,U_770),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ! [U_769,U_770] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_769,U_770),
    inference(definitional_conversion,[status(esa)],[f_186_2]) ).

cnf(f_186_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_769,U_770),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I20_J]) ).

fof(f_187_2,plain,
    ! [U_773,U_772,U_771] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_771,U_772,U_773),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_772,U_771,U_773] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_771,U_772,U_773),
    inference(definitional_conversion,[status(esa)],[f_187_2]) ).

cnf(f_187_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_771,U_772,U_773),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I10_J]) ).

fof(f_188_2,plain,
    ! [U_776,U_775,U_774] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_774,U_775,U_776),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_775,U_774,U_776] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_774,U_775,U_776),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_774,U_775,U_776),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I21_J]) ).

fof(f_189_2,plain,
    ! [U_779,U_778,U_777] : c_Com_Ocom_OCall(U_777,U_778,U_779) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_777,U_778,U_779] : c_Com_Ocom_OCall(U_777,U_778,U_779) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    c_Com_Ocom_OCall(U_777,U_778,U_779) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I11_J]) ).

fof(f_190_2,plain,
    ! [U_782,U_781,U_780] : c_Com_Ocom_OLocal(U_780,U_781,U_782) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_781,U_780,U_782] : c_Com_Ocom_OLocal(U_780,U_781,U_782) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    c_Com_Ocom_OLocal(U_780,U_781,U_782) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
        | ( ( V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).

fof(f_191_2,plain,
    ! [U_784,U_783] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_783),U_784)
        | ( ( U_784 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_783 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_783 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_784 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_783 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_783),U_784) ) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ( ! [U_788,U_786] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_786),U_788)
        | ( ( U_788 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_786 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_786 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_787,U_785] :
        ( ( U_787 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_785 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_785),U_787) ) ),
    inference(miniscope,[status(thm)],[f_191_2]) ).

fof(f_191_4,plain,
    ( ! [U_788,U_786] :
        ( U_788 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_786 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP32(U_788,U_786) )
    & ! [U_788,U_786] :
        ( U_788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_786 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP32(U_788,U_786) )
    & ! [U_785,U_787] :
        ( U_787 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP31(U_785,U_787) )
    & ! [U_785,U_787] :
        ( U_785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP31(U_785,U_787) )
    & ! [U_785,U_787] :
        ( U_787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP30(U_785,U_787) )
    & ! [U_785,U_787] :
        ( U_785 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP30(U_785,U_787) )
    & ! [U_788,U_786] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_786),U_788)
        | sP32(U_788,U_786) )
    & ! [U_785,U_787] :
        ( sP31(U_785,U_787)
        | sP30(U_785,U_787)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_785),U_787) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31,sP32])],[f_191_3]) ).

cnf(f_191_5,plain,
    ( sP31(U_785,U_787)
    | sP30(U_785,U_787)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_785),U_787) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_6,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_786),U_788)
    | sP32(U_788,U_786) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_7,plain,
    ( U_785 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP30(U_785,U_787) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_8,plain,
    ( U_787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP30(U_785,U_787) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_9,plain,
    ( U_785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP31(U_785,U_787) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_10,plain,
    ( U_787 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP31(U_785,U_787) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_11,plain,
    ( U_788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_786 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP32(U_788,U_786) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

cnf(f_191_12,plain,
    ( U_788 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_786 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP32(U_788,U_786) ),
    inference(clausify,[status(thm)],[f_191_4]) ).

fof(f_192_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).

fof(f_192_2,plain,
    ! [U_790,U_789] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_789),U_790) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_790 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_789 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_790 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_789 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_790 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_789 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_789),U_790) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ( ! [U_794,U_792] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_792),U_794) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_794 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_794 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_792 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_793,U_791] :
        ( ( U_793 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_791 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_791),U_793) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_192_2]) ).

fof(f_192_4,plain,
    ( ! [U_792,U_794] :
        ( U_794 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP35(U_792,U_794) )
    & ! [U_792,U_794] :
        ( U_794 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_792 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP35(U_792,U_794) )
    & ! [U_793,U_791] :
        ( U_793 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP34(U_793,U_791) )
    & ! [U_793,U_791] :
        ( U_791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP34(U_793,U_791) )
    & ! [U_793,U_791] :
        ( U_793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP33(U_793,U_791) )
    & ! [U_793,U_791] :
        ( U_791 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP33(U_793,U_791) )
    & ! [U_792,U_794] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_792),U_794) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP35(U_792,U_794) )
    & ! [U_793,U_791] :
        ( sP34(U_793,U_791)
        | sP33(U_793,U_791)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_791),U_793) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34,sP35])],[f_192_3]) ).

cnf(f_192_5,plain,
    ( sP34(U_793,U_791)
    | sP33(U_793,U_791)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_791),U_793) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_792),U_794) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP35(U_792,U_794) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_7,plain,
    ( U_791 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP33(U_793,U_791) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_8,plain,
    ( U_793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP33(U_793,U_791) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_9,plain,
    ( U_791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP34(U_793,U_791) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_10,plain,
    ( U_793 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP34(U_793,U_791) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_11,plain,
    ( U_794 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_792 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP35(U_792,U_794) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

cnf(f_192_12,plain,
    ( U_794 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP35(U_792,U_794) ),
    inference(clausify,[status(thm)],[f_192_4]) ).

fof(f_193_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | ! [B_m] : V_n_2 != hAPP(c_Nat_OSuc,B_m) )
      & ( ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).

fof(f_193_2,plain,
    ! [U_797] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_797))
        | ! [U_796] : U_797 != hAPP(c_Nat_OSuc,U_796) )
      & ( ? [U_795] : U_797 = hAPP(c_Nat_OSuc,U_795)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_797)) ) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ( ! [U_799] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_799))
        | ! [U_796] : U_799 != hAPP(c_Nat_OSuc,U_796) )
    & ! [U_798] :
        ( ? [U_795] : U_798 = hAPP(c_Nat_OSuc,U_795)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_798)) ) ),
    inference(miniscope,[status(thm)],[f_193_2]) ).

fof(f_193_4,plain,
    ( ! [U_799] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_799))
        | ! [U_796] : U_799 != hAPP(c_Nat_OSuc,U_796) )
    & ! [U_798] :
        ( U_798 = hAPP(c_Nat_OSuc,sK18(U_798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_798)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_795,sK18(U_798))],[f_193_3]) ).

fof(f_193_5,plain,
    ( ! [U_799,U_796] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_799))
        | U_799 != hAPP(c_Nat_OSuc,U_796) )
    & ! [U_798] :
        ( U_798 = hAPP(c_Nat_OSuc,sK18(U_798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_798)) ) ),
    inference(definitional_conversion,[status(esa)],[f_193_4]) ).

cnf(f_193_6,plain,
    ( U_798 = hAPP(c_Nat_OSuc,sK18(U_798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_798)) ),
    inference(clausify,[status(thm)],[f_193_5]) ).

cnf(f_193_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_799))
    | U_799 != hAPP(c_Nat_OSuc,U_796) ),
    inference(clausify,[status(thm)],[f_193_5]) ).

fof(f_194_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).

fof(f_194_2,plain,
    ! [U_800] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_800),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_800 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_800),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ( ! [U_802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_802),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_802 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_801] :
        ( U_801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_801),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_194_2]) ).

fof(f_194_4,plain,
    ( ! [U_802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_802),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_802 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_801] :
        ( U_801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_801),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_194_3]) ).

cnf(f_194_5,plain,
    ( U_801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_801),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_194_4]) ).

cnf(f_194_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_802),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_802 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_194_4]) ).

fof(f_195_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ( ! [B_j] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
              | V_m_2 != hAPP(c_Nat_OSuc,B_j) )
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
            & V_m_2 = hAPP(c_Nat_OSuc,B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).

fof(f_195_2,plain,
    ! [U_806,U_805] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_805),hAPP(c_Nat_OSuc,U_806)))
        | ( ! [U_804] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_804),U_806))
              | U_805 != hAPP(c_Nat_OSuc,U_804) )
          & U_805 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_803] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_803),U_806))
            & U_805 = hAPP(c_Nat_OSuc,U_803) )
        | U_805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_805),hAPP(c_Nat_OSuc,U_806))) ) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ( ! [U_810,U_808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_808),hAPP(c_Nat_OSuc,U_810)))
        | ( ! [U_804] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_804),U_810))
              | U_808 != hAPP(c_Nat_OSuc,U_804) )
          & U_808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_809,U_807] :
        ( ? [U_803] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_803),U_809))
            & U_807 = hAPP(c_Nat_OSuc,U_803) )
        | U_807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_807),hAPP(c_Nat_OSuc,U_809))) ) ),
    inference(miniscope,[status(thm)],[f_195_2]) ).

fof(f_195_4,plain,
    ( ! [U_810,U_808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_808),hAPP(c_Nat_OSuc,U_810)))
        | ( ! [U_804] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_804),U_810))
              | U_808 != hAPP(c_Nat_OSuc,U_804) )
          & U_808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_809,U_807] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK19(U_809,U_807)),U_809))
          & U_807 = hAPP(c_Nat_OSuc,sK19(U_809,U_807)) )
        | U_807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_807),hAPP(c_Nat_OSuc,U_809))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_803,sK19(U_809,U_807))],[f_195_3]) ).

fof(f_195_5,plain,
    ( ! [U_804,U_810,U_808] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_804),U_810))
        | U_808 != hAPP(c_Nat_OSuc,U_804)
        | ~ sP37(U_804,U_810,U_808) )
    & ! [U_804,U_810,U_808] :
        ( U_808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP37(U_804,U_810,U_808) )
    & ! [U_809,U_807] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK19(U_809,U_807)),U_809))
        | ~ sP36(U_809,U_807) )
    & ! [U_809,U_807] :
        ( U_807 = hAPP(c_Nat_OSuc,sK19(U_809,U_807))
        | ~ sP36(U_809,U_807) )
    & ! [U_804,U_810,U_808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_808),hAPP(c_Nat_OSuc,U_810)))
        | sP37(U_804,U_810,U_808) )
    & ! [U_809,U_807] :
        ( sP36(U_809,U_807)
        | U_807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_807),hAPP(c_Nat_OSuc,U_809))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36,sP37])],[f_195_4]) ).

cnf(f_195_6,plain,
    ( sP36(U_809,U_807)
    | U_807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_807),hAPP(c_Nat_OSuc,U_809))) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

cnf(f_195_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_808),hAPP(c_Nat_OSuc,U_810)))
    | sP37(U_804,U_810,U_808) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

cnf(f_195_8,plain,
    ( U_807 = hAPP(c_Nat_OSuc,sK19(U_809,U_807))
    | ~ sP36(U_809,U_807) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

cnf(f_195_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK19(U_809,U_807)),U_809))
    | ~ sP36(U_809,U_807) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

cnf(f_195_10,plain,
    ( U_808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP37(U_804,U_810,U_808) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

cnf(f_195_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_804),U_810))
    | U_808 != hAPP(c_Nat_OSuc,U_804)
    | ~ sP37(U_804,U_810,U_808) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

fof(f_196_1,plain,
    ! [V_b,V_pn] :
      ( hBOOL(hAPP(c_Com_OWT,V_b))
      | hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
      | ~ c_Com_OWT__bodies ),
    inference(fof_nnf,[status(thm)],[fact_WT__bodiesD]) ).

fof(f_196_2,plain,
    ! [U_812,U_811] :
      ( hBOOL(hAPP(c_Com_OWT,U_812))
      | hAPP(c_Com_Obody,U_811) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_812)
      | ~ c_Com_OWT__bodies ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ( ! [U_812] :
        ( ! [U_811] : hAPP(c_Com_Obody,U_811) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_812)
        | hBOOL(hAPP(c_Com_OWT,U_812)) )
    | ~ c_Com_OWT__bodies ),
    inference(miniscope,[status(thm)],[f_196_2]) ).

fof(f_196_4,plain,
    ! [U_811,U_812] :
      ( hAPP(c_Com_Obody,U_811) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_812)
      | hBOOL(hAPP(c_Com_OWT,U_812))
      | ~ c_Com_OWT__bodies ),
    inference(definitional_conversion,[status(esa)],[f_196_3]) ).

cnf(f_196_5,plain,
    ( hAPP(c_Com_Obody,U_811) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_812)
    | hBOOL(hAPP(c_Com_OWT,U_812))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_196_4]) ).

fof(f_197_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).

fof(f_197_2,plain,
    ! [U_816,U_815,U_814,U_813] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),U_815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_813),U_814),U_816)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),U_815),U_816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),c_Groups_Ozero__class_Ozero(U_813)),U_814))
      | ~ class_Rings_Olinordered__semidom(U_813) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ! [U_813,U_814,U_815,U_816] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),U_815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_813),U_814),U_816)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),U_815),U_816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),c_Groups_Ozero__class_Ozero(U_813)),U_814))
      | ~ class_Rings_Olinordered__semidom(U_813) ),
    inference(definitional_conversion,[status(esa)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),U_815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_813),U_814),U_816)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),U_815),U_816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_813),c_Groups_Ozero__class_Ozero(U_813)),U_814))
    | ~ class_Rings_Olinordered__semidom(U_813) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).

fof(f_198_2,plain,
    ! [U_818,U_817] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_817),U_818),U_818)),c_Groups_Ozero__class_Ozero(U_817)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),U_818),c_Groups_Ozero__class_Ozero(U_817))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),U_818),c_Groups_Ozero__class_Ozero(U_817)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_817),U_818),U_818)),c_Groups_Ozero__class_Ozero(U_817))) ) )
      | ~ class_Rings_Olinordered__idom(U_817) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ( ! [U_818,U_817] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_817),U_818),U_818)),c_Groups_Ozero__class_Ozero(U_817)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),U_818),c_Groups_Ozero__class_Ozero(U_817)))
        | ~ sP38(U_818,U_817) )
    & ! [U_818,U_817] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),U_818),c_Groups_Ozero__class_Ozero(U_817)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_817),U_818),U_818)),c_Groups_Ozero__class_Ozero(U_817)))
        | ~ sP38(U_818,U_817) )
    & ! [U_818,U_817] :
        ( sP38(U_818,U_817)
        | ~ class_Rings_Olinordered__idom(U_817) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_198_2]) ).

cnf(f_198_4,plain,
    ( sP38(U_818,U_817)
    | ~ class_Rings_Olinordered__idom(U_817) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),U_818),c_Groups_Ozero__class_Ozero(U_817)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_817),U_818),U_818)),c_Groups_Ozero__class_Ozero(U_817)))
    | ~ sP38(U_818,U_817) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_817),U_818),U_818)),c_Groups_Ozero__class_Ozero(U_817)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_817),U_818),c_Groups_Ozero__class_Ozero(U_817)))
    | ~ sP38(U_818,U_817) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_1,plain,
    ! [V_P] :
      ( ? [B_y] : hAPP(c_Com_Obody,V_P) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I7_J]) ).

fof(f_199_2,plain,
    ! [U_820] :
      ( ? [U_819] : hAPP(c_Com_Obody,U_820) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_819)
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_820))) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_820] :
      ( hAPP(c_Com_Obody,U_820) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK20(U_820))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_820))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_819,sK20(U_820))],[f_199_2]) ).

fof(f_199_4,plain,
    ! [U_820] :
      ( hAPP(c_Com_Obody,U_820) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK20(U_820))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_820))) ),
    inference(definitional_conversion,[status(esa)],[f_199_3]) ).

cnf(f_199_5,plain,
    ( hAPP(c_Com_Obody,U_820) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK20(U_820))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_820))) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

fof(f_200_1,plain,
    ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_the_Osimps]) ).

fof(f_200_2,plain,
    ! [U_822,U_821] : hAPP(c_Option_Othe(U_821),hAPP(c_Option_Ooption_OSome(U_821),U_822)) = U_822,
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_821,U_822] : hAPP(c_Option_Othe(U_821),hAPP(c_Option_Ooption_OSome(U_821),U_822)) = U_822,
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    hAPP(c_Option_Othe(U_821),hAPP(c_Option_Ooption_OSome(U_821),U_822)) = U_822,
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_1,plain,
    ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H),
    inference(fof_nnf,[status(thm)],[fact_option_Osimps_I2_J]) ).

fof(f_201_2,plain,
    ! [U_824,U_823] : c_Option_Ooption_ONone(U_823) != hAPP(c_Option_Ooption_OSome(U_823),U_824),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_823,U_824] : c_Option_Ooption_ONone(U_823) != hAPP(c_Option_Ooption_OSome(U_823),U_824),
    inference(definitional_conversion,[status(esa)],[f_201_2]) ).

cnf(f_201_4,plain,
    c_Option_Ooption_ONone(U_823) != hAPP(c_Option_Ooption_OSome(U_823),U_824),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_1,plain,
    ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_option_Osimps_I3_J]) ).

fof(f_202_2,plain,
    ! [U_826,U_825] : hAPP(c_Option_Ooption_OSome(U_825),U_826) != c_Option_Ooption_ONone(U_825),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_825,U_826] : hAPP(c_Option_Ooption_OSome(U_825),U_826) != c_Option_Ooption_ONone(U_825),
    inference(definitional_conversion,[status(esa)],[f_202_2]) ).

cnf(f_202_4,plain,
    hAPP(c_Option_Ooption_OSome(U_825),U_826) != c_Option_Ooption_ONone(U_825),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [T_b,V_x_2] :
      ( ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
        | V_x_2 != c_Option_Ooption_ONone(T_b) )
      & ( V_x_2 = c_Option_Ooption_ONone(T_b)
        | ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__Some__eq]) ).

fof(f_203_2,plain,
    ! [U_830,U_829] :
      ( ( ! [U_828] : U_829 != hAPP(c_Option_Ooption_OSome(U_830),U_828)
        | U_829 != c_Option_Ooption_ONone(U_830) )
      & ( U_829 = c_Option_Ooption_ONone(U_830)
        | ? [U_827] : U_829 = hAPP(c_Option_Ooption_OSome(U_830),U_827) ) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_834,U_832] :
        ( ! [U_828] : U_832 != hAPP(c_Option_Ooption_OSome(U_834),U_828)
        | U_832 != c_Option_Ooption_ONone(U_834) )
    & ! [U_833,U_831] :
        ( U_831 = c_Option_Ooption_ONone(U_833)
        | ? [U_827] : U_831 = hAPP(c_Option_Ooption_OSome(U_833),U_827) ) ),
    inference(miniscope,[status(thm)],[f_203_2]) ).

fof(f_203_4,plain,
    ( ! [U_834,U_832] :
        ( ! [U_828] : U_832 != hAPP(c_Option_Ooption_OSome(U_834),U_828)
        | U_832 != c_Option_Ooption_ONone(U_834) )
    & ! [U_833,U_831] :
        ( U_831 = c_Option_Ooption_ONone(U_833)
        | U_831 = hAPP(c_Option_Ooption_OSome(U_833),sK21(U_833,U_831)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_827,sK21(U_833,U_831))],[f_203_3]) ).

fof(f_203_5,plain,
    ( ! [U_828,U_832,U_834] :
        ( U_832 != hAPP(c_Option_Ooption_OSome(U_834),U_828)
        | U_832 != c_Option_Ooption_ONone(U_834) )
    & ! [U_831,U_833] :
        ( U_831 = c_Option_Ooption_ONone(U_833)
        | U_831 = hAPP(c_Option_Ooption_OSome(U_833),sK21(U_833,U_831)) ) ),
    inference(definitional_conversion,[status(esa)],[f_203_4]) ).

cnf(f_203_6,plain,
    ( U_831 = c_Option_Ooption_ONone(U_833)
    | U_831 = hAPP(c_Option_Ooption_OSome(U_833),sK21(U_833,U_831)) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_7,plain,
    ( U_832 != hAPP(c_Option_Ooption_OSome(U_834),U_828)
    | U_832 != c_Option_Ooption_ONone(U_834) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

fof(f_204_1,plain,
    ! [T_b,V_x_2] :
      ( ( V_x_2 != c_Option_Ooption_ONone(T_b)
        | ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y) )
      & ( ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y)
        | V_x_2 = c_Option_Ooption_ONone(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__None__eq]) ).

fof(f_204_2,plain,
    ! [U_838,U_837] :
      ( ( U_837 != c_Option_Ooption_ONone(U_838)
        | ! [U_836] : U_837 != hAPP(c_Option_Ooption_OSome(U_838),U_836) )
      & ( ? [U_835] : U_837 = hAPP(c_Option_Ooption_OSome(U_838),U_835)
        | U_837 = c_Option_Ooption_ONone(U_838) ) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_842,U_840] :
        ( U_840 != c_Option_Ooption_ONone(U_842)
        | ! [U_836] : U_840 != hAPP(c_Option_Ooption_OSome(U_842),U_836) )
    & ! [U_841,U_839] :
        ( ? [U_835] : U_839 = hAPP(c_Option_Ooption_OSome(U_841),U_835)
        | U_839 = c_Option_Ooption_ONone(U_841) ) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

fof(f_204_4,plain,
    ( ! [U_842,U_840] :
        ( U_840 != c_Option_Ooption_ONone(U_842)
        | ! [U_836] : U_840 != hAPP(c_Option_Ooption_OSome(U_842),U_836) )
    & ! [U_841,U_839] :
        ( U_839 = hAPP(c_Option_Ooption_OSome(U_841),sK22(U_841,U_839))
        | U_839 = c_Option_Ooption_ONone(U_841) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_835,sK22(U_841,U_839))],[f_204_3]) ).

fof(f_204_5,plain,
    ( ! [U_836,U_840,U_842] :
        ( U_840 != c_Option_Ooption_ONone(U_842)
        | U_840 != hAPP(c_Option_Ooption_OSome(U_842),U_836) )
    & ! [U_841,U_839] :
        ( U_839 = hAPP(c_Option_Ooption_OSome(U_841),sK22(U_841,U_839))
        | U_839 = c_Option_Ooption_ONone(U_841) ) ),
    inference(definitional_conversion,[status(esa)],[f_204_4]) ).

cnf(f_204_6,plain,
    ( U_839 = hAPP(c_Option_Ooption_OSome(U_841),sK22(U_841,U_839))
    | U_839 = c_Option_Ooption_ONone(U_841) ),
    inference(clausify,[status(thm)],[f_204_5]) ).

cnf(f_204_7,plain,
    ( U_840 != c_Option_Ooption_ONone(U_842)
    | U_840 != hAPP(c_Option_Ooption_OSome(U_842),U_836) ),
    inference(clausify,[status(thm)],[f_204_5]) ).

fof(f_205_1,plain,
    ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_option_Osize_I2_J]) ).

fof(f_205_2,plain,
    ! [U_845,U_844,U_843] : c_Option_Ooption_Ooption__size(U_843,U_844,hAPP(c_Option_Ooption_OSome(U_843),U_845)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_844,U_845)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_843,U_844,U_845] : c_Option_Ooption_Ooption__size(U_843,U_844,hAPP(c_Option_Ooption_OSome(U_843),U_845)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_844,U_845)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_205_2]) ).

cnf(f_205_4,plain,
    c_Option_Ooption_Ooption__size(U_843,U_844,hAPP(c_Option_Ooption_OSome(U_843),U_845)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_844,U_845)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_1,plain,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).

fof(f_206_2,plain,
    ! [U_848,U_847,U_846] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_847),U_848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_846),U_847)) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ! [U_846,U_847,U_848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_847),U_848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_846),U_847)) ),
    inference(definitional_conversion,[status(esa)],[f_206_2]) ).

cnf(f_206_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_847),U_848)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_846),U_847)) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | V_x = V_y
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(f_207_2,plain,
    ! [U_851,U_850,U_849] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),U_851),U_850))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),U_850),U_851))
      | U_850 = U_851
      | ~ class_Rings_Olinordered__idom(U_849) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ! [U_849,U_850,U_851] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),U_851),U_850))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),U_850),U_851))
      | U_850 = U_851
      | ~ class_Rings_Olinordered__idom(U_849) ),
    inference(definitional_conversion,[status(esa)],[f_207_2]) ).

cnf(f_207_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),U_851),U_850))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),U_850),U_851))
    | U_850 = U_851
    | ~ class_Rings_Olinordered__idom(U_849) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_1,plain,
    ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_option_Osize_I1_J]) ).

fof(f_208_2,plain,
    ! [U_853,U_852] : c_Option_Ooption_Ooption__size(U_852,U_853,c_Option_Ooption_ONone(U_852)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_852,U_853] : c_Option_Ooption_Ooption__size(U_852,U_853,c_Option_Ooption_ONone(U_852)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    c_Option_Ooption_Ooption__size(U_852,U_853,c_Option_Ooption_ONone(U_852)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_1,plain,
    ! [V_a_H_2,V_a_2,T_b] :
      ( ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
        | V_a_2 != V_a_H_2 )
      & ( V_a_2 = V_a_H_2
        | hAPP(c_Option_Ooption_OSome(T_b),V_a_2) != hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_option_Oinject]) ).

fof(f_209_2,plain,
    ! [U_856,U_855,U_854] :
      ( ( hAPP(c_Option_Ooption_OSome(U_854),U_855) = hAPP(c_Option_Ooption_OSome(U_854),U_856)
        | U_855 != U_856 )
      & ( U_855 = U_856
        | hAPP(c_Option_Ooption_OSome(U_854),U_855) != hAPP(c_Option_Ooption_OSome(U_854),U_856) ) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ( ! [U_862,U_860] :
        ( ! [U_858] : hAPP(c_Option_Ooption_OSome(U_858),U_860) = hAPP(c_Option_Ooption_OSome(U_858),U_862)
        | U_860 != U_862 )
    & ! [U_861,U_859] :
        ( ! [U_857] : hAPP(c_Option_Ooption_OSome(U_857),U_859) != hAPP(c_Option_Ooption_OSome(U_857),U_861)
        | U_859 = U_861 ) ),
    inference(miniscope,[status(thm)],[f_209_2]) ).

fof(f_209_4,plain,
    ( ! [U_858,U_862,U_860] :
        ( hAPP(c_Option_Ooption_OSome(U_858),U_860) = hAPP(c_Option_Ooption_OSome(U_858),U_862)
        | U_860 != U_862 )
    & ! [U_861,U_859,U_857] :
        ( hAPP(c_Option_Ooption_OSome(U_857),U_859) != hAPP(c_Option_Ooption_OSome(U_857),U_861)
        | U_859 = U_861 ) ),
    inference(definitional_conversion,[status(esa)],[f_209_3]) ).

cnf(f_209_5,plain,
    ( hAPP(c_Option_Ooption_OSome(U_857),U_859) != hAPP(c_Option_Ooption_OSome(U_857),U_861)
    | U_859 = U_861 ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_6,plain,
    ( hAPP(c_Option_Ooption_OSome(U_858),U_860) = hAPP(c_Option_Ooption_OSome(U_858),U_862)
    | U_860 != U_862 ),
    inference(clausify,[status(thm)],[f_209_4]) ).

fof(f_210_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).

fof(f_210_2,plain,
    ! [U_864,U_863] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),U_864) = c_Groups_Ozero__class_Ozero(U_863)
          | U_864 != c_Groups_Ozero__class_Ozero(U_863) )
        & ( U_864 = c_Groups_Ozero__class_Ozero(U_863)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),U_864) != c_Groups_Ozero__class_Ozero(U_863) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_863) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ( ! [U_863,U_864] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),U_864) = c_Groups_Ozero__class_Ozero(U_863)
        | U_864 != c_Groups_Ozero__class_Ozero(U_863)
        | ~ sP39(U_863,U_864) )
    & ! [U_863,U_864] :
        ( U_864 = c_Groups_Ozero__class_Ozero(U_863)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),U_864) != c_Groups_Ozero__class_Ozero(U_863)
        | ~ sP39(U_863,U_864) )
    & ! [U_863,U_864] :
        ( sP39(U_863,U_864)
        | ~ class_Groups_Olinordered__ab__group__add(U_863) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_210_2]) ).

cnf(f_210_4,plain,
    ( sP39(U_863,U_864)
    | ~ class_Groups_Olinordered__ab__group__add(U_863) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_5,plain,
    ( U_864 = c_Groups_Ozero__class_Ozero(U_863)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),U_864) != c_Groups_Ozero__class_Ozero(U_863)
    | ~ sP39(U_863,U_864) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),U_864) = c_Groups_Ozero__class_Ozero(U_863)
    | U_864 != c_Groups_Ozero__class_Ozero(U_863)
    | ~ sP39(U_863,U_864) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).

fof(f_211_2,plain,
    ! [U_867,U_866,U_865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_867),U_866)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_865),U_866)) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_867,U_866,U_865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_867),U_866)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_865),U_866)) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_867),U_866)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_865),U_866)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I2_J]) ).

fof(f_212_2,plain,
    ! [U_868] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_868)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_868] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_868)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_868)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I4_J]) ).

fof(f_213_2,plain,
    ! [U_869] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_869)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_869] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_869)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_869)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_1,plain,
    ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_option_Osize_I4_J]) ).

fof(f_214_2,plain,
    ! [U_871,U_870] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_870)),hAPP(c_Option_Ooption_OSome(U_870),U_871)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_870,U_871] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_870)),hAPP(c_Option_Ooption_OSome(U_870),U_871)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_870)),hAPP(c_Option_Ooption_OSome(U_870),U_871)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_option_Osize_I3_J]) ).

fof(f_215_2,plain,
    ! [U_872] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_872)),c_Option_Ooption_ONone(U_872)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_872] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_872)),c_Option_Ooption_ONone(U_872)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_215_2]) ).

cnf(f_215_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_872)),c_Option_Ooption_ONone(U_872)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).

fof(f_216_2,plain,
    ! [U_875,U_874,U_873] :
      ( ( ( U_874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_873),U_874),U_875)
          | U_875 != c_Groups_Ozero__class_Ozero(U_873) )
        & ( U_875 = c_Groups_Ozero__class_Ozero(U_873)
          | U_874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_873),U_874),U_875) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_873) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ( ! [U_873,U_874,U_875] :
        ( U_874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_873),U_874),U_875)
        | U_875 != c_Groups_Ozero__class_Ozero(U_873)
        | ~ sP40(U_873,U_874,U_875) )
    & ! [U_873,U_874,U_875] :
        ( U_875 = c_Groups_Ozero__class_Ozero(U_873)
        | U_874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_873),U_874),U_875)
        | ~ sP40(U_873,U_874,U_875) )
    & ! [U_873,U_874,U_875] :
        ( sP40(U_873,U_874,U_875)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_873) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_216_2]) ).

cnf(f_216_4,plain,
    ( sP40(U_873,U_874,U_875)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_873) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

cnf(f_216_5,plain,
    ( U_875 = c_Groups_Ozero__class_Ozero(U_873)
    | U_874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_873),U_874),U_875)
    | ~ sP40(U_873,U_874,U_875) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

cnf(f_216_6,plain,
    ( U_874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_873),U_874),U_875)
    | U_875 != c_Groups_Ozero__class_Ozero(U_873)
    | ~ sP40(U_873,U_874,U_875) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).

fof(f_217_2,plain,
    ! [U_877,U_876] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_876),U_877),c_Groups_Ozero__class_Ozero(U_876)) = U_877
      | ~ class_Rings_Ocomm__semiring__1(U_876) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_877,U_876] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_876),U_877),c_Groups_Ozero__class_Ozero(U_876)) = U_877
      | ~ class_Rings_Ocomm__semiring__1(U_876) ),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_876),U_877),c_Groups_Ozero__class_Ozero(U_876)) = U_877
    | ~ class_Rings_Ocomm__semiring__1(U_876) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).

fof(f_218_2,plain,
    ! [U_879,U_878] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_878),c_Groups_Ozero__class_Ozero(U_878)),U_879) = U_879
      | ~ class_Rings_Ocomm__semiring__1(U_878) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ! [U_878,U_879] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_878),c_Groups_Ozero__class_Ozero(U_878)),U_879) = U_879
      | ~ class_Rings_Ocomm__semiring__1(U_878) ),
    inference(definitional_conversion,[status(esa)],[f_218_2]) ).

cnf(f_218_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_878),c_Groups_Ozero__class_Ozero(U_878)),U_879) = U_879
    | ~ class_Rings_Ocomm__semiring__1(U_878) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_1,plain,
    ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I12_J]) ).

fof(f_219_2,plain,
    ! [U_881,U_880] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_880,U_881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_880)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_881))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ! [U_880,U_881] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_880,U_881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_880)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_881))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_219_2]) ).

cnf(f_219_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_880,U_881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_880)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_881))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I4_J]) ).

fof(f_220_2,plain,
    ! [U_883,U_882] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_882,U_883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_882)),c_Com_Ocom_Ocom__size(U_883))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_882,U_883] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_882,U_883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_882)),c_Com_Ocom_Ocom__size(U_883))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_882,U_883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_882)),c_Com_Ocom_Ocom__size(U_883))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I13_J]) ).

fof(f_221_2,plain,
    ! [U_886,U_885,U_884] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_884,U_885,U_886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_885)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_886))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ! [U_884,U_885,U_886] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_884,U_885,U_886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_885)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_886))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_221_2]) ).

cnf(f_221_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_884,U_885,U_886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_885)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_886))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I5_J]) ).

fof(f_222_2,plain,
    ! [U_889,U_888,U_887] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_887,U_888,U_889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_888)),c_Com_Ocom_Ocom__size(U_889))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_887,U_888,U_889] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_887,U_888,U_889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_888)),c_Com_Ocom_Ocom__size(U_889))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_887,U_888,U_889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_888)),c_Com_Ocom_Ocom__size(U_889))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( ( c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2)
        & ~ hBOOL(hAPP(V_b_2,V_s_2)) )
      | ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2)
        & hBOOL(hAPP(V_b_2,V_s_2)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I5_J]) ).

fof(f_223_2,plain,
    ! [U_895,U_894,U_893,U_892,U_891,U_890] :
      ( ( c_Natural_Oevaln(U_892,U_893,U_894,U_895)
        & ~ hBOOL(hAPP(U_890,U_893)) )
      | ( c_Natural_Oevaln(U_891,U_893,U_894,U_895)
        & hBOOL(hAPP(U_890,U_893)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_890,U_891,U_892),U_893,U_894,U_895) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ( ! [U_890,U_892,U_893,U_894,U_895] :
        ( c_Natural_Oevaln(U_892,U_893,U_894,U_895)
        | ~ sP42(U_890,U_892,U_893,U_894,U_895) )
    & ! [U_890,U_892,U_893,U_894,U_895] :
        ( ~ hBOOL(hAPP(U_890,U_893))
        | ~ sP42(U_890,U_892,U_893,U_894,U_895) )
    & ! [U_890,U_891,U_893,U_894,U_895] :
        ( c_Natural_Oevaln(U_891,U_893,U_894,U_895)
        | ~ sP41(U_890,U_891,U_893,U_894,U_895) )
    & ! [U_890,U_891,U_893,U_894,U_895] :
        ( hBOOL(hAPP(U_890,U_893))
        | ~ sP41(U_890,U_891,U_893,U_894,U_895) )
    & ! [U_890,U_891,U_892,U_893,U_894,U_895] :
        ( sP42(U_890,U_892,U_893,U_894,U_895)
        | sP41(U_890,U_891,U_893,U_894,U_895)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_890,U_891,U_892),U_893,U_894,U_895) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42])],[f_223_2]) ).

cnf(f_223_4,plain,
    ( sP42(U_890,U_892,U_893,U_894,U_895)
    | sP41(U_890,U_891,U_893,U_894,U_895)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_890,U_891,U_892),U_893,U_894,U_895) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( hBOOL(hAPP(U_890,U_893))
    | ~ sP41(U_890,U_891,U_893,U_894,U_895) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_6,plain,
    ( c_Natural_Oevaln(U_891,U_893,U_894,U_895)
    | ~ sP41(U_890,U_891,U_893,U_894,U_895) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_7,plain,
    ( ~ hBOOL(hAPP(U_890,U_893))
    | ~ sP42(U_890,U_892,U_893,U_894,U_895) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_8,plain,
    ( c_Natural_Oevaln(U_892,U_893,U_894,U_895)
    | ~ sP42(U_890,U_892,U_893,U_894,U_895) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2)
      | ~ c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
      | ~ hBOOL(hAPP(V_b_2,V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OIfTrue]) ).

fof(f_224_2,plain,
    ! [U_901,U_900,U_899,U_898,U_897,U_896] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_896,U_898,U_901),U_897,U_899,U_900)
      | ~ c_Natural_Oevaln(U_898,U_897,U_899,U_900)
      | ~ hBOOL(hAPP(U_896,U_897)) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ! [U_900,U_901,U_899,U_897,U_896,U_898] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_896,U_898,U_901),U_897,U_899,U_900)
      | ~ c_Natural_Oevaln(U_898,U_897,U_899,U_900)
      | ~ hBOOL(hAPP(U_896,U_897)) ),
    inference(definitional_conversion,[status(esa)],[f_224_2]) ).

cnf(f_224_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_896,U_898,U_901),U_897,U_899,U_900)
    | ~ c_Natural_Oevaln(U_898,U_897,U_899,U_900)
    | ~ hBOOL(hAPP(U_896,U_897)) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_1,plain,
    ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2)
      | ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
      | hBOOL(hAPP(V_b_2,V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OIfFalse]) ).

fof(f_225_2,plain,
    ! [U_907,U_906,U_905,U_904,U_903,U_902] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_902,U_907,U_904),U_903,U_905,U_906)
      | ~ c_Natural_Oevaln(U_904,U_903,U_905,U_906)
      | hBOOL(hAPP(U_902,U_903)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_903,U_902,U_906,U_904,U_905,U_907] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_902,U_907,U_904),U_903,U_905,U_906)
      | ~ c_Natural_Oevaln(U_904,U_903,U_905,U_906)
      | hBOOL(hAPP(U_902,U_903)) ),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_902,U_907,U_904),U_903,U_905,U_906)
    | ~ c_Natural_Oevaln(U_904,U_903,U_905,U_906)
    | hBOOL(hAPP(U_902,U_903)) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_1,plain,
    ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
      | hBOOL(hAPP(V_b_2,V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OIfFalse]) ).

fof(f_226_2,plain,
    ! [U_912,U_911,U_910,U_909,U_908] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_908,U_912,U_910)),U_909),U_911))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_910),U_909),U_911))
      | hBOOL(hAPP(U_908,U_909)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_909,U_908,U_910,U_911,U_912] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_908,U_912,U_910)),U_909),U_911))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_910),U_909),U_911))
      | hBOOL(hAPP(U_908,U_909)) ),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_908,U_912,U_910)),U_909),U_911))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_910),U_909),U_911))
    | hBOOL(hAPP(U_908,U_909)) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_1,plain,
    ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
      | ~ hBOOL(hAPP(V_b_2,V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OIfTrue]) ).

fof(f_227_2,plain,
    ! [U_917,U_916,U_915,U_914,U_913] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_913,U_915,U_917)),U_914),U_916))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_915),U_914),U_916))
      | ~ hBOOL(hAPP(U_913,U_914)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_914,U_913,U_915,U_916,U_917] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_913,U_915,U_917)),U_914),U_916))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_915),U_914),U_916))
      | ~ hBOOL(hAPP(U_913,U_914)) ),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_913,U_915,U_917)),U_914),U_916))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_915),U_914),U_916))
    | ~ hBOOL(hAPP(U_913,U_914)) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_1,plain,
    ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2))
        & ~ hBOOL(hAPP(V_b_2,V_s_2)) )
      | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2))
        & hBOOL(hAPP(V_b_2,V_s_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I5_J]) ).

fof(f_228_2,plain,
    ! [U_922,U_921,U_920,U_919,U_918] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_920),U_921),U_922))
        & ~ hBOOL(hAPP(U_918,U_921)) )
      | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_919),U_921),U_922))
        & hBOOL(hAPP(U_918,U_921)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_918,U_919,U_920)),U_921),U_922)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_918,U_920,U_921,U_922] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_920),U_921),U_922))
        | ~ sP44(U_918,U_920,U_921,U_922) )
    & ! [U_918,U_920,U_921,U_922] :
        ( ~ hBOOL(hAPP(U_918,U_921))
        | ~ sP44(U_918,U_920,U_921,U_922) )
    & ! [U_919,U_918,U_921,U_922] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_919),U_921),U_922))
        | ~ sP43(U_919,U_918,U_921,U_922) )
    & ! [U_919,U_918,U_921,U_922] :
        ( hBOOL(hAPP(U_918,U_921))
        | ~ sP43(U_919,U_918,U_921,U_922) )
    & ! [U_919,U_918,U_920,U_921,U_922] :
        ( sP44(U_918,U_920,U_921,U_922)
        | sP43(U_919,U_918,U_921,U_922)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_918,U_919,U_920)),U_921),U_922)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43,sP44])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP44(U_918,U_920,U_921,U_922)
    | sP43(U_919,U_918,U_921,U_922)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_918,U_919,U_920)),U_921),U_922)) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( hBOOL(hAPP(U_918,U_921))
    | ~ sP43(U_919,U_918,U_921,U_922) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_919),U_921),U_922))
    | ~ sP43(U_919,U_918,U_921,U_922) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_7,plain,
    ( ~ hBOOL(hAPP(U_918,U_921))
    | ~ sP44(U_918,U_920,U_921,U_922) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_920),U_921),U_922))
    | ~ sP44(U_918,U_920,U_921,U_922) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_1,plain,
    ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2)
      | ~ c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
      | ~ c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OSemi]) ).

fof(f_229_2,plain,
    ! [U_928,U_927,U_926,U_925,U_924,U_923] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_923,U_927),U_924,U_925,U_928)
      | ~ c_Natural_Oevaln(U_927,U_926,U_925,U_928)
      | ~ c_Natural_Oevaln(U_923,U_924,U_925,U_926) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_925,U_924,U_923,U_926,U_927,U_928] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_923,U_927),U_924,U_925,U_928)
      | ~ c_Natural_Oevaln(U_927,U_926,U_925,U_928)
      | ~ c_Natural_Oevaln(U_923,U_924,U_925,U_926) ),
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_923,U_927),U_924,U_925,U_928)
    | ~ c_Natural_Oevaln(U_927,U_926,U_925,U_928)
    | ~ c_Natural_Oevaln(U_923,U_924,U_925,U_926) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_1,plain,
    ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OSemi]) ).

fof(f_230_2,plain,
    ! [U_933,U_932,U_931,U_930,U_929] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_929,U_932)),U_930),U_933))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_932),U_931),U_933))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_929),U_930),U_931)) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_931,U_930,U_929,U_932,U_933] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_929,U_932)),U_930),U_933))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_932),U_931),U_933))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_929),U_930),U_931)) ),
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_929,U_932)),U_930),U_933))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_932),U_931),U_933))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_929),U_930),U_931)) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_1,plain,
    ! [V_c2_2,V_c1_2,V_b_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,V_c2_2))
        & hBOOL(hAPP(c_Com_OWT,V_c1_2)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I5_J]) ).

fof(f_231_2,plain,
    ! [U_936,U_935,U_934] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_936))
        & hBOOL(hAPP(c_Com_OWT,U_935)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_934,U_935,U_936))) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_936,U_935] :
      ( ! [U_934] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_934,U_935,U_936)))
      | ( hBOOL(hAPP(c_Com_OWT,U_936))
        & hBOOL(hAPP(c_Com_OWT,U_935)) ) ),
    inference(miniscope,[status(thm)],[f_231_2]) ).

fof(f_231_4,plain,
    ( ! [U_935,U_936] :
        ( hBOOL(hAPP(c_Com_OWT,U_936))
        | ~ sP45(U_935,U_936) )
    & ! [U_935,U_936] :
        ( hBOOL(hAPP(c_Com_OWT,U_935))
        | ~ sP45(U_935,U_936) )
    & ! [U_934,U_935,U_936] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_934,U_935,U_936)))
        | sP45(U_935,U_936) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_231_3]) ).

cnf(f_231_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_934,U_935,U_936)))
    | sP45(U_935,U_936) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

cnf(f_231_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_935))
    | ~ sP45(U_935,U_936) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

cnf(f_231_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_936))
    | ~ sP45(U_935,U_936) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

fof(f_232_1,plain,
    ! [V_c2,V_c1] :
      ( ( hBOOL(hAPP(c_Com_OWT,V_c2))
        & hBOOL(hAPP(c_Com_OWT,V_c1)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I4_J]) ).

fof(f_232_2,plain,
    ! [U_938,U_937] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_938))
        & hBOOL(hAPP(c_Com_OWT,U_937)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_937,U_938))) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ( ! [U_938,U_937] :
        ( hBOOL(hAPP(c_Com_OWT,U_938))
        | ~ sP46(U_938,U_937) )
    & ! [U_938,U_937] :
        ( hBOOL(hAPP(c_Com_OWT,U_937))
        | ~ sP46(U_938,U_937) )
    & ! [U_938,U_937] :
        ( sP46(U_938,U_937)
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_937,U_938))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_232_2]) ).

cnf(f_232_4,plain,
    ( sP46(U_938,U_937)
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_937,U_938))) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

cnf(f_232_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_937))
    | ~ sP46(U_938,U_937) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

cnf(f_232_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_938))
    | ~ sP46(U_938,U_937) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
      ( ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
        | V_com2_2 != V_com2_H_2
        | V_com1_2 != V_com1_H_2
        | V_fun_2 != V_fun_H_2 )
      & ( ( V_com2_2 = V_com2_H_2
          & V_com1_2 = V_com1_H_2
          & V_fun_2 = V_fun_H_2 )
        | c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J]) ).

fof(f_233_2,plain,
    ! [U_944,U_943,U_942,U_941,U_940,U_939] :
      ( ( c_Com_Ocom_OCond(U_939,U_940,U_941) = c_Com_Ocom_OCond(U_942,U_943,U_944)
        | U_941 != U_944
        | U_940 != U_943
        | U_939 != U_942 )
      & ( ( U_941 = U_944
          & U_940 = U_943
          & U_939 = U_942 )
        | c_Com_Ocom_OCond(U_939,U_940,U_941) != c_Com_Ocom_OCond(U_942,U_943,U_944) ) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ( ! [U_956,U_954,U_952,U_950,U_948,U_946] :
        ( c_Com_Ocom_OCond(U_946,U_948,U_950) = c_Com_Ocom_OCond(U_952,U_954,U_956)
        | U_950 != U_956
        | U_948 != U_954
        | U_946 != U_952 )
    & ! [U_955,U_953,U_951,U_949,U_947,U_945] :
        ( ( U_949 = U_955
          & U_947 = U_953
          & U_945 = U_951 )
        | c_Com_Ocom_OCond(U_945,U_947,U_949) != c_Com_Ocom_OCond(U_951,U_953,U_955) ) ),
    inference(miniscope,[status(thm)],[f_233_2]) ).

fof(f_233_4,plain,
    ( ! [U_949,U_955,U_951,U_945,U_947,U_953] :
        ( U_949 = U_955
        | ~ sP47(U_949,U_955,U_951,U_945,U_947,U_953) )
    & ! [U_949,U_955,U_951,U_945,U_947,U_953] :
        ( U_947 = U_953
        | ~ sP47(U_949,U_955,U_951,U_945,U_947,U_953) )
    & ! [U_949,U_955,U_951,U_945,U_947,U_953] :
        ( U_945 = U_951
        | ~ sP47(U_949,U_955,U_951,U_945,U_947,U_953) )
    & ! [U_950,U_952,U_948,U_946,U_954,U_956] :
        ( c_Com_Ocom_OCond(U_946,U_948,U_950) = c_Com_Ocom_OCond(U_952,U_954,U_956)
        | U_950 != U_956
        | U_948 != U_954
        | U_946 != U_952 )
    & ! [U_949,U_955,U_951,U_945,U_947,U_953] :
        ( sP47(U_949,U_955,U_951,U_945,U_947,U_953)
        | c_Com_Ocom_OCond(U_945,U_947,U_949) != c_Com_Ocom_OCond(U_951,U_953,U_955) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_233_3]) ).

cnf(f_233_5,plain,
    ( sP47(U_949,U_955,U_951,U_945,U_947,U_953)
    | c_Com_Ocom_OCond(U_945,U_947,U_949) != c_Com_Ocom_OCond(U_951,U_953,U_955) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_6,plain,
    ( c_Com_Ocom_OCond(U_946,U_948,U_950) = c_Com_Ocom_OCond(U_952,U_954,U_956)
    | U_950 != U_956
    | U_948 != U_954
    | U_946 != U_952 ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_7,plain,
    ( U_945 = U_951
    | ~ sP47(U_949,U_955,U_951,U_945,U_947,U_953) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_8,plain,
    ( U_947 = U_953
    | ~ sP47(U_949,U_955,U_951,U_945,U_947,U_953) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_9,plain,
    ( U_949 = U_955
    | ~ sP47(U_949,U_955,U_951,U_945,U_947,U_953) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

fof(f_234_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
      ( ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
        | V_com2_2 != V_com2_H_2
        | V_com1_2 != V_com1_H_2 )
      & ( ( V_com2_2 = V_com2_H_2
          & V_com1_2 = V_com1_H_2 )
        | c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J]) ).

fof(f_234_2,plain,
    ! [U_960,U_959,U_958,U_957] :
      ( ( c_Com_Ocom_OSemi(U_957,U_958) = c_Com_Ocom_OSemi(U_959,U_960)
        | U_958 != U_960
        | U_957 != U_959 )
      & ( ( U_958 = U_960
          & U_957 = U_959 )
        | c_Com_Ocom_OSemi(U_957,U_958) != c_Com_Ocom_OSemi(U_959,U_960) ) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ( ! [U_968,U_966,U_964,U_962] :
        ( c_Com_Ocom_OSemi(U_962,U_964) = c_Com_Ocom_OSemi(U_966,U_968)
        | U_964 != U_968
        | U_962 != U_966 )
    & ! [U_967,U_965,U_963,U_961] :
        ( ( U_963 = U_967
          & U_961 = U_965 )
        | c_Com_Ocom_OSemi(U_961,U_963) != c_Com_Ocom_OSemi(U_965,U_967) ) ),
    inference(miniscope,[status(thm)],[f_234_2]) ).

fof(f_234_4,plain,
    ( ! [U_961,U_967,U_963,U_965] :
        ( U_963 = U_967
        | ~ sP48(U_961,U_967,U_963,U_965) )
    & ! [U_961,U_967,U_963,U_965] :
        ( U_961 = U_965
        | ~ sP48(U_961,U_967,U_963,U_965) )
    & ! [U_968,U_964,U_966,U_962] :
        ( c_Com_Ocom_OSemi(U_962,U_964) = c_Com_Ocom_OSemi(U_966,U_968)
        | U_964 != U_968
        | U_962 != U_966 )
    & ! [U_961,U_967,U_963,U_965] :
        ( sP48(U_961,U_967,U_963,U_965)
        | c_Com_Ocom_OSemi(U_961,U_963) != c_Com_Ocom_OSemi(U_965,U_967) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_234_3]) ).

cnf(f_234_5,plain,
    ( sP48(U_961,U_967,U_963,U_965)
    | c_Com_Ocom_OSemi(U_961,U_963) != c_Com_Ocom_OSemi(U_965,U_967) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

cnf(f_234_6,plain,
    ( c_Com_Ocom_OSemi(U_962,U_964) = c_Com_Ocom_OSemi(U_966,U_968)
    | U_964 != U_968
    | U_962 != U_966 ),
    inference(clausify,[status(thm)],[f_234_4]) ).

cnf(f_234_7,plain,
    ( U_961 = U_965
    | ~ sP48(U_961,U_967,U_963,U_965) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

cnf(f_234_8,plain,
    ( U_963 = U_967
    | ~ sP48(U_961,U_967,U_963,U_965) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

fof(f_235_1,plain,
    ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I45_J]) ).

fof(f_235_2,plain,
    ! [U_973,U_972,U_971,U_970,U_969] : c_Com_Ocom_OCond(U_969,U_970,U_971) != c_Com_Ocom_OSemi(U_972,U_973),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_971,U_970,U_973,U_972,U_969] : c_Com_Ocom_OCond(U_969,U_970,U_971) != c_Com_Ocom_OSemi(U_972,U_973),
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    c_Com_Ocom_OCond(U_969,U_970,U_971) != c_Com_Ocom_OSemi(U_972,U_973),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I44_J]) ).

fof(f_236_2,plain,
    ! [U_978,U_977,U_976,U_975,U_974] : c_Com_Ocom_OSemi(U_974,U_975) != c_Com_Ocom_OCond(U_976,U_977,U_978),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ! [U_976,U_974,U_977,U_978,U_975] : c_Com_Ocom_OSemi(U_974,U_975) != c_Com_Ocom_OCond(U_976,U_977,U_978),
    inference(definitional_conversion,[status(esa)],[f_236_2]) ).

cnf(f_236_4,plain,
    c_Com_Ocom_OSemi(U_974,U_975) != c_Com_Ocom_OCond(U_976,U_977,U_978),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__size]) ).

fof(f_237_2,plain,
    ! [U_979] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_979) = U_979,
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_979] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_979) = U_979,
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_979) = U_979,
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_1,plain,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2),V_a2_2,V_a4_2,V_a5_2)
        | ( ( ~ c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2)
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2)
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) )
      & ( ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2)
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2)
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2),V_a2_2,V_a4_2,V_a5_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I6_J]) ).

fof(f_238_2,plain,
    ! [U_985,U_984,U_983,U_982,U_981,U_980] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_980,U_981,U_982),U_983,U_984,U_985)
        | ( ( ~ c_Natural_Oevaln(U_982,U_983,U_984,U_985)
            | hBOOL(hAPP(U_980,U_983)) )
          & ( ~ c_Natural_Oevaln(U_981,U_983,U_984,U_985)
            | ~ hBOOL(hAPP(U_980,U_983)) ) ) )
      & ( ( c_Natural_Oevaln(U_982,U_983,U_984,U_985)
          & ~ hBOOL(hAPP(U_980,U_983)) )
        | ( c_Natural_Oevaln(U_981,U_983,U_984,U_985)
          & hBOOL(hAPP(U_980,U_983)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_980,U_981,U_982),U_983,U_984,U_985) ) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ( ! [U_997,U_995,U_993,U_991,U_989,U_987] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_987,U_989,U_991),U_993,U_995,U_997)
        | ( ( ~ c_Natural_Oevaln(U_991,U_993,U_995,U_997)
            | hBOOL(hAPP(U_987,U_993)) )
          & ( ~ c_Natural_Oevaln(U_989,U_993,U_995,U_997)
            | ~ hBOOL(hAPP(U_987,U_993)) ) ) )
    & ! [U_996,U_994,U_992,U_990,U_988,U_986] :
        ( ( c_Natural_Oevaln(U_990,U_992,U_994,U_996)
          & ~ hBOOL(hAPP(U_986,U_992)) )
        | ( c_Natural_Oevaln(U_988,U_992,U_994,U_996)
          & hBOOL(hAPP(U_986,U_992)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_986,U_988,U_990),U_992,U_994,U_996) ) ),
    inference(miniscope,[status(thm)],[f_238_2]) ).

fof(f_238_4,plain,
    ( ! [U_993,U_989,U_997,U_991,U_987,U_995] :
        ( ~ c_Natural_Oevaln(U_991,U_993,U_995,U_997)
        | hBOOL(hAPP(U_987,U_993))
        | ~ sP51(U_993,U_989,U_997,U_991,U_987,U_995) )
    & ! [U_993,U_989,U_997,U_991,U_987,U_995] :
        ( ~ c_Natural_Oevaln(U_989,U_993,U_995,U_997)
        | ~ hBOOL(hAPP(U_987,U_993))
        | ~ sP51(U_993,U_989,U_997,U_991,U_987,U_995) )
    & ! [U_990,U_994,U_996,U_986,U_992] :
        ( c_Natural_Oevaln(U_990,U_992,U_994,U_996)
        | ~ sP50(U_990,U_994,U_996,U_986,U_992) )
    & ! [U_990,U_994,U_996,U_986,U_992] :
        ( ~ hBOOL(hAPP(U_986,U_992))
        | ~ sP50(U_990,U_994,U_996,U_986,U_992) )
    & ! [U_994,U_988,U_996,U_986,U_992] :
        ( c_Natural_Oevaln(U_988,U_992,U_994,U_996)
        | ~ sP49(U_994,U_988,U_996,U_986,U_992) )
    & ! [U_994,U_988,U_996,U_986,U_992] :
        ( hBOOL(hAPP(U_986,U_992))
        | ~ sP49(U_994,U_988,U_996,U_986,U_992) )
    & ! [U_993,U_989,U_997,U_991,U_987,U_995] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_987,U_989,U_991),U_993,U_995,U_997)
        | sP51(U_993,U_989,U_997,U_991,U_987,U_995) )
    & ! [U_990,U_994,U_988,U_996,U_986,U_992] :
        ( sP50(U_990,U_994,U_996,U_986,U_992)
        | sP49(U_994,U_988,U_996,U_986,U_992)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_986,U_988,U_990),U_992,U_994,U_996) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50,sP51])],[f_238_3]) ).

cnf(f_238_5,plain,
    ( sP50(U_990,U_994,U_996,U_986,U_992)
    | sP49(U_994,U_988,U_996,U_986,U_992)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_986,U_988,U_990),U_992,U_994,U_996) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_6,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_987,U_989,U_991),U_993,U_995,U_997)
    | sP51(U_993,U_989,U_997,U_991,U_987,U_995) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_7,plain,
    ( hBOOL(hAPP(U_986,U_992))
    | ~ sP49(U_994,U_988,U_996,U_986,U_992) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_8,plain,
    ( c_Natural_Oevaln(U_988,U_992,U_994,U_996)
    | ~ sP49(U_994,U_988,U_996,U_986,U_992) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_9,plain,
    ( ~ hBOOL(hAPP(U_986,U_992))
    | ~ sP50(U_990,U_994,U_996,U_986,U_992) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_10,plain,
    ( c_Natural_Oevaln(U_990,U_992,U_994,U_996)
    | ~ sP50(U_990,U_994,U_996,U_986,U_992) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_11,plain,
    ( ~ c_Natural_Oevaln(U_989,U_993,U_995,U_997)
    | ~ hBOOL(hAPP(U_987,U_993))
    | ~ sP51(U_993,U_989,U_997,U_991,U_987,U_995) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_12,plain,
    ( ~ c_Natural_Oevaln(U_991,U_993,U_995,U_997)
    | hBOOL(hAPP(U_987,U_993))
    | ~ sP51(U_993,U_989,U_997,U_991,U_987,U_995) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

fof(f_239_1,plain,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2),V_a2_2,V_a4_2,V_a5_2)
        | ( ( ~ c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2)
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2)
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) )
      & ( ( c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2)
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2)
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2),V_a2_2,V_a4_2,V_a5_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I5_J]) ).

fof(f_239_2,plain,
    ! [U_1003,U_1002,U_1001,U_1000,U_999,U_998] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_998,U_999,U_1000),U_1001,U_1002,U_1003)
        | ( ( ~ c_Natural_Oevaln(U_1000,U_1001,U_1002,U_1003)
            | hBOOL(hAPP(U_998,U_1001)) )
          & ( ~ c_Natural_Oevaln(U_999,U_1001,U_1002,U_1003)
            | ~ hBOOL(hAPP(U_998,U_1001)) ) ) )
      & ( ( c_Natural_Oevaln(U_1000,U_1001,U_1002,U_1003)
          & ~ hBOOL(hAPP(U_998,U_1001)) )
        | ( c_Natural_Oevaln(U_999,U_1001,U_1002,U_1003)
          & hBOOL(hAPP(U_998,U_1001)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_998,U_999,U_1000),U_1001,U_1002,U_1003) ) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ( ! [U_1015,U_1013,U_1011,U_1009,U_1007,U_1005] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_1005,U_1007,U_1009),U_1011,U_1013,U_1015)
        | ( ( ~ c_Natural_Oevaln(U_1009,U_1011,U_1013,U_1015)
            | hBOOL(hAPP(U_1005,U_1011)) )
          & ( ~ c_Natural_Oevaln(U_1007,U_1011,U_1013,U_1015)
            | ~ hBOOL(hAPP(U_1005,U_1011)) ) ) )
    & ! [U_1014,U_1012,U_1010,U_1008,U_1006,U_1004] :
        ( ( c_Natural_Oevaln(U_1008,U_1010,U_1012,U_1014)
          & ~ hBOOL(hAPP(U_1004,U_1010)) )
        | ( c_Natural_Oevaln(U_1006,U_1010,U_1012,U_1014)
          & hBOOL(hAPP(U_1004,U_1010)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_1004,U_1006,U_1008),U_1010,U_1012,U_1014) ) ),
    inference(miniscope,[status(thm)],[f_239_2]) ).

fof(f_239_4,plain,
    ( ! [U_1011,U_1015,U_1013,U_1007,U_1009,U_1005] :
        ( ~ c_Natural_Oevaln(U_1009,U_1011,U_1013,U_1015)
        | hBOOL(hAPP(U_1005,U_1011))
        | ~ sP54(U_1011,U_1015,U_1013,U_1007,U_1009,U_1005) )
    & ! [U_1011,U_1015,U_1013,U_1007,U_1009,U_1005] :
        ( ~ c_Natural_Oevaln(U_1007,U_1011,U_1013,U_1015)
        | ~ hBOOL(hAPP(U_1005,U_1011))
        | ~ sP54(U_1011,U_1015,U_1013,U_1007,U_1009,U_1005) )
    & ! [U_1008,U_1012,U_1004,U_1014,U_1010] :
        ( c_Natural_Oevaln(U_1008,U_1010,U_1012,U_1014)
        | ~ sP53(U_1008,U_1012,U_1004,U_1014,U_1010) )
    & ! [U_1008,U_1012,U_1004,U_1014,U_1010] :
        ( ~ hBOOL(hAPP(U_1004,U_1010))
        | ~ sP53(U_1008,U_1012,U_1004,U_1014,U_1010) )
    & ! [U_1012,U_1006,U_1004,U_1014,U_1010] :
        ( c_Natural_Oevaln(U_1006,U_1010,U_1012,U_1014)
        | ~ sP52(U_1012,U_1006,U_1004,U_1014,U_1010) )
    & ! [U_1012,U_1006,U_1004,U_1014,U_1010] :
        ( hBOOL(hAPP(U_1004,U_1010))
        | ~ sP52(U_1012,U_1006,U_1004,U_1014,U_1010) )
    & ! [U_1011,U_1015,U_1013,U_1007,U_1009,U_1005] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_1005,U_1007,U_1009),U_1011,U_1013,U_1015)
        | sP54(U_1011,U_1015,U_1013,U_1007,U_1009,U_1005) )
    & ! [U_1008,U_1012,U_1006,U_1004,U_1014,U_1010] :
        ( sP53(U_1008,U_1012,U_1004,U_1014,U_1010)
        | sP52(U_1012,U_1006,U_1004,U_1014,U_1010)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_1004,U_1006,U_1008),U_1010,U_1012,U_1014) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52,sP53,sP54])],[f_239_3]) ).

cnf(f_239_5,plain,
    ( sP53(U_1008,U_1012,U_1004,U_1014,U_1010)
    | sP52(U_1012,U_1006,U_1004,U_1014,U_1010)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_1004,U_1006,U_1008),U_1010,U_1012,U_1014) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_6,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_1005,U_1007,U_1009),U_1011,U_1013,U_1015)
    | sP54(U_1011,U_1015,U_1013,U_1007,U_1009,U_1005) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_7,plain,
    ( hBOOL(hAPP(U_1004,U_1010))
    | ~ sP52(U_1012,U_1006,U_1004,U_1014,U_1010) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_8,plain,
    ( c_Natural_Oevaln(U_1006,U_1010,U_1012,U_1014)
    | ~ sP52(U_1012,U_1006,U_1004,U_1014,U_1010) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_9,plain,
    ( ~ hBOOL(hAPP(U_1004,U_1010))
    | ~ sP53(U_1008,U_1012,U_1004,U_1014,U_1010) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_10,plain,
    ( c_Natural_Oevaln(U_1008,U_1010,U_1012,U_1014)
    | ~ sP53(U_1008,U_1012,U_1004,U_1014,U_1010) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_11,plain,
    ( ~ c_Natural_Oevaln(U_1007,U_1011,U_1013,U_1015)
    | ~ hBOOL(hAPP(U_1005,U_1011))
    | ~ sP54(U_1011,U_1015,U_1013,U_1007,U_1009,U_1005) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_12,plain,
    ( ~ c_Natural_Oevaln(U_1009,U_1011,U_1013,U_1015)
    | hBOOL(hAPP(U_1005,U_1011))
    | ~ sP54(U_1011,U_1015,U_1013,U_1007,U_1009,U_1005) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

fof(f_240_1,plain,
    ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I5_J]) ).

fof(f_240_2,plain,
    ! [U_1020,U_1019,U_1018,U_1017,U_1016] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1016,U_1017,U_1018)),U_1019),U_1020))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1018),U_1019),U_1020))
            | hBOOL(hAPP(U_1016,U_1019)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1017),U_1019),U_1020))
            | ~ hBOOL(hAPP(U_1016,U_1019)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1018),U_1019),U_1020))
          & ~ hBOOL(hAPP(U_1016,U_1019)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1017),U_1019),U_1020))
          & hBOOL(hAPP(U_1016,U_1019)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1016,U_1017,U_1018)),U_1019),U_1020)) ) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ( ! [U_1030,U_1028,U_1026,U_1024,U_1022] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1022,U_1024,U_1026)),U_1028),U_1030))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1026),U_1028),U_1030))
            | hBOOL(hAPP(U_1022,U_1028)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1024),U_1028),U_1030))
            | ~ hBOOL(hAPP(U_1022,U_1028)) ) ) )
    & ! [U_1029,U_1027,U_1025,U_1023,U_1021] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1025),U_1027),U_1029))
          & ~ hBOOL(hAPP(U_1021,U_1027)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1023),U_1027),U_1029))
          & hBOOL(hAPP(U_1021,U_1027)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1021,U_1023,U_1025)),U_1027),U_1029)) ) ),
    inference(miniscope,[status(thm)],[f_240_2]) ).

fof(f_240_4,plain,
    ( ! [U_1024,U_1022,U_1026,U_1028,U_1030] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1026),U_1028),U_1030))
        | hBOOL(hAPP(U_1022,U_1028))
        | ~ sP57(U_1024,U_1022,U_1026,U_1028,U_1030) )
    & ! [U_1024,U_1022,U_1026,U_1028,U_1030] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1024),U_1028),U_1030))
        | ~ hBOOL(hAPP(U_1022,U_1028))
        | ~ sP57(U_1024,U_1022,U_1026,U_1028,U_1030) )
    & ! [U_1021,U_1025,U_1027,U_1029] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1025),U_1027),U_1029))
        | ~ sP56(U_1021,U_1025,U_1027,U_1029) )
    & ! [U_1021,U_1025,U_1027,U_1029] :
        ( ~ hBOOL(hAPP(U_1021,U_1027))
        | ~ sP56(U_1021,U_1025,U_1027,U_1029) )
    & ! [U_1021,U_1023,U_1027,U_1029] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1023),U_1027),U_1029))
        | ~ sP55(U_1021,U_1023,U_1027,U_1029) )
    & ! [U_1021,U_1023,U_1027,U_1029] :
        ( hBOOL(hAPP(U_1021,U_1027))
        | ~ sP55(U_1021,U_1023,U_1027,U_1029) )
    & ! [U_1024,U_1022,U_1026,U_1028,U_1030] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1022,U_1024,U_1026)),U_1028),U_1030))
        | sP57(U_1024,U_1022,U_1026,U_1028,U_1030) )
    & ! [U_1021,U_1023,U_1025,U_1027,U_1029] :
        ( sP56(U_1021,U_1025,U_1027,U_1029)
        | sP55(U_1021,U_1023,U_1027,U_1029)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1021,U_1023,U_1025)),U_1027),U_1029)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55,sP56,sP57])],[f_240_3]) ).

cnf(f_240_5,plain,
    ( sP56(U_1021,U_1025,U_1027,U_1029)
    | sP55(U_1021,U_1023,U_1027,U_1029)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1021,U_1023,U_1025)),U_1027),U_1029)) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1022,U_1024,U_1026)),U_1028),U_1030))
    | sP57(U_1024,U_1022,U_1026,U_1028,U_1030) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_7,plain,
    ( hBOOL(hAPP(U_1021,U_1027))
    | ~ sP55(U_1021,U_1023,U_1027,U_1029) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1023),U_1027),U_1029))
    | ~ sP55(U_1021,U_1023,U_1027,U_1029) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_9,plain,
    ( ~ hBOOL(hAPP(U_1021,U_1027))
    | ~ sP56(U_1021,U_1025,U_1027,U_1029) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1025),U_1027),U_1029))
    | ~ sP56(U_1021,U_1025,U_1027,U_1029) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1024),U_1028),U_1030))
    | ~ hBOOL(hAPP(U_1022,U_1028))
    | ~ sP57(U_1024,U_1022,U_1026,U_1028,U_1030) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1026),U_1028),U_1030))
    | hBOOL(hAPP(U_1022,U_1028))
    | ~ sP57(U_1024,U_1022,U_1026,U_1028,U_1030) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

fof(f_241_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I6_J]) ).

fof(f_241_2,plain,
    ! [U_1035,U_1034,U_1033,U_1032,U_1031] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1031,U_1032,U_1033)),U_1034),U_1035))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1033),U_1034),U_1035))
            | hBOOL(hAPP(U_1031,U_1034)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1032),U_1034),U_1035))
            | ~ hBOOL(hAPP(U_1031,U_1034)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1033),U_1034),U_1035))
          & ~ hBOOL(hAPP(U_1031,U_1034)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1032),U_1034),U_1035))
          & hBOOL(hAPP(U_1031,U_1034)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1031,U_1032,U_1033)),U_1034),U_1035)) ) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ( ! [U_1045,U_1043,U_1041,U_1039,U_1037] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1037,U_1039,U_1041)),U_1043),U_1045))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1041),U_1043),U_1045))
            | hBOOL(hAPP(U_1037,U_1043)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1039),U_1043),U_1045))
            | ~ hBOOL(hAPP(U_1037,U_1043)) ) ) )
    & ! [U_1044,U_1042,U_1040,U_1038,U_1036] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1040),U_1042),U_1044))
          & ~ hBOOL(hAPP(U_1036,U_1042)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1038),U_1042),U_1044))
          & hBOOL(hAPP(U_1036,U_1042)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1036,U_1038,U_1040)),U_1042),U_1044)) ) ),
    inference(miniscope,[status(thm)],[f_241_2]) ).

fof(f_241_4,plain,
    ( ! [U_1041,U_1037,U_1039,U_1045,U_1043] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1041),U_1043),U_1045))
        | hBOOL(hAPP(U_1037,U_1043))
        | ~ sP60(U_1041,U_1037,U_1039,U_1045,U_1043) )
    & ! [U_1041,U_1037,U_1039,U_1045,U_1043] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1039),U_1043),U_1045))
        | ~ hBOOL(hAPP(U_1037,U_1043))
        | ~ sP60(U_1041,U_1037,U_1039,U_1045,U_1043) )
    & ! [U_1042,U_1040,U_1036,U_1044] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1040),U_1042),U_1044))
        | ~ sP59(U_1042,U_1040,U_1036,U_1044) )
    & ! [U_1042,U_1040,U_1036,U_1044] :
        ( ~ hBOOL(hAPP(U_1036,U_1042))
        | ~ sP59(U_1042,U_1040,U_1036,U_1044) )
    & ! [U_1042,U_1036,U_1038,U_1044] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1038),U_1042),U_1044))
        | ~ sP58(U_1042,U_1036,U_1038,U_1044) )
    & ! [U_1042,U_1036,U_1038,U_1044] :
        ( hBOOL(hAPP(U_1036,U_1042))
        | ~ sP58(U_1042,U_1036,U_1038,U_1044) )
    & ! [U_1041,U_1037,U_1039,U_1045,U_1043] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1037,U_1039,U_1041)),U_1043),U_1045))
        | sP60(U_1041,U_1037,U_1039,U_1045,U_1043) )
    & ! [U_1042,U_1040,U_1036,U_1038,U_1044] :
        ( sP59(U_1042,U_1040,U_1036,U_1044)
        | sP58(U_1042,U_1036,U_1038,U_1044)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1036,U_1038,U_1040)),U_1042),U_1044)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58,sP59,sP60])],[f_241_3]) ).

cnf(f_241_5,plain,
    ( sP59(U_1042,U_1040,U_1036,U_1044)
    | sP58(U_1042,U_1036,U_1038,U_1044)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1036,U_1038,U_1040)),U_1042),U_1044)) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1037,U_1039,U_1041)),U_1043),U_1045))
    | sP60(U_1041,U_1037,U_1039,U_1045,U_1043) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_7,plain,
    ( hBOOL(hAPP(U_1036,U_1042))
    | ~ sP58(U_1042,U_1036,U_1038,U_1044) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1038),U_1042),U_1044))
    | ~ sP58(U_1042,U_1036,U_1038,U_1044) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_9,plain,
    ( ~ hBOOL(hAPP(U_1036,U_1042))
    | ~ sP59(U_1042,U_1040,U_1036,U_1044) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1040),U_1042),U_1044))
    | ~ sP59(U_1042,U_1040,U_1036,U_1044) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1039),U_1043),U_1045))
    | ~ hBOOL(hAPP(U_1037,U_1043))
    | ~ sP60(U_1041,U_1037,U_1039,U_1045,U_1043) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1041),U_1043),U_1045))
    | hBOOL(hAPP(U_1037,U_1043))
    | ~ sP60(U_1041,U_1037,U_1039,U_1045,U_1043) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

fof(f_242_1,plain,
    ! [V_b_2,V_c1_2,V_c0_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c1_2))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c0_2)) ),
    inference(fof_nnf,[status(thm)],[fact_WT_OIf]) ).

fof(f_242_2,plain,
    ! [U_1048,U_1047,U_1046] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1048,U_1046,U_1047)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1047))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1046)) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_1046,U_1047,U_1048] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1048,U_1046,U_1047)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1047))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1046)) ),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1048,U_1046,U_1047)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1047))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1046)) ),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_1,plain,
    ! [V_a2_2,V_a1_2,V_a3_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
        | ~ hBOOL(hAPP(c_Com_OWT,V_a2_2))
        | ~ hBOOL(hAPP(c_Com_OWT,V_a1_2)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,V_a2_2))
          & hBOOL(hAPP(c_Com_OWT,V_a1_2)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I5_J]) ).

fof(f_243_2,plain,
    ! [U_1051,U_1050,U_1049] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1049,U_1050,U_1051)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1051))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1050)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_1051))
          & hBOOL(hAPP(c_Com_OWT,U_1050)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1049,U_1050,U_1051))) ) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ( ! [U_1057,U_1055] :
        ( ! [U_1053] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1053,U_1055,U_1057)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1057))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1055)) )
    & ! [U_1056,U_1054] :
        ( ! [U_1052] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1052,U_1054,U_1056)))
        | ( hBOOL(hAPP(c_Com_OWT,U_1056))
          & hBOOL(hAPP(c_Com_OWT,U_1054)) ) ) ),
    inference(miniscope,[status(thm)],[f_243_2]) ).

fof(f_243_4,plain,
    ( ! [U_1056,U_1054] :
        ( hBOOL(hAPP(c_Com_OWT,U_1056))
        | ~ sP61(U_1056,U_1054) )
    & ! [U_1056,U_1054] :
        ( hBOOL(hAPP(c_Com_OWT,U_1054))
        | ~ sP61(U_1056,U_1054) )
    & ! [U_1057,U_1055,U_1053] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1053,U_1055,U_1057)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1057))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1055)) )
    & ! [U_1056,U_1054,U_1052] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1052,U_1054,U_1056)))
        | sP61(U_1056,U_1054) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_243_3]) ).

cnf(f_243_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1052,U_1054,U_1056)))
    | sP61(U_1056,U_1054) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1053,U_1055,U_1057)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1057))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1055)) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_1054))
    | ~ sP61(U_1056,U_1054) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_8,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_1056))
    | ~ sP61(U_1056,U_1054) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

fof(f_244_1,plain,
    ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I54_J]) ).

fof(f_244_2,plain,
    ! [U_1061,U_1060,U_1059,U_1058] : c_Com_Ocom_OCond(U_1058,U_1059,U_1060) != hAPP(c_Com_Ocom_OBODY,U_1061),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_1061,U_1059,U_1058,U_1060] : c_Com_Ocom_OCond(U_1058,U_1059,U_1060) != hAPP(c_Com_Ocom_OBODY,U_1061),
    inference(definitional_conversion,[status(esa)],[f_244_2]) ).

cnf(f_244_4,plain,
    c_Com_Ocom_OCond(U_1058,U_1059,U_1060) != hAPP(c_Com_Ocom_OBODY,U_1061),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I55_J]) ).

fof(f_245_2,plain,
    ! [U_1065,U_1064,U_1063,U_1062] : hAPP(c_Com_Ocom_OBODY,U_1062) != c_Com_Ocom_OCond(U_1063,U_1064,U_1065),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_1062,U_1063,U_1064,U_1065] : hAPP(c_Com_Ocom_OBODY,U_1062) != c_Com_Ocom_OCond(U_1063,U_1064,U_1065),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_1062) != c_Com_Ocom_OCond(U_1063,U_1064,U_1065),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
        | ! [B_s1] :
            ( ~ c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2)
            | ~ c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1) ) )
      & ( ? [B_s1] :
            ( c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2)
            & c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I4_J]) ).

fof(f_246_2,plain,
    ! [U_1072,U_1071,U_1070,U_1069,U_1068] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1068,U_1069),U_1070,U_1071,U_1072)
        | ! [U_1067] :
            ( ~ c_Natural_Oevaln(U_1069,U_1067,U_1071,U_1072)
            | ~ c_Natural_Oevaln(U_1068,U_1070,U_1071,U_1067) ) )
      & ( ? [U_1066] :
            ( c_Natural_Oevaln(U_1069,U_1066,U_1071,U_1072)
            & c_Natural_Oevaln(U_1068,U_1070,U_1071,U_1066) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1068,U_1069),U_1070,U_1071,U_1072) ) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ( ! [U_1082,U_1080,U_1078,U_1076,U_1074] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1074,U_1076),U_1078,U_1080,U_1082)
        | ! [U_1067] :
            ( ~ c_Natural_Oevaln(U_1076,U_1067,U_1080,U_1082)
            | ~ c_Natural_Oevaln(U_1074,U_1078,U_1080,U_1067) ) )
    & ! [U_1081,U_1079,U_1077,U_1075,U_1073] :
        ( ? [U_1066] :
            ( c_Natural_Oevaln(U_1075,U_1066,U_1079,U_1081)
            & c_Natural_Oevaln(U_1073,U_1077,U_1079,U_1066) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1073,U_1075),U_1077,U_1079,U_1081) ) ),
    inference(miniscope,[status(thm)],[f_246_2]) ).

fof(f_246_4,plain,
    ( ! [U_1082,U_1080,U_1078,U_1076,U_1074] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1074,U_1076),U_1078,U_1080,U_1082)
        | ! [U_1067] :
            ( ~ c_Natural_Oevaln(U_1076,U_1067,U_1080,U_1082)
            | ~ c_Natural_Oevaln(U_1074,U_1078,U_1080,U_1067) ) )
    & ! [U_1081,U_1079,U_1077,U_1075,U_1073] :
        ( ( c_Natural_Oevaln(U_1075,sK23(U_1081,U_1079,U_1077,U_1075,U_1073),U_1079,U_1081)
          & c_Natural_Oevaln(U_1073,U_1077,U_1079,sK23(U_1081,U_1079,U_1077,U_1075,U_1073)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1073,U_1075),U_1077,U_1079,U_1081) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1066,sK23(U_1081,U_1079,U_1077,U_1075,U_1073))],[f_246_3]) ).

fof(f_246_5,plain,
    ( ! [U_1081,U_1077,U_1075,U_1073,U_1079] :
        ( c_Natural_Oevaln(U_1075,sK23(U_1081,U_1079,U_1077,U_1075,U_1073),U_1079,U_1081)
        | ~ sP62(U_1081,U_1077,U_1075,U_1073,U_1079) )
    & ! [U_1081,U_1077,U_1075,U_1073,U_1079] :
        ( c_Natural_Oevaln(U_1073,U_1077,U_1079,sK23(U_1081,U_1079,U_1077,U_1075,U_1073))
        | ~ sP62(U_1081,U_1077,U_1075,U_1073,U_1079) )
    & ! [U_1082,U_1067,U_1078,U_1076,U_1080,U_1074] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1074,U_1076),U_1078,U_1080,U_1082)
        | ~ c_Natural_Oevaln(U_1076,U_1067,U_1080,U_1082)
        | ~ c_Natural_Oevaln(U_1074,U_1078,U_1080,U_1067) )
    & ! [U_1081,U_1077,U_1075,U_1073,U_1079] :
        ( sP62(U_1081,U_1077,U_1075,U_1073,U_1079)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1073,U_1075),U_1077,U_1079,U_1081) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_246_4]) ).

cnf(f_246_6,plain,
    ( sP62(U_1081,U_1077,U_1075,U_1073,U_1079)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1073,U_1075),U_1077,U_1079,U_1081) ),
    inference(clausify,[status(thm)],[f_246_5]) ).

cnf(f_246_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1074,U_1076),U_1078,U_1080,U_1082)
    | ~ c_Natural_Oevaln(U_1076,U_1067,U_1080,U_1082)
    | ~ c_Natural_Oevaln(U_1074,U_1078,U_1080,U_1067) ),
    inference(clausify,[status(thm)],[f_246_5]) ).

cnf(f_246_8,plain,
    ( c_Natural_Oevaln(U_1073,U_1077,U_1079,sK23(U_1081,U_1079,U_1077,U_1075,U_1073))
    | ~ sP62(U_1081,U_1077,U_1075,U_1073,U_1079) ),
    inference(clausify,[status(thm)],[f_246_5]) ).

cnf(f_246_9,plain,
    ( c_Natural_Oevaln(U_1075,sK23(U_1081,U_1079,U_1077,U_1075,U_1073),U_1079,U_1081)
    | ~ sP62(U_1081,U_1077,U_1075,U_1073,U_1079) ),
    inference(clausify,[status(thm)],[f_246_5]) ).

fof(f_247_1,plain,
    ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
        | ! [B_s1] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I4_J]) ).

fof(f_247_2,plain,
    ! [U_1088,U_1087,U_1086,U_1085] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1085,U_1086)),U_1087),U_1088))
        | ! [U_1084] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1086),U_1084),U_1088))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1085),U_1087),U_1084)) ) )
      & ( ? [U_1083] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1086),U_1083),U_1088))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1085),U_1087),U_1083)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1085,U_1086)),U_1087),U_1088)) ) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ( ! [U_1096,U_1094,U_1092,U_1090] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1090,U_1092)),U_1094),U_1096))
        | ! [U_1084] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1092),U_1084),U_1096))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1090),U_1094),U_1084)) ) )
    & ! [U_1095,U_1093,U_1091,U_1089] :
        ( ? [U_1083] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1091),U_1083),U_1095))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1089),U_1093),U_1083)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1089,U_1091)),U_1093),U_1095)) ) ),
    inference(miniscope,[status(thm)],[f_247_2]) ).

fof(f_247_4,plain,
    ( ! [U_1096,U_1094,U_1092,U_1090] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1090,U_1092)),U_1094),U_1096))
        | ! [U_1084] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1092),U_1084),U_1096))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1090),U_1094),U_1084)) ) )
    & ! [U_1095,U_1093,U_1091,U_1089] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1091),sK24(U_1095,U_1093,U_1091,U_1089)),U_1095))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1089),U_1093),sK24(U_1095,U_1093,U_1091,U_1089))) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1089,U_1091)),U_1093),U_1095)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1083,sK24(U_1095,U_1093,U_1091,U_1089))],[f_247_3]) ).

fof(f_247_5,plain,
    ( ! [U_1095,U_1091,U_1089,U_1093] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1091),sK24(U_1095,U_1093,U_1091,U_1089)),U_1095))
        | ~ sP63(U_1095,U_1091,U_1089,U_1093) )
    & ! [U_1095,U_1091,U_1089,U_1093] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1089),U_1093),sK24(U_1095,U_1093,U_1091,U_1089)))
        | ~ sP63(U_1095,U_1091,U_1089,U_1093) )
    & ! [U_1084,U_1094,U_1092,U_1090,U_1096] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1090,U_1092)),U_1094),U_1096))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1092),U_1084),U_1096))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1090),U_1094),U_1084)) )
    & ! [U_1095,U_1091,U_1089,U_1093] :
        ( sP63(U_1095,U_1091,U_1089,U_1093)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1089,U_1091)),U_1093),U_1095)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_247_4]) ).

cnf(f_247_6,plain,
    ( sP63(U_1095,U_1091,U_1089,U_1093)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1089,U_1091)),U_1093),U_1095)) ),
    inference(clausify,[status(thm)],[f_247_5]) ).

cnf(f_247_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1090,U_1092)),U_1094),U_1096))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1092),U_1084),U_1096))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1090),U_1094),U_1084)) ),
    inference(clausify,[status(thm)],[f_247_5]) ).

cnf(f_247_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1089),U_1093),sK24(U_1095,U_1093,U_1091,U_1089)))
    | ~ sP63(U_1095,U_1091,U_1089,U_1093) ),
    inference(clausify,[status(thm)],[f_247_5]) ).

cnf(f_247_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1091),sK24(U_1095,U_1093,U_1091,U_1089)),U_1095))
    | ~ sP63(U_1095,U_1091,U_1089,U_1093) ),
    inference(clausify,[status(thm)],[f_247_5]) ).

fof(f_248_1,plain,
    ! [V_c1,V_c0] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1)))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c1))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c0)) ),
    inference(fof_nnf,[status(thm)],[fact_WT_OSemi]) ).

fof(f_248_2,plain,
    ! [U_1098,U_1097] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1097,U_1098)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1098))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1097)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_1097,U_1098] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1097,U_1098)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1098))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1097)) ),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1097,U_1098)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1098))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1097)) ),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_1,plain,
    ! [V_a2_2,V_a1_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
        | ~ hBOOL(hAPP(c_Com_OWT,V_a2_2))
        | ~ hBOOL(hAPP(c_Com_OWT,V_a1_2)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,V_a2_2))
          & hBOOL(hAPP(c_Com_OWT,V_a1_2)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I4_J]) ).

fof(f_249_2,plain,
    ! [U_1100,U_1099] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1099,U_1100)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1100))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1099)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_1100))
          & hBOOL(hAPP(c_Com_OWT,U_1099)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1099,U_1100))) ) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ( ! [U_1104,U_1102] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1102,U_1104)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1104))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1102)) )
    & ! [U_1103,U_1101] :
        ( ( hBOOL(hAPP(c_Com_OWT,U_1103))
          & hBOOL(hAPP(c_Com_OWT,U_1101)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1101,U_1103))) ) ),
    inference(miniscope,[status(thm)],[f_249_2]) ).

fof(f_249_4,plain,
    ( ! [U_1103,U_1101] :
        ( hBOOL(hAPP(c_Com_OWT,U_1103))
        | ~ sP64(U_1103,U_1101) )
    & ! [U_1103,U_1101] :
        ( hBOOL(hAPP(c_Com_OWT,U_1101))
        | ~ sP64(U_1103,U_1101) )
    & ! [U_1102,U_1104] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1102,U_1104)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1104))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1102)) )
    & ! [U_1103,U_1101] :
        ( sP64(U_1103,U_1101)
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1101,U_1103))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_249_3]) ).

cnf(f_249_5,plain,
    ( sP64(U_1103,U_1101)
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1101,U_1103))) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_1102,U_1104)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1104))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1102)) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_1101))
    | ~ sP64(U_1103,U_1101) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_8,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_1103))
    | ~ sP64(U_1103,U_1101) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

fof(f_250_1,plain,
    ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I48_J]) ).

fof(f_250_2,plain,
    ! [U_1107,U_1106,U_1105] : c_Com_Ocom_OSemi(U_1105,U_1106) != hAPP(c_Com_Ocom_OBODY,U_1107),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_1105,U_1107,U_1106] : c_Com_Ocom_OSemi(U_1105,U_1106) != hAPP(c_Com_Ocom_OBODY,U_1107),
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    c_Com_Ocom_OSemi(U_1105,U_1106) != hAPP(c_Com_Ocom_OBODY,U_1107),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I49_J]) ).

fof(f_251_2,plain,
    ! [U_1110,U_1109,U_1108] : hAPP(c_Com_Ocom_OBODY,U_1108) != c_Com_Ocom_OSemi(U_1109,U_1110),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_1108,U_1109,U_1110] : hAPP(c_Com_Ocom_OBODY,U_1108) != c_Com_Ocom_OSemi(U_1109,U_1110),
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_1108) != c_Com_Ocom_OSemi(U_1109,U_1110),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I27_J]) ).

fof(f_252_2,plain,
    ! [U_1115,U_1114,U_1113,U_1112,U_1111] : c_Com_Ocom_OCond(U_1111,U_1112,U_1113) != c_Com_Ocom_OAss(U_1114,U_1115),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_1112,U_1111,U_1113,U_1114,U_1115] : c_Com_Ocom_OCond(U_1111,U_1112,U_1113) != c_Com_Ocom_OAss(U_1114,U_1115),
    inference(definitional_conversion,[status(esa)],[f_252_2]) ).

cnf(f_252_4,plain,
    c_Com_Ocom_OCond(U_1111,U_1112,U_1113) != c_Com_Ocom_OAss(U_1114,U_1115),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I26_J]) ).

fof(f_253_2,plain,
    ! [U_1120,U_1119,U_1118,U_1117,U_1116] : c_Com_Ocom_OAss(U_1116,U_1117) != c_Com_Ocom_OCond(U_1118,U_1119,U_1120),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_1116,U_1117,U_1118,U_1119,U_1120] : c_Com_Ocom_OAss(U_1116,U_1117) != c_Com_Ocom_OCond(U_1118,U_1119,U_1120),
    inference(definitional_conversion,[status(esa)],[f_253_2]) ).

cnf(f_253_4,plain,
    c_Com_Ocom_OAss(U_1116,U_1117) != c_Com_Ocom_OCond(U_1118,U_1119,U_1120),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I57_J]) ).

fof(f_254_2,plain,
    ! [U_1126,U_1125,U_1124,U_1123,U_1122,U_1121] : c_Com_Ocom_OCall(U_1121,U_1122,U_1123) != c_Com_Ocom_OCond(U_1124,U_1125,U_1126),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_1122,U_1121,U_1123,U_1124,U_1125,U_1126] : c_Com_Ocom_OCall(U_1121,U_1122,U_1123) != c_Com_Ocom_OCond(U_1124,U_1125,U_1126),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    c_Com_Ocom_OCall(U_1121,U_1122,U_1123) != c_Com_Ocom_OCond(U_1124,U_1125,U_1126),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I56_J]) ).

fof(f_255_2,plain,
    ! [U_1132,U_1131,U_1130,U_1129,U_1128,U_1127] : c_Com_Ocom_OCond(U_1127,U_1128,U_1129) != c_Com_Ocom_OCall(U_1130,U_1131,U_1132),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_1128,U_1127,U_1129,U_1130,U_1131,U_1132] : c_Com_Ocom_OCond(U_1127,U_1128,U_1129) != c_Com_Ocom_OCall(U_1130,U_1131,U_1132),
    inference(definitional_conversion,[status(esa)],[f_255_2]) ).

cnf(f_255_4,plain,
    c_Com_Ocom_OCond(U_1127,U_1128,U_1129) != c_Com_Ocom_OCall(U_1130,U_1131,U_1132),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I37_J]) ).

fof(f_256_2,plain,
    ! [U_1138,U_1137,U_1136,U_1135,U_1134,U_1133] : c_Com_Ocom_OCond(U_1133,U_1134,U_1135) != c_Com_Ocom_OLocal(U_1136,U_1137,U_1138),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_1134,U_1133,U_1135,U_1136,U_1137,U_1138] : c_Com_Ocom_OCond(U_1133,U_1134,U_1135) != c_Com_Ocom_OLocal(U_1136,U_1137,U_1138),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    c_Com_Ocom_OCond(U_1133,U_1134,U_1135) != c_Com_Ocom_OLocal(U_1136,U_1137,U_1138),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I36_J]) ).

fof(f_257_2,plain,
    ! [U_1144,U_1143,U_1142,U_1141,U_1140,U_1139] : c_Com_Ocom_OLocal(U_1139,U_1140,U_1141) != c_Com_Ocom_OCond(U_1142,U_1143,U_1144),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_1140,U_1139,U_1141,U_1142,U_1143,U_1144] : c_Com_Ocom_OLocal(U_1139,U_1140,U_1141) != c_Com_Ocom_OCond(U_1142,U_1143,U_1144),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    c_Com_Ocom_OLocal(U_1139,U_1140,U_1141) != c_Com_Ocom_OCond(U_1142,U_1143,U_1144),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I15_J]) ).

fof(f_258_2,plain,
    ! [U_1147,U_1146,U_1145] : c_Com_Ocom_OCond(U_1145,U_1146,U_1147) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_1146,U_1145,U_1147] : c_Com_Ocom_OCond(U_1145,U_1146,U_1147) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    c_Com_Ocom_OCond(U_1145,U_1146,U_1147) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I14_J]) ).

fof(f_259_2,plain,
    ! [U_1150,U_1149,U_1148] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_1148,U_1149,U_1150),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_1149,U_1150,U_1148] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_1148,U_1149,U_1150),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_1148,U_1149,U_1150),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_1,plain,
    ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I25_J]) ).

fof(f_260_2,plain,
    ! [U_1154,U_1153,U_1152,U_1151] : c_Com_Ocom_OSemi(U_1151,U_1152) != c_Com_Ocom_OAss(U_1153,U_1154),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_1151,U_1152,U_1153,U_1154] : c_Com_Ocom_OSemi(U_1151,U_1152) != c_Com_Ocom_OAss(U_1153,U_1154),
    inference(definitional_conversion,[status(esa)],[f_260_2]) ).

cnf(f_260_4,plain,
    c_Com_Ocom_OSemi(U_1151,U_1152) != c_Com_Ocom_OAss(U_1153,U_1154),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I24_J]) ).

fof(f_261_2,plain,
    ! [U_1158,U_1157,U_1156,U_1155] : c_Com_Ocom_OAss(U_1155,U_1156) != c_Com_Ocom_OSemi(U_1157,U_1158),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_1155,U_1156,U_1157,U_1158] : c_Com_Ocom_OAss(U_1155,U_1156) != c_Com_Ocom_OSemi(U_1157,U_1158),
    inference(definitional_conversion,[status(esa)],[f_261_2]) ).

cnf(f_261_4,plain,
    c_Com_Ocom_OAss(U_1155,U_1156) != c_Com_Ocom_OSemi(U_1157,U_1158),
    inference(clausify,[status(thm)],[f_261_3]) ).

fof(f_262_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I50_J]) ).

fof(f_262_2,plain,
    ! [U_1163,U_1162,U_1161,U_1160,U_1159] : c_Com_Ocom_OSemi(U_1159,U_1160) != c_Com_Ocom_OCall(U_1161,U_1162,U_1163),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_1159,U_1160,U_1161,U_1162,U_1163] : c_Com_Ocom_OSemi(U_1159,U_1160) != c_Com_Ocom_OCall(U_1161,U_1162,U_1163),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    c_Com_Ocom_OSemi(U_1159,U_1160) != c_Com_Ocom_OCall(U_1161,U_1162,U_1163),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I35_J]) ).

fof(f_263_2,plain,
    ! [U_1168,U_1167,U_1166,U_1165,U_1164] : c_Com_Ocom_OSemi(U_1164,U_1165) != c_Com_Ocom_OLocal(U_1166,U_1167,U_1168),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_1164,U_1165,U_1166,U_1167,U_1168] : c_Com_Ocom_OSemi(U_1164,U_1165) != c_Com_Ocom_OLocal(U_1166,U_1167,U_1168),
    inference(definitional_conversion,[status(esa)],[f_263_2]) ).

cnf(f_263_4,plain,
    c_Com_Ocom_OSemi(U_1164,U_1165) != c_Com_Ocom_OLocal(U_1166,U_1167,U_1168),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I51_J]) ).

fof(f_264_2,plain,
    ! [U_1173,U_1172,U_1171,U_1170,U_1169] : c_Com_Ocom_OCall(U_1169,U_1170,U_1171) != c_Com_Ocom_OSemi(U_1172,U_1173),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_1170,U_1169,U_1171,U_1172,U_1173] : c_Com_Ocom_OCall(U_1169,U_1170,U_1171) != c_Com_Ocom_OSemi(U_1172,U_1173),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    c_Com_Ocom_OCall(U_1169,U_1170,U_1171) != c_Com_Ocom_OSemi(U_1172,U_1173),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I34_J]) ).

fof(f_265_2,plain,
    ! [U_1178,U_1177,U_1176,U_1175,U_1174] : c_Com_Ocom_OLocal(U_1174,U_1175,U_1176) != c_Com_Ocom_OSemi(U_1177,U_1178),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_1175,U_1174,U_1176,U_1177,U_1178] : c_Com_Ocom_OLocal(U_1174,U_1175,U_1176) != c_Com_Ocom_OSemi(U_1177,U_1178),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    c_Com_Ocom_OLocal(U_1174,U_1175,U_1176) != c_Com_Ocom_OSemi(U_1177,U_1178),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_1,plain,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I13_J]) ).

fof(f_266_2,plain,
    ! [U_1180,U_1179] : c_Com_Ocom_OSemi(U_1179,U_1180) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ! [U_1179,U_1180] : c_Com_Ocom_OSemi(U_1179,U_1180) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_266_2]) ).

cnf(f_266_4,plain,
    c_Com_Ocom_OSemi(U_1179,U_1180) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_266_3]) ).

fof(f_267_1,plain,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I12_J]) ).

fof(f_267_2,plain,
    ! [U_1182,U_1181] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_1181,U_1182),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_1181,U_1182] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_1181,U_1182),
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_1181,U_1182),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I3_J]) ).

fof(f_268_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_268_1]) ).

cnf(f_268_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_268_2]) ).

fof(f_269_1,plain,
    ! [V_c,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).

fof(f_269_2,plain,
    ! [U_1185,U_1184,U_1183] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1183),U_1184),U_1185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1183),U_1185),U_1184)
      | ~ class_Rings_Ocomm__semiring__1(U_1183) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ! [U_1183,U_1184,U_1185] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1183),U_1184),U_1185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1183),U_1185),U_1184)
      | ~ class_Rings_Ocomm__semiring__1(U_1183) ),
    inference(definitional_conversion,[status(esa)],[f_269_2]) ).

cnf(f_269_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1183),U_1184),U_1185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1183),U_1185),U_1184)
    | ~ class_Rings_Ocomm__semiring__1(U_1183) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

fof(f_270_1,plain,
    ! [V_d,V_c,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).

fof(f_270_2,plain,
    ! [U_1189,U_1188,U_1187,U_1186] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1188),U_1189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1187),U_1189))
      | ~ class_Rings_Ocomm__semiring__1(U_1186) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_1186,U_1187,U_1188,U_1189] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1188),U_1189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1187),U_1189))
      | ~ class_Rings_Ocomm__semiring__1(U_1186) ),
    inference(definitional_conversion,[status(esa)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1188),U_1189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1186),U_1187),U_1189))
    | ~ class_Rings_Ocomm__semiring__1(U_1186) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_1,plain,
    ! [V_d,V_c,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).

fof(f_271_2,plain,
    ! [U_1193,U_1192,U_1191,U_1190] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1192),U_1193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1191),U_1192)),U_1193)
      | ~ class_Rings_Ocomm__semiring__1(U_1190) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_1190,U_1191,U_1192,U_1193] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1192),U_1193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1191),U_1192)),U_1193)
      | ~ class_Rings_Ocomm__semiring__1(U_1190) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1192),U_1193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1190),U_1191),U_1192)),U_1193)
    | ~ class_Rings_Ocomm__semiring__1(U_1190) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).

fof(f_272_2,plain,
    ! [U_1197,U_1196,U_1195,U_1194] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1195),U_1196)),U_1197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1195),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1196),U_1197))
      | ~ class_Rings_Ocomm__semiring__1(U_1194) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_1194,U_1195,U_1196,U_1197] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1195),U_1196)),U_1197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1195),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1196),U_1197))
      | ~ class_Rings_Ocomm__semiring__1(U_1194) ),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1195),U_1196)),U_1197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1195),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1194),U_1196),U_1197))
    | ~ class_Rings_Ocomm__semiring__1(U_1194) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).

fof(f_273_2,plain,
    ! [U_1201,U_1200,U_1199,U_1198] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),U_1199),U_1200)),U_1201) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),U_1199),U_1201)),U_1200)
      | ~ class_Rings_Ocomm__semiring__1(U_1198) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_1198,U_1199,U_1200,U_1201] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),U_1199),U_1200)),U_1201) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),U_1199),U_1201)),U_1200)
      | ~ class_Rings_Ocomm__semiring__1(U_1198) ),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),U_1199),U_1200)),U_1201) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1198),U_1199),U_1201)),U_1200)
    | ~ class_Rings_Ocomm__semiring__1(U_1198) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).

fof(f_274_2,plain,
    ! [U_1206,U_1205,U_1204,U_1203,U_1202] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1203),U_1204)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1205),U_1206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1203),U_1205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1204),U_1206))
      | ~ class_Rings_Ocomm__semiring__1(U_1202) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_1202,U_1203,U_1204,U_1205,U_1206] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1203),U_1204)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1205),U_1206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1203),U_1205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1204),U_1206))
      | ~ class_Rings_Ocomm__semiring__1(U_1202) ),
    inference(definitional_conversion,[status(esa)],[f_274_2]) ).

cnf(f_274_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1203),U_1204)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1205),U_1206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1203),U_1205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1202),U_1204),U_1206))
    | ~ class_Rings_Ocomm__semiring__1(U_1202) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_1,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I1_J]) ).

fof(f_275_2,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_275_1]) ).

cnf(f_275_3,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_275_2]) ).

fof(f_276_1,plain,
    ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_option_Orecs_I2_J]) ).

fof(f_276_2,plain,
    ! [U_1211,U_1210,U_1209,U_1208,U_1207] : c_Option_Ooption_Ooption__rec(U_1207,U_1208,U_1209,U_1210,hAPP(c_Option_Ooption_OSome(U_1208),U_1211)) = hAPP(U_1210,U_1211),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_1208,U_1207,U_1209,U_1210,U_1211] : c_Option_Ooption_Ooption__rec(U_1207,U_1208,U_1209,U_1210,hAPP(c_Option_Ooption_OSome(U_1208),U_1211)) = hAPP(U_1210,U_1211),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    c_Option_Ooption_Ooption__rec(U_1207,U_1208,U_1209,U_1210,hAPP(c_Option_Ooption_OSome(U_1208),U_1211)) = hAPP(U_1210,U_1211),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_1,plain,
    ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_option_Osimps_I5_J]) ).

fof(f_277_2,plain,
    ! [U_1216,U_1215,U_1214,U_1213,U_1212] : hAPP(c_Option_Ooption_Ooption__case(U_1212,U_1213,U_1214,U_1215),hAPP(c_Option_Ooption_OSome(U_1213),U_1216)) = hAPP(U_1215,U_1216),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_1213,U_1212,U_1214,U_1215,U_1216] : hAPP(c_Option_Ooption_Ooption__case(U_1212,U_1213,U_1214,U_1215),hAPP(c_Option_Ooption_OSome(U_1213),U_1216)) = hAPP(U_1215,U_1216),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_1212,U_1213,U_1214,U_1215),hAPP(c_Option_Ooption_OSome(U_1213),U_1216)) = hAPP(U_1215,U_1216),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_option_Orecs_I1_J]) ).

fof(f_278_2,plain,
    ! [U_1220,U_1219,U_1218,U_1217] : c_Option_Ooption_Ooption__rec(U_1217,U_1218,U_1219,U_1220,c_Option_Ooption_ONone(U_1218)) = U_1219,
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_1217,U_1218,U_1219,U_1220] : c_Option_Ooption_Ooption__rec(U_1217,U_1218,U_1219,U_1220,c_Option_Ooption_ONone(U_1218)) = U_1219,
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    c_Option_Ooption_Ooption__rec(U_1217,U_1218,U_1219,U_1220,c_Option_Ooption_ONone(U_1218)) = U_1219,
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_1,plain,
    ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_option_Osimps_I4_J]) ).

fof(f_279_2,plain,
    ! [U_1224,U_1223,U_1222,U_1221] : hAPP(c_Option_Ooption_Ooption__case(U_1221,U_1222,U_1223,U_1224),c_Option_Ooption_ONone(U_1222)) = U_1223,
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_1221,U_1222,U_1223,U_1224] : hAPP(c_Option_Ooption_Ooption__case(U_1221,U_1222,U_1223,U_1224),c_Option_Ooption_ONone(U_1222)) = U_1223,
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_1221,U_1222,U_1223,U_1224),c_Option_Ooption_ONone(U_1222)) = U_1223,
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_1,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I1_J]) ).

fof(f_280_2,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_280_1]) ).

cnf(f_280_3,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_1,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I2_J]) ).

fof(f_281_2,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_281_1]) ).

cnf(f_281_3,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_281_2]) ).

fof(f_282_1,plain,
    ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I6_J]) ).

fof(f_282_2,plain,
    ! [U_1226,U_1225] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_1225,U_1226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1226)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_1225,U_1226] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_1225,U_1226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1226)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_282_2]) ).

cnf(f_282_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_1225,U_1226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1226)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_1,plain,
    ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I14_J]) ).

fof(f_283_2,plain,
    ! [U_1228,U_1227] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_1227,U_1228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1228)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_1227,U_1228] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_1227,U_1228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1228)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_1227,U_1228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1228)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)),
    inference(fof_nnf,[status(thm)],[fact_is__none__code_I2_J]) ).

fof(f_284_2,plain,
    ! [U_1230,U_1229] : ~ c_Option_Ois__none(U_1229,hAPP(c_Option_Ooption_OSome(U_1229),U_1230)),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_1229,U_1230] : ~ c_Option_Ois__none(U_1229,hAPP(c_Option_Ooption_OSome(U_1229),U_1230)),
    inference(definitional_conversion,[status(esa)],[f_284_2]) ).

cnf(f_284_4,plain,
    ~ c_Option_Ois__none(U_1229,hAPP(c_Option_Ooption_OSome(U_1229),U_1230)),
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_1,plain,
    ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)),
    inference(fof_nnf,[status(thm)],[fact_is__none__code_I1_J]) ).

fof(f_285_2,plain,
    ! [U_1231] : c_Option_Ois__none(U_1231,c_Option_Ooption_ONone(U_1231)),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_1231] : c_Option_Ois__none(U_1231,c_Option_Ooption_ONone(U_1231)),
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    c_Option_Ois__none(U_1231,c_Option_Ooption_ONone(U_1231)),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_Option_Ois__none(T_b,V_x_2)
        | V_x_2 != c_Option_Ooption_ONone(T_b) )
      & ( V_x_2 = c_Option_Ooption_ONone(T_b)
        | ~ c_Option_Ois__none(T_b,V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_is__none__def]) ).

fof(f_286_2,plain,
    ! [U_1233,U_1232] :
      ( ( c_Option_Ois__none(U_1232,U_1233)
        | U_1233 != c_Option_Ooption_ONone(U_1232) )
      & ( U_1233 = c_Option_Ooption_ONone(U_1232)
        | ~ c_Option_Ois__none(U_1232,U_1233) ) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ( ! [U_1237,U_1235] :
        ( c_Option_Ois__none(U_1235,U_1237)
        | U_1237 != c_Option_Ooption_ONone(U_1235) )
    & ! [U_1236,U_1234] :
        ( U_1236 = c_Option_Ooption_ONone(U_1234)
        | ~ c_Option_Ois__none(U_1234,U_1236) ) ),
    inference(miniscope,[status(thm)],[f_286_2]) ).

fof(f_286_4,plain,
    ( ! [U_1235,U_1237] :
        ( c_Option_Ois__none(U_1235,U_1237)
        | U_1237 != c_Option_Ooption_ONone(U_1235) )
    & ! [U_1236,U_1234] :
        ( U_1236 = c_Option_Ooption_ONone(U_1234)
        | ~ c_Option_Ois__none(U_1234,U_1236) ) ),
    inference(definitional_conversion,[status(esa)],[f_286_3]) ).

cnf(f_286_5,plain,
    ( U_1236 = c_Option_Ooption_ONone(U_1234)
    | ~ c_Option_Ois__none(U_1234,U_1236) ),
    inference(clausify,[status(thm)],[f_286_4]) ).

cnf(f_286_6,plain,
    ( c_Option_Ois__none(U_1235,U_1237)
    | U_1237 != c_Option_Ooption_ONone(U_1235) ),
    inference(clausify,[status(thm)],[f_286_4]) ).

fof(f_287_1,plain,
    ! [V_n_2,V_c_2,V_s_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2)
      | hBOOL(hAPP(V_b_2,V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OWhileFalse]) ).

fof(f_287_2,plain,
    ! [U_1241,U_1240,U_1239,U_1238] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1238,U_1240),U_1239,U_1241,U_1239)
      | hBOOL(hAPP(U_1238,U_1239)) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_1238,U_1239,U_1240,U_1241] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1238,U_1240),U_1239,U_1241,U_1239)
      | hBOOL(hAPP(U_1238,U_1239)) ),
    inference(definitional_conversion,[status(esa)],[f_287_2]) ).

cnf(f_287_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1238,U_1240),U_1239,U_1241,U_1239)
    | hBOOL(hAPP(U_1238,U_1239)) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_1,plain,
    ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
      | ~ c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
      | ~ hBOOL(hAPP(V_b_2,V_s0_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OWhileTrue]) ).

fof(f_288_2,plain,
    ! [U_1247,U_1246,U_1245,U_1244,U_1243,U_1242] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1242,U_1244),U_1243,U_1245,U_1247)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1242,U_1244),U_1246,U_1245,U_1247)
      | ~ c_Natural_Oevaln(U_1244,U_1243,U_1245,U_1246)
      | ~ hBOOL(hAPP(U_1242,U_1243)) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_1242,U_1243,U_1244,U_1245,U_1246,U_1247] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1242,U_1244),U_1243,U_1245,U_1247)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1242,U_1244),U_1246,U_1245,U_1247)
      | ~ c_Natural_Oevaln(U_1244,U_1243,U_1245,U_1246)
      | ~ hBOOL(hAPP(U_1242,U_1243)) ),
    inference(definitional_conversion,[status(esa)],[f_288_2]) ).

cnf(f_288_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1242,U_1244),U_1243,U_1245,U_1247)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1242,U_1244),U_1246,U_1245,U_1247)
    | ~ c_Natural_Oevaln(U_1244,U_1243,U_1245,U_1246)
    | ~ hBOOL(hAPP(U_1242,U_1243)) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

fof(f_289_1,plain,
    ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
      | ~ hBOOL(hAPP(V_b_2,V_s0_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OWhileTrue]) ).

fof(f_289_2,plain,
    ! [U_1252,U_1251,U_1250,U_1249,U_1248] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1248,U_1250)),U_1249),U_1252))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1248,U_1250)),U_1251),U_1252))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1250),U_1249),U_1251))
      | ~ hBOOL(hAPP(U_1248,U_1249)) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_1250,U_1248,U_1249,U_1251,U_1252] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1248,U_1250)),U_1249),U_1252))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1248,U_1250)),U_1251),U_1252))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1250),U_1249),U_1251))
      | ~ hBOOL(hAPP(U_1248,U_1249)) ),
    inference(definitional_conversion,[status(esa)],[f_289_2]) ).

cnf(f_289_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1248,U_1250)),U_1249),U_1252))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1248,U_1250)),U_1251),U_1252))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1250),U_1249),U_1251))
    | ~ hBOOL(hAPP(U_1248,U_1249)) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_1,plain,
    ! [V_c_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2))
      | hBOOL(hAPP(V_b_2,V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OWhileFalse]) ).

fof(f_290_2,plain,
    ! [U_1255,U_1254,U_1253] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1253,U_1255)),U_1254),U_1254))
      | hBOOL(hAPP(U_1253,U_1254)) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_1255,U_1253,U_1254] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1253,U_1255)),U_1254),U_1254))
      | hBOOL(hAPP(U_1253,U_1254)) ),
    inference(definitional_conversion,[status(esa)],[f_290_2]) ).

cnf(f_290_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1253,U_1255)),U_1254),U_1254))
    | hBOOL(hAPP(U_1253,U_1254)) ),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [V_c_2,V_b_2] :
      ( hBOOL(hAPP(c_Com_OWT,V_c_2))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I6_J]) ).

fof(f_291_2,plain,
    ! [U_1257,U_1256] :
      ( hBOOL(hAPP(c_Com_OWT,U_1257))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1256,U_1257))) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_1257] :
      ( ! [U_1256] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1256,U_1257)))
      | hBOOL(hAPP(c_Com_OWT,U_1257)) ),
    inference(miniscope,[status(thm)],[f_291_2]) ).

fof(f_291_4,plain,
    ! [U_1256,U_1257] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1256,U_1257)))
      | hBOOL(hAPP(c_Com_OWT,U_1257)) ),
    inference(definitional_conversion,[status(esa)],[f_291_3]) ).

cnf(f_291_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1256,U_1257)))
    | hBOOL(hAPP(c_Com_OWT,U_1257)) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

fof(f_292_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
      ( ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
        | V_com_2 != V_com_H_2
        | V_fun_2 != V_fun_H_2 )
      & ( ( V_com_2 = V_com_H_2
          & V_fun_2 = V_fun_H_2 )
        | c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J]) ).

fof(f_292_2,plain,
    ! [U_1261,U_1260,U_1259,U_1258] :
      ( ( c_Com_Ocom_OWhile(U_1258,U_1259) = c_Com_Ocom_OWhile(U_1260,U_1261)
        | U_1259 != U_1261
        | U_1258 != U_1260 )
      & ( ( U_1259 = U_1261
          & U_1258 = U_1260 )
        | c_Com_Ocom_OWhile(U_1258,U_1259) != c_Com_Ocom_OWhile(U_1260,U_1261) ) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ( ! [U_1269,U_1267,U_1265,U_1263] :
        ( c_Com_Ocom_OWhile(U_1263,U_1265) = c_Com_Ocom_OWhile(U_1267,U_1269)
        | U_1265 != U_1269
        | U_1263 != U_1267 )
    & ! [U_1268,U_1266,U_1264,U_1262] :
        ( ( U_1264 = U_1268
          & U_1262 = U_1266 )
        | c_Com_Ocom_OWhile(U_1262,U_1264) != c_Com_Ocom_OWhile(U_1266,U_1268) ) ),
    inference(miniscope,[status(thm)],[f_292_2]) ).

fof(f_292_4,plain,
    ( ! [U_1268,U_1264,U_1262,U_1266] :
        ( U_1264 = U_1268
        | ~ sP65(U_1268,U_1264,U_1262,U_1266) )
    & ! [U_1268,U_1264,U_1262,U_1266] :
        ( U_1262 = U_1266
        | ~ sP65(U_1268,U_1264,U_1262,U_1266) )
    & ! [U_1269,U_1267,U_1263,U_1265] :
        ( c_Com_Ocom_OWhile(U_1263,U_1265) = c_Com_Ocom_OWhile(U_1267,U_1269)
        | U_1265 != U_1269
        | U_1263 != U_1267 )
    & ! [U_1268,U_1264,U_1262,U_1266] :
        ( sP65(U_1268,U_1264,U_1262,U_1266)
        | c_Com_Ocom_OWhile(U_1262,U_1264) != c_Com_Ocom_OWhile(U_1266,U_1268) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_292_3]) ).

cnf(f_292_5,plain,
    ( sP65(U_1268,U_1264,U_1262,U_1266)
    | c_Com_Ocom_OWhile(U_1262,U_1264) != c_Com_Ocom_OWhile(U_1266,U_1268) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_6,plain,
    ( c_Com_Ocom_OWhile(U_1263,U_1265) = c_Com_Ocom_OWhile(U_1267,U_1269)
    | U_1265 != U_1269
    | U_1263 != U_1267 ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_7,plain,
    ( U_1262 = U_1266
    | ~ sP65(U_1268,U_1264,U_1262,U_1266) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_8,plain,
    ( U_1264 = U_1268
    | ~ sP65(U_1268,U_1264,U_1262,U_1266) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

fof(f_293_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
        | ( ! [B_s1] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2)
              | ~ c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) )
      & ( ? [B_s1] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2)
            & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) )
        | ~ hBOOL(hAPP(V_a1_2,V_a2_2))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I7_J]) ).

fof(f_293_2,plain,
    ! [U_1275,U_1274,U_1273,U_1272] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1272,U_1273),U_1274,U_1275,U_1274)
        | ( ! [U_1271] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1272,U_1273),U_1271,U_1275,U_1274)
              | ~ c_Natural_Oevaln(U_1273,U_1274,U_1275,U_1271) )
          & hBOOL(hAPP(U_1272,U_1274)) ) )
      & ( ? [U_1270] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1272,U_1273),U_1270,U_1275,U_1274)
            & c_Natural_Oevaln(U_1273,U_1274,U_1275,U_1270) )
        | ~ hBOOL(hAPP(U_1272,U_1274))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1272,U_1273),U_1274,U_1275,U_1274) ) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ( ! [U_1283,U_1281,U_1279,U_1277] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1281,U_1283,U_1281)
        | ( ! [U_1271] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1271,U_1283,U_1281)
              | ~ c_Natural_Oevaln(U_1279,U_1281,U_1283,U_1271) )
          & hBOOL(hAPP(U_1277,U_1281)) ) )
    & ! [U_1282,U_1280,U_1278,U_1276] :
        ( ? [U_1270] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),U_1270,U_1282,U_1280)
            & c_Natural_Oevaln(U_1278,U_1280,U_1282,U_1270) )
        | ~ hBOOL(hAPP(U_1276,U_1280))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),U_1280,U_1282,U_1280) ) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

fof(f_293_4,plain,
    ( ! [U_1283,U_1281,U_1279,U_1277] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1281,U_1283,U_1281)
        | ( ! [U_1271] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1271,U_1283,U_1281)
              | ~ c_Natural_Oevaln(U_1279,U_1281,U_1283,U_1271) )
          & hBOOL(hAPP(U_1277,U_1281)) ) )
    & ! [U_1282,U_1280,U_1278,U_1276] :
        ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),sK25(U_1282,U_1280,U_1278,U_1276),U_1282,U_1280)
          & c_Natural_Oevaln(U_1278,U_1280,U_1282,sK25(U_1282,U_1280,U_1278,U_1276)) )
        | ~ hBOOL(hAPP(U_1276,U_1280))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),U_1280,U_1282,U_1280) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1270,sK25(U_1282,U_1280,U_1278,U_1276))],[f_293_3]) ).

fof(f_293_5,plain,
    ( ! [U_1271,U_1283,U_1279,U_1281,U_1277] :
        ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1271,U_1283,U_1281)
        | ~ c_Natural_Oevaln(U_1279,U_1281,U_1283,U_1271)
        | ~ sP67(U_1271,U_1283,U_1279,U_1281,U_1277) )
    & ! [U_1271,U_1283,U_1279,U_1281,U_1277] :
        ( hBOOL(hAPP(U_1277,U_1281))
        | ~ sP67(U_1271,U_1283,U_1279,U_1281,U_1277) )
    & ! [U_1280,U_1278,U_1276,U_1282] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),sK25(U_1282,U_1280,U_1278,U_1276),U_1282,U_1280)
        | ~ sP66(U_1280,U_1278,U_1276,U_1282) )
    & ! [U_1280,U_1278,U_1276,U_1282] :
        ( c_Natural_Oevaln(U_1278,U_1280,U_1282,sK25(U_1282,U_1280,U_1278,U_1276))
        | ~ sP66(U_1280,U_1278,U_1276,U_1282) )
    & ! [U_1271,U_1283,U_1279,U_1281,U_1277] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1281,U_1283,U_1281)
        | sP67(U_1271,U_1283,U_1279,U_1281,U_1277) )
    & ! [U_1280,U_1278,U_1276,U_1282] :
        ( sP66(U_1280,U_1278,U_1276,U_1282)
        | ~ hBOOL(hAPP(U_1276,U_1280))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),U_1280,U_1282,U_1280) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66,sP67])],[f_293_4]) ).

cnf(f_293_6,plain,
    ( sP66(U_1280,U_1278,U_1276,U_1282)
    | ~ hBOOL(hAPP(U_1276,U_1280))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),U_1280,U_1282,U_1280) ),
    inference(clausify,[status(thm)],[f_293_5]) ).

cnf(f_293_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1281,U_1283,U_1281)
    | sP67(U_1271,U_1283,U_1279,U_1281,U_1277) ),
    inference(clausify,[status(thm)],[f_293_5]) ).

cnf(f_293_8,plain,
    ( c_Natural_Oevaln(U_1278,U_1280,U_1282,sK25(U_1282,U_1280,U_1278,U_1276))
    | ~ sP66(U_1280,U_1278,U_1276,U_1282) ),
    inference(clausify,[status(thm)],[f_293_5]) ).

cnf(f_293_9,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1276,U_1278),sK25(U_1282,U_1280,U_1278,U_1276),U_1282,U_1280)
    | ~ sP66(U_1280,U_1278,U_1276,U_1282) ),
    inference(clausify,[status(thm)],[f_293_5]) ).

cnf(f_293_10,plain,
    ( hBOOL(hAPP(U_1277,U_1281))
    | ~ sP67(U_1271,U_1283,U_1279,U_1281,U_1277) ),
    inference(clausify,[status(thm)],[f_293_5]) ).

cnf(f_293_11,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1277,U_1279),U_1271,U_1283,U_1281)
    | ~ c_Natural_Oevaln(U_1279,U_1281,U_1283,U_1271)
    | ~ sP67(U_1271,U_1283,U_1279,U_1281,U_1277) ),
    inference(clausify,[status(thm)],[f_293_5]) ).

fof(f_294_1,plain,
    ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
        | ( ( ! [B_s1] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2)
                | ~ c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) )
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( hBOOL(hAPP(V_a1_2,V_a2_2))
            | V_a6_2 != V_a2_2 ) ) )
      & ( ( ? [B_s1] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2)
              & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
          & V_a6_2 = V_a2_2 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I8_J]) ).

fof(f_294_2,plain,
    ! [U_1290,U_1289,U_1288,U_1287,U_1286] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1286,U_1287),U_1288,U_1289,U_1290)
        | ( ( ! [U_1285] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1286,U_1287),U_1285,U_1289,U_1290)
                | ~ c_Natural_Oevaln(U_1287,U_1288,U_1289,U_1285) )
            | ~ hBOOL(hAPP(U_1286,U_1288)) )
          & ( hBOOL(hAPP(U_1286,U_1288))
            | U_1290 != U_1288 ) ) )
      & ( ( ? [U_1284] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1286,U_1287),U_1284,U_1289,U_1290)
              & c_Natural_Oevaln(U_1287,U_1288,U_1289,U_1284) )
          & hBOOL(hAPP(U_1286,U_1288)) )
        | ( ~ hBOOL(hAPP(U_1286,U_1288))
          & U_1290 = U_1288 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1286,U_1287),U_1288,U_1289,U_1290) ) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ( ! [U_1300,U_1298,U_1296,U_1294,U_1292] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1296,U_1298,U_1300)
        | ( ( ! [U_1285] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1285,U_1298,U_1300)
                | ~ c_Natural_Oevaln(U_1294,U_1296,U_1298,U_1285) )
            | ~ hBOOL(hAPP(U_1292,U_1296)) )
          & ( hBOOL(hAPP(U_1292,U_1296))
            | U_1300 != U_1296 ) ) )
    & ! [U_1299,U_1297,U_1295,U_1293,U_1291] :
        ( ( ? [U_1284] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),U_1284,U_1297,U_1299)
              & c_Natural_Oevaln(U_1293,U_1295,U_1297,U_1284) )
          & hBOOL(hAPP(U_1291,U_1295)) )
        | ( ~ hBOOL(hAPP(U_1291,U_1295))
          & U_1299 = U_1295 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),U_1295,U_1297,U_1299) ) ),
    inference(miniscope,[status(thm)],[f_294_2]) ).

fof(f_294_4,plain,
    ( ! [U_1300,U_1298,U_1296,U_1294,U_1292] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1296,U_1298,U_1300)
        | ( ( ! [U_1285] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1285,U_1298,U_1300)
                | ~ c_Natural_Oevaln(U_1294,U_1296,U_1298,U_1285) )
            | ~ hBOOL(hAPP(U_1292,U_1296)) )
          & ( hBOOL(hAPP(U_1292,U_1296))
            | U_1300 != U_1296 ) ) )
    & ! [U_1299,U_1297,U_1295,U_1293,U_1291] :
        ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),sK26(U_1299,U_1297,U_1295,U_1293,U_1291),U_1297,U_1299)
          & c_Natural_Oevaln(U_1293,U_1295,U_1297,sK26(U_1299,U_1297,U_1295,U_1293,U_1291))
          & hBOOL(hAPP(U_1291,U_1295)) )
        | ( ~ hBOOL(hAPP(U_1291,U_1295))
          & U_1299 = U_1295 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),U_1295,U_1297,U_1299) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1284,sK26(U_1299,U_1297,U_1295,U_1293,U_1291))],[f_294_3]) ).

fof(f_294_5,plain,
    ( ! [U_1298,U_1285,U_1296,U_1294,U_1292,U_1300] :
        ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1285,U_1298,U_1300)
        | ~ c_Natural_Oevaln(U_1294,U_1296,U_1298,U_1285)
        | ~ hBOOL(hAPP(U_1292,U_1296))
        | ~ sP70(U_1298,U_1285,U_1296,U_1294,U_1292,U_1300) )
    & ! [U_1298,U_1285,U_1296,U_1294,U_1292,U_1300] :
        ( hBOOL(hAPP(U_1292,U_1296))
        | U_1300 != U_1296
        | ~ sP70(U_1298,U_1285,U_1296,U_1294,U_1292,U_1300) )
    & ! [U_1293,U_1295,U_1291,U_1297,U_1299] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),sK26(U_1299,U_1297,U_1295,U_1293,U_1291),U_1297,U_1299)
        | ~ sP69(U_1293,U_1295,U_1291,U_1297,U_1299) )
    & ! [U_1293,U_1295,U_1291,U_1297,U_1299] :
        ( c_Natural_Oevaln(U_1293,U_1295,U_1297,sK26(U_1299,U_1297,U_1295,U_1293,U_1291))
        | ~ sP69(U_1293,U_1295,U_1291,U_1297,U_1299) )
    & ! [U_1293,U_1295,U_1291,U_1297,U_1299] :
        ( hBOOL(hAPP(U_1291,U_1295))
        | ~ sP69(U_1293,U_1295,U_1291,U_1297,U_1299) )
    & ! [U_1295,U_1291,U_1299] :
        ( ~ hBOOL(hAPP(U_1291,U_1295))
        | ~ sP68(U_1295,U_1291,U_1299) )
    & ! [U_1295,U_1291,U_1299] :
        ( U_1299 = U_1295
        | ~ sP68(U_1295,U_1291,U_1299) )
    & ! [U_1298,U_1285,U_1296,U_1294,U_1292,U_1300] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1296,U_1298,U_1300)
        | sP70(U_1298,U_1285,U_1296,U_1294,U_1292,U_1300) )
    & ! [U_1293,U_1295,U_1291,U_1297,U_1299] :
        ( sP69(U_1293,U_1295,U_1291,U_1297,U_1299)
        | sP68(U_1295,U_1291,U_1299)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),U_1295,U_1297,U_1299) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68,sP69,sP70])],[f_294_4]) ).

cnf(f_294_6,plain,
    ( sP69(U_1293,U_1295,U_1291,U_1297,U_1299)
    | sP68(U_1295,U_1291,U_1299)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),U_1295,U_1297,U_1299) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1296,U_1298,U_1300)
    | sP70(U_1298,U_1285,U_1296,U_1294,U_1292,U_1300) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_8,plain,
    ( U_1299 = U_1295
    | ~ sP68(U_1295,U_1291,U_1299) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_9,plain,
    ( ~ hBOOL(hAPP(U_1291,U_1295))
    | ~ sP68(U_1295,U_1291,U_1299) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_10,plain,
    ( hBOOL(hAPP(U_1291,U_1295))
    | ~ sP69(U_1293,U_1295,U_1291,U_1297,U_1299) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_11,plain,
    ( c_Natural_Oevaln(U_1293,U_1295,U_1297,sK26(U_1299,U_1297,U_1295,U_1293,U_1291))
    | ~ sP69(U_1293,U_1295,U_1291,U_1297,U_1299) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_12,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1291,U_1293),sK26(U_1299,U_1297,U_1295,U_1293,U_1291),U_1297,U_1299)
    | ~ sP69(U_1293,U_1295,U_1291,U_1297,U_1299) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_13,plain,
    ( hBOOL(hAPP(U_1292,U_1296))
    | U_1300 != U_1296
    | ~ sP70(U_1298,U_1285,U_1296,U_1294,U_1292,U_1300) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

cnf(f_294_14,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_1292,U_1294),U_1285,U_1298,U_1300)
    | ~ c_Natural_Oevaln(U_1294,U_1296,U_1298,U_1285)
    | ~ hBOOL(hAPP(U_1292,U_1296))
    | ~ sP70(U_1298,U_1285,U_1296,U_1294,U_1292,U_1300) ),
    inference(clausify,[status(thm)],[f_294_5]) ).

fof(f_295_1,plain,
    ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
        | ( ( ! [B_s1] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) )
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( hBOOL(hAPP(V_a1_2,V_a2_2))
            | V_a5_2 != V_a2_2 ) ) )
      & ( ( ? [B_s1] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
          & V_a5_2 = V_a2_2 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I8_J]) ).

fof(f_295_2,plain,
    ! [U_1306,U_1305,U_1304,U_1303] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1303,U_1304)),U_1305),U_1306))
        | ( ( ! [U_1302] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1303,U_1304)),U_1302),U_1306))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1304),U_1305),U_1302)) )
            | ~ hBOOL(hAPP(U_1303,U_1305)) )
          & ( hBOOL(hAPP(U_1303,U_1305))
            | U_1306 != U_1305 ) ) )
      & ( ( ? [U_1301] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1303,U_1304)),U_1301),U_1306))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1304),U_1305),U_1301)) )
          & hBOOL(hAPP(U_1303,U_1305)) )
        | ( ~ hBOOL(hAPP(U_1303,U_1305))
          & U_1306 = U_1305 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1303,U_1304)),U_1305),U_1306)) ) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ( ! [U_1314,U_1312,U_1310,U_1308] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1312),U_1314))
        | ( ( ! [U_1302] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1302),U_1314))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1310),U_1312),U_1302)) )
            | ~ hBOOL(hAPP(U_1308,U_1312)) )
          & ( hBOOL(hAPP(U_1308,U_1312))
            | U_1314 != U_1312 ) ) )
    & ! [U_1313,U_1311,U_1309,U_1307] :
        ( ( ? [U_1301] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),U_1301),U_1313))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1309),U_1311),U_1301)) )
          & hBOOL(hAPP(U_1307,U_1311)) )
        | ( ~ hBOOL(hAPP(U_1307,U_1311))
          & U_1313 = U_1311 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),U_1311),U_1313)) ) ),
    inference(miniscope,[status(thm)],[f_295_2]) ).

fof(f_295_4,plain,
    ( ! [U_1314,U_1312,U_1310,U_1308] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1312),U_1314))
        | ( ( ! [U_1302] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1302),U_1314))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1310),U_1312),U_1302)) )
            | ~ hBOOL(hAPP(U_1308,U_1312)) )
          & ( hBOOL(hAPP(U_1308,U_1312))
            | U_1314 != U_1312 ) ) )
    & ! [U_1313,U_1311,U_1309,U_1307] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),sK27(U_1313,U_1311,U_1309,U_1307)),U_1313))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1309),U_1311),sK27(U_1313,U_1311,U_1309,U_1307)))
          & hBOOL(hAPP(U_1307,U_1311)) )
        | ( ~ hBOOL(hAPP(U_1307,U_1311))
          & U_1313 = U_1311 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),U_1311),U_1313)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1301,sK27(U_1313,U_1311,U_1309,U_1307))],[f_295_3]) ).

fof(f_295_5,plain,
    ( ! [U_1312,U_1302,U_1308,U_1314,U_1310] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1302),U_1314))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1310),U_1312),U_1302))
        | ~ hBOOL(hAPP(U_1308,U_1312))
        | ~ sP73(U_1312,U_1302,U_1308,U_1314,U_1310) )
    & ! [U_1312,U_1302,U_1308,U_1314,U_1310] :
        ( hBOOL(hAPP(U_1308,U_1312))
        | U_1314 != U_1312
        | ~ sP73(U_1312,U_1302,U_1308,U_1314,U_1310) )
    & ! [U_1309,U_1307,U_1311,U_1313] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),sK27(U_1313,U_1311,U_1309,U_1307)),U_1313))
        | ~ sP72(U_1309,U_1307,U_1311,U_1313) )
    & ! [U_1309,U_1307,U_1311,U_1313] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1309),U_1311),sK27(U_1313,U_1311,U_1309,U_1307)))
        | ~ sP72(U_1309,U_1307,U_1311,U_1313) )
    & ! [U_1309,U_1307,U_1311,U_1313] :
        ( hBOOL(hAPP(U_1307,U_1311))
        | ~ sP72(U_1309,U_1307,U_1311,U_1313) )
    & ! [U_1307,U_1311,U_1313] :
        ( ~ hBOOL(hAPP(U_1307,U_1311))
        | ~ sP71(U_1307,U_1311,U_1313) )
    & ! [U_1307,U_1311,U_1313] :
        ( U_1313 = U_1311
        | ~ sP71(U_1307,U_1311,U_1313) )
    & ! [U_1312,U_1302,U_1308,U_1314,U_1310] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1312),U_1314))
        | sP73(U_1312,U_1302,U_1308,U_1314,U_1310) )
    & ! [U_1309,U_1307,U_1311,U_1313] :
        ( sP72(U_1309,U_1307,U_1311,U_1313)
        | sP71(U_1307,U_1311,U_1313)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),U_1311),U_1313)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71,sP72,sP73])],[f_295_4]) ).

cnf(f_295_6,plain,
    ( sP72(U_1309,U_1307,U_1311,U_1313)
    | sP71(U_1307,U_1311,U_1313)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),U_1311),U_1313)) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1312),U_1314))
    | sP73(U_1312,U_1302,U_1308,U_1314,U_1310) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_8,plain,
    ( U_1313 = U_1311
    | ~ sP71(U_1307,U_1311,U_1313) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_9,plain,
    ( ~ hBOOL(hAPP(U_1307,U_1311))
    | ~ sP71(U_1307,U_1311,U_1313) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_10,plain,
    ( hBOOL(hAPP(U_1307,U_1311))
    | ~ sP72(U_1309,U_1307,U_1311,U_1313) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_11,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1309),U_1311),sK27(U_1313,U_1311,U_1309,U_1307)))
    | ~ sP72(U_1309,U_1307,U_1311,U_1313) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_12,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1307,U_1309)),sK27(U_1313,U_1311,U_1309,U_1307)),U_1313))
    | ~ sP72(U_1309,U_1307,U_1311,U_1313) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_13,plain,
    ( hBOOL(hAPP(U_1308,U_1312))
    | U_1314 != U_1312
    | ~ sP73(U_1312,U_1302,U_1308,U_1314,U_1310) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

cnf(f_295_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1308,U_1310)),U_1302),U_1314))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1310),U_1312),U_1302))
    | ~ hBOOL(hAPP(U_1308,U_1312))
    | ~ sP73(U_1312,U_1302,U_1308,U_1314,U_1310) ),
    inference(clausify,[status(thm)],[f_295_5]) ).

fof(f_296_1,plain,
    ! [V_a2_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
        | ( ! [B_s1] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) )
        | ~ hBOOL(hAPP(V_a1_2,V_a2_2))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I7_J]) ).

fof(f_296_2,plain,
    ! [U_1319,U_1318,U_1317] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1317,U_1318)),U_1319),U_1319))
        | ( ! [U_1316] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1317,U_1318)),U_1316),U_1319))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1318),U_1319),U_1316)) )
          & hBOOL(hAPP(U_1317,U_1319)) ) )
      & ( ? [U_1315] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1317,U_1318)),U_1315),U_1319))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1318),U_1319),U_1315)) )
        | ~ hBOOL(hAPP(U_1317,U_1319))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1317,U_1318)),U_1319),U_1319)) ) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ( ! [U_1325,U_1323,U_1321] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1325),U_1325))
        | ( ! [U_1316] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1316),U_1325))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1323),U_1325),U_1316)) )
          & hBOOL(hAPP(U_1321,U_1325)) ) )
    & ! [U_1324,U_1322,U_1320] :
        ( ? [U_1315] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),U_1315),U_1324))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1322),U_1324),U_1315)) )
        | ~ hBOOL(hAPP(U_1320,U_1324))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),U_1324),U_1324)) ) ),
    inference(miniscope,[status(thm)],[f_296_2]) ).

fof(f_296_4,plain,
    ( ! [U_1325,U_1323,U_1321] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1325),U_1325))
        | ( ! [U_1316] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1316),U_1325))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1323),U_1325),U_1316)) )
          & hBOOL(hAPP(U_1321,U_1325)) ) )
    & ! [U_1324,U_1322,U_1320] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),sK28(U_1324,U_1322,U_1320)),U_1324))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1322),U_1324),sK28(U_1324,U_1322,U_1320))) )
        | ~ hBOOL(hAPP(U_1320,U_1324))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),U_1324),U_1324)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1315,sK28(U_1324,U_1322,U_1320))],[f_296_3]) ).

fof(f_296_5,plain,
    ( ! [U_1323,U_1321,U_1316,U_1325] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1316),U_1325))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1323),U_1325),U_1316))
        | ~ sP75(U_1323,U_1321,U_1316,U_1325) )
    & ! [U_1323,U_1321,U_1316,U_1325] :
        ( hBOOL(hAPP(U_1321,U_1325))
        | ~ sP75(U_1323,U_1321,U_1316,U_1325) )
    & ! [U_1322,U_1320,U_1324] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),sK28(U_1324,U_1322,U_1320)),U_1324))
        | ~ sP74(U_1322,U_1320,U_1324) )
    & ! [U_1322,U_1320,U_1324] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1322),U_1324),sK28(U_1324,U_1322,U_1320)))
        | ~ sP74(U_1322,U_1320,U_1324) )
    & ! [U_1323,U_1321,U_1316,U_1325] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1325),U_1325))
        | sP75(U_1323,U_1321,U_1316,U_1325) )
    & ! [U_1322,U_1320,U_1324] :
        ( sP74(U_1322,U_1320,U_1324)
        | ~ hBOOL(hAPP(U_1320,U_1324))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),U_1324),U_1324)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75])],[f_296_4]) ).

cnf(f_296_6,plain,
    ( sP74(U_1322,U_1320,U_1324)
    | ~ hBOOL(hAPP(U_1320,U_1324))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),U_1324),U_1324)) ),
    inference(clausify,[status(thm)],[f_296_5]) ).

cnf(f_296_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1325),U_1325))
    | sP75(U_1323,U_1321,U_1316,U_1325) ),
    inference(clausify,[status(thm)],[f_296_5]) ).

cnf(f_296_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1322),U_1324),sK28(U_1324,U_1322,U_1320)))
    | ~ sP74(U_1322,U_1320,U_1324) ),
    inference(clausify,[status(thm)],[f_296_5]) ).

cnf(f_296_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1320,U_1322)),sK28(U_1324,U_1322,U_1320)),U_1324))
    | ~ sP74(U_1322,U_1320,U_1324) ),
    inference(clausify,[status(thm)],[f_296_5]) ).

cnf(f_296_10,plain,
    ( hBOOL(hAPP(U_1321,U_1325))
    | ~ sP75(U_1323,U_1321,U_1316,U_1325) ),
    inference(clausify,[status(thm)],[f_296_5]) ).

cnf(f_296_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1321,U_1323)),U_1316),U_1325))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1323),U_1325),U_1316))
    | ~ sP75(U_1323,U_1321,U_1316,U_1325) ),
    inference(clausify,[status(thm)],[f_296_5]) ).

fof(f_297_1,plain,
    ! [V_a1_2,V_a2_2] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
        | ~ hBOOL(hAPP(c_Com_OWT,V_a1_2)) )
      & ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I6_J]) ).

fof(f_297_2,plain,
    ! [U_1327,U_1326] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1326,U_1327)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1327)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_1327))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1326,U_1327))) ) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ( ! [U_1331] :
        ( ! [U_1329] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1329,U_1331)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1331)) )
    & ! [U_1330] :
        ( ! [U_1328] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1328,U_1330)))
        | hBOOL(hAPP(c_Com_OWT,U_1330)) ) ),
    inference(miniscope,[status(thm)],[f_297_2]) ).

fof(f_297_4,plain,
    ( ! [U_1329,U_1331] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1329,U_1331)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1331)) )
    & ! [U_1330,U_1328] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1328,U_1330)))
        | hBOOL(hAPP(c_Com_OWT,U_1330)) ) ),
    inference(definitional_conversion,[status(esa)],[f_297_3]) ).

cnf(f_297_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1328,U_1330)))
    | hBOOL(hAPP(c_Com_OWT,U_1330)) ),
    inference(clausify,[status(thm)],[f_297_4]) ).

cnf(f_297_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1329,U_1331)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1331)) ),
    inference(clausify,[status(thm)],[f_297_4]) ).

fof(f_298_1,plain,
    ! [V_b_2,V_c_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_While]) ).

fof(f_298_2,plain,
    ! [U_1333,U_1332] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1333,U_1332)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1332)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_1333,U_1332] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1333,U_1332)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1332)) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_1333,U_1332)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1332)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_1,plain,
    ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I59_J]) ).

fof(f_299_2,plain,
    ! [U_1336,U_1335,U_1334] : hAPP(c_Com_Ocom_OBODY,U_1334) != c_Com_Ocom_OWhile(U_1335,U_1336),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_1334,U_1335,U_1336] : hAPP(c_Com_Ocom_OBODY,U_1334) != c_Com_Ocom_OWhile(U_1335,U_1336),
    inference(definitional_conversion,[status(esa)],[f_299_2]) ).

cnf(f_299_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_1334) != c_Com_Ocom_OWhile(U_1335,U_1336),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_1,plain,
    ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I58_J]) ).

fof(f_300_2,plain,
    ! [U_1339,U_1338,U_1337] : c_Com_Ocom_OWhile(U_1337,U_1338) != hAPP(c_Com_Ocom_OBODY,U_1339),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_1337,U_1338,U_1339] : c_Com_Ocom_OWhile(U_1337,U_1338) != hAPP(c_Com_Ocom_OBODY,U_1339),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    c_Com_Ocom_OWhile(U_1337,U_1338) != hAPP(c_Com_Ocom_OBODY,U_1339),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I53_J]) ).

fof(f_301_2,plain,
    ! [U_1344,U_1343,U_1342,U_1341,U_1340] : c_Com_Ocom_OWhile(U_1340,U_1341) != c_Com_Ocom_OCond(U_1342,U_1343,U_1344),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_1340,U_1341,U_1342,U_1343,U_1344] : c_Com_Ocom_OWhile(U_1340,U_1341) != c_Com_Ocom_OCond(U_1342,U_1343,U_1344),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_4,plain,
    c_Com_Ocom_OWhile(U_1340,U_1341) != c_Com_Ocom_OCond(U_1342,U_1343,U_1344),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I52_J]) ).

fof(f_302_2,plain,
    ! [U_1349,U_1348,U_1347,U_1346,U_1345] : c_Com_Ocom_OCond(U_1345,U_1346,U_1347) != c_Com_Ocom_OWhile(U_1348,U_1349),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_1346,U_1345,U_1347,U_1348,U_1349] : c_Com_Ocom_OCond(U_1345,U_1346,U_1347) != c_Com_Ocom_OWhile(U_1348,U_1349),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    c_Com_Ocom_OCond(U_1345,U_1346,U_1347) != c_Com_Ocom_OWhile(U_1348,U_1349),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I28_J]) ).

fof(f_303_2,plain,
    ! [U_1353,U_1352,U_1351,U_1350] : c_Com_Ocom_OAss(U_1350,U_1351) != c_Com_Ocom_OWhile(U_1352,U_1353),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_1350,U_1351,U_1352,U_1353] : c_Com_Ocom_OAss(U_1350,U_1351) != c_Com_Ocom_OWhile(U_1352,U_1353),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    c_Com_Ocom_OAss(U_1350,U_1351) != c_Com_Ocom_OWhile(U_1352,U_1353),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I29_J]) ).

fof(f_304_2,plain,
    ! [U_1357,U_1356,U_1355,U_1354] : c_Com_Ocom_OWhile(U_1354,U_1355) != c_Com_Ocom_OAss(U_1356,U_1357),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_1354,U_1355,U_1356,U_1357] : c_Com_Ocom_OWhile(U_1354,U_1355) != c_Com_Ocom_OAss(U_1356,U_1357),
    inference(definitional_conversion,[status(esa)],[f_304_2]) ).

cnf(f_304_4,plain,
    c_Com_Ocom_OWhile(U_1354,U_1355) != c_Com_Ocom_OAss(U_1356,U_1357),
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I38_J]) ).

fof(f_305_2,plain,
    ! [U_1362,U_1361,U_1360,U_1359,U_1358] : c_Com_Ocom_OLocal(U_1358,U_1359,U_1360) != c_Com_Ocom_OWhile(U_1361,U_1362),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_1359,U_1358,U_1360,U_1361,U_1362] : c_Com_Ocom_OLocal(U_1358,U_1359,U_1360) != c_Com_Ocom_OWhile(U_1361,U_1362),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    c_Com_Ocom_OLocal(U_1358,U_1359,U_1360) != c_Com_Ocom_OWhile(U_1361,U_1362),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_1,plain,
    ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I61_J]) ).

fof(f_306_2,plain,
    ! [U_1367,U_1366,U_1365,U_1364,U_1363] : c_Com_Ocom_OCall(U_1363,U_1364,U_1365) != c_Com_Ocom_OWhile(U_1366,U_1367),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_1364,U_1363,U_1365,U_1366,U_1367] : c_Com_Ocom_OCall(U_1363,U_1364,U_1365) != c_Com_Ocom_OWhile(U_1366,U_1367),
    inference(definitional_conversion,[status(esa)],[f_306_2]) ).

cnf(f_306_4,plain,
    c_Com_Ocom_OCall(U_1363,U_1364,U_1365) != c_Com_Ocom_OWhile(U_1366,U_1367),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I39_J]) ).

fof(f_307_2,plain,
    ! [U_1372,U_1371,U_1370,U_1369,U_1368] : c_Com_Ocom_OWhile(U_1368,U_1369) != c_Com_Ocom_OLocal(U_1370,U_1371,U_1372),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_1368,U_1369,U_1370,U_1371,U_1372] : c_Com_Ocom_OWhile(U_1368,U_1369) != c_Com_Ocom_OLocal(U_1370,U_1371,U_1372),
    inference(definitional_conversion,[status(esa)],[f_307_2]) ).

cnf(f_307_4,plain,
    c_Com_Ocom_OWhile(U_1368,U_1369) != c_Com_Ocom_OLocal(U_1370,U_1371,U_1372),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I60_J]) ).

fof(f_308_2,plain,
    ! [U_1377,U_1376,U_1375,U_1374,U_1373] : c_Com_Ocom_OWhile(U_1373,U_1374) != c_Com_Ocom_OCall(U_1375,U_1376,U_1377),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_1373,U_1374,U_1375,U_1376,U_1377] : c_Com_Ocom_OWhile(U_1373,U_1374) != c_Com_Ocom_OCall(U_1375,U_1376,U_1377),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    c_Com_Ocom_OWhile(U_1373,U_1374) != c_Com_Ocom_OCall(U_1375,U_1376,U_1377),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I46_J]) ).

fof(f_309_2,plain,
    ! [U_1381,U_1380,U_1379,U_1378] : c_Com_Ocom_OSemi(U_1378,U_1379) != c_Com_Ocom_OWhile(U_1380,U_1381),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1378,U_1379,U_1380,U_1381] : c_Com_Ocom_OSemi(U_1378,U_1379) != c_Com_Ocom_OWhile(U_1380,U_1381),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    c_Com_Ocom_OSemi(U_1378,U_1379) != c_Com_Ocom_OWhile(U_1380,U_1381),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_1,plain,
    ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I47_J]) ).

fof(f_310_2,plain,
    ! [U_1385,U_1384,U_1383,U_1382] : c_Com_Ocom_OWhile(U_1382,U_1383) != c_Com_Ocom_OSemi(U_1384,U_1385),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_1382,U_1383,U_1384,U_1385] : c_Com_Ocom_OWhile(U_1382,U_1383) != c_Com_Ocom_OSemi(U_1384,U_1385),
    inference(definitional_conversion,[status(esa)],[f_310_2]) ).

cnf(f_310_4,plain,
    c_Com_Ocom_OWhile(U_1382,U_1383) != c_Com_Ocom_OSemi(U_1384,U_1385),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_1,plain,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I16_J]) ).

fof(f_311_2,plain,
    ! [U_1387,U_1386] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_1386,U_1387),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_1386,U_1387] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_1386,U_1387),
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_1386,U_1387),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_1,plain,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I17_J]) ).

fof(f_312_2,plain,
    ! [U_1389,U_1388] : c_Com_Ocom_OWhile(U_1388,U_1389) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_1388,U_1389] : c_Com_Ocom_OWhile(U_1388,U_1389) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    c_Com_Ocom_OWhile(U_1388,U_1389) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [V_n_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).

fof(f_313_2,plain,
    ! [U_1391,U_1390] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1390),c_Groups_Ozero__class_Ozero(U_1390)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1390),U_1391)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1391)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1391))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1390),c_Groups_Ozero__class_Ozero(U_1390)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1390),U_1391))) ) )
      | ~ class_Rings_Olinordered__semidom(U_1390) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ( ! [U_1390,U_1391] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1390),c_Groups_Ozero__class_Ozero(U_1390)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1390),U_1391)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1391))
        | ~ sP76(U_1390,U_1391) )
    & ! [U_1390,U_1391] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1391))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1390),c_Groups_Ozero__class_Ozero(U_1390)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1390),U_1391)))
        | ~ sP76(U_1390,U_1391) )
    & ! [U_1390,U_1391] :
        ( sP76(U_1390,U_1391)
        | ~ class_Rings_Olinordered__semidom(U_1390) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_313_2]) ).

cnf(f_313_4,plain,
    ( sP76(U_1390,U_1391)
    | ~ class_Rings_Olinordered__semidom(U_1390) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

cnf(f_313_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1390),c_Groups_Ozero__class_Ozero(U_1390)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1390),U_1391)))
    | ~ sP76(U_1390,U_1391) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

cnf(f_313_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1390),c_Groups_Ozero__class_Ozero(U_1390)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1390),U_1391)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1391))
    | ~ sP76(U_1390,U_1391) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I4_J]) ).

fof(f_314_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_314_1]) ).

cnf(f_314_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_314_2]) ).

fof(f_315_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I3_J]) ).

fof(f_315_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_315_1]) ).

cnf(f_315_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_315_2]) ).

fof(f_316_1,plain,
    ! [V_n,V_m] :
      ( ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__Suc__add]) ).

fof(f_316_2,plain,
    ! [U_1394,U_1393] :
      ( ? [U_1392] : U_1394 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1393),U_1392))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1393),U_1394)) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_1394,U_1393] :
      ( U_1394 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1393),sK29(U_1394,U_1393)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1393),U_1394)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1392,sK29(U_1394,U_1393))],[f_316_2]) ).

fof(f_316_4,plain,
    ! [U_1393,U_1394] :
      ( U_1394 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1393),sK29(U_1394,U_1393)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1393),U_1394)) ),
    inference(definitional_conversion,[status(esa)],[f_316_3]) ).

cnf(f_316_5,plain,
    ( U_1394 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1393),sK29(U_1394,U_1393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1393),U_1394)) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

fof(f_317_1,plain,
    ! [V_j,V_i] :
      ( ? [B_k] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__add__positive]) ).

fof(f_317_2,plain,
    ! [U_1397,U_1396] :
      ( ? [U_1395] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1396),U_1395) = U_1397
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1395)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1396),U_1397)) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_1397,U_1396] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1396),sK30(U_1397,U_1396)) = U_1397
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK30(U_1397,U_1396))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1396),U_1397)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1395,sK30(U_1397,U_1396))],[f_317_2]) ).

fof(f_317_4,plain,
    ( ! [U_1396,U_1397] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1396),sK30(U_1397,U_1396)) = U_1397
        | ~ sP77(U_1396,U_1397) )
    & ! [U_1396,U_1397] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK30(U_1397,U_1396)))
        | ~ sP77(U_1396,U_1397) )
    & ! [U_1396,U_1397] :
        ( sP77(U_1396,U_1397)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1396),U_1397)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_317_3]) ).

cnf(f_317_5,plain,
    ( sP77(U_1396,U_1397)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1396),U_1397)) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

cnf(f_317_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK30(U_1397,U_1396)))
    | ~ sP77(U_1396,U_1397) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

cnf(f_317_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1396),sK30(U_1397,U_1396)) = U_1397
    | ~ sP77(U_1396,U_1397) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

fof(f_318_1,plain,
    ! [V_n] :
      ( ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_gr0__implies__Suc]) ).

fof(f_318_2,plain,
    ! [U_1399] :
      ( ? [U_1398] : U_1399 = hAPP(c_Nat_OSuc,U_1398)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399)) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_1399] :
      ( U_1399 = hAPP(c_Nat_OSuc,sK31(U_1399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1398,sK31(U_1399))],[f_318_2]) ).

fof(f_318_4,plain,
    ! [U_1399] :
      ( U_1399 = hAPP(c_Nat_OSuc,sK31(U_1399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399)) ),
    inference(definitional_conversion,[status(esa)],[f_318_3]) ).

cnf(f_318_5,plain,
    ( U_1399 = hAPP(c_Nat_OSuc,sK31(U_1399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399)) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

fof(f_319_1,plain,
    ! [V_t,V_s,V_c2,V_c1] :
      ( ? [B_s1] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I4_J]) ).

fof(f_319_2,plain,
    ! [U_1404,U_1403,U_1402,U_1401] :
      ( ? [U_1400] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1402),U_1400),U_1404))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1401),U_1403),U_1400)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1401,U_1402)),U_1403),U_1404)) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_1404,U_1403,U_1402,U_1401] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1402),sK32(U_1404,U_1403,U_1402,U_1401)),U_1404))
        & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1401),U_1403),sK32(U_1404,U_1403,U_1402,U_1401))) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1401,U_1402)),U_1403),U_1404)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1400,sK32(U_1404,U_1403,U_1402,U_1401))],[f_319_2]) ).

fof(f_319_4,plain,
    ( ! [U_1401,U_1402,U_1403,U_1404] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1402),sK32(U_1404,U_1403,U_1402,U_1401)),U_1404))
        | ~ sP78(U_1401,U_1402,U_1403,U_1404) )
    & ! [U_1401,U_1402,U_1403,U_1404] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1401),U_1403),sK32(U_1404,U_1403,U_1402,U_1401)))
        | ~ sP78(U_1401,U_1402,U_1403,U_1404) )
    & ! [U_1401,U_1402,U_1403,U_1404] :
        ( sP78(U_1401,U_1402,U_1403,U_1404)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1401,U_1402)),U_1403),U_1404)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_319_3]) ).

cnf(f_319_5,plain,
    ( sP78(U_1401,U_1402,U_1403,U_1404)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1401,U_1402)),U_1403),U_1404)) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

cnf(f_319_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1401),U_1403),sK32(U_1404,U_1403,U_1402,U_1401)))
    | ~ sP78(U_1401,U_1402,U_1403,U_1404) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

cnf(f_319_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1402),sK32(U_1404,U_1403,U_1402,U_1401)),U_1404))
    | ~ sP78(U_1401,U_1402,U_1403,U_1404) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

fof(f_320_1,plain,
    ! [V_m_2,V_n_2,V_f_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2))) ) )
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less__iff]) ).

fof(f_320_2,plain,
    ! [U_1409,U_1408,U_1407,U_1406] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409))) ) )
      | ? [U_1405] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1405)),hAPP(U_1407,hAPP(c_Nat_OSuc,U_1405))))
      | ~ class_Orderings_Oorder(U_1406) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_1409,U_1408,U_1407,U_1406] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,sK33(U_1409,U_1408,U_1407,U_1406))),hAPP(U_1407,hAPP(c_Nat_OSuc,sK33(U_1409,U_1408,U_1407,U_1406)))))
      | ~ class_Orderings_Oorder(U_1406) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1405,sK33(U_1409,U_1408,U_1407,U_1406))],[f_320_2]) ).

fof(f_320_4,plain,
    ( ! [U_1406,U_1407,U_1408,U_1409] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409))
        | ~ sP79(U_1406,U_1407,U_1408,U_1409) )
    & ! [U_1406,U_1407,U_1408,U_1409] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409)))
        | ~ sP79(U_1406,U_1407,U_1408,U_1409) )
    & ! [U_1406,U_1407,U_1408,U_1409] :
        ( sP79(U_1406,U_1407,U_1408,U_1409)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,sK33(U_1409,U_1408,U_1407,U_1406))),hAPP(U_1407,hAPP(c_Nat_OSuc,sK33(U_1409,U_1408,U_1407,U_1406)))))
        | ~ class_Orderings_Oorder(U_1406) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_320_3]) ).

cnf(f_320_5,plain,
    ( sP79(U_1406,U_1407,U_1408,U_1409)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,sK33(U_1409,U_1408,U_1407,U_1406))),hAPP(U_1407,hAPP(c_Nat_OSuc,sK33(U_1409,U_1408,U_1407,U_1406)))))
    | ~ class_Orderings_Oorder(U_1406) ),
    inference(clausify,[status(thm)],[f_320_4]) ).

cnf(f_320_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409)))
    | ~ sP79(U_1406,U_1407,U_1408,U_1409) ),
    inference(clausify,[status(thm)],[f_320_4]) ).

cnf(f_320_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(U_1407,U_1408)),hAPP(U_1407,U_1409)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1408),U_1409))
    | ~ sP79(U_1406,U_1407,U_1408,U_1409) ),
    inference(clausify,[status(thm)],[f_320_4]) ).

fof(f_321_1,plain,
    ! [V_n_H_2,V_n_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less]) ).

fof(f_321_2,plain,
    ! [U_1414,U_1413,U_1412,U_1411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,U_1413)),hAPP(U_1412,U_1414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1413),U_1414))
      | ? [U_1410] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,U_1410)),hAPP(U_1412,hAPP(c_Nat_OSuc,U_1410))))
      | ~ class_Orderings_Oorder(U_1411) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_1414,U_1413,U_1412,U_1411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,U_1413)),hAPP(U_1412,U_1414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1413),U_1414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,sK34(U_1414,U_1413,U_1412,U_1411))),hAPP(U_1412,hAPP(c_Nat_OSuc,sK34(U_1414,U_1413,U_1412,U_1411)))))
      | ~ class_Orderings_Oorder(U_1411) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1410,sK34(U_1414,U_1413,U_1412,U_1411))],[f_321_2]) ).

fof(f_321_4,plain,
    ! [U_1412,U_1414,U_1413,U_1411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,U_1413)),hAPP(U_1412,U_1414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1413),U_1414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,sK34(U_1414,U_1413,U_1412,U_1411))),hAPP(U_1412,hAPP(c_Nat_OSuc,sK34(U_1414,U_1413,U_1412,U_1411)))))
      | ~ class_Orderings_Oorder(U_1411) ),
    inference(definitional_conversion,[status(esa)],[f_321_3]) ).

cnf(f_321_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,U_1413)),hAPP(U_1412,U_1414)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1413),U_1414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(U_1412,sK34(U_1414,U_1413,U_1412,U_1411))),hAPP(U_1412,hAPP(c_Nat_OSuc,sK34(U_1414,U_1413,U_1412,U_1411)))))
    | ~ class_Orderings_Oorder(U_1411) ),
    inference(clausify,[status(thm)],[f_321_4]) ).

fof(f_322_1,plain,
    ! [V_t,V_n,V_s,V_c2,V_c1] :
      ( ? [B_s1] :
          ( c_Natural_Oevaln(V_c2,B_s1,V_n,V_t)
          & c_Natural_Oevaln(V_c1,V_s,V_n,B_s1) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I4_J]) ).

fof(f_322_2,plain,
    ! [U_1420,U_1419,U_1418,U_1417,U_1416] :
      ( ? [U_1415] :
          ( c_Natural_Oevaln(U_1417,U_1415,U_1419,U_1420)
          & c_Natural_Oevaln(U_1416,U_1418,U_1419,U_1415) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1416,U_1417),U_1418,U_1419,U_1420) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_1420,U_1419,U_1418,U_1417,U_1416] :
      ( ( c_Natural_Oevaln(U_1417,sK35(U_1420,U_1419,U_1418,U_1417,U_1416),U_1419,U_1420)
        & c_Natural_Oevaln(U_1416,U_1418,U_1419,sK35(U_1420,U_1419,U_1418,U_1417,U_1416)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1416,U_1417),U_1418,U_1419,U_1420) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1415,sK35(U_1420,U_1419,U_1418,U_1417,U_1416))],[f_322_2]) ).

fof(f_322_4,plain,
    ( ! [U_1419,U_1420,U_1417,U_1418,U_1416] :
        ( c_Natural_Oevaln(U_1417,sK35(U_1420,U_1419,U_1418,U_1417,U_1416),U_1419,U_1420)
        | ~ sP80(U_1419,U_1420,U_1417,U_1418,U_1416) )
    & ! [U_1419,U_1420,U_1417,U_1418,U_1416] :
        ( c_Natural_Oevaln(U_1416,U_1418,U_1419,sK35(U_1420,U_1419,U_1418,U_1417,U_1416))
        | ~ sP80(U_1419,U_1420,U_1417,U_1418,U_1416) )
    & ! [U_1419,U_1420,U_1417,U_1418,U_1416] :
        ( sP80(U_1419,U_1420,U_1417,U_1418,U_1416)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1416,U_1417),U_1418,U_1419,U_1420) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_322_3]) ).

cnf(f_322_5,plain,
    ( sP80(U_1419,U_1420,U_1417,U_1418,U_1416)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_1416,U_1417),U_1418,U_1419,U_1420) ),
    inference(clausify,[status(thm)],[f_322_4]) ).

cnf(f_322_6,plain,
    ( c_Natural_Oevaln(U_1416,U_1418,U_1419,sK35(U_1420,U_1419,U_1418,U_1417,U_1416))
    | ~ sP80(U_1419,U_1420,U_1417,U_1418,U_1416) ),
    inference(clausify,[status(thm)],[f_322_4]) ).

cnf(f_322_7,plain,
    ( c_Natural_Oevaln(U_1417,sK35(U_1420,U_1419,U_1418,U_1417,U_1416),U_1419,U_1420)
    | ~ sP80(U_1419,U_1420,U_1417,U_1418,U_1416) ),
    inference(clausify,[status(thm)],[f_322_4]) ).

fof(f_323_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) ) )
      | ~ class_Nat_Osemiring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).

fof(f_323_2,plain,
    ! [U_1423,U_1422,U_1421] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1422) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1423)
          | U_1422 != U_1423 )
        & ( U_1422 = U_1423
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1422) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1423) ) )
      | ~ class_Nat_Osemiring__char__0(U_1421) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ( ! [U_1423,U_1422,U_1421] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1422) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1423)
        | U_1422 != U_1423
        | ~ sP81(U_1423,U_1422,U_1421) )
    & ! [U_1423,U_1422,U_1421] :
        ( U_1422 = U_1423
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1422) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1423)
        | ~ sP81(U_1423,U_1422,U_1421) )
    & ! [U_1423,U_1422,U_1421] :
        ( sP81(U_1423,U_1422,U_1421)
        | ~ class_Nat_Osemiring__char__0(U_1421) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_323_2]) ).

cnf(f_323_4,plain,
    ( sP81(U_1423,U_1422,U_1421)
    | ~ class_Nat_Osemiring__char__0(U_1421) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

cnf(f_323_5,plain,
    ( U_1422 = U_1423
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1422) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1423)
    | ~ sP81(U_1423,U_1422,U_1421) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

cnf(f_323_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1422) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1421),U_1423)
    | U_1422 != U_1423
    | ~ sP81(U_1423,U_1422,U_1421) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_1,plain,
    ! [V_n_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv]) ).

fof(f_324_2,plain,
    ! [U_1424] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1424 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1424) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ( ! [U_1426] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1426 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1425] :
        ( U_1425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1425) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_324_2]) ).

fof(f_324_4,plain,
    ( ! [U_1426] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1426 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1425] :
        ( U_1425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1425) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_324_3]) ).

cnf(f_324_5,plain,
    ( U_1425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1425) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_324_4]) ).

cnf(f_324_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_1426 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_324_4]) ).

fof(f_325_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__0]) ).

fof(f_325_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_325_1]) ).

cnf(f_325_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_325_2]) ).

fof(f_326_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ! [B_n] : V_z_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) )
      & ( ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd]) ).

fof(f_326_2,plain,
    ! [U_1430,U_1429] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1429),U_1430))
        | ! [U_1428] : U_1430 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1429),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1428))) )
      & ( ? [U_1427] : U_1430 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1429),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1427)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1429),U_1430)) ) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ( ! [U_1434,U_1432] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1432),U_1434))
        | ! [U_1428] : U_1434 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1432),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1428))) )
    & ! [U_1433,U_1431] :
        ( ? [U_1427] : U_1433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1431),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1427)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1431),U_1433)) ) ),
    inference(miniscope,[status(thm)],[f_326_2]) ).

fof(f_326_4,plain,
    ( ! [U_1434,U_1432] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1432),U_1434))
        | ! [U_1428] : U_1434 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1432),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1428))) )
    & ! [U_1433,U_1431] :
        ( U_1433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1431),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK36(U_1433,U_1431))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1431),U_1433)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1427,sK36(U_1433,U_1431))],[f_326_3]) ).

fof(f_326_5,plain,
    ( ! [U_1434,U_1428,U_1432] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1432),U_1434))
        | U_1434 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1432),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1428))) )
    & ! [U_1433,U_1431] :
        ( U_1433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1431),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK36(U_1433,U_1431))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1431),U_1433)) ) ),
    inference(definitional_conversion,[status(esa)],[f_326_4]) ).

cnf(f_326_6,plain,
    ( U_1433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1431),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK36(U_1433,U_1431))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1431),U_1433)) ),
    inference(clausify,[status(thm)],[f_326_5]) ).

cnf(f_326_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1432),U_1434))
    | U_1434 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1432),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1428))) ),
    inference(clausify,[status(thm)],[f_326_5]) ).

fof(f_327_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__int]) ).

fof(f_327_2,plain,
    ! [U_1436,U_1435] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1435)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1436)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1435),U_1436)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1435),U_1436))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1435)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1436))) ) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ( ! [U_1440,U_1438] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1438)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1440)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1438),U_1440)) )
    & ! [U_1439,U_1437] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1437),U_1439))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1437)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1439))) ) ),
    inference(miniscope,[status(thm)],[f_327_2]) ).

fof(f_327_4,plain,
    ( ! [U_1438,U_1440] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1438)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1440)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1438),U_1440)) )
    & ! [U_1439,U_1437] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1437),U_1439))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1437)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1439))) ) ),
    inference(definitional_conversion,[status(esa)],[f_327_3]) ).

cnf(f_327_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1437),U_1439))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1437)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1439))) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1438)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1440)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1438),U_1440)) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

fof(f_328_1,plain,
    ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z),
    inference(fof_nnf,[status(thm)],[fact_zadd__int__left]) ).

fof(f_328_2,plain,
    ! [U_1443,U_1442,U_1441] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1441)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1442)),U_1443)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1441),U_1442))),U_1443),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_1441,U_1442,U_1443] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1441)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1442)),U_1443)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1441),U_1442))),U_1443),
    inference(definitional_conversion,[status(esa)],[f_328_2]) ).

cnf(f_328_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1441)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1442)),U_1443)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1441),U_1442))),U_1443),
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zadd__int]) ).

fof(f_329_2,plain,
    ! [U_1445,U_1444] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1444)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1445)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1444),U_1445)),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_1444,U_1445] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1444)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1445)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1444),U_1445)),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1444)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1445)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1444),U_1445)),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv]) ).

fof(f_330_2,plain,
    ! [U_1446] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1446)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1446))) ) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ( ! [U_1448] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1448)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1448)) )
    & ! [U_1447] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1447))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1447))) ) ),
    inference(miniscope,[status(thm)],[f_330_2]) ).

fof(f_330_4,plain,
    ( ! [U_1448] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1448)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1448)) )
    & ! [U_1447] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1447))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1447))) ) ),
    inference(definitional_conversion,[status(esa)],[f_330_3]) ).

cnf(f_330_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1447))) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

cnf(f_330_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1448)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1448)) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

fof(f_331_1,plain,
    ! [V_m,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(f_331_2,plain,
    ! [U_1450,U_1449] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1449),U_1450)),c_Groups_Ozero__class_Ozero(U_1449)))
      | ~ class_Rings_Olinordered__semidom(U_1449) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_1449,U_1450] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1449),U_1450)),c_Groups_Ozero__class_Ozero(U_1449)))
      | ~ class_Rings_Olinordered__semidom(U_1449) ),
    inference(definitional_conversion,[status(esa)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1449),U_1450)),c_Groups_Ozero__class_Ozero(U_1449)))
    | ~ class_Rings_Olinordered__semidom(U_1449) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_1,plain,
    ! [T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0]) ).

fof(f_332_2,plain,
    ! [U_1451] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1451),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1451)
      | ~ class_Rings_Osemiring__1(U_1451) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1451] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1451),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1451)
      | ~ class_Rings_Osemiring__1(U_1451) ),
    inference(definitional_conversion,[status(esa)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1451),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1451)
    | ~ class_Rings_Osemiring__1(U_1451) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_1,plain,
    ! [V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less]) ).

fof(f_333_2,plain,
    ! [U_1454,U_1453,U_1452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1453),U_1454))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1452),U_1453)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1452),U_1454)))
      | ~ class_Rings_Olinordered__semidom(U_1452) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_1452,U_1453,U_1454] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1453),U_1454))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1452),U_1453)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1452),U_1454)))
      | ~ class_Rings_Olinordered__semidom(U_1452) ),
    inference(definitional_conversion,[status(esa)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1453),U_1454))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1452),U_1453)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1452),U_1454)))
    | ~ class_Rings_Olinordered__semidom(U_1452) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_1,plain,
    ! [V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less]) ).

fof(f_334_2,plain,
    ! [U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1455),U_1456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1455),U_1457)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1456),U_1457))
      | ~ class_Rings_Olinordered__semidom(U_1455) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1455,U_1456,U_1457] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1455),U_1456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1455),U_1457)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1456),U_1457))
      | ~ class_Rings_Olinordered__semidom(U_1455) ),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1455),U_1456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1455),U_1457)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1456),U_1457))
    | ~ class_Rings_Olinordered__semidom(U_1455) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).

fof(f_335_2,plain,
    ! [U_1460,U_1459,U_1458] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1458),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1459)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1460)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1459),U_1460)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1459),U_1460))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1458),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1459)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1460))) ) )
      | ~ class_Rings_Olinordered__semidom(U_1458) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ( ! [U_1459,U_1458,U_1460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1458),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1459)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1460)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1459),U_1460))
        | ~ sP82(U_1459,U_1458,U_1460) )
    & ! [U_1459,U_1458,U_1460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1459),U_1460))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1458),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1459)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1460)))
        | ~ sP82(U_1459,U_1458,U_1460) )
    & ! [U_1459,U_1458,U_1460] :
        ( sP82(U_1459,U_1458,U_1460)
        | ~ class_Rings_Olinordered__semidom(U_1458) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_335_2]) ).

cnf(f_335_4,plain,
    ( sP82(U_1459,U_1458,U_1460)
    | ~ class_Rings_Olinordered__semidom(U_1458) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

cnf(f_335_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1459),U_1460))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1458),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1459)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1460)))
    | ~ sP82(U_1459,U_1458,U_1460) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

cnf(f_335_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1458),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1459)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1458),U_1460)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1459),U_1460))
    | ~ sP82(U_1459,U_1458,U_1460) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__add]) ).

fof(f_336_2,plain,
    ! [U_1463,U_1462,U_1461] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1462),U_1463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),U_1462)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),U_1463))
      | ~ class_Rings_Osemiring__1(U_1461) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_1462,U_1461,U_1463] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1462),U_1463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),U_1462)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),U_1463))
      | ~ class_Rings_Osemiring__1(U_1461) ),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1462),U_1463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),U_1462)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1461),U_1463))
    | ~ class_Rings_Osemiring__1(U_1461) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(f_337_2,plain,
    ! [U_1465,U_1464] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1464)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1465)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1464),U_1465)),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1464,U_1465] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1464)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1465)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1464),U_1465)),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1464)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1465)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1464),U_1465)),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J]) ).

fof(f_338_2,plain,
    ! [U_1467,U_1466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1466)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1466),U_1467)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1466),U_1467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1466)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1467))) ) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ( ! [U_1471,U_1469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1469)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1471)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1469),U_1471)) )
    & ! [U_1470,U_1468] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1468),U_1470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1470))) ) ),
    inference(miniscope,[status(thm)],[f_338_2]) ).

fof(f_338_4,plain,
    ( ! [U_1469,U_1471] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1469)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1471)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1469),U_1471)) )
    & ! [U_1468,U_1470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1468),U_1470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1470))) ) ),
    inference(definitional_conversion,[status(esa)],[f_338_3]) ).

cnf(f_338_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1468),U_1470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1470))) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

cnf(f_338_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1469)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1469),U_1471)) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

fof(f_339_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]) ).

fof(f_339_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_339_1]) ).

cnf(f_339_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_1,plain,
    ! [V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).

fof(f_340_2,plain,
    ! [U_1473,U_1472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1472),U_1473),U_1473))
      | ~ class_Orderings_Opreorder(U_1472) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ! [U_1472,U_1473] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1472),U_1473),U_1473))
      | ~ class_Orderings_Opreorder(U_1472) ),
    inference(definitional_conversion,[status(esa)],[f_340_2]) ).

cnf(f_340_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1472),U_1473),U_1473))
    | ~ class_Orderings_Opreorder(U_1472) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( V_x_2 != V_y_2
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 = V_y_2 ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).

fof(f_341_2,plain,
    ! [U_1476,U_1475,U_1474] :
      ( ( ( U_1475 != U_1476
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1476),U_1475))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1475),U_1476)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1476),U_1475))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1475),U_1476))
          | U_1475 = U_1476 ) )
      | ~ class_Orderings_Olinorder(U_1474) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ( ! [U_1474,U_1475,U_1476] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1476),U_1475))
        | ~ sP83(U_1474,U_1475,U_1476) )
    & ! [U_1474,U_1475,U_1476] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1475),U_1476))
        | ~ sP83(U_1474,U_1475,U_1476) )
    & ! [U_1474,U_1475,U_1476] :
        ( U_1475 != U_1476
        | sP83(U_1474,U_1475,U_1476)
        | ~ sP84(U_1474,U_1475,U_1476) )
    & ! [U_1474,U_1475,U_1476] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1476),U_1475))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1475),U_1476))
        | U_1475 = U_1476
        | ~ sP84(U_1474,U_1475,U_1476) )
    & ! [U_1474,U_1475,U_1476] :
        ( sP84(U_1474,U_1475,U_1476)
        | ~ class_Orderings_Olinorder(U_1474) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83,sP84])],[f_341_2]) ).

cnf(f_341_4,plain,
    ( sP84(U_1474,U_1475,U_1476)
    | ~ class_Orderings_Olinorder(U_1474) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

cnf(f_341_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1476),U_1475))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1475),U_1476))
    | U_1475 = U_1476
    | ~ sP84(U_1474,U_1475,U_1476) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

cnf(f_341_6,plain,
    ( U_1475 != U_1476
    | sP83(U_1474,U_1475,U_1476)
    | ~ sP84(U_1474,U_1475,U_1476) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

cnf(f_341_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1475),U_1476))
    | ~ sP83(U_1474,U_1475,U_1476) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

cnf(f_341_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1474),U_1476),U_1475))
    | ~ sP83(U_1474,U_1475,U_1476) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ( V_x_2 != V_y_2
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(f_342_2,plain,
    ! [U_1479,U_1478,U_1477] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1478),U_1479))
          | ( U_1478 != U_1479
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1479),U_1478)) ) )
        & ( U_1478 = U_1479
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1479),U_1478))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1478),U_1479)) ) )
      | ~ class_Orderings_Olinorder(U_1477) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ( ! [U_1478,U_1479,U_1477] :
        ( U_1478 != U_1479
        | ~ sP85(U_1478,U_1479,U_1477) )
    & ! [U_1478,U_1479,U_1477] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1479),U_1478))
        | ~ sP85(U_1478,U_1479,U_1477) )
    & ! [U_1478,U_1479,U_1477] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1478),U_1479))
        | sP85(U_1478,U_1479,U_1477)
        | ~ sP86(U_1478,U_1479,U_1477) )
    & ! [U_1478,U_1479,U_1477] :
        ( U_1478 = U_1479
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1479),U_1478))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1478),U_1479))
        | ~ sP86(U_1478,U_1479,U_1477) )
    & ! [U_1478,U_1479,U_1477] :
        ( sP86(U_1478,U_1479,U_1477)
        | ~ class_Orderings_Olinorder(U_1477) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85,sP86])],[f_342_2]) ).

cnf(f_342_4,plain,
    ( sP86(U_1478,U_1479,U_1477)
    | ~ class_Orderings_Olinorder(U_1477) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

cnf(f_342_5,plain,
    ( U_1478 = U_1479
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1479),U_1478))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1478),U_1479))
    | ~ sP86(U_1478,U_1479,U_1477) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

cnf(f_342_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1478),U_1479))
    | sP85(U_1478,U_1479,U_1477)
    | ~ sP86(U_1478,U_1479,U_1477) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

cnf(f_342_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1477),U_1479),U_1478))
    | ~ sP85(U_1478,U_1479,U_1477) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

cnf(f_342_8,plain,
    ( U_1478 != U_1479
    | ~ sP85(U_1478,U_1479,U_1477) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).

fof(f_343_2,plain,
    ! [U_1482,U_1481,U_1480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1480),U_1482),U_1481))
      | U_1481 = U_1482
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1480),U_1481),U_1482))
      | ~ class_Orderings_Olinorder(U_1480) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_1482,U_1480,U_1481] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1480),U_1482),U_1481))
      | U_1481 = U_1482
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1480),U_1481),U_1482))
      | ~ class_Orderings_Olinorder(U_1480) ),
    inference(definitional_conversion,[status(esa)],[f_343_2]) ).

cnf(f_343_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1480),U_1482),U_1481))
    | U_1481 = U_1482
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1480),U_1481),U_1482))
    | ~ class_Orderings_Olinorder(U_1480) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_1,plain,
    ! [V_x_2,V_y_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(f_344_2,plain,
    ! [U_1485,U_1484,U_1483] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1485),U_1484))
          | U_1485 != U_1484 )
        & ( U_1485 = U_1484
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1485),U_1484)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1484),U_1485))
      | ~ class_Orderings_Olinorder(U_1483) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ( ! [U_1483,U_1484,U_1485] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1485),U_1484))
        | U_1485 != U_1484
        | ~ sP87(U_1483,U_1484,U_1485) )
    & ! [U_1483,U_1484,U_1485] :
        ( U_1485 = U_1484
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1485),U_1484))
        | ~ sP87(U_1483,U_1484,U_1485) )
    & ! [U_1483,U_1484,U_1485] :
        ( sP87(U_1483,U_1484,U_1485)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1484),U_1485))
        | ~ class_Orderings_Olinorder(U_1483) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_344_2]) ).

cnf(f_344_4,plain,
    ( sP87(U_1483,U_1484,U_1485)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1484),U_1485))
    | ~ class_Orderings_Olinorder(U_1483) ),
    inference(clausify,[status(thm)],[f_344_3]) ).

cnf(f_344_5,plain,
    ( U_1485 = U_1484
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1485),U_1484))
    | ~ sP87(U_1483,U_1484,U_1485) ),
    inference(clausify,[status(thm)],[f_344_3]) ).

cnf(f_344_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1483),U_1485),U_1484))
    | U_1485 != U_1484
    | ~ sP87(U_1483,U_1484,U_1485) ),
    inference(clausify,[status(thm)],[f_344_3]) ).

fof(f_345_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | V_x = V_y
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).

fof(f_345_2,plain,
    ! [U_1488,U_1487,U_1486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1486),U_1488),U_1487))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1486),U_1487),U_1488))
      | U_1487 = U_1488
      | ~ class_Orderings_Olinorder(U_1486) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_1487,U_1488,U_1486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1486),U_1488),U_1487))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1486),U_1487),U_1488))
      | U_1487 = U_1488
      | ~ class_Orderings_Olinorder(U_1486) ),
    inference(definitional_conversion,[status(esa)],[f_345_2]) ).

cnf(f_345_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1486),U_1488),U_1487))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1486),U_1487),U_1488))
    | U_1487 = U_1488
    | ~ class_Orderings_Olinorder(U_1486) ),
    inference(clausify,[status(thm)],[f_345_3]) ).

fof(f_346_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x != V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).

fof(f_346_2,plain,
    ! [U_1491,U_1490,U_1489] :
      ( U_1490 != U_1491
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1489),U_1490),U_1491))
      | ~ class_Orderings_Oorder(U_1489) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_1491,U_1490,U_1489] :
      ( U_1490 != U_1491
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1489),U_1490),U_1491))
      | ~ class_Orderings_Oorder(U_1489) ),
    inference(definitional_conversion,[status(esa)],[f_346_2]) ).

cnf(f_346_4,plain,
    ( U_1490 != U_1491
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1489),U_1490),U_1491))
    | ~ class_Orderings_Oorder(U_1489) ),
    inference(clausify,[status(thm)],[f_346_3]) ).

fof(f_347_1,plain,
    ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_int__less__0__conv]) ).

fof(f_347_2,plain,
    ! [U_1492] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1492)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1492] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1492)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1492)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__int__eq]) ).

fof(f_348_2,plain,
    ! [U_1494,U_1493] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1493) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1494)
        | U_1493 != U_1494 )
      & ( U_1493 = U_1494
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1493) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1494) ) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ( ! [U_1498,U_1496] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1496) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1498)
        | U_1496 != U_1498 )
    & ! [U_1497,U_1495] :
        ( U_1495 = U_1497
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1495) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1497) ) ),
    inference(miniscope,[status(thm)],[f_348_2]) ).

fof(f_348_4,plain,
    ( ! [U_1496,U_1498] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1496) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1498)
        | U_1496 != U_1498 )
    & ! [U_1497,U_1495] :
        ( U_1495 = U_1497
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1495) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1497) ) ),
    inference(definitional_conversion,[status(esa)],[f_348_3]) ).

cnf(f_348_5,plain,
    ( U_1495 = U_1497
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1495) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1497) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1496) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1498)
    | U_1496 != U_1498 ),
    inference(clausify,[status(thm)],[f_348_4]) ).

fof(f_349_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J]) ).

fof(f_349_2,plain,
    ! [U_1500,U_1499] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1499) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1500)
        | U_1499 != U_1500 )
      & ( U_1499 = U_1500
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1499) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1500) ) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ( ! [U_1504,U_1502] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1502) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1504)
        | U_1502 != U_1504 )
    & ! [U_1503,U_1501] :
        ( U_1501 = U_1503
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1501) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1503) ) ),
    inference(miniscope,[status(thm)],[f_349_2]) ).

fof(f_349_4,plain,
    ( ! [U_1502,U_1504] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1502) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1504)
        | U_1502 != U_1504 )
    & ! [U_1503,U_1501] :
        ( U_1501 = U_1503
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1501) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1503) ) ),
    inference(definitional_conversion,[status(esa)],[f_349_3]) ).

cnf(f_349_5,plain,
    ( U_1501 = U_1503
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1501) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1503) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1502) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1504)
    | U_1502 != U_1504 ),
    inference(clausify,[status(thm)],[f_349_4]) ).

fof(f_350_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).

fof(f_350_2,plain,
    ! [U_1505] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1505) = U_1505,
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_1505] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1505) = U_1505,
    inference(definitional_conversion,[status(esa)],[f_350_2]) ).

cnf(f_350_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1505) = U_1505,
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).

fof(f_351_2,plain,
    ! [U_1506] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1506),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1506,
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1506] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1506),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1506,
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1506),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1506,
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).

fof(f_352_2,plain,
    ! [U_1509,U_1508,U_1507] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1507),U_1509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1508),U_1509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1507),U_1508)) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ! [U_1507,U_1508,U_1509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1507),U_1509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1508),U_1509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1507),U_1508)) ),
    inference(definitional_conversion,[status(esa)],[f_352_2]) ).

cnf(f_352_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1507),U_1509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1508),U_1509)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1507),U_1508)) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_1,plain,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
    inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).

fof(f_353_2,plain,
    ! [U_1512,U_1511,U_1510] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),U_1511)),U_1512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1511),U_1512)),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_1510,U_1511,U_1512] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),U_1511)),U_1512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1511),U_1512)),
    inference(definitional_conversion,[status(esa)],[f_353_2]) ).

cnf(f_353_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),U_1511)),U_1512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1511),U_1512)),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).

fof(f_354_2,plain,
    ! [U_1515,U_1514,U_1513] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1514),U_1515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1513),U_1515)),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_1513,U_1514,U_1515] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1514),U_1515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1513),U_1515)),
    inference(definitional_conversion,[status(esa)],[f_354_2]) ).

cnf(f_354_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1514),U_1515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1513),U_1515)),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).

fof(f_355_2,plain,
    ! [U_1517,U_1516] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1517),U_1516))
      | U_1516 = U_1517
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1516),U_1517)) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_1516,U_1517] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1517),U_1516))
      | U_1516 = U_1517
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1516),U_1517)) ),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1517),U_1516))
    | U_1516 = U_1517
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1516),U_1517)) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
    inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).

fof(f_356_2,plain,
    ! [U_1519,U_1518] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1518),U_1519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1519),U_1518),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1518,U_1519] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1518),U_1519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1519),U_1518),
    inference(definitional_conversion,[status(esa)],[f_356_2]) ).

cnf(f_356_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1518),U_1519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1519),U_1518),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).

fof(f_357_2,plain,
    ! [U_1522,U_1521,U_1520] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1520),U_1522),U_1521))
      | U_1521 = U_1522
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1520),U_1521),U_1522))
      | ~ class_Orderings_Olinorder(U_1520) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1520,U_1521,U_1522] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1520),U_1522),U_1521))
      | U_1521 = U_1522
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1520),U_1521),U_1522))
      | ~ class_Orderings_Olinorder(U_1520) ),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1520),U_1522),U_1521))
    | U_1521 = U_1522
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1520),U_1521),U_1522))
    | ~ class_Orderings_Olinorder(U_1520) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).

fof(f_358_2,plain,
    ! [U_1525,U_1524,U_1523] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1523),U_1525),U_1524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1523),U_1524),U_1525))
      | ~ class_Orderings_Opreorder(U_1523) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_1523,U_1524,U_1525] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1523),U_1525),U_1524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1523),U_1524),U_1525))
      | ~ class_Orderings_Opreorder(U_1523) ),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1523),U_1525),U_1524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1523),U_1524),U_1525))
    | ~ class_Orderings_Opreorder(U_1523) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).

fof(f_359_2,plain,
    ! [U_1529,U_1528,U_1527,U_1526] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1529),U_1528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1529),U_1527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1527),U_1528))
      | ~ class_Orderings_Oorder(U_1526) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ! [U_1526,U_1527,U_1528,U_1529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1529),U_1528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1529),U_1527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1527),U_1528))
      | ~ class_Orderings_Oorder(U_1526) ),
    inference(definitional_conversion,[status(esa)],[f_359_2]) ).

cnf(f_359_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1529),U_1528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1529),U_1527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1526),U_1527),U_1528))
    | ~ class_Orderings_Oorder(U_1526) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).

fof(f_360_2,plain,
    ! [U_1533,U_1532,U_1531,U_1530] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1532),U_1533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1532))
      | ~ class_Orderings_Opreorder(U_1530) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_1531,U_1530,U_1532,U_1533] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1532),U_1533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1532))
      | ~ class_Orderings_Opreorder(U_1530) ),
    inference(definitional_conversion,[status(esa)],[f_360_2]) ).

cnf(f_360_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1532),U_1533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1532))
    | ~ class_Orderings_Opreorder(U_1530) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).

fof(f_361_2,plain,
    ! [U_1537,U_1536,U_1535,U_1534] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1537),U_1536))
      | U_1535 != U_1537
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1535),U_1536))
      | ~ class_Orderings_Oorder(U_1534) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_1535,U_1536,U_1534,U_1537] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1537),U_1536))
      | U_1535 != U_1537
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1535),U_1536))
      | ~ class_Orderings_Oorder(U_1534) ),
    inference(definitional_conversion,[status(esa)],[f_361_2]) ).

cnf(f_361_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1537),U_1536))
    | U_1535 != U_1537
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1535),U_1536))
    | ~ class_Orderings_Oorder(U_1534) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).

fof(f_362_2,plain,
    ! [U_1541,U_1540,U_1539,U_1538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1541))
      | U_1540 != U_1541
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1540))
      | ~ class_Orderings_Oord(U_1538) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_1541,U_1539,U_1540,U_1538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1541))
      | U_1540 != U_1541
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1540))
      | ~ class_Orderings_Oord(U_1538) ),
    inference(definitional_conversion,[status(esa)],[f_362_2]) ).

cnf(f_362_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1541))
    | U_1540 != U_1541
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1540))
    | ~ class_Orderings_Oord(U_1538) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

fof(f_363_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
      | V_a != V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).

fof(f_363_2,plain,
    ! [U_1545,U_1544,U_1543,U_1542] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1545),U_1543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1545),U_1544))
      | U_1543 != U_1544
      | ~ class_Orderings_Oorder(U_1542) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_1545,U_1544,U_1543,U_1542] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1545),U_1543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1545),U_1544))
      | U_1543 != U_1544
      | ~ class_Orderings_Oorder(U_1542) ),
    inference(definitional_conversion,[status(esa)],[f_363_2]) ).

cnf(f_363_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1545),U_1543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1545),U_1544))
    | U_1543 != U_1544
    | ~ class_Orderings_Oorder(U_1542) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
      | V_a != V_b
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).

fof(f_364_2,plain,
    ! [U_1549,U_1548,U_1547,U_1546] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1547),U_1549))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1548),U_1549))
      | U_1547 != U_1548
      | ~ class_Orderings_Oord(U_1546) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ! [U_1548,U_1546,U_1547,U_1549] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1547),U_1549))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1548),U_1549))
      | U_1547 != U_1548
      | ~ class_Orderings_Oord(U_1546) ),
    inference(definitional_conversion,[status(esa)],[f_364_2]) ).

cnf(f_364_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1547),U_1549))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1548),U_1549))
    | U_1547 != U_1548
    | ~ class_Orderings_Oord(U_1546) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_1,plain,
    ! [V_a,V_b,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).

fof(f_365_2,plain,
    ! [U_1552,U_1551,U_1550] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1550),U_1552),U_1551))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1550),U_1551),U_1552))
      | ~ class_Orderings_Oorder(U_1550) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_1552,U_1551,U_1550] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1550),U_1552),U_1551))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1550),U_1551),U_1552))
      | ~ class_Orderings_Oorder(U_1550) ),
    inference(definitional_conversion,[status(esa)],[f_365_2]) ).

cnf(f_365_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1550),U_1552),U_1551))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1550),U_1551),U_1552))
    | ~ class_Orderings_Oorder(U_1550) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [V_b,V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).

fof(f_366_2,plain,
    ! [U_1555,U_1554,U_1553] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1553),U_1555),U_1554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1553),U_1554),U_1555))
      | ~ class_Orderings_Opreorder(U_1553) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1553,U_1554,U_1555] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1553),U_1555),U_1554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1553),U_1554),U_1555))
      | ~ class_Orderings_Opreorder(U_1553) ),
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1553),U_1555),U_1554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1553),U_1554),U_1555))
    | ~ class_Orderings_Opreorder(U_1553) ),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_y != V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).

fof(f_367_2,plain,
    ! [U_1558,U_1557,U_1556] :
      ( U_1558 != U_1557
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1556),U_1557),U_1558))
      | ~ class_Orderings_Oorder(U_1556) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_1556,U_1557,U_1558] :
      ( U_1558 != U_1557
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1556),U_1557),U_1558))
      | ~ class_Orderings_Oorder(U_1556) ),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_4,plain,
    ( U_1558 != U_1557
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1556),U_1557),U_1558))
    | ~ class_Orderings_Oorder(U_1556) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x != V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).

fof(f_368_2,plain,
    ! [U_1561,U_1560,U_1559] :
      ( U_1560 != U_1561
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1559),U_1560),U_1561))
      | ~ class_Orderings_Oorder(U_1559) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_1559,U_1560,U_1561] :
      ( U_1560 != U_1561
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1559),U_1560),U_1561))
      | ~ class_Orderings_Oorder(U_1559) ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( U_1560 != U_1561
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1559),U_1560),U_1561))
    | ~ class_Orderings_Oorder(U_1559) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(f_369_2,plain,
    ! [U_1564,U_1563,U_1562] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1564),U_1563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1563),U_1564))
      | ~ class_Orderings_Opreorder(U_1562) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_1562,U_1563,U_1564] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1564),U_1563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1563),U_1564))
      | ~ class_Orderings_Opreorder(U_1562) ),
    inference(definitional_conversion,[status(esa)],[f_369_2]) ).

cnf(f_369_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1564),U_1563))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1563),U_1564))
    | ~ class_Orderings_Opreorder(U_1562) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).

fof(f_370_2,plain,
    ! [U_1567,U_1566,U_1565] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1565),U_1567),U_1566))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1565),U_1566),U_1567))
      | ~ class_Orderings_Opreorder(U_1565) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_1565,U_1566,U_1567] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1565),U_1567),U_1566))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1565),U_1566),U_1567))
      | ~ class_Orderings_Opreorder(U_1565) ),
    inference(definitional_conversion,[status(esa)],[f_370_2]) ).

cnf(f_370_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1565),U_1567),U_1566))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1565),U_1566),U_1567))
    | ~ class_Orderings_Opreorder(U_1565) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_1,plain,
    ! [V_k] :
      ( ? [B_n] :
          ( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int]) ).

fof(f_371_2,plain,
    ! [U_1569] :
      ( ? [U_1568] :
          ( U_1569 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1568)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1568)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1569)) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_1569] :
      ( ( U_1569 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK37(U_1569))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK37(U_1569))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1569)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1568,sK37(U_1569))],[f_371_2]) ).

fof(f_371_4,plain,
    ( ! [U_1569] :
        ( U_1569 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK37(U_1569))
        | ~ sP88(U_1569) )
    & ! [U_1569] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK37(U_1569)))
        | ~ sP88(U_1569) )
    & ! [U_1569] :
        ( sP88(U_1569)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1569)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_371_3]) ).

cnf(f_371_5,plain,
    ( sP88(U_1569)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1569)) ),
    inference(clausify,[status(thm)],[f_371_4]) ).

cnf(f_371_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK37(U_1569)))
    | ~ sP88(U_1569) ),
    inference(clausify,[status(thm)],[f_371_4]) ).

cnf(f_371_7,plain,
    ( U_1569 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK37(U_1569))
    | ~ sP88(U_1569) ),
    inference(clausify,[status(thm)],[f_371_4]) ).

fof(f_372_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff]) ).

fof(f_372_2,plain,
    ! [U_1571,U_1570] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1570),c_Groups_Ozero__class_Ozero(U_1570)),hAPP(c_Int_Oring__1__class_Oof__int(U_1570),U_1571)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1571)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1571))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1570),c_Groups_Ozero__class_Ozero(U_1570)),hAPP(c_Int_Oring__1__class_Oof__int(U_1570),U_1571))) ) )
      | ~ class_Rings_Olinordered__idom(U_1570) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ( ! [U_1571,U_1570] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1570),c_Groups_Ozero__class_Ozero(U_1570)),hAPP(c_Int_Oring__1__class_Oof__int(U_1570),U_1571)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1571))
        | ~ sP89(U_1571,U_1570) )
    & ! [U_1571,U_1570] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1571))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1570),c_Groups_Ozero__class_Ozero(U_1570)),hAPP(c_Int_Oring__1__class_Oof__int(U_1570),U_1571)))
        | ~ sP89(U_1571,U_1570) )
    & ! [U_1571,U_1570] :
        ( sP89(U_1571,U_1570)
        | ~ class_Rings_Olinordered__idom(U_1570) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_372_2]) ).

cnf(f_372_4,plain,
    ( sP89(U_1571,U_1570)
    | ~ class_Rings_Olinordered__idom(U_1570) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1571))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1570),c_Groups_Ozero__class_Ozero(U_1570)),hAPP(c_Int_Oring__1__class_Oof__int(U_1570),U_1571)))
    | ~ sP89(U_1571,U_1570) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1570),c_Groups_Ozero__class_Ozero(U_1570)),hAPP(c_Int_Oring__1__class_Oof__int(U_1570),U_1571)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1571))
    | ~ sP89(U_1571,U_1570) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff]) ).

fof(f_373_2,plain,
    ! [U_1573,U_1572] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1572),hAPP(c_Int_Oring__1__class_Oof__int(U_1572),U_1573)),c_Groups_Ozero__class_Ozero(U_1572)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1573),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1573),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1572),hAPP(c_Int_Oring__1__class_Oof__int(U_1572),U_1573)),c_Groups_Ozero__class_Ozero(U_1572))) ) )
      | ~ class_Rings_Olinordered__idom(U_1572) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ( ! [U_1573,U_1572] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1572),hAPP(c_Int_Oring__1__class_Oof__int(U_1572),U_1573)),c_Groups_Ozero__class_Ozero(U_1572)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1573),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP90(U_1573,U_1572) )
    & ! [U_1573,U_1572] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1573),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1572),hAPP(c_Int_Oring__1__class_Oof__int(U_1572),U_1573)),c_Groups_Ozero__class_Ozero(U_1572)))
        | ~ sP90(U_1573,U_1572) )
    & ! [U_1573,U_1572] :
        ( sP90(U_1573,U_1572)
        | ~ class_Rings_Olinordered__idom(U_1572) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_373_2]) ).

cnf(f_373_4,plain,
    ( sP90(U_1573,U_1572)
    | ~ class_Rings_Olinordered__idom(U_1572) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1573),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1572),hAPP(c_Int_Oring__1__class_Oof__int(U_1572),U_1573)),c_Groups_Ozero__class_Ozero(U_1572)))
    | ~ sP90(U_1573,U_1572) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1572),hAPP(c_Int_Oring__1__class_Oof__int(U_1572),U_1573)),c_Groups_Ozero__class_Ozero(U_1572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1573),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP90(U_1573,U_1572) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma]) ).

fof(f_374_2,plain,
    ! [U_1576,U_1575,U_1574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1576)),U_1574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1576)),U_1575)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1576))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1574),U_1575)) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ! [U_1575,U_1574,U_1576] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1576)),U_1574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1576)),U_1575)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1576))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1574),U_1575)) ),
    inference(definitional_conversion,[status(esa)],[f_374_2]) ).

cnf(f_374_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1576)),U_1574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1576)),U_1575)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1576))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1574),U_1575)) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_negative__zless__0]) ).

fof(f_375_2,plain,
    ! [U_1577] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1577)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_1577] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1577)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_375_2]) ).

cnf(f_375_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1577)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_1,plain,
    ! [V_i_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,B_n))
            & V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [B_n] :
              ( hBOOL(hAPP(V_P_2,B_n))
              | V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__nat]) ).

fof(f_376_2,plain,
    ! [U_1581,U_1580] :
      ( ( hBOOL(hAPP(U_1580,hAPP(c_Int_Onat,U_1581)))
        | ( ~ hBOOL(hAPP(U_1580,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1581),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_1579] :
            ( ~ hBOOL(hAPP(U_1580,U_1579))
            & U_1581 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1579) ) )
      & ( ( ( hBOOL(hAPP(U_1580,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1581),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1578] :
              ( hBOOL(hAPP(U_1580,U_1578))
              | U_1581 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1578) ) )
        | ~ hBOOL(hAPP(U_1580,hAPP(c_Int_Onat,U_1581))) ) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ( ! [U_1585,U_1583] :
        ( hBOOL(hAPP(U_1583,hAPP(c_Int_Onat,U_1585)))
        | ( ~ hBOOL(hAPP(U_1583,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1585),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_1579] :
            ( ~ hBOOL(hAPP(U_1583,U_1579))
            & U_1585 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1579) ) )
    & ! [U_1584,U_1582] :
        ( ( ( hBOOL(hAPP(U_1582,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1578] :
              ( hBOOL(hAPP(U_1582,U_1578))
              | U_1584 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1578) ) )
        | ~ hBOOL(hAPP(U_1582,hAPP(c_Int_Onat,U_1584))) ) ),
    inference(miniscope,[status(thm)],[f_376_2]) ).

fof(f_376_4,plain,
    ( ! [U_1585,U_1583] :
        ( hBOOL(hAPP(U_1583,hAPP(c_Int_Onat,U_1585)))
        | ( ~ hBOOL(hAPP(U_1583,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1585),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_1583,sK38(U_1585,U_1583)))
          & U_1585 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK38(U_1585,U_1583)) ) )
    & ! [U_1584,U_1582] :
        ( ( ( hBOOL(hAPP(U_1582,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1578] :
              ( hBOOL(hAPP(U_1582,U_1578))
              | U_1584 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1578) ) )
        | ~ hBOOL(hAPP(U_1582,hAPP(c_Int_Onat,U_1584))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1579,sK38(U_1585,U_1583))],[f_376_3]) ).

fof(f_376_5,plain,
    ( ! [U_1583,U_1585] :
        ( ~ hBOOL(hAPP(U_1583,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP93(U_1583,U_1585) )
    & ! [U_1583,U_1585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1585),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP93(U_1583,U_1585) )
    & ! [U_1583,U_1585] :
        ( ~ hBOOL(hAPP(U_1583,sK38(U_1585,U_1583)))
        | ~ sP92(U_1583,U_1585) )
    & ! [U_1583,U_1585] :
        ( U_1585 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK38(U_1585,U_1583))
        | ~ sP92(U_1583,U_1585) )
    & ! [U_1578,U_1582,U_1584] :
        ( hBOOL(hAPP(U_1582,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1584),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP91(U_1578,U_1582,U_1584) )
    & ! [U_1578,U_1582,U_1584] :
        ( hBOOL(hAPP(U_1582,U_1578))
        | U_1584 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1578)
        | ~ sP91(U_1578,U_1582,U_1584) )
    & ! [U_1583,U_1585] :
        ( hBOOL(hAPP(U_1583,hAPP(c_Int_Onat,U_1585)))
        | sP93(U_1583,U_1585)
        | sP92(U_1583,U_1585) )
    & ! [U_1578,U_1582,U_1584] :
        ( sP91(U_1578,U_1582,U_1584)
        | ~ hBOOL(hAPP(U_1582,hAPP(c_Int_Onat,U_1584))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91,sP92,sP93])],[f_376_4]) ).

cnf(f_376_6,plain,
    ( sP91(U_1578,U_1582,U_1584)
    | ~ hBOOL(hAPP(U_1582,hAPP(c_Int_Onat,U_1584))) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_7,plain,
    ( hBOOL(hAPP(U_1583,hAPP(c_Int_Onat,U_1585)))
    | sP93(U_1583,U_1585)
    | sP92(U_1583,U_1585) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_8,plain,
    ( hBOOL(hAPP(U_1582,U_1578))
    | U_1584 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1578)
    | ~ sP91(U_1578,U_1582,U_1584) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_9,plain,
    ( hBOOL(hAPP(U_1582,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1584),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP91(U_1578,U_1582,U_1584) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_10,plain,
    ( U_1585 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK38(U_1585,U_1583))
    | ~ sP92(U_1583,U_1585) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_11,plain,
    ( ~ hBOOL(hAPP(U_1583,sK38(U_1585,U_1583)))
    | ~ sP92(U_1583,U_1585) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1585),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP93(U_1583,U_1585) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

cnf(f_376_13,plain,
    ( ~ hBOOL(hAPP(U_1583,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP93(U_1583,U_1585) ),
    inference(clausify,[status(thm)],[f_376_5]) ).

fof(f_377_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq]) ).

fof(f_377_2,plain,
    ! [U_1586] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1586)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1586)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1586))) ) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ( ! [U_1588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1588)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1588)) )
    & ! [U_1587] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1587))) ) ),
    inference(miniscope,[status(thm)],[f_377_2]) ).

fof(f_377_4,plain,
    ( ! [U_1588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1588)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1588)) )
    & ! [U_1587] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1587))) ) ),
    inference(definitional_conversion,[status(esa)],[f_377_3]) ).

cnf(f_377_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1587))) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

cnf(f_377_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1588)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1588)) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

fof(f_378_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    inference(fof_nnf,[status(thm)],[fact_negative__zless]) ).

fof(f_378_2,plain,
    ! [U_1590,U_1589] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1589)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1590))),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_1590,U_1589] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1589)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1590))),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1589)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1590))),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_1,plain,
    ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
    inference(fof_nnf,[status(thm)],[fact_int__Suc]) ).

fof(f_379_2,plain,
    ! [U_1591] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1591)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1591)),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_1591] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1591)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1591)),
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1591)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1591)),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).

fof(f_380_2,plain,
    ! [U_1592] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1592)),U_1592)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1592),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1592),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1592)),U_1592)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ( ! [U_1594] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1594)),U_1594)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1594),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_1593] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1593),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1593)),U_1593)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_380_2]) ).

fof(f_380_4,plain,
    ( ! [U_1594] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1594)),U_1594)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1594),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_1593] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1593),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1593)),U_1593)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_380_3]) ).

cnf(f_380_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1593),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1593)),U_1593)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

cnf(f_380_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1594)),U_1594)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1594),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

fof(f_381_1,plain,
    ! [V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).

fof(f_381_2,plain,
    ! [U_1597,U_1596,U_1595] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1595),U_1596),U_1597)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),U_1597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),U_1596))
      | ~ class_Rings_Olinordered__semidom(U_1595) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1596,U_1595,U_1597] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1595),U_1596),U_1597)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),U_1597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),U_1596))
      | ~ class_Rings_Olinordered__semidom(U_1595) ),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1595),U_1596),U_1597)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),U_1597))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1595),c_Groups_Oone__class_Oone(U_1595)),U_1596))
    | ~ class_Rings_Olinordered__semidom(U_1595) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_1,plain,
    ! [V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).

fof(f_382_2,plain,
    ! [U_1600,U_1599,U_1598] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1598),U_1599),U_1600)),U_1600) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),U_1599),c_Groups_Oone__class_Oone(U_1598))),U_1600)
      | ~ class_Rings_Ocomm__semiring__1(U_1598) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1598,U_1599,U_1600] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1598),U_1599),U_1600)),U_1600) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),U_1599),c_Groups_Oone__class_Oone(U_1598))),U_1600)
      | ~ class_Rings_Ocomm__semiring__1(U_1598) ),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1598),U_1599),U_1600)),U_1600) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),U_1599),c_Groups_Oone__class_Oone(U_1598))),U_1600)
    | ~ class_Rings_Ocomm__semiring__1(U_1598) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_1,plain,
    ! [V_a,V_m,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).

fof(f_383_2,plain,
    ! [U_1603,U_1602,U_1601] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1601),U_1603),U_1602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),U_1603),c_Groups_Oone__class_Oone(U_1601))),U_1602)
      | ~ class_Rings_Ocomm__semiring__1(U_1601) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1601,U_1602,U_1603] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1601),U_1603),U_1602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),U_1603),c_Groups_Oone__class_Oone(U_1601))),U_1602)
      | ~ class_Rings_Ocomm__semiring__1(U_1601) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1601),U_1603),U_1602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),U_1603),c_Groups_Oone__class_Oone(U_1601))),U_1602)
    | ~ class_Rings_Ocomm__semiring__1(U_1601) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_1,plain,
    ! [V_m,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).

fof(f_384_2,plain,
    ! [U_1605,U_1604] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1605) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),c_Groups_Oone__class_Oone(U_1604)),c_Groups_Oone__class_Oone(U_1604))),U_1605)
      | ~ class_Rings_Ocomm__semiring__1(U_1604) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1604,U_1605] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1605) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),c_Groups_Oone__class_Oone(U_1604)),c_Groups_Oone__class_Oone(U_1604))),U_1605)
      | ~ class_Rings_Ocomm__semiring__1(U_1604) ),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1605) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),c_Groups_Oone__class_Oone(U_1604)),c_Groups_Oone__class_Oone(U_1604))),U_1605)
    | ~ class_Rings_Ocomm__semiring__1(U_1604) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
          | ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
            & V_a_2 != V_b_2 ) )
        & ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) ) )
      | ~ class_Rings_Oidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).

fof(f_385_2,plain,
    ! [U_1608,U_1607,U_1606] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1608),U_1608)
          | ( U_1607 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1606),U_1608)
            & U_1607 != U_1608 ) )
        & ( U_1607 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1606),U_1608)
          | U_1607 = U_1608
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1608),U_1608) ) )
      | ~ class_Rings_Oidom(U_1606) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ( ! [U_1606,U_1607,U_1608] :
        ( U_1607 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1606),U_1608)
        | ~ sP94(U_1606,U_1607,U_1608) )
    & ! [U_1606,U_1607,U_1608] :
        ( U_1607 != U_1608
        | ~ sP94(U_1606,U_1607,U_1608) )
    & ! [U_1606,U_1607,U_1608] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1608),U_1608)
        | sP94(U_1606,U_1607,U_1608)
        | ~ sP95(U_1606,U_1607,U_1608) )
    & ! [U_1606,U_1607,U_1608] :
        ( U_1607 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1606),U_1608)
        | U_1607 = U_1608
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1608),U_1608)
        | ~ sP95(U_1606,U_1607,U_1608) )
    & ! [U_1606,U_1607,U_1608] :
        ( sP95(U_1606,U_1607,U_1608)
        | ~ class_Rings_Oidom(U_1606) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95])],[f_385_2]) ).

cnf(f_385_4,plain,
    ( sP95(U_1606,U_1607,U_1608)
    | ~ class_Rings_Oidom(U_1606) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

cnf(f_385_5,plain,
    ( U_1607 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1606),U_1608)
    | U_1607 = U_1608
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1608),U_1608)
    | ~ sP95(U_1606,U_1607,U_1608) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

cnf(f_385_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1608),U_1608)
    | sP94(U_1606,U_1607,U_1608)
    | ~ sP95(U_1606,U_1607,U_1608) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

cnf(f_385_7,plain,
    ( U_1607 != U_1608
    | ~ sP94(U_1606,U_1607,U_1608) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

cnf(f_385_8,plain,
    ( U_1607 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1606),U_1608)
    | ~ sP94(U_1606,U_1607,U_1608) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
    inference(fof_nnf,[status(thm)],[fact_zmult__assoc]) ).

fof(f_386_2,plain,
    ! [U_1611,U_1610,U_1609] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1609),U_1610)),U_1611) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1610),U_1611)),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1610,U_1611,U_1609] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1609),U_1610)),U_1611) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1610),U_1611)),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1609),U_1610)),U_1611) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1610),U_1611)),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
          | ( V_x_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
            & V_x_2 != c_Groups_Oone__class_Oone(T_b) ) )
        & ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_x_2 = c_Groups_Oone__class_Oone(T_b)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).

fof(f_387_2,plain,
    ! [U_1613,U_1612] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1612),U_1613),U_1613) = c_Groups_Oone__class_Oone(U_1612)
          | ( U_1613 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1612),c_Groups_Oone__class_Oone(U_1612))
            & U_1613 != c_Groups_Oone__class_Oone(U_1612) ) )
        & ( U_1613 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1612),c_Groups_Oone__class_Oone(U_1612))
          | U_1613 = c_Groups_Oone__class_Oone(U_1612)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1612),U_1613),U_1613) != c_Groups_Oone__class_Oone(U_1612) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_1612) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ( ! [U_1612,U_1613] :
        ( U_1613 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1612),c_Groups_Oone__class_Oone(U_1612))
        | ~ sP96(U_1612,U_1613) )
    & ! [U_1612,U_1613] :
        ( U_1613 != c_Groups_Oone__class_Oone(U_1612)
        | ~ sP96(U_1612,U_1613) )
    & ! [U_1612,U_1613] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1612),U_1613),U_1613) = c_Groups_Oone__class_Oone(U_1612)
        | sP96(U_1612,U_1613)
        | ~ sP97(U_1612,U_1613) )
    & ! [U_1612,U_1613] :
        ( U_1613 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1612),c_Groups_Oone__class_Oone(U_1612))
        | U_1613 = c_Groups_Oone__class_Oone(U_1612)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1612),U_1613),U_1613) != c_Groups_Oone__class_Oone(U_1612)
        | ~ sP97(U_1612,U_1613) )
    & ! [U_1612,U_1613] :
        ( sP97(U_1612,U_1613)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_1612) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97])],[f_387_2]) ).

cnf(f_387_4,plain,
    ( sP97(U_1612,U_1613)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_1612) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_5,plain,
    ( U_1613 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1612),c_Groups_Oone__class_Oone(U_1612))
    | U_1613 = c_Groups_Oone__class_Oone(U_1612)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1612),U_1613),U_1613) != c_Groups_Oone__class_Oone(U_1612)
    | ~ sP97(U_1612,U_1613) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1612),U_1613),U_1613) = c_Groups_Oone__class_Oone(U_1612)
    | sP96(U_1612,U_1613)
    | ~ sP97(U_1612,U_1613) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_7,plain,
    ( U_1613 != c_Groups_Oone__class_Oone(U_1612)
    | ~ sP96(U_1612,U_1613) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_8,plain,
    ( U_1613 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1612),c_Groups_Oone__class_Oone(U_1612))
    | ~ sP96(U_1612,U_1613) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).

fof(f_388_2,plain,
    ! [U_1616,U_1615,U_1614] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1614),hAPP(c_Groups_Ouminus__class_Ouminus(U_1614),U_1615)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1614),U_1616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1614),U_1615),U_1616)
      | ~ class_Rings_Oring(U_1614) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1615,U_1616,U_1614] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1614),hAPP(c_Groups_Ouminus__class_Ouminus(U_1614),U_1615)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1614),U_1616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1614),U_1615),U_1616)
      | ~ class_Rings_Oring(U_1614) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1614),hAPP(c_Groups_Ouminus__class_Ouminus(U_1614),U_1615)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1614),U_1616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1614),U_1615),U_1616)
    | ~ class_Rings_Oring(U_1614) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
          | V_w_2 != V_z_2 )
        & ( V_w_2 = V_z_2
          | hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff]) ).

fof(f_389_2,plain,
    ! [U_1619,U_1618,U_1617] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1618) = hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1619)
          | U_1618 != U_1619 )
        & ( U_1618 = U_1619
          | hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1618) != hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1619) ) )
      | ~ class_Int_Oring__char__0(U_1617) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ( ! [U_1617,U_1618,U_1619] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1618) = hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1619)
        | U_1618 != U_1619
        | ~ sP98(U_1617,U_1618,U_1619) )
    & ! [U_1617,U_1618,U_1619] :
        ( U_1618 = U_1619
        | hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1618) != hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1619)
        | ~ sP98(U_1617,U_1618,U_1619) )
    & ! [U_1617,U_1618,U_1619] :
        ( sP98(U_1617,U_1618,U_1619)
        | ~ class_Int_Oring__char__0(U_1617) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_389_2]) ).

cnf(f_389_4,plain,
    ( sP98(U_1617,U_1618,U_1619)
    | ~ class_Int_Oring__char__0(U_1617) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_5,plain,
    ( U_1618 = U_1619
    | hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1618) != hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1619)
    | ~ sP98(U_1617,U_1618,U_1619) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1618) = hAPP(c_Int_Oring__1__class_Oof__int(U_1617),U_1619)
    | U_1618 != U_1619
    | ~ sP98(U_1617,U_1618,U_1619) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).

fof(f_390_2,plain,
    ! [U_1622,U_1621,U_1620] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),hAPP(c_Groups_Ouminus__class_Ouminus(U_1620),U_1621)),U_1622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),hAPP(c_Groups_Ouminus__class_Ouminus(U_1620),U_1622))
      | ~ class_Rings_Oring(U_1620) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_1621,U_1622,U_1620] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),hAPP(c_Groups_Ouminus__class_Ouminus(U_1620),U_1621)),U_1622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),hAPP(c_Groups_Ouminus__class_Ouminus(U_1620),U_1622))
      | ~ class_Rings_Oring(U_1620) ),
    inference(definitional_conversion,[status(esa)],[f_390_2]) ).

cnf(f_390_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),hAPP(c_Groups_Ouminus__class_Ouminus(U_1620),U_1621)),U_1622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),hAPP(c_Groups_Ouminus__class_Ouminus(U_1620),U_1622))
    | ~ class_Rings_Oring(U_1620) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).

fof(f_391_2,plain,
    ! [U_1624,U_1623] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1623)),U_1624) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1623),U_1624)),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1623,U_1624] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1623)),U_1624) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1623),U_1624)),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1623)),U_1624) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1623),U_1624)),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
    inference(fof_nnf,[status(thm)],[fact_zmult__commute]) ).

fof(f_392_2,plain,
    ! [U_1626,U_1625] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1625),U_1626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1626),U_1625),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_1625,U_1626] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1625),U_1626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1626),U_1625),
    inference(definitional_conversion,[status(esa)],[f_392_2]) ).

cnf(f_392_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1625),U_1626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1626),U_1625),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zmult__1__right]) ).

fof(f_393_2,plain,
    ! [U_1627] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1627),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1627,
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1627] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1627),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1627,
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1627),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1627,
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zmult__1]) ).

fof(f_394_2,plain,
    ! [U_1628] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1628) = U_1628,
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1628] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1628) = U_1628,
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1628) = U_1628,
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__mult]) ).

fof(f_395_2,plain,
    ! [U_1631,U_1630,U_1629] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1630),U_1631)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1629),hAPP(c_Int_Oring__1__class_Oof__int(U_1629),U_1630)),hAPP(c_Int_Oring__1__class_Oof__int(U_1629),U_1631))
      | ~ class_Rings_Oring__1(U_1629) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1629,U_1630,U_1631] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1630),U_1631)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1629),hAPP(c_Int_Oring__1__class_Oof__int(U_1629),U_1630)),hAPP(c_Int_Oring__1__class_Oof__int(U_1629),U_1631))
      | ~ class_Rings_Oring__1(U_1629) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1630),U_1631)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1629),hAPP(c_Int_Oring__1__class_Oof__int(U_1629),U_1630)),hAPP(c_Int_Oring__1__class_Oof__int(U_1629),U_1631))
    | ~ class_Rings_Oring__1(U_1629) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).

fof(f_396_2,plain,
    ! [U_1634,U_1633,U_1632] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),hAPP(c_Groups_Ouminus__class_Ouminus(U_1632),U_1633)),U_1634)
      | ~ class_Rings_Oring(U_1632) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1632,U_1633,U_1634] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),hAPP(c_Groups_Ouminus__class_Ouminus(U_1632),U_1633)),U_1634)
      | ~ class_Rings_Oring(U_1632) ),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),hAPP(c_Groups_Ouminus__class_Ouminus(U_1632),U_1633)),U_1634)
    | ~ class_Rings_Oring(U_1632) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).

fof(f_397_2,plain,
    ! [U_1637,U_1636,U_1635] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1635),U_1636),U_1637)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1635),U_1636),hAPP(c_Groups_Ouminus__class_Ouminus(U_1635),U_1637))
      | ~ class_Rings_Oring(U_1635) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1635,U_1636,U_1637] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1635),U_1636),U_1637)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1635),U_1636),hAPP(c_Groups_Ouminus__class_Ouminus(U_1635),U_1637))
      | ~ class_Rings_Oring(U_1635) ),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1635),U_1636),U_1637)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1635),U_1636),hAPP(c_Groups_Ouminus__class_Ouminus(U_1635),U_1637))
    | ~ class_Rings_Oring(U_1635) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [V_z,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__minus]) ).

fof(f_398_2,plain,
    ! [U_1639,U_1638] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1639)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1638),hAPP(c_Int_Oring__1__class_Oof__int(U_1638),U_1639))
      | ~ class_Rings_Oring__1(U_1638) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1638,U_1639] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1639)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1638),hAPP(c_Int_Oring__1__class_Oof__int(U_1638),U_1639))
      | ~ class_Rings_Oring__1(U_1638) ),
    inference(definitional_conversion,[status(esa)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1639)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1638),hAPP(c_Int_Oring__1__class_Oof__int(U_1638),U_1639))
    | ~ class_Rings_Oring__1(U_1638) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_1,plain,
    ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).

fof(f_399_2,plain,
    ! [U_1640] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1640)) = U_1640,
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1640] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1640)) = U_1640,
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1640)) = U_1640,
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__1]) ).

fof(f_400_2,plain,
    ! [U_1641] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1641),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1641)
      | ~ class_Rings_Oring__1(U_1641) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ! [U_1641] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1641),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1641)
      | ~ class_Rings_Oring__1(U_1641) ),
    inference(definitional_conversion,[status(esa)],[f_400_2]) ).

cnf(f_400_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1641),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1641)
    | ~ class_Rings_Oring__1(U_1641) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J]) ).

fof(f_401_2,plain,
    ! [U_1645,U_1644,U_1643,U_1642] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1643),U_1644)),U_1645) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1644),U_1645))
      | ~ class_Groups_Oab__semigroup__mult(U_1642) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_1642,U_1643,U_1644,U_1645] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1643),U_1644)),U_1645) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1644),U_1645))
      | ~ class_Groups_Oab__semigroup__mult(U_1642) ),
    inference(definitional_conversion,[status(esa)],[f_401_2]) ).

cnf(f_401_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1643),U_1644)),U_1645) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1642),U_1644),U_1645))
    | ~ class_Groups_Oab__semigroup__mult(U_1642) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).

fof(f_402_2,plain,
    ! [U_1648,U_1647,U_1646] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1647) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1648)
          | U_1647 != U_1648 )
        & ( U_1647 = U_1648
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1647) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1648) ) )
      | ~ class_Groups_Ogroup__add(U_1646) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ( ! [U_1646,U_1647,U_1648] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1647) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1648)
        | U_1647 != U_1648
        | ~ sP99(U_1646,U_1647,U_1648) )
    & ! [U_1646,U_1647,U_1648] :
        ( U_1647 = U_1648
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1647) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1648)
        | ~ sP99(U_1646,U_1647,U_1648) )
    & ! [U_1646,U_1647,U_1648] :
        ( sP99(U_1646,U_1647,U_1648)
        | ~ class_Groups_Ogroup__add(U_1646) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_402_2]) ).

cnf(f_402_4,plain,
    ( sP99(U_1646,U_1647,U_1648)
    | ~ class_Groups_Ogroup__add(U_1646) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

cnf(f_402_5,plain,
    ( U_1647 = U_1648
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1647) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1648)
    | ~ sP99(U_1646,U_1647,U_1648) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

cnf(f_402_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1647) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1646),U_1648)
    | U_1647 != U_1648
    | ~ sP99(U_1646,U_1647,U_1648) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) != V_a_2 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_b_2 ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).

fof(f_403_2,plain,
    ! [U_1651,U_1650,U_1649] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1650) = U_1651
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1651) != U_1650 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1651) = U_1650
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1650) != U_1651 ) )
      | ~ class_Groups_Ogroup__add(U_1649) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ( ! [U_1651,U_1650,U_1649] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1650) = U_1651
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1651) != U_1650
        | ~ sP100(U_1651,U_1650,U_1649) )
    & ! [U_1651,U_1650,U_1649] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1651) = U_1650
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1650) != U_1651
        | ~ sP100(U_1651,U_1650,U_1649) )
    & ! [U_1651,U_1650,U_1649] :
        ( sP100(U_1651,U_1650,U_1649)
        | ~ class_Groups_Ogroup__add(U_1649) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_403_2]) ).

cnf(f_403_4,plain,
    ( sP100(U_1651,U_1650,U_1649)
    | ~ class_Groups_Ogroup__add(U_1649) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

cnf(f_403_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1651) = U_1650
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1650) != U_1651
    | ~ sP100(U_1651,U_1650,U_1649) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

cnf(f_403_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1650) = U_1651
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1649),U_1651) != U_1650
    | ~ sP100(U_1651,U_1650,U_1649) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_b_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) )
        & ( V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).

fof(f_404_2,plain,
    ! [U_1654,U_1653,U_1652] :
      ( ( ( U_1653 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1654)
          | U_1654 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1653) )
        & ( U_1654 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1653)
          | U_1653 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1654) ) )
      | ~ class_Groups_Ogroup__add(U_1652) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ( ! [U_1653,U_1654,U_1652] :
        ( U_1653 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1654)
        | U_1654 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1653)
        | ~ sP101(U_1653,U_1654,U_1652) )
    & ! [U_1653,U_1654,U_1652] :
        ( U_1654 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1653)
        | U_1653 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1654)
        | ~ sP101(U_1653,U_1654,U_1652) )
    & ! [U_1653,U_1654,U_1652] :
        ( sP101(U_1653,U_1654,U_1652)
        | ~ class_Groups_Ogroup__add(U_1652) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_404_2]) ).

cnf(f_404_4,plain,
    ( sP101(U_1653,U_1654,U_1652)
    | ~ class_Groups_Ogroup__add(U_1652) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_5,plain,
    ( U_1654 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1653)
    | U_1653 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1654)
    | ~ sP101(U_1653,U_1654,U_1652) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_6,plain,
    ( U_1653 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1654)
    | U_1654 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1652),U_1653)
    | ~ sP101(U_1653,U_1654,U_1652) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral]) ).

fof(f_405_2,plain,
    ! [U_1656,U_1655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1656),c_Groups_Oone__class_Oone(U_1655)) = U_1656
      | ~ class_Groups_Ocomm__monoid__mult(U_1655) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ! [U_1656,U_1655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1656),c_Groups_Oone__class_Oone(U_1655)) = U_1656
      | ~ class_Groups_Ocomm__monoid__mult(U_1655) ),
    inference(definitional_conversion,[status(esa)],[f_405_2]) ).

cnf(f_405_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1656),c_Groups_Oone__class_Oone(U_1655)) = U_1656
    | ~ class_Groups_Ocomm__monoid__mult(U_1655) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1__right]) ).

fof(f_406_2,plain,
    ! [U_1658,U_1657] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1657),U_1658),c_Groups_Oone__class_Oone(U_1657)) = U_1658
      | ~ class_Groups_Omonoid__mult(U_1657) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1657,U_1658] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1657),U_1658),c_Groups_Oone__class_Oone(U_1657)) = U_1658
      | ~ class_Groups_Omonoid__mult(U_1657) ),
    inference(definitional_conversion,[status(esa)],[f_406_2]) ).

cnf(f_406_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1657),U_1658),c_Groups_Oone__class_Oone(U_1657)) = U_1658
    | ~ class_Groups_Omonoid__mult(U_1657) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( c_Groups_Oone__class_Oone(T_b) = V_x_2
          | V_x_2 != c_Groups_Oone__class_Oone(T_b) )
        & ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
          | c_Groups_Oone__class_Oone(T_b) != V_x_2 ) )
      | ~ class_Groups_Oone(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).

fof(f_407_2,plain,
    ! [U_1660,U_1659] :
      ( ( ( c_Groups_Oone__class_Oone(U_1659) = U_1660
          | U_1660 != c_Groups_Oone__class_Oone(U_1659) )
        & ( U_1660 = c_Groups_Oone__class_Oone(U_1659)
          | c_Groups_Oone__class_Oone(U_1659) != U_1660 ) )
      | ~ class_Groups_Oone(U_1659) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ( ! [U_1659,U_1660] :
        ( c_Groups_Oone__class_Oone(U_1659) = U_1660
        | U_1660 != c_Groups_Oone__class_Oone(U_1659)
        | ~ sP102(U_1659,U_1660) )
    & ! [U_1659,U_1660] :
        ( U_1660 = c_Groups_Oone__class_Oone(U_1659)
        | c_Groups_Oone__class_Oone(U_1659) != U_1660
        | ~ sP102(U_1659,U_1660) )
    & ! [U_1659,U_1660] :
        ( sP102(U_1659,U_1660)
        | ~ class_Groups_Oone(U_1659) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_407_2]) ).

cnf(f_407_4,plain,
    ( sP102(U_1659,U_1660)
    | ~ class_Groups_Oone(U_1659) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

cnf(f_407_5,plain,
    ( U_1660 = c_Groups_Oone__class_Oone(U_1659)
    | c_Groups_Oone__class_Oone(U_1659) != U_1660
    | ~ sP102(U_1659,U_1660) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

cnf(f_407_6,plain,
    ( c_Groups_Oone__class_Oone(U_1659) = U_1660
    | U_1660 != c_Groups_Oone__class_Oone(U_1659)
    | ~ sP102(U_1659,U_1660) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1]) ).

fof(f_408_2,plain,
    ! [U_1662,U_1661] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1661),c_Groups_Oone__class_Oone(U_1661)),U_1662) = U_1662
      | ~ class_Groups_Ocomm__monoid__mult(U_1661) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1662,U_1661] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1661),c_Groups_Oone__class_Oone(U_1661)),U_1662) = U_1662
      | ~ class_Groups_Ocomm__monoid__mult(U_1661) ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1661),c_Groups_Oone__class_Oone(U_1661)),U_1662) = U_1662
    | ~ class_Groups_Ocomm__monoid__mult(U_1661) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1__left]) ).

fof(f_409_2,plain,
    ! [U_1664,U_1663] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),c_Groups_Oone__class_Oone(U_1663)),U_1664) = U_1664
      | ~ class_Groups_Omonoid__mult(U_1663) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1663,U_1664] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),c_Groups_Oone__class_Oone(U_1663)),U_1664) = U_1664
      | ~ class_Groups_Omonoid__mult(U_1663) ),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),c_Groups_Oone__class_Oone(U_1663)),U_1664) = U_1664
    | ~ class_Groups_Omonoid__mult(U_1663) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).

fof(f_410_2,plain,
    ! [U_1666,U_1665] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1665),hAPP(c_Groups_Ouminus__class_Ouminus(U_1665),U_1666)) = U_1666
      | ~ class_Groups_Ogroup__add(U_1665) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1665,U_1666] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1665),hAPP(c_Groups_Ouminus__class_Ouminus(U_1665),U_1666)) = U_1666
      | ~ class_Groups_Ogroup__add(U_1665) ),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1665),hAPP(c_Groups_Ouminus__class_Ouminus(U_1665),U_1666)) = U_1666
    | ~ class_Groups_Ogroup__add(U_1665) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).

fof(f_411_2,plain,
    ! [U_1671,U_1670,U_1669,U_1668,U_1667] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1668),U_1669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1670),U_1671)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1668),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1669),U_1671))
      | ~ class_Rings_Ocomm__semiring__1(U_1667) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1667,U_1668,U_1669,U_1670,U_1671] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1668),U_1669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1670),U_1671)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1668),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1669),U_1671))
      | ~ class_Rings_Ocomm__semiring__1(U_1667) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1668),U_1669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1670),U_1671)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1668),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1667),U_1669),U_1671))
    | ~ class_Rings_Ocomm__semiring__1(U_1667) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).

fof(f_412_2,plain,
    ! [U_1676,U_1675,U_1674,U_1673,U_1672] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1673),U_1674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1675),U_1676)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1673),U_1674)),U_1676))
      | ~ class_Rings_Ocomm__semiring__1(U_1672) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1672,U_1673,U_1674,U_1675,U_1676] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1673),U_1674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1675),U_1676)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1673),U_1674)),U_1676))
      | ~ class_Rings_Ocomm__semiring__1(U_1672) ),
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1673),U_1674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1675),U_1676)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1672),U_1673),U_1674)),U_1676))
    | ~ class_Rings_Ocomm__semiring__1(U_1672) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).

fof(f_413_2,plain,
    ! [U_1681,U_1680,U_1679,U_1678,U_1677] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),U_1679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1680),U_1681)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1680),U_1681)))
      | ~ class_Rings_Ocomm__semiring__1(U_1677) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1677,U_1678,U_1679,U_1680,U_1681] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),U_1679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1680),U_1681)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1680),U_1681)))
      | ~ class_Rings_Ocomm__semiring__1(U_1677) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),U_1679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1680),U_1681)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1680),U_1681)))
    | ~ class_Rings_Ocomm__semiring__1(U_1677) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).

fof(f_414_2,plain,
    ! [U_1685,U_1684,U_1683,U_1682] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),U_1683),U_1684)),U_1685) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),U_1683),U_1685)),U_1684)
      | ~ class_Rings_Ocomm__semiring__1(U_1682) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1682,U_1683,U_1684,U_1685] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),U_1683),U_1684)),U_1685) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),U_1683),U_1685)),U_1684)
      | ~ class_Rings_Ocomm__semiring__1(U_1682) ),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),U_1683),U_1684)),U_1685) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1682),U_1683),U_1685)),U_1684)
    | ~ class_Rings_Ocomm__semiring__1(U_1682) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).

fof(f_415_2,plain,
    ! [U_1689,U_1688,U_1687,U_1686] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1687),U_1688)),U_1689) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1688),U_1689))
      | ~ class_Rings_Ocomm__semiring__1(U_1686) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1686,U_1687,U_1688,U_1689] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1687),U_1688)),U_1689) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1688),U_1689))
      | ~ class_Rings_Ocomm__semiring__1(U_1686) ),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1687),U_1688)),U_1689) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1686),U_1688),U_1689))
    | ~ class_Rings_Ocomm__semiring__1(U_1686) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_1,plain,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).

fof(f_416_2,plain,
    ! [U_1693,U_1692,U_1691,U_1690] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1692),U_1693)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1691),U_1692)),U_1693)
      | ~ class_Rings_Ocomm__semiring__1(U_1690) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1690,U_1691,U_1692,U_1693] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1692),U_1693)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1691),U_1692)),U_1693)
      | ~ class_Rings_Ocomm__semiring__1(U_1690) ),
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1692),U_1693)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1690),U_1691),U_1692)),U_1693)
    | ~ class_Rings_Ocomm__semiring__1(U_1690) ),
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_1,plain,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).

fof(f_417_2,plain,
    ! [U_1697,U_1696,U_1695,U_1694] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1696),U_1697)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1695),U_1697))
      | ~ class_Rings_Ocomm__semiring__1(U_1694) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1694,U_1695,U_1696,U_1697] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1696),U_1697)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1695),U_1697))
      | ~ class_Rings_Ocomm__semiring__1(U_1694) ),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1696),U_1697)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1694),U_1695),U_1697))
    | ~ class_Rings_Ocomm__semiring__1(U_1694) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).

fof(f_418_2,plain,
    ! [U_1700,U_1699,U_1698] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1698),U_1699),U_1700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1698),U_1700),U_1699)
      | ~ class_Rings_Ocomm__semiring__1(U_1698) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1698,U_1699,U_1700] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1698),U_1699),U_1700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1698),U_1700),U_1699)
      | ~ class_Rings_Ocomm__semiring__1(U_1698) ),
    inference(definitional_conversion,[status(esa)],[f_418_2]) ).

cnf(f_418_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1698),U_1699),U_1700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1698),U_1700),U_1699)
    | ~ class_Rings_Ocomm__semiring__1(U_1698) ),
    inference(clausify,[status(thm)],[f_418_3]) ).

fof(f_419_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).

fof(f_419_2,plain,
    ! [U_1702,U_1701] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),c_Groups_Oone__class_Oone(U_1701)) = U_1702
      | ~ class_Rings_Ocomm__semiring__1(U_1701) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1701,U_1702] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),c_Groups_Oone__class_Oone(U_1701)) = U_1702
      | ~ class_Rings_Ocomm__semiring__1(U_1701) ),
    inference(definitional_conversion,[status(esa)],[f_419_2]) ).

cnf(f_419_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),c_Groups_Oone__class_Oone(U_1701)) = U_1702
    | ~ class_Rings_Ocomm__semiring__1(U_1701) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).

fof(f_420_2,plain,
    ! [U_1704,U_1703] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1703),c_Groups_Oone__class_Oone(U_1703)),U_1704) = U_1704
      | ~ class_Rings_Ocomm__semiring__1(U_1703) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1703,U_1704] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1703),c_Groups_Oone__class_Oone(U_1703)),U_1704) = U_1704
      | ~ class_Rings_Ocomm__semiring__1(U_1703) ),
    inference(definitional_conversion,[status(esa)],[f_420_2]) ).

cnf(f_420_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1703),c_Groups_Oone__class_Oone(U_1703)),U_1704) = U_1704
    | ~ class_Rings_Ocomm__semiring__1(U_1703) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x)
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).

fof(f_421_2,plain,
    ! [U_1706,U_1705] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1705),U_1706) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),hAPP(c_Groups_Ouminus__class_Ouminus(U_1705),c_Groups_Oone__class_Oone(U_1705))),U_1706)
      | ~ class_Rings_Ocomm__ring__1(U_1705) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ! [U_1705,U_1706] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1705),U_1706) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),hAPP(c_Groups_Ouminus__class_Ouminus(U_1705),c_Groups_Oone__class_Oone(U_1705))),U_1706)
      | ~ class_Rings_Ocomm__ring__1(U_1705) ),
    inference(definitional_conversion,[status(esa)],[f_421_2]) ).

cnf(f_421_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1705),U_1706) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),hAPP(c_Groups_Ouminus__class_Ouminus(U_1705),c_Groups_Oone__class_Oone(U_1705))),U_1706)
    | ~ class_Rings_Ocomm__ring__1(U_1705) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__mult]) ).

fof(f_422_2,plain,
    ! [U_1709,U_1708,U_1707] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1708),U_1709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1707),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),U_1708)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),U_1709))
      | ~ class_Rings_Osemiring__1(U_1707) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1707,U_1708,U_1709] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1708),U_1709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1707),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),U_1708)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),U_1709))
      | ~ class_Rings_Osemiring__1(U_1707) ),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1708),U_1709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1707),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),U_1708)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1707),U_1709))
    | ~ class_Rings_Osemiring__1(U_1707) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_1,plain,
    ! [T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__1]) ).

fof(f_423_2,plain,
    ! [U_1710] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1710),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1710)
      | ~ class_Rings_Osemiring__1(U_1710) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ! [U_1710] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1710),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1710)
      | ~ class_Rings_Osemiring__1(U_1710) ),
    inference(definitional_conversion,[status(esa)],[f_423_2]) ).

cnf(f_423_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1710),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1710)
    | ~ class_Rings_Osemiring__1(U_1710) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_1,plain,
    ! [V_k,T_a] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__of__nat]) ).

fof(f_424_2,plain,
    ! [U_1712,U_1711] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1711),U_1712) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(c_Int_Onat,U_1712))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_1711),U_1712) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1711),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1712))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(U_1711) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ( ! [U_1711,U_1712] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1711),U_1712) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(c_Int_Onat,U_1712))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP103(U_1711,U_1712) )
    & ! [U_1711,U_1712] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1711),U_1712) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1711),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1712))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP103(U_1711,U_1712) )
    & ! [U_1711,U_1712] :
        ( sP103(U_1711,U_1712)
        | ~ class_Rings_Oring__1(U_1711) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_424_2]) ).

cnf(f_424_4,plain,
    ( sP103(U_1711,U_1712)
    | ~ class_Rings_Oring__1(U_1711) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

cnf(f_424_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1711),U_1712) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1711),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1712))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP103(U_1711,U_1712) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

cnf(f_424_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1711),U_1712) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(c_Int_Onat,U_1712))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP103(U_1711,U_1712) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_1,plain,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__zminus__int]) ).

fof(f_425_2,plain,
    ! [U_1713] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1713))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1713] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1713))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1713))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_1,plain,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_nat__1]) ).

fof(f_426_2,plain,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_426_1]) ).

cnf(f_426_3,plain,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).

fof(f_427_2,plain,
    ! [U_1715,U_1714] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1714),U_1715) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_1715 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_1714 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_1715 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_1714 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1714),U_1715) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1714)) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ( ! [U_1715,U_1714] :
        ( U_1715 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP104(U_1715,U_1714) )
    & ! [U_1715,U_1714] :
        ( U_1714 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP104(U_1715,U_1714) )
    & ! [U_1715,U_1714] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1714),U_1715) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_1715 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_1714 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP105(U_1715,U_1714) )
    & ! [U_1715,U_1714] :
        ( sP104(U_1715,U_1714)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1714),U_1715) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP105(U_1715,U_1714) )
    & ! [U_1715,U_1714] :
        ( sP105(U_1715,U_1714)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1714)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104,sP105])],[f_427_2]) ).

cnf(f_427_4,plain,
    ( sP105(U_1715,U_1714)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1714)) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_5,plain,
    ( sP104(U_1715,U_1714)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1714),U_1715) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP105(U_1715,U_1714) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1714),U_1715) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_1715 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_1714 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP105(U_1715,U_1714) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_7,plain,
    ( U_1714 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP104(U_1715,U_1714) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_8,plain,
    ( U_1715 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP104(U_1715,U_1714) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).

fof(f_428_2,plain,
    ! [U_1716] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1716),c_Groups_Ozero__class_Ozero(U_1716)) = c_Groups_Ozero__class_Ozero(U_1716)
      | ~ class_Groups_Ogroup__add(U_1716) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ! [U_1716] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1716),c_Groups_Ozero__class_Ozero(U_1716)) = c_Groups_Ozero__class_Ozero(U_1716)
      | ~ class_Groups_Ogroup__add(U_1716) ),
    inference(definitional_conversion,[status(esa)],[f_428_2]) ).

cnf(f_428_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1716),c_Groups_Ozero__class_Ozero(U_1716)) = c_Groups_Ozero__class_Ozero(U_1716)
    | ~ class_Groups_Ogroup__add(U_1716) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

fof(f_429_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
          | c_Groups_Ozero__class_Ozero(T_b) != V_a_2 )
        & ( c_Groups_Ozero__class_Ozero(T_b) = V_a_2
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).

fof(f_429_2,plain,
    ! [U_1718,U_1717] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1717) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1717),U_1718)
          | c_Groups_Ozero__class_Ozero(U_1717) != U_1718 )
        & ( c_Groups_Ozero__class_Ozero(U_1717) = U_1718
          | c_Groups_Ozero__class_Ozero(U_1717) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1717),U_1718) ) )
      | ~ class_Groups_Ogroup__add(U_1717) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ( ! [U_1718,U_1717] :
        ( c_Groups_Ozero__class_Ozero(U_1717) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1717),U_1718)
        | c_Groups_Ozero__class_Ozero(U_1717) != U_1718
        | ~ sP106(U_1718,U_1717) )
    & ! [U_1718,U_1717] :
        ( c_Groups_Ozero__class_Ozero(U_1717) = U_1718
        | c_Groups_Ozero__class_Ozero(U_1717) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1717),U_1718)
        | ~ sP106(U_1718,U_1717) )
    & ! [U_1718,U_1717] :
        ( sP106(U_1718,U_1717)
        | ~ class_Groups_Ogroup__add(U_1717) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_429_2]) ).

cnf(f_429_4,plain,
    ( sP106(U_1718,U_1717)
    | ~ class_Groups_Ogroup__add(U_1717) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

cnf(f_429_5,plain,
    ( c_Groups_Ozero__class_Ozero(U_1717) = U_1718
    | c_Groups_Ozero__class_Ozero(U_1717) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1717),U_1718)
    | ~ sP106(U_1718,U_1717) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

cnf(f_429_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1717) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1717),U_1718)
    | c_Groups_Ozero__class_Ozero(U_1717) != U_1718
    | ~ sP106(U_1718,U_1717) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).

fof(f_430_2,plain,
    ! [U_1720,U_1719] :
      ( ( ( U_1720 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1719),U_1720)
          | U_1720 != c_Groups_Ozero__class_Ozero(U_1719) )
        & ( U_1720 = c_Groups_Ozero__class_Ozero(U_1719)
          | U_1720 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1719),U_1720) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1719) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ( ! [U_1720,U_1719] :
        ( U_1720 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1719),U_1720)
        | U_1720 != c_Groups_Ozero__class_Ozero(U_1719)
        | ~ sP107(U_1720,U_1719) )
    & ! [U_1720,U_1719] :
        ( U_1720 = c_Groups_Ozero__class_Ozero(U_1719)
        | U_1720 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1719),U_1720)
        | ~ sP107(U_1720,U_1719) )
    & ! [U_1720,U_1719] :
        ( sP107(U_1720,U_1719)
        | ~ class_Groups_Olinordered__ab__group__add(U_1719) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_430_2]) ).

cnf(f_430_4,plain,
    ( sP107(U_1720,U_1719)
    | ~ class_Groups_Olinordered__ab__group__add(U_1719) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

cnf(f_430_5,plain,
    ( U_1720 = c_Groups_Ozero__class_Ozero(U_1719)
    | U_1720 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1719),U_1720)
    | ~ sP107(U_1720,U_1719) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

cnf(f_430_6,plain,
    ( U_1720 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1719),U_1720)
    | U_1720 != c_Groups_Ozero__class_Ozero(U_1719)
    | ~ sP107(U_1720,U_1719) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).

fof(f_431_2,plain,
    ! [U_1722,U_1721] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1721),U_1722) = c_Groups_Ozero__class_Ozero(U_1721)
          | U_1722 != c_Groups_Ozero__class_Ozero(U_1721) )
        & ( U_1722 = c_Groups_Ozero__class_Ozero(U_1721)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1721),U_1722) != c_Groups_Ozero__class_Ozero(U_1721) ) )
      | ~ class_Groups_Ogroup__add(U_1721) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ( ! [U_1722,U_1721] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1721),U_1722) = c_Groups_Ozero__class_Ozero(U_1721)
        | U_1722 != c_Groups_Ozero__class_Ozero(U_1721)
        | ~ sP108(U_1722,U_1721) )
    & ! [U_1722,U_1721] :
        ( U_1722 = c_Groups_Ozero__class_Ozero(U_1721)
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1721),U_1722) != c_Groups_Ozero__class_Ozero(U_1721)
        | ~ sP108(U_1722,U_1721) )
    & ! [U_1722,U_1721] :
        ( sP108(U_1722,U_1721)
        | ~ class_Groups_Ogroup__add(U_1721) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_431_2]) ).

cnf(f_431_4,plain,
    ( sP108(U_1722,U_1721)
    | ~ class_Groups_Ogroup__add(U_1721) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_5,plain,
    ( U_1722 = c_Groups_Ozero__class_Ozero(U_1721)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1721),U_1722) != c_Groups_Ozero__class_Ozero(U_1721)
    | ~ sP108(U_1722,U_1721) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1721),U_1722) = c_Groups_Ozero__class_Ozero(U_1721)
    | U_1722 != c_Groups_Ozero__class_Ozero(U_1721)
    | ~ sP108(U_1722,U_1721) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_a_2 ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).

fof(f_432_2,plain,
    ! [U_1724,U_1723] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1723),U_1724) = U_1724
          | U_1724 != c_Groups_Ozero__class_Ozero(U_1723) )
        & ( U_1724 = c_Groups_Ozero__class_Ozero(U_1723)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1723),U_1724) != U_1724 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1723) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ( ! [U_1724,U_1723] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1723),U_1724) = U_1724
        | U_1724 != c_Groups_Ozero__class_Ozero(U_1723)
        | ~ sP109(U_1724,U_1723) )
    & ! [U_1724,U_1723] :
        ( U_1724 = c_Groups_Ozero__class_Ozero(U_1723)
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1723),U_1724) != U_1724
        | ~ sP109(U_1724,U_1723) )
    & ! [U_1724,U_1723] :
        ( sP109(U_1724,U_1723)
        | ~ class_Groups_Olinordered__ab__group__add(U_1723) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_432_2]) ).

cnf(f_432_4,plain,
    ( sP109(U_1724,U_1723)
    | ~ class_Groups_Olinordered__ab__group__add(U_1723) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

cnf(f_432_5,plain,
    ( U_1724 = c_Groups_Ozero__class_Ozero(U_1723)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1723),U_1724) != U_1724
    | ~ sP109(U_1724,U_1723) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

cnf(f_432_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1723),U_1724) = U_1724
    | U_1724 != c_Groups_Ozero__class_Ozero(U_1723)
    | ~ sP109(U_1724,U_1723) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).

fof(f_433_2,plain,
    ! [U_1727,U_1726,U_1725] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1726),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1727)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1727),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1726))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1727),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1726)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1726),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1727))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1725) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ( ! [U_1725,U_1726,U_1727] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1726),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1727)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1727),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1726)))
        | ~ sP110(U_1725,U_1726,U_1727) )
    & ! [U_1725,U_1726,U_1727] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1727),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1726)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1726),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1727)))
        | ~ sP110(U_1725,U_1726,U_1727) )
    & ! [U_1725,U_1726,U_1727] :
        ( sP110(U_1725,U_1726,U_1727)
        | ~ class_Groups_Oordered__ab__group__add(U_1725) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_433_2]) ).

cnf(f_433_4,plain,
    ( sP110(U_1725,U_1726,U_1727)
    | ~ class_Groups_Oordered__ab__group__add(U_1725) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

cnf(f_433_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1727),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1726)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1726),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1727)))
    | ~ sP110(U_1725,U_1726,U_1727) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

cnf(f_433_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1726),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1727)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1725),U_1727),hAPP(c_Groups_Ouminus__class_Ouminus(U_1725),U_1726)))
    | ~ sP110(U_1725,U_1726,U_1727) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).

fof(f_434_2,plain,
    ! [U_1730,U_1729,U_1728] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1729)),U_1730))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1730)),U_1729)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1730)),U_1729))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1729)),U_1730)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1728) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ( ! [U_1728,U_1729,U_1730] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1729)),U_1730))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1730)),U_1729))
        | ~ sP111(U_1728,U_1729,U_1730) )
    & ! [U_1728,U_1729,U_1730] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1730)),U_1729))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1729)),U_1730))
        | ~ sP111(U_1728,U_1729,U_1730) )
    & ! [U_1728,U_1729,U_1730] :
        ( sP111(U_1728,U_1729,U_1730)
        | ~ class_Groups_Oordered__ab__group__add(U_1728) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_434_2]) ).

cnf(f_434_4,plain,
    ( sP111(U_1728,U_1729,U_1730)
    | ~ class_Groups_Oordered__ab__group__add(U_1728) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

cnf(f_434_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1730)),U_1729))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1729)),U_1730))
    | ~ sP111(U_1728,U_1729,U_1730) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

cnf(f_434_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1729)),U_1730))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1728),hAPP(c_Groups_Ouminus__class_Ouminus(U_1728),U_1730)),U_1729))
    | ~ sP111(U_1728,U_1729,U_1730) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).

fof(f_435_2,plain,
    ! [U_1733,U_1732,U_1731] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1732)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1733)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1733),U_1732)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1733),U_1732))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1732)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1733))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1731) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ( ! [U_1733,U_1731,U_1732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1732)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1733)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1733),U_1732))
        | ~ sP112(U_1733,U_1731,U_1732) )
    & ! [U_1733,U_1731,U_1732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1733),U_1732))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1732)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1733)))
        | ~ sP112(U_1733,U_1731,U_1732) )
    & ! [U_1733,U_1731,U_1732] :
        ( sP112(U_1733,U_1731,U_1732)
        | ~ class_Groups_Oordered__ab__group__add(U_1731) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_435_2]) ).

cnf(f_435_4,plain,
    ( sP112(U_1733,U_1731,U_1732)
    | ~ class_Groups_Oordered__ab__group__add(U_1731) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1733),U_1732))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1732)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1733)))
    | ~ sP112(U_1733,U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1732)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1731),U_1733)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1733),U_1732))
    | ~ sP112(U_1733,U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).

fof(f_436_2,plain,
    ! [U_1736,U_1735,U_1734] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1734),U_1735),U_1736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1734),hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),U_1735)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),U_1736))
      | ~ class_Groups_Oab__group__add(U_1734) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1734,U_1735,U_1736] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1734),U_1735),U_1736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1734),hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),U_1735)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),U_1736))
      | ~ class_Groups_Oab__group__add(U_1734) ),
    inference(definitional_conversion,[status(esa)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1734),U_1735),U_1736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1734),hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),U_1735)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1734),U_1736))
    | ~ class_Groups_Oab__group__add(U_1734) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add]) ).

fof(f_437_2,plain,
    ! [U_1739,U_1738,U_1737] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),U_1738),U_1739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),U_1739)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),U_1738))
      | ~ class_Groups_Ogroup__add(U_1737) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ! [U_1737,U_1738,U_1739] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),U_1738),U_1739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),U_1739)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),U_1738))
      | ~ class_Groups_Ogroup__add(U_1737) ),
    inference(definitional_conversion,[status(esa)],[f_437_2]) ).

cnf(f_437_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),U_1738),U_1739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),U_1739)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1737),U_1738))
    | ~ class_Groups_Ogroup__add(U_1737) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).

fof(f_438_2,plain,
    ! [U_1742,U_1741,U_1740] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1740),U_1741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1740),hAPP(c_Groups_Ouminus__class_Ouminus(U_1740),U_1741)),U_1742)) = U_1742
      | ~ class_Groups_Ogroup__add(U_1740) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1740,U_1741,U_1742] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1740),U_1741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1740),hAPP(c_Groups_Ouminus__class_Ouminus(U_1740),U_1741)),U_1742)) = U_1742
      | ~ class_Groups_Ogroup__add(U_1740) ),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1740),U_1741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1740),hAPP(c_Groups_Ouminus__class_Ouminus(U_1740),U_1741)),U_1742)) = U_1742
    | ~ class_Groups_Ogroup__add(U_1740) ),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).

fof(f_439_2,plain,
    ! [U_1745,U_1744,U_1743] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(c_Groups_Ouminus__class_Ouminus(U_1743),U_1744)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),U_1744),U_1745)) = U_1745
      | ~ class_Groups_Ogroup__add(U_1743) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1743,U_1744,U_1745] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(c_Groups_Ouminus__class_Ouminus(U_1743),U_1744)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),U_1744),U_1745)) = U_1745
      | ~ class_Groups_Ogroup__add(U_1743) ),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(c_Groups_Ouminus__class_Ouminus(U_1743),U_1744)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),U_1744),U_1745)) = U_1745
    | ~ class_Groups_Ogroup__add(U_1743) ),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).

fof(f_440_2,plain,
    ! [U_1747,U_1746] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1746),c_Groups_Ozero__class_Ozero(U_1746)),U_1747) = c_Groups_Ozero__class_Ozero(U_1746)
      | ~ class_Rings_Ocomm__semiring__1(U_1746) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1746,U_1747] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1746),c_Groups_Ozero__class_Ozero(U_1746)),U_1747) = c_Groups_Ozero__class_Ozero(U_1746)
      | ~ class_Rings_Ocomm__semiring__1(U_1746) ),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1746),c_Groups_Ozero__class_Ozero(U_1746)),U_1747) = c_Groups_Ozero__class_Ozero(U_1746)
    | ~ class_Rings_Ocomm__semiring__1(U_1746) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).

fof(f_441_2,plain,
    ! [U_1749,U_1748] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),c_Groups_Ozero__class_Ozero(U_1748)) = c_Groups_Ozero__class_Ozero(U_1748)
      | ~ class_Rings_Ocomm__semiring__1(U_1748) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1748,U_1749] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),c_Groups_Ozero__class_Ozero(U_1748)) = c_Groups_Ozero__class_Ozero(U_1748)
      | ~ class_Rings_Ocomm__semiring__1(U_1748) ),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),c_Groups_Ozero__class_Ozero(U_1748)) = c_Groups_Ozero__class_Ozero(U_1748)
    | ~ class_Rings_Ocomm__semiring__1(U_1748) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Omult__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__zero__left]) ).

fof(f_442_2,plain,
    ! [U_1751,U_1750] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1750),c_Groups_Ozero__class_Ozero(U_1750)),U_1751) = c_Groups_Ozero__class_Ozero(U_1750)
      | ~ class_Rings_Omult__zero(U_1750) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1750,U_1751] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1750),c_Groups_Ozero__class_Ozero(U_1750)),U_1751) = c_Groups_Ozero__class_Ozero(U_1750)
      | ~ class_Rings_Omult__zero(U_1750) ),
    inference(definitional_conversion,[status(esa)],[f_442_2]) ).

cnf(f_442_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1750),c_Groups_Ozero__class_Ozero(U_1750)),U_1751) = c_Groups_Ozero__class_Ozero(U_1750)
    | ~ class_Rings_Omult__zero(U_1750) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Omult__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__zero__right]) ).

fof(f_443_2,plain,
    ! [U_1753,U_1752] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),c_Groups_Ozero__class_Ozero(U_1752)) = c_Groups_Ozero__class_Ozero(U_1752)
      | ~ class_Rings_Omult__zero(U_1752) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1752,U_1753] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),c_Groups_Ozero__class_Ozero(U_1752)) = c_Groups_Ozero__class_Ozero(U_1752)
      | ~ class_Rings_Omult__zero(U_1752) ),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),c_Groups_Ozero__class_Ozero(U_1752)) = c_Groups_Ozero__class_Ozero(U_1752)
    | ~ class_Rings_Omult__zero(U_1752) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Oring__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).

fof(f_444_2,plain,
    ! [U_1756,U_1755,U_1754] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756) = c_Groups_Ozero__class_Ozero(U_1754)
          | ( U_1756 != c_Groups_Ozero__class_Ozero(U_1754)
            & U_1755 != c_Groups_Ozero__class_Ozero(U_1754) ) )
        & ( U_1756 = c_Groups_Ozero__class_Ozero(U_1754)
          | U_1755 = c_Groups_Ozero__class_Ozero(U_1754)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756) != c_Groups_Ozero__class_Ozero(U_1754) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_1754) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ( ! [U_1754,U_1755,U_1756] :
        ( U_1756 != c_Groups_Ozero__class_Ozero(U_1754)
        | ~ sP113(U_1754,U_1755,U_1756) )
    & ! [U_1754,U_1755,U_1756] :
        ( U_1755 != c_Groups_Ozero__class_Ozero(U_1754)
        | ~ sP113(U_1754,U_1755,U_1756) )
    & ! [U_1754,U_1755,U_1756] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756) = c_Groups_Ozero__class_Ozero(U_1754)
        | sP113(U_1754,U_1755,U_1756)
        | ~ sP114(U_1754,U_1755,U_1756) )
    & ! [U_1754,U_1755,U_1756] :
        ( U_1756 = c_Groups_Ozero__class_Ozero(U_1754)
        | U_1755 = c_Groups_Ozero__class_Ozero(U_1754)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756) != c_Groups_Ozero__class_Ozero(U_1754)
        | ~ sP114(U_1754,U_1755,U_1756) )
    & ! [U_1754,U_1755,U_1756] :
        ( sP114(U_1754,U_1755,U_1756)
        | ~ class_Rings_Oring__no__zero__divisors(U_1754) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113,sP114])],[f_444_2]) ).

cnf(f_444_4,plain,
    ( sP114(U_1754,U_1755,U_1756)
    | ~ class_Rings_Oring__no__zero__divisors(U_1754) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_5,plain,
    ( U_1756 = c_Groups_Ozero__class_Ozero(U_1754)
    | U_1755 = c_Groups_Ozero__class_Ozero(U_1754)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756) != c_Groups_Ozero__class_Ozero(U_1754)
    | ~ sP114(U_1754,U_1755,U_1756) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756) = c_Groups_Ozero__class_Ozero(U_1754)
    | sP113(U_1754,U_1755,U_1756)
    | ~ sP114(U_1754,U_1755,U_1756) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_7,plain,
    ( U_1755 != c_Groups_Ozero__class_Ozero(U_1754)
    | ~ sP113(U_1754,U_1755,U_1756) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_8,plain,
    ( U_1756 != c_Groups_Ozero__class_Ozero(U_1754)
    | ~ sP113(U_1754,U_1755,U_1756) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_no__zero__divisors]) ).

fof(f_445_2,plain,
    ! [U_1759,U_1758,U_1757] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1757),U_1758),U_1759) != c_Groups_Ozero__class_Ozero(U_1757)
      | U_1759 = c_Groups_Ozero__class_Ozero(U_1757)
      | U_1758 = c_Groups_Ozero__class_Ozero(U_1757)
      | ~ class_Rings_Ono__zero__divisors(U_1757) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1757,U_1758,U_1759] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1757),U_1758),U_1759) != c_Groups_Ozero__class_Ozero(U_1757)
      | U_1759 = c_Groups_Ozero__class_Ozero(U_1757)
      | U_1758 = c_Groups_Ozero__class_Ozero(U_1757)
      | ~ class_Rings_Ono__zero__divisors(U_1757) ),
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1757),U_1758),U_1759) != c_Groups_Ozero__class_Ozero(U_1757)
    | U_1759 = c_Groups_Ozero__class_Ozero(U_1757)
    | U_1758 = c_Groups_Ozero__class_Ozero(U_1757)
    | ~ class_Rings_Ono__zero__divisors(U_1757) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_1,plain,
    ! [V_b,V_a,T_a] :
      ( V_b = c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divisors__zero]) ).

fof(f_446_2,plain,
    ! [U_1762,U_1761,U_1760] :
      ( U_1762 = c_Groups_Ozero__class_Ozero(U_1760)
      | U_1761 = c_Groups_Ozero__class_Ozero(U_1760)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),U_1762) != c_Groups_Ozero__class_Ozero(U_1760)
      | ~ class_Rings_Ono__zero__divisors(U_1760) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1761,U_1760,U_1762] :
      ( U_1762 = c_Groups_Ozero__class_Ozero(U_1760)
      | U_1761 = c_Groups_Ozero__class_Ozero(U_1760)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),U_1762) != c_Groups_Ozero__class_Ozero(U_1760)
      | ~ class_Rings_Ono__zero__divisors(U_1760) ),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( U_1762 = c_Groups_Ozero__class_Ozero(U_1760)
    | U_1761 = c_Groups_Ozero__class_Ozero(U_1760)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),U_1762) != c_Groups_Ozero__class_Ozero(U_1760)
    | ~ class_Rings_Ono__zero__divisors(U_1760) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [T_a] :
      ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ozero__neq__one(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__neq__zero]) ).

fof(f_447_2,plain,
    ! [U_1763] :
      ( c_Groups_Oone__class_Oone(U_1763) != c_Groups_Ozero__class_Ozero(U_1763)
      | ~ class_Rings_Ozero__neq__one(U_1763) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1763] :
      ( c_Groups_Oone__class_Oone(U_1763) != c_Groups_Ozero__class_Ozero(U_1763)
      | ~ class_Rings_Ozero__neq__one(U_1763) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( c_Groups_Oone__class_Oone(U_1763) != c_Groups_Ozero__class_Ozero(U_1763)
    | ~ class_Rings_Ozero__neq__one(U_1763) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_1,plain,
    ! [T_a] :
      ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ozero__neq__one(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__neq__one]) ).

fof(f_448_2,plain,
    ! [U_1764] :
      ( c_Groups_Ozero__class_Ozero(U_1764) != c_Groups_Oone__class_Oone(U_1764)
      | ~ class_Rings_Ozero__neq__one(U_1764) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1764] :
      ( c_Groups_Ozero__class_Ozero(U_1764) != c_Groups_Oone__class_Oone(U_1764)
      | ~ class_Rings_Ozero__neq__one(U_1764) ),
    inference(definitional_conversion,[status(esa)],[f_448_2]) ).

cnf(f_448_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_1764) != c_Groups_Oone__class_Oone(U_1764)
    | ~ class_Rings_Ozero__neq__one(U_1764) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_1,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).

fof(f_449_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_449_1]) ).

cnf(f_449_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_1,plain,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__int]) ).

fof(f_450_2,plain,
    ! [U_1765] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1765)) = U_1765,
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ! [U_1765] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1765)) = U_1765,
    inference(definitional_conversion,[status(esa)],[f_450_2]) ).

cnf(f_450_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1765)) = U_1765,
    inference(clausify,[status(thm)],[f_450_3]) ).

fof(f_451_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).

fof(f_451_2,plain,
    ! [U_1769,U_1768,U_1767,U_1766] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1766),U_1768),U_1769)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),U_1768)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),U_1769))
      | ~ class_Rings_Ocomm__semiring__1(U_1766) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ! [U_1766,U_1767,U_1768,U_1769] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1766),U_1768),U_1769)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),U_1768)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),U_1769))
      | ~ class_Rings_Ocomm__semiring__1(U_1766) ),
    inference(definitional_conversion,[status(esa)],[f_451_2]) ).

cnf(f_451_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1766),U_1768),U_1769)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),U_1768)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1767),U_1769))
    | ~ class_Rings_Ocomm__semiring__1(U_1766) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

fof(f_452_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( ( V_c_2 != V_d_2
            & V_a_2 != V_b_2 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))
          | V_c_2 = V_d_2
          | V_a_2 = V_b_2 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).

fof(f_452_2,plain,
    ! [U_1774,U_1773,U_1772,U_1771,U_1770] :
      ( ( ( ( U_1773 != U_1774
            & U_1771 != U_1772 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1773)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1774)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1773))
          | U_1773 = U_1774
          | U_1771 = U_1772 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1770) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ( ! [U_1771,U_1772,U_1773,U_1774] :
        ( U_1773 != U_1774
        | ~ sP115(U_1771,U_1772,U_1773,U_1774) )
    & ! [U_1771,U_1772,U_1773,U_1774] :
        ( U_1771 != U_1772
        | ~ sP115(U_1771,U_1772,U_1773,U_1774) )
    & ! [U_1770,U_1771,U_1772,U_1773,U_1774] :
        ( sP115(U_1771,U_1772,U_1773,U_1774)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1773))
        | ~ sP116(U_1770,U_1771,U_1772,U_1773,U_1774) )
    & ! [U_1770,U_1771,U_1772,U_1773,U_1774] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1774)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1773))
        | U_1773 = U_1774
        | U_1771 = U_1772
        | ~ sP116(U_1770,U_1771,U_1772,U_1773,U_1774) )
    & ! [U_1770,U_1771,U_1772,U_1773,U_1774] :
        ( sP116(U_1770,U_1771,U_1772,U_1773,U_1774)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1770) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115,sP116])],[f_452_2]) ).

cnf(f_452_4,plain,
    ( sP116(U_1770,U_1771,U_1772,U_1773,U_1774)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1770) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

cnf(f_452_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1774)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1773))
    | U_1773 = U_1774
    | U_1771 = U_1772
    | ~ sP116(U_1770,U_1771,U_1772,U_1773,U_1774) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

cnf(f_452_6,plain,
    ( sP115(U_1771,U_1772,U_1773,U_1774)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1771),U_1774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1773))
    | ~ sP116(U_1770,U_1771,U_1772,U_1773,U_1774) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

cnf(f_452_7,plain,
    ( U_1771 != U_1772
    | ~ sP115(U_1771,U_1772,U_1773,U_1774) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

cnf(f_452_8,plain,
    ( U_1773 != U_1774
    | ~ sP115(U_1771,U_1772,U_1773,U_1774) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).

fof(f_453_2,plain,
    ! [U_1778,U_1777,U_1776,U_1775] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1775),U_1776),U_1777)),U_1778) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),U_1776),U_1778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),U_1777),U_1778))
      | ~ class_Rings_Ocomm__semiring__1(U_1775) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1777,U_1776,U_1778,U_1775] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1775),U_1776),U_1777)),U_1778) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),U_1776),U_1778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),U_1777),U_1778))
      | ~ class_Rings_Ocomm__semiring__1(U_1775) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1775),U_1776),U_1777)),U_1778) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),U_1776),U_1778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1775),U_1777),U_1778))
    | ~ class_Rings_Ocomm__semiring__1(U_1775) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_1,plain,
    ! [V_b,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).

fof(f_454_2,plain,
    ! [U_1782,U_1781,U_1780,U_1779] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1780),U_1781)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1782),U_1781)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1779),U_1780),U_1782)),U_1781)
      | ~ class_Rings_Ocomm__semiring__1(U_1779) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ! [U_1779,U_1780,U_1781,U_1782] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1780),U_1781)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1782),U_1781)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1779),U_1780),U_1782)),U_1781)
      | ~ class_Rings_Ocomm__semiring__1(U_1779) ),
    inference(definitional_conversion,[status(esa)],[f_454_2]) ).

cnf(f_454_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1780),U_1781)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1782),U_1781)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1779),U_1780),U_1782)),U_1781)
    | ~ class_Rings_Ocomm__semiring__1(U_1779) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_1,plain,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
          | ( V_y_2 != V_z_2
            & V_w_2 != V_x_2 ) )
        & ( V_y_2 = V_z_2
          | V_w_2 = V_x_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).

fof(f_455_2,plain,
    ! [U_1787,U_1786,U_1785,U_1784,U_1783] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1787)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1785))
          | ( U_1785 != U_1787
            & U_1784 != U_1786 ) )
        & ( U_1785 = U_1787
          | U_1784 = U_1786
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1787)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1785)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1783) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ( ! [U_1784,U_1785,U_1786,U_1787] :
        ( U_1785 != U_1787
        | ~ sP117(U_1784,U_1785,U_1786,U_1787) )
    & ! [U_1784,U_1785,U_1786,U_1787] :
        ( U_1784 != U_1786
        | ~ sP117(U_1784,U_1785,U_1786,U_1787) )
    & ! [U_1783,U_1784,U_1785,U_1786,U_1787] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1787)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1785))
        | sP117(U_1784,U_1785,U_1786,U_1787)
        | ~ sP118(U_1783,U_1784,U_1785,U_1786,U_1787) )
    & ! [U_1783,U_1784,U_1785,U_1786,U_1787] :
        ( U_1785 = U_1787
        | U_1784 = U_1786
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1787)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1785))
        | ~ sP118(U_1783,U_1784,U_1785,U_1786,U_1787) )
    & ! [U_1783,U_1784,U_1785,U_1786,U_1787] :
        ( sP118(U_1783,U_1784,U_1785,U_1786,U_1787)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1783) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117,sP118])],[f_455_2]) ).

cnf(f_455_4,plain,
    ( sP118(U_1783,U_1784,U_1785,U_1786,U_1787)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1783) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

cnf(f_455_5,plain,
    ( U_1785 = U_1787
    | U_1784 = U_1786
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1787)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1785))
    | ~ sP118(U_1783,U_1784,U_1785,U_1786,U_1787) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

cnf(f_455_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1787)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1786),U_1785))
    | sP117(U_1784,U_1785,U_1786,U_1787)
    | ~ sP118(U_1783,U_1784,U_1785,U_1786,U_1787) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

cnf(f_455_7,plain,
    ( U_1784 != U_1786
    | ~ sP117(U_1784,U_1785,U_1786,U_1787) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

cnf(f_455_8,plain,
    ( U_1785 != U_1787
    | ~ sP117(U_1784,U_1785,U_1786,U_1787) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).

fof(f_456_2,plain,
    ! [U_1791,U_1790,U_1789,U_1788] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1788),U_1789),U_1790)),U_1791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1788),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),U_1789),U_1791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),U_1790),U_1791))
      | ~ class_Rings_Ocomm__semiring(U_1788) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1791,U_1790,U_1789,U_1788] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1788),U_1789),U_1790)),U_1791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1788),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),U_1789),U_1791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),U_1790),U_1791))
      | ~ class_Rings_Ocomm__semiring(U_1788) ),
    inference(definitional_conversion,[status(esa)],[f_456_2]) ).

cnf(f_456_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1788),U_1789),U_1790)),U_1791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1788),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),U_1789),U_1791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1788),U_1790),U_1791))
    | ~ class_Rings_Ocomm__semiring(U_1788) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_1,plain,
    ! [V_c,V_b,V_e,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c)
      | ~ class_Rings_Osemiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).

fof(f_457_2,plain,
    ! [U_1796,U_1795,U_1794,U_1793,U_1792] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),U_1793),U_1794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),U_1795),U_1794)),U_1796)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),U_1793),U_1795)),U_1794)),U_1796)
      | ~ class_Rings_Osemiring(U_1792) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1792,U_1793,U_1794,U_1795,U_1796] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),U_1793),U_1794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),U_1795),U_1794)),U_1796)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),U_1793),U_1795)),U_1794)),U_1796)
      | ~ class_Rings_Osemiring(U_1792) ),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),U_1793),U_1794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),U_1795),U_1794)),U_1796)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1792),U_1793),U_1795)),U_1794)),U_1796)
    | ~ class_Rings_Osemiring(U_1792) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_1,plain,
    ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(f_458_2,plain,
    ! [U_1798,U_1797] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1797),U_1798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1797)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1798)),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ! [U_1797,U_1798] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1797),U_1798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1797)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1798)),
    inference(definitional_conversion,[status(esa)],[f_458_2]) ).

cnf(f_458_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1797),U_1798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1797)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1798)),
    inference(clausify,[status(thm)],[f_458_3]) ).

fof(f_459_1,plain,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(f_459_2,plain,
    ! [U_1801,U_1800,U_1799] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1800),U_1801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),U_1800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),U_1801)),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1801,U_1799,U_1800] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1800),U_1801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),U_1800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),U_1801)),
    inference(definitional_conversion,[status(esa)],[f_459_2]) ).

cnf(f_459_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1800),U_1801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),U_1800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1799),U_1801)),
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(f_460_2,plain,
    ! [U_1804,U_1803,U_1802] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1802),U_1803)),U_1804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1802),U_1804)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1803),U_1804)),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1802,U_1803,U_1804] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1802),U_1803)),U_1804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1802),U_1804)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1803),U_1804)),
    inference(definitional_conversion,[status(esa)],[f_460_2]) ).

cnf(f_460_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1802),U_1803)),U_1804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1802),U_1804)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1803),U_1804)),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).

fof(f_461_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_461_1]) ).

cnf(f_461_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_461_2]) ).

fof(f_462_1,plain,
    ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),
    inference(fof_nnf,[status(thm)],[fact_of__int__int__eq]) ).

fof(f_462_2,plain,
    ! [U_1805] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1805)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1805),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1805] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1805)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1805),
    inference(definitional_conversion,[status(esa)],[f_462_2]) ).

cnf(f_462_4,plain,
    hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1805)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1805),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq]) ).

fof(f_463_2,plain,
    ! [U_1806] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1806)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1806)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1806))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1806))) ) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ( ! [U_1808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1808)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1808)) )
    & ! [U_1807] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1807))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1807))) ) ),
    inference(miniscope,[status(thm)],[f_463_2]) ).

fof(f_463_4,plain,
    ( ! [U_1808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1808)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1808)) )
    & ! [U_1807] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1807))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1807))) ) ),
    inference(definitional_conversion,[status(esa)],[f_463_3]) ).

cnf(f_463_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1807))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1807))) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

cnf(f_463_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_1808)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1808)) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

fof(f_464_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).

fof(f_464_2,plain,
    ! [U_1810,U_1809] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),hAPP(c_Groups_Ouminus__class_Ouminus(U_1809),U_1810)),U_1810))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),c_Groups_Ozero__class_Ozero(U_1809)),U_1810)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),c_Groups_Ozero__class_Ozero(U_1809)),U_1810))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),hAPP(c_Groups_Ouminus__class_Ouminus(U_1809),U_1810)),U_1810)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1809) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ( ! [U_1809,U_1810] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),hAPP(c_Groups_Ouminus__class_Ouminus(U_1809),U_1810)),U_1810))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),c_Groups_Ozero__class_Ozero(U_1809)),U_1810))
        | ~ sP119(U_1809,U_1810) )
    & ! [U_1809,U_1810] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),c_Groups_Ozero__class_Ozero(U_1809)),U_1810))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),hAPP(c_Groups_Ouminus__class_Ouminus(U_1809),U_1810)),U_1810))
        | ~ sP119(U_1809,U_1810) )
    & ! [U_1809,U_1810] :
        ( sP119(U_1809,U_1810)
        | ~ class_Groups_Olinordered__ab__group__add(U_1809) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_464_2]) ).

cnf(f_464_4,plain,
    ( sP119(U_1809,U_1810)
    | ~ class_Groups_Olinordered__ab__group__add(U_1809) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

cnf(f_464_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),c_Groups_Ozero__class_Ozero(U_1809)),U_1810))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),hAPP(c_Groups_Ouminus__class_Ouminus(U_1809),U_1810)),U_1810))
    | ~ sP119(U_1809,U_1810) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

cnf(f_464_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),hAPP(c_Groups_Ouminus__class_Ouminus(U_1809),U_1810)),U_1810))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1809),c_Groups_Ozero__class_Ozero(U_1809)),U_1810))
    | ~ sP119(U_1809,U_1810) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

fof(f_465_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).

fof(f_465_2,plain,
    ! [U_1812,U_1811] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),hAPP(c_Groups_Ouminus__class_Ouminus(U_1811),U_1812)),c_Groups_Ozero__class_Ozero(U_1811)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),c_Groups_Ozero__class_Ozero(U_1811)),U_1812)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),c_Groups_Ozero__class_Ozero(U_1811)),U_1812))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),hAPP(c_Groups_Ouminus__class_Ouminus(U_1811),U_1812)),c_Groups_Ozero__class_Ozero(U_1811))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1811) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ( ! [U_1812,U_1811] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),hAPP(c_Groups_Ouminus__class_Ouminus(U_1811),U_1812)),c_Groups_Ozero__class_Ozero(U_1811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),c_Groups_Ozero__class_Ozero(U_1811)),U_1812))
        | ~ sP120(U_1812,U_1811) )
    & ! [U_1812,U_1811] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),c_Groups_Ozero__class_Ozero(U_1811)),U_1812))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),hAPP(c_Groups_Ouminus__class_Ouminus(U_1811),U_1812)),c_Groups_Ozero__class_Ozero(U_1811)))
        | ~ sP120(U_1812,U_1811) )
    & ! [U_1812,U_1811] :
        ( sP120(U_1812,U_1811)
        | ~ class_Groups_Oordered__ab__group__add(U_1811) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_465_2]) ).

cnf(f_465_4,plain,
    ( sP120(U_1812,U_1811)
    | ~ class_Groups_Oordered__ab__group__add(U_1811) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),c_Groups_Ozero__class_Ozero(U_1811)),U_1812))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),hAPP(c_Groups_Ouminus__class_Ouminus(U_1811),U_1812)),c_Groups_Ozero__class_Ozero(U_1811)))
    | ~ sP120(U_1812,U_1811) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),hAPP(c_Groups_Ouminus__class_Ouminus(U_1811),U_1812)),c_Groups_Ozero__class_Ozero(U_1811)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),c_Groups_Ozero__class_Ozero(U_1811)),U_1812))
    | ~ sP120(U_1812,U_1811) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).

fof(f_466_2,plain,
    ! [U_1814,U_1813] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),c_Groups_Ozero__class_Ozero(U_1813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1813),U_1814)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1814),c_Groups_Ozero__class_Ozero(U_1813))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1814),c_Groups_Ozero__class_Ozero(U_1813)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),c_Groups_Ozero__class_Ozero(U_1813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1813),U_1814))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1813) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ( ! [U_1813,U_1814] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),c_Groups_Ozero__class_Ozero(U_1813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1813),U_1814)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1814),c_Groups_Ozero__class_Ozero(U_1813)))
        | ~ sP121(U_1813,U_1814) )
    & ! [U_1813,U_1814] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1814),c_Groups_Ozero__class_Ozero(U_1813)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),c_Groups_Ozero__class_Ozero(U_1813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1813),U_1814)))
        | ~ sP121(U_1813,U_1814) )
    & ! [U_1813,U_1814] :
        ( sP121(U_1813,U_1814)
        | ~ class_Groups_Oordered__ab__group__add(U_1813) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_466_2]) ).

cnf(f_466_4,plain,
    ( sP121(U_1813,U_1814)
    | ~ class_Groups_Oordered__ab__group__add(U_1813) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

cnf(f_466_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1814),c_Groups_Ozero__class_Ozero(U_1813)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),c_Groups_Ozero__class_Ozero(U_1813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1813),U_1814)))
    | ~ sP121(U_1813,U_1814) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

cnf(f_466_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),c_Groups_Ozero__class_Ozero(U_1813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1813),U_1814)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1813),U_1814),c_Groups_Ozero__class_Ozero(U_1813)))
    | ~ sP121(U_1813,U_1814) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

fof(f_467_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).

fof(f_467_2,plain,
    ! [U_1816,U_1815] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),hAPP(c_Groups_Ouminus__class_Ouminus(U_1815),U_1816)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),c_Groups_Ozero__class_Ozero(U_1815))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),c_Groups_Ozero__class_Ozero(U_1815)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),hAPP(c_Groups_Ouminus__class_Ouminus(U_1815),U_1816))) ) )
      | ~ class_Rings_Olinordered__idom(U_1815) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ( ! [U_1816,U_1815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),hAPP(c_Groups_Ouminus__class_Ouminus(U_1815),U_1816)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),c_Groups_Ozero__class_Ozero(U_1815)))
        | ~ sP122(U_1816,U_1815) )
    & ! [U_1816,U_1815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),c_Groups_Ozero__class_Ozero(U_1815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),hAPP(c_Groups_Ouminus__class_Ouminus(U_1815),U_1816)))
        | ~ sP122(U_1816,U_1815) )
    & ! [U_1816,U_1815] :
        ( sP122(U_1816,U_1815)
        | ~ class_Rings_Olinordered__idom(U_1815) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_467_2]) ).

cnf(f_467_4,plain,
    ( sP122(U_1816,U_1815)
    | ~ class_Rings_Olinordered__idom(U_1815) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

cnf(f_467_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),c_Groups_Ozero__class_Ozero(U_1815)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),hAPP(c_Groups_Ouminus__class_Ouminus(U_1815),U_1816)))
    | ~ sP122(U_1816,U_1815) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

cnf(f_467_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),hAPP(c_Groups_Ouminus__class_Ouminus(U_1815),U_1816)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1815),U_1816),c_Groups_Ozero__class_Ozero(U_1815)))
    | ~ sP122(U_1816,U_1815) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).

fof(f_468_2,plain,
    ! [U_1819,U_1818,U_1817] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1817),U_1818) = U_1819
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1817),U_1818),U_1819) != c_Groups_Ozero__class_Ozero(U_1817)
      | ~ class_Groups_Ogroup__add(U_1817) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1819,U_1818,U_1817] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1817),U_1818) = U_1819
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1817),U_1818),U_1819) != c_Groups_Ozero__class_Ozero(U_1817)
      | ~ class_Groups_Ogroup__add(U_1817) ),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1817),U_1818) = U_1819
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1817),U_1818),U_1819) != c_Groups_Ozero__class_Ozero(U_1817)
    | ~ class_Groups_Ogroup__add(U_1817) ),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).

fof(f_469_2,plain,
    ! [U_1821,U_1820] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1820),hAPP(c_Groups_Ouminus__class_Ouminus(U_1820),U_1821)),U_1821) = c_Groups_Ozero__class_Ozero(U_1820)
      | ~ class_Groups_Oab__group__add(U_1820) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_1820,U_1821] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1820),hAPP(c_Groups_Ouminus__class_Ouminus(U_1820),U_1821)),U_1821) = c_Groups_Ozero__class_Ozero(U_1820)
      | ~ class_Groups_Oab__group__add(U_1820) ),
    inference(definitional_conversion,[status(esa)],[f_469_2]) ).

cnf(f_469_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1820),hAPP(c_Groups_Ouminus__class_Ouminus(U_1820),U_1821)),U_1821) = c_Groups_Ozero__class_Ozero(U_1820)
    | ~ class_Groups_Oab__group__add(U_1820) ),
    inference(clausify,[status(thm)],[f_469_3]) ).

fof(f_470_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_left__minus]) ).

fof(f_470_2,plain,
    ! [U_1823,U_1822] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1822),hAPP(c_Groups_Ouminus__class_Ouminus(U_1822),U_1823)),U_1823) = c_Groups_Ozero__class_Ozero(U_1822)
      | ~ class_Groups_Ogroup__add(U_1822) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1822,U_1823] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1822),hAPP(c_Groups_Ouminus__class_Ouminus(U_1822),U_1823)),U_1823) = c_Groups_Ozero__class_Ozero(U_1822)
      | ~ class_Groups_Ogroup__add(U_1822) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1822),hAPP(c_Groups_Ouminus__class_Ouminus(U_1822),U_1823)),U_1823) = c_Groups_Ozero__class_Ozero(U_1822)
    | ~ class_Groups_Ogroup__add(U_1822) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).

fof(f_471_2,plain,
    ! [U_1826,U_1825,U_1824] :
      ( ( ( U_1825 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1824),U_1826)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1824),U_1825),U_1826) != c_Groups_Ozero__class_Ozero(U_1824) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1824),U_1825),U_1826) = c_Groups_Ozero__class_Ozero(U_1824)
          | U_1825 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1824),U_1826) ) )
      | ~ class_Groups_Ogroup__add(U_1824) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ( ! [U_1824,U_1825,U_1826] :
        ( U_1825 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1824),U_1826)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1824),U_1825),U_1826) != c_Groups_Ozero__class_Ozero(U_1824)
        | ~ sP123(U_1824,U_1825,U_1826) )
    & ! [U_1824,U_1825,U_1826] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1824),U_1825),U_1826) = c_Groups_Ozero__class_Ozero(U_1824)
        | U_1825 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1824),U_1826)
        | ~ sP123(U_1824,U_1825,U_1826) )
    & ! [U_1824,U_1825,U_1826] :
        ( sP123(U_1824,U_1825,U_1826)
        | ~ class_Groups_Ogroup__add(U_1824) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_471_2]) ).

cnf(f_471_4,plain,
    ( sP123(U_1824,U_1825,U_1826)
    | ~ class_Groups_Ogroup__add(U_1824) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

cnf(f_471_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1824),U_1825),U_1826) = c_Groups_Ozero__class_Ozero(U_1824)
    | U_1825 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1824),U_1826)
    | ~ sP123(U_1824,U_1825,U_1826) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

cnf(f_471_6,plain,
    ( U_1825 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1824),U_1826)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1824),U_1825),U_1826) != c_Groups_Ozero__class_Ozero(U_1824)
    | ~ sP123(U_1824,U_1825,U_1826) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus]) ).

fof(f_472_2,plain,
    ! [U_1828,U_1827] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1827),U_1828),hAPP(c_Groups_Ouminus__class_Ouminus(U_1827),U_1828)) = c_Groups_Ozero__class_Ozero(U_1827)
      | ~ class_Groups_Ogroup__add(U_1827) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1828,U_1827] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1827),U_1828),hAPP(c_Groups_Ouminus__class_Ouminus(U_1827),U_1828)) = c_Groups_Ozero__class_Ozero(U_1827)
      | ~ class_Groups_Ogroup__add(U_1827) ),
    inference(definitional_conversion,[status(esa)],[f_472_2]) ).

cnf(f_472_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1827),U_1828),hAPP(c_Groups_Ouminus__class_Ouminus(U_1827),U_1828)) = c_Groups_Ozero__class_Ozero(U_1827)
    | ~ class_Groups_Ogroup__add(U_1827) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_1,plain,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__0]) ).

fof(f_473_2,plain,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_473_1]) ).

cnf(f_473_3,plain,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_473_2]) ).

fof(f_474_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).

fof(f_474_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_474_1]) ).

cnf(f_474_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).

fof(f_475_2,plain,
    ! [U_1832,U_1831,U_1830,U_1829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),U_1832),U_1831)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),U_1832),U_1830)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1832),c_Groups_Ozero__class_Ozero(U_1829)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
      | ~ class_Rings_Olinordered__ring__strict(U_1829) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1829,U_1830,U_1831,U_1832] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),U_1832),U_1831)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),U_1832),U_1830)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1832),c_Groups_Ozero__class_Ozero(U_1829)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
      | ~ class_Rings_Olinordered__ring__strict(U_1829) ),
    inference(definitional_conversion,[status(esa)],[f_475_2]) ).

cnf(f_475_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),U_1832),U_1831)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),U_1832),U_1830)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1832),c_Groups_Ozero__class_Ozero(U_1829)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
    | ~ class_Rings_Olinordered__ring__strict(U_1829) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).

fof(f_476_2,plain,
    ! [U_1836,U_1835,U_1834,U_1833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1835),U_1836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1836)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),U_1836),c_Groups_Ozero__class_Ozero(U_1833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),U_1834),U_1835))
      | ~ class_Rings_Olinordered__ring__strict(U_1833) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1833,U_1834,U_1835,U_1836] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1835),U_1836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1836)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),U_1836),c_Groups_Ozero__class_Ozero(U_1833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),U_1834),U_1835))
      | ~ class_Rings_Olinordered__ring__strict(U_1833) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1835),U_1836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1836)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),U_1836),c_Groups_Ozero__class_Ozero(U_1833)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1833),U_1834),U_1835))
    | ~ class_Rings_Olinordered__ring__strict(U_1833) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).

fof(f_477_2,plain,
    ! [U_1840,U_1839,U_1838,U_1837] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1837),U_1840),U_1838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1837),U_1840),U_1839)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),c_Groups_Ozero__class_Ozero(U_1837)),U_1840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),U_1838),U_1839))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_1837) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1837,U_1838,U_1839,U_1840] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1837),U_1840),U_1838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1837),U_1840),U_1839)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),c_Groups_Ozero__class_Ozero(U_1837)),U_1840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),U_1838),U_1839))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_1837) ),
    inference(definitional_conversion,[status(esa)],[f_477_2]) ).

cnf(f_477_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1837),U_1840),U_1838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1837),U_1840),U_1839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),c_Groups_Ozero__class_Ozero(U_1837)),U_1840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1837),U_1838),U_1839))
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_1837) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).

fof(f_478_2,plain,
    ! [U_1844,U_1843,U_1842,U_1841] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1841),U_1844),U_1842)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1841),U_1844),U_1843)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),c_Groups_Ozero__class_Ozero(U_1841)),U_1844))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843))
      | ~ class_Rings_Olinordered__semiring__strict(U_1841) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_1841,U_1842,U_1843,U_1844] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1841),U_1844),U_1842)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1841),U_1844),U_1843)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),c_Groups_Ozero__class_Ozero(U_1841)),U_1844))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843))
      | ~ class_Rings_Olinordered__semiring__strict(U_1841) ),
    inference(definitional_conversion,[status(esa)],[f_478_2]) ).

cnf(f_478_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1841),U_1844),U_1842)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1841),U_1844),U_1843)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),c_Groups_Ozero__class_Ozero(U_1841)),U_1844))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843))
    | ~ class_Rings_Olinordered__semiring__strict(U_1841) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).

fof(f_479_2,plain,
    ! [U_1848,U_1847,U_1846,U_1845] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1848)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),c_Groups_Ozero__class_Ozero(U_1845)),U_1848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),U_1846),U_1847))
      | ~ class_Rings_Olinordered__semiring__strict(U_1845) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1845,U_1846,U_1847,U_1848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1848)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),c_Groups_Ozero__class_Ozero(U_1845)),U_1848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),U_1846),U_1847))
      | ~ class_Rings_Olinordered__semiring__strict(U_1845) ),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1848)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1848)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),c_Groups_Ozero__class_Ozero(U_1845)),U_1848))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),U_1846),U_1847))
    | ~ class_Rings_Olinordered__semiring__strict(U_1845) ),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).

fof(f_480_2,plain,
    ! [U_1851,U_1850,U_1849] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),c_Groups_Ozero__class_Ozero(U_1849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),U_1850),U_1851)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),U_1851),c_Groups_Ozero__class_Ozero(U_1849)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),U_1850),c_Groups_Ozero__class_Ozero(U_1849)))
      | ~ class_Rings_Olinordered__ring__strict(U_1849) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1850,U_1849,U_1851] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),c_Groups_Ozero__class_Ozero(U_1849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),U_1850),U_1851)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),U_1851),c_Groups_Ozero__class_Ozero(U_1849)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),U_1850),c_Groups_Ozero__class_Ozero(U_1849)))
      | ~ class_Rings_Olinordered__ring__strict(U_1849) ),
    inference(definitional_conversion,[status(esa)],[f_480_2]) ).

cnf(f_480_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),c_Groups_Ozero__class_Ozero(U_1849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),U_1850),U_1851)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),U_1851),c_Groups_Ozero__class_Ozero(U_1849)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1849),U_1850),c_Groups_Ozero__class_Ozero(U_1849)))
    | ~ class_Rings_Olinordered__ring__strict(U_1849) ),
    inference(clausify,[status(thm)],[f_480_3]) ).

fof(f_481_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).

fof(f_481_2,plain,
    ! [U_1854,U_1853,U_1852] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1852),U_1853),U_1854)),c_Groups_Ozero__class_Ozero(U_1852)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),c_Groups_Ozero__class_Ozero(U_1852)),U_1854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),U_1853),c_Groups_Ozero__class_Ozero(U_1852)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1852) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1852,U_1853,U_1854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1852),U_1853),U_1854)),c_Groups_Ozero__class_Ozero(U_1852)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),c_Groups_Ozero__class_Ozero(U_1852)),U_1854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),U_1853),c_Groups_Ozero__class_Ozero(U_1852)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1852) ),
    inference(definitional_conversion,[status(esa)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1852),U_1853),U_1854)),c_Groups_Ozero__class_Ozero(U_1852)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),c_Groups_Ozero__class_Ozero(U_1852)),U_1854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1852),U_1853),c_Groups_Ozero__class_Ozero(U_1852)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1852) ),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).

fof(f_482_2,plain,
    ! [U_1858,U_1857,U_1856,U_1855] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1858)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1858),U_1857)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1858),U_1857))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1858))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1856),c_Groups_Ozero__class_Ozero(U_1855)))
      | ~ class_Rings_Olinordered__ring__strict(U_1855) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ( ! [U_1855,U_1856,U_1857,U_1858] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1858)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1858),U_1857))
        | ~ sP124(U_1855,U_1856,U_1857,U_1858) )
    & ! [U_1855,U_1856,U_1857,U_1858] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1858),U_1857))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1858)))
        | ~ sP124(U_1855,U_1856,U_1857,U_1858) )
    & ! [U_1855,U_1856,U_1857,U_1858] :
        ( sP124(U_1855,U_1856,U_1857,U_1858)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1856),c_Groups_Ozero__class_Ozero(U_1855)))
        | ~ class_Rings_Olinordered__ring__strict(U_1855) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_482_2]) ).

cnf(f_482_4,plain,
    ( sP124(U_1855,U_1856,U_1857,U_1858)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1856),c_Groups_Ozero__class_Ozero(U_1855)))
    | ~ class_Rings_Olinordered__ring__strict(U_1855) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

cnf(f_482_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1858),U_1857))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1858)))
    | ~ sP124(U_1855,U_1856,U_1857,U_1858) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

cnf(f_482_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1855),U_1856),U_1858)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1855),U_1858),U_1857))
    | ~ sP124(U_1855,U_1856,U_1857,U_1858) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_1,plain,
    ! [V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).

fof(f_483_2,plain,
    ! [U_1861,U_1860,U_1859] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),U_1860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),U_1861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1859),U_1860),U_1861)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1859) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_1860,U_1861,U_1859] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),U_1860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),U_1861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1859),U_1860),U_1861)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1859) ),
    inference(definitional_conversion,[status(esa)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),U_1860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),U_1861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1859),c_Groups_Ozero__class_Ozero(U_1859)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1859),U_1860),U_1861)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1859) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

fof(f_484_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).

fof(f_484_2,plain,
    ! [U_1864,U_1863,U_1862] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),U_1864))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),U_1863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1862),U_1863),U_1864)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1862) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ! [U_1862,U_1863,U_1864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),U_1864))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),U_1863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1862),U_1863),U_1864)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1862) ),
    inference(definitional_conversion,[status(esa)],[f_484_2]) ).

cnf(f_484_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),U_1864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),U_1863))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1862),c_Groups_Ozero__class_Ozero(U_1862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1862),U_1863),U_1864)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1862) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).

fof(f_485_2,plain,
    ! [U_1867,U_1866,U_1865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1865),U_1867),U_1866)),c_Groups_Ozero__class_Ozero(U_1865)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),U_1867),c_Groups_Ozero__class_Ozero(U_1865)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),c_Groups_Ozero__class_Ozero(U_1865)),U_1866))
      | ~ class_Rings_Olinordered__semiring__strict(U_1865) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1865,U_1866,U_1867] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1865),U_1867),U_1866)),c_Groups_Ozero__class_Ozero(U_1865)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),U_1867),c_Groups_Ozero__class_Ozero(U_1865)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),c_Groups_Ozero__class_Ozero(U_1865)),U_1866))
      | ~ class_Rings_Olinordered__semiring__strict(U_1865) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1865),U_1867),U_1866)),c_Groups_Ozero__class_Ozero(U_1865)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),U_1867),c_Groups_Ozero__class_Ozero(U_1865)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1865),c_Groups_Ozero__class_Ozero(U_1865)),U_1866))
    | ~ class_Rings_Olinordered__semiring__strict(U_1865) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).

fof(f_486_2,plain,
    ! [U_1870,U_1869,U_1868] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1868),U_1869),U_1870)),c_Groups_Ozero__class_Ozero(U_1868)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),U_1870),c_Groups_Ozero__class_Ozero(U_1868)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),c_Groups_Ozero__class_Ozero(U_1868)),U_1869))
      | ~ class_Rings_Olinordered__semiring__strict(U_1868) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1868,U_1869,U_1870] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1868),U_1869),U_1870)),c_Groups_Ozero__class_Ozero(U_1868)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),U_1870),c_Groups_Ozero__class_Ozero(U_1868)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),c_Groups_Ozero__class_Ozero(U_1868)),U_1869))
      | ~ class_Rings_Olinordered__semiring__strict(U_1868) ),
    inference(definitional_conversion,[status(esa)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1868),U_1869),U_1870)),c_Groups_Ozero__class_Ozero(U_1868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),U_1870),c_Groups_Ozero__class_Ozero(U_1868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1868),c_Groups_Ozero__class_Ozero(U_1868)),U_1869))
    | ~ class_Rings_Olinordered__semiring__strict(U_1868) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

fof(f_487_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).

fof(f_487_2,plain,
    ! [U_1873,U_1872,U_1871] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1872),U_1873)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),U_1873))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),U_1872))
      | ~ class_Rings_Olinordered__semiring__strict(U_1871) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1872,U_1871,U_1873] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1872),U_1873)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),U_1873))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),U_1872))
      | ~ class_Rings_Olinordered__semiring__strict(U_1871) ),
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1872),U_1873)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),U_1873))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1871),c_Groups_Ozero__class_Ozero(U_1871)),U_1872))
    | ~ class_Rings_Olinordered__semiring__strict(U_1871) ),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).

fof(f_488_2,plain,
    ! [U_1877,U_1876,U_1875,U_1874] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1877)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),U_1876),U_1877)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),U_1876),U_1877))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1877))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),c_Groups_Ozero__class_Ozero(U_1874)),U_1875))
      | ~ class_Rings_Olinordered__ring__strict(U_1874) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ( ! [U_1875,U_1874,U_1876,U_1877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1877)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),U_1876),U_1877))
        | ~ sP125(U_1875,U_1874,U_1876,U_1877) )
    & ! [U_1875,U_1874,U_1876,U_1877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),U_1876),U_1877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1877)))
        | ~ sP125(U_1875,U_1874,U_1876,U_1877) )
    & ! [U_1875,U_1874,U_1876,U_1877] :
        ( sP125(U_1875,U_1874,U_1876,U_1877)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),c_Groups_Ozero__class_Ozero(U_1874)),U_1875))
        | ~ class_Rings_Olinordered__ring__strict(U_1874) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_488_2]) ).

cnf(f_488_4,plain,
    ( sP125(U_1875,U_1874,U_1876,U_1877)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),c_Groups_Ozero__class_Ozero(U_1874)),U_1875))
    | ~ class_Rings_Olinordered__ring__strict(U_1874) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

cnf(f_488_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),U_1876),U_1877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1877)))
    | ~ sP125(U_1875,U_1874,U_1876,U_1877) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

cnf(f_488_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1874),U_1875),U_1877)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1874),U_1876),U_1877))
    | ~ sP125(U_1875,U_1874,U_1876,U_1877) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).

fof(f_489_2,plain,
    ! [U_1881,U_1880,U_1879,U_1878] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1881)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1881),U_1880))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),c_Groups_Ozero__class_Ozero(U_1878))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1880),U_1881))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),c_Groups_Ozero__class_Ozero(U_1878)),U_1879)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1881),U_1880))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),c_Groups_Ozero__class_Ozero(U_1878))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1880),U_1881))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),c_Groups_Ozero__class_Ozero(U_1878)),U_1879)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1881))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1878) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ( ! [U_1879,U_1878,U_1880,U_1881] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1881),U_1880))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),c_Groups_Ozero__class_Ozero(U_1878)))
        | ~ sP128(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1880),U_1881))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),c_Groups_Ozero__class_Ozero(U_1878)),U_1879))
        | ~ sP128(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1881),U_1880))
        | ~ sP127(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),c_Groups_Ozero__class_Ozero(U_1878)))
        | ~ sP127(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1880),U_1881))
        | ~ sP126(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),c_Groups_Ozero__class_Ozero(U_1878)),U_1879))
        | ~ sP126(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1881)))
        | sP128(U_1879,U_1878,U_1880,U_1881)
        | ~ sP129(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( sP127(U_1879,U_1878,U_1880,U_1881)
        | sP126(U_1879,U_1878,U_1880,U_1881)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1881)))
        | ~ sP129(U_1879,U_1878,U_1880,U_1881) )
    & ! [U_1879,U_1878,U_1880,U_1881] :
        ( sP129(U_1879,U_1878,U_1880,U_1881)
        | ~ class_Rings_Olinordered__ring__strict(U_1878) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126,sP127,sP128,sP129])],[f_489_2]) ).

cnf(f_489_4,plain,
    ( sP129(U_1879,U_1878,U_1880,U_1881)
    | ~ class_Rings_Olinordered__ring__strict(U_1878) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_5,plain,
    ( sP127(U_1879,U_1878,U_1880,U_1881)
    | sP126(U_1879,U_1878,U_1880,U_1881)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1881)))
    | ~ sP129(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1881)))
    | sP128(U_1879,U_1878,U_1880,U_1881)
    | ~ sP129(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),c_Groups_Ozero__class_Ozero(U_1878)),U_1879))
    | ~ sP126(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1880),U_1881))
    | ~ sP126(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),c_Groups_Ozero__class_Ozero(U_1878)))
    | ~ sP127(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1881),U_1880))
    | ~ sP127(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1880),U_1881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),c_Groups_Ozero__class_Ozero(U_1878)),U_1879))
    | ~ sP128(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1881),U_1880))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),U_1879),c_Groups_Ozero__class_Ozero(U_1878)))
    | ~ sP128(U_1879,U_1878,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

fof(f_490_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).

fof(f_490_2,plain,
    ! [U_1885,U_1884,U_1883,U_1882] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1883),U_1884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1885),U_1884)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1885),U_1883))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1884),c_Groups_Ozero__class_Ozero(U_1882))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1883),U_1885))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),c_Groups_Ozero__class_Ozero(U_1882)),U_1884)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1885),U_1883))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1884),c_Groups_Ozero__class_Ozero(U_1882))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1883),U_1885))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),c_Groups_Ozero__class_Ozero(U_1882)),U_1884)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1883),U_1884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1885),U_1884))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1882) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ( ! [U_1884,U_1885,U_1882,U_1883] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1885),U_1883))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1884),c_Groups_Ozero__class_Ozero(U_1882)))
        | ~ sP132(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1883),U_1885))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),c_Groups_Ozero__class_Ozero(U_1882)),U_1884))
        | ~ sP132(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1885),U_1883))
        | ~ sP131(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1884),c_Groups_Ozero__class_Ozero(U_1882)))
        | ~ sP131(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1883),U_1885))
        | ~ sP130(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),c_Groups_Ozero__class_Ozero(U_1882)),U_1884))
        | ~ sP130(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1883),U_1884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1885),U_1884)))
        | sP132(U_1884,U_1885,U_1882,U_1883)
        | ~ sP133(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( sP131(U_1884,U_1885,U_1882,U_1883)
        | sP130(U_1884,U_1885,U_1882,U_1883)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1883),U_1884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1885),U_1884)))
        | ~ sP133(U_1884,U_1885,U_1882,U_1883) )
    & ! [U_1884,U_1885,U_1882,U_1883] :
        ( sP133(U_1884,U_1885,U_1882,U_1883)
        | ~ class_Rings_Olinordered__ring__strict(U_1882) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130,sP131,sP132,sP133])],[f_490_2]) ).

cnf(f_490_4,plain,
    ( sP133(U_1884,U_1885,U_1882,U_1883)
    | ~ class_Rings_Olinordered__ring__strict(U_1882) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_5,plain,
    ( sP131(U_1884,U_1885,U_1882,U_1883)
    | sP130(U_1884,U_1885,U_1882,U_1883)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1883),U_1884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1885),U_1884)))
    | ~ sP133(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1883),U_1884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1882),U_1885),U_1884)))
    | sP132(U_1884,U_1885,U_1882,U_1883)
    | ~ sP133(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),c_Groups_Ozero__class_Ozero(U_1882)),U_1884))
    | ~ sP130(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1883),U_1885))
    | ~ sP130(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1884),c_Groups_Ozero__class_Ozero(U_1882)))
    | ~ sP131(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1885),U_1883))
    | ~ sP131(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1883),U_1885))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),c_Groups_Ozero__class_Ozero(U_1882)),U_1884))
    | ~ sP132(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1885),U_1883))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1882),U_1884),c_Groups_Ozero__class_Ozero(U_1882)))
    | ~ sP132(U_1884,U_1885,U_1882,U_1883) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

fof(f_491_1,plain,
    ! [V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).

fof(f_491_2,plain,
    ! [U_1887,U_1886] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1886),U_1887),U_1887)),c_Groups_Ozero__class_Ozero(U_1886)))
      | ~ class_Rings_Olinordered__ring(U_1886) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ! [U_1886,U_1887] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1886),U_1887),U_1887)),c_Groups_Ozero__class_Ozero(U_1886)))
      | ~ class_Rings_Olinordered__ring(U_1886) ),
    inference(definitional_conversion,[status(esa)],[f_491_2]) ).

cnf(f_491_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1886),U_1887),U_1887)),c_Groups_Ozero__class_Ozero(U_1886)))
    | ~ class_Rings_Olinordered__ring(U_1886) ),
    inference(clausify,[status(thm)],[f_491_3]) ).

fof(f_492_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).

fof(f_492_2,plain,
    ! [U_1888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),c_Groups_Ozero__class_Ozero(U_1888)),c_Groups_Oone__class_Oone(U_1888)))
      | ~ class_Rings_Olinordered__semidom(U_1888) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ! [U_1888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),c_Groups_Ozero__class_Ozero(U_1888)),c_Groups_Oone__class_Oone(U_1888)))
      | ~ class_Rings_Olinordered__semidom(U_1888) ),
    inference(definitional_conversion,[status(esa)],[f_492_2]) ).

cnf(f_492_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1888),c_Groups_Ozero__class_Ozero(U_1888)),c_Groups_Oone__class_Oone(U_1888)))
    | ~ class_Rings_Olinordered__semidom(U_1888) ),
    inference(clausify,[status(thm)],[f_492_3]) ).

fof(f_493_1,plain,
    ! [T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).

fof(f_493_2,plain,
    ! [U_1889] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1889),c_Groups_Oone__class_Oone(U_1889)),c_Groups_Ozero__class_Ozero(U_1889)))
      | ~ class_Rings_Olinordered__semidom(U_1889) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ! [U_1889] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1889),c_Groups_Oone__class_Oone(U_1889)),c_Groups_Ozero__class_Ozero(U_1889)))
      | ~ class_Rings_Olinordered__semidom(U_1889) ),
    inference(definitional_conversion,[status(esa)],[f_493_2]) ).

cnf(f_493_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1889),c_Groups_Oone__class_Oone(U_1889)),c_Groups_Ozero__class_Ozero(U_1889)))
    | ~ class_Rings_Olinordered__semidom(U_1889) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

fof(f_494_1,plain,
    ! [V_d,V_c,V_b,V_a,V_r,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))
      | V_c = V_d
      | V_a != V_b
      | V_r = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).

fof(f_494_2,plain,
    ! [U_1895,U_1894,U_1893,U_1892,U_1891,U_1890] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1890),U_1892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1894)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1890),U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1895))
      | U_1894 = U_1895
      | U_1892 != U_1893
      | U_1891 = c_Groups_Ozero__class_Ozero(U_1890)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1890) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ! [U_1890,U_1891,U_1892,U_1893,U_1894,U_1895] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1890),U_1892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1894)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1890),U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1895))
      | U_1894 = U_1895
      | U_1892 != U_1893
      | U_1891 = c_Groups_Ozero__class_Ozero(U_1890)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1890) ),
    inference(definitional_conversion,[status(esa)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1890),U_1892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1894)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1890),U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1895))
    | U_1894 = U_1895
    | U_1892 != U_1893
    | U_1891 = c_Groups_Ozero__class_Ozero(U_1890)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1890) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

fof(f_495_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).

fof(f_495_2,plain,
    ! [U_1898,U_1897,U_1896] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1898)) = c_Groups_Ozero__class_Ozero(U_1896)
          | U_1898 != c_Groups_Ozero__class_Ozero(U_1896)
          | U_1897 != c_Groups_Ozero__class_Ozero(U_1896) )
        & ( ( U_1898 = c_Groups_Ozero__class_Ozero(U_1896)
            & U_1897 = c_Groups_Ozero__class_Ozero(U_1896) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1898)) != c_Groups_Ozero__class_Ozero(U_1896) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1896) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ( ! [U_1896,U_1897,U_1898] :
        ( U_1898 = c_Groups_Ozero__class_Ozero(U_1896)
        | ~ sP134(U_1896,U_1897,U_1898) )
    & ! [U_1896,U_1897,U_1898] :
        ( U_1897 = c_Groups_Ozero__class_Ozero(U_1896)
        | ~ sP134(U_1896,U_1897,U_1898) )
    & ! [U_1896,U_1897,U_1898] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1898)) = c_Groups_Ozero__class_Ozero(U_1896)
        | U_1898 != c_Groups_Ozero__class_Ozero(U_1896)
        | U_1897 != c_Groups_Ozero__class_Ozero(U_1896)
        | ~ sP135(U_1896,U_1897,U_1898) )
    & ! [U_1896,U_1897,U_1898] :
        ( sP134(U_1896,U_1897,U_1898)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1898)) != c_Groups_Ozero__class_Ozero(U_1896)
        | ~ sP135(U_1896,U_1897,U_1898) )
    & ! [U_1896,U_1897,U_1898] :
        ( sP135(U_1896,U_1897,U_1898)
        | ~ class_Rings_Olinordered__ring__strict(U_1896) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134,sP135])],[f_495_2]) ).

cnf(f_495_4,plain,
    ( sP135(U_1896,U_1897,U_1898)
    | ~ class_Rings_Olinordered__ring__strict(U_1896) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_5,plain,
    ( sP134(U_1896,U_1897,U_1898)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1898)) != c_Groups_Ozero__class_Ozero(U_1896)
    | ~ sP135(U_1896,U_1897,U_1898) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1898)) = c_Groups_Ozero__class_Ozero(U_1896)
    | U_1898 != c_Groups_Ozero__class_Ozero(U_1896)
    | U_1897 != c_Groups_Ozero__class_Ozero(U_1896)
    | ~ sP135(U_1896,U_1897,U_1898) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_7,plain,
    ( U_1897 = c_Groups_Ozero__class_Ozero(U_1896)
    | ~ sP134(U_1896,U_1897,U_1898) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_8,plain,
    ( U_1898 = c_Groups_Ozero__class_Ozero(U_1896)
    | ~ sP134(U_1896,U_1897,U_1898) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).

fof(f_496_2,plain,
    ! [U_1900,U_1899] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1899),U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),U_1900),c_Groups_Oone__class_Oone(U_1899))))
      | ~ class_Rings_Olinordered__semidom(U_1899) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ! [U_1899,U_1900] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1899),U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),U_1900),c_Groups_Oone__class_Oone(U_1899))))
      | ~ class_Rings_Olinordered__semidom(U_1899) ),
    inference(definitional_conversion,[status(esa)],[f_496_2]) ).

cnf(f_496_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1899),U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),U_1900),c_Groups_Oone__class_Oone(U_1899))))
    | ~ class_Rings_Olinordered__semidom(U_1899) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(f_497_2,plain,
    ! [U_1901] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1901)),U_1901) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ! [U_1901] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1901)),U_1901) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_497_2]) ).

cnf(f_497_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1901)),U_1901) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_negative__eq__positive]) ).

fof(f_498_2,plain,
    ! [U_1903,U_1902] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1902)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1903)
        | U_1903 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1902 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_1903 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1902)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1903) ) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ( ! [U_1907,U_1905] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1905)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1907)
        | U_1907 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1905 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1906,U_1904] :
        ( ( U_1906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1904)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1906) ) ),
    inference(miniscope,[status(thm)],[f_498_2]) ).

fof(f_498_4,plain,
    ( ! [U_1904,U_1906] :
        ( U_1906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP136(U_1904,U_1906) )
    & ! [U_1904,U_1906] :
        ( U_1904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP136(U_1904,U_1906) )
    & ! [U_1907,U_1905] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1905)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1907)
        | U_1907 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1905 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1904,U_1906] :
        ( sP136(U_1904,U_1906)
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1904)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_498_3]) ).

cnf(f_498_5,plain,
    ( sP136(U_1904,U_1906)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1904)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1906) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1905)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1907)
    | U_1907 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1905 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_7,plain,
    ( U_1904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP136(U_1904,U_1906) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_8,plain,
    ( U_1906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP136(U_1904,U_1906) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

fof(f_499_1,plain,
    ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))),
    inference(fof_nnf,[status(thm)],[fact_not__int__zless__negative]) ).

fof(f_499_2,plain,
    ! [U_1909,U_1908] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1908)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1909)))),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ! [U_1908,U_1909] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1908)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1909)))),
    inference(definitional_conversion,[status(esa)],[f_499_2]) ).

cnf(f_499_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1908)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1909)))),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).

fof(f_500_2,plain,
    ! [U_1912,U_1911,U_1910] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1912),U_1910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1912),U_1911)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1910),U_1911)) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1912,U_1910,U_1911] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1912),U_1910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1912),U_1911)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1910),U_1911)) ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1912),U_1910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1912),U_1911)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1912))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1910),U_1911)) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).

fof(f_501_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_501_1]) ).

cnf(f_501_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_501_2]) ).

fof(f_502_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).

fof(f_502_2,plain,
    ! [U_1913] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1913)),U_1913) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ! [U_1913] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1913)),U_1913) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_502_2]) ).

cnf(f_502_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1913)),U_1913) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( V_w_2 != V_z_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) )
      & ( V_w_2 = V_z_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).

fof(f_503_2,plain,
    ! [U_1915,U_1914] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1915),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_1914 != U_1915
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1914),U_1915)) ) )
      & ( U_1914 = U_1915
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1914),U_1915))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1915),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ( ! [U_1919,U_1917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1919),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_1917 != U_1919
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1917),U_1919)) ) )
    & ! [U_1918,U_1916] :
        ( U_1916 = U_1918
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1916),U_1918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1918),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_503_2]) ).

fof(f_503_4,plain,
    ( ! [U_1919,U_1917] :
        ( U_1917 != U_1919
        | ~ sP137(U_1919,U_1917) )
    & ! [U_1919,U_1917] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1917),U_1919))
        | ~ sP137(U_1919,U_1917) )
    & ! [U_1919,U_1917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1919),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | sP137(U_1919,U_1917) )
    & ! [U_1918,U_1916] :
        ( U_1916 = U_1918
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1916),U_1918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1918),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_503_3]) ).

cnf(f_503_5,plain,
    ( U_1916 = U_1918
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1916),U_1918))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1918),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

cnf(f_503_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1919),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | sP137(U_1919,U_1917) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

cnf(f_503_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1917),U_1919))
    | ~ sP137(U_1919,U_1917) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

cnf(f_503_8,plain,
    ( U_1917 != U_1919
    | ~ sP137(U_1919,U_1917) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

fof(f_504_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0]) ).

fof(f_504_2,plain,
    ! [U_1920] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1920),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_1920)
      | ~ class_Rings_Oring__1(U_1920) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ! [U_1920] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1920),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_1920)
      | ~ class_Rings_Oring__1(U_1920) ),
    inference(definitional_conversion,[status(esa)],[f_504_2]) ).

cnf(f_504_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1920),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_1920)
    | ~ class_Rings_Oring__1(U_1920) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
          | V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff]) ).

fof(f_505_2,plain,
    ! [U_1922,U_1921] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1921) = hAPP(c_Int_Oring__1__class_Oof__int(U_1921),U_1922)
          | U_1922 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_1922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(U_1921) != hAPP(c_Int_Oring__1__class_Oof__int(U_1921),U_1922) ) )
      | ~ class_Int_Oring__char__0(U_1921) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1922,U_1921] :
        ( c_Groups_Ozero__class_Ozero(U_1921) = hAPP(c_Int_Oring__1__class_Oof__int(U_1921),U_1922)
        | U_1922 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP138(U_1922,U_1921) )
    & ! [U_1922,U_1921] :
        ( U_1922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(U_1921) != hAPP(c_Int_Oring__1__class_Oof__int(U_1921),U_1922)
        | ~ sP138(U_1922,U_1921) )
    & ! [U_1922,U_1921] :
        ( sP138(U_1922,U_1921)
        | ~ class_Int_Oring__char__0(U_1921) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_505_2]) ).

cnf(f_505_4,plain,
    ( sP138(U_1922,U_1921)
    | ~ class_Int_Oring__char__0(U_1921) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_5,plain,
    ( U_1922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(U_1921) != hAPP(c_Int_Oring__1__class_Oof__int(U_1921),U_1922)
    | ~ sP138(U_1922,U_1921) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1921) = hAPP(c_Int_Oring__1__class_Oof__int(U_1921),U_1922)
    | U_1922 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP138(U_1922,U_1921) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff]) ).

fof(f_506_2,plain,
    ! [U_1924,U_1923] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1923),U_1924) = c_Groups_Ozero__class_Ozero(U_1923)
          | U_1924 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_1924 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(U_1923),U_1924) != c_Groups_Ozero__class_Ozero(U_1923) ) )
      | ~ class_Int_Oring__char__0(U_1923) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_1924,U_1923] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1923),U_1924) = c_Groups_Ozero__class_Ozero(U_1923)
        | U_1924 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP139(U_1924,U_1923) )
    & ! [U_1924,U_1923] :
        ( U_1924 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(U_1923),U_1924) != c_Groups_Ozero__class_Ozero(U_1923)
        | ~ sP139(U_1924,U_1923) )
    & ! [U_1924,U_1923] :
        ( sP139(U_1924,U_1923)
        | ~ class_Int_Oring__char__0(U_1923) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_506_2]) ).

cnf(f_506_4,plain,
    ( sP139(U_1924,U_1923)
    | ~ class_Int_Oring__char__0(U_1923) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

cnf(f_506_5,plain,
    ( U_1924 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(U_1923),U_1924) != c_Groups_Ozero__class_Ozero(U_1923)
    | ~ sP139(U_1924,U_1923) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

cnf(f_506_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1923),U_1924) = c_Groups_Ozero__class_Ozero(U_1923)
    | U_1924 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP139(U_1924,U_1923) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__less__iff]) ).

fof(f_507_2,plain,
    ! [U_1927,U_1926,U_1925] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1926)),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1927)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1926),U_1927)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1926),U_1927))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1926)),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1927))) ) )
      | ~ class_Rings_Olinordered__idom(U_1925) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ( ! [U_1926,U_1927,U_1925] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1926)),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1927)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1926),U_1927))
        | ~ sP140(U_1926,U_1927,U_1925) )
    & ! [U_1926,U_1927,U_1925] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1926),U_1927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1926)),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1927)))
        | ~ sP140(U_1926,U_1927,U_1925) )
    & ! [U_1926,U_1927,U_1925] :
        ( sP140(U_1926,U_1927,U_1925)
        | ~ class_Rings_Olinordered__idom(U_1925) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_507_2]) ).

cnf(f_507_4,plain,
    ( sP140(U_1926,U_1927,U_1925)
    | ~ class_Rings_Olinordered__idom(U_1925) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1926),U_1927))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1926)),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1927)))
    | ~ sP140(U_1926,U_1927,U_1925) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1926)),hAPP(c_Int_Oring__1__class_Oof__int(U_1925),U_1927)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1926),U_1927))
    | ~ sP140(U_1926,U_1927,U_1925) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__add]) ).

fof(f_508_2,plain,
    ! [U_1930,U_1929,U_1928] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1929),U_1930)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1928),hAPP(c_Int_Oring__1__class_Oof__int(U_1928),U_1929)),hAPP(c_Int_Oring__1__class_Oof__int(U_1928),U_1930))
      | ~ class_Rings_Oring__1(U_1928) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1929,U_1928,U_1930] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1929),U_1930)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1928),hAPP(c_Int_Oring__1__class_Oof__int(U_1928),U_1929)),hAPP(c_Int_Oring__1__class_Oof__int(U_1928),U_1930))
      | ~ class_Rings_Oring__1(U_1928) ),
    inference(definitional_conversion,[status(esa)],[f_508_2]) ).

cnf(f_508_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1929),U_1930)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1928),hAPP(c_Int_Oring__1__class_Oof__int(U_1928),U_1929)),hAPP(c_Int_Oring__1__class_Oof__int(U_1928),U_1930))
    | ~ class_Rings_Oring__1(U_1928) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_1,plain,
    ! [V_n,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq]) ).

fof(f_509_2,plain,
    ! [U_1932,U_1931] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1931),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1932)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1931),U_1932)
      | ~ class_Rings_Oring__1(U_1931) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_1931,U_1932] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1931),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1932)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1931),U_1932)
      | ~ class_Rings_Oring__1(U_1931) ),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1931),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1932)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1931),U_1932)
    | ~ class_Rings_Oring__1(U_1931) ),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__nat__conj]) ).

fof(f_510_2,plain,
    ! [U_1934,U_1933] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1933)),hAPP(c_Int_Onat,U_1934)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1933),U_1934))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1934)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1933),U_1934))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1934)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1933)),hAPP(c_Int_Onat,U_1934))) ) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ( ! [U_1938,U_1936] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1936)),hAPP(c_Int_Onat,U_1938)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1936),U_1938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1938)) )
    & ! [U_1937,U_1935] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1935),U_1937))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1937)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1935)),hAPP(c_Int_Onat,U_1937))) ) ),
    inference(miniscope,[status(thm)],[f_510_2]) ).

fof(f_510_4,plain,
    ( ! [U_1937,U_1935] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1935),U_1937))
        | ~ sP141(U_1937,U_1935) )
    & ! [U_1937,U_1935] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1937))
        | ~ sP141(U_1937,U_1935) )
    & ! [U_1938,U_1936] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1936)),hAPP(c_Int_Onat,U_1938)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1936),U_1938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1938)) )
    & ! [U_1937,U_1935] :
        ( sP141(U_1937,U_1935)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1935)),hAPP(c_Int_Onat,U_1937))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_510_3]) ).

cnf(f_510_5,plain,
    ( sP141(U_1937,U_1935)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1935)),hAPP(c_Int_Onat,U_1937))) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1936)),hAPP(c_Int_Onat,U_1938)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1936),U_1938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1938)) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1937))
    | ~ sP141(U_1937,U_1935) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1935),U_1937))
    | ~ sP141(U_1937,U_1935) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

fof(f_511_1,plain,
    ! [V_w_2,V_z_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mono__iff]) ).

fof(f_511_2,plain,
    ! [U_1940,U_1939] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1940)),hAPP(c_Int_Onat,U_1939)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1940),U_1939)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1940),U_1939))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1940)),hAPP(c_Int_Onat,U_1939))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1939)) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ( ! [U_1940,U_1939] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1940)),hAPP(c_Int_Onat,U_1939)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1940),U_1939))
        | ~ sP142(U_1940,U_1939) )
    & ! [U_1940,U_1939] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1940),U_1939))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1940)),hAPP(c_Int_Onat,U_1939)))
        | ~ sP142(U_1940,U_1939) )
    & ! [U_1940,U_1939] :
        ( sP142(U_1940,U_1939)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1939)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142])],[f_511_2]) ).

cnf(f_511_4,plain,
    ( sP142(U_1940,U_1939)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1939)) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

cnf(f_511_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1940),U_1939))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1940)),hAPP(c_Int_Onat,U_1939)))
    | ~ sP142(U_1940,U_1939) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

cnf(f_511_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1940)),hAPP(c_Int_Onat,U_1939)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1940),U_1939))
    | ~ sP142(U_1940,U_1939) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

fof(f_512_1,plain,
    ! [V_z_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless]) ).

fof(f_512_2,plain,
    ! [U_1942,U_1941] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1941),hAPP(c_Int_Onat,U_1942)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1941)),U_1942)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1941)),U_1942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1941),hAPP(c_Int_Onat,U_1942))) ) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ( ! [U_1946,U_1944] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1944),hAPP(c_Int_Onat,U_1946)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1944)),U_1946)) )
    & ! [U_1945,U_1943] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1943)),U_1945))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),hAPP(c_Int_Onat,U_1945))) ) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

fof(f_512_4,plain,
    ( ! [U_1944,U_1946] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1944),hAPP(c_Int_Onat,U_1946)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1944)),U_1946)) )
    & ! [U_1943,U_1945] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1943)),U_1945))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),hAPP(c_Int_Onat,U_1945))) ) ),
    inference(definitional_conversion,[status(esa)],[f_512_3]) ).

cnf(f_512_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1943)),U_1945))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),hAPP(c_Int_Onat,U_1945))) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1944),hAPP(c_Int_Onat,U_1946)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1944)),U_1946)) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

fof(f_513_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(f_513_2,plain,
    ! [U_1949,U_1948,U_1947] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),U_1948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1949),U_1949))),c_Groups_Ozero__class_Ozero(U_1947)))
      | ~ class_Rings_Olinordered__ring(U_1947) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_1947,U_1948,U_1949] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),U_1948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1949),U_1949))),c_Groups_Ozero__class_Ozero(U_1947)))
      | ~ class_Rings_Olinordered__ring(U_1947) ),
    inference(definitional_conversion,[status(esa)],[f_513_2]) ).

cnf(f_513_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),U_1948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1949),U_1949))),c_Groups_Ozero__class_Ozero(U_1947)))
    | ~ class_Rings_Olinordered__ring(U_1947) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

fof(f_514_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
          | ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).

fof(f_514_2,plain,
    ! [U_1952,U_1951,U_1950] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),c_Groups_Ozero__class_Ozero(U_1950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1951),U_1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1952),U_1952))))
          | ( U_1952 = c_Groups_Ozero__class_Ozero(U_1950)
            & U_1951 = c_Groups_Ozero__class_Ozero(U_1950) ) )
        & ( U_1952 != c_Groups_Ozero__class_Ozero(U_1950)
          | U_1951 != c_Groups_Ozero__class_Ozero(U_1950)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),c_Groups_Ozero__class_Ozero(U_1950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1951),U_1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1952),U_1952)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1950) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ( ! [U_1951,U_1952,U_1950] :
        ( U_1952 = c_Groups_Ozero__class_Ozero(U_1950)
        | ~ sP143(U_1951,U_1952,U_1950) )
    & ! [U_1951,U_1952,U_1950] :
        ( U_1951 = c_Groups_Ozero__class_Ozero(U_1950)
        | ~ sP143(U_1951,U_1952,U_1950) )
    & ! [U_1951,U_1952,U_1950] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),c_Groups_Ozero__class_Ozero(U_1950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1951),U_1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1952),U_1952))))
        | sP143(U_1951,U_1952,U_1950)
        | ~ sP144(U_1951,U_1952,U_1950) )
    & ! [U_1951,U_1952,U_1950] :
        ( U_1952 != c_Groups_Ozero__class_Ozero(U_1950)
        | U_1951 != c_Groups_Ozero__class_Ozero(U_1950)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),c_Groups_Ozero__class_Ozero(U_1950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1951),U_1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1952),U_1952))))
        | ~ sP144(U_1951,U_1952,U_1950) )
    & ! [U_1951,U_1952,U_1950] :
        ( sP144(U_1951,U_1952,U_1950)
        | ~ class_Rings_Olinordered__ring__strict(U_1950) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143,sP144])],[f_514_2]) ).

cnf(f_514_4,plain,
    ( sP144(U_1951,U_1952,U_1950)
    | ~ class_Rings_Olinordered__ring__strict(U_1950) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_5,plain,
    ( U_1952 != c_Groups_Ozero__class_Ozero(U_1950)
    | U_1951 != c_Groups_Ozero__class_Ozero(U_1950)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),c_Groups_Ozero__class_Ozero(U_1950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1951),U_1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1952),U_1952))))
    | ~ sP144(U_1951,U_1952,U_1950) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),c_Groups_Ozero__class_Ozero(U_1950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1951),U_1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1952),U_1952))))
    | sP143(U_1951,U_1952,U_1950)
    | ~ sP144(U_1951,U_1952,U_1950) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_7,plain,
    ( U_1951 = c_Groups_Ozero__class_Ozero(U_1950)
    | ~ sP143(U_1951,U_1952,U_1950) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_8,plain,
    ( U_1952 = c_Groups_Ozero__class_Ozero(U_1950)
    | ~ sP143(U_1951,U_1952,U_1950) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).

fof(f_515_2,plain,
    ! [U_1953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),c_Groups_Ozero__class_Ozero(U_1953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),c_Groups_Oone__class_Oone(U_1953)),c_Groups_Oone__class_Oone(U_1953))))
      | ~ class_Rings_Olinordered__semidom(U_1953) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ! [U_1953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),c_Groups_Ozero__class_Ozero(U_1953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),c_Groups_Oone__class_Oone(U_1953)),c_Groups_Oone__class_Oone(U_1953))))
      | ~ class_Rings_Olinordered__semidom(U_1953) ),
    inference(definitional_conversion,[status(esa)],[f_515_2]) ).

cnf(f_515_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),c_Groups_Ozero__class_Ozero(U_1953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),c_Groups_Oone__class_Oone(U_1953)),c_Groups_Oone__class_Oone(U_1953))))
    | ~ class_Rings_Olinordered__semidom(U_1953) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_1,plain,
    ! [V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__Suc]) ).

fof(f_516_2,plain,
    ! [U_1955,U_1954] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1954),hAPP(c_Nat_OSuc,U_1955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1954),c_Groups_Oone__class_Oone(U_1954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1954),U_1955))
      | ~ class_Rings_Osemiring__1(U_1954) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_1954,U_1955] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1954),hAPP(c_Nat_OSuc,U_1955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1954),c_Groups_Oone__class_Oone(U_1954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1954),U_1955))
      | ~ class_Rings_Osemiring__1(U_1954) ),
    inference(definitional_conversion,[status(esa)],[f_516_2]) ).

cnf(f_516_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1954),hAPP(c_Nat_OSuc,U_1955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1954),c_Groups_Oone__class_Oone(U_1954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1954),U_1955))
    | ~ class_Rings_Osemiring__1(U_1954) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__Suc0__eq__1]) ).

fof(f_517_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_517_1]) ).

cnf(f_517_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_517_2]) ).

fof(f_518_1,plain,
    ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n),
    inference(fof_nnf,[status(thm)],[fact_nat__aux__def]) ).

fof(f_518_2,plain,
    ! [U_1957,U_1956] : c_Int_Onat__aux(U_1956,U_1957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_1956)),U_1957),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1956,U_1957] : c_Int_Onat__aux(U_1956,U_1957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_1956)),U_1957),
    inference(definitional_conversion,[status(esa)],[f_518_2]) ).

cnf(f_518_4,plain,
    c_Int_Onat__aux(U_1956,U_1957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_1956)),U_1957),
    inference(clausify,[status(thm)],[f_518_3]) ).

fof(f_519_1,plain,
    ! [V_x] :
      ( ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_negD]) ).

fof(f_519_2,plain,
    ! [U_1959] :
      ( ? [U_1958] : U_1959 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1958)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1959] :
      ( U_1959 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK39(U_1959))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1958,sK39(U_1959))],[f_519_2]) ).

fof(f_519_4,plain,
    ! [U_1959] :
      ( U_1959 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK39(U_1959))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_519_3]) ).

cnf(f_519_5,plain,
    ( U_1959 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK39(U_1959))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

fof(f_520_1,plain,
    ! [V_x,T_a] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) )
            & ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) ) )
          | V_x = c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)
          | V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Osgn__if(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__if]) ).

fof(f_520_2,plain,
    ! [U_1961,U_1960] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1960),c_Groups_Oone__class_Oone(U_1960))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1960),c_Groups_Ozero__class_Ozero(U_1960)),U_1961)) )
            & ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = c_Groups_Oone__class_Oone(U_1960)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1960),c_Groups_Ozero__class_Ozero(U_1960)),U_1961)) ) )
          | U_1961 = c_Groups_Ozero__class_Ozero(U_1960) )
        & ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = c_Groups_Ozero__class_Ozero(U_1960)
          | U_1961 != c_Groups_Ozero__class_Ozero(U_1960) ) )
      | ~ class_Groups_Osgn__if(U_1960) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ( ! [U_1960,U_1961] :
        ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1960),c_Groups_Oone__class_Oone(U_1960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1960),c_Groups_Ozero__class_Ozero(U_1960)),U_1961))
        | ~ sP145(U_1960,U_1961) )
    & ! [U_1960,U_1961] :
        ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = c_Groups_Oone__class_Oone(U_1960)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1960),c_Groups_Ozero__class_Ozero(U_1960)),U_1961))
        | ~ sP145(U_1960,U_1961) )
    & ! [U_1960,U_1961] :
        ( sP145(U_1960,U_1961)
        | U_1961 = c_Groups_Ozero__class_Ozero(U_1960)
        | ~ sP146(U_1960,U_1961) )
    & ! [U_1960,U_1961] :
        ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = c_Groups_Ozero__class_Ozero(U_1960)
        | U_1961 != c_Groups_Ozero__class_Ozero(U_1960)
        | ~ sP146(U_1960,U_1961) )
    & ! [U_1960,U_1961] :
        ( sP146(U_1960,U_1961)
        | ~ class_Groups_Osgn__if(U_1960) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145,sP146])],[f_520_2]) ).

cnf(f_520_4,plain,
    ( sP146(U_1960,U_1961)
    | ~ class_Groups_Osgn__if(U_1960) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_5,plain,
    ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = c_Groups_Ozero__class_Ozero(U_1960)
    | U_1961 != c_Groups_Ozero__class_Ozero(U_1960)
    | ~ sP146(U_1960,U_1961) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_6,plain,
    ( sP145(U_1960,U_1961)
    | U_1961 = c_Groups_Ozero__class_Ozero(U_1960)
    | ~ sP146(U_1960,U_1961) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_7,plain,
    ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = c_Groups_Oone__class_Oone(U_1960)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1960),c_Groups_Ozero__class_Ozero(U_1960)),U_1961))
    | ~ sP145(U_1960,U_1961) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_8,plain,
    ( c_Groups_Osgn__class_Osgn(U_1960,U_1961) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1960),c_Groups_Oone__class_Oone(U_1960))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1960),c_Groups_Ozero__class_Ozero(U_1960)),U_1961))
    | ~ sP145(U_1960,U_1961) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__neg]) ).

fof(f_521_2,plain,
    ! [U_1963,U_1962] :
      ( c_Groups_Osgn__class_Osgn(U_1962,U_1963) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),c_Groups_Oone__class_Oone(U_1962))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),U_1963),c_Groups_Ozero__class_Ozero(U_1962)))
      | ~ class_Rings_Olinordered__idom(U_1962) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1963,U_1962] :
      ( c_Groups_Osgn__class_Osgn(U_1962,U_1963) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),c_Groups_Oone__class_Oone(U_1962))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),U_1963),c_Groups_Ozero__class_Ozero(U_1962)))
      | ~ class_Rings_Olinordered__idom(U_1962) ),
    inference(definitional_conversion,[status(esa)],[f_521_2]) ).

cnf(f_521_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_1962,U_1963) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),c_Groups_Oone__class_Oone(U_1962))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),U_1963),c_Groups_Ozero__class_Ozero(U_1962)))
    | ~ class_Rings_Olinordered__idom(U_1962) ),
    inference(clausify,[status(thm)],[f_521_3]) ).

fof(f_522_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | c_Groups_Osgn__class_Osgn(T_b,V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).

fof(f_522_2,plain,
    ! [U_1965,U_1964] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_1964,U_1965) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1964),c_Groups_Oone__class_Oone(U_1964))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1964),U_1965),c_Groups_Ozero__class_Ozero(U_1964))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1964),U_1965),c_Groups_Ozero__class_Ozero(U_1964)))
          | c_Groups_Osgn__class_Osgn(U_1964,U_1965) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1964),c_Groups_Oone__class_Oone(U_1964)) ) )
      | ~ class_Rings_Olinordered__idom(U_1964) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ( ! [U_1964,U_1965] :
        ( c_Groups_Osgn__class_Osgn(U_1964,U_1965) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1964),c_Groups_Oone__class_Oone(U_1964))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1964),U_1965),c_Groups_Ozero__class_Ozero(U_1964)))
        | ~ sP147(U_1964,U_1965) )
    & ! [U_1964,U_1965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1964),U_1965),c_Groups_Ozero__class_Ozero(U_1964)))
        | c_Groups_Osgn__class_Osgn(U_1964,U_1965) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1964),c_Groups_Oone__class_Oone(U_1964))
        | ~ sP147(U_1964,U_1965) )
    & ! [U_1964,U_1965] :
        ( sP147(U_1964,U_1965)
        | ~ class_Rings_Olinordered__idom(U_1964) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_522_2]) ).

cnf(f_522_4,plain,
    ( sP147(U_1964,U_1965)
    | ~ class_Rings_Olinordered__idom(U_1964) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

cnf(f_522_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1964),U_1965),c_Groups_Ozero__class_Ozero(U_1964)))
    | c_Groups_Osgn__class_Osgn(U_1964,U_1965) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1964),c_Groups_Oone__class_Oone(U_1964))
    | ~ sP147(U_1964,U_1965) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

cnf(f_522_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_1964,U_1965) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1964),c_Groups_Oone__class_Oone(U_1964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1964),U_1965),c_Groups_Ozero__class_Ozero(U_1964)))
    | ~ sP147(U_1964,U_1965) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_1,plain,
    ! [V_i] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) ) )
        | V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zsgn__def]) ).

fof(f_523_2,plain,
    ! [U_1966] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1966) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1966)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1966) = c_Groups_Oone__class_Oone(tc_Int_Oint)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1966)) ) )
        | U_1966 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1966) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1966 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ( ! [U_1968] :
        ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1968) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1968)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1968) = c_Groups_Oone__class_Oone(tc_Int_Oint)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1968)) ) )
        | U_1968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_1967] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1967) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1967 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_523_2]) ).

fof(f_523_4,plain,
    ( ! [U_1968] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1968) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1968))
        | ~ sP148(U_1968) )
    & ! [U_1968] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1968) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1968))
        | ~ sP148(U_1968) )
    & ! [U_1968] :
        ( sP148(U_1968)
        | U_1968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_1967] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1967) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1967 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148])],[f_523_3]) ).

cnf(f_523_5,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1967) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_1967 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

cnf(f_523_6,plain,
    ( sP148(U_1968)
    | U_1968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

cnf(f_523_7,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1968) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1968))
    | ~ sP148(U_1968) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

cnf(f_523_8,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1968) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1968))
    | ~ sP148(U_1968) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

fof(f_524_1,plain,
    ! [V_z] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1]) ).

fof(f_524_2,plain,
    ! [U_1969] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_1969)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1969)) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_1969] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_1969)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1969)) ),
    inference(definitional_conversion,[status(esa)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_1969)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1969))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1969)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_1,plain,
    ! [V_m_2,V_w_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__iff]) ).

fof(f_525_2,plain,
    ! [U_1971,U_1970] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1970)),U_1971))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1970),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1971))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1970),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1971)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1970)),U_1971)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1970)) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ( ! [U_1970,U_1971] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1970)),U_1971))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1970),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1971)))
        | ~ sP149(U_1970,U_1971) )
    & ! [U_1970,U_1971] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1970),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1971)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1970)),U_1971))
        | ~ sP149(U_1970,U_1971) )
    & ! [U_1970,U_1971] :
        ( sP149(U_1970,U_1971)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1970)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_525_2]) ).

cnf(f_525_4,plain,
    ( sP149(U_1970,U_1971)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1970)) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

cnf(f_525_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1970),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1971)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1970)),U_1971))
    | ~ sP149(U_1970,U_1971) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

cnf(f_525_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1970)),U_1971))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1970),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1971)))
    | ~ sP149(U_1970,U_1971) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_1,plain,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
      | ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).

fof(f_526_2,plain,
    ! [U_1977,U_1976,U_1975,U_1974,U_1973,U_1972] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1972),U_1976),U_1973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1972),U_1977),U_1975))),U_1974))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1972),U_1976),U_1977) != c_Groups_Oone__class_Oone(U_1972)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1972),c_Groups_Ozero__class_Ozero(U_1972)),U_1977))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1972),c_Groups_Ozero__class_Ozero(U_1972)),U_1976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),U_1975),U_1974))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),U_1973),U_1974))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_1972) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_1972,U_1973,U_1974,U_1975,U_1976,U_1977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1972),U_1976),U_1973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1972),U_1977),U_1975))),U_1974))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1972),U_1976),U_1977) != c_Groups_Oone__class_Oone(U_1972)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1972),c_Groups_Ozero__class_Ozero(U_1972)),U_1977))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1972),c_Groups_Ozero__class_Ozero(U_1972)),U_1976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),U_1975),U_1974))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),U_1973),U_1974))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_1972) ),
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1972),U_1976),U_1973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1972),U_1977),U_1975))),U_1974))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1972),U_1976),U_1977) != c_Groups_Oone__class_Oone(U_1972)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1972),c_Groups_Ozero__class_Ozero(U_1972)),U_1977))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1972),c_Groups_Ozero__class_Ozero(U_1972)),U_1976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),U_1975),U_1974))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1972),U_1973),U_1974))
    | ~ class_Rings_Olinordered__semiring__1__strict(U_1972) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__pos]) ).

fof(f_527_2,plain,
    ! [U_1979,U_1978] :
      ( c_Groups_Osgn__class_Osgn(U_1978,U_1979) = c_Groups_Oone__class_Oone(U_1978)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1978),c_Groups_Ozero__class_Ozero(U_1978)),U_1979))
      | ~ class_Rings_Olinordered__idom(U_1978) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_1979,U_1978] :
      ( c_Groups_Osgn__class_Osgn(U_1978,U_1979) = c_Groups_Oone__class_Oone(U_1978)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1978),c_Groups_Ozero__class_Ozero(U_1978)),U_1979))
      | ~ class_Rings_Olinordered__idom(U_1978) ),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_1978,U_1979) = c_Groups_Oone__class_Oone(U_1978)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1978),c_Groups_Ozero__class_Ozero(U_1978)),U_1979))
    | ~ class_Rings_Olinordered__idom(U_1978) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__refl]) ).

fof(f_528_2,plain,
    ! [U_1981,U_1980] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1980),U_1981),U_1981))
      | ~ class_Orderings_Opreorder(U_1980) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ! [U_1980,U_1981] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1980),U_1981),U_1981))
      | ~ class_Orderings_Opreorder(U_1980) ),
    inference(definitional_conversion,[status(esa)],[f_528_2]) ).

cnf(f_528_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1980),U_1981),U_1981))
    | ~ class_Orderings_Opreorder(U_1980) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_le0]) ).

fof(f_529_2,plain,
    ! [U_1982] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1982)),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_1982] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1982)),
    inference(definitional_conversion,[status(esa)],[f_529_2]) ).

cnf(f_529_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1982)),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    inference(fof_nnf,[status(thm)],[fact_negative__zle]) ).

fof(f_530_2,plain,
    ! [U_1984,U_1983] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1983))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1984))),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_1983,U_1984] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1983))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1984))),
    inference(definitional_conversion,[status(esa)],[f_530_2]) ).

cnf(f_530_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1983))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1984))),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).

fof(f_531_2,plain,
    ! [U_1988,U_1987,U_1986,U_1985] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1985),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1986),U_1988)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1987),U_1988))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1985),U_1986)) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_1985,U_1986,U_1987,U_1988] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1985),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1986),U_1988)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1987),U_1988))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1985),U_1986)) ),
    inference(definitional_conversion,[status(esa)],[f_531_2]) ).

cnf(f_531_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1985),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1986),U_1988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1987),U_1988))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1985),U_1986)) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).

fof(f_532_2,plain,
    ! [U_1991,U_1990,U_1989] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1991),U_1989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1991),U_1990)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1989),U_1990)) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_1989,U_1990,U_1991] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1991),U_1989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1991),U_1990)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1989),U_1990)) ),
    inference(definitional_conversion,[status(esa)],[f_532_2]) ).

cnf(f_532_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1991),U_1989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1991),U_1990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1989),U_1990)) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).

fof(f_533_2,plain,
    ! [U_1994,U_1993,U_1992] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1992),U_1994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1993),U_1994)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1992),U_1993)) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_1992,U_1993,U_1994] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1992),U_1994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1993),U_1994)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1992),U_1993)) ),
    inference(definitional_conversion,[status(esa)],[f_533_2]) ).

cnf(f_533_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1992),U_1994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1993),U_1994)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1992),U_1993)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__assoc]) ).

fof(f_534_2,plain,
    ! [U_1997,U_1996,U_1995] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1995),U_1996)),U_1997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1996),U_1997)),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_1995,U_1996,U_1997] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1995),U_1996)),U_1997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1996),U_1997)),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1995),U_1996)),U_1997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1996),U_1997)),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).

fof(f_535_2,plain,
    ! [U_1999,U_1998] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1998),U_1999) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1999 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1998 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_1999 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_1998 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1998),U_1999) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ( ! [U_2003,U_2001] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2001),U_2003) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2003 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2001 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2002,U_2000] :
        ( ( U_2002 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2000 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2000),U_2002) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_535_2]) ).

fof(f_535_4,plain,
    ( ! [U_2002,U_2000] :
        ( U_2002 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP150(U_2002,U_2000) )
    & ! [U_2002,U_2000] :
        ( U_2000 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP150(U_2002,U_2000) )
    & ! [U_2003,U_2001] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2001),U_2003) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2003 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2001 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2002,U_2000] :
        ( sP150(U_2002,U_2000)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2000),U_2002) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_535_3]) ).

cnf(f_535_5,plain,
    ( sP150(U_2002,U_2000)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2000),U_2002) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_535_4]) ).

cnf(f_535_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2001),U_2003) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2003 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2001 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_535_4]) ).

cnf(f_535_7,plain,
    ( U_2000 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP150(U_2002,U_2000) ),
    inference(clausify,[status(thm)],[f_535_4]) ).

cnf(f_535_8,plain,
    ( U_2002 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP150(U_2002,U_2000) ),
    inference(clausify,[status(thm)],[f_535_4]) ).

fof(f_536_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__commute]) ).

fof(f_536_2,plain,
    ! [U_2005,U_2004] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2004),U_2005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2005),U_2004),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ! [U_2005,U_2004] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2004),U_2005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2005),U_2004),
    inference(definitional_conversion,[status(esa)],[f_536_2]) ).

cnf(f_536_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2004),U_2005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2005),U_2004),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__mult__1__right]) ).

fof(f_537_2,plain,
    ! [U_2006] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2006),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2006,
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ! [U_2006] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2006),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2006,
    inference(definitional_conversion,[status(esa)],[f_537_2]) ).

cnf(f_537_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2006),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2006,
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
        | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).

fof(f_538_2,plain,
    ! [U_2008,U_2007] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2007),U_2008)
        | U_2008 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2007 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2008 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2007 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2007),U_2008) ) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ( ! [U_2012,U_2010] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2010),U_2012)
        | U_2012 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2010 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2011,U_2009] :
        ( ( U_2011 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2009 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2009),U_2011) ) ),
    inference(miniscope,[status(thm)],[f_538_2]) ).

fof(f_538_4,plain,
    ( ! [U_2011,U_2009] :
        ( U_2011 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP151(U_2011,U_2009) )
    & ! [U_2011,U_2009] :
        ( U_2009 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP151(U_2011,U_2009) )
    & ! [U_2012,U_2010] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2010),U_2012)
        | U_2012 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2010 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2011,U_2009] :
        ( sP151(U_2011,U_2009)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2009),U_2011) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_538_3]) ).

cnf(f_538_5,plain,
    ( sP151(U_2011,U_2009)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2009),U_2011) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

cnf(f_538_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2010),U_2012)
    | U_2012 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2010 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

cnf(f_538_7,plain,
    ( U_2009 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP151(U_2011,U_2009) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

cnf(f_538_8,plain,
    ( U_2011 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP151(U_2011,U_2009) ),
    inference(clausify,[status(thm)],[f_538_4]) ).

fof(f_539_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__mult__1]) ).

fof(f_539_2,plain,
    ! [U_2013] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2013) = U_2013,
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ! [U_2013] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2013) = U_2013,
    inference(definitional_conversion,[status(esa)],[f_539_2]) ).

cnf(f_539_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2013) = U_2013,
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_1,plain,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
    inference(fof_nnf,[status(thm)],[fact_le__cube]) ).

fof(f_540_2,plain,
    ! [U_2014] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2014),U_2014)))),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ! [U_2014] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2014),U_2014)))),
    inference(definitional_conversion,[status(esa)],[f_540_2]) ).

cnf(f_540_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2014),U_2014)))),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_1,plain,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
    inference(fof_nnf,[status(thm)],[fact_le__square]) ).

fof(f_541_2,plain,
    ! [U_2015] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2015),U_2015))),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ! [U_2015] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2015),U_2015))),
    inference(definitional_conversion,[status(esa)],[f_541_2]) ).

cnf(f_541_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2015),U_2015))),
    inference(clausify,[status(thm)],[f_541_3]) ).

fof(f_542_1,plain,
    ! [V_n,V_m] :
      ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | V_m != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10]) ).

fof(f_542_2,plain,
    ! [U_2017,U_2016] :
      ( U_2016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2017 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2016 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2016),U_2017) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_2016,U_2017] :
      ( U_2016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2017 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2016 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2016),U_2017) ),
    inference(definitional_conversion,[status(esa)],[f_542_2]) ).

cnf(f_542_4,plain,
    ( U_2016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2017 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2016 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2016),U_2017) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_1,plain,
    ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).

fof(f_543_2,plain,
    ! [U_2018] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2018),U_2018)),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_2018] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2018),U_2018)),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2018),U_2018)),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__sgn]) ).

fof(f_544_2,plain,
    ! [U_2020,U_2019] :
      ( c_Groups_Osgn__class_Osgn(U_2019,c_Groups_Osgn__class_Osgn(U_2019,U_2020)) = c_Groups_Osgn__class_Osgn(U_2019,U_2020)
      | ~ class_Rings_Olinordered__idom(U_2019) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_2019,U_2020] :
      ( c_Groups_Osgn__class_Osgn(U_2019,c_Groups_Osgn__class_Osgn(U_2019,U_2020)) = c_Groups_Osgn__class_Osgn(U_2019,U_2020)
      | ~ class_Rings_Olinordered__idom(U_2019) ),
    inference(definitional_conversion,[status(esa)],[f_544_2]) ).

cnf(f_544_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2019,c_Groups_Osgn__class_Osgn(U_2019,U_2020)) = c_Groups_Osgn__class_Osgn(U_2019,U_2020)
    | ~ class_Rings_Olinordered__idom(U_2019) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_1,plain,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
    inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).

fof(f_545_2,plain,
    ! [U_2022,U_2021] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2022),U_2021))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2021),U_2022)) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ! [U_2021,U_2022] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2022),U_2021))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2021),U_2022)) ),
    inference(definitional_conversion,[status(esa)],[f_545_2]) ).

cnf(f_545_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2022),U_2021))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2021),U_2022)) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).

fof(f_546_2,plain,
    ! [U_2025,U_2024,U_2023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2023),U_2025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2024),U_2025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2023),U_2024)) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ! [U_2023,U_2024,U_2025] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2023),U_2025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2024),U_2025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2023),U_2024)) ),
    inference(definitional_conversion,[status(esa)],[f_546_2]) ).

cnf(f_546_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2023),U_2025))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2024),U_2025))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2023),U_2024)) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [V_w,V_z] :
      ( V_z = V_w
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
    inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).

fof(f_547_2,plain,
    ! [U_2027,U_2026] :
      ( U_2026 = U_2027
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2027),U_2026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2026),U_2027)) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_2027,U_2026] :
      ( U_2026 = U_2027
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2027),U_2026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2026),U_2027)) ),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_4,plain,
    ( U_2026 = U_2027
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2027),U_2026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2026),U_2027)) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
          | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
        & ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).

fof(f_548_2,plain,
    ! [U_2033,U_2032,U_2031,U_2030] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033))
          | ? [U_2029] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,U_2029)),hAPP(U_2033,U_2029))) )
        & ( ! [U_2028] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,U_2028)),hAPP(U_2033,U_2028)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033)) ) )
      | ~ class_Orderings_Oord(U_2030) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ! [U_2033,U_2032,U_2031,U_2030] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,sK40(U_2033,U_2032,U_2031,U_2030))),hAPP(U_2033,sK40(U_2033,U_2032,U_2031,U_2030)))) )
        & ( ! [U_2028] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,U_2028)),hAPP(U_2033,U_2028)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033)) ) )
      | ~ class_Orderings_Oord(U_2030) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2029,sK40(U_2033,U_2032,U_2031,U_2030))],[f_548_2]) ).

fof(f_548_4,plain,
    ( ! [U_2033,U_2032,U_2028,U_2030,U_2031] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,sK40(U_2033,U_2032,U_2031,U_2030))),hAPP(U_2033,sK40(U_2033,U_2032,U_2031,U_2030))))
        | ~ sP152(U_2033,U_2032,U_2028,U_2030,U_2031) )
    & ! [U_2033,U_2032,U_2028,U_2030,U_2031] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,U_2028)),hAPP(U_2033,U_2028)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033))
        | ~ sP152(U_2033,U_2032,U_2028,U_2030,U_2031) )
    & ! [U_2033,U_2032,U_2028,U_2030,U_2031] :
        ( sP152(U_2033,U_2032,U_2028,U_2030,U_2031)
        | ~ class_Orderings_Oord(U_2030) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_548_3]) ).

cnf(f_548_5,plain,
    ( sP152(U_2033,U_2032,U_2028,U_2030,U_2031)
    | ~ class_Orderings_Oord(U_2030) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

cnf(f_548_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,U_2028)),hAPP(U_2033,U_2028)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033))
    | ~ sP152(U_2033,U_2032,U_2028,U_2030,U_2031) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

cnf(f_548_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2031,U_2030)),U_2032),U_2033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2030),hAPP(U_2032,sK40(U_2033,U_2032,U_2031,U_2030))),hAPP(U_2033,sK40(U_2033,U_2032,U_2031,U_2030))))
    | ~ sP152(U_2033,U_2032,U_2028,U_2030,U_2031) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

fof(f_549_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).

fof(f_549_2,plain,
    ! [U_2036,U_2035,U_2034] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2034),U_2036),U_2035))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2034),U_2035),U_2036))
      | ~ class_Orderings_Olinorder(U_2034) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ! [U_2034,U_2035,U_2036] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2034),U_2036),U_2035))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2034),U_2035),U_2036))
      | ~ class_Orderings_Olinorder(U_2034) ),
    inference(definitional_conversion,[status(esa)],[f_549_2]) ).

cnf(f_549_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2034),U_2036),U_2035))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2034),U_2035),U_2036))
    | ~ class_Orderings_Olinorder(U_2034) ),
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | V_x_2 != V_y_2 ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).

fof(f_550_2,plain,
    ! [U_2039,U_2038,U_2037] :
      ( ( ( U_2038 = U_2039
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2039),U_2038))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2038),U_2039)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2039),U_2038))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2038),U_2039)) )
          | U_2038 != U_2039 ) )
      | ~ class_Orderings_Oorder(U_2037) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ( ! [U_2037,U_2038,U_2039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2039),U_2038))
        | ~ sP153(U_2037,U_2038,U_2039) )
    & ! [U_2037,U_2038,U_2039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2038),U_2039))
        | ~ sP153(U_2037,U_2038,U_2039) )
    & ! [U_2037,U_2038,U_2039] :
        ( U_2038 = U_2039
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2039),U_2038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2038),U_2039))
        | ~ sP154(U_2037,U_2038,U_2039) )
    & ! [U_2037,U_2038,U_2039] :
        ( sP153(U_2037,U_2038,U_2039)
        | U_2038 != U_2039
        | ~ sP154(U_2037,U_2038,U_2039) )
    & ! [U_2037,U_2038,U_2039] :
        ( sP154(U_2037,U_2038,U_2039)
        | ~ class_Orderings_Oorder(U_2037) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153,sP154])],[f_550_2]) ).

cnf(f_550_4,plain,
    ( sP154(U_2037,U_2038,U_2039)
    | ~ class_Orderings_Oorder(U_2037) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_5,plain,
    ( sP153(U_2037,U_2038,U_2039)
    | U_2038 != U_2039
    | ~ sP154(U_2037,U_2038,U_2039) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_6,plain,
    ( U_2038 = U_2039
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2039),U_2038))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2038),U_2039))
    | ~ sP154(U_2037,U_2038,U_2039) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2038),U_2039))
    | ~ sP153(U_2037,U_2038,U_2039) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2037),U_2039),U_2038))
    | ~ sP153(U_2037,U_2038,U_2039) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | V_x != V_y
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).

fof(f_551_2,plain,
    ! [U_2042,U_2041,U_2040] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2040),U_2041),U_2042))
      | U_2041 != U_2042
      | ~ class_Orderings_Opreorder(U_2040) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_2040,U_2042,U_2041] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2040),U_2041),U_2042))
      | U_2041 != U_2042
      | ~ class_Orderings_Opreorder(U_2040) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2040),U_2041),U_2042))
    | U_2041 != U_2042
    | ~ class_Orderings_Opreorder(U_2040) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__funD]) ).

fof(f_552_2,plain,
    ! [U_2047,U_2046,U_2045,U_2044,U_2043] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2043),hAPP(U_2045,U_2047)),hAPP(U_2046,U_2047)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2044,U_2043)),U_2045),U_2046))
      | ~ class_Orderings_Oord(U_2043) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_2043,U_2044,U_2045,U_2046,U_2047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2043),hAPP(U_2045,U_2047)),hAPP(U_2046,U_2047)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2044,U_2043)),U_2045),U_2046))
      | ~ class_Orderings_Oord(U_2043) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2043),hAPP(U_2045,U_2047)),hAPP(U_2046,U_2047)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2044,U_2043)),U_2045),U_2046))
    | ~ class_Orderings_Oord(U_2043) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_1,plain,
    ! [V_x_2,V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).

fof(f_553_2,plain,
    ! [U_2050,U_2049,U_2048] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2050),U_2049))
          | U_2050 != U_2049 )
        & ( U_2050 = U_2049
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2050),U_2049)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2049),U_2050))
      | ~ class_Orderings_Oorder(U_2048) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ( ! [U_2048,U_2049,U_2050] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2050),U_2049))
        | U_2050 != U_2049
        | ~ sP155(U_2048,U_2049,U_2050) )
    & ! [U_2048,U_2049,U_2050] :
        ( U_2050 = U_2049
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2050),U_2049))
        | ~ sP155(U_2048,U_2049,U_2050) )
    & ! [U_2048,U_2049,U_2050] :
        ( sP155(U_2048,U_2049,U_2050)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2049),U_2050))
        | ~ class_Orderings_Oorder(U_2048) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_553_2]) ).

cnf(f_553_4,plain,
    ( sP155(U_2048,U_2049,U_2050)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2049),U_2050))
    | ~ class_Orderings_Oorder(U_2048) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

cnf(f_553_5,plain,
    ( U_2050 = U_2049
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2050),U_2049))
    | ~ sP155(U_2048,U_2049,U_2050) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

cnf(f_553_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2048),U_2050),U_2049))
    | U_2050 != U_2049
    | ~ sP155(U_2048,U_2049,U_2050) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
      | V_a != V_b
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).

fof(f_554_2,plain,
    ! [U_2054,U_2053,U_2052,U_2051] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2051),U_2052),U_2054))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2051),U_2053),U_2054))
      | U_2052 != U_2053
      | ~ class_Orderings_Oord(U_2051) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_2053,U_2054,U_2052,U_2051] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2051),U_2052),U_2054))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2051),U_2053),U_2054))
      | U_2052 != U_2053
      | ~ class_Orderings_Oord(U_2051) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2051),U_2052),U_2054))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2051),U_2053),U_2054))
    | U_2052 != U_2053
    | ~ class_Orderings_Oord(U_2051) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
      | V_a != V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).

fof(f_555_2,plain,
    ! [U_2058,U_2057,U_2056,U_2055] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2055),U_2058),U_2056))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2055),U_2058),U_2057))
      | U_2056 != U_2057
      | ~ class_Orderings_Oorder(U_2055) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_2056,U_2055,U_2057,U_2058] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2055),U_2058),U_2056))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2055),U_2058),U_2057))
      | U_2056 != U_2057
      | ~ class_Orderings_Oorder(U_2055) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2055),U_2058),U_2056))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2055),U_2058),U_2057))
    | U_2056 != U_2057
    | ~ class_Orderings_Oorder(U_2055) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).

fof(f_556_2,plain,
    ! [U_2062,U_2061,U_2060,U_2059] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2059),U_2060),U_2062))
      | U_2061 != U_2062
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2059),U_2060),U_2061))
      | ~ class_Orderings_Oord(U_2059) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ! [U_2062,U_2060,U_2061,U_2059] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2059),U_2060),U_2062))
      | U_2061 != U_2062
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2059),U_2060),U_2061))
      | ~ class_Orderings_Oord(U_2059) ),
    inference(definitional_conversion,[status(esa)],[f_556_2]) ).

cnf(f_556_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2059),U_2060),U_2062))
    | U_2061 != U_2062
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2059),U_2060),U_2061))
    | ~ class_Orderings_Oord(U_2059) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).

fof(f_557_2,plain,
    ! [U_2066,U_2065,U_2064,U_2063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2063),U_2066),U_2065))
      | U_2064 != U_2066
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2063),U_2064),U_2065))
      | ~ class_Orderings_Oorder(U_2063) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ! [U_2064,U_2065,U_2063,U_2066] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2063),U_2066),U_2065))
      | U_2064 != U_2066
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2063),U_2064),U_2065))
      | ~ class_Orderings_Oorder(U_2063) ),
    inference(definitional_conversion,[status(esa)],[f_557_2]) ).

cnf(f_557_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2063),U_2066),U_2065))
    | U_2064 != U_2066
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2063),U_2064),U_2065))
    | ~ class_Orderings_Oorder(U_2063) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

fof(f_558_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).

fof(f_558_2,plain,
    ! [U_2069,U_2068,U_2067] :
      ( U_2068 = U_2069
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2067),U_2069),U_2068))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2067),U_2068),U_2069))
      | ~ class_Orderings_Oorder(U_2067) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ! [U_2069,U_2067,U_2068] :
      ( U_2068 = U_2069
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2067),U_2069),U_2068))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2067),U_2068),U_2069))
      | ~ class_Orderings_Oorder(U_2067) ),
    inference(definitional_conversion,[status(esa)],[f_558_2]) ).

cnf(f_558_4,plain,
    ( U_2068 = U_2069
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2067),U_2069),U_2068))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2067),U_2068),U_2069))
    | ~ class_Orderings_Oorder(U_2067) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__trans]) ).

fof(f_559_2,plain,
    ! [U_2073,U_2072,U_2071,U_2070] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2071),U_2073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2072),U_2073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2071),U_2072))
      | ~ class_Orderings_Opreorder(U_2070) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_2071,U_2070,U_2072,U_2073] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2071),U_2073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2072),U_2073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2071),U_2072))
      | ~ class_Orderings_Opreorder(U_2070) ),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2071),U_2073))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2072),U_2073))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2070),U_2071),U_2072))
    | ~ class_Orderings_Opreorder(U_2070) ),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_1,plain,
    ! [V_x,V_y,T_a] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).

fof(f_560_2,plain,
    ! [U_2076,U_2075,U_2074] :
      ( U_2076 = U_2075
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2076),U_2075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2075),U_2076))
      | ~ class_Orderings_Oorder(U_2074) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ! [U_2076,U_2074,U_2075] :
      ( U_2076 = U_2075
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2076),U_2075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2075),U_2076))
      | ~ class_Orderings_Oorder(U_2074) ),
    inference(definitional_conversion,[status(esa)],[f_560_2]) ).

cnf(f_560_4,plain,
    ( U_2076 = U_2075
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2076),U_2075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2075),U_2076))
    | ~ class_Orderings_Oorder(U_2074) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).

fof(f_561_2,plain,
    ! [U_2080,U_2079,U_2078,U_2077] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2080),U_2079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2080),U_2078))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2078),U_2079))
      | ~ class_Orderings_Oorder(U_2077) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ! [U_2078,U_2077,U_2079,U_2080] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2080),U_2079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2080),U_2078))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2078),U_2079))
      | ~ class_Orderings_Oorder(U_2077) ),
    inference(definitional_conversion,[status(esa)],[f_561_2]) ).

cnf(f_561_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2080),U_2079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2080),U_2078))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2077),U_2078),U_2079))
    | ~ class_Orderings_Oorder(U_2077) ),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__funE]) ).

fof(f_562_2,plain,
    ! [U_2085,U_2084,U_2083,U_2082,U_2081] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2081),hAPP(U_2083,U_2085)),hAPP(U_2084,U_2085)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2082,U_2081)),U_2083),U_2084))
      | ~ class_Orderings_Oord(U_2081) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_2081,U_2082,U_2083,U_2084,U_2085] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2081),hAPP(U_2083,U_2085)),hAPP(U_2084,U_2085)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2082,U_2081)),U_2083),U_2084))
      | ~ class_Orderings_Oord(U_2081) ),
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2081),hAPP(U_2083,U_2085)),hAPP(U_2084,U_2085)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2082,U_2081)),U_2083),U_2084))
    | ~ class_Orderings_Oord(U_2081) ),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).

fof(f_563_2,plain,
    ! [U_2088,U_2087,U_2086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2086),U_2088),U_2087))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2086),U_2087),U_2088))
      | ~ class_Orderings_Olinorder(U_2086) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ! [U_2087,U_2086,U_2088] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2086),U_2088),U_2087))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2086),U_2087),U_2088))
      | ~ class_Orderings_Olinorder(U_2086) ),
    inference(definitional_conversion,[status(esa)],[f_563_2]) ).

cnf(f_563_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2086),U_2088),U_2087))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2086),U_2087),U_2088))
    | ~ class_Orderings_Olinorder(U_2086) ),
    inference(clausify,[status(thm)],[f_563_3]) ).

fof(f_564_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).

fof(f_564_2,plain,
    ! [U_2091,U_2090,U_2089] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2090)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2091)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2090),U_2091)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2090),U_2091))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2090)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2091))) ) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ( ! [U_2097,U_2095] :
        ( ! [U_2093] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2095),U_2097)) )
    & ! [U_2096,U_2094] :
        ( ! [U_2092] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2094)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2096)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ) ),
    inference(miniscope,[status(thm)],[f_564_2]) ).

fof(f_564_4,plain,
    ( ! [U_2097,U_2093,U_2095] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2095),U_2097)) )
    & ! [U_2092,U_2094,U_2096] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2094)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2096)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ) ),
    inference(definitional_conversion,[status(esa)],[f_564_3]) ).

cnf(f_564_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2094)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2096)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

cnf(f_564_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2095),U_2097)) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

fof(f_565_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).

fof(f_565_2,plain,
    ! [U_2100,U_2099,U_2098] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2099)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2100)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2099),U_2100)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2099),U_2100))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2099)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2100))) ) )
      | ~ class_Rings_Olinordered__semidom(U_2098) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ( ! [U_2098,U_2099,U_2100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2099)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2099),U_2100))
        | ~ sP156(U_2098,U_2099,U_2100) )
    & ! [U_2098,U_2099,U_2100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2099),U_2100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2099)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2100)))
        | ~ sP156(U_2098,U_2099,U_2100) )
    & ! [U_2098,U_2099,U_2100] :
        ( sP156(U_2098,U_2099,U_2100)
        | ~ class_Rings_Olinordered__semidom(U_2098) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_565_2]) ).

cnf(f_565_4,plain,
    ( sP156(U_2098,U_2099,U_2100)
    | ~ class_Rings_Olinordered__semidom(U_2098) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

cnf(f_565_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2099),U_2100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2099)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2100)))
    | ~ sP156(U_2098,U_2099,U_2100) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

cnf(f_565_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2099)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2098),U_2100)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2099),U_2100))
    | ~ sP156(U_2098,U_2099,U_2100) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__int]) ).

fof(f_566_2,plain,
    ! [U_2102,U_2101] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2102)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2101),U_2102)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2101),U_2102))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2102))) ) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ( ! [U_2106,U_2104] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2104)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2106)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2104),U_2106)) )
    & ! [U_2105,U_2103] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2103),U_2105))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2103)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2105))) ) ),
    inference(miniscope,[status(thm)],[f_566_2]) ).

fof(f_566_4,plain,
    ( ! [U_2104,U_2106] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2104)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2106)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2104),U_2106)) )
    & ! [U_2105,U_2103] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2103),U_2105))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2103)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2105))) ) ),
    inference(definitional_conversion,[status(esa)],[f_566_3]) ).

cnf(f_566_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2103),U_2105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2103)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2105))) ),
    inference(clausify,[status(thm)],[f_566_4]) ).

cnf(f_566_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2104)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2104),U_2106)) ),
    inference(clausify,[status(thm)],[f_566_4]) ).

fof(f_567_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J]) ).

fof(f_567_2,plain,
    ! [U_2108,U_2107] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2108)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2107),U_2108)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2107),U_2108))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2108))) ) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ( ! [U_2112,U_2110] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2112)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2110),U_2112)) )
    & ! [U_2111,U_2109] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2109),U_2111))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2109)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2111))) ) ),
    inference(miniscope,[status(thm)],[f_567_2]) ).

fof(f_567_4,plain,
    ( ! [U_2110,U_2112] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2112)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2110),U_2112)) )
    & ! [U_2109,U_2111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2109),U_2111))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2109)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2111))) ) ),
    inference(definitional_conversion,[status(esa)],[f_567_3]) ).

cnf(f_567_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2109),U_2111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2109)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2111))) ),
    inference(clausify,[status(thm)],[f_567_4]) ).

cnf(f_567_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2110),U_2112)) ),
    inference(clausify,[status(thm)],[f_567_4]) ).

fof(f_568_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__le__iff]) ).

fof(f_568_2,plain,
    ! [U_2115,U_2114,U_2113] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2113),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2114)),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2115)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2114),U_2115)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2114),U_2115))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2113),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2114)),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2115))) ) )
      | ~ class_Rings_Olinordered__idom(U_2113) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ( ! [U_2113,U_2114,U_2115] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2113),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2114)),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2115)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2114),U_2115))
        | ~ sP157(U_2113,U_2114,U_2115) )
    & ! [U_2113,U_2114,U_2115] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2114),U_2115))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2113),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2114)),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2115)))
        | ~ sP157(U_2113,U_2114,U_2115) )
    & ! [U_2113,U_2114,U_2115] :
        ( sP157(U_2113,U_2114,U_2115)
        | ~ class_Rings_Olinordered__idom(U_2113) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157])],[f_568_2]) ).

cnf(f_568_4,plain,
    ( sP157(U_2113,U_2114,U_2115)
    | ~ class_Rings_Olinordered__idom(U_2113) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

cnf(f_568_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2114),U_2115))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2113),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2114)),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2115)))
    | ~ sP157(U_2113,U_2114,U_2115) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

cnf(f_568_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2113),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2114)),hAPP(c_Int_Oring__1__class_Oof__int(U_2113),U_2115)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2114),U_2115))
    | ~ sP157(U_2113,U_2114,U_2115) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

fof(f_569_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).

fof(f_569_2,plain,
    ! [U_2117,U_2116] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2116),U_2117)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2117))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2116)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2117))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2116)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2116),U_2117))) ) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ( ! [U_2121,U_2119] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2119),U_2121)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2119)) )
    & ! [U_2120,U_2118] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2120))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2118)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2118),U_2120))) ) ),
    inference(miniscope,[status(thm)],[f_569_2]) ).

fof(f_569_4,plain,
    ( ! [U_2118,U_2120] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2120))
        | ~ sP158(U_2118,U_2120) )
    & ! [U_2118,U_2120] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2118))
        | ~ sP158(U_2118,U_2120) )
    & ! [U_2119,U_2121] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2119),U_2121)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2119)) )
    & ! [U_2118,U_2120] :
        ( sP158(U_2118,U_2120)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2118),U_2120))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158])],[f_569_3]) ).

cnf(f_569_5,plain,
    ( sP158(U_2118,U_2120)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2118),U_2120))) ),
    inference(clausify,[status(thm)],[f_569_4]) ).

cnf(f_569_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2119),U_2121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2121))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2119)) ),
    inference(clausify,[status(thm)],[f_569_4]) ).

cnf(f_569_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2118))
    | ~ sP158(U_2118,U_2120) ),
    inference(clausify,[status(thm)],[f_569_4]) ).

cnf(f_569_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2120))
    | ~ sP158(U_2118,U_2120) ),
    inference(clausify,[status(thm)],[f_569_4]) ).

fof(f_570_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).

fof(f_570_2,plain,
    ! [U_2124,U_2123,U_2122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2122),U_2123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2122),U_2124)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2123),U_2124))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2123),U_2124))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2122),U_2123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2122),U_2124))) ) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ( ! [U_2130,U_2128,U_2126] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2126),U_2128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2126),U_2130)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2128),U_2130))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2126)) ) )
    & ! [U_2129,U_2127,U_2125] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2127),U_2129))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2125))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2125),U_2127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2125),U_2129))) ) ),
    inference(miniscope,[status(thm)],[f_570_2]) ).

fof(f_570_4,plain,
    ( ! [U_2130,U_2126,U_2128] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2128),U_2130))
        | ~ sP159(U_2130,U_2126,U_2128) )
    & ! [U_2130,U_2126,U_2128] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2126))
        | ~ sP159(U_2130,U_2126,U_2128) )
    & ! [U_2130,U_2126,U_2128] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2126),U_2128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2126),U_2130)))
        | sP159(U_2130,U_2126,U_2128) )
    & ! [U_2125,U_2127,U_2129] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2127),U_2129))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2125))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2125),U_2127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2125),U_2129))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_570_3]) ).

cnf(f_570_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2127),U_2129))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2125),U_2127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2125),U_2129))) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2126),U_2128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2126),U_2130)))
    | sP159(U_2130,U_2126,U_2128) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2126))
    | ~ sP159(U_2130,U_2126,U_2128) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2128),U_2130))
    | ~ sP159(U_2130,U_2126,U_2128) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

fof(f_571_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).

fof(f_571_2,plain,
    ! [U_2133,U_2132,U_2131] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2131),U_2132)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2133),U_2132)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2131),U_2133))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2132)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2131),U_2133))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2132))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2131),U_2132)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2133),U_2132))) ) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ( ! [U_2139,U_2137,U_2135] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2135),U_2137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2139),U_2137)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2135),U_2139))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2137)) ) )
    & ! [U_2138,U_2136,U_2134] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2134),U_2138))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2136))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2134),U_2136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2138),U_2136))) ) ),
    inference(miniscope,[status(thm)],[f_571_2]) ).

fof(f_571_4,plain,
    ( ! [U_2139,U_2135,U_2137] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2135),U_2139))
        | ~ sP160(U_2139,U_2135,U_2137) )
    & ! [U_2139,U_2135,U_2137] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2137))
        | ~ sP160(U_2139,U_2135,U_2137) )
    & ! [U_2139,U_2135,U_2137] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2135),U_2137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2139),U_2137)))
        | sP160(U_2139,U_2135,U_2137) )
    & ! [U_2136,U_2134,U_2138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2134),U_2138))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2136))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2134),U_2136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2138),U_2136))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_571_3]) ).

cnf(f_571_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2134),U_2138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2136))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2134),U_2136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2138),U_2136))) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

cnf(f_571_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2135),U_2137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2139),U_2137)))
    | sP160(U_2139,U_2135,U_2137) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

cnf(f_571_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2137))
    | ~ sP160(U_2139,U_2135,U_2137) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

cnf(f_571_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2135),U_2139))
    | ~ sP160(U_2139,U_2135,U_2137) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

fof(f_572_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J]) ).

fof(f_572_2,plain,
    ! [U_2141,U_2140] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2140)),hAPP(c_Int_Onat,U_2141)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2140),U_2141)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2140),U_2141))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2140)),hAPP(c_Int_Onat,U_2141))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2141))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2140)) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ( ! [U_2141,U_2140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2140)),hAPP(c_Int_Onat,U_2141)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2140),U_2141))
        | ~ sP161(U_2141,U_2140) )
    & ! [U_2141,U_2140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2140),U_2141))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2140)),hAPP(c_Int_Onat,U_2141)))
        | ~ sP161(U_2141,U_2140) )
    & ! [U_2141,U_2140] :
        ( sP161(U_2141,U_2140)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2141))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2140)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_572_2]) ).

cnf(f_572_4,plain,
    ( sP161(U_2141,U_2140)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2141))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2140)) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

cnf(f_572_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2140),U_2141))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2140)),hAPP(c_Int_Onat,U_2141)))
    | ~ sP161(U_2141,U_2140) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

cnf(f_572_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2140)),hAPP(c_Int_Onat,U_2141)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2140),U_2141))
    | ~ sP161(U_2141,U_2140) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).

fof(f_573_2,plain,
    ! [U_2145,U_2144,U_2143,U_2142] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2142),U_2145),U_2144))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2142),U_2145),U_2143))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2142),U_2143),U_2144))
      | ~ class_Orderings_Oorder(U_2142) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_2144,U_2143,U_2145,U_2142] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2142),U_2145),U_2144))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2142),U_2145),U_2143))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2142),U_2143),U_2144))
      | ~ class_Orderings_Oorder(U_2142) ),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2142),U_2145),U_2144))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2142),U_2145),U_2143))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2142),U_2143),U_2144))
    | ~ class_Orderings_Oorder(U_2142) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).

fof(f_574_2,plain,
    ! [U_2149,U_2148,U_2147,U_2146] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2146),U_2147),U_2149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2146),U_2148),U_2149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),U_2147),U_2148))
      | ~ class_Orderings_Opreorder(U_2146) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_2146,U_2147,U_2148,U_2149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2146),U_2147),U_2149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2146),U_2148),U_2149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),U_2147),U_2148))
      | ~ class_Orderings_Opreorder(U_2146) ),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2146),U_2147),U_2149))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2146),U_2148),U_2149))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),U_2147),U_2148))
    | ~ class_Orderings_Opreorder(U_2146) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).

fof(f_575_2,plain,
    ! [U_2153,U_2152,U_2151,U_2150] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2150),U_2153),U_2152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2150),U_2153),U_2151))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2150),U_2151),U_2152))
      | ~ class_Orderings_Oorder(U_2150) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ! [U_2151,U_2150,U_2152,U_2153] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2150),U_2153),U_2152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2150),U_2153),U_2151))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2150),U_2151),U_2152))
      | ~ class_Orderings_Oorder(U_2150) ),
    inference(definitional_conversion,[status(esa)],[f_575_2]) ).

cnf(f_575_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2150),U_2153),U_2152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2150),U_2153),U_2151))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2150),U_2151),U_2152))
    | ~ class_Orderings_Oorder(U_2150) ),
    inference(clausify,[status(thm)],[f_575_3]) ).

fof(f_576_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).

fof(f_576_2,plain,
    ! [U_2157,U_2156,U_2155,U_2154] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2154),U_2155),U_2157))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2154),U_2156),U_2157))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2154),U_2155),U_2156))
      | ~ class_Orderings_Opreorder(U_2154) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ! [U_2155,U_2154,U_2156,U_2157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2154),U_2155),U_2157))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2154),U_2156),U_2157))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2154),U_2155),U_2156))
      | ~ class_Orderings_Opreorder(U_2154) ),
    inference(definitional_conversion,[status(esa)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2154),U_2155),U_2157))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2154),U_2156),U_2157))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2154),U_2155),U_2156))
    | ~ class_Orderings_Opreorder(U_2154) ),
    inference(clausify,[status(thm)],[f_576_3]) ).

fof(f_577_1,plain,
    ! [V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).

fof(f_577_2,plain,
    ! [U_2160,U_2159,U_2158] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2158),U_2159),U_2160))
      | U_2160 = U_2159
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2158),U_2159),U_2160))
      | ~ class_Orderings_Oorder(U_2158) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ! [U_2158,U_2159,U_2160] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2158),U_2159),U_2160))
      | U_2160 = U_2159
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2158),U_2159),U_2160))
      | ~ class_Orderings_Oorder(U_2158) ),
    inference(definitional_conversion,[status(esa)],[f_577_2]) ).

cnf(f_577_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2158),U_2159),U_2160))
    | U_2160 = U_2159
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2158),U_2159),U_2160))
    | ~ class_Orderings_Oorder(U_2158) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).

fof(f_578_2,plain,
    ! [U_2163,U_2162,U_2161] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2161),U_2162),U_2163))
      | U_2162 = U_2163
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2161),U_2162),U_2163))
      | ~ class_Orderings_Oorder(U_2161) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ! [U_2161,U_2162,U_2163] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2161),U_2162),U_2163))
      | U_2162 = U_2163
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2161),U_2162),U_2163))
      | ~ class_Orderings_Oorder(U_2161) ),
    inference(definitional_conversion,[status(esa)],[f_578_2]) ).

cnf(f_578_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2161),U_2162),U_2163))
    | U_2162 = U_2163
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2161),U_2162),U_2163))
    | ~ class_Orderings_Oorder(U_2161) ),
    inference(clausify,[status(thm)],[f_578_3]) ).

fof(f_579_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).

fof(f_579_2,plain,
    ! [U_2166,U_2165,U_2164] :
      ( U_2165 = U_2166
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2164),U_2165),U_2166))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2164),U_2165),U_2166))
      | ~ class_Orderings_Oorder(U_2164) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_2164,U_2165,U_2166] :
      ( U_2165 = U_2166
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2164),U_2165),U_2166))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2164),U_2165),U_2166))
      | ~ class_Orderings_Oorder(U_2164) ),
    inference(definitional_conversion,[status(esa)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( U_2165 = U_2166
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2164),U_2165),U_2166))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2164),U_2165),U_2166))
    | ~ class_Orderings_Oorder(U_2164) ),
    inference(clausify,[status(thm)],[f_579_3]) ).

fof(f_580_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(f_580_2,plain,
    ! [U_2169,U_2168,U_2167] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2167),U_2168),U_2169))
          | U_2168 != U_2169 )
        & ( U_2168 = U_2169
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2167),U_2168),U_2169)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2168),U_2169))
      | ~ class_Orderings_Olinorder(U_2167) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ( ! [U_2167,U_2168,U_2169] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2167),U_2168),U_2169))
        | U_2168 != U_2169
        | ~ sP162(U_2167,U_2168,U_2169) )
    & ! [U_2167,U_2168,U_2169] :
        ( U_2168 = U_2169
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2167),U_2168),U_2169))
        | ~ sP162(U_2167,U_2168,U_2169) )
    & ! [U_2167,U_2168,U_2169] :
        ( sP162(U_2167,U_2168,U_2169)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2168),U_2169))
        | ~ class_Orderings_Olinorder(U_2167) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_580_2]) ).

cnf(f_580_4,plain,
    ( sP162(U_2167,U_2168,U_2169)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2168),U_2169))
    | ~ class_Orderings_Olinorder(U_2167) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

cnf(f_580_5,plain,
    ( U_2168 = U_2169
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2167),U_2168),U_2169))
    | ~ sP162(U_2167,U_2168,U_2169) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

cnf(f_580_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2167),U_2168),U_2169))
    | U_2168 != U_2169
    | ~ sP162(U_2167,U_2168,U_2169) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).

fof(f_581_2,plain,
    ! [U_2172,U_2171,U_2170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2170),U_2171),U_2172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2170),U_2171),U_2172))
      | ~ class_Orderings_Opreorder(U_2170) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_2172,U_2171,U_2170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2170),U_2171),U_2172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2170),U_2171),U_2172))
      | ~ class_Orderings_Opreorder(U_2170) ),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2170),U_2171),U_2172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2170),U_2171),U_2172))
    | ~ class_Orderings_Opreorder(U_2170) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_1,plain,
    ! [V_x,V_y,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_leD]) ).

fof(f_582_2,plain,
    ! [U_2175,U_2174,U_2173] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2173),U_2175),U_2174))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2173),U_2174),U_2175))
      | ~ class_Orderings_Olinorder(U_2173) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ! [U_2173,U_2174,U_2175] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2173),U_2175),U_2174))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2173),U_2174),U_2175))
      | ~ class_Orderings_Olinorder(U_2173) ),
    inference(definitional_conversion,[status(esa)],[f_582_2]) ).

cnf(f_582_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2173),U_2175),U_2174))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2173),U_2174),U_2175))
    | ~ class_Orderings_Olinorder(U_2173) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

fof(f_583_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | V_a = V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).

fof(f_583_2,plain,
    ! [U_2178,U_2177,U_2176] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),U_2178),U_2177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2178),U_2177))
      | U_2177 = U_2178
      | ~ class_Orderings_Oorder(U_2176) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_2176,U_2177,U_2178] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),U_2178),U_2177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2178),U_2177))
      | U_2177 = U_2178
      | ~ class_Orderings_Oorder(U_2176) ),
    inference(definitional_conversion,[status(esa)],[f_583_2]) ).

cnf(f_583_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),U_2178),U_2177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2178),U_2177))
    | U_2177 = U_2178
    | ~ class_Orderings_Oorder(U_2176) ),
    inference(clausify,[status(thm)],[f_583_3]) ).

fof(f_584_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | V_a = V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).

fof(f_584_2,plain,
    ! [U_2181,U_2180,U_2179] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2179),U_2180),U_2181))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2179),U_2180),U_2181))
      | U_2180 = U_2181
      | ~ class_Orderings_Oorder(U_2179) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ! [U_2180,U_2179,U_2181] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2179),U_2180),U_2181))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2179),U_2180),U_2181))
      | U_2180 = U_2181
      | ~ class_Orderings_Oorder(U_2179) ),
    inference(definitional_conversion,[status(esa)],[f_584_2]) ).

cnf(f_584_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2179),U_2180),U_2181))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2179),U_2180),U_2181))
    | U_2180 = U_2181
    | ~ class_Orderings_Oorder(U_2179) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

fof(f_585_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(f_585_2,plain,
    ! [U_2184,U_2183,U_2182] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2182),U_2183),U_2184))
          | U_2183 != U_2184 )
        & ( U_2183 = U_2184
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2182),U_2183),U_2184)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2182),U_2183),U_2184))
      | ~ class_Orderings_Olinorder(U_2182) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ( ! [U_2182,U_2183,U_2184] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2182),U_2183),U_2184))
        | U_2183 != U_2184
        | ~ sP163(U_2182,U_2183,U_2184) )
    & ! [U_2182,U_2183,U_2184] :
        ( U_2183 = U_2184
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2182),U_2183),U_2184))
        | ~ sP163(U_2182,U_2183,U_2184) )
    & ! [U_2182,U_2183,U_2184] :
        ( sP163(U_2182,U_2183,U_2184)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2182),U_2183),U_2184))
        | ~ class_Orderings_Olinorder(U_2182) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_585_2]) ).

cnf(f_585_4,plain,
    ( sP163(U_2182,U_2183,U_2184)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2182),U_2183),U_2184))
    | ~ class_Orderings_Olinorder(U_2182) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

cnf(f_585_5,plain,
    ( U_2183 = U_2184
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2182),U_2183),U_2184))
    | ~ sP163(U_2182,U_2183,U_2184) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

cnf(f_585_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2182),U_2183),U_2184))
    | U_2183 != U_2184
    | ~ sP163(U_2182,U_2183,U_2184) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__leE]) ).

fof(f_586_2,plain,
    ! [U_2187,U_2186,U_2185] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2185),U_2187),U_2186))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2185),U_2186),U_2187))
      | ~ class_Orderings_Olinorder(U_2185) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_2187,U_2186,U_2185] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2185),U_2187),U_2186))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2185),U_2186),U_2187))
      | ~ class_Orderings_Olinorder(U_2185) ),
    inference(definitional_conversion,[status(esa)],[f_586_2]) ).

cnf(f_586_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2185),U_2187),U_2186))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2185),U_2186),U_2187))
    | ~ class_Orderings_Olinorder(U_2185) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_leI]) ).

fof(f_587_2,plain,
    ! [U_2190,U_2189,U_2188] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2188),U_2190),U_2189))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2188),U_2189),U_2190))
      | ~ class_Orderings_Olinorder(U_2188) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_2188,U_2189,U_2190] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2188),U_2190),U_2189))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2188),U_2189),U_2190))
      | ~ class_Orderings_Olinorder(U_2188) ),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2188),U_2190),U_2189))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2188),U_2189),U_2190))
    | ~ class_Orderings_Olinorder(U_2188) ),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ( V_x_2 != V_y_2
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).

fof(f_588_2,plain,
    ! [U_2193,U_2192,U_2191] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2191),U_2192),U_2193))
          | ( U_2192 != U_2193
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2191),U_2192),U_2193)) ) )
        & ( U_2192 = U_2193
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2191),U_2192),U_2193))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2191),U_2192),U_2193)) ) )
      | ~ class_Orderings_Oorder(U_2191) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ( ! [U_2191,U_2192,U_2193] :
        ( U_2192 != U_2193
        | ~ sP164(U_2191,U_2192,U_2193) )
    & ! [U_2191,U_2192,U_2193] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2191),U_2192),U_2193))
        | ~ sP164(U_2191,U_2192,U_2193) )
    & ! [U_2191,U_2192,U_2193] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2191),U_2192),U_2193))
        | sP164(U_2191,U_2192,U_2193)
        | ~ sP165(U_2191,U_2192,U_2193) )
    & ! [U_2191,U_2192,U_2193] :
        ( U_2192 = U_2193
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2191),U_2192),U_2193))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2191),U_2192),U_2193))
        | ~ sP165(U_2191,U_2192,U_2193) )
    & ! [U_2191,U_2192,U_2193] :
        ( sP165(U_2191,U_2192,U_2193)
        | ~ class_Orderings_Oorder(U_2191) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164,sP165])],[f_588_2]) ).

cnf(f_588_4,plain,
    ( sP165(U_2191,U_2192,U_2193)
    | ~ class_Orderings_Oorder(U_2191) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_5,plain,
    ( U_2192 = U_2193
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2191),U_2192),U_2193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2191),U_2192),U_2193))
    | ~ sP165(U_2191,U_2192,U_2193) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2191),U_2192),U_2193))
    | sP164(U_2191,U_2192,U_2193)
    | ~ sP165(U_2191,U_2192,U_2193) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2191),U_2192),U_2193))
    | ~ sP164(U_2191,U_2192,U_2193) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_8,plain,
    ( U_2192 != U_2193
    | ~ sP164(U_2191,U_2192,U_2193) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Opreorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).

fof(f_589_2,plain,
    ! [U_2196,U_2195,U_2194] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2194),U_2195),U_2196))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2196),U_2195))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2196),U_2195))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2194),U_2195),U_2196)) ) )
      | ~ class_Orderings_Opreorder(U_2194) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ( ! [U_2196,U_2195,U_2194] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2196),U_2195))
        | ~ sP166(U_2196,U_2195,U_2194) )
    & ! [U_2196,U_2195,U_2194] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
        | ~ sP166(U_2196,U_2195,U_2194) )
    & ! [U_2196,U_2195,U_2194] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2194),U_2195),U_2196))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2196),U_2195))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
        | ~ sP167(U_2196,U_2195,U_2194) )
    & ! [U_2196,U_2195,U_2194] :
        ( sP166(U_2196,U_2195,U_2194)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2194),U_2195),U_2196))
        | ~ sP167(U_2196,U_2195,U_2194) )
    & ! [U_2196,U_2195,U_2194] :
        ( sP167(U_2196,U_2195,U_2194)
        | ~ class_Orderings_Opreorder(U_2194) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166,sP167])],[f_589_2]) ).

cnf(f_589_4,plain,
    ( sP167(U_2196,U_2195,U_2194)
    | ~ class_Orderings_Opreorder(U_2194) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

cnf(f_589_5,plain,
    ( sP166(U_2196,U_2195,U_2194)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2194),U_2195),U_2196))
    | ~ sP167(U_2196,U_2195,U_2194) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

cnf(f_589_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2194),U_2195),U_2196))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2196),U_2195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
    | ~ sP167(U_2196,U_2195,U_2194) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

cnf(f_589_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
    | ~ sP166(U_2196,U_2195,U_2194) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

cnf(f_589_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2196),U_2195))
    | ~ sP166(U_2196,U_2195,U_2194) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( V_x_2 != V_y_2
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).

fof(f_590_2,plain,
    ! [U_2199,U_2198,U_2197] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2197),U_2198),U_2199))
          | U_2198 = U_2199
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2197),U_2198),U_2199)) )
        & ( ( U_2198 != U_2199
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2197),U_2198),U_2199)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2197),U_2198),U_2199)) ) )
      | ~ class_Orderings_Oorder(U_2197) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ( ! [U_2198,U_2197,U_2199] :
        ( U_2198 != U_2199
        | ~ sP168(U_2198,U_2197,U_2199) )
    & ! [U_2198,U_2197,U_2199] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2197),U_2198),U_2199))
        | ~ sP168(U_2198,U_2197,U_2199) )
    & ! [U_2198,U_2197,U_2199] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2197),U_2198),U_2199))
        | U_2198 = U_2199
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2197),U_2198),U_2199))
        | ~ sP169(U_2198,U_2197,U_2199) )
    & ! [U_2198,U_2197,U_2199] :
        ( sP168(U_2198,U_2197,U_2199)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2197),U_2198),U_2199))
        | ~ sP169(U_2198,U_2197,U_2199) )
    & ! [U_2198,U_2197,U_2199] :
        ( sP169(U_2198,U_2197,U_2199)
        | ~ class_Orderings_Oorder(U_2197) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169])],[f_590_2]) ).

cnf(f_590_4,plain,
    ( sP169(U_2198,U_2197,U_2199)
    | ~ class_Orderings_Oorder(U_2197) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

cnf(f_590_5,plain,
    ( sP168(U_2198,U_2197,U_2199)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2197),U_2198),U_2199))
    | ~ sP169(U_2198,U_2197,U_2199) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

cnf(f_590_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2197),U_2198),U_2199))
    | U_2198 = U_2199
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2197),U_2198),U_2199))
    | ~ sP169(U_2198,U_2197,U_2199) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

cnf(f_590_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2197),U_2198),U_2199))
    | ~ sP168(U_2198,U_2197,U_2199) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

cnf(f_590_8,plain,
    ( U_2198 != U_2199
    | ~ sP168(U_2198,U_2197,U_2199) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

fof(f_591_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).

fof(f_591_2,plain,
    ! [U_2202,U_2201,U_2200] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2200),U_2202),U_2201))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2200),U_2201),U_2202))
      | ~ class_Orderings_Olinorder(U_2200) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_2200,U_2202,U_2201] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2200),U_2202),U_2201))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2200),U_2201),U_2202))
      | ~ class_Orderings_Olinorder(U_2200) ),
    inference(definitional_conversion,[status(esa)],[f_591_2]) ).

cnf(f_591_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2200),U_2202),U_2201))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2200),U_2201),U_2202))
    | ~ class_Orderings_Olinorder(U_2200) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

fof(f_592_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).

fof(f_592_2,plain,
    ! [U_2205,U_2204,U_2203] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203),U_2204),U_2205))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2203),U_2205),U_2204)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2203),U_2205),U_2204))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203),U_2204),U_2205)) ) )
      | ~ class_Orderings_Olinorder(U_2203) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ( ! [U_2204,U_2203,U_2205] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203),U_2204),U_2205))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2203),U_2205),U_2204))
        | ~ sP170(U_2204,U_2203,U_2205) )
    & ! [U_2204,U_2203,U_2205] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2203),U_2205),U_2204))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203),U_2204),U_2205))
        | ~ sP170(U_2204,U_2203,U_2205) )
    & ! [U_2204,U_2203,U_2205] :
        ( sP170(U_2204,U_2203,U_2205)
        | ~ class_Orderings_Olinorder(U_2203) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_592_2]) ).

cnf(f_592_4,plain,
    ( sP170(U_2204,U_2203,U_2205)
    | ~ class_Orderings_Olinorder(U_2203) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2203),U_2205),U_2204))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203),U_2204),U_2205))
    | ~ sP170(U_2204,U_2203,U_2205) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203),U_2204),U_2205))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2203),U_2205),U_2204))
    | ~ sP170(U_2204,U_2203,U_2205) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).

fof(f_593_2,plain,
    ! [U_2208,U_2207,U_2206] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2206),U_2207),U_2208))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2206),U_2208),U_2207)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2206),U_2208),U_2207))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2206),U_2207),U_2208)) ) )
      | ~ class_Orderings_Olinorder(U_2206) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ( ! [U_2208,U_2207,U_2206] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2206),U_2207),U_2208))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2206),U_2208),U_2207))
        | ~ sP171(U_2208,U_2207,U_2206) )
    & ! [U_2208,U_2207,U_2206] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2206),U_2208),U_2207))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2206),U_2207),U_2208))
        | ~ sP171(U_2208,U_2207,U_2206) )
    & ! [U_2208,U_2207,U_2206] :
        ( sP171(U_2208,U_2207,U_2206)
        | ~ class_Orderings_Olinorder(U_2206) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_593_2]) ).

cnf(f_593_4,plain,
    ( sP171(U_2208,U_2207,U_2206)
    | ~ class_Orderings_Olinorder(U_2206) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

cnf(f_593_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2206),U_2208),U_2207))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2206),U_2207),U_2208))
    | ~ sP171(U_2208,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

cnf(f_593_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2206),U_2207),U_2208))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2206),U_2208),U_2207))
    | ~ sP171(U_2208,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).

fof(f_594_2,plain,
    ! [U_2212,U_2211,U_2210,U_2209] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209),U_2211),U_2212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2209),U_2210),U_2211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2209),U_2210),U_2212)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2209) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_2211,U_2210,U_2209,U_2212] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209),U_2211),U_2212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2209),U_2210),U_2211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2209),U_2210),U_2212)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2209) ),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209),U_2211),U_2212))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2209),U_2210),U_2211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2209),U_2210),U_2212)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2209) ),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).

fof(f_595_2,plain,
    ! [U_2216,U_2215,U_2214,U_2213] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2213),U_2214),U_2216))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2213),U_2214),U_2215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2213),U_2216),U_2215)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2213) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_2213,U_2214,U_2215,U_2216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2213),U_2214),U_2216))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2213),U_2214),U_2215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2213),U_2216),U_2215)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2213) ),
    inference(definitional_conversion,[status(esa)],[f_595_2]) ).

cnf(f_595_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2213),U_2214),U_2216))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2213),U_2214),U_2215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2213),U_2216),U_2215)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2213) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__mono]) ).

fof(f_596_2,plain,
    ! [U_2221,U_2220,U_2219,U_2218,U_2217] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2218),U_2220)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2219),U_2221)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2220),U_2221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2218),U_2219))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2217) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

fof(f_596_3,plain,
    ! [U_2217,U_2218,U_2219,U_2220,U_2221] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2218),U_2220)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2219),U_2221)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2220),U_2221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2218),U_2219))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2217) ),
    inference(definitional_conversion,[status(esa)],[f_596_2]) ).

cnf(f_596_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2218),U_2220)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2219),U_2221)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2220),U_2221))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2217),U_2218),U_2219))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_2217) ),
    inference(clausify,[status(thm)],[f_596_3]) ).

fof(f_597_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__mono]) ).

fof(f_597_2,plain,
    ! [U_2225,U_2224,U_2223,U_2222] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2225),U_2223)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2225),U_2224)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2222),U_2223),U_2224))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2222) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_2222,U_2223,U_2224,U_2225] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2225),U_2223)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2225),U_2224)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2222),U_2223),U_2224))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2222) ),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2225),U_2223)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2225),U_2224)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2222),U_2223),U_2224))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_2222) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__mono]) ).

fof(f_598_2,plain,
    ! [U_2229,U_2228,U_2227,U_2226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2227),U_2229)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2228),U_2229)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2226),U_2227),U_2228))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2226) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_2226,U_2227,U_2228,U_2229] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2227),U_2229)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2228),U_2229)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2226),U_2227),U_2228))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2226) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2227),U_2229)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2228),U_2229)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2226),U_2227),U_2228))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_2226) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).

fof(f_599_2,plain,
    ! [U_2233,U_2232,U_2231,U_2230] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2233)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2232),U_2233)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2232),U_2233))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2233))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2230) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ( ! [U_2232,U_2231,U_2230,U_2233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2233)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2232),U_2233))
        | ~ sP172(U_2232,U_2231,U_2230,U_2233) )
    & ! [U_2232,U_2231,U_2230,U_2233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2232),U_2233))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2233)))
        | ~ sP172(U_2232,U_2231,U_2230,U_2233) )
    & ! [U_2232,U_2231,U_2230,U_2233] :
        ( sP172(U_2232,U_2231,U_2230,U_2233)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2230) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_599_2]) ).

cnf(f_599_4,plain,
    ( sP172(U_2232,U_2231,U_2230,U_2233)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2230) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

cnf(f_599_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2232),U_2233))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2233)))
    | ~ sP172(U_2232,U_2231,U_2230,U_2233) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

cnf(f_599_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2230),U_2231),U_2233)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2232),U_2233))
    | ~ sP172(U_2232,U_2231,U_2230,U_2233) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).

fof(f_600_2,plain,
    ! [U_2237,U_2236,U_2235,U_2234] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2235),U_2236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2237),U_2236)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),U_2235),U_2237)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),U_2235),U_2237))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2235),U_2236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2237),U_2236))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2234) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ( ! [U_2235,U_2236,U_2237,U_2234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2235),U_2236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2237),U_2236)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),U_2235),U_2237))
        | ~ sP173(U_2235,U_2236,U_2237,U_2234) )
    & ! [U_2235,U_2236,U_2237,U_2234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),U_2235),U_2237))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2235),U_2236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2237),U_2236)))
        | ~ sP173(U_2235,U_2236,U_2237,U_2234) )
    & ! [U_2235,U_2236,U_2237,U_2234] :
        ( sP173(U_2235,U_2236,U_2237,U_2234)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2234) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_600_2]) ).

cnf(f_600_4,plain,
    ( sP173(U_2235,U_2236,U_2237,U_2234)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2234) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),U_2235),U_2237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2235),U_2236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2237),U_2236)))
    | ~ sP173(U_2235,U_2236,U_2237,U_2234) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2235),U_2236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2234),U_2237),U_2236)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2234),U_2235),U_2237))
    | ~ sP173(U_2235,U_2236,U_2237,U_2234) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
        | ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != V_n_2 ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).

fof(f_601_2,plain,
    ! [U_2240,U_2239,U_2238] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2238),U_2239) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2239)
        | ( U_2239 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2238 != U_2240 ) )
      & ( U_2239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2238 = U_2240
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2238),U_2239) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2239) ) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ( ! [U_2246,U_2244,U_2242] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2244)
        | ( U_2244 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2242 != U_2246 ) )
    & ! [U_2245,U_2243,U_2241] :
        ( U_2243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2241 = U_2245
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2243) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2245),U_2243) ) ),
    inference(miniscope,[status(thm)],[f_601_2]) ).

fof(f_601_4,plain,
    ( ! [U_2246,U_2244,U_2242] :
        ( U_2244 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP174(U_2246,U_2244,U_2242) )
    & ! [U_2246,U_2244,U_2242] :
        ( U_2242 != U_2246
        | ~ sP174(U_2246,U_2244,U_2242) )
    & ! [U_2246,U_2244,U_2242] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2244)
        | sP174(U_2246,U_2244,U_2242) )
    & ! [U_2243,U_2241,U_2245] :
        ( U_2243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2241 = U_2245
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2243) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2245),U_2243) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_601_3]) ).

cnf(f_601_5,plain,
    ( U_2243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2241 = U_2245
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2243) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2245),U_2243) ),
    inference(clausify,[status(thm)],[f_601_4]) ).

cnf(f_601_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2244)
    | sP174(U_2246,U_2244,U_2242) ),
    inference(clausify,[status(thm)],[f_601_4]) ).

cnf(f_601_7,plain,
    ( U_2242 != U_2246
    | ~ sP174(U_2246,U_2244,U_2242) ),
    inference(clausify,[status(thm)],[f_601_4]) ).

cnf(f_601_8,plain,
    ( U_2244 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP174(U_2246,U_2244,U_2242) ),
    inference(clausify,[status(thm)],[f_601_4]) ).

fof(f_602_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
        | ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != V_n_2 ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).

fof(f_602_2,plain,
    ! [U_2249,U_2248,U_2247] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2247),U_2248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2247),U_2249)
        | ( U_2247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2248 != U_2249 ) )
      & ( U_2247 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2248 = U_2249
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2247),U_2248) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2247),U_2249) ) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ( ! [U_2255,U_2253,U_2251] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2251),U_2253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2251),U_2255)
        | ( U_2251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2253 != U_2255 ) )
    & ! [U_2254,U_2252,U_2250] :
        ( U_2250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2252 = U_2254
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2250),U_2252) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2250),U_2254) ) ),
    inference(miniscope,[status(thm)],[f_602_2]) ).

fof(f_602_4,plain,
    ( ! [U_2255,U_2253,U_2251] :
        ( U_2251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP175(U_2255,U_2253,U_2251) )
    & ! [U_2255,U_2253,U_2251] :
        ( U_2253 != U_2255
        | ~ sP175(U_2255,U_2253,U_2251) )
    & ! [U_2255,U_2253,U_2251] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2251),U_2253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2251),U_2255)
        | sP175(U_2255,U_2253,U_2251) )
    & ! [U_2252,U_2250,U_2254] :
        ( U_2250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2252 = U_2254
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2250),U_2252) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2250),U_2254) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_602_3]) ).

cnf(f_602_5,plain,
    ( U_2250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2252 = U_2254
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2250),U_2252) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2250),U_2254) ),
    inference(clausify,[status(thm)],[f_602_4]) ).

cnf(f_602_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2251),U_2253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2251),U_2255)
    | sP175(U_2255,U_2253,U_2251) ),
    inference(clausify,[status(thm)],[f_602_4]) ).

cnf(f_602_7,plain,
    ( U_2253 != U_2255
    | ~ sP175(U_2255,U_2253,U_2251) ),
    inference(clausify,[status(thm)],[f_602_4]) ).

cnf(f_602_8,plain,
    ( U_2251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP175(U_2255,U_2253,U_2251) ),
    inference(clausify,[status(thm)],[f_602_4]) ).

fof(f_603_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).

fof(f_603_2,plain,
    ! [U_2257,U_2256] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2256),U_2257) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_2257 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2256),U_2257) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ( ! [U_2261,U_2259] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2259),U_2261) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_2261 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2260,U_2258] :
        ( U_2260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2258),U_2260) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_603_2]) ).

fof(f_603_4,plain,
    ( ! [U_2261,U_2259] :
        ( U_2261 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP176(U_2261,U_2259) )
    & ! [U_2261,U_2259] :
        ( U_2259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP176(U_2261,U_2259) )
    & ! [U_2261,U_2259] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2259),U_2261) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP176(U_2261,U_2259) )
    & ! [U_2260,U_2258] :
        ( U_2260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2258),U_2260) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_603_3]) ).

cnf(f_603_5,plain,
    ( U_2260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2258),U_2260) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_603_4]) ).

cnf(f_603_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2259),U_2261) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP176(U_2261,U_2259) ),
    inference(clausify,[status(thm)],[f_603_4]) ).

cnf(f_603_7,plain,
    ( U_2259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP176(U_2261,U_2259) ),
    inference(clausify,[status(thm)],[f_603_4]) ).

cnf(f_603_8,plain,
    ( U_2261 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP176(U_2261,U_2259) ),
    inference(clausify,[status(thm)],[f_603_4]) ).

fof(f_604_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mult__0__right]) ).

fof(f_604_2,plain,
    ! [U_2262] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2262),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_2262] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2262),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_604_2]) ).

cnf(f_604_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2262),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mult__0]) ).

fof(f_605_2,plain,
    ! [U_2263] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ! [U_2263] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_605_2]) ).

cnf(f_605_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).

fof(f_606_2,plain,
    ! [U_2266,U_2265,U_2264] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2264)),U_2265) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2264)),U_2266)
        | U_2265 != U_2266 )
      & ( U_2265 = U_2266
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2264)),U_2265) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2264)),U_2266) ) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ( ! [U_2272,U_2270] :
        ( ! [U_2268] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2268)),U_2270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2268)),U_2272)
        | U_2270 != U_2272 )
    & ! [U_2271,U_2269] :
        ( ! [U_2267] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2267)),U_2269) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2267)),U_2271)
        | U_2269 = U_2271 ) ),
    inference(miniscope,[status(thm)],[f_606_2]) ).

fof(f_606_4,plain,
    ( ! [U_2272,U_2268,U_2270] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2268)),U_2270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2268)),U_2272)
        | U_2270 != U_2272 )
    & ! [U_2271,U_2267,U_2269] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2267)),U_2269) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2267)),U_2271)
        | U_2269 = U_2271 ) ),
    inference(definitional_conversion,[status(esa)],[f_606_3]) ).

cnf(f_606_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2267)),U_2269) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2267)),U_2271)
    | U_2269 = U_2271 ),
    inference(clausify,[status(thm)],[f_606_4]) ).

cnf(f_606_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2268)),U_2270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2268)),U_2272)
    | U_2270 != U_2272 ),
    inference(clausify,[status(thm)],[f_606_4]) ).

fof(f_607_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).

fof(f_607_2,plain,
    ! [U_2273] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2273 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ( ! [U_2275] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2275),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2274] :
        ( U_2274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2274),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_607_2]) ).

fof(f_607_4,plain,
    ( ! [U_2275] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2275),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2274] :
        ( U_2274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2274),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_607_3]) ).

cnf(f_607_5,plain,
    ( U_2274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2274),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_607_4]) ).

cnf(f_607_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2275),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_2275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_607_4]) ).

fof(f_608_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(f_608_2,plain,
    ! [U_2276] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2276)),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_2276] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2276)),
    inference(definitional_conversion,[status(esa)],[f_608_2]) ).

cnf(f_608_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2276)),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).

fof(f_609_2,plain,
    ! [U_2279,U_2278,U_2277] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2279)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2278))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2278)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2279))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2277) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ( ! [U_2278,U_2279,U_2277] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2279)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2278)))
        | ~ sP177(U_2278,U_2279,U_2277) )
    & ! [U_2278,U_2279,U_2277] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2278)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2279)))
        | ~ sP177(U_2278,U_2279,U_2277) )
    & ! [U_2278,U_2279,U_2277] :
        ( sP177(U_2278,U_2279,U_2277)
        | ~ class_Groups_Oordered__ab__group__add(U_2277) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_609_2]) ).

cnf(f_609_4,plain,
    ( sP177(U_2278,U_2279,U_2277)
    | ~ class_Groups_Oordered__ab__group__add(U_2277) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

cnf(f_609_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2278)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2279)))
    | ~ sP177(U_2278,U_2279,U_2277) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

cnf(f_609_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2279)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),hAPP(c_Groups_Ouminus__class_Ouminus(U_2277),U_2278)))
    | ~ sP177(U_2278,U_2279,U_2277) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).

fof(f_610_2,plain,
    ! [U_2282,U_2281,U_2280] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2281)),U_2282))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2282)),U_2281)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2282)),U_2281))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2281)),U_2282)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2280) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ( ! [U_2282,U_2281,U_2280] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2281)),U_2282))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2282)),U_2281))
        | ~ sP178(U_2282,U_2281,U_2280) )
    & ! [U_2282,U_2281,U_2280] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2282)),U_2281))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2281)),U_2282))
        | ~ sP178(U_2282,U_2281,U_2280) )
    & ! [U_2282,U_2281,U_2280] :
        ( sP178(U_2282,U_2281,U_2280)
        | ~ class_Groups_Oordered__ab__group__add(U_2280) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_610_2]) ).

cnf(f_610_4,plain,
    ( sP178(U_2282,U_2281,U_2280)
    | ~ class_Groups_Oordered__ab__group__add(U_2280) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

cnf(f_610_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2282)),U_2281))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2281)),U_2282))
    | ~ sP178(U_2282,U_2281,U_2280) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

cnf(f_610_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2281)),U_2282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280),hAPP(c_Groups_Ouminus__class_Ouminus(U_2280),U_2282)),U_2281))
    | ~ sP178(U_2282,U_2281,U_2280) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).

fof(f_611_2,plain,
    ! [U_2285,U_2284,U_2283] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2284)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2285)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),U_2285),U_2284)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),U_2285),U_2284))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2284)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2285))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2283) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ( ! [U_2283,U_2284,U_2285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2284)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2285)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),U_2285),U_2284))
        | ~ sP179(U_2283,U_2284,U_2285) )
    & ! [U_2283,U_2284,U_2285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),U_2285),U_2284))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2284)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2285)))
        | ~ sP179(U_2283,U_2284,U_2285) )
    & ! [U_2283,U_2284,U_2285] :
        ( sP179(U_2283,U_2284,U_2285)
        | ~ class_Groups_Oordered__ab__group__add(U_2283) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_611_2]) ).

cnf(f_611_4,plain,
    ( sP179(U_2283,U_2284,U_2285)
    | ~ class_Groups_Oordered__ab__group__add(U_2283) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

cnf(f_611_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),U_2285),U_2284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2284)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2285)))
    | ~ sP179(U_2283,U_2284,U_2285) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

cnf(f_611_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2284)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2283),U_2285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283),U_2285),U_2284))
    | ~ sP179(U_2283,U_2284,U_2285) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).

fof(f_612_2,plain,
    ! [U_2288,U_2287,U_2286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2286),hAPP(c_Groups_Ouminus__class_Ouminus(U_2286),U_2288)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2286),U_2287)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2286),U_2287),U_2288))
      | ~ class_Groups_Oordered__ab__group__add(U_2286) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_2287,U_2288,U_2286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2286),hAPP(c_Groups_Ouminus__class_Ouminus(U_2286),U_2288)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2286),U_2287)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2286),U_2287),U_2288))
      | ~ class_Groups_Oordered__ab__group__add(U_2286) ),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2286),hAPP(c_Groups_Ouminus__class_Ouminus(U_2286),U_2288)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2286),U_2287)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2286),U_2287),U_2288))
    | ~ class_Groups_Oordered__ab__group__add(U_2286) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).

fof(f_613_2,plain,
    ! [U_2291,U_2290,U_2289] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2290),U_2291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),U_2290)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),U_2291)),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_2289,U_2290,U_2291] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2290),U_2291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),U_2290)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),U_2291)),
    inference(definitional_conversion,[status(esa)],[f_613_2]) ).

cnf(f_613_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2290),U_2291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),U_2290)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2289),U_2291)),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).

fof(f_614_2,plain,
    ! [U_2294,U_2293,U_2292] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2292),U_2293)),U_2294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2292),U_2294)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2293),U_2294)),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_2292,U_2293,U_2294] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2292),U_2293)),U_2294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2292),U_2294)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2293),U_2294)),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2292),U_2293)),U_2294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2292),U_2294)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2293),U_2294)),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(f_615_2,plain,
    ! [U_2295] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2295)),U_2295)),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_2295] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2295)),U_2295)),
    inference(definitional_conversion,[status(esa)],[f_615_2]) ).

cnf(f_615_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2295)),U_2295)),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).

fof(f_616_2,plain,
    ! [U_2297,U_2296] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2296),U_2297))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2297)),U_2296)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2297)),U_2296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2296),U_2297)) ) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ( ! [U_2301,U_2299] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2299),U_2301))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2301)),U_2299)) )
    & ! [U_2300,U_2298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2300)),U_2298))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2298),U_2300)) ) ),
    inference(miniscope,[status(thm)],[f_616_2]) ).

fof(f_616_4,plain,
    ( ! [U_2299,U_2301] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2299),U_2301))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2301)),U_2299)) )
    & ! [U_2300,U_2298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2300)),U_2298))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2298),U_2300)) ) ),
    inference(definitional_conversion,[status(esa)],[f_616_3]) ).

cnf(f_616_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2300)),U_2298))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2298),U_2300)) ),
    inference(clausify,[status(thm)],[f_616_4]) ).

cnf(f_616_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2299),U_2301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2301)),U_2299)) ),
    inference(clausify,[status(thm)],[f_616_4]) ).

fof(f_617_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ( V_m_2 != hAPP(c_Nat_OSuc,V_n_2)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).

fof(f_617_2,plain,
    ! [U_2303,U_2302] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2302),hAPP(c_Nat_OSuc,U_2303)))
        | ( U_2302 != hAPP(c_Nat_OSuc,U_2303)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2302),U_2303)) ) )
      & ( U_2302 = hAPP(c_Nat_OSuc,U_2303)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2302),U_2303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2302),hAPP(c_Nat_OSuc,U_2303))) ) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ( ! [U_2307,U_2305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2305),hAPP(c_Nat_OSuc,U_2307)))
        | ( U_2305 != hAPP(c_Nat_OSuc,U_2307)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2305),U_2307)) ) )
    & ! [U_2306,U_2304] :
        ( U_2304 = hAPP(c_Nat_OSuc,U_2306)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2304),U_2306))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2304),hAPP(c_Nat_OSuc,U_2306))) ) ),
    inference(miniscope,[status(thm)],[f_617_2]) ).

fof(f_617_4,plain,
    ( ! [U_2307,U_2305] :
        ( U_2305 != hAPP(c_Nat_OSuc,U_2307)
        | ~ sP180(U_2307,U_2305) )
    & ! [U_2307,U_2305] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2305),U_2307))
        | ~ sP180(U_2307,U_2305) )
    & ! [U_2307,U_2305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2305),hAPP(c_Nat_OSuc,U_2307)))
        | sP180(U_2307,U_2305) )
    & ! [U_2306,U_2304] :
        ( U_2304 = hAPP(c_Nat_OSuc,U_2306)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2304),U_2306))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2304),hAPP(c_Nat_OSuc,U_2306))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_617_3]) ).

cnf(f_617_5,plain,
    ( U_2304 = hAPP(c_Nat_OSuc,U_2306)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2304),U_2306))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2304),hAPP(c_Nat_OSuc,U_2306))) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

cnf(f_617_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2305),hAPP(c_Nat_OSuc,U_2307)))
    | sP180(U_2307,U_2305) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

cnf(f_617_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2305),U_2307))
    | ~ sP180(U_2307,U_2305) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

cnf(f_617_8,plain,
    ( U_2305 != hAPP(c_Nat_OSuc,U_2307)
    | ~ sP180(U_2307,U_2305) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

fof(f_618_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).

fof(f_618_2,plain,
    ! [U_2309,U_2308] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2308)),hAPP(c_Nat_OSuc,U_2309)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2308),U_2309)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2308),U_2309))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2308)),hAPP(c_Nat_OSuc,U_2309))) ) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ( ! [U_2313,U_2311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2311)),hAPP(c_Nat_OSuc,U_2313)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2311),U_2313)) )
    & ! [U_2312,U_2310] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2310),U_2312))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2310)),hAPP(c_Nat_OSuc,U_2312))) ) ),
    inference(miniscope,[status(thm)],[f_618_2]) ).

fof(f_618_4,plain,
    ( ! [U_2311,U_2313] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2311)),hAPP(c_Nat_OSuc,U_2313)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2311),U_2313)) )
    & ! [U_2312,U_2310] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2310),U_2312))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2310)),hAPP(c_Nat_OSuc,U_2312))) ) ),
    inference(definitional_conversion,[status(esa)],[f_618_3]) ).

cnf(f_618_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2310),U_2312))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2310)),hAPP(c_Nat_OSuc,U_2312))) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

cnf(f_618_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2311)),hAPP(c_Nat_OSuc,U_2313)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2311),U_2313)) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

fof(f_619_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).

fof(f_619_2,plain,
    ! [U_2315,U_2314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2314),hAPP(c_Nat_OSuc,U_2315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2314),U_2315)) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ! [U_2315,U_2314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2314),hAPP(c_Nat_OSuc,U_2315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2314),U_2315)) ),
    inference(definitional_conversion,[status(esa)],[f_619_2]) ).

cnf(f_619_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2314),hAPP(c_Nat_OSuc,U_2315)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2314),U_2315)) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_1,plain,
    ! [V_n,V_m] :
      ( V_m = hAPP(c_Nat_OSuc,V_n)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).

fof(f_620_2,plain,
    ! [U_2317,U_2316] :
      ( U_2316 = hAPP(c_Nat_OSuc,U_2317)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2316),U_2317))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2316),hAPP(c_Nat_OSuc,U_2317))) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_2316,U_2317] :
      ( U_2316 = hAPP(c_Nat_OSuc,U_2317)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2316),U_2317))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2316),hAPP(c_Nat_OSuc,U_2317))) ),
    inference(definitional_conversion,[status(esa)],[f_620_2]) ).

cnf(f_620_4,plain,
    ( U_2316 = hAPP(c_Nat_OSuc,U_2317)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2316),U_2317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2316),hAPP(c_Nat_OSuc,U_2317))) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).

fof(f_621_2,plain,
    ! [U_2319,U_2318] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2318),U_2319))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2318)),U_2319)) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ! [U_2318,U_2319] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2318),U_2319))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2318)),U_2319)) ),
    inference(definitional_conversion,[status(esa)],[f_621_2]) ).

cnf(f_621_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2318),U_2319))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2318)),U_2319)) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).

fof(f_622_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_622_1]) ).

cnf(f_622_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_622_2]) ).

fof(f_623_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).

fof(f_623_2,plain,
    ! [U_2321,U_2320] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2320),U_2321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2320),U_2321)) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ! [U_2320,U_2321] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2320),U_2321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2320),U_2321)) ),
    inference(definitional_conversion,[status(esa)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2320),U_2321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2320),U_2321)) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | V_m_2 = V_n_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( ( V_m_2 != V_n_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).

fof(f_624_2,plain,
    ! [U_2323,U_2322] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2322),U_2323))
        | U_2322 = U_2323
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2322),U_2323)) )
      & ( ( U_2322 != U_2323
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2322),U_2323)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2322),U_2323)) ) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ( ! [U_2327,U_2325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2325),U_2327))
        | U_2325 = U_2327
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2325),U_2327)) )
    & ! [U_2326,U_2324] :
        ( ( U_2324 != U_2326
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2324),U_2326)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2324),U_2326)) ) ),
    inference(miniscope,[status(thm)],[f_624_2]) ).

fof(f_624_4,plain,
    ( ! [U_2326,U_2324] :
        ( U_2324 != U_2326
        | ~ sP181(U_2326,U_2324) )
    & ! [U_2326,U_2324] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2324),U_2326))
        | ~ sP181(U_2326,U_2324) )
    & ! [U_2325,U_2327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2325),U_2327))
        | U_2325 = U_2327
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2325),U_2327)) )
    & ! [U_2326,U_2324] :
        ( sP181(U_2326,U_2324)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2324),U_2326)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_624_3]) ).

cnf(f_624_5,plain,
    ( sP181(U_2326,U_2324)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2324),U_2326)) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

cnf(f_624_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2325),U_2327))
    | U_2325 = U_2327
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2325),U_2327)) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

cnf(f_624_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2324),U_2326))
    | ~ sP181(U_2326,U_2324) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

cnf(f_624_8,plain,
    ( U_2324 != U_2326
    | ~ sP181(U_2326,U_2324) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

fof(f_625_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ( V_m_2 != V_n_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).

fof(f_625_2,plain,
    ! [U_2329,U_2328] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2328),U_2329))
        | ( U_2328 != U_2329
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2328),U_2329)) ) )
      & ( U_2328 = U_2329
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2328),U_2329))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2328),U_2329)) ) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ( ! [U_2333,U_2331] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2331),U_2333))
        | ( U_2331 != U_2333
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2331),U_2333)) ) )
    & ! [U_2332,U_2330] :
        ( U_2330 = U_2332
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2330),U_2332))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2330),U_2332)) ) ),
    inference(miniscope,[status(thm)],[f_625_2]) ).

fof(f_625_4,plain,
    ( ! [U_2331,U_2333] :
        ( U_2331 != U_2333
        | ~ sP182(U_2331,U_2333) )
    & ! [U_2331,U_2333] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2331),U_2333))
        | ~ sP182(U_2331,U_2333) )
    & ! [U_2331,U_2333] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2331),U_2333))
        | sP182(U_2331,U_2333) )
    & ! [U_2330,U_2332] :
        ( U_2330 = U_2332
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2330),U_2332))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2330),U_2332)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_625_3]) ).

cnf(f_625_5,plain,
    ( U_2330 = U_2332
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2330),U_2332))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2330),U_2332)) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

cnf(f_625_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2331),U_2333))
    | sP182(U_2331,U_2333) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

cnf(f_625_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2331),U_2333))
    | ~ sP182(U_2331,U_2333) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

cnf(f_625_8,plain,
    ( U_2331 != U_2333
    | ~ sP182(U_2331,U_2333) ),
    inference(clausify,[status(thm)],[f_625_4]) ).

fof(f_626_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).

fof(f_626_2,plain,
    ! [U_2335,U_2334] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2334),U_2335))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2334),U_2335)) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ! [U_2334,U_2335] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2334),U_2335))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2334),U_2335)) ),
    inference(definitional_conversion,[status(esa)],[f_626_2]) ).

cnf(f_626_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2334),U_2335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2334),U_2335)) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).

fof(f_627_2,plain,
    ! [U_2337,U_2336] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2336),U_2337))
      | U_2336 = U_2337
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2336),U_2337)) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ! [U_2336,U_2337] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2336),U_2337))
      | U_2336 = U_2337
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2336),U_2337)) ),
    inference(definitional_conversion,[status(esa)],[f_627_2]) ).

cnf(f_627_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2336),U_2337))
    | U_2336 = U_2337
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2336),U_2337)) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ( V_m != V_n
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).

fof(f_628_2,plain,
    ! [U_2339,U_2338] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2338),U_2339))
      | ( U_2338 != U_2339
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2338),U_2339)) ) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ( ! [U_2338,U_2339] :
        ( U_2338 != U_2339
        | ~ sP183(U_2338,U_2339) )
    & ! [U_2338,U_2339] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2338),U_2339))
        | ~ sP183(U_2338,U_2339) )
    & ! [U_2338,U_2339] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2338),U_2339))
        | sP183(U_2338,U_2339) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_628_2]) ).

cnf(f_628_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2338),U_2339))
    | sP183(U_2338,U_2339) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

cnf(f_628_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2338),U_2339))
    | ~ sP183(U_2338,U_2339) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

cnf(f_628_6,plain,
    ( U_2338 != U_2339
    | ~ sP183(U_2338,U_2339) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_1,plain,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).

fof(f_629_2,plain,
    ! [U_2342,U_2341,U_2340] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2340),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2341)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2340),U_2341)) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ! [U_2341,U_2340,U_2342] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2340),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2341)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2340),U_2341)) ),
    inference(definitional_conversion,[status(esa)],[f_629_2]) ).

cnf(f_629_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2340),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2341)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2340),U_2341)) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

fof(f_630_1,plain,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).

fof(f_630_2,plain,
    ! [U_2345,U_2344,U_2343] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2343),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2344),U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2343),U_2344)) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_2343,U_2344,U_2345] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2343),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2344),U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2343),U_2344)) ),
    inference(definitional_conversion,[status(esa)],[f_630_2]) ).

cnf(f_630_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2343),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2344),U_2345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2343),U_2344)) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
    inference(fof_nnf,[status(thm)],[fact_le__add2]) ).

fof(f_631_2,plain,
    ! [U_2347,U_2346] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),U_2346))),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_2346,U_2347] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),U_2346))),
    inference(definitional_conversion,[status(esa)],[f_631_2]) ).

cnf(f_631_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),U_2346))),
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
    inference(fof_nnf,[status(thm)],[fact_le__add1]) ).

fof(f_632_2,plain,
    ! [U_2349,U_2348] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2348),U_2349))),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_2348,U_2349] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2348),U_2349))),
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2348),U_2349))),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ! [B_k] : V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) )
      & ( ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).

fof(f_633_2,plain,
    ! [U_2353,U_2352] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2352),U_2353))
        | ! [U_2351] : U_2353 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2352),U_2351) )
      & ( ? [U_2350] : U_2353 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2352),U_2350)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2352),U_2353)) ) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ( ! [U_2357,U_2355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),U_2357))
        | ! [U_2351] : U_2357 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2355),U_2351) )
    & ! [U_2356,U_2354] :
        ( ? [U_2350] : U_2356 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2354),U_2350)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2354),U_2356)) ) ),
    inference(miniscope,[status(thm)],[f_633_2]) ).

fof(f_633_4,plain,
    ( ! [U_2357,U_2355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),U_2357))
        | ! [U_2351] : U_2357 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2355),U_2351) )
    & ! [U_2356,U_2354] :
        ( U_2356 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2354),sK41(U_2356,U_2354))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2354),U_2356)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2350,sK41(U_2356,U_2354))],[f_633_3]) ).

fof(f_633_5,plain,
    ( ! [U_2351,U_2355,U_2357] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),U_2357))
        | U_2357 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2355),U_2351) )
    & ! [U_2356,U_2354] :
        ( U_2356 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2354),sK41(U_2356,U_2354))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2354),U_2356)) ) ),
    inference(definitional_conversion,[status(esa)],[f_633_4]) ).

cnf(f_633_6,plain,
    ( U_2356 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2354),sK41(U_2356,U_2354))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2354),U_2356)) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

cnf(f_633_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),U_2357))
    | U_2357 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2355),U_2351) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

fof(f_634_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).

fof(f_634_2,plain,
    ! [U_2360,U_2359,U_2358] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2358),U_2359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2358),U_2360)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2359),U_2360)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2359),U_2360))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2358),U_2359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2358),U_2360))) ) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ( ! [U_2366,U_2364] :
        ( ! [U_2362] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2362),U_2364)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2362),U_2366)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2364),U_2366)) )
    & ! [U_2365,U_2363] :
        ( ! [U_2361] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2365)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365)) ) ),
    inference(miniscope,[status(thm)],[f_634_2]) ).

fof(f_634_4,plain,
    ( ! [U_2366,U_2364,U_2362] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2362),U_2364)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2362),U_2366)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2364),U_2366)) )
    & ! [U_2363,U_2365,U_2361] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2365)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365)) ) ),
    inference(definitional_conversion,[status(esa)],[f_634_3]) ).

cnf(f_634_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2365)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365)) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2362),U_2364)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2362),U_2366)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2364),U_2366)) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

fof(f_635_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).

fof(f_635_2,plain,
    ! [U_2369,U_2368,U_2367] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2368),U_2369)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2367),U_2368)) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ! [U_2368,U_2367,U_2369] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2368),U_2369)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2367),U_2368)) ),
    inference(definitional_conversion,[status(esa)],[f_635_2]) ).

cnf(f_635_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2368),U_2369)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2367),U_2368)) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).

fof(f_636_2,plain,
    ! [U_2372,U_2371,U_2370] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),U_2371)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2370),U_2371)) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ! [U_2370,U_2371,U_2372] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),U_2371)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2370),U_2371)) ),
    inference(definitional_conversion,[status(esa)],[f_636_2]) ).

cnf(f_636_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),U_2371)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2370),U_2371)) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

fof(f_637_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).

fof(f_637_2,plain,
    ! [U_2375,U_2374,U_2373] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2373),U_2375)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2374),U_2375)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2373),U_2374)) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_2373,U_2374,U_2375] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2373),U_2375)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2374),U_2375)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2373),U_2374)) ),
    inference(definitional_conversion,[status(esa)],[f_637_2]) ).

cnf(f_637_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2373),U_2375)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2374),U_2375)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2373),U_2374)) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).

fof(f_638_2,plain,
    ! [U_2379,U_2378,U_2377,U_2376] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2376),U_2378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2377),U_2379)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2378),U_2379))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),U_2377)) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_2376,U_2377,U_2378,U_2379] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2376),U_2378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2377),U_2379)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2378),U_2379))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),U_2377)) ),
    inference(definitional_conversion,[status(esa)],[f_638_2]) ).

cnf(f_638_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2376),U_2378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2377),U_2379)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2378),U_2379))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),U_2377)) ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_1,plain,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).

fof(f_639_2,plain,
    ! [U_2382,U_2381,U_2380] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2381),U_2382))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2381)),U_2382)) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ! [U_2382,U_2381] :
      ( ! [U_2380] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2381)),U_2382))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2381),U_2382)) ),
    inference(miniscope,[status(thm)],[f_639_2]) ).

fof(f_639_4,plain,
    ! [U_2380,U_2381,U_2382] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2381)),U_2382))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2381),U_2382)) ),
    inference(definitional_conversion,[status(esa)],[f_639_3]) ).

cnf(f_639_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2381)),U_2382))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2381),U_2382)) ),
    inference(clausify,[status(thm)],[f_639_4]) ).

fof(f_640_1,plain,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).

fof(f_640_2,plain,
    ! [U_2385,U_2384,U_2383] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2383),U_2385))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384)),U_2385)) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_2383,U_2384,U_2385] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2383),U_2385))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384)),U_2385)) ),
    inference(definitional_conversion,[status(esa)],[f_640_2]) ).

cnf(f_640_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2383),U_2385))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384)),U_2385)) ),
    inference(clausify,[status(thm)],[f_640_3]) ).

fof(f_641_1,plain,
    ! [V_n,V_k,V_m] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__leE]) ).

fof(f_641_2,plain,
    ! [U_2388,U_2387,U_2386] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2387),U_2388))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2386),U_2388)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2387)),U_2388)) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ( ! [U_2386,U_2387,U_2388] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2387),U_2388))
        | ~ sP184(U_2386,U_2387,U_2388) )
    & ! [U_2386,U_2387,U_2388] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2386),U_2388))
        | ~ sP184(U_2386,U_2387,U_2388) )
    & ! [U_2386,U_2387,U_2388] :
        ( sP184(U_2386,U_2387,U_2388)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2387)),U_2388)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_641_2]) ).

cnf(f_641_4,plain,
    ( sP184(U_2386,U_2387,U_2388)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2387)),U_2388)) ),
    inference(clausify,[status(thm)],[f_641_3]) ).

cnf(f_641_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2386),U_2388))
    | ~ sP184(U_2386,U_2387,U_2388) ),
    inference(clausify,[status(thm)],[f_641_3]) ).

cnf(f_641_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2387),U_2388))
    | ~ sP184(U_2386,U_2387,U_2388) ),
    inference(clausify,[status(thm)],[f_641_3]) ).

fof(f_642_1,plain,
    ! [V_w_2,V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
        | V_z_2 = V_w_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) )
      & ( ( V_z_2 != V_w_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__le]) ).

fof(f_642_2,plain,
    ! [U_2390,U_2389] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2389),U_2390))
        | U_2389 = U_2390
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2389),U_2390)) )
      & ( ( U_2389 != U_2390
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2389),U_2390)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2389),U_2390)) ) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ( ! [U_2394,U_2392] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2392),U_2394))
        | U_2392 = U_2394
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2392),U_2394)) )
    & ! [U_2393,U_2391] :
        ( ( U_2391 != U_2393
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2391),U_2393)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2391),U_2393)) ) ),
    inference(miniscope,[status(thm)],[f_642_2]) ).

fof(f_642_4,plain,
    ( ! [U_2391,U_2393] :
        ( U_2391 != U_2393
        | ~ sP185(U_2391,U_2393) )
    & ! [U_2391,U_2393] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2391),U_2393))
        | ~ sP185(U_2391,U_2393) )
    & ! [U_2394,U_2392] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2392),U_2394))
        | U_2392 = U_2394
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2392),U_2394)) )
    & ! [U_2391,U_2393] :
        ( sP185(U_2391,U_2393)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2391),U_2393)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_642_3]) ).

cnf(f_642_5,plain,
    ( sP185(U_2391,U_2393)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2391),U_2393)) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2392),U_2394))
    | U_2392 = U_2394
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2392),U_2394)) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2391),U_2393))
    | ~ sP185(U_2391,U_2393) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_8,plain,
    ( U_2391 != U_2393
    | ~ sP185(U_2391,U_2393) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

fof(f_643_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).

fof(f_643_2,plain,
    ! [U_2397,U_2396,U_2395] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2397),U_2395)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2397),U_2396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2395),U_2396)) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ! [U_2396,U_2395,U_2397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2397),U_2395)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2397),U_2396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2395),U_2396)) ),
    inference(definitional_conversion,[status(esa)],[f_643_2]) ).

cnf(f_643_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2397),U_2395)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2397),U_2396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2395),U_2396)) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

fof(f_644_1,plain,
    ! [V_m,V_t,V_n,V_s,V_c] :
      ( c_Natural_Oevaln(V_c,V_s,V_m,V_t)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__nonstrict]) ).

fof(f_644_2,plain,
    ! [U_2402,U_2401,U_2400,U_2399,U_2398] :
      ( c_Natural_Oevaln(U_2398,U_2399,U_2402,U_2401)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2400),U_2402))
      | ~ c_Natural_Oevaln(U_2398,U_2399,U_2400,U_2401) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ! [U_2398,U_2400,U_2399,U_2401,U_2402] :
      ( c_Natural_Oevaln(U_2398,U_2399,U_2402,U_2401)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2400),U_2402))
      | ~ c_Natural_Oevaln(U_2398,U_2399,U_2400,U_2401) ),
    inference(definitional_conversion,[status(esa)],[f_644_2]) ).

cnf(f_644_4,plain,
    ( c_Natural_Oevaln(U_2398,U_2399,U_2402,U_2401)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2400),U_2402))
    | ~ c_Natural_Oevaln(U_2398,U_2399,U_2400,U_2401) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

fof(f_645_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle]) ).

fof(f_645_2,plain,
    ! [U_2404,U_2403] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2403)),hAPP(c_Int_Onat,U_2404)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2403),U_2404)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2403),U_2404))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2403)),hAPP(c_Int_Onat,U_2404))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2404))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2403)) ) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ( ! [U_2404,U_2403] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2403)),hAPP(c_Int_Onat,U_2404)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2403),U_2404))
        | ~ sP187(U_2404,U_2403) )
    & ! [U_2404,U_2403] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2403),U_2404))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2403)),hAPP(c_Int_Onat,U_2404)))
        | ~ sP187(U_2404,U_2403) )
    & ! [U_2404,U_2403] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2404))
        | ~ sP186(U_2404,U_2403) )
    & ! [U_2404,U_2403] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2403))
        | ~ sP186(U_2404,U_2403) )
    & ! [U_2404,U_2403] :
        ( sP187(U_2404,U_2403)
        | sP186(U_2404,U_2403) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186,sP187])],[f_645_2]) ).

cnf(f_645_4,plain,
    ( sP187(U_2404,U_2403)
    | sP186(U_2404,U_2403) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2403))
    | ~ sP186(U_2404,U_2403) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2404))
    | ~ sP186(U_2404,U_2403) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2403),U_2404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2403)),hAPP(c_Int_Onat,U_2404)))
    | ~ sP187(U_2404,U_2403) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2403)),hAPP(c_Int_Onat,U_2404)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2403),U_2404))
    | ~ sP187(U_2404,U_2403) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_1,plain,
    ! [V_z_H,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib]) ).

fof(f_646_2,plain,
    ! [U_2406,U_2405] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2405),U_2406)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2405)),hAPP(c_Int_Onat,U_2406))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2405)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ! [U_2406,U_2405] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2405),U_2406)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2405)),hAPP(c_Int_Onat,U_2406))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2405)) ),
    inference(definitional_conversion,[status(esa)],[f_646_2]) ).

cnf(f_646_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2405),U_2406)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2405)),hAPP(c_Int_Onat,U_2406))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2405)) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J]) ).

fof(f_647_2,plain,
    ! [U_2408,U_2407] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2407)),hAPP(c_Int_Onat,U_2408)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2407),U_2408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ! [U_2407,U_2408] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2407)),hAPP(c_Int_Onat,U_2408)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2407),U_2408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407)) ),
    inference(definitional_conversion,[status(esa)],[f_647_2]) ).

cnf(f_647_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2407)),hAPP(c_Int_Onat,U_2408)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2407),U_2408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407)) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

fof(f_648_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff]) ).

fof(f_648_2,plain,
    ! [U_2410,U_2409] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),hAPP(c_Int_Oring__1__class_Oof__int(U_2409),U_2410)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2410)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2410))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),hAPP(c_Int_Oring__1__class_Oof__int(U_2409),U_2410))) ) )
      | ~ class_Rings_Olinordered__idom(U_2409) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ( ! [U_2409,U_2410] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),hAPP(c_Int_Oring__1__class_Oof__int(U_2409),U_2410)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2410))
        | ~ sP188(U_2409,U_2410) )
    & ! [U_2409,U_2410] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2410))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),hAPP(c_Int_Oring__1__class_Oof__int(U_2409),U_2410)))
        | ~ sP188(U_2409,U_2410) )
    & ! [U_2409,U_2410] :
        ( sP188(U_2409,U_2410)
        | ~ class_Rings_Olinordered__idom(U_2409) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_648_2]) ).

cnf(f_648_4,plain,
    ( sP188(U_2409,U_2410)
    | ~ class_Rings_Olinordered__idom(U_2409) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

cnf(f_648_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),hAPP(c_Int_Oring__1__class_Oof__int(U_2409),U_2410)))
    | ~ sP188(U_2409,U_2410) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

cnf(f_648_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),hAPP(c_Int_Oring__1__class_Oof__int(U_2409),U_2410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2410))
    | ~ sP188(U_2409,U_2410) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

fof(f_649_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff]) ).

fof(f_649_2,plain,
    ! [U_2412,U_2411] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Int_Oring__1__class_Oof__int(U_2411),U_2412)),c_Groups_Ozero__class_Ozero(U_2411)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2412),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Int_Oring__1__class_Oof__int(U_2411),U_2412)),c_Groups_Ozero__class_Ozero(U_2411))) ) )
      | ~ class_Rings_Olinordered__idom(U_2411) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ( ! [U_2411,U_2412] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Int_Oring__1__class_Oof__int(U_2411),U_2412)),c_Groups_Ozero__class_Ozero(U_2411)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP189(U_2411,U_2412) )
    & ! [U_2411,U_2412] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Int_Oring__1__class_Oof__int(U_2411),U_2412)),c_Groups_Ozero__class_Ozero(U_2411)))
        | ~ sP189(U_2411,U_2412) )
    & ! [U_2411,U_2412] :
        ( sP189(U_2411,U_2412)
        | ~ class_Rings_Olinordered__idom(U_2411) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_649_2]) ).

cnf(f_649_4,plain,
    ( sP189(U_2411,U_2412)
    | ~ class_Rings_Olinordered__idom(U_2411) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Int_Oring__1__class_Oof__int(U_2411),U_2412)),c_Groups_Ozero__class_Ozero(U_2411)))
    | ~ sP189(U_2411,U_2412) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Int_Oring__1__class_Oof__int(U_2411),U_2412)),c_Groups_Ozero__class_Ozero(U_2411)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP189(U_2411,U_2412) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

fof(f_650_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).

fof(f_650_2,plain,
    ! [U_2414,U_2413] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_2413,U_2414) = c_Groups_Ozero__class_Ozero(U_2413)
          | U_2414 != c_Groups_Ozero__class_Ozero(U_2413) )
        & ( U_2414 = c_Groups_Ozero__class_Ozero(U_2413)
          | c_Groups_Osgn__class_Osgn(U_2413,U_2414) != c_Groups_Ozero__class_Ozero(U_2413) ) )
      | ~ class_Rings_Olinordered__idom(U_2413) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ( ! [U_2414,U_2413] :
        ( c_Groups_Osgn__class_Osgn(U_2413,U_2414) = c_Groups_Ozero__class_Ozero(U_2413)
        | U_2414 != c_Groups_Ozero__class_Ozero(U_2413)
        | ~ sP190(U_2414,U_2413) )
    & ! [U_2414,U_2413] :
        ( U_2414 = c_Groups_Ozero__class_Ozero(U_2413)
        | c_Groups_Osgn__class_Osgn(U_2413,U_2414) != c_Groups_Ozero__class_Ozero(U_2413)
        | ~ sP190(U_2414,U_2413) )
    & ! [U_2414,U_2413] :
        ( sP190(U_2414,U_2413)
        | ~ class_Rings_Olinordered__idom(U_2413) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_650_2]) ).

cnf(f_650_4,plain,
    ( sP190(U_2414,U_2413)
    | ~ class_Rings_Olinordered__idom(U_2413) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_5,plain,
    ( U_2414 = c_Groups_Ozero__class_Ozero(U_2413)
    | c_Groups_Osgn__class_Osgn(U_2413,U_2414) != c_Groups_Ozero__class_Ozero(U_2413)
    | ~ sP190(U_2414,U_2413) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_2413,U_2414) = c_Groups_Ozero__class_Ozero(U_2413)
    | U_2414 != c_Groups_Ozero__class_Ozero(U_2413)
    | ~ sP190(U_2414,U_2413) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_1,plain,
    ! [T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Osgn__if(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn0]) ).

fof(f_651_2,plain,
    ! [U_2415] :
      ( c_Groups_Osgn__class_Osgn(U_2415,c_Groups_Ozero__class_Ozero(U_2415)) = c_Groups_Ozero__class_Ozero(U_2415)
      | ~ class_Groups_Osgn__if(U_2415) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_2415] :
      ( c_Groups_Osgn__class_Osgn(U_2415,c_Groups_Ozero__class_Ozero(U_2415)) = c_Groups_Ozero__class_Ozero(U_2415)
      | ~ class_Groups_Osgn__if(U_2415) ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2415,c_Groups_Ozero__class_Ozero(U_2415)) = c_Groups_Ozero__class_Ozero(U_2415)
    | ~ class_Groups_Osgn__if(U_2415) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__times]) ).

fof(f_652_2,plain,
    ! [U_2418,U_2417,U_2416] :
      ( c_Groups_Osgn__class_Osgn(U_2416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),U_2417),U_2418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),c_Groups_Osgn__class_Osgn(U_2416,U_2417)),c_Groups_Osgn__class_Osgn(U_2416,U_2418))
      | ~ class_Rings_Olinordered__idom(U_2416) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_2416,U_2417,U_2418] :
      ( c_Groups_Osgn__class_Osgn(U_2416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),U_2417),U_2418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),c_Groups_Osgn__class_Osgn(U_2416,U_2417)),c_Groups_Osgn__class_Osgn(U_2416,U_2418))
      | ~ class_Rings_Olinordered__idom(U_2416) ),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),U_2417),U_2418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),c_Groups_Osgn__class_Osgn(U_2416,U_2417)),c_Groups_Osgn__class_Osgn(U_2416,U_2418))
    | ~ class_Rings_Olinordered__idom(U_2416) ),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_1,plain,
    ! [V_z_H,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg]) ).

fof(f_653_2,plain,
    ! [U_2420,U_2419] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2419),U_2420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2419))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2420)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2419),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_2419,U_2420] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2419),U_2420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2419))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2420)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2419),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2419),U_2420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2419))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2420)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2419),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_654_2,plain,
    ! [U_2422,U_2421] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),U_2422)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),U_2422)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),U_2422))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),U_2422))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2421) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ( ! [U_2421,U_2422] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),U_2422)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),U_2422))
        | ~ sP191(U_2421,U_2422) )
    & ! [U_2421,U_2422] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),U_2422))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),U_2422)))
        | ~ sP191(U_2421,U_2422) )
    & ! [U_2421,U_2422] :
        ( sP191(U_2421,U_2422)
        | ~ class_Groups_Olinordered__ab__group__add(U_2421) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_654_2]) ).

cnf(f_654_4,plain,
    ( sP191(U_2421,U_2422)
    | ~ class_Groups_Olinordered__ab__group__add(U_2421) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

cnf(f_654_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),U_2422))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),U_2422)))
    | ~ sP191(U_2421,U_2422) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

cnf(f_654_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),U_2422)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2421),c_Groups_Ozero__class_Ozero(U_2421)),U_2422))
    | ~ sP191(U_2421,U_2422) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_655_2,plain,
    ! [U_2424,U_2423] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2423),U_2424),U_2424)),c_Groups_Ozero__class_Ozero(U_2423)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),U_2424),c_Groups_Ozero__class_Ozero(U_2423))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),U_2424),c_Groups_Ozero__class_Ozero(U_2423)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2423),U_2424),U_2424)),c_Groups_Ozero__class_Ozero(U_2423))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2423) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ( ! [U_2423,U_2424] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2423),U_2424),U_2424)),c_Groups_Ozero__class_Ozero(U_2423)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),U_2424),c_Groups_Ozero__class_Ozero(U_2423)))
        | ~ sP192(U_2423,U_2424) )
    & ! [U_2423,U_2424] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),U_2424),c_Groups_Ozero__class_Ozero(U_2423)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2423),U_2424),U_2424)),c_Groups_Ozero__class_Ozero(U_2423)))
        | ~ sP192(U_2423,U_2424) )
    & ! [U_2423,U_2424] :
        ( sP192(U_2423,U_2424)
        | ~ class_Groups_Olinordered__ab__group__add(U_2423) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_655_2]) ).

cnf(f_655_4,plain,
    ( sP192(U_2423,U_2424)
    | ~ class_Groups_Olinordered__ab__group__add(U_2423) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

cnf(f_655_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),U_2424),c_Groups_Ozero__class_Ozero(U_2423)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2423),U_2424),U_2424)),c_Groups_Ozero__class_Ozero(U_2423)))
    | ~ sP192(U_2423,U_2424) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

cnf(f_655_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2423),U_2424),U_2424)),c_Groups_Ozero__class_Ozero(U_2423)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2423),U_2424),c_Groups_Ozero__class_Ozero(U_2423)))
    | ~ sP192(U_2423,U_2424) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).

fof(f_656_2,plain,
    ! [U_2427,U_2426,U_2425] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2425),U_2426),U_2427)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),U_2427))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),U_2426))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2425) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ! [U_2425,U_2426,U_2427] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2425),U_2426),U_2427)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),U_2427))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),U_2426))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2425) ),
    inference(definitional_conversion,[status(esa)],[f_656_2]) ).

cnf(f_656_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2425),U_2426),U_2427)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),U_2427))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2425),c_Groups_Ozero__class_Ozero(U_2425)),U_2426))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2425) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
      | ~ class_Groups_Oordered__comm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).

fof(f_657_2,plain,
    ! [U_2430,U_2429,U_2428] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2428),U_2429),U_2430) = c_Groups_Ozero__class_Ozero(U_2428)
          | U_2430 != c_Groups_Ozero__class_Ozero(U_2428)
          | U_2429 != c_Groups_Ozero__class_Ozero(U_2428) )
        & ( ( U_2430 = c_Groups_Ozero__class_Ozero(U_2428)
            & U_2429 = c_Groups_Ozero__class_Ozero(U_2428) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2428),U_2429),U_2430) != c_Groups_Ozero__class_Ozero(U_2428) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2428),c_Groups_Ozero__class_Ozero(U_2428)),U_2430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2428),c_Groups_Ozero__class_Ozero(U_2428)),U_2429))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2428) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ( ! [U_2428,U_2429,U_2430] :
        ( U_2430 = c_Groups_Ozero__class_Ozero(U_2428)
        | ~ sP193(U_2428,U_2429,U_2430) )
    & ! [U_2428,U_2429,U_2430] :
        ( U_2429 = c_Groups_Ozero__class_Ozero(U_2428)
        | ~ sP193(U_2428,U_2429,U_2430) )
    & ! [U_2428,U_2429,U_2430] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2428),U_2429),U_2430) = c_Groups_Ozero__class_Ozero(U_2428)
        | U_2430 != c_Groups_Ozero__class_Ozero(U_2428)
        | U_2429 != c_Groups_Ozero__class_Ozero(U_2428)
        | ~ sP194(U_2428,U_2429,U_2430) )
    & ! [U_2428,U_2429,U_2430] :
        ( sP193(U_2428,U_2429,U_2430)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2428),U_2429),U_2430) != c_Groups_Ozero__class_Ozero(U_2428)
        | ~ sP194(U_2428,U_2429,U_2430) )
    & ! [U_2428,U_2429,U_2430] :
        ( sP194(U_2428,U_2429,U_2430)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2428),c_Groups_Ozero__class_Ozero(U_2428)),U_2430))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2428),c_Groups_Ozero__class_Ozero(U_2428)),U_2429))
        | ~ class_Groups_Oordered__comm__monoid__add(U_2428) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193,sP194])],[f_657_2]) ).

cnf(f_657_4,plain,
    ( sP194(U_2428,U_2429,U_2430)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2428),c_Groups_Ozero__class_Ozero(U_2428)),U_2430))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2428),c_Groups_Ozero__class_Ozero(U_2428)),U_2429))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2428) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_5,plain,
    ( sP193(U_2428,U_2429,U_2430)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2428),U_2429),U_2430) != c_Groups_Ozero__class_Ozero(U_2428)
    | ~ sP194(U_2428,U_2429,U_2430) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2428),U_2429),U_2430) = c_Groups_Ozero__class_Ozero(U_2428)
    | U_2430 != c_Groups_Ozero__class_Ozero(U_2428)
    | U_2429 != c_Groups_Ozero__class_Ozero(U_2428)
    | ~ sP194(U_2428,U_2429,U_2430) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_7,plain,
    ( U_2429 = c_Groups_Ozero__class_Ozero(U_2428)
    | ~ sP193(U_2428,U_2429,U_2430) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_8,plain,
    ( U_2430 = c_Groups_Ozero__class_Ozero(U_2428)
    | ~ sP193(U_2428,U_2429,U_2430) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

fof(f_658_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).

fof(f_658_2,plain,
    ! [U_2434,U_2433,U_2432,U_2431] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),U_2433),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2431),U_2432),U_2434)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),U_2433),U_2434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),c_Groups_Ozero__class_Ozero(U_2431)),U_2432))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2431) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ! [U_2432,U_2433,U_2434,U_2431] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),U_2433),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2431),U_2432),U_2434)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),U_2433),U_2434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),c_Groups_Ozero__class_Ozero(U_2431)),U_2432))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2431) ),
    inference(definitional_conversion,[status(esa)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),U_2433),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2431),U_2432),U_2434)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),U_2433),U_2434))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2431),c_Groups_Ozero__class_Ozero(U_2431)),U_2432))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2431) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).

fof(f_659_2,plain,
    ! [U_2438,U_2437,U_2436,U_2435] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),U_2437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),U_2438),U_2436)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),U_2437),U_2438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),c_Groups_Ozero__class_Ozero(U_2435)),U_2436))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2435) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_2436,U_2437,U_2435,U_2438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),U_2437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),U_2438),U_2436)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),U_2437),U_2438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),c_Groups_Ozero__class_Ozero(U_2435)),U_2436))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2435) ),
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),U_2437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),U_2438),U_2436)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),U_2437),U_2438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435),c_Groups_Ozero__class_Ozero(U_2435)),U_2436))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2435) ),
    inference(clausify,[status(thm)],[f_659_3]) ).

fof(f_660_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).

fof(f_660_2,plain,
    ! [U_2441,U_2440,U_2439] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2439),U_2440),U_2441)),c_Groups_Ozero__class_Ozero(U_2439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),U_2441),c_Groups_Ozero__class_Ozero(U_2439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),U_2440),c_Groups_Ozero__class_Ozero(U_2439)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2439) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_2440,U_2439,U_2441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2439),U_2440),U_2441)),c_Groups_Ozero__class_Ozero(U_2439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),U_2441),c_Groups_Ozero__class_Ozero(U_2439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),U_2440),c_Groups_Ozero__class_Ozero(U_2439)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2439) ),
    inference(definitional_conversion,[status(esa)],[f_660_2]) ).

cnf(f_660_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2439),U_2440),U_2441)),c_Groups_Ozero__class_Ozero(U_2439)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),U_2441),c_Groups_Ozero__class_Ozero(U_2439)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2439),U_2440),c_Groups_Ozero__class_Ozero(U_2439)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2439) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).

fof(f_661_2,plain,
    ! [U_2444,U_2443,U_2442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2442),U_2443),U_2444)),c_Groups_Ozero__class_Ozero(U_2442)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),c_Groups_Ozero__class_Ozero(U_2442)),U_2444))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),U_2443),c_Groups_Ozero__class_Ozero(U_2442))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),U_2444),c_Groups_Ozero__class_Ozero(U_2442)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),c_Groups_Ozero__class_Ozero(U_2442)),U_2443)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_2442) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ( ! [U_2442,U_2443,U_2444] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),c_Groups_Ozero__class_Ozero(U_2442)),U_2444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),U_2443),c_Groups_Ozero__class_Ozero(U_2442)))
        | ~ sP195(U_2442,U_2443,U_2444) )
    & ! [U_2442,U_2443,U_2444] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),U_2444),c_Groups_Ozero__class_Ozero(U_2442)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),c_Groups_Ozero__class_Ozero(U_2442)),U_2443))
        | ~ sP195(U_2442,U_2443,U_2444) )
    & ! [U_2442,U_2443,U_2444] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2442),U_2443),U_2444)),c_Groups_Ozero__class_Ozero(U_2442)))
        | sP195(U_2442,U_2443,U_2444)
        | ~ class_Rings_Oordered__cancel__semiring(U_2442) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_661_2]) ).

cnf(f_661_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2442),U_2443),U_2444)),c_Groups_Ozero__class_Ozero(U_2442)))
    | sP195(U_2442,U_2443,U_2444)
    | ~ class_Rings_Oordered__cancel__semiring(U_2442) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),U_2444),c_Groups_Ozero__class_Ozero(U_2442)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),c_Groups_Ozero__class_Ozero(U_2442)),U_2443))
    | ~ sP195(U_2442,U_2443,U_2444) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),c_Groups_Ozero__class_Ozero(U_2442)),U_2444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2442),U_2443),c_Groups_Ozero__class_Ozero(U_2442)))
    | ~ sP195(U_2442,U_2443,U_2444) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).

fof(f_662_2,plain,
    ! [U_2447,U_2446,U_2445] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2445),U_2446),U_2447)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),U_2447),c_Groups_Ozero__class_Ozero(U_2445)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),U_2446),c_Groups_Ozero__class_Ozero(U_2445))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),U_2447))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),U_2446)) ) )
      | ~ class_Rings_Oordered__ring(U_2445) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ( ! [U_2445,U_2446,U_2447] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),U_2447),c_Groups_Ozero__class_Ozero(U_2445)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),U_2446),c_Groups_Ozero__class_Ozero(U_2445)))
        | ~ sP196(U_2445,U_2446,U_2447) )
    & ! [U_2445,U_2446,U_2447] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),U_2447))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),U_2446))
        | ~ sP196(U_2445,U_2446,U_2447) )
    & ! [U_2445,U_2446,U_2447] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2445),U_2446),U_2447)))
        | sP196(U_2445,U_2446,U_2447)
        | ~ class_Rings_Oordered__ring(U_2445) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_662_2]) ).

cnf(f_662_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2445),U_2446),U_2447)))
    | sP196(U_2445,U_2446,U_2447)
    | ~ class_Rings_Oordered__ring(U_2445) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

cnf(f_662_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),U_2447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),c_Groups_Ozero__class_Ozero(U_2445)),U_2446))
    | ~ sP196(U_2445,U_2446,U_2447) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

cnf(f_662_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),U_2447),c_Groups_Ozero__class_Ozero(U_2445)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2445),U_2446),c_Groups_Ozero__class_Ozero(U_2445)))
    | ~ sP196(U_2445,U_2446,U_2447) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).

fof(f_663_2,plain,
    ! [U_2452,U_2451,U_2450,U_2449,U_2448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2448),U_2449),U_2451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2448),U_2450),U_2452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),U_2451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),U_2450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),U_2451),U_2452))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),U_2449),U_2450))
      | ~ class_Rings_Oordered__semiring(U_2448) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_2448,U_2449,U_2450,U_2451,U_2452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2448),U_2449),U_2451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2448),U_2450),U_2452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),U_2451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),U_2450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),U_2451),U_2452))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),U_2449),U_2450))
      | ~ class_Rings_Oordered__semiring(U_2448) ),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2448),U_2449),U_2451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2448),U_2450),U_2452)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),U_2451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),U_2450))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),U_2451),U_2452))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),U_2449),U_2450))
    | ~ class_Rings_Oordered__semiring(U_2448) ),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).

fof(f_664_2,plain,
    ! [U_2457,U_2456,U_2455,U_2454,U_2453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2454),U_2456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2455),U_2457)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2456))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2454))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),U_2456),U_2457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),U_2454),U_2455))
      | ~ class_Rings_Oordered__semiring(U_2453) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_2453,U_2454,U_2455,U_2456,U_2457] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2454),U_2456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2455),U_2457)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2456))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2454))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),U_2456),U_2457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),U_2454),U_2455))
      | ~ class_Rings_Oordered__semiring(U_2453) ),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2454),U_2456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2455),U_2457)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2456))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2454))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),U_2456),U_2457))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),U_2454),U_2455))
    | ~ class_Rings_Oordered__semiring(U_2453) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).

fof(f_665_2,plain,
    ! [U_2461,U_2460,U_2459,U_2458] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2458),U_2461),U_2460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2458),U_2461),U_2459)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),U_2461),c_Groups_Ozero__class_Ozero(U_2458)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),U_2459),U_2460))
      | ~ class_Rings_Oordered__ring(U_2458) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ! [U_2460,U_2461,U_2459,U_2458] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2458),U_2461),U_2460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2458),U_2461),U_2459)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),U_2461),c_Groups_Ozero__class_Ozero(U_2458)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),U_2459),U_2460))
      | ~ class_Rings_Oordered__ring(U_2458) ),
    inference(definitional_conversion,[status(esa)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2458),U_2461),U_2460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2458),U_2461),U_2459)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),U_2461),c_Groups_Ozero__class_Ozero(U_2458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),U_2459),U_2460))
    | ~ class_Rings_Oordered__ring(U_2458) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).

fof(f_666_2,plain,
    ! [U_2465,U_2464,U_2463,U_2462] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2462),U_2464),U_2465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2462),U_2463),U_2465)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),U_2465),c_Groups_Ozero__class_Ozero(U_2462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),U_2463),U_2464))
      | ~ class_Rings_Oordered__ring(U_2462) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_2462,U_2463,U_2464,U_2465] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2462),U_2464),U_2465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2462),U_2463),U_2465)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),U_2465),c_Groups_Ozero__class_Ozero(U_2462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),U_2463),U_2464))
      | ~ class_Rings_Oordered__ring(U_2462) ),
    inference(definitional_conversion,[status(esa)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2462),U_2464),U_2465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2462),U_2463),U_2465)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),U_2465),c_Groups_Ozero__class_Ozero(U_2462)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2462),U_2463),U_2464))
    | ~ class_Rings_Oordered__ring(U_2462) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__comm__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).

fof(f_667_2,plain,
    ! [U_2469,U_2468,U_2467,U_2466] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2469),U_2467)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2469),U_2468)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),c_Groups_Ozero__class_Ozero(U_2466)),U_2469))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),U_2467),U_2468))
      | ~ class_Rings_Oordered__comm__semiring(U_2466) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_2466,U_2467,U_2468,U_2469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2469),U_2467)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2469),U_2468)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),c_Groups_Ozero__class_Ozero(U_2466)),U_2469))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),U_2467),U_2468))
      | ~ class_Rings_Oordered__comm__semiring(U_2466) ),
    inference(definitional_conversion,[status(esa)],[f_667_2]) ).

cnf(f_667_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2469),U_2467)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2469),U_2468)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),c_Groups_Ozero__class_Ozero(U_2466)),U_2469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),U_2467),U_2468))
    | ~ class_Rings_Oordered__comm__semiring(U_2466) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).

fof(f_668_2,plain,
    ! [U_2473,U_2472,U_2471,U_2470] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2470),U_2473),U_2471)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2470),U_2473),U_2472)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),c_Groups_Ozero__class_Ozero(U_2470)),U_2473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),U_2471),U_2472))
      | ~ class_Rings_Oordered__semiring(U_2470) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ! [U_2470,U_2471,U_2472,U_2473] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2470),U_2473),U_2471)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2470),U_2473),U_2472)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),c_Groups_Ozero__class_Ozero(U_2470)),U_2473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),U_2471),U_2472))
      | ~ class_Rings_Oordered__semiring(U_2470) ),
    inference(definitional_conversion,[status(esa)],[f_668_2]) ).

cnf(f_668_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2470),U_2473),U_2471)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2470),U_2473),U_2472)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),c_Groups_Ozero__class_Ozero(U_2470)),U_2473))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2470),U_2471),U_2472))
    | ~ class_Rings_Oordered__semiring(U_2470) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).

fof(f_669_2,plain,
    ! [U_2477,U_2476,U_2475,U_2474] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2474),U_2475),U_2477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2474),U_2476),U_2477)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),c_Groups_Ozero__class_Ozero(U_2474)),U_2477))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),U_2475),U_2476))
      | ~ class_Rings_Oordered__semiring(U_2474) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_2474,U_2475,U_2476,U_2477] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2474),U_2475),U_2477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2474),U_2476),U_2477)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),c_Groups_Ozero__class_Ozero(U_2474)),U_2477))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),U_2475),U_2476))
      | ~ class_Rings_Oordered__semiring(U_2474) ),
    inference(definitional_conversion,[status(esa)],[f_669_2]) ).

cnf(f_669_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2474),U_2475),U_2477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2474),U_2476),U_2477)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),c_Groups_Ozero__class_Ozero(U_2474)),U_2477))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2474),U_2475),U_2476))
    | ~ class_Rings_Oordered__semiring(U_2474) ),
    inference(clausify,[status(thm)],[f_669_3]) ).

fof(f_670_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).

fof(f_670_2,plain,
    ! [U_2480,U_2479,U_2478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),c_Groups_Ozero__class_Ozero(U_2478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2480)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2480),c_Groups_Ozero__class_Ozero(U_2478)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2479),c_Groups_Ozero__class_Ozero(U_2478)))
      | ~ class_Rings_Oordered__ring(U_2478) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_2478,U_2479,U_2480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),c_Groups_Ozero__class_Ozero(U_2478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2480)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2480),c_Groups_Ozero__class_Ozero(U_2478)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2479),c_Groups_Ozero__class_Ozero(U_2478)))
      | ~ class_Rings_Oordered__ring(U_2478) ),
    inference(definitional_conversion,[status(esa)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),c_Groups_Ozero__class_Ozero(U_2478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2480)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2480),c_Groups_Ozero__class_Ozero(U_2478)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2479),c_Groups_Ozero__class_Ozero(U_2478)))
    | ~ class_Rings_Oordered__ring(U_2478) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).

fof(f_671_2,plain,
    ! [U_2483,U_2482,U_2481] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2482),U_2483)),c_Groups_Ozero__class_Ozero(U_2481)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),c_Groups_Ozero__class_Ozero(U_2481)),U_2483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),U_2482),c_Groups_Ozero__class_Ozero(U_2481)))
      | ~ class_Rings_Oordered__cancel__semiring(U_2481) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_2481,U_2482,U_2483] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2482),U_2483)),c_Groups_Ozero__class_Ozero(U_2481)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),c_Groups_Ozero__class_Ozero(U_2481)),U_2483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),U_2482),c_Groups_Ozero__class_Ozero(U_2481)))
      | ~ class_Rings_Oordered__cancel__semiring(U_2481) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2482),U_2483)),c_Groups_Ozero__class_Ozero(U_2481)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),c_Groups_Ozero__class_Ozero(U_2481)),U_2483))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),U_2482),c_Groups_Ozero__class_Ozero(U_2481)))
    | ~ class_Rings_Oordered__cancel__semiring(U_2481) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).

fof(f_672_2,plain,
    ! [U_2486,U_2485,U_2484] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2485)),c_Groups_Ozero__class_Ozero(U_2484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),U_2486),c_Groups_Ozero__class_Ozero(U_2484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),U_2485))
      | ~ class_Rings_Oordered__cancel__semiring(U_2484) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ! [U_2484,U_2485,U_2486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2485)),c_Groups_Ozero__class_Ozero(U_2484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),U_2486),c_Groups_Ozero__class_Ozero(U_2484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),U_2485))
      | ~ class_Rings_Oordered__cancel__semiring(U_2484) ),
    inference(definitional_conversion,[status(esa)],[f_672_2]) ).

cnf(f_672_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2485)),c_Groups_Ozero__class_Ozero(U_2484)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),U_2486),c_Groups_Ozero__class_Ozero(U_2484)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),U_2485))
    | ~ class_Rings_Oordered__cancel__semiring(U_2484) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).

fof(f_673_2,plain,
    ! [U_2489,U_2488,U_2487] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489)),c_Groups_Ozero__class_Ozero(U_2487)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),U_2489),c_Groups_Ozero__class_Ozero(U_2487)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),c_Groups_Ozero__class_Ozero(U_2487)),U_2488))
      | ~ class_Rings_Oordered__cancel__semiring(U_2487) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ! [U_2487,U_2488,U_2489] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489)),c_Groups_Ozero__class_Ozero(U_2487)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),U_2489),c_Groups_Ozero__class_Ozero(U_2487)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),c_Groups_Ozero__class_Ozero(U_2487)),U_2488))
      | ~ class_Rings_Oordered__cancel__semiring(U_2487) ),
    inference(definitional_conversion,[status(esa)],[f_673_2]) ).

cnf(f_673_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489)),c_Groups_Ozero__class_Ozero(U_2487)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),U_2489),c_Groups_Ozero__class_Ozero(U_2487)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2487),c_Groups_Ozero__class_Ozero(U_2487)),U_2488))
    | ~ class_Rings_Oordered__cancel__semiring(U_2487) ),
    inference(clausify,[status(thm)],[f_673_3]) ).

fof(f_674_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).

fof(f_674_2,plain,
    ! [U_2492,U_2491,U_2490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2491),U_2492)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),U_2492))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),U_2491))
      | ~ class_Rings_Oordered__cancel__semiring(U_2490) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ! [U_2490,U_2491,U_2492] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2491),U_2492)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),U_2492))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),U_2491))
      | ~ class_Rings_Oordered__cancel__semiring(U_2490) ),
    inference(definitional_conversion,[status(esa)],[f_674_2]) ).

cnf(f_674_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2491),U_2492)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),U_2492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),c_Groups_Ozero__class_Ozero(U_2490)),U_2491))
    | ~ class_Rings_Oordered__cancel__semiring(U_2490) ),
    inference(clausify,[status(thm)],[f_674_3]) ).

fof(f_675_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).

fof(f_675_2,plain,
    ! [U_2495,U_2494,U_2493] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495)),c_Groups_Ozero__class_Ozero(U_2493)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2495))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2494),c_Groups_Ozero__class_Ozero(U_2493))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2495),c_Groups_Ozero__class_Ozero(U_2493)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2494)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2495))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2494),c_Groups_Ozero__class_Ozero(U_2493))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2495),c_Groups_Ozero__class_Ozero(U_2493)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2494)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495)),c_Groups_Ozero__class_Ozero(U_2493))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2493) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ( ! [U_2495,U_2493,U_2494] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2495))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2494),c_Groups_Ozero__class_Ozero(U_2493)))
        | ~ sP199(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2495),c_Groups_Ozero__class_Ozero(U_2493)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2494))
        | ~ sP199(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2495))
        | ~ sP198(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2494),c_Groups_Ozero__class_Ozero(U_2493)))
        | ~ sP198(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2495),c_Groups_Ozero__class_Ozero(U_2493)))
        | ~ sP197(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2494))
        | ~ sP197(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495)),c_Groups_Ozero__class_Ozero(U_2493)))
        | sP199(U_2495,U_2493,U_2494)
        | ~ sP200(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( sP198(U_2495,U_2493,U_2494)
        | sP197(U_2495,U_2493,U_2494)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495)),c_Groups_Ozero__class_Ozero(U_2493)))
        | ~ sP200(U_2495,U_2493,U_2494) )
    & ! [U_2495,U_2493,U_2494] :
        ( sP200(U_2495,U_2493,U_2494)
        | ~ class_Rings_Olinordered__ring__strict(U_2493) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197,sP198,sP199,sP200])],[f_675_2]) ).

cnf(f_675_4,plain,
    ( sP200(U_2495,U_2493,U_2494)
    | ~ class_Rings_Olinordered__ring__strict(U_2493) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_5,plain,
    ( sP198(U_2495,U_2493,U_2494)
    | sP197(U_2495,U_2493,U_2494)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495)),c_Groups_Ozero__class_Ozero(U_2493)))
    | ~ sP200(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495)),c_Groups_Ozero__class_Ozero(U_2493)))
    | sP199(U_2495,U_2493,U_2494)
    | ~ sP200(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2494))
    | ~ sP197(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2495),c_Groups_Ozero__class_Ozero(U_2493)))
    | ~ sP197(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2494),c_Groups_Ozero__class_Ozero(U_2493)))
    | ~ sP198(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2495))
    | ~ sP198(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2495),c_Groups_Ozero__class_Ozero(U_2493)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2494))
    | ~ sP199(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

cnf(f_675_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),U_2495))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2493),U_2494),c_Groups_Ozero__class_Ozero(U_2493)))
    | ~ sP199(U_2495,U_2493,U_2494) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).

fof(f_676_2,plain,
    ! [U_2498,U_2497,U_2496] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),U_2498)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2498),c_Groups_Ozero__class_Ozero(U_2496)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2497),c_Groups_Ozero__class_Ozero(U_2496))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2498))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2497)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2498),c_Groups_Ozero__class_Ozero(U_2496)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2497),c_Groups_Ozero__class_Ozero(U_2496))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2498))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2497)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),U_2498))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2496) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ( ! [U_2498,U_2496,U_2497] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2498),c_Groups_Ozero__class_Ozero(U_2496)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2497),c_Groups_Ozero__class_Ozero(U_2496)))
        | ~ sP203(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2498))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2497))
        | ~ sP203(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2498),c_Groups_Ozero__class_Ozero(U_2496)))
        | ~ sP202(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2497),c_Groups_Ozero__class_Ozero(U_2496)))
        | ~ sP202(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2498))
        | ~ sP201(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2497))
        | ~ sP201(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),U_2498)))
        | sP203(U_2498,U_2496,U_2497)
        | ~ sP204(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( sP202(U_2498,U_2496,U_2497)
        | sP201(U_2498,U_2496,U_2497)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),U_2498)))
        | ~ sP204(U_2498,U_2496,U_2497) )
    & ! [U_2498,U_2496,U_2497] :
        ( sP204(U_2498,U_2496,U_2497)
        | ~ class_Rings_Olinordered__ring__strict(U_2496) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201,sP202,sP203,sP204])],[f_676_2]) ).

cnf(f_676_4,plain,
    ( sP204(U_2498,U_2496,U_2497)
    | ~ class_Rings_Olinordered__ring__strict(U_2496) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_5,plain,
    ( sP202(U_2498,U_2496,U_2497)
    | sP201(U_2498,U_2496,U_2497)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),U_2498)))
    | ~ sP204(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),U_2498)))
    | sP203(U_2498,U_2496,U_2497)
    | ~ sP204(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2497))
    | ~ sP201(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2498))
    | ~ sP201(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2497),c_Groups_Ozero__class_Ozero(U_2496)))
    | ~ sP202(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2498),c_Groups_Ozero__class_Ozero(U_2496)))
    | ~ sP202(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2498))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),c_Groups_Ozero__class_Ozero(U_2496)),U_2497))
    | ~ sP203(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2498),c_Groups_Ozero__class_Ozero(U_2496)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2496),U_2497),c_Groups_Ozero__class_Ozero(U_2496)))
    | ~ sP203(U_2498,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).

fof(f_677_2,plain,
    ! [U_2500,U_2499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2499),c_Groups_Ozero__class_Ozero(U_2499)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),U_2500)))
      | ~ class_Rings_Olinordered__ring(U_2499) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ! [U_2500,U_2499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2499),c_Groups_Ozero__class_Ozero(U_2499)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),U_2500)))
      | ~ class_Rings_Olinordered__ring(U_2499) ),
    inference(definitional_conversion,[status(esa)],[f_677_2]) ).

cnf(f_677_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2499),c_Groups_Ozero__class_Ozero(U_2499)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),U_2500)))
    | ~ class_Rings_Olinordered__ring(U_2499) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).

fof(f_678_2,plain,
    ! [U_2505,U_2504,U_2503,U_2502,U_2501] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2501),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2501),U_2502),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2501),U_2503),U_2505)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2501),U_2504),U_2505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2501),U_2502),U_2503))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2501) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ! [U_2504,U_2502,U_2505,U_2503,U_2501] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2501),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2501),U_2502),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2501),U_2503),U_2505)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2501),U_2504),U_2505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2501),U_2502),U_2503))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2501) ),
    inference(definitional_conversion,[status(esa)],[f_678_2]) ).

cnf(f_678_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2501),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2501),U_2502),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2501),U_2503),U_2505)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2501),U_2504),U_2505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2501),U_2502),U_2503))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2501) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).

fof(f_679_2,plain,
    ! [U_2510,U_2509,U_2508,U_2507,U_2506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2506),U_2507),U_2509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2506),U_2508),U_2510)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2506),U_2509),U_2510))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2506),U_2507),U_2508))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2506) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_2510,U_2506,U_2507,U_2508,U_2509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2506),U_2507),U_2509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2506),U_2508),U_2510)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2506),U_2509),U_2510))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2506),U_2507),U_2508))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2506) ),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2506),U_2507),U_2509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2506),U_2508),U_2510)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2506),U_2509),U_2510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2506),U_2507),U_2508))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2506) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).

fof(f_680_2,plain,
    ! [U_2511] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),c_Groups_Oone__class_Oone(U_2511)))
      | ~ class_Rings_Olinordered__semidom(U_2511) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_2511] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),c_Groups_Oone__class_Oone(U_2511)))
      | ~ class_Rings_Olinordered__semidom(U_2511) ),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),c_Groups_Oone__class_Oone(U_2511)))
    | ~ class_Rings_Olinordered__semidom(U_2511) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_1,plain,
    ! [T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).

fof(f_681_2,plain,
    ! [U_2512] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2512),c_Groups_Oone__class_Oone(U_2512)),c_Groups_Ozero__class_Ozero(U_2512)))
      | ~ class_Rings_Olinordered__semidom(U_2512) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ! [U_2512] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2512),c_Groups_Oone__class_Oone(U_2512)),c_Groups_Ozero__class_Ozero(U_2512)))
      | ~ class_Rings_Olinordered__semidom(U_2512) ),
    inference(definitional_conversion,[status(esa)],[f_681_2]) ).

cnf(f_681_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2512),c_Groups_Oone__class_Oone(U_2512)),c_Groups_Ozero__class_Ozero(U_2512)))
    | ~ class_Rings_Olinordered__semidom(U_2512) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).

fof(f_682_2,plain,
    ! [U_2514,U_2513] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),c_Groups_Ozero__class_Ozero(U_2513)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2513),U_2514)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),U_2514),c_Groups_Ozero__class_Ozero(U_2513))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),U_2514),c_Groups_Ozero__class_Ozero(U_2513)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),c_Groups_Ozero__class_Ozero(U_2513)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2513),U_2514))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2513) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ( ! [U_2513,U_2514] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),c_Groups_Ozero__class_Ozero(U_2513)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2513),U_2514)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),U_2514),c_Groups_Ozero__class_Ozero(U_2513)))
        | ~ sP205(U_2513,U_2514) )
    & ! [U_2513,U_2514] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),U_2514),c_Groups_Ozero__class_Ozero(U_2513)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),c_Groups_Ozero__class_Ozero(U_2513)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2513),U_2514)))
        | ~ sP205(U_2513,U_2514) )
    & ! [U_2513,U_2514] :
        ( sP205(U_2513,U_2514)
        | ~ class_Groups_Oordered__ab__group__add(U_2513) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_682_2]) ).

cnf(f_682_4,plain,
    ( sP205(U_2513,U_2514)
    | ~ class_Groups_Oordered__ab__group__add(U_2513) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

cnf(f_682_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),U_2514),c_Groups_Ozero__class_Ozero(U_2513)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),c_Groups_Ozero__class_Ozero(U_2513)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2513),U_2514)))
    | ~ sP205(U_2513,U_2514) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

cnf(f_682_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),c_Groups_Ozero__class_Ozero(U_2513)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2513),U_2514)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2513),U_2514),c_Groups_Ozero__class_Ozero(U_2513)))
    | ~ sP205(U_2513,U_2514) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).

fof(f_683_2,plain,
    ! [U_2516,U_2515] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),hAPP(c_Groups_Ouminus__class_Ouminus(U_2515),U_2516)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),c_Groups_Ozero__class_Ozero(U_2515))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),c_Groups_Ozero__class_Ozero(U_2515)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),hAPP(c_Groups_Ouminus__class_Ouminus(U_2515),U_2516))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2515) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_2515,U_2516] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),hAPP(c_Groups_Ouminus__class_Ouminus(U_2515),U_2516)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),c_Groups_Ozero__class_Ozero(U_2515)))
        | ~ sP206(U_2515,U_2516) )
    & ! [U_2515,U_2516] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),c_Groups_Ozero__class_Ozero(U_2515)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),hAPP(c_Groups_Ouminus__class_Ouminus(U_2515),U_2516)))
        | ~ sP206(U_2515,U_2516) )
    & ! [U_2515,U_2516] :
        ( sP206(U_2515,U_2516)
        | ~ class_Groups_Olinordered__ab__group__add(U_2515) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_683_2]) ).

cnf(f_683_4,plain,
    ( sP206(U_2515,U_2516)
    | ~ class_Groups_Olinordered__ab__group__add(U_2515) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),c_Groups_Ozero__class_Ozero(U_2515)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),hAPP(c_Groups_Ouminus__class_Ouminus(U_2515),U_2516)))
    | ~ sP206(U_2515,U_2516) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),hAPP(c_Groups_Ouminus__class_Ouminus(U_2515),U_2516)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2515),U_2516),c_Groups_Ozero__class_Ozero(U_2515)))
    | ~ sP206(U_2515,U_2516) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).

fof(f_684_2,plain,
    ! [U_2518,U_2517] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),hAPP(c_Groups_Ouminus__class_Ouminus(U_2517),U_2518)),c_Groups_Ozero__class_Ozero(U_2517)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),c_Groups_Ozero__class_Ozero(U_2517)),U_2518)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),c_Groups_Ozero__class_Ozero(U_2517)),U_2518))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),hAPP(c_Groups_Ouminus__class_Ouminus(U_2517),U_2518)),c_Groups_Ozero__class_Ozero(U_2517))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2517) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ( ! [U_2517,U_2518] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),hAPP(c_Groups_Ouminus__class_Ouminus(U_2517),U_2518)),c_Groups_Ozero__class_Ozero(U_2517)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),c_Groups_Ozero__class_Ozero(U_2517)),U_2518))
        | ~ sP207(U_2517,U_2518) )
    & ! [U_2517,U_2518] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),c_Groups_Ozero__class_Ozero(U_2517)),U_2518))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),hAPP(c_Groups_Ouminus__class_Ouminus(U_2517),U_2518)),c_Groups_Ozero__class_Ozero(U_2517)))
        | ~ sP207(U_2517,U_2518) )
    & ! [U_2517,U_2518] :
        ( sP207(U_2517,U_2518)
        | ~ class_Groups_Oordered__ab__group__add(U_2517) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_684_2]) ).

cnf(f_684_4,plain,
    ( sP207(U_2517,U_2518)
    | ~ class_Groups_Oordered__ab__group__add(U_2517) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

cnf(f_684_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),c_Groups_Ozero__class_Ozero(U_2517)),U_2518))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),hAPP(c_Groups_Ouminus__class_Ouminus(U_2517),U_2518)),c_Groups_Ozero__class_Ozero(U_2517)))
    | ~ sP207(U_2517,U_2518) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

cnf(f_684_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),hAPP(c_Groups_Ouminus__class_Ouminus(U_2517),U_2518)),c_Groups_Ozero__class_Ozero(U_2517)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2517),c_Groups_Ozero__class_Ozero(U_2517)),U_2518))
    | ~ sP207(U_2517,U_2518) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).

fof(f_685_2,plain,
    ! [U_2520,U_2519] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),hAPP(c_Groups_Ouminus__class_Ouminus(U_2519),U_2520)),U_2520))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),c_Groups_Ozero__class_Ozero(U_2519)),U_2520)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),c_Groups_Ozero__class_Ozero(U_2519)),U_2520))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),hAPP(c_Groups_Ouminus__class_Ouminus(U_2519),U_2520)),U_2520)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2519) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ( ! [U_2519,U_2520] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),hAPP(c_Groups_Ouminus__class_Ouminus(U_2519),U_2520)),U_2520))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),c_Groups_Ozero__class_Ozero(U_2519)),U_2520))
        | ~ sP208(U_2519,U_2520) )
    & ! [U_2519,U_2520] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),c_Groups_Ozero__class_Ozero(U_2519)),U_2520))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),hAPP(c_Groups_Ouminus__class_Ouminus(U_2519),U_2520)),U_2520))
        | ~ sP208(U_2519,U_2520) )
    & ! [U_2519,U_2520] :
        ( sP208(U_2519,U_2520)
        | ~ class_Groups_Olinordered__ab__group__add(U_2519) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_685_2]) ).

cnf(f_685_4,plain,
    ( sP208(U_2519,U_2520)
    | ~ class_Groups_Olinordered__ab__group__add(U_2519) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

cnf(f_685_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),c_Groups_Ozero__class_Ozero(U_2519)),U_2520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),hAPP(c_Groups_Ouminus__class_Ouminus(U_2519),U_2520)),U_2520))
    | ~ sP208(U_2519,U_2520) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

cnf(f_685_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),hAPP(c_Groups_Ouminus__class_Ouminus(U_2519),U_2520)),U_2520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),c_Groups_Ozero__class_Ozero(U_2519)),U_2520))
    | ~ sP208(U_2519,U_2520) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

fof(f_686_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).

fof(f_686_2,plain,
    ! [U_2522,U_2521] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2521),U_2522) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2522 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2521 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_2522 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2521 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2521),U_2522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ( ! [U_2526,U_2524] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2524),U_2526) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2526 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2524 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2525,U_2523] :
        ( ( U_2525 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2523 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2523),U_2525) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_686_2]) ).

fof(f_686_4,plain,
    ( ! [U_2525,U_2523] :
        ( U_2525 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP209(U_2525,U_2523) )
    & ! [U_2525,U_2523] :
        ( U_2523 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP209(U_2525,U_2523) )
    & ! [U_2526,U_2524] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2524),U_2526) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2526 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2524 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2525,U_2523] :
        ( sP209(U_2525,U_2523)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2523),U_2525) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_686_3]) ).

cnf(f_686_5,plain,
    ( sP209(U_2525,U_2523)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2523),U_2525) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

cnf(f_686_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2524),U_2526) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2526 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2524 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

cnf(f_686_7,plain,
    ( U_2523 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP209(U_2525,U_2523) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

cnf(f_686_8,plain,
    ( U_2525 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP209(U_2525,U_2523) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

fof(f_687_1,plain,
    ! [V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff]) ).

fof(f_687_2,plain,
    ! [U_2528,U_2527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2527),c_Groups_Ozero__class_Ozero(U_2527)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2527),U_2528)))
      | ~ class_Rings_Olinordered__semidom(U_2527) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_2527,U_2528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2527),c_Groups_Ozero__class_Ozero(U_2527)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2527),U_2528)))
      | ~ class_Rings_Olinordered__semidom(U_2527) ),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2527),c_Groups_Ozero__class_Ozero(U_2527)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2527),U_2528)))
    | ~ class_Rings_Olinordered__semidom(U_2527) ),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_1,plain,
    ! [V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat]) ).

fof(f_688_2,plain,
    ! [U_2530,U_2529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2529),c_Groups_Ozero__class_Ozero(U_2529)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2529),U_2530)))
      | ~ class_Rings_Olinordered__semidom(U_2529) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_2529,U_2530] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2529),c_Groups_Ozero__class_Ozero(U_2529)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2529),U_2530)))
      | ~ class_Rings_Olinordered__semidom(U_2529) ),
    inference(definitional_conversion,[status(esa)],[f_688_2]) ).

cnf(f_688_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2529),c_Groups_Ozero__class_Ozero(U_2529)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2529),U_2530)))
    | ~ class_Rings_Olinordered__semidom(U_2529) ),
    inference(clausify,[status(thm)],[f_688_3]) ).

fof(f_689_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).

fof(f_689_2,plain,
    ! [U_2533,U_2532,U_2531] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2533),U_2531)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2533),U_2532)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2531),U_2532)) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_2531,U_2532,U_2533] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2533),U_2531)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2533),U_2532)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2531),U_2532)) ),
    inference(definitional_conversion,[status(esa)],[f_689_2]) ).

cnf(f_689_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2533),U_2531)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2533),U_2532)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2531),U_2532)) ),
    inference(clausify,[status(thm)],[f_689_3]) ).

fof(f_690_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).

fof(f_690_2,plain,
    ! [U_2536,U_2535,U_2534] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2534),U_2536)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2535),U_2536)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2534),U_2535)) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ! [U_2534,U_2535,U_2536] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2534),U_2536)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2535),U_2536)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2534),U_2535)) ),
    inference(definitional_conversion,[status(esa)],[f_690_2]) ).

cnf(f_690_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2534),U_2536)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2535),U_2536)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2534),U_2535)) ),
    inference(clausify,[status(thm)],[f_690_3]) ).

fof(f_691_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).

fof(f_691_2,plain,
    ! [U_2539,U_2538,U_2537] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2537),U_2538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2539),U_2538)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2537),U_2539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2538)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2537),U_2539))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2538)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2537),U_2538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2539),U_2538))) ) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ( ! [U_2545,U_2543,U_2541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2541),U_2543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2545),U_2543)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2541),U_2545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2543)) )
    & ! [U_2544,U_2542,U_2540] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2540),U_2544))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2542)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2540),U_2542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2544),U_2542))) ) ),
    inference(miniscope,[status(thm)],[f_691_2]) ).

fof(f_691_4,plain,
    ( ! [U_2542,U_2540,U_2544] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2540),U_2544))
        | ~ sP210(U_2542,U_2540,U_2544) )
    & ! [U_2542,U_2540,U_2544] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2542))
        | ~ sP210(U_2542,U_2540,U_2544) )
    & ! [U_2543,U_2541,U_2545] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2541),U_2543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2545),U_2543)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2541),U_2545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2543)) )
    & ! [U_2542,U_2540,U_2544] :
        ( sP210(U_2542,U_2540,U_2544)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2540),U_2542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2544),U_2542))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_691_3]) ).

cnf(f_691_5,plain,
    ( sP210(U_2542,U_2540,U_2544)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2540),U_2542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2544),U_2542))) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2541),U_2543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2545),U_2543)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2541),U_2545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2543)) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2542))
    | ~ sP210(U_2542,U_2540,U_2544) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2540),U_2544))
    | ~ sP210(U_2542,U_2540,U_2544) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

fof(f_692_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).

fof(f_692_2,plain,
    ! [U_2548,U_2547,U_2546] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2546),U_2547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2546),U_2548)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2547),U_2548))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2546)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2547),U_2548))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2546)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2546),U_2547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2546),U_2548))) ) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ( ! [U_2554,U_2552,U_2550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2554)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2552),U_2554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2550)) )
    & ! [U_2553,U_2551,U_2549] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2551),U_2553))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2549)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2553))) ) ),
    inference(miniscope,[status(thm)],[f_692_2]) ).

fof(f_692_4,plain,
    ( ! [U_2549,U_2553,U_2551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2551),U_2553))
        | ~ sP211(U_2549,U_2553,U_2551) )
    & ! [U_2549,U_2553,U_2551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2549))
        | ~ sP211(U_2549,U_2553,U_2551) )
    & ! [U_2554,U_2552,U_2550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2554)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2552),U_2554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2550)) )
    & ! [U_2549,U_2553,U_2551] :
        ( sP211(U_2549,U_2553,U_2551)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2553))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_692_3]) ).

cnf(f_692_5,plain,
    ( sP211(U_2549,U_2553,U_2551)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2553))) ),
    inference(clausify,[status(thm)],[f_692_4]) ).

cnf(f_692_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2554)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2552),U_2554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2550)) ),
    inference(clausify,[status(thm)],[f_692_4]) ).

cnf(f_692_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2549))
    | ~ sP211(U_2549,U_2553,U_2551) ),
    inference(clausify,[status(thm)],[f_692_4]) ).

cnf(f_692_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2551),U_2553))
    | ~ sP211(U_2549,U_2553,U_2551) ),
    inference(clausify,[status(thm)],[f_692_4]) ).

fof(f_693_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).

fof(f_693_2,plain,
    ! [U_2556,U_2555] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2555),U_2556)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2556))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2555)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2556))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2555)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2555),U_2556))) ) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ( ! [U_2560,U_2558] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2560)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2558)) )
    & ! [U_2559,U_2557] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2559))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2557)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2557),U_2559))) ) ),
    inference(miniscope,[status(thm)],[f_693_2]) ).

fof(f_693_4,plain,
    ( ! [U_2557,U_2559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2559))
        | ~ sP212(U_2557,U_2559) )
    & ! [U_2557,U_2559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2557))
        | ~ sP212(U_2557,U_2559) )
    & ! [U_2558,U_2560] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2560)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2558)) )
    & ! [U_2557,U_2559] :
        ( sP212(U_2557,U_2559)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2557),U_2559))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_693_3]) ).

cnf(f_693_5,plain,
    ( sP212(U_2557,U_2559)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2557),U_2559))) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

cnf(f_693_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2560)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2560))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2558)) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

cnf(f_693_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2557))
    | ~ sP212(U_2557,U_2559) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

cnf(f_693_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2559))
    | ~ sP212(U_2557,U_2559) ),
    inference(clausify,[status(thm)],[f_693_4]) ).

fof(f_694_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).

fof(f_694_2,plain,
    ! [U_2563,U_2562,U_2561] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2561)),U_2562)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2561)),U_2563)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2562),U_2563)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2562),U_2563))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2561)),U_2562)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2561)),U_2563))) ) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ( ! [U_2569,U_2567] :
        ( ! [U_2565] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2565)),U_2567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2565)),U_2569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2567),U_2569)) )
    & ! [U_2568,U_2566] :
        ( ! [U_2564] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2564)),U_2566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2564)),U_2568)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2566),U_2568)) ) ),
    inference(miniscope,[status(thm)],[f_694_2]) ).

fof(f_694_4,plain,
    ( ! [U_2569,U_2565,U_2567] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2565)),U_2567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2565)),U_2569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2567),U_2569)) )
    & ! [U_2564,U_2566,U_2568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2564)),U_2566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2564)),U_2568)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2566),U_2568)) ) ),
    inference(definitional_conversion,[status(esa)],[f_694_3]) ).

cnf(f_694_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2564)),U_2566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2564)),U_2568)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2566),U_2568)) ),
    inference(clausify,[status(thm)],[f_694_4]) ).

cnf(f_694_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2565)),U_2567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2565)),U_2569)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2567),U_2569)) ),
    inference(clausify,[status(thm)],[f_694_4]) ).

fof(f_695_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).

fof(f_695_2,plain,
    ! [U_2571,U_2570] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2570)),U_2571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571)),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_2570,U_2571] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2570)),U_2571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571)),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2570)),U_2571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571)),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).

fof(f_696_2,plain,
    ! [U_2573,U_2572] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2572),hAPP(c_Nat_OSuc,U_2573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2572),U_2573)),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_2572,U_2573] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2572),hAPP(c_Nat_OSuc,U_2573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2572),U_2573)),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2572),hAPP(c_Nat_OSuc,U_2573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2572),U_2573)),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_One__nat__def]) ).

fof(f_697_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_697_1]) ).

cnf(f_697_3,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_697_2]) ).

fof(f_698_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).

fof(f_698_2,plain,
    ! [U_2575,U_2574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2574),U_2575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2574)),U_2575)) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_2574,U_2575] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2574),U_2575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2574)),U_2575)) ),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2574),U_2575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2574)),U_2575)) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
          | V_n_2 != V_m_2 )
        & ( V_n_2 = V_m_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).

fof(f_699_2,plain,
    ! [U_2577,U_2576] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),hAPP(c_Nat_OSuc,U_2576)))
          | U_2577 != U_2576 )
        & ( U_2577 = U_2576
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),hAPP(c_Nat_OSuc,U_2576))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2576),U_2577)) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ( ! [U_2576,U_2577] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),hAPP(c_Nat_OSuc,U_2576)))
        | U_2577 != U_2576
        | ~ sP213(U_2576,U_2577) )
    & ! [U_2576,U_2577] :
        ( U_2577 = U_2576
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),hAPP(c_Nat_OSuc,U_2576)))
        | ~ sP213(U_2576,U_2577) )
    & ! [U_2576,U_2577] :
        ( sP213(U_2576,U_2577)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2576),U_2577)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_699_2]) ).

cnf(f_699_4,plain,
    ( sP213(U_2576,U_2577)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2576),U_2577)) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

cnf(f_699_5,plain,
    ( U_2577 = U_2576
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),hAPP(c_Nat_OSuc,U_2576)))
    | ~ sP213(U_2576,U_2577) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

cnf(f_699_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),hAPP(c_Nat_OSuc,U_2576)))
    | U_2577 != U_2576
    | ~ sP213(U_2576,U_2577) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).

fof(f_700_2,plain,
    ! [U_2579,U_2578] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2578)),U_2579))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2578),U_2579)) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_2579,U_2578] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2578)),U_2579))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2578),U_2579)) ),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2578)),U_2579))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2578),U_2579)) ),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).

fof(f_701_2,plain,
    ! [U_2581,U_2580] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2580),hAPP(c_Nat_OSuc,U_2581)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2580),U_2581)) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_2580,U_2581] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2580),hAPP(c_Nat_OSuc,U_2581)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2580),U_2581)) ),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2580),hAPP(c_Nat_OSuc,U_2581)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2580),U_2581)) ),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).

fof(f_702_2,plain,
    ! [U_2583,U_2582] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2582)),U_2583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2582),U_2583)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2582),U_2583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2582)),U_2583)) ) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ( ! [U_2587,U_2585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2585)),U_2587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2585),U_2587)) )
    & ! [U_2586,U_2584] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2584),U_2586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2584)),U_2586)) ) ),
    inference(miniscope,[status(thm)],[f_702_2]) ).

fof(f_702_4,plain,
    ( ! [U_2585,U_2587] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2585)),U_2587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2585),U_2587)) )
    & ! [U_2586,U_2584] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2584),U_2586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2584)),U_2586)) ) ),
    inference(definitional_conversion,[status(esa)],[f_702_3]) ).

cnf(f_702_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2584),U_2586))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2584)),U_2586)) ),
    inference(clausify,[status(thm)],[f_702_4]) ).

cnf(f_702_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2585)),U_2587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2585),U_2587)) ),
    inference(clausify,[status(thm)],[f_702_4]) ).

fof(f_703_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).

fof(f_703_2,plain,
    ! [U_2589,U_2588] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2588),hAPP(c_Nat_OSuc,U_2589)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2588),U_2589)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2588),U_2589))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2588),hAPP(c_Nat_OSuc,U_2589))) ) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ( ! [U_2593,U_2591] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2591),hAPP(c_Nat_OSuc,U_2593)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2591),U_2593)) )
    & ! [U_2592,U_2590] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2590),U_2592))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2590),hAPP(c_Nat_OSuc,U_2592))) ) ),
    inference(miniscope,[status(thm)],[f_703_2]) ).

fof(f_703_4,plain,
    ( ! [U_2591,U_2593] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2591),hAPP(c_Nat_OSuc,U_2593)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2591),U_2593)) )
    & ! [U_2592,U_2590] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2590),U_2592))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2590),hAPP(c_Nat_OSuc,U_2592))) ) ),
    inference(definitional_conversion,[status(esa)],[f_703_3]) ).

cnf(f_703_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2590),U_2592))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2590),hAPP(c_Nat_OSuc,U_2592))) ),
    inference(clausify,[status(thm)],[f_703_4]) ).

cnf(f_703_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2591),hAPP(c_Nat_OSuc,U_2593)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2591),U_2593)) ),
    inference(clausify,[status(thm)],[f_703_4]) ).

fof(f_704_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).

fof(f_704_2,plain,
    ! [U_2595,U_2594] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2594),U_2595))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2594)),U_2595)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2594)),U_2595))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2594),U_2595)) ) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ( ! [U_2599,U_2597] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2597),U_2599))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2597)),U_2599)) )
    & ! [U_2598,U_2596] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2596)),U_2598))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2596),U_2598)) ) ),
    inference(miniscope,[status(thm)],[f_704_2]) ).

fof(f_704_4,plain,
    ( ! [U_2597,U_2599] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2597),U_2599))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2597)),U_2599)) )
    & ! [U_2598,U_2596] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2596)),U_2598))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2596),U_2598)) ) ),
    inference(definitional_conversion,[status(esa)],[f_704_3]) ).

cnf(f_704_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2596)),U_2598))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2596),U_2598)) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2597),U_2599))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2597)),U_2599)) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

fof(f_705_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(f_705_2,plain,
    ! [U_2600] : hAPP(c_Nat_OSuc,U_2600) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2600),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_2600] : hAPP(c_Nat_OSuc,U_2600) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2600),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    hAPP(c_Nat_OSuc,U_2600) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2600),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(f_706_2,plain,
    ! [U_2601] : hAPP(c_Nat_OSuc,U_2601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2601),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_2601] : hAPP(c_Nat_OSuc,U_2601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2601),
    inference(definitional_conversion,[status(esa)],[f_706_2]) ).

cnf(f_706_4,plain,
    hAPP(c_Nat_OSuc,U_2601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2601),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_707_2,plain,
    ! [U_2603,U_2602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2602),U_2603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2603))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2602)) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2602,U_2603] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2602),U_2603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2603))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2602)) ),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2602),U_2603)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2603))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2602)) ),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    inference(fof_nnf,[status(thm)],[fact_zero__zle__int]) ).

fof(f_708_2,plain,
    ! [U_2604] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2604))),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_2604] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2604))),
    inference(definitional_conversion,[status(esa)],[f_708_2]) ).

cnf(f_708_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2604))),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_1,plain,
    ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(f_709_2,plain,
    ! [U_2605] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2605))),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_2605] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2605))),
    inference(definitional_conversion,[status(esa)],[f_709_2]) ).

cnf(f_709_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2605))),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J]) ).

fof(f_710_2,plain,
    ! [U_2610] :
      ( ( ? [U_2609] :
            ( hBOOL(hAPP(U_2610,U_2609))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2609)) )
        | ! [U_2608] : ~ hBOOL(hAPP(U_2610,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2608))) )
      & ( ? [U_2607] : hBOOL(hAPP(U_2610,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2607)))
        | ! [U_2606] :
            ( ~ hBOOL(hAPP(U_2610,U_2606))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2606)) ) ) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ( ! [U_2612] :
        ( ? [U_2609] :
            ( hBOOL(hAPP(U_2612,U_2609))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2609)) )
        | ! [U_2608] : ~ hBOOL(hAPP(U_2612,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2608))) )
    & ! [U_2611] :
        ( ? [U_2607] : hBOOL(hAPP(U_2611,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2607)))
        | ! [U_2606] :
            ( ~ hBOOL(hAPP(U_2611,U_2606))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2606)) ) ) ),
    inference(miniscope,[status(thm)],[f_710_2]) ).

fof(f_710_4,plain,
    ( ! [U_2612] :
        ( ? [U_2609] :
            ( hBOOL(hAPP(U_2612,U_2609))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2609)) )
        | ! [U_2608] : ~ hBOOL(hAPP(U_2612,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2608))) )
    & ! [U_2611] :
        ( hBOOL(hAPP(U_2611,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK42(U_2611))))
        | ! [U_2606] :
            ( ~ hBOOL(hAPP(U_2611,U_2606))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2606)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2607,sK42(U_2611))],[f_710_3]) ).

fof(f_710_5,plain,
    ( ! [U_2612] :
        ( ( hBOOL(hAPP(U_2612,sK43(U_2612)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2612))) )
        | ! [U_2608] : ~ hBOOL(hAPP(U_2612,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2608))) )
    & ! [U_2611] :
        ( hBOOL(hAPP(U_2611,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK42(U_2611))))
        | ! [U_2606] :
            ( ~ hBOOL(hAPP(U_2611,U_2606))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2606)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2609,sK43(U_2612))],[f_710_4]) ).

fof(f_710_6,plain,
    ( ! [U_2612] :
        ( hBOOL(hAPP(U_2612,sK43(U_2612)))
        | ~ sP214(U_2612) )
    & ! [U_2612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2612)))
        | ~ sP214(U_2612) )
    & ! [U_2608,U_2612] :
        ( sP214(U_2612)
        | ~ hBOOL(hAPP(U_2612,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2608))) )
    & ! [U_2606,U_2611] :
        ( hBOOL(hAPP(U_2611,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK42(U_2611))))
        | ~ hBOOL(hAPP(U_2611,U_2606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2606)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_710_5]) ).

cnf(f_710_7,plain,
    ( hBOOL(hAPP(U_2611,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK42(U_2611))))
    | ~ hBOOL(hAPP(U_2611,U_2606))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2606)) ),
    inference(clausify,[status(thm)],[f_710_6]) ).

cnf(f_710_8,plain,
    ( sP214(U_2612)
    | ~ hBOOL(hAPP(U_2612,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2608))) ),
    inference(clausify,[status(thm)],[f_710_6]) ).

cnf(f_710_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2612)))
    | ~ sP214(U_2612) ),
    inference(clausify,[status(thm)],[f_710_6]) ).

cnf(f_710_10,plain,
    ( hBOOL(hAPP(U_2612,sK43(U_2612)))
    | ~ sP214(U_2612) ),
    inference(clausify,[status(thm)],[f_710_6]) ).

fof(f_711_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J]) ).

fof(f_711_2,plain,
    ! [U_2617] :
      ( ( ! [U_2616] :
            ( hBOOL(hAPP(U_2617,U_2616))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2616)) )
        | ? [U_2615] : ~ hBOOL(hAPP(U_2617,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2615))) )
      & ( ! [U_2614] : hBOOL(hAPP(U_2617,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2614)))
        | ? [U_2613] :
            ( ~ hBOOL(hAPP(U_2617,U_2613))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2613)) ) ) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ( ! [U_2619] :
        ( ! [U_2616] :
            ( hBOOL(hAPP(U_2619,U_2616))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2616)) )
        | ? [U_2615] : ~ hBOOL(hAPP(U_2619,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2615))) )
    & ! [U_2618] :
        ( ! [U_2614] : hBOOL(hAPP(U_2618,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2614)))
        | ? [U_2613] :
            ( ~ hBOOL(hAPP(U_2618,U_2613))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2613)) ) ) ),
    inference(miniscope,[status(thm)],[f_711_2]) ).

fof(f_711_4,plain,
    ( ! [U_2619] :
        ( ! [U_2616] :
            ( hBOOL(hAPP(U_2619,U_2616))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2616)) )
        | ? [U_2615] : ~ hBOOL(hAPP(U_2619,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2615))) )
    & ! [U_2618] :
        ( ! [U_2614] : hBOOL(hAPP(U_2618,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2614)))
        | ( ~ hBOOL(hAPP(U_2618,sK44(U_2618)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK44(U_2618))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2613,sK44(U_2618))],[f_711_3]) ).

fof(f_711_5,plain,
    ( ! [U_2619] :
        ( ! [U_2616] :
            ( hBOOL(hAPP(U_2619,U_2616))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2616)) )
        | ~ hBOOL(hAPP(U_2619,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK45(U_2619)))) )
    & ! [U_2618] :
        ( ! [U_2614] : hBOOL(hAPP(U_2618,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2614)))
        | ( ~ hBOOL(hAPP(U_2618,sK44(U_2618)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK44(U_2618))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2615,sK45(U_2619))],[f_711_4]) ).

fof(f_711_6,plain,
    ( ! [U_2618] :
        ( ~ hBOOL(hAPP(U_2618,sK44(U_2618)))
        | ~ sP215(U_2618) )
    & ! [U_2618] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK44(U_2618)))
        | ~ sP215(U_2618) )
    & ! [U_2616,U_2619] :
        ( hBOOL(hAPP(U_2619,U_2616))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2616))
        | ~ hBOOL(hAPP(U_2619,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK45(U_2619)))) )
    & ! [U_2614,U_2618] :
        ( hBOOL(hAPP(U_2618,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2614)))
        | sP215(U_2618) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_711_5]) ).

cnf(f_711_7,plain,
    ( hBOOL(hAPP(U_2618,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2614)))
    | sP215(U_2618) ),
    inference(clausify,[status(thm)],[f_711_6]) ).

cnf(f_711_8,plain,
    ( hBOOL(hAPP(U_2619,U_2616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2616))
    | ~ hBOOL(hAPP(U_2619,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK45(U_2619)))) ),
    inference(clausify,[status(thm)],[f_711_6]) ).

cnf(f_711_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK44(U_2618)))
    | ~ sP215(U_2618) ),
    inference(clausify,[status(thm)],[f_711_6]) ).

cnf(f_711_10,plain,
    ( ~ hBOOL(hAPP(U_2618,sK44(U_2618)))
    | ~ sP215(U_2618) ),
    inference(clausify,[status(thm)],[f_711_6]) ).

fof(f_712_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).

fof(f_712_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_712_1]) ).

cnf(f_712_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_712_2]) ).

fof(f_713_1,plain,
    ! [V_z_H_2,V_z_2] :
      ( ( ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
          | V_z_2 != V_z_H_2 )
        & ( V_z_2 = V_z_H_2
          | hAPP(c_Int_Onat,V_z_2) != hAPP(c_Int_Onat,V_z_H_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff]) ).

fof(f_713_2,plain,
    ! [U_2621,U_2620] :
      ( ( ( hAPP(c_Int_Onat,U_2620) = hAPP(c_Int_Onat,U_2621)
          | U_2620 != U_2621 )
        & ( U_2620 = U_2621
          | hAPP(c_Int_Onat,U_2620) != hAPP(c_Int_Onat,U_2621) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2621))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ( ! [U_2620,U_2621] :
        ( hAPP(c_Int_Onat,U_2620) = hAPP(c_Int_Onat,U_2621)
        | U_2620 != U_2621
        | ~ sP216(U_2620,U_2621) )
    & ! [U_2620,U_2621] :
        ( U_2620 = U_2621
        | hAPP(c_Int_Onat,U_2620) != hAPP(c_Int_Onat,U_2621)
        | ~ sP216(U_2620,U_2621) )
    & ! [U_2620,U_2621] :
        ( sP216(U_2620,U_2621)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2621))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_713_2]) ).

cnf(f_713_4,plain,
    ( sP216(U_2620,U_2621)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2621))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

cnf(f_713_5,plain,
    ( U_2620 = U_2621
    | hAPP(c_Int_Onat,U_2620) != hAPP(c_Int_Onat,U_2621)
    | ~ sP216(U_2620,U_2621) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

cnf(f_713_6,plain,
    ( hAPP(c_Int_Onat,U_2620) = hAPP(c_Int_Onat,U_2621)
    | U_2620 != U_2621
    | ~ sP216(U_2620,U_2621) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).

fof(f_714_2,plain,
    ! [U_2626] :
      ( ( ? [U_2625] : hBOOL(hAPP(U_2626,U_2625))
        | ! [U_2624] :
            ( ~ hBOOL(hAPP(U_2626,hAPP(c_Int_Onat,U_2624)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2624)) ) )
      & ( ? [U_2623] :
            ( hBOOL(hAPP(U_2626,hAPP(c_Int_Onat,U_2623)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2623)) )
        | ! [U_2622] : ~ hBOOL(hAPP(U_2626,U_2622)) ) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ( ! [U_2628] :
        ( ? [U_2625] : hBOOL(hAPP(U_2628,U_2625))
        | ! [U_2624] :
            ( ~ hBOOL(hAPP(U_2628,hAPP(c_Int_Onat,U_2624)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2624)) ) )
    & ! [U_2627] :
        ( ? [U_2623] :
            ( hBOOL(hAPP(U_2627,hAPP(c_Int_Onat,U_2623)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2623)) )
        | ! [U_2622] : ~ hBOOL(hAPP(U_2627,U_2622)) ) ),
    inference(miniscope,[status(thm)],[f_714_2]) ).

fof(f_714_4,plain,
    ( ! [U_2628] :
        ( ? [U_2625] : hBOOL(hAPP(U_2628,U_2625))
        | ! [U_2624] :
            ( ~ hBOOL(hAPP(U_2628,hAPP(c_Int_Onat,U_2624)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2624)) ) )
    & ! [U_2627] :
        ( ( hBOOL(hAPP(U_2627,hAPP(c_Int_Onat,sK46(U_2627))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK46(U_2627))) )
        | ! [U_2622] : ~ hBOOL(hAPP(U_2627,U_2622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_2623,sK46(U_2627))],[f_714_3]) ).

fof(f_714_5,plain,
    ( ! [U_2628] :
        ( hBOOL(hAPP(U_2628,sK47(U_2628)))
        | ! [U_2624] :
            ( ~ hBOOL(hAPP(U_2628,hAPP(c_Int_Onat,U_2624)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2624)) ) )
    & ! [U_2627] :
        ( ( hBOOL(hAPP(U_2627,hAPP(c_Int_Onat,sK46(U_2627))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK46(U_2627))) )
        | ! [U_2622] : ~ hBOOL(hAPP(U_2627,U_2622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_2625,sK47(U_2628))],[f_714_4]) ).

fof(f_714_6,plain,
    ( ! [U_2627] :
        ( hBOOL(hAPP(U_2627,hAPP(c_Int_Onat,sK46(U_2627))))
        | ~ sP217(U_2627) )
    & ! [U_2627] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK46(U_2627)))
        | ~ sP217(U_2627) )
    & ! [U_2624,U_2628] :
        ( hBOOL(hAPP(U_2628,sK47(U_2628)))
        | ~ hBOOL(hAPP(U_2628,hAPP(c_Int_Onat,U_2624)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2624)) )
    & ! [U_2622,U_2627] :
        ( sP217(U_2627)
        | ~ hBOOL(hAPP(U_2627,U_2622)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_714_5]) ).

cnf(f_714_7,plain,
    ( sP217(U_2627)
    | ~ hBOOL(hAPP(U_2627,U_2622)) ),
    inference(clausify,[status(thm)],[f_714_6]) ).

cnf(f_714_8,plain,
    ( hBOOL(hAPP(U_2628,sK47(U_2628)))
    | ~ hBOOL(hAPP(U_2628,hAPP(c_Int_Onat,U_2624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2624)) ),
    inference(clausify,[status(thm)],[f_714_6]) ).

cnf(f_714_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK46(U_2627)))
    | ~ sP217(U_2627) ),
    inference(clausify,[status(thm)],[f_714_6]) ).

cnf(f_714_10,plain,
    ( hBOOL(hAPP(U_2627,hAPP(c_Int_Onat,sK46(U_2627))))
    | ~ sP217(U_2627) ),
    inference(clausify,[status(thm)],[f_714_6]) ).

fof(f_715_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat]) ).

fof(f_715_2,plain,
    ! [U_2633] :
      ( ( ! [U_2632] : hBOOL(hAPP(U_2633,U_2632))
        | ? [U_2631] :
            ( ~ hBOOL(hAPP(U_2633,hAPP(c_Int_Onat,U_2631)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2631)) ) )
      & ( ! [U_2630] :
            ( hBOOL(hAPP(U_2633,hAPP(c_Int_Onat,U_2630)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2630)) )
        | ? [U_2629] : ~ hBOOL(hAPP(U_2633,U_2629)) ) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ( ! [U_2635] :
        ( ! [U_2632] : hBOOL(hAPP(U_2635,U_2632))
        | ? [U_2631] :
            ( ~ hBOOL(hAPP(U_2635,hAPP(c_Int_Onat,U_2631)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2631)) ) )
    & ! [U_2634] :
        ( ! [U_2630] :
            ( hBOOL(hAPP(U_2634,hAPP(c_Int_Onat,U_2630)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2630)) )
        | ? [U_2629] : ~ hBOOL(hAPP(U_2634,U_2629)) ) ),
    inference(miniscope,[status(thm)],[f_715_2]) ).

fof(f_715_4,plain,
    ( ! [U_2635] :
        ( ! [U_2632] : hBOOL(hAPP(U_2635,U_2632))
        | ? [U_2631] :
            ( ~ hBOOL(hAPP(U_2635,hAPP(c_Int_Onat,U_2631)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2631)) ) )
    & ! [U_2634] :
        ( ! [U_2630] :
            ( hBOOL(hAPP(U_2634,hAPP(c_Int_Onat,U_2630)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2630)) )
        | ~ hBOOL(hAPP(U_2634,sK48(U_2634))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_2629,sK48(U_2634))],[f_715_3]) ).

fof(f_715_5,plain,
    ( ! [U_2635] :
        ( ! [U_2632] : hBOOL(hAPP(U_2635,U_2632))
        | ( ~ hBOOL(hAPP(U_2635,hAPP(c_Int_Onat,sK49(U_2635))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK49(U_2635))) ) )
    & ! [U_2634] :
        ( ! [U_2630] :
            ( hBOOL(hAPP(U_2634,hAPP(c_Int_Onat,U_2630)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2630)) )
        | ~ hBOOL(hAPP(U_2634,sK48(U_2634))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_2631,sK49(U_2635))],[f_715_4]) ).

fof(f_715_6,plain,
    ( ! [U_2635] :
        ( ~ hBOOL(hAPP(U_2635,hAPP(c_Int_Onat,sK49(U_2635))))
        | ~ sP218(U_2635) )
    & ! [U_2635] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK49(U_2635)))
        | ~ sP218(U_2635) )
    & ! [U_2632,U_2635] :
        ( hBOOL(hAPP(U_2635,U_2632))
        | sP218(U_2635) )
    & ! [U_2630,U_2634] :
        ( hBOOL(hAPP(U_2634,hAPP(c_Int_Onat,U_2630)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2630))
        | ~ hBOOL(hAPP(U_2634,sK48(U_2634))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_715_5]) ).

cnf(f_715_7,plain,
    ( hBOOL(hAPP(U_2634,hAPP(c_Int_Onat,U_2630)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2630))
    | ~ hBOOL(hAPP(U_2634,sK48(U_2634))) ),
    inference(clausify,[status(thm)],[f_715_6]) ).

cnf(f_715_8,plain,
    ( hBOOL(hAPP(U_2635,U_2632))
    | sP218(U_2635) ),
    inference(clausify,[status(thm)],[f_715_6]) ).

cnf(f_715_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK49(U_2635)))
    | ~ sP218(U_2635) ),
    inference(clausify,[status(thm)],[f_715_6]) ).

cnf(f_715_10,plain,
    ( ~ hBOOL(hAPP(U_2635,hAPP(c_Int_Onat,sK49(U_2635))))
    | ~ sP218(U_2635) ),
    inference(clausify,[status(thm)],[f_715_6]) ).

fof(f_716_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Int_Onat,V_x_2) != hAPP(c_Int_Onat,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J]) ).

fof(f_716_2,plain,
    ! [U_2637,U_2636] :
      ( ( ( hAPP(c_Int_Onat,U_2636) = hAPP(c_Int_Onat,U_2637)
          | U_2636 != U_2637 )
        & ( U_2636 = U_2637
          | hAPP(c_Int_Onat,U_2636) != hAPP(c_Int_Onat,U_2637) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2637))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2636)) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ( ! [U_2637,U_2636] :
        ( hAPP(c_Int_Onat,U_2636) = hAPP(c_Int_Onat,U_2637)
        | U_2636 != U_2637
        | ~ sP219(U_2637,U_2636) )
    & ! [U_2637,U_2636] :
        ( U_2636 = U_2637
        | hAPP(c_Int_Onat,U_2636) != hAPP(c_Int_Onat,U_2637)
        | ~ sP219(U_2637,U_2636) )
    & ! [U_2637,U_2636] :
        ( sP219(U_2637,U_2636)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2637))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2636)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_716_2]) ).

cnf(f_716_4,plain,
    ( sP219(U_2637,U_2636)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2637))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2636)) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

cnf(f_716_5,plain,
    ( U_2636 = U_2637
    | hAPP(c_Int_Onat,U_2636) != hAPP(c_Int_Onat,U_2637)
    | ~ sP219(U_2637,U_2636) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

cnf(f_716_6,plain,
    ( hAPP(c_Int_Onat,U_2636) = hAPP(c_Int_Onat,U_2637)
    | U_2636 != U_2637
    | ~ sP219(U_2637,U_2636) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_1,plain,
    ! [V_z,V_z_H,V_w,V_w_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).

fof(f_717_2,plain,
    ! [U_2641,U_2640,U_2639,U_2638] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2638),U_2640)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2639),U_2641)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2640),U_2641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),U_2639)) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_2638,U_2639,U_2641,U_2640] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2638),U_2640)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2639),U_2641)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2640),U_2641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),U_2639)) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2638),U_2640)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2639),U_2641)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2640),U_2641))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),U_2639)) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_718_2,plain,
    ! [U_2643,U_2642] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2642),U_2643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2642)) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ! [U_2642,U_2643] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2642),U_2643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2642)) ),
    inference(definitional_conversion,[status(esa)],[f_718_2]) ).

cnf(f_718_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2642),U_2643)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2643))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2642)) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmult__int]) ).

fof(f_719_2,plain,
    ! [U_2645,U_2644] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2644)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2644),U_2645)),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ! [U_2644,U_2645] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2644)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2644),U_2645)),
    inference(definitional_conversion,[status(esa)],[f_719_2]) ).

cnf(f_719_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2644)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2644),U_2645)),
    inference(clausify,[status(thm)],[f_719_3]) ).

fof(f_720_1,plain,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    inference(fof_nnf,[status(thm)],[fact_int__mult]) ).

fof(f_720_2,plain,
    ! [U_2647,U_2646] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2646),U_2647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2646)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2647)),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ! [U_2646,U_2647] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2646),U_2647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2646)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2647)),
    inference(definitional_conversion,[status(esa)],[f_720_2]) ).

cnf(f_720_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2646),U_2647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2646)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2647)),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(f_721_2,plain,
    ! [U_2649,U_2648] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2648)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2649)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2648),U_2649)),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_2648,U_2649] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2648)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2649)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2648),U_2649)),
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2648)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2649)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2648),U_2649)),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
        | ! [B_n] : V_z_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) )
      & ( ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd]) ).

fof(f_722_2,plain,
    ! [U_2653,U_2652] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2652),U_2653))
        | ! [U_2651] : U_2653 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2652),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)) )
      & ( ? [U_2650] : U_2653 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2652),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2650))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2652),U_2653)) ) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ( ! [U_2657,U_2655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2655),U_2657))
        | ! [U_2651] : U_2657 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2655),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)) )
    & ! [U_2656,U_2654] :
        ( ? [U_2650] : U_2656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2654),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2650))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2654),U_2656)) ) ),
    inference(miniscope,[status(thm)],[f_722_2]) ).

fof(f_722_4,plain,
    ( ! [U_2657,U_2655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2655),U_2657))
        | ! [U_2651] : U_2657 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2655),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)) )
    & ! [U_2656,U_2654] :
        ( U_2656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2654),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK50(U_2656,U_2654)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2654),U_2656)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_2650,sK50(U_2656,U_2654))],[f_722_3]) ).

fof(f_722_5,plain,
    ( ! [U_2657,U_2651,U_2655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2655),U_2657))
        | U_2657 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2655),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)) )
    & ! [U_2656,U_2654] :
        ( U_2656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2654),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK50(U_2656,U_2654)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2654),U_2656)) ) ),
    inference(definitional_conversion,[status(esa)],[f_722_4]) ).

cnf(f_722_6,plain,
    ( U_2656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2654),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK50(U_2656,U_2654)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2654),U_2656)) ),
    inference(clausify,[status(thm)],[f_722_5]) ).

cnf(f_722_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2655),U_2657))
    | U_2657 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2655),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)) ),
    inference(clausify,[status(thm)],[f_722_5]) ).

fof(f_723_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__1]) ).

fof(f_723_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_723_1]) ).

cnf(f_723_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_723_2]) ).

fof(f_724_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).

fof(f_724_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_724_1]) ).

cnf(f_724_3,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_724_2]) ).

fof(f_725_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I2_J]) ).

fof(f_725_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_725_1]) ).

cnf(f_725_3,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_725_2]) ).

fof(f_726_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).

fof(f_726_2,plain,
    ! [U_2660,U_2659,U_2658] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2658),U_2659),U_2660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),U_2660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),U_2659))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2658) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2658,U_2659,U_2660] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2658),U_2659),U_2660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),U_2660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),U_2659))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2658) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2658),U_2659),U_2660)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),U_2660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2658),c_Groups_Ozero__class_Ozero(U_2658)),U_2659))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2658) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).

fof(f_727_2,plain,
    ! [U_2663,U_2662,U_2661] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2661),U_2662),U_2663)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),U_2663))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),U_2662))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2661) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ! [U_2661,U_2662,U_2663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2661),U_2662),U_2663)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),U_2663))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),U_2662))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2661) ),
    inference(definitional_conversion,[status(esa)],[f_727_2]) ).

cnf(f_727_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2661),U_2662),U_2663)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),U_2663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2661),c_Groups_Ozero__class_Ozero(U_2661)),U_2662))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2661) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).

fof(f_728_2,plain,
    ! [U_2667,U_2666,U_2665,U_2664] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2664),U_2666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2664),U_2665),U_2667)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2664),U_2666),U_2667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2664),c_Groups_Ozero__class_Ozero(U_2664)),U_2665))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2664) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2664,U_2665,U_2666,U_2667] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2664),U_2666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2664),U_2665),U_2667)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2664),U_2666),U_2667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2664),c_Groups_Ozero__class_Ozero(U_2664)),U_2665))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2664) ),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2664),U_2666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2664),U_2665),U_2667)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2664),U_2666),U_2667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2664),c_Groups_Ozero__class_Ozero(U_2664)),U_2665))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2664) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).

fof(f_729_2,plain,
    ! [U_2671,U_2670,U_2669,U_2668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2668),U_2670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2668),U_2669),U_2671)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2668),U_2670),U_2671))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2668),c_Groups_Ozero__class_Ozero(U_2668)),U_2669))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2668) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ! [U_2668,U_2669,U_2670,U_2671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2668),U_2670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2668),U_2669),U_2671)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2668),U_2670),U_2671))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2668),c_Groups_Ozero__class_Ozero(U_2668)),U_2669))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2668) ),
    inference(definitional_conversion,[status(esa)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2668),U_2670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2668),U_2669),U_2671)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2668),U_2670),U_2671))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2668),c_Groups_Ozero__class_Ozero(U_2668)),U_2669))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2668) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).

fof(f_730_2,plain,
    ! [U_2674,U_2673,U_2672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2672),U_2673),U_2674)),c_Groups_Ozero__class_Ozero(U_2672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2672),U_2674),c_Groups_Ozero__class_Ozero(U_2672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2672),U_2673),c_Groups_Ozero__class_Ozero(U_2672)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2672) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2672,U_2673,U_2674] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2672),U_2673),U_2674)),c_Groups_Ozero__class_Ozero(U_2672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2672),U_2674),c_Groups_Ozero__class_Ozero(U_2672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2672),U_2673),c_Groups_Ozero__class_Ozero(U_2672)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2672) ),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2672),U_2673),U_2674)),c_Groups_Ozero__class_Ozero(U_2672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2672),U_2674),c_Groups_Ozero__class_Ozero(U_2672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2672),U_2673),c_Groups_Ozero__class_Ozero(U_2672)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2672) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).

fof(f_731_2,plain,
    ! [U_2677,U_2676,U_2675] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2675),U_2676),U_2677)),c_Groups_Ozero__class_Ozero(U_2675)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2675),U_2677),c_Groups_Ozero__class_Ozero(U_2675)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2675),U_2676),c_Groups_Ozero__class_Ozero(U_2675)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2675) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2675,U_2676,U_2677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2675),U_2676),U_2677)),c_Groups_Ozero__class_Ozero(U_2675)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2675),U_2677),c_Groups_Ozero__class_Ozero(U_2675)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2675),U_2676),c_Groups_Ozero__class_Ozero(U_2675)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2675) ),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2675),U_2676),U_2677)),c_Groups_Ozero__class_Ozero(U_2675)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2675),U_2677),c_Groups_Ozero__class_Ozero(U_2675)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2675),U_2676),c_Groups_Ozero__class_Ozero(U_2675)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2675) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).

fof(f_732_2,plain,
    ! [U_2681,U_2680,U_2679,U_2678] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2681)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),U_2680),U_2681)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),U_2680),U_2681))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2681))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2678),c_Groups_Ozero__class_Ozero(U_2678)),U_2679))
      | ~ class_Rings_Olinordered__ring__strict(U_2678) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ( ! [U_2678,U_2679,U_2680,U_2681] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2681)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),U_2680),U_2681))
        | ~ sP220(U_2678,U_2679,U_2680,U_2681) )
    & ! [U_2678,U_2679,U_2680,U_2681] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),U_2680),U_2681))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2681)))
        | ~ sP220(U_2678,U_2679,U_2680,U_2681) )
    & ! [U_2678,U_2679,U_2680,U_2681] :
        ( sP220(U_2678,U_2679,U_2680,U_2681)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2678),c_Groups_Ozero__class_Ozero(U_2678)),U_2679))
        | ~ class_Rings_Olinordered__ring__strict(U_2678) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_732_2]) ).

cnf(f_732_4,plain,
    ( sP220(U_2678,U_2679,U_2680,U_2681)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2678),c_Groups_Ozero__class_Ozero(U_2678)),U_2679))
    | ~ class_Rings_Olinordered__ring__strict(U_2678) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),U_2680),U_2681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2681)))
    | ~ sP220(U_2678,U_2679,U_2680,U_2681) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2678),U_2679),U_2681)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2678),U_2680),U_2681))
    | ~ sP220(U_2678,U_2679,U_2680,U_2681) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).

fof(f_733_2,plain,
    ! [U_2685,U_2684,U_2683,U_2682] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2685)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),U_2685),U_2684)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),U_2685),U_2684))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2685))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2682),U_2683),c_Groups_Ozero__class_Ozero(U_2682)))
      | ~ class_Rings_Olinordered__ring__strict(U_2682) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ( ! [U_2683,U_2682,U_2684,U_2685] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2685)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),U_2685),U_2684))
        | ~ sP221(U_2683,U_2682,U_2684,U_2685) )
    & ! [U_2683,U_2682,U_2684,U_2685] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),U_2685),U_2684))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2685)))
        | ~ sP221(U_2683,U_2682,U_2684,U_2685) )
    & ! [U_2683,U_2682,U_2684,U_2685] :
        ( sP221(U_2683,U_2682,U_2684,U_2685)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2682),U_2683),c_Groups_Ozero__class_Ozero(U_2682)))
        | ~ class_Rings_Olinordered__ring__strict(U_2682) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_733_2]) ).

cnf(f_733_4,plain,
    ( sP221(U_2683,U_2682,U_2684,U_2685)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2682),U_2683),c_Groups_Ozero__class_Ozero(U_2682)))
    | ~ class_Rings_Olinordered__ring__strict(U_2682) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

cnf(f_733_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),U_2685),U_2684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2685)))
    | ~ sP221(U_2683,U_2682,U_2684,U_2685) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

cnf(f_733_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2682),U_2685),U_2684))
    | ~ sP221(U_2683,U_2682,U_2684,U_2685) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__mono]) ).

fof(f_734_2,plain,
    ! [U_2690,U_2689,U_2688,U_2687,U_2686] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),U_2687),U_2689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),U_2688),U_2690)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),U_2689),U_2690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),U_2687),U_2688))
      | ~ class_Rings_Olinordered__semiring__strict(U_2686) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ! [U_2687,U_2686,U_2689,U_2688,U_2690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),U_2687),U_2689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),U_2688),U_2690)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),U_2689),U_2690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),U_2687),U_2688))
      | ~ class_Rings_Olinordered__semiring__strict(U_2686) ),
    inference(definitional_conversion,[status(esa)],[f_734_2]) ).

cnf(f_734_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),U_2687),U_2689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),U_2688),U_2690)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2688))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),U_2689),U_2690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2686),U_2687),U_2688))
    | ~ class_Rings_Olinordered__semiring__strict(U_2686) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H]) ).

fof(f_735_2,plain,
    ! [U_2695,U_2694,U_2693,U_2692,U_2691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2691),U_2692),U_2694)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2691),U_2693),U_2695)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2691),c_Groups_Ozero__class_Ozero(U_2691)),U_2694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2691),c_Groups_Ozero__class_Ozero(U_2691)),U_2692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),U_2694),U_2695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),U_2692),U_2693))
      | ~ class_Rings_Olinordered__semiring__strict(U_2691) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2694,U_2691,U_2692,U_2693,U_2695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2691),U_2692),U_2694)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2691),U_2693),U_2695)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2691),c_Groups_Ozero__class_Ozero(U_2691)),U_2694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2691),c_Groups_Ozero__class_Ozero(U_2691)),U_2692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),U_2694),U_2695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),U_2692),U_2693))
      | ~ class_Rings_Olinordered__semiring__strict(U_2691) ),
    inference(definitional_conversion,[status(esa)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2691),U_2692),U_2694)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2691),U_2693),U_2695)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2691),c_Groups_Ozero__class_Ozero(U_2691)),U_2694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2691),c_Groups_Ozero__class_Ozero(U_2691)),U_2692))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),U_2694),U_2695))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2691),U_2692),U_2693))
    | ~ class_Rings_Olinordered__semiring__strict(U_2691) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).

fof(f_736_2,plain,
    ! [U_2700,U_2699,U_2698,U_2697,U_2696] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2698),U_2700)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),U_2699),U_2700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),U_2697),U_2698))
      | ~ class_Rings_Olinordered__semiring__strict(U_2696) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2697,U_2698,U_2696,U_2699,U_2700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2698),U_2700)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),U_2699),U_2700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),U_2697),U_2698))
      | ~ class_Rings_Olinordered__semiring__strict(U_2696) ),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2698),U_2700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2699))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),U_2699),U_2700))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),U_2697),U_2698))
    | ~ class_Rings_Olinordered__semiring__strict(U_2696) ),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).

fof(f_737_2,plain,
    ! [U_2705,U_2704,U_2703,U_2702,U_2701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2702),U_2704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2703),U_2705)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2702))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),U_2704),U_2705))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),U_2702),U_2703))
      | ~ class_Rings_Olinordered__semiring__strict(U_2701) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ! [U_2702,U_2704,U_2703,U_2701,U_2705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2702),U_2704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2703),U_2705)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2702))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),U_2704),U_2705))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),U_2702),U_2703))
      | ~ class_Rings_Olinordered__semiring__strict(U_2701) ),
    inference(definitional_conversion,[status(esa)],[f_737_2]) ).

cnf(f_737_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2702),U_2704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2703),U_2705)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2704))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2702))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),U_2704),U_2705))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),U_2702),U_2703))
    | ~ class_Rings_Olinordered__semiring__strict(U_2701) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ class_Rings_Olinordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).

fof(f_738_2,plain,
    ! [U_2709,U_2708,U_2707,U_2706] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2706),U_2707),U_2709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2706),c_Groups_Ozero__class_Ozero(U_2706)),U_2708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2706),U_2707),U_2708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2706),U_2709),U_2708)))
      | ~ class_Rings_Olinordered__semiring(U_2706) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ! [U_2707,U_2708,U_2709,U_2706] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2706),U_2707),U_2709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2706),c_Groups_Ozero__class_Ozero(U_2706)),U_2708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2706),U_2707),U_2708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2706),U_2709),U_2708)))
      | ~ class_Rings_Olinordered__semiring(U_2706) ),
    inference(definitional_conversion,[status(esa)],[f_738_2]) ).

cnf(f_738_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2706),U_2707),U_2709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2706),c_Groups_Ozero__class_Ozero(U_2706)),U_2708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2706),U_2707),U_2708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2706),U_2709),U_2708)))
    | ~ class_Rings_Olinordered__semiring(U_2706) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

fof(f_739_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).

fof(f_739_2,plain,
    ! [U_2713,U_2712,U_2711,U_2710] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2710),U_2711),U_2713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2710),c_Groups_Ozero__class_Ozero(U_2710)),U_2712))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2710),U_2711),U_2712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2710),U_2713),U_2712)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2710) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ! [U_2710,U_2711,U_2712,U_2713] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2710),U_2711),U_2713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2710),c_Groups_Ozero__class_Ozero(U_2710)),U_2712))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2710),U_2711),U_2712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2710),U_2713),U_2712)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2710) ),
    inference(definitional_conversion,[status(esa)],[f_739_2]) ).

cnf(f_739_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2710),U_2711),U_2713))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2710),c_Groups_Ozero__class_Ozero(U_2710)),U_2712))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2710),U_2711),U_2712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2710),U_2713),U_2712)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2710) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

fof(f_740_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ class_Rings_Olinordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).

fof(f_740_2,plain,
    ! [U_2717,U_2716,U_2715,U_2714] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2714),U_2716),U_2717))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2714),c_Groups_Ozero__class_Ozero(U_2714)),U_2715))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2717)))
      | ~ class_Rings_Olinordered__semiring(U_2714) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ! [U_2714,U_2715,U_2716,U_2717] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2714),U_2716),U_2717))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2714),c_Groups_Ozero__class_Ozero(U_2714)),U_2715))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2717)))
      | ~ class_Rings_Olinordered__semiring(U_2714) ),
    inference(definitional_conversion,[status(esa)],[f_740_2]) ).

cnf(f_740_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2714),U_2716),U_2717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2714),c_Groups_Ozero__class_Ozero(U_2714)),U_2715))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2717)))
    | ~ class_Rings_Olinordered__semiring(U_2714) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

fof(f_741_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).

fof(f_741_2,plain,
    ! [U_2721,U_2720,U_2719,U_2718] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2720),U_2721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2718),c_Groups_Ozero__class_Ozero(U_2718)),U_2719))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2718),U_2719),U_2720)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2718),U_2719),U_2721)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2718) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_2718,U_2719,U_2720,U_2721] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2720),U_2721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2718),c_Groups_Ozero__class_Ozero(U_2718)),U_2719))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2718),U_2719),U_2720)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2718),U_2719),U_2721)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2718) ),
    inference(definitional_conversion,[status(esa)],[f_741_2]) ).

cnf(f_741_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2720),U_2721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2718),c_Groups_Ozero__class_Ozero(U_2718)),U_2719))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2718),U_2719),U_2720)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2718),U_2719),U_2721)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2718) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).

fof(f_742_2,plain,
    ! [U_2725,U_2724,U_2723,U_2722] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2722),U_2723),U_2725))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2722),c_Groups_Ozero__class_Ozero(U_2722)),U_2724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2722),U_2723),U_2724)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2722),U_2725),U_2724)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2722) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_2722,U_2723,U_2724,U_2725] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2722),U_2723),U_2725))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2722),c_Groups_Ozero__class_Ozero(U_2722)),U_2724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2722),U_2723),U_2724)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2722),U_2725),U_2724)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2722) ),
    inference(definitional_conversion,[status(esa)],[f_742_2]) ).

cnf(f_742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2722),U_2723),U_2725))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2722),c_Groups_Ozero__class_Ozero(U_2722)),U_2724))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2722),U_2723),U_2724)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2722),U_2725),U_2724)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2722) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

fof(f_743_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).

fof(f_743_2,plain,
    ! [U_2729,U_2728,U_2727,U_2726] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2726),U_2728),U_2729))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2726),c_Groups_Ozero__class_Ozero(U_2726)),U_2727))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2726),U_2727),U_2728)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2726),U_2727),U_2729)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2726) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2726,U_2727,U_2728,U_2729] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2726),U_2728),U_2729))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2726),c_Groups_Ozero__class_Ozero(U_2726)),U_2727))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2726),U_2727),U_2728)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2726),U_2727),U_2729)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2726) ),
    inference(definitional_conversion,[status(esa)],[f_743_2]) ).

cnf(f_743_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2726),U_2728),U_2729))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2726),c_Groups_Ozero__class_Ozero(U_2726)),U_2727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2726),U_2727),U_2728)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2726),U_2727),U_2729)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2726) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).

fof(f_744_2,plain,
    ! [U_2732,U_2731,U_2730] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2731),U_2731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2732),U_2732))),c_Groups_Ozero__class_Ozero(U_2730)))
          | U_2732 != c_Groups_Ozero__class_Ozero(U_2730)
          | U_2731 != c_Groups_Ozero__class_Ozero(U_2730) )
        & ( ( U_2732 = c_Groups_Ozero__class_Ozero(U_2730)
            & U_2731 = c_Groups_Ozero__class_Ozero(U_2730) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2731),U_2731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2732),U_2732))),c_Groups_Ozero__class_Ozero(U_2730))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2730) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ( ! [U_2730,U_2731,U_2732] :
        ( U_2732 = c_Groups_Ozero__class_Ozero(U_2730)
        | ~ sP222(U_2730,U_2731,U_2732) )
    & ! [U_2730,U_2731,U_2732] :
        ( U_2731 = c_Groups_Ozero__class_Ozero(U_2730)
        | ~ sP222(U_2730,U_2731,U_2732) )
    & ! [U_2730,U_2731,U_2732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2731),U_2731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2732),U_2732))),c_Groups_Ozero__class_Ozero(U_2730)))
        | U_2732 != c_Groups_Ozero__class_Ozero(U_2730)
        | U_2731 != c_Groups_Ozero__class_Ozero(U_2730)
        | ~ sP223(U_2730,U_2731,U_2732) )
    & ! [U_2730,U_2731,U_2732] :
        ( sP222(U_2730,U_2731,U_2732)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2731),U_2731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2732),U_2732))),c_Groups_Ozero__class_Ozero(U_2730)))
        | ~ sP223(U_2730,U_2731,U_2732) )
    & ! [U_2730,U_2731,U_2732] :
        ( sP223(U_2730,U_2731,U_2732)
        | ~ class_Rings_Olinordered__ring__strict(U_2730) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222,sP223])],[f_744_2]) ).

cnf(f_744_4,plain,
    ( sP223(U_2730,U_2731,U_2732)
    | ~ class_Rings_Olinordered__ring__strict(U_2730) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_5,plain,
    ( sP222(U_2730,U_2731,U_2732)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2731),U_2731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2732),U_2732))),c_Groups_Ozero__class_Ozero(U_2730)))
    | ~ sP223(U_2730,U_2731,U_2732) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2731),U_2731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2730),U_2732),U_2732))),c_Groups_Ozero__class_Ozero(U_2730)))
    | U_2732 != c_Groups_Ozero__class_Ozero(U_2730)
    | U_2731 != c_Groups_Ozero__class_Ozero(U_2730)
    | ~ sP223(U_2730,U_2731,U_2732) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_7,plain,
    ( U_2731 = c_Groups_Ozero__class_Ozero(U_2730)
    | ~ sP222(U_2730,U_2731,U_2732) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_8,plain,
    ( U_2732 = c_Groups_Ozero__class_Ozero(U_2730)
    | ~ sP222(U_2730,U_2731,U_2732) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).

fof(f_745_2,plain,
    ! [U_2735,U_2734,U_2733] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2733),c_Groups_Ozero__class_Ozero(U_2733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2733),U_2734),U_2734)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2733),U_2735),U_2735))))
      | ~ class_Rings_Olinordered__ring(U_2733) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2733,U_2734,U_2735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2733),c_Groups_Ozero__class_Ozero(U_2733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2733),U_2734),U_2734)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2733),U_2735),U_2735))))
      | ~ class_Rings_Olinordered__ring(U_2733) ),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2733),c_Groups_Ozero__class_Ozero(U_2733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2733),U_2734),U_2734)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2733),U_2735),U_2735))))
    | ~ class_Rings_Olinordered__ring(U_2733) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).

fof(f_746_2,plain,
    ! [U_2738,U_2737,U_2736] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2736),U_2738),U_2737)),U_2737))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),U_2738),c_Groups_Oone__class_Oone(U_2736)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),c_Groups_Ozero__class_Ozero(U_2736)),U_2738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),c_Groups_Ozero__class_Ozero(U_2736)),U_2737))
      | ~ class_Rings_Olinordered__idom(U_2736) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ! [U_2736,U_2738,U_2737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2736),U_2738),U_2737)),U_2737))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),U_2738),c_Groups_Oone__class_Oone(U_2736)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),c_Groups_Ozero__class_Ozero(U_2736)),U_2738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),c_Groups_Ozero__class_Ozero(U_2736)),U_2737))
      | ~ class_Rings_Olinordered__idom(U_2736) ),
    inference(definitional_conversion,[status(esa)],[f_746_2]) ).

cnf(f_746_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2736),U_2738),U_2737)),U_2737))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),U_2738),c_Groups_Oone__class_Oone(U_2736)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),c_Groups_Ozero__class_Ozero(U_2736)),U_2738))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2736),c_Groups_Ozero__class_Ozero(U_2736)),U_2737))
    | ~ class_Rings_Olinordered__idom(U_2736) ),
    inference(clausify,[status(thm)],[f_746_3]) ).

fof(f_747_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).

fof(f_747_2,plain,
    ! [U_2741,U_2740,U_2739] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2739),U_2740),U_2741)),U_2740))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),U_2741),c_Groups_Oone__class_Oone(U_2739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),c_Groups_Ozero__class_Ozero(U_2739)),U_2741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),c_Groups_Ozero__class_Ozero(U_2739)),U_2740))
      | ~ class_Rings_Olinordered__idom(U_2739) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2740,U_2741,U_2739] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2739),U_2740),U_2741)),U_2740))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),U_2741),c_Groups_Oone__class_Oone(U_2739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),c_Groups_Ozero__class_Ozero(U_2739)),U_2741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),c_Groups_Ozero__class_Ozero(U_2739)),U_2740))
      | ~ class_Rings_Olinordered__idom(U_2739) ),
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2739),U_2740),U_2741)),U_2740))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),U_2741),c_Groups_Oone__class_Oone(U_2739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),c_Groups_Ozero__class_Ozero(U_2739)),U_2741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2739),c_Groups_Ozero__class_Ozero(U_2739)),U_2740))
    | ~ class_Rings_Olinordered__idom(U_2739) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).

fof(f_748_2,plain,
    ! [U_2743,U_2742] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),c_Groups_Osgn__class_Osgn(U_2742,U_2743)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),U_2743)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),U_2743))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),c_Groups_Osgn__class_Osgn(U_2742,U_2743))) ) )
      | ~ class_Rings_Olinordered__idom(U_2742) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ( ! [U_2743,U_2742] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),c_Groups_Osgn__class_Osgn(U_2742,U_2743)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),U_2743))
        | ~ sP224(U_2743,U_2742) )
    & ! [U_2743,U_2742] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),U_2743))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),c_Groups_Osgn__class_Osgn(U_2742,U_2743)))
        | ~ sP224(U_2743,U_2742) )
    & ! [U_2743,U_2742] :
        ( sP224(U_2743,U_2742)
        | ~ class_Rings_Olinordered__idom(U_2742) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_748_2]) ).

cnf(f_748_4,plain,
    ( sP224(U_2743,U_2742)
    | ~ class_Rings_Olinordered__idom(U_2742) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),U_2743))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),c_Groups_Osgn__class_Osgn(U_2742,U_2743)))
    | ~ sP224(U_2743,U_2742) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),c_Groups_Osgn__class_Osgn(U_2742,U_2743)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2742),c_Groups_Ozero__class_Ozero(U_2742)),U_2743))
    | ~ sP224(U_2743,U_2742) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).

fof(f_749_2,plain,
    ! [U_2745,U_2744] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),c_Groups_Osgn__class_Osgn(U_2744,U_2745)),c_Groups_Ozero__class_Ozero(U_2744)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2745),c_Groups_Ozero__class_Ozero(U_2744))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2745),c_Groups_Ozero__class_Ozero(U_2744)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),c_Groups_Osgn__class_Osgn(U_2744,U_2745)),c_Groups_Ozero__class_Ozero(U_2744))) ) )
      | ~ class_Rings_Olinordered__idom(U_2744) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ( ! [U_2744,U_2745] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),c_Groups_Osgn__class_Osgn(U_2744,U_2745)),c_Groups_Ozero__class_Ozero(U_2744)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2745),c_Groups_Ozero__class_Ozero(U_2744)))
        | ~ sP225(U_2744,U_2745) )
    & ! [U_2744,U_2745] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2745),c_Groups_Ozero__class_Ozero(U_2744)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),c_Groups_Osgn__class_Osgn(U_2744,U_2745)),c_Groups_Ozero__class_Ozero(U_2744)))
        | ~ sP225(U_2744,U_2745) )
    & ! [U_2744,U_2745] :
        ( sP225(U_2744,U_2745)
        | ~ class_Rings_Olinordered__idom(U_2744) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_749_2]) ).

cnf(f_749_4,plain,
    ( sP225(U_2744,U_2745)
    | ~ class_Rings_Olinordered__idom(U_2744) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

cnf(f_749_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2745),c_Groups_Ozero__class_Ozero(U_2744)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),c_Groups_Osgn__class_Osgn(U_2744,U_2745)),c_Groups_Ozero__class_Ozero(U_2744)))
    | ~ sP225(U_2744,U_2745) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

cnf(f_749_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),c_Groups_Osgn__class_Osgn(U_2744,U_2745)),c_Groups_Ozero__class_Ozero(U_2744)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2745),c_Groups_Ozero__class_Ozero(U_2744)))
    | ~ sP225(U_2744,U_2745) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).

fof(f_750_2,plain,
    ! [U_2747,U_2746] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2747),U_2746)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2746)) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ! [U_2747,U_2746] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2747),U_2746)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2746)) ),
    inference(definitional_conversion,[status(esa)],[f_750_2]) ).

cnf(f_750_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2747),U_2746)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2747))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2746)) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m]) ).

fof(f_751_2,plain,
    ! [U_2749,U_2748] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2748),U_2749)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2748)) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2748,U_2749] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2748),U_2749)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2748)) ),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2748),U_2749)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2749))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2748)) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n]) ).

fof(f_752_2,plain,
    ! [U_2751,U_2750] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2751),U_2750)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2751))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2750)) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ! [U_2750,U_2751] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2751),U_2750)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2751))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2750)) ),
    inference(definitional_conversion,[status(esa)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2751),U_2750)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2751))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2750)) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__le__0__conv]) ).

fof(f_753_2,plain,
    ! [U_2752] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2752)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_2752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2752 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2752)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ( ! [U_2754] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2754)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_2754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2753] :
        ( U_2753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2753)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_753_2]) ).

fof(f_753_4,plain,
    ( ! [U_2754] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2754)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_2754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2753] :
        ( U_2753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2753)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_753_3]) ).

cnf(f_753_5,plain,
    ( U_2753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2753)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_753_4]) ).

cnf(f_753_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2754)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_2754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_753_4]) ).

fof(f_754_1,plain,
    ! [V_i_2] :
      ( ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,V_i_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__iff]) ).

fof(f_754_2,plain,
    ! [U_2755] :
      ( ( hAPP(c_Int_Onat,U_2755) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2755),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2755),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_2755) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ( ! [U_2757] :
        ( hAPP(c_Int_Onat,U_2757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2756] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2756),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_2756) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_754_2]) ).

fof(f_754_4,plain,
    ( ! [U_2757] :
        ( hAPP(c_Int_Onat,U_2757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2756] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2756),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_2756) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_754_3]) ).

cnf(f_754_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2756),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,U_2756) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_754_4]) ).

cnf(f_754_6,plain,
    ( hAPP(c_Int_Onat,U_2757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_754_4]) ).

fof(f_755_1,plain,
    ! [V_z] :
      ( hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__0]) ).

fof(f_755_2,plain,
    ! [U_2758] :
      ( hAPP(c_Int_Onat,U_2758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2758),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ! [U_2758] :
      ( hAPP(c_Int_Onat,U_2758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2758),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hAPP(c_Int_Onat,U_2758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2758),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).

fof(f_756_2,plain,
    ! [U_2759] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2759))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2759)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2759))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2759)) ) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ( ! [U_2761] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2761)) )
    & ! [U_2760] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2760))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2760)) ) ),
    inference(miniscope,[status(thm)],[f_756_2]) ).

fof(f_756_4,plain,
    ( ! [U_2761] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2761)) )
    & ! [U_2760] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2760))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2760)) ) ),
    inference(definitional_conversion,[status(esa)],[f_756_3]) ).

cnf(f_756_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2760))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2760)) ),
    inference(clausify,[status(thm)],[f_756_4]) ).

cnf(f_756_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2761))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2761)) ),
    inference(clausify,[status(thm)],[f_756_4]) ).

fof(f_757_1,plain,
    ! [V_z] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__le]) ).

fof(f_757_2,plain,
    ! [U_2762] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2762)) = U_2762
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2762)) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_2762] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2762)) = U_2762
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2762)) ),
    inference(definitional_conversion,[status(esa)],[f_757_2]) ).

cnf(f_757_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2762)) = U_2762
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2762)) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_1,plain,
    ! [V_z_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | V_m_2 != hAPP(c_Int_Onat,V_z_2) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
          & V_m_2 = hAPP(c_Int_Onat,V_z_2) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != V_z_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__iff]) ).

fof(f_758_2,plain,
    ! [U_2764,U_2763] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2763) = U_2764
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2764))
        | U_2763 != hAPP(c_Int_Onat,U_2764) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2764))
          & U_2763 = hAPP(c_Int_Onat,U_2764) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2763) != U_2764 ) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ( ! [U_2768,U_2766] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2766) = U_2768
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2768))
        | U_2766 != hAPP(c_Int_Onat,U_2768) )
    & ! [U_2767,U_2765] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
          & U_2765 = hAPP(c_Int_Onat,U_2767) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2765) != U_2767 ) ),
    inference(miniscope,[status(thm)],[f_758_2]) ).

fof(f_758_4,plain,
    ( ! [U_2767,U_2765] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
        | ~ sP226(U_2767,U_2765) )
    & ! [U_2767,U_2765] :
        ( U_2765 = hAPP(c_Int_Onat,U_2767)
        | ~ sP226(U_2767,U_2765) )
    & ! [U_2766,U_2768] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2766) = U_2768
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2768))
        | U_2766 != hAPP(c_Int_Onat,U_2768) )
    & ! [U_2767,U_2765] :
        ( sP226(U_2767,U_2765)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2765) != U_2767 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_758_3]) ).

cnf(f_758_5,plain,
    ( sP226(U_2767,U_2765)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2765) != U_2767 ),
    inference(clausify,[status(thm)],[f_758_4]) ).

cnf(f_758_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2766) = U_2768
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2768))
    | U_2766 != hAPP(c_Int_Onat,U_2768) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

cnf(f_758_7,plain,
    ( U_2765 = hAPP(c_Int_Onat,U_2767)
    | ~ sP226(U_2767,U_2765) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

cnf(f_758_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
    | ~ sP226(U_2767,U_2765) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

fof(f_759_1,plain,
    ! [V_z] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__nat__eq]) ).

fof(f_759_2,plain,
    ! [U_2769] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2769)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2769)) = U_2769
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769)) ) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ( ! [U_2771] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2771)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771)) )
    & ! [U_2770] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2770)) = U_2770
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2770)) ) ),
    inference(miniscope,[status(thm)],[f_759_2]) ).

fof(f_759_4,plain,
    ( ! [U_2771] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2771)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771)) )
    & ! [U_2770] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2770)) = U_2770
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2770)) ) ),
    inference(definitional_conversion,[status(esa)],[f_759_3]) ).

cnf(f_759_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2770)) = U_2770
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2770)) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2771)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771)) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

fof(f_760_1,plain,
    ! [V_z,V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).

fof(f_760_2,plain,
    ! [U_2773,U_2772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2772),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2772),U_2773)) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_2773,U_2772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2772),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2772),U_2773)) ),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2772),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2772),U_2773)) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).

fof(f_761_2,plain,
    ! [U_2775,U_2774] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2774),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2775))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2774),U_2775)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2774),U_2775))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2774),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2775)) ) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ( ! [U_2779,U_2777] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2777),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2779))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2777),U_2779)) )
    & ! [U_2778,U_2776] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2776),U_2778))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2776),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2778)) ) ),
    inference(miniscope,[status(thm)],[f_761_2]) ).

fof(f_761_4,plain,
    ( ! [U_2779,U_2777] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2777),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2779))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2777),U_2779)) )
    & ! [U_2778,U_2776] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2776),U_2778))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2776),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2778)) ) ),
    inference(definitional_conversion,[status(esa)],[f_761_3]) ).

cnf(f_761_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2776),U_2778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2776),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2778)) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2777),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2777),U_2779)) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

fof(f_762_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).

fof(f_762_2,plain,
    ! [U_2781,U_2780] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2781),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2780),U_2781)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2780),U_2781))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2781),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ( ! [U_2785,U_2783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2783),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2785),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2783),U_2785)) )
    & ! [U_2784,U_2782] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2782),U_2784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2784),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_762_2]) ).

fof(f_762_4,plain,
    ( ! [U_2785,U_2783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2783),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2785),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2783),U_2785)) )
    & ! [U_2782,U_2784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2782),U_2784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2784),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2782),U_2784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2784),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

cnf(f_762_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2783),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2785),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2783),U_2785)) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

fof(f_763_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__zle__neg]) ).

fof(f_763_2,plain,
    ! [U_2787,U_2786] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2786)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2787))))
        | U_2787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2786 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_2787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2786)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2787)))) ) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ( ! [U_2791,U_2789] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2789)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2791))))
        | U_2791 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2789 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2790,U_2788] :
        ( ( U_2790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2788)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2790)))) ) ),
    inference(miniscope,[status(thm)],[f_763_2]) ).

fof(f_763_4,plain,
    ( ! [U_2790,U_2788] :
        ( U_2790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP227(U_2790,U_2788) )
    & ! [U_2790,U_2788] :
        ( U_2788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP227(U_2790,U_2788) )
    & ! [U_2791,U_2789] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2789)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2791))))
        | U_2791 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2789 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2790,U_2788] :
        ( sP227(U_2790,U_2788)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2788)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2790)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_763_3]) ).

cnf(f_763_5,plain,
    ( sP227(U_2790,U_2788)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2788)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2790)))) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

cnf(f_763_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2789)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2791))))
    | U_2791 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2789 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

cnf(f_763_7,plain,
    ( U_2788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP227(U_2790,U_2788) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

cnf(f_763_8,plain,
    ( U_2790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP227(U_2790,U_2788) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

fof(f_764_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_negative__zle__0]) ).

fof(f_764_2,plain,
    ! [U_2792] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2792))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ! [U_2792] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2792))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_764_2]) ).

cnf(f_764_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2792))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_764_3]) ).

fof(f_765_1,plain,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Rings_Olinordered__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).

fof(f_765_2,plain,
    ! [U_2798,U_2797,U_2796,U_2795,U_2794,U_2793] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2797),U_2794)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2798),U_2796))),U_2795))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2793),U_2797),U_2798) != c_Groups_Oone__class_Oone(U_2793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),c_Groups_Ozero__class_Ozero(U_2793)),U_2798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),c_Groups_Ozero__class_Ozero(U_2793)),U_2797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),U_2796),U_2795))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),U_2794),U_2795))
      | ~ class_Rings_Olinordered__semiring__1(U_2793) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_2793,U_2794,U_2795,U_2796,U_2797,U_2798] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2797),U_2794)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2798),U_2796))),U_2795))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2793),U_2797),U_2798) != c_Groups_Oone__class_Oone(U_2793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),c_Groups_Ozero__class_Ozero(U_2793)),U_2798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),c_Groups_Ozero__class_Ozero(U_2793)),U_2797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),U_2796),U_2795))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),U_2794),U_2795))
      | ~ class_Rings_Olinordered__semiring__1(U_2793) ),
    inference(definitional_conversion,[status(esa)],[f_765_2]) ).

cnf(f_765_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2797),U_2794)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2798),U_2796))),U_2795))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2793),U_2797),U_2798) != c_Groups_Oone__class_Oone(U_2793)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),c_Groups_Ozero__class_Ozero(U_2793)),U_2798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),c_Groups_Ozero__class_Ozero(U_2793)),U_2797))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),U_2796),U_2795))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2793),U_2794),U_2795))
    | ~ class_Rings_Olinordered__semiring__1(U_2793) ),
    inference(clausify,[status(thm)],[f_765_3]) ).

fof(f_766_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J]) ).

fof(f_766_2,plain,
    ! [U_2800,U_2799] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2799)),hAPP(c_Int_Onat,U_2800)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2799),U_2800)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2799),U_2800))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2799)),hAPP(c_Int_Onat,U_2800))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2800))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799)) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ( ! [U_2799,U_2800] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2799)),hAPP(c_Int_Onat,U_2800)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2799),U_2800))
        | ~ sP228(U_2799,U_2800) )
    & ! [U_2799,U_2800] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2799),U_2800))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2799)),hAPP(c_Int_Onat,U_2800)))
        | ~ sP228(U_2799,U_2800) )
    & ! [U_2799,U_2800] :
        ( sP228(U_2799,U_2800)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2800))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_766_2]) ).

cnf(f_766_4,plain,
    ( sP228(U_2799,U_2800)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799)) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

cnf(f_766_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2799),U_2800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2799)),hAPP(c_Int_Onat,U_2800)))
    | ~ sP228(U_2799,U_2800) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

cnf(f_766_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2799)),hAPP(c_Int_Onat,U_2800)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2799),U_2800))
    | ~ sP228(U_2799,U_2800) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

fof(f_767_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless]) ).

fof(f_767_2,plain,
    ! [U_2802,U_2801] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2801)),hAPP(c_Int_Onat,U_2802)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2801),U_2802)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2801),U_2802))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2801)),hAPP(c_Int_Onat,U_2802))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2801)) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ( ! [U_2802,U_2801] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2801)),hAPP(c_Int_Onat,U_2802)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2801),U_2802))
        | ~ sP229(U_2802,U_2801) )
    & ! [U_2802,U_2801] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2801),U_2802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2801)),hAPP(c_Int_Onat,U_2802)))
        | ~ sP229(U_2802,U_2801) )
    & ! [U_2802,U_2801] :
        ( sP229(U_2802,U_2801)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2801)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_767_2]) ).

cnf(f_767_4,plain,
    ( sP229(U_2802,U_2801)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2801)) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2801),U_2802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2801)),hAPP(c_Int_Onat,U_2802)))
    | ~ sP229(U_2802,U_2801) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2801)),hAPP(c_Int_Onat,U_2802)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2801),U_2802))
    | ~ sP229(U_2802,U_2801) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_1,plain,
    ! [V_m_2,V_w_2] :
      ( ( hAPP(c_Int_Onat,V_w_2) = V_m_2
        | ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
        | ( V_w_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
      & ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
          & ( V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
        | hAPP(c_Int_Onat,V_w_2) != V_m_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__iff]) ).

fof(f_768_2,plain,
    ! [U_2804,U_2803] :
      ( ( hAPP(c_Int_Onat,U_2803) = U_2804
        | ( U_2804 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803)) )
        | ( U_2803 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2804)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803)) ) )
      & ( ( ( U_2804 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803)) )
          & ( U_2803 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2804)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803)) ) )
        | hAPP(c_Int_Onat,U_2803) != U_2804 ) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ( ! [U_2808,U_2806] :
        ( hAPP(c_Int_Onat,U_2806) = U_2808
        | ( U_2808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2806)) )
        | ( U_2806 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2808)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2806)) ) )
    & ! [U_2807,U_2805] :
        ( ( ( U_2807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805)) )
          & ( U_2805 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2807)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805)) ) )
        | hAPP(c_Int_Onat,U_2805) != U_2807 ) ),
    inference(miniscope,[status(thm)],[f_768_2]) ).

fof(f_768_4,plain,
    ( ! [U_2806,U_2808] :
        ( U_2808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP232(U_2806,U_2808) )
    & ! [U_2806,U_2808] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2806))
        | ~ sP232(U_2806,U_2808) )
    & ! [U_2806,U_2808] :
        ( U_2806 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2808)
        | ~ sP231(U_2806,U_2808) )
    & ! [U_2806,U_2808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2806))
        | ~ sP231(U_2806,U_2808) )
    & ! [U_2807,U_2805] :
        ( U_2807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
        | ~ sP230(U_2807,U_2805) )
    & ! [U_2807,U_2805] :
        ( U_2805 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2807)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
        | ~ sP230(U_2807,U_2805) )
    & ! [U_2806,U_2808] :
        ( hAPP(c_Int_Onat,U_2806) = U_2808
        | sP232(U_2806,U_2808)
        | sP231(U_2806,U_2808) )
    & ! [U_2807,U_2805] :
        ( sP230(U_2807,U_2805)
        | hAPP(c_Int_Onat,U_2805) != U_2807 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230,sP231,sP232])],[f_768_3]) ).

cnf(f_768_5,plain,
    ( sP230(U_2807,U_2805)
    | hAPP(c_Int_Onat,U_2805) != U_2807 ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_6,plain,
    ( hAPP(c_Int_Onat,U_2806) = U_2808
    | sP232(U_2806,U_2808)
    | sP231(U_2806,U_2808) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_7,plain,
    ( U_2805 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2807)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
    | ~ sP230(U_2807,U_2805) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_8,plain,
    ( U_2807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
    | ~ sP230(U_2807,U_2805) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2806))
    | ~ sP231(U_2806,U_2808) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_10,plain,
    ( U_2806 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2808)
    | ~ sP231(U_2806,U_2808) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2806))
    | ~ sP232(U_2806,U_2808) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_12,plain,
    ( U_2808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP232(U_2806,U_2808) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

fof(f_769_1,plain,
    ! [V_w_2,V_m_2] :
      ( ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
        | ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
        | ( V_w_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
      & ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
          & ( V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
        | V_m_2 != hAPP(c_Int_Onat,V_w_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__iff2]) ).

fof(f_769_2,plain,
    ! [U_2810,U_2809] :
      ( ( U_2809 = hAPP(c_Int_Onat,U_2810)
        | ( U_2809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2810)) )
        | ( U_2810 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2809)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2810)) ) )
      & ( ( ( U_2809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2810)) )
          & ( U_2810 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2809)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2810)) ) )
        | U_2809 != hAPP(c_Int_Onat,U_2810) ) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ( ! [U_2814,U_2812] :
        ( U_2812 = hAPP(c_Int_Onat,U_2814)
        | ( U_2812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2814)) )
        | ( U_2814 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2812)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2814)) ) )
    & ! [U_2813,U_2811] :
        ( ( ( U_2811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2813)) )
          & ( U_2813 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2811)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2813)) ) )
        | U_2811 != hAPP(c_Int_Onat,U_2813) ) ),
    inference(miniscope,[status(thm)],[f_769_2]) ).

fof(f_769_4,plain,
    ( ! [U_2814,U_2812] :
        ( U_2812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP235(U_2814,U_2812) )
    & ! [U_2814,U_2812] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2814))
        | ~ sP235(U_2814,U_2812) )
    & ! [U_2814,U_2812] :
        ( U_2814 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2812)
        | ~ sP234(U_2814,U_2812) )
    & ! [U_2814,U_2812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2814))
        | ~ sP234(U_2814,U_2812) )
    & ! [U_2813,U_2811] :
        ( U_2811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2813))
        | ~ sP233(U_2813,U_2811) )
    & ! [U_2813,U_2811] :
        ( U_2813 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2811)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2813))
        | ~ sP233(U_2813,U_2811) )
    & ! [U_2814,U_2812] :
        ( U_2812 = hAPP(c_Int_Onat,U_2814)
        | sP235(U_2814,U_2812)
        | sP234(U_2814,U_2812) )
    & ! [U_2813,U_2811] :
        ( sP233(U_2813,U_2811)
        | U_2811 != hAPP(c_Int_Onat,U_2813) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233,sP234,sP235])],[f_769_3]) ).

cnf(f_769_5,plain,
    ( sP233(U_2813,U_2811)
    | U_2811 != hAPP(c_Int_Onat,U_2813) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_6,plain,
    ( U_2812 = hAPP(c_Int_Onat,U_2814)
    | sP235(U_2814,U_2812)
    | sP234(U_2814,U_2812) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_7,plain,
    ( U_2813 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2811)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2813))
    | ~ sP233(U_2813,U_2811) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_8,plain,
    ( U_2811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2813))
    | ~ sP233(U_2813,U_2811) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2814))
    | ~ sP234(U_2814,U_2812) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_10,plain,
    ( U_2814 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2812)
    | ~ sP234(U_2814,U_2812) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2814))
    | ~ sP235(U_2814,U_2812) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_12,plain,
    ( U_2812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP235(U_2814,U_2812) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

fof(f_770_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J]) ).

fof(f_770_2,plain,
    ! [U_2816,U_2815] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2815)),hAPP(c_Int_Onat,U_2816)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2815),U_2816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2815)) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_2815,U_2816] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2815)),hAPP(c_Int_Onat,U_2816)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2815),U_2816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2815)) ),
    inference(definitional_conversion,[status(esa)],[f_770_2]) ).

cnf(f_770_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2815)),hAPP(c_Int_Onat,U_2816)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2815),U_2816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2815)) ),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_1,plain,
    ! [V_z_H,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__distrib]) ).

fof(f_771_2,plain,
    ! [U_2818,U_2817] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2817),U_2818)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2817)),hAPP(c_Int_Onat,U_2818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2817)) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ! [U_2817,U_2818] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2817),U_2818)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2817)),hAPP(c_Int_Onat,U_2818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2817)) ),
    inference(definitional_conversion,[status(esa)],[f_771_2]) ).

cnf(f_771_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2817),U_2818)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2817)),hAPP(c_Int_Onat,U_2818))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2818))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2817)) ),
    inference(clausify,[status(thm)],[f_771_3]) ).

fof(f_772_1,plain,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).

fof(f_772_2,plain,
    ! [U_2819] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2819)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2819)) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2819] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2819)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2819)) ),
    inference(definitional_conversion,[status(esa)],[f_772_2]) ).

cnf(f_772_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2819)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2819)) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    inference(fof_nnf,[status(thm)],[fact_not__zle__0__negative]) ).

fof(f_773_2,plain,
    ! [U_2820] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2820))))),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2820] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2820))))),
    inference(definitional_conversion,[status(esa)],[f_773_2]) ).

cnf(f_773_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2820))))),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [V_z,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__nat]) ).

fof(f_774_2,plain,
    ! [U_2822,U_2821] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2821),hAPP(c_Int_Onat,U_2822)) = hAPP(c_Int_Oring__1__class_Oof__int(U_2821),U_2822)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2822))
      | ~ class_Rings_Oring__1(U_2821) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2821,U_2822] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2821),hAPP(c_Int_Onat,U_2822)) = hAPP(c_Int_Oring__1__class_Oof__int(U_2821),U_2822)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2822))
      | ~ class_Rings_Oring__1(U_2821) ),
    inference(definitional_conversion,[status(esa)],[f_774_2]) ).

cnf(f_774_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2821),hAPP(c_Int_Onat,U_2822)) = hAPP(c_Int_Oring__1__class_Oof__int(U_2821),U_2822)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2822))
    | ~ class_Rings_Oring__1(U_2821) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).

fof(f_775_2,plain,
    ! [U_2824,U_2823] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_2823,U_2824) = c_Groups_Oone__class_Oone(U_2823)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2823),c_Groups_Ozero__class_Ozero(U_2823)),U_2824)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2823),c_Groups_Ozero__class_Ozero(U_2823)),U_2824))
          | c_Groups_Osgn__class_Osgn(U_2823,U_2824) != c_Groups_Oone__class_Oone(U_2823) ) )
      | ~ class_Rings_Olinordered__idom(U_2823) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ( ! [U_2823,U_2824] :
        ( c_Groups_Osgn__class_Osgn(U_2823,U_2824) = c_Groups_Oone__class_Oone(U_2823)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2823),c_Groups_Ozero__class_Ozero(U_2823)),U_2824))
        | ~ sP236(U_2823,U_2824) )
    & ! [U_2823,U_2824] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2823),c_Groups_Ozero__class_Ozero(U_2823)),U_2824))
        | c_Groups_Osgn__class_Osgn(U_2823,U_2824) != c_Groups_Oone__class_Oone(U_2823)
        | ~ sP236(U_2823,U_2824) )
    & ! [U_2823,U_2824] :
        ( sP236(U_2823,U_2824)
        | ~ class_Rings_Olinordered__idom(U_2823) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_775_2]) ).

cnf(f_775_4,plain,
    ( sP236(U_2823,U_2824)
    | ~ class_Rings_Olinordered__idom(U_2823) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2823),c_Groups_Ozero__class_Ozero(U_2823)),U_2824))
    | c_Groups_Osgn__class_Osgn(U_2823,U_2824) != c_Groups_Oone__class_Oone(U_2823)
    | ~ sP236(U_2823,U_2824) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_2823,U_2824) = c_Groups_Oone__class_Oone(U_2823)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2823),c_Groups_Ozero__class_Ozero(U_2823)),U_2824))
    | ~ sP236(U_2823,U_2824) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_1,plain,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2]) ).

fof(f_776_2,plain,
    ! [U_2827,U_2826,U_2825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2827),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2826))
      | U_2825 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2825),U_2827))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2825)) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ! [U_2826,U_2825,U_2827] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2827),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2826))
      | U_2825 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2825),U_2827))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2825)) ),
    inference(definitional_conversion,[status(esa)],[f_776_2]) ).

cnf(f_776_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2827),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2826))
    | U_2825 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2825),U_2827))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2825)) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_1,plain,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
      | V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1]) ).

fof(f_777_2,plain,
    ! [U_2830,U_2829,U_2828] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2830))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2829),U_2828))
      | U_2828 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2828),U_2830))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2828)) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2828,U_2829,U_2830] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2830))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2829),U_2828))
      | U_2828 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2828),U_2830))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2828)) ),
    inference(definitional_conversion,[status(esa)],[f_777_2]) ).

cnf(f_777_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2830))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2829),U_2828))
    | U_2828 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2828),U_2830))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2828)) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_1,plain,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) ),
    inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).

fof(f_778_2,plain,
    ! [U_2833,U_2832,U_2831] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2832))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2833),U_2831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2831),U_2832)),U_2833))) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_2831,U_2832,U_2833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2832))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2833),U_2831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2831),U_2832)),U_2833))) ),
    inference(definitional_conversion,[status(esa)],[f_778_2]) ).

cnf(f_778_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2832))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2833),U_2831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2831),U_2832)),U_2833))) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_1,plain,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).

fof(f_779_2,plain,
    ! [U_2836,U_2835,U_2834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2835),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2834),U_2835)),U_2836)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_2834,U_2835,U_2836] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2835),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2834),U_2835)),U_2836)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_779_2]) ).

cnf(f_779_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2835),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2834))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2836))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2834),U_2835)),U_2836)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_1,plain,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).

fof(f_780_2,plain,
    ! [U_2841,U_2840,U_2839,U_2838,U_2837] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2838),U_2840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2841),U_2837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2839),U_2837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2839))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2837),U_2838)),U_2839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2837),U_2840)),U_2841))) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2837,U_2838,U_2839,U_2840,U_2841] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2838),U_2840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2841),U_2837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2839),U_2837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2839))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2837),U_2838)),U_2839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2837),U_2840)),U_2841))) ),
    inference(definitional_conversion,[status(esa)],[f_780_2]) ).

cnf(f_780_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2838),U_2840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2841),U_2837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2839),U_2837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2839))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2837),U_2838)),U_2839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2837),U_2840)),U_2841))) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_1,plain,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).

fof(f_781_2,plain,
    ! [U_2847,U_2846,U_2845,U_2844,U_2843,U_2842] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2843),U_2846))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2845),U_2842))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2844))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2847),U_2845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2845),U_2846)),U_2847)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2842),U_2843)),U_2844) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2845),U_2846)),U_2847) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2842,U_2843,U_2845,U_2844,U_2846,U_2847] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2843),U_2846))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2845),U_2842))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2844))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2847),U_2845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2845),U_2846)),U_2847)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2842),U_2843)),U_2844) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2845),U_2846)),U_2847) ),
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2843),U_2846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2845),U_2842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2844))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2847),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2845),U_2846)),U_2847)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2842),U_2843)),U_2844) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2845),U_2846)),U_2847) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_1,plain,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).

fof(f_782_2,plain,
    ! [U_2852,U_2851,U_2850,U_2849,U_2848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2851),U_2849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2848),U_2850))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2848),U_2852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2848),U_2849)),U_2850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2848),U_2851)),U_2852))) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2849,U_2851,U_2848,U_2850,U_2852] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2851),U_2849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2848),U_2850))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2848),U_2852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2848),U_2849)),U_2850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2848),U_2851)),U_2852))) ),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2851),U_2849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2848),U_2850))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2848),U_2852))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2848),U_2849)),U_2850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2848),U_2851)),U_2852))) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_1,plain,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).

fof(f_783_2,plain,
    ! [U_2858,U_2857,U_2856,U_2855,U_2854,U_2853] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2857),U_2854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2856),U_2853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2856))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2858))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2855),U_2853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2856),U_2857)),U_2858)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2853),U_2854)),U_2855) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2856),U_2857)),U_2858) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_2853,U_2855,U_2854,U_2856,U_2857,U_2858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2857),U_2854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2856),U_2853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2856))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2858))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2855),U_2853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2856),U_2857)),U_2858)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2853),U_2854)),U_2855) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2856),U_2857)),U_2858) ),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2857),U_2854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2856),U_2853))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2856))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2858))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2855),U_2853))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2856),U_2857)),U_2858)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2853),U_2854)),U_2855) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2856),U_2857)),U_2858) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1]) ).

fof(f_784_2,plain,
    ! [U_2861,U_2860,U_2859] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2861)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2861)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2861))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2861))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2859)) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ( ! [U_2861,U_2860,U_2859] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2861)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2861))
        | ~ sP237(U_2861,U_2860,U_2859) )
    & ! [U_2861,U_2860,U_2859] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2861)))
        | ~ sP237(U_2861,U_2860,U_2859) )
    & ! [U_2861,U_2860,U_2859] :
        ( sP237(U_2861,U_2860,U_2859)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2859)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_784_2]) ).

cnf(f_784_4,plain,
    ( sP237(U_2861,U_2860,U_2859)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2859)) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

cnf(f_784_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2861)))
    | ~ sP237(U_2861,U_2860,U_2859) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

cnf(f_784_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2859),U_2861)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2861))
    | ~ sP237(U_2861,U_2860,U_2859) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)),
    inference(fof_nnf,[status(thm)],[fact_le__refl]) ).

fof(f_785_2,plain,
    ! [U_2862] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2862),U_2862)),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_2862] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2862),U_2862)),
    inference(definitional_conversion,[status(esa)],[f_785_2]) ).

cnf(f_785_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2862),U_2862)),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).

fof(f_786_2,plain,
    ! [U_2864,U_2863] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2863))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2863),U_2864)) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_2863,U_2864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2863))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2863),U_2864)) ),
    inference(definitional_conversion,[status(esa)],[f_786_2]) ).

cnf(f_786_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2863))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2863),U_2864)) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | V_m != V_n ),
    inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).

fof(f_787_2,plain,
    ! [U_2866,U_2865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2865),U_2866))
      | U_2865 != U_2866 ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_2865,U_2866] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2865),U_2866))
      | U_2865 != U_2866 ),
    inference(definitional_conversion,[status(esa)],[f_787_2]) ).

cnf(f_787_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2865),U_2866))
    | U_2865 != U_2866 ),
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_le__trans]) ).

fof(f_788_2,plain,
    ! [U_2869,U_2868,U_2867] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2867),U_2869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2868),U_2869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2867),U_2868)) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ! [U_2867,U_2868,U_2869] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2867),U_2869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2868),U_2869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2867),U_2868)) ),
    inference(definitional_conversion,[status(esa)],[f_788_2]) ).

cnf(f_788_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2867),U_2869))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2868),U_2869))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2867),U_2868)) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

fof(f_789_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).

fof(f_789_2,plain,
    ! [U_2871,U_2870] :
      ( U_2870 = U_2871
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2871),U_2870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),U_2871)) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_2870,U_2871] :
      ( U_2870 = U_2871
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2871),U_2870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),U_2871)) ),
    inference(definitional_conversion,[status(esa)],[f_789_2]) ).

cnf(f_789_4,plain,
    ( U_2870 = U_2871
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2871),U_2870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),U_2871)) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).

fof(f_790_2,plain,
    ! [U_2875,U_2874,U_2873,U_2872] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2873,U_2872)),U_2874),U_2875))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2875),U_2874))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2874),U_2875)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2875),U_2874))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2874),U_2875)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2873,U_2872)),U_2874),U_2875)) ) )
      | ~ class_Orderings_Oord(U_2872) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ( ! [U_2872,U_2873,U_2874,U_2875] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2875),U_2874))
        | ~ sP238(U_2872,U_2873,U_2874,U_2875) )
    & ! [U_2872,U_2873,U_2874,U_2875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2874),U_2875))
        | ~ sP238(U_2872,U_2873,U_2874,U_2875) )
    & ! [U_2872,U_2873,U_2874,U_2875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2873,U_2872)),U_2874),U_2875))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2875),U_2874))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2874),U_2875))
        | ~ sP239(U_2872,U_2873,U_2874,U_2875) )
    & ! [U_2872,U_2873,U_2874,U_2875] :
        ( sP238(U_2872,U_2873,U_2874,U_2875)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2873,U_2872)),U_2874),U_2875))
        | ~ sP239(U_2872,U_2873,U_2874,U_2875) )
    & ! [U_2872,U_2873,U_2874,U_2875] :
        ( sP239(U_2872,U_2873,U_2874,U_2875)
        | ~ class_Orderings_Oord(U_2872) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238,sP239])],[f_790_2]) ).

cnf(f_790_4,plain,
    ( sP239(U_2872,U_2873,U_2874,U_2875)
    | ~ class_Orderings_Oord(U_2872) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

cnf(f_790_5,plain,
    ( sP238(U_2872,U_2873,U_2874,U_2875)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2873,U_2872)),U_2874),U_2875))
    | ~ sP239(U_2872,U_2873,U_2874,U_2875) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

cnf(f_790_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2873,U_2872)),U_2874),U_2875))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2875),U_2874))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2874),U_2875))
    | ~ sP239(U_2872,U_2873,U_2874,U_2875) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

cnf(f_790_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2874),U_2875))
    | ~ sP238(U_2872,U_2873,U_2874,U_2875) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

cnf(f_790_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2873,U_2872)),U_2875),U_2874))
    | ~ sP238(U_2872,U_2873,U_2874,U_2875) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

fof(f_791_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
        | ( V_m_2 != V_n_2
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_m_2 = V_n_2
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).

fof(f_791_2,plain,
    ! [U_2878,U_2877,U_2876] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2876),U_2877) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2876),U_2878)
        | ( U_2877 != U_2878
          & U_2876 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2877 = U_2878
        | U_2876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2876),U_2877) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2876),U_2878) ) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ( ! [U_2884,U_2882,U_2880] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2884)
        | ( U_2882 != U_2884
          & U_2880 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2883,U_2881,U_2879] :
        ( U_2881 = U_2883
        | U_2879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2881) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2883) ) ),
    inference(miniscope,[status(thm)],[f_791_2]) ).

fof(f_791_4,plain,
    ( ! [U_2882,U_2884,U_2880] :
        ( U_2882 != U_2884
        | ~ sP240(U_2882,U_2884,U_2880) )
    & ! [U_2882,U_2884,U_2880] :
        ( U_2880 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP240(U_2882,U_2884,U_2880) )
    & ! [U_2882,U_2884,U_2880] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2884)
        | sP240(U_2882,U_2884,U_2880) )
    & ! [U_2879,U_2881,U_2883] :
        ( U_2881 = U_2883
        | U_2879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2881) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2883) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_791_3]) ).

cnf(f_791_5,plain,
    ( U_2881 = U_2883
    | U_2879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2881) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2883) ),
    inference(clausify,[status(thm)],[f_791_4]) ).

cnf(f_791_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2884)
    | sP240(U_2882,U_2884,U_2880) ),
    inference(clausify,[status(thm)],[f_791_4]) ).

cnf(f_791_7,plain,
    ( U_2880 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP240(U_2882,U_2884,U_2880) ),
    inference(clausify,[status(thm)],[f_791_4]) ).

cnf(f_791_8,plain,
    ( U_2882 != U_2884
    | ~ sP240(U_2882,U_2884,U_2880) ),
    inference(clausify,[status(thm)],[f_791_4]) ).

fof(f_792_1,plain,
    ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
    inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(f_792_2,plain,
    ! [U_2888,U_2887,U_2886,U_2885] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2885),U_2886)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2886)),U_2888)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2887)),U_2886)),U_2888),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_2885,U_2886,U_2887,U_2888] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2885),U_2886)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2886)),U_2888)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2887)),U_2886)),U_2888),
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2885),U_2886)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2886)),U_2888)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2887)),U_2886)),U_2888),
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1]) ).

fof(f_793_2,plain,
    ! [U_2891,U_2890,U_2889] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2890),U_2891)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2890),U_2891))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2889)) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ( ! [U_2889,U_2890,U_2891] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2890),U_2891))
        | ~ sP241(U_2889,U_2890,U_2891) )
    & ! [U_2889,U_2890,U_2891] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2890),U_2891))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)))
        | ~ sP241(U_2889,U_2890,U_2891) )
    & ! [U_2889,U_2890,U_2891] :
        ( sP241(U_2889,U_2890,U_2891)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2889)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_793_2]) ).

cnf(f_793_4,plain,
    ( sP241(U_2889,U_2890,U_2891)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2889)) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

cnf(f_793_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2890),U_2891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)))
    | ~ sP241(U_2889,U_2890,U_2891) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

cnf(f_793_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2890),U_2891))
    | ~ sP241(U_2889,U_2890,U_2891) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

fof(f_794_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1]) ).

fof(f_794_2,plain,
    ! [U_2894,U_2893,U_2892] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2894)
          | U_2893 != U_2894 )
        & ( U_2893 = U_2894
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2893) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2894) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2892)) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ( ! [U_2894,U_2893,U_2892] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2894)
        | U_2893 != U_2894
        | ~ sP242(U_2894,U_2893,U_2892) )
    & ! [U_2894,U_2893,U_2892] :
        ( U_2893 = U_2894
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2893) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2894)
        | ~ sP242(U_2894,U_2893,U_2892) )
    & ! [U_2894,U_2893,U_2892] :
        ( sP242(U_2894,U_2893,U_2892)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2892)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_794_2]) ).

cnf(f_794_4,plain,
    ( sP242(U_2894,U_2893,U_2892)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2892)) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

cnf(f_794_5,plain,
    ( U_2893 = U_2894
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2893) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2894)
    | ~ sP242(U_2894,U_2893,U_2892) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

cnf(f_794_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2892),U_2894)
    | U_2893 != U_2894
    | ~ sP242(U_2894,U_2893,U_2892) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

fof(f_795_1,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_transfer__morphism__nat__int]) ).

fof(f_795_2,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_795_1]) ).

cnf(f_795_3,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_795_2]) ).

fof(f_796_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) ) )
      | ~ class_Lattices_Oboolean__algebra(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).

fof(f_796_2,plain,
    ! [U_2897,U_2896,U_2895] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2897)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),U_2897),U_2896)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),U_2897),U_2896))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2897))) ) )
      | ~ class_Lattices_Oboolean__algebra(U_2895) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ( ! [U_2895,U_2896,U_2897] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2897)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),U_2897),U_2896))
        | ~ sP243(U_2895,U_2896,U_2897) )
    & ! [U_2895,U_2896,U_2897] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),U_2897),U_2896))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2897)))
        | ~ sP243(U_2895,U_2896,U_2897) )
    & ! [U_2895,U_2896,U_2897] :
        ( sP243(U_2895,U_2896,U_2897)
        | ~ class_Lattices_Oboolean__algebra(U_2895) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_796_2]) ).

cnf(f_796_4,plain,
    ( sP243(U_2895,U_2896,U_2897)
    | ~ class_Lattices_Oboolean__algebra(U_2895) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),U_2897),U_2896))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2897)))
    | ~ sP243(U_2895,U_2896,U_2897) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2897)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2895),U_2897),U_2896))
    | ~ sP243(U_2895,U_2896,U_2897) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__mono]) ).

fof(f_797_2,plain,
    ! [U_2900,U_2899,U_2898] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2898),hAPP(c_Groups_Ouminus__class_Ouminus(U_2898),U_2900)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2898),U_2899)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2898),U_2899),U_2900))
      | ~ class_Lattices_Oboolean__algebra(U_2898) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2898,U_2899,U_2900] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2898),hAPP(c_Groups_Ouminus__class_Ouminus(U_2898),U_2900)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2898),U_2899)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2898),U_2899),U_2900))
      | ~ class_Lattices_Oboolean__algebra(U_2898) ),
    inference(definitional_conversion,[status(esa)],[f_797_2]) ).

cnf(f_797_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2898),hAPP(c_Groups_Ouminus__class_Ouminus(U_2898),U_2900)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2898),U_2899)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2898),U_2899),U_2900))
    | ~ class_Lattices_Oboolean__algebra(U_2898) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_1,plain,
    ! [V_n_2,V_P_2] :
      ( ? [B_k] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) )
      | ~ hBOOL(hAPP(V_P_2,V_n_2))
      | hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).

fof(f_798_2,plain,
    ! [U_2904,U_2903] :
      ( ? [U_2902] :
          ( hBOOL(hAPP(U_2903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2902),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_2901] :
              ( ~ hBOOL(hAPP(U_2903,U_2901))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2901),U_2902)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2902),U_2904)) )
      | ~ hBOOL(hAPP(U_2903,U_2904))
      | hBOOL(hAPP(U_2903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2904,U_2903] :
      ( ( hBOOL(hAPP(U_2903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK51(U_2904,U_2903)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_2901] :
            ( ~ hBOOL(hAPP(U_2903,U_2901))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2901),sK51(U_2904,U_2903))) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK51(U_2904,U_2903)),U_2904)) )
      | ~ hBOOL(hAPP(U_2903,U_2904))
      | hBOOL(hAPP(U_2903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_2902,sK51(U_2904,U_2903))],[f_798_2]) ).

fof(f_798_4,plain,
    ( ! [U_2901,U_2903,U_2904] :
        ( hBOOL(hAPP(U_2903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK51(U_2904,U_2903)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ sP244(U_2901,U_2903,U_2904) )
    & ! [U_2901,U_2903,U_2904] :
        ( ~ hBOOL(hAPP(U_2903,U_2901))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2901),sK51(U_2904,U_2903)))
        | ~ sP244(U_2901,U_2903,U_2904) )
    & ! [U_2901,U_2903,U_2904] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK51(U_2904,U_2903)),U_2904))
        | ~ sP244(U_2901,U_2903,U_2904) )
    & ! [U_2901,U_2903,U_2904] :
        ( sP244(U_2901,U_2903,U_2904)
        | ~ hBOOL(hAPP(U_2903,U_2904))
        | hBOOL(hAPP(U_2903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_798_3]) ).

cnf(f_798_5,plain,
    ( sP244(U_2901,U_2903,U_2904)
    | ~ hBOOL(hAPP(U_2903,U_2904))
    | hBOOL(hAPP(U_2903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

cnf(f_798_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK51(U_2904,U_2903)),U_2904))
    | ~ sP244(U_2901,U_2903,U_2904) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

cnf(f_798_7,plain,
    ( ~ hBOOL(hAPP(U_2903,U_2901))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2901),sK51(U_2904,U_2903)))
    | ~ sP244(U_2901,U_2903,U_2904) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

cnf(f_798_8,plain,
    ( hBOOL(hAPP(U_2903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK51(U_2904,U_2903)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ sP244(U_2901,U_2903,U_2904) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

fof(f_799_1,plain,
    ! [V_y,V_q_1,V_b_1,V_a_1] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y
      | V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | V_a_1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).

fof(f_799_2,plain,
    ! [U_2908,U_2907,U_2906,U_2905] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2905,U_2906) = U_2908
      | U_2906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2908),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2906),U_2908)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2906)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2908),U_2906))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2908)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2906)) )
      | U_2905 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2906),U_2907)),U_2908) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ( ! [U_2906,U_2908] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2908),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2906),U_2908))
        | ~ sP246(U_2906,U_2908) )
    & ! [U_2906,U_2908] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2906))
        | ~ sP246(U_2906,U_2908) )
    & ! [U_2906,U_2908] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2908),U_2906))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2908))
        | ~ sP245(U_2906,U_2908) )
    & ! [U_2906,U_2908] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2906))
        | ~ sP245(U_2906,U_2908) )
    & ! [U_2906,U_2905,U_2907,U_2908] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2905,U_2906) = U_2908
        | U_2906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP246(U_2906,U_2908)
        | sP245(U_2906,U_2908)
        | U_2905 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2906),U_2907)),U_2908) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245,sP246])],[f_799_2]) ).

cnf(f_799_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2905,U_2906) = U_2908
    | U_2906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP246(U_2906,U_2908)
    | sP245(U_2906,U_2908)
    | U_2905 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2906),U_2907)),U_2908) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

cnf(f_799_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2906))
    | ~ sP245(U_2906,U_2908) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

cnf(f_799_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2908),U_2906))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2908))
    | ~ sP245(U_2906,U_2908) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

cnf(f_799_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2906))
    | ~ sP246(U_2906,U_2908) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

cnf(f_799_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2908),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2906),U_2908))
    | ~ sP246(U_2906,U_2908) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

fof(f_800_1,plain,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2]) ).

fof(f_800_2,plain,
    ! [U_2912,U_2911,U_2910,U_2909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2910),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2912,U_2909))),U_2911)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2911),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2910),U_2911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2909)) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_2911,U_2910,U_2912,U_2909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2910),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2912,U_2909))),U_2911)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2911),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2910),U_2911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2909)) ),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2910),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2912,U_2909))),U_2911)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2911),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2910),U_2911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2909)) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_1,plain,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1]) ).

fof(f_801_2,plain,
    ! [U_2916,U_2915,U_2914,U_2913] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2913)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2913))),U_2915)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2915),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2915))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2913)) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_2915,U_2913,U_2914,U_2916] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2913)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2913))),U_2915)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2915),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2915))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2913)) ),
    inference(definitional_conversion,[status(esa)],[f_801_2]) ).

cnf(f_801_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2913)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2913))),U_2915)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2915),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2915))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2913)) ),
    inference(clausify,[status(thm)],[f_801_3]) ).

fof(f_802_1,plain,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4]) ).

fof(f_802_2,plain,
    ! [U_2920,U_2919,U_2918,U_2917] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2919),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2920,U_2917))),U_2918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2919),U_2917)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2918),U_2919))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2918))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2917)) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_2917,U_2918,U_2919,U_2920] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2919),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2920,U_2917))),U_2918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2919),U_2917)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2918),U_2919))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2918))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2917)) ),
    inference(definitional_conversion,[status(esa)],[f_802_2]) ).

cnf(f_802_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2919),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2920,U_2917))),U_2918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2919),U_2917)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2918),U_2919))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2918))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2917)) ),
    inference(clausify,[status(thm)],[f_802_3]) ).

fof(f_803_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial]) ).

fof(f_803_2,plain,
    ! [U_2923,U_2922,U_2921] :
      ( c_Divides_Odiv__class_Omod(U_2921,c_Divides_Odiv__class_Omod(U_2921,U_2922,U_2923),U_2923) = c_Divides_Odiv__class_Omod(U_2921,U_2922,U_2923)
      | ~ class_Divides_Osemiring__div(U_2921) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2921,U_2923,U_2922] :
      ( c_Divides_Odiv__class_Omod(U_2921,c_Divides_Odiv__class_Omod(U_2921,U_2922,U_2923),U_2923) = c_Divides_Odiv__class_Omod(U_2921,U_2922,U_2923)
      | ~ class_Divides_Osemiring__div(U_2921) ),
    inference(definitional_conversion,[status(esa)],[f_803_2]) ).

cnf(f_803_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2921,c_Divides_Odiv__class_Omod(U_2921,U_2922,U_2923),U_2923) = c_Divides_Odiv__class_Omod(U_2921,U_2922,U_2923)
    | ~ class_Divides_Osemiring__div(U_2921) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__0]) ).

fof(f_804_2,plain,
    ! [U_2925,U_2924] :
      ( c_Divides_Odiv__class_Omod(U_2924,c_Groups_Ozero__class_Ozero(U_2924),U_2925) = c_Groups_Ozero__class_Ozero(U_2924)
      | ~ class_Divides_Osemiring__div(U_2924) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2924,U_2925] :
      ( c_Divides_Odiv__class_Omod(U_2924,c_Groups_Ozero__class_Ozero(U_2924),U_2925) = c_Groups_Ozero__class_Ozero(U_2924)
      | ~ class_Divides_Osemiring__div(U_2924) ),
    inference(definitional_conversion,[status(esa)],[f_804_2]) ).

cnf(f_804_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2924,c_Groups_Ozero__class_Ozero(U_2924),U_2925) = c_Groups_Ozero__class_Ozero(U_2924)
    | ~ class_Divides_Osemiring__div(U_2924) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__by__0]) ).

fof(f_805_2,plain,
    ! [U_2927,U_2926] :
      ( c_Divides_Odiv__class_Omod(U_2926,U_2927,c_Groups_Ozero__class_Ozero(U_2926)) = U_2927
      | ~ class_Divides_Osemiring__div(U_2926) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_2926,U_2927] :
      ( c_Divides_Odiv__class_Omod(U_2926,U_2927,c_Groups_Ozero__class_Ozero(U_2926)) = U_2927
      | ~ class_Divides_Osemiring__div(U_2926) ),
    inference(definitional_conversion,[status(esa)],[f_805_2]) ).

cnf(f_805_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2926,U_2927,c_Groups_Ozero__class_Ozero(U_2926)) = U_2927
    | ~ class_Divides_Osemiring__div(U_2926) ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__self]) ).

fof(f_806_2,plain,
    ! [U_2929,U_2928] :
      ( c_Divides_Odiv__class_Omod(U_2928,U_2929,U_2929) = c_Groups_Ozero__class_Ozero(U_2928)
      | ~ class_Divides_Osemiring__div(U_2928) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_2928,U_2929] :
      ( c_Divides_Odiv__class_Omod(U_2928,U_2929,U_2929) = c_Groups_Ozero__class_Ozero(U_2928)
      | ~ class_Divides_Osemiring__div(U_2928) ),
    inference(definitional_conversion,[status(esa)],[f_806_2]) ).

cnf(f_806_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2928,U_2929,U_2929) = c_Groups_Ozero__class_Ozero(U_2928)
    | ~ class_Divides_Osemiring__div(U_2928) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__self2]) ).

fof(f_807_2,plain,
    ! [U_2932,U_2931,U_2930] :
      ( c_Divides_Odiv__class_Omod(U_2930,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2930),U_2931),U_2932),U_2932) = c_Divides_Odiv__class_Omod(U_2930,U_2931,U_2932)
      | ~ class_Divides_Osemiring__div(U_2930) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_2930,U_2931,U_2932] :
      ( c_Divides_Odiv__class_Omod(U_2930,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2930),U_2931),U_2932),U_2932) = c_Divides_Odiv__class_Omod(U_2930,U_2931,U_2932)
      | ~ class_Divides_Osemiring__div(U_2930) ),
    inference(definitional_conversion,[status(esa)],[f_807_2]) ).

cnf(f_807_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2930,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2930),U_2931),U_2932),U_2932) = c_Divides_Odiv__class_Omod(U_2930,U_2931,U_2932)
    | ~ class_Divides_Osemiring__div(U_2930) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__self1]) ).

fof(f_808_2,plain,
    ! [U_2935,U_2934,U_2933] :
      ( c_Divides_Odiv__class_Omod(U_2933,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2933),U_2934),U_2935),U_2934) = c_Divides_Odiv__class_Omod(U_2933,U_2935,U_2934)
      | ~ class_Divides_Osemiring__div(U_2933) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ! [U_2933,U_2934,U_2935] :
      ( c_Divides_Odiv__class_Omod(U_2933,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2933),U_2934),U_2935),U_2934) = c_Divides_Odiv__class_Omod(U_2933,U_2935,U_2934)
      | ~ class_Divides_Osemiring__div(U_2933) ),
    inference(definitional_conversion,[status(esa)],[f_808_2]) ).

cnf(f_808_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2933,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2933),U_2934),U_2935),U_2934) = c_Divides_Odiv__class_Omod(U_2933,U_2935,U_2934)
    | ~ class_Divides_Osemiring__div(U_2933) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

fof(f_809_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq]) ).

fof(f_809_2,plain,
    ! [U_2939,U_2938,U_2937,U_2936] :
      ( c_Divides_Odiv__class_Omod(U_2936,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2936),U_2937),U_2938),U_2939) = c_Divides_Odiv__class_Omod(U_2936,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2936),U_2937),c_Divides_Odiv__class_Omod(U_2936,U_2938,U_2939)),U_2939)
      | ~ class_Divides_Osemiring__div(U_2936) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_2936,U_2937,U_2938,U_2939] :
      ( c_Divides_Odiv__class_Omod(U_2936,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2936),U_2937),U_2938),U_2939) = c_Divides_Odiv__class_Omod(U_2936,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2936),U_2937),c_Divides_Odiv__class_Omod(U_2936,U_2938,U_2939)),U_2939)
      | ~ class_Divides_Osemiring__div(U_2936) ),
    inference(definitional_conversion,[status(esa)],[f_809_2]) ).

cnf(f_809_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2936,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2936),U_2937),U_2938),U_2939) = c_Divides_Odiv__class_Omod(U_2936,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2936),U_2937),c_Divides_Odiv__class_Omod(U_2936,U_2938,U_2939)),U_2939)
    | ~ class_Divides_Osemiring__div(U_2936) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq]) ).

fof(f_810_2,plain,
    ! [U_2943,U_2942,U_2941,U_2940] :
      ( c_Divides_Odiv__class_Omod(U_2940,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2940),U_2941),U_2942),U_2943) = c_Divides_Odiv__class_Omod(U_2940,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2940),c_Divides_Odiv__class_Omod(U_2940,U_2941,U_2943)),U_2942),U_2943)
      | ~ class_Divides_Osemiring__div(U_2940) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_2940,U_2941,U_2942,U_2943] :
      ( c_Divides_Odiv__class_Omod(U_2940,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2940),U_2941),U_2942),U_2943) = c_Divides_Odiv__class_Omod(U_2940,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2940),c_Divides_Odiv__class_Omod(U_2940,U_2941,U_2943)),U_2942),U_2943)
      | ~ class_Divides_Osemiring__div(U_2940) ),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2940,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2940),U_2941),U_2942),U_2943) = c_Divides_Odiv__class_Omod(U_2940,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2940),c_Divides_Odiv__class_Omod(U_2940,U_2941,U_2943)),U_2942),U_2943)
    | ~ class_Divides_Osemiring__div(U_2940) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__eq]) ).

fof(f_811_2,plain,
    ! [U_2947,U_2946,U_2945,U_2944] :
      ( c_Divides_Odiv__class_Omod(U_2944,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2944),U_2945),U_2946),U_2947) = c_Divides_Odiv__class_Omod(U_2944,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2944),c_Divides_Odiv__class_Omod(U_2944,U_2945,U_2947)),c_Divides_Odiv__class_Omod(U_2944,U_2946,U_2947)),U_2947)
      | ~ class_Divides_Osemiring__div(U_2944) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_2944,U_2945,U_2946,U_2947] :
      ( c_Divides_Odiv__class_Omod(U_2944,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2944),U_2945),U_2946),U_2947) = c_Divides_Odiv__class_Omod(U_2944,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2944),c_Divides_Odiv__class_Omod(U_2944,U_2945,U_2947)),c_Divides_Odiv__class_Omod(U_2944,U_2946,U_2947)),U_2947)
      | ~ class_Divides_Osemiring__div(U_2944) ),
    inference(definitional_conversion,[status(esa)],[f_811_2]) ).

cnf(f_811_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2944,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2944),U_2945),U_2946),U_2947) = c_Divides_Odiv__class_Omod(U_2944,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2944),c_Divides_Odiv__class_Omod(U_2944,U_2945,U_2947)),c_Divides_Odiv__class_Omod(U_2944,U_2946,U_2947)),U_2947)
    | ~ class_Divides_Osemiring__div(U_2944) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

fof(f_812_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J]) ).

fof(f_812_2,plain,
    ! [U_2951,U_2950,U_2949,U_2948] :
      ( c_Divides_Odiv__class_Omod(U_2948,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2948),U_2949),c_Divides_Odiv__class_Omod(U_2948,U_2950,U_2951)),U_2951) = c_Divides_Odiv__class_Omod(U_2948,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2948),U_2949),U_2950),U_2951)
      | ~ class_Divides_Osemiring__div(U_2948) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_2948,U_2949,U_2950,U_2951] :
      ( c_Divides_Odiv__class_Omod(U_2948,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2948),U_2949),c_Divides_Odiv__class_Omod(U_2948,U_2950,U_2951)),U_2951) = c_Divides_Odiv__class_Omod(U_2948,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2948),U_2949),U_2950),U_2951)
      | ~ class_Divides_Osemiring__div(U_2948) ),
    inference(definitional_conversion,[status(esa)],[f_812_2]) ).

cnf(f_812_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2948,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2948),U_2949),c_Divides_Odiv__class_Omod(U_2948,U_2950,U_2951)),U_2951) = c_Divides_Odiv__class_Omod(U_2948,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2948),U_2949),U_2950),U_2951)
    | ~ class_Divides_Osemiring__div(U_2948) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J]) ).

fof(f_813_2,plain,
    ! [U_2955,U_2954,U_2953,U_2952] :
      ( c_Divides_Odiv__class_Omod(U_2952,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2952),c_Divides_Odiv__class_Omod(U_2952,U_2953,U_2954)),U_2955),U_2954) = c_Divides_Odiv__class_Omod(U_2952,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2952),U_2953),U_2955),U_2954)
      | ~ class_Divides_Osemiring__div(U_2952) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ! [U_2952,U_2953,U_2954,U_2955] :
      ( c_Divides_Odiv__class_Omod(U_2952,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2952),c_Divides_Odiv__class_Omod(U_2952,U_2953,U_2954)),U_2955),U_2954) = c_Divides_Odiv__class_Omod(U_2952,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2952),U_2953),U_2955),U_2954)
      | ~ class_Divides_Osemiring__div(U_2952) ),
    inference(definitional_conversion,[status(esa)],[f_813_2]) ).

cnf(f_813_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2952,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2952),c_Divides_Odiv__class_Omod(U_2952,U_2953,U_2954)),U_2955),U_2954) = c_Divides_Odiv__class_Omod(U_2952,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2952),U_2953),U_2955),U_2954)
    | ~ class_Divides_Osemiring__div(U_2952) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_1,plain,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__cong]) ).

fof(f_814_2,plain,
    ! [U_2961,U_2960,U_2959,U_2958,U_2957,U_2956] :
      ( c_Divides_Odiv__class_Omod(U_2956,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2956),U_2957),U_2960),U_2958) = c_Divides_Odiv__class_Omod(U_2956,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2956),U_2959),U_2961),U_2958)
      | c_Divides_Odiv__class_Omod(U_2956,U_2960,U_2958) != c_Divides_Odiv__class_Omod(U_2956,U_2961,U_2958)
      | c_Divides_Odiv__class_Omod(U_2956,U_2957,U_2958) != c_Divides_Odiv__class_Omod(U_2956,U_2959,U_2958)
      | ~ class_Divides_Osemiring__div(U_2956) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_2956,U_2957,U_2958,U_2959,U_2960,U_2961] :
      ( c_Divides_Odiv__class_Omod(U_2956,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2956),U_2957),U_2960),U_2958) = c_Divides_Odiv__class_Omod(U_2956,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2956),U_2959),U_2961),U_2958)
      | c_Divides_Odiv__class_Omod(U_2956,U_2960,U_2958) != c_Divides_Odiv__class_Omod(U_2956,U_2961,U_2958)
      | c_Divides_Odiv__class_Omod(U_2956,U_2957,U_2958) != c_Divides_Odiv__class_Omod(U_2956,U_2959,U_2958)
      | ~ class_Divides_Osemiring__div(U_2956) ),
    inference(definitional_conversion,[status(esa)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2956,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2956),U_2957),U_2960),U_2958) = c_Divides_Odiv__class_Omod(U_2956,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2956),U_2959),U_2961),U_2958)
    | c_Divides_Odiv__class_Omod(U_2956,U_2960,U_2958) != c_Divides_Odiv__class_Omod(U_2956,U_2961,U_2958)
    | c_Divides_Odiv__class_Omod(U_2956,U_2957,U_2958) != c_Divides_Odiv__class_Omod(U_2956,U_2959,U_2958)
    | ~ class_Divides_Osemiring__div(U_2956) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq]) ).

fof(f_815_2,plain,
    ! [U_2965,U_2964,U_2963,U_2962] :
      ( c_Divides_Odiv__class_Omod(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2963),U_2964),U_2965) = c_Divides_Odiv__class_Omod(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2963),c_Divides_Odiv__class_Omod(U_2962,U_2964,U_2965)),U_2965)
      | ~ class_Divides_Osemiring__div(U_2962) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_2962,U_2963,U_2964,U_2965] :
      ( c_Divides_Odiv__class_Omod(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2963),U_2964),U_2965) = c_Divides_Odiv__class_Omod(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2963),c_Divides_Odiv__class_Omod(U_2962,U_2964,U_2965)),U_2965)
      | ~ class_Divides_Osemiring__div(U_2962) ),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2963),U_2964),U_2965) = c_Divides_Odiv__class_Omod(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2963),c_Divides_Odiv__class_Omod(U_2962,U_2964,U_2965)),U_2965)
    | ~ class_Divides_Osemiring__div(U_2962) ),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq]) ).

fof(f_816_2,plain,
    ! [U_2969,U_2968,U_2967,U_2966] :
      ( c_Divides_Odiv__class_Omod(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),U_2969) = c_Divides_Odiv__class_Omod(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),c_Divides_Odiv__class_Omod(U_2966,U_2967,U_2969)),U_2968),U_2969)
      | ~ class_Divides_Osemiring__div(U_2966) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2966,U_2967,U_2968,U_2969] :
      ( c_Divides_Odiv__class_Omod(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),U_2969) = c_Divides_Odiv__class_Omod(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),c_Divides_Odiv__class_Omod(U_2966,U_2967,U_2969)),U_2968),U_2969)
      | ~ class_Divides_Osemiring__div(U_2966) ),
    inference(definitional_conversion,[status(esa)],[f_816_2]) ).

cnf(f_816_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),U_2969) = c_Divides_Odiv__class_Omod(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),c_Divides_Odiv__class_Omod(U_2966,U_2967,U_2969)),U_2968),U_2969)
    | ~ class_Divides_Osemiring__div(U_2966) ),
    inference(clausify,[status(thm)],[f_816_3]) ).

fof(f_817_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__eq]) ).

fof(f_817_2,plain,
    ! [U_2973,U_2972,U_2971,U_2970] :
      ( c_Divides_Odiv__class_Omod(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2971),U_2972),U_2973) = c_Divides_Odiv__class_Omod(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),c_Divides_Odiv__class_Omod(U_2970,U_2971,U_2973)),c_Divides_Odiv__class_Omod(U_2970,U_2972,U_2973)),U_2973)
      | ~ class_Divides_Osemiring__div(U_2970) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2970,U_2971,U_2972,U_2973] :
      ( c_Divides_Odiv__class_Omod(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2971),U_2972),U_2973) = c_Divides_Odiv__class_Omod(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),c_Divides_Odiv__class_Omod(U_2970,U_2971,U_2973)),c_Divides_Odiv__class_Omod(U_2970,U_2972,U_2973)),U_2973)
      | ~ class_Divides_Osemiring__div(U_2970) ),
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2971),U_2972),U_2973) = c_Divides_Odiv__class_Omod(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),c_Divides_Odiv__class_Omod(U_2970,U_2971,U_2973)),c_Divides_Odiv__class_Omod(U_2970,U_2972,U_2973)),U_2973)
    | ~ class_Divides_Osemiring__div(U_2970) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1]) ).

fof(f_818_2,plain,
    ! [U_2977,U_2976,U_2975,U_2974] :
      ( c_Divides_Odiv__class_Omod(U_2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),c_Divides_Odiv__class_Omod(U_2974,U_2976,U_2977))
      | ~ class_Divides_Osemiring__div(U_2974) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2974,U_2975,U_2976,U_2977] :
      ( c_Divides_Odiv__class_Omod(U_2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),c_Divides_Odiv__class_Omod(U_2974,U_2976,U_2977))
      | ~ class_Divides_Osemiring__div(U_2974) ),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),c_Divides_Odiv__class_Omod(U_2974,U_2976,U_2977))
    | ~ class_Divides_Osemiring__div(U_2974) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2]) ).

fof(f_819_2,plain,
    ! [U_2981,U_2980,U_2979,U_2978] :
      ( c_Divides_Odiv__class_Omod(U_2978,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),U_2979),U_2980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),U_2981),U_2980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),c_Divides_Odiv__class_Omod(U_2978,U_2979,U_2981)),U_2980)
      | ~ class_Divides_Osemiring__div(U_2978) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2978,U_2979,U_2980,U_2981] :
      ( c_Divides_Odiv__class_Omod(U_2978,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),U_2979),U_2980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),U_2981),U_2980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),c_Divides_Odiv__class_Omod(U_2978,U_2979,U_2981)),U_2980)
      | ~ class_Divides_Osemiring__div(U_2978) ),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2978,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),U_2979),U_2980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),U_2981),U_2980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2978),c_Divides_Odiv__class_Omod(U_2978,U_2979,U_2981)),U_2980)
    | ~ class_Divides_Osemiring__div(U_2978) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J]) ).

fof(f_820_2,plain,
    ! [U_2985,U_2984,U_2983,U_2982] :
      ( c_Divides_Odiv__class_Omod(U_2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2982),c_Divides_Odiv__class_Omod(U_2982,U_2983,U_2984)),U_2985),U_2984) = c_Divides_Odiv__class_Omod(U_2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2982),U_2983),U_2985),U_2984)
      | ~ class_Divides_Osemiring__div(U_2982) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2982,U_2983,U_2984,U_2985] :
      ( c_Divides_Odiv__class_Omod(U_2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2982),c_Divides_Odiv__class_Omod(U_2982,U_2983,U_2984)),U_2985),U_2984) = c_Divides_Odiv__class_Omod(U_2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2982),U_2983),U_2985),U_2984)
      | ~ class_Divides_Osemiring__div(U_2982) ),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2982),c_Divides_Odiv__class_Omod(U_2982,U_2983,U_2984)),U_2985),U_2984) = c_Divides_Odiv__class_Omod(U_2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2982),U_2983),U_2985),U_2984)
    | ~ class_Divides_Osemiring__div(U_2982) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_1,plain,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__cong]) ).

fof(f_821_2,plain,
    ! [U_2991,U_2990,U_2989,U_2988,U_2987,U_2986] :
      ( c_Divides_Odiv__class_Omod(U_2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2986),U_2987),U_2990),U_2988) = c_Divides_Odiv__class_Omod(U_2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2986),U_2989),U_2991),U_2988)
      | c_Divides_Odiv__class_Omod(U_2986,U_2990,U_2988) != c_Divides_Odiv__class_Omod(U_2986,U_2991,U_2988)
      | c_Divides_Odiv__class_Omod(U_2986,U_2987,U_2988) != c_Divides_Odiv__class_Omod(U_2986,U_2989,U_2988)
      | ~ class_Divides_Osemiring__div(U_2986) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2986,U_2987,U_2988,U_2989,U_2990,U_2991] :
      ( c_Divides_Odiv__class_Omod(U_2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2986),U_2987),U_2990),U_2988) = c_Divides_Odiv__class_Omod(U_2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2986),U_2989),U_2991),U_2988)
      | c_Divides_Odiv__class_Omod(U_2986,U_2990,U_2988) != c_Divides_Odiv__class_Omod(U_2986,U_2991,U_2988)
      | c_Divides_Odiv__class_Omod(U_2986,U_2987,U_2988) != c_Divides_Odiv__class_Omod(U_2986,U_2989,U_2988)
      | ~ class_Divides_Osemiring__div(U_2986) ),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2986),U_2987),U_2990),U_2988) = c_Divides_Odiv__class_Omod(U_2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2986),U_2989),U_2991),U_2988)
    | c_Divides_Odiv__class_Omod(U_2986,U_2990,U_2988) != c_Divides_Odiv__class_Omod(U_2986,U_2991,U_2988)
    | c_Divides_Odiv__class_Omod(U_2986,U_2987,U_2988) != c_Divides_Odiv__class_Omod(U_2986,U_2989,U_2988)
    | ~ class_Divides_Osemiring__div(U_2986) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__minus__eq]) ).

fof(f_822_2,plain,
    ! [U_2994,U_2993,U_2992] :
      ( c_Divides_Odiv__class_Omod(U_2992,hAPP(c_Groups_Ouminus__class_Ouminus(U_2992),U_2993),U_2994) = c_Divides_Odiv__class_Omod(U_2992,hAPP(c_Groups_Ouminus__class_Ouminus(U_2992),c_Divides_Odiv__class_Omod(U_2992,U_2993,U_2994)),U_2994)
      | ~ class_Divides_Oring__div(U_2992) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_2993,U_2992,U_2994] :
      ( c_Divides_Odiv__class_Omod(U_2992,hAPP(c_Groups_Ouminus__class_Ouminus(U_2992),U_2993),U_2994) = c_Divides_Odiv__class_Omod(U_2992,hAPP(c_Groups_Ouminus__class_Ouminus(U_2992),c_Divides_Odiv__class_Omod(U_2992,U_2993,U_2994)),U_2994)
      | ~ class_Divides_Oring__div(U_2992) ),
    inference(definitional_conversion,[status(esa)],[f_822_2]) ).

cnf(f_822_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2992,hAPP(c_Groups_Ouminus__class_Ouminus(U_2992),U_2993),U_2994) = c_Divides_Odiv__class_Omod(U_2992,hAPP(c_Groups_Ouminus__class_Ouminus(U_2992),c_Divides_Odiv__class_Omod(U_2992,U_2993,U_2994)),U_2994)
    | ~ class_Divides_Oring__div(U_2992) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_1,plain,
    ! [V_a_H,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_b) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__minus__cong]) ).

fof(f_823_2,plain,
    ! [U_2998,U_2997,U_2996,U_2995] :
      ( c_Divides_Odiv__class_Omod(U_2995,hAPP(c_Groups_Ouminus__class_Ouminus(U_2995),U_2996),U_2997) = c_Divides_Odiv__class_Omod(U_2995,hAPP(c_Groups_Ouminus__class_Ouminus(U_2995),U_2998),U_2997)
      | c_Divides_Odiv__class_Omod(U_2995,U_2996,U_2997) != c_Divides_Odiv__class_Omod(U_2995,U_2998,U_2997)
      | ~ class_Divides_Oring__div(U_2995) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2995,U_2996,U_2997,U_2998] :
      ( c_Divides_Odiv__class_Omod(U_2995,hAPP(c_Groups_Ouminus__class_Ouminus(U_2995),U_2996),U_2997) = c_Divides_Odiv__class_Omod(U_2995,hAPP(c_Groups_Ouminus__class_Ouminus(U_2995),U_2998),U_2997)
      | c_Divides_Odiv__class_Omod(U_2995,U_2996,U_2997) != c_Divides_Odiv__class_Omod(U_2995,U_2998,U_2997)
      | ~ class_Divides_Oring__div(U_2995) ),
    inference(definitional_conversion,[status(esa)],[f_823_2]) ).

cnf(f_823_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2995,hAPP(c_Groups_Ouminus__class_Ouminus(U_2995),U_2996),U_2997) = c_Divides_Odiv__class_Omod(U_2995,hAPP(c_Groups_Ouminus__class_Ouminus(U_2995),U_2998),U_2997)
    | c_Divides_Odiv__class_Omod(U_2995,U_2996,U_2997) != c_Divides_Odiv__class_Omod(U_2995,U_2998,U_2997)
    | ~ class_Divides_Oring__div(U_2995) ),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_1,plain,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__self]) ).

fof(f_824_2,plain,
    ! [U_2999] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2999,U_2999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2999] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2999,U_2999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_824_2]) ).

cnf(f_824_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2999,U_2999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_1,plain,
    ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__zero]) ).

fof(f_825_2,plain,
    ! [U_3000] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3000) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_3000] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3000) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_825_2]) ).

cnf(f_825_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3000) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I3_J]) ).

fof(f_826_2,plain,
    ! [U_3003,U_3002,U_3001] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3001),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3002,U_3003)),U_3003) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3001),U_3002),U_3003),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_3001,U_3002,U_3003] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3001),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3002,U_3003)),U_3003) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3001),U_3002),U_3003),
    inference(definitional_conversion,[status(esa)],[f_826_2]) ).

cnf(f_826_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3001),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3002,U_3003)),U_3003) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3001),U_3002),U_3003),
    inference(clausify,[status(thm)],[f_826_3]) ).

fof(f_827_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c),
    inference(fof_nnf,[status(thm)],[fact_zmod__zmult1__eq]) ).

fof(f_827_2,plain,
    ! [U_3006,U_3005,U_3004] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3004),U_3005),U_3006) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3004),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3005,U_3006)),U_3006),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_3004,U_3005,U_3006] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3004),U_3005),U_3006) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3004),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3005,U_3006)),U_3006),
    inference(definitional_conversion,[status(esa)],[f_827_2]) ).

cnf(f_827_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3004),U_3005),U_3006) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3004),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3005,U_3006)),U_3006),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_1,plain,
    ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m),
    inference(fof_nnf,[status(thm)],[fact_zminus__zmod]) ).

fof(f_828_2,plain,
    ! [U_3008,U_3007] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3007,U_3008)),U_3008) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3007),U_3008),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_3007,U_3008] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3007,U_3008)),U_3008) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3007),U_3008),
    inference(definitional_conversion,[status(esa)],[f_828_2]) ).

cnf(f_828_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3007,U_3008)),U_3008) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3007),U_3008),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_1,plain,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus__zminus]) ).

fof(f_829_2,plain,
    ! [U_3010,U_3009] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3009),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3010)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3009,U_3010)),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ! [U_3009,U_3010] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3009),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3010)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3009,U_3010)),
    inference(definitional_conversion,[status(esa)],[f_829_2]) ).

cnf(f_829_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3009),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3010)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3009,U_3010)),
    inference(clausify,[status(thm)],[f_829_3]) ).

fof(f_830_1,plain,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus2]) ).

fof(f_830_2,plain,
    ! [U_3012,U_3011] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3011,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3012)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3011),U_3012)),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ! [U_3011,U_3012] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3011,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3012)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3011),U_3012)),
    inference(definitional_conversion,[status(esa)],[f_830_2]) ).

cnf(f_830_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3011,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3012)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3011),U_3012)),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0]) ).

fof(f_831_2,plain,
    ! [U_3015,U_3014,U_3013] :
      ( c_Divides_Odiv__class_Omod(U_3013,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3013),U_3014),U_3015),U_3015) = c_Groups_Ozero__class_Ozero(U_3013)
      | ~ class_Divides_Osemiring__div(U_3013) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_3013,U_3014,U_3015] :
      ( c_Divides_Odiv__class_Omod(U_3013,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3013),U_3014),U_3015),U_3015) = c_Groups_Ozero__class_Ozero(U_3013)
      | ~ class_Divides_Osemiring__div(U_3013) ),
    inference(definitional_conversion,[status(esa)],[f_831_2]) ).

cnf(f_831_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3013,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3013),U_3014),U_3015),U_3015) = c_Groups_Ozero__class_Ozero(U_3013)
    | ~ class_Divides_Osemiring__div(U_3013) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0]) ).

fof(f_832_2,plain,
    ! [U_3018,U_3017,U_3016] :
      ( c_Divides_Odiv__class_Omod(U_3016,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3016),U_3017),U_3018),U_3017) = c_Groups_Ozero__class_Ozero(U_3016)
      | ~ class_Divides_Osemiring__div(U_3016) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_3016,U_3017,U_3018] :
      ( c_Divides_Odiv__class_Omod(U_3016,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3016),U_3017),U_3018),U_3017) = c_Groups_Ozero__class_Ozero(U_3016)
      | ~ class_Divides_Osemiring__div(U_3016) ),
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3016,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3016),U_3017),U_3018),U_3017) = c_Groups_Ozero__class_Ozero(U_3016)
    | ~ class_Divides_Osemiring__div(U_3016) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self2]) ).

fof(f_833_2,plain,
    ! [U_3022,U_3021,U_3020,U_3019] :
      ( c_Divides_Odiv__class_Omod(U_3019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3019),U_3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3019),U_3021),U_3022)),U_3021) = c_Divides_Odiv__class_Omod(U_3019,U_3020,U_3021)
      | ~ class_Divides_Osemiring__div(U_3019) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ! [U_3019,U_3020,U_3021,U_3022] :
      ( c_Divides_Odiv__class_Omod(U_3019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3019),U_3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3019),U_3021),U_3022)),U_3021) = c_Divides_Odiv__class_Omod(U_3019,U_3020,U_3021)
      | ~ class_Divides_Osemiring__div(U_3019) ),
    inference(definitional_conversion,[status(esa)],[f_833_2]) ).

cnf(f_833_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3019),U_3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3019),U_3021),U_3022)),U_3021) = c_Divides_Odiv__class_Omod(U_3019,U_3020,U_3021)
    | ~ class_Divides_Osemiring__div(U_3019) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self1]) ).

fof(f_834_2,plain,
    ! [U_3026,U_3025,U_3024,U_3023] :
      ( c_Divides_Odiv__class_Omod(U_3023,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3023),U_3024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3023),U_3025),U_3026)),U_3026) = c_Divides_Odiv__class_Omod(U_3023,U_3024,U_3026)
      | ~ class_Divides_Osemiring__div(U_3023) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ! [U_3023,U_3024,U_3025,U_3026] :
      ( c_Divides_Odiv__class_Omod(U_3023,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3023),U_3024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3023),U_3025),U_3026)),U_3026) = c_Divides_Odiv__class_Omod(U_3023,U_3024,U_3026)
      | ~ class_Divides_Osemiring__div(U_3023) ),
    inference(definitional_conversion,[status(esa)],[f_834_2]) ).

cnf(f_834_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3023,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3023),U_3024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3023),U_3025),U_3026)),U_3026) = c_Divides_Odiv__class_Omod(U_3023,U_3024,U_3026)
    | ~ class_Divides_Osemiring__div(U_3023) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

fof(f_835_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__by__1]) ).

fof(f_835_2,plain,
    ! [U_3028,U_3027] :
      ( c_Divides_Odiv__class_Omod(U_3027,U_3028,c_Groups_Oone__class_Oone(U_3027)) = c_Groups_Ozero__class_Ozero(U_3027)
      | ~ class_Divides_Osemiring__div(U_3027) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_3027,U_3028] :
      ( c_Divides_Odiv__class_Omod(U_3027,U_3028,c_Groups_Oone__class_Oone(U_3027)) = c_Groups_Ozero__class_Ozero(U_3027)
      | ~ class_Divides_Osemiring__div(U_3027) ),
    inference(definitional_conversion,[status(esa)],[f_835_2]) ).

cnf(f_835_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3027,U_3028,c_Groups_Oone__class_Oone(U_3027)) = c_Groups_Ozero__class_Ozero(U_3027)
    | ~ class_Divides_Osemiring__div(U_3027) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

fof(f_836_1,plain,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend]) ).

fof(f_836_2,plain,
    ! [U_3030,U_3029] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3029,U_3030)),U_3029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3029)) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_3029,U_3030] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3029,U_3030)),U_3029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3029)) ),
    inference(definitional_conversion,[status(esa)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3029,U_3030)),U_3029))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3029)) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_837_2,plain,
    ! [U_3032,U_3031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3031,U_3032)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3031)) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_3031,U_3032] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3031,U_3032)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3031)) ),
    inference(definitional_conversion,[status(esa)],[f_837_2]) ).

cnf(f_837_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3031,U_3032)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3031)) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__mod__bound]) ).

fof(f_838_2,plain,
    ! [U_3034,U_3033] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3034,U_3033)),U_3033))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3033)) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_3033,U_3034] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3034,U_3033)),U_3033))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3033)) ),
    inference(definitional_conversion,[status(esa)],[f_838_2]) ).

cnf(f_838_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3034,U_3033)),U_3033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3033)) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__mod__bound]) ).

fof(f_839_2,plain,
    ! [U_3036,U_3035] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3035),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3036,U_3035)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3035),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_3035,U_3036] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3035),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3036,U_3035)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3035),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_839_2]) ).

cnf(f_839_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3035),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3036,U_3035)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3035),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_1,plain,
    ! [V_d_2,V_m_2] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [B_q] : V_m_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) )
      & ( ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff]) ).

fof(f_840_2,plain,
    ! [U_3040,U_3039] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3039,U_3040) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_3038] : U_3039 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3040),U_3038) )
      & ( ? [U_3037] : U_3039 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3040),U_3037)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3039,U_3040) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ( ! [U_3044,U_3042] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3042,U_3044) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_3038] : U_3042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3038) )
    & ! [U_3043,U_3041] :
        ( ? [U_3037] : U_3041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3043),U_3037)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3041,U_3043) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_840_2]) ).

fof(f_840_4,plain,
    ( ! [U_3044,U_3042] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3042,U_3044) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_3038] : U_3042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3038) )
    & ! [U_3043,U_3041] :
        ( U_3041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3043),sK52(U_3043,U_3041))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3041,U_3043) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3037,sK52(U_3043,U_3041))],[f_840_3]) ).

fof(f_840_5,plain,
    ( ! [U_3038,U_3042,U_3044] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3042,U_3044) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_3042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3038) )
    & ! [U_3041,U_3043] :
        ( U_3041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3043),sK52(U_3043,U_3041))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3041,U_3043) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_840_4]) ).

cnf(f_840_6,plain,
    ( U_3041 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3043),sK52(U_3043,U_3041))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3041,U_3043) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_840_5]) ).

cnf(f_840_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3042,U_3044) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_3042 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3038) ),
    inference(clausify,[status(thm)],[f_840_5]) ).

fof(f_841_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero]) ).

fof(f_841_2,plain,
    ! [U_3046,U_3045] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3045,U_3046) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3045,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3046)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_3046,U_3045] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3045,U_3046) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3045,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3046)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_841_2]) ).

cnf(f_841_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3045,U_3046) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3045,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3046)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero]) ).

fof(f_842_2,plain,
    ! [U_3048,U_3047] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3047,U_3048) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3047),U_3048) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_3047,U_3048] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3047,U_3048) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3047),U_3048) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_842_2]) ).

cnf(f_842_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3047,U_3048) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3047),U_3048) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__mod__sign]) ).

fof(f_843_2,plain,
    ! [U_3050,U_3049] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3050,U_3049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3049)) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_3049,U_3050] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3050,U_3049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3049)) ),
    inference(definitional_conversion,[status(esa)],[f_843_2]) ).

cnf(f_843_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3050,U_3049)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3049)) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

fof(f_844_1,plain,
    ! [V_a,V_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__mod__conj]) ).

fof(f_844_2,plain,
    ! [U_3052,U_3051] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3052,U_3051)),U_3051))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3052,U_3051))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3051)) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ( ! [U_3051,U_3052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3052,U_3051)),U_3051))
        | ~ sP247(U_3051,U_3052) )
    & ! [U_3051,U_3052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3052,U_3051)))
        | ~ sP247(U_3051,U_3052) )
    & ! [U_3051,U_3052] :
        ( sP247(U_3051,U_3052)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3051)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247])],[f_844_2]) ).

cnf(f_844_4,plain,
    ( sP247(U_3051,U_3052)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3051)) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3052,U_3051)))
    | ~ sP247(U_3051,U_3052) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3052,U_3051)),U_3051))
    | ~ sP247(U_3051,U_3052) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial]) ).

fof(f_845_2,plain,
    ! [U_3054,U_3053] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3053,U_3054) = U_3053
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3053),U_3054))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3053)) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_3054,U_3053] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3053,U_3054) = U_3053
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3053),U_3054))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3053)) ),
    inference(definitional_conversion,[status(esa)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3053,U_3054) = U_3053
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3053),U_3054))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3053)) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__mod__sign]) ).

fof(f_846_2,plain,
    ! [U_3056,U_3055] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3056,U_3055)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3055),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ! [U_3055,U_3056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3056,U_3055)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3055),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_846_2]) ).

cnf(f_846_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3056,U_3055)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3055),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_1,plain,
    ! [V_a,V_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__mod__conj]) ).

fof(f_847_2,plain,
    ! [U_3058,U_3057] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3057),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3058,U_3057)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3058,U_3057)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3057),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ( ! [U_3057,U_3058] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3057),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3058,U_3057)))
        | ~ sP248(U_3057,U_3058) )
    & ! [U_3057,U_3058] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3058,U_3057)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP248(U_3057,U_3058) )
    & ! [U_3057,U_3058] :
        ( sP248(U_3057,U_3058)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3057),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248])],[f_847_2]) ).

cnf(f_847_4,plain,
    ( sP248(U_3057,U_3058)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3057),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

cnf(f_847_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3058,U_3057)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP248(U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

cnf(f_847_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3057),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3058,U_3057)))
    | ~ sP248(U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial]) ).

fof(f_848_2,plain,
    ! [U_3060,U_3059] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3059,U_3060) = U_3059
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3060),U_3059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3059),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_3059,U_3060] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3059,U_3060) = U_3059
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3060),U_3059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3059),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_848_2]) ).

cnf(f_848_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3059,U_3060) = U_3059
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3060),U_3059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3059),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__idem]) ).

fof(f_849_2,plain,
    ! [U_3063,U_3062,U_3061] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),U_3063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),U_3063)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3061) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_3061,U_3062,U_3063] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),U_3063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),U_3063)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3061) ),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),U_3063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3061),U_3062),U_3063)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3061) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__idem]) ).

fof(f_850_2,plain,
    ! [U_3065,U_3064] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3064),U_3065),U_3065) = U_3065
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3064) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_3064,U_3065] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3064),U_3065),U_3065) = U_3065
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3064) ),
    inference(definitional_conversion,[status(esa)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3064),U_3065),U_3065) = U_3065
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3064) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_times_Oidem]) ).

fof(f_851_2,plain,
    ! [U_3067,U_3066] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3066),U_3067),U_3067) = U_3067
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3066) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_3066,U_3067] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3066),U_3067),U_3067) = U_3067
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3066) ),
    inference(definitional_conversion,[status(esa)],[f_851_2]) ).

cnf(f_851_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3066),U_3067),U_3067) = U_3067
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3066) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) ) )
      | ~ class_Lattices_Oboolean__algebra(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).

fof(f_852_2,plain,
    ! [U_3070,U_3069,U_3068] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3069) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3070)
          | U_3069 != U_3070 )
        & ( U_3069 = U_3070
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3069) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3070) ) )
      | ~ class_Lattices_Oboolean__algebra(U_3068) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ( ! [U_3068,U_3069,U_3070] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3069) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3070)
        | U_3069 != U_3070
        | ~ sP249(U_3068,U_3069,U_3070) )
    & ! [U_3068,U_3069,U_3070] :
        ( U_3069 = U_3070
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3069) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3070)
        | ~ sP249(U_3068,U_3069,U_3070) )
    & ! [U_3068,U_3069,U_3070] :
        ( sP249(U_3068,U_3069,U_3070)
        | ~ class_Lattices_Oboolean__algebra(U_3068) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249])],[f_852_2]) ).

cnf(f_852_4,plain,
    ( sP249(U_3068,U_3069,U_3070)
    | ~ class_Lattices_Oboolean__algebra(U_3068) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_5,plain,
    ( U_3069 = U_3070
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3069) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3070)
    | ~ sP249(U_3068,U_3069,U_3070) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3069) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3068),U_3070)
    | U_3069 != U_3070
    | ~ sP249(U_3068,U_3069,U_3070) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))
      | ~ class_Groups_Ouminus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).

fof(f_853_2,plain,
    ! [U_3074,U_3073,U_3072,U_3071] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3072,U_3071)),U_3073),U_3074) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3071),hAPP(U_3073,U_3074))
      | ~ class_Groups_Ouminus(U_3071) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_3072,U_3073,U_3071,U_3074] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3072,U_3071)),U_3073),U_3074) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3071),hAPP(U_3073,U_3074))
      | ~ class_Groups_Ouminus(U_3071) ),
    inference(definitional_conversion,[status(esa)],[f_853_2]) ).

cnf(f_853_4,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3072,U_3071)),U_3073),U_3074) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3071),hAPP(U_3073,U_3074))
    | ~ class_Groups_Ouminus(U_3071) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__compl]) ).

fof(f_854_2,plain,
    ! [U_3076,U_3075] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3075),hAPP(c_Groups_Ouminus__class_Ouminus(U_3075),U_3076)) = U_3076
      | ~ class_Lattices_Oboolean__algebra(U_3075) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ! [U_3075,U_3076] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3075),hAPP(c_Groups_Ouminus__class_Ouminus(U_3075),U_3076)) = U_3076
      | ~ class_Lattices_Oboolean__algebra(U_3075) ),
    inference(definitional_conversion,[status(esa)],[f_854_2]) ).

cnf(f_854_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3075),hAPP(c_Groups_Ouminus__class_Ouminus(U_3075),U_3076)) = U_3076
    | ~ class_Lattices_Oboolean__algebra(U_3075) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

fof(f_855_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial]) ).

fof(f_855_2,plain,
    ! [U_3078,U_3077] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3077,U_3078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3077),U_3078)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3077),U_3078)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3077)) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ! [U_3077,U_3078] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3077,U_3078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3077),U_3078)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3077),U_3078)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3077)) ),
    inference(definitional_conversion,[status(esa)],[f_855_2]) ).

cnf(f_855_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3077,U_3078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3077),U_3078)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3077),U_3078)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3077)) ),
    inference(clausify,[status(thm)],[f_855_3]) ).

fof(f_856_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
          & ( hBOOL(hAPP(V_P_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zmod]) ).

fof(f_856_2,plain,
    ! [U_3089,U_3088,U_3087] :
      ( ( hBOOL(hAPP(U_3087,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3088,U_3089)))
        | ( ? [U_3086,U_3085] :
              ( ~ hBOOL(hAPP(U_3087,U_3085))
              & U_3088 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3089),U_3086)),U_3085)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3089),U_3085)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3089),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3084,U_3083] :
              ( ~ hBOOL(hAPP(U_3087,U_3083))
              & U_3088 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3089),U_3084)),U_3083)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3083),U_3089))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3083)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3089)) )
        | ( ~ hBOOL(hAPP(U_3087,U_3088))
          & U_3089 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_3082,U_3081] :
                ( hBOOL(hAPP(U_3087,U_3081))
                | U_3088 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3089),U_3082)),U_3081)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3089),U_3081)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3089),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3080,U_3079] :
                ( hBOOL(hAPP(U_3087,U_3079))
                | U_3088 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3089),U_3080)),U_3079)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3089))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3089)) )
          & ( hBOOL(hAPP(U_3087,U_3088))
            | U_3089 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3087,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3088,U_3089))) ) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ( ! [U_3095,U_3093,U_3091] :
        ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
        | ( ? [U_3086,U_3085] :
              ( ~ hBOOL(hAPP(U_3091,U_3085))
              & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),U_3086)),U_3085)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),U_3085)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3084,U_3083] :
              ( ~ hBOOL(hAPP(U_3091,U_3083))
              & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),U_3084)),U_3083)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3083),U_3095))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3083)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095)) )
        | ( ~ hBOOL(hAPP(U_3091,U_3093))
          & U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3094,U_3092,U_3090] :
        ( ( ( ! [U_3082,U_3081] :
                ( hBOOL(hAPP(U_3090,U_3081))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3080,U_3079] :
                ( hBOOL(hAPP(U_3090,U_3079))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094)) )
          & ( hBOOL(hAPP(U_3090,U_3092))
            | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ) ),
    inference(miniscope,[status(thm)],[f_856_2]) ).

fof(f_856_4,plain,
    ( ! [U_3095,U_3093,U_3091] :
        ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
        | ( ? [U_3086,U_3085] :
              ( ~ hBOOL(hAPP(U_3091,U_3085))
              & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),U_3086)),U_3085)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),U_3085)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3083] :
              ( ~ hBOOL(hAPP(U_3091,U_3083))
              & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK53(U_3095,U_3093,U_3091))),U_3083)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3083),U_3095))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3083)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095)) )
        | ( ~ hBOOL(hAPP(U_3091,U_3093))
          & U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3094,U_3092,U_3090] :
        ( ( ( ! [U_3082,U_3081] :
                ( hBOOL(hAPP(U_3090,U_3081))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3080,U_3079] :
                ( hBOOL(hAPP(U_3090,U_3079))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094)) )
          & ( hBOOL(hAPP(U_3090,U_3092))
            | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_3084,sK53(U_3095,U_3093,U_3091))],[f_856_3]) ).

fof(f_856_5,plain,
    ( ! [U_3095,U_3093,U_3091] :
        ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
        | ( ? [U_3086,U_3085] :
              ( ~ hBOOL(hAPP(U_3091,U_3085))
              & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),U_3086)),U_3085)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),U_3085)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3091,sK54(U_3095,U_3093,U_3091)))
          & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK53(U_3095,U_3093,U_3091))),sK54(U_3095,U_3093,U_3091))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK54(U_3095,U_3093,U_3091)),U_3095))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_3095,U_3093,U_3091)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095)) )
        | ( ~ hBOOL(hAPP(U_3091,U_3093))
          & U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3094,U_3092,U_3090] :
        ( ( ( ! [U_3082,U_3081] :
                ( hBOOL(hAPP(U_3090,U_3081))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3080,U_3079] :
                ( hBOOL(hAPP(U_3090,U_3079))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094)) )
          & ( hBOOL(hAPP(U_3090,U_3092))
            | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_3083,sK54(U_3095,U_3093,U_3091))],[f_856_4]) ).

fof(f_856_6,plain,
    ( ! [U_3095,U_3093,U_3091] :
        ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
        | ( ? [U_3085] :
              ( ~ hBOOL(hAPP(U_3091,U_3085))
              & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK55(U_3095,U_3093,U_3091))),U_3085)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),U_3085)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3091,sK54(U_3095,U_3093,U_3091)))
          & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK53(U_3095,U_3093,U_3091))),sK54(U_3095,U_3093,U_3091))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK54(U_3095,U_3093,U_3091)),U_3095))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_3095,U_3093,U_3091)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095)) )
        | ( ~ hBOOL(hAPP(U_3091,U_3093))
          & U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3094,U_3092,U_3090] :
        ( ( ( ! [U_3082,U_3081] :
                ( hBOOL(hAPP(U_3090,U_3081))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3080,U_3079] :
                ( hBOOL(hAPP(U_3090,U_3079))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094)) )
          & ( hBOOL(hAPP(U_3090,U_3092))
            | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_3086,sK55(U_3095,U_3093,U_3091))],[f_856_5]) ).

fof(f_856_7,plain,
    ( ! [U_3095,U_3093,U_3091] :
        ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
        | ( ~ hBOOL(hAPP(U_3091,sK56(U_3095,U_3093,U_3091)))
          & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK55(U_3095,U_3093,U_3091))),sK56(U_3095,U_3093,U_3091))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK56(U_3095,U_3093,U_3091)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),sK56(U_3095,U_3093,U_3091)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3091,sK54(U_3095,U_3093,U_3091)))
          & U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK53(U_3095,U_3093,U_3091))),sK54(U_3095,U_3093,U_3091))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK54(U_3095,U_3093,U_3091)),U_3095))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_3095,U_3093,U_3091)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095)) )
        | ( ~ hBOOL(hAPP(U_3091,U_3093))
          & U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3094,U_3092,U_3090] :
        ( ( ( ! [U_3082,U_3081] :
                ( hBOOL(hAPP(U_3090,U_3081))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3080,U_3079] :
                ( hBOOL(hAPP(U_3090,U_3079))
                | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094)) )
          & ( hBOOL(hAPP(U_3090,U_3092))
            | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_3085,sK56(U_3095,U_3093,U_3091))],[f_856_6]) ).

fof(f_856_8,plain,
    ( ! [U_3095,U_3091,U_3093] :
        ( ~ hBOOL(hAPP(U_3091,sK56(U_3095,U_3093,U_3091)))
        | ~ sP253(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK55(U_3095,U_3093,U_3091))),sK56(U_3095,U_3093,U_3091))
        | ~ sP253(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK56(U_3095,U_3093,U_3091)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP253(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),sK56(U_3095,U_3093,U_3091)))
        | ~ sP253(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP253(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( ~ hBOOL(hAPP(U_3091,sK54(U_3095,U_3093,U_3091)))
        | ~ sP252(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK53(U_3095,U_3093,U_3091))),sK54(U_3095,U_3093,U_3091))
        | ~ sP252(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK54(U_3095,U_3093,U_3091)),U_3095))
        | ~ sP252(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_3095,U_3093,U_3091)))
        | ~ sP252(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095))
        | ~ sP252(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( ~ hBOOL(hAPP(U_3091,U_3093))
        | ~ sP251(U_3095,U_3091,U_3093) )
    & ! [U_3095,U_3091,U_3093] :
        ( U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP251(U_3095,U_3091,U_3093) )
    & ! [U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092] :
        ( hBOOL(hAPP(U_3090,U_3081))
        | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092) )
    & ! [U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092] :
        ( hBOOL(hAPP(U_3090,U_3079))
        | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094))
        | ~ sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092) )
    & ! [U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092] :
        ( hBOOL(hAPP(U_3090,U_3092))
        | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092) )
    & ! [U_3095,U_3091,U_3093] :
        ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
        | sP253(U_3095,U_3091,U_3093)
        | sP252(U_3095,U_3091,U_3093)
        | sP251(U_3095,U_3091,U_3093) )
    & ! [U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092] :
        ( sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092)
        | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250,sP251,sP252,sP253])],[f_856_7]) ).

cnf(f_856_9,plain,
    ( sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092)
    | ~ hBOOL(hAPP(U_3090,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3092,U_3094))) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_10,plain,
    ( hBOOL(hAPP(U_3091,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095)))
    | sP253(U_3095,U_3091,U_3093)
    | sP252(U_3095,U_3091,U_3093)
    | sP251(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_11,plain,
    ( hBOOL(hAPP(U_3090,U_3092))
    | U_3094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_12,plain,
    ( hBOOL(hAPP(U_3090,U_3079))
    | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3080)),U_3079)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3079),U_3094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3094))
    | ~ sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_13,plain,
    ( hBOOL(hAPP(U_3090,U_3081))
    | U_3092 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3094),U_3082)),U_3081)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),U_3081))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3094),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP250(U_3079,U_3080,U_3081,U_3082,U_3090,U_3094,U_3092) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_14,plain,
    ( U_3095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP251(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_15,plain,
    ( ~ hBOOL(hAPP(U_3091,U_3093))
    | ~ sP251(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3095))
    | ~ sP252(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_3095,U_3093,U_3091)))
    | ~ sP252(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK54(U_3095,U_3093,U_3091)),U_3095))
    | ~ sP252(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_19,plain,
    ( U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK53(U_3095,U_3093,U_3091))),sK54(U_3095,U_3093,U_3091))
    | ~ sP252(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_20,plain,
    ( ~ hBOOL(hAPP(U_3091,sK54(U_3095,U_3093,U_3091)))
    | ~ sP252(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP253(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3095),sK56(U_3095,U_3093,U_3091)))
    | ~ sP253(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK56(U_3095,U_3093,U_3091)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP253(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_24,plain,
    ( U_3093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK55(U_3095,U_3093,U_3091))),sK56(U_3095,U_3093,U_3091))
    | ~ sP253(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

cnf(f_856_25,plain,
    ( ~ hBOOL(hAPP(U_3091,sK56(U_3095,U_3093,U_3091)))
    | ~ sP253(U_3095,U_3091,U_3093) ),
    inference(clausify,[status(thm)],[f_856_8]) ).

fof(f_857_1,plain,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3]) ).

fof(f_857_2,plain,
    ! [U_3099,U_3098,U_3097,U_3096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3098),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3099,U_3096))),U_3097)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3097),U_3098))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3096)) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ! [U_3098,U_3097,U_3096,U_3099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3098),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3099,U_3096))),U_3097)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3097),U_3098))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3096)) ),
    inference(definitional_conversion,[status(esa)],[f_857_2]) ).

cnf(f_857_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3098),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3099,U_3096))),U_3097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3097),U_3098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3096)) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_1,plain,
    ! [V_k,V_l] :
      ( ( c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) )
      & ( c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_z3mod__def]) ).

fof(f_858_2,plain,
    ! [U_3101,U_3100] :
      ( ( c_SMT_Oz3mod(U_3101,U_3100) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3101,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3100))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3100)) )
      & ( c_SMT_Oz3mod(U_3101,U_3100) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3101,U_3100)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3100)) ) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ( ! [U_3105,U_3103] :
        ( c_SMT_Oz3mod(U_3105,U_3103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3105,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3103))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3103)) )
    & ! [U_3104,U_3102] :
        ( c_SMT_Oz3mod(U_3104,U_3102) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3104,U_3102)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3102)) ) ),
    inference(miniscope,[status(thm)],[f_858_2]) ).

fof(f_858_4,plain,
    ( ! [U_3105,U_3103] :
        ( c_SMT_Oz3mod(U_3105,U_3103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3105,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3103))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3103)) )
    & ! [U_3102,U_3104] :
        ( c_SMT_Oz3mod(U_3104,U_3102) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3104,U_3102)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3102)) ) ),
    inference(definitional_conversion,[status(esa)],[f_858_3]) ).

cnf(f_858_5,plain,
    ( c_SMT_Oz3mod(U_3104,U_3102) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3104,U_3102)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3102)) ),
    inference(clausify,[status(thm)],[f_858_4]) ).

cnf(f_858_6,plain,
    ( c_SMT_Oz3mod(U_3105,U_3103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3105,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3103))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3103)) ),
    inference(clausify,[status(thm)],[f_858_4]) ).

fof(f_859_1,plain,
    ! [V_n_2,V_P_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
          | ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
        & ( ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
          | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_split__pos__lemma]) ).

fof(f_859_2,plain,
    ! [U_3112,U_3111,U_3110] :
      ( ( ( hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
          | ? [U_3109,U_3108] :
              ( ~ hBOOL(hAPP(hAPP(U_3111,U_3109),U_3108))
              & U_3112 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),U_3109)),U_3108)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3108),U_3110))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3108)) ) )
        & ( ! [U_3107,U_3106] :
              ( hBOOL(hAPP(hAPP(U_3111,U_3107),U_3106))
              | U_3112 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),U_3107)),U_3106)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3106),U_3110))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3106)) )
          | ~ hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3110)) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_3112,U_3111,U_3110] :
      ( ( ( hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
          | ? [U_3108] :
              ( ~ hBOOL(hAPP(hAPP(U_3111,sK57(U_3112,U_3111,U_3110)),U_3108))
              & U_3112 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),sK57(U_3112,U_3111,U_3110))),U_3108)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3108),U_3110))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3108)) ) )
        & ( ! [U_3107,U_3106] :
              ( hBOOL(hAPP(hAPP(U_3111,U_3107),U_3106))
              | U_3112 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),U_3107)),U_3106)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3106),U_3110))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3106)) )
          | ~ hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3110)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_3109,sK57(U_3112,U_3111,U_3110))],[f_859_2]) ).

fof(f_859_4,plain,
    ! [U_3112,U_3111,U_3110] :
      ( ( ( hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
          | ( ~ hBOOL(hAPP(hAPP(U_3111,sK57(U_3112,U_3111,U_3110)),sK58(U_3112,U_3111,U_3110)))
            & U_3112 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),sK57(U_3112,U_3111,U_3110))),sK58(U_3112,U_3111,U_3110))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK58(U_3112,U_3111,U_3110)),U_3110))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK58(U_3112,U_3111,U_3110))) ) )
        & ( ! [U_3107,U_3106] :
              ( hBOOL(hAPP(hAPP(U_3111,U_3107),U_3106))
              | U_3112 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),U_3107)),U_3106)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3106),U_3110))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3106)) )
          | ~ hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3110)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_3108,sK58(U_3112,U_3111,U_3110))],[f_859_3]) ).

fof(f_859_5,plain,
    ( ! [U_3110,U_3112,U_3111] :
        ( ~ hBOOL(hAPP(hAPP(U_3111,sK57(U_3112,U_3111,U_3110)),sK58(U_3112,U_3111,U_3110)))
        | ~ sP254(U_3110,U_3112,U_3111) )
    & ! [U_3110,U_3112,U_3111] :
        ( U_3112 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),sK57(U_3112,U_3111,U_3110))),sK58(U_3112,U_3111,U_3110))
        | ~ sP254(U_3110,U_3112,U_3111) )
    & ! [U_3110,U_3112,U_3111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK58(U_3112,U_3111,U_3110)),U_3110))
        | ~ sP254(U_3110,U_3112,U_3111) )
    & ! [U_3110,U_3112,U_3111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK58(U_3112,U_3111,U_3110)))
        | ~ sP254(U_3110,U_3112,U_3111) )
    & ! [U_3107,U_3106,U_3110,U_3112,U_3111] :
        ( hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
        | sP254(U_3110,U_3112,U_3111)
        | ~ sP255(U_3107,U_3106,U_3110,U_3112,U_3111) )
    & ! [U_3107,U_3106,U_3110,U_3112,U_3111] :
        ( hBOOL(hAPP(hAPP(U_3111,U_3107),U_3106))
        | U_3112 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),U_3107)),U_3106)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3106),U_3110))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3106))
        | ~ hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
        | ~ sP255(U_3107,U_3106,U_3110,U_3112,U_3111) )
    & ! [U_3107,U_3106,U_3110,U_3112,U_3111] :
        ( sP255(U_3107,U_3106,U_3110,U_3112,U_3111)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3110)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254,sP255])],[f_859_4]) ).

cnf(f_859_6,plain,
    ( sP255(U_3107,U_3106,U_3110,U_3112,U_3111)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3110)) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

cnf(f_859_7,plain,
    ( hBOOL(hAPP(hAPP(U_3111,U_3107),U_3106))
    | U_3112 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),U_3107)),U_3106)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3106),U_3110))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3106))
    | ~ hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
    | ~ sP255(U_3107,U_3106,U_3110,U_3112,U_3111) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

cnf(f_859_8,plain,
    ( hBOOL(hAPP(hAPP(U_3111,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3112),U_3110)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3112,U_3110)))
    | sP254(U_3110,U_3112,U_3111)
    | ~ sP255(U_3107,U_3106,U_3110,U_3112,U_3111) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

cnf(f_859_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK58(U_3112,U_3111,U_3110)))
    | ~ sP254(U_3110,U_3112,U_3111) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

cnf(f_859_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK58(U_3112,U_3111,U_3110)),U_3110))
    | ~ sP254(U_3110,U_3112,U_3111) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

cnf(f_859_11,plain,
    ( U_3112 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3110),sK57(U_3112,U_3111,U_3110))),sK58(U_3112,U_3111,U_3110))
    | ~ sP254(U_3110,U_3112,U_3111) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

cnf(f_859_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3111,sK57(U_3112,U_3111,U_3110)),sK58(U_3112,U_3111,U_3110)))
    | ~ sP254(U_3110,U_3112,U_3111) ),
    inference(clausify,[status(thm)],[f_859_5]) ).

fof(f_860_1,plain,
    ! [V_n_2,V_P_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
          | ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
        & ( ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
          | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_split__neg__lemma]) ).

fof(f_860_2,plain,
    ! [U_3119,U_3118,U_3117] :
      ( ( ( hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
          | ? [U_3116,U_3115] :
              ( ~ hBOOL(hAPP(hAPP(U_3118,U_3116),U_3115))
              & U_3119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),U_3116)),U_3115)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3115),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3115)) ) )
        & ( ! [U_3114,U_3113] :
              ( hBOOL(hAPP(hAPP(U_3118,U_3114),U_3113))
              | U_3119 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),U_3114)),U_3113)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3113)) )
          | ~ hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_3119,U_3118,U_3117] :
      ( ( ( hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
          | ? [U_3115] :
              ( ~ hBOOL(hAPP(hAPP(U_3118,sK59(U_3119,U_3118,U_3117)),U_3115))
              & U_3119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),sK59(U_3119,U_3118,U_3117))),U_3115)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3115),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3115)) ) )
        & ( ! [U_3114,U_3113] :
              ( hBOOL(hAPP(hAPP(U_3118,U_3114),U_3113))
              | U_3119 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),U_3114)),U_3113)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3113)) )
          | ~ hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_3116,sK59(U_3119,U_3118,U_3117))],[f_860_2]) ).

fof(f_860_4,plain,
    ! [U_3119,U_3118,U_3117] :
      ( ( ( hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
          | ( ~ hBOOL(hAPP(hAPP(U_3118,sK59(U_3119,U_3118,U_3117)),sK60(U_3119,U_3118,U_3117)))
            & U_3119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),sK59(U_3119,U_3118,U_3117))),sK60(U_3119,U_3118,U_3117))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK60(U_3119,U_3118,U_3117)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),sK60(U_3119,U_3118,U_3117))) ) )
        & ( ! [U_3114,U_3113] :
              ( hBOOL(hAPP(hAPP(U_3118,U_3114),U_3113))
              | U_3119 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),U_3114)),U_3113)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3113)) )
          | ~ hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_3115,sK60(U_3119,U_3118,U_3117))],[f_860_3]) ).

fof(f_860_5,plain,
    ( ! [U_3117,U_3118,U_3119] :
        ( ~ hBOOL(hAPP(hAPP(U_3118,sK59(U_3119,U_3118,U_3117)),sK60(U_3119,U_3118,U_3117)))
        | ~ sP256(U_3117,U_3118,U_3119) )
    & ! [U_3117,U_3118,U_3119] :
        ( U_3119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),sK59(U_3119,U_3118,U_3117))),sK60(U_3119,U_3118,U_3117))
        | ~ sP256(U_3117,U_3118,U_3119) )
    & ! [U_3117,U_3118,U_3119] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK60(U_3119,U_3118,U_3117)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP256(U_3117,U_3118,U_3119) )
    & ! [U_3117,U_3118,U_3119] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),sK60(U_3119,U_3118,U_3117)))
        | ~ sP256(U_3117,U_3118,U_3119) )
    & ! [U_3117,U_3118,U_3114,U_3113,U_3119] :
        ( hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
        | sP256(U_3117,U_3118,U_3119)
        | ~ sP257(U_3117,U_3118,U_3114,U_3113,U_3119) )
    & ! [U_3117,U_3118,U_3114,U_3113,U_3119] :
        ( hBOOL(hAPP(hAPP(U_3118,U_3114),U_3113))
        | U_3119 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),U_3114)),U_3113)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3113))
        | ~ hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
        | ~ sP257(U_3117,U_3118,U_3114,U_3113,U_3119) )
    & ! [U_3117,U_3118,U_3114,U_3113,U_3119] :
        ( sP257(U_3117,U_3118,U_3114,U_3113,U_3119)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256,sP257])],[f_860_4]) ).

cnf(f_860_6,plain,
    ( sP257(U_3117,U_3118,U_3114,U_3113,U_3119)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

cnf(f_860_7,plain,
    ( hBOOL(hAPP(hAPP(U_3118,U_3114),U_3113))
    | U_3119 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),U_3114)),U_3113)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),U_3113))
    | ~ hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
    | ~ sP257(U_3117,U_3118,U_3114,U_3113,U_3119) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

cnf(f_860_8,plain,
    ( hBOOL(hAPP(hAPP(U_3118,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3119),U_3117)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3119,U_3117)))
    | sP256(U_3117,U_3118,U_3119)
    | ~ sP257(U_3117,U_3118,U_3114,U_3113,U_3119) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

cnf(f_860_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3117),sK60(U_3119,U_3118,U_3117)))
    | ~ sP256(U_3117,U_3118,U_3119) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

cnf(f_860_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK60(U_3119,U_3118,U_3117)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP256(U_3117,U_3118,U_3119) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

cnf(f_860_11,plain,
    ( U_3119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3117),sK59(U_3119,U_3118,U_3117))),sK60(U_3119,U_3118,U_3117))
    | ~ sP256(U_3117,U_3118,U_3119) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

cnf(f_860_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3118,sK59(U_3119,U_3118,U_3117)),sK60(U_3119,U_3118,U_3117)))
    | ~ sP256(U_3117,U_3118,U_3119) ),
    inference(clausify,[status(thm)],[f_860_5]) ).

fof(f_861_1,plain,
    ! [V_b,V_a,V_c] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq]) ).

fof(f_861_2,plain,
    ! [U_3122,U_3121,U_3120] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3121,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3122),U_3120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3122),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3121),U_3122),U_3120))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3121,U_3122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3120)) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_3121,U_3122,U_3120] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3121,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3122),U_3120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3122),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3121),U_3122),U_3120))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3121,U_3122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3120)) ),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3121,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3122),U_3120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3122),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3121),U_3122),U_3120))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3121,U_3122))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3120)) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).

fof(f_862_2,plain,
    ! [U_3124,U_3123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_3123,U_3124)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3124))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3123)) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_3124,U_3123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_3123,U_3124)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3124))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3123)) ),
    inference(definitional_conversion,[status(esa)],[f_862_2]) ).

cnf(f_862_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_3123,U_3124)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3124))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3123)) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).

fof(f_863_2,plain,
    ! [U_3135,U_3134,U_3133] :
      ( ( hBOOL(hAPP(U_3133,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3134),U_3135)))
        | ( ? [U_3132] :
              ( ~ hBOOL(hAPP(U_3133,U_3132))
              & ? [U_3131] :
                  ( U_3134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3135),U_3132)),U_3131)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3131),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3135),U_3131)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3135),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3130] :
              ( ~ hBOOL(hAPP(U_3133,U_3130))
              & ? [U_3129] :
                  ( U_3134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3135),U_3130)),U_3129)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3129),U_3135))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3129)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3135)) )
        | ( ~ hBOOL(hAPP(U_3133,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3135 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_3128] :
                ( hBOOL(hAPP(U_3133,U_3128))
                | ! [U_3127] :
                    ( U_3134 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3135),U_3128)),U_3127)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3135),U_3127)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3135),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3126] :
                ( hBOOL(hAPP(U_3133,U_3126))
                | ! [U_3125] :
                    ( U_3134 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3135),U_3126)),U_3125)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3135))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3135)) )
          & ( hBOOL(hAPP(U_3133,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3135 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3133,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3134),U_3135))) ) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ( ! [U_3141,U_3139,U_3137] :
        ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
        | ( ? [U_3132] :
              ( ~ hBOOL(hAPP(U_3137,U_3132))
              & ? [U_3131] :
                  ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),U_3132)),U_3131)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3131),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),U_3131)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3130] :
              ( ~ hBOOL(hAPP(U_3137,U_3130))
              & ? [U_3129] :
                  ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),U_3130)),U_3129)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3129),U_3141))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3129)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141)) )
        | ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3140,U_3138,U_3136] :
        ( ( ( ! [U_3128] :
                ( hBOOL(hAPP(U_3136,U_3128))
                | ! [U_3127] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3126] :
                ( hBOOL(hAPP(U_3136,U_3126))
                | ! [U_3125] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140)) )
          & ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ) ),
    inference(miniscope,[status(thm)],[f_863_2]) ).

fof(f_863_4,plain,
    ( ! [U_3141,U_3139,U_3137] :
        ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
        | ( ? [U_3132] :
              ( ~ hBOOL(hAPP(U_3137,U_3132))
              & ? [U_3131] :
                  ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),U_3132)),U_3131)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3131),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),U_3131)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3137,sK61(U_3141,U_3139,U_3137)))
          & ? [U_3129] :
              ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK61(U_3141,U_3139,U_3137))),U_3129)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3129),U_3141))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3129)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141)) )
        | ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3140,U_3138,U_3136] :
        ( ( ( ! [U_3128] :
                ( hBOOL(hAPP(U_3136,U_3128))
                | ! [U_3127] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3126] :
                ( hBOOL(hAPP(U_3136,U_3126))
                | ! [U_3125] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140)) )
          & ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3130,sK61(U_3141,U_3139,U_3137))],[f_863_3]) ).

fof(f_863_5,plain,
    ( ! [U_3141,U_3139,U_3137] :
        ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
        | ( ? [U_3132] :
              ( ~ hBOOL(hAPP(U_3137,U_3132))
              & ? [U_3131] :
                  ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),U_3132)),U_3131)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3131),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),U_3131)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3137,sK61(U_3141,U_3139,U_3137)))
          & U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK61(U_3141,U_3139,U_3137))),sK62(U_3141,U_3139,U_3137))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK62(U_3141,U_3139,U_3137)),U_3141))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK62(U_3141,U_3139,U_3137)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141)) )
        | ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3140,U_3138,U_3136] :
        ( ( ( ! [U_3128] :
                ( hBOOL(hAPP(U_3136,U_3128))
                | ! [U_3127] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3126] :
                ( hBOOL(hAPP(U_3136,U_3126))
                | ! [U_3125] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140)) )
          & ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3129,sK62(U_3141,U_3139,U_3137))],[f_863_4]) ).

fof(f_863_6,plain,
    ( ! [U_3141,U_3139,U_3137] :
        ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
        | ( ~ hBOOL(hAPP(U_3137,sK63(U_3141,U_3139,U_3137)))
          & ? [U_3131] :
              ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK63(U_3141,U_3139,U_3137))),U_3131)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3131),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),U_3131)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3137,sK61(U_3141,U_3139,U_3137)))
          & U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK61(U_3141,U_3139,U_3137))),sK62(U_3141,U_3139,U_3137))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK62(U_3141,U_3139,U_3137)),U_3141))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK62(U_3141,U_3139,U_3137)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141)) )
        | ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3140,U_3138,U_3136] :
        ( ( ( ! [U_3128] :
                ( hBOOL(hAPP(U_3136,U_3128))
                | ! [U_3127] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3126] :
                ( hBOOL(hAPP(U_3136,U_3126))
                | ! [U_3125] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140)) )
          & ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3132,sK63(U_3141,U_3139,U_3137))],[f_863_5]) ).

fof(f_863_7,plain,
    ( ! [U_3141,U_3139,U_3137] :
        ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
        | ( ~ hBOOL(hAPP(U_3137,sK63(U_3141,U_3139,U_3137)))
          & U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK63(U_3141,U_3139,U_3137))),sK64(U_3141,U_3139,U_3137))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK64(U_3141,U_3139,U_3137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),sK64(U_3141,U_3139,U_3137)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3137,sK61(U_3141,U_3139,U_3137)))
          & U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK61(U_3141,U_3139,U_3137))),sK62(U_3141,U_3139,U_3137))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK62(U_3141,U_3139,U_3137)),U_3141))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK62(U_3141,U_3139,U_3137)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141)) )
        | ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3140,U_3138,U_3136] :
        ( ( ( ! [U_3128] :
                ( hBOOL(hAPP(U_3136,U_3128))
                | ! [U_3127] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3126] :
                ( hBOOL(hAPP(U_3136,U_3126))
                | ! [U_3125] :
                    ( U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140)) )
          & ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3131,sK64(U_3141,U_3139,U_3137))],[f_863_6]) ).

fof(f_863_8,plain,
    ( ! [U_3137,U_3139,U_3141] :
        ( ~ hBOOL(hAPP(U_3137,sK63(U_3141,U_3139,U_3137)))
        | ~ sP261(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK63(U_3141,U_3139,U_3137))),sK64(U_3141,U_3139,U_3137))
        | ~ sP261(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK64(U_3141,U_3139,U_3137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP261(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),sK64(U_3141,U_3139,U_3137)))
        | ~ sP261(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP261(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( ~ hBOOL(hAPP(U_3137,sK61(U_3141,U_3139,U_3137)))
        | ~ sP260(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK61(U_3141,U_3139,U_3137))),sK62(U_3141,U_3139,U_3137))
        | ~ sP260(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK62(U_3141,U_3139,U_3137)),U_3141))
        | ~ sP260(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK62(U_3141,U_3139,U_3137)))
        | ~ sP260(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141))
        | ~ sP260(U_3137,U_3139,U_3141) )
    & ! [U_3137,U_3141] :
        ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP259(U_3137,U_3141) )
    & ! [U_3137,U_3141] :
        ( U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP259(U_3137,U_3141) )
    & ! [U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140] :
        ( hBOOL(hAPP(U_3136,U_3128))
        | U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140) )
    & ! [U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140] :
        ( hBOOL(hAPP(U_3136,U_3126))
        | U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140))
        | ~ sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140) )
    & ! [U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140] :
        ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140) )
    & ! [U_3137,U_3139,U_3141] :
        ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
        | sP261(U_3137,U_3139,U_3141)
        | sP260(U_3137,U_3139,U_3141)
        | sP259(U_3137,U_3141) )
    & ! [U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140] :
        ( sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140)
        | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258,sP259,sP260,sP261])],[f_863_7]) ).

cnf(f_863_9,plain,
    ( sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140)
    | ~ hBOOL(hAPP(U_3136,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3138),U_3140))) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_10,plain,
    ( hBOOL(hAPP(U_3137,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3139),U_3141)))
    | sP261(U_3137,U_3139,U_3141)
    | sP260(U_3137,U_3139,U_3141)
    | sP259(U_3137,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_11,plain,
    ( hBOOL(hAPP(U_3136,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_3140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_12,plain,
    ( hBOOL(hAPP(U_3136,U_3126))
    | U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3126)),U_3125)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3125),U_3140))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3140))
    | ~ sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_13,plain,
    ( hBOOL(hAPP(U_3136,U_3128))
    | U_3138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3140),U_3128)),U_3127)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3127),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),U_3127))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3140),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP258(U_3125,U_3126,U_3127,U_3128,U_3136,U_3138,U_3140) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_14,plain,
    ( U_3141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP259(U_3137,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_15,plain,
    ( ~ hBOOL(hAPP(U_3137,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP259(U_3137,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3141))
    | ~ sP260(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK62(U_3141,U_3139,U_3137)))
    | ~ sP260(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK62(U_3141,U_3139,U_3137)),U_3141))
    | ~ sP260(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_19,plain,
    ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK61(U_3141,U_3139,U_3137))),sK62(U_3141,U_3139,U_3137))
    | ~ sP260(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_20,plain,
    ( ~ hBOOL(hAPP(U_3137,sK61(U_3141,U_3139,U_3137)))
    | ~ sP260(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP261(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3141),sK64(U_3141,U_3139,U_3137)))
    | ~ sP261(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK64(U_3141,U_3139,U_3137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP261(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_24,plain,
    ( U_3139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3141),sK63(U_3141,U_3139,U_3137))),sK64(U_3141,U_3139,U_3137))
    | ~ sP261(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

cnf(f_863_25,plain,
    ( ~ hBOOL(hAPP(U_3137,sK63(U_3141,U_3139,U_3137)))
    | ~ sP261(U_3137,U_3139,U_3141) ),
    inference(clausify,[status(thm)],[f_863_8]) ).

fof(f_864_1,plain,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y
      | V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | V_a_1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(f_864_2,plain,
    ! [U_3145,U_3144,U_3143,U_3142] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3142),U_3143) = U_3144
      | U_3143 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3145),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3143),U_3145)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3143)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3145),U_3143))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3145)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3143)) )
      | U_3142 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3143),U_3144)),U_3145) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ( ! [U_3143,U_3145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3145),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3143),U_3145))
        | ~ sP263(U_3143,U_3145) )
    & ! [U_3143,U_3145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3143))
        | ~ sP263(U_3143,U_3145) )
    & ! [U_3143,U_3145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3145),U_3143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3145))
        | ~ sP262(U_3143,U_3145) )
    & ! [U_3143,U_3145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3143))
        | ~ sP262(U_3143,U_3145) )
    & ! [U_3144,U_3143,U_3145,U_3142] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3142),U_3143) = U_3144
        | U_3143 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP263(U_3143,U_3145)
        | sP262(U_3143,U_3145)
        | U_3142 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3143),U_3144)),U_3145) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262,sP263])],[f_864_2]) ).

cnf(f_864_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3142),U_3143) = U_3144
    | U_3143 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP263(U_3143,U_3145)
    | sP262(U_3143,U_3145)
    | U_3142 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3143),U_3144)),U_3145) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

cnf(f_864_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3143))
    | ~ sP262(U_3143,U_3145) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

cnf(f_864_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3145),U_3143))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3145))
    | ~ sP262(U_3143,U_3145) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

cnf(f_864_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3143))
    | ~ sP263(U_3143,U_3145) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

cnf(f_864_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3145),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3143),U_3145))
    | ~ sP263(U_3143,U_3145) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_1,plain,
    ! [V_n_2,V_m_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ! [B_q] :
              ( ~ hBOOL(hAPP(V_P_2,B_q))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
          & ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).

fof(f_865_2,plain,
    ! [U_3150,U_3149,U_3148] :
      ( ( hBOOL(hAPP(U_3148,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3149),U_3150)))
        | ( ! [U_3147] :
              ( ~ hBOOL(hAPP(U_3148,U_3147))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3150),hAPP(c_Nat_OSuc,U_3147))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3150),U_3147)),U_3149)) )
          & ( ~ hBOOL(hAPP(U_3148,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3150 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_3146] :
            ( hBOOL(hAPP(U_3148,U_3146))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3150),hAPP(c_Nat_OSuc,U_3146))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3150),U_3146)),U_3149)) )
        | ( hBOOL(hAPP(U_3148,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3148,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3149),U_3150))) ) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ( ! [U_3156,U_3154,U_3152] :
        ( hBOOL(hAPP(U_3152,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3154),U_3156)))
        | ( ! [U_3147] :
              ( ~ hBOOL(hAPP(U_3152,U_3147))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),hAPP(c_Nat_OSuc,U_3147))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),U_3147)),U_3154)) )
          & ( ~ hBOOL(hAPP(U_3152,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3155,U_3153,U_3151] :
        ( ? [U_3146] :
            ( hBOOL(hAPP(U_3151,U_3146))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),hAPP(c_Nat_OSuc,U_3146))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),U_3146)),U_3153)) )
        | ( hBOOL(hAPP(U_3151,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3151,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3153),U_3155))) ) ),
    inference(miniscope,[status(thm)],[f_865_2]) ).

fof(f_865_4,plain,
    ( ! [U_3156,U_3154,U_3152] :
        ( hBOOL(hAPP(U_3152,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3154),U_3156)))
        | ( ! [U_3147] :
              ( ~ hBOOL(hAPP(U_3152,U_3147))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),hAPP(c_Nat_OSuc,U_3147))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),U_3147)),U_3154)) )
          & ( ~ hBOOL(hAPP(U_3152,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3155,U_3153,U_3151] :
        ( ( hBOOL(hAPP(U_3151,sK65(U_3155,U_3153,U_3151)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),hAPP(c_Nat_OSuc,sK65(U_3155,U_3153,U_3151)))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),sK65(U_3155,U_3153,U_3151))),U_3153)) )
        | ( hBOOL(hAPP(U_3151,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3151,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3153),U_3155))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3146,sK65(U_3155,U_3153,U_3151))],[f_865_3]) ).

fof(f_865_5,plain,
    ( ! [U_3147,U_3152,U_3154,U_3156] :
        ( ~ hBOOL(hAPP(U_3152,U_3147))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),hAPP(c_Nat_OSuc,U_3147))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),U_3147)),U_3154))
        | ~ sP266(U_3147,U_3152,U_3154,U_3156) )
    & ! [U_3147,U_3152,U_3154,U_3156] :
        ( ~ hBOOL(hAPP(U_3152,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP266(U_3147,U_3152,U_3154,U_3156) )
    & ! [U_3153,U_3155,U_3151] :
        ( hBOOL(hAPP(U_3151,sK65(U_3155,U_3153,U_3151)))
        | ~ sP265(U_3153,U_3155,U_3151) )
    & ! [U_3153,U_3155,U_3151] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),hAPP(c_Nat_OSuc,sK65(U_3155,U_3153,U_3151)))))
        | ~ sP265(U_3153,U_3155,U_3151) )
    & ! [U_3153,U_3155,U_3151] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),sK65(U_3155,U_3153,U_3151))),U_3153))
        | ~ sP265(U_3153,U_3155,U_3151) )
    & ! [U_3155,U_3151] :
        ( hBOOL(hAPP(U_3151,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP264(U_3155,U_3151) )
    & ! [U_3155,U_3151] :
        ( U_3155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP264(U_3155,U_3151) )
    & ! [U_3147,U_3152,U_3154,U_3156] :
        ( hBOOL(hAPP(U_3152,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3154),U_3156)))
        | sP266(U_3147,U_3152,U_3154,U_3156) )
    & ! [U_3153,U_3155,U_3151] :
        ( sP265(U_3153,U_3155,U_3151)
        | sP264(U_3155,U_3151)
        | ~ hBOOL(hAPP(U_3151,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3153),U_3155))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264,sP265,sP266])],[f_865_4]) ).

cnf(f_865_6,plain,
    ( sP265(U_3153,U_3155,U_3151)
    | sP264(U_3155,U_3151)
    | ~ hBOOL(hAPP(U_3151,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3153),U_3155))) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_7,plain,
    ( hBOOL(hAPP(U_3152,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3154),U_3156)))
    | sP266(U_3147,U_3152,U_3154,U_3156) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_8,plain,
    ( U_3155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP264(U_3155,U_3151) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_9,plain,
    ( hBOOL(hAPP(U_3151,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP264(U_3155,U_3151) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),sK65(U_3155,U_3153,U_3151))),U_3153))
    | ~ sP265(U_3153,U_3155,U_3151) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3155),hAPP(c_Nat_OSuc,sK65(U_3155,U_3153,U_3151)))))
    | ~ sP265(U_3153,U_3155,U_3151) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_12,plain,
    ( hBOOL(hAPP(U_3151,sK65(U_3155,U_3153,U_3151)))
    | ~ sP265(U_3153,U_3155,U_3151) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_13,plain,
    ( ~ hBOOL(hAPP(U_3152,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3156 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP266(U_3147,U_3152,U_3154,U_3156) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_14,plain,
    ( ~ hBOOL(hAPP(U_3152,U_3147))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),hAPP(c_Nat_OSuc,U_3147))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3156),U_3147)),U_3154))
    | ~ sP266(U_3147,U_3152,U_3154,U_3156) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

fof(f_866_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_div__add1__eq]) ).

fof(f_866_2,plain,
    ! [U_3159,U_3158,U_3157] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3157),U_3158)),U_3159) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3157),U_3159)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3158),U_3159))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3157,U_3159)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3158,U_3159))),U_3159)),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_3159,U_3157,U_3158] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3157),U_3158)),U_3159) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3157),U_3159)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3158),U_3159))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3157,U_3159)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3158,U_3159))),U_3159)),
    inference(definitional_conversion,[status(esa)],[f_866_2]) ).

cnf(f_866_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3157),U_3158)),U_3159) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3157),U_3159)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3158),U_3159))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3157,U_3159)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3158,U_3159))),U_3159)),
    inference(clausify,[status(thm)],[f_866_3]) ).

fof(f_867_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(f_867_2,plain,
    ! [U_3161,U_3160] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3160)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3161)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3160),U_3161)),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_3160,U_3161] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3160)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3161)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3160),U_3161)),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3160)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3161)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3160),U_3161)),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_1,plain,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__int]) ).

fof(f_868_2,plain,
    ! [U_3163,U_3162] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3162),U_3163)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3162)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3163)),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_3163,U_3162] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3162),U_3163)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3162)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3163)),
    inference(definitional_conversion,[status(esa)],[f_868_2]) ).

cnf(f_868_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3162),U_3163)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3162)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3163)),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_mod__mult2__eq]) ).

fof(f_869_2,plain,
    ! [U_3166,U_3165,U_3164] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3165),U_3166)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3165),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3164),U_3165),U_3166))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3164,U_3165)),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ! [U_3164,U_3165,U_3166] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3165),U_3166)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3165),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3164),U_3165),U_3166))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3164,U_3165)),
    inference(definitional_conversion,[status(esa)],[f_869_2]) ).

cnf(f_869_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3165),U_3166)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3165),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3164),U_3165),U_3166))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3164,U_3165)),
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_div__mult1__eq]) ).

fof(f_870_2,plain,
    ! [U_3169,U_3168,U_3167] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),U_3168)),U_3169) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3168),U_3169))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3168,U_3169))),U_3169)),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_3167,U_3168,U_3169] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),U_3168)),U_3169) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3168),U_3169))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3168,U_3169))),U_3169)),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),U_3168)),U_3169) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3168),U_3169))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3167),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3168,U_3169))),U_3169)),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_1,plain,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).

fof(f_871_2,plain,
    ! [U_3172,U_3171,U_3170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3170),U_3172)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3171),U_3172)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3170),U_3171)) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ! [U_3170,U_3171,U_3172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3170),U_3172)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3171),U_3172)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3170),U_3171)) ),
    inference(definitional_conversion,[status(esa)],[f_871_2]) ).

cnf(f_871_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3170),U_3172)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3171),U_3172)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3170),U_3171)) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)),
    inference(fof_nnf,[status(thm)],[fact_div__le__dividend]) ).

fof(f_872_2,plain,
    ! [U_3174,U_3173] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3173),U_3174)),U_3173)),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_3173,U_3174] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3173),U_3174)),U_3173)),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3173),U_3174)),U_3173)),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_1,plain,
    ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zero]) ).

fof(f_873_2,plain,
    ! [U_3175] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3175) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_3175] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3175) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3175) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n),
    inference(fof_nnf,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).

fof(f_874_2,plain,
    ! [U_3177,U_3176] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3176),U_3177) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3176,U_3177)),U_3177),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_3176,U_3177] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3176),U_3177) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3176,U_3177)),U_3177),
    inference(definitional_conversion,[status(esa)],[f_874_2]) ).

cnf(f_874_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3176),U_3177) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3176,U_3177)),U_3177),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c),
    inference(fof_nnf,[status(thm)],[fact_div__mult2__eq]) ).

fof(f_875_2,plain,
    ! [U_3180,U_3179,U_3178] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3179),U_3180)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3178),U_3179)),U_3180),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_3178,U_3179,U_3180] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3179),U_3180)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3178),U_3179)),U_3180),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3179),U_3180)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3178),U_3179)),U_3180),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__less]) ).

fof(f_876_2,plain,
    ! [U_3182,U_3181] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3181,U_3182) = U_3181
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3181),U_3182)) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_3181,U_3182] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3181,U_3182) = U_3181
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3181),U_3182)) ),
    inference(definitional_conversion,[status(esa)],[f_876_2]) ).

cnf(f_876_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3181,U_3182) = U_3181
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3181),U_3182)) ),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)),
    inference(fof_nnf,[status(thm)],[fact_mod__less__eq__dividend]) ).

fof(f_877_2,plain,
    ! [U_3184,U_3183] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3183,U_3184)),U_3183)),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_3183,U_3184] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3183,U_3184)),U_3183)),
    inference(definitional_conversion,[status(esa)],[f_877_2]) ).

cnf(f_877_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3183,U_3184)),U_3183)),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__distrib]) ).

fof(f_878_2,plain,
    ! [U_3187,U_3186,U_3185] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3185,U_3186)),U_3187) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3185),U_3187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3186),U_3187)),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_3185,U_3186,U_3187] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3185,U_3186)),U_3187) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3185),U_3187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3186),U_3187)),
    inference(definitional_conversion,[status(esa)],[f_878_2]) ).

cnf(f_878_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3185,U_3186)),U_3187) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3185),U_3187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3186),U_3187)),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__distrib2]) ).

fof(f_879_2,plain,
    ! [U_3190,U_3189,U_3188] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3189,U_3190)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),U_3189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),U_3190)),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ! [U_3188,U_3189,U_3190] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3189,U_3190)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),U_3189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),U_3190)),
    inference(definitional_conversion,[status(esa)],[f_879_2]) ).

cnf(f_879_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3189,U_3190)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),U_3189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3188),U_3190)),
    inference(clausify,[status(thm)],[f_879_3]) ).

fof(f_880_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2]) ).

fof(f_880_2,plain,
    ! [U_3192,U_3191] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3191),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3192)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3191)),U_3192),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_3191,U_3192] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3191),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3192)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3191)),U_3192),
    inference(definitional_conversion,[status(esa)],[f_880_2]) ).

cnf(f_880_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3191),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3192)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3191)),U_3192),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(f_881_2,plain,
    ! [U_3194,U_3193] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3193)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3194)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3193),U_3194),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_3193,U_3194] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3193)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3194)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3193),U_3194),
    inference(definitional_conversion,[status(esa)],[f_881_2]) ).

cnf(f_881_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3193)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3194)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3193),U_3194),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__0]) ).

fof(f_882_2,plain,
    ! [U_3196,U_3195] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3195),c_Groups_Ozero__class_Ozero(U_3195)),U_3196) = c_Groups_Ozero__class_Ozero(U_3195)
      | ~ class_Divides_Osemiring__div(U_3195) ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_3195,U_3196] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3195),c_Groups_Ozero__class_Ozero(U_3195)),U_3196) = c_Groups_Ozero__class_Ozero(U_3195)
      | ~ class_Divides_Osemiring__div(U_3195) ),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3195),c_Groups_Ozero__class_Ozero(U_3195)),U_3196) = c_Groups_Ozero__class_Ozero(U_3195)
    | ~ class_Divides_Osemiring__div(U_3195) ),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__by__0]) ).

fof(f_883_2,plain,
    ! [U_3198,U_3197] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3197),U_3198),c_Groups_Ozero__class_Ozero(U_3197)) = c_Groups_Ozero__class_Ozero(U_3197)
      | ~ class_Divides_Osemiring__div(U_3197) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ! [U_3197,U_3198] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3197),U_3198),c_Groups_Ozero__class_Ozero(U_3197)) = c_Groups_Ozero__class_Ozero(U_3197)
      | ~ class_Divides_Osemiring__div(U_3197) ),
    inference(definitional_conversion,[status(esa)],[f_883_2]) ).

cnf(f_883_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3197),U_3198),c_Groups_Ozero__class_Ozero(U_3197)) = c_Groups_Ozero__class_Ozero(U_3197)
    | ~ class_Divides_Osemiring__div(U_3197) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__by__1]) ).

fof(f_884_2,plain,
    ! [U_3200,U_3199] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3199),U_3200),c_Groups_Oone__class_Oone(U_3199)) = U_3200
      | ~ class_Divides_Osemiring__div(U_3199) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ! [U_3199,U_3200] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3199),U_3200),c_Groups_Oone__class_Oone(U_3199)) = U_3200
      | ~ class_Divides_Osemiring__div(U_3199) ),
    inference(definitional_conversion,[status(esa)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3199),U_3200),c_Groups_Oone__class_Oone(U_3199)) = U_3200
    | ~ class_Divides_Osemiring__div(U_3199) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_1,plain,
    ! [V_y,V_x] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__div__distrib]) ).

fof(f_885_2,plain,
    ! [U_3202,U_3201] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3201),U_3202)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3201)),hAPP(c_Int_Onat,U_3202))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3201)) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ! [U_3201,U_3202] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3201),U_3202)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3201)),hAPP(c_Int_Onat,U_3202))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3201)) ),
    inference(definitional_conversion,[status(esa)],[f_885_2]) ).

cnf(f_885_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3201),U_3202)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3201)),hAPP(c_Int_Onat,U_3202))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3201)) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J]) ).

fof(f_886_2,plain,
    ! [U_3204,U_3203] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3203)),hAPP(c_Int_Onat,U_3204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3203),U_3204))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3204))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3203)) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_3203,U_3204] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3203)),hAPP(c_Int_Onat,U_3204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3203),U_3204))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3204))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3203)) ),
    inference(definitional_conversion,[status(esa)],[f_886_2]) ).

cnf(f_886_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3203)),hAPP(c_Int_Onat,U_3204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3203),U_3204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3203)) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_1,plain,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
    inference(fof_nnf,[status(thm)],[fact_div__1]) ).

fof(f_887_2,plain,
    ! [U_3205] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3205),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3205,
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_3205] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3205),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3205,
    inference(definitional_conversion,[status(esa)],[f_887_2]) ).

cnf(f_887_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3205),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3205,
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_1,plain,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__less]) ).

fof(f_888_2,plain,
    ! [U_3207,U_3206] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3206),U_3207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3206),U_3207)) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_3206,U_3207] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3206),U_3207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3206),U_3207)) ),
    inference(definitional_conversion,[status(esa)],[f_888_2]) ).

cnf(f_888_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3206),U_3207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3206),U_3207)) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_1,plain,
    ! [V_n,V_m,V_k] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)
        | V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj]) ).

fof(f_889_2,plain,
    ! [U_3210,U_3209,U_3208] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3208),U_3209)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3208),U_3210)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3209),U_3210)
        | U_3208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3208),U_3209)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3208),U_3210)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3208 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ( ! [U_3216,U_3214,U_3212] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3214)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3214),U_3216)
        | U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3215,U_3213,U_3211] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3211),U_3213)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3211),U_3215)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3211 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_889_2]) ).

fof(f_889_4,plain,
    ( ! [U_3212,U_3214,U_3216] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3214)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3214),U_3216)
        | U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3215,U_3211,U_3213] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3211),U_3213)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3211),U_3215)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3211 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_889_3]) ).

cnf(f_889_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3211),U_3213)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3211),U_3215)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3211 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_889_4]) ).

cnf(f_889_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3214)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3214),U_3216)
    | U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_889_4]) ).

fof(f_890_1,plain,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mod__1]) ).

fof(f_890_2,plain,
    ! [U_3217] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3217,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_3217] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3217,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_890_2]) ).

cnf(f_890_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3217,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_1,plain,
    ! [V_n,V_m] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__Suc]) ).

fof(f_891_2,plain,
    ! [U_3219,U_3218] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3218),U_3219) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3218,U_3219))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3218,U_3219)) = U_3219 )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3218),U_3219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3218,U_3219)) != U_3219 ) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ( ! [U_3223,U_3221] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3221),U_3223) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3221,U_3223))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3221,U_3223)) = U_3223 )
    & ! [U_3222,U_3220] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3220),U_3222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3220,U_3222)) != U_3222 ) ),
    inference(miniscope,[status(thm)],[f_891_2]) ).

fof(f_891_4,plain,
    ( ! [U_3221,U_3223] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3221),U_3223) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3221,U_3223))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3221,U_3223)) = U_3223 )
    & ! [U_3220,U_3222] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3220),U_3222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3220,U_3222)) != U_3222 ) ),
    inference(definitional_conversion,[status(esa)],[f_891_3]) ).

cnf(f_891_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3220),U_3222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3220,U_3222)) != U_3222 ),
    inference(clausify,[status(thm)],[f_891_4]) ).

cnf(f_891_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3221),U_3223) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3221,U_3223))
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3221,U_3223)) = U_3223 ),
    inference(clausify,[status(thm)],[f_891_4]) ).

fof(f_892_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_892_2,plain,
    ! [U_3225,U_3224] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3224),U_3225)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3224)) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_3224,U_3225] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3224),U_3225)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3224)) ),
    inference(definitional_conversion,[status(esa)],[f_892_2]) ).

cnf(f_892_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3224),U_3225)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3224)) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__less__divisor]) ).

fof(f_893_2,plain,
    ! [U_3227,U_3226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3226)),U_3226))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3226)) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_3226,U_3227] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3226)),U_3226))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3226)) ),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3226)),U_3226))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3226)) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0]) ).

fof(f_894_2,plain,
    ! [U_3229,U_3228] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3228),U_3229)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3229))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3228),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_3228,U_3229] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3228),U_3229)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3229))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3228),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_894_2]) ).

cnf(f_894_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3228),U_3229)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3229))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3228),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff]) ).

fof(f_895_2,plain,
    ! [U_3231,U_3230] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3231),U_3230)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3231),U_3230)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3230),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ( ! [U_3231,U_3230] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3231),U_3230)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
        | ~ sP267(U_3231,U_3230) )
    & ! [U_3231,U_3230] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3231),U_3230)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP267(U_3231,U_3230) )
    & ! [U_3231,U_3230] :
        ( sP267(U_3231,U_3230)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3230),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_895_2]) ).

cnf(f_895_4,plain,
    ( sP267(U_3231,U_3230)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3230),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

cnf(f_895_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3231),U_3230)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP267(U_3231,U_3230) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

cnf(f_895_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3231),U_3230)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
    | ~ sP267(U_3231,U_3230) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

fof(f_896_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff]) ).

fof(f_896_2,plain,
    ! [U_3233,U_3232] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3233),U_3232)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3233),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3233),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3233),U_3232)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3232)) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ( ! [U_3233,U_3232] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3233),U_3232)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3233),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP268(U_3233,U_3232) )
    & ! [U_3233,U_3232] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3233),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3233),U_3232)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP268(U_3233,U_3232) )
    & ! [U_3233,U_3232] :
        ( sP268(U_3233,U_3232)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3232)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_896_2]) ).

cnf(f_896_4,plain,
    ( sP268(U_3233,U_3232)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3232)) ),
    inference(clausify,[status(thm)],[f_896_3]) ).

cnf(f_896_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3233),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3233),U_3232)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP268(U_3233,U_3232) ),
    inference(clausify,[status(thm)],[f_896_3]) ).

cnf(f_896_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3233),U_3232)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3233),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP268(U_3233,U_3232) ),
    inference(clausify,[status(thm)],[f_896_3]) ).

fof(f_897_1,plain,
    ! [V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__self]) ).

fof(f_897_2,plain,
    ! [U_3234] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3234),U_3234) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_3234 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_3234] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3234),U_3234) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_3234 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_897_2]) ).

cnf(f_897_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3234),U_3234) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_3234 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_897_3]) ).

fof(f_898_1,plain,
    ! [V_d_2,V_m_2] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [B_q] : V_m_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) )
      & ( ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff]) ).

fof(f_898_2,plain,
    ! [U_3238,U_3237] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3237,U_3238) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3236] : U_3237 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3238),U_3236) )
      & ( ? [U_3235] : U_3237 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3238),U_3235)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3237,U_3238) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ( ! [U_3242,U_3240] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3240,U_3242) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3236] : U_3240 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3236) )
    & ! [U_3241,U_3239] :
        ( ? [U_3235] : U_3239 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),U_3235)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3239,U_3241) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_898_2]) ).

fof(f_898_4,plain,
    ( ! [U_3242,U_3240] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3240,U_3242) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3236] : U_3240 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3236) )
    & ! [U_3241,U_3239] :
        ( U_3239 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),sK66(U_3241,U_3239))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3239,U_3241) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3235,sK66(U_3241,U_3239))],[f_898_3]) ).

fof(f_898_5,plain,
    ( ! [U_3240,U_3236,U_3242] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3240,U_3242) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3240 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3236) )
    & ! [U_3239,U_3241] :
        ( U_3239 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),sK66(U_3241,U_3239))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3239,U_3241) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_898_4]) ).

cnf(f_898_6,plain,
    ( U_3239 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),sK66(U_3241,U_3239))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3239,U_3241) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_898_5]) ).

cnf(f_898_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3240,U_3242) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3240 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3236) ),
    inference(clausify,[status(thm)],[f_898_5]) ).

fof(f_899_1,plain,
    ! [V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_DIVISION__BY__ZERO]) ).

fof(f_899_2,plain,
    ! [U_3243] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3243,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3243
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3243),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ( ! [U_3245] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3245,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3245
    & ! [U_3244] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3244),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(miniscope,[status(thm)],[f_899_2]) ).

fof(f_899_4,plain,
    ( ! [U_3245] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3245,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3245
    & ! [U_3244] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3244),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_899_3]) ).

cnf(f_899_5,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3244),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_899_4]) ).

cnf(f_899_6,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3245,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3245,
    inference(clausify,[status(thm)],[f_899_4]) ).

fof(f_900_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__trivial]) ).

fof(f_900_2,plain,
    ! [U_3247,U_3246] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3246,U_3247)),U_3247) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_3246,U_3247] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3246,U_3247)),U_3247) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3246,U_3247)),U_3247) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_1,plain,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self3]) ).

fof(f_901_2,plain,
    ! [U_3250,U_3249,U_3248] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3249)),U_3250),U_3249) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3250,U_3249),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_3248,U_3249,U_3250] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3249)),U_3250),U_3249) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3250,U_3249),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3249)),U_3250),U_3249) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3250,U_3249),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zadd1__eq]) ).

fof(f_902_2,plain,
    ! [U_3253,U_3252,U_3251] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3251),U_3252)),U_3253) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3251),U_3253)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3252),U_3253))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3251,U_3253)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3252,U_3253))),U_3253)),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_3251,U_3252,U_3253] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3251),U_3252)),U_3253) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3251),U_3253)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3252),U_3253))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3251,U_3253)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3252,U_3253))),U_3253)),
    inference(definitional_conversion,[status(esa)],[f_902_2]) ).

cnf(f_902_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3251),U_3252)),U_3253) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3251),U_3253)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3252),U_3253))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3251,U_3253)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3252,U_3253))),U_3253)),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_1,plain,
    ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).

fof(f_903_2,plain,
    ! [U_3255,U_3254] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3254),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3255)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3254,U_3255)),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_3255,U_3254] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3254),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3255)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3254,U_3255)),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3254),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3255)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3254,U_3255)),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_1,plain,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__int]) ).

fof(f_904_2,plain,
    ! [U_3257,U_3256] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3256,U_3257)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3256),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3257)),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_3257,U_3256] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3256,U_3257)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3256),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3257)),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3256,U_3257)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3256),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3257)),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult1]) ).

fof(f_905_2,plain,
    ! [U_3261,U_3260,U_3259,U_3258] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3258),U_3259),U_3260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3258),U_3259),U_3261)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3258),U_3260),U_3261)
      | U_3259 = c_Groups_Ozero__class_Ozero(U_3258)
      | ~ class_Divides_Osemiring__div(U_3258) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_3258,U_3259,U_3260,U_3261] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3258),U_3259),U_3260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3258),U_3259),U_3261)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3258),U_3260),U_3261)
      | U_3259 = c_Groups_Ozero__class_Ozero(U_3258)
      | ~ class_Divides_Osemiring__div(U_3258) ),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3258),U_3259),U_3260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3258),U_3259),U_3261)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3258),U_3260),U_3261)
    | U_3259 = c_Groups_Ozero__class_Ozero(U_3258)
    | ~ class_Divides_Osemiring__div(U_3258) ),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult2]) ).

fof(f_906_2,plain,
    ! [U_3265,U_3264,U_3263,U_3262] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3262),U_3264),U_3263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3262),U_3265),U_3263)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3262),U_3264),U_3265)
      | U_3263 = c_Groups_Ozero__class_Ozero(U_3262)
      | ~ class_Divides_Osemiring__div(U_3262) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_3262,U_3263,U_3264,U_3265] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3262),U_3264),U_3263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3262),U_3265),U_3263)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3262),U_3264),U_3265)
      | U_3263 = c_Groups_Ozero__class_Ozero(U_3262)
      | ~ class_Divides_Osemiring__div(U_3262) ),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3262),U_3264),U_3263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3262),U_3265),U_3263)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3262),U_3264),U_3265)
    | U_3263 = c_Groups_Ozero__class_Ozero(U_3262)
    | ~ class_Divides_Osemiring__div(U_3262) ),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id]) ).

fof(f_907_2,plain,
    ! [U_3268,U_3267,U_3266] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3266),U_3267),U_3268)),U_3267) = U_3268
      | U_3267 = c_Groups_Ozero__class_Ozero(U_3266)
      | ~ class_Divides_Osemiring__div(U_3266) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_3266,U_3267,U_3268] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3266),U_3267),U_3268)),U_3267) = U_3268
      | U_3267 = c_Groups_Ozero__class_Ozero(U_3266)
      | ~ class_Divides_Osemiring__div(U_3266) ),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3266),U_3267),U_3268)),U_3267) = U_3268
    | U_3267 = c_Groups_Ozero__class_Ozero(U_3266)
    | ~ class_Divides_Osemiring__div(U_3266) ),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id]) ).

fof(f_908_2,plain,
    ! [U_3271,U_3270,U_3269] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3269),U_3271),U_3270)),U_3270) = U_3271
      | U_3270 = c_Groups_Ozero__class_Ozero(U_3269)
      | ~ class_Divides_Osemiring__div(U_3269) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ! [U_3269,U_3270,U_3271] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3269),U_3271),U_3270)),U_3270) = U_3271
      | U_3270 = c_Groups_Ozero__class_Ozero(U_3269)
      | ~ class_Divides_Osemiring__div(U_3269) ),
    inference(definitional_conversion,[status(esa)],[f_908_2]) ).

cnf(f_908_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3269),U_3271),U_3270)),U_3270) = U_3271
    | U_3270 = c_Groups_Ozero__class_Ozero(U_3269)
    | ~ class_Divides_Osemiring__div(U_3269) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)
          | V_c = c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a)
          | V_c != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if]) ).

fof(f_909_2,plain,
    ! [U_3275,U_3274,U_3273,U_3272] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3275)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),U_3274),U_3275)
          | U_3273 = c_Groups_Ozero__class_Ozero(U_3272) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3275)) = c_Groups_Ozero__class_Ozero(U_3272)
          | U_3273 != c_Groups_Ozero__class_Ozero(U_3272) ) )
      | ~ class_Divides_Osemiring__div(U_3272) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ( ! [U_3272,U_3273,U_3274,U_3275] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3275)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),U_3274),U_3275)
        | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
        | ~ sP269(U_3272,U_3273,U_3274,U_3275) )
    & ! [U_3272,U_3273,U_3274,U_3275] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3275)) = c_Groups_Ozero__class_Ozero(U_3272)
        | U_3273 != c_Groups_Ozero__class_Ozero(U_3272)
        | ~ sP269(U_3272,U_3273,U_3274,U_3275) )
    & ! [U_3272,U_3273,U_3274,U_3275] :
        ( sP269(U_3272,U_3273,U_3274,U_3275)
        | ~ class_Divides_Osemiring__div(U_3272) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269])],[f_909_2]) ).

cnf(f_909_4,plain,
    ( sP269(U_3272,U_3273,U_3274,U_3275)
    | ~ class_Divides_Osemiring__div(U_3272) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

cnf(f_909_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3275)) = c_Groups_Ozero__class_Ozero(U_3272)
    | U_3273 != c_Groups_Ozero__class_Ozero(U_3272)
    | ~ sP269(U_3272,U_3273,U_3274,U_3275) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

cnf(f_909_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3275)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),U_3274),U_3275)
    | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
    | ~ sP269(U_3272,U_3273,U_3274,U_3275) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

fof(f_910_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__self]) ).

fof(f_910_2,plain,
    ! [U_3277,U_3276] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3276),U_3277),U_3277) = c_Groups_Oone__class_Oone(U_3276)
      | U_3277 = c_Groups_Ozero__class_Ozero(U_3276)
      | ~ class_Divides_Osemiring__div(U_3276) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ! [U_3276,U_3277] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3276),U_3277),U_3277) = c_Groups_Oone__class_Oone(U_3276)
      | U_3277 = c_Groups_Ozero__class_Ozero(U_3276)
      | ~ class_Divides_Osemiring__div(U_3276) ),
    inference(definitional_conversion,[status(esa)],[f_910_2]) ).

cnf(f_910_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3276),U_3277),U_3277) = c_Groups_Oone__class_Oone(U_3276)
    | U_3277 = c_Groups_Ozero__class_Ozero(U_3276)
    | ~ class_Divides_Osemiring__div(U_3276) ),
    inference(clausify,[status(thm)],[f_910_3]) ).

fof(f_911_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__trivial]) ).

fof(f_911_2,plain,
    ! [U_3280,U_3279,U_3278] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),c_Divides_Odiv__class_Omod(U_3278,U_3279,U_3280)),U_3280) = c_Groups_Ozero__class_Ozero(U_3278)
      | ~ class_Divides_Osemiring__div(U_3278) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_3278,U_3279,U_3280] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),c_Divides_Odiv__class_Omod(U_3278,U_3279,U_3280)),U_3280) = c_Groups_Ozero__class_Ozero(U_3278)
      | ~ class_Divides_Osemiring__div(U_3278) ),
    inference(definitional_conversion,[status(esa)],[f_911_2]) ).

cnf(f_911_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),c_Divides_Odiv__class_Omod(U_3278,U_3279,U_3280)),U_3280) = c_Groups_Ozero__class_Ozero(U_3278)
    | ~ class_Divides_Osemiring__div(U_3278) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

fof(f_912_1,plain,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_div__le__mono2]) ).

fof(f_912_2,plain,
    ! [U_3283,U_3282,U_3281] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3283),U_3282)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3283),U_3281)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3281)) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_3281,U_3282,U_3283] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3283),U_3282)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3283),U_3281)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3281)) ),
    inference(definitional_conversion,[status(esa)],[f_912_2]) ).

cnf(f_912_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3283),U_3282)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3283),U_3281)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3281)) ),
    inference(clausify,[status(thm)],[f_912_3]) ).

fof(f_913_1,plain,
    ! [V_n,V_m,V_k] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1]) ).

fof(f_913_2,plain,
    ! [U_3286,U_3285,U_3284] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3284),U_3285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3284),U_3286)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3285),U_3286)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3284)) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ! [U_3284,U_3285,U_3286] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3284),U_3285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3284),U_3286)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3285),U_3286)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3284)) ),
    inference(definitional_conversion,[status(esa)],[f_913_2]) ).

cnf(f_913_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3284),U_3285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3284),U_3286)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3285),U_3286)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3284)) ),
    inference(clausify,[status(thm)],[f_913_3]) ).

fof(f_914_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m]) ).

fof(f_914_2,plain,
    ! [U_3288,U_3287] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3287),U_3288)),U_3287) = U_3288
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3287)) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ! [U_3287,U_3288] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3287),U_3288)),U_3287) = U_3288
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3287)) ),
    inference(definitional_conversion,[status(esa)],[f_914_2]) ).

cnf(f_914_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3287),U_3288)),U_3287) = U_3288
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3287)) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

fof(f_915_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m]) ).

fof(f_915_2,plain,
    ! [U_3290,U_3289] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3290),U_3289)),U_3289) = U_3290
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3289)) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_3289,U_3290] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3290),U_3289)),U_3289) = U_3290
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3289)) ),
    inference(definitional_conversion,[status(esa)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3290),U_3289)),U_3289) = U_3290
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3289)) ),
    inference(clausify,[status(thm)],[f_915_3]) ).

fof(f_916_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__less__dividend]) ).

fof(f_916_2,plain,
    ! [U_3292,U_3291] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3292),U_3291)),U_3292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3291)) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_3291,U_3292] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3292),U_3291)),U_3292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3291)) ),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3292),U_3291)),U_3292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3291)) ),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_1,plain,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg]) ).

fof(f_917_2,plain,
    ! [U_3295,U_3294,U_3293] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3294),U_3295)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3293),U_3295)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3295),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3293),U_3294)) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ! [U_3293,U_3294,U_3295] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3294),U_3295)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3293),U_3295)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3295),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3293),U_3294)) ),
    inference(definitional_conversion,[status(esa)],[f_917_2]) ).

cnf(f_917_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3294),U_3295)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3293),U_3295)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3295),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3293),U_3294)) ),
    inference(clausify,[status(thm)],[f_917_3]) ).

fof(f_918_1,plain,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).

fof(f_918_2,plain,
    ! [U_3298,U_3297,U_3296] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3296),U_3298)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3297),U_3298)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3296),U_3297)) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ! [U_3296,U_3297,U_3298] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3296),U_3298)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3297),U_3298)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3296),U_3297)) ),
    inference(definitional_conversion,[status(esa)],[f_918_2]) ).

cnf(f_918_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3296),U_3298)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3297),U_3298)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3296),U_3297)) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

fof(f_919_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial]) ).

fof(f_919_2,plain,
    ! [U_3300,U_3299] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3300),U_3299))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3299),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ! [U_3299,U_3300] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3300),U_3299))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3299),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_919_2]) ).

cnf(f_919_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3300),U_3299))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3299),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_919_3]) ).

fof(f_920_1,plain,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg]) ).

fof(f_920_2,plain,
    ! [U_3303,U_3302,U_3301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3301),U_3302)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3301),U_3303)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3302),U_3303))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3302))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3301),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_3301,U_3302,U_3303] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3301),U_3302)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3301),U_3303)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3302),U_3303))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3302))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3301),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3301),U_3302)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3301),U_3303)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3302),U_3303))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3302))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3301),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0]) ).

fof(f_921_2,plain,
    ! [U_3305,U_3304] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3304),U_3305)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3304),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_3304,U_3305] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3304),U_3305)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3304),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_921_2]) ).

cnf(f_921_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3304),U_3305)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3304),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_921_3]) ).

fof(f_922_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff]) ).

fof(f_922_2,plain,
    ! [U_3307,U_3306] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3306),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ( ! [U_3306,U_3307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP270(U_3306,U_3307) )
    & ! [U_3306,U_3307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
        | ~ sP270(U_3306,U_3307) )
    & ! [U_3306,U_3307] :
        ( sP270(U_3306,U_3307)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3306),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP270])],[f_922_2]) ).

cnf(f_922_4,plain,
    ( sP270(U_3306,U_3307)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3306),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

cnf(f_922_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
    | ~ sP270(U_3306,U_3307) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

cnf(f_922_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP270(U_3306,U_3307) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

fof(f_923_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial]) ).

fof(f_923_2,plain,
    ! [U_3309,U_3308] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3308),U_3309) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3308),U_3309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3308)) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_3308,U_3309] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3308),U_3309) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3308),U_3309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3308)) ),
    inference(definitional_conversion,[status(esa)],[f_923_2]) ).

cnf(f_923_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3308),U_3309) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3308),U_3309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3308)) ),
    inference(clausify,[status(thm)],[f_923_3]) ).

fof(f_924_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0]) ).

fof(f_924_2,plain,
    ! [U_3311,U_3310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3311)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3311),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3310)) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_3310,U_3311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3311)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3311),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3310)) ),
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3311)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3311),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3310)) ),
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_1,plain,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2]) ).

fof(f_925_2,plain,
    ! [U_3314,U_3313,U_3312] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3312),U_3314)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3312),U_3313)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3313),U_3314))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3312)) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_3312,U_3313,U_3314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3312),U_3314)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3312),U_3313)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3313),U_3314))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3312)) ),
    inference(definitional_conversion,[status(esa)],[f_925_2]) ).

cnf(f_925_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3312),U_3314)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3312),U_3313)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3313),U_3314))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3313))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3312)) ),
    inference(clausify,[status(thm)],[f_925_3]) ).

fof(f_926_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).

fof(f_926_2,plain,
    ! [U_3316,U_3315] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3316)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3316))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3316),U_3315)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3316))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3316),U_3315)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3316))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3315)) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ( ! [U_3315,U_3316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3316))
        | ~ sP271(U_3315,U_3316) )
    & ! [U_3315,U_3316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3316),U_3315))
        | ~ sP271(U_3315,U_3316) )
    & ! [U_3315,U_3316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3316)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3316))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3316),U_3315))
        | ~ sP272(U_3315,U_3316) )
    & ! [U_3315,U_3316] :
        ( sP271(U_3315,U_3316)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3316)))
        | ~ sP272(U_3315,U_3316) )
    & ! [U_3315,U_3316] :
        ( sP272(U_3315,U_3316)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3315)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271,sP272])],[f_926_2]) ).

cnf(f_926_4,plain,
    ( sP272(U_3315,U_3316)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3315)) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

cnf(f_926_5,plain,
    ( sP271(U_3315,U_3316)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3316)))
    | ~ sP272(U_3315,U_3316) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

cnf(f_926_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3316)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3316))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3316),U_3315))
    | ~ sP272(U_3315,U_3316) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

cnf(f_926_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3316),U_3315))
    | ~ sP271(U_3315,U_3316) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

cnf(f_926_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3316))
    | ~ sP271(U_3315,U_3316) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

fof(f_927_1,plain,
    ! [V_i_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff]) ).

fof(f_927_2,plain,
    ! [U_3318,U_3317] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3317)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3317),U_3318)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3317),U_3318))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3317))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3317)) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ( ! [U_3318,U_3317] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3317)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3317),U_3318))
        | ~ sP273(U_3318,U_3317) )
    & ! [U_3318,U_3317] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3317),U_3318))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3317)))
        | ~ sP273(U_3318,U_3317) )
    & ! [U_3318,U_3317] :
        ( sP273(U_3318,U_3317)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3317)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273])],[f_927_2]) ).

cnf(f_927_4,plain,
    ( sP273(U_3318,U_3317)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3317)) ),
    inference(clausify,[status(thm)],[f_927_3]) ).

cnf(f_927_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3317),U_3318))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3317)))
    | ~ sP273(U_3318,U_3317) ),
    inference(clausify,[status(thm)],[f_927_3]) ).

cnf(f_927_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3317)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3317),U_3318))
    | ~ sP273(U_3318,U_3317) ),
    inference(clausify,[status(thm)],[f_927_3]) ).

fof(f_928_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff]) ).

fof(f_928_2,plain,
    ! [U_3320,U_3319] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3320),U_3319)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3320)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3320))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3320),U_3319))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3319)) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ( ! [U_3319,U_3320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3320),U_3319)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3320))
        | ~ sP274(U_3319,U_3320) )
    & ! [U_3319,U_3320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3320))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3320),U_3319)))
        | ~ sP274(U_3319,U_3320) )
    & ! [U_3319,U_3320] :
        ( sP274(U_3319,U_3320)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3319)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_928_2]) ).

cnf(f_928_4,plain,
    ( sP274(U_3319,U_3320)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3319)) ),
    inference(clausify,[status(thm)],[f_928_3]) ).

cnf(f_928_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3320))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3320),U_3319)))
    | ~ sP274(U_3319,U_3320) ),
    inference(clausify,[status(thm)],[f_928_3]) ).

cnf(f_928_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3320),U_3319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3320))
    | ~ sP274(U_3319,U_3320) ),
    inference(clausify,[status(thm)],[f_928_3]) ).

fof(f_929_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff]) ).

fof(f_929_2,plain,
    ! [U_3322,U_3321] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3321),U_3322) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3322),U_3321))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3321),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3321),U_3322))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3321)) )
          & U_3322 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3322),U_3321))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3321),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3321),U_3322))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3321)) )
        | U_3322 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3321),U_3322) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ( ! [U_3326,U_3324] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3324),U_3326) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3326),U_3324))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3324),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3324),U_3326))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3324)) )
          & U_3326 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3325,U_3323] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3325),U_3323))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3323),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3323),U_3325))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3323)) )
        | U_3325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3323),U_3325) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_929_2]) ).

fof(f_929_4,plain,
    ( ! [U_3326,U_3324] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3326),U_3324))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3324),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP277(U_3326,U_3324) )
    & ! [U_3326,U_3324] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3324),U_3326))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3324))
        | ~ sP277(U_3326,U_3324) )
    & ! [U_3326,U_3324] :
        ( U_3326 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP277(U_3326,U_3324) )
    & ! [U_3323,U_3325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3325),U_3323))
        | ~ sP276(U_3323,U_3325) )
    & ! [U_3323,U_3325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3323),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP276(U_3323,U_3325) )
    & ! [U_3323,U_3325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3323),U_3325))
        | ~ sP275(U_3323,U_3325) )
    & ! [U_3323,U_3325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3323))
        | ~ sP275(U_3323,U_3325) )
    & ! [U_3326,U_3324] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3324),U_3326) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP277(U_3326,U_3324) )
    & ! [U_3323,U_3325] :
        ( sP276(U_3323,U_3325)
        | sP275(U_3323,U_3325)
        | U_3325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3323),U_3325) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275,sP276,sP277])],[f_929_3]) ).

cnf(f_929_5,plain,
    ( sP276(U_3323,U_3325)
    | sP275(U_3323,U_3325)
    | U_3325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3323),U_3325) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3324),U_3326) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP277(U_3326,U_3324) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3323))
    | ~ sP275(U_3323,U_3325) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3323),U_3325))
    | ~ sP275(U_3323,U_3325) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3323),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP276(U_3323,U_3325) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3325),U_3323))
    | ~ sP276(U_3323,U_3325) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_11,plain,
    ( U_3326 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP277(U_3326,U_3324) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3324),U_3326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3324))
    | ~ sP277(U_3326,U_3324) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3326),U_3324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3324),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP277(U_3326,U_3324) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

fof(f_930_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__le__divisor]) ).

fof(f_930_2,plain,
    ! [U_3328,U_3327] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3328,U_3327)),U_3327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3327)) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_3328,U_3327] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3328,U_3327)),U_3327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3327)) ),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3328,U_3327)),U_3327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3327)) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_1,plain,
    ! [V_k,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_int__div__less__self]) ).

fof(f_931_2,plain,
    ! [U_3330,U_3329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3329),U_3330)),U_3329))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3329)) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ! [U_3330,U_3329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3329),U_3330)),U_3329))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3329)) ),
    inference(definitional_conversion,[status(esa)],[f_931_2]) ).

cnf(f_931_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3329),U_3330)),U_3329))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3329)) ),
    inference(clausify,[status(thm)],[f_931_3]) ).

fof(f_932_1,plain,
    ! [V_b,V_a,V_c] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq]) ).

fof(f_932_2,plain,
    ! [U_3333,U_3332,U_3331] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3333),U_3331)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3332),U_3333)),U_3331)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3331)) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ! [U_3333,U_3331,U_3332] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3333),U_3331)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3332),U_3333)),U_3331)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3331)) ),
    inference(definitional_conversion,[status(esa)],[f_932_2]) ).

cnf(f_932_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3333),U_3331)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3332),U_3333)),U_3331)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3331)) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

fof(f_933_1,plain,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self4]) ).

fof(f_933_2,plain,
    ! [U_3336,U_3335,U_3334] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3334),U_3335)),U_3336)),U_3335) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3336),U_3335),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ! [U_3334,U_3335,U_3336] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3334),U_3335)),U_3336)),U_3335) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3336),U_3335),
    inference(definitional_conversion,[status(esa)],[f_933_2]) ).

cnf(f_933_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3334),U_3335)),U_3336)),U_3335) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3336),U_3335),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_1,plain,
    ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmod__equality2]) ).

fof(f_934_2,plain,
    ! [U_3339,U_3338,U_3337] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3337),U_3338)),U_3338)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3337,U_3338))),U_3339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3337),U_3339),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ! [U_3337,U_3338,U_3339] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3337),U_3338)),U_3338)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3337,U_3338))),U_3339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3337),U_3339),
    inference(definitional_conversion,[status(esa)],[f_934_2]) ).

cnf(f_934_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3337),U_3338)),U_3338)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3337,U_3338))),U_3339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3337),U_3339),
    inference(clausify,[status(thm)],[f_934_3]) ).

fof(f_935_1,plain,
    ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmod__equality]) ).

fof(f_935_2,plain,
    ! [U_3342,U_3341,U_3340] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3340),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3341),U_3340))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3341,U_3340))),U_3342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3341),U_3342),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_3340,U_3341,U_3342] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3340),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3341),U_3340))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3341,U_3340))),U_3342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3341),U_3342),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3340),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3341),U_3340))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3341,U_3340))),U_3342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3341),U_3342),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmult1__eq]) ).

fof(f_936_2,plain,
    ! [U_3345,U_3344,U_3343] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),U_3344)),U_3345) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3344),U_3345))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3344,U_3345))),U_3345)),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_3343,U_3344,U_3345] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),U_3344)),U_3345) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3344),U_3345))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3344,U_3345))),U_3345)),
    inference(definitional_conversion,[status(esa)],[f_936_2]) ).

cnf(f_936_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),U_3344)),U_3345) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3344),U_3345))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3343),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3344,U_3345))),U_3345)),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_1,plain,
    ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality]) ).

fof(f_937_2,plain,
    ! [U_3347,U_3346] : U_3346 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3347),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3346),U_3347))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3346,U_3347)),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_3347,U_3346] : U_3346 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3347),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3346),U_3347))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3346,U_3347)),
    inference(definitional_conversion,[status(esa)],[f_937_2]) ).

cnf(f_937_4,plain,
    U_3346 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3347),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3346),U_3347))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3346,U_3347)),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1]) ).

fof(f_938_2,plain,
    ! [U_3351,U_3350,U_3349,U_3348] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3348),U_3350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),U_3351),U_3349))),U_3349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3348),U_3351),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3348),U_3350),U_3349))
      | U_3349 = c_Groups_Ozero__class_Ozero(U_3348)
      | ~ class_Divides_Osemiring__div(U_3348) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ! [U_3348,U_3349,U_3350,U_3351] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3348),U_3350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),U_3351),U_3349))),U_3349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3348),U_3351),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3348),U_3350),U_3349))
      | U_3349 = c_Groups_Ozero__class_Ozero(U_3348)
      | ~ class_Divides_Osemiring__div(U_3348) ),
    inference(definitional_conversion,[status(esa)],[f_938_2]) ).

cnf(f_938_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3348),U_3350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),U_3351),U_3349))),U_3349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3348),U_3351),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3348),U_3350),U_3349))
    | U_3349 = c_Groups_Ozero__class_Ozero(U_3348)
    | ~ class_Divides_Osemiring__div(U_3348) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self2]) ).

fof(f_939_2,plain,
    ! [U_3355,U_3354,U_3353,U_3352] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3352),U_3354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3355))),U_3353) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3352),U_3355),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3352),U_3354),U_3353))
      | U_3353 = c_Groups_Ozero__class_Ozero(U_3352)
      | ~ class_Divides_Osemiring__div(U_3352) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ! [U_3352,U_3353,U_3354,U_3355] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3352),U_3354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3355))),U_3353) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3352),U_3355),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3352),U_3354),U_3353))
      | U_3353 = c_Groups_Ozero__class_Ozero(U_3352)
      | ~ class_Divides_Osemiring__div(U_3352) ),
    inference(definitional_conversion,[status(esa)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3352),U_3354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3355))),U_3353) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3352),U_3355),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3352),U_3354),U_3353))
    | U_3353 = c_Groups_Ozero__class_Ozero(U_3352)
    | ~ class_Divides_Osemiring__div(U_3352) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add__self1]) ).

fof(f_940_2,plain,
    ! [U_3358,U_3357,U_3356] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),U_3357),U_3358)),U_3357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),U_3358),U_3357)),c_Groups_Oone__class_Oone(U_3356))
      | U_3357 = c_Groups_Ozero__class_Ozero(U_3356)
      | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ! [U_3356,U_3357,U_3358] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),U_3357),U_3358)),U_3357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),U_3358),U_3357)),c_Groups_Oone__class_Oone(U_3356))
      | U_3357 = c_Groups_Ozero__class_Ozero(U_3356)
      | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(definitional_conversion,[status(esa)],[f_940_2]) ).

cnf(f_940_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),U_3357),U_3358)),U_3357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),U_3358),U_3357)),c_Groups_Oone__class_Oone(U_3356))
    | U_3357 = c_Groups_Ozero__class_Ozero(U_3356)
    | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

fof(f_941_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add__self2]) ).

fof(f_941_2,plain,
    ! [U_3361,U_3360,U_3359] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),U_3361),U_3360)),U_3360) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),U_3361),U_3360)),c_Groups_Oone__class_Oone(U_3359))
      | U_3360 = c_Groups_Ozero__class_Ozero(U_3359)
      | ~ class_Divides_Osemiring__div(U_3359) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ! [U_3359,U_3360,U_3361] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),U_3361),U_3360)),U_3360) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),U_3361),U_3360)),c_Groups_Oone__class_Oone(U_3359))
      | U_3360 = c_Groups_Ozero__class_Ozero(U_3359)
      | ~ class_Divides_Osemiring__div(U_3359) ),
    inference(definitional_conversion,[status(esa)],[f_941_2]) ).

cnf(f_941_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),U_3361),U_3360)),U_3360) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),U_3361),U_3360)),c_Groups_Oone__class_Oone(U_3359))
    | U_3360 = c_Groups_Ozero__class_Ozero(U_3359)
    | ~ class_Divides_Osemiring__div(U_3359) ),
    inference(clausify,[status(thm)],[f_941_3]) ).

fof(f_942_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mod__equality]) ).

fof(f_942_2,plain,
    ! [U_3365,U_3364,U_3363,U_3362] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3362),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3362),U_3363),U_3364)),U_3364)),c_Divides_Odiv__class_Omod(U_3362,U_3363,U_3364))),U_3365) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3363),U_3365)
      | ~ class_Divides_Osemiring__div(U_3362) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_3362,U_3363,U_3364,U_3365] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3362),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3362),U_3363),U_3364)),U_3364)),c_Divides_Odiv__class_Omod(U_3362,U_3363,U_3364))),U_3365) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3363),U_3365)
      | ~ class_Divides_Osemiring__div(U_3362) ),
    inference(definitional_conversion,[status(esa)],[f_942_2]) ).

cnf(f_942_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3362),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3362),U_3363),U_3364)),U_3364)),c_Divides_Odiv__class_Omod(U_3362,U_3363,U_3364))),U_3365) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),U_3363),U_3365)
    | ~ class_Divides_Osemiring__div(U_3362) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mod__equality2]) ).

fof(f_943_2,plain,
    ! [U_3369,U_3368,U_3367,U_3366] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3366),U_3367),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3366),U_3368),U_3367))),c_Divides_Odiv__class_Omod(U_3366,U_3368,U_3367))),U_3369) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),U_3368),U_3369)
      | ~ class_Divides_Osemiring__div(U_3366) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ! [U_3366,U_3367,U_3368,U_3369] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3366),U_3367),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3366),U_3368),U_3367))),c_Divides_Odiv__class_Omod(U_3366,U_3368,U_3367))),U_3369) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),U_3368),U_3369)
      | ~ class_Divides_Osemiring__div(U_3366) ),
    inference(definitional_conversion,[status(esa)],[f_943_2]) ).

cnf(f_943_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3366),U_3367),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3366),U_3368),U_3367))),c_Divides_Odiv__class_Omod(U_3366,U_3368,U_3367))),U_3369) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),U_3368),U_3369)
    | ~ class_Divides_Osemiring__div(U_3366) ),
    inference(clausify,[status(thm)],[f_943_3]) ).

fof(f_944_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__equality]) ).

fof(f_944_2,plain,
    ! [U_3372,U_3371,U_3370] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3370),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3370),U_3371),U_3372)),U_3372)),c_Divides_Odiv__class_Omod(U_3370,U_3371,U_3372)) = U_3371
      | ~ class_Divides_Osemiring__div(U_3370) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_3370,U_3371,U_3372] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3370),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3370),U_3371),U_3372)),U_3372)),c_Divides_Odiv__class_Omod(U_3370,U_3371,U_3372)) = U_3371
      | ~ class_Divides_Osemiring__div(U_3370) ),
    inference(definitional_conversion,[status(esa)],[f_944_2]) ).

cnf(f_944_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3370),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3370),U_3371),U_3372)),U_3372)),c_Divides_Odiv__class_Omod(U_3370,U_3371,U_3372)) = U_3371
    | ~ class_Divides_Osemiring__div(U_3370) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__equality2]) ).

fof(f_945_2,plain,
    ! [U_3375,U_3374,U_3373] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3373),U_3374),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3373),U_3375),U_3374))),c_Divides_Odiv__class_Omod(U_3373,U_3375,U_3374)) = U_3375
      | ~ class_Divides_Osemiring__div(U_3373) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_3373,U_3374,U_3375] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3373),U_3374),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3373),U_3375),U_3374))),c_Divides_Odiv__class_Omod(U_3373,U_3375,U_3374)) = U_3375
      | ~ class_Divides_Osemiring__div(U_3373) ),
    inference(definitional_conversion,[status(esa)],[f_945_2]) ).

cnf(f_945_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3373),U_3374),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3373),U_3375),U_3374))),c_Divides_Odiv__class_Omod(U_3373,U_3375,U_3374)) = U_3375
    | ~ class_Divides_Osemiring__div(U_3373) ),
    inference(clausify,[status(thm)],[f_945_3]) ).

fof(f_946_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H]) ).

fof(f_946_2,plain,
    ! [U_3378,U_3377,U_3376] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),c_Divides_Odiv__class_Omod(U_3376,U_3377,U_3378)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3376),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3376),U_3377),U_3378)),U_3378)) = U_3377
      | ~ class_Divides_Osemiring__div(U_3376) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ! [U_3376,U_3377,U_3378] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),c_Divides_Odiv__class_Omod(U_3376,U_3377,U_3378)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3376),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3376),U_3377),U_3378)),U_3378)) = U_3377
      | ~ class_Divides_Osemiring__div(U_3376) ),
    inference(definitional_conversion,[status(esa)],[f_946_2]) ).

cnf(f_946_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),c_Divides_Odiv__class_Omod(U_3376,U_3377,U_3378)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3376),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3376),U_3377),U_3378)),U_3378)) = U_3377
    | ~ class_Divides_Osemiring__div(U_3376) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

fof(f_947_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div]) ).

fof(f_947_2,plain,
    ! [U_3385,U_3384,U_3383] :
      ( ( hBOOL(hAPP(U_3383,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3384),U_3385)))
        | ( ? [U_3382,U_3381] :
              ( ~ hBOOL(hAPP(U_3383,U_3382))
              & U_3384 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3385),U_3382)),U_3381)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3381),U_3385)) )
          & U_3385 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3383,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3380,U_3379] :
                ( hBOOL(hAPP(U_3383,U_3380))
                | U_3384 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3385),U_3380)),U_3379)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3385)) )
            | U_3385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3383,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3385 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3383,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3384),U_3385))) ) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ( ! [U_3391,U_3389,U_3387] :
        ( hBOOL(hAPP(U_3387,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3389),U_3391)))
        | ( ? [U_3382,U_3381] :
              ( ~ hBOOL(hAPP(U_3387,U_3382))
              & U_3389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3391),U_3382)),U_3381)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3381),U_3391)) )
          & U_3391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3387,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3390,U_3388,U_3386] :
        ( ( ( ! [U_3380,U_3379] :
                ( hBOOL(hAPP(U_3386,U_3380))
                | U_3388 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3380)),U_3379)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3390)) )
            | U_3390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3386,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3386,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3388),U_3390))) ) ),
    inference(miniscope,[status(thm)],[f_947_2]) ).

fof(f_947_4,plain,
    ( ! [U_3391,U_3389,U_3387] :
        ( hBOOL(hAPP(U_3387,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3389),U_3391)))
        | ( ? [U_3381] :
              ( ~ hBOOL(hAPP(U_3387,sK67(U_3391,U_3389,U_3387)))
              & U_3389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3391),sK67(U_3391,U_3389,U_3387))),U_3381)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3381),U_3391)) )
          & U_3391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3387,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3390,U_3388,U_3386] :
        ( ( ( ! [U_3380,U_3379] :
                ( hBOOL(hAPP(U_3386,U_3380))
                | U_3388 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3380)),U_3379)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3390)) )
            | U_3390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3386,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3386,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3388),U_3390))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3382,sK67(U_3391,U_3389,U_3387))],[f_947_3]) ).

fof(f_947_5,plain,
    ( ! [U_3391,U_3389,U_3387] :
        ( hBOOL(hAPP(U_3387,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3389),U_3391)))
        | ( ~ hBOOL(hAPP(U_3387,sK67(U_3391,U_3389,U_3387)))
          & U_3389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3391),sK67(U_3391,U_3389,U_3387))),sK68(U_3391,U_3389,U_3387))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK68(U_3391,U_3389,U_3387)),U_3391))
          & U_3391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3387,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3390,U_3388,U_3386] :
        ( ( ( ! [U_3380,U_3379] :
                ( hBOOL(hAPP(U_3386,U_3380))
                | U_3388 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3380)),U_3379)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3390)) )
            | U_3390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3386,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3386,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3388),U_3390))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3381,sK68(U_3391,U_3389,U_3387))],[f_947_4]) ).

fof(f_947_6,plain,
    ( ! [U_3387,U_3389,U_3391] :
        ( ~ hBOOL(hAPP(U_3387,sK67(U_3391,U_3389,U_3387)))
        | ~ sP280(U_3387,U_3389,U_3391) )
    & ! [U_3387,U_3389,U_3391] :
        ( U_3389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3391),sK67(U_3391,U_3389,U_3387))),sK68(U_3391,U_3389,U_3387))
        | ~ sP280(U_3387,U_3389,U_3391) )
    & ! [U_3387,U_3389,U_3391] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK68(U_3391,U_3389,U_3387)),U_3391))
        | ~ sP280(U_3387,U_3389,U_3391) )
    & ! [U_3387,U_3389,U_3391] :
        ( U_3391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP280(U_3387,U_3389,U_3391) )
    & ! [U_3387,U_3391] :
        ( ~ hBOOL(hAPP(U_3387,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP279(U_3387,U_3391) )
    & ! [U_3387,U_3391] :
        ( U_3391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP279(U_3387,U_3391) )
    & ! [U_3380,U_3379,U_3386,U_3390,U_3388] :
        ( hBOOL(hAPP(U_3386,U_3380))
        | U_3388 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3380)),U_3379)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3390))
        | U_3390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP278(U_3380,U_3379,U_3386,U_3390,U_3388) )
    & ! [U_3380,U_3379,U_3386,U_3390,U_3388] :
        ( hBOOL(hAPP(U_3386,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP278(U_3380,U_3379,U_3386,U_3390,U_3388) )
    & ! [U_3387,U_3389,U_3391] :
        ( hBOOL(hAPP(U_3387,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3389),U_3391)))
        | sP280(U_3387,U_3389,U_3391)
        | sP279(U_3387,U_3391) )
    & ! [U_3380,U_3379,U_3386,U_3390,U_3388] :
        ( sP278(U_3380,U_3379,U_3386,U_3390,U_3388)
        | ~ hBOOL(hAPP(U_3386,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3388),U_3390))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278,sP279,sP280])],[f_947_5]) ).

cnf(f_947_7,plain,
    ( sP278(U_3380,U_3379,U_3386,U_3390,U_3388)
    | ~ hBOOL(hAPP(U_3386,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3388),U_3390))) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_8,plain,
    ( hBOOL(hAPP(U_3387,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3389),U_3391)))
    | sP280(U_3387,U_3389,U_3391)
    | sP279(U_3387,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_9,plain,
    ( hBOOL(hAPP(U_3386,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP278(U_3380,U_3379,U_3386,U_3390,U_3388) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_10,plain,
    ( hBOOL(hAPP(U_3386,U_3380))
    | U_3388 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3380)),U_3379)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3390))
    | U_3390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP278(U_3380,U_3379,U_3386,U_3390,U_3388) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_11,plain,
    ( U_3391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP279(U_3387,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_12,plain,
    ( ~ hBOOL(hAPP(U_3387,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP279(U_3387,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_13,plain,
    ( U_3391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP280(U_3387,U_3389,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK68(U_3391,U_3389,U_3387)),U_3391))
    | ~ sP280(U_3387,U_3389,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_15,plain,
    ( U_3389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3391),sK67(U_3391,U_3389,U_3387))),sK68(U_3391,U_3389,U_3387))
    | ~ sP280(U_3387,U_3389,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

cnf(f_947_16,plain,
    ( ~ hBOOL(hAPP(U_3387,sK67(U_3391,U_3389,U_3387)))
    | ~ sP280(U_3387,U_3389,U_3391) ),
    inference(clausify,[status(thm)],[f_947_6]) ).

fof(f_948_1,plain,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__lemma]) ).

fof(f_948_2,plain,
    ! [U_3395,U_3394,U_3393,U_3392] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3394),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3395,U_3392))),U_3393)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3394),U_3392)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3393),U_3394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3392)) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_3392,U_3393,U_3394,U_3395] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3394),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3395,U_3392))),U_3393)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3394),U_3392)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3393),U_3394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3392)) ),
    inference(definitional_conversion,[status(esa)],[f_948_2]) ).

cnf(f_948_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3394),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3395,U_3392))),U_3393)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3394),U_3392)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3393),U_3394))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3392)) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

fof(f_949_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__mod]) ).

fof(f_949_2,plain,
    ! [U_3402,U_3401,U_3400] :
      ( ( hBOOL(hAPP(U_3400,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3401,U_3402)))
        | ( ? [U_3399,U_3398] :
              ( ~ hBOOL(hAPP(U_3400,U_3398))
              & U_3401 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3402),U_3399)),U_3398)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3398),U_3402)) )
          & U_3402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3400,U_3401))
          & U_3402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3397,U_3396] :
                ( hBOOL(hAPP(U_3400,U_3396))
                | U_3401 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3402),U_3397)),U_3396)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3396),U_3402)) )
            | U_3402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3400,U_3401))
            | U_3402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3400,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3401,U_3402))) ) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ( ! [U_3408,U_3406,U_3404] :
        ( hBOOL(hAPP(U_3404,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3406,U_3408)))
        | ( ? [U_3399,U_3398] :
              ( ~ hBOOL(hAPP(U_3404,U_3398))
              & U_3406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3408),U_3399)),U_3398)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3398),U_3408)) )
          & U_3408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3404,U_3406))
          & U_3408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3407,U_3405,U_3403] :
        ( ( ( ! [U_3397,U_3396] :
                ( hBOOL(hAPP(U_3403,U_3396))
                | U_3405 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3407),U_3397)),U_3396)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3396),U_3407)) )
            | U_3407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3403,U_3405))
            | U_3407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3403,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3405,U_3407))) ) ),
    inference(miniscope,[status(thm)],[f_949_2]) ).

fof(f_949_4,plain,
    ( ! [U_3408,U_3406,U_3404] :
        ( hBOOL(hAPP(U_3404,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3406,U_3408)))
        | ( ? [U_3398] :
              ( ~ hBOOL(hAPP(U_3404,U_3398))
              & U_3406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3408),sK69(U_3408,U_3406,U_3404))),U_3398)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3398),U_3408)) )
          & U_3408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3404,U_3406))
          & U_3408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3407,U_3405,U_3403] :
        ( ( ( ! [U_3397,U_3396] :
                ( hBOOL(hAPP(U_3403,U_3396))
                | U_3405 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3407),U_3397)),U_3396)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3396),U_3407)) )
            | U_3407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3403,U_3405))
            | U_3407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3403,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3405,U_3407))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3399,sK69(U_3408,U_3406,U_3404))],[f_949_3]) ).

fof(f_949_5,plain,
    ( ! [U_3408,U_3406,U_3404] :
        ( hBOOL(hAPP(U_3404,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3406,U_3408)))
        | ( ~ hBOOL(hAPP(U_3404,sK70(U_3408,U_3406,U_3404)))
          & U_3406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3408),sK69(U_3408,U_3406,U_3404))),sK70(U_3408,U_3406,U_3404))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK70(U_3408,U_3406,U_3404)),U_3408))
          & U_3408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3404,U_3406))
          & U_3408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3407,U_3405,U_3403] :
        ( ( ( ! [U_3397,U_3396] :
                ( hBOOL(hAPP(U_3403,U_3396))
                | U_3405 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3407),U_3397)),U_3396)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3396),U_3407)) )
            | U_3407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3403,U_3405))
            | U_3407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3403,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3405,U_3407))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3398,sK70(U_3408,U_3406,U_3404))],[f_949_4]) ).

fof(f_949_6,plain,
    ( ! [U_3404,U_3408,U_3406] :
        ( ~ hBOOL(hAPP(U_3404,sK70(U_3408,U_3406,U_3404)))
        | ~ sP283(U_3404,U_3408,U_3406) )
    & ! [U_3404,U_3408,U_3406] :
        ( U_3406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3408),sK69(U_3408,U_3406,U_3404))),sK70(U_3408,U_3406,U_3404))
        | ~ sP283(U_3404,U_3408,U_3406) )
    & ! [U_3404,U_3408,U_3406] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK70(U_3408,U_3406,U_3404)),U_3408))
        | ~ sP283(U_3404,U_3408,U_3406) )
    & ! [U_3404,U_3408,U_3406] :
        ( U_3408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP283(U_3404,U_3408,U_3406) )
    & ! [U_3404,U_3408,U_3406] :
        ( ~ hBOOL(hAPP(U_3404,U_3406))
        | ~ sP282(U_3404,U_3408,U_3406) )
    & ! [U_3404,U_3408,U_3406] :
        ( U_3408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP282(U_3404,U_3408,U_3406) )
    & ! [U_3407,U_3396,U_3403,U_3397,U_3405] :
        ( hBOOL(hAPP(U_3403,U_3396))
        | U_3405 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3407),U_3397)),U_3396)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3396),U_3407))
        | U_3407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP281(U_3407,U_3396,U_3403,U_3397,U_3405) )
    & ! [U_3407,U_3396,U_3403,U_3397,U_3405] :
        ( hBOOL(hAPP(U_3403,U_3405))
        | U_3407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP281(U_3407,U_3396,U_3403,U_3397,U_3405) )
    & ! [U_3404,U_3408,U_3406] :
        ( hBOOL(hAPP(U_3404,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3406,U_3408)))
        | sP283(U_3404,U_3408,U_3406)
        | sP282(U_3404,U_3408,U_3406) )
    & ! [U_3407,U_3396,U_3403,U_3397,U_3405] :
        ( sP281(U_3407,U_3396,U_3403,U_3397,U_3405)
        | ~ hBOOL(hAPP(U_3403,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3405,U_3407))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281,sP282,sP283])],[f_949_5]) ).

cnf(f_949_7,plain,
    ( sP281(U_3407,U_3396,U_3403,U_3397,U_3405)
    | ~ hBOOL(hAPP(U_3403,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3405,U_3407))) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_8,plain,
    ( hBOOL(hAPP(U_3404,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3406,U_3408)))
    | sP283(U_3404,U_3408,U_3406)
    | sP282(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_9,plain,
    ( hBOOL(hAPP(U_3403,U_3405))
    | U_3407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP281(U_3407,U_3396,U_3403,U_3397,U_3405) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_10,plain,
    ( hBOOL(hAPP(U_3403,U_3396))
    | U_3405 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3407),U_3397)),U_3396)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3396),U_3407))
    | U_3407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP281(U_3407,U_3396,U_3403,U_3397,U_3405) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_11,plain,
    ( U_3408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP282(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_12,plain,
    ( ~ hBOOL(hAPP(U_3404,U_3406))
    | ~ sP282(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_13,plain,
    ( U_3408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP283(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK70(U_3408,U_3406,U_3404)),U_3408))
    | ~ sP283(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_15,plain,
    ( U_3406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3408),sK69(U_3408,U_3406,U_3404))),sK70(U_3408,U_3406,U_3404))
    | ~ sP283(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

cnf(f_949_16,plain,
    ( ~ hBOOL(hAPP(U_3404,sK70(U_3408,U_3406,U_3404)))
    | ~ sP283(U_3404,U_3408,U_3406) ),
    inference(clausify,[status(thm)],[f_949_6]) ).

fof(f_950_1,plain,
    ! [V_m,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq]) ).

fof(f_950_2,plain,
    ! [U_3410,U_3409] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3409),U_3410)),U_3409) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3409)) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_3410,U_3409] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3409),U_3410)),U_3409) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3409)) ),
    inference(definitional_conversion,[status(esa)],[f_950_2]) ).

cnf(f_950_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3409),U_3410)),U_3409) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3409)) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_1,plain,
    ! [V_y,V_x] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib]) ).

fof(f_951_2,plain,
    ! [U_3412,U_3411] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3411,U_3412)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3411),hAPP(c_Int_Onat,U_3412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3411)) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_3412,U_3411] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3411,U_3412)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3411),hAPP(c_Int_Onat,U_3412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3411)) ),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3411,U_3412)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3411),hAPP(c_Int_Onat,U_3412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3411)) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_1,plain,
    ! [V_y,V_x] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J]) ).

fof(f_952_2,plain,
    ! [U_3414,U_3413] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3413),hAPP(c_Int_Onat,U_3414)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3413,U_3414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3413)) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_3414,U_3413] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3413),hAPP(c_Int_Onat,U_3414)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3413,U_3414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3413)) ),
    inference(definitional_conversion,[status(esa)],[f_952_2]) ).

cnf(f_952_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3413),hAPP(c_Int_Onat,U_3414)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3413,U_3414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3413)) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_1,plain,
    ! [V_m_2,V_q_2,V_n_2] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) )
          | V_q_2 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) )
        & ( V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_split__div__lemma]) ).

fof(f_953_2,plain,
    ! [U_3417,U_3416,U_3415] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),hAPP(c_Nat_OSuc,U_3416))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),U_3416)),U_3417)) )
          | U_3416 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3415) )
        & ( U_3416 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3415)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),hAPP(c_Nat_OSuc,U_3416))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),U_3416)),U_3417)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3415)) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ( ! [U_3415,U_3416,U_3417] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),hAPP(c_Nat_OSuc,U_3416))))
        | ~ sP284(U_3415,U_3416,U_3417) )
    & ! [U_3415,U_3416,U_3417] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),U_3416)),U_3417))
        | ~ sP284(U_3415,U_3416,U_3417) )
    & ! [U_3415,U_3416,U_3417] :
        ( sP284(U_3415,U_3416,U_3417)
        | U_3416 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3415)
        | ~ sP285(U_3415,U_3416,U_3417) )
    & ! [U_3415,U_3416,U_3417] :
        ( U_3416 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3415)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),hAPP(c_Nat_OSuc,U_3416))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),U_3416)),U_3417))
        | ~ sP285(U_3415,U_3416,U_3417) )
    & ! [U_3415,U_3416,U_3417] :
        ( sP285(U_3415,U_3416,U_3417)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3415)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284,sP285])],[f_953_2]) ).

cnf(f_953_4,plain,
    ( sP285(U_3415,U_3416,U_3417)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3415)) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

cnf(f_953_5,plain,
    ( U_3416 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3415)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),hAPP(c_Nat_OSuc,U_3416))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),U_3416)),U_3417))
    | ~ sP285(U_3415,U_3416,U_3417) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

cnf(f_953_6,plain,
    ( sP284(U_3415,U_3416,U_3417)
    | U_3416 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3415)
    | ~ sP285(U_3415,U_3416,U_3417) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

cnf(f_953_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),U_3416)),U_3417))
    | ~ sP284(U_3415,U_3416,U_3417) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

cnf(f_953_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3415),hAPP(c_Nat_OSuc,U_3416))))
    | ~ sP284(U_3415,U_3416,U_3417) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_1,plain,
    ! [V_k,V_l] :
      ( ( c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) )
      & ( c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_z3div__def]) ).

fof(f_954_2,plain,
    ! [U_3419,U_3418] :
      ( ( c_SMT_Oz3div(U_3419,U_3418) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3419),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3418)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3418)) )
      & ( c_SMT_Oz3div(U_3419,U_3418) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3419),U_3418)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3418)) ) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ( ! [U_3423,U_3421] :
        ( c_SMT_Oz3div(U_3423,U_3421) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3423),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3421)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3421)) )
    & ! [U_3422,U_3420] :
        ( c_SMT_Oz3div(U_3422,U_3420) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3422),U_3420)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3420)) ) ),
    inference(miniscope,[status(thm)],[f_954_2]) ).

fof(f_954_4,plain,
    ( ! [U_3421,U_3423] :
        ( c_SMT_Oz3div(U_3423,U_3421) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3423),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3421)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3421)) )
    & ! [U_3420,U_3422] :
        ( c_SMT_Oz3div(U_3422,U_3420) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3422),U_3420)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3420)) ) ),
    inference(definitional_conversion,[status(esa)],[f_954_3]) ).

cnf(f_954_5,plain,
    ( c_SMT_Oz3div(U_3422,U_3420) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3422),U_3420)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3420)) ),
    inference(clausify,[status(thm)],[f_954_4]) ).

cnf(f_954_6,plain,
    ( c_SMT_Oz3div(U_3423,U_3421) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3423),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3421)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3421)) ),
    inference(clausify,[status(thm)],[f_954_4]) ).

fof(f_955_1,plain,
    ! [V_a,V_b] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus1__eq__if]) ).

fof(f_955_2,plain,
    ! [U_3425,U_3424] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3425)),U_3424) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3425),U_3424))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3425)),U_3424) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3425),U_3424))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3424) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_3424 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ( ! [U_3424,U_3425] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3425)),U_3424) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3425),U_3424))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP286(U_3424,U_3425) )
    & ! [U_3424,U_3425] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3425)),U_3424) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3425),U_3424))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3424) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP286(U_3424,U_3425) )
    & ! [U_3424,U_3425] :
        ( sP286(U_3424,U_3425)
        | U_3424 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_955_2]) ).

cnf(f_955_4,plain,
    ( sP286(U_3424,U_3425)
    | U_3424 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

cnf(f_955_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3425)),U_3424) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3425),U_3424))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3424) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP286(U_3424,U_3425) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

cnf(f_955_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3425)),U_3424) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3425),U_3424))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP286(U_3424,U_3425) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_1,plain,
    ! [V_a,V_b] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if]) ).

fof(f_956_2,plain,
    ! [U_3427,U_3426] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3426)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),U_3426))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3427,U_3426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3426)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),U_3426))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3427,U_3426) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_3426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ( ! [U_3427,U_3426] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3426)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),U_3426))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3427,U_3426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP287(U_3427,U_3426) )
    & ! [U_3427,U_3426] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3426)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),U_3426))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3427,U_3426) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP287(U_3427,U_3426) )
    & ! [U_3427,U_3426] :
        ( sP287(U_3427,U_3426)
        | U_3426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_956_2]) ).

cnf(f_956_4,plain,
    ( sP287(U_3427,U_3426)
    | U_3426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

cnf(f_956_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3426)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),U_3426))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3427,U_3426) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP287(U_3427,U_3426) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

cnf(f_956_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3426)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3427),U_3426))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3427,U_3426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP287(U_3427,U_3426) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__div__geq]) ).

fof(f_957_2,plain,
    ! [U_3429,U_3428] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3429),U_3428) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3429),U_3428)),U_3428))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3428),U_3429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3428)) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_3429,U_3428] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3429),U_3428) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3429),U_3428)),U_3428))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3428),U_3429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3428)) ),
    inference(definitional_conversion,[status(esa)],[f_957_2]) ).

cnf(f_957_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3429),U_3428) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3429),U_3428)),U_3428))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3428),U_3429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3428)) ),
    inference(clausify,[status(thm)],[f_957_3]) ).

fof(f_958_1,plain,
    ! [V_b,V_a,T_a] :
      ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__decomp]) ).

fof(f_958_2,plain,
    ! [U_3432,U_3431,U_3430] :
      ( U_3431 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3430),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3430),U_3431),U_3432)),U_3432)),c_Divides_Odiv__class_Omod(U_3430,U_3431,U_3432))
      | ~ class_Divides_Osemiring__div(U_3430) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_3430,U_3431,U_3432] :
      ( U_3431 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3430),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3430),U_3431),U_3432)),U_3432)),c_Divides_Odiv__class_Omod(U_3430,U_3431,U_3432))
      | ~ class_Divides_Osemiring__div(U_3430) ),
    inference(definitional_conversion,[status(esa)],[f_958_2]) ).

cnf(f_958_4,plain,
    ( U_3431 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3430),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3430),U_3431),U_3432)),U_3432)),c_Divides_Odiv__class_Omod(U_3430,U_3431,U_3432))
    | ~ class_Divides_Osemiring__div(U_3430) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J]) ).

fof(f_959_2,plain,
    ! [U_3434,U_3433] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3433)),hAPP(c_Int_Onat,U_3434)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3433,U_3434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3433)) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_3433,U_3434] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3433)),hAPP(c_Int_Onat,U_3434)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3433,U_3434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3433)) ),
    inference(definitional_conversion,[status(esa)],[f_959_2]) ).

cnf(f_959_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3433)),hAPP(c_Int_Onat,U_3434)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3433,U_3434))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3434))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3433)) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

fof(f_960_1,plain,
    ! [V_k_2,V_P_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).

fof(f_960_2,plain,
    ! [U_3439,U_3438,U_3437] :
      ( ! [U_3436] :
          ( hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3439),U_3437))))
          | ~ hBOOL(hAPP(U_3438,U_3436)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439))
      | ? [U_3435] :
          ( ~ hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3435),U_3437)))
          & hBOOL(hAPP(U_3438,U_3435)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3437)) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_3439,U_3438,U_3437] :
      ( ! [U_3436] :
          ( hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3439),U_3437))))
          | ~ hBOOL(hAPP(U_3438,U_3436)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439))
      | ( ~ hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK71(U_3439,U_3438,U_3437)),U_3437)))
        & hBOOL(hAPP(U_3438,sK71(U_3439,U_3438,U_3437))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3437)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3435,sK71(U_3439,U_3438,U_3437))],[f_960_2]) ).

fof(f_960_4,plain,
    ( ! [U_3437,U_3438,U_3439] :
        ( ~ hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK71(U_3439,U_3438,U_3437)),U_3437)))
        | ~ sP288(U_3437,U_3438,U_3439) )
    & ! [U_3437,U_3438,U_3439] :
        ( hBOOL(hAPP(U_3438,sK71(U_3439,U_3438,U_3437)))
        | ~ sP288(U_3437,U_3438,U_3439) )
    & ! [U_3436,U_3437,U_3438,U_3439] :
        ( hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3439),U_3437))))
        | ~ hBOOL(hAPP(U_3438,U_3436))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439))
        | sP288(U_3437,U_3438,U_3439)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3437)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_960_3]) ).

cnf(f_960_5,plain,
    ( hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3439),U_3437))))
    | ~ hBOOL(hAPP(U_3438,U_3436))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439))
    | sP288(U_3437,U_3438,U_3439)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3437)) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

cnf(f_960_6,plain,
    ( hBOOL(hAPP(U_3438,sK71(U_3439,U_3438,U_3437)))
    | ~ sP288(U_3437,U_3438,U_3439) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

cnf(f_960_7,plain,
    ( ~ hBOOL(hAPP(U_3438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK71(U_3439,U_3438,U_3437)),U_3437)))
    | ~ sP288(U_3437,U_3438,U_3439) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

fof(f_961_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ? [B_z] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval]) ).

fof(f_961_2,plain,
    ! [U_3443,U_3442,U_3441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),U_3442),U_3443))
      | ? [U_3440] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3440),U_3442)),U_3443))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),U_3440),c_Groups_Oone__class_Oone(U_3441)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),c_Groups_Ozero__class_Ozero(U_3441)),U_3440)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3441) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_3443,U_3442,U_3441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),U_3442),U_3443))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),sK72(U_3443,U_3442,U_3441)),U_3442)),U_3443))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),sK72(U_3443,U_3442,U_3441)),c_Groups_Oone__class_Oone(U_3441)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),c_Groups_Ozero__class_Ozero(U_3441)),sK72(U_3443,U_3442,U_3441))) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3441) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3440,sK72(U_3443,U_3442,U_3441))],[f_961_2]) ).

fof(f_961_4,plain,
    ( ! [U_3441,U_3442,U_3443] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),sK72(U_3443,U_3442,U_3441)),U_3442)),U_3443))
        | ~ sP289(U_3441,U_3442,U_3443) )
    & ! [U_3441,U_3442,U_3443] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),sK72(U_3443,U_3442,U_3441)),c_Groups_Oone__class_Oone(U_3441)))
        | ~ sP289(U_3441,U_3442,U_3443) )
    & ! [U_3441,U_3442,U_3443] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),c_Groups_Ozero__class_Ozero(U_3441)),sK72(U_3443,U_3442,U_3441)))
        | ~ sP289(U_3441,U_3442,U_3443) )
    & ! [U_3441,U_3442,U_3443] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),U_3442),U_3443))
        | sP289(U_3441,U_3442,U_3443)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_3441) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289])],[f_961_3]) ).

cnf(f_961_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),U_3442),U_3443))
    | sP289(U_3441,U_3442,U_3443)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3441) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),c_Groups_Ozero__class_Ozero(U_3441)),sK72(U_3443,U_3442,U_3441)))
    | ~ sP289(U_3441,U_3442,U_3443) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),sK72(U_3443,U_3442,U_3441)),c_Groups_Oone__class_Oone(U_3441)))
    | ~ sP289(U_3441,U_3442,U_3443) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),sK72(U_3443,U_3442,U_3441)),U_3442)),U_3443))
    | ~ sP289(U_3441,U_3442,U_3443) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

fof(f_962_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = V_b_2
          | V_c_2 != V_d_2 )
        & ( V_c_2 = V_d_2
          | V_a_2 != V_b_2 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).

fof(f_962_2,plain,
    ! [U_3448,U_3447,U_3446,U_3445,U_3444] :
      ( ( ( U_3445 = U_3446
          | U_3447 != U_3448 )
        & ( U_3447 = U_3448
          | U_3445 != U_3446 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3444),U_3445),U_3446) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3444),U_3447),U_3448)
      | ~ class_Groups_Oab__group__add(U_3444) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ( ! [U_3447,U_3448,U_3446,U_3445] :
        ( U_3445 = U_3446
        | U_3447 != U_3448
        | ~ sP290(U_3447,U_3448,U_3446,U_3445) )
    & ! [U_3447,U_3448,U_3446,U_3445] :
        ( U_3447 = U_3448
        | U_3445 != U_3446
        | ~ sP290(U_3447,U_3448,U_3446,U_3445) )
    & ! [U_3447,U_3448,U_3446,U_3445,U_3444] :
        ( sP290(U_3447,U_3448,U_3446,U_3445)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3444),U_3445),U_3446) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3444),U_3447),U_3448)
        | ~ class_Groups_Oab__group__add(U_3444) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290])],[f_962_2]) ).

cnf(f_962_4,plain,
    ( sP290(U_3447,U_3448,U_3446,U_3445)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3444),U_3445),U_3446) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3444),U_3447),U_3448)
    | ~ class_Groups_Oab__group__add(U_3444) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

cnf(f_962_5,plain,
    ( U_3447 = U_3448
    | U_3445 != U_3446
    | ~ sP290(U_3447,U_3448,U_3446,U_3445) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

cnf(f_962_6,plain,
    ( U_3445 = U_3446
    | U_3447 != U_3448
    | ~ sP290(U_3447,U_3448,U_3446,U_3445) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

fof(f_963_1,plain,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j),
    inference(fof_nnf,[status(thm)],[fact_diff__commute]) ).

fof(f_963_2,plain,
    ! [U_3451,U_3450,U_3449] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3449),U_3450)),U_3451) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3449),U_3451)),U_3450),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_3449,U_3451,U_3450] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3449),U_3450)),U_3451) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3449),U_3451)),U_3450),
    inference(definitional_conversion,[status(esa)],[f_963_2]) ).

cnf(f_963_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3449),U_3450)),U_3451) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3449),U_3451)),U_3450),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__diff]) ).

fof(f_964_2,plain,
    ! [U_3454,U_3453,U_3452] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3453),U_3454)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3452),hAPP(c_Int_Oring__1__class_Oof__int(U_3452),U_3453)),hAPP(c_Int_Oring__1__class_Oof__int(U_3452),U_3454))
      | ~ class_Rings_Oring__1(U_3452) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3452,U_3453,U_3454] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3453),U_3454)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3452),hAPP(c_Int_Oring__1__class_Oof__int(U_3452),U_3453)),hAPP(c_Int_Oring__1__class_Oof__int(U_3452),U_3454))
      | ~ class_Rings_Oring__1(U_3452) ),
    inference(definitional_conversion,[status(esa)],[f_964_2]) ).

cnf(f_964_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3453),U_3454)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3452),hAPP(c_Int_Oring__1__class_Oof__int(U_3452),U_3453)),hAPP(c_Int_Oring__1__class_Oof__int(U_3452),U_3454))
    | ~ class_Rings_Oring__1(U_3452) ),
    inference(clausify,[status(thm)],[f_964_3]) ).

fof(f_965_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
      | ~ class_Groups_Ominus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).

fof(f_965_2,plain,
    ! [U_3459,U_3458,U_3457,U_3456,U_3455] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3456,U_3455)),U_3457),U_3458),U_3459) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3455),hAPP(U_3457,U_3459)),hAPP(U_3458,U_3459))
      | ~ class_Groups_Ominus(U_3455) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_3455,U_3456,U_3457,U_3458,U_3459] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3456,U_3455)),U_3457),U_3458),U_3459) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3455),hAPP(U_3457,U_3459)),hAPP(U_3458,U_3459))
      | ~ class_Groups_Ominus(U_3455) ),
    inference(definitional_conversion,[status(esa)],[f_965_2]) ).

cnf(f_965_4,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3456,U_3455)),U_3457),U_3458),U_3459) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3455),hAPP(U_3457,U_3459)),hAPP(U_3458,U_3459))
    | ~ class_Groups_Ominus(U_3455) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_1,plain,
    ! [V_m,V_n,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__diff]) ).

fof(f_966_2,plain,
    ! [U_3462,U_3461,U_3460] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3462),U_3461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),U_3462)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),U_3461))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3461),U_3462))
      | ~ class_Rings_Oring__1(U_3460) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ! [U_3460,U_3461,U_3462] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3462),U_3461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),U_3462)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),U_3461))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3461),U_3462))
      | ~ class_Rings_Oring__1(U_3460) ),
    inference(definitional_conversion,[status(esa)],[f_966_2]) ).

cnf(f_966_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3462),U_3461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),U_3462)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3460),U_3461))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3461),U_3462))
    | ~ class_Rings_Oring__1(U_3460) ),
    inference(clausify,[status(thm)],[f_966_3]) ).

fof(f_967_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiff__int]) ).

fof(f_967_2,plain,
    ! [U_3464,U_3463] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3464)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3463)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3464),U_3463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3463),U_3464)) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_3463,U_3464] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3464)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3463)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3464),U_3463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3463),U_3464)) ),
    inference(definitional_conversion,[status(esa)],[f_967_2]) ).

cnf(f_967_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3464)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3463)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3464),U_3463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3463),U_3464)) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).

fof(f_968_2,plain,
    ! [U_3469,U_3468,U_3467,U_3466,U_3465] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3466),U_3467))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3468),U_3469)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3468),U_3469))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3466),U_3467)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3468),U_3469)
      | ~ class_Groups_Oordered__ab__group__add(U_3465) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ( ! [U_3465,U_3466,U_3467,U_3468,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3466),U_3467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3468),U_3469))
        | ~ sP291(U_3465,U_3466,U_3467,U_3468,U_3469) )
    & ! [U_3465,U_3466,U_3467,U_3468,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3468),U_3469))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3466),U_3467))
        | ~ sP291(U_3465,U_3466,U_3467,U_3468,U_3469) )
    & ! [U_3465,U_3466,U_3467,U_3468,U_3469] :
        ( sP291(U_3465,U_3466,U_3467,U_3468,U_3469)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3468),U_3469)
        | ~ class_Groups_Oordered__ab__group__add(U_3465) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_968_2]) ).

cnf(f_968_4,plain,
    ( sP291(U_3465,U_3466,U_3467,U_3468,U_3469)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3468),U_3469)
    | ~ class_Groups_Oordered__ab__group__add(U_3465) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

cnf(f_968_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3468),U_3469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3466),U_3467))
    | ~ sP291(U_3465,U_3466,U_3467,U_3468,U_3469) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

cnf(f_968_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3466),U_3467))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3465),U_3468),U_3469))
    | ~ sP291(U_3465,U_3466,U_3467,U_3468,U_3469) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

fof(f_969_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).

fof(f_969_2,plain,
    ! [U_3472,U_3471,U_3470] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),U_3472) = c_Groups_Ozero__class_Ozero(U_3470)
          | U_3471 != U_3472 )
        & ( U_3471 = U_3472
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),U_3472) != c_Groups_Ozero__class_Ozero(U_3470) ) )
      | ~ class_Groups_Ogroup__add(U_3470) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ( ! [U_3471,U_3470,U_3472] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),U_3472) = c_Groups_Ozero__class_Ozero(U_3470)
        | U_3471 != U_3472
        | ~ sP292(U_3471,U_3470,U_3472) )
    & ! [U_3471,U_3470,U_3472] :
        ( U_3471 = U_3472
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),U_3472) != c_Groups_Ozero__class_Ozero(U_3470)
        | ~ sP292(U_3471,U_3470,U_3472) )
    & ! [U_3471,U_3470,U_3472] :
        ( sP292(U_3471,U_3470,U_3472)
        | ~ class_Groups_Ogroup__add(U_3470) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_969_2]) ).

cnf(f_969_4,plain,
    ( sP292(U_3471,U_3470,U_3472)
    | ~ class_Groups_Ogroup__add(U_3470) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

cnf(f_969_5,plain,
    ( U_3471 = U_3472
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),U_3472) != c_Groups_Ozero__class_Ozero(U_3470)
    | ~ sP292(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

cnf(f_969_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),U_3472) = c_Groups_Ozero__class_Ozero(U_3470)
    | U_3471 != U_3472
    | ~ sP292(U_3471,U_3470,U_3472) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

fof(f_970_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != V_b_2 ) )
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).

fof(f_970_2,plain,
    ! [U_3475,U_3474,U_3473] :
      ( ( ( U_3474 = U_3475
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3475) != c_Groups_Ozero__class_Ozero(U_3473) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3475) = c_Groups_Ozero__class_Ozero(U_3473)
          | U_3474 != U_3475 ) )
      | ~ class_Groups_Oab__group__add(U_3473) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ( ! [U_3473,U_3474,U_3475] :
        ( U_3474 = U_3475
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3475) != c_Groups_Ozero__class_Ozero(U_3473)
        | ~ sP293(U_3473,U_3474,U_3475) )
    & ! [U_3473,U_3474,U_3475] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3475) = c_Groups_Ozero__class_Ozero(U_3473)
        | U_3474 != U_3475
        | ~ sP293(U_3473,U_3474,U_3475) )
    & ! [U_3473,U_3474,U_3475] :
        ( sP293(U_3473,U_3474,U_3475)
        | ~ class_Groups_Oab__group__add(U_3473) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_970_2]) ).

cnf(f_970_4,plain,
    ( sP293(U_3473,U_3474,U_3475)
    | ~ class_Groups_Oab__group__add(U_3473) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3475) = c_Groups_Ozero__class_Ozero(U_3473)
    | U_3474 != U_3475
    | ~ sP293(U_3473,U_3474,U_3475) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_6,plain,
    ( U_3474 = U_3475
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3475) != c_Groups_Ozero__class_Ozero(U_3473)
    | ~ sP293(U_3473,U_3474,U_3475) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__self]) ).

fof(f_971_2,plain,
    ! [U_3477,U_3476] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3476),U_3477),U_3477) = c_Groups_Ozero__class_Ozero(U_3476)
      | ~ class_Groups_Ogroup__add(U_3476) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ! [U_3477,U_3476] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3476),U_3477),U_3477) = c_Groups_Ozero__class_Ozero(U_3476)
      | ~ class_Groups_Ogroup__add(U_3476) ),
    inference(definitional_conversion,[status(esa)],[f_971_2]) ).

cnf(f_971_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3476),U_3477),U_3477) = c_Groups_Ozero__class_Ozero(U_3476)
    | ~ class_Groups_Ogroup__add(U_3476) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__0__right]) ).

fof(f_972_2,plain,
    ! [U_3479,U_3478] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3478),U_3479),c_Groups_Ozero__class_Ozero(U_3478)) = U_3479
      | ~ class_Groups_Ogroup__add(U_3478) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ! [U_3478,U_3479] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3478),U_3479),c_Groups_Ozero__class_Ozero(U_3478)) = U_3479
      | ~ class_Groups_Ogroup__add(U_3478) ),
    inference(definitional_conversion,[status(esa)],[f_972_2]) ).

cnf(f_972_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3478),U_3479),c_Groups_Ozero__class_Ozero(U_3478)) = U_3479
    | ~ class_Groups_Ogroup__add(U_3478) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).

fof(f_973_2,plain,
    ! [U_3484,U_3483,U_3482,U_3481,U_3480] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3481),U_3482))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3483),U_3484)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3483),U_3484))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3481),U_3482)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),U_3481),U_3482) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),U_3483),U_3484)
      | ~ class_Groups_Oordered__ab__group__add(U_3480) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ( ! [U_3480,U_3481,U_3482,U_3483,U_3484] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3481),U_3482))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3483),U_3484))
        | ~ sP294(U_3480,U_3481,U_3482,U_3483,U_3484) )
    & ! [U_3480,U_3481,U_3482,U_3483,U_3484] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3483),U_3484))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3481),U_3482))
        | ~ sP294(U_3480,U_3481,U_3482,U_3483,U_3484) )
    & ! [U_3480,U_3481,U_3482,U_3483,U_3484] :
        ( sP294(U_3480,U_3481,U_3482,U_3483,U_3484)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),U_3481),U_3482) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),U_3483),U_3484)
        | ~ class_Groups_Oordered__ab__group__add(U_3480) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_973_2]) ).

cnf(f_973_4,plain,
    ( sP294(U_3480,U_3481,U_3482,U_3483,U_3484)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),U_3481),U_3482) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),U_3483),U_3484)
    | ~ class_Groups_Oordered__ab__group__add(U_3480) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

cnf(f_973_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3483),U_3484))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3481),U_3482))
    | ~ sP294(U_3480,U_3481,U_3482,U_3483,U_3484) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

cnf(f_973_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3481),U_3482))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3480),U_3483),U_3484))
    | ~ sP294(U_3480,U_3481,U_3482,U_3483,U_3484) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

fof(f_974_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).

fof(f_974_2,plain,
    ! [U_3487,U_3486,U_3485] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3485),U_3486),U_3487)),U_3487) = U_3486
      | ~ class_Groups_Ogroup__add(U_3485) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ! [U_3487,U_3486,U_3485] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3485),U_3486),U_3487)),U_3487) = U_3486
      | ~ class_Groups_Ogroup__add(U_3485) ),
    inference(definitional_conversion,[status(esa)],[f_974_2]) ).

cnf(f_974_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3485),U_3486),U_3487)),U_3487) = U_3486
    | ~ class_Groups_Ogroup__add(U_3485) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

fof(f_975_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__cancel]) ).

fof(f_975_2,plain,
    ! [U_3490,U_3489,U_3488] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3488),U_3489),U_3490)),U_3490) = U_3489
      | ~ class_Groups_Ogroup__add(U_3488) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ! [U_3489,U_3488,U_3490] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3488),U_3489),U_3490)),U_3490) = U_3489
      | ~ class_Groups_Ogroup__add(U_3488) ),
    inference(definitional_conversion,[status(esa)],[f_975_2]) ).

cnf(f_975_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3488),U_3489),U_3490)),U_3490) = U_3489
    | ~ class_Groups_Ogroup__add(U_3488) ),
    inference(clausify,[status(thm)],[f_975_3]) ).

fof(f_976_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).

fof(f_976_2,plain,
    ! [U_3493,U_3492,U_3491] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3491),U_3492),U_3493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3491),U_3493),U_3492)
      | ~ class_Groups_Oab__group__add(U_3491) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_3491,U_3492,U_3493] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3491),U_3492),U_3493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3491),U_3493),U_3492)
      | ~ class_Groups_Oab__group__add(U_3491) ),
    inference(definitional_conversion,[status(esa)],[f_976_2]) ).

cnf(f_976_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3491),U_3492),U_3493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3491),U_3493),U_3492)
    | ~ class_Groups_Oab__group__add(U_3491) ),
    inference(clausify,[status(thm)],[f_976_3]) ).

fof(f_977_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq]) ).

fof(f_977_2,plain,
    ! [U_3497,U_3496,U_3495,U_3494] :
      ( c_Divides_Odiv__class_Omod(U_3494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3494),U_3495),U_3496),U_3497) = c_Divides_Odiv__class_Omod(U_3494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3494),U_3495),c_Divides_Odiv__class_Omod(U_3494,U_3496,U_3497)),U_3497)
      | ~ class_Divides_Oring__div(U_3494) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3494,U_3495,U_3496,U_3497] :
      ( c_Divides_Odiv__class_Omod(U_3494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3494),U_3495),U_3496),U_3497) = c_Divides_Odiv__class_Omod(U_3494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3494),U_3495),c_Divides_Odiv__class_Omod(U_3494,U_3496,U_3497)),U_3497)
      | ~ class_Divides_Oring__div(U_3494) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3494),U_3495),U_3496),U_3497) = c_Divides_Odiv__class_Omod(U_3494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3494),U_3495),c_Divides_Odiv__class_Omod(U_3494,U_3496,U_3497)),U_3497)
    | ~ class_Divides_Oring__div(U_3494) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq]) ).

fof(f_978_2,plain,
    ! [U_3501,U_3500,U_3499,U_3498] :
      ( c_Divides_Odiv__class_Omod(U_3498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3498),U_3499),U_3500),U_3501) = c_Divides_Odiv__class_Omod(U_3498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3498),c_Divides_Odiv__class_Omod(U_3498,U_3499,U_3501)),U_3500),U_3501)
      | ~ class_Divides_Oring__div(U_3498) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_3498,U_3499,U_3500,U_3501] :
      ( c_Divides_Odiv__class_Omod(U_3498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3498),U_3499),U_3500),U_3501) = c_Divides_Odiv__class_Omod(U_3498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3498),c_Divides_Odiv__class_Omod(U_3498,U_3499,U_3501)),U_3500),U_3501)
      | ~ class_Divides_Oring__div(U_3498) ),
    inference(definitional_conversion,[status(esa)],[f_978_2]) ).

cnf(f_978_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3498),U_3499),U_3500),U_3501) = c_Divides_Odiv__class_Omod(U_3498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3498),c_Divides_Odiv__class_Omod(U_3498,U_3499,U_3501)),U_3500),U_3501)
    | ~ class_Divides_Oring__div(U_3498) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

fof(f_979_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__eq]) ).

fof(f_979_2,plain,
    ! [U_3505,U_3504,U_3503,U_3502] :
      ( c_Divides_Odiv__class_Omod(U_3502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3502),U_3503),U_3504),U_3505) = c_Divides_Odiv__class_Omod(U_3502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3502),c_Divides_Odiv__class_Omod(U_3502,U_3503,U_3505)),c_Divides_Odiv__class_Omod(U_3502,U_3504,U_3505)),U_3505)
      | ~ class_Divides_Oring__div(U_3502) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3502,U_3503,U_3504,U_3505] :
      ( c_Divides_Odiv__class_Omod(U_3502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3502),U_3503),U_3504),U_3505) = c_Divides_Odiv__class_Omod(U_3502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3502),c_Divides_Odiv__class_Omod(U_3502,U_3503,U_3505)),c_Divides_Odiv__class_Omod(U_3502,U_3504,U_3505)),U_3505)
      | ~ class_Divides_Oring__div(U_3502) ),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3502),U_3503),U_3504),U_3505) = c_Divides_Odiv__class_Omod(U_3502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3502),c_Divides_Odiv__class_Omod(U_3502,U_3503,U_3505)),c_Divides_Odiv__class_Omod(U_3502,U_3504,U_3505)),U_3505)
    | ~ class_Divides_Oring__div(U_3502) ),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_1,plain,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__cong]) ).

fof(f_980_2,plain,
    ! [U_3511,U_3510,U_3509,U_3508,U_3507,U_3506] :
      ( c_Divides_Odiv__class_Omod(U_3506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3506),U_3507),U_3510),U_3508) = c_Divides_Odiv__class_Omod(U_3506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3506),U_3509),U_3511),U_3508)
      | c_Divides_Odiv__class_Omod(U_3506,U_3510,U_3508) != c_Divides_Odiv__class_Omod(U_3506,U_3511,U_3508)
      | c_Divides_Odiv__class_Omod(U_3506,U_3507,U_3508) != c_Divides_Odiv__class_Omod(U_3506,U_3509,U_3508)
      | ~ class_Divides_Oring__div(U_3506) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_3506,U_3507,U_3508,U_3509,U_3510,U_3511] :
      ( c_Divides_Odiv__class_Omod(U_3506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3506),U_3507),U_3510),U_3508) = c_Divides_Odiv__class_Omod(U_3506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3506),U_3509),U_3511),U_3508)
      | c_Divides_Odiv__class_Omod(U_3506,U_3510,U_3508) != c_Divides_Odiv__class_Omod(U_3506,U_3511,U_3508)
      | c_Divides_Odiv__class_Omod(U_3506,U_3507,U_3508) != c_Divides_Odiv__class_Omod(U_3506,U_3509,U_3508)
      | ~ class_Divides_Oring__div(U_3506) ),
    inference(definitional_conversion,[status(esa)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3506),U_3507),U_3510),U_3508) = c_Divides_Odiv__class_Omod(U_3506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3506),U_3509),U_3511),U_3508)
    | c_Divides_Odiv__class_Omod(U_3506,U_3510,U_3508) != c_Divides_Odiv__class_Omod(U_3506,U_3511,U_3508)
    | c_Divides_Odiv__class_Omod(U_3506,U_3507,U_3508) != c_Divides_Odiv__class_Omod(U_3506,U_3509,U_3508)
    | ~ class_Divides_Oring__div(U_3506) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal]) ).

fof(f_981_2,plain,
    ! [U_3513,U_3512] :
      ( U_3512 = U_3513
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3513),U_3512) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3512),U_3513) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3513,U_3512] :
      ( U_3512 = U_3513
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3513),U_3512) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3512),U_3513) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( U_3512 = U_3513
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3513),U_3512) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3512),U_3513) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_981_3]) ).

fof(f_982_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__self__eq__0]) ).

fof(f_982_2,plain,
    ! [U_3514] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3514),U_3514) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_3514] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3514),U_3514) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_982_2]) ).

cnf(f_982_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3514),U_3514) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_982_3]) ).

fof(f_983_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    inference(fof_nnf,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(f_983_2,plain,
    ! [U_3515] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3515,
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ! [U_3515] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3515,
    inference(definitional_conversion,[status(esa)],[f_983_2]) ).

cnf(f_983_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3515,
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__0__eq__0]) ).

fof(f_984_2,plain,
    ! [U_3516] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ! [U_3516] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_984_2]) ).

cnf(f_984_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(f_985_2,plain,
    ! [U_3518,U_3517] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3517)),hAPP(c_Nat_OSuc,U_3518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3518),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ! [U_3517,U_3518] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3517)),hAPP(c_Nat_OSuc,U_3518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3518),
    inference(definitional_conversion,[status(esa)],[f_985_2]) ).

cnf(f_985_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3517)),hAPP(c_Nat_OSuc,U_3518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3518),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__diff]) ).

fof(f_986_2,plain,
    ! [U_3521,U_3520,U_3519] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3519)),U_3520)),hAPP(c_Nat_OSuc,U_3521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3519),U_3520)),U_3521),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3519,U_3520,U_3521] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3519)),U_3520)),hAPP(c_Nat_OSuc,U_3521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3519),U_3520)),U_3521),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3519)),U_3520)),hAPP(c_Nat_OSuc,U_3521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3519),U_3520)),U_3521),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_1,plain,
    ! [V_n,V_k,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).

fof(f_987_2,plain,
    ! [U_3524,U_3523,U_3522] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3522),U_3524)),U_3523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3522),U_3523)) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_3522,U_3523,U_3524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3522),U_3524)),U_3523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3522),U_3523)) ),
    inference(definitional_conversion,[status(esa)],[f_987_2]) ).

cnf(f_987_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3522),U_3524)),U_3523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3522),U_3523)) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_1,plain,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).

fof(f_988_2,plain,
    ! [U_3527,U_3526,U_3525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3527),U_3526)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3527),U_3525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ! [U_3525,U_3526,U_3527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3527),U_3526)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3527),U_3525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ),
    inference(definitional_conversion,[status(esa)],[f_988_2]) ).

cnf(f_988_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3527),U_3526)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3527),U_3525)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_1,plain,
    ! [V_n,V_m] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__if]) ).

fof(f_989_2,plain,
    ! [U_3529,U_3528] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3528,U_3529) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3528),U_3529),U_3529)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3529)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3528,U_3529) = U_3528
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3529)) ) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ( ! [U_3533,U_3531] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3531,U_3533) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3533),U_3533)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3531),U_3533)) )
    & ! [U_3532,U_3530] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3530,U_3532) = U_3530
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3530),U_3532)) ) ),
    inference(miniscope,[status(thm)],[f_989_2]) ).

fof(f_989_4,plain,
    ( ! [U_3533,U_3531] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3531,U_3533) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3533),U_3533)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3531),U_3533)) )
    & ! [U_3530,U_3532] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3530,U_3532) = U_3530
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3530),U_3532)) ) ),
    inference(definitional_conversion,[status(esa)],[f_989_3]) ).

cnf(f_989_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3530,U_3532) = U_3530
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3530),U_3532)) ),
    inference(clausify,[status(thm)],[f_989_4]) ).

cnf(f_989_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3531,U_3533) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3533),U_3533)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3531),U_3533)) ),
    inference(clausify,[status(thm)],[f_989_4]) ).

fof(f_990_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__geq]) ).

fof(f_990_2,plain,
    ! [U_3535,U_3534] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3534,U_3535) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3534),U_3535),U_3535)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),U_3535)) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_3535,U_3534] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3534,U_3535) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3534),U_3535),U_3535)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),U_3535)) ),
    inference(definitional_conversion,[status(esa)],[f_990_2]) ).

cnf(f_990_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3534,U_3535) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3534),U_3535),U_3535)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),U_3535)) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m,
    inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).

fof(f_991_2,plain,
    ! [U_3537,U_3536] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3536),U_3537)),U_3537) = U_3536,
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3536,U_3537] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3536),U_3537)),U_3537) = U_3536,
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3536),U_3537)),U_3537) = U_3536,
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m,
    inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).

fof(f_992_2,plain,
    ! [U_3539,U_3538] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3538),U_3539)),U_3538) = U_3539,
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3538,U_3539] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3538),U_3539)),U_3538) = U_3539,
    inference(definitional_conversion,[status(esa)],[f_992_2]) ).

cnf(f_992_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3538),U_3539)),U_3538) = U_3539,
    inference(clausify,[status(thm)],[f_992_3]) ).

fof(f_993_1,plain,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).

fof(f_993_2,plain,
    ! [U_3542,U_3541,U_3540] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3540),U_3541)),U_3542) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3540),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3541),U_3542)),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3540,U_3541,U_3542] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3540),U_3541)),U_3542) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3540),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3541),U_3542)),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3540),U_3541)),U_3542) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3540),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3541),U_3542)),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).

fof(f_994_2,plain,
    ! [U_3545,U_3544,U_3543] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3544),U_3545),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3543,U_3544,U_3545] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3544),U_3545),
    inference(definitional_conversion,[status(esa)],[f_994_2]) ).

cnf(f_994_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3544),U_3545),
    inference(clausify,[status(thm)],[f_994_3]) ).

fof(f_995_1,plain,
    ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).

fof(f_995_2,plain,
    ! [U_3548,U_3547,U_3546] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3548),U_3547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3546),U_3548),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3546,U_3547,U_3548] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3548),U_3547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3546),U_3548),
    inference(definitional_conversion,[status(esa)],[f_995_2]) ).

cnf(f_995_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3548),U_3547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3546),U_3548),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).

fof(f_996_2,plain,
    ! [U_3551,U_3550,U_3549] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3550),U_3549)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3551),U_3549)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3550),U_3549)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3551),U_3549))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3549),U_3551))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3549),U_3550)) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ( ! [U_3549,U_3550,U_3551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3550),U_3549)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3551),U_3549)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551))
        | ~ sP295(U_3549,U_3550,U_3551) )
    & ! [U_3549,U_3550,U_3551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3550),U_3549)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3551),U_3549)))
        | ~ sP295(U_3549,U_3550,U_3551) )
    & ! [U_3549,U_3550,U_3551] :
        ( sP295(U_3549,U_3550,U_3551)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3549),U_3551))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3549),U_3550)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_996_2]) ).

cnf(f_996_4,plain,
    ( sP295(U_3549,U_3550,U_3551)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3549),U_3551))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3549),U_3550)) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

cnf(f_996_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3550),U_3549)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3551),U_3549)))
    | ~ sP295(U_3549,U_3550,U_3551) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

cnf(f_996_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3550),U_3549)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3551),U_3549)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551))
    | ~ sP295(U_3549,U_3550,U_3551) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_1,plain,
    ! [V_n,V_m,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).

fof(f_997_2,plain,
    ! [U_3554,U_3553,U_3552] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3554)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3553)) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

fof(f_997_3,plain,
    ! [U_3554,U_3552,U_3553] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3554)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3553)) ),
    inference(definitional_conversion,[status(esa)],[f_997_2]) ).

cnf(f_997_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3554)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3553)) ),
    inference(clausify,[status(thm)],[f_997_3]) ).

fof(f_998_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).

fof(f_998_2,plain,
    ! [U_3557,U_3556,U_3555] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)
          | U_3556 != U_3557 )
        & ( U_3556 = U_3557
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3556)) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ( ! [U_3555,U_3556,U_3557] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)
        | U_3556 != U_3557
        | ~ sP296(U_3555,U_3556,U_3557) )
    & ! [U_3555,U_3556,U_3557] :
        ( U_3556 = U_3557
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)
        | ~ sP296(U_3555,U_3556,U_3557) )
    & ! [U_3555,U_3556,U_3557] :
        ( sP296(U_3555,U_3556,U_3557)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3557))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3556)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296])],[f_998_2]) ).

cnf(f_998_4,plain,
    ( sP296(U_3555,U_3556,U_3557)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3557))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3556)) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

cnf(f_998_5,plain,
    ( U_3556 = U_3557
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)
    | ~ sP296(U_3555,U_3556,U_3557) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

cnf(f_998_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)
    | U_3556 != U_3557
    | ~ sP296(U_3555,U_3556,U_3557) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_1,plain,
    ! [V_n,V_i] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).

fof(f_999_2,plain,
    ! [U_3559,U_3558] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558)) = U_3558
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3559)) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_3559,U_3558] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558)) = U_3558
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3559)) ),
    inference(definitional_conversion,[status(esa)],[f_999_2]) ).

cnf(f_999_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558)) = U_3558
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3559)) ),
    inference(clausify,[status(thm)],[f_999_3]) ).

fof(f_1000_1,plain,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).

fof(f_1000_2,plain,
    ! [U_3562,U_3561,U_3560] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3562)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3561),U_3562)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3560),U_3561)) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

fof(f_1000_3,plain,
    ! [U_3560,U_3561,U_3562] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3562)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3561),U_3562)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3560),U_3561)) ),
    inference(definitional_conversion,[status(esa)],[f_1000_2]) ).

cnf(f_1000_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3562)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3561),U_3562)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3560),U_3561)) ),
    inference(clausify,[status(thm)],[f_1000_3]) ).

fof(f_1001_1,plain,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).

fof(f_1001_2,plain,
    ! [U_3565,U_3564,U_3563] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3565),U_3564)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3565),U_3563)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3563),U_3564)) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ! [U_3563,U_3564,U_3565] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3565),U_3564)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3565),U_3563)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3563),U_3564)) ),
    inference(definitional_conversion,[status(esa)],[f_1001_2]) ).

cnf(f_1001_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3565),U_3564)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3565),U_3563)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3563),U_3564)) ),
    inference(clausify,[status(thm)],[f_1001_3]) ).

fof(f_1002_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)),
    inference(fof_nnf,[status(thm)],[fact_diff__le__self]) ).

fof(f_1002_2,plain,
    ! [U_3567,U_3566] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3566),U_3567)),U_3566)),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ! [U_3566,U_3567] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3566),U_3567)),U_3566)),
    inference(definitional_conversion,[status(esa)],[f_1002_2]) ).

cnf(f_1002_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3566),U_3567)),U_3566)),
    inference(clausify,[status(thm)],[f_1002_3]) ).

fof(f_1003_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_le__mod__geq]) ).

fof(f_1003_2,plain,
    ! [U_3569,U_3568] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3569,U_3568) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3569),U_3568),U_3568)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3568),U_3569)) ),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ! [U_3568,U_3569] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3569,U_3568) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3569),U_3568),U_3568)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3568),U_3569)) ),
    inference(definitional_conversion,[status(esa)],[f_1003_2]) ).

cnf(f_1003_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3569,U_3568) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3569),U_3568),U_3568)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3568),U_3569)) ),
    inference(clausify,[status(thm)],[f_1003_3]) ).

fof(f_1004_1,plain,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(f_1004_2,plain,
    ! [U_3572,U_3571,U_3570] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3571),U_3572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),U_3572)),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

fof(f_1004_3,plain,
    ! [U_3570,U_3571,U_3572] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3571),U_3572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),U_3572)),
    inference(definitional_conversion,[status(esa)],[f_1004_2]) ).

cnf(f_1004_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3571),U_3572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3570),U_3572)),
    inference(clausify,[status(thm)],[f_1004_3]) ).

fof(f_1005_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib]) ).

fof(f_1005_2,plain,
    ! [U_3575,U_3574,U_3573] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3573),U_3574)),U_3575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3575)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3574),U_3575)),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

fof(f_1005_3,plain,
    ! [U_3573,U_3574,U_3575] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3573),U_3574)),U_3575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3575)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3574),U_3575)),
    inference(definitional_conversion,[status(esa)],[f_1005_2]) ).

cnf(f_1005_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3573),U_3574)),U_3575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3575)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3574),U_3575)),
    inference(clausify,[status(thm)],[f_1005_3]) ).

fof(f_1006_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib]) ).

fof(f_1006_2,plain,
    ! [U_3578,U_3577,U_3576] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3576),U_3577)),U_3578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3576),U_3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3577),U_3578)),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

fof(f_1006_3,plain,
    ! [U_3576,U_3577,U_3578] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3576),U_3577)),U_3578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3576),U_3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3577),U_3578)),
    inference(definitional_conversion,[status(esa)],[f_1006_2]) ).

cnf(f_1006_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3576),U_3577)),U_3578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3576),U_3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3577),U_3578)),
    inference(clausify,[status(thm)],[f_1006_3]) ).

fof(f_1007_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(f_1007_2,plain,
    ! [U_3581,U_3580,U_3579] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3580),U_3581)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3580)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3581)),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

fof(f_1007_3,plain,
    ! [U_3579,U_3580,U_3581] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3580),U_3581)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3580)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3581)),
    inference(definitional_conversion,[status(esa)],[f_1007_2]) ).

cnf(f_1007_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3580),U_3581)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3580)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3581)),
    inference(clausify,[status(thm)],[f_1007_3]) ).

fof(f_1008_1,plain,
    ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmod__right]) ).

fof(f_1008_2,plain,
    ! [U_3584,U_3583,U_3582] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3582),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3583,U_3584)),U_3584) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3582),U_3583),U_3584),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

fof(f_1008_3,plain,
    ! [U_3582,U_3583,U_3584] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3582),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3583,U_3584)),U_3584) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3582),U_3583),U_3584),
    inference(definitional_conversion,[status(esa)],[f_1008_2]) ).

cnf(f_1008_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3582),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3583,U_3584)),U_3584) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3582),U_3583),U_3584),
    inference(clausify,[status(thm)],[f_1008_3]) ).

fof(f_1009_1,plain,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmod__left]) ).

fof(f_1009_2,plain,
    ! [U_3587,U_3586,U_3585] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3585,U_3586)),U_3587),U_3586) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),U_3587),U_3586),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

fof(f_1009_3,plain,
    ! [U_3585,U_3586,U_3587] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3585,U_3586)),U_3587),U_3586) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),U_3587),U_3586),
    inference(definitional_conversion,[status(esa)],[f_1009_2]) ).

cnf(f_1009_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3585,U_3586)),U_3587),U_3586) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),U_3587),U_3586),
    inference(clausify,[status(thm)],[f_1009_3]) ).

fof(f_1010_1,plain,
    ! [V_z,V_z_H] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib]) ).

fof(f_1010_2,plain,
    ! [U_3589,U_3588] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3589),U_3588)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3589)),hAPP(c_Int_Onat,U_3588))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3588),U_3589))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3588)) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

fof(f_1010_3,plain,
    ! [U_3588,U_3589] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3589),U_3588)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3589)),hAPP(c_Int_Onat,U_3588))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3588),U_3589))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3588)) ),
    inference(definitional_conversion,[status(esa)],[f_1010_2]) ).

cnf(f_1010_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3589),U_3588)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3589)),hAPP(c_Int_Onat,U_3588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3588),U_3589))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3588)) ),
    inference(clausify,[status(thm)],[f_1010_3]) ).

fof(f_1011_1,plain,
    ! [V_y_2,V_x_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
          & ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiff__int__split]) ).

fof(f_1011_2,plain,
    ! [U_3592,U_3591,U_3590] :
      ( ( hBOOL(hAPP(U_3590,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3591),U_3592))))
        | ( ~ hBOOL(hAPP(U_3590,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3591),U_3592)) )
        | ( ~ hBOOL(hAPP(U_3590,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3591)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3592))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3592),U_3591)) ) )
      & ( ( ( hBOOL(hAPP(U_3590,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3591),U_3592)) )
          & ( hBOOL(hAPP(U_3590,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3591)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3592))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3592),U_3591)) ) )
        | ~ hBOOL(hAPP(U_3590,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3591),U_3592)))) ) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ( ! [U_3598,U_3596,U_3594] :
        ( hBOOL(hAPP(U_3594,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3598))))
        | ( ~ hBOOL(hAPP(U_3594,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3596),U_3598)) )
        | ( ~ hBOOL(hAPP(U_3594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3596)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3598))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3598),U_3596)) ) )
    & ! [U_3597,U_3595,U_3593] :
        ( ( ( hBOOL(hAPP(U_3593,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3595),U_3597)) )
          & ( hBOOL(hAPP(U_3593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3595)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3597))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3597),U_3595)) ) )
        | ~ hBOOL(hAPP(U_3593,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3595),U_3597)))) ) ),
    inference(miniscope,[status(thm)],[f_1011_2]) ).

fof(f_1011_4,plain,
    ( ! [U_3594,U_3598,U_3596] :
        ( ~ hBOOL(hAPP(U_3594,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP299(U_3594,U_3598,U_3596) )
    & ! [U_3594,U_3598,U_3596] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3596),U_3598))
        | ~ sP299(U_3594,U_3598,U_3596) )
    & ! [U_3594,U_3598,U_3596] :
        ( ~ hBOOL(hAPP(U_3594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3596)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3598))))
        | ~ sP298(U_3594,U_3598,U_3596) )
    & ! [U_3594,U_3598,U_3596] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3598),U_3596))
        | ~ sP298(U_3594,U_3598,U_3596) )
    & ! [U_3593,U_3595,U_3597] :
        ( hBOOL(hAPP(U_3593,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3595),U_3597))
        | ~ sP297(U_3593,U_3595,U_3597) )
    & ! [U_3593,U_3595,U_3597] :
        ( hBOOL(hAPP(U_3593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3595)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3597))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3597),U_3595))
        | ~ sP297(U_3593,U_3595,U_3597) )
    & ! [U_3594,U_3598,U_3596] :
        ( hBOOL(hAPP(U_3594,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3598))))
        | sP299(U_3594,U_3598,U_3596)
        | sP298(U_3594,U_3598,U_3596) )
    & ! [U_3593,U_3595,U_3597] :
        ( sP297(U_3593,U_3595,U_3597)
        | ~ hBOOL(hAPP(U_3593,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3595),U_3597)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297,sP298,sP299])],[f_1011_3]) ).

cnf(f_1011_5,plain,
    ( sP297(U_3593,U_3595,U_3597)
    | ~ hBOOL(hAPP(U_3593,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3595),U_3597)))) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_6,plain,
    ( hBOOL(hAPP(U_3594,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3598))))
    | sP299(U_3594,U_3598,U_3596)
    | sP298(U_3594,U_3598,U_3596) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_7,plain,
    ( hBOOL(hAPP(U_3593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3595)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3597))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3597),U_3595))
    | ~ sP297(U_3593,U_3595,U_3597) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_8,plain,
    ( hBOOL(hAPP(U_3593,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3595),U_3597))
    | ~ sP297(U_3593,U_3595,U_3597) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3598),U_3596))
    | ~ sP298(U_3594,U_3598,U_3596) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_10,plain,
    ( ~ hBOOL(hAPP(U_3594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3596)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3598))))
    | ~ sP298(U_3594,U_3598,U_3596) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3596),U_3598))
    | ~ sP299(U_3594,U_3598,U_3596) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_12,plain,
    ( ~ hBOOL(hAPP(U_3594,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP299(U_3594,U_3598,U_3596) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

fof(f_1012_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).

fof(f_1012_2,plain,
    ! [U_3601,U_3600,U_3599] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3600),U_3601))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3599),U_3600),U_3601)),c_Groups_Ozero__class_Ozero(U_3599))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3599),U_3600),U_3601)),c_Groups_Ozero__class_Ozero(U_3599)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3600),U_3601)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3599) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

fof(f_1012_3,plain,
    ( ! [U_3600,U_3599,U_3601] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3600),U_3601))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3599),U_3600),U_3601)),c_Groups_Ozero__class_Ozero(U_3599)))
        | ~ sP300(U_3600,U_3599,U_3601) )
    & ! [U_3600,U_3599,U_3601] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3599),U_3600),U_3601)),c_Groups_Ozero__class_Ozero(U_3599)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3600),U_3601))
        | ~ sP300(U_3600,U_3599,U_3601) )
    & ! [U_3600,U_3599,U_3601] :
        ( sP300(U_3600,U_3599,U_3601)
        | ~ class_Groups_Oordered__ab__group__add(U_3599) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300])],[f_1012_2]) ).

cnf(f_1012_4,plain,
    ( sP300(U_3600,U_3599,U_3601)
    | ~ class_Groups_Oordered__ab__group__add(U_3599) ),
    inference(clausify,[status(thm)],[f_1012_3]) ).

cnf(f_1012_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3599),U_3600),U_3601)),c_Groups_Ozero__class_Ozero(U_3599)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3600),U_3601))
    | ~ sP300(U_3600,U_3599,U_3601) ),
    inference(clausify,[status(thm)],[f_1012_3]) ).

cnf(f_1012_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3600),U_3601))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3599),U_3600),U_3601)),c_Groups_Ozero__class_Ozero(U_3599)))
    | ~ sP300(U_3600,U_3599,U_3601) ),
    inference(clausify,[status(thm)],[f_1012_3]) ).

fof(f_1013_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).

fof(f_1013_2,plain,
    ! [U_3604,U_3603,U_3602] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),U_3603),U_3604))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3602),U_3603),U_3604)),c_Groups_Ozero__class_Ozero(U_3602))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3602),U_3603),U_3604)),c_Groups_Ozero__class_Ozero(U_3602)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),U_3603),U_3604)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3602) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ( ! [U_3602,U_3603,U_3604] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),U_3603),U_3604))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3602),U_3603),U_3604)),c_Groups_Ozero__class_Ozero(U_3602)))
        | ~ sP301(U_3602,U_3603,U_3604) )
    & ! [U_3602,U_3603,U_3604] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3602),U_3603),U_3604)),c_Groups_Ozero__class_Ozero(U_3602)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),U_3603),U_3604))
        | ~ sP301(U_3602,U_3603,U_3604) )
    & ! [U_3602,U_3603,U_3604] :
        ( sP301(U_3602,U_3603,U_3604)
        | ~ class_Groups_Oordered__ab__group__add(U_3602) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP301])],[f_1013_2]) ).

cnf(f_1013_4,plain,
    ( sP301(U_3602,U_3603,U_3604)
    | ~ class_Groups_Oordered__ab__group__add(U_3602) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3602),U_3603),U_3604)),c_Groups_Ozero__class_Ozero(U_3602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),U_3603),U_3604))
    | ~ sP301(U_3602,U_3603,U_3604) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),U_3603),U_3604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3602),U_3603),U_3604)),c_Groups_Ozero__class_Ozero(U_3602)))
    | ~ sP301(U_3602,U_3603,U_3604) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

fof(f_1014_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
          | V_c_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) )
        & ( V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
      | ~ class_Rings_Oring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).

fof(f_1014_2,plain,
    ! [U_3610,U_3609,U_3608,U_3607,U_3606,U_3605] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3606),U_3607)),U_3608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3609),U_3607)),U_3610)
          | U_3608 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3605),U_3609),U_3606)),U_3607)),U_3610) )
        & ( U_3608 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3605),U_3609),U_3606)),U_3607)),U_3610)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3606),U_3607)),U_3608) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3609),U_3607)),U_3610) ) )
      | ~ class_Rings_Oring(U_3605) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ( ! [U_3605,U_3606,U_3607,U_3608,U_3609,U_3610] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3606),U_3607)),U_3608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3609),U_3607)),U_3610)
        | U_3608 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3605),U_3609),U_3606)),U_3607)),U_3610)
        | ~ sP302(U_3605,U_3606,U_3607,U_3608,U_3609,U_3610) )
    & ! [U_3605,U_3606,U_3607,U_3608,U_3609,U_3610] :
        ( U_3608 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3605),U_3609),U_3606)),U_3607)),U_3610)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3606),U_3607)),U_3608) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3609),U_3607)),U_3610)
        | ~ sP302(U_3605,U_3606,U_3607,U_3608,U_3609,U_3610) )
    & ! [U_3605,U_3606,U_3607,U_3608,U_3609,U_3610] :
        ( sP302(U_3605,U_3606,U_3607,U_3608,U_3609,U_3610)
        | ~ class_Rings_Oring(U_3605) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_1014_2]) ).

cnf(f_1014_4,plain,
    ( sP302(U_3605,U_3606,U_3607,U_3608,U_3609,U_3610)
    | ~ class_Rings_Oring(U_3605) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

cnf(f_1014_5,plain,
    ( U_3608 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3605),U_3609),U_3606)),U_3607)),U_3610)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3606),U_3607)),U_3608) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3609),U_3607)),U_3610)
    | ~ sP302(U_3605,U_3606,U_3607,U_3608,U_3609,U_3610) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

cnf(f_1014_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3606),U_3607)),U_3608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),U_3609),U_3607)),U_3610)
    | U_3608 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3605),U_3609),U_3606)),U_3607)),U_3610)
    | ~ sP302(U_3605,U_3606,U_3607,U_3608,U_3609,U_3610) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

fof(f_1015_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) != V_d_2 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
      | ~ class_Rings_Oring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).

fof(f_1015_2,plain,
    ! [U_3616,U_3615,U_3614,U_3613,U_3612,U_3611] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3615),U_3613)),U_3616)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3615)),U_3613)),U_3614) != U_3616 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3615)),U_3613)),U_3614) = U_3616
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3615),U_3613)),U_3616) ) )
      | ~ class_Rings_Oring(U_3611) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ( ! [U_3612,U_3611,U_3613,U_3614,U_3615,U_3616] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3615),U_3613)),U_3616)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3615)),U_3613)),U_3614) != U_3616
        | ~ sP303(U_3612,U_3611,U_3613,U_3614,U_3615,U_3616) )
    & ! [U_3612,U_3611,U_3613,U_3614,U_3615,U_3616] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3615)),U_3613)),U_3614) = U_3616
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3615),U_3613)),U_3616)
        | ~ sP303(U_3612,U_3611,U_3613,U_3614,U_3615,U_3616) )
    & ! [U_3612,U_3611,U_3613,U_3614,U_3615,U_3616] :
        ( sP303(U_3612,U_3611,U_3613,U_3614,U_3615,U_3616)
        | ~ class_Rings_Oring(U_3611) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_1015_2]) ).

cnf(f_1015_4,plain,
    ( sP303(U_3612,U_3611,U_3613,U_3614,U_3615,U_3616)
    | ~ class_Rings_Oring(U_3611) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

cnf(f_1015_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3615)),U_3613)),U_3614) = U_3616
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3615),U_3613)),U_3616)
    | ~ sP303(U_3612,U_3611,U_3613,U_3614,U_3615,U_3616) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

cnf(f_1015_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),U_3615),U_3613)),U_3616)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3615)),U_3613)),U_3614) != U_3616
    | ~ sP303(U_3612,U_3611,U_3613,U_3614,U_3615,U_3616) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

fof(f_1016_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__0]) ).

fof(f_1016_2,plain,
    ! [U_3618,U_3617] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3617),c_Groups_Ozero__class_Ozero(U_3617)),U_3618) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3617),U_3618)
      | ~ class_Groups_Ogroup__add(U_3617) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ! [U_3617,U_3618] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3617),c_Groups_Ozero__class_Ozero(U_3617)),U_3618) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3617),U_3618)
      | ~ class_Groups_Ogroup__add(U_3617) ),
    inference(definitional_conversion,[status(esa)],[f_1016_2]) ).

cnf(f_1016_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3617),c_Groups_Ozero__class_Ozero(U_3617)),U_3618) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3617),U_3618)
    | ~ class_Groups_Ogroup__add(U_3617) ),
    inference(clausify,[status(thm)],[f_1016_3]) ).

fof(f_1017_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).

fof(f_1017_2,plain,
    ! [U_3621,U_3620,U_3619] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3619),U_3620),hAPP(c_Groups_Ouminus__class_Ouminus(U_3619),U_3621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3619),U_3620),U_3621)
      | ~ class_Groups_Ogroup__add(U_3619) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

fof(f_1017_3,plain,
    ! [U_3619,U_3620,U_3621] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3619),U_3620),hAPP(c_Groups_Ouminus__class_Ouminus(U_3619),U_3621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3619),U_3620),U_3621)
      | ~ class_Groups_Ogroup__add(U_3619) ),
    inference(definitional_conversion,[status(esa)],[f_1017_2]) ).

cnf(f_1017_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3619),U_3620),hAPP(c_Groups_Ouminus__class_Ouminus(U_3619),U_3621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3619),U_3620),U_3621)
    | ~ class_Groups_Ogroup__add(U_3619) ),
    inference(clausify,[status(thm)],[f_1017_3]) ).

fof(f_1018_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).

fof(f_1018_2,plain,
    ! [U_3624,U_3623,U_3622] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3622),U_3623),U_3624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3623),hAPP(c_Groups_Ouminus__class_Ouminus(U_3622),U_3624))
      | ~ class_Groups_Oab__group__add(U_3622) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ! [U_3622,U_3623,U_3624] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3622),U_3623),U_3624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3623),hAPP(c_Groups_Ouminus__class_Ouminus(U_3622),U_3624))
      | ~ class_Groups_Oab__group__add(U_3622) ),
    inference(definitional_conversion,[status(esa)],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3622),U_3623),U_3624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3623),hAPP(c_Groups_Ouminus__class_Ouminus(U_3622),U_3624))
    | ~ class_Groups_Oab__group__add(U_3622) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

fof(f_1019_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__def]) ).

fof(f_1019_2,plain,
    ! [U_3627,U_3626,U_3625] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3625),U_3626),U_3627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3625),U_3626),hAPP(c_Groups_Ouminus__class_Ouminus(U_3625),U_3627))
      | ~ class_Groups_Ogroup__add(U_3625) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ! [U_3625,U_3626,U_3627] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3625),U_3626),U_3627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3625),U_3626),hAPP(c_Groups_Ouminus__class_Ouminus(U_3625),U_3627))
      | ~ class_Groups_Ogroup__add(U_3625) ),
    inference(definitional_conversion,[status(esa)],[f_1019_2]) ).

cnf(f_1019_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3625),U_3626),U_3627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3625),U_3626),hAPP(c_Groups_Ouminus__class_Ouminus(U_3625),U_3627))
    | ~ class_Groups_Ogroup__add(U_3625) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

fof(f_1020_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).

fof(f_1020_2,plain,
    ! [U_3630,U_3629,U_3628] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3628),U_3629),U_3630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),U_3629),hAPP(c_Groups_Ouminus__class_Ouminus(U_3628),U_3630))
      | ~ class_Rings_Ocomm__ring__1(U_3628) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

fof(f_1020_3,plain,
    ! [U_3628,U_3629,U_3630] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3628),U_3629),U_3630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),U_3629),hAPP(c_Groups_Ouminus__class_Ouminus(U_3628),U_3630))
      | ~ class_Rings_Ocomm__ring__1(U_3628) ),
    inference(definitional_conversion,[status(esa)],[f_1020_2]) ).

cnf(f_1020_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3628),U_3629),U_3630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),U_3629),hAPP(c_Groups_Ouminus__class_Ouminus(U_3628),U_3630))
    | ~ class_Rings_Ocomm__ring__1(U_3628) ),
    inference(clausify,[status(thm)],[f_1020_3]) ).

fof(f_1021_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).

fof(f_1021_2,plain,
    ! [U_3632,U_3631] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3631),U_3632))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3631),U_3632)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3631),U_3632)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3631),U_3632)) ) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

fof(f_1021_3,plain,
    ( ! [U_3636,U_3634] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3634),U_3636))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3634),U_3636)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_3635,U_3633] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3633),U_3635)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3633),U_3635)) ) ),
    inference(miniscope,[status(thm)],[f_1021_2]) ).

fof(f_1021_4,plain,
    ( ! [U_3634,U_3636] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3634),U_3636))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3634),U_3636)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_3635,U_3633] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3633),U_3635)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3633),U_3635)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1021_3]) ).

cnf(f_1021_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3633),U_3635)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3633),U_3635)) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

cnf(f_1021_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3634),U_3636))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3634),U_3636)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

fof(f_1022_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less]) ).

fof(f_1022_2,plain,
    ! [U_3638,U_3637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3638),U_3637)),U_3638))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3638))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3637)) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

fof(f_1022_3,plain,
    ! [U_3638,U_3637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3638),U_3637)),U_3638))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3638))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3637)) ),
    inference(definitional_conversion,[status(esa)],[f_1022_2]) ).

cnf(f_1022_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3638),U_3637)),U_3638))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3638))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3637)) ),
    inference(clausify,[status(thm)],[f_1022_3]) ).

fof(f_1023_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).

fof(f_1023_2,plain,
    ! [U_3640,U_3639] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3639),U_3640)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3640),U_3639)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3640),U_3639))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3639),U_3640))) ) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

fof(f_1023_3,plain,
    ( ! [U_3644,U_3642] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3642),U_3644)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3644),U_3642)) )
    & ! [U_3643,U_3641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3643),U_3641))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3641),U_3643))) ) ),
    inference(miniscope,[status(thm)],[f_1023_2]) ).

fof(f_1023_4,plain,
    ( ! [U_3642,U_3644] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3642),U_3644)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3644),U_3642)) )
    & ! [U_3643,U_3641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3643),U_3641))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3641),U_3643))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1023_3]) ).

cnf(f_1023_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3643),U_3641))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3641),U_3643))) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

cnf(f_1023_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3642),U_3644)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3644),U_3642)) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

fof(f_1024_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))),
    inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).

fof(f_1024_2,plain,
    ! [U_3646,U_3645] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3646)),hAPP(c_Nat_OSuc,U_3645))),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ! [U_3645,U_3646] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3646)),hAPP(c_Nat_OSuc,U_3645))),
    inference(definitional_conversion,[status(esa)],[f_1024_2]) ).

cnf(f_1024_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3646)),hAPP(c_Nat_OSuc,U_3645))),
    inference(clausify,[status(thm)],[f_1024_3]) ).

fof(f_1025_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).

fof(f_1025_2,plain,
    ! [U_3648,U_3647] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3647),U_3648)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

fof(f_1025_3,plain,
    ! [U_3647,U_3648] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3647),U_3648)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1025_2]) ).

cnf(f_1025_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3647),U_3648)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1025_3]) ).

fof(f_1026_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).

fof(f_1026_2,plain,
    ! [U_3650,U_3649] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3649),U_3650) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3649),U_3650)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3649),U_3650))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3649),U_3650) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

fof(f_1026_3,plain,
    ( ! [U_3654,U_3652] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3652),U_3654) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3654)) )
    & ! [U_3653,U_3651] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3651),U_3653))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3651),U_3653) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1026_2]) ).

fof(f_1026_4,plain,
    ( ! [U_3652,U_3654] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3652),U_3654) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3654)) )
    & ! [U_3651,U_3653] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3651),U_3653))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3651),U_3653) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1026_3]) ).

cnf(f_1026_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3651),U_3653))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3651),U_3653) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

cnf(f_1026_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3652),U_3654) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3654)) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

fof(f_1027_1,plain,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).

fof(f_1027_2,plain,
    ! [U_3656,U_3655] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3655),U_3656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3655),U_3656)) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

fof(f_1027_3,plain,
    ! [U_3655,U_3656] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3655),U_3656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3655),U_3656)) ),
    inference(definitional_conversion,[status(esa)],[f_1027_2]) ).

cnf(f_1027_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3655),U_3656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3655),U_3656)) ),
    inference(clausify,[status(thm)],[f_1027_3]) ).

fof(f_1028_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).

fof(f_1028_2,plain,
    ! [U_3659,U_3658,U_3657] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3657),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3658),U_3659)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3657),U_3659)),U_3658)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3657),U_3659)),U_3658))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3657),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3658),U_3659))) ) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

fof(f_1028_3,plain,
    ( ! [U_3665,U_3663,U_3661] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3663),U_3665)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3661),U_3665)),U_3663)) )
    & ! [U_3664,U_3662,U_3660] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3660),U_3664)),U_3662))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3662),U_3664))) ) ),
    inference(miniscope,[status(thm)],[f_1028_2]) ).

fof(f_1028_4,plain,
    ( ! [U_3661,U_3663,U_3665] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3663),U_3665)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3661),U_3665)),U_3663)) )
    & ! [U_3664,U_3662,U_3660] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3660),U_3664)),U_3662))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3662),U_3664))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1028_3]) ).

cnf(f_1028_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3660),U_3664)),U_3662))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3662),U_3664))) ),
    inference(clausify,[status(thm)],[f_1028_4]) ).

cnf(f_1028_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3663),U_3665)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3661),U_3665)),U_3663)) ),
    inference(clausify,[status(thm)],[f_1028_4]) ).

fof(f_1029_1,plain,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).

fof(f_1029_2,plain,
    ! [U_3667,U_3666] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3667),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3666),U_3667)) = U_3666
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3666),U_3667)) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

fof(f_1029_3,plain,
    ! [U_3667,U_3666] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3667),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3666),U_3667)) = U_3666
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3666),U_3667)) ),
    inference(definitional_conversion,[status(esa)],[f_1029_2]) ).

cnf(f_1029_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3667),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3666),U_3667)) = U_3666
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3666),U_3667)) ),
    inference(clausify,[status(thm)],[f_1029_3]) ).

fof(f_1030_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).

fof(f_1030_2,plain,
    ! [U_3669,U_3668] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3669)),U_3668) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3669),U_3668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3668),U_3669)) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

fof(f_1030_3,plain,
    ! [U_3668,U_3669] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3669)),U_3668) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3669),U_3668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3668),U_3669)) ),
    inference(definitional_conversion,[status(esa)],[f_1030_2]) ).

cnf(f_1030_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3669)),U_3668) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3669),U_3668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3668),U_3669)) ),
    inference(clausify,[status(thm)],[f_1030_3]) ).

fof(f_1031_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).

fof(f_1031_2,plain,
    ! [U_3672,U_3671,U_3670] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3671),U_3670)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3672),U_3670)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3672)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3672))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3671),U_3670)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3672),U_3670))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3670),U_3672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3670),U_3671)) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

fof(f_1031_3,plain,
    ( ! [U_3670,U_3671,U_3672] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3671),U_3670)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3672),U_3670)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3672))
        | ~ sP304(U_3670,U_3671,U_3672) )
    & ! [U_3670,U_3671,U_3672] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3672))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3671),U_3670)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3672),U_3670)))
        | ~ sP304(U_3670,U_3671,U_3672) )
    & ! [U_3670,U_3671,U_3672] :
        ( sP304(U_3670,U_3671,U_3672)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3670),U_3672))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3670),U_3671)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304])],[f_1031_2]) ).

cnf(f_1031_4,plain,
    ( sP304(U_3670,U_3671,U_3672)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3670),U_3672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3670),U_3671)) ),
    inference(clausify,[status(thm)],[f_1031_3]) ).

cnf(f_1031_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3671),U_3670)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3672),U_3670)))
    | ~ sP304(U_3670,U_3671,U_3672) ),
    inference(clausify,[status(thm)],[f_1031_3]) ).

cnf(f_1031_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3671),U_3670)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3672),U_3670)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3672))
    | ~ sP304(U_3670,U_3671,U_3672) ),
    inference(clausify,[status(thm)],[f_1031_3]) ).

fof(f_1032_1,plain,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).

fof(f_1032_2,plain,
    ! [U_3675,U_3674,U_3673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3675)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3674),U_3675)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3675),U_3673))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3673),U_3674)) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

fof(f_1032_3,plain,
    ! [U_3675,U_3674,U_3673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3675)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3674),U_3675)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3675),U_3673))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3673),U_3674)) ),
    inference(definitional_conversion,[status(esa)],[f_1032_2]) ).

cnf(f_1032_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3675)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3674),U_3675)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3675),U_3673))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3673),U_3674)) ),
    inference(clausify,[status(thm)],[f_1032_3]) ).

fof(f_1033_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).

fof(f_1033_2,plain,
    ! [U_3678,U_3677,U_3676] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),U_3678)),U_3676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3677),U_3676)),U_3678)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3676),U_3677)) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

fof(f_1033_3,plain,
    ! [U_3676,U_3677,U_3678] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),U_3678)),U_3676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3677),U_3676)),U_3678)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3676),U_3677)) ),
    inference(definitional_conversion,[status(esa)],[f_1033_2]) ).

cnf(f_1033_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),U_3678)),U_3676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3677),U_3676)),U_3678)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3676),U_3677)) ),
    inference(clausify,[status(thm)],[f_1033_3]) ).

fof(f_1034_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).

fof(f_1034_2,plain,
    ! [U_3681,U_3680,U_3679] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3680),U_3679)),U_3681) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3680),U_3681)),U_3679)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),U_3680)) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

fof(f_1034_3,plain,
    ! [U_3679,U_3680,U_3681] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3680),U_3679)),U_3681) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3680),U_3681)),U_3679)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),U_3680)) ),
    inference(definitional_conversion,[status(esa)],[f_1034_2]) ).

cnf(f_1034_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3680),U_3679)),U_3681) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3680),U_3681)),U_3679)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3679),U_3680)) ),
    inference(clausify,[status(thm)],[f_1034_3]) ).

fof(f_1035_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).

fof(f_1035_2,plain,
    ! [U_3684,U_3683,U_3682] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3683)),U_3682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

fof(f_1035_3,plain,
    ! [U_3682,U_3683,U_3684] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3683)),U_3682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) ),
    inference(definitional_conversion,[status(esa)],[f_1035_2]) ).

cnf(f_1035_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),U_3683)),U_3682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3684),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3683),U_3682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) ),
    inference(clausify,[status(thm)],[f_1035_3]) ).

fof(f_1036_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
          | V_j_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) )
        & ( V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) != V_k_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).

fof(f_1036_2,plain,
    ! [U_3687,U_3686,U_3685] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3686),U_3685) = U_3687
          | U_3686 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3687),U_3685) )
        & ( U_3686 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3687),U_3685)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3686),U_3685) != U_3687 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3685),U_3686)) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

fof(f_1036_3,plain,
    ( ! [U_3685,U_3686,U_3687] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3686),U_3685) = U_3687
        | U_3686 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3687),U_3685)
        | ~ sP305(U_3685,U_3686,U_3687) )
    & ! [U_3685,U_3686,U_3687] :
        ( U_3686 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3687),U_3685)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3686),U_3685) != U_3687
        | ~ sP305(U_3685,U_3686,U_3687) )
    & ! [U_3685,U_3686,U_3687] :
        ( sP305(U_3685,U_3686,U_3687)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3685),U_3686)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP305])],[f_1036_2]) ).

cnf(f_1036_4,plain,
    ( sP305(U_3685,U_3686,U_3687)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3685),U_3686)) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

cnf(f_1036_5,plain,
    ( U_3686 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3687),U_3685)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3686),U_3685) != U_3687
    | ~ sP305(U_3685,U_3686,U_3687) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

cnf(f_1036_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3686),U_3685) = U_3687
    | U_3686 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3687),U_3685)
    | ~ sP305(U_3685,U_3686,U_3687) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

fof(f_1037_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).

fof(f_1037_2,plain,
    ! [U_3689,U_3688] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3689),U_3688)),U_3688) = U_3689
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3688),U_3689)) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

fof(f_1037_3,plain,
    ! [U_3689,U_3688] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3689),U_3688)),U_3688) = U_3689
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3688),U_3689)) ),
    inference(definitional_conversion,[status(esa)],[f_1037_2]) ).

cnf(f_1037_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3689),U_3688)),U_3688) = U_3689
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3688),U_3689)) ),
    inference(clausify,[status(thm)],[f_1037_3]) ).

fof(f_1038_1,plain,
    ! [V_i_2,V_j_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).

fof(f_1038_2,plain,
    ! [U_3692,U_3691,U_3690] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3691),U_3690)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3690)),U_3691)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3690)),U_3691))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3691),U_3690))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3690),U_3691)) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

fof(f_1038_3,plain,
    ( ! [U_3690,U_3691,U_3692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3691),U_3690)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3690)),U_3691))
        | ~ sP306(U_3690,U_3691,U_3692) )
    & ! [U_3690,U_3691,U_3692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3690)),U_3691))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3691),U_3690)))
        | ~ sP306(U_3690,U_3691,U_3692) )
    & ! [U_3690,U_3691,U_3692] :
        ( sP306(U_3690,U_3691,U_3692)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3690),U_3691)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306])],[f_1038_2]) ).

cnf(f_1038_4,plain,
    ( sP306(U_3690,U_3691,U_3692)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3690),U_3691)) ),
    inference(clausify,[status(thm)],[f_1038_3]) ).

cnf(f_1038_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3690)),U_3691))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3691),U_3690)))
    | ~ sP306(U_3690,U_3691,U_3692) ),
    inference(clausify,[status(thm)],[f_1038_3]) ).

cnf(f_1038_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3691),U_3690)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3690)),U_3691))
    | ~ sP306(U_3690,U_3691,U_3692) ),
    inference(clausify,[status(thm)],[f_1038_3]) ).

fof(f_1039_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).

fof(f_1039_2,plain,
    ! [U_3695,U_3694,U_3693] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),U_3693)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),U_3694)),U_3693)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3693),U_3694)) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

fof(f_1039_3,plain,
    ! [U_3695,U_3694,U_3693] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),U_3693)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),U_3694)),U_3693)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3693),U_3694)) ),
    inference(definitional_conversion,[status(esa)],[f_1039_2]) ).

cnf(f_1039_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),U_3693)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),U_3694)),U_3693)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3693),U_3694)) ),
    inference(clausify,[status(thm)],[f_1039_3]) ).

fof(f_1040_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).

fof(f_1040_2,plain,
    ! [U_3697,U_3696] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3697),U_3696)) = U_3697
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3696),U_3697)) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

fof(f_1040_3,plain,
    ! [U_3696,U_3697] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3697),U_3696)) = U_3697
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3696),U_3697)) ),
    inference(definitional_conversion,[status(esa)],[f_1040_2]) ).

cnf(f_1040_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3697),U_3696)) = U_3697
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3696),U_3697)) ),
    inference(clausify,[status(thm)],[f_1040_3]) ).

fof(f_1041_1,plain,
    ! [V_m,V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).

fof(f_1041_2,plain,
    ! [U_3700,U_3699,U_3698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3699),U_3700)),U_3698)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3698),U_3699)) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

fof(f_1041_3,plain,
    ! [U_3698,U_3699,U_3700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3699),U_3700)),U_3698)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3698),U_3699)) ),
    inference(definitional_conversion,[status(esa)],[f_1041_2]) ).

cnf(f_1041_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3699),U_3700)),U_3698)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3698),U_3699)) ),
    inference(clausify,[status(thm)],[f_1041_3]) ).

fof(f_1042_1,plain,
    ! [V_i_2,V_k_2,V_j_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__conv]) ).

fof(f_1042_2,plain,
    ! [U_3703,U_3702,U_3701] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3701),U_3702)),U_3703))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3701),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3703),U_3702))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3701),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3703),U_3702)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3701),U_3702)),U_3703)) ) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

fof(f_1042_3,plain,
    ( ! [U_3709,U_3707,U_3705] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3707)),U_3709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3709),U_3707))) )
    & ! [U_3708,U_3706,U_3704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3704),U_3706)),U_3708)) ) ),
    inference(miniscope,[status(thm)],[f_1042_2]) ).

fof(f_1042_4,plain,
    ( ! [U_3705,U_3707,U_3709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3707)),U_3709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3709),U_3707))) )
    & ! [U_3706,U_3704,U_3708] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3704),U_3706)),U_3708)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1042_3]) ).

cnf(f_1042_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3706)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3704),U_3706)),U_3708)) ),
    inference(clausify,[status(thm)],[f_1042_4]) ).

cnf(f_1042_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3707)),U_3709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3709),U_3707))) ),
    inference(clausify,[status(thm)],[f_1042_4]) ).

fof(f_1043_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).

fof(f_1043_2,plain,
    ! [U_3712,U_3711,U_3710] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3712),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3711),U_3710)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3712),U_3710)),U_3711)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3710),U_3711)) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

fof(f_1043_3,plain,
    ! [U_3710,U_3712,U_3711] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3712),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3711),U_3710)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3712),U_3710)),U_3711)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3710),U_3711)) ),
    inference(definitional_conversion,[status(esa)],[f_1043_2]) ).

cnf(f_1043_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3712),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3711),U_3710)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3712),U_3710)),U_3711)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3710),U_3711)) ),
    inference(clausify,[status(thm)],[f_1043_3]) ).

fof(f_1044_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).

fof(f_1044_2,plain,
    ! [U_3714,U_3713] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3713),U_3714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3713),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3714)),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

fof(f_1044_3,plain,
    ! [U_3713,U_3714] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3713),U_3714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3713),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3714)),
    inference(definitional_conversion,[status(esa)],[f_1044_2]) ).

cnf(f_1044_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3713),U_3714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3713),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3714)),
    inference(clausify,[status(thm)],[f_1044_3]) ).

fof(f_1045_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w),
    inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(f_1045_2,plain,
    ! [U_3716,U_3715] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3715),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3715),U_3716),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

fof(f_1045_3,plain,
    ! [U_3715,U_3716] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3715),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3715),U_3716),
    inference(definitional_conversion,[status(esa)],[f_1045_2]) ).

cnf(f_1045_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3715),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3715),U_3716),
    inference(clausify,[status(thm)],[f_1045_3]) ).

fof(f_1046_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__1]) ).

fof(f_1046_2,plain,
    ! [U_3717] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3717)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3717,
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

fof(f_1046_3,plain,
    ! [U_3717] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3717)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3717,
    inference(definitional_conversion,[status(esa)],[f_1046_2]) ).

cnf(f_1046_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3717)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3717,
    inference(clausify,[status(thm)],[f_1046_3]) ).

fof(f_1047_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(f_1047_2,plain,
    ! [U_3719,U_3718] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3718),hAPP(c_Nat_OSuc,U_3719)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3718),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3719),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

fof(f_1047_3,plain,
    ! [U_3718,U_3719] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3718),hAPP(c_Nat_OSuc,U_3719)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3718),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3719),
    inference(definitional_conversion,[status(esa)],[f_1047_2]) ).

cnf(f_1047_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3718),hAPP(c_Nat_OSuc,U_3719)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3718),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3719),
    inference(clausify,[status(thm)],[f_1047_3]) ).

fof(f_1048_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_div__mod__equality_H]) ).

fof(f_1048_2,plain,
    ! [U_3721,U_3720] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3720),U_3721)),U_3721) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3720,U_3721)),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

fof(f_1048_3,plain,
    ! [U_3720,U_3721] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3720),U_3721)),U_3721) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3720,U_3721)),
    inference(definitional_conversion,[status(esa)],[f_1048_2]) ).

cnf(f_1048_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3720),U_3721)),U_3721) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3720,U_3721)),
    inference(clausify,[status(thm)],[f_1048_3]) ).

fof(f_1049_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__div__cancel]) ).

fof(f_1049_2,plain,
    ! [U_3723,U_3722] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3722),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3723),U_3722)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3723),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3723,U_3722)),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

fof(f_1049_3,plain,
    ! [U_3722,U_3723] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3722),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3723),U_3722)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3723),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3723,U_3722)),
    inference(definitional_conversion,[status(esa)],[f_1049_2]) ).

cnf(f_1049_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3722),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3723),U_3722)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3723),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3723,U_3722)),
    inference(clausify,[status(thm)],[f_1049_3]) ).

fof(f_1050_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).

fof(f_1050_2,plain,
    ! [U_3725,U_3724] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3724,U_3725) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3724),U_3725)),U_3725)),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

fof(f_1050_3,plain,
    ! [U_3724,U_3725] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3724,U_3725) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3724),U_3725)),U_3725)),
    inference(definitional_conversion,[status(esa)],[f_1050_2]) ).

cnf(f_1050_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3724,U_3725) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3724),U_3725)),U_3725)),
    inference(clausify,[status(thm)],[f_1050_3]) ).

fof(f_1051_1,plain,
    ! [V_x,V_y] :
      ( c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).

fof(f_1051_2,plain,
    ! [U_3727,U_3726] :
      ( c_Nat__Transfer_Otsub(U_3727,U_3726) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3727),U_3726)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3726),U_3727)) ),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

fof(f_1051_3,plain,
    ! [U_3726,U_3727] :
      ( c_Nat__Transfer_Otsub(U_3727,U_3726) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3727),U_3726)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3726),U_3727)) ),
    inference(definitional_conversion,[status(esa)],[f_1051_2]) ).

cnf(f_1051_4,plain,
    ( c_Nat__Transfer_Otsub(U_3727,U_3726) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3727),U_3726)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3726),U_3727)) ),
    inference(clausify,[status(thm)],[f_1051_3]) ).

fof(f_1052_1,plain,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(f_1052_2,plain,
    ! [U_3729,U_3728] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3728),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3729)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3728),U_3729)),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

fof(f_1052_3,plain,
    ! [U_3728,U_3729] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3728),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3729)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3728),U_3729)),
    inference(definitional_conversion,[status(esa)],[f_1052_2]) ).

cnf(f_1052_4,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3728),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3729)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3728),U_3729)),
    inference(clausify,[status(thm)],[f_1052_3]) ).

fof(f_1053_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).

fof(f_1053_2,plain,
    ! [U_3735,U_3734,U_3733,U_3732,U_3731,U_3730] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3731),U_3732)),U_3733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3734),U_3732)),U_3735)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),U_3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3730),U_3734),U_3731)),U_3732)),U_3735))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),U_3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3730),U_3734),U_3731)),U_3732)),U_3735)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3731),U_3732)),U_3733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3734),U_3732)),U_3735))) ) )
      | ~ class_Rings_Oordered__ring(U_3730) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ( ! [U_3730,U_3731,U_3732,U_3733,U_3734,U_3735] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3731),U_3732)),U_3733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3734),U_3732)),U_3735)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),U_3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3730),U_3734),U_3731)),U_3732)),U_3735)))
        | ~ sP307(U_3730,U_3731,U_3732,U_3733,U_3734,U_3735) )
    & ! [U_3730,U_3731,U_3732,U_3733,U_3734,U_3735] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),U_3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3730),U_3734),U_3731)),U_3732)),U_3735)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3731),U_3732)),U_3733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3734),U_3732)),U_3735)))
        | ~ sP307(U_3730,U_3731,U_3732,U_3733,U_3734,U_3735) )
    & ! [U_3730,U_3731,U_3732,U_3733,U_3734,U_3735] :
        ( sP307(U_3730,U_3731,U_3732,U_3733,U_3734,U_3735)
        | ~ class_Rings_Oordered__ring(U_3730) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP307])],[f_1053_2]) ).

cnf(f_1053_4,plain,
    ( sP307(U_3730,U_3731,U_3732,U_3733,U_3734,U_3735)
    | ~ class_Rings_Oordered__ring(U_3730) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

cnf(f_1053_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),U_3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3730),U_3734),U_3731)),U_3732)),U_3735)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3731),U_3732)),U_3733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3734),U_3732)),U_3735)))
    | ~ sP307(U_3730,U_3731,U_3732,U_3733,U_3734,U_3735) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

cnf(f_1053_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3731),U_3732)),U_3733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),U_3734),U_3732)),U_3735)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3730),U_3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3730),U_3734),U_3731)),U_3732)),U_3735)))
    | ~ sP307(U_3730,U_3731,U_3732,U_3733,U_3734,U_3735) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

fof(f_1054_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).

fof(f_1054_2,plain,
    ! [U_3741,U_3740,U_3739,U_3738,U_3737,U_3736] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3737),U_3738)),U_3739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3740),U_3738)),U_3741)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3736),U_3737),U_3740)),U_3738)),U_3739)),U_3741)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3736),U_3737),U_3740)),U_3738)),U_3739)),U_3741))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3737),U_3738)),U_3739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3740),U_3738)),U_3741))) ) )
      | ~ class_Rings_Oordered__ring(U_3736) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

fof(f_1054_3,plain,
    ( ! [U_3736,U_3737,U_3738,U_3739,U_3740,U_3741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3737),U_3738)),U_3739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3740),U_3738)),U_3741)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3736),U_3737),U_3740)),U_3738)),U_3739)),U_3741))
        | ~ sP308(U_3736,U_3737,U_3738,U_3739,U_3740,U_3741) )
    & ! [U_3736,U_3737,U_3738,U_3739,U_3740,U_3741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3736),U_3737),U_3740)),U_3738)),U_3739)),U_3741))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3737),U_3738)),U_3739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3740),U_3738)),U_3741)))
        | ~ sP308(U_3736,U_3737,U_3738,U_3739,U_3740,U_3741) )
    & ! [U_3736,U_3737,U_3738,U_3739,U_3740,U_3741] :
        ( sP308(U_3736,U_3737,U_3738,U_3739,U_3740,U_3741)
        | ~ class_Rings_Oordered__ring(U_3736) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_1054_2]) ).

cnf(f_1054_4,plain,
    ( sP308(U_3736,U_3737,U_3738,U_3739,U_3740,U_3741)
    | ~ class_Rings_Oordered__ring(U_3736) ),
    inference(clausify,[status(thm)],[f_1054_3]) ).

cnf(f_1054_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3736),U_3737),U_3740)),U_3738)),U_3739)),U_3741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3737),U_3738)),U_3739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3740),U_3738)),U_3741)))
    | ~ sP308(U_3736,U_3737,U_3738,U_3739,U_3740,U_3741) ),
    inference(clausify,[status(thm)],[f_1054_3]) ).

cnf(f_1054_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3737),U_3738)),U_3739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),U_3740),U_3738)),U_3741)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3736),U_3737),U_3740)),U_3738)),U_3739)),U_3741))
    | ~ sP308(U_3736,U_3737,U_3738,U_3739,U_3740,U_3741) ),
    inference(clausify,[status(thm)],[f_1054_3]) ).

fof(f_1055_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).

fof(f_1055_2,plain,
    ! [U_3747,U_3746,U_3745,U_3744,U_3743,U_3742] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3743),U_3744)),U_3745)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3746),U_3744)),U_3747)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3742),U_3743),U_3746)),U_3744)),U_3745)),U_3747)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3742),U_3743),U_3746)),U_3744)),U_3745)),U_3747))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3743),U_3744)),U_3745)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3746),U_3744)),U_3747))) ) )
      | ~ class_Rings_Oordered__ring(U_3742) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

fof(f_1055_3,plain,
    ( ! [U_3742,U_3743,U_3744,U_3745,U_3746,U_3747] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3743),U_3744)),U_3745)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3746),U_3744)),U_3747)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3742),U_3743),U_3746)),U_3744)),U_3745)),U_3747))
        | ~ sP309(U_3742,U_3743,U_3744,U_3745,U_3746,U_3747) )
    & ! [U_3742,U_3743,U_3744,U_3745,U_3746,U_3747] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3742),U_3743),U_3746)),U_3744)),U_3745)),U_3747))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3743),U_3744)),U_3745)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3746),U_3744)),U_3747)))
        | ~ sP309(U_3742,U_3743,U_3744,U_3745,U_3746,U_3747) )
    & ! [U_3742,U_3743,U_3744,U_3745,U_3746,U_3747] :
        ( sP309(U_3742,U_3743,U_3744,U_3745,U_3746,U_3747)
        | ~ class_Rings_Oordered__ring(U_3742) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309])],[f_1055_2]) ).

cnf(f_1055_4,plain,
    ( sP309(U_3742,U_3743,U_3744,U_3745,U_3746,U_3747)
    | ~ class_Rings_Oordered__ring(U_3742) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

cnf(f_1055_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3742),U_3743),U_3746)),U_3744)),U_3745)),U_3747))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3743),U_3744)),U_3745)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3746),U_3744)),U_3747)))
    | ~ sP309(U_3742,U_3743,U_3744,U_3745,U_3746,U_3747) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

cnf(f_1055_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3743),U_3744)),U_3745)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),U_3746),U_3744)),U_3747)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3742),U_3743),U_3746)),U_3744)),U_3745)),U_3747))
    | ~ sP309(U_3742,U_3743,U_3744,U_3745,U_3746,U_3747) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

fof(f_1056_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).

fof(f_1056_2,plain,
    ! [U_3753,U_3752,U_3751,U_3750,U_3749,U_3748] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3749),U_3750)),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3752),U_3750)),U_3753)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),U_3751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3748),U_3752),U_3749)),U_3750)),U_3753))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),U_3751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3748),U_3752),U_3749)),U_3750)),U_3753)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3749),U_3750)),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3752),U_3750)),U_3753))) ) )
      | ~ class_Rings_Oordered__ring(U_3748) ),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

fof(f_1056_3,plain,
    ( ! [U_3749,U_3748,U_3750,U_3751,U_3752,U_3753] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3749),U_3750)),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3752),U_3750)),U_3753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),U_3751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3748),U_3752),U_3749)),U_3750)),U_3753)))
        | ~ sP310(U_3749,U_3748,U_3750,U_3751,U_3752,U_3753) )
    & ! [U_3749,U_3748,U_3750,U_3751,U_3752,U_3753] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),U_3751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3748),U_3752),U_3749)),U_3750)),U_3753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3749),U_3750)),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3752),U_3750)),U_3753)))
        | ~ sP310(U_3749,U_3748,U_3750,U_3751,U_3752,U_3753) )
    & ! [U_3749,U_3748,U_3750,U_3751,U_3752,U_3753] :
        ( sP310(U_3749,U_3748,U_3750,U_3751,U_3752,U_3753)
        | ~ class_Rings_Oordered__ring(U_3748) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310])],[f_1056_2]) ).

cnf(f_1056_4,plain,
    ( sP310(U_3749,U_3748,U_3750,U_3751,U_3752,U_3753)
    | ~ class_Rings_Oordered__ring(U_3748) ),
    inference(clausify,[status(thm)],[f_1056_3]) ).

cnf(f_1056_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),U_3751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3748),U_3752),U_3749)),U_3750)),U_3753)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3749),U_3750)),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3752),U_3750)),U_3753)))
    | ~ sP310(U_3749,U_3748,U_3750,U_3751,U_3752,U_3753) ),
    inference(clausify,[status(thm)],[f_1056_3]) ).

cnf(f_1056_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3749),U_3750)),U_3751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),U_3752),U_3750)),U_3753)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3748),U_3751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3748),U_3752),U_3749)),U_3750)),U_3753)))
    | ~ sP310(U_3749,U_3748,U_3750,U_3751,U_3752,U_3753) ),
    inference(clausify,[status(thm)],[f_1056_3]) ).

fof(f_1057_1,plain,
    ! [V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).

fof(f_1057_2,plain,
    ! [U_3755,U_3754] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3754),hAPP(c_Nat_OSuc,U_3755))),U_3754))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3754)) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ! [U_3755,U_3754] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3754),hAPP(c_Nat_OSuc,U_3755))),U_3754))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3754)) ),
    inference(definitional_conversion,[status(esa)],[f_1057_2]) ).

cnf(f_1057_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3754),hAPP(c_Nat_OSuc,U_3755))),U_3754))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3754)) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

fof(f_1058_1,plain,
    ! [V_n] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).

fof(f_1058_2,plain,
    ! [U_3756] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3756),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3756
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3756)) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

fof(f_1058_3,plain,
    ! [U_3756] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3756),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3756
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3756)) ),
    inference(definitional_conversion,[status(esa)],[f_1058_2]) ).

cnf(f_1058_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3756),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3756
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3756)) ),
    inference(clausify,[status(thm)],[f_1058_3]) ).

fof(f_1059_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(f_1059_2,plain,
    ! [U_3761,U_3760,U_3759] :
      ( ( hBOOL(hAPP(U_3759,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3760),U_3761)))
        | ? [U_3758] :
            ( ~ hBOOL(hAPP(U_3759,U_3758))
            & U_3760 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3761),U_3758) )
        | ( ~ hBOOL(hAPP(U_3759,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3760),U_3761)) ) )
      & ( ( ! [U_3757] :
              ( hBOOL(hAPP(U_3759,U_3757))
              | U_3760 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3761),U_3757) )
          & ( hBOOL(hAPP(U_3759,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3760),U_3761)) ) )
        | ~ hBOOL(hAPP(U_3759,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3760),U_3761))) ) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

fof(f_1059_3,plain,
    ( ! [U_3767,U_3765,U_3763] :
        ( hBOOL(hAPP(U_3763,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3765),U_3767)))
        | ? [U_3758] :
            ( ~ hBOOL(hAPP(U_3763,U_3758))
            & U_3765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3767),U_3758) )
        | ( ~ hBOOL(hAPP(U_3763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3767)) ) )
    & ! [U_3766,U_3764,U_3762] :
        ( ( ! [U_3757] :
              ( hBOOL(hAPP(U_3762,U_3757))
              | U_3764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3757) )
          & ( hBOOL(hAPP(U_3762,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3764),U_3766)) ) )
        | ~ hBOOL(hAPP(U_3762,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3764),U_3766))) ) ),
    inference(miniscope,[status(thm)],[f_1059_2]) ).

fof(f_1059_4,plain,
    ( ! [U_3767,U_3765,U_3763] :
        ( hBOOL(hAPP(U_3763,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3765),U_3767)))
        | ( ~ hBOOL(hAPP(U_3763,sK73(U_3767,U_3765,U_3763)))
          & U_3765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3767),sK73(U_3767,U_3765,U_3763)) )
        | ( ~ hBOOL(hAPP(U_3763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3767)) ) )
    & ! [U_3766,U_3764,U_3762] :
        ( ( ! [U_3757] :
              ( hBOOL(hAPP(U_3762,U_3757))
              | U_3764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3757) )
          & ( hBOOL(hAPP(U_3762,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3764),U_3766)) ) )
        | ~ hBOOL(hAPP(U_3762,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3764),U_3766))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3758,sK73(U_3767,U_3765,U_3763))],[f_1059_3]) ).

fof(f_1059_5,plain,
    ( ! [U_3763,U_3765,U_3767] :
        ( ~ hBOOL(hAPP(U_3763,sK73(U_3767,U_3765,U_3763)))
        | ~ sP313(U_3763,U_3765,U_3767) )
    & ! [U_3763,U_3765,U_3767] :
        ( U_3765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3767),sK73(U_3767,U_3765,U_3763))
        | ~ sP313(U_3763,U_3765,U_3767) )
    & ! [U_3763,U_3765,U_3767] :
        ( ~ hBOOL(hAPP(U_3763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP312(U_3763,U_3765,U_3767) )
    & ! [U_3763,U_3765,U_3767] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3767))
        | ~ sP312(U_3763,U_3765,U_3767) )
    & ! [U_3764,U_3757,U_3762,U_3766] :
        ( hBOOL(hAPP(U_3762,U_3757))
        | U_3764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3757)
        | ~ sP311(U_3764,U_3757,U_3762,U_3766) )
    & ! [U_3764,U_3757,U_3762,U_3766] :
        ( hBOOL(hAPP(U_3762,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3764),U_3766))
        | ~ sP311(U_3764,U_3757,U_3762,U_3766) )
    & ! [U_3763,U_3765,U_3767] :
        ( hBOOL(hAPP(U_3763,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3765),U_3767)))
        | sP313(U_3763,U_3765,U_3767)
        | sP312(U_3763,U_3765,U_3767) )
    & ! [U_3764,U_3757,U_3762,U_3766] :
        ( sP311(U_3764,U_3757,U_3762,U_3766)
        | ~ hBOOL(hAPP(U_3762,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3764),U_3766))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311,sP312,sP313])],[f_1059_4]) ).

cnf(f_1059_6,plain,
    ( sP311(U_3764,U_3757,U_3762,U_3766)
    | ~ hBOOL(hAPP(U_3762,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3764),U_3766))) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_7,plain,
    ( hBOOL(hAPP(U_3763,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3765),U_3767)))
    | sP313(U_3763,U_3765,U_3767)
    | sP312(U_3763,U_3765,U_3767) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_8,plain,
    ( hBOOL(hAPP(U_3762,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3764),U_3766))
    | ~ sP311(U_3764,U_3757,U_3762,U_3766) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_9,plain,
    ( hBOOL(hAPP(U_3762,U_3757))
    | U_3764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3766),U_3757)
    | ~ sP311(U_3764,U_3757,U_3762,U_3766) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3765),U_3767))
    | ~ sP312(U_3763,U_3765,U_3767) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_11,plain,
    ( ~ hBOOL(hAPP(U_3763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP312(U_3763,U_3765,U_3767) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_12,plain,
    ( U_3765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3767),sK73(U_3767,U_3765,U_3763))
    | ~ sP313(U_3763,U_3765,U_3767) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

cnf(f_1059_13,plain,
    ( ~ hBOOL(hAPP(U_3763,sK73(U_3767,U_3765,U_3763)))
    | ~ sP313(U_3763,U_3765,U_3767) ),
    inference(clausify,[status(thm)],[f_1059_5]) ).

fof(f_1060_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).

fof(f_1060_2,plain,
    ! [U_3772,U_3771,U_3770] :
      ( ( hBOOL(hAPP(U_3770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3771),U_3772)))
        | ? [U_3769] :
            ( ~ hBOOL(hAPP(U_3770,U_3769))
            & U_3771 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3772),U_3769) )
        | ( ~ hBOOL(hAPP(U_3770,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3771),U_3772)) ) )
      & ( ( ! [U_3768] :
              ( hBOOL(hAPP(U_3770,U_3768))
              | U_3771 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3772),U_3768) )
          & ( hBOOL(hAPP(U_3770,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3771),U_3772)) ) )
        | ~ hBOOL(hAPP(U_3770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3771),U_3772))) ) ),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

fof(f_1060_3,plain,
    ( ! [U_3778,U_3776,U_3774] :
        ( hBOOL(hAPP(U_3774,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3778)))
        | ? [U_3769] :
            ( ~ hBOOL(hAPP(U_3774,U_3769))
            & U_3776 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3778),U_3769) )
        | ( ~ hBOOL(hAPP(U_3774,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778)) ) )
    & ! [U_3777,U_3775,U_3773] :
        ( ( ! [U_3768] :
              ( hBOOL(hAPP(U_3773,U_3768))
              | U_3775 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3777),U_3768) )
          & ( hBOOL(hAPP(U_3773,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3775),U_3777)) ) )
        | ~ hBOOL(hAPP(U_3773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3775),U_3777))) ) ),
    inference(miniscope,[status(thm)],[f_1060_2]) ).

fof(f_1060_4,plain,
    ( ! [U_3778,U_3776,U_3774] :
        ( hBOOL(hAPP(U_3774,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3778)))
        | ( ~ hBOOL(hAPP(U_3774,sK74(U_3778,U_3776,U_3774)))
          & U_3776 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3778),sK74(U_3778,U_3776,U_3774)) )
        | ( ~ hBOOL(hAPP(U_3774,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778)) ) )
    & ! [U_3777,U_3775,U_3773] :
        ( ( ! [U_3768] :
              ( hBOOL(hAPP(U_3773,U_3768))
              | U_3775 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3777),U_3768) )
          & ( hBOOL(hAPP(U_3773,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3775),U_3777)) ) )
        | ~ hBOOL(hAPP(U_3773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3775),U_3777))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3769,sK74(U_3778,U_3776,U_3774))],[f_1060_3]) ).

fof(f_1060_5,plain,
    ( ! [U_3778,U_3776,U_3774] :
        ( ~ hBOOL(hAPP(U_3774,sK74(U_3778,U_3776,U_3774)))
        | ~ sP316(U_3778,U_3776,U_3774) )
    & ! [U_3778,U_3776,U_3774] :
        ( U_3776 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3778),sK74(U_3778,U_3776,U_3774))
        | ~ sP316(U_3778,U_3776,U_3774) )
    & ! [U_3778,U_3776,U_3774] :
        ( ~ hBOOL(hAPP(U_3774,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP315(U_3778,U_3776,U_3774) )
    & ! [U_3778,U_3776,U_3774] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778))
        | ~ sP315(U_3778,U_3776,U_3774) )
    & ! [U_3768,U_3773,U_3777,U_3775] :
        ( hBOOL(hAPP(U_3773,U_3768))
        | U_3775 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3777),U_3768)
        | ~ sP314(U_3768,U_3773,U_3777,U_3775) )
    & ! [U_3768,U_3773,U_3777,U_3775] :
        ( hBOOL(hAPP(U_3773,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3775),U_3777))
        | ~ sP314(U_3768,U_3773,U_3777,U_3775) )
    & ! [U_3778,U_3776,U_3774] :
        ( hBOOL(hAPP(U_3774,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3778)))
        | sP316(U_3778,U_3776,U_3774)
        | sP315(U_3778,U_3776,U_3774) )
    & ! [U_3768,U_3773,U_3777,U_3775] :
        ( sP314(U_3768,U_3773,U_3777,U_3775)
        | ~ hBOOL(hAPP(U_3773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3775),U_3777))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314,sP315,sP316])],[f_1060_4]) ).

cnf(f_1060_6,plain,
    ( sP314(U_3768,U_3773,U_3777,U_3775)
    | ~ hBOOL(hAPP(U_3773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3775),U_3777))) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_7,plain,
    ( hBOOL(hAPP(U_3774,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3778)))
    | sP316(U_3778,U_3776,U_3774)
    | sP315(U_3778,U_3776,U_3774) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_8,plain,
    ( hBOOL(hAPP(U_3773,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3775),U_3777))
    | ~ sP314(U_3768,U_3773,U_3777,U_3775) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_9,plain,
    ( hBOOL(hAPP(U_3773,U_3768))
    | U_3775 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3777),U_3768)
    | ~ sP314(U_3768,U_3773,U_3777,U_3775) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3778))
    | ~ sP315(U_3778,U_3776,U_3774) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_11,plain,
    ( ~ hBOOL(hAPP(U_3774,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP315(U_3778,U_3776,U_3774) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_12,plain,
    ( U_3776 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3778),sK74(U_3778,U_3776,U_3774))
    | ~ sP316(U_3778,U_3776,U_3774) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

cnf(f_1060_13,plain,
    ( ~ hBOOL(hAPP(U_3774,sK74(U_3778,U_3776,U_3774)))
    | ~ sP316(U_3778,U_3776,U_3774) ),
    inference(clausify,[status(thm)],[f_1060_5]) ).

fof(f_1061_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).

fof(f_1061_2,plain,
    ! [U_3780,U_3779] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3780),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3779),U_3780)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3779),U_3780))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3780),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

fof(f_1061_3,plain,
    ( ! [U_3784,U_3782] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3782),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3784),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3782),U_3784)) )
    & ! [U_3783,U_3781] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3781),U_3783))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3783),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1061_2]) ).

fof(f_1061_4,plain,
    ( ! [U_3784,U_3782] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3782),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3784),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3782),U_3784)) )
    & ! [U_3781,U_3783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3781),U_3783))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3783),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1061_3]) ).

cnf(f_1061_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3781),U_3783))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3783),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1061_4]) ).

cnf(f_1061_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3782),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3784),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3782),U_3784)) ),
    inference(clausify,[status(thm)],[f_1061_4]) ).

fof(f_1062_1,plain,
    ! [V_m,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).

fof(f_1062_2,plain,
    ! [U_3787,U_3786,U_3785] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3787),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3787),U_3785)),hAPP(c_Nat_OSuc,U_3786))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

fof(f_1062_3,plain,
    ! [U_3786,U_3787,U_3785] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3787),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3787),U_3785)),hAPP(c_Nat_OSuc,U_3786))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ),
    inference(definitional_conversion,[status(esa)],[f_1062_2]) ).

cnf(f_1062_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3787),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3787),U_3785)),hAPP(c_Nat_OSuc,U_3786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ),
    inference(clausify,[status(thm)],[f_1062_3]) ).

fof(f_1063_1,plain,
    ! [V_m,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).

fof(f_1063_2,plain,
    ! [U_3790,U_3789,U_3788] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3789),U_3788))),U_3790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3788),U_3790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3788),U_3789)) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

fof(f_1063_3,plain,
    ! [U_3788,U_3789,U_3790] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3789),U_3788))),U_3790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3788),U_3790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3788),U_3789)) ),
    inference(definitional_conversion,[status(esa)],[f_1063_2]) ).

cnf(f_1063_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3789),U_3788))),U_3790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3788),U_3790))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3788),U_3789)) ),
    inference(clausify,[status(thm)],[f_1063_3]) ).

fof(f_1064_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1]) ).

fof(f_1064_2,plain,
    ! [U_3795,U_3794,U_3793,U_3792,U_3791] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3792),U_3793)),U_3794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3793)),U_3795)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3792),U_3791)),U_3793)),U_3794)),U_3795)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3792),U_3791)),U_3793)),U_3794)),U_3795))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3792),U_3793)),U_3794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3793)),U_3795))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3791),U_3792)) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

fof(f_1064_3,plain,
    ( ! [U_3791,U_3792,U_3793,U_3794,U_3795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3792),U_3793)),U_3794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3793)),U_3795)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3792),U_3791)),U_3793)),U_3794)),U_3795))
        | ~ sP317(U_3791,U_3792,U_3793,U_3794,U_3795) )
    & ! [U_3791,U_3792,U_3793,U_3794,U_3795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3792),U_3791)),U_3793)),U_3794)),U_3795))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3792),U_3793)),U_3794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3793)),U_3795)))
        | ~ sP317(U_3791,U_3792,U_3793,U_3794,U_3795) )
    & ! [U_3791,U_3792,U_3793,U_3794,U_3795] :
        ( sP317(U_3791,U_3792,U_3793,U_3794,U_3795)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3791),U_3792)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP317])],[f_1064_2]) ).

cnf(f_1064_4,plain,
    ( sP317(U_3791,U_3792,U_3793,U_3794,U_3795)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3791),U_3792)) ),
    inference(clausify,[status(thm)],[f_1064_3]) ).

cnf(f_1064_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3792),U_3791)),U_3793)),U_3794)),U_3795))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3792),U_3793)),U_3794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3793)),U_3795)))
    | ~ sP317(U_3791,U_3792,U_3793,U_3794,U_3795) ),
    inference(clausify,[status(thm)],[f_1064_3]) ).

cnf(f_1064_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3792),U_3793)),U_3794)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3793)),U_3795)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3792),U_3791)),U_3793)),U_3794)),U_3795))
    | ~ sP317(U_3791,U_3792,U_3793,U_3794,U_3795) ),
    inference(clausify,[status(thm)],[f_1064_3]) ).

fof(f_1065_1,plain,
    ! [V_n,V_m,V_u,V_i,V_j] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).

fof(f_1065_2,plain,
    ! [U_3800,U_3799,U_3798,U_3797,U_3796] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3797),U_3798)),U_3799)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3796),U_3798)),U_3800)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3797),U_3796)),U_3798)),U_3799)),U_3800)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3796),U_3797)) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

fof(f_1065_3,plain,
    ! [U_3797,U_3796,U_3798,U_3799,U_3800] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3797),U_3798)),U_3799)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3796),U_3798)),U_3800)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3797),U_3796)),U_3798)),U_3799)),U_3800)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3796),U_3797)) ),
    inference(definitional_conversion,[status(esa)],[f_1065_2]) ).

cnf(f_1065_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3797),U_3798)),U_3799)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3796),U_3798)),U_3800)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3797),U_3796)),U_3798)),U_3799)),U_3800)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3796),U_3797)) ),
    inference(clausify,[status(thm)],[f_1065_3]) ).

fof(f_1066_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) != V_n_2 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1]) ).

fof(f_1066_2,plain,
    ! [U_3805,U_3804,U_3803,U_3802,U_3801] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3802),U_3803)),U_3804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3801),U_3803)),U_3805)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3802),U_3801)),U_3803)),U_3804) != U_3805 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3802),U_3801)),U_3803)),U_3804) = U_3805
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3802),U_3803)),U_3804) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3801),U_3803)),U_3805) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3801),U_3802)) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

fof(f_1066_3,plain,
    ( ! [U_3801,U_3802,U_3803,U_3804,U_3805] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3802),U_3803)),U_3804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3801),U_3803)),U_3805)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3802),U_3801)),U_3803)),U_3804) != U_3805
        | ~ sP318(U_3801,U_3802,U_3803,U_3804,U_3805) )
    & ! [U_3801,U_3802,U_3803,U_3804,U_3805] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3802),U_3801)),U_3803)),U_3804) = U_3805
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3802),U_3803)),U_3804) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3801),U_3803)),U_3805)
        | ~ sP318(U_3801,U_3802,U_3803,U_3804,U_3805) )
    & ! [U_3801,U_3802,U_3803,U_3804,U_3805] :
        ( sP318(U_3801,U_3802,U_3803,U_3804,U_3805)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3801),U_3802)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP318])],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( sP318(U_3801,U_3802,U_3803,U_3804,U_3805)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3801),U_3802)) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

cnf(f_1066_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3802),U_3801)),U_3803)),U_3804) = U_3805
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3802),U_3803)),U_3804) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3801),U_3803)),U_3805)
    | ~ sP318(U_3801,U_3802,U_3803,U_3804,U_3805) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

cnf(f_1066_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3802),U_3803)),U_3804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3801),U_3803)),U_3805)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3802),U_3801)),U_3803)),U_3804) != U_3805
    | ~ sP318(U_3801,U_3802,U_3803,U_3804,U_3805) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

fof(f_1067_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2]) ).

fof(f_1067_2,plain,
    ! [U_3810,U_3809,U_3808,U_3807,U_3806] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3806),U_3808)),U_3809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3807),U_3808)),U_3810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3807),U_3806)),U_3808)),U_3810))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3807),U_3806)),U_3808)),U_3810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3806),U_3808)),U_3809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3807),U_3808)),U_3810))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3806),U_3807)) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

fof(f_1067_3,plain,
    ( ! [U_3807,U_3806,U_3809,U_3808,U_3810] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3806),U_3808)),U_3809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3807),U_3808)),U_3810)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3807),U_3806)),U_3808)),U_3810)))
        | ~ sP319(U_3807,U_3806,U_3809,U_3808,U_3810) )
    & ! [U_3807,U_3806,U_3809,U_3808,U_3810] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3807),U_3806)),U_3808)),U_3810)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3806),U_3808)),U_3809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3807),U_3808)),U_3810)))
        | ~ sP319(U_3807,U_3806,U_3809,U_3808,U_3810) )
    & ! [U_3807,U_3806,U_3809,U_3808,U_3810] :
        ( sP319(U_3807,U_3806,U_3809,U_3808,U_3810)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3806),U_3807)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319])],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( sP319(U_3807,U_3806,U_3809,U_3808,U_3810)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3806),U_3807)) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3807),U_3806)),U_3808)),U_3810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3806),U_3808)),U_3809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3807),U_3808)),U_3810)))
    | ~ sP319(U_3807,U_3806,U_3809,U_3808,U_3810) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3806),U_3808)),U_3809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3807),U_3808)),U_3810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3807),U_3806)),U_3808)),U_3810)))
    | ~ sP319(U_3807,U_3806,U_3809,U_3808,U_3810) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

fof(f_1068_1,plain,
    ! [V_n,V_m,V_u,V_j,V_i] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).

fof(f_1068_2,plain,
    ! [U_3815,U_3814,U_3813,U_3812,U_3811] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3811),U_3813)),U_3814)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3812),U_3813)),U_3815)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3812),U_3811)),U_3813)),U_3815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3811),U_3812)) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

fof(f_1068_3,plain,
    ! [U_3812,U_3813,U_3811,U_3814,U_3815] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3811),U_3813)),U_3814)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3812),U_3813)),U_3815)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3812),U_3811)),U_3813)),U_3815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3811),U_3812)) ),
    inference(definitional_conversion,[status(esa)],[f_1068_2]) ).

cnf(f_1068_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3811),U_3813)),U_3814)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3812),U_3813)),U_3815)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3812),U_3811)),U_3813)),U_3815))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3811),U_3812)) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

fof(f_1069_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
          | V_m_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) )
        & ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2]) ).

fof(f_1069_2,plain,
    ! [U_3820,U_3819,U_3818,U_3817,U_3816] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3816),U_3818)),U_3819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3817),U_3818)),U_3820)
          | U_3819 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3817),U_3816)),U_3818)),U_3820) )
        & ( U_3819 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3817),U_3816)),U_3818)),U_3820)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3816),U_3818)),U_3819) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3817),U_3818)),U_3820) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),U_3817)) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

fof(f_1069_3,plain,
    ( ! [U_3816,U_3817,U_3818,U_3819,U_3820] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3816),U_3818)),U_3819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3817),U_3818)),U_3820)
        | U_3819 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3817),U_3816)),U_3818)),U_3820)
        | ~ sP320(U_3816,U_3817,U_3818,U_3819,U_3820) )
    & ! [U_3816,U_3817,U_3818,U_3819,U_3820] :
        ( U_3819 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3817),U_3816)),U_3818)),U_3820)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3816),U_3818)),U_3819) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3817),U_3818)),U_3820)
        | ~ sP320(U_3816,U_3817,U_3818,U_3819,U_3820) )
    & ! [U_3816,U_3817,U_3818,U_3819,U_3820] :
        ( sP320(U_3816,U_3817,U_3818,U_3819,U_3820)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),U_3817)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP320])],[f_1069_2]) ).

cnf(f_1069_4,plain,
    ( sP320(U_3816,U_3817,U_3818,U_3819,U_3820)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3816),U_3817)) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_5,plain,
    ( U_3819 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3817),U_3816)),U_3818)),U_3820)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3816),U_3818)),U_3819) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3817),U_3818)),U_3820)
    | ~ sP320(U_3816,U_3817,U_3818,U_3819,U_3820) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3816),U_3818)),U_3819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3817),U_3818)),U_3820)
    | U_3819 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3817),U_3816)),U_3818)),U_3820)
    | ~ sP320(U_3816,U_3817,U_3818,U_3819,U_3820) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

fof(f_1070_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if]) ).

fof(f_1070_2,plain,
    ! [U_3822,U_3821] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3821,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3822)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3821,U_3822)),U_3822)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3821,U_3822) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3821,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3822)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3821,U_3822) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

fof(f_1070_3,plain,
    ( ! [U_3826,U_3824] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3826)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,U_3826)),U_3826)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,U_3826) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3825,U_3823] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3823,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3825)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3823,U_3825) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1070_2]) ).

fof(f_1070_4,plain,
    ( ! [U_3826,U_3824] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3826)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,U_3826)),U_3826)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,U_3826) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3825,U_3823] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3823,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3825)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3823,U_3825) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1070_3]) ).

cnf(f_1070_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3823,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3825)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3823,U_3825) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1070_4]) ).

cnf(f_1070_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3826)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,U_3826)),U_3826)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3824,U_3826) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1070_4]) ).

fof(f_1071_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if]) ).

fof(f_1071_2,plain,
    ! [U_3828,U_3827] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3827),U_3828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3828),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3827,U_3828))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3827,U_3828) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3827),U_3828) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3827,U_3828) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

fof(f_1071_3,plain,
    ( ! [U_3832,U_3830] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3830),U_3832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3832),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3830,U_3832))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3830,U_3832) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3831,U_3829] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3829),U_3831) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3829,U_3831) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1071_2]) ).

fof(f_1071_4,plain,
    ( ! [U_3832,U_3830] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3830),U_3832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3832),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3830,U_3832))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3830,U_3832) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3829,U_3831] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3829),U_3831) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3829,U_3831) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1071_3]) ).

cnf(f_1071_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3829),U_3831) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3829,U_3831) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1071_4]) ).

cnf(f_1071_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3830),U_3832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3832),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3830,U_3832))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3830,U_3832) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1071_4]) ).

fof(f_1072_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality_H]) ).

fof(f_1072_2,plain,
    ! [U_3834,U_3833] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3833,U_3834) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3833),U_3834)),U_3834)),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

fof(f_1072_3,plain,
    ! [U_3833,U_3834] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3833,U_3834) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3833),U_3834)),U_3834)),
    inference(definitional_conversion,[status(esa)],[f_1072_2]) ).

cnf(f_1072_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3833,U_3834) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3833),U_3834)),U_3834)),
    inference(clausify,[status(thm)],[f_1072_3]) ).

fof(f_1073_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmult__div__cancel]) ).

fof(f_1073_2,plain,
    ! [U_3836,U_3835] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3835),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3836),U_3835)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3836),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3836,U_3835)),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

fof(f_1073_3,plain,
    ! [U_3835,U_3836] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3835),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3836),U_3835)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3836),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3836,U_3835)),
    inference(definitional_conversion,[status(esa)],[f_1073_2]) ).

cnf(f_1073_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3835),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3836),U_3835)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3836),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3836,U_3835)),
    inference(clausify,[status(thm)],[f_1073_3]) ).

fof(f_1074_1,plain,
    ! [V_x,V_y] :
      ( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) )
      & ( c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).

fof(f_1074_2,plain,
    ! [U_3838,U_3837] :
      ( ( c_Nat__Transfer_Otsub(U_3838,U_3837) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3837),U_3838)) )
      & ( c_Nat__Transfer_Otsub(U_3838,U_3837) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3838),U_3837)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3837),U_3838)) ) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

fof(f_1074_3,plain,
    ( ! [U_3842,U_3840] :
        ( c_Nat__Transfer_Otsub(U_3842,U_3840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3840),U_3842)) )
    & ! [U_3841,U_3839] :
        ( c_Nat__Transfer_Otsub(U_3841,U_3839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3841),U_3839)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3839),U_3841)) ) ),
    inference(miniscope,[status(thm)],[f_1074_2]) ).

fof(f_1074_4,plain,
    ( ! [U_3840,U_3842] :
        ( c_Nat__Transfer_Otsub(U_3842,U_3840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3840),U_3842)) )
    & ! [U_3841,U_3839] :
        ( c_Nat__Transfer_Otsub(U_3841,U_3839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3841),U_3839)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3839),U_3841)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1074_3]) ).

cnf(f_1074_5,plain,
    ( c_Nat__Transfer_Otsub(U_3841,U_3839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3841),U_3839)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3839),U_3841)) ),
    inference(clausify,[status(thm)],[f_1074_4]) ).

cnf(f_1074_6,plain,
    ( c_Nat__Transfer_Otsub(U_3842,U_3840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3840),U_3842)) ),
    inference(clausify,[status(thm)],[f_1074_4]) ).

fof(f_1075_1,plain,
    ! [V_n] :
      ( V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).

fof(f_1075_2,plain,
    ! [U_3843] :
      ( U_3843 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3843),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3843)) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

fof(f_1075_3,plain,
    ! [U_3843] :
      ( U_3843 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3843),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3843)) ),
    inference(definitional_conversion,[status(esa)],[f_1075_2]) ).

cnf(f_1075_4,plain,
    ( U_3843 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3843),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3843)) ),
    inference(clausify,[status(thm)],[f_1075_3]) ).

fof(f_1076_1,plain,
    ! [V_n] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).

fof(f_1076_2,plain,
    ! [U_3844] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3844),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3844
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3844)) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

fof(f_1076_3,plain,
    ! [U_3844] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3844),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3844
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3844)) ),
    inference(definitional_conversion,[status(esa)],[f_1076_2]) ).

cnf(f_1076_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3844),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3844
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3844)) ),
    inference(clausify,[status(thm)],[f_1076_3]) ).

fof(f_1077_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2]) ).

fof(f_1077_2,plain,
    ! [U_3849,U_3848,U_3847,U_3846,U_3845] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3845),U_3847)),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3847)),U_3849)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3845)),U_3847)),U_3849))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3845)),U_3847)),U_3849)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3845),U_3847)),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3847)),U_3849))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3845),U_3846)) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

fof(f_1077_3,plain,
    ( ! [U_3845,U_3846,U_3847,U_3848,U_3849] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3845),U_3847)),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3847)),U_3849)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3845)),U_3847)),U_3849)))
        | ~ sP321(U_3845,U_3846,U_3847,U_3848,U_3849) )
    & ! [U_3845,U_3846,U_3847,U_3848,U_3849] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3845)),U_3847)),U_3849)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3845),U_3847)),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3847)),U_3849)))
        | ~ sP321(U_3845,U_3846,U_3847,U_3848,U_3849) )
    & ! [U_3845,U_3846,U_3847,U_3848,U_3849] :
        ( sP321(U_3845,U_3846,U_3847,U_3848,U_3849)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3845),U_3846)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP321])],[f_1077_2]) ).

cnf(f_1077_4,plain,
    ( sP321(U_3845,U_3846,U_3847,U_3848,U_3849)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3845),U_3846)) ),
    inference(clausify,[status(thm)],[f_1077_3]) ).

cnf(f_1077_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3845)),U_3847)),U_3849)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3845),U_3847)),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3847)),U_3849)))
    | ~ sP321(U_3845,U_3846,U_3847,U_3848,U_3849) ),
    inference(clausify,[status(thm)],[f_1077_3]) ).

cnf(f_1077_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3845),U_3847)),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3847)),U_3849)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3846),U_3845)),U_3847)),U_3849)))
    | ~ sP321(U_3845,U_3846,U_3847,U_3848,U_3849) ),
    inference(clausify,[status(thm)],[f_1077_3]) ).

fof(f_1078_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1]) ).

fof(f_1078_2,plain,
    ! [U_3854,U_3853,U_3852,U_3851,U_3850] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3852)),U_3853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3850),U_3852)),U_3854)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3851),U_3850)),U_3852)),U_3853)),U_3854)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3851),U_3850)),U_3852)),U_3853)),U_3854))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3852)),U_3853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3850),U_3852)),U_3854))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3850),U_3851)) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

fof(f_1078_3,plain,
    ( ! [U_3850,U_3851,U_3853,U_3852,U_3854] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3852)),U_3853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3850),U_3852)),U_3854)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3851),U_3850)),U_3852)),U_3853)),U_3854))
        | ~ sP322(U_3850,U_3851,U_3853,U_3852,U_3854) )
    & ! [U_3850,U_3851,U_3853,U_3852,U_3854] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3851),U_3850)),U_3852)),U_3853)),U_3854))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3852)),U_3853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3850),U_3852)),U_3854)))
        | ~ sP322(U_3850,U_3851,U_3853,U_3852,U_3854) )
    & ! [U_3850,U_3851,U_3853,U_3852,U_3854] :
        ( sP322(U_3850,U_3851,U_3853,U_3852,U_3854)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3850),U_3851)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP322])],[f_1078_2]) ).

cnf(f_1078_4,plain,
    ( sP322(U_3850,U_3851,U_3853,U_3852,U_3854)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3850),U_3851)) ),
    inference(clausify,[status(thm)],[f_1078_3]) ).

cnf(f_1078_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3851),U_3850)),U_3852)),U_3853)),U_3854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3852)),U_3853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3850),U_3852)),U_3854)))
    | ~ sP322(U_3850,U_3851,U_3853,U_3852,U_3854) ),
    inference(clausify,[status(thm)],[f_1078_3]) ).

cnf(f_1078_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3852)),U_3853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3850),U_3852)),U_3854)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3851),U_3850)),U_3852)),U_3853)),U_3854))
    | ~ sP322(U_3850,U_3851,U_3853,U_3852,U_3854) ),
    inference(clausify,[status(thm)],[f_1078_3]) ).

fof(f_1079_1,plain,
    ! [V_n,V_m] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).

fof(f_1079_2,plain,
    ! [U_3856,U_3855] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3856) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3855),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3856))
        | U_3855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3856) = U_3856
        | U_3855 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

fof(f_1079_3,plain,
    ( ! [U_3860,U_3858] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3858),U_3860) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3858),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3860))
        | U_3858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3859,U_3857] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3859) = U_3859
        | U_3857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1079_2]) ).

fof(f_1079_4,plain,
    ( ! [U_3860,U_3858] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3858),U_3860) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3858),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3860))
        | U_3858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3857,U_3859] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3859) = U_3859
        | U_3857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1079_3]) ).

cnf(f_1079_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3859) = U_3859
    | U_3857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1079_4]) ).

cnf(f_1079_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3858),U_3860) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3858),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3860))
    | U_3858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1079_4]) ).

fof(f_1080_1,plain,
    ! [V_m,V_n] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__if]) ).

fof(f_1080_2,plain,
    ! [U_3862,U_3861] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3862),U_3861) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3862),U_3861)),U_3861))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3862),U_3861)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3862),U_3861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3862),U_3861)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3861)) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

fof(f_1080_3,plain,
    ( ! [U_3861,U_3862] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3862),U_3861) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3862),U_3861)),U_3861))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3862),U_3861))
        | ~ sP323(U_3861,U_3862) )
    & ! [U_3861,U_3862] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3862),U_3861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3862),U_3861))
        | ~ sP323(U_3861,U_3862) )
    & ! [U_3861,U_3862] :
        ( sP323(U_3861,U_3862)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3861)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323])],[f_1080_2]) ).

cnf(f_1080_4,plain,
    ( sP323(U_3861,U_3862)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3861)) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

cnf(f_1080_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3862),U_3861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3862),U_3861))
    | ~ sP323(U_3861,U_3862) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

cnf(f_1080_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3862),U_3861) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3862),U_3861)),U_3861))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3862),U_3861))
    | ~ sP323(U_3861,U_3862) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

fof(f_1081_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__geq]) ).

fof(f_1081_2,plain,
    ! [U_3864,U_3863] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3864),U_3863) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3864),U_3863)),U_3863))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3864),U_3863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3863)) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

fof(f_1081_3,plain,
    ! [U_3863,U_3864] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3864),U_3863) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3864),U_3863)),U_3863))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3864),U_3863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3863)) ),
    inference(definitional_conversion,[status(esa)],[f_1081_2]) ).

cnf(f_1081_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3864),U_3863) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3864),U_3863)),U_3863))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3864),U_3863))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3863)) ),
    inference(clausify,[status(thm)],[f_1081_3]) ).

fof(f_1082_1,plain,
    ! [V_n,V_m] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__if]) ).

fof(f_1082_2,plain,
    ! [U_3866,U_3865] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3865),U_3866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3866),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3865),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3866))
        | U_3865 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3865),U_3866) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3865 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

fof(f_1082_3,plain,
    ( ! [U_3870,U_3868] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3868),U_3870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3870),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3868),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3870))
        | U_3868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3869,U_3867] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3867),U_3869) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1082_2]) ).

fof(f_1082_4,plain,
    ( ! [U_3870,U_3868] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3868),U_3870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3870),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3868),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3870))
        | U_3868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3869,U_3867] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3867),U_3869) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1082_3]) ).

cnf(f_1082_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3867),U_3869) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3868),U_3870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3870),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3868),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3870))
    | U_3868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

fof(f_1083_1,plain,
    ! [V_k,V_m] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_int__power__div__base]) ).

fof(f_1083_2,plain,
    ! [U_3872,U_3871] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3872),U_3871)),U_3872) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3871),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3872))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3871)) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

fof(f_1083_3,plain,
    ! [U_3871,U_3872] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3872),U_3871)),U_3872) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3871),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3872))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3871)) ),
    inference(definitional_conversion,[status(esa)],[f_1083_2]) ).

cnf(f_1083_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3872),U_3871)),U_3872) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3871),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3872))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3871)) ),
    inference(clausify,[status(thm)],[f_1083_3]) ).

fof(f_1084_1,plain,
    ! [V_k_2,V_P_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).

fof(f_1084_2,plain,
    ! [U_3877,U_3876,U_3875] :
      ( ! [U_3874] :
          ( hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3877),U_3875))))
          | ~ hBOOL(hAPP(U_3876,U_3874)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3877))
      | ? [U_3873] :
          ( ~ hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3873),U_3875)))
          & hBOOL(hAPP(U_3876,U_3873)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3875)) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

fof(f_1084_3,plain,
    ! [U_3877,U_3876,U_3875] :
      ( ! [U_3874] :
          ( hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3877),U_3875))))
          | ~ hBOOL(hAPP(U_3876,U_3874)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3877))
      | ( ~ hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK75(U_3877,U_3876,U_3875)),U_3875)))
        & hBOOL(hAPP(U_3876,sK75(U_3877,U_3876,U_3875))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3875)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3873,sK75(U_3877,U_3876,U_3875))],[f_1084_2]) ).

fof(f_1084_4,plain,
    ( ! [U_3875,U_3876,U_3877] :
        ( ~ hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK75(U_3877,U_3876,U_3875)),U_3875)))
        | ~ sP324(U_3875,U_3876,U_3877) )
    & ! [U_3875,U_3876,U_3877] :
        ( hBOOL(hAPP(U_3876,sK75(U_3877,U_3876,U_3875)))
        | ~ sP324(U_3875,U_3876,U_3877) )
    & ! [U_3874,U_3875,U_3876,U_3877] :
        ( hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3877),U_3875))))
        | ~ hBOOL(hAPP(U_3876,U_3874))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3877))
        | sP324(U_3875,U_3876,U_3877)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3875)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP324])],[f_1084_3]) ).

cnf(f_1084_5,plain,
    ( hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3877),U_3875))))
    | ~ hBOOL(hAPP(U_3876,U_3874))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3877))
    | sP324(U_3875,U_3876,U_3877)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3875)) ),
    inference(clausify,[status(thm)],[f_1084_4]) ).

cnf(f_1084_6,plain,
    ( hBOOL(hAPP(U_3876,sK75(U_3877,U_3876,U_3875)))
    | ~ sP324(U_3875,U_3876,U_3877) ),
    inference(clausify,[status(thm)],[f_1084_4]) ).

cnf(f_1084_7,plain,
    ( ~ hBOOL(hAPP(U_3876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK75(U_3877,U_3876,U_3875)),U_3875)))
    | ~ sP324(U_3875,U_3876,U_3877) ),
    inference(clausify,[status(thm)],[f_1084_4]) ).

fof(f_1085_1,plain,
    ! [V_x,V_z,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
    inference(fof_nnf,[status(thm)],[fact_incr__lemma]) ).

fof(f_1085_2,plain,
    ! [U_3880,U_3879,U_3878] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3880),U_3879))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3878))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3878)) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

fof(f_1085_3,plain,
    ! [U_3879,U_3880,U_3878] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3880),U_3879))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3878))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3878)) ),
    inference(definitional_conversion,[status(esa)],[f_1085_2]) ).

cnf(f_1085_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3880),U_3879))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3878))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3878)) ),
    inference(clausify,[status(thm)],[f_1085_3]) ).

fof(f_1086_1,plain,
    ! [V_z,V_x,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
    inference(fof_nnf,[status(thm)],[fact_decr__lemma]) ).

fof(f_1086_2,plain,
    ! [U_3883,U_3882,U_3881] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3882),U_3883))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3881))),U_3883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3881)) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

fof(f_1086_3,plain,
    ! [U_3882,U_3881,U_3883] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3882),U_3883))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3881))),U_3883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3881)) ),
    inference(definitional_conversion,[status(esa)],[f_1086_2]) ).

cnf(f_1086_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3882),U_3883))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3881))),U_3883))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3881)) ),
    inference(clausify,[status(thm)],[f_1086_3]) ).

fof(f_1087_1,plain,
    ! [V_y,V_n,V_x] :
      ( ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma]) ).

fof(f_1087_2,plain,
    ! [U_3887,U_3886,U_3885] :
      ( ? [U_3884] : U_3885 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),U_3884))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),U_3885))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3885,U_3886) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3887,U_3886) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

fof(f_1087_3,plain,
    ! [U_3887,U_3886,U_3885] :
      ( U_3885 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),sK76(U_3887,U_3886,U_3885)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),U_3885))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3885,U_3886) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3887,U_3886) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3884,sK76(U_3887,U_3886,U_3885))],[f_1087_2]) ).

fof(f_1087_4,plain,
    ! [U_3885,U_3886,U_3887] :
      ( U_3885 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),sK76(U_3887,U_3886,U_3885)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),U_3885))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3885,U_3886) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3887,U_3886) ),
    inference(definitional_conversion,[status(esa)],[f_1087_3]) ).

cnf(f_1087_5,plain,
    ( U_3885 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3886),sK76(U_3887,U_3886,U_3885)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),U_3885))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3885,U_3886) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3887,U_3886) ),
    inference(clausify,[status(thm)],[f_1087_4]) ).

fof(f_1088_1,plain,
    ! [V_i_2,V_P_2,V_p_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
      | ~ hBOOL(hAPP(V_P_2,V_i_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
          & hBOOL(hAPP(V_P_2,B_i))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__induct__0]) ).

fof(f_1088_2,plain,
    ! [U_3891,U_3890,U_3889] :
      ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3891),U_3889))
      | ~ hBOOL(hAPP(U_3890,U_3891))
      | ? [U_3888] :
          ( ~ hBOOL(hAPP(U_3890,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3888),U_3889)))
          & hBOOL(hAPP(U_3890,U_3888))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3888),U_3889)) ) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

fof(f_1088_3,plain,
    ! [U_3891,U_3890,U_3889] :
      ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3891),U_3889))
      | ~ hBOOL(hAPP(U_3890,U_3891))
      | ( ~ hBOOL(hAPP(U_3890,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK77(U_3891,U_3890,U_3889)),U_3889)))
        & hBOOL(hAPP(U_3890,sK77(U_3891,U_3890,U_3889)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK77(U_3891,U_3890,U_3889)),U_3889)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3888,sK77(U_3891,U_3890,U_3889))],[f_1088_2]) ).

fof(f_1088_4,plain,
    ( ! [U_3889,U_3890,U_3891] :
        ( ~ hBOOL(hAPP(U_3890,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK77(U_3891,U_3890,U_3889)),U_3889)))
        | ~ sP325(U_3889,U_3890,U_3891) )
    & ! [U_3889,U_3890,U_3891] :
        ( hBOOL(hAPP(U_3890,sK77(U_3891,U_3890,U_3889)))
        | ~ sP325(U_3889,U_3890,U_3891) )
    & ! [U_3889,U_3890,U_3891] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK77(U_3891,U_3890,U_3889)),U_3889))
        | ~ sP325(U_3889,U_3890,U_3891) )
    & ! [U_3889,U_3890,U_3891] :
        ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3891),U_3889))
        | ~ hBOOL(hAPP(U_3890,U_3891))
        | sP325(U_3889,U_3890,U_3891) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325])],[f_1088_3]) ).

cnf(f_1088_5,plain,
    ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3891),U_3889))
    | ~ hBOOL(hAPP(U_3890,U_3891))
    | sP325(U_3889,U_3890,U_3891) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK77(U_3891,U_3890,U_3889)),U_3889))
    | ~ sP325(U_3889,U_3890,U_3891) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_7,plain,
    ( hBOOL(hAPP(U_3890,sK77(U_3891,U_3890,U_3889)))
    | ~ sP325(U_3889,U_3890,U_3891) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_8,plain,
    ( ~ hBOOL(hAPP(U_3890,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK77(U_3891,U_3890,U_3889)),U_3889)))
    | ~ sP325(U_3889,U_3890,U_3891) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

fof(f_1089_1,plain,
    ! [V_v] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_expand__Suc]) ).

fof(f_1089_2,plain,
    ! [U_3892] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892))) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

fof(f_1089_3,plain,
    ! [U_3892] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892))) ),
    inference(definitional_conversion,[status(esa)],[f_1089_2]) ).

cnf(f_1089_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3892))) ),
    inference(clausify,[status(thm)],[f_1089_3]) ).

fof(f_1090_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ? [B_e] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) )
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__le__epsilon]) ).

fof(f_1090_2,plain,
    ! [U_3896,U_3895,U_3894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),U_3896))
      | ? [U_3893] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3896),U_3893)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3894),c_Groups_Ozero__class_Ozero(U_3894)),U_3893)) )
      | ~ class_Fields_Olinordered__field(U_3894) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

fof(f_1090_3,plain,
    ! [U_3896,U_3895,U_3894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),U_3896))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3896),sK78(U_3896,U_3895,U_3894))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3894),c_Groups_Ozero__class_Ozero(U_3894)),sK78(U_3896,U_3895,U_3894))) )
      | ~ class_Fields_Olinordered__field(U_3894) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_3893,sK78(U_3896,U_3895,U_3894))],[f_1090_2]) ).

fof(f_1090_4,plain,
    ( ! [U_3894,U_3895,U_3896] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3896),sK78(U_3896,U_3895,U_3894))))
        | ~ sP326(U_3894,U_3895,U_3896) )
    & ! [U_3894,U_3895,U_3896] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3894),c_Groups_Ozero__class_Ozero(U_3894)),sK78(U_3896,U_3895,U_3894)))
        | ~ sP326(U_3894,U_3895,U_3896) )
    & ! [U_3894,U_3895,U_3896] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),U_3896))
        | sP326(U_3894,U_3895,U_3896)
        | ~ class_Fields_Olinordered__field(U_3894) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326])],[f_1090_3]) ).

cnf(f_1090_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),U_3896))
    | sP326(U_3894,U_3895,U_3896)
    | ~ class_Fields_Olinordered__field(U_3894) ),
    inference(clausify,[status(thm)],[f_1090_4]) ).

cnf(f_1090_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3894),c_Groups_Ozero__class_Ozero(U_3894)),sK78(U_3896,U_3895,U_3894)))
    | ~ sP326(U_3894,U_3895,U_3896) ),
    inference(clausify,[status(thm)],[f_1090_4]) ).

cnf(f_1090_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3894),U_3895),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3896),sK78(U_3896,U_3895,U_3894))))
    | ~ sP326(U_3894,U_3895,U_3896) ),
    inference(clausify,[status(thm)],[f_1090_4]) ).

fof(f_1091_1,plain,
    ! [V_n,V_z,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__power]) ).

fof(f_1091_2,plain,
    ! [U_3899,U_3898,U_3897] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3897),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3898),U_3899)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3897),hAPP(c_Int_Oring__1__class_Oof__int(U_3897),U_3898)),U_3899)
      | ~ class_Rings_Oring__1(U_3897) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

fof(f_1091_3,plain,
    ! [U_3897,U_3898,U_3899] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3897),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3898),U_3899)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3897),hAPP(c_Int_Oring__1__class_Oof__int(U_3897),U_3898)),U_3899)
      | ~ class_Rings_Oring__1(U_3897) ),
    inference(definitional_conversion,[status(esa)],[f_1091_2]) ).

cnf(f_1091_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3897),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3898),U_3899)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3897),hAPP(c_Int_Oring__1__class_Oof__int(U_3897),U_3898)),U_3899)
    | ~ class_Rings_Oring__1(U_3897) ),
    inference(clausify,[status(thm)],[f_1091_3]) ).

fof(f_1092_1,plain,
    ! [V_v,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq]) ).

fof(f_1092_2,plain,
    ! [U_3901,U_3900] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3900),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3901)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3900),U_3901)
      | ~ class_Int_Onumber__ring(U_3900) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

fof(f_1092_3,plain,
    ! [U_3900,U_3901] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3900),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3901)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3900),U_3901)
      | ~ class_Int_Onumber__ring(U_3900) ),
    inference(definitional_conversion,[status(esa)],[f_1092_2]) ).

cnf(f_1092_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3900),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3901)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3900),U_3901)
    | ~ class_Int_Onumber__ring(U_3900) ),
    inference(clausify,[status(thm)],[f_1092_3]) ).

fof(f_1093_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Oring__char__0(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).

fof(f_1093_2,plain,
    ! [U_3904,U_3903,U_3902] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3903) = hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3904)
          | U_3903 != U_3904 )
        & ( U_3903 = U_3904
          | hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3903) != hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3904) ) )
      | ~ class_Int_Oring__char__0(U_3902)
      | ~ class_Int_Onumber__ring(U_3902) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

fof(f_1093_3,plain,
    ( ! [U_3902,U_3903,U_3904] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3903) = hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3904)
        | U_3903 != U_3904
        | ~ sP327(U_3902,U_3903,U_3904) )
    & ! [U_3902,U_3903,U_3904] :
        ( U_3903 = U_3904
        | hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3903) != hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3904)
        | ~ sP327(U_3902,U_3903,U_3904) )
    & ! [U_3902,U_3903,U_3904] :
        ( sP327(U_3902,U_3903,U_3904)
        | ~ class_Int_Oring__char__0(U_3902)
        | ~ class_Int_Onumber__ring(U_3902) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP327])],[f_1093_2]) ).

cnf(f_1093_4,plain,
    ( sP327(U_3902,U_3903,U_3904)
    | ~ class_Int_Oring__char__0(U_3902)
    | ~ class_Int_Onumber__ring(U_3902) ),
    inference(clausify,[status(thm)],[f_1093_3]) ).

cnf(f_1093_5,plain,
    ( U_3903 = U_3904
    | hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3903) != hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3904)
    | ~ sP327(U_3902,U_3903,U_3904) ),
    inference(clausify,[status(thm)],[f_1093_3]) ).

cnf(f_1093_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3903) = hAPP(c_Int_Onumber__class_Onumber__of(U_3902),U_3904)
    | U_3903 != U_3904
    | ~ sP327(U_3902,U_3903,U_3904) ),
    inference(clausify,[status(thm)],[f_1093_3]) ).

fof(f_1094_1,plain,
    ! [V_x_2,V_w_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
          | V_x_2 != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) )
        & ( V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != V_x_2 ) )
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).

fof(f_1094_2,plain,
    ! [U_3907,U_3906,U_3905] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) = U_3907
          | U_3907 != hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) )
        & ( U_3907 = hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906)
          | hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) != U_3907 ) )
      | ~ class_Int_Onumber(U_3905) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

fof(f_1094_3,plain,
    ( ! [U_3906,U_3907,U_3905] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) = U_3907
        | U_3907 != hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906)
        | ~ sP328(U_3906,U_3907,U_3905) )
    & ! [U_3906,U_3907,U_3905] :
        ( U_3907 = hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) != U_3907
        | ~ sP328(U_3906,U_3907,U_3905) )
    & ! [U_3906,U_3907,U_3905] :
        ( sP328(U_3906,U_3907,U_3905)
        | ~ class_Int_Onumber(U_3905) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP328])],[f_1094_2]) ).

cnf(f_1094_4,plain,
    ( sP328(U_3906,U_3907,U_3905)
    | ~ class_Int_Onumber(U_3905) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

cnf(f_1094_5,plain,
    ( U_3907 = hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) != U_3907
    | ~ sP328(U_3906,U_3907,U_3905) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

cnf(f_1094_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906) = U_3907
    | U_3907 != hAPP(c_Int_Onumber__class_Onumber__of(U_3905),U_3906)
    | ~ sP328(U_3906,U_3907,U_3905) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

fof(f_1095_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__idempotent]) ).

fof(f_1095_2,plain,
    ! [U_3909,U_3908] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3908),hAPP(c_Groups_Oabs__class_Oabs(U_3908),U_3909)) = hAPP(c_Groups_Oabs__class_Oabs(U_3908),U_3909)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3908) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

fof(f_1095_3,plain,
    ! [U_3909,U_3908] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3908),hAPP(c_Groups_Oabs__class_Oabs(U_3908),U_3909)) = hAPP(c_Groups_Oabs__class_Oabs(U_3908),U_3909)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3908) ),
    inference(definitional_conversion,[status(esa)],[f_1095_2]) ).

cnf(f_1095_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3908),hAPP(c_Groups_Oabs__class_Oabs(U_3908),U_3909)) = hAPP(c_Groups_Oabs__class_Oabs(U_3908),U_3909)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3908) ),
    inference(clausify,[status(thm)],[f_1095_3]) ).

fof(f_1096_1,plain,
    ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))),
    inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(f_1096_2,plain,
    ! [U_3911,U_3910] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3910)),U_3911))),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

fof(f_1096_3,plain,
    ! [U_3910,U_3911] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3910)),U_3911))),
    inference(definitional_conversion,[status(esa)],[f_1096_2]) ).

cnf(f_1096_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3910)),U_3911))),
    inference(clausify,[status(thm)],[f_1096_3]) ).

fof(f_1097_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__D1]) ).

fof(f_1097_2,plain,
    ! [U_3914,U_3913,U_3912] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3912),U_3913),U_3914))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3912),hAPP(c_Groups_Oabs__class_Oabs(U_3912),U_3913)),U_3914))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3912) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

fof(f_1097_3,plain,
    ! [U_3912,U_3913,U_3914] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3912),U_3913),U_3914))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3912),hAPP(c_Groups_Oabs__class_Oabs(U_3912),U_3913)),U_3914))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3912) ),
    inference(definitional_conversion,[status(esa)],[f_1097_2]) ).

cnf(f_1097_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3912),U_3913),U_3914))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3912),hAPP(c_Groups_Oabs__class_Oabs(U_3912),U_3913)),U_3914))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3912) ),
    inference(clausify,[status(thm)],[f_1097_3]) ).

fof(f_1098_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__self]) ).

fof(f_1098_2,plain,
    ! [U_3916,U_3915] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3915),U_3916),hAPP(c_Groups_Oabs__class_Oabs(U_3915),U_3916)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3915) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

fof(f_1098_3,plain,
    ! [U_3915,U_3916] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3915),U_3916),hAPP(c_Groups_Oabs__class_Oabs(U_3915),U_3916)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3915) ),
    inference(definitional_conversion,[status(esa)],[f_1098_2]) ).

cnf(f_1098_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3915),U_3916),hAPP(c_Groups_Oabs__class_Oabs(U_3915),U_3916)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3915) ),
    inference(clausify,[status(thm)],[f_1098_3]) ).

fof(f_1099_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__zero]) ).

fof(f_1099_2,plain,
    ! [U_3917] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3917),c_Groups_Ozero__class_Ozero(U_3917)) = c_Groups_Ozero__class_Ozero(U_3917)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3917) ),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

fof(f_1099_3,plain,
    ! [U_3917] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3917),c_Groups_Ozero__class_Ozero(U_3917)) = c_Groups_Ozero__class_Ozero(U_3917)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3917) ),
    inference(definitional_conversion,[status(esa)],[f_1099_2]) ).

cnf(f_1099_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3917),c_Groups_Ozero__class_Ozero(U_3917)) = c_Groups_Ozero__class_Ozero(U_3917)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3917) ),
    inference(clausify,[status(thm)],[f_1099_3]) ).

fof(f_1100_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).

fof(f_1100_2,plain,
    ! [U_3919,U_3918] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_3918),U_3919) = c_Groups_Ozero__class_Ozero(U_3918)
          | U_3919 != c_Groups_Ozero__class_Ozero(U_3918) )
        & ( U_3919 = c_Groups_Ozero__class_Ozero(U_3918)
          | hAPP(c_Groups_Oabs__class_Oabs(U_3918),U_3919) != c_Groups_Ozero__class_Ozero(U_3918) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3918) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

fof(f_1100_3,plain,
    ( ! [U_3918,U_3919] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_3918),U_3919) = c_Groups_Ozero__class_Ozero(U_3918)
        | U_3919 != c_Groups_Ozero__class_Ozero(U_3918)
        | ~ sP329(U_3918,U_3919) )
    & ! [U_3918,U_3919] :
        ( U_3919 = c_Groups_Ozero__class_Ozero(U_3918)
        | hAPP(c_Groups_Oabs__class_Oabs(U_3918),U_3919) != c_Groups_Ozero__class_Ozero(U_3918)
        | ~ sP329(U_3918,U_3919) )
    & ! [U_3918,U_3919] :
        ( sP329(U_3918,U_3919)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_3918) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP329])],[f_1100_2]) ).

cnf(f_1100_4,plain,
    ( sP329(U_3918,U_3919)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3918) ),
    inference(clausify,[status(thm)],[f_1100_3]) ).

cnf(f_1100_5,plain,
    ( U_3919 = c_Groups_Ozero__class_Ozero(U_3918)
    | hAPP(c_Groups_Oabs__class_Oabs(U_3918),U_3919) != c_Groups_Ozero__class_Ozero(U_3918)
    | ~ sP329(U_3918,U_3919) ),
    inference(clausify,[status(thm)],[f_1100_3]) ).

cnf(f_1100_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3918),U_3919) = c_Groups_Ozero__class_Ozero(U_3918)
    | U_3919 != c_Groups_Ozero__class_Ozero(U_3918)
    | ~ sP329(U_3918,U_3919) ),
    inference(clausify,[status(thm)],[f_1100_3]) ).

fof(f_1101_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__add__abs]) ).

fof(f_1101_2,plain,
    ! [U_3922,U_3921,U_3920] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3920),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3921)),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3922))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3920),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3921)),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3922))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3920) ),
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

fof(f_1101_3,plain,
    ! [U_3921,U_3920,U_3922] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3920),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3921)),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3922))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3920),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3921)),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3922))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3920) ),
    inference(definitional_conversion,[status(esa)],[f_1101_2]) ).

cnf(f_1101_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3920),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3921)),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3922))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3920),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3921)),hAPP(c_Groups_Oabs__class_Oabs(U_3920),U_3922))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3920) ),
    inference(clausify,[status(thm)],[f_1101_3]) ).

fof(f_1102_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__self]) ).

fof(f_1102_2,plain,
    ! [U_3924,U_3923] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),hAPP(c_Groups_Oabs__class_Oabs(U_3923),U_3924)),hAPP(c_Groups_Oabs__class_Oabs(U_3923),U_3924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3924),U_3924)
      | ~ class_Rings_Olinordered__idom(U_3923) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

fof(f_1102_3,plain,
    ! [U_3923,U_3924] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),hAPP(c_Groups_Oabs__class_Oabs(U_3923),U_3924)),hAPP(c_Groups_Oabs__class_Oabs(U_3923),U_3924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3924),U_3924)
      | ~ class_Rings_Olinordered__idom(U_3923) ),
    inference(definitional_conversion,[status(esa)],[f_1102_2]) ).

cnf(f_1102_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),hAPP(c_Groups_Oabs__class_Oabs(U_3923),U_3924)),hAPP(c_Groups_Oabs__class_Oabs(U_3923),U_3924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3924),U_3924)
    | ~ class_Rings_Olinordered__idom(U_3923) ),
    inference(clausify,[status(thm)],[f_1102_3]) ).

fof(f_1103_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult]) ).

fof(f_1103_2,plain,
    ! [U_3927,U_3926,U_3925] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3925),U_3926),U_3927)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3925),hAPP(c_Groups_Oabs__class_Oabs(U_3925),U_3926)),hAPP(c_Groups_Oabs__class_Oabs(U_3925),U_3927))
      | ~ class_Rings_Olinordered__idom(U_3925) ),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

fof(f_1103_3,plain,
    ! [U_3925,U_3926,U_3927] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3925),U_3926),U_3927)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3925),hAPP(c_Groups_Oabs__class_Oabs(U_3925),U_3926)),hAPP(c_Groups_Oabs__class_Oabs(U_3925),U_3927))
      | ~ class_Rings_Olinordered__idom(U_3925) ),
    inference(definitional_conversion,[status(esa)],[f_1103_2]) ).

cnf(f_1103_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3925),U_3926),U_3927)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3925),hAPP(c_Groups_Oabs__class_Oabs(U_3925),U_3926)),hAPP(c_Groups_Oabs__class_Oabs(U_3925),U_3927))
    | ~ class_Rings_Olinordered__idom(U_3925) ),
    inference(clausify,[status(thm)],[f_1103_3]) ).

fof(f_1104_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__commute]) ).

fof(f_1104_2,plain,
    ! [U_3930,U_3929,U_3928] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3928),U_3929),U_3930)) = hAPP(c_Groups_Oabs__class_Oabs(U_3928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3928),U_3930),U_3929))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3928) ),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

fof(f_1104_3,plain,
    ! [U_3928,U_3929,U_3930] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3928),U_3929),U_3930)) = hAPP(c_Groups_Oabs__class_Oabs(U_3928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3928),U_3930),U_3929))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3928) ),
    inference(definitional_conversion,[status(esa)],[f_1104_2]) ).

cnf(f_1104_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3928),U_3929),U_3930)) = hAPP(c_Groups_Oabs__class_Oabs(U_3928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3928),U_3930),U_3929))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3928) ),
    inference(clausify,[status(thm)],[f_1104_3]) ).

fof(f_1105_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__one]) ).

fof(f_1105_2,plain,
    ! [U_3931] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3931),c_Groups_Oone__class_Oone(U_3931)) = c_Groups_Oone__class_Oone(U_3931)
      | ~ class_Rings_Olinordered__idom(U_3931) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

fof(f_1105_3,plain,
    ! [U_3931] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3931),c_Groups_Oone__class_Oone(U_3931)) = c_Groups_Oone__class_Oone(U_3931)
      | ~ class_Rings_Olinordered__idom(U_3931) ),
    inference(definitional_conversion,[status(esa)],[f_1105_2]) ).

cnf(f_1105_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3931),c_Groups_Oone__class_Oone(U_3931)) = c_Groups_Oone__class_Oone(U_3931)
    | ~ class_Rings_Olinordered__idom(U_3931) ),
    inference(clausify,[status(thm)],[f_1105_3]) ).

fof(f_1106_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel]) ).

fof(f_1106_2,plain,
    ! [U_3933,U_3932] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3932),hAPP(c_Groups_Ouminus__class_Ouminus(U_3932),U_3933)) = hAPP(c_Groups_Oabs__class_Oabs(U_3932),U_3933)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3932) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

fof(f_1106_3,plain,
    ! [U_3932,U_3933] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3932),hAPP(c_Groups_Ouminus__class_Ouminus(U_3932),U_3933)) = hAPP(c_Groups_Oabs__class_Oabs(U_3932),U_3933)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3932) ),
    inference(definitional_conversion,[status(esa)],[f_1106_2]) ).

cnf(f_1106_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3932),hAPP(c_Groups_Ouminus__class_Ouminus(U_3932),U_3933)) = hAPP(c_Groups_Oabs__class_Oabs(U_3932),U_3933)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3932) ),
    inference(clausify,[status(thm)],[f_1106_3]) ).

fof(f_1107_1,plain,
    ! [V_q,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).

fof(f_1107_2,plain,
    ! [U_3937,U_3936,U_3935,U_3934] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3934),U_3935),U_3936)),U_3937) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3934),hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3935),U_3937)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3936),U_3937))
      | ~ class_Rings_Ocomm__semiring__1(U_3934) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

fof(f_1107_3,plain,
    ! [U_3934,U_3935,U_3936,U_3937] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3934),U_3935),U_3936)),U_3937) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3934),hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3935),U_3937)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3936),U_3937))
      | ~ class_Rings_Ocomm__semiring__1(U_3934) ),
    inference(definitional_conversion,[status(esa)],[f_1107_2]) ).

cnf(f_1107_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3934),U_3935),U_3936)),U_3937) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3934),hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3935),U_3937)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3936),U_3937))
    | ~ class_Rings_Ocomm__semiring__1(U_3934) ),
    inference(clausify,[status(thm)],[f_1107_3]) ).

fof(f_1108_1,plain,
    ! [V_n,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nat]) ).

fof(f_1108_2,plain,
    ! [U_3939,U_3938] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3938),U_3939)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3938),U_3939)
      | ~ class_Rings_Olinordered__idom(U_3938) ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

fof(f_1108_3,plain,
    ! [U_3939,U_3938] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3938),U_3939)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3938),U_3939)
      | ~ class_Rings_Olinordered__idom(U_3938) ),
    inference(definitional_conversion,[status(esa)],[f_1108_2]) ).

cnf(f_1108_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3938),U_3939)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3938),U_3939)
    | ~ class_Rings_Olinordered__idom(U_3938) ),
    inference(clausify,[status(thm)],[f_1108_3]) ).

fof(f_1109_1,plain,
    ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),
    inference(fof_nnf,[status(thm)],[fact_abs__int__eq]) ).

fof(f_1109_2,plain,
    ! [U_3940] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3940)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3940),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

fof(f_1109_3,plain,
    ! [U_3940] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3940)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3940),
    inference(definitional_conversion,[status(esa)],[f_1109_2]) ).

cnf(f_1109_4,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3940)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3940),
    inference(clausify,[status(thm)],[f_1109_3]) ).

fof(f_1110_1,plain,
    ! [V_q,V_p,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).

fof(f_1110_2,plain,
    ! [U_3944,U_3943,U_3942,U_3941] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),U_3944) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3943),U_3944))
      | ~ class_Rings_Ocomm__semiring__1(U_3941) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

fof(f_1110_3,plain,
    ! [U_3941,U_3942,U_3943,U_3944] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),U_3944) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3943),U_3944))
      | ~ class_Rings_Ocomm__semiring__1(U_3941) ),
    inference(definitional_conversion,[status(esa)],[f_1110_2]) ).

cnf(f_1110_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),U_3944) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3943),U_3944))
    | ~ class_Rings_Ocomm__semiring__1(U_3941) ),
    inference(clausify,[status(thm)],[f_1110_3]) ).

fof(f_1111_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zpower__zpower]) ).

fof(f_1111_2,plain,
    ! [U_3947,U_3946,U_3945] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3945),U_3946)),U_3947) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3946),U_3947)),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

fof(f_1111_3,plain,
    ! [U_3945,U_3946,U_3947] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3945),U_3946)),U_3947) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3946),U_3947)),
    inference(definitional_conversion,[status(esa)],[f_1111_2]) ).

cnf(f_1111_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3945),U_3946)),U_3947) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3946),U_3947)),
    inference(clausify,[status(thm)],[f_1111_3]) ).

fof(f_1112_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).

fof(f_1112_2,plain,
    ! [U_3949,U_3948] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3949),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3949
      | ~ class_Rings_Ocomm__semiring__1(U_3948) ),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

fof(f_1112_3,plain,
    ! [U_3948,U_3949] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3949),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3949
      | ~ class_Rings_Ocomm__semiring__1(U_3948) ),
    inference(definitional_conversion,[status(esa)],[f_1112_2]) ).

cnf(f_1112_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3949),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3949
    | ~ class_Rings_Ocomm__semiring__1(U_3948) ),
    inference(clausify,[status(thm)],[f_1112_3]) ).

fof(f_1113_1,plain,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m),
    inference(fof_nnf,[status(thm)],[fact_zpower__zmod]) ).

fof(f_1113_2,plain,
    ! [U_3952,U_3951,U_3950] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3950,U_3951)),U_3952),U_3951) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3950),U_3952),U_3951),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

fof(f_1113_3,plain,
    ! [U_3950,U_3951,U_3952] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3950,U_3951)),U_3952),U_3951) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3950),U_3952),U_3951),
    inference(definitional_conversion,[status(esa)],[f_1113_2]) ).

cnf(f_1113_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3950,U_3951)),U_3952),U_3951) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3950),U_3952),U_3951),
    inference(clausify,[status(thm)],[f_1113_3]) ).

fof(f_1114_1,plain,
    ! [V_v,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(f_1114_2,plain,
    ! [U_3954,U_3953] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3954)) = c_Groups_Ozero__class_Ozero(U_3953)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3954))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3954)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3953),U_3954)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3954))) ) )
      | ~ class_Int_Onumber__ring(U_3953) ),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

fof(f_1114_3,plain,
    ( ! [U_3954,U_3953] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3954)) = c_Groups_Ozero__class_Ozero(U_3953)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3954)))
        | ~ sP330(U_3954,U_3953) )
    & ! [U_3954,U_3953] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3954)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3953),U_3954)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3954)))
        | ~ sP330(U_3954,U_3953) )
    & ! [U_3954,U_3953] :
        ( sP330(U_3954,U_3953)
        | ~ class_Int_Onumber__ring(U_3953) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330])],[f_1114_2]) ).

cnf(f_1114_4,plain,
    ( sP330(U_3954,U_3953)
    | ~ class_Int_Onumber__ring(U_3953) ),
    inference(clausify,[status(thm)],[f_1114_3]) ).

cnf(f_1114_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3954)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3953),U_3954)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3954)))
    | ~ sP330(U_3954,U_3953) ),
    inference(clausify,[status(thm)],[f_1114_3]) ).

cnf(f_1114_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3954)) = c_Groups_Ozero__class_Ozero(U_3953)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3954)))
    | ~ sP330(U_3954,U_3953) ),
    inference(clausify,[status(thm)],[f_1114_3]) ).

fof(f_1115_1,plain,
    ! [V_k,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__eq]) ).

fof(f_1115_2,plain,
    ! [U_3956,U_3955] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_3955),U_3956) = hAPP(c_Int_Oring__1__class_Oof__int(U_3955),U_3956)
      | ~ class_Int_Onumber__ring(U_3955) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

fof(f_1115_3,plain,
    ! [U_3956,U_3955] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_3955),U_3956) = hAPP(c_Int_Oring__1__class_Oof__int(U_3955),U_3956)
      | ~ class_Int_Onumber__ring(U_3955) ),
    inference(definitional_conversion,[status(esa)],[f_1115_2]) ).

cnf(f_1115_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_3955),U_3956) = hAPP(c_Int_Oring__1__class_Oof__int(U_3955),U_3956)
    | ~ class_Int_Onumber__ring(U_3955) ),
    inference(clausify,[status(thm)],[f_1115_3]) ).

fof(f_1116_1,plain,
    ! [V_x,T_a] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__number__of]) ).

fof(f_1116_2,plain,
    ! [U_3958,U_3957] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)),c_Groups_Ozero__class_Ozero(U_3957))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)),c_Groups_Ozero__class_Ozero(U_3957))) ) )
      | ~ class_Rings_Olinordered__idom(U_3957)
      | ~ class_Int_Onumber__ring(U_3957) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

fof(f_1116_3,plain,
    ( ! [U_3957,U_3958] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)),c_Groups_Ozero__class_Ozero(U_3957)))
        | ~ sP331(U_3957,U_3958) )
    & ! [U_3957,U_3958] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)),c_Groups_Ozero__class_Ozero(U_3957)))
        | ~ sP331(U_3957,U_3958) )
    & ! [U_3957,U_3958] :
        ( sP331(U_3957,U_3958)
        | ~ class_Rings_Olinordered__idom(U_3957)
        | ~ class_Int_Onumber__ring(U_3957) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP331])],[f_1116_2]) ).

cnf(f_1116_4,plain,
    ( sP331(U_3957,U_3958)
    | ~ class_Rings_Olinordered__idom(U_3957)
    | ~ class_Int_Onumber__ring(U_3957) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

cnf(f_1116_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)),c_Groups_Ozero__class_Ozero(U_3957)))
    | ~ sP331(U_3957,U_3958) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

cnf(f_1116_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),hAPP(c_Int_Onumber__class_Onumber__of(U_3957),U_3958)),c_Groups_Ozero__class_Ozero(U_3957)))
    | ~ sP331(U_3957,U_3958) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

fof(f_1117_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).

fof(f_1117_2,plain,
    ! [U_3960,U_3959] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3959)),U_3960)))
        | ( U_3960 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3959 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_3960 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3959 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3959)),U_3960))) ) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

fof(f_1117_3,plain,
    ( ! [U_3964,U_3962] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3962)),U_3964)))
        | ( U_3964 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3963,U_3961] :
        ( U_3963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3961 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3961)),U_3963))) ) ),
    inference(miniscope,[status(thm)],[f_1117_2]) ).

fof(f_1117_4,plain,
    ( ! [U_3962,U_3964] :
        ( U_3964 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP332(U_3962,U_3964) )
    & ! [U_3962,U_3964] :
        ( U_3962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP332(U_3962,U_3964) )
    & ! [U_3962,U_3964] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3962)),U_3964)))
        | sP332(U_3962,U_3964) )
    & ! [U_3963,U_3961] :
        ( U_3963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3961 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3961)),U_3963))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP332])],[f_1117_3]) ).

cnf(f_1117_5,plain,
    ( U_3963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3961 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3961)),U_3963))) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

cnf(f_1117_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3962)),U_3964)))
    | sP332(U_3962,U_3964) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

cnf(f_1117_7,plain,
    ( U_3962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP332(U_3962,U_3964) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

cnf(f_1117_8,plain,
    ( U_3964 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP332(U_3962,U_3964) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

fof(f_1118_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg]) ).

fof(f_1118_2,plain,
    ! [U_3966,U_3965] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3965),U_3966) = U_3966
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),U_3966))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3965) ),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

fof(f_1118_3,plain,
    ! [U_3965,U_3966] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3965),U_3966) = U_3966
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),U_3966))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3965) ),
    inference(definitional_conversion,[status(esa)],[f_1118_2]) ).

cnf(f_1118_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3965),U_3966) = U_3966
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),U_3966))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3965) ),
    inference(clausify,[status(thm)],[f_1118_3]) ).

fof(f_1119_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).

fof(f_1119_2,plain,
    ! [U_3968,U_3967] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3967),hAPP(c_Groups_Oabs__class_Oabs(U_3967),U_3968)),c_Groups_Ozero__class_Ozero(U_3967)))
          | U_3968 != c_Groups_Ozero__class_Ozero(U_3967) )
        & ( U_3968 = c_Groups_Ozero__class_Ozero(U_3967)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3967),hAPP(c_Groups_Oabs__class_Oabs(U_3967),U_3968)),c_Groups_Ozero__class_Ozero(U_3967))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3967) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

fof(f_1119_3,plain,
    ( ! [U_3967,U_3968] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3967),hAPP(c_Groups_Oabs__class_Oabs(U_3967),U_3968)),c_Groups_Ozero__class_Ozero(U_3967)))
        | U_3968 != c_Groups_Ozero__class_Ozero(U_3967)
        | ~ sP333(U_3967,U_3968) )
    & ! [U_3967,U_3968] :
        ( U_3968 = c_Groups_Ozero__class_Ozero(U_3967)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3967),hAPP(c_Groups_Oabs__class_Oabs(U_3967),U_3968)),c_Groups_Ozero__class_Ozero(U_3967)))
        | ~ sP333(U_3967,U_3968) )
    & ! [U_3967,U_3968] :
        ( sP333(U_3967,U_3968)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_3967) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP333])],[f_1119_2]) ).

cnf(f_1119_4,plain,
    ( sP333(U_3967,U_3968)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3967) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

cnf(f_1119_5,plain,
    ( U_3968 = c_Groups_Ozero__class_Ozero(U_3967)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3967),hAPP(c_Groups_Oabs__class_Oabs(U_3967),U_3968)),c_Groups_Ozero__class_Ozero(U_3967)))
    | ~ sP333(U_3967,U_3968) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

cnf(f_1119_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3967),hAPP(c_Groups_Oabs__class_Oabs(U_3967),U_3968)),c_Groups_Ozero__class_Ozero(U_3967)))
    | U_3968 != c_Groups_Ozero__class_Ozero(U_3967)
    | ~ sP333(U_3967,U_3968) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

fof(f_1120_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__zero]) ).

fof(f_1120_2,plain,
    ! [U_3970,U_3969] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),c_Groups_Ozero__class_Ozero(U_3969)),hAPP(c_Groups_Oabs__class_Oabs(U_3969),U_3970)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3969) ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

fof(f_1120_3,plain,
    ! [U_3970,U_3969] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),c_Groups_Ozero__class_Ozero(U_3969)),hAPP(c_Groups_Oabs__class_Oabs(U_3969),U_3970)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3969) ),
    inference(definitional_conversion,[status(esa)],[f_1120_2]) ).

cnf(f_1120_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),c_Groups_Ozero__class_Ozero(U_3969)),hAPP(c_Groups_Oabs__class_Oabs(U_3969),U_3970)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3969) ),
    inference(clausify,[status(thm)],[f_1120_3]) ).

fof(f_1121_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__pos]) ).

fof(f_1121_2,plain,
    ! [U_3972,U_3971] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3971),U_3972) = U_3972
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3971),c_Groups_Ozero__class_Ozero(U_3971)),U_3972))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3971) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

fof(f_1121_3,plain,
    ! [U_3971,U_3972] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3971),U_3972) = U_3972
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3971),c_Groups_Ozero__class_Ozero(U_3971)),U_3972))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3971) ),
    inference(definitional_conversion,[status(esa)],[f_1121_2]) ).

cnf(f_1121_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3971),U_3972) = U_3972
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3971),c_Groups_Ozero__class_Ozero(U_3971)),U_3972))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3971) ),
    inference(clausify,[status(thm)],[f_1121_3]) ).

fof(f_1122_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).

fof(f_1122_2,plain,
    ! [U_3974,U_3973] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),hAPP(c_Groups_Oabs__class_Oabs(U_3973),U_3974)))
          | U_3974 = c_Groups_Ozero__class_Ozero(U_3973) )
        & ( U_3974 != c_Groups_Ozero__class_Ozero(U_3973)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),hAPP(c_Groups_Oabs__class_Oabs(U_3973),U_3974))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3973) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

fof(f_1122_3,plain,
    ( ! [U_3973,U_3974] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),hAPP(c_Groups_Oabs__class_Oabs(U_3973),U_3974)))
        | U_3974 = c_Groups_Ozero__class_Ozero(U_3973)
        | ~ sP334(U_3973,U_3974) )
    & ! [U_3973,U_3974] :
        ( U_3974 != c_Groups_Ozero__class_Ozero(U_3973)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),hAPP(c_Groups_Oabs__class_Oabs(U_3973),U_3974)))
        | ~ sP334(U_3973,U_3974) )
    & ! [U_3973,U_3974] :
        ( sP334(U_3973,U_3974)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_3973) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP334])],[f_1122_2]) ).

cnf(f_1122_4,plain,
    ( sP334(U_3973,U_3974)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3973) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

cnf(f_1122_5,plain,
    ( U_3974 != c_Groups_Ozero__class_Ozero(U_3973)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),hAPP(c_Groups_Oabs__class_Oabs(U_3973),U_3974)))
    | ~ sP334(U_3973,U_3974) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

cnf(f_1122_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),hAPP(c_Groups_Oabs__class_Oabs(U_3973),U_3974)))
    | U_3974 = c_Groups_Ozero__class_Ozero(U_3973)
    | ~ sP334(U_3973,U_3974) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

fof(f_1123_1,plain,
    ! [V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__not__less__zero]) ).

fof(f_1123_2,plain,
    ! [U_3976,U_3975] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3975),hAPP(c_Groups_Oabs__class_Oabs(U_3975),U_3976)),c_Groups_Ozero__class_Ozero(U_3975)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3975) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

fof(f_1123_3,plain,
    ! [U_3976,U_3975] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3975),hAPP(c_Groups_Oabs__class_Oabs(U_3975),U_3976)),c_Groups_Ozero__class_Ozero(U_3975)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3975) ),
    inference(definitional_conversion,[status(esa)],[f_1123_2]) ).

cnf(f_1123_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3975),hAPP(c_Groups_Oabs__class_Oabs(U_3975),U_3976)),c_Groups_Ozero__class_Ozero(U_3975)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3975) ),
    inference(clausify,[status(thm)],[f_1123_3]) ).

fof(f_1124_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq]) ).

fof(f_1124_2,plain,
    ! [U_3979,U_3978,U_3977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),hAPP(c_Groups_Oabs__class_Oabs(U_3977),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3977),U_3978),U_3979))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3977),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3978)),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3979))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3977) ),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

fof(f_1124_3,plain,
    ! [U_3977,U_3978,U_3979] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),hAPP(c_Groups_Oabs__class_Oabs(U_3977),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3977),U_3978),U_3979))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3977),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3978)),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3979))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3977) ),
    inference(definitional_conversion,[status(esa)],[f_1124_2]) ).

cnf(f_1124_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),hAPP(c_Groups_Oabs__class_Oabs(U_3977),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3977),U_3978),U_3979))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3977),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3978)),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3979))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3977) ),
    inference(clausify,[status(thm)],[f_1124_3]) ).

fof(f_1125_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__less]) ).

fof(f_1125_2,plain,
    ! [U_3984,U_3983,U_3982,U_3981,U_3980] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981)),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3983))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3980),U_3982),U_3984)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3983)),U_3984))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981)),U_3982))
      | ~ class_Rings_Olinordered__idom(U_3980) ),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

fof(f_1125_3,plain,
    ! [U_3980,U_3981,U_3982,U_3983,U_3984] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981)),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3983))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3980),U_3982),U_3984)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3983)),U_3984))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981)),U_3982))
      | ~ class_Rings_Olinordered__idom(U_3980) ),
    inference(definitional_conversion,[status(esa)],[f_1125_2]) ).

cnf(f_1125_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981)),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3983))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3980),U_3982),U_3984)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3983)),U_3984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3980),hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981)),U_3982))
    | ~ class_Rings_Olinordered__idom(U_3980) ),
    inference(clausify,[status(thm)],[f_1125_3]) ).

fof(f_1126_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym]) ).

fof(f_1126_2,plain,
    ! [U_3987,U_3986,U_3985] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3987))),hAPP(c_Groups_Oabs__class_Oabs(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3987),U_3986))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3985) ),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

fof(f_1126_3,plain,
    ! [U_3986,U_3985,U_3987] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3987))),hAPP(c_Groups_Oabs__class_Oabs(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3987),U_3986))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3985) ),
    inference(definitional_conversion,[status(esa)],[f_1126_2]) ).

cnf(f_1126_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3987))),hAPP(c_Groups_Oabs__class_Oabs(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3987),U_3986))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3985) ),
    inference(clausify,[status(thm)],[f_1126_3]) ).

fof(f_1127_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2]) ).

fof(f_1127_2,plain,
    ! [U_3990,U_3989,U_3988] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3988),hAPP(c_Groups_Oabs__class_Oabs(U_3988),U_3989)),hAPP(c_Groups_Oabs__class_Oabs(U_3988),U_3990))),hAPP(c_Groups_Oabs__class_Oabs(U_3988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3988),U_3989),U_3990))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3988) ),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

fof(f_1127_3,plain,
    ! [U_3988,U_3989,U_3990] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3988),hAPP(c_Groups_Oabs__class_Oabs(U_3988),U_3989)),hAPP(c_Groups_Oabs__class_Oabs(U_3988),U_3990))),hAPP(c_Groups_Oabs__class_Oabs(U_3988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3988),U_3989),U_3990))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3988) ),
    inference(definitional_conversion,[status(esa)],[f_1127_2]) ).

cnf(f_1127_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3988),hAPP(c_Groups_Oabs__class_Oabs(U_3988),U_3989)),hAPP(c_Groups_Oabs__class_Oabs(U_3988),U_3990))),hAPP(c_Groups_Oabs__class_Oabs(U_3988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3988),U_3989),U_3990))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3988) ),
    inference(clausify,[status(thm)],[f_1127_3]) ).

fof(f_1128_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3]) ).

fof(f_1128_2,plain,
    ! [U_3993,U_3992,U_3991] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3991),hAPP(c_Groups_Oabs__class_Oabs(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),hAPP(c_Groups_Oabs__class_Oabs(U_3991),U_3992)),hAPP(c_Groups_Oabs__class_Oabs(U_3991),U_3993)))),hAPP(c_Groups_Oabs__class_Oabs(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3992),U_3993))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3991) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

fof(f_1128_3,plain,
    ! [U_3991,U_3992,U_3993] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3991),hAPP(c_Groups_Oabs__class_Oabs(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),hAPP(c_Groups_Oabs__class_Oabs(U_3991),U_3992)),hAPP(c_Groups_Oabs__class_Oabs(U_3991),U_3993)))),hAPP(c_Groups_Oabs__class_Oabs(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3992),U_3993))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3991) ),
    inference(definitional_conversion,[status(esa)],[f_1128_2]) ).

cnf(f_1128_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3991),hAPP(c_Groups_Oabs__class_Oabs(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),hAPP(c_Groups_Oabs__class_Oabs(U_3991),U_3992)),hAPP(c_Groups_Oabs__class_Oabs(U_3991),U_3993)))),hAPP(c_Groups_Oabs__class_Oabs(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3992),U_3993))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3991) ),
    inference(clausify,[status(thm)],[f_1128_3]) ).

fof(f_1129_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self]) ).

fof(f_1129_2,plain,
    ! [U_3995,U_3994] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),hAPP(c_Groups_Ouminus__class_Ouminus(U_3994),U_3995)),hAPP(c_Groups_Oabs__class_Oabs(U_3994),U_3995)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3994) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

fof(f_1129_3,plain,
    ! [U_3994,U_3995] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),hAPP(c_Groups_Ouminus__class_Ouminus(U_3994),U_3995)),hAPP(c_Groups_Oabs__class_Oabs(U_3994),U_3995)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3994) ),
    inference(definitional_conversion,[status(esa)],[f_1129_2]) ).

cnf(f_1129_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),hAPP(c_Groups_Ouminus__class_Ouminus(U_3994),U_3995)),hAPP(c_Groups_Oabs__class_Oabs(U_3994),U_3995)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3994) ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

fof(f_1130_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).

fof(f_1130_2,plain,
    ! [U_3998,U_3997,U_3996] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Oabs__class_Oabs(U_3996),U_3997)),U_3998))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Ouminus__class_Ouminus(U_3996),U_3997)),U_3998))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),U_3997),U_3998)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Ouminus__class_Ouminus(U_3996),U_3997)),U_3998))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),U_3997),U_3998)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Oabs__class_Oabs(U_3996),U_3997)),U_3998)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3996) ),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

fof(f_1130_3,plain,
    ( ! [U_3996,U_3997,U_3998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Ouminus__class_Ouminus(U_3996),U_3997)),U_3998))
        | ~ sP335(U_3996,U_3997,U_3998) )
    & ! [U_3996,U_3997,U_3998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),U_3997),U_3998))
        | ~ sP335(U_3996,U_3997,U_3998) )
    & ! [U_3996,U_3997,U_3998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Oabs__class_Oabs(U_3996),U_3997)),U_3998))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Ouminus__class_Ouminus(U_3996),U_3997)),U_3998))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),U_3997),U_3998))
        | ~ sP336(U_3996,U_3997,U_3998) )
    & ! [U_3996,U_3997,U_3998] :
        ( sP335(U_3996,U_3997,U_3998)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Oabs__class_Oabs(U_3996),U_3997)),U_3998))
        | ~ sP336(U_3996,U_3997,U_3998) )
    & ! [U_3996,U_3997,U_3998] :
        ( sP336(U_3996,U_3997,U_3998)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_3996) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP335,sP336])],[f_1130_2]) ).

cnf(f_1130_4,plain,
    ( sP336(U_3996,U_3997,U_3998)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3996) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

cnf(f_1130_5,plain,
    ( sP335(U_3996,U_3997,U_3998)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Oabs__class_Oabs(U_3996),U_3997)),U_3998))
    | ~ sP336(U_3996,U_3997,U_3998) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

cnf(f_1130_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Oabs__class_Oabs(U_3996),U_3997)),U_3998))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Ouminus__class_Ouminus(U_3996),U_3997)),U_3998))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),U_3997),U_3998))
    | ~ sP336(U_3996,U_3997,U_3998) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

cnf(f_1130_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),U_3997),U_3998))
    | ~ sP335(U_3996,U_3997,U_3998) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

cnf(f_1130_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3996),hAPP(c_Groups_Ouminus__class_Ouminus(U_3996),U_3997)),U_3998))
    | ~ sP335(U_3996,U_3997,U_3998) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

fof(f_1131_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__leI]) ).

fof(f_1131_2,plain,
    ! [U_4001,U_4000,U_3999] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),hAPP(c_Groups_Oabs__class_Oabs(U_3999),U_4000)),U_4001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),hAPP(c_Groups_Ouminus__class_Ouminus(U_3999),U_4000)),U_4001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),U_4000),U_4001))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3999) ),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

fof(f_1131_3,plain,
    ! [U_3999,U_4000,U_4001] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),hAPP(c_Groups_Oabs__class_Oabs(U_3999),U_4000)),U_4001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),hAPP(c_Groups_Ouminus__class_Ouminus(U_3999),U_4000)),U_4001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),U_4000),U_4001))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3999) ),
    inference(definitional_conversion,[status(esa)],[f_1131_2]) ).

cnf(f_1131_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),hAPP(c_Groups_Oabs__class_Oabs(U_3999),U_4000)),U_4001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),hAPP(c_Groups_Ouminus__class_Ouminus(U_3999),U_4000)),U_4001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),U_4000),U_4001))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3999) ),
    inference(clausify,[status(thm)],[f_1131_3]) ).

fof(f_1132_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__D2]) ).

fof(f_1132_2,plain,
    ! [U_4004,U_4003,U_4002] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4002),hAPP(c_Groups_Ouminus__class_Ouminus(U_4002),U_4003)),U_4004))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4002),hAPP(c_Groups_Oabs__class_Oabs(U_4002),U_4003)),U_4004))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4002) ),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

fof(f_1132_3,plain,
    ! [U_4002,U_4003,U_4004] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4002),hAPP(c_Groups_Ouminus__class_Ouminus(U_4002),U_4003)),U_4004))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4002),hAPP(c_Groups_Oabs__class_Oabs(U_4002),U_4003)),U_4004))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4002) ),
    inference(definitional_conversion,[status(esa)],[f_1132_2]) ).

cnf(f_1132_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4002),hAPP(c_Groups_Ouminus__class_Ouminus(U_4002),U_4003)),U_4004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4002),hAPP(c_Groups_Oabs__class_Oabs(U_4002),U_4003)),U_4004))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4002) ),
    inference(clausify,[status(thm)],[f_1132_3]) ).

fof(f_1133_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).

fof(f_1133_2,plain,
    ! [U_4007,U_4006,U_4005] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Oabs__class_Oabs(U_4005),U_4006)),U_4007))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4006)),U_4007))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),U_4006),U_4007)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4006)),U_4007))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),U_4006),U_4007)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Oabs__class_Oabs(U_4005),U_4006)),U_4007)) ) )
      | ~ class_Rings_Olinordered__idom(U_4005) ),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

fof(f_1133_3,plain,
    ( ! [U_4005,U_4006,U_4007] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4006)),U_4007))
        | ~ sP337(U_4005,U_4006,U_4007) )
    & ! [U_4005,U_4006,U_4007] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),U_4006),U_4007))
        | ~ sP337(U_4005,U_4006,U_4007) )
    & ! [U_4005,U_4006,U_4007] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Oabs__class_Oabs(U_4005),U_4006)),U_4007))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4006)),U_4007))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),U_4006),U_4007))
        | ~ sP338(U_4005,U_4006,U_4007) )
    & ! [U_4005,U_4006,U_4007] :
        ( sP337(U_4005,U_4006,U_4007)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Oabs__class_Oabs(U_4005),U_4006)),U_4007))
        | ~ sP338(U_4005,U_4006,U_4007) )
    & ! [U_4005,U_4006,U_4007] :
        ( sP338(U_4005,U_4006,U_4007)
        | ~ class_Rings_Olinordered__idom(U_4005) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP337,sP338])],[f_1133_2]) ).

cnf(f_1133_4,plain,
    ( sP338(U_4005,U_4006,U_4007)
    | ~ class_Rings_Olinordered__idom(U_4005) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

cnf(f_1133_5,plain,
    ( sP337(U_4005,U_4006,U_4007)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Oabs__class_Oabs(U_4005),U_4006)),U_4007))
    | ~ sP338(U_4005,U_4006,U_4007) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

cnf(f_1133_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Oabs__class_Oabs(U_4005),U_4006)),U_4007))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4006)),U_4007))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),U_4006),U_4007))
    | ~ sP338(U_4005,U_4006,U_4007) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

cnf(f_1133_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),U_4006),U_4007))
    | ~ sP337(U_4005,U_4006,U_4007) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

cnf(f_1133_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4005),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4006)),U_4007))
    | ~ sP337(U_4005,U_4006,U_4007) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

fof(f_1134_1,plain,
    ! [V_w_2,V_v_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(f_1134_2,plain,
    ! [U_4010,U_4009,U_4008] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010))) ) )
      | ~ class_Orderings_Olinorder(U_4008)
      | ~ class_Int_Onumber(U_4008) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

fof(f_1134_3,plain,
    ( ! [U_4009,U_4010,U_4008] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)))
        | ~ sP339(U_4009,U_4010,U_4008) )
    & ! [U_4009,U_4010,U_4008] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)))
        | ~ sP339(U_4009,U_4010,U_4008) )
    & ! [U_4009,U_4010,U_4008] :
        ( sP339(U_4009,U_4010,U_4008)
        | ~ class_Orderings_Olinorder(U_4008)
        | ~ class_Int_Onumber(U_4008) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP339])],[f_1134_2]) ).

cnf(f_1134_4,plain,
    ( sP339(U_4009,U_4010,U_4008)
    | ~ class_Orderings_Olinorder(U_4008)
    | ~ class_Int_Onumber(U_4008) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

cnf(f_1134_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)))
    | ~ sP339(U_4009,U_4010,U_4008) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

cnf(f_1134_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4008),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4010)),hAPP(c_Int_Onumber__class_Onumber__of(U_4008),U_4009)))
    | ~ sP339(U_4009,U_4010,U_4008) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

fof(f_1135_1,plain,
    ! [V_v,V_b,V_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
      | ~ class_Rings_Osemiring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of]) ).

fof(f_1135_2,plain,
    ! [U_4014,U_4013,U_4012,U_4011] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4011),U_4012),U_4013)),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),U_4012),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),U_4013),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014)))
      | ~ class_Rings_Osemiring(U_4011)
      | ~ class_Int_Onumber(U_4011) ),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

fof(f_1135_3,plain,
    ! [U_4012,U_4011,U_4013,U_4014] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4011),U_4012),U_4013)),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),U_4012),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),U_4013),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014)))
      | ~ class_Rings_Osemiring(U_4011)
      | ~ class_Int_Onumber(U_4011) ),
    inference(definitional_conversion,[status(esa)],[f_1135_2]) ).

cnf(f_1135_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4011),U_4012),U_4013)),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),U_4012),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4011),U_4013),hAPP(c_Int_Onumber__class_Onumber__of(U_4011),U_4014)))
    | ~ class_Rings_Osemiring(U_4011)
    | ~ class_Int_Onumber(U_4011) ),
    inference(clausify,[status(thm)],[f_1135_3]) ).

fof(f_1136_1,plain,
    ! [V_c,V_b,V_v,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c))
      | ~ class_Rings_Osemiring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of]) ).

fof(f_1136_2,plain,
    ! [U_4018,U_4017,U_4016,U_4015] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4015),U_4017),U_4018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),U_4017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),U_4018))
      | ~ class_Rings_Osemiring(U_4015)
      | ~ class_Int_Onumber(U_4015) ),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

fof(f_1136_3,plain,
    ! [U_4016,U_4015,U_4017,U_4018] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4015),U_4017),U_4018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),U_4017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),U_4018))
      | ~ class_Rings_Osemiring(U_4015)
      | ~ class_Int_Onumber(U_4015) ),
    inference(definitional_conversion,[status(esa)],[f_1136_2]) ).

cnf(f_1136_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4015),U_4017),U_4018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),U_4017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4015),hAPP(c_Int_Onumber__class_Onumber__of(U_4015),U_4016)),U_4018))
    | ~ class_Rings_Osemiring(U_4015)
    | ~ class_Int_Onumber(U_4015) ),
    inference(clausify,[status(thm)],[f_1136_3]) ).

fof(f_1137_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J]) ).

fof(f_1137_2,plain,
    ! [U_4021,U_4020,U_4019] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4019),hAPP(hAPP(c_Power_Opower__class_Opower(U_4019),U_4020),U_4021)),U_4020) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4019),U_4020),hAPP(c_Nat_OSuc,U_4021))
      | ~ class_Rings_Ocomm__semiring__1(U_4019) ),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

fof(f_1137_3,plain,
    ! [U_4020,U_4019,U_4021] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4019),hAPP(hAPP(c_Power_Opower__class_Opower(U_4019),U_4020),U_4021)),U_4020) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4019),U_4020),hAPP(c_Nat_OSuc,U_4021))
      | ~ class_Rings_Ocomm__semiring__1(U_4019) ),
    inference(definitional_conversion,[status(esa)],[f_1137_2]) ).

cnf(f_1137_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4019),hAPP(hAPP(c_Power_Opower__class_Opower(U_4019),U_4020),U_4021)),U_4020) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4019),U_4020),hAPP(c_Nat_OSuc,U_4021))
    | ~ class_Rings_Ocomm__semiring__1(U_4019) ),
    inference(clausify,[status(thm)],[f_1137_3]) ).

fof(f_1138_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J]) ).

fof(f_1138_2,plain,
    ! [U_4024,U_4023,U_4022] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4022),U_4023),hAPP(hAPP(c_Power_Opower__class_Opower(U_4022),U_4023),U_4024)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4022),U_4023),hAPP(c_Nat_OSuc,U_4024))
      | ~ class_Rings_Ocomm__semiring__1(U_4022) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

fof(f_1138_3,plain,
    ! [U_4022,U_4023,U_4024] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4022),U_4023),hAPP(hAPP(c_Power_Opower__class_Opower(U_4022),U_4023),U_4024)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4022),U_4023),hAPP(c_Nat_OSuc,U_4024))
      | ~ class_Rings_Ocomm__semiring__1(U_4022) ),
    inference(definitional_conversion,[status(esa)],[f_1138_2]) ).

cnf(f_1138_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4022),U_4023),hAPP(hAPP(c_Power_Opower__class_Opower(U_4022),U_4023),U_4024)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4022),U_4023),hAPP(c_Nat_OSuc,U_4024))
    | ~ class_Rings_Ocomm__semiring__1(U_4022) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

fof(f_1139_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J]) ).

fof(f_1139_2,plain,
    ! [U_4027,U_4026,U_4025] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4025),U_4026),hAPP(c_Nat_OSuc,U_4027)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4025),U_4026),hAPP(hAPP(c_Power_Opower__class_Opower(U_4025),U_4026),U_4027))
      | ~ class_Rings_Ocomm__semiring__1(U_4025) ),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

fof(f_1139_3,plain,
    ! [U_4025,U_4026,U_4027] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4025),U_4026),hAPP(c_Nat_OSuc,U_4027)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4025),U_4026),hAPP(hAPP(c_Power_Opower__class_Opower(U_4025),U_4026),U_4027))
      | ~ class_Rings_Ocomm__semiring__1(U_4025) ),
    inference(definitional_conversion,[status(esa)],[f_1139_2]) ).

cnf(f_1139_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4025),U_4026),hAPP(c_Nat_OSuc,U_4027)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4025),U_4026),hAPP(hAPP(c_Power_Opower__class_Opower(U_4025),U_4026),U_4027))
    | ~ class_Rings_Ocomm__semiring__1(U_4025) ),
    inference(clausify,[status(thm)],[f_1139_3]) ).

fof(f_1140_1,plain,
    ! [V_v,V_b,V_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
      | ~ class_Rings_Oring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of]) ).

fof(f_1140_2,plain,
    ! [U_4031,U_4030,U_4029,U_4028] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4028),U_4029),U_4030)),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),U_4029),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),U_4030),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031)))
      | ~ class_Rings_Oring(U_4028)
      | ~ class_Int_Onumber(U_4028) ),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

fof(f_1140_3,plain,
    ! [U_4028,U_4029,U_4030,U_4031] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4028),U_4029),U_4030)),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),U_4029),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),U_4030),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031)))
      | ~ class_Rings_Oring(U_4028)
      | ~ class_Int_Onumber(U_4028) ),
    inference(definitional_conversion,[status(esa)],[f_1140_2]) ).

cnf(f_1140_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4028),U_4029),U_4030)),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),U_4029),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4028),U_4030),hAPP(c_Int_Onumber__class_Onumber__of(U_4028),U_4031)))
    | ~ class_Rings_Oring(U_4028)
    | ~ class_Int_Onumber(U_4028) ),
    inference(clausify,[status(thm)],[f_1140_3]) ).

fof(f_1141_1,plain,
    ! [V_c,V_b,V_v,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c))
      | ~ class_Rings_Oring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of]) ).

fof(f_1141_2,plain,
    ! [U_4035,U_4034,U_4033,U_4032] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4032),U_4034),U_4035)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),U_4034)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),U_4035))
      | ~ class_Rings_Oring(U_4032)
      | ~ class_Int_Onumber(U_4032) ),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

fof(f_1141_3,plain,
    ! [U_4033,U_4032,U_4034,U_4035] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4032),U_4034),U_4035)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),U_4034)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),U_4035))
      | ~ class_Rings_Oring(U_4032)
      | ~ class_Int_Onumber(U_4032) ),
    inference(definitional_conversion,[status(esa)],[f_1141_2]) ).

cnf(f_1141_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4032),U_4034),U_4035)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),U_4034)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4032),hAPP(c_Int_Onumber__class_Onumber__of(U_4032),U_4033)),U_4035))
    | ~ class_Rings_Oring(U_4032)
    | ~ class_Int_Onumber(U_4032) ),
    inference(clausify,[status(thm)],[f_1141_3]) ).

fof(f_1142_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).

fof(f_1142_2,plain,
    ! [U_4038,U_4037,U_4036] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4036),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4037)),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4038)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4037),U_4038)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4037),U_4038))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4036),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4037)),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4038))) ) )
      | ~ class_Rings_Olinordered__idom(U_4036)
      | ~ class_Int_Onumber__ring(U_4036) ),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

fof(f_1142_3,plain,
    ( ! [U_4037,U_4036,U_4038] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4036),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4037)),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4038)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4037),U_4038))
        | ~ sP340(U_4037,U_4036,U_4038) )
    & ! [U_4037,U_4036,U_4038] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4037),U_4038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4036),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4037)),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4038)))
        | ~ sP340(U_4037,U_4036,U_4038) )
    & ! [U_4037,U_4036,U_4038] :
        ( sP340(U_4037,U_4036,U_4038)
        | ~ class_Rings_Olinordered__idom(U_4036)
        | ~ class_Int_Onumber__ring(U_4036) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP340])],[f_1142_2]) ).

cnf(f_1142_4,plain,
    ( sP340(U_4037,U_4036,U_4038)
    | ~ class_Rings_Olinordered__idom(U_4036)
    | ~ class_Int_Onumber__ring(U_4036) ),
    inference(clausify,[status(thm)],[f_1142_3]) ).

cnf(f_1142_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4037),U_4038))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4036),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4037)),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4038)))
    | ~ sP340(U_4037,U_4036,U_4038) ),
    inference(clausify,[status(thm)],[f_1142_3]) ).

cnf(f_1142_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4036),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4037)),hAPP(c_Int_Onumber__class_Onumber__of(U_4036),U_4038)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4037),U_4038))
    | ~ sP340(U_4037,U_4036,U_4038) ),
    inference(clausify,[status(thm)],[f_1142_3]) ).

fof(f_1143_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).

fof(f_1143_2,plain,
    ! [U_4040,U_4039] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4039),U_4040),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4039)
      | ~ class_Rings_Ocomm__semiring__1(U_4039) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

fof(f_1143_3,plain,
    ! [U_4040,U_4039] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4039),U_4040),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4039)
      | ~ class_Rings_Ocomm__semiring__1(U_4039) ),
    inference(definitional_conversion,[status(esa)],[f_1143_2]) ).

cnf(f_1143_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4039),U_4040),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4039)
    | ~ class_Rings_Ocomm__semiring__1(U_4039) ),
    inference(clausify,[status(thm)],[f_1143_3]) ).

fof(f_1144_1,plain,
    ! [V_q,V_p,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).

fof(f_1144_2,plain,
    ! [U_4044,U_4043,U_4042,U_4041] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4041),hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),U_4043)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),U_4044)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4043),U_4044))
      | ~ class_Rings_Ocomm__semiring__1(U_4041) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

fof(f_1144_3,plain,
    ! [U_4042,U_4041,U_4043,U_4044] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4041),hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),U_4043)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),U_4044)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4043),U_4044))
      | ~ class_Rings_Ocomm__semiring__1(U_4041) ),
    inference(definitional_conversion,[status(esa)],[f_1144_2]) ).

cnf(f_1144_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4041),hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),U_4043)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),U_4044)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4041),U_4042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4043),U_4044))
    | ~ class_Rings_Ocomm__semiring__1(U_4041) ),
    inference(clausify,[status(thm)],[f_1144_3]) ).

fof(f_1145_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).

fof(f_1145_2,plain,
    ! [U_4047,U_4046,U_4045] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4045),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4046)),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4047)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4046),U_4047)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4046),U_4047))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4045),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4046)),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4047))) ) )
      | ~ class_Rings_Olinordered__idom(U_4045)
      | ~ class_Int_Onumber__ring(U_4045) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

fof(f_1145_3,plain,
    ( ! [U_4045,U_4046,U_4047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4045),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4046)),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4047)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4046),U_4047))
        | ~ sP341(U_4045,U_4046,U_4047) )
    & ! [U_4045,U_4046,U_4047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4046),U_4047))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4045),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4046)),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4047)))
        | ~ sP341(U_4045,U_4046,U_4047) )
    & ! [U_4045,U_4046,U_4047] :
        ( sP341(U_4045,U_4046,U_4047)
        | ~ class_Rings_Olinordered__idom(U_4045)
        | ~ class_Int_Onumber__ring(U_4045) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP341])],[f_1145_2]) ).

cnf(f_1145_4,plain,
    ( sP341(U_4045,U_4046,U_4047)
    | ~ class_Rings_Olinordered__idom(U_4045)
    | ~ class_Int_Onumber__ring(U_4045) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4046),U_4047))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4045),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4046)),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4047)))
    | ~ sP341(U_4045,U_4046,U_4047) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4045),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4046)),hAPP(c_Int_Onumber__class_Onumber__of(U_4045),U_4047)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4046),U_4047))
    | ~ sP341(U_4045,U_4046,U_4047) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

fof(f_1146_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__add]) ).

fof(f_1146_2,plain,
    ! [U_4050,U_4049,U_4048] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4048),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4049),U_4050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4048),hAPP(c_Int_Onumber__class_Onumber__of(U_4048),U_4049)),hAPP(c_Int_Onumber__class_Onumber__of(U_4048),U_4050))
      | ~ class_Int_Onumber__ring(U_4048) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

fof(f_1146_3,plain,
    ! [U_4050,U_4049,U_4048] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4048),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4049),U_4050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4048),hAPP(c_Int_Onumber__class_Onumber__of(U_4048),U_4049)),hAPP(c_Int_Onumber__class_Onumber__of(U_4048),U_4050))
      | ~ class_Int_Onumber__ring(U_4048) ),
    inference(definitional_conversion,[status(esa)],[f_1146_2]) ).

cnf(f_1146_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4048),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4049),U_4050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4048),hAPP(c_Int_Onumber__class_Onumber__of(U_4048),U_4049)),hAPP(c_Int_Onumber__class_Onumber__of(U_4048),U_4050))
    | ~ class_Int_Onumber__ring(U_4048) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

fof(f_1147_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__eq]) ).

fof(f_1147_2,plain,
    ! [U_4053,U_4052,U_4051] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4051),hAPP(c_Int_Onumber__class_Onumber__of(U_4051),U_4052)),hAPP(c_Int_Onumber__class_Onumber__of(U_4051),U_4053)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4052),U_4053))
      | ~ class_Int_Onumber__ring(U_4051) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

fof(f_1147_3,plain,
    ! [U_4051,U_4052,U_4053] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4051),hAPP(c_Int_Onumber__class_Onumber__of(U_4051),U_4052)),hAPP(c_Int_Onumber__class_Onumber__of(U_4051),U_4053)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4052),U_4053))
      | ~ class_Int_Onumber__ring(U_4051) ),
    inference(definitional_conversion,[status(esa)],[f_1147_2]) ).

cnf(f_1147_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4051),hAPP(c_Int_Onumber__class_Onumber__of(U_4051),U_4052)),hAPP(c_Int_Onumber__class_Onumber__of(U_4051),U_4053)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4052),U_4053))
    | ~ class_Int_Onumber__ring(U_4051) ),
    inference(clausify,[status(thm)],[f_1147_3]) ).

fof(f_1148_1,plain,
    ! [V_z,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__left]) ).

fof(f_1148_2,plain,
    ! [U_4057,U_4056,U_4055,U_4054] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),U_4055)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),U_4056)),U_4057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4055),U_4056))),U_4057)
      | ~ class_Int_Onumber__ring(U_4054) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

fof(f_1148_3,plain,
    ! [U_4054,U_4055,U_4056,U_4057] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),U_4055)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),U_4056)),U_4057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4055),U_4056))),U_4057)
      | ~ class_Int_Onumber__ring(U_4054) ),
    inference(definitional_conversion,[status(esa)],[f_1148_2]) ).

cnf(f_1148_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),U_4055)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),U_4056)),U_4057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4054),hAPP(c_Int_Onumber__class_Onumber__of(U_4054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4055),U_4056))),U_4057)
    | ~ class_Int_Onumber__ring(U_4054) ),
    inference(clausify,[status(thm)],[f_1148_3]) ).

fof(f_1149_1,plain,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).

fof(f_1149_2,plain,
    ! [U_4059,U_4058] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4058),U_4059)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4058)) ),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

fof(f_1149_3,plain,
    ! [U_4058,U_4059] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4058),U_4059)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4058)) ),
    inference(definitional_conversion,[status(esa)],[f_1149_2]) ).

cnf(f_1149_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4058),U_4059)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4058)) ),
    inference(clausify,[status(thm)],[f_1149_3]) ).

fof(f_1150_1,plain,
    ! [V_z,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__number__of__left]) ).

fof(f_1150_2,plain,
    ! [U_4063,U_4062,U_4061,U_4060] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),U_4061)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),U_4062)),U_4063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4061),U_4062))),U_4063)
      | ~ class_Int_Onumber__ring(U_4060) ),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

fof(f_1150_3,plain,
    ! [U_4060,U_4061,U_4062,U_4063] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),U_4061)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),U_4062)),U_4063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4061),U_4062))),U_4063)
      | ~ class_Int_Onumber__ring(U_4060) ),
    inference(definitional_conversion,[status(esa)],[f_1150_2]) ).

cnf(f_1150_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),U_4061)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),U_4062)),U_4063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4060),hAPP(c_Int_Onumber__class_Onumber__of(U_4060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4061),U_4062))),U_4063)
    | ~ class_Int_Onumber__ring(U_4060) ),
    inference(clausify,[status(thm)],[f_1150_3]) ).

fof(f_1151_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J]) ).

fof(f_1151_2,plain,
    ! [U_4066,U_4065,U_4064] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),hAPP(c_Int_Onumber__class_Onumber__of(U_4064),U_4065)),hAPP(c_Int_Onumber__class_Onumber__of(U_4064),U_4066)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4065),U_4066))
      | ~ class_Int_Onumber__ring(U_4064) ),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

fof(f_1151_3,plain,
    ! [U_4064,U_4065,U_4066] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),hAPP(c_Int_Onumber__class_Onumber__of(U_4064),U_4065)),hAPP(c_Int_Onumber__class_Onumber__of(U_4064),U_4066)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4065),U_4066))
      | ~ class_Int_Onumber__ring(U_4064) ),
    inference(definitional_conversion,[status(esa)],[f_1151_2]) ).

cnf(f_1151_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),hAPP(c_Int_Onumber__class_Onumber__of(U_4064),U_4065)),hAPP(c_Int_Onumber__class_Onumber__of(U_4064),U_4066)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4065),U_4066))
    | ~ class_Int_Onumber__ring(U_4064) ),
    inference(clausify,[status(thm)],[f_1151_3]) ).

fof(f_1152_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__mult]) ).

fof(f_1152_2,plain,
    ! [U_4069,U_4068,U_4067] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4068),U_4069)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4067),hAPP(c_Int_Onumber__class_Onumber__of(U_4067),U_4068)),hAPP(c_Int_Onumber__class_Onumber__of(U_4067),U_4069))
      | ~ class_Int_Onumber__ring(U_4067) ),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

fof(f_1152_3,plain,
    ! [U_4067,U_4068,U_4069] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4068),U_4069)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4067),hAPP(c_Int_Onumber__class_Onumber__of(U_4067),U_4068)),hAPP(c_Int_Onumber__class_Onumber__of(U_4067),U_4069))
      | ~ class_Int_Onumber__ring(U_4067) ),
    inference(definitional_conversion,[status(esa)],[f_1152_2]) ).

cnf(f_1152_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4068),U_4069)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4067),hAPP(c_Int_Onumber__class_Onumber__of(U_4067),U_4068)),hAPP(c_Int_Onumber__class_Onumber__of(U_4067),U_4069))
    | ~ class_Int_Onumber__ring(U_4067) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

fof(f_1153_1,plain,
    ! [V_n,V_m] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1]) ).

fof(f_1153_2,plain,
    ! [U_4071,U_4070] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4070) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4070),U_4071)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ! [U_4070,U_4071] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4070) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4070),U_4071)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1153_2]) ).

cnf(f_1153_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4070) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4070),U_4071)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

fof(f_1154_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__diff]) ).

fof(f_1154_2,plain,
    ! [U_4074,U_4073,U_4072] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4073),U_4074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4072),hAPP(c_Int_Onumber__class_Onumber__of(U_4072),U_4073)),hAPP(c_Int_Onumber__class_Onumber__of(U_4072),U_4074))
      | ~ class_Int_Onumber__ring(U_4072) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

fof(f_1154_3,plain,
    ! [U_4072,U_4073,U_4074] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4073),U_4074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4072),hAPP(c_Int_Onumber__class_Onumber__of(U_4072),U_4073)),hAPP(c_Int_Onumber__class_Onumber__of(U_4072),U_4074))
      | ~ class_Int_Onumber__ring(U_4072) ),
    inference(definitional_conversion,[status(esa)],[f_1154_2]) ).

cnf(f_1154_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4073),U_4074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4072),hAPP(c_Int_Onumber__class_Onumber__of(U_4072),U_4073)),hAPP(c_Int_Onumber__class_Onumber__of(U_4072),U_4074))
    | ~ class_Int_Onumber__ring(U_4072) ),
    inference(clausify,[status(thm)],[f_1154_3]) ).

fof(f_1155_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(f_1155_2,plain,
    ! [U_4077,U_4076,U_4075] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4076),U_4077)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),U_4076)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),U_4077)),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

fof(f_1155_3,plain,
    ! [U_4075,U_4076,U_4077] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4076),U_4077)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),U_4076)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),U_4077)),
    inference(definitional_conversion,[status(esa)],[f_1155_2]) ).

cnf(f_1155_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4076),U_4077)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),U_4076)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4075),U_4077)),
    inference(clausify,[status(thm)],[f_1155_3]) ).

fof(f_1156_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__minus]) ).

fof(f_1156_2,plain,
    ! [U_4079,U_4078] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4078),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4079)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4078),hAPP(c_Int_Onumber__class_Onumber__of(U_4078),U_4079))
      | ~ class_Int_Onumber__ring(U_4078) ),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

fof(f_1156_3,plain,
    ! [U_4078,U_4079] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4078),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4079)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4078),hAPP(c_Int_Onumber__class_Onumber__of(U_4078),U_4079))
      | ~ class_Int_Onumber__ring(U_4078) ),
    inference(definitional_conversion,[status(esa)],[f_1156_2]) ).

cnf(f_1156_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4078),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4079)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4078),hAPP(c_Int_Onumber__class_Onumber__of(U_4078),U_4079))
    | ~ class_Int_Onumber__ring(U_4078) ),
    inference(clausify,[status(thm)],[f_1156_3]) ).

fof(f_1157_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J]) ).

fof(f_1157_2,plain,
    ! [U_4081,U_4080] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),hAPP(c_Int_Onumber__class_Onumber__of(U_4080),U_4081)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4080),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4081))
      | ~ class_Int_Onumber__ring(U_4080) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

fof(f_1157_3,plain,
    ! [U_4080,U_4081] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),hAPP(c_Int_Onumber__class_Onumber__of(U_4080),U_4081)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4080),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4081))
      | ~ class_Int_Onumber__ring(U_4080) ),
    inference(definitional_conversion,[status(esa)],[f_1157_2]) ).

cnf(f_1157_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),hAPP(c_Int_Onumber__class_Onumber__of(U_4080),U_4081)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4080),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4081))
    | ~ class_Int_Onumber__ring(U_4080) ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

fof(f_1158_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs]) ).

fof(f_1158_2,plain,
    ! [U_4083,U_4082] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4082),c_Groups_Osgn__class_Osgn(U_4082,U_4083)),hAPP(c_Groups_Oabs__class_Oabs(U_4082),U_4083)) = U_4083
      | ~ class_Rings_Olinordered__idom(U_4082) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

fof(f_1158_3,plain,
    ! [U_4082,U_4083] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4082),c_Groups_Osgn__class_Osgn(U_4082,U_4083)),hAPP(c_Groups_Oabs__class_Oabs(U_4082),U_4083)) = U_4083
      | ~ class_Rings_Olinordered__idom(U_4082) ),
    inference(definitional_conversion,[status(esa)],[f_1158_2]) ).

cnf(f_1158_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4082),c_Groups_Osgn__class_Osgn(U_4082,U_4083)),hAPP(c_Groups_Oabs__class_Oabs(U_4082),U_4083)) = U_4083
    | ~ class_Rings_Olinordered__idom(U_4082) ),
    inference(clausify,[status(thm)],[f_1158_3]) ).

fof(f_1159_1,plain,
    ! [V_k,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__sgn]) ).

fof(f_1159_2,plain,
    ! [U_4085,U_4084] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4084),U_4085) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4084),U_4085),c_Groups_Osgn__class_Osgn(U_4084,U_4085))
      | ~ class_Rings_Olinordered__idom(U_4084) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

fof(f_1159_3,plain,
    ! [U_4084,U_4085] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4084),U_4085) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4084),U_4085),c_Groups_Osgn__class_Osgn(U_4084,U_4085))
      | ~ class_Rings_Olinordered__idom(U_4084) ),
    inference(definitional_conversion,[status(esa)],[f_1159_2]) ).

cnf(f_1159_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4084),U_4085) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4084),U_4085),c_Groups_Osgn__class_Osgn(U_4084,U_4085))
    | ~ class_Rings_Olinordered__idom(U_4084) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

fof(f_1160_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__pos]) ).

fof(f_1160_2,plain,
    ! [U_4088,U_4087,U_4086] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4088)),U_4087) = hAPP(c_Groups_Oabs__class_Oabs(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4088),U_4087))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4086),c_Groups_Ozero__class_Ozero(U_4086)),U_4087))
      | ~ class_Rings_Olinordered__idom(U_4086) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

fof(f_1160_3,plain,
    ! [U_4086,U_4087,U_4088] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4088)),U_4087) = hAPP(c_Groups_Oabs__class_Oabs(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4088),U_4087))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4086),c_Groups_Ozero__class_Ozero(U_4086)),U_4087))
      | ~ class_Rings_Olinordered__idom(U_4086) ),
    inference(definitional_conversion,[status(esa)],[f_1160_2]) ).

cnf(f_1160_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4088)),U_4087) = hAPP(c_Groups_Oabs__class_Oabs(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4088),U_4087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4086),c_Groups_Ozero__class_Ozero(U_4086)),U_4087))
    | ~ class_Rings_Olinordered__idom(U_4086) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

fof(f_1161_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
      | ~ class_Rings_Oordered__ring__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__mult]) ).

fof(f_1161_2,plain,
    ! [U_4091,U_4090,U_4089] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4089),U_4090),U_4091)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4089),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4090)),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4091))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),U_4091),c_Groups_Ozero__class_Ozero(U_4089)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),c_Groups_Ozero__class_Ozero(U_4089)),U_4091)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),U_4090),c_Groups_Ozero__class_Ozero(U_4089)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),c_Groups_Ozero__class_Ozero(U_4089)),U_4090)) )
      | ~ class_Rings_Oordered__ring__abs(U_4089) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

fof(f_1161_3,plain,
    ( ! [U_4089,U_4091] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),U_4091),c_Groups_Ozero__class_Ozero(U_4089)))
        | ~ sP343(U_4089,U_4091) )
    & ! [U_4089,U_4091] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),c_Groups_Ozero__class_Ozero(U_4089)),U_4091))
        | ~ sP343(U_4089,U_4091) )
    & ! [U_4089,U_4090] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),U_4090),c_Groups_Ozero__class_Ozero(U_4089)))
        | ~ sP342(U_4089,U_4090) )
    & ! [U_4089,U_4090] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),c_Groups_Ozero__class_Ozero(U_4089)),U_4090))
        | ~ sP342(U_4089,U_4090) )
    & ! [U_4089,U_4090,U_4091] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4089),U_4090),U_4091)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4089),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4090)),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4091))
        | sP343(U_4089,U_4091)
        | sP342(U_4089,U_4090)
        | ~ class_Rings_Oordered__ring__abs(U_4089) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP342,sP343])],[f_1161_2]) ).

cnf(f_1161_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4089),U_4090),U_4091)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4089),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4090)),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4091))
    | sP343(U_4089,U_4091)
    | sP342(U_4089,U_4090)
    | ~ class_Rings_Oordered__ring__abs(U_4089) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

cnf(f_1161_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),c_Groups_Ozero__class_Ozero(U_4089)),U_4090))
    | ~ sP342(U_4089,U_4090) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

cnf(f_1161_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),U_4090),c_Groups_Ozero__class_Ozero(U_4089)))
    | ~ sP342(U_4089,U_4090) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

cnf(f_1161_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),c_Groups_Ozero__class_Ozero(U_4089)),U_4091))
    | ~ sP343(U_4089,U_4091) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

cnf(f_1161_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),U_4091),c_Groups_Ozero__class_Ozero(U_4089)))
    | ~ sP343(U_4089,U_4091) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

fof(f_1162_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq]) ).

fof(f_1162_2,plain,
    ! [U_4096,U_4095,U_4094,U_4093,U_4092] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),U_4093),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),U_4095),U_4096)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),U_4093),U_4095))),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),U_4094),U_4096)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4092) ),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

fof(f_1162_3,plain,
    ! [U_4092,U_4093,U_4094,U_4095,U_4096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),U_4093),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),U_4095),U_4096)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),U_4093),U_4095))),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),U_4094),U_4096)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4092) ),
    inference(definitional_conversion,[status(esa)],[f_1162_2]) ).

cnf(f_1162_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),U_4093),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),U_4095),U_4096)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),U_4093),U_4095))),hAPP(c_Groups_Oabs__class_Oabs(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4092),U_4094),U_4096)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4092) ),
    inference(clausify,[status(thm)],[f_1162_3]) ).

fof(f_1163_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4]) ).

fof(f_1163_2,plain,
    ! [U_4099,U_4098,U_4097] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4097),hAPP(c_Groups_Oabs__class_Oabs(U_4097),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4097),U_4098),U_4099))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4097),hAPP(c_Groups_Oabs__class_Oabs(U_4097),U_4098)),hAPP(c_Groups_Oabs__class_Oabs(U_4097),U_4099))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4097) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ! [U_4097,U_4098,U_4099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4097),hAPP(c_Groups_Oabs__class_Oabs(U_4097),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4097),U_4098),U_4099))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4097),hAPP(c_Groups_Oabs__class_Oabs(U_4097),U_4098)),hAPP(c_Groups_Oabs__class_Oabs(U_4097),U_4099))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4097) ),
    inference(definitional_conversion,[status(esa)],[f_1163_2]) ).

cnf(f_1163_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4097),hAPP(c_Groups_Oabs__class_Oabs(U_4097),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4097),U_4098),U_4099))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4097),hAPP(c_Groups_Oabs__class_Oabs(U_4097),U_4098)),hAPP(c_Groups_Oabs__class_Oabs(U_4097),U_4099))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4097) ),
    inference(clausify,[status(thm)],[f_1163_3]) ).

fof(f_1164_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos]) ).

fof(f_1164_2,plain,
    ! [U_4101,U_4100] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4100),U_4101) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4100),U_4101)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4100),U_4101),c_Groups_Ozero__class_Ozero(U_4100)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4100) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

fof(f_1164_3,plain,
    ! [U_4100,U_4101] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4100),U_4101) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4100),U_4101)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4100),U_4101),c_Groups_Ozero__class_Ozero(U_4100)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4100) ),
    inference(definitional_conversion,[status(esa)],[f_1164_2]) ).

cnf(f_1164_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4100),U_4101) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4100),U_4101)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4100),U_4101),c_Groups_Ozero__class_Ozero(U_4100)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4100) ),
    inference(clausify,[status(thm)],[f_1164_3]) ).

fof(f_1165_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero]) ).

fof(f_1165_2,plain,
    ! [U_4103,U_4102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4102),hAPP(c_Groups_Ouminus__class_Ouminus(U_4102),hAPP(c_Groups_Oabs__class_Oabs(U_4102),U_4103))),c_Groups_Ozero__class_Ozero(U_4102)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4102) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

fof(f_1165_3,plain,
    ! [U_4102,U_4103] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4102),hAPP(c_Groups_Ouminus__class_Ouminus(U_4102),hAPP(c_Groups_Oabs__class_Oabs(U_4102),U_4103))),c_Groups_Ozero__class_Ozero(U_4102)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4102) ),
    inference(definitional_conversion,[status(esa)],[f_1165_2]) ).

cnf(f_1165_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4102),hAPP(c_Groups_Ouminus__class_Ouminus(U_4102),hAPP(c_Groups_Oabs__class_Oabs(U_4102),U_4103))),c_Groups_Ozero__class_Ozero(U_4102)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4102) ),
    inference(clausify,[status(thm)],[f_1165_3]) ).

fof(f_1166_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__neg]) ).

fof(f_1166_2,plain,
    ! [U_4105,U_4104] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4104),U_4105) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4104),U_4105)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4104),U_4105),c_Groups_Ozero__class_Ozero(U_4104)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4104) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

fof(f_1166_3,plain,
    ! [U_4104,U_4105] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4104),U_4105) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4104),U_4105)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4104),U_4105),c_Groups_Ozero__class_Ozero(U_4104)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4104) ),
    inference(definitional_conversion,[status(esa)],[f_1166_2]) ).

cnf(f_1166_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4104),U_4105) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4104),U_4105)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4104),U_4105),c_Groups_Ozero__class_Ozero(U_4104)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4104) ),
    inference(clausify,[status(thm)],[f_1166_3]) ).

fof(f_1167_1,plain,
    ! [V_a,T_a] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Oabs__if(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__if]) ).

fof(f_1167_2,plain,
    ! [U_4107,U_4106] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_4106),U_4107) = U_4107
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4107),c_Groups_Ozero__class_Ozero(U_4106))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_4106),U_4107) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4106),U_4107)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4107),c_Groups_Ozero__class_Ozero(U_4106))) ) )
      | ~ class_Groups_Oabs__if(U_4106) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

fof(f_1167_3,plain,
    ( ! [U_4106,U_4107] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4106),U_4107) = U_4107
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4107),c_Groups_Ozero__class_Ozero(U_4106)))
        | ~ sP344(U_4106,U_4107) )
    & ! [U_4106,U_4107] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4106),U_4107) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4106),U_4107)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4107),c_Groups_Ozero__class_Ozero(U_4106)))
        | ~ sP344(U_4106,U_4107) )
    & ! [U_4106,U_4107] :
        ( sP344(U_4106,U_4107)
        | ~ class_Groups_Oabs__if(U_4106) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP344])],[f_1167_2]) ).

cnf(f_1167_4,plain,
    ( sP344(U_4106,U_4107)
    | ~ class_Groups_Oabs__if(U_4106) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4106),U_4107) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4106),U_4107)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4107),c_Groups_Ozero__class_Ozero(U_4106)))
    | ~ sP344(U_4106,U_4107) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4106),U_4107) = U_4107
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4107),c_Groups_Ozero__class_Ozero(U_4106)))
    | ~ sP344(U_4106,U_4107) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

fof(f_1168_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff]) ).

fof(f_1168_2,plain,
    ! [U_4108] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4108)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4108 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_4108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4108)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

fof(f_1168_3,plain,
    ( ! [U_4110] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4110)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4110 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4109] :
        ( U_4109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4109)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1168_2]) ).

fof(f_1168_4,plain,
    ( ! [U_4110] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4110)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4110 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4109] :
        ( U_4109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4109)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1168_3]) ).

cnf(f_1168_5,plain,
    ( U_4109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4109)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1168_4]) ).

cnf(f_1168_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4110)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | U_4110 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1168_4]) ).

fof(f_1169_1,plain,
    ! [V_c,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1]) ).

fof(f_1169_2,plain,
    ! [U_4114,U_4113,U_4112,U_4111] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),U_4112)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),U_4113)),U_4114)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4112),U_4113))),U_4114)
      | ~ class_Int_Onumber__ring(U_4111) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

fof(f_1169_3,plain,
    ! [U_4111,U_4112,U_4113,U_4114] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),U_4112)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),U_4113)),U_4114)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4112),U_4113))),U_4114)
      | ~ class_Int_Onumber__ring(U_4111) ),
    inference(definitional_conversion,[status(esa)],[f_1169_2]) ).

cnf(f_1169_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),U_4112)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),U_4113)),U_4114)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4111),hAPP(c_Int_Onumber__class_Onumber__of(U_4111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4112),U_4113))),U_4114)
    | ~ class_Int_Onumber__ring(U_4111) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

fof(f_1170_1,plain,
    ! [V_i] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zabs__def]) ).

fof(f_1170_2,plain,
    ! [U_4115] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4115) = U_4115
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4115),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4115) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4115)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4115),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

fof(f_1170_3,plain,
    ( ! [U_4117] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4117) = U_4117
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4116] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4116) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4116)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4116),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1170_2]) ).

fof(f_1170_4,plain,
    ( ! [U_4117] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4117) = U_4117
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4116] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4116) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4116)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4116),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1170_3]) ).

cnf(f_1170_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4116) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4116)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4116),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1170_4]) ).

cnf(f_1170_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4117) = U_4117
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4117),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1170_4]) ).

fof(f_1171_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult]) ).

fof(f_1171_2,plain,
    ! [U_4120,U_4119,U_4118] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(c_Groups_Ouminus__class_Ouminus(U_4118),hAPP(c_Int_Onumber__class_Onumber__of(U_4118),U_4119))),U_4120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(c_Int_Onumber__class_Onumber__of(U_4118),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4119))),U_4120)
      | ~ class_Int_Onumber__ring(U_4118) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ! [U_4118,U_4119,U_4120] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(c_Groups_Ouminus__class_Ouminus(U_4118),hAPP(c_Int_Onumber__class_Onumber__of(U_4118),U_4119))),U_4120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(c_Int_Onumber__class_Onumber__of(U_4118),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4119))),U_4120)
      | ~ class_Int_Onumber__ring(U_4118) ),
    inference(definitional_conversion,[status(esa)],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(c_Groups_Ouminus__class_Ouminus(U_4118),hAPP(c_Int_Onumber__class_Onumber__of(U_4118),U_4119))),U_4120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),hAPP(c_Int_Onumber__class_Onumber__of(U_4118),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4119))),U_4120)
    | ~ class_Int_Onumber__ring(U_4118) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_1,plain,
    ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))),
    inference(fof_nnf,[status(thm)],[fact_nat__abs__mult__distrib]) ).

fof(f_1172_2,plain,
    ! [U_4122,U_4121] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4121),U_4122))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4121))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4122))),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

fof(f_1172_3,plain,
    ! [U_4121,U_4122] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4121),U_4122))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4121))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4122))),
    inference(definitional_conversion,[status(esa)],[f_1172_2]) ).

cnf(f_1172_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4121),U_4122))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4121))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4122))),
    inference(clausify,[status(thm)],[f_1172_3]) ).

fof(f_1173_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq]) ).

fof(f_1173_2,plain,
    ! [U_4125,U_4124,U_4123] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4123),hAPP(c_Int_Onumber__class_Onumber__of(U_4123),U_4124)),hAPP(c_Int_Onumber__class_Onumber__of(U_4123),U_4125)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4124),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4125)))
      | ~ class_Int_Onumber__ring(U_4123) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

fof(f_1173_3,plain,
    ! [U_4123,U_4124,U_4125] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4123),hAPP(c_Int_Onumber__class_Onumber__of(U_4123),U_4124)),hAPP(c_Int_Onumber__class_Onumber__of(U_4123),U_4125)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4124),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4125)))
      | ~ class_Int_Onumber__ring(U_4123) ),
    inference(definitional_conversion,[status(esa)],[f_1173_2]) ).

cnf(f_1173_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4123),hAPP(c_Int_Onumber__class_Onumber__of(U_4123),U_4124)),hAPP(c_Int_Onumber__class_Onumber__of(U_4123),U_4125)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4124),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4125)))
    | ~ class_Int_Onumber__ring(U_4123) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

fof(f_1174_1,plain,
    ! [V_w,V_c,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2]) ).

fof(f_1174_2,plain,
    ! [U_4129,U_4128,U_4127,U_4126] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),U_4128),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4129))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4127),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4129)))),U_4128)
      | ~ class_Int_Onumber__ring(U_4126) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

fof(f_1174_3,plain,
    ! [U_4126,U_4127,U_4128,U_4129] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),U_4128),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4129))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4127),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4129)))),U_4128)
      | ~ class_Int_Onumber__ring(U_4126) ),
    inference(definitional_conversion,[status(esa)],[f_1174_2]) ).

cnf(f_1174_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),U_4128),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4129))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4127),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4129)))),U_4128)
    | ~ class_Int_Onumber__ring(U_4126) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

fof(f_1175_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).

fof(f_1175_2,plain,
    ! [U_4133,U_4132,U_4131,U_4130] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4130),hAPP(hAPP(c_Power_Opower__class_Opower(U_4130),U_4131),U_4133)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4130),U_4132),U_4133)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4133))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4130),c_Groups_Ozero__class_Ozero(U_4130)),U_4131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4130),U_4131),U_4132))
      | ~ class_Rings_Olinordered__semidom(U_4130) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ! [U_4130,U_4131,U_4132,U_4133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4130),hAPP(hAPP(c_Power_Opower__class_Opower(U_4130),U_4131),U_4133)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4130),U_4132),U_4133)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4133))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4130),c_Groups_Ozero__class_Ozero(U_4130)),U_4131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4130),U_4131),U_4132))
      | ~ class_Rings_Olinordered__semidom(U_4130) ),
    inference(definitional_conversion,[status(esa)],[f_1175_2]) ).

cnf(f_1175_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4130),hAPP(hAPP(c_Power_Opower__class_Opower(U_4130),U_4131),U_4133)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4130),U_4132),U_4133)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4133))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4130),c_Groups_Ozero__class_Ozero(U_4130)),U_4131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4130),U_4131),U_4132))
    | ~ class_Rings_Olinordered__semidom(U_4130) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

fof(f_1176_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).

fof(f_1176_2,plain,
    ! [U_4136,U_4135,U_4134] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4134),c_Groups_Oone__class_Oone(U_4134)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4134),U_4135),U_4136)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4136))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4134),c_Groups_Oone__class_Oone(U_4134)),U_4135))
      | ~ class_Rings_Olinordered__semidom(U_4134) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ! [U_4135,U_4134,U_4136] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4134),c_Groups_Oone__class_Oone(U_4134)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4134),U_4135),U_4136)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4136))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4134),c_Groups_Oone__class_Oone(U_4134)),U_4135))
      | ~ class_Rings_Olinordered__semidom(U_4134) ),
    inference(definitional_conversion,[status(esa)],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4134),c_Groups_Oone__class_Oone(U_4134)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4134),U_4135),U_4136)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4136))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4134),c_Groups_Oone__class_Oone(U_4134)),U_4135))
    | ~ class_Rings_Olinordered__semidom(U_4134) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

fof(f_1177_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).

fof(f_1177_2,plain,
    ! [U_4140,U_4139,U_4138,U_4137] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4137),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4139)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4140)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4139),U_4140)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4139),U_4140))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4137),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4139)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4140))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4137),c_Groups_Oone__class_Oone(U_4137)),U_4138))
      | ~ class_Rings_Olinordered__semidom(U_4137) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ( ! [U_4137,U_4138,U_4139,U_4140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4137),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4139)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4140)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4139),U_4140))
        | ~ sP345(U_4137,U_4138,U_4139,U_4140) )
    & ! [U_4137,U_4138,U_4139,U_4140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4139),U_4140))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4137),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4139)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4140)))
        | ~ sP345(U_4137,U_4138,U_4139,U_4140) )
    & ! [U_4137,U_4138,U_4139,U_4140] :
        ( sP345(U_4137,U_4138,U_4139,U_4140)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4137),c_Groups_Oone__class_Oone(U_4137)),U_4138))
        | ~ class_Rings_Olinordered__semidom(U_4137) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP345])],[f_1177_2]) ).

cnf(f_1177_4,plain,
    ( sP345(U_4137,U_4138,U_4139,U_4140)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4137),c_Groups_Oone__class_Oone(U_4137)),U_4138))
    | ~ class_Rings_Olinordered__semidom(U_4137) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

cnf(f_1177_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4139),U_4140))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4137),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4139)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4140)))
    | ~ sP345(U_4137,U_4138,U_4139,U_4140) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

cnf(f_1177_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4137),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4139)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),U_4140)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4139),U_4140))
    | ~ sP345(U_4137,U_4138,U_4139,U_4140) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

fof(f_1178_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).

fof(f_1178_2,plain,
    ! [U_4144,U_4143,U_4142,U_4141] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4143),U_4144))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4141),hAPP(hAPP(c_Power_Opower__class_Opower(U_4141),U_4142),U_4143)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4141),U_4142),U_4144)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4141),c_Groups_Oone__class_Oone(U_4141)),U_4142))
      | ~ class_Rings_Olinordered__semidom(U_4141) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

fof(f_1178_3,plain,
    ! [U_4142,U_4141,U_4144,U_4143] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4143),U_4144))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4141),hAPP(hAPP(c_Power_Opower__class_Opower(U_4141),U_4142),U_4143)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4141),U_4142),U_4144)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4141),c_Groups_Oone__class_Oone(U_4141)),U_4142))
      | ~ class_Rings_Olinordered__semidom(U_4141) ),
    inference(definitional_conversion,[status(esa)],[f_1178_2]) ).

cnf(f_1178_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4143),U_4144))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4141),hAPP(hAPP(c_Power_Opower__class_Opower(U_4141),U_4142),U_4143)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4141),U_4142),U_4144)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4141),c_Groups_Oone__class_Oone(U_4141)),U_4142))
    | ~ class_Rings_Olinordered__semidom(U_4141) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

fof(f_1179_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).

fof(f_1179_2,plain,
    ! [U_4148,U_4147,U_4146,U_4145] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),hAPP(hAPP(c_Power_Opower__class_Opower(U_4145),U_4148),U_4147)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4145),U_4148),U_4146)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),U_4148),c_Groups_Oone__class_Oone(U_4145)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),c_Groups_Ozero__class_Ozero(U_4145)),U_4148))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4146),U_4147))
      | ~ class_Rings_Olinordered__semidom(U_4145) ),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

fof(f_1179_3,plain,
    ! [U_4146,U_4145,U_4147,U_4148] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),hAPP(hAPP(c_Power_Opower__class_Opower(U_4145),U_4148),U_4147)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4145),U_4148),U_4146)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),U_4148),c_Groups_Oone__class_Oone(U_4145)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),c_Groups_Ozero__class_Ozero(U_4145)),U_4148))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4146),U_4147))
      | ~ class_Rings_Olinordered__semidom(U_4145) ),
    inference(definitional_conversion,[status(esa)],[f_1179_2]) ).

cnf(f_1179_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),hAPP(hAPP(c_Power_Opower__class_Opower(U_4145),U_4148),U_4147)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4145),U_4148),U_4146)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),U_4148),c_Groups_Oone__class_Oone(U_4145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4145),c_Groups_Ozero__class_Ozero(U_4145)),U_4148))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4146),U_4147))
    | ~ class_Rings_Olinordered__semidom(U_4145) ),
    inference(clausify,[status(thm)],[f_1179_3]) ).

fof(f_1180_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).

fof(f_1180_2,plain,
    ! [U_4152,U_4151,U_4150,U_4149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),hAPP(hAPP(c_Power_Opower__class_Opower(U_4149),U_4152),U_4151)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4149),U_4152),U_4150)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),U_4152),c_Groups_Oone__class_Oone(U_4149)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),c_Groups_Ozero__class_Ozero(U_4149)),U_4152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4150),U_4151))
      | ~ class_Rings_Olinordered__semidom(U_4149) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

fof(f_1180_3,plain,
    ! [U_4150,U_4149,U_4151,U_4152] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),hAPP(hAPP(c_Power_Opower__class_Opower(U_4149),U_4152),U_4151)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4149),U_4152),U_4150)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),U_4152),c_Groups_Oone__class_Oone(U_4149)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),c_Groups_Ozero__class_Ozero(U_4149)),U_4152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4150),U_4151))
      | ~ class_Rings_Olinordered__semidom(U_4149) ),
    inference(definitional_conversion,[status(esa)],[f_1180_2]) ).

cnf(f_1180_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),hAPP(hAPP(c_Power_Opower__class_Opower(U_4149),U_4152),U_4151)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4149),U_4152),U_4150)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),U_4152),c_Groups_Oone__class_Oone(U_4149)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4149),c_Groups_Ozero__class_Ozero(U_4149)),U_4152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4150),U_4151))
    | ~ class_Rings_Olinordered__semidom(U_4149) ),
    inference(clausify,[status(thm)],[f_1180_3]) ).

fof(f_1181_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).

fof(f_1181_2,plain,
    ! [U_4155,U_4154,U_4153] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Power_Opower__class_Opower(U_4153),U_4154),hAPP(c_Nat_OSuc,U_4155))),c_Groups_Oone__class_Oone(U_4153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),c_Groups_Oone__class_Oone(U_4153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),c_Groups_Ozero__class_Ozero(U_4153)),U_4154))
      | ~ class_Rings_Olinordered__semidom(U_4153) ),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

fof(f_1181_3,plain,
    ! [U_4154,U_4153,U_4155] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Power_Opower__class_Opower(U_4153),U_4154),hAPP(c_Nat_OSuc,U_4155))),c_Groups_Oone__class_Oone(U_4153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),c_Groups_Oone__class_Oone(U_4153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),c_Groups_Ozero__class_Ozero(U_4153)),U_4154))
      | ~ class_Rings_Olinordered__semidom(U_4153) ),
    inference(definitional_conversion,[status(esa)],[f_1181_2]) ).

cnf(f_1181_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Power_Opower__class_Opower(U_4153),U_4154),hAPP(c_Nat_OSuc,U_4155))),c_Groups_Oone__class_Oone(U_4153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),c_Groups_Oone__class_Oone(U_4153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),c_Groups_Ozero__class_Ozero(U_4153)),U_4154))
    | ~ class_Rings_Olinordered__semidom(U_4153) ),
    inference(clausify,[status(thm)],[f_1181_3]) ).

fof(f_1182_1,plain,
    ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
    inference(fof_nnf,[status(thm)],[fact_number__of__is__id]) ).

fof(f_1182_2,plain,
    ! [U_4156] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4156) = U_4156,
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

fof(f_1182_3,plain,
    ! [U_4156] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4156) = U_4156,
    inference(definitional_conversion,[status(esa)],[f_1182_2]) ).

cnf(f_1182_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4156) = U_4156,
    inference(clausify,[status(thm)],[f_1182_3]) ).

fof(f_1183_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code]) ).

fof(f_1183_2,plain,
    ! [U_4158,U_4157] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4157)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4158)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4157),U_4158)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4157),U_4158))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4157)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4158))) ) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

fof(f_1183_3,plain,
    ( ! [U_4162,U_4160] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4162)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4160),U_4162)) )
    & ! [U_4161,U_4159] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4159),U_4161))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4159)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4161))) ) ),
    inference(miniscope,[status(thm)],[f_1183_2]) ).

fof(f_1183_4,plain,
    ( ! [U_4160,U_4162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4162)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4160),U_4162)) )
    & ! [U_4161,U_4159] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4159),U_4161))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4159)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4161))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1183_3]) ).

cnf(f_1183_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4159),U_4161))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4159)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4161))) ),
    inference(clausify,[status(thm)],[f_1183_4]) ).

cnf(f_1183_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4162)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4160),U_4162)) ),
    inference(clausify,[status(thm)],[f_1183_4]) ).

fof(f_1184_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code]) ).

fof(f_1184_2,plain,
    ! [U_4164,U_4163] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4163),U_4164)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4163),U_4164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4164))) ) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

fof(f_1184_3,plain,
    ( ! [U_4168,U_4166] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4166)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4168)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4166),U_4168)) )
    & ! [U_4167,U_4165] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4165),U_4167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4167))) ) ),
    inference(miniscope,[status(thm)],[f_1184_2]) ).

fof(f_1184_4,plain,
    ( ! [U_4166,U_4168] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4166)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4168)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4166),U_4168)) )
    & ! [U_4167,U_4165] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4165),U_4167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4167))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1184_3]) ).

cnf(f_1184_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4165),U_4167))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4167))) ),
    inference(clausify,[status(thm)],[f_1184_4]) ).

cnf(f_1184_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4166)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4168)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4166),U_4168)) ),
    inference(clausify,[status(thm)],[f_1184_4]) ).

fof(f_1185_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)),
    inference(fof_nnf,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(f_1185_2,plain,
    ! [U_4170,U_4169] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4169)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4169),U_4170)),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

fof(f_1185_3,plain,
    ! [U_4170,U_4169] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4169)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4169),U_4170)),
    inference(definitional_conversion,[status(esa)],[f_1185_2]) ).

cnf(f_1185_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4169)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4169),U_4170)),
    inference(clausify,[status(thm)],[f_1185_3]) ).

fof(f_1186_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    inference(fof_nnf,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(f_1186_2,plain,
    ! [U_4172,U_4171] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4171)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4172)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4171),U_4172)),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

fof(f_1186_3,plain,
    ! [U_4171,U_4172] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4171)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4172)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4171),U_4172)),
    inference(definitional_conversion,[status(esa)],[f_1186_2]) ).

cnf(f_1186_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4171)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4172)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4171),U_4172)),
    inference(clausify,[status(thm)],[f_1186_3]) ).

fof(f_1187_1,plain,
    ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(f_1187_2,plain,
    ! [U_4173] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4173)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4173)),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

fof(f_1187_3,plain,
    ! [U_4173] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4173)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4173)),
    inference(definitional_conversion,[status(esa)],[f_1187_2]) ).

cnf(f_1187_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4173)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4173)),
    inference(clausify,[status(thm)],[f_1187_3]) ).

fof(f_1188_1,plain,
    ! [V_m_2,V_x_2] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( V_x_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff]) ).

fof(f_1188_2,plain,
    ! [U_4175,U_4174] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4174),U_4175) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_4174 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4175 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_4174 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4174),U_4175) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

fof(f_1188_3,plain,
    ( ! [U_4179,U_4177] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4177),U_4179) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_4177 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4178,U_4176] :
        ( U_4176 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4176),U_4178) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1188_2]) ).

fof(f_1188_4,plain,
    ( ! [U_4179,U_4177] :
        ( U_4177 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP346(U_4179,U_4177) )
    & ! [U_4179,U_4177] :
        ( U_4179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP346(U_4179,U_4177) )
    & ! [U_4179,U_4177] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4177),U_4179) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP346(U_4179,U_4177) )
    & ! [U_4178,U_4176] :
        ( U_4176 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4176),U_4178) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP346])],[f_1188_3]) ).

cnf(f_1188_5,plain,
    ( U_4176 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4176),U_4178) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

cnf(f_1188_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4177),U_4179) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP346(U_4179,U_4177) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

cnf(f_1188_7,plain,
    ( U_4179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP346(U_4179,U_4177) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

cnf(f_1188_8,plain,
    ( U_4177 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP346(U_4179,U_4177) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

fof(f_1189_1,plain,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__0]) ).

fof(f_1189_2,plain,
    ! [U_4180] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4180) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

fof(f_1189_3,plain,
    ! [U_4180] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4180) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1189_2]) ).

cnf(f_1189_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4180) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1189_3]) ).

fof(f_1190_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).

fof(f_1190_2,plain,
    ! [U_4182,U_4181] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4181),U_4182)))
        | ( U_4182 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4181)) ) )
      & ( U_4182 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4181))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4181),U_4182))) ) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

fof(f_1190_3,plain,
    ( ! [U_4186,U_4184] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4184),U_4186)))
        | ( U_4186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4184)) ) )
    & ! [U_4185,U_4183] :
        ( U_4185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4183),U_4185))) ) ),
    inference(miniscope,[status(thm)],[f_1190_2]) ).

fof(f_1190_4,plain,
    ( ! [U_4186,U_4184] :
        ( U_4186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP347(U_4186,U_4184) )
    & ! [U_4186,U_4184] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4184))
        | ~ sP347(U_4186,U_4184) )
    & ! [U_4186,U_4184] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4184),U_4186)))
        | sP347(U_4186,U_4184) )
    & ! [U_4183,U_4185] :
        ( U_4185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4183),U_4185))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP347])],[f_1190_3]) ).

cnf(f_1190_5,plain,
    ( U_4185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4183))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4183),U_4185))) ),
    inference(clausify,[status(thm)],[f_1190_4]) ).

cnf(f_1190_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4184),U_4186)))
    | sP347(U_4186,U_4184) ),
    inference(clausify,[status(thm)],[f_1190_4]) ).

cnf(f_1190_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4184))
    | ~ sP347(U_4186,U_4184) ),
    inference(clausify,[status(thm)],[f_1190_4]) ).

cnf(f_1190_8,plain,
    ( U_4186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP347(U_4186,U_4184) ),
    inference(clausify,[status(thm)],[f_1190_4]) ).

fof(f_1191_1,plain,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).

fof(f_1191_2,plain,
    ! [U_4189,U_4188,U_4187] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4188),U_4189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4187),U_4188)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4187),U_4189)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4187)) ),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

fof(f_1191_3,plain,
    ! [U_4188,U_4187,U_4189] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4188),U_4189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4187),U_4188)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4187),U_4189)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4187)) ),
    inference(definitional_conversion,[status(esa)],[f_1191_2]) ).

cnf(f_1191_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4188),U_4189))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4187),U_4188)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4187),U_4189)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4187)) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

fof(f_1192_1,plain,
    ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w),
    inference(fof_nnf,[status(thm)],[fact_int__number__of__def]) ).

fof(f_1192_2,plain,
    ! [U_4190] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4190) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4190),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

fof(f_1192_3,plain,
    ! [U_4190] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4190) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4190),
    inference(definitional_conversion,[status(esa)],[f_1192_2]) ).

cnf(f_1192_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4190) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4190),
    inference(clausify,[status(thm)],[f_1192_3]) ).

fof(f_1193_1,plain,
    ! [V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__one__le__power]) ).

fof(f_1193_2,plain,
    ! [U_4192,U_4191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4191),U_4192)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4191)) ),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

fof(f_1193_3,plain,
    ! [U_4191,U_4192] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4191),U_4192)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4191)) ),
    inference(definitional_conversion,[status(esa)],[f_1193_2]) ).

cnf(f_1193_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4191),U_4192)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4191)) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

fof(f_1194_1,plain,
    ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of]) ).

fof(f_1194_2,plain,
    ! [U_4193] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4193)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4193),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ! [U_4193] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4193)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4193),
    inference(definitional_conversion,[status(esa)],[f_1194_2]) ).

cnf(f_1194_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4193)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4193),
    inference(clausify,[status(thm)],[f_1194_3]) ).

fof(f_1195_1,plain,
    ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__def]) ).

fof(f_1195_2,plain,
    ! [U_4194] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4194) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4194)),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

fof(f_1195_3,plain,
    ! [U_4194] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4194) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4194)),
    inference(definitional_conversion,[status(esa)],[f_1195_2]) ).

cnf(f_1195_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4194) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4194)),
    inference(clausify,[status(thm)],[f_1195_3]) ).

fof(f_1196_1,plain,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(f_1196_2,plain,
    ! [U_4196,U_4195] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4195)),U_4196) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4195),U_4196)),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

fof(f_1196_3,plain,
    ! [U_4195,U_4196] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4195)),U_4196) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4195),U_4196)),
    inference(definitional_conversion,[status(esa)],[f_1196_2]) ).

cnf(f_1196_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4195)),U_4196) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4195),U_4196)),
    inference(clausify,[status(thm)],[f_1196_3]) ).

fof(f_1197_1,plain,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_int__power]) ).

fof(f_1197_2,plain,
    ! [U_4198,U_4197] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4197),U_4198)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4197)),U_4198),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

fof(f_1197_3,plain,
    ! [U_4197,U_4198] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4197),U_4198)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4197)),U_4198),
    inference(definitional_conversion,[status(esa)],[f_1197_2]) ).

cnf(f_1197_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4197),U_4198)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4197)),U_4198),
    inference(clausify,[status(thm)],[f_1197_3]) ).

fof(f_1198_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zpower__int]) ).

fof(f_1198_2,plain,
    ! [U_4200,U_4199] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4199)),U_4200) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4199),U_4200)),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

fof(f_1198_3,plain,
    ! [U_4199,U_4200] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4199)),U_4200) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4199),U_4200)),
    inference(definitional_conversion,[status(esa)],[f_1198_2]) ).

cnf(f_1198_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4199)),U_4200) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4199),U_4200)),
    inference(clausify,[status(thm)],[f_1198_3]) ).

fof(f_1199_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),
    inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(f_1199_2,plain,
    ! [U_4202,U_4201] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4201)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4202)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4201),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4202))),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

fof(f_1199_3,plain,
    ! [U_4201,U_4202] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4201)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4202)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4201),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4202))),
    inference(definitional_conversion,[status(esa)],[f_1199_2]) ).

cnf(f_1199_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4201)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4202)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4201),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4202))),
    inference(clausify,[status(thm)],[f_1199_3]) ).

fof(f_1200_1,plain,
    ! [V_p,V_m] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__if]) ).

fof(f_1200_2,plain,
    ! [U_4204,U_4203] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4204),U_4203) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4204),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4203),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4204),U_4203) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

fof(f_1200_3,plain,
    ( ! [U_4208,U_4206] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4208),U_4206) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4208),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4206),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4207,U_4205] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4207),U_4205) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1200_2]) ).

fof(f_1200_4,plain,
    ( ! [U_4206,U_4208] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4208),U_4206) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4208),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4206),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4205,U_4207] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4207),U_4205) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1200_3]) ).

cnf(f_1200_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4207),U_4205) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1200_4]) ).

cnf(f_1200_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4208),U_4206) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4208),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4206),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_4206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1200_4]) ).

fof(f_1201_1,plain,
    ! [V_v_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
        | V_m_2 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
          & V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of]) ).

fof(f_1201_2,plain,
    ! [U_4210,U_4209] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4209) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4210)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4210)))
        | U_4209 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4210)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4210)))
          & U_4209 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4210)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4209) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4210) ) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

fof(f_1201_3,plain,
    ( ! [U_4214,U_4212] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4212) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)))
        | U_4212 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)) )
    & ! [U_4213,U_4211] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213)))
          & U_4211 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4211) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213) ) ),
    inference(miniscope,[status(thm)],[f_1201_2]) ).

fof(f_1201_4,plain,
    ( ! [U_4211,U_4213] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213)))
        | ~ sP348(U_4211,U_4213) )
    & ! [U_4211,U_4213] :
        ( U_4211 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213))
        | ~ sP348(U_4211,U_4213) )
    & ! [U_4212,U_4214] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4212) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)))
        | U_4212 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)) )
    & ! [U_4211,U_4213] :
        ( sP348(U_4211,U_4213)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4211) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP348])],[f_1201_3]) ).

cnf(f_1201_5,plain,
    ( sP348(U_4211,U_4213)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4211) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213) ),
    inference(clausify,[status(thm)],[f_1201_4]) ).

cnf(f_1201_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4212) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)))
    | U_4212 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4214)) ),
    inference(clausify,[status(thm)],[f_1201_4]) ).

cnf(f_1201_7,plain,
    ( U_4211 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213))
    | ~ sP348(U_4211,U_4213) ),
    inference(clausify,[status(thm)],[f_1201_4]) ).

cnf(f_1201_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4213)))
    | ~ sP348(U_4211,U_4213) ),
    inference(clausify,[status(thm)],[f_1201_4]) ).

fof(f_1202_1,plain,
    ! [V_n,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__eq]) ).

fof(f_1202_2,plain,
    ! [U_4216,U_4215] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4215),U_4216)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4215)),U_4216)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4215)) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

fof(f_1202_3,plain,
    ! [U_4216,U_4215] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4215),U_4216)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4215)),U_4216)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4215)) ),
    inference(definitional_conversion,[status(esa)],[f_1202_2]) ).

cnf(f_1202_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4215),U_4216)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4215)),U_4216)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4215)) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

fof(f_1203_1,plain,
    ! [V_n,V_x] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J]) ).

fof(f_1203_2,plain,
    ! [U_4218,U_4217] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4217)),U_4218) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4217),U_4218))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4217)) ),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

fof(f_1203_3,plain,
    ! [U_4217,U_4218] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4217)),U_4218) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4217),U_4218))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4217)) ),
    inference(definitional_conversion,[status(esa)],[f_1203_2]) ).

cnf(f_1203_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4217)),U_4218) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4217),U_4218))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4217)) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

fof(f_1204_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__power__not__zero]) ).

fof(f_1204_2,plain,
    ! [U_4221,U_4220,U_4219] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4219),U_4220),U_4221) != c_Groups_Ozero__class_Ozero(U_4219)
      | U_4220 = c_Groups_Ozero__class_Ozero(U_4219)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4219) ),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

fof(f_1204_3,plain,
    ! [U_4219,U_4220,U_4221] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4219),U_4220),U_4221) != c_Groups_Ozero__class_Ozero(U_4219)
      | U_4220 = c_Groups_Ozero__class_Ozero(U_4219)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4219) ),
    inference(definitional_conversion,[status(esa)],[f_1204_2]) ).

cnf(f_1204_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4219),U_4220),U_4221) != c_Groups_Ozero__class_Ozero(U_4219)
    | U_4220 = c_Groups_Ozero__class_Ozero(U_4219)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4219) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

fof(f_1205_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__commutes]) ).

fof(f_1205_2,plain,
    ! [U_4224,U_4223,U_4222] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4222),hAPP(hAPP(c_Power_Opower__class_Opower(U_4222),U_4223),U_4224)),U_4223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4222),U_4223),hAPP(hAPP(c_Power_Opower__class_Opower(U_4222),U_4223),U_4224))
      | ~ class_Groups_Omonoid__mult(U_4222) ),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

fof(f_1205_3,plain,
    ! [U_4222,U_4223,U_4224] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4222),hAPP(hAPP(c_Power_Opower__class_Opower(U_4222),U_4223),U_4224)),U_4223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4222),U_4223),hAPP(hAPP(c_Power_Opower__class_Opower(U_4222),U_4223),U_4224))
      | ~ class_Groups_Omonoid__mult(U_4222) ),
    inference(definitional_conversion,[status(esa)],[f_1205_2]) ).

cnf(f_1205_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4222),hAPP(hAPP(c_Power_Opower__class_Opower(U_4222),U_4223),U_4224)),U_4223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4222),U_4223),hAPP(hAPP(c_Power_Opower__class_Opower(U_4222),U_4223),U_4224))
    | ~ class_Groups_Omonoid__mult(U_4222) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

fof(f_1206_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mult__distrib]) ).

fof(f_1206_2,plain,
    ! [U_4228,U_4227,U_4226,U_4225] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4225),U_4226),U_4227)),U_4228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4225),hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),U_4226),U_4228)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),U_4227),U_4228))
      | ~ class_Groups_Ocomm__monoid__mult(U_4225) ),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

fof(f_1206_3,plain,
    ! [U_4225,U_4226,U_4227,U_4228] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4225),U_4226),U_4227)),U_4228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4225),hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),U_4226),U_4228)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),U_4227),U_4228))
      | ~ class_Groups_Ocomm__monoid__mult(U_4225) ),
    inference(definitional_conversion,[status(esa)],[f_1206_2]) ).

cnf(f_1206_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4225),U_4226),U_4227)),U_4228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4225),hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),U_4226),U_4228)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4225),U_4227),U_4228))
    | ~ class_Groups_Ocomm__monoid__mult(U_4225) ),
    inference(clausify,[status(thm)],[f_1206_3]) ).

fof(f_1207_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one]) ).

fof(f_1207_2,plain,
    ! [U_4230,U_4229] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4229),c_Groups_Oone__class_Oone(U_4229)),U_4230) = c_Groups_Oone__class_Oone(U_4229)
      | ~ class_Groups_Omonoid__mult(U_4229) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

fof(f_1207_3,plain,
    ! [U_4230,U_4229] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4229),c_Groups_Oone__class_Oone(U_4229)),U_4230) = c_Groups_Oone__class_Oone(U_4229)
      | ~ class_Groups_Omonoid__mult(U_4229) ),
    inference(definitional_conversion,[status(esa)],[f_1207_2]) ).

cnf(f_1207_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4229),c_Groups_Oone__class_Oone(U_4229)),U_4230) = c_Groups_Oone__class_Oone(U_4229)
    | ~ class_Groups_Omonoid__mult(U_4229) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

fof(f_1208_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__power]) ).

fof(f_1208_2,plain,
    ! [U_4233,U_4232,U_4231] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4231),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4232),U_4233)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4231),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4231),U_4232)),U_4233)
      | ~ class_Rings_Osemiring__1(U_4231) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

fof(f_1208_3,plain,
    ! [U_4231,U_4232,U_4233] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4231),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4232),U_4233)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4231),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4231),U_4232)),U_4233)
      | ~ class_Rings_Osemiring__1(U_4231) ),
    inference(definitional_conversion,[status(esa)],[f_1208_2]) ).

cnf(f_1208_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4231),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4232),U_4233)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4231),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4231),U_4232)),U_4233)
    | ~ class_Rings_Osemiring__1(U_4231) ),
    inference(clausify,[status(thm)],[f_1208_3]) ).

fof(f_1209_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mult]) ).

fof(f_1209_2,plain,
    ! [U_4237,U_4236,U_4235,U_4234] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),U_4235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4236),U_4237)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),U_4235),U_4236)),U_4237)
      | ~ class_Groups_Omonoid__mult(U_4234) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

fof(f_1209_3,plain,
    ! [U_4234,U_4235,U_4236,U_4237] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),U_4235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4236),U_4237)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),U_4235),U_4236)),U_4237)
      | ~ class_Groups_Omonoid__mult(U_4234) ),
    inference(definitional_conversion,[status(esa)],[f_1209_2]) ).

cnf(f_1209_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),U_4235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4236),U_4237)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),hAPP(hAPP(c_Power_Opower__class_Opower(U_4234),U_4235),U_4236)),U_4237)
    | ~ class_Groups_Omonoid__mult(U_4234) ),
    inference(clausify,[status(thm)],[f_1209_3]) ).

fof(f_1210_1,plain,
    ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))),
    inference(fof_nnf,[status(thm)],[fact_one__div__nat__number__of]) ).

fof(f_1210_2,plain,
    ! [U_4238] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4238))),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

fof(f_1210_3,plain,
    ! [U_4238] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4238))),
    inference(definitional_conversion,[status(esa)],[f_1210_2]) ).

cnf(f_1210_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4238))),
    inference(clausify,[status(thm)],[f_1210_3]) ).

fof(f_1211_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__abs]) ).

fof(f_1211_2,plain,
    ! [U_4241,U_4240,U_4239] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4239),hAPP(hAPP(c_Power_Opower__class_Opower(U_4239),U_4240),U_4241)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4239),hAPP(c_Groups_Oabs__class_Oabs(U_4239),U_4240)),U_4241)
      | ~ class_Rings_Olinordered__idom(U_4239) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

fof(f_1211_3,plain,
    ! [U_4239,U_4240,U_4241] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4239),hAPP(hAPP(c_Power_Opower__class_Opower(U_4239),U_4240),U_4241)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4239),hAPP(c_Groups_Oabs__class_Oabs(U_4239),U_4240)),U_4241)
      | ~ class_Rings_Olinordered__idom(U_4239) ),
    inference(definitional_conversion,[status(esa)],[f_1211_2]) ).

cnf(f_1211_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4239),hAPP(hAPP(c_Power_Opower__class_Opower(U_4239),U_4240),U_4241)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4239),hAPP(c_Groups_Oabs__class_Oabs(U_4239),U_4240)),U_4241)
    | ~ class_Rings_Olinordered__idom(U_4239) ),
    inference(clausify,[status(thm)],[f_1211_3]) ).

fof(f_1212_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one__right]) ).

fof(f_1212_2,plain,
    ! [U_4243,U_4242] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4242),U_4243),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4243
      | ~ class_Groups_Omonoid__mult(U_4242) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

fof(f_1212_3,plain,
    ! [U_4242,U_4243] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4242),U_4243),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4243
      | ~ class_Groups_Omonoid__mult(U_4242) ),
    inference(definitional_conversion,[status(esa)],[f_1212_2]) ).

cnf(f_1212_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4242),U_4243),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4243
    | ~ class_Groups_Omonoid__mult(U_4242) ),
    inference(clausify,[status(thm)],[f_1212_3]) ).

fof(f_1213_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).

fof(f_1213_2,plain,
    ! [U_4246,U_4245,U_4244] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),c_Groups_Ozero__class_Ozero(U_4244)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),c_Groups_Ozero__class_Ozero(U_4244)),U_4245))
      | ~ class_Rings_Olinordered__semidom(U_4244) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

fof(f_1213_3,plain,
    ! [U_4244,U_4245,U_4246] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),c_Groups_Ozero__class_Ozero(U_4244)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),c_Groups_Ozero__class_Ozero(U_4244)),U_4245))
      | ~ class_Rings_Olinordered__semidom(U_4244) ),
    inference(definitional_conversion,[status(esa)],[f_1213_2]) ).

cnf(f_1213_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),c_Groups_Ozero__class_Ozero(U_4244)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),c_Groups_Ozero__class_Ozero(U_4244)),U_4245))
    | ~ class_Rings_Olinordered__semidom(U_4244) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

fof(f_1214_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mono]) ).

fof(f_1214_2,plain,
    ! [U_4250,U_4249,U_4248,U_4247] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),hAPP(hAPP(c_Power_Opower__class_Opower(U_4247),U_4248),U_4250)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4247),U_4249),U_4250)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),c_Groups_Ozero__class_Ozero(U_4247)),U_4248))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),U_4248),U_4249))
      | ~ class_Rings_Olinordered__semidom(U_4247) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

fof(f_1214_3,plain,
    ! [U_4247,U_4248,U_4249,U_4250] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),hAPP(hAPP(c_Power_Opower__class_Opower(U_4247),U_4248),U_4250)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4247),U_4249),U_4250)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),c_Groups_Ozero__class_Ozero(U_4247)),U_4248))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),U_4248),U_4249))
      | ~ class_Rings_Olinordered__semidom(U_4247) ),
    inference(definitional_conversion,[status(esa)],[f_1214_2]) ).

cnf(f_1214_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),hAPP(hAPP(c_Power_Opower__class_Opower(U_4247),U_4248),U_4250)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4247),U_4249),U_4250)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),c_Groups_Ozero__class_Ozero(U_4247)),U_4248))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4247),U_4248),U_4249))
    | ~ class_Rings_Olinordered__semidom(U_4247) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

fof(f_1215_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).

fof(f_1215_2,plain,
    ! [U_4253,U_4252,U_4251] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4251),U_4252),U_4253)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),U_4252))
      | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

fof(f_1215_3,plain,
    ! [U_4252,U_4251,U_4253] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4251),U_4252),U_4253)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),U_4252))
      | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(definitional_conversion,[status(esa)],[f_1215_2]) ).

cnf(f_1215_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4251),U_4252),U_4253)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),U_4252))
    | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(clausify,[status(thm)],[f_1215_3]) ).

fof(f_1216_1,plain,
    ! [V_n_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Ozero__neq__one(T_b)
      | ~ class_Rings_Ono__zero__divisors(T_b)
      | ~ class_Rings_Omult__zero(T_b)
      | ~ class_Power_Opower(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).

fof(f_1216_2,plain,
    ! [U_4256,U_4255,U_4254] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4254),U_4255),U_4256) = c_Groups_Ozero__class_Ozero(U_4254)
          | U_4256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_4255 != c_Groups_Ozero__class_Ozero(U_4254) )
        & ( ( U_4256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_4255 = c_Groups_Ozero__class_Ozero(U_4254) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4254),U_4255),U_4256) != c_Groups_Ozero__class_Ozero(U_4254) ) )
      | ~ class_Rings_Ozero__neq__one(U_4254)
      | ~ class_Rings_Ono__zero__divisors(U_4254)
      | ~ class_Rings_Omult__zero(U_4254)
      | ~ class_Power_Opower(U_4254) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ( ! [U_4254,U_4255,U_4256] :
        ( U_4256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP349(U_4254,U_4255,U_4256) )
    & ! [U_4254,U_4255,U_4256] :
        ( U_4255 = c_Groups_Ozero__class_Ozero(U_4254)
        | ~ sP349(U_4254,U_4255,U_4256) )
    & ! [U_4254,U_4255,U_4256] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4254),U_4255),U_4256) = c_Groups_Ozero__class_Ozero(U_4254)
        | U_4256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4255 != c_Groups_Ozero__class_Ozero(U_4254)
        | ~ sP350(U_4254,U_4255,U_4256) )
    & ! [U_4254,U_4255,U_4256] :
        ( sP349(U_4254,U_4255,U_4256)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4254),U_4255),U_4256) != c_Groups_Ozero__class_Ozero(U_4254)
        | ~ sP350(U_4254,U_4255,U_4256) )
    & ! [U_4254,U_4255,U_4256] :
        ( sP350(U_4254,U_4255,U_4256)
        | ~ class_Rings_Ozero__neq__one(U_4254)
        | ~ class_Rings_Ono__zero__divisors(U_4254)
        | ~ class_Rings_Omult__zero(U_4254)
        | ~ class_Power_Opower(U_4254) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP349,sP350])],[f_1216_2]) ).

cnf(f_1216_4,plain,
    ( sP350(U_4254,U_4255,U_4256)
    | ~ class_Rings_Ozero__neq__one(U_4254)
    | ~ class_Rings_Ono__zero__divisors(U_4254)
    | ~ class_Rings_Omult__zero(U_4254)
    | ~ class_Power_Opower(U_4254) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

cnf(f_1216_5,plain,
    ( sP349(U_4254,U_4255,U_4256)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4254),U_4255),U_4256) != c_Groups_Ozero__class_Ozero(U_4254)
    | ~ sP350(U_4254,U_4255,U_4256) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

cnf(f_1216_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4254),U_4255),U_4256) = c_Groups_Ozero__class_Ozero(U_4254)
    | U_4256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4255 != c_Groups_Ozero__class_Ozero(U_4254)
    | ~ sP350(U_4254,U_4255,U_4256) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

cnf(f_1216_7,plain,
    ( U_4255 = c_Groups_Ozero__class_Ozero(U_4254)
    | ~ sP349(U_4254,U_4255,U_4256) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

cnf(f_1216_8,plain,
    ( U_4256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP349(U_4254,U_4255,U_4256) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

fof(f_1217_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).

fof(f_1217_2,plain,
    ! [U_4259,U_4258,U_4257] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4257),c_Groups_Oone__class_Oone(U_4257)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4257),U_4258),U_4259)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4257),c_Groups_Oone__class_Oone(U_4257)),U_4258))
      | ~ class_Rings_Olinordered__semidom(U_4257) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ! [U_4258,U_4259,U_4257] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4257),c_Groups_Oone__class_Oone(U_4257)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4257),U_4258),U_4259)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4257),c_Groups_Oone__class_Oone(U_4257)),U_4258))
      | ~ class_Rings_Olinordered__semidom(U_4257) ),
    inference(definitional_conversion,[status(esa)],[f_1217_2]) ).

cnf(f_1217_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4257),c_Groups_Oone__class_Oone(U_4257)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4257),U_4258),U_4259)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4257),c_Groups_Oone__class_Oone(U_4257)),U_4258))
    | ~ class_Rings_Olinordered__semidom(U_4257) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

fof(f_1218_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0__Suc]) ).

fof(f_1218_2,plain,
    ! [U_4261,U_4260] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4260),c_Groups_Ozero__class_Ozero(U_4260)),hAPP(c_Nat_OSuc,U_4261)) = c_Groups_Ozero__class_Ozero(U_4260)
      | ~ class_Rings_Osemiring__0(U_4260)
      | ~ class_Power_Opower(U_4260) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ! [U_4260,U_4261] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4260),c_Groups_Ozero__class_Ozero(U_4260)),hAPP(c_Nat_OSuc,U_4261)) = c_Groups_Ozero__class_Ozero(U_4260)
      | ~ class_Rings_Osemiring__0(U_4260)
      | ~ class_Power_Opower(U_4260) ),
    inference(definitional_conversion,[status(esa)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4260),c_Groups_Ozero__class_Ozero(U_4260)),hAPP(c_Nat_OSuc,U_4261)) = c_Groups_Ozero__class_Ozero(U_4260)
    | ~ class_Rings_Osemiring__0(U_4260)
    | ~ class_Power_Opower(U_4260) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [V_n_2,V_m_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).

fof(f_1219_2,plain,
    ! [U_4265,U_4264,U_4263,U_4262] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4264) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4265)
          | U_4264 != U_4265 )
        & ( U_4264 = U_4265
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4264) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4265) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Oone__class_Oone(U_4262)),U_4263))
      | ~ class_Rings_Olinordered__semidom(U_4262) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ( ! [U_4262,U_4263,U_4264,U_4265] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4264) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4265)
        | U_4264 != U_4265
        | ~ sP351(U_4262,U_4263,U_4264,U_4265) )
    & ! [U_4262,U_4263,U_4264,U_4265] :
        ( U_4264 = U_4265
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4264) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4265)
        | ~ sP351(U_4262,U_4263,U_4264,U_4265) )
    & ! [U_4262,U_4263,U_4264,U_4265] :
        ( sP351(U_4262,U_4263,U_4264,U_4265)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Oone__class_Oone(U_4262)),U_4263))
        | ~ class_Rings_Olinordered__semidom(U_4262) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP351])],[f_1219_2]) ).

cnf(f_1219_4,plain,
    ( sP351(U_4262,U_4263,U_4264,U_4265)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Oone__class_Oone(U_4262)),U_4263))
    | ~ class_Rings_Olinordered__semidom(U_4262) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

cnf(f_1219_5,plain,
    ( U_4264 = U_4265
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4264) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4265)
    | ~ sP351(U_4262,U_4263,U_4264,U_4265) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

cnf(f_1219_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4264) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4262),U_4263),U_4265)
    | U_4264 != U_4265
    | ~ sP351(U_4262,U_4263,U_4264,U_4265) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc2]) ).

fof(f_1220_2,plain,
    ! [U_4268,U_4267,U_4266] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4266),U_4267),hAPP(c_Nat_OSuc,U_4268)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),hAPP(hAPP(c_Power_Opower__class_Opower(U_4266),U_4267),U_4268)),U_4267)
      | ~ class_Groups_Omonoid__mult(U_4266) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ! [U_4268,U_4267,U_4266] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4266),U_4267),hAPP(c_Nat_OSuc,U_4268)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),hAPP(hAPP(c_Power_Opower__class_Opower(U_4266),U_4267),U_4268)),U_4267)
      | ~ class_Groups_Omonoid__mult(U_4266) ),
    inference(definitional_conversion,[status(esa)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4266),U_4267),hAPP(c_Nat_OSuc,U_4268)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),hAPP(hAPP(c_Power_Opower__class_Opower(U_4266),U_4267),U_4268)),U_4267)
    | ~ class_Groups_Omonoid__mult(U_4266) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc]) ).

fof(f_1221_2,plain,
    ! [U_4271,U_4270,U_4269] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4269),U_4270),hAPP(c_Nat_OSuc,U_4271)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4269),U_4270),hAPP(hAPP(c_Power_Opower__class_Opower(U_4269),U_4270),U_4271))
      | ~ class_Power_Opower(U_4269) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

fof(f_1221_3,plain,
    ! [U_4270,U_4271,U_4269] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4269),U_4270),hAPP(c_Nat_OSuc,U_4271)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4269),U_4270),hAPP(hAPP(c_Power_Opower__class_Opower(U_4269),U_4270),U_4271))
      | ~ class_Power_Opower(U_4269) ),
    inference(definitional_conversion,[status(esa)],[f_1221_2]) ).

cnf(f_1221_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4269),U_4270),hAPP(c_Nat_OSuc,U_4271)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4269),U_4270),hAPP(hAPP(c_Power_Opower__class_Opower(U_4269),U_4270),U_4271))
    | ~ class_Power_Opower(U_4269) ),
    inference(clausify,[status(thm)],[f_1221_3]) ).

fof(f_1222_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0]) ).

fof(f_1222_2,plain,
    ! [U_4273,U_4272] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4272),U_4273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4272)
      | ~ class_Power_Opower(U_4272) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

fof(f_1222_3,plain,
    ! [U_4272,U_4273] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4272),U_4273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4272)
      | ~ class_Power_Opower(U_4272) ),
    inference(definitional_conversion,[status(esa)],[f_1222_2]) ).

cnf(f_1222_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4272),U_4273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4272)
    | ~ class_Power_Opower(U_4272) ),
    inference(clausify,[status(thm)],[f_1222_3]) ).

fof(f_1223_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__add]) ).

fof(f_1223_2,plain,
    ! [U_4277,U_4276,U_4275,U_4274] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4276),U_4277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4274),hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),U_4276)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),U_4277))
      | ~ class_Groups_Omonoid__mult(U_4274) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

fof(f_1223_3,plain,
    ! [U_4274,U_4275,U_4276,U_4277] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4276),U_4277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4274),hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),U_4276)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),U_4277))
      | ~ class_Groups_Omonoid__mult(U_4274) ),
    inference(definitional_conversion,[status(esa)],[f_1223_2]) ).

cnf(f_1223_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4276),U_4277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4274),hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),U_4276)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4274),U_4275),U_4277))
    | ~ class_Groups_Omonoid__mult(U_4274) ),
    inference(clausify,[status(thm)],[f_1223_3]) ).

fof(f_1224_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__power__minus]) ).

fof(f_1224_2,plain,
    ! [U_4280,U_4279,U_4278] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4278),hAPP(hAPP(c_Power_Opower__class_Opower(U_4278),hAPP(c_Groups_Ouminus__class_Ouminus(U_4278),U_4279)),U_4280)) = hAPP(c_Groups_Oabs__class_Oabs(U_4278),hAPP(hAPP(c_Power_Opower__class_Opower(U_4278),U_4279),U_4280))
      | ~ class_Rings_Olinordered__idom(U_4278) ),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

fof(f_1224_3,plain,
    ! [U_4278,U_4279,U_4280] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4278),hAPP(hAPP(c_Power_Opower__class_Opower(U_4278),hAPP(c_Groups_Ouminus__class_Ouminus(U_4278),U_4279)),U_4280)) = hAPP(c_Groups_Oabs__class_Oabs(U_4278),hAPP(hAPP(c_Power_Opower__class_Opower(U_4278),U_4279),U_4280))
      | ~ class_Rings_Olinordered__idom(U_4278) ),
    inference(definitional_conversion,[status(esa)],[f_1224_2]) ).

cnf(f_1224_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4278),hAPP(hAPP(c_Power_Opower__class_Opower(U_4278),hAPP(c_Groups_Ouminus__class_Ouminus(U_4278),U_4279)),U_4280)) = hAPP(c_Groups_Oabs__class_Oabs(U_4278),hAPP(hAPP(c_Power_Opower__class_Opower(U_4278),U_4279),U_4280))
    | ~ class_Rings_Olinordered__idom(U_4278) ),
    inference(clausify,[status(thm)],[f_1224_3]) ).

fof(f_1225_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).

fof(f_1225_2,plain,
    ! [U_4284,U_4283,U_4282,U_4281] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4281),U_4282),U_4284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4281),c_Groups_Ozero__class_Ozero(U_4281)),U_4284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4281),hAPP(hAPP(c_Power_Opower__class_Opower(U_4281),U_4282),U_4283)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4281),U_4284),U_4283)))
      | ~ class_Rings_Olinordered__semidom(U_4281) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ! [U_4281,U_4282,U_4283,U_4284] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4281),U_4282),U_4284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4281),c_Groups_Ozero__class_Ozero(U_4281)),U_4284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4281),hAPP(hAPP(c_Power_Opower__class_Opower(U_4281),U_4282),U_4283)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4281),U_4284),U_4283)))
      | ~ class_Rings_Olinordered__semidom(U_4281) ),
    inference(definitional_conversion,[status(esa)],[f_1225_2]) ).

cnf(f_1225_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4281),U_4282),U_4284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4281),c_Groups_Ozero__class_Ozero(U_4281)),U_4284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4281),hAPP(hAPP(c_Power_Opower__class_Opower(U_4281),U_4282),U_4283)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4281),U_4284),U_4283)))
    | ~ class_Rings_Olinordered__semidom(U_4281) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).

fof(f_1226_2,plain,
    ! [U_4288,U_4287,U_4286,U_4285] :
      ( U_4286 = U_4288
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4285),c_Groups_Ozero__class_Ozero(U_4285)),U_4288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4285),c_Groups_Ozero__class_Ozero(U_4285)),U_4286))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4285),U_4286),hAPP(c_Nat_OSuc,U_4287)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4285),U_4288),hAPP(c_Nat_OSuc,U_4287))
      | ~ class_Rings_Olinordered__semidom(U_4285) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ! [U_4285,U_4286,U_4287,U_4288] :
      ( U_4286 = U_4288
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4285),c_Groups_Ozero__class_Ozero(U_4285)),U_4288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4285),c_Groups_Ozero__class_Ozero(U_4285)),U_4286))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4285),U_4286),hAPP(c_Nat_OSuc,U_4287)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4285),U_4288),hAPP(c_Nat_OSuc,U_4287))
      | ~ class_Rings_Olinordered__semidom(U_4285) ),
    inference(definitional_conversion,[status(esa)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( U_4286 = U_4288
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4285),c_Groups_Ozero__class_Ozero(U_4285)),U_4288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4285),c_Groups_Ozero__class_Ozero(U_4285)),U_4286))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4285),U_4286),hAPP(c_Nat_OSuc,U_4287)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4285),U_4288),hAPP(c_Nat_OSuc,U_4287))
    | ~ class_Rings_Olinordered__semidom(U_4285) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).

fof(f_1227_2,plain,
    ! [U_4292,U_4291,U_4290,U_4289] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),U_4290),U_4292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),c_Groups_Ozero__class_Ozero(U_4289)),U_4292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),hAPP(hAPP(c_Power_Opower__class_Opower(U_4289),U_4290),hAPP(c_Nat_OSuc,U_4291))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4289),U_4292),hAPP(c_Nat_OSuc,U_4291))))
      | ~ class_Rings_Olinordered__semidom(U_4289) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ! [U_4289,U_4290,U_4291,U_4292] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),U_4290),U_4292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),c_Groups_Ozero__class_Ozero(U_4289)),U_4292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),hAPP(hAPP(c_Power_Opower__class_Opower(U_4289),U_4290),hAPP(c_Nat_OSuc,U_4291))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4289),U_4292),hAPP(c_Nat_OSuc,U_4291))))
      | ~ class_Rings_Olinordered__semidom(U_4289) ),
    inference(definitional_conversion,[status(esa)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),U_4290),U_4292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),c_Groups_Ozero__class_Ozero(U_4289)),U_4292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4289),hAPP(hAPP(c_Power_Opower__class_Opower(U_4289),U_4290),hAPP(c_Nat_OSuc,U_4291))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4289),U_4292),hAPP(c_Nat_OSuc,U_4291))))
    | ~ class_Rings_Olinordered__semidom(U_4289) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

fof(f_1228_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma]) ).

fof(f_1228_2,plain,
    ! [U_4295,U_4294,U_4293] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4293),c_Groups_Oone__class_Oone(U_4293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4293),U_4294),hAPP(hAPP(c_Power_Opower__class_Opower(U_4293),U_4294),U_4295))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4293),c_Groups_Oone__class_Oone(U_4293)),U_4294))
      | ~ class_Rings_Olinordered__semidom(U_4293) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ! [U_4293,U_4294,U_4295] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4293),c_Groups_Oone__class_Oone(U_4293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4293),U_4294),hAPP(hAPP(c_Power_Opower__class_Opower(U_4293),U_4294),U_4295))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4293),c_Groups_Oone__class_Oone(U_4293)),U_4294))
      | ~ class_Rings_Olinordered__semidom(U_4293) ),
    inference(definitional_conversion,[status(esa)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4293),c_Groups_Oone__class_Oone(U_4293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4293),U_4294),hAPP(hAPP(c_Power_Opower__class_Opower(U_4293),U_4294),U_4295))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4293),c_Groups_Oone__class_Oone(U_4293)),U_4294))
    | ~ class_Rings_Olinordered__semidom(U_4293) ),
    inference(clausify,[status(thm)],[f_1228_3]) ).

fof(f_1229_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc]) ).

fof(f_1229_2,plain,
    ! [U_4298,U_4297,U_4296] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4296),hAPP(hAPP(c_Power_Opower__class_Opower(U_4296),U_4297),U_4298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4296),U_4297),hAPP(hAPP(c_Power_Opower__class_Opower(U_4296),U_4297),U_4298))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4296),c_Groups_Oone__class_Oone(U_4296)),U_4297))
      | ~ class_Rings_Olinordered__semidom(U_4296) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ! [U_4296,U_4297,U_4298] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4296),hAPP(hAPP(c_Power_Opower__class_Opower(U_4296),U_4297),U_4298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4296),U_4297),hAPP(hAPP(c_Power_Opower__class_Opower(U_4296),U_4297),U_4298))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4296),c_Groups_Oone__class_Oone(U_4296)),U_4297))
      | ~ class_Rings_Olinordered__semidom(U_4296) ),
    inference(definitional_conversion,[status(esa)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4296),hAPP(hAPP(c_Power_Opower__class_Opower(U_4296),U_4297),U_4298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4296),U_4297),hAPP(hAPP(c_Power_Opower__class_Opower(U_4296),U_4297),U_4298))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4296),c_Groups_Oone__class_Oone(U_4296)),U_4297))
    | ~ class_Rings_Olinordered__semidom(U_4296) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_1,plain,
    ! [V_n,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)
          | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)
          | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0__left]) ).

fof(f_1230_2,plain,
    ! [U_4300,U_4299] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4299),c_Groups_Ozero__class_Ozero(U_4299)),U_4300) = c_Groups_Ozero__class_Ozero(U_4299)
          | U_4300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4299),c_Groups_Ozero__class_Ozero(U_4299)),U_4300) = c_Groups_Oone__class_Oone(U_4299)
          | U_4300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_4299)
      | ~ class_Power_Opower(U_4299) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

fof(f_1230_3,plain,
    ( ! [U_4299,U_4300] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4299),c_Groups_Ozero__class_Ozero(U_4299)),U_4300) = c_Groups_Ozero__class_Ozero(U_4299)
        | U_4300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP352(U_4299,U_4300) )
    & ! [U_4299,U_4300] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4299),c_Groups_Ozero__class_Ozero(U_4299)),U_4300) = c_Groups_Oone__class_Oone(U_4299)
        | U_4300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP352(U_4299,U_4300) )
    & ! [U_4299,U_4300] :
        ( sP352(U_4299,U_4300)
        | ~ class_Rings_Osemiring__0(U_4299)
        | ~ class_Power_Opower(U_4299) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP352])],[f_1230_2]) ).

cnf(f_1230_4,plain,
    ( sP352(U_4299,U_4300)
    | ~ class_Rings_Osemiring__0(U_4299)
    | ~ class_Power_Opower(U_4299) ),
    inference(clausify,[status(thm)],[f_1230_3]) ).

cnf(f_1230_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4299),c_Groups_Ozero__class_Ozero(U_4299)),U_4300) = c_Groups_Oone__class_Oone(U_4299)
    | U_4300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP352(U_4299,U_4300) ),
    inference(clausify,[status(thm)],[f_1230_3]) ).

cnf(f_1230_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4299),c_Groups_Ozero__class_Ozero(U_4299)),U_4300) = c_Groups_Ozero__class_Ozero(U_4299)
    | U_4300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP352(U_4299,U_4300) ),
    inference(clausify,[status(thm)],[f_1230_3]) ).

fof(f_1231_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).

fof(f_1231_2,plain,
    ! [U_4303,U_4302,U_4301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4301),c_Groups_Oone__class_Oone(U_4301)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4301),U_4302),hAPP(c_Nat_OSuc,U_4303))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4301),c_Groups_Oone__class_Oone(U_4301)),U_4302))
      | ~ class_Rings_Olinordered__semidom(U_4301) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ! [U_4302,U_4301,U_4303] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4301),c_Groups_Oone__class_Oone(U_4301)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4301),U_4302),hAPP(c_Nat_OSuc,U_4303))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4301),c_Groups_Oone__class_Oone(U_4301)),U_4302))
      | ~ class_Rings_Olinordered__semidom(U_4301) ),
    inference(definitional_conversion,[status(esa)],[f_1231_2]) ).

cnf(f_1231_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4301),c_Groups_Oone__class_Oone(U_4301)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4301),U_4302),hAPP(c_Nat_OSuc,U_4303))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4301),c_Groups_Oone__class_Oone(U_4301)),U_4302))
    | ~ class_Rings_Olinordered__semidom(U_4301) ),
    inference(clausify,[status(thm)],[f_1231_3]) ).

fof(f_1232_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).

fof(f_1232_2,plain,
    ! [U_4307,U_4306,U_4305,U_4304] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4304),hAPP(hAPP(c_Power_Opower__class_Opower(U_4304),U_4307),U_4305)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4304),U_4307),U_4306)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4304),c_Groups_Oone__class_Oone(U_4304)),U_4307))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4305),U_4306))
      | ~ class_Rings_Olinordered__semidom(U_4304) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ! [U_4304,U_4305,U_4306,U_4307] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4304),hAPP(hAPP(c_Power_Opower__class_Opower(U_4304),U_4307),U_4305)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4304),U_4307),U_4306)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4304),c_Groups_Oone__class_Oone(U_4304)),U_4307))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4305),U_4306))
      | ~ class_Rings_Olinordered__semidom(U_4304) ),
    inference(definitional_conversion,[status(esa)],[f_1232_2]) ).

cnf(f_1232_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4304),hAPP(hAPP(c_Power_Opower__class_Opower(U_4304),U_4307),U_4305)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4304),U_4307),U_4306)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4304),c_Groups_Oone__class_Oone(U_4304)),U_4307))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4305),U_4306))
    | ~ class_Rings_Olinordered__semidom(U_4304) ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

fof(f_1233_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).

fof(f_1233_2,plain,
    ! [U_4311,U_4310,U_4309,U_4308] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4310),U_4311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4308),hAPP(hAPP(c_Power_Opower__class_Opower(U_4308),U_4309),U_4310)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4308),U_4309),U_4311)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4308),c_Groups_Oone__class_Oone(U_4308)),U_4309))
      | ~ class_Rings_Olinordered__semidom(U_4308) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ! [U_4308,U_4309,U_4310,U_4311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4310),U_4311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4308),hAPP(hAPP(c_Power_Opower__class_Opower(U_4308),U_4309),U_4310)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4308),U_4309),U_4311)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4308),c_Groups_Oone__class_Oone(U_4308)),U_4309))
      | ~ class_Rings_Olinordered__semidom(U_4308) ),
    inference(definitional_conversion,[status(esa)],[f_1233_2]) ).

cnf(f_1233_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4310),U_4311))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4308),hAPP(hAPP(c_Power_Opower__class_Opower(U_4308),U_4309),U_4310)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4308),U_4309),U_4311)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4308),c_Groups_Oone__class_Oone(U_4308)),U_4309))
    | ~ class_Rings_Olinordered__semidom(U_4308) ),
    inference(clausify,[status(thm)],[f_1233_3]) ).

fof(f_1234_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).

fof(f_1234_2,plain,
    ! [U_4315,U_4314,U_4313,U_4312] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4315)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4315))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),c_Groups_Oone__class_Oone(U_4312)),U_4313))
      | ~ class_Rings_Olinordered__semidom(U_4312) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ( ! [U_4313,U_4312,U_4314,U_4315] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4315)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315))
        | ~ sP353(U_4313,U_4312,U_4314,U_4315) )
    & ! [U_4313,U_4312,U_4314,U_4315] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4315)))
        | ~ sP353(U_4313,U_4312,U_4314,U_4315) )
    & ! [U_4313,U_4312,U_4314,U_4315] :
        ( sP353(U_4313,U_4312,U_4314,U_4315)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),c_Groups_Oone__class_Oone(U_4312)),U_4313))
        | ~ class_Rings_Olinordered__semidom(U_4312) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP353])],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( sP353(U_4313,U_4312,U_4314,U_4315)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),c_Groups_Oone__class_Oone(U_4312)),U_4313))
    | ~ class_Rings_Olinordered__semidom(U_4312) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4315)))
    | ~ sP353(U_4313,U_4312,U_4314,U_4315) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4312),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4312),U_4313),U_4315)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315))
    | ~ sP353(U_4313,U_4312,U_4314,U_4315) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs]) ).

fof(f_1235_2,plain,
    ! [U_4318,U_4317,U_4316] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4316),c_Groups_Ozero__class_Ozero(U_4316)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4316),hAPP(c_Groups_Oabs__class_Oabs(U_4316),U_4317)),U_4318)))
      | ~ class_Rings_Olinordered__idom(U_4316) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_4316,U_4317,U_4318] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4316),c_Groups_Ozero__class_Ozero(U_4316)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4316),hAPP(c_Groups_Oabs__class_Oabs(U_4316),U_4317)),U_4318)))
      | ~ class_Rings_Olinordered__idom(U_4316) ),
    inference(definitional_conversion,[status(esa)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4316),c_Groups_Ozero__class_Ozero(U_4316)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4316),hAPP(c_Groups_Oabs__class_Oabs(U_4316),U_4317)),U_4318)))
    | ~ class_Rings_Olinordered__idom(U_4316) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).

fof(f_1236_2,plain,
    ! [U_4322,U_4321,U_4320,U_4319] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4319),hAPP(hAPP(c_Power_Opower__class_Opower(U_4319),U_4322),U_4320)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4319),U_4322),U_4321)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4319),c_Groups_Oone__class_Oone(U_4319)),U_4322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4320),U_4321))
      | ~ class_Rings_Olinordered__semidom(U_4319) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

fof(f_1236_3,plain,
    ! [U_4319,U_4320,U_4321,U_4322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4319),hAPP(hAPP(c_Power_Opower__class_Opower(U_4319),U_4322),U_4320)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4319),U_4322),U_4321)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4319),c_Groups_Oone__class_Oone(U_4319)),U_4322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4320),U_4321))
      | ~ class_Rings_Olinordered__semidom(U_4319) ),
    inference(definitional_conversion,[status(esa)],[f_1236_2]) ).

cnf(f_1236_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4319),hAPP(hAPP(c_Power_Opower__class_Opower(U_4319),U_4322),U_4320)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4319),U_4322),U_4321)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4319),c_Groups_Oone__class_Oone(U_4319)),U_4322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4320),U_4321))
    | ~ class_Rings_Olinordered__semidom(U_4319) ),
    inference(clausify,[status(thm)],[f_1236_3]) ).

fof(f_1237_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus]) ).

fof(f_1237_2,plain,
    ! [U_4325,U_4324,U_4323] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),hAPP(c_Groups_Ouminus__class_Ouminus(U_4323),U_4324)),U_4325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4323),hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),hAPP(c_Groups_Ouminus__class_Ouminus(U_4323),c_Groups_Oone__class_Oone(U_4323))),U_4325)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),U_4324),U_4325))
      | ~ class_Rings_Oring__1(U_4323) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ! [U_4323,U_4324,U_4325] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),hAPP(c_Groups_Ouminus__class_Ouminus(U_4323),U_4324)),U_4325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4323),hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),hAPP(c_Groups_Ouminus__class_Ouminus(U_4323),c_Groups_Oone__class_Oone(U_4323))),U_4325)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),U_4324),U_4325))
      | ~ class_Rings_Oring__1(U_4323) ),
    inference(definitional_conversion,[status(esa)],[f_1237_2]) ).

cnf(f_1237_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),hAPP(c_Groups_Ouminus__class_Ouminus(U_4323),U_4324)),U_4325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4323),hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),hAPP(c_Groups_Ouminus__class_Ouminus(U_4323),c_Groups_Oone__class_Oone(U_4323))),U_4325)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4323),U_4324),U_4325))
    | ~ class_Rings_Oring__1(U_4323) ),
    inference(clausify,[status(thm)],[f_1237_3]) ).

fof(f_1238_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).

fof(f_1238_2,plain,
    ! [U_4328,U_4327,U_4326] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4326),U_4327),hAPP(hAPP(c_Power_Opower__class_Opower(U_4326),U_4327),U_4328))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4326),U_4327),U_4328)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),c_Groups_Oone__class_Oone(U_4326)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),U_4327))
      | ~ class_Rings_Olinordered__semidom(U_4326) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ! [U_4326,U_4327,U_4328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4326),U_4327),hAPP(hAPP(c_Power_Opower__class_Opower(U_4326),U_4327),U_4328))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4326),U_4327),U_4328)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),c_Groups_Oone__class_Oone(U_4326)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),U_4327))
      | ~ class_Rings_Olinordered__semidom(U_4326) ),
    inference(definitional_conversion,[status(esa)],[f_1238_2]) ).

cnf(f_1238_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4326),U_4327),hAPP(hAPP(c_Power_Opower__class_Opower(U_4326),U_4327),U_4328))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4326),U_4327),U_4328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),c_Groups_Oone__class_Oone(U_4326)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),U_4327))
    | ~ class_Rings_Olinordered__semidom(U_4326) ),
    inference(clausify,[status(thm)],[f_1238_3]) ).

fof(f_1239_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).

fof(f_1239_2,plain,
    ! [U_4332,U_4331,U_4330,U_4329] :
      ( U_4330 = U_4332
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4329),c_Groups_Ozero__class_Ozero(U_4329)),U_4332))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4329),c_Groups_Ozero__class_Ozero(U_4329)),U_4330))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4329),U_4330),U_4331) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4329),U_4332),U_4331)
      | ~ class_Rings_Olinordered__semidom(U_4329) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ! [U_4329,U_4330,U_4331,U_4332] :
      ( U_4330 = U_4332
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4329),c_Groups_Ozero__class_Ozero(U_4329)),U_4332))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4329),c_Groups_Ozero__class_Ozero(U_4329)),U_4330))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4329),U_4330),U_4331) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4329),U_4332),U_4331)
      | ~ class_Rings_Olinordered__semidom(U_4329) ),
    inference(definitional_conversion,[status(esa)],[f_1239_2]) ).

cnf(f_1239_4,plain,
    ( U_4330 = U_4332
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4329),c_Groups_Ozero__class_Ozero(U_4329)),U_4332))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4329),c_Groups_Ozero__class_Ozero(U_4329)),U_4330))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4329),U_4330),U_4331) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4329),U_4332),U_4331)
    | ~ class_Rings_Olinordered__semidom(U_4329) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

fof(f_1240_1,plain,
    ! [V_v_H] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__mod__nat__number__of]) ).

fof(f_1240_2,plain,
    ! [U_4333] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4333)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4333)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333))) ) ),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ( ! [U_4335] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4335)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4335)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4335))) )
    & ! [U_4334] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4334)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4334))) ) ),
    inference(miniscope,[status(thm)],[f_1240_2]) ).

fof(f_1240_4,plain,
    ( ! [U_4335] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4335)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4335)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4335))) )
    & ! [U_4334] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4334)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4334))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1240_3]) ).

cnf(f_1240_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4334)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4334))) ),
    inference(clausify,[status(thm)],[f_1240_4]) ).

cnf(f_1240_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4335)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4335)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4335))) ),
    inference(clausify,[status(thm)],[f_1240_4]) ).

fof(f_1241_1,plain,
    ! [T_b] :
      ( c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b))
      | ~ class_Power_Opower(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).

fof(f_1241_2,plain,
    ! [U_4336] :
      ( c_Power_Opower__class_Opower(U_4336) = c_Power_Opower_Opower(U_4336,c_Groups_Oone__class_Oone(U_4336),c_Groups_Otimes__class_Otimes(U_4336))
      | ~ class_Power_Opower(U_4336) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ! [U_4336] :
      ( c_Power_Opower__class_Opower(U_4336) = c_Power_Opower_Opower(U_4336,c_Groups_Oone__class_Oone(U_4336),c_Groups_Otimes__class_Otimes(U_4336))
      | ~ class_Power_Opower(U_4336) ),
    inference(definitional_conversion,[status(esa)],[f_1241_2]) ).

cnf(f_1241_4,plain,
    ( c_Power_Opower__class_Opower(U_4336) = c_Power_Opower_Opower(U_4336,c_Groups_Oone__class_Oone(U_4336),c_Groups_Otimes__class_Otimes(U_4336))
    | ~ class_Power_Opower(U_4336) ),
    inference(clausify,[status(thm)],[f_1241_3]) ).

fof(f_1242_1,plain,
    ! [V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_div__nat__number__of]) ).

fof(f_1242_2,plain,
    ! [U_4338,U_4337] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4337)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4338)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4337)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4338)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4337))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4337)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4338)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4337))) ) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

fof(f_1242_3,plain,
    ( ! [U_4342,U_4340] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4340)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4342)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340))) )
    & ! [U_4341,U_4339] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4339)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4341)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339))) ) ),
    inference(miniscope,[status(thm)],[f_1242_2]) ).

fof(f_1242_4,plain,
    ( ! [U_4340,U_4342] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4340)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4342)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340))) )
    & ! [U_4341,U_4339] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4339)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4341)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1242_3]) ).

cnf(f_1242_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4339)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4341)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339))) ),
    inference(clausify,[status(thm)],[f_1242_4]) ).

cnf(f_1242_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4340)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4342)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340))) ),
    inference(clausify,[status(thm)],[f_1242_4]) ).

fof(f_1243_1,plain,
    ! [V_v_H,V_v] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__nat__number__of]) ).

fof(f_1243_2,plain,
    ! [U_4344,U_4343] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4344)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4344))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4344))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343))) ) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ( ! [U_4348,U_4346] :
        ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4346))) )
    & ! [U_4347,U_4345] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4347)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4345))) ) ),
    inference(miniscope,[status(thm)],[f_1243_2]) ).

fof(f_1243_4,plain,
    ( ! [U_4348,U_4346] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
        | ~ sP354(U_4348,U_4346) )
    & ! [U_4348,U_4346] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
        | ~ sP354(U_4348,U_4346) )
    & ! [U_4348,U_4346] :
        ( sP354(U_4348,U_4346)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4346))) )
    & ! [U_4345,U_4347] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4347)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4345))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP354])],[f_1243_3]) ).

cnf(f_1243_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4347)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4345))) ),
    inference(clausify,[status(thm)],[f_1243_4]) ).

cnf(f_1243_6,plain,
    ( sP354(U_4348,U_4346)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4346))) ),
    inference(clausify,[status(thm)],[f_1243_4]) ).

cnf(f_1243_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
    | ~ sP354(U_4348,U_4346) ),
    inference(clausify,[status(thm)],[f_1243_4]) ).

cnf(f_1243_8,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348)))
    | ~ sP354(U_4348,U_4346) ),
    inference(clausify,[status(thm)],[f_1243_4]) ).

fof(f_1244_1,plain,
    ! [V_n,V_v] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__nat__number__of]) ).

fof(f_1244_2,plain,
    ! [U_4350,U_4349] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4350) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4349)),U_4350))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4349))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4350) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4350)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4349))) ) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ( ! [U_4354,U_4352] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4352)),U_4354) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4352)),U_4354))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4352))) )
    & ! [U_4353,U_4351] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4351)),U_4353) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4353)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4351))) ) ),
    inference(miniscope,[status(thm)],[f_1244_2]) ).

fof(f_1244_4,plain,
    ( ! [U_4354,U_4352] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4352)),U_4354) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4352)),U_4354))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4352))) )
    & ! [U_4351,U_4353] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4351)),U_4353) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4353)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4351))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1244_3]) ).

cnf(f_1244_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4351)),U_4353) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4353)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4351))) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

cnf(f_1244_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4352)),U_4354) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4352)),U_4354))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4352))) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

fof(f_1245_1,plain,
    ! [V_w,V_v] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__nat__number__of__number__of]) ).

fof(f_1245_2,plain,
    ! [U_4356,U_4355] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4355)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4355)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355))) ) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

fof(f_1245_3,plain,
    ( ! [U_4360,U_4358] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4358))) )
    & ! [U_4359,U_4357] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4357)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4357))) ) ),
    inference(miniscope,[status(thm)],[f_1245_2]) ).

fof(f_1245_4,plain,
    ( ! [U_4358,U_4360] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4358))) )
    & ! [U_4357,U_4359] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4357)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4357))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1245_3]) ).

cnf(f_1245_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4357)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4357))) ),
    inference(clausify,[status(thm)],[f_1245_4]) ).

cnf(f_1245_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4358))) ),
    inference(clausify,[status(thm)],[f_1245_4]) ).

fof(f_1246_1,plain,
    ! [V_b] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__minus1]) ).

fof(f_1246_2,plain,
    ! [U_4361] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4361) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4361),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4361)) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ! [U_4361] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4361) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4361),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4361)) ),
    inference(definitional_conversion,[status(esa)],[f_1246_2]) ).

cnf(f_1246_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4361) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4361),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4361)) ),
    inference(clausify,[status(thm)],[f_1246_3]) ).

fof(f_1247_1,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__Min]) ).

fof(f_1247_2,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(definitional_conversion,[status(esa)],[f_1247_1]) ).

cnf(f_1247_3,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(clausify,[status(thm)],[f_1247_2]) ).

fof(f_1248_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I24_J]) ).

fof(f_1248_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(definitional_conversion,[status(esa)],[f_1248_1]) ).

cnf(f_1248_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1248_2]) ).

fof(f_1249_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I7_J]) ).

fof(f_1249_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(definitional_conversion,[status(esa)],[f_1249_1]) ).

cnf(f_1249_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1249_2]) ).

fof(f_1250_1,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__0]) ).

fof(f_1250_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1250_1]) ).

cnf(f_1250_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1250_2]) ).

fof(f_1251_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__int]) ).

fof(f_1251_2,plain,
    ! [U_4362] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4362))),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

fof(f_1251_3,plain,
    ! [U_4362] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4362))),
    inference(definitional_conversion,[status(esa)],[f_1251_2]) ).

cnf(f_1251_4,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4362))),
    inference(clausify,[status(thm)],[f_1251_3]) ).

fof(f_1252_1,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__1]) ).

fof(f_1252_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1252_1]) ).

cnf(f_1252_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1252_2]) ).

fof(f_1253_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I2_J]) ).

fof(f_1253_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1253_1]) ).

cnf(f_1253_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1253_2]) ).

fof(f_1254_1,plain,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Int_OMin__def]) ).

fof(f_1254_2,plain,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1254_1]) ).

cnf(f_1254_3,plain,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1254_2]) ).

fof(f_1255_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),
    inference(fof_nnf,[status(thm)],[fact_mult__Min]) ).

fof(f_1255_2,plain,
    ! [U_4363] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4363) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4363),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

fof(f_1255_3,plain,
    ! [U_4363] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4363) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4363),
    inference(definitional_conversion,[status(esa)],[f_1255_2]) ).

cnf(f_1255_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4363) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4363),
    inference(clausify,[status(thm)],[f_1255_3]) ).

fof(f_1256_1,plain,
    ! [V_x_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(f_1256_2,plain,
    ! [U_4364] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4364))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4364)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4364))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4364)) ) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

fof(f_1256_3,plain,
    ( ! [U_4366] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4366))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4366)) )
    & ! [U_4365] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4365))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4365)) ) ),
    inference(miniscope,[status(thm)],[f_1256_2]) ).

fof(f_1256_4,plain,
    ( ! [U_4366] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4366))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4366)) )
    & ! [U_4365] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4365))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4365)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1256_3]) ).

cnf(f_1256_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4365))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4365)) ),
    inference(clausify,[status(thm)],[f_1256_4]) ).

cnf(f_1256_6,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4366))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4366)) ),
    inference(clausify,[status(thm)],[f_1256_4]) ).

fof(f_1257_1,plain,
    ! [V_Z_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__def]) ).

fof(f_1257_2,plain,
    ! [U_4367] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4367))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4367),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4367),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4367)) ) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

fof(f_1257_3,plain,
    ( ! [U_4369] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4369))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4369),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4368] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4368)) ) ),
    inference(miniscope,[status(thm)],[f_1257_2]) ).

fof(f_1257_4,plain,
    ( ! [U_4369] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4369))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4369),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4368] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4368)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1257_3]) ).

cnf(f_1257_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4368)) ),
    inference(clausify,[status(thm)],[f_1257_4]) ).

cnf(f_1257_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4369),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1257_4]) ).

fof(f_1258_1,plain,
    ! [V_z] :
      ( hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_neg__nat]) ).

fof(f_1258_2,plain,
    ! [U_4370] :
      ( hAPP(c_Int_Onat,U_4370) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4370)) ),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

fof(f_1258_3,plain,
    ! [U_4370] :
      ( hAPP(c_Int_Onat,U_4370) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4370)) ),
    inference(definitional_conversion,[status(esa)],[f_1258_2]) ).

cnf(f_1258_4,plain,
    ( hAPP(c_Int_Onat,U_4370) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4370)) ),
    inference(clausify,[status(thm)],[f_1258_3]) ).

fof(f_1259_1,plain,
    ! [V_z] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_not__neg__nat]) ).

fof(f_1259_2,plain,
    ! [U_4371] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_4371)) = U_4371
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4371)) ),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

fof(f_1259_3,plain,
    ! [U_4371] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_4371)) = U_4371
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4371)) ),
    inference(definitional_conversion,[status(esa)],[f_1259_2]) ).

cnf(f_1259_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_4371)) = U_4371
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4371)) ),
    inference(clausify,[status(thm)],[f_1259_3]) ).

fof(f_1260_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__minus1]) ).

fof(f_1260_2,plain,
    ! [U_4373,U_4372] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),hAPP(c_Int_Onumber__class_Onumber__of(U_4372),c_Int_OMin)),U_4373) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)
      | ~ class_Int_Onumber__ring(U_4372) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

fof(f_1260_3,plain,
    ! [U_4372,U_4373] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),hAPP(c_Int_Onumber__class_Onumber__of(U_4372),c_Int_OMin)),U_4373) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)
      | ~ class_Int_Onumber__ring(U_4372) ),
    inference(definitional_conversion,[status(esa)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),hAPP(c_Int_Onumber__class_Onumber__of(U_4372),c_Int_OMin)),U_4373) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)
    | ~ class_Int_Onumber__ring(U_4372) ),
    inference(clausify,[status(thm)],[f_1260_3]) ).

fof(f_1261_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__minus1__right]) ).

fof(f_1261_2,plain,
    ! [U_4375,U_4374] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),U_4375),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4374),U_4375)
      | ~ class_Int_Onumber__ring(U_4374) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

fof(f_1261_3,plain,
    ! [U_4374,U_4375] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),U_4375),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4374),U_4375)
      | ~ class_Int_Onumber__ring(U_4374) ),
    inference(definitional_conversion,[status(esa)],[f_1261_2]) ).

cnf(f_1261_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),U_4375),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4374),U_4375)
    | ~ class_Int_Onumber__ring(U_4374) ),
    inference(clausify,[status(thm)],[f_1261_3]) ).

fof(f_1262_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Min]) ).

fof(f_1262_2,plain,
    ! [U_4376] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4376),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4376),c_Groups_Oone__class_Oone(U_4376))
      | ~ class_Int_Onumber__ring(U_4376) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

fof(f_1262_3,plain,
    ! [U_4376] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4376),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4376),c_Groups_Oone__class_Oone(U_4376))
      | ~ class_Int_Onumber__ring(U_4376) ),
    inference(definitional_conversion,[status(esa)],[f_1262_2]) ).

cnf(f_1262_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4376),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4376),c_Groups_Oone__class_Oone(U_4376))
    | ~ class_Int_Onumber__ring(U_4376) ),
    inference(clausify,[status(thm)],[f_1262_3]) ).

fof(f_1263_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J]) ).

fof(f_1263_2,plain,
    ! [U_4377] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4377),c_Groups_Oone__class_Oone(U_4377)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4377),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4377) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ! [U_4377] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4377),c_Groups_Oone__class_Oone(U_4377)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4377),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4377) ),
    inference(definitional_conversion,[status(esa)],[f_1263_2]) ).

cnf(f_1263_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4377),c_Groups_Oone__class_Oone(U_4377)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4377),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4377) ),
    inference(clausify,[status(thm)],[f_1263_3]) ).

fof(f_1264_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__one]) ).

fof(f_1264_2,plain,
    ! [U_4378] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4378),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4378)
      | ~ class_Rings_Olinordered__idom(U_4378)
      | ~ class_Int_Onumber__ring(U_4378) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

fof(f_1264_3,plain,
    ! [U_4378] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4378),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4378)
      | ~ class_Rings_Olinordered__idom(U_4378)
      | ~ class_Int_Onumber__ring(U_4378) ),
    inference(definitional_conversion,[status(esa)],[f_1264_2]) ).

cnf(f_1264_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4378),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4378)
    | ~ class_Rings_Olinordered__idom(U_4378)
    | ~ class_Int_Onumber__ring(U_4378) ),
    inference(clausify,[status(thm)],[f_1264_3]) ).

fof(f_1265_1,plain,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__minus1__right]) ).

fof(f_1265_2,plain,
    ! [U_4379] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4379,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

fof(f_1265_3,plain,
    ! [U_4379] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4379,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1265_2]) ).

cnf(f_1265_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4379,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1265_3]) ).

fof(f_1266_1,plain,
    ! [V_n,V_m] :
      ( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma]) ).

fof(f_1266_2,plain,
    ! [U_4381,U_4380] :
      ( U_4380 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_4380 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4380),U_4381) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

fof(f_1266_3,plain,
    ! [U_4380,U_4381] :
      ( U_4380 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_4380 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4380),U_4381) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1266_2]) ).

cnf(f_1266_4,plain,
    ( U_4380 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_4380 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4380),U_4381) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1266_3]) ).

fof(f_1267_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( V_n_2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | V_m_2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff]) ).

fof(f_1267_2,plain,
    ! [U_4383,U_4382] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4382),U_4383) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_4383 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_4382 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_4383 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_4382 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( U_4383 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_4382 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_4383 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_4382 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4382),U_4383) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

fof(f_1267_3,plain,
    ( ! [U_4387,U_4385] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4385),U_4387) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_4387 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_4385 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_4387 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_4385 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
    & ! [U_4386,U_4384] :
        ( ( U_4386 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_4384 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_4386 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_4384 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4384),U_4386) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1267_2]) ).

fof(f_1267_4,plain,
    ( ! [U_4385,U_4387] :
        ( U_4387 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | U_4385 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP357(U_4385,U_4387) )
    & ! [U_4385,U_4387] :
        ( U_4387 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_4385 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP357(U_4385,U_4387) )
    & ! [U_4384,U_4386] :
        ( U_4386 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP356(U_4384,U_4386) )
    & ! [U_4384,U_4386] :
        ( U_4384 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP356(U_4384,U_4386) )
    & ! [U_4384,U_4386] :
        ( U_4386 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP355(U_4384,U_4386) )
    & ! [U_4384,U_4386] :
        ( U_4384 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP355(U_4384,U_4386) )
    & ! [U_4385,U_4387] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4385),U_4387) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | sP357(U_4385,U_4387) )
    & ! [U_4384,U_4386] :
        ( sP356(U_4384,U_4386)
        | sP355(U_4384,U_4386)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4384),U_4386) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP355,sP356,sP357])],[f_1267_3]) ).

cnf(f_1267_5,plain,
    ( sP356(U_4384,U_4386)
    | sP355(U_4384,U_4386)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4384),U_4386) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4385),U_4387) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | sP357(U_4385,U_4387) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_7,plain,
    ( U_4384 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP355(U_4384,U_4386) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_8,plain,
    ( U_4386 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP355(U_4384,U_4386) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_9,plain,
    ( U_4384 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP356(U_4384,U_4386) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_10,plain,
    ( U_4386 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP356(U_4384,U_4386) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_11,plain,
    ( U_4387 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_4385 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP357(U_4385,U_4387) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

cnf(f_1267_12,plain,
    ( U_4387 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_4385 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP357(U_4385,U_4387) ),
    inference(clausify,[status(thm)],[f_1267_4]) ).

fof(f_1268_1,plain,
    ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(f_1268_2,plain,
    ! [U_4391,U_4390,U_4389,U_4388] : hAPP(hAPP(c_Power_Opower_Opower(U_4388,U_4389,U_4390),U_4391),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4389,
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

fof(f_1268_3,plain,
    ! [U_4390,U_4391,U_4388,U_4389] : hAPP(hAPP(c_Power_Opower_Opower(U_4388,U_4389,U_4390),U_4391),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4389,
    inference(definitional_conversion,[status(esa)],[f_1268_2]) ).

cnf(f_1268_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_4388,U_4389,U_4390),U_4391),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4389,
    inference(clausify,[status(thm)],[f_1268_3]) ).

fof(f_1269_1,plain,
    ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(f_1269_2,plain,
    ! [U_4396,U_4395,U_4394,U_4393,U_4392] : hAPP(hAPP(c_Power_Opower_Opower(U_4392,U_4393,U_4394),U_4395),hAPP(c_Nat_OSuc,U_4396)) = hAPP(hAPP(U_4394,U_4395),hAPP(hAPP(c_Power_Opower_Opower(U_4392,U_4393,U_4394),U_4395),U_4396)),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

fof(f_1269_3,plain,
    ! [U_4394,U_4393,U_4396,U_4395,U_4392] : hAPP(hAPP(c_Power_Opower_Opower(U_4392,U_4393,U_4394),U_4395),hAPP(c_Nat_OSuc,U_4396)) = hAPP(hAPP(U_4394,U_4395),hAPP(hAPP(c_Power_Opower_Opower(U_4392,U_4393,U_4394),U_4395),U_4396)),
    inference(definitional_conversion,[status(esa)],[f_1269_2]) ).

cnf(f_1269_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_4392,U_4393,U_4394),U_4395),hAPP(c_Nat_OSuc,U_4396)) = hAPP(hAPP(U_4394,U_4395),hAPP(hAPP(c_Power_Opower_Opower(U_4392,U_4393,U_4394),U_4395),U_4396)),
    inference(clausify,[status(thm)],[f_1269_3]) ).

fof(f_1270_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__m1]) ).

fof(f_1270_2,plain,
    ! [U_4397] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4397),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4397),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4397) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

fof(f_1270_3,plain,
    ! [U_4397] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4397),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4397),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4397) ),
    inference(definitional_conversion,[status(esa)],[f_1270_2]) ).

cnf(f_1270_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_4397),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4397),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4397) ),
    inference(clausify,[status(thm)],[f_1270_3]) ).

fof(f_1271_1,plain,
    ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),
    inference(fof_nnf,[status(thm)],[fact_zdiv__minus1__right]) ).

fof(f_1271_2,plain,
    ! [U_4398] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4398),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4398),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

fof(f_1271_3,plain,
    ! [U_4398] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4398),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4398),
    inference(definitional_conversion,[status(esa)],[f_1271_2]) ).

cnf(f_1271_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4398),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4398),
    inference(clausify,[status(thm)],[f_1271_3]) ).

fof(f_1272_1,plain,
    ! [V_v] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0]) ).

fof(f_1272_2,plain,
    ! [U_4399] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4399))) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

fof(f_1272_3,plain,
    ! [U_4399] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4399))) ),
    inference(definitional_conversion,[status(esa)],[f_1272_2]) ).

cnf(f_1272_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4399))) ),
    inference(clausify,[status(thm)],[f_1272_3]) ).

fof(f_1273_1,plain,
    ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    inference(fof_nnf,[status(thm)],[fact_neg__zminus__int]) ).

fof(f_1273_2,plain,
    ! [U_4400] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4400))))),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

fof(f_1273_3,plain,
    ! [U_4400] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4400))))),
    inference(definitional_conversion,[status(esa)],[f_1273_2]) ).

cnf(f_1273_4,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4400))))),
    inference(clausify,[status(thm)],[f_1273_3]) ).

fof(f_1274_1,plain,
    ! [V_n,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one]) ).

fof(f_1274_2,plain,
    ! [U_4402,U_4401] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4401),hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4401),c_Int_OMin)),U_4402)) = c_Groups_Oone__class_Oone(U_4401)
      | ~ class_Rings_Olinordered__idom(U_4401)
      | ~ class_Int_Onumber__ring(U_4401) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

fof(f_1274_3,plain,
    ! [U_4401,U_4402] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4401),hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4401),c_Int_OMin)),U_4402)) = c_Groups_Oone__class_Oone(U_4401)
      | ~ class_Rings_Olinordered__idom(U_4401)
      | ~ class_Int_Onumber__ring(U_4401) ),
    inference(definitional_conversion,[status(esa)],[f_1274_2]) ).

cnf(f_1274_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4401),hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4401),c_Int_OMin)),U_4402)) = c_Groups_Oone__class_Oone(U_4401)
    | ~ class_Rings_Olinordered__idom(U_4401)
    | ~ class_Int_Onumber__ring(U_4401) ),
    inference(clausify,[status(thm)],[f_1274_3]) ).

fof(f_1275_1,plain,
    ! [V_b] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_div__eq__minus1]) ).

fof(f_1275_2,plain,
    ! [U_4403] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4403) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4403)) ),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

fof(f_1275_3,plain,
    ! [U_4403] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4403) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4403)) ),
    inference(definitional_conversion,[status(esa)],[f_1275_2]) ).

cnf(f_1275_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4403) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4403)) ),
    inference(clausify,[status(thm)],[f_1275_3]) ).

fof(f_1276_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
        | ( ( ( V_v_2 != V_v_H_2
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) )
      & ( ( ( ( ( V_v_2 = V_v_H_2
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__nat__number__of]) ).

fof(f_1276_2,plain,
    ! [U_4405,U_4404] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4404) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4405)
        | ( ( ( U_4404 != U_4405
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4405))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4404) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4405))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4404))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4405)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4404))) ) )
      & ( ( ( ( ( U_4404 = U_4405
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4405))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4404) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4405))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4404))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4405)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4404))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4404) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4405) ) ),
    inference(variable_rename,[status(thm)],[f_1276_1]) ).

fof(f_1276_3,plain,
    ( ! [U_4409,U_4407] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4407) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4409)
        | ( ( ( U_4407 != U_4409
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407))) ) )
    & ! [U_4408,U_4406] :
        ( ( ( ( ( U_4406 = U_4408
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4406) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4408) ) ),
    inference(miniscope,[status(thm)],[f_1276_2]) ).

fof(f_1276_4,plain,
    ( ! [U_4407,U_4409] :
        ( U_4407 != U_4409
        | ~ sP362(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)))
        | ~ sP362(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP361(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)))
        | ~ sP361(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( sP362(U_4407,U_4409)
        | sP361(U_4407,U_4409)
        | ~ sP363(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407)))
        | ~ sP363(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP360(U_4407,U_4409) )
    & ! [U_4407,U_4409] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407)))
        | ~ sP360(U_4407,U_4409) )
    & ! [U_4406,U_4408] :
        ( U_4406 = U_4408
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)))
        | ~ sP358(U_4406,U_4408) )
    & ! [U_4406,U_4408] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)))
        | ~ sP358(U_4406,U_4408) )
    & ! [U_4406,U_4408] :
        ( sP358(U_4406,U_4408)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406)))
        | ~ sP359(U_4406,U_4408) )
    & ! [U_4406,U_4408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406)))
        | ~ sP359(U_4406,U_4408) )
    & ! [U_4407,U_4409] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4407) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4409)
        | sP363(U_4407,U_4409)
        | sP360(U_4407,U_4409) )
    & ! [U_4406,U_4408] :
        ( sP359(U_4406,U_4408)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4406) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4408) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP358,sP359,sP360,sP361,sP362,sP363])],[f_1276_3]) ).

cnf(f_1276_5,plain,
    ( sP359(U_4406,U_4408)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4406) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4408) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4407) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4409)
    | sP363(U_4407,U_4409)
    | sP360(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406)))
    | ~ sP359(U_4406,U_4408) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_8,plain,
    ( sP358(U_4406,U_4408)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406)))
    | ~ sP359(U_4406,U_4408) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4406) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)))
    | ~ sP358(U_4406,U_4408) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_10,plain,
    ( U_4406 = U_4408
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4408)))
    | ~ sP358(U_4406,U_4408) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_11,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407)))
    | ~ sP360(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP360(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_13,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407)))
    | ~ sP363(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_14,plain,
    ( sP362(U_4407,U_4409)
    | sP361(U_4407,U_4409)
    | ~ sP363(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_15,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)))
    | ~ sP361(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_16,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4407) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP361(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_17,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4409)))
    | ~ sP362(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

cnf(f_1276_18,plain,
    ( U_4407 != U_4409
    | ~ sP362(U_4407,U_4409) ),
    inference(clausify,[status(thm)],[f_1276_4]) ).

fof(f_1277_1,plain,
    ! [V_k,V_v_H,V_v] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(f_1277_2,plain,
    ! [U_4412,U_4411,U_4410] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4411)),U_4412)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4410),U_4411))),U_4412)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4411))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4411)),U_4412)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4410)),U_4412)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4411))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4410))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4411)),U_4412)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4411)),U_4412)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4410))) ) ),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

fof(f_1277_3,plain,
    ( ! [U_4418,U_4416,U_4414] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4416)),U_4418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4414),U_4416))),U_4418)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4416))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4416)),U_4418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),U_4418)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4416))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4414))) )
    & ! [U_4417,U_4415,U_4413] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4413)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4415)),U_4417)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4415)),U_4417)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4413))) ) ),
    inference(miniscope,[status(thm)],[f_1277_2]) ).

fof(f_1277_4,plain,
    ( ! [U_4414,U_4416,U_4418] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4416)),U_4418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4414),U_4416))),U_4418)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4416)))
        | ~ sP364(U_4414,U_4416,U_4418) )
    & ! [U_4414,U_4416,U_4418] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4416)),U_4418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),U_4418)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4416)))
        | ~ sP364(U_4414,U_4416,U_4418) )
    & ! [U_4414,U_4416,U_4418] :
        ( sP364(U_4414,U_4416,U_4418)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4414))) )
    & ! [U_4413,U_4415,U_4417] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4413)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4415)),U_4417)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4415)),U_4417)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4413))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP364])],[f_1277_3]) ).

cnf(f_1277_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4413)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4415)),U_4417)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4415)),U_4417)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4413))) ),
    inference(clausify,[status(thm)],[f_1277_4]) ).

cnf(f_1277_6,plain,
    ( sP364(U_4414,U_4416,U_4418)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4414))) ),
    inference(clausify,[status(thm)],[f_1277_4]) ).

cnf(f_1277_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4416)),U_4418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),U_4418)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4416)))
    | ~ sP364(U_4414,U_4416,U_4418) ),
    inference(clausify,[status(thm)],[f_1277_4]) ).

cnf(f_1277_8,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4416)),U_4418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4414),U_4416))),U_4418)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4416)))
    | ~ sP364(U_4414,U_4416,U_4418) ),
    inference(clausify,[status(thm)],[f_1277_4]) ).

fof(f_1278_1,plain,
    ! [V_v] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__nat__number__of]) ).

fof(f_1278_2,plain,
    ! [U_4419] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4419)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4419)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4419))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4419)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4419))) ) ),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

fof(f_1278_3,plain,
    ( ! [U_4421] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4421)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4421)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4421))) )
    & ! [U_4420] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4420)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4420))) ) ),
    inference(miniscope,[status(thm)],[f_1278_2]) ).

fof(f_1278_4,plain,
    ( ! [U_4421] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4421)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4421)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4421))) )
    & ! [U_4420] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4420)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4420))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1278_3]) ).

cnf(f_1278_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4420)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4420))) ),
    inference(clausify,[status(thm)],[f_1278_4]) ).

cnf(f_1278_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4421)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4421)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4421))) ),
    inference(clausify,[status(thm)],[f_1278_4]) ).

fof(f_1279_1,plain,
    ! [V_v,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(f_1279_2,plain,
    ! [U_4423,U_4422] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4422),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4422),U_4423)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4423))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4422),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423)) = c_Groups_Ozero__class_Ozero(U_4422)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4423))) ) )
      | ~ class_Int_Onumber__ring(U_4422) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

fof(f_1279_3,plain,
    ( ! [U_4423,U_4422] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4422),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4422),U_4423)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4423)))
        | ~ sP365(U_4423,U_4422) )
    & ! [U_4423,U_4422] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4422),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423)) = c_Groups_Ozero__class_Ozero(U_4422)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4423)))
        | ~ sP365(U_4423,U_4422) )
    & ! [U_4423,U_4422] :
        ( sP365(U_4423,U_4422)
        | ~ class_Int_Onumber__ring(U_4422) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP365])],[f_1279_2]) ).

cnf(f_1279_4,plain,
    ( sP365(U_4423,U_4422)
    | ~ class_Int_Onumber__ring(U_4422) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

cnf(f_1279_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4422),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423)) = c_Groups_Ozero__class_Ozero(U_4422)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4423)))
    | ~ sP365(U_4423,U_4422) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

cnf(f_1279_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4422),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4422),U_4423)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4423)))
    | ~ sP365(U_4423,U_4422) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

fof(f_1280_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__neg__trivial]) ).

fof(f_1280_2,plain,
    ! [U_4425,U_4424] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4424),U_4425) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4424),U_4425)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4424)) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

fof(f_1280_3,plain,
    ! [U_4425,U_4424] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4424),U_4425) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4424),U_4425)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4424)) ),
    inference(definitional_conversion,[status(esa)],[f_1280_2]) ).

cnf(f_1280_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4424),U_4425) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4424),U_4425)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4424)) ),
    inference(clausify,[status(thm)],[f_1280_3]) ).

fof(f_1281_1,plain,
    ! [V_n,V_v] :
      ( ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(f_1281_2,plain,
    ! [U_4427,U_4426] :
      ( ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4426)),U_4427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4426))),U_4427)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4426))) )
      & ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4426)),U_4427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4427)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4426))) ) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

fof(f_1281_3,plain,
    ( ! [U_4431,U_4429] :
        ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4429)),U_4431)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4429))),U_4431)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4429))) )
    & ! [U_4430,U_4428] :
        ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4428)),U_4430)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4430)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4428))) ) ),
    inference(miniscope,[status(thm)],[f_1281_2]) ).

fof(f_1281_4,plain,
    ( ! [U_4429,U_4431] :
        ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4429)),U_4431)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4429))),U_4431)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4429))) )
    & ! [U_4430,U_4428] :
        ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4428)),U_4430)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4430)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4428))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1281_3]) ).

cnf(f_1281_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4428)),U_4430)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4430)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4428))) ),
    inference(clausify,[status(thm)],[f_1281_4]) ).

cnf(f_1281_6,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4429)),U_4431)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4429))),U_4431)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4429))) ),
    inference(clausify,[status(thm)],[f_1281_4]) ).

fof(f_1282_1,plain,
    ! [V_v] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(f_1282_2,plain,
    ! [U_4432] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4432)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4432))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4432))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4432)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4432))) ) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

fof(f_1282_3,plain,
    ( ! [U_4434] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4434)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4434))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4434))) )
    & ! [U_4433] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4433)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4433))) ) ),
    inference(miniscope,[status(thm)],[f_1282_2]) ).

fof(f_1282_4,plain,
    ( ! [U_4434] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4434)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4434))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4434))) )
    & ! [U_4433] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4433)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4433))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1282_3]) ).

cnf(f_1282_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4433)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4433))) ),
    inference(clausify,[status(thm)],[f_1282_4]) ).

cnf(f_1282_6,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4434)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4434))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4434))) ),
    inference(clausify,[status(thm)],[f_1282_4]) ).

fof(f_1283_1,plain,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ? [B_i] :
          ( hAPP(V_f_2,B_i) = V_k_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val]) ).

fof(f_1283_2,plain,
    ! [U_4439,U_4438,U_4437] :
      ( ? [U_4436] :
          ( hAPP(U_4438,U_4436) = U_4439
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4436),U_4437)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4439),hAPP(U_4438,U_4437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4438,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4439))
      | ? [U_4435] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4435),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4438,U_4435)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4435),U_4437)) ) ),
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

fof(f_1283_3,plain,
    ! [U_4439,U_4438,U_4437] :
      ( ? [U_4436] :
          ( hAPP(U_4438,U_4436) = U_4439
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4436),U_4437)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4439),hAPP(U_4438,U_4437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4438,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4439))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4438,sK79(U_4439,U_4438,U_4437))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),U_4437)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_4435,sK79(U_4439,U_4438,U_4437))],[f_1283_2]) ).

fof(f_1283_4,plain,
    ! [U_4439,U_4438,U_4437] :
      ( ( hAPP(U_4438,sK80(U_4439,U_4438,U_4437)) = U_4439
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK80(U_4439,U_4438,U_4437)),U_4437)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4439),hAPP(U_4438,U_4437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4438,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4439))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4438,sK79(U_4439,U_4438,U_4437))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),U_4437)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_4436,sK80(U_4439,U_4438,U_4437))],[f_1283_3]) ).

fof(f_1283_5,plain,
    ( ! [U_4437,U_4438,U_4439] :
        ( hAPP(U_4438,sK80(U_4439,U_4438,U_4437)) = U_4439
        | ~ sP367(U_4437,U_4438,U_4439) )
    & ! [U_4437,U_4438,U_4439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK80(U_4439,U_4438,U_4437)),U_4437))
        | ~ sP367(U_4437,U_4438,U_4439) )
    & ! [U_4437,U_4438,U_4439] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4438,sK79(U_4439,U_4438,U_4437))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP366(U_4437,U_4438,U_4439) )
    & ! [U_4437,U_4438,U_4439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),U_4437))
        | ~ sP366(U_4437,U_4438,U_4439) )
    & ! [U_4437,U_4438,U_4439] :
        ( sP367(U_4437,U_4438,U_4439)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4439),hAPP(U_4438,U_4437)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4438,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4439))
        | sP366(U_4437,U_4438,U_4439) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP366,sP367])],[f_1283_4]) ).

cnf(f_1283_6,plain,
    ( sP367(U_4437,U_4438,U_4439)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4439),hAPP(U_4438,U_4437)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4438,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4439))
    | sP366(U_4437,U_4438,U_4439) ),
    inference(clausify,[status(thm)],[f_1283_5]) ).

cnf(f_1283_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),U_4437))
    | ~ sP366(U_4437,U_4438,U_4439) ),
    inference(clausify,[status(thm)],[f_1283_5]) ).

cnf(f_1283_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK79(U_4439,U_4438,U_4437)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4438,sK79(U_4439,U_4438,U_4437))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP366(U_4437,U_4438,U_4439) ),
    inference(clausify,[status(thm)],[f_1283_5]) ).

cnf(f_1283_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK80(U_4439,U_4438,U_4437)),U_4437))
    | ~ sP367(U_4437,U_4438,U_4439) ),
    inference(clausify,[status(thm)],[f_1283_5]) ).

cnf(f_1283_10,plain,
    ( hAPP(U_4438,sK80(U_4439,U_4438,U_4437)) = U_4439
    | ~ sP367(U_4437,U_4438,U_4439) ),
    inference(clausify,[status(thm)],[f_1283_5]) ).

fof(f_1284_1,plain,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ? [B_i] :
          ( hAPP(V_f_2,B_i) = V_k_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__val__lemma]) ).

fof(f_1284_2,plain,
    ! [U_4444,U_4443,U_4442] :
      ( ? [U_4441] :
          ( hAPP(U_4443,U_4441) = U_4444
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4441),U_4442)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4444),hAPP(U_4443,U_4442)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4443,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4444))
      | ? [U_4440] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4443,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4440),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4443,U_4440)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4440),U_4442)) ) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

fof(f_1284_3,plain,
    ! [U_4444,U_4443,U_4442] :
      ( ? [U_4441] :
          ( hAPP(U_4443,U_4441) = U_4444
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4441),U_4442)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4444),hAPP(U_4443,U_4442)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4443,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4444))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4443,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4443,sK81(U_4444,U_4443,U_4442))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),U_4442)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_4440,sK81(U_4444,U_4443,U_4442))],[f_1284_2]) ).

fof(f_1284_4,plain,
    ! [U_4444,U_4443,U_4442] :
      ( ( hAPP(U_4443,sK82(U_4444,U_4443,U_4442)) = U_4444
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK82(U_4444,U_4443,U_4442)),U_4442)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4444),hAPP(U_4443,U_4442)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4443,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4444))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4443,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4443,sK81(U_4444,U_4443,U_4442))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),U_4442)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_4441,sK82(U_4444,U_4443,U_4442))],[f_1284_3]) ).

fof(f_1284_5,plain,
    ( ! [U_4443,U_4442,U_4444] :
        ( hAPP(U_4443,sK82(U_4444,U_4443,U_4442)) = U_4444
        | ~ sP369(U_4443,U_4442,U_4444) )
    & ! [U_4443,U_4442,U_4444] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK82(U_4444,U_4443,U_4442)),U_4442))
        | ~ sP369(U_4443,U_4442,U_4444) )
    & ! [U_4443,U_4442,U_4444] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4443,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4443,sK81(U_4444,U_4443,U_4442))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP368(U_4443,U_4442,U_4444) )
    & ! [U_4443,U_4442,U_4444] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),U_4442))
        | ~ sP368(U_4443,U_4442,U_4444) )
    & ! [U_4443,U_4442,U_4444] :
        ( sP369(U_4443,U_4442,U_4444)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4444),hAPP(U_4443,U_4442)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4443,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4444))
        | sP368(U_4443,U_4442,U_4444) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP368,sP369])],[f_1284_4]) ).

cnf(f_1284_6,plain,
    ( sP369(U_4443,U_4442,U_4444)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4444),hAPP(U_4443,U_4442)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4443,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4444))
    | sP368(U_4443,U_4442,U_4444) ),
    inference(clausify,[status(thm)],[f_1284_5]) ).

cnf(f_1284_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),U_4442))
    | ~ sP368(U_4443,U_4442,U_4444) ),
    inference(clausify,[status(thm)],[f_1284_5]) ).

cnf(f_1284_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4443,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK81(U_4444,U_4443,U_4442)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4443,sK81(U_4444,U_4443,U_4442))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP368(U_4443,U_4442,U_4444) ),
    inference(clausify,[status(thm)],[f_1284_5]) ).

cnf(f_1284_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK82(U_4444,U_4443,U_4442)),U_4442))
    | ~ sP369(U_4443,U_4442,U_4444) ),
    inference(clausify,[status(thm)],[f_1284_5]) ).

cnf(f_1284_10,plain,
    ( hAPP(U_4443,sK82(U_4444,U_4443,U_4442)) = U_4444
    | ~ sP369(U_4443,U_4442,U_4444) ),
    inference(clausify,[status(thm)],[f_1284_5]) ).

fof(f_1285_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).

fof(f_1285_2,plain,
    ! [U_4447,U_4446,U_4445] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) = hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4447)
          | ~ c_Int_Oiszero(U_4445,hAPP(c_Int_Onumber__class_Onumber__of(U_4445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4447)))) )
        & ( c_Int_Oiszero(U_4445,hAPP(c_Int_Onumber__class_Onumber__of(U_4445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4447))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) != hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4447) ) )
      | ~ class_Int_Onumber__ring(U_4445) ),
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

fof(f_1285_3,plain,
    ( ! [U_4445,U_4446,U_4447] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) = hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4447)
        | ~ c_Int_Oiszero(U_4445,hAPP(c_Int_Onumber__class_Onumber__of(U_4445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4447))))
        | ~ sP370(U_4445,U_4446,U_4447) )
    & ! [U_4445,U_4446,U_4447] :
        ( c_Int_Oiszero(U_4445,hAPP(c_Int_Onumber__class_Onumber__of(U_4445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4447))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) != hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4447)
        | ~ sP370(U_4445,U_4446,U_4447) )
    & ! [U_4445,U_4446,U_4447] :
        ( sP370(U_4445,U_4446,U_4447)
        | ~ class_Int_Onumber__ring(U_4445) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP370])],[f_1285_2]) ).

cnf(f_1285_4,plain,
    ( sP370(U_4445,U_4446,U_4447)
    | ~ class_Int_Onumber__ring(U_4445) ),
    inference(clausify,[status(thm)],[f_1285_3]) ).

cnf(f_1285_5,plain,
    ( c_Int_Oiszero(U_4445,hAPP(c_Int_Onumber__class_Onumber__of(U_4445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4447))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) != hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4447)
    | ~ sP370(U_4445,U_4446,U_4447) ),
    inference(clausify,[status(thm)],[f_1285_3]) ).

cnf(f_1285_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) = hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4447)
    | ~ c_Int_Oiszero(U_4445,hAPP(c_Int_Onumber__class_Onumber__of(U_4445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4447))))
    | ~ sP370(U_4445,U_4446,U_4447) ),
    inference(clausify,[status(thm)],[f_1285_3]) ).

fof(f_1286_1,plain,
    ! [V_v_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0]) ).

fof(f_1286_2,plain,
    ! [U_4448] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4448))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4448) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4448) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4448)))) ) ),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

fof(f_1286_3,plain,
    ( ! [U_4450] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4450))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4450) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4449] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4449)))) ) ),
    inference(miniscope,[status(thm)],[f_1286_2]) ).

fof(f_1286_4,plain,
    ( ! [U_4450] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4450))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4450) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4449] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4449)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1286_3]) ).

cnf(f_1286_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4449)))) ),
    inference(clausify,[status(thm)],[f_1286_4]) ).

cnf(f_1286_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4450))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4450) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1286_4]) ).

fof(f_1287_1,plain,
    ! [V_k,V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(f_1287_2,plain,
    ! [U_4453,U_4452,U_4451] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4452)),U_4453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4451),U_4452))),U_4453)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4451),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4452)),U_4453)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4451),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

fof(f_1287_3,plain,
    ( ! [U_4459,U_4457,U_4455] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4457)),U_4459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4455),U_4457))),U_4459)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4455),c_Int_OPls)) )
    & ! [U_4458,U_4456,U_4454] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4456)),U_4458)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4454),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1287_2]) ).

fof(f_1287_4,plain,
    ( ! [U_4455,U_4457,U_4459] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4457)),U_4459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4455),U_4457))),U_4459)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4455),c_Int_OPls)) )
    & ! [U_4456,U_4454,U_4458] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4456)),U_4458)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4454),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1287_3]) ).

cnf(f_1287_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4456)),U_4458)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4454),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1287_4]) ).

cnf(f_1287_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4457)),U_4459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4455),U_4457))),U_4459)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4455),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1287_4]) ).

fof(f_1288_1,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).

fof(f_1288_2,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1288_1]) ).

cnf(f_1288_3,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1288_2]) ).

fof(f_1289_1,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).

fof(f_1289_2,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1289_1]) ).

cnf(f_1289_3,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1289_2]) ).

fof(f_1290_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_1290_2,plain,
    ! [U_4460] : c_Int_Osucc(c_Int_Opred(U_4460)) = U_4460,
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ! [U_4460] : c_Int_Osucc(c_Int_Opred(U_4460)) = U_4460,
    inference(definitional_conversion,[status(esa)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    c_Int_Osucc(c_Int_Opred(U_4460)) = U_4460,
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_1,plain,
    ! [T_a] :
      ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0]) ).

fof(f_1291_2,plain,
    ! [U_4461] :
      ( c_Int_Oiszero(U_4461,hAPP(c_Int_Onumber__class_Onumber__of(U_4461),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4461) ),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

fof(f_1291_3,plain,
    ! [U_4461] :
      ( c_Int_Oiszero(U_4461,hAPP(c_Int_Onumber__class_Onumber__of(U_4461),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4461) ),
    inference(definitional_conversion,[status(esa)],[f_1291_2]) ).

cnf(f_1291_4,plain,
    ( c_Int_Oiszero(U_4461,hAPP(c_Int_Onumber__class_Onumber__of(U_4461),c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_4461) ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

fof(f_1292_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

fof(f_1292_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1292_1]) ).

cnf(f_1292_3,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1292_2]) ).

fof(f_1293_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I19_J]) ).

fof(f_1293_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1293_1]) ).

cnf(f_1293_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1293_2]) ).

fof(f_1294_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I2_J]) ).

fof(f_1294_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1294_1]) ).

cnf(f_1294_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1294_2]) ).

fof(f_1295_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    inference(fof_nnf,[status(thm)],[fact_add__Pls__right]) ).

fof(f_1295_2,plain,
    ! [U_4462] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4462),c_Int_OPls) = U_4462,
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

fof(f_1295_3,plain,
    ! [U_4462] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4462),c_Int_OPls) = U_4462,
    inference(definitional_conversion,[status(esa)],[f_1295_2]) ).

cnf(f_1295_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4462),c_Int_OPls) = U_4462,
    inference(clausify,[status(thm)],[f_1295_3]) ).

fof(f_1296_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
    inference(fof_nnf,[status(thm)],[fact_add__Pls]) ).

fof(f_1296_2,plain,
    ! [U_4463] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4463) = U_4463,
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

fof(f_1296_3,plain,
    ! [U_4463] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4463) = U_4463,
    inference(definitional_conversion,[status(esa)],[f_1296_2]) ).

cnf(f_1296_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4463) = U_4463,
    inference(clausify,[status(thm)],[f_1296_3]) ).

fof(f_1297_1,plain,
    ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_mult__Pls]) ).

fof(f_1297_2,plain,
    ! [U_4464] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4464) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ! [U_4464] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4464) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1297_2]) ).

cnf(f_1297_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4464) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1297_3]) ).

fof(f_1298_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(f_1298_2,plain,
    ! [U_4465] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4465),c_Int_OPls) = U_4465,
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

fof(f_1298_3,plain,
    ! [U_4465] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4465),c_Int_OPls) = U_4465,
    inference(definitional_conversion,[status(esa)],[f_1298_2]) ).

cnf(f_1298_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4465),c_Int_OPls) = U_4465,
    inference(clausify,[status(thm)],[f_1298_3]) ).

fof(f_1299_1,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_minus__Pls]) ).

fof(f_1299_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1299_1]) ).

cnf(f_1299_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1299_2]) ).

fof(f_1300_1,plain,
    c_Int_OMin != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).

fof(f_1300_2,plain,
    c_Int_OMin != c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1300_1]) ).

cnf(f_1300_3,plain,
    c_Int_OMin != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1300_2]) ).

fof(f_1301_1,plain,
    c_Int_OPls != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).

fof(f_1301_2,plain,
    c_Int_OPls != c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1301_1]) ).

cnf(f_1301_3,plain,
    c_Int_OPls != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1301_2]) ).

fof(f_1302_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( c_Int_Oiszero(T_b,V_z_2)
          | V_z_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
          | ~ c_Int_Oiszero(T_b,V_z_2) ) )
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).

fof(f_1302_2,plain,
    ! [U_4467,U_4466] :
      ( ( ( c_Int_Oiszero(U_4466,U_4467)
          | U_4467 != c_Groups_Ozero__class_Ozero(U_4466) )
        & ( U_4467 = c_Groups_Ozero__class_Ozero(U_4466)
          | ~ c_Int_Oiszero(U_4466,U_4467) ) )
      | ~ class_Rings_Osemiring__1(U_4466) ),
    inference(variable_rename,[status(thm)],[f_1302_1]) ).

fof(f_1302_3,plain,
    ( ! [U_4466,U_4467] :
        ( c_Int_Oiszero(U_4466,U_4467)
        | U_4467 != c_Groups_Ozero__class_Ozero(U_4466)
        | ~ sP371(U_4466,U_4467) )
    & ! [U_4466,U_4467] :
        ( U_4467 = c_Groups_Ozero__class_Ozero(U_4466)
        | ~ c_Int_Oiszero(U_4466,U_4467)
        | ~ sP371(U_4466,U_4467) )
    & ! [U_4466,U_4467] :
        ( sP371(U_4466,U_4467)
        | ~ class_Rings_Osemiring__1(U_4466) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP371])],[f_1302_2]) ).

cnf(f_1302_4,plain,
    ( sP371(U_4466,U_4467)
    | ~ class_Rings_Osemiring__1(U_4466) ),
    inference(clausify,[status(thm)],[f_1302_3]) ).

cnf(f_1302_5,plain,
    ( U_4467 = c_Groups_Ozero__class_Ozero(U_4466)
    | ~ c_Int_Oiszero(U_4466,U_4467)
    | ~ sP371(U_4466,U_4467) ),
    inference(clausify,[status(thm)],[f_1302_3]) ).

cnf(f_1302_6,plain,
    ( c_Int_Oiszero(U_4466,U_4467)
    | U_4467 != c_Groups_Ozero__class_Ozero(U_4466)
    | ~ sP371(U_4466,U_4467) ),
    inference(clausify,[status(thm)],[f_1302_3]) ).

fof(f_1303_1,plain,
    ! [T_a] :
      ( c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__0]) ).

fof(f_1303_2,plain,
    ! [U_4468] :
      ( c_Int_Oiszero(U_4468,c_Groups_Ozero__class_Ozero(U_4468))
      | ~ class_Rings_Osemiring__1(U_4468) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ! [U_4468] :
      ( c_Int_Oiszero(U_4468,c_Groups_Ozero__class_Ozero(U_4468))
      | ~ class_Rings_Osemiring__1(U_4468) ),
    inference(definitional_conversion,[status(esa)],[f_1303_2]) ).

cnf(f_1303_4,plain,
    ( c_Int_Oiszero(U_4468,c_Groups_Ozero__class_Ozero(U_4468))
    | ~ class_Rings_Osemiring__1(U_4468) ),
    inference(clausify,[status(thm)],[f_1303_3]) ).

fof(f_1304_1,plain,
    ! [T_a] :
      ( ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__iszero__1]) ).

fof(f_1304_2,plain,
    ! [U_4469] :
      ( ~ c_Int_Oiszero(U_4469,c_Groups_Oone__class_Oone(U_4469))
      | ~ class_Rings_Osemiring__1(U_4469) ),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

fof(f_1304_3,plain,
    ! [U_4469] :
      ( ~ c_Int_Oiszero(U_4469,c_Groups_Oone__class_Oone(U_4469))
      | ~ class_Rings_Osemiring__1(U_4469) ),
    inference(definitional_conversion,[status(esa)],[f_1304_2]) ).

cnf(f_1304_4,plain,
    ( ~ c_Int_Oiszero(U_4469,c_Groups_Oone__class_Oone(U_4469))
    | ~ class_Rings_Osemiring__1(U_4469) ),
    inference(clausify,[status(thm)],[f_1304_3]) ).

fof(f_1305_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Pls]) ).

fof(f_1305_2,plain,
    ! [U_4470] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4470),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4470)
      | ~ class_Int_Onumber__ring(U_4470) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

fof(f_1305_3,plain,
    ! [U_4470] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4470),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4470)
      | ~ class_Int_Onumber__ring(U_4470) ),
    inference(definitional_conversion,[status(esa)],[f_1305_2]) ).

cnf(f_1305_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4470),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4470)
    | ~ class_Int_Onumber__ring(U_4470) ),
    inference(clausify,[status(thm)],[f_1305_3]) ).

fof(f_1306_1,plain,
    ! [T_a] :
      ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J]) ).

fof(f_1306_2,plain,
    ! [U_4471] :
      ( c_Groups_Ozero__class_Ozero(U_4471) = hAPP(c_Int_Onumber__class_Onumber__of(U_4471),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_4471) ),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

fof(f_1306_3,plain,
    ! [U_4471] :
      ( c_Groups_Ozero__class_Ozero(U_4471) = hAPP(c_Int_Onumber__class_Onumber__of(U_4471),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_4471) ),
    inference(definitional_conversion,[status(esa)],[f_1306_2]) ).

cnf(f_1306_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_4471) = hAPP(c_Int_Onumber__class_Onumber__of(U_4471),c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_4471) ),
    inference(clausify,[status(thm)],[f_1306_3]) ).

fof(f_1307_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right]) ).

fof(f_1307_2,plain,
    ! [U_4473,U_4472] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4472),U_4473),hAPP(c_Int_Onumber__class_Onumber__of(U_4472),c_Int_OPls)) = U_4473
      | ~ class_Int_Onumber__ring(U_4472) ),
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

fof(f_1307_3,plain,
    ! [U_4472,U_4473] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4472),U_4473),hAPP(c_Int_Onumber__class_Onumber__of(U_4472),c_Int_OPls)) = U_4473
      | ~ class_Int_Onumber__ring(U_4472) ),
    inference(definitional_conversion,[status(esa)],[f_1307_2]) ).

cnf(f_1307_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4472),U_4473),hAPP(c_Int_Onumber__class_Onumber__of(U_4472),c_Int_OPls)) = U_4473
    | ~ class_Int_Onumber__ring(U_4472) ),
    inference(clausify,[status(thm)],[f_1307_3]) ).

fof(f_1308_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__numeral__0]) ).

fof(f_1308_2,plain,
    ! [U_4475,U_4474] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),c_Int_OPls)),U_4475) = U_4475
      | ~ class_Int_Onumber__ring(U_4474) ),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

fof(f_1308_3,plain,
    ! [U_4474,U_4475] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),c_Int_OPls)),U_4475) = U_4475
      | ~ class_Int_Onumber__ring(U_4474) ),
    inference(definitional_conversion,[status(esa)],[f_1308_2]) ).

cnf(f_1308_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),c_Int_OPls)),U_4475) = U_4475
    | ~ class_Int_Onumber__ring(U_4474) ),
    inference(clausify,[status(thm)],[f_1308_3]) ).

fof(f_1309_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).

fof(f_1309_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1309_1]) ).

cnf(f_1309_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1309_2]) ).

fof(f_1310_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Pls]) ).

fof(f_1310_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1310_1]) ).

cnf(f_1310_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1310_2]) ).

fof(f_1311_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I113_J]) ).

fof(f_1311_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1311_1]) ).

cnf(f_1311_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    inference(clausify,[status(thm)],[f_1311_2]) ).

fof(f_1312_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_zero__is__num__zero]) ).

fof(f_1312_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1312_1]) ).

cnf(f_1312_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    inference(clausify,[status(thm)],[f_1312_2]) ).

fof(f_1313_1,plain,
    ! [V_m,V_v] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of]) ).

fof(f_1313_2,plain,
    ! [U_4477,U_4476] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4477)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4477),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4476)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4476)) ),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

fof(f_1313_3,plain,
    ! [U_4476,U_4477] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4477)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4477),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4476)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4476)) ),
    inference(definitional_conversion,[status(esa)],[f_1313_2]) ).

cnf(f_1313_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4477)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4477),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4476)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4476)) ),
    inference(clausify,[status(thm)],[f_1313_3]) ).

fof(f_1314_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I23_J]) ).

fof(f_1314_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1314_1]) ).

cnf(f_1314_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1314_2]) ).

fof(f_1315_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I20_J]) ).

fof(f_1315_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(definitional_conversion,[status(esa)],[f_1315_1]) ).

cnf(f_1315_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1315_2]) ).

fof(f_1316_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I3_J]) ).

fof(f_1316_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(definitional_conversion,[status(esa)],[f_1316_1]) ).

cnf(f_1316_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1316_2]) ).

fof(f_1317_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I6_J]) ).

fof(f_1317_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1317_1]) ).

cnf(f_1317_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1317_2]) ).

fof(f_1318_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__Pls__Min]) ).

fof(f_1318_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    inference(definitional_conversion,[status(esa)],[f_1318_1]) ).

cnf(f_1318_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    inference(clausify,[status(thm)],[f_1318_2]) ).

fof(f_1319_1,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__number__of__Pls]) ).

fof(f_1319_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(definitional_conversion,[status(esa)],[f_1319_1]) ).

cnf(f_1319_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(clausify,[status(thm)],[f_1319_2]) ).

fof(f_1320_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).

fof(f_1320_2,plain,
    ! [U_4479,U_4478] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4478),U_4479) = c_Groups_Ozero__class_Ozero(U_4478)
          | ~ c_Int_Oiszero(U_4478,hAPP(c_Int_Onumber__class_Onumber__of(U_4478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(U_4478,hAPP(c_Int_Onumber__class_Onumber__of(U_4478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4478),U_4479) != c_Groups_Ozero__class_Ozero(U_4478) ) )
      | ~ class_Int_Onumber__ring(U_4478) ),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

fof(f_1320_3,plain,
    ( ! [U_4479,U_4478] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4478),U_4479) = c_Groups_Ozero__class_Ozero(U_4478)
        | ~ c_Int_Oiszero(U_4478,hAPP(c_Int_Onumber__class_Onumber__of(U_4478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ sP372(U_4479,U_4478) )
    & ! [U_4479,U_4478] :
        ( c_Int_Oiszero(U_4478,hAPP(c_Int_Onumber__class_Onumber__of(U_4478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4478),U_4479) != c_Groups_Ozero__class_Ozero(U_4478)
        | ~ sP372(U_4479,U_4478) )
    & ! [U_4479,U_4478] :
        ( sP372(U_4479,U_4478)
        | ~ class_Int_Onumber__ring(U_4478) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP372])],[f_1320_2]) ).

cnf(f_1320_4,plain,
    ( sP372(U_4479,U_4478)
    | ~ class_Int_Onumber__ring(U_4478) ),
    inference(clausify,[status(thm)],[f_1320_3]) ).

cnf(f_1320_5,plain,
    ( c_Int_Oiszero(U_4478,hAPP(c_Int_Onumber__class_Onumber__of(U_4478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4478),U_4479) != c_Groups_Ozero__class_Ozero(U_4478)
    | ~ sP372(U_4479,U_4478) ),
    inference(clausify,[status(thm)],[f_1320_3]) ).

cnf(f_1320_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4478),U_4479) = c_Groups_Ozero__class_Ozero(U_4478)
    | ~ c_Int_Oiszero(U_4478,hAPP(c_Int_Onumber__class_Onumber__of(U_4478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ sP372(U_4479,U_4478) ),
    inference(clausify,[status(thm)],[f_1320_3]) ).

fof(f_1321_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).

fof(f_1321_2,plain,
    ! [U_4481,U_4480] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_4480) = hAPP(c_Int_Onumber__class_Onumber__of(U_4480),U_4481)
          | ~ c_Int_Oiszero(U_4480,hAPP(c_Int_Onumber__class_Onumber__of(U_4480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4481)))) )
        & ( c_Int_Oiszero(U_4480,hAPP(c_Int_Onumber__class_Onumber__of(U_4480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4481))))
          | c_Groups_Ozero__class_Ozero(U_4480) != hAPP(c_Int_Onumber__class_Onumber__of(U_4480),U_4481) ) )
      | ~ class_Int_Onumber__ring(U_4480) ),
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

fof(f_1321_3,plain,
    ( ! [U_4481,U_4480] :
        ( c_Groups_Ozero__class_Ozero(U_4480) = hAPP(c_Int_Onumber__class_Onumber__of(U_4480),U_4481)
        | ~ c_Int_Oiszero(U_4480,hAPP(c_Int_Onumber__class_Onumber__of(U_4480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4481))))
        | ~ sP373(U_4481,U_4480) )
    & ! [U_4481,U_4480] :
        ( c_Int_Oiszero(U_4480,hAPP(c_Int_Onumber__class_Onumber__of(U_4480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4481))))
        | c_Groups_Ozero__class_Ozero(U_4480) != hAPP(c_Int_Onumber__class_Onumber__of(U_4480),U_4481)
        | ~ sP373(U_4481,U_4480) )
    & ! [U_4481,U_4480] :
        ( sP373(U_4481,U_4480)
        | ~ class_Int_Onumber__ring(U_4480) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP373])],[f_1321_2]) ).

cnf(f_1321_4,plain,
    ( sP373(U_4481,U_4480)
    | ~ class_Int_Onumber__ring(U_4480) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

cnf(f_1321_5,plain,
    ( c_Int_Oiszero(U_4480,hAPP(c_Int_Onumber__class_Onumber__of(U_4480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4481))))
    | c_Groups_Ozero__class_Ozero(U_4480) != hAPP(c_Int_Onumber__class_Onumber__of(U_4480),U_4481)
    | ~ sP373(U_4481,U_4480) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

cnf(f_1321_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_4480) = hAPP(c_Int_Onumber__class_Onumber__of(U_4480),U_4481)
    | ~ c_Int_Oiszero(U_4480,hAPP(c_Int_Onumber__class_Onumber__of(U_4480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4481))))
    | ~ sP373(U_4481,U_4480) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

fof(f_1322_1,plain,
    ! [V_v] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(f_1322_2,plain,
    ! [U_4482] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4482)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4482))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4482),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4482)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4482),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

fof(f_1322_3,plain,
    ( ! [U_4484] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4484))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4484),c_Int_OPls)) )
    & ! [U_4483] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4483)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4483),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1322_2]) ).

fof(f_1322_4,plain,
    ( ! [U_4484] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4484))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4484),c_Int_OPls)) )
    & ! [U_4483] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4483)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4483),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1322_3]) ).

cnf(f_1322_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4483)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4483),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1322_4]) ).

cnf(f_1322_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4484))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4484),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1322_4]) ).

fof(f_1323_1,plain,
    ! [V_v] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(f_1323_2,plain,
    ! [U_4485] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4485)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4485))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4485),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4485)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4485),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1323_1]) ).

fof(f_1323_3,plain,
    ( ! [U_4487] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4487)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4487))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4487),c_Int_OPls)) )
    & ! [U_4486] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4486)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4486),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1323_2]) ).

fof(f_1323_4,plain,
    ( ! [U_4487] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4487)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4487))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4487),c_Int_OPls)) )
    & ! [U_4486] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4486)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4486),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1323_3]) ).

cnf(f_1323_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4486)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4486),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1323_4]) ).

cnf(f_1323_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4487)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4487))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4487),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1323_4]) ).

fof(f_1324_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less]) ).

fof(f_1324_2,plain,
    ! [U_4489,U_4488] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4488),U_4489))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4488)),U_4489)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4488)),U_4489))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4488),U_4489)) ) ),
    inference(variable_rename,[status(thm)],[f_1324_1]) ).

fof(f_1324_3,plain,
    ( ! [U_4493,U_4491] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4491),U_4493))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4491)),U_4493)) )
    & ! [U_4492,U_4490] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4490)),U_4492))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4490),U_4492)) ) ),
    inference(miniscope,[status(thm)],[f_1324_2]) ).

fof(f_1324_4,plain,
    ( ! [U_4491,U_4493] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4491),U_4493))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4491)),U_4493)) )
    & ! [U_4492,U_4490] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4490)),U_4492))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4490),U_4492)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1324_3]) ).

cnf(f_1324_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4490)),U_4492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4490),U_4492)) ),
    inference(clausify,[status(thm)],[f_1324_4]) ).

cnf(f_1324_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4491),U_4493))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4491)),U_4493)) ),
    inference(clausify,[status(thm)],[f_1324_4]) ).

fof(f_1325_1,plain,
    ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_pred__def]) ).

fof(f_1325_2,plain,
    ! [U_4494] : c_Int_Opred(U_4494) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4494),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1325_1]) ).

fof(f_1325_3,plain,
    ! [U_4494] : c_Int_Opred(U_4494) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4494),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1325_2]) ).

cnf(f_1325_4,plain,
    c_Int_Opred(U_4494) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4494),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1325_3]) ).

fof(f_1326_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
    inference(fof_nnf,[status(thm)],[fact_add__Min]) ).

fof(f_1326_2,plain,
    ! [U_4495] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_4495) = c_Int_Opred(U_4495),
    inference(variable_rename,[status(thm)],[f_1326_1]) ).

fof(f_1326_3,plain,
    ! [U_4495] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_4495) = c_Int_Opred(U_4495),
    inference(definitional_conversion,[status(esa)],[f_1326_2]) ).

cnf(f_1326_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_4495) = c_Int_Opred(U_4495),
    inference(clausify,[status(thm)],[f_1326_3]) ).

fof(f_1327_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
    inference(fof_nnf,[status(thm)],[fact_add__Min__right]) ).

fof(f_1327_2,plain,
    ! [U_4496] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4496),c_Int_OMin) = c_Int_Opred(U_4496),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

fof(f_1327_3,plain,
    ! [U_4496] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4496),c_Int_OMin) = c_Int_Opred(U_4496),
    inference(definitional_conversion,[status(esa)],[f_1327_2]) ).

cnf(f_1327_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4496),c_Int_OMin) = c_Int_Opred(U_4496),
    inference(clausify,[status(thm)],[f_1327_3]) ).

fof(f_1328_1,plain,
    ! [V_v] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(f_1328_2,plain,
    ! [U_4497] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4497)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4497))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4497),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4497)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4497),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

fof(f_1328_3,plain,
    ( ! [U_4499] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4499)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4499))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4499),c_Int_OPls)) )
    & ! [U_4498] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4498)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4498),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1328_2]) ).

fof(f_1328_4,plain,
    ( ! [U_4499] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4499)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4499))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4499),c_Int_OPls)) )
    & ! [U_4498] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4498)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4498),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1328_3]) ).

cnf(f_1328_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4498)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4498),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1328_4]) ).

cnf(f_1328_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4499)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4499))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4499),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1328_4]) ).

fof(f_1329_1,plain,
    ! [V_v_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__0]) ).

fof(f_1329_2,plain,
    ! [U_4500] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4500) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4500),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4500),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4500) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

fof(f_1329_3,plain,
    ( ! [U_4502] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4502) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4502),c_Int_OPls)) )
    & ! [U_4501] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4501),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1329_2]) ).

fof(f_1329_4,plain,
    ( ! [U_4502] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4502) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4502),c_Int_OPls)) )
    & ! [U_4501] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4501),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1329_3]) ).

cnf(f_1329_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4501),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1329_4]) ).

cnf(f_1329_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4502) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4502),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1329_4]) ).

fof(f_1330_1,plain,
    ! [V_v_2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__0__number__of]) ).

fof(f_1330_2,plain,
    ! [U_4503] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4503)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4503),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4503),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4503) ) ),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

fof(f_1330_3,plain,
    ( ! [U_4505] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4505)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4505),c_Int_OPls)) )
    & ! [U_4504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4504),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4504) ) ),
    inference(miniscope,[status(thm)],[f_1330_2]) ).

fof(f_1330_4,plain,
    ( ! [U_4505] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4505)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4505),c_Int_OPls)) )
    & ! [U_4504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4504),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4504) ) ),
    inference(definitional_conversion,[status(esa)],[f_1330_3]) ).

cnf(f_1330_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4504),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4504) ),
    inference(clausify,[status(thm)],[f_1330_4]) ).

cnf(f_1330_6,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4505)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4505),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1330_4]) ).

fof(f_1331_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_number__of2]) ).

fof(f_1331_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(definitional_conversion,[status(esa)],[f_1331_1]) ).

cnf(f_1331_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(clausify,[status(thm)],[f_1331_2]) ).

fof(f_1332_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__nat__number__of]) ).

fof(f_1332_2,plain,
    ! [U_4507,U_4506] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4506)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4507)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4506),U_4507))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4507))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4506),U_4507)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4506),U_4507))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4507))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4506),U_4507)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4506)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4507))) ) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

fof(f_1332_3,plain,
    ( ! [U_4511,U_4509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4511)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4509),U_4511))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4511))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4509),U_4511)) ) )
    & ! [U_4510,U_4508] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4508),U_4510))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4510))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4508),U_4510)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4508)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4510))) ) ),
    inference(miniscope,[status(thm)],[f_1332_2]) ).

fof(f_1332_4,plain,
    ( ! [U_4511,U_4509] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4511))
        | ~ sP375(U_4511,U_4509) )
    & ! [U_4511,U_4509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4509),U_4511))
        | ~ sP375(U_4511,U_4509) )
    & ! [U_4510,U_4508] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4508),U_4510))
        | ~ sP374(U_4510,U_4508) )
    & ! [U_4510,U_4508] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4510))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4508),U_4510))
        | ~ sP374(U_4510,U_4508) )
    & ! [U_4511,U_4509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4511)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4509),U_4511))
        | sP375(U_4511,U_4509) )
    & ! [U_4510,U_4508] :
        ( sP374(U_4510,U_4508)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4508)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4510))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP374,sP375])],[f_1332_3]) ).

cnf(f_1332_5,plain,
    ( sP374(U_4510,U_4508)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4508)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4510))) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

cnf(f_1332_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4511)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4509),U_4511))
    | sP375(U_4511,U_4509) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

cnf(f_1332_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4508),U_4510))
    | ~ sP374(U_4510,U_4508) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

cnf(f_1332_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4508),U_4510))
    | ~ sP374(U_4510,U_4508) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

cnf(f_1332_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4509),U_4511))
    | ~ sP375(U_4511,U_4509) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

cnf(f_1332_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4511))
    | ~ sP375(U_4511,U_4509) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

fof(f_1333_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__nat__number__of]) ).

fof(f_1333_2,plain,
    ! [U_4513,U_4512] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4512)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4513)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4512),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4512),U_4513)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4512),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4512),U_4513))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4512)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4513))) ) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

fof(f_1333_3,plain,
    ( ! [U_4517,U_4515] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4515)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4517)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4515),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4515),U_4517)) ) )
    & ! [U_4516,U_4514] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4514),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4514),U_4516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4514)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4516))) ) ),
    inference(miniscope,[status(thm)],[f_1333_2]) ).

fof(f_1333_4,plain,
    ( ! [U_4515,U_4517] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4515),c_Int_OPls))
        | ~ sP376(U_4515,U_4517) )
    & ! [U_4515,U_4517] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4515),U_4517))
        | ~ sP376(U_4515,U_4517) )
    & ! [U_4515,U_4517] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4515)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4517)))
        | sP376(U_4515,U_4517) )
    & ! [U_4516,U_4514] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4514),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4514),U_4516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4514)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4516))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP376])],[f_1333_3]) ).

cnf(f_1333_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4514),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4514),U_4516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4514)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4516))) ),
    inference(clausify,[status(thm)],[f_1333_4]) ).

cnf(f_1333_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4515)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4517)))
    | sP376(U_4515,U_4517) ),
    inference(clausify,[status(thm)],[f_1333_4]) ).

cnf(f_1333_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4515),U_4517))
    | ~ sP376(U_4515,U_4517) ),
    inference(clausify,[status(thm)],[f_1333_4]) ).

cnf(f_1333_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4515),c_Int_OPls))
    | ~ sP376(U_4515,U_4517) ),
    inference(clausify,[status(thm)],[f_1333_4]) ).

fof(f_1334_1,plain,
    ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_succ__def]) ).

fof(f_1334_2,plain,
    ! [U_4518] : c_Int_Osucc(U_4518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4518),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1334_1]) ).

fof(f_1334_3,plain,
    ! [U_4518] : c_Int_Osucc(U_4518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4518),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1334_2]) ).

cnf(f_1334_4,plain,
    c_Int_Osucc(U_4518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4518),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1334_3]) ).

fof(f_1335_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I2_J]) ).

fof(f_1335_2,plain,
    ! [U_4519] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4519),c_Int_OMin) = c_Int_Osucc(U_4519),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

fof(f_1335_3,plain,
    ! [U_4519] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4519),c_Int_OMin) = c_Int_Osucc(U_4519),
    inference(definitional_conversion,[status(esa)],[f_1335_2]) ).

cnf(f_1335_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4519),c_Int_OMin) = c_Int_Osucc(U_4519),
    inference(clausify,[status(thm)],[f_1335_3]) ).

fof(f_1336_1,plain,
    ! [T_a] :
      ( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__number__of__Min]) ).

fof(f_1336_2,plain,
    ! [U_4520] :
      ( ~ c_Int_Oiszero(U_4520,hAPP(c_Int_Onumber__class_Onumber__of(U_4520),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_4520) ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

fof(f_1336_3,plain,
    ! [U_4520] :
      ( ~ c_Int_Oiszero(U_4520,hAPP(c_Int_Onumber__class_Onumber__of(U_4520),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_4520) ),
    inference(definitional_conversion,[status(esa)],[f_1336_2]) ).

cnf(f_1336_4,plain,
    ( ~ c_Int_Oiszero(U_4520,hAPP(c_Int_Onumber__class_Onumber__of(U_4520),c_Int_OMin))
    | ~ class_Int_Onumber__ring(U_4520) ),
    inference(clausify,[status(thm)],[f_1336_3]) ).

fof(f_1337_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).

fof(f_1337_2,plain,
    ! [U_4522,U_4521] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(c_Int_Onumber__class_Onumber__of(U_4521),U_4522)),c_Groups_Ozero__class_Ozero(U_4521)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4522),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4522),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(c_Int_Onumber__class_Onumber__of(U_4521),U_4522)),c_Groups_Ozero__class_Ozero(U_4521))) ) )
      | ~ class_Rings_Olinordered__idom(U_4521)
      | ~ class_Int_Onumber__ring(U_4521) ),
    inference(variable_rename,[status(thm)],[f_1337_1]) ).

fof(f_1337_3,plain,
    ( ! [U_4521,U_4522] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(c_Int_Onumber__class_Onumber__of(U_4521),U_4522)),c_Groups_Ozero__class_Ozero(U_4521)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4522),c_Int_OPls))
        | ~ sP377(U_4521,U_4522) )
    & ! [U_4521,U_4522] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4522),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(c_Int_Onumber__class_Onumber__of(U_4521),U_4522)),c_Groups_Ozero__class_Ozero(U_4521)))
        | ~ sP377(U_4521,U_4522) )
    & ! [U_4521,U_4522] :
        ( sP377(U_4521,U_4522)
        | ~ class_Rings_Olinordered__idom(U_4521)
        | ~ class_Int_Onumber__ring(U_4521) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP377])],[f_1337_2]) ).

cnf(f_1337_4,plain,
    ( sP377(U_4521,U_4522)
    | ~ class_Rings_Olinordered__idom(U_4521)
    | ~ class_Int_Onumber__ring(U_4521) ),
    inference(clausify,[status(thm)],[f_1337_3]) ).

cnf(f_1337_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4522),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(c_Int_Onumber__class_Onumber__of(U_4521),U_4522)),c_Groups_Ozero__class_Ozero(U_4521)))
    | ~ sP377(U_4521,U_4522) ),
    inference(clausify,[status(thm)],[f_1337_3]) ).

cnf(f_1337_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(c_Int_Onumber__class_Onumber__of(U_4521),U_4522)),c_Groups_Ozero__class_Ozero(U_4521)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4522),c_Int_OPls))
    | ~ sP377(U_4521,U_4522) ),
    inference(clausify,[status(thm)],[f_1337_3]) ).

fof(f_1338_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).

fof(f_1338_2,plain,
    ! [U_4524,U_4523] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4523),c_Groups_Ozero__class_Ozero(U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(U_4523),U_4524)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4524)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4524))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4523),c_Groups_Ozero__class_Ozero(U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(U_4523),U_4524))) ) )
      | ~ class_Rings_Olinordered__idom(U_4523)
      | ~ class_Int_Onumber__ring(U_4523) ),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

fof(f_1338_3,plain,
    ( ! [U_4524,U_4523] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4523),c_Groups_Ozero__class_Ozero(U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(U_4523),U_4524)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4524))
        | ~ sP378(U_4524,U_4523) )
    & ! [U_4524,U_4523] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4524))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4523),c_Groups_Ozero__class_Ozero(U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(U_4523),U_4524)))
        | ~ sP378(U_4524,U_4523) )
    & ! [U_4524,U_4523] :
        ( sP378(U_4524,U_4523)
        | ~ class_Rings_Olinordered__idom(U_4523)
        | ~ class_Int_Onumber__ring(U_4523) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP378])],[f_1338_2]) ).

cnf(f_1338_4,plain,
    ( sP378(U_4524,U_4523)
    | ~ class_Rings_Olinordered__idom(U_4523)
    | ~ class_Int_Onumber__ring(U_4523) ),
    inference(clausify,[status(thm)],[f_1338_3]) ).

cnf(f_1338_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4523),c_Groups_Ozero__class_Ozero(U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(U_4523),U_4524)))
    | ~ sP378(U_4524,U_4523) ),
    inference(clausify,[status(thm)],[f_1338_3]) ).

cnf(f_1338_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4523),c_Groups_Ozero__class_Ozero(U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(U_4523),U_4524)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4524))
    | ~ sP378(U_4524,U_4523) ),
    inference(clausify,[status(thm)],[f_1338_3]) ).

fof(f_1339_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).

fof(f_1339_2,plain,
    ! [U_4526,U_4525] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(U_4525),U_4526)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4526)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4526))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(U_4525),U_4526))) ) )
      | ~ class_Rings_Olinordered__idom(U_4525)
      | ~ class_Int_Onumber__ring(U_4525) ),
    inference(variable_rename,[status(thm)],[f_1339_1]) ).

fof(f_1339_3,plain,
    ( ! [U_4526,U_4525] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(U_4525),U_4526)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4526))
        | ~ sP379(U_4526,U_4525) )
    & ! [U_4526,U_4525] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4526))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(U_4525),U_4526)))
        | ~ sP379(U_4526,U_4525) )
    & ! [U_4526,U_4525] :
        ( sP379(U_4526,U_4525)
        | ~ class_Rings_Olinordered__idom(U_4525)
        | ~ class_Int_Onumber__ring(U_4525) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP379])],[f_1339_2]) ).

cnf(f_1339_4,plain,
    ( sP379(U_4526,U_4525)
    | ~ class_Rings_Olinordered__idom(U_4525)
    | ~ class_Int_Onumber__ring(U_4525) ),
    inference(clausify,[status(thm)],[f_1339_3]) ).

cnf(f_1339_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4526))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(U_4525),U_4526)))
    | ~ sP379(U_4526,U_4525) ),
    inference(clausify,[status(thm)],[f_1339_3]) ).

cnf(f_1339_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(U_4525),U_4526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4526))
    | ~ sP379(U_4526,U_4525) ),
    inference(clausify,[status(thm)],[f_1339_3]) ).

fof(f_1340_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).

fof(f_1340_2,plain,
    ! [U_4528,U_4527] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4527),hAPP(c_Int_Onumber__class_Onumber__of(U_4527),U_4528)),c_Groups_Ozero__class_Ozero(U_4527)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4527),hAPP(c_Int_Onumber__class_Onumber__of(U_4527),U_4528)),c_Groups_Ozero__class_Ozero(U_4527))) ) )
      | ~ class_Rings_Olinordered__idom(U_4527)
      | ~ class_Int_Onumber__ring(U_4527) ),
    inference(variable_rename,[status(thm)],[f_1340_1]) ).

fof(f_1340_3,plain,
    ( ! [U_4528,U_4527] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4527),hAPP(c_Int_Onumber__class_Onumber__of(U_4527),U_4528)),c_Groups_Ozero__class_Ozero(U_4527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),c_Int_OPls))
        | ~ sP380(U_4528,U_4527) )
    & ! [U_4528,U_4527] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4527),hAPP(c_Int_Onumber__class_Onumber__of(U_4527),U_4528)),c_Groups_Ozero__class_Ozero(U_4527)))
        | ~ sP380(U_4528,U_4527) )
    & ! [U_4528,U_4527] :
        ( sP380(U_4528,U_4527)
        | ~ class_Rings_Olinordered__idom(U_4527)
        | ~ class_Int_Onumber__ring(U_4527) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP380])],[f_1340_2]) ).

cnf(f_1340_4,plain,
    ( sP380(U_4528,U_4527)
    | ~ class_Rings_Olinordered__idom(U_4527)
    | ~ class_Int_Onumber__ring(U_4527) ),
    inference(clausify,[status(thm)],[f_1340_3]) ).

cnf(f_1340_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4527),hAPP(c_Int_Onumber__class_Onumber__of(U_4527),U_4528)),c_Groups_Ozero__class_Ozero(U_4527)))
    | ~ sP380(U_4528,U_4527) ),
    inference(clausify,[status(thm)],[f_1340_3]) ).

cnf(f_1340_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4527),hAPP(c_Int_Onumber__class_Onumber__of(U_4527),U_4528)),c_Groups_Ozero__class_Ozero(U_4527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),c_Int_OPls))
    | ~ sP380(U_4528,U_4527) ),
    inference(clausify,[status(thm)],[f_1340_3]) ).

fof(f_1341_1,plain,
    ! [V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__0__number__of]) ).

fof(f_1341_2,plain,
    ! [U_4529] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4529)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4529)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4529))) ) ),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

fof(f_1341_3,plain,
    ( ! [U_4531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4531)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4531)) )
    & ! [U_4530] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4530))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4530))) ) ),
    inference(miniscope,[status(thm)],[f_1341_2]) ).

fof(f_1341_4,plain,
    ( ! [U_4531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4531)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4531)) )
    & ! [U_4530] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4530))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4530))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1341_3]) ).

cnf(f_1341_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4530))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4530))) ),
    inference(clausify,[status(thm)],[f_1341_4]) ).

cnf(f_1341_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4531)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4531)) ),
    inference(clausify,[status(thm)],[f_1341_4]) ).

fof(f_1342_1,plain,
    ! [V_v_H,V_v] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__nat__number__of]) ).

fof(f_1342_2,plain,
    ! [U_4533,U_4532] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4532)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4533)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4532),U_4533))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4533),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4532)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4533)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4532)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4533),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4532),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4532)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4533)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4533)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4532),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1342_1]) ).

fof(f_1342_3,plain,
    ( ! [U_4537,U_4535] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4537)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4535),U_4537))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4537),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4537)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4537),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4535),c_Int_OPls)) )
    & ! [U_4536,U_4534] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4536)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4536)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4534),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1342_2]) ).

fof(f_1342_4,plain,
    ( ! [U_4537,U_4535] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4537)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4535),U_4537))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4537),c_Int_OPls))
        | ~ sP381(U_4537,U_4535) )
    & ! [U_4537,U_4535] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4537)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4537),c_Int_OPls))
        | ~ sP381(U_4537,U_4535) )
    & ! [U_4537,U_4535] :
        ( sP381(U_4537,U_4535)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4535),c_Int_OPls)) )
    & ! [U_4536,U_4534] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4536)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4536)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4534),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP381])],[f_1342_3]) ).

cnf(f_1342_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4536)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4536)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4534),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1342_4]) ).

cnf(f_1342_6,plain,
    ( sP381(U_4537,U_4535)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4535),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1342_4]) ).

cnf(f_1342_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4537)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4537),c_Int_OPls))
    | ~ sP381(U_4537,U_4535) ),
    inference(clausify,[status(thm)],[f_1342_4]) ).

cnf(f_1342_8,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4537)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4535),U_4537))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4537),c_Int_OPls))
    | ~ sP381(U_4537,U_4535) ),
    inference(clausify,[status(thm)],[f_1342_4]) ).

fof(f_1343_1,plain,
    ! [V_k,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__succ]) ).

fof(f_1343_2,plain,
    ! [U_4539,U_4538] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4538),c_Int_Osucc(U_4539)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4538),c_Groups_Oone__class_Oone(U_4538)),hAPP(c_Int_Onumber__class_Onumber__of(U_4538),U_4539))
      | ~ class_Int_Onumber__ring(U_4538) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

fof(f_1343_3,plain,
    ! [U_4538,U_4539] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4538),c_Int_Osucc(U_4539)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4538),c_Groups_Oone__class_Oone(U_4538)),hAPP(c_Int_Onumber__class_Onumber__of(U_4538),U_4539))
      | ~ class_Int_Onumber__ring(U_4538) ),
    inference(definitional_conversion,[status(esa)],[f_1343_2]) ).

cnf(f_1343_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4538),c_Int_Osucc(U_4539)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4538),c_Groups_Oone__class_Oone(U_4538)),hAPP(c_Int_Onumber__class_Onumber__of(U_4538),U_4539))
    | ~ class_Int_Onumber__ring(U_4538) ),
    inference(clausify,[status(thm)],[f_1343_3]) ).

fof(f_1344_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__pred]) ).

fof(f_1344_2,plain,
    ! [U_4541,U_4540] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4540),c_Int_Opred(U_4541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4540),hAPP(c_Groups_Ouminus__class_Ouminus(U_4540),c_Groups_Oone__class_Oone(U_4540))),hAPP(c_Int_Onumber__class_Onumber__of(U_4540),U_4541))
      | ~ class_Int_Onumber__ring(U_4540) ),
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

fof(f_1344_3,plain,
    ! [U_4540,U_4541] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4540),c_Int_Opred(U_4541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4540),hAPP(c_Groups_Ouminus__class_Ouminus(U_4540),c_Groups_Oone__class_Oone(U_4540))),hAPP(c_Int_Onumber__class_Onumber__of(U_4540),U_4541))
      | ~ class_Int_Onumber__ring(U_4540) ),
    inference(definitional_conversion,[status(esa)],[f_1344_2]) ).

cnf(f_1344_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4540),c_Int_Opred(U_4541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4540),hAPP(c_Groups_Ouminus__class_Ouminus(U_4540),c_Groups_Oone__class_Oone(U_4540))),hAPP(c_Int_Onumber__class_Onumber__of(U_4540),U_4541))
    | ~ class_Int_Onumber__ring(U_4540) ),
    inference(clausify,[status(thm)],[f_1344_3]) ).

fof(f_1345_1,plain,
    ! [V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nat__number__of]) ).

fof(f_1345_2,plain,
    ! [U_4543,U_4542] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4543)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4542),U_4543))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4542),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4543)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4542),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

fof(f_1345_3,plain,
    ( ! [U_4547,U_4545] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4545),U_4547))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4545),c_Int_OPls)) )
    & ! [U_4546,U_4544] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4546)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4544),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1345_2]) ).

fof(f_1345_4,plain,
    ( ! [U_4545,U_4547] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4545),U_4547))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4545),c_Int_OPls)) )
    & ! [U_4546,U_4544] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4546)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4544),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1345_3]) ).

cnf(f_1345_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4546)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4544),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1345_4]) ).

cnf(f_1345_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4545),U_4547))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4545),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1345_4]) ).

fof(f_1346_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
          | c_Groups_Oone__class_Oone(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).

fof(f_1346_2,plain,
    ! [U_4549,U_4548] :
      ( ( ( c_Groups_Oone__class_Oone(U_4548) = hAPP(c_Int_Onumber__class_Onumber__of(U_4548),U_4549)
          | ~ c_Int_Oiszero(U_4548,hAPP(c_Int_Onumber__class_Onumber__of(U_4548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549)))) )
        & ( c_Int_Oiszero(U_4548,hAPP(c_Int_Onumber__class_Onumber__of(U_4548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549))))
          | c_Groups_Oone__class_Oone(U_4548) != hAPP(c_Int_Onumber__class_Onumber__of(U_4548),U_4549) ) )
      | ~ class_Int_Onumber__ring(U_4548) ),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

fof(f_1346_3,plain,
    ( ! [U_4548,U_4549] :
        ( c_Groups_Oone__class_Oone(U_4548) = hAPP(c_Int_Onumber__class_Onumber__of(U_4548),U_4549)
        | ~ c_Int_Oiszero(U_4548,hAPP(c_Int_Onumber__class_Onumber__of(U_4548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549))))
        | ~ sP382(U_4548,U_4549) )
    & ! [U_4548,U_4549] :
        ( c_Int_Oiszero(U_4548,hAPP(c_Int_Onumber__class_Onumber__of(U_4548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549))))
        | c_Groups_Oone__class_Oone(U_4548) != hAPP(c_Int_Onumber__class_Onumber__of(U_4548),U_4549)
        | ~ sP382(U_4548,U_4549) )
    & ! [U_4548,U_4549] :
        ( sP382(U_4548,U_4549)
        | ~ class_Int_Onumber__ring(U_4548) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP382])],[f_1346_2]) ).

cnf(f_1346_4,plain,
    ( sP382(U_4548,U_4549)
    | ~ class_Int_Onumber__ring(U_4548) ),
    inference(clausify,[status(thm)],[f_1346_3]) ).

cnf(f_1346_5,plain,
    ( c_Int_Oiszero(U_4548,hAPP(c_Int_Onumber__class_Onumber__of(U_4548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549))))
    | c_Groups_Oone__class_Oone(U_4548) != hAPP(c_Int_Onumber__class_Onumber__of(U_4548),U_4549)
    | ~ sP382(U_4548,U_4549) ),
    inference(clausify,[status(thm)],[f_1346_3]) ).

cnf(f_1346_6,plain,
    ( c_Groups_Oone__class_Oone(U_4548) = hAPP(c_Int_Onumber__class_Onumber__of(U_4548),U_4549)
    | ~ c_Int_Oiszero(U_4548,hAPP(c_Int_Onumber__class_Onumber__of(U_4548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549))))
    | ~ sP382(U_4548,U_4549) ),
    inference(clausify,[status(thm)],[f_1346_3]) ).

fof(f_1347_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).

fof(f_1347_2,plain,
    ! [U_4551,U_4550] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4550),U_4551) = c_Groups_Oone__class_Oone(U_4550)
          | ~ c_Int_Oiszero(U_4550,hAPP(c_Int_Onumber__class_Onumber__of(U_4550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4551),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(U_4550,hAPP(c_Int_Onumber__class_Onumber__of(U_4550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4551),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4550),U_4551) != c_Groups_Oone__class_Oone(U_4550) ) )
      | ~ class_Int_Onumber__ring(U_4550) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

fof(f_1347_3,plain,
    ( ! [U_4551,U_4550] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4550),U_4551) = c_Groups_Oone__class_Oone(U_4550)
        | ~ c_Int_Oiszero(U_4550,hAPP(c_Int_Onumber__class_Onumber__of(U_4550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4551),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ sP383(U_4551,U_4550) )
    & ! [U_4551,U_4550] :
        ( c_Int_Oiszero(U_4550,hAPP(c_Int_Onumber__class_Onumber__of(U_4550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4551),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4550),U_4551) != c_Groups_Oone__class_Oone(U_4550)
        | ~ sP383(U_4551,U_4550) )
    & ! [U_4551,U_4550] :
        ( sP383(U_4551,U_4550)
        | ~ class_Int_Onumber__ring(U_4550) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP383])],[f_1347_2]) ).

cnf(f_1347_4,plain,
    ( sP383(U_4551,U_4550)
    | ~ class_Int_Onumber__ring(U_4550) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

cnf(f_1347_5,plain,
    ( c_Int_Oiszero(U_4550,hAPP(c_Int_Onumber__class_Onumber__of(U_4550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4551),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4550),U_4551) != c_Groups_Oone__class_Oone(U_4550)
    | ~ sP383(U_4551,U_4550) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

cnf(f_1347_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4550),U_4551) = c_Groups_Oone__class_Oone(U_4550)
    | ~ c_Int_Oiszero(U_4550,hAPP(c_Int_Onumber__class_Onumber__of(U_4550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4551),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ sP383(U_4551,U_4550) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

fof(f_1348_1,plain,
    ! [V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J]) ).

fof(f_1348_2,plain,
    ! [U_4553,U_4552] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4552),c_Groups_Oone__class_Oone(U_4552)),hAPP(c_Int_Onumber__class_Onumber__of(U_4552),U_4553)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4553)))
      | ~ class_Int_Onumber__ring(U_4552) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

fof(f_1348_3,plain,
    ! [U_4553,U_4552] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4552),c_Groups_Oone__class_Oone(U_4552)),hAPP(c_Int_Onumber__class_Onumber__of(U_4552),U_4553)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4553)))
      | ~ class_Int_Onumber__ring(U_4552) ),
    inference(definitional_conversion,[status(esa)],[f_1348_2]) ).

cnf(f_1348_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4552),c_Groups_Oone__class_Oone(U_4552)),hAPP(c_Int_Onumber__class_Onumber__of(U_4552),U_4553)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4553)))
    | ~ class_Int_Onumber__ring(U_4552) ),
    inference(clausify,[status(thm)],[f_1348_3]) ).

fof(f_1349_1,plain,
    ! [V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J]) ).

fof(f_1349_2,plain,
    ! [U_4555,U_4554] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4554),hAPP(c_Int_Onumber__class_Onumber__of(U_4554),U_4555)),c_Groups_Oone__class_Oone(U_4554)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4554),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4555),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_4554) ),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

fof(f_1349_3,plain,
    ! [U_4554,U_4555] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4554),hAPP(c_Int_Onumber__class_Onumber__of(U_4554),U_4555)),c_Groups_Oone__class_Oone(U_4554)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4554),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4555),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_4554) ),
    inference(definitional_conversion,[status(esa)],[f_1349_2]) ).

cnf(f_1349_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4554),hAPP(c_Int_Onumber__class_Onumber__of(U_4554),U_4555)),c_Groups_Oone__class_Oone(U_4554)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4554),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4555),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_4554) ),
    inference(clausify,[status(thm)],[f_1349_3]) ).

fof(f_1350_1,plain,
    ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    inference(fof_nnf,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(f_1350_2,plain,
    ! [U_4557,U_4556] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4556)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4556)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4557)),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

fof(f_1350_3,plain,
    ! [U_4556,U_4557] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4556)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4556)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4557)),
    inference(definitional_conversion,[status(esa)],[f_1350_2]) ).

cnf(f_1350_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4556)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4556)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4557)),
    inference(clausify,[status(thm)],[f_1350_3]) ).

fof(f_1351_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(f_1351_2,plain,
    ! [U_4559,U_4558] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4558)))),U_4559) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4558)),U_4559),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

fof(f_1351_3,plain,
    ! [U_4558,U_4559] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4558)))),U_4559) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4558)),U_4559),
    inference(definitional_conversion,[status(esa)],[f_1351_2]) ).

cnf(f_1351_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4558)))),U_4559) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4558)),U_4559),
    inference(clausify,[status(thm)],[f_1351_3]) ).

fof(f_1352_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    inference(fof_nnf,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(f_1352_2,plain,
    ! [U_4561,U_4560] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4560),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4561)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4561)),
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

fof(f_1352_3,plain,
    ! [U_4560,U_4561] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4560),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4561)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4561)),
    inference(definitional_conversion,[status(esa)],[f_1352_2]) ).

cnf(f_1352_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4560),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4561)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4561)),
    inference(clausify,[status(thm)],[f_1352_3]) ).

fof(f_1353_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
        | V_k_2 != V_l_2 )
      & ( V_k_2 = V_l_2
        | c_Int_OBit1(V_k_2) != c_Int_OBit1(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J]) ).

fof(f_1353_2,plain,
    ! [U_4563,U_4562] :
      ( ( c_Int_OBit1(U_4562) = c_Int_OBit1(U_4563)
        | U_4562 != U_4563 )
      & ( U_4562 = U_4563
        | c_Int_OBit1(U_4562) != c_Int_OBit1(U_4563) ) ),
    inference(variable_rename,[status(thm)],[f_1353_1]) ).

fof(f_1353_3,plain,
    ( ! [U_4567,U_4565] :
        ( c_Int_OBit1(U_4565) = c_Int_OBit1(U_4567)
        | U_4565 != U_4567 )
    & ! [U_4566,U_4564] :
        ( U_4564 = U_4566
        | c_Int_OBit1(U_4564) != c_Int_OBit1(U_4566) ) ),
    inference(miniscope,[status(thm)],[f_1353_2]) ).

fof(f_1353_4,plain,
    ( ! [U_4565,U_4567] :
        ( c_Int_OBit1(U_4565) = c_Int_OBit1(U_4567)
        | U_4565 != U_4567 )
    & ! [U_4566,U_4564] :
        ( U_4564 = U_4566
        | c_Int_OBit1(U_4564) != c_Int_OBit1(U_4566) ) ),
    inference(definitional_conversion,[status(esa)],[f_1353_3]) ).

cnf(f_1353_5,plain,
    ( U_4564 = U_4566
    | c_Int_OBit1(U_4564) != c_Int_OBit1(U_4566) ),
    inference(clausify,[status(thm)],[f_1353_4]) ).

cnf(f_1353_6,plain,
    ( c_Int_OBit1(U_4565) = c_Int_OBit1(U_4567)
    | U_4565 != U_4567 ),
    inference(clausify,[status(thm)],[f_1353_4]) ).

fof(f_1354_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J]) ).

fof(f_1354_2,plain,
    ! [U_4569,U_4568] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4568)),c_Int_OBit1(U_4569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4568),U_4569)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4568),U_4569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4568)),c_Int_OBit1(U_4569))) ) ),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

fof(f_1354_3,plain,
    ( ! [U_4573,U_4571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4571)),c_Int_OBit1(U_4573)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4571),U_4573)) )
    & ! [U_4572,U_4570] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4570),U_4572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4570)),c_Int_OBit1(U_4572))) ) ),
    inference(miniscope,[status(thm)],[f_1354_2]) ).

fof(f_1354_4,plain,
    ( ! [U_4571,U_4573] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4571)),c_Int_OBit1(U_4573)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4571),U_4573)) )
    & ! [U_4572,U_4570] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4570),U_4572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4570)),c_Int_OBit1(U_4572))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1354_3]) ).

cnf(f_1354_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4570),U_4572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4570)),c_Int_OBit1(U_4572))) ),
    inference(clausify,[status(thm)],[f_1354_4]) ).

cnf(f_1354_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4571)),c_Int_OBit1(U_4573)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4571),U_4573)) ),
    inference(clausify,[status(thm)],[f_1354_4]) ).

fof(f_1355_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J]) ).

fof(f_1355_2,plain,
    ! [U_4575,U_4574] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4574)),c_Int_OBit1(U_4575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4574),U_4575)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4574),U_4575))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4574)),c_Int_OBit1(U_4575))) ) ),
    inference(variable_rename,[status(thm)],[f_1355_1]) ).

fof(f_1355_3,plain,
    ( ! [U_4579,U_4577] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4577)),c_Int_OBit1(U_4579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4577),U_4579)) )
    & ! [U_4578,U_4576] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4576),U_4578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4576)),c_Int_OBit1(U_4578))) ) ),
    inference(miniscope,[status(thm)],[f_1355_2]) ).

fof(f_1355_4,plain,
    ( ! [U_4577,U_4579] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4577)),c_Int_OBit1(U_4579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4577),U_4579)) )
    & ! [U_4578,U_4576] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4576),U_4578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4576)),c_Int_OBit1(U_4578))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1355_3]) ).

cnf(f_1355_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4576),U_4578))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4576)),c_Int_OBit1(U_4578))) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4577)),c_Int_OBit1(U_4579)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4577),U_4579)) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

fof(f_1356_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J]) ).

fof(f_1356_2,plain,
    ! [U_4581,U_4580] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4580)),c_Int_OBit1(U_4581)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4580),U_4581)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4580),U_4581))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4580)),c_Int_OBit1(U_4581))) ) ),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ( ! [U_4585,U_4583] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4583)),c_Int_OBit1(U_4585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4583),U_4585)) )
    & ! [U_4584,U_4582] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4582),U_4584))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4582)),c_Int_OBit1(U_4584))) ) ),
    inference(miniscope,[status(thm)],[f_1356_2]) ).

fof(f_1356_4,plain,
    ( ! [U_4583,U_4585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4583)),c_Int_OBit1(U_4585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4583),U_4585)) )
    & ! [U_4584,U_4582] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4582),U_4584))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4582)),c_Int_OBit1(U_4584))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1356_3]) ).

cnf(f_1356_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4582),U_4584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4582)),c_Int_OBit1(U_4584))) ),
    inference(clausify,[status(thm)],[f_1356_4]) ).

cnf(f_1356_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4583)),c_Int_OBit1(U_4585)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4583),U_4585)) ),
    inference(clausify,[status(thm)],[f_1356_4]) ).

fof(f_1357_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J]) ).

fof(f_1357_2,plain,
    ! [U_4587,U_4586] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4586)),c_Int_OBit1(U_4587)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4586),U_4587)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4586),U_4587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4586)),c_Int_OBit1(U_4587))) ) ),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

fof(f_1357_3,plain,
    ( ! [U_4591,U_4589] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4589)),c_Int_OBit1(U_4591)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4589),U_4591)) )
    & ! [U_4590,U_4588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4588),U_4590))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4588)),c_Int_OBit1(U_4590))) ) ),
    inference(miniscope,[status(thm)],[f_1357_2]) ).

fof(f_1357_4,plain,
    ( ! [U_4589,U_4591] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4589)),c_Int_OBit1(U_4591)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4589),U_4591)) )
    & ! [U_4590,U_4588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4588),U_4590))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4588)),c_Int_OBit1(U_4590))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1357_3]) ).

cnf(f_1357_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4588),U_4590))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4588)),c_Int_OBit1(U_4590))) ),
    inference(clausify,[status(thm)],[f_1357_4]) ).

cnf(f_1357_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4589)),c_Int_OBit1(U_4591)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4589),U_4591)) ),
    inference(clausify,[status(thm)],[f_1357_4]) ).

fof(f_1358_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(f_1358_2,plain,
    ! [U_4592] : c_Int_OBit1(U_4592) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

fof(f_1358_3,plain,
    ! [U_4592] : c_Int_OBit1(U_4592) != c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1358_2]) ).

cnf(f_1358_4,plain,
    c_Int_OBit1(U_4592) != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1358_3]) ).

fof(f_1359_1,plain,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(f_1359_2,plain,
    ! [U_4593] : c_Int_OPls != c_Int_OBit1(U_4593),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

fof(f_1359_3,plain,
    ! [U_4593] : c_Int_OPls != c_Int_OBit1(U_4593),
    inference(definitional_conversion,[status(esa)],[f_1359_2]) ).

cnf(f_1359_4,plain,
    c_Int_OPls != c_Int_OBit1(U_4593),
    inference(clausify,[status(thm)],[f_1359_3]) ).

fof(f_1360_1,plain,
    ! [V_k_2] :
      ( ( c_Int_OBit1(V_k_2) = c_Int_OMin
        | V_k_2 != c_Int_OMin )
      & ( V_k_2 = c_Int_OMin
        | c_Int_OBit1(V_k_2) != c_Int_OMin ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J]) ).

fof(f_1360_2,plain,
    ! [U_4594] :
      ( ( c_Int_OBit1(U_4594) = c_Int_OMin
        | U_4594 != c_Int_OMin )
      & ( U_4594 = c_Int_OMin
        | c_Int_OBit1(U_4594) != c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

fof(f_1360_3,plain,
    ( ! [U_4596] :
        ( c_Int_OBit1(U_4596) = c_Int_OMin
        | U_4596 != c_Int_OMin )
    & ! [U_4595] :
        ( U_4595 = c_Int_OMin
        | c_Int_OBit1(U_4595) != c_Int_OMin ) ),
    inference(miniscope,[status(thm)],[f_1360_2]) ).

fof(f_1360_4,plain,
    ( ! [U_4596] :
        ( c_Int_OBit1(U_4596) = c_Int_OMin
        | U_4596 != c_Int_OMin )
    & ! [U_4595] :
        ( U_4595 = c_Int_OMin
        | c_Int_OBit1(U_4595) != c_Int_OMin ) ),
    inference(definitional_conversion,[status(esa)],[f_1360_3]) ).

cnf(f_1360_5,plain,
    ( U_4595 = c_Int_OMin
    | c_Int_OBit1(U_4595) != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1360_4]) ).

cnf(f_1360_6,plain,
    ( c_Int_OBit1(U_4596) = c_Int_OMin
    | U_4596 != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1360_4]) ).

fof(f_1361_1,plain,
    ! [V_l_2] :
      ( ( c_Int_OMin = c_Int_OBit1(V_l_2)
        | c_Int_OMin != V_l_2 )
      & ( c_Int_OMin = V_l_2
        | c_Int_OMin != c_Int_OBit1(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J]) ).

fof(f_1361_2,plain,
    ! [U_4597] :
      ( ( c_Int_OMin = c_Int_OBit1(U_4597)
        | c_Int_OMin != U_4597 )
      & ( c_Int_OMin = U_4597
        | c_Int_OMin != c_Int_OBit1(U_4597) ) ),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

fof(f_1361_3,plain,
    ( ! [U_4599] :
        ( c_Int_OMin = c_Int_OBit1(U_4599)
        | c_Int_OMin != U_4599 )
    & ! [U_4598] :
        ( c_Int_OMin = U_4598
        | c_Int_OMin != c_Int_OBit1(U_4598) ) ),
    inference(miniscope,[status(thm)],[f_1361_2]) ).

fof(f_1361_4,plain,
    ( ! [U_4599] :
        ( c_Int_OMin = c_Int_OBit1(U_4599)
        | c_Int_OMin != U_4599 )
    & ! [U_4598] :
        ( c_Int_OMin = U_4598
        | c_Int_OMin != c_Int_OBit1(U_4598) ) ),
    inference(definitional_conversion,[status(esa)],[f_1361_3]) ).

cnf(f_1361_5,plain,
    ( c_Int_OMin = U_4598
    | c_Int_OMin != c_Int_OBit1(U_4598) ),
    inference(clausify,[status(thm)],[f_1361_4]) ).

cnf(f_1361_6,plain,
    ( c_Int_OMin = c_Int_OBit1(U_4599)
    | c_Int_OMin != U_4599 ),
    inference(clausify,[status(thm)],[f_1361_4]) ).

fof(f_1362_1,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).

fof(f_1362_2,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1362_1]) ).

cnf(f_1362_3,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1362_2]) ).

fof(f_1363_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J]) ).

fof(f_1363_2,plain,
    ! [U_4600] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4600)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4600),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4600),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4600)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

fof(f_1363_3,plain,
    ( ! [U_4602] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4602)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4602),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4601] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4601),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1363_2]) ).

fof(f_1363_4,plain,
    ( ! [U_4602] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4602)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4602),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4601] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4601),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1363_3]) ).

cnf(f_1363_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4601),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1363_4]) ).

cnf(f_1363_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4602)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4602),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1363_4]) ).

fof(f_1364_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J]) ).

fof(f_1364_2,plain,
    ! [U_4603] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4603)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4603)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4603))) ) ),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

fof(f_1364_3,plain,
    ( ! [U_4605] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4605)) )
    & ! [U_4604] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4604))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4604))) ) ),
    inference(miniscope,[status(thm)],[f_1364_2]) ).

fof(f_1364_4,plain,
    ( ! [U_4605] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4605)) )
    & ! [U_4604] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4604))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4604))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1364_3]) ).

cnf(f_1364_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4604))) ),
    inference(clausify,[status(thm)],[f_1364_4]) ).

cnf(f_1364_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4605)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4605)) ),
    inference(clausify,[status(thm)],[f_1364_4]) ).

fof(f_1365_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J]) ).

fof(f_1365_2,plain,
    ! [U_4606] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4606)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4606),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4606),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4606)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

fof(f_1365_3,plain,
    ( ! [U_4608] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4608)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4608),c_Int_OPls)) )
    & ! [U_4607] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4607),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4607)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1365_2]) ).

fof(f_1365_4,plain,
    ( ! [U_4608] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4608)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4608),c_Int_OPls)) )
    & ! [U_4607] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4607),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4607)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1365_3]) ).

cnf(f_1365_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4607),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4607)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4608)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4608),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

fof(f_1366_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k),
    inference(fof_nnf,[status(thm)],[fact_Bit1__def]) ).

fof(f_1366_2,plain,
    ! [U_4609] : c_Int_OBit1(U_4609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4609)),U_4609),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

fof(f_1366_3,plain,
    ! [U_4609] : c_Int_OBit1(U_4609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4609)),U_4609),
    inference(definitional_conversion,[status(esa)],[f_1366_2]) ).

cnf(f_1366_4,plain,
    c_Int_OBit1(U_4609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4609)),U_4609),
    inference(clausify,[status(thm)],[f_1366_3]) ).

fof(f_1367_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J]) ).

fof(f_1367_2,plain,
    ! [U_4610] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4610)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4610),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4610),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4610)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

fof(f_1367_3,plain,
    ( ! [U_4612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4612)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4612),c_Int_OMin)) )
    & ! [U_4611] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4611),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4611)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1367_2]) ).

fof(f_1367_4,plain,
    ( ! [U_4612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4612)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4612),c_Int_OMin)) )
    & ! [U_4611] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4611),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4611)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1367_3]) ).

cnf(f_1367_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4611),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4611)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1367_4]) ).

cnf(f_1367_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4612)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4612),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1367_4]) ).

fof(f_1368_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J]) ).

fof(f_1368_2,plain,
    ! [U_4613] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4613)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4613))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4613))) ) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

fof(f_1368_3,plain,
    ( ! [U_4615] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4615)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4615)) )
    & ! [U_4614] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4614))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4614))) ) ),
    inference(miniscope,[status(thm)],[f_1368_2]) ).

fof(f_1368_4,plain,
    ( ! [U_4615] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4615)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4615)) )
    & ! [U_4614] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4614))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4614))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1368_3]) ).

cnf(f_1368_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4614))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4614))) ),
    inference(clausify,[status(thm)],[f_1368_4]) ).

cnf(f_1368_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4615)) ),
    inference(clausify,[status(thm)],[f_1368_4]) ).

fof(f_1369_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J]) ).

fof(f_1369_2,plain,
    ! [U_4616] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4616)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4616)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4616))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4616))) ) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

fof(f_1369_3,plain,
    ( ! [U_4618] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4618)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4618)) )
    & ! [U_4617] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4617))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4617))) ) ),
    inference(miniscope,[status(thm)],[f_1369_2]) ).

fof(f_1369_4,plain,
    ( ! [U_4618] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4618)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4618)) )
    & ! [U_4617] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4617))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4617))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1369_3]) ).

cnf(f_1369_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4617))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4617))) ),
    inference(clausify,[status(thm)],[f_1369_4]) ).

cnf(f_1369_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4618)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4618)) ),
    inference(clausify,[status(thm)],[f_1369_4]) ).

fof(f_1370_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J]) ).

fof(f_1370_2,plain,
    ! [U_4619] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4619)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4619),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4619),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4619)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

fof(f_1370_3,plain,
    ( ! [U_4621] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4621)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4621),c_Int_OMin)) )
    & ! [U_4620] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4620),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4620)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1370_2]) ).

fof(f_1370_4,plain,
    ( ! [U_4621] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4621)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4621),c_Int_OMin)) )
    & ! [U_4620] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4620),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4620)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1370_3]) ).

cnf(f_1370_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4620),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4620)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1370_4]) ).

cnf(f_1370_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4621)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4621),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1370_4]) ).

fof(f_1371_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1]) ).

fof(f_1371_2,plain,
    ! [U_4622] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4622))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4622))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4622)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4622)))) ) ),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

fof(f_1371_3,plain,
    ( ! [U_4624] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4624))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4624))) )
    & ! [U_4623] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4623)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4623)))) ) ),
    inference(miniscope,[status(thm)],[f_1371_2]) ).

fof(f_1371_4,plain,
    ( ! [U_4624] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4624))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4624))) )
    & ! [U_4623] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4623)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4623)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1371_3]) ).

cnf(f_1371_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4623)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4623)))) ),
    inference(clausify,[status(thm)],[f_1371_4]) ).

cnf(f_1371_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4624))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4624))) ),
    inference(clausify,[status(thm)],[f_1371_4]) ).

fof(f_1372_1,plain,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))),
    inference(fof_nnf,[status(thm)],[fact_minus__Bit1]) ).

fof(f_1372_2,plain,
    ! [U_4625] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_4625)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4625))),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

fof(f_1372_3,plain,
    ! [U_4625] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_4625)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4625))),
    inference(definitional_conversion,[status(esa)],[f_1372_2]) ).

cnf(f_1372_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_4625)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4625))),
    inference(clausify,[status(thm)],[f_1372_3]) ).

fof(f_1373_1,plain,
    ! [V_w,T_a] :
      ( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)))
      | ~ class_Int_Oring__char__0(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(f_1373_2,plain,
    ! [U_4627,U_4626] :
      ( ~ c_Int_Oiszero(U_4626,hAPP(c_Int_Onumber__class_Onumber__of(U_4626),c_Int_OBit1(U_4627)))
      | ~ class_Int_Oring__char__0(U_4626)
      | ~ class_Int_Onumber__ring(U_4626) ),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

fof(f_1373_3,plain,
    ! [U_4626,U_4627] :
      ( ~ c_Int_Oiszero(U_4626,hAPP(c_Int_Onumber__class_Onumber__of(U_4626),c_Int_OBit1(U_4627)))
      | ~ class_Int_Oring__char__0(U_4626)
      | ~ class_Int_Onumber__ring(U_4626) ),
    inference(definitional_conversion,[status(esa)],[f_1373_2]) ).

cnf(f_1373_4,plain,
    ( ~ c_Int_Oiszero(U_4626,hAPP(c_Int_Onumber__class_Onumber__of(U_4626),c_Int_OBit1(U_4627)))
    | ~ class_Int_Oring__char__0(U_4626)
    | ~ class_Int_Onumber__ring(U_4626) ),
    inference(clausify,[status(thm)],[f_1373_3]) ).

fof(f_1374_1,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).

fof(f_1374_2,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1374_1]) ).

cnf(f_1374_3,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_1374_2]) ).

fof(f_1375_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Bit1]) ).

fof(f_1375_2,plain,
    ! [U_4629,U_4628] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4628),c_Int_OBit1(U_4629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4628),c_Groups_Oone__class_Oone(U_4628)),hAPP(c_Int_Onumber__class_Onumber__of(U_4628),U_4629))),hAPP(c_Int_Onumber__class_Onumber__of(U_4628),U_4629))
      | ~ class_Int_Onumber__ring(U_4628) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

fof(f_1375_3,plain,
    ! [U_4628,U_4629] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4628),c_Int_OBit1(U_4629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4628),c_Groups_Oone__class_Oone(U_4628)),hAPP(c_Int_Onumber__class_Onumber__of(U_4628),U_4629))),hAPP(c_Int_Onumber__class_Onumber__of(U_4628),U_4629))
      | ~ class_Int_Onumber__ring(U_4628) ),
    inference(definitional_conversion,[status(esa)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4628),c_Int_OBit1(U_4629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4628),c_Groups_Oone__class_Oone(U_4628)),hAPP(c_Int_Onumber__class_Onumber__of(U_4628),U_4629))),hAPP(c_Int_Onumber__class_Onumber__of(U_4628),U_4629))
    | ~ class_Int_Onumber__ring(U_4628) ),
    inference(clausify,[status(thm)],[f_1375_3]) ).

fof(f_1376_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__numeral__1]) ).

fof(f_1376_2,plain,
    ! [U_4631,U_4630] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),hAPP(c_Int_Onumber__class_Onumber__of(U_4630),c_Int_OBit1(c_Int_OPls))),U_4631) = U_4631
      | ~ class_Int_Onumber__ring(U_4630) ),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

fof(f_1376_3,plain,
    ! [U_4630,U_4631] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),hAPP(c_Int_Onumber__class_Onumber__of(U_4630),c_Int_OBit1(c_Int_OPls))),U_4631) = U_4631
      | ~ class_Int_Onumber__ring(U_4630) ),
    inference(definitional_conversion,[status(esa)],[f_1376_2]) ).

cnf(f_1376_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4630),hAPP(c_Int_Onumber__class_Onumber__of(U_4630),c_Int_OBit1(c_Int_OPls))),U_4631) = U_4631
    | ~ class_Int_Onumber__ring(U_4630) ),
    inference(clausify,[status(thm)],[f_1376_3]) ).

fof(f_1377_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right]) ).

fof(f_1377_2,plain,
    ! [U_4633,U_4632] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4632),U_4633),hAPP(c_Int_Onumber__class_Onumber__of(U_4632),c_Int_OBit1(c_Int_OPls))) = U_4633
      | ~ class_Int_Onumber__ring(U_4632) ),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

fof(f_1377_3,plain,
    ! [U_4632,U_4633] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4632),U_4633),hAPP(c_Int_Onumber__class_Onumber__of(U_4632),c_Int_OBit1(c_Int_OPls))) = U_4633
      | ~ class_Int_Onumber__ring(U_4632) ),
    inference(definitional_conversion,[status(esa)],[f_1377_2]) ).

cnf(f_1377_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4632),U_4633),hAPP(c_Int_Onumber__class_Onumber__of(U_4632),c_Int_OBit1(c_Int_OPls))) = U_4633
    | ~ class_Int_Onumber__ring(U_4632) ),
    inference(clausify,[status(thm)],[f_1377_3]) ).

fof(f_1378_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1]) ).

fof(f_1378_2,plain,
    ! [U_4634] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4634),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_4634)
      | ~ class_Int_Onumber__ring(U_4634) ),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

fof(f_1378_3,plain,
    ! [U_4634] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4634),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_4634)
      | ~ class_Int_Onumber__ring(U_4634) ),
    inference(definitional_conversion,[status(esa)],[f_1378_2]) ).

cnf(f_1378_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4634),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_4634)
    | ~ class_Int_Onumber__ring(U_4634) ),
    inference(clausify,[status(thm)],[f_1378_3]) ).

fof(f_1379_1,plain,
    ! [T_a] :
      ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J]) ).

fof(f_1379_2,plain,
    ! [U_4635] :
      ( c_Groups_Oone__class_Oone(U_4635) = hAPP(c_Int_Onumber__class_Onumber__of(U_4635),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4635) ),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

fof(f_1379_3,plain,
    ! [U_4635] :
      ( c_Groups_Oone__class_Oone(U_4635) = hAPP(c_Int_Onumber__class_Onumber__of(U_4635),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4635) ),
    inference(definitional_conversion,[status(esa)],[f_1379_2]) ).

cnf(f_1379_4,plain,
    ( c_Groups_Oone__class_Oone(U_4635) = hAPP(c_Int_Onumber__class_Onumber__of(U_4635),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_4635) ),
    inference(clausify,[status(thm)],[f_1379_3]) ).

fof(f_1380_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J]) ).

fof(f_1380_2,plain,
    ! [U_4636] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4636)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4636),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4636),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4636)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

fof(f_1380_3,plain,
    ( ! [U_4638] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4638)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4638),c_Int_OPls)) )
    & ! [U_4637] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4637),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4637)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1380_2]) ).

fof(f_1380_4,plain,
    ( ! [U_4638] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4638)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4638),c_Int_OPls)) )
    & ! [U_4637] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4637),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4637)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1380_3]) ).

cnf(f_1380_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4637),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4637)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1380_4]) ).

cnf(f_1380_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4638)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4638),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1380_4]) ).

fof(f_1381_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J]) ).

fof(f_1381_2,plain,
    ! [U_4639] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4639)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4639)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4639))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4639))) ) ),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

fof(f_1381_3,plain,
    ( ! [U_4641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4641)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4641)) )
    & ! [U_4640] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4640))) ) ),
    inference(miniscope,[status(thm)],[f_1381_2]) ).

fof(f_1381_4,plain,
    ( ! [U_4641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4641)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4641)) )
    & ! [U_4640] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4640))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1381_3]) ).

cnf(f_1381_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4640))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4640))) ),
    inference(clausify,[status(thm)],[f_1381_4]) ).

cnf(f_1381_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4641)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4641)) ),
    inference(clausify,[status(thm)],[f_1381_4]) ).

fof(f_1382_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_one__is__num__one]) ).

fof(f_1382_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1382_1]) ).

cnf(f_1382_3,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1382_2]) ).

fof(f_1383_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__numeral__1__eq__1]) ).

fof(f_1383_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1383_1]) ).

cnf(f_1383_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1383_2]) ).

fof(f_1384_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_Numeral1__eq1__nat]) ).

fof(f_1384_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1384_1]) ).

cnf(f_1384_3,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1384_2]) ).

fof(f_1385_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I4_J]) ).

fof(f_1385_2,plain,
    ! [U_4642] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4642)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4642)),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

fof(f_1385_3,plain,
    ! [U_4642] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4642)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4642)),
    inference(definitional_conversion,[status(esa)],[f_1385_2]) ).

cnf(f_1385_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4642)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4642)),
    inference(clausify,[status(thm)],[f_1385_3]) ).

fof(f_1386_1,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_minus__Min]) ).

fof(f_1386_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1386_1]) ).

cnf(f_1386_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_1386_2]) ).

fof(f_1387_1,plain,
    ! [T_a] :
      ( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(f_1387_2,plain,
    ! [U_4643] :
      ( ~ c_Int_Oiszero(U_4643,hAPP(c_Int_Onumber__class_Onumber__of(U_4643),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_4643) ),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

fof(f_1387_3,plain,
    ! [U_4643] :
      ( ~ c_Int_Oiszero(U_4643,hAPP(c_Int_Onumber__class_Onumber__of(U_4643),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_4643) ),
    inference(definitional_conversion,[status(esa)],[f_1387_2]) ).

cnf(f_1387_4,plain,
    ( ~ c_Int_Oiszero(U_4643,hAPP(c_Int_Onumber__class_Onumber__of(U_4643),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_4643) ),
    inference(clausify,[status(thm)],[f_1387_3]) ).

fof(f_1388_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).

fof(f_1388_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1388_1]) ).

cnf(f_1388_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1388_2]) ).

fof(f_1389_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_numeral__3__eq__3]) ).

fof(f_1389_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1389_1]) ).

cnf(f_1389_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_1389_2]) ).

fof(f_1390_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power3__eq__cube]) ).

fof(f_1390_2,plain,
    ! [U_4645,U_4644] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4644),U_4645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4644),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4644),U_4645),U_4645)),U_4645)
      | ~ class_Groups_Omonoid__mult(U_4644) ),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

fof(f_1390_3,plain,
    ! [U_4644,U_4645] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4644),U_4645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4644),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4644),U_4645),U_4645)),U_4645)
      | ~ class_Groups_Omonoid__mult(U_4644) ),
    inference(definitional_conversion,[status(esa)],[f_1390_2]) ).

cnf(f_1390_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4644),U_4645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4644),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4644),U_4645),U_4645)),U_4645)
    | ~ class_Groups_Omonoid__mult(U_4644) ),
    inference(clausify,[status(thm)],[f_1390_3]) ).

fof(f_1391_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).

fof(f_1391_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    inference(definitional_conversion,[status(esa)],[f_1391_1]) ).

cnf(f_1391_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_1391_2]) ).

fof(f_1392_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(f_1392_2,plain,
    ! [U_4646] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4646))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4646),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

fof(f_1392_3,plain,
    ! [U_4646] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4646))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4646),
    inference(definitional_conversion,[status(esa)],[f_1392_2]) ).

cnf(f_1392_4,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4646))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4646),
    inference(clausify,[status(thm)],[f_1392_3]) ).

fof(f_1393_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I4_J]) ).

fof(f_1393_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1393_1]) ).

cnf(f_1393_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1393_2]) ).

fof(f_1394_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I4_J]) ).

fof(f_1394_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1394_1]) ).

cnf(f_1394_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1394_2]) ).

fof(f_1395_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).

fof(f_1395_2,plain,
    ! [U_4648,U_4647] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4647),c_Groups_Oone__class_Oone(U_4647)),hAPP(c_Int_Onumber__class_Onumber__of(U_4647),U_4648)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4648)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4648))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4647),c_Groups_Oone__class_Oone(U_4647)),hAPP(c_Int_Onumber__class_Onumber__of(U_4647),U_4648))) ) )
      | ~ class_Rings_Olinordered__idom(U_4647)
      | ~ class_Int_Onumber__ring(U_4647) ),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

fof(f_1395_3,plain,
    ( ! [U_4647,U_4648] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4647),c_Groups_Oone__class_Oone(U_4647)),hAPP(c_Int_Onumber__class_Onumber__of(U_4647),U_4648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4648))
        | ~ sP384(U_4647,U_4648) )
    & ! [U_4647,U_4648] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4648))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4647),c_Groups_Oone__class_Oone(U_4647)),hAPP(c_Int_Onumber__class_Onumber__of(U_4647),U_4648)))
        | ~ sP384(U_4647,U_4648) )
    & ! [U_4647,U_4648] :
        ( sP384(U_4647,U_4648)
        | ~ class_Rings_Olinordered__idom(U_4647)
        | ~ class_Int_Onumber__ring(U_4647) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP384])],[f_1395_2]) ).

cnf(f_1395_4,plain,
    ( sP384(U_4647,U_4648)
    | ~ class_Rings_Olinordered__idom(U_4647)
    | ~ class_Int_Onumber__ring(U_4647) ),
    inference(clausify,[status(thm)],[f_1395_3]) ).

cnf(f_1395_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4648))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4647),c_Groups_Oone__class_Oone(U_4647)),hAPP(c_Int_Onumber__class_Onumber__of(U_4647),U_4648)))
    | ~ sP384(U_4647,U_4648) ),
    inference(clausify,[status(thm)],[f_1395_3]) ).

cnf(f_1395_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4647),c_Groups_Oone__class_Oone(U_4647)),hAPP(c_Int_Onumber__class_Onumber__of(U_4647),U_4648)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4648))
    | ~ sP384(U_4647,U_4648) ),
    inference(clausify,[status(thm)],[f_1395_3]) ).

fof(f_1396_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).

fof(f_1396_2,plain,
    ! [U_4650,U_4649] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4649),hAPP(c_Int_Onumber__class_Onumber__of(U_4649),U_4650)),c_Groups_Oone__class_Oone(U_4649)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4650),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4650),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4649),hAPP(c_Int_Onumber__class_Onumber__of(U_4649),U_4650)),c_Groups_Oone__class_Oone(U_4649))) ) )
      | ~ class_Rings_Olinordered__idom(U_4649)
      | ~ class_Int_Onumber__ring(U_4649) ),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

fof(f_1396_3,plain,
    ( ! [U_4650,U_4649] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4649),hAPP(c_Int_Onumber__class_Onumber__of(U_4649),U_4650)),c_Groups_Oone__class_Oone(U_4649)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4650),c_Int_OBit1(c_Int_OPls)))
        | ~ sP385(U_4650,U_4649) )
    & ! [U_4650,U_4649] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4650),c_Int_OBit1(c_Int_OPls)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4649),hAPP(c_Int_Onumber__class_Onumber__of(U_4649),U_4650)),c_Groups_Oone__class_Oone(U_4649)))
        | ~ sP385(U_4650,U_4649) )
    & ! [U_4650,U_4649] :
        ( sP385(U_4650,U_4649)
        | ~ class_Rings_Olinordered__idom(U_4649)
        | ~ class_Int_Onumber__ring(U_4649) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP385])],[f_1396_2]) ).

cnf(f_1396_4,plain,
    ( sP385(U_4650,U_4649)
    | ~ class_Rings_Olinordered__idom(U_4649)
    | ~ class_Int_Onumber__ring(U_4649) ),
    inference(clausify,[status(thm)],[f_1396_3]) ).

cnf(f_1396_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4650),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4649),hAPP(c_Int_Onumber__class_Onumber__of(U_4649),U_4650)),c_Groups_Oone__class_Oone(U_4649)))
    | ~ sP385(U_4650,U_4649) ),
    inference(clausify,[status(thm)],[f_1396_3]) ).

cnf(f_1396_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4649),hAPP(c_Int_Onumber__class_Onumber__of(U_4649),U_4650)),c_Groups_Oone__class_Oone(U_4649)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4650),c_Int_OBit1(c_Int_OPls)))
    | ~ sP385(U_4650,U_4649) ),
    inference(clausify,[status(thm)],[f_1396_3]) ).

fof(f_1397_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).

fof(f_1397_2,plain,
    ! [U_4652,U_4651] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4651),hAPP(c_Int_Onumber__class_Onumber__of(U_4651),U_4652)),c_Groups_Oone__class_Oone(U_4651)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4652),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4652),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4651),hAPP(c_Int_Onumber__class_Onumber__of(U_4651),U_4652)),c_Groups_Oone__class_Oone(U_4651))) ) )
      | ~ class_Rings_Olinordered__idom(U_4651)
      | ~ class_Int_Onumber__ring(U_4651) ),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

fof(f_1397_3,plain,
    ( ! [U_4651,U_4652] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4651),hAPP(c_Int_Onumber__class_Onumber__of(U_4651),U_4652)),c_Groups_Oone__class_Oone(U_4651)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4652),c_Int_OBit1(c_Int_OPls)))
        | ~ sP386(U_4651,U_4652) )
    & ! [U_4651,U_4652] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4652),c_Int_OBit1(c_Int_OPls)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4651),hAPP(c_Int_Onumber__class_Onumber__of(U_4651),U_4652)),c_Groups_Oone__class_Oone(U_4651)))
        | ~ sP386(U_4651,U_4652) )
    & ! [U_4651,U_4652] :
        ( sP386(U_4651,U_4652)
        | ~ class_Rings_Olinordered__idom(U_4651)
        | ~ class_Int_Onumber__ring(U_4651) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP386])],[f_1397_2]) ).

cnf(f_1397_4,plain,
    ( sP386(U_4651,U_4652)
    | ~ class_Rings_Olinordered__idom(U_4651)
    | ~ class_Int_Onumber__ring(U_4651) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4652),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4651),hAPP(c_Int_Onumber__class_Onumber__of(U_4651),U_4652)),c_Groups_Oone__class_Oone(U_4651)))
    | ~ sP386(U_4651,U_4652) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4651),hAPP(c_Int_Onumber__class_Onumber__of(U_4651),U_4652)),c_Groups_Oone__class_Oone(U_4651)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4652),c_Int_OBit1(c_Int_OPls)))
    | ~ sP386(U_4651,U_4652) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

fof(f_1398_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).

fof(f_1398_2,plain,
    ! [U_4654,U_4653] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Oone__class_Oone(U_4653)),hAPP(c_Int_Onumber__class_Onumber__of(U_4653),U_4654)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4654)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4654))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Oone__class_Oone(U_4653)),hAPP(c_Int_Onumber__class_Onumber__of(U_4653),U_4654))) ) )
      | ~ class_Rings_Olinordered__idom(U_4653)
      | ~ class_Int_Onumber__ring(U_4653) ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

fof(f_1398_3,plain,
    ( ! [U_4654,U_4653] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Oone__class_Oone(U_4653)),hAPP(c_Int_Onumber__class_Onumber__of(U_4653),U_4654)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4654))
        | ~ sP387(U_4654,U_4653) )
    & ! [U_4654,U_4653] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4654))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Oone__class_Oone(U_4653)),hAPP(c_Int_Onumber__class_Onumber__of(U_4653),U_4654)))
        | ~ sP387(U_4654,U_4653) )
    & ! [U_4654,U_4653] :
        ( sP387(U_4654,U_4653)
        | ~ class_Rings_Olinordered__idom(U_4653)
        | ~ class_Int_Onumber__ring(U_4653) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP387])],[f_1398_2]) ).

cnf(f_1398_4,plain,
    ( sP387(U_4654,U_4653)
    | ~ class_Rings_Olinordered__idom(U_4653)
    | ~ class_Int_Onumber__ring(U_4653) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

cnf(f_1398_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Oone__class_Oone(U_4653)),hAPP(c_Int_Onumber__class_Onumber__of(U_4653),U_4654)))
    | ~ sP387(U_4654,U_4653) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

cnf(f_1398_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4653),c_Groups_Oone__class_Oone(U_4653)),hAPP(c_Int_Onumber__class_Onumber__of(U_4653),U_4654)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4654))
    | ~ sP387(U_4654,U_4653) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

fof(f_1399_1,plain,
    ! [V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__special_I3_J]) ).

fof(f_1399_2,plain,
    ! [U_4656,U_4655] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4655),hAPP(c_Int_Onumber__class_Onumber__of(U_4655),U_4656)),c_Groups_Oone__class_Oone(U_4655)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4656),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_4655) ),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

fof(f_1399_3,plain,
    ! [U_4655,U_4656] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4655),hAPP(c_Int_Onumber__class_Onumber__of(U_4655),U_4656)),c_Groups_Oone__class_Oone(U_4655)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4656),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_4655) ),
    inference(definitional_conversion,[status(esa)],[f_1399_2]) ).

cnf(f_1399_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4655),hAPP(c_Int_Onumber__class_Onumber__of(U_4655),U_4656)),c_Groups_Oone__class_Oone(U_4655)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4656),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_4655) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

fof(f_1400_1,plain,
    ! [V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__special_I2_J]) ).

fof(f_1400_2,plain,
    ! [U_4658,U_4657] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4657),c_Groups_Oone__class_Oone(U_4657)),hAPP(c_Int_Onumber__class_Onumber__of(U_4657),U_4658)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4658))
      | ~ class_Int_Onumber__ring(U_4657) ),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

fof(f_1400_3,plain,
    ! [U_4657,U_4658] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4657),c_Groups_Oone__class_Oone(U_4657)),hAPP(c_Int_Onumber__class_Onumber__of(U_4657),U_4658)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4658))
      | ~ class_Int_Onumber__ring(U_4657) ),
    inference(definitional_conversion,[status(esa)],[f_1400_2]) ).

cnf(f_1400_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4657),c_Groups_Oone__class_Oone(U_4657)),hAPP(c_Int_Onumber__class_Onumber__of(U_4657),U_4658)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_4658))
    | ~ class_Int_Onumber__ring(U_4657) ),
    inference(clausify,[status(thm)],[f_1400_3]) ).

fof(f_1401_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred]) ).

fof(f_1401_2,plain,
    ! [U_4660,U_4659] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4660)),U_4659) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_4659)) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

fof(f_1401_3,plain,
    ! [U_4659,U_4660] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4660)),U_4659) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_4659)) ),
    inference(definitional_conversion,[status(esa)],[f_1401_2]) ).

cnf(f_1401_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4660)),U_4659) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_4659)) ),
    inference(clausify,[status(thm)],[f_1401_3]) ).

fof(f_1402_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).

fof(f_1402_2,plain,
    ! [U_4662,U_4661] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4661,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4662)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4661,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4662)),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

fof(f_1402_3,plain,
    ! [U_4662,U_4661] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4661,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4662)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4661,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4662)),
    inference(definitional_conversion,[status(esa)],[f_1402_2]) ).

cnf(f_1402_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4661,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4662)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4661,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4662)),
    inference(clausify,[status(thm)],[f_1402_3]) ).

fof(f_1403_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).

fof(f_1403_2,plain,
    ! [U_4664,U_4663] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4663))),U_4664) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4663),U_4664),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ! [U_4663,U_4664] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4663))),U_4664) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4663),U_4664),
    inference(definitional_conversion,[status(esa)],[f_1403_2]) ).

cnf(f_1403_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4663))),U_4664) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4663),U_4664),
    inference(clausify,[status(thm)],[f_1403_3]) ).

fof(f_1404_1,plain,
    ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    inference(fof_nnf,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).

fof(f_1404_2,plain,
    ! [U_4666,U_4665] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4665))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4666)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4665),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4666)),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ! [U_4665,U_4666] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4665))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4666)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4665),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4666)),
    inference(definitional_conversion,[status(esa)],[f_1404_2]) ).

cnf(f_1404_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4665))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4666)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_4665),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4666)),
    inference(clausify,[status(thm)],[f_1404_3]) ).

fof(f_1405_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2]) ).

fof(f_1405_2,plain,
    ! [U_4668,U_4667] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4668)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4668),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4667))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4667),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ! [U_4668,U_4667] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4668)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4668),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4667))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4667),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1405_2]) ).

cnf(f_1405_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4668)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4668),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4667))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4667),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1405_3]) ).

fof(f_1406_1,plain,
    ! [V_v,V_w] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__number__of__Bit1]) ).

fof(f_1406_2,plain,
    ! [U_4670,U_4669] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4670)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4669))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4669)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4669))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4670)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4669))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4669)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4669))) ) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ( ! [U_4674,U_4672] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4674)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4672))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4674)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4672)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4672))) )
    & ! [U_4673,U_4671] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4673)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4673),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671))) ) ),
    inference(miniscope,[status(thm)],[f_1406_2]) ).

fof(f_1406_4,plain,
    ( ! [U_4672,U_4674] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4674)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4672))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4674)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4672)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4672))) )
    & ! [U_4673,U_4671] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4673)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4673),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1406_3]) ).

cnf(f_1406_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4673)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4673),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4674)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4672))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4674)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4672)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4672))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

fof(f_1407_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2]) ).

fof(f_1407_2,plain,
    ! [U_4676,U_4675] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4676))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4675)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4676),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4675)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

fof(f_1407_3,plain,
    ! [U_4676,U_4675] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4676))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4675)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4676),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4675)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1407_2]) ).

cnf(f_1407_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4676))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4675)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4676),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4675)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

fof(f_1408_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2]) ).

fof(f_1408_2,plain,
    ! [U_4678,U_4677] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4678))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4677)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4678),U_4677)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4677)) ),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

fof(f_1408_3,plain,
    ! [U_4677,U_4678] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4678))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4677)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4678),U_4677)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4677)) ),
    inference(definitional_conversion,[status(esa)],[f_1408_2]) ).

cnf(f_1408_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4678))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4677)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4678),U_4677)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4677)) ),
    inference(clausify,[status(thm)],[f_1408_3]) ).

fof(f_1409_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2]) ).

fof(f_1409_2,plain,
    ! [U_4680,U_4679] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4679)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4680,U_4679)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4679)) ),
    inference(variable_rename,[status(thm)],[f_1409_1]) ).

fof(f_1409_3,plain,
    ! [U_4679,U_4680] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4679)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4680,U_4679)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4679)) ),
    inference(definitional_conversion,[status(esa)],[f_1409_2]) ).

cnf(f_1409_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4679)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4680,U_4679)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4679)) ),
    inference(clausify,[status(thm)],[f_1409_3]) ).

fof(f_1410_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__double]) ).

fof(f_1410_2,plain,
    ! [U_4682,U_4681] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4682))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,U_4682))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,U_4682)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4682))
      | ~ class_Rings_Osemiring__1(U_4681) ),
    inference(variable_rename,[status(thm)],[f_1410_1]) ).

fof(f_1410_3,plain,
    ! [U_4681,U_4682] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4682))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,U_4682))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,U_4682)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4682))
      | ~ class_Rings_Osemiring__1(U_4681) ),
    inference(definitional_conversion,[status(esa)],[f_1410_2]) ).

cnf(f_1410_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4682))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,U_4682))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4681),hAPP(c_Int_Onat,U_4682)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4682))
    | ~ class_Rings_Osemiring__1(U_4681) ),
    inference(clausify,[status(thm)],[f_1410_3]) ).

fof(f_1411_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
        | V_k_2 != V_l_2 )
      & ( V_k_2 = V_l_2
        | c_Int_OBit0(V_k_2) != c_Int_OBit0(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J]) ).

fof(f_1411_2,plain,
    ! [U_4684,U_4683] :
      ( ( c_Int_OBit0(U_4683) = c_Int_OBit0(U_4684)
        | U_4683 != U_4684 )
      & ( U_4683 = U_4684
        | c_Int_OBit0(U_4683) != c_Int_OBit0(U_4684) ) ),
    inference(variable_rename,[status(thm)],[f_1411_1]) ).

fof(f_1411_3,plain,
    ( ! [U_4688,U_4686] :
        ( c_Int_OBit0(U_4686) = c_Int_OBit0(U_4688)
        | U_4686 != U_4688 )
    & ! [U_4687,U_4685] :
        ( U_4685 = U_4687
        | c_Int_OBit0(U_4685) != c_Int_OBit0(U_4687) ) ),
    inference(miniscope,[status(thm)],[f_1411_2]) ).

fof(f_1411_4,plain,
    ( ! [U_4686,U_4688] :
        ( c_Int_OBit0(U_4686) = c_Int_OBit0(U_4688)
        | U_4686 != U_4688 )
    & ! [U_4687,U_4685] :
        ( U_4685 = U_4687
        | c_Int_OBit0(U_4685) != c_Int_OBit0(U_4687) ) ),
    inference(definitional_conversion,[status(esa)],[f_1411_3]) ).

cnf(f_1411_5,plain,
    ( U_4685 = U_4687
    | c_Int_OBit0(U_4685) != c_Int_OBit0(U_4687) ),
    inference(clausify,[status(thm)],[f_1411_4]) ).

cnf(f_1411_6,plain,
    ( c_Int_OBit0(U_4686) = c_Int_OBit0(U_4688)
    | U_4686 != U_4688 ),
    inference(clausify,[status(thm)],[f_1411_4]) ).

fof(f_1412_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J]) ).

fof(f_1412_2,plain,
    ! [U_4690,U_4689] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4689)),c_Int_OBit0(U_4690)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4689),U_4690)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4689),U_4690))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4689)),c_Int_OBit0(U_4690))) ) ),
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

fof(f_1412_3,plain,
    ( ! [U_4694,U_4692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4692)),c_Int_OBit0(U_4694)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4692),U_4694)) )
    & ! [U_4693,U_4691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4691),U_4693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4691)),c_Int_OBit0(U_4693))) ) ),
    inference(miniscope,[status(thm)],[f_1412_2]) ).

fof(f_1412_4,plain,
    ( ! [U_4692,U_4694] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4692)),c_Int_OBit0(U_4694)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4692),U_4694)) )
    & ! [U_4693,U_4691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4691),U_4693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4691)),c_Int_OBit0(U_4693))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1412_3]) ).

cnf(f_1412_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4691),U_4693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4691)),c_Int_OBit0(U_4693))) ),
    inference(clausify,[status(thm)],[f_1412_4]) ).

cnf(f_1412_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4692)),c_Int_OBit0(U_4694)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4692),U_4694)) ),
    inference(clausify,[status(thm)],[f_1412_4]) ).

fof(f_1413_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J]) ).

fof(f_1413_2,plain,
    ! [U_4696,U_4695] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4695)),c_Int_OBit0(U_4696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4695),U_4696)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4695),U_4696))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4695)),c_Int_OBit0(U_4696))) ) ),
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

fof(f_1413_3,plain,
    ( ! [U_4700,U_4698] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4698)),c_Int_OBit0(U_4700)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4698),U_4700)) )
    & ! [U_4699,U_4697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4697),U_4699))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4697)),c_Int_OBit0(U_4699))) ) ),
    inference(miniscope,[status(thm)],[f_1413_2]) ).

fof(f_1413_4,plain,
    ( ! [U_4698,U_4700] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4698)),c_Int_OBit0(U_4700)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4698),U_4700)) )
    & ! [U_4699,U_4697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4697),U_4699))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4697)),c_Int_OBit0(U_4699))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1413_3]) ).

cnf(f_1413_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4697),U_4699))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4697)),c_Int_OBit0(U_4699))) ),
    inference(clausify,[status(thm)],[f_1413_4]) ).

cnf(f_1413_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4698)),c_Int_OBit0(U_4700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4698),U_4700)) ),
    inference(clausify,[status(thm)],[f_1413_4]) ).

fof(f_1414_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J]) ).

fof(f_1414_2,plain,
    ! [U_4702,U_4701] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4701)),c_Int_OBit0(U_4702)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4701),U_4702)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4701),U_4702))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4701)),c_Int_OBit0(U_4702))) ) ),
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

fof(f_1414_3,plain,
    ( ! [U_4706,U_4704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4704)),c_Int_OBit0(U_4706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4704),U_4706)) )
    & ! [U_4705,U_4703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4703),U_4705))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4703)),c_Int_OBit0(U_4705))) ) ),
    inference(miniscope,[status(thm)],[f_1414_2]) ).

fof(f_1414_4,plain,
    ( ! [U_4704,U_4706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4704)),c_Int_OBit0(U_4706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4704),U_4706)) )
    & ! [U_4705,U_4703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4703),U_4705))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4703)),c_Int_OBit0(U_4705))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1414_3]) ).

cnf(f_1414_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4703),U_4705))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4703)),c_Int_OBit0(U_4705))) ),
    inference(clausify,[status(thm)],[f_1414_4]) ).

cnf(f_1414_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4704)),c_Int_OBit0(U_4706)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4704),U_4706)) ),
    inference(clausify,[status(thm)],[f_1414_4]) ).

fof(f_1415_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J]) ).

fof(f_1415_2,plain,
    ! [U_4708,U_4707] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4707)),c_Int_OBit0(U_4708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4707),U_4708)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4707),U_4708))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4707)),c_Int_OBit0(U_4708))) ) ),
    inference(variable_rename,[status(thm)],[f_1415_1]) ).

fof(f_1415_3,plain,
    ( ! [U_4712,U_4710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4710)),c_Int_OBit0(U_4712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4710),U_4712)) )
    & ! [U_4711,U_4709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4709),U_4711))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4709)),c_Int_OBit0(U_4711))) ) ),
    inference(miniscope,[status(thm)],[f_1415_2]) ).

fof(f_1415_4,plain,
    ( ! [U_4710,U_4712] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4710)),c_Int_OBit0(U_4712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4710),U_4712)) )
    & ! [U_4711,U_4709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4709),U_4711))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4709)),c_Int_OBit0(U_4711))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1415_3]) ).

cnf(f_1415_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4709),U_4711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4709)),c_Int_OBit0(U_4711))) ),
    inference(clausify,[status(thm)],[f_1415_4]) ).

cnf(f_1415_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4710)),c_Int_OBit0(U_4712)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4710),U_4712)) ),
    inference(clausify,[status(thm)],[f_1415_4]) ).

fof(f_1416_1,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).

fof(f_1416_2,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1416_1]) ).

cnf(f_1416_3,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1416_2]) ).

fof(f_1417_1,plain,
    ! [V_l_2] :
      ( ( c_Int_OPls = c_Int_OBit0(V_l_2)
        | c_Int_OPls != V_l_2 )
      & ( c_Int_OPls = V_l_2
        | c_Int_OPls != c_Int_OBit0(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J]) ).

fof(f_1417_2,plain,
    ! [U_4713] :
      ( ( c_Int_OPls = c_Int_OBit0(U_4713)
        | c_Int_OPls != U_4713 )
      & ( c_Int_OPls = U_4713
        | c_Int_OPls != c_Int_OBit0(U_4713) ) ),
    inference(variable_rename,[status(thm)],[f_1417_1]) ).

fof(f_1417_3,plain,
    ( ! [U_4715] :
        ( c_Int_OPls = c_Int_OBit0(U_4715)
        | c_Int_OPls != U_4715 )
    & ! [U_4714] :
        ( c_Int_OPls = U_4714
        | c_Int_OPls != c_Int_OBit0(U_4714) ) ),
    inference(miniscope,[status(thm)],[f_1417_2]) ).

fof(f_1417_4,plain,
    ( ! [U_4715] :
        ( c_Int_OPls = c_Int_OBit0(U_4715)
        | c_Int_OPls != U_4715 )
    & ! [U_4714] :
        ( c_Int_OPls = U_4714
        | c_Int_OPls != c_Int_OBit0(U_4714) ) ),
    inference(definitional_conversion,[status(esa)],[f_1417_3]) ).

cnf(f_1417_5,plain,
    ( c_Int_OPls = U_4714
    | c_Int_OPls != c_Int_OBit0(U_4714) ),
    inference(clausify,[status(thm)],[f_1417_4]) ).

cnf(f_1417_6,plain,
    ( c_Int_OPls = c_Int_OBit0(U_4715)
    | c_Int_OPls != U_4715 ),
    inference(clausify,[status(thm)],[f_1417_4]) ).

fof(f_1418_1,plain,
    ! [V_k_2] :
      ( ( c_Int_OBit0(V_k_2) = c_Int_OPls
        | V_k_2 != c_Int_OPls )
      & ( V_k_2 = c_Int_OPls
        | c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J]) ).

fof(f_1418_2,plain,
    ! [U_4716] :
      ( ( c_Int_OBit0(U_4716) = c_Int_OPls
        | U_4716 != c_Int_OPls )
      & ( U_4716 = c_Int_OPls
        | c_Int_OBit0(U_4716) != c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[f_1418_1]) ).

fof(f_1418_3,plain,
    ( ! [U_4718] :
        ( c_Int_OBit0(U_4718) = c_Int_OPls
        | U_4718 != c_Int_OPls )
    & ! [U_4717] :
        ( U_4717 = c_Int_OPls
        | c_Int_OBit0(U_4717) != c_Int_OPls ) ),
    inference(miniscope,[status(thm)],[f_1418_2]) ).

fof(f_1418_4,plain,
    ( ! [U_4718] :
        ( c_Int_OBit0(U_4718) = c_Int_OPls
        | U_4718 != c_Int_OPls )
    & ! [U_4717] :
        ( U_4717 = c_Int_OPls
        | c_Int_OBit0(U_4717) != c_Int_OPls ) ),
    inference(definitional_conversion,[status(esa)],[f_1418_3]) ).

cnf(f_1418_5,plain,
    ( U_4717 = c_Int_OPls
    | c_Int_OBit0(U_4717) != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1418_4]) ).

cnf(f_1418_6,plain,
    ( c_Int_OBit0(U_4718) = c_Int_OPls
    | U_4718 != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1418_4]) ).

fof(f_1419_1,plain,
    ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(f_1419_2,plain,
    ! [U_4720,U_4719] : c_Int_OBit0(U_4719) != c_Int_OBit1(U_4720),
    inference(variable_rename,[status(thm)],[f_1419_1]) ).

fof(f_1419_3,plain,
    ! [U_4719,U_4720] : c_Int_OBit0(U_4719) != c_Int_OBit1(U_4720),
    inference(definitional_conversion,[status(esa)],[f_1419_2]) ).

cnf(f_1419_4,plain,
    c_Int_OBit0(U_4719) != c_Int_OBit1(U_4720),
    inference(clausify,[status(thm)],[f_1419_3]) ).

fof(f_1420_1,plain,
    ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(f_1420_2,plain,
    ! [U_4722,U_4721] : c_Int_OBit1(U_4721) != c_Int_OBit0(U_4722),
    inference(variable_rename,[status(thm)],[f_1420_1]) ).

fof(f_1420_3,plain,
    ! [U_4721,U_4722] : c_Int_OBit1(U_4721) != c_Int_OBit0(U_4722),
    inference(definitional_conversion,[status(esa)],[f_1420_2]) ).

cnf(f_1420_4,plain,
    c_Int_OBit1(U_4721) != c_Int_OBit0(U_4722),
    inference(clausify,[status(thm)],[f_1420_3]) ).

fof(f_1421_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(f_1421_2,plain,
    ! [U_4724,U_4723] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_4723)),c_Int_OBit0(U_4724)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4723),U_4724)),
    inference(variable_rename,[status(thm)],[f_1421_1]) ).

fof(f_1421_3,plain,
    ! [U_4723,U_4724] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_4723)),c_Int_OBit0(U_4724)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4723),U_4724)),
    inference(definitional_conversion,[status(esa)],[f_1421_2]) ).

cnf(f_1421_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_4723)),c_Int_OBit0(U_4724)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4723),U_4724)),
    inference(clausify,[status(thm)],[f_1421_3]) ).

fof(f_1422_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
    inference(fof_nnf,[status(thm)],[fact_Bit0__def]) ).

fof(f_1422_2,plain,
    ! [U_4725] : c_Int_OBit0(U_4725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4725),U_4725),
    inference(variable_rename,[status(thm)],[f_1422_1]) ).

fof(f_1422_3,plain,
    ! [U_4725] : c_Int_OBit0(U_4725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4725),U_4725),
    inference(definitional_conversion,[status(esa)],[f_1422_2]) ).

cnf(f_1422_4,plain,
    c_Int_OBit0(U_4725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4725),U_4725),
    inference(clausify,[status(thm)],[f_1422_3]) ).

fof(f_1423_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_mult__Bit0]) ).

fof(f_1423_2,plain,
    ! [U_4727,U_4726] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_4726)),U_4727) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4726),U_4727)),
    inference(variable_rename,[status(thm)],[f_1423_1]) ).

fof(f_1423_3,plain,
    ! [U_4727,U_4726] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_4726)),U_4727) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4726),U_4727)),
    inference(definitional_conversion,[status(esa)],[f_1423_2]) ).

cnf(f_1423_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_4726)),U_4727) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4726),U_4727)),
    inference(clausify,[status(thm)],[f_1423_3]) ).

fof(f_1424_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(f_1424_2,plain,
    ! [U_4729,U_4728] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_4728)),c_Int_OBit0(U_4729)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4728),U_4729)),
    inference(variable_rename,[status(thm)],[f_1424_1]) ).

fof(f_1424_3,plain,
    ! [U_4728,U_4729] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_4728)),c_Int_OBit0(U_4729)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4728),U_4729)),
    inference(definitional_conversion,[status(esa)],[f_1424_2]) ).

cnf(f_1424_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_4728)),c_Int_OBit0(U_4729)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4728),U_4729)),
    inference(clausify,[status(thm)],[f_1424_3]) ).

fof(f_1425_1,plain,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)),
    inference(fof_nnf,[status(thm)],[fact_minus__Bit0]) ).

fof(f_1425_2,plain,
    ! [U_4730] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_4730)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4730)),
    inference(variable_rename,[status(thm)],[f_1425_1]) ).

fof(f_1425_3,plain,
    ! [U_4730] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_4730)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4730)),
    inference(definitional_conversion,[status(esa)],[f_1425_2]) ).

cnf(f_1425_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_4730)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4730)),
    inference(clausify,[status(thm)],[f_1425_3]) ).

fof(f_1426_1,plain,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(f_1426_2,plain,
    ! [U_4731] : c_Int_OMin != c_Int_OBit0(U_4731),
    inference(variable_rename,[status(thm)],[f_1426_1]) ).

fof(f_1426_3,plain,
    ! [U_4731] : c_Int_OMin != c_Int_OBit0(U_4731),
    inference(definitional_conversion,[status(esa)],[f_1426_2]) ).

cnf(f_1426_4,plain,
    c_Int_OMin != c_Int_OBit0(U_4731),
    inference(clausify,[status(thm)],[f_1426_3]) ).

fof(f_1427_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(f_1427_2,plain,
    ! [U_4732] : c_Int_OBit0(U_4732) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[f_1427_1]) ).

fof(f_1427_3,plain,
    ! [U_4732] : c_Int_OBit0(U_4732) != c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1427_2]) ).

cnf(f_1427_4,plain,
    c_Int_OBit0(U_4732) != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1427_3]) ).

fof(f_1428_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J]) ).

fof(f_1428_2,plain,
    ! [U_4733] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4733)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4733),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4733),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4733)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1428_1]) ).

fof(f_1428_3,plain,
    ( ! [U_4735] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4735)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4735),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4734),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4734)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1428_2]) ).

fof(f_1428_4,plain,
    ( ! [U_4735] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4735)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4735),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4734),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4734)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1428_3]) ).

cnf(f_1428_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4734),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4734)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1428_4]) ).

cnf(f_1428_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4735)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4735),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1428_4]) ).

fof(f_1429_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J]) ).

fof(f_1429_2,plain,
    ! [U_4736] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4736)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4736)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4736))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4736))) ) ),
    inference(variable_rename,[status(thm)],[f_1429_1]) ).

fof(f_1429_3,plain,
    ( ! [U_4738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4738)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4738)) )
    & ! [U_4737] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4737))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4737))) ) ),
    inference(miniscope,[status(thm)],[f_1429_2]) ).

fof(f_1429_4,plain,
    ( ! [U_4738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4738)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4738)) )
    & ! [U_4737] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4737))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4737))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1429_3]) ).

cnf(f_1429_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4737))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4737))) ),
    inference(clausify,[status(thm)],[f_1429_4]) ).

cnf(f_1429_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4738)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4738)) ),
    inference(clausify,[status(thm)],[f_1429_4]) ).

fof(f_1430_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J]) ).

fof(f_1430_2,plain,
    ! [U_4739] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4739)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4739),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4739),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4739)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1430_1]) ).

fof(f_1430_3,plain,
    ( ! [U_4741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4741)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4741),c_Int_OPls)) )
    & ! [U_4740] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4740),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4740)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1430_2]) ).

fof(f_1430_4,plain,
    ( ! [U_4741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4741)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4741),c_Int_OPls)) )
    & ! [U_4740] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4740),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4740)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1430_3]) ).

cnf(f_1430_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4740),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4740)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1430_4]) ).

cnf(f_1430_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4741)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4741),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1430_4]) ).

fof(f_1431_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J]) ).

fof(f_1431_2,plain,
    ! [U_4743,U_4742] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4742)),c_Int_OBit1(U_4743)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4742),U_4743)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4742),U_4743))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4742)),c_Int_OBit1(U_4743))) ) ),
    inference(variable_rename,[status(thm)],[f_1431_1]) ).

fof(f_1431_3,plain,
    ( ! [U_4747,U_4745] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4745)),c_Int_OBit1(U_4747)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4745),U_4747)) )
    & ! [U_4746,U_4744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4744),U_4746))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4744)),c_Int_OBit1(U_4746))) ) ),
    inference(miniscope,[status(thm)],[f_1431_2]) ).

fof(f_1431_4,plain,
    ( ! [U_4745,U_4747] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4745)),c_Int_OBit1(U_4747)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4745),U_4747)) )
    & ! [U_4746,U_4744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4744),U_4746))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4744)),c_Int_OBit1(U_4746))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1431_3]) ).

cnf(f_1431_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4744),U_4746))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4744)),c_Int_OBit1(U_4746))) ),
    inference(clausify,[status(thm)],[f_1431_4]) ).

cnf(f_1431_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4745)),c_Int_OBit1(U_4747)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4745),U_4747)) ),
    inference(clausify,[status(thm)],[f_1431_4]) ).

fof(f_1432_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J]) ).

fof(f_1432_2,plain,
    ! [U_4749,U_4748] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4748)),c_Int_OBit1(U_4749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4748),U_4749)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4748),U_4749))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4748)),c_Int_OBit1(U_4749))) ) ),
    inference(variable_rename,[status(thm)],[f_1432_1]) ).

fof(f_1432_3,plain,
    ( ! [U_4753,U_4751] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4751)),c_Int_OBit1(U_4753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4751),U_4753)) )
    & ! [U_4752,U_4750] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4750),U_4752))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4750)),c_Int_OBit1(U_4752))) ) ),
    inference(miniscope,[status(thm)],[f_1432_2]) ).

fof(f_1432_4,plain,
    ( ! [U_4751,U_4753] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4751)),c_Int_OBit1(U_4753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4751),U_4753)) )
    & ! [U_4752,U_4750] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4750),U_4752))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4750)),c_Int_OBit1(U_4752))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1432_3]) ).

cnf(f_1432_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4750),U_4752))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4750)),c_Int_OBit1(U_4752))) ),
    inference(clausify,[status(thm)],[f_1432_4]) ).

cnf(f_1432_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4751)),c_Int_OBit1(U_4753)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4751),U_4753)) ),
    inference(clausify,[status(thm)],[f_1432_4]) ).

fof(f_1433_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J]) ).

fof(f_1433_2,plain,
    ! [U_4754] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4754)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4754),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4754),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4754)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1433_1]) ).

fof(f_1433_3,plain,
    ( ! [U_4756] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4756)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4756),c_Int_OPls)) )
    & ! [U_4755] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4755),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4755)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1433_2]) ).

fof(f_1433_4,plain,
    ( ! [U_4756] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4756)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4756),c_Int_OPls)) )
    & ! [U_4755] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4755),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4755)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1433_3]) ).

cnf(f_1433_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4755),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4755)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1433_4]) ).

cnf(f_1433_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4756)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4756),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1433_4]) ).

fof(f_1434_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J]) ).

fof(f_1434_2,plain,
    ! [U_4757] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4757)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4757)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4757))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4757))) ) ),
    inference(variable_rename,[status(thm)],[f_1434_1]) ).

fof(f_1434_3,plain,
    ( ! [U_4759] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4759)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4759)) )
    & ! [U_4758] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4758))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4758))) ) ),
    inference(miniscope,[status(thm)],[f_1434_2]) ).

fof(f_1434_4,plain,
    ( ! [U_4759] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4759)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4759)) )
    & ! [U_4758] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4758))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4758))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1434_3]) ).

cnf(f_1434_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4758))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4758))) ),
    inference(clausify,[status(thm)],[f_1434_4]) ).

cnf(f_1434_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4759)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4759)) ),
    inference(clausify,[status(thm)],[f_1434_4]) ).

fof(f_1435_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J]) ).

fof(f_1435_2,plain,
    ! [U_4761,U_4760] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4760)),c_Int_OBit0(U_4761)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4760),U_4761)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4760),U_4761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4760)),c_Int_OBit0(U_4761))) ) ),
    inference(variable_rename,[status(thm)],[f_1435_1]) ).

fof(f_1435_3,plain,
    ( ! [U_4765,U_4763] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4763)),c_Int_OBit0(U_4765)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4763),U_4765)) )
    & ! [U_4764,U_4762] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4762),U_4764))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4762)),c_Int_OBit0(U_4764))) ) ),
    inference(miniscope,[status(thm)],[f_1435_2]) ).

fof(f_1435_4,plain,
    ( ! [U_4763,U_4765] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4763)),c_Int_OBit0(U_4765)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4763),U_4765)) )
    & ! [U_4764,U_4762] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4762),U_4764))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4762)),c_Int_OBit0(U_4764))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1435_3]) ).

cnf(f_1435_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4762),U_4764))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4762)),c_Int_OBit0(U_4764))) ),
    inference(clausify,[status(thm)],[f_1435_4]) ).

cnf(f_1435_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4763)),c_Int_OBit0(U_4765)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4763),U_4765)) ),
    inference(clausify,[status(thm)],[f_1435_4]) ).

fof(f_1436_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J]) ).

fof(f_1436_2,plain,
    ! [U_4767,U_4766] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4766)),c_Int_OBit0(U_4767)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4766),U_4767)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4766),U_4767))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4766)),c_Int_OBit0(U_4767))) ) ),
    inference(variable_rename,[status(thm)],[f_1436_1]) ).

fof(f_1436_3,plain,
    ( ! [U_4771,U_4769] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4769)),c_Int_OBit0(U_4771)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4769),U_4771)) )
    & ! [U_4770,U_4768] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4768),U_4770))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4768)),c_Int_OBit0(U_4770))) ) ),
    inference(miniscope,[status(thm)],[f_1436_2]) ).

fof(f_1436_4,plain,
    ( ! [U_4771,U_4769] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4769)),c_Int_OBit0(U_4771)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4769),U_4771)) )
    & ! [U_4770,U_4768] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4768),U_4770))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4768)),c_Int_OBit0(U_4770))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1436_3]) ).

cnf(f_1436_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4768),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4768)),c_Int_OBit0(U_4770))) ),
    inference(clausify,[status(thm)],[f_1436_4]) ).

cnf(f_1436_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4769)),c_Int_OBit0(U_4771)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4769),U_4771)) ),
    inference(clausify,[status(thm)],[f_1436_4]) ).

fof(f_1437_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(f_1437_2,plain,
    ! [U_4773,U_4772] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_4772)),c_Int_OBit1(U_4773)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4772),U_4773)),
    inference(variable_rename,[status(thm)],[f_1437_1]) ).

fof(f_1437_3,plain,
    ! [U_4773,U_4772] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_4772)),c_Int_OBit1(U_4773)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4772),U_4773)),
    inference(definitional_conversion,[status(esa)],[f_1437_2]) ).

cnf(f_1437_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_4772)),c_Int_OBit1(U_4773)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4772),U_4773)),
    inference(clausify,[status(thm)],[f_1437_3]) ).

fof(f_1438_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(f_1438_2,plain,
    ! [U_4775,U_4774] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_4774)),c_Int_OBit0(U_4775)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4774),U_4775)),
    inference(variable_rename,[status(thm)],[f_1438_1]) ).

fof(f_1438_3,plain,
    ! [U_4774,U_4775] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_4774)),c_Int_OBit0(U_4775)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4774),U_4775)),
    inference(definitional_conversion,[status(esa)],[f_1438_2]) ).

cnf(f_1438_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_4774)),c_Int_OBit0(U_4775)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4774),U_4775)),
    inference(clausify,[status(thm)],[f_1438_3]) ).

fof(f_1439_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(f_1439_2,plain,
    ! [U_4776] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4776)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_4776)),
    inference(variable_rename,[status(thm)],[f_1439_1]) ).

fof(f_1439_3,plain,
    ! [U_4776] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4776)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_4776)),
    inference(definitional_conversion,[status(esa)],[f_1439_2]) ).

cnf(f_1439_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_4776)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_4776)),
    inference(clausify,[status(thm)],[f_1439_3]) ).

fof(f_1440_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(f_1440_2,plain,
    ! [U_4778,U_4777] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_4777)),c_Int_OBit0(U_4778)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4777),U_4778)),
    inference(variable_rename,[status(thm)],[f_1440_1]) ).

fof(f_1440_3,plain,
    ! [U_4777,U_4778] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_4777)),c_Int_OBit0(U_4778)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4777),U_4778)),
    inference(definitional_conversion,[status(esa)],[f_1440_2]) ).

cnf(f_1440_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_4777)),c_Int_OBit0(U_4778)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4777),U_4778)),
    inference(clausify,[status(thm)],[f_1440_3]) ).

fof(f_1441_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(f_1441_2,plain,
    ! [U_4780,U_4779] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_4779)),c_Int_OBit1(U_4780)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4779),U_4780)),
    inference(variable_rename,[status(thm)],[f_1441_1]) ).

fof(f_1441_3,plain,
    ! [U_4779,U_4780] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_4779)),c_Int_OBit1(U_4780)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4779),U_4780)),
    inference(definitional_conversion,[status(esa)],[f_1441_2]) ).

cnf(f_1441_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_4779)),c_Int_OBit1(U_4780)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4779),U_4780)),
    inference(clausify,[status(thm)],[f_1441_3]) ).

fof(f_1442_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J]) ).

fof(f_1442_2,plain,
    ! [U_4781] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4781)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4781),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4781),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4781)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1442_1]) ).

fof(f_1442_3,plain,
    ( ! [U_4783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4783)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4783),c_Int_OMin)) )
    & ! [U_4782] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4782),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4782)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1442_2]) ).

fof(f_1442_4,plain,
    ( ! [U_4783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4783)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4783),c_Int_OMin)) )
    & ! [U_4782] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4782),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4782)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1442_3]) ).

cnf(f_1442_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4782),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4782)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

cnf(f_1442_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_4783)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4783),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

fof(f_1443_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J]) ).

fof(f_1443_2,plain,
    ! [U_4784] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4784)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4784)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4784))) ) ),
    inference(variable_rename,[status(thm)],[f_1443_1]) ).

fof(f_1443_3,plain,
    ( ! [U_4786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4786)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4786)) )
    & ! [U_4785] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4785))) ) ),
    inference(miniscope,[status(thm)],[f_1443_2]) ).

fof(f_1443_4,plain,
    ( ! [U_4786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4786)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4786)) )
    & ! [U_4785] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4785))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1443_3]) ).

cnf(f_1443_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4785))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4785))) ),
    inference(clausify,[status(thm)],[f_1443_4]) ).

cnf(f_1443_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4786)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4786)) ),
    inference(clausify,[status(thm)],[f_1443_4]) ).

fof(f_1444_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(f_1444_2,plain,
    ! [U_4788,U_4787] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4787))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4788))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4787)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4788)),
    inference(variable_rename,[status(thm)],[f_1444_1]) ).

fof(f_1444_3,plain,
    ! [U_4788,U_4787] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4787))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4788))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4787)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4788)),
    inference(definitional_conversion,[status(esa)],[f_1444_2]) ).

cnf(f_1444_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4787))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4788))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4787)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4788)),
    inference(clausify,[status(thm)],[f_1444_3]) ).

fof(f_1445_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0]) ).

fof(f_1445_2,plain,
    ! [U_4789] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4789))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4789))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4789)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4789)))) ) ),
    inference(variable_rename,[status(thm)],[f_1445_1]) ).

fof(f_1445_3,plain,
    ( ! [U_4791] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4791))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4791))) )
    & ! [U_4790] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4790)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4790)))) ) ),
    inference(miniscope,[status(thm)],[f_1445_2]) ).

fof(f_1445_4,plain,
    ( ! [U_4791] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4791))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4791))) )
    & ! [U_4790] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4790)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4790)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1445_3]) ).

cnf(f_1445_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4790)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4790)))) ),
    inference(clausify,[status(thm)],[f_1445_4]) ).

cnf(f_1445_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4791))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4791))) ),
    inference(clausify,[status(thm)],[f_1445_4]) ).

fof(f_1446_1,plain,
    ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
    inference(fof_nnf,[status(thm)],[fact_pred__Bit0]) ).

fof(f_1446_2,plain,
    ! [U_4792] : c_Int_Opred(c_Int_OBit0(U_4792)) = c_Int_OBit1(c_Int_Opred(U_4792)),
    inference(variable_rename,[status(thm)],[f_1446_1]) ).

fof(f_1446_3,plain,
    ! [U_4792] : c_Int_Opred(c_Int_OBit0(U_4792)) = c_Int_OBit1(c_Int_Opred(U_4792)),
    inference(definitional_conversion,[status(esa)],[f_1446_2]) ).

cnf(f_1446_4,plain,
    c_Int_Opred(c_Int_OBit0(U_4792)) = c_Int_OBit1(c_Int_Opred(U_4792)),
    inference(clausify,[status(thm)],[f_1446_3]) ).

fof(f_1447_1,plain,
    ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
    inference(fof_nnf,[status(thm)],[fact_pred__Bit1]) ).

fof(f_1447_2,plain,
    ! [U_4793] : c_Int_Opred(c_Int_OBit1(U_4793)) = c_Int_OBit0(U_4793),
    inference(variable_rename,[status(thm)],[f_1447_1]) ).

fof(f_1447_3,plain,
    ! [U_4793] : c_Int_Opred(c_Int_OBit1(U_4793)) = c_Int_OBit0(U_4793),
    inference(definitional_conversion,[status(esa)],[f_1447_2]) ).

cnf(f_1447_4,plain,
    c_Int_Opred(c_Int_OBit1(U_4793)) = c_Int_OBit0(U_4793),
    inference(clausify,[status(thm)],[f_1447_3]) ).

fof(f_1448_1,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).

fof(f_1448_2,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(definitional_conversion,[status(esa)],[f_1448_1]) ).

cnf(f_1448_3,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(clausify,[status(thm)],[f_1448_2]) ).

fof(f_1449_1,plain,
    ! [V_w_2,T_b] :
      ( ( ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) ) )
      | ~ class_Int_Oring__char__0(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).

fof(f_1449_2,plain,
    ! [U_4795,U_4794] :
      ( ( ( c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),c_Int_OBit0(U_4795)))
          | ~ c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),U_4795)) )
        & ( c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),U_4795))
          | ~ c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),c_Int_OBit0(U_4795))) ) )
      | ~ class_Int_Oring__char__0(U_4794)
      | ~ class_Int_Onumber__ring(U_4794) ),
    inference(variable_rename,[status(thm)],[f_1449_1]) ).

fof(f_1449_3,plain,
    ( ! [U_4794,U_4795] :
        ( c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),c_Int_OBit0(U_4795)))
        | ~ c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),U_4795))
        | ~ sP388(U_4794,U_4795) )
    & ! [U_4794,U_4795] :
        ( c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),U_4795))
        | ~ c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),c_Int_OBit0(U_4795)))
        | ~ sP388(U_4794,U_4795) )
    & ! [U_4794,U_4795] :
        ( sP388(U_4794,U_4795)
        | ~ class_Int_Oring__char__0(U_4794)
        | ~ class_Int_Onumber__ring(U_4794) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP388])],[f_1449_2]) ).

cnf(f_1449_4,plain,
    ( sP388(U_4794,U_4795)
    | ~ class_Int_Oring__char__0(U_4794)
    | ~ class_Int_Onumber__ring(U_4794) ),
    inference(clausify,[status(thm)],[f_1449_3]) ).

cnf(f_1449_5,plain,
    ( c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),U_4795))
    | ~ c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),c_Int_OBit0(U_4795)))
    | ~ sP388(U_4794,U_4795) ),
    inference(clausify,[status(thm)],[f_1449_3]) ).

cnf(f_1449_6,plain,
    ( c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),c_Int_OBit0(U_4795)))
    | ~ c_Int_Oiszero(U_4794,hAPP(c_Int_Onumber__class_Onumber__of(U_4794),U_4795))
    | ~ sP388(U_4794,U_4795) ),
    inference(clausify,[status(thm)],[f_1449_3]) ).

fof(f_1450_1,plain,
    ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
    inference(fof_nnf,[status(thm)],[fact_succ__Bit1]) ).

fof(f_1450_2,plain,
    ! [U_4796] : c_Int_Osucc(c_Int_OBit1(U_4796)) = c_Int_OBit0(c_Int_Osucc(U_4796)),
    inference(variable_rename,[status(thm)],[f_1450_1]) ).

fof(f_1450_3,plain,
    ! [U_4796] : c_Int_Osucc(c_Int_OBit1(U_4796)) = c_Int_OBit0(c_Int_Osucc(U_4796)),
    inference(definitional_conversion,[status(esa)],[f_1450_2]) ).

cnf(f_1450_4,plain,
    c_Int_Osucc(c_Int_OBit1(U_4796)) = c_Int_OBit0(c_Int_Osucc(U_4796)),
    inference(clausify,[status(thm)],[f_1450_3]) ).

fof(f_1451_1,plain,
    ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
    inference(fof_nnf,[status(thm)],[fact_succ__Bit0]) ).

fof(f_1451_2,plain,
    ! [U_4797] : c_Int_Osucc(c_Int_OBit0(U_4797)) = c_Int_OBit1(U_4797),
    inference(variable_rename,[status(thm)],[f_1451_1]) ).

fof(f_1451_3,plain,
    ! [U_4797] : c_Int_Osucc(c_Int_OBit0(U_4797)) = c_Int_OBit1(U_4797),
    inference(definitional_conversion,[status(esa)],[f_1451_2]) ).

cnf(f_1451_4,plain,
    c_Int_Osucc(c_Int_OBit0(U_4797)) = c_Int_OBit1(U_4797),
    inference(clausify,[status(thm)],[f_1451_3]) ).

fof(f_1452_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Bit0]) ).

fof(f_1452_2,plain,
    ! [U_4799,U_4798] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4798),c_Int_OBit0(U_4799)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4798),c_Groups_Ozero__class_Ozero(U_4798)),hAPP(c_Int_Onumber__class_Onumber__of(U_4798),U_4799))),hAPP(c_Int_Onumber__class_Onumber__of(U_4798),U_4799))
      | ~ class_Int_Onumber__ring(U_4798) ),
    inference(variable_rename,[status(thm)],[f_1452_1]) ).

fof(f_1452_3,plain,
    ! [U_4798,U_4799] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4798),c_Int_OBit0(U_4799)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4798),c_Groups_Ozero__class_Ozero(U_4798)),hAPP(c_Int_Onumber__class_Onumber__of(U_4798),U_4799))),hAPP(c_Int_Onumber__class_Onumber__of(U_4798),U_4799))
      | ~ class_Int_Onumber__ring(U_4798) ),
    inference(definitional_conversion,[status(esa)],[f_1452_2]) ).

cnf(f_1452_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4798),c_Int_OBit0(U_4799)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4798),c_Groups_Ozero__class_Ozero(U_4798)),hAPP(c_Int_Onumber__class_Onumber__of(U_4798),U_4799))),hAPP(c_Int_Onumber__class_Onumber__of(U_4798),U_4799))
    | ~ class_Int_Onumber__ring(U_4798) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

fof(f_1453_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J]) ).

fof(f_1453_2,plain,
    ! [U_4801,U_4800] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4800)),c_Int_OBit1(U_4801)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4800),U_4801)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4800),U_4801))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4800)),c_Int_OBit1(U_4801))) ) ),
    inference(variable_rename,[status(thm)],[f_1453_1]) ).

fof(f_1453_3,plain,
    ( ! [U_4805,U_4803] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4803)),c_Int_OBit1(U_4805)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4803),U_4805)) )
    & ! [U_4804,U_4802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),U_4804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4802)),c_Int_OBit1(U_4804))) ) ),
    inference(miniscope,[status(thm)],[f_1453_2]) ).

fof(f_1453_4,plain,
    ( ! [U_4803,U_4805] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4803)),c_Int_OBit1(U_4805)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4803),U_4805)) )
    & ! [U_4804,U_4802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),U_4804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4802)),c_Int_OBit1(U_4804))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1453_3]) ).

cnf(f_1453_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),U_4804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4802)),c_Int_OBit1(U_4804))) ),
    inference(clausify,[status(thm)],[f_1453_4]) ).

cnf(f_1453_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4803)),c_Int_OBit1(U_4805)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4803),U_4805)) ),
    inference(clausify,[status(thm)],[f_1453_4]) ).

fof(f_1454_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J]) ).

fof(f_1454_2,plain,
    ! [U_4807,U_4806] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4806)),c_Int_OBit1(U_4807)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4806),U_4807)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4806),U_4807))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4806)),c_Int_OBit1(U_4807))) ) ),
    inference(variable_rename,[status(thm)],[f_1454_1]) ).

fof(f_1454_3,plain,
    ( ! [U_4811,U_4809] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4809)),c_Int_OBit1(U_4811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4809),U_4811)) )
    & ! [U_4810,U_4808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4808),U_4810))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4808)),c_Int_OBit1(U_4810))) ) ),
    inference(miniscope,[status(thm)],[f_1454_2]) ).

fof(f_1454_4,plain,
    ( ! [U_4809,U_4811] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4809)),c_Int_OBit1(U_4811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4809),U_4811)) )
    & ! [U_4810,U_4808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4808),U_4810))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4808)),c_Int_OBit1(U_4810))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1454_3]) ).

cnf(f_1454_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4808),U_4810))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4808)),c_Int_OBit1(U_4810))) ),
    inference(clausify,[status(thm)],[f_1454_4]) ).

cnf(f_1454_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4809)),c_Int_OBit1(U_4811)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4809),U_4811)) ),
    inference(clausify,[status(thm)],[f_1454_4]) ).

fof(f_1455_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J]) ).

fof(f_1455_2,plain,
    ! [U_4813,U_4812] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4812)),c_Int_OBit0(U_4813)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4812),U_4813)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4812),U_4813))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4812)),c_Int_OBit0(U_4813))) ) ),
    inference(variable_rename,[status(thm)],[f_1455_1]) ).

fof(f_1455_3,plain,
    ( ! [U_4817,U_4815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4815)),c_Int_OBit0(U_4817)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4815),U_4817)) )
    & ! [U_4816,U_4814] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4814),U_4816))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4814)),c_Int_OBit0(U_4816))) ) ),
    inference(miniscope,[status(thm)],[f_1455_2]) ).

fof(f_1455_4,plain,
    ( ! [U_4815,U_4817] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4815)),c_Int_OBit0(U_4817)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4815),U_4817)) )
    & ! [U_4816,U_4814] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4814),U_4816))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4814)),c_Int_OBit0(U_4816))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1455_3]) ).

cnf(f_1455_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4814),U_4816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4814)),c_Int_OBit0(U_4816))) ),
    inference(clausify,[status(thm)],[f_1455_4]) ).

cnf(f_1455_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4815)),c_Int_OBit0(U_4817)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4815),U_4817)) ),
    inference(clausify,[status(thm)],[f_1455_4]) ).

fof(f_1456_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J]) ).

fof(f_1456_2,plain,
    ! [U_4819,U_4818] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4818)),c_Int_OBit0(U_4819)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4818),U_4819)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4818),U_4819))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4818)),c_Int_OBit0(U_4819))) ) ),
    inference(variable_rename,[status(thm)],[f_1456_1]) ).

fof(f_1456_3,plain,
    ( ! [U_4823,U_4821] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4821)),c_Int_OBit0(U_4823)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4821),U_4823)) )
    & ! [U_4822,U_4820] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4820),U_4822))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4820)),c_Int_OBit0(U_4822))) ) ),
    inference(miniscope,[status(thm)],[f_1456_2]) ).

fof(f_1456_4,plain,
    ( ! [U_4821,U_4823] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4821)),c_Int_OBit0(U_4823)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4821),U_4823)) )
    & ! [U_4822,U_4820] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4820),U_4822))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4820)),c_Int_OBit0(U_4822))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1456_3]) ).

cnf(f_1456_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4820),U_4822))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4820)),c_Int_OBit0(U_4822))) ),
    inference(clausify,[status(thm)],[f_1456_4]) ).

cnf(f_1456_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4821)),c_Int_OBit0(U_4823)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4821),U_4823)) ),
    inference(clausify,[status(thm)],[f_1456_4]) ).

fof(f_1457_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l),
    inference(fof_nnf,[status(thm)],[fact_mult__Bit1]) ).

fof(f_1457_2,plain,
    ! [U_4825,U_4824] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_4824)),U_4825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4824),U_4825))),U_4825),
    inference(variable_rename,[status(thm)],[f_1457_1]) ).

fof(f_1457_3,plain,
    ! [U_4824,U_4825] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_4824)),U_4825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4824),U_4825))),U_4825),
    inference(definitional_conversion,[status(esa)],[f_1457_2]) ).

cnf(f_1457_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_4824)),U_4825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4824),U_4825))),U_4825),
    inference(clausify,[status(thm)],[f_1457_3]) ).

fof(f_1458_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J]) ).

fof(f_1458_2,plain,
    ! [U_4826] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4826)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4826)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4826))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4826))) ) ),
    inference(variable_rename,[status(thm)],[f_1458_1]) ).

fof(f_1458_3,plain,
    ( ! [U_4828] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4828)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4828)) )
    & ! [U_4827] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4827))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4827))) ) ),
    inference(miniscope,[status(thm)],[f_1458_2]) ).

fof(f_1458_4,plain,
    ( ! [U_4828] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4828)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4828)) )
    & ! [U_4827] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4827))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4827))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1458_3]) ).

cnf(f_1458_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4827))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4827))) ),
    inference(clausify,[status(thm)],[f_1458_4]) ).

cnf(f_1458_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4828)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_4828)) ),
    inference(clausify,[status(thm)],[f_1458_4]) ).

fof(f_1459_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J]) ).

fof(f_1459_2,plain,
    ! [U_4829] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4829)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4829),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4829),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4829)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1459_1]) ).

fof(f_1459_3,plain,
    ( ! [U_4831] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4831)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4831),c_Int_OMin)) )
    & ! [U_4830] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4830),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4830)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1459_2]) ).

fof(f_1459_4,plain,
    ( ! [U_4831] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4831)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4831),c_Int_OMin)) )
    & ! [U_4830] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4830),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4830)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1459_3]) ).

cnf(f_1459_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4830),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4830)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1459_4]) ).

cnf(f_1459_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_4831)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4831),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1459_4]) ).

fof(f_1460_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I5_J]) ).

fof(f_1460_2,plain,
    ! [U_4832] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4832)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4832)),
    inference(variable_rename,[status(thm)],[f_1460_1]) ).

fof(f_1460_3,plain,
    ! [U_4832] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4832)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4832)),
    inference(definitional_conversion,[status(esa)],[f_1460_2]) ).

cnf(f_1460_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_4832)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4832)),
    inference(clausify,[status(thm)],[f_1460_3]) ).

fof(f_1461_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I6_J]) ).

fof(f_1461_2,plain,
    ! [U_4833] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4833)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4833)),
    inference(variable_rename,[status(thm)],[f_1461_1]) ).

fof(f_1461_3,plain,
    ! [U_4833] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4833)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4833)),
    inference(definitional_conversion,[status(esa)],[f_1461_2]) ).

cnf(f_1461_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4833)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_4833)),
    inference(clausify,[status(thm)],[f_1461_3]) ).

fof(f_1462_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I8_J]) ).

fof(f_1462_2,plain,
    ! [U_4835,U_4834] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_4834)),c_Int_OBit1(U_4835)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_4834)),U_4835)),
    inference(variable_rename,[status(thm)],[f_1462_1]) ).

fof(f_1462_3,plain,
    ! [U_4834,U_4835] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_4834)),c_Int_OBit1(U_4835)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_4834)),U_4835)),
    inference(definitional_conversion,[status(esa)],[f_1462_2]) ).

cnf(f_1462_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_4834)),c_Int_OBit1(U_4835)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_4834)),U_4835)),
    inference(clausify,[status(thm)],[f_1462_3]) ).

fof(f_1463_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))),
    inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(f_1463_2,plain,
    ! [U_4837,U_4836] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_4836)),c_Int_OBit1(U_4837)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4836),c_Int_Osucc(U_4837))),
    inference(variable_rename,[status(thm)],[f_1463_1]) ).

fof(f_1463_3,plain,
    ! [U_4836,U_4837] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_4836)),c_Int_OBit1(U_4837)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4836),c_Int_Osucc(U_4837))),
    inference(definitional_conversion,[status(esa)],[f_1463_2]) ).

cnf(f_1463_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_4836)),c_Int_OBit1(U_4837)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4836),c_Int_Osucc(U_4837))),
    inference(clausify,[status(thm)],[f_1463_3]) ).

fof(f_1464_1,plain,
    ! [V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0]) ).

fof(f_1464_2,plain,
    ! [U_4839,U_4838] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4838),c_Groups_Oone__class_Oone(U_4838)),c_Groups_Oone__class_Oone(U_4838))),hAPP(c_Int_Onumber__class_Onumber__of(U_4838),U_4839)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4838),c_Int_OBit0(U_4839))
      | ~ class_Int_Onumber__ring(U_4838) ),
    inference(variable_rename,[status(thm)],[f_1464_1]) ).

fof(f_1464_3,plain,
    ! [U_4838,U_4839] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4838),c_Groups_Oone__class_Oone(U_4838)),c_Groups_Oone__class_Oone(U_4838))),hAPP(c_Int_Onumber__class_Onumber__of(U_4838),U_4839)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4838),c_Int_OBit0(U_4839))
      | ~ class_Int_Onumber__ring(U_4838) ),
    inference(definitional_conversion,[status(esa)],[f_1464_2]) ).

cnf(f_1464_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4838),c_Groups_Oone__class_Oone(U_4838)),c_Groups_Oone__class_Oone(U_4838))),hAPP(c_Int_Onumber__class_Onumber__of(U_4838),U_4839)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4838),c_Int_OBit0(U_4839))
    | ~ class_Int_Onumber__ring(U_4838) ),
    inference(clausify,[status(thm)],[f_1464_3]) ).

fof(f_1465_1,plain,
    ! [V_n] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_number__of1]) ).

fof(f_1465_2,plain,
    ! [U_4840] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4840))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4840)))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4840))) ),
    inference(variable_rename,[status(thm)],[f_1465_1]) ).

fof(f_1465_3,plain,
    ( ! [U_4840] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4840))))
        | ~ sP389(U_4840) )
    & ! [U_4840] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4840))))
        | ~ sP389(U_4840) )
    & ! [U_4840] :
        ( sP389(U_4840)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4840))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP389])],[f_1465_2]) ).

cnf(f_1465_4,plain,
    ( sP389(U_4840)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4840))) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

cnf(f_1465_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4840))))
    | ~ sP389(U_4840) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

cnf(f_1465_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4840))))
    | ~ sP389(U_4840) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

fof(f_1466_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__2__right]) ).

fof(f_1466_2,plain,
    ! [U_4842,U_4841] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4841),U_4842),hAPP(c_Int_Onumber__class_Onumber__of(U_4841),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4841),U_4842),U_4842)
      | ~ class_Int_Onumber__ring(U_4841) ),
    inference(variable_rename,[status(thm)],[f_1466_1]) ).

fof(f_1466_3,plain,
    ! [U_4841,U_4842] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4841),U_4842),hAPP(c_Int_Onumber__class_Onumber__of(U_4841),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4841),U_4842),U_4842)
      | ~ class_Int_Onumber__ring(U_4841) ),
    inference(definitional_conversion,[status(esa)],[f_1466_2]) ).

cnf(f_1466_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4841),U_4842),hAPP(c_Int_Onumber__class_Onumber__of(U_4841),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4841),U_4842),U_4842)
    | ~ class_Int_Onumber__ring(U_4841) ),
    inference(clausify,[status(thm)],[f_1466_3]) ).

fof(f_1467_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__2]) ).

fof(f_1467_2,plain,
    ! [U_4844,U_4843] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4843),hAPP(c_Int_Onumber__class_Onumber__of(U_4843),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4843),U_4844),U_4844)
      | ~ class_Int_Onumber__ring(U_4843) ),
    inference(variable_rename,[status(thm)],[f_1467_1]) ).

fof(f_1467_3,plain,
    ! [U_4843,U_4844] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4843),hAPP(c_Int_Onumber__class_Onumber__of(U_4843),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4843),U_4844),U_4844)
      | ~ class_Int_Onumber__ring(U_4843) ),
    inference(definitional_conversion,[status(esa)],[f_1467_2]) ).

cnf(f_1467_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4843),hAPP(c_Int_Onumber__class_Onumber__of(U_4843),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4843),U_4844),U_4844)
    | ~ class_Int_Onumber__ring(U_4843) ),
    inference(clausify,[status(thm)],[f_1467_3]) ).

fof(f_1468_1,plain,
    ! [T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two]) ).

fof(f_1468_2,plain,
    ! [U_4845] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4845),c_Groups_Oone__class_Oone(U_4845)),c_Groups_Oone__class_Oone(U_4845)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4845),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_4845) ),
    inference(variable_rename,[status(thm)],[f_1468_1]) ).

fof(f_1468_3,plain,
    ! [U_4845] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4845),c_Groups_Oone__class_Oone(U_4845)),c_Groups_Oone__class_Oone(U_4845)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4845),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_4845) ),
    inference(definitional_conversion,[status(esa)],[f_1468_2]) ).

cnf(f_1468_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4845),c_Groups_Oone__class_Oone(U_4845)),c_Groups_Oone__class_Oone(U_4845)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4845),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_4845) ),
    inference(clausify,[status(thm)],[f_1468_3]) ).

fof(f_1469_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).

fof(f_1469_2,plain,
    ! [U_4847,U_4846] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4846),U_4847),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_4846)
          | U_4847 != c_Groups_Ozero__class_Ozero(U_4846) )
        & ( U_4847 = c_Groups_Ozero__class_Ozero(U_4846)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4846),U_4847),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_4846) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4846) ),
    inference(variable_rename,[status(thm)],[f_1469_1]) ).

fof(f_1469_3,plain,
    ( ! [U_4846,U_4847] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4846),U_4847),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_4846)
        | U_4847 != c_Groups_Ozero__class_Ozero(U_4846)
        | ~ sP390(U_4846,U_4847) )
    & ! [U_4846,U_4847] :
        ( U_4847 = c_Groups_Ozero__class_Ozero(U_4846)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4846),U_4847),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_4846)
        | ~ sP390(U_4846,U_4847) )
    & ! [U_4846,U_4847] :
        ( sP390(U_4846,U_4847)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_4846) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP390])],[f_1469_2]) ).

cnf(f_1469_4,plain,
    ( sP390(U_4846,U_4847)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4846) ),
    inference(clausify,[status(thm)],[f_1469_3]) ).

cnf(f_1469_5,plain,
    ( U_4847 = c_Groups_Ozero__class_Ozero(U_4846)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4846),U_4847),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_4846)
    | ~ sP390(U_4846,U_4847) ),
    inference(clausify,[status(thm)],[f_1469_3]) ).

cnf(f_1469_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4846),U_4847),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_4846)
    | U_4847 != c_Groups_Ozero__class_Ozero(U_4846)
    | ~ sP390(U_4846,U_4847) ),
    inference(clausify,[status(thm)],[f_1469_3]) ).

fof(f_1470_1,plain,
    ! [T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__power2]) ).

fof(f_1470_2,plain,
    ! [U_4848] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4848),c_Groups_Ozero__class_Ozero(U_4848)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_4848)
      | ~ class_Rings_Osemiring__1(U_4848) ),
    inference(variable_rename,[status(thm)],[f_1470_1]) ).

fof(f_1470_3,plain,
    ! [U_4848] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4848),c_Groups_Ozero__class_Ozero(U_4848)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_4848)
      | ~ class_Rings_Osemiring__1(U_4848) ),
    inference(definitional_conversion,[status(esa)],[f_1470_2]) ).

cnf(f_1470_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4848),c_Groups_Ozero__class_Ozero(U_4848)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_4848)
    | ~ class_Rings_Osemiring__1(U_4848) ),
    inference(clausify,[status(thm)],[f_1470_3]) ).

fof(f_1471_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_numeral__2__eq__2]) ).

fof(f_1471_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1471_1]) ).

cnf(f_1471_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1471_2]) ).

fof(f_1472_1,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I115_J]) ).

fof(f_1472_2,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(definitional_conversion,[status(esa)],[f_1472_1]) ).

cnf(f_1472_3,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(clausify,[status(thm)],[f_1472_2]) ).

fof(f_1473_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).

fof(f_1473_2,plain,
    ! [U_4850,U_4849] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4849),U_4850),U_4850) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4849),U_4850),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Ocomm__semiring__1(U_4849) ),
    inference(variable_rename,[status(thm)],[f_1473_1]) ).

fof(f_1473_3,plain,
    ! [U_4849,U_4850] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4849),U_4850),U_4850) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4849),U_4850),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Ocomm__semiring__1(U_4849) ),
    inference(definitional_conversion,[status(esa)],[f_1473_2]) ).

cnf(f_1473_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4849),U_4850),U_4850) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4849),U_4850),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Ocomm__semiring__1(U_4849) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

fof(f_1474_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__square]) ).

fof(f_1474_2,plain,
    ! [U_4852,U_4851] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4851),U_4852),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4851),U_4852),U_4852)
      | ~ class_Groups_Omonoid__mult(U_4851) ),
    inference(variable_rename,[status(thm)],[f_1474_1]) ).

fof(f_1474_3,plain,
    ! [U_4851,U_4852] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4851),U_4852),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4851),U_4852),U_4852)
      | ~ class_Groups_Omonoid__mult(U_4851) ),
    inference(definitional_conversion,[status(esa)],[f_1474_2]) ).

cnf(f_1474_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4851),U_4852),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4851),U_4852),U_4852)
    | ~ class_Groups_Omonoid__mult(U_4851) ),
    inference(clausify,[status(thm)],[f_1474_3]) ).

fof(f_1475_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).

fof(f_1475_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(definitional_conversion,[status(esa)],[f_1475_1]) ).

cnf(f_1475_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_1475_2]) ).

fof(f_1476_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(f_1476_2,plain,
    ! [U_4853] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4853) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4853)),
    inference(variable_rename,[status(thm)],[f_1476_1]) ).

fof(f_1476_3,plain,
    ! [U_4853] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4853) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4853)),
    inference(definitional_conversion,[status(esa)],[f_1476_2]) ).

cnf(f_1476_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4853) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4853)),
    inference(clausify,[status(thm)],[f_1476_3]) ).

fof(f_1477_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(f_1477_2,plain,
    ! [U_4854] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4854),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4854)),
    inference(variable_rename,[status(thm)],[f_1477_1]) ).

fof(f_1477_3,plain,
    ! [U_4854] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4854),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4854)),
    inference(definitional_conversion,[status(esa)],[f_1477_2]) ).

cnf(f_1477_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4854),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4854)),
    inference(clausify,[status(thm)],[f_1477_3]) ).

fof(f_1478_1,plain,
    ! [T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__power2]) ).

fof(f_1478_2,plain,
    ! [U_4855] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4855),c_Groups_Oone__class_Oone(U_4855)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_4855)
      | ~ class_Rings_Osemiring__1(U_4855) ),
    inference(variable_rename,[status(thm)],[f_1478_1]) ).

fof(f_1478_3,plain,
    ! [U_4855] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4855),c_Groups_Oone__class_Oone(U_4855)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_4855)
      | ~ class_Rings_Osemiring__1(U_4855) ),
    inference(definitional_conversion,[status(esa)],[f_1478_2]) ).

cnf(f_1478_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4855),c_Groups_Oone__class_Oone(U_4855)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_4855)
    | ~ class_Rings_Osemiring__1(U_4855) ),
    inference(clausify,[status(thm)],[f_1478_3]) ).

fof(f_1479_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__minus]) ).

fof(f_1479_2,plain,
    ! [U_4857,U_4856] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4856),hAPP(c_Groups_Ouminus__class_Ouminus(U_4856),U_4857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4856),U_4857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_4856) ),
    inference(variable_rename,[status(thm)],[f_1479_1]) ).

fof(f_1479_3,plain,
    ! [U_4856,U_4857] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4856),hAPP(c_Groups_Ouminus__class_Ouminus(U_4856),U_4857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4856),U_4857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_4856) ),
    inference(definitional_conversion,[status(esa)],[f_1479_2]) ).

cnf(f_1479_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4856),hAPP(c_Groups_Ouminus__class_Ouminus(U_4856),U_4857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4856),U_4857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(U_4856) ),
    inference(clausify,[status(thm)],[f_1479_3]) ).

fof(f_1480_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__2]) ).

fof(f_1480_2,plain,
    ! [U_4858] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4858) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4858),U_4858),
    inference(variable_rename,[status(thm)],[f_1480_1]) ).

fof(f_1480_3,plain,
    ! [U_4858] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4858) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4858),U_4858),
    inference(definitional_conversion,[status(esa)],[f_1480_2]) ).

cnf(f_1480_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4858) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4858),U_4858),
    inference(clausify,[status(thm)],[f_1480_3]) ).

fof(f_1481_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__2__right]) ).

fof(f_1481_2,plain,
    ! [U_4859] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4859),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4859),U_4859),
    inference(variable_rename,[status(thm)],[f_1481_1]) ).

fof(f_1481_3,plain,
    ! [U_4859] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4859),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4859),U_4859),
    inference(definitional_conversion,[status(esa)],[f_1481_2]) ).

cnf(f_1481_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4859),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4859),U_4859),
    inference(clausify,[status(thm)],[f_1481_3]) ).

fof(f_1482_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__even__eq]) ).

fof(f_1482_2,plain,
    ! [U_4862,U_4861,U_4860] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),U_4861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4862)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),U_4861),U_4862)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_4860) ),
    inference(variable_rename,[status(thm)],[f_1482_1]) ).

fof(f_1482_3,plain,
    ! [U_4860,U_4861,U_4862] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),U_4861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4862)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),U_4861),U_4862)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_4860) ),
    inference(definitional_conversion,[status(esa)],[f_1482_2]) ).

cnf(f_1482_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),U_4861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4862)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),hAPP(hAPP(c_Power_Opower__class_Opower(U_4860),U_4861),U_4862)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(U_4860) ),
    inference(clausify,[status(thm)],[f_1482_3]) ).

fof(f_1483_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I3_J]) ).

fof(f_1483_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1483_1]) ).

cnf(f_1483_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1483_2]) ).

fof(f_1484_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I3_J]) ).

fof(f_1484_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1484_1]) ).

cnf(f_1484_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1484_2]) ).

fof(f_1485_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__power2]) ).

fof(f_1485_2,plain,
    ! [U_4864,U_4863] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4863),hAPP(hAPP(c_Power_Opower__class_Opower(U_4863),U_4864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4863),U_4864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_4863) ),
    inference(variable_rename,[status(thm)],[f_1485_1]) ).

fof(f_1485_3,plain,
    ! [U_4863,U_4864] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4863),hAPP(hAPP(c_Power_Opower__class_Opower(U_4863),U_4864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4863),U_4864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_4863) ),
    inference(definitional_conversion,[status(esa)],[f_1485_2]) ).

cnf(f_1485_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4863),hAPP(hAPP(c_Power_Opower__class_Opower(U_4863),U_4864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4863),U_4864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_4863) ),
    inference(clausify,[status(thm)],[f_1485_3]) ).

fof(f_1486_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__abs]) ).

fof(f_1486_2,plain,
    ! [U_4866,U_4865] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4865),hAPP(c_Groups_Oabs__class_Oabs(U_4865),U_4866)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4865),U_4866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_4865) ),
    inference(variable_rename,[status(thm)],[f_1486_1]) ).

fof(f_1486_3,plain,
    ! [U_4865,U_4866] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4865),hAPP(c_Groups_Oabs__class_Oabs(U_4865),U_4866)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4865),U_4866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_4865) ),
    inference(definitional_conversion,[status(esa)],[f_1486_2]) ).

cnf(f_1486_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4865),hAPP(c_Groups_Oabs__class_Oabs(U_4865),U_4866)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4865),U_4866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_4865) ),
    inference(clausify,[status(thm)],[f_1486_3]) ).

fof(f_1487_1,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_nat__1__add__1]) ).

fof(f_1487_2,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(definitional_conversion,[status(esa)],[f_1487_1]) ).

cnf(f_1487_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(clausify,[status(thm)],[f_1487_2]) ).

fof(f_1488_1,plain,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_mod2__Suc__Suc]) ).

fof(f_1488_2,plain,
    ! [U_4867] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4867)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4867,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(variable_rename,[status(thm)],[f_1488_1]) ).

fof(f_1488_3,plain,
    ! [U_4867] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4867)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4867,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1488_2]) ).

cnf(f_1488_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4867)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4867,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1488_3]) ).

fof(f_1489_1,plain,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_nnf,[status(thm)],[fact_div2__Suc__Suc]) ).

fof(f_1489_2,plain,
    ! [U_4868] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4868))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4868),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(variable_rename,[status(thm)],[f_1489_1]) ).

fof(f_1489_3,plain,
    ! [U_4868] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4868))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4868),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(definitional_conversion,[status(esa)],[f_1489_2]) ).

cnf(f_1489_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4868))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4868),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_1489_3]) ).

fof(f_1490_1,plain,
    ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))),
    inference(fof_nnf,[status(thm)],[fact_zmod__number__of__Bit0]) ).

fof(f_1490_2,plain,
    ! [U_4870,U_4869] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4869)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4870))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4869),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4870))),
    inference(variable_rename,[status(thm)],[f_1490_1]) ).

fof(f_1490_3,plain,
    ! [U_4869,U_4870] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4869)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4870))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4869),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4870))),
    inference(definitional_conversion,[status(esa)],[f_1490_2]) ).

cnf(f_1490_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4869)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4870))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4869),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4870))),
    inference(clausify,[status(thm)],[f_1490_3]) ).

fof(f_1491_1,plain,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m,
    inference(fof_nnf,[status(thm)],[fact_add__self__div__2]) ).

fof(f_1491_2,plain,
    ! [U_4871] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4871),U_4871)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_4871,
    inference(variable_rename,[status(thm)],[f_1491_1]) ).

fof(f_1491_3,plain,
    ! [U_4871] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4871),U_4871)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_4871,
    inference(definitional_conversion,[status(esa)],[f_1491_2]) ).

cnf(f_1491_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4871),U_4871)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_4871,
    inference(clausify,[status(thm)],[f_1491_3]) ).

fof(f_1492_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq]) ).

fof(f_1492_2,plain,
    ! [U_4874,U_4873,U_4872] :
      ( U_4873 = U_4874
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4874))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4873))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4872),U_4873),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4872),U_4874),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_4872) ),
    inference(variable_rename,[status(thm)],[f_1492_1]) ).

fof(f_1492_3,plain,
    ! [U_4872,U_4873,U_4874] :
      ( U_4873 = U_4874
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4874))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4873))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4872),U_4873),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4872),U_4874),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_4872) ),
    inference(definitional_conversion,[status(esa)],[f_1492_2]) ).

cnf(f_1492_4,plain,
    ( U_4873 = U_4874
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4874))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),c_Groups_Ozero__class_Ozero(U_4872)),U_4873))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4872),U_4873),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4872),U_4874),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(U_4872) ),
    inference(clausify,[status(thm)],[f_1492_3]) ).

fof(f_1493_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le]) ).

fof(f_1493_2,plain,
    ! [U_4877,U_4876,U_4875] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),U_4876),U_4877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),c_Groups_Ozero__class_Ozero(U_4875)),U_4877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),hAPP(hAPP(c_Power_Opower__class_Opower(U_4875),U_4876),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4875),U_4877),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_4875) ),
    inference(variable_rename,[status(thm)],[f_1493_1]) ).

fof(f_1493_3,plain,
    ! [U_4877,U_4876,U_4875] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),U_4876),U_4877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),c_Groups_Ozero__class_Ozero(U_4875)),U_4877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),hAPP(hAPP(c_Power_Opower__class_Opower(U_4875),U_4876),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4875),U_4877),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_4875) ),
    inference(definitional_conversion,[status(esa)],[f_1493_2]) ).

cnf(f_1493_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),U_4876),U_4877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),c_Groups_Ozero__class_Ozero(U_4875)),U_4877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4875),hAPP(hAPP(c_Power_Opower__class_Opower(U_4875),U_4876),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4875),U_4877),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_4875) ),
    inference(clausify,[status(thm)],[f_1493_3]) ).

fof(f_1494_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power2]) ).

fof(f_1494_2,plain,
    ! [U_4879,U_4878] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4878),c_Groups_Ozero__class_Ozero(U_4878)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4878),U_4879),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_4878) ),
    inference(variable_rename,[status(thm)],[f_1494_1]) ).

fof(f_1494_3,plain,
    ! [U_4878,U_4879] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4878),c_Groups_Ozero__class_Ozero(U_4878)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4878),U_4879),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_4878) ),
    inference(definitional_conversion,[status(esa)],[f_1494_2]) ).

cnf(f_1494_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4878),c_Groups_Ozero__class_Ozero(U_4878)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4878),U_4879),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_4878) ),
    inference(clausify,[status(thm)],[f_1494_3]) ).

fof(f_1495_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).

fof(f_1495_2,plain,
    ! [U_4881,U_4880] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4880),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | U_4881 = c_Groups_Ozero__class_Ozero(U_4880) )
        & ( U_4881 != c_Groups_Ozero__class_Ozero(U_4880)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4880),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(U_4880) ),
    inference(variable_rename,[status(thm)],[f_1495_1]) ).

fof(f_1495_3,plain,
    ( ! [U_4880,U_4881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4880),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | U_4881 = c_Groups_Ozero__class_Ozero(U_4880)
        | ~ sP391(U_4880,U_4881) )
    & ! [U_4880,U_4881] :
        ( U_4881 != c_Groups_Ozero__class_Ozero(U_4880)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4880),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ sP391(U_4880,U_4881) )
    & ! [U_4880,U_4881] :
        ( sP391(U_4880,U_4881)
        | ~ class_Rings_Olinordered__idom(U_4880) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP391])],[f_1495_2]) ).

cnf(f_1495_4,plain,
    ( sP391(U_4880,U_4881)
    | ~ class_Rings_Olinordered__idom(U_4880) ),
    inference(clausify,[status(thm)],[f_1495_3]) ).

cnf(f_1495_5,plain,
    ( U_4881 != c_Groups_Ozero__class_Ozero(U_4880)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4880),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ sP391(U_4880,U_4881) ),
    inference(clausify,[status(thm)],[f_1495_3]) ).

cnf(f_1495_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4880),c_Groups_Ozero__class_Ozero(U_4880)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4880),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | U_4881 = c_Groups_Ozero__class_Ozero(U_4880)
    | ~ sP391(U_4880,U_4881) ),
    inference(clausify,[status(thm)],[f_1495_3]) ).

fof(f_1496_1,plain,
    ! [V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__less__0]) ).

fof(f_1496_2,plain,
    ! [U_4883,U_4882] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4882),hAPP(hAPP(c_Power_Opower__class_Opower(U_4882),U_4883),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_4882)))
      | ~ class_Rings_Olinordered__idom(U_4882) ),
    inference(variable_rename,[status(thm)],[f_1496_1]) ).

fof(f_1496_3,plain,
    ! [U_4882,U_4883] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4882),hAPP(hAPP(c_Power_Opower__class_Opower(U_4882),U_4883),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_4882)))
      | ~ class_Rings_Olinordered__idom(U_4882) ),
    inference(definitional_conversion,[status(esa)],[f_1496_2]) ).

cnf(f_1496_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4882),hAPP(hAPP(c_Power_Opower__class_Opower(U_4882),U_4883),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_4882)))
    | ~ class_Rings_Olinordered__idom(U_4882) ),
    inference(clausify,[status(thm)],[f_1496_3]) ).

fof(f_1497_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).

fof(f_1497_2,plain,
    ! [U_4886,U_4885,U_4884] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4884),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4885),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4886),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_4884)
          | U_4886 != c_Groups_Ozero__class_Ozero(U_4884)
          | U_4885 != c_Groups_Ozero__class_Ozero(U_4884) )
        & ( ( U_4886 = c_Groups_Ozero__class_Ozero(U_4884)
            & U_4885 = c_Groups_Ozero__class_Ozero(U_4884) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4884),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4885),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4886),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_4884) ) )
      | ~ class_Rings_Olinordered__idom(U_4884) ),
    inference(variable_rename,[status(thm)],[f_1497_1]) ).

fof(f_1497_3,plain,
    ( ! [U_4884,U_4885,U_4886] :
        ( U_4886 = c_Groups_Ozero__class_Ozero(U_4884)
        | ~ sP392(U_4884,U_4885,U_4886) )
    & ! [U_4884,U_4885,U_4886] :
        ( U_4885 = c_Groups_Ozero__class_Ozero(U_4884)
        | ~ sP392(U_4884,U_4885,U_4886) )
    & ! [U_4884,U_4885,U_4886] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4884),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4885),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4886),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_4884)
        | U_4886 != c_Groups_Ozero__class_Ozero(U_4884)
        | U_4885 != c_Groups_Ozero__class_Ozero(U_4884)
        | ~ sP393(U_4884,U_4885,U_4886) )
    & ! [U_4884,U_4885,U_4886] :
        ( sP392(U_4884,U_4885,U_4886)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4884),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4885),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4886),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_4884)
        | ~ sP393(U_4884,U_4885,U_4886) )
    & ! [U_4884,U_4885,U_4886] :
        ( sP393(U_4884,U_4885,U_4886)
        | ~ class_Rings_Olinordered__idom(U_4884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP392,sP393])],[f_1497_2]) ).

cnf(f_1497_4,plain,
    ( sP393(U_4884,U_4885,U_4886)
    | ~ class_Rings_Olinordered__idom(U_4884) ),
    inference(clausify,[status(thm)],[f_1497_3]) ).

cnf(f_1497_5,plain,
    ( sP392(U_4884,U_4885,U_4886)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4884),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4885),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4886),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_4884)
    | ~ sP393(U_4884,U_4885,U_4886) ),
    inference(clausify,[status(thm)],[f_1497_3]) ).

cnf(f_1497_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4884),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4885),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4884),U_4886),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_4884)
    | U_4886 != c_Groups_Ozero__class_Ozero(U_4884)
    | U_4885 != c_Groups_Ozero__class_Ozero(U_4884)
    | ~ sP393(U_4884,U_4885,U_4886) ),
    inference(clausify,[status(thm)],[f_1497_3]) ).

cnf(f_1497_7,plain,
    ( U_4885 = c_Groups_Ozero__class_Ozero(U_4884)
    | ~ sP392(U_4884,U_4885,U_4886) ),
    inference(clausify,[status(thm)],[f_1497_3]) ).

cnf(f_1497_8,plain,
    ( U_4886 = c_Groups_Ozero__class_Ozero(U_4884)
    | ~ sP392(U_4884,U_4885,U_4886) ),
    inference(clausify,[status(thm)],[f_1497_3]) ).

fof(f_1498_1,plain,
    ! [V_w,T_b] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w))
      | ~ class_Int_Onumber(T_b)
      | ~ class_Groups_Omonoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of]) ).

fof(f_1498_2,plain,
    ! [U_4888,U_4887] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4887),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4887),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888)),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888))
      | ~ class_Int_Onumber(U_4887)
      | ~ class_Groups_Omonoid__mult(U_4887) ),
    inference(variable_rename,[status(thm)],[f_1498_1]) ).

fof(f_1498_3,plain,
    ! [U_4888,U_4887] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4887),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4887),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888)),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888))
      | ~ class_Int_Onumber(U_4887)
      | ~ class_Groups_Omonoid__mult(U_4887) ),
    inference(definitional_conversion,[status(esa)],[f_1498_2]) ).

cnf(f_1498_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4887),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4887),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888)),hAPP(c_Int_Onumber__class_Onumber__of(U_4887),U_4888))
    | ~ class_Int_Onumber(U_4887)
    | ~ class_Groups_Omonoid__mult(U_4887) ),
    inference(clausify,[status(thm)],[f_1498_3]) ).

fof(f_1499_1,plain,
    ! [V_n] :
      ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(fof_nnf,[status(thm)],[fact_less__2__cases]) ).

fof(f_1499_2,plain,
    ! [U_4889] :
      ( U_4889 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_4889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4889),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[f_1499_1]) ).

fof(f_1499_3,plain,
    ! [U_4889] :
      ( U_4889 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_4889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4889),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(definitional_conversion,[status(esa)],[f_1499_2]) ).

cnf(f_1499_4,plain,
    ( U_4889 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4889),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(clausify,[status(thm)],[f_1499_3]) ).

fof(f_1500_1,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__2]) ).

fof(f_1500_2,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1500_1]) ).

cnf(f_1500_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1500_2]) ).

fof(f_1501_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
          | ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
            & V_a_2 != c_Groups_Oone__class_Oone(T_b) ) )
        & ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_a_2 = c_Groups_Oone__class_Oone(T_b)
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).

fof(f_1501_2,plain,
    ! [U_4891,U_4890] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4890),U_4891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_4890)
          | ( U_4891 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4890),c_Groups_Oone__class_Oone(U_4890))
            & U_4891 != c_Groups_Oone__class_Oone(U_4890) ) )
        & ( U_4891 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4890),c_Groups_Oone__class_Oone(U_4890))
          | U_4891 = c_Groups_Oone__class_Oone(U_4890)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4890),U_4891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_4890) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4890) ),
    inference(variable_rename,[status(thm)],[f_1501_1]) ).

fof(f_1501_3,plain,
    ( ! [U_4890,U_4891] :
        ( U_4891 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4890),c_Groups_Oone__class_Oone(U_4890))
        | ~ sP394(U_4890,U_4891) )
    & ! [U_4890,U_4891] :
        ( U_4891 != c_Groups_Oone__class_Oone(U_4890)
        | ~ sP394(U_4890,U_4891) )
    & ! [U_4890,U_4891] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4890),U_4891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_4890)
        | sP394(U_4890,U_4891)
        | ~ sP395(U_4890,U_4891) )
    & ! [U_4890,U_4891] :
        ( U_4891 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4890),c_Groups_Oone__class_Oone(U_4890))
        | U_4891 = c_Groups_Oone__class_Oone(U_4890)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4890),U_4891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_4890)
        | ~ sP395(U_4890,U_4891) )
    & ! [U_4890,U_4891] :
        ( sP395(U_4890,U_4891)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_4890) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP394,sP395])],[f_1501_2]) ).

cnf(f_1501_4,plain,
    ( sP395(U_4890,U_4891)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4890) ),
    inference(clausify,[status(thm)],[f_1501_3]) ).

cnf(f_1501_5,plain,
    ( U_4891 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4890),c_Groups_Oone__class_Oone(U_4890))
    | U_4891 = c_Groups_Oone__class_Oone(U_4890)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4890),U_4891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_4890)
    | ~ sP395(U_4890,U_4891) ),
    inference(clausify,[status(thm)],[f_1501_3]) ).

cnf(f_1501_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4890),U_4891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_4890)
    | sP394(U_4890,U_4891)
    | ~ sP395(U_4890,U_4891) ),
    inference(clausify,[status(thm)],[f_1501_3]) ).

cnf(f_1501_7,plain,
    ( U_4891 != c_Groups_Oone__class_Oone(U_4890)
    | ~ sP394(U_4890,U_4891) ),
    inference(clausify,[status(thm)],[f_1501_3]) ).

cnf(f_1501_8,plain,
    ( U_4891 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4890),c_Groups_Oone__class_Oone(U_4890))
    | ~ sP394(U_4890,U_4891) ),
    inference(clausify,[status(thm)],[f_1501_3]) ).

fof(f_1502_1,plain,
    ! [V_n,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).

fof(f_1502_2,plain,
    ! [U_4894,U_4893,U_4892] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4892),hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),U_4894)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),U_4894))
      | ~ class_Rings_Ocomm__semiring__1(U_4892) ),
    inference(variable_rename,[status(thm)],[f_1502_1]) ).

fof(f_1502_3,plain,
    ! [U_4893,U_4894,U_4892] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4892),hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),U_4894)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),U_4894))
      | ~ class_Rings_Ocomm__semiring__1(U_4892) ),
    inference(definitional_conversion,[status(esa)],[f_1502_2]) ).

cnf(f_1502_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4892),hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),U_4894)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4892),U_4893),U_4894))
    | ~ class_Rings_Ocomm__semiring__1(U_4892) ),
    inference(clausify,[status(thm)],[f_1502_3]) ).

fof(f_1503_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus__even]) ).

fof(f_1503_2,plain,
    ! [U_4897,U_4896,U_4895] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4895),hAPP(c_Groups_Ouminus__class_Ouminus(U_4895),U_4896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4897)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4895),U_4896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4897))
      | ~ class_Rings_Oring__1(U_4895) ),
    inference(variable_rename,[status(thm)],[f_1503_1]) ).

fof(f_1503_3,plain,
    ! [U_4896,U_4895,U_4897] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4895),hAPP(c_Groups_Ouminus__class_Ouminus(U_4895),U_4896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4897)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4895),U_4896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4897))
      | ~ class_Rings_Oring__1(U_4895) ),
    inference(definitional_conversion,[status(esa)],[f_1503_2]) ).

cnf(f_1503_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4895),hAPP(c_Groups_Ouminus__class_Ouminus(U_4895),U_4896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4897)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4895),U_4896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4897))
    | ~ class_Rings_Oring__1(U_4895) ),
    inference(clausify,[status(thm)],[f_1503_3]) ).

fof(f_1504_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less]) ).

fof(f_1504_2,plain,
    ! [U_4900,U_4899,U_4898] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4899),U_4900))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4900))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),hAPP(hAPP(c_Power_Opower__class_Opower(U_4898),U_4899),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4898),U_4900),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_4898) ),
    inference(variable_rename,[status(thm)],[f_1504_1]) ).

fof(f_1504_3,plain,
    ! [U_4898,U_4899,U_4900] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4899),U_4900))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4900))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),hAPP(hAPP(c_Power_Opower__class_Opower(U_4898),U_4899),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4898),U_4900),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_4898) ),
    inference(definitional_conversion,[status(esa)],[f_1504_2]) ).

cnf(f_1504_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),U_4899),U_4900))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4898),c_Groups_Ozero__class_Ozero(U_4898)),U_4900))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4898),hAPP(hAPP(c_Power_Opower__class_Opower(U_4898),U_4899),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4898),U_4900),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_4898) ),
    inference(clausify,[status(thm)],[f_1504_3]) ).

fof(f_1505_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero]) ).

fof(f_1505_2,plain,
    ! [U_4903,U_4902,U_4901] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4901),c_Groups_Ozero__class_Ozero(U_4901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4901),hAPP(hAPP(c_Power_Opower__class_Opower(U_4901),U_4902),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4901),U_4903),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_4901) ),
    inference(variable_rename,[status(thm)],[f_1505_1]) ).

fof(f_1505_3,plain,
    ! [U_4902,U_4901,U_4903] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4901),c_Groups_Ozero__class_Ozero(U_4901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4901),hAPP(hAPP(c_Power_Opower__class_Opower(U_4901),U_4902),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4901),U_4903),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_4901) ),
    inference(definitional_conversion,[status(esa)],[f_1505_2]) ).

cnf(f_1505_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4901),c_Groups_Ozero__class_Ozero(U_4901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4901),hAPP(hAPP(c_Power_Opower__class_Opower(U_4901),U_4902),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4901),U_4903),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_4901) ),
    inference(clausify,[status(thm)],[f_1505_3]) ).

fof(f_1506_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).

fof(f_1506_2,plain,
    ! [U_4906,U_4905,U_4904] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4904),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4906),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4904)))
          | U_4906 != c_Groups_Ozero__class_Ozero(U_4904)
          | U_4905 != c_Groups_Ozero__class_Ozero(U_4904) )
        & ( ( U_4906 = c_Groups_Ozero__class_Ozero(U_4904)
            & U_4905 = c_Groups_Ozero__class_Ozero(U_4904) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4904),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4906),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4904))) ) )
      | ~ class_Rings_Olinordered__idom(U_4904) ),
    inference(variable_rename,[status(thm)],[f_1506_1]) ).

fof(f_1506_3,plain,
    ( ! [U_4904,U_4905,U_4906] :
        ( U_4906 = c_Groups_Ozero__class_Ozero(U_4904)
        | ~ sP396(U_4904,U_4905,U_4906) )
    & ! [U_4904,U_4905,U_4906] :
        ( U_4905 = c_Groups_Ozero__class_Ozero(U_4904)
        | ~ sP396(U_4904,U_4905,U_4906) )
    & ! [U_4904,U_4905,U_4906] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4904),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4906),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4904)))
        | U_4906 != c_Groups_Ozero__class_Ozero(U_4904)
        | U_4905 != c_Groups_Ozero__class_Ozero(U_4904)
        | ~ sP397(U_4904,U_4905,U_4906) )
    & ! [U_4904,U_4905,U_4906] :
        ( sP396(U_4904,U_4905,U_4906)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4904),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4906),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4904)))
        | ~ sP397(U_4904,U_4905,U_4906) )
    & ! [U_4904,U_4905,U_4906] :
        ( sP397(U_4904,U_4905,U_4906)
        | ~ class_Rings_Olinordered__idom(U_4904) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP396,sP397])],[f_1506_2]) ).

cnf(f_1506_4,plain,
    ( sP397(U_4904,U_4905,U_4906)
    | ~ class_Rings_Olinordered__idom(U_4904) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_5,plain,
    ( sP396(U_4904,U_4905,U_4906)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4904),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4906),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4904)))
    | ~ sP397(U_4904,U_4905,U_4906) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4904),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4904),U_4906),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4904)))
    | U_4906 != c_Groups_Ozero__class_Ozero(U_4904)
    | U_4905 != c_Groups_Ozero__class_Ozero(U_4904)
    | ~ sP397(U_4904,U_4905,U_4906) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_7,plain,
    ( U_4905 = c_Groups_Ozero__class_Ozero(U_4904)
    | ~ sP396(U_4904,U_4905,U_4906) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_8,plain,
    ( U_4906 = c_Groups_Ozero__class_Ozero(U_4904)
    | ~ sP396(U_4904,U_4905,U_4906) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

fof(f_1507_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(f_1507_2,plain,
    ! [U_4909,U_4908,U_4907] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4907),hAPP(hAPP(c_Power_Opower__class_Opower(U_4907),U_4908),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4907),U_4909),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4907)))
      | ~ class_Rings_Olinordered__idom(U_4907) ),
    inference(variable_rename,[status(thm)],[f_1507_1]) ).

fof(f_1507_3,plain,
    ! [U_4908,U_4909,U_4907] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4907),hAPP(hAPP(c_Power_Opower__class_Opower(U_4907),U_4908),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4907),U_4909),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4907)))
      | ~ class_Rings_Olinordered__idom(U_4907) ),
    inference(definitional_conversion,[status(esa)],[f_1507_2]) ).

cnf(f_1507_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4907),hAPP(hAPP(c_Power_Opower__class_Opower(U_4907),U_4908),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4907),U_4909),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_4907)))
    | ~ class_Rings_Olinordered__idom(U_4907) ),
    inference(clausify,[status(thm)],[f_1507_3]) ).

fof(f_1508_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).

fof(f_1508_2,plain,
    ! [U_4912,U_4911,U_4910] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4910),c_Groups_Ozero__class_Ozero(U_4910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4911),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4912),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( U_4912 = c_Groups_Ozero__class_Ozero(U_4910)
            & U_4911 = c_Groups_Ozero__class_Ozero(U_4910) ) )
        & ( U_4912 != c_Groups_Ozero__class_Ozero(U_4910)
          | U_4911 != c_Groups_Ozero__class_Ozero(U_4910)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4910),c_Groups_Ozero__class_Ozero(U_4910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4911),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4912),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(U_4910) ),
    inference(variable_rename,[status(thm)],[f_1508_1]) ).

fof(f_1508_3,plain,
    ( ! [U_4910,U_4911,U_4912] :
        ( U_4912 = c_Groups_Ozero__class_Ozero(U_4910)
        | ~ sP398(U_4910,U_4911,U_4912) )
    & ! [U_4910,U_4911,U_4912] :
        ( U_4911 = c_Groups_Ozero__class_Ozero(U_4910)
        | ~ sP398(U_4910,U_4911,U_4912) )
    & ! [U_4910,U_4911,U_4912] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4910),c_Groups_Ozero__class_Ozero(U_4910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4911),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4912),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | sP398(U_4910,U_4911,U_4912)
        | ~ sP399(U_4910,U_4911,U_4912) )
    & ! [U_4910,U_4911,U_4912] :
        ( U_4912 != c_Groups_Ozero__class_Ozero(U_4910)
        | U_4911 != c_Groups_Ozero__class_Ozero(U_4910)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4910),c_Groups_Ozero__class_Ozero(U_4910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4911),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4912),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ sP399(U_4910,U_4911,U_4912) )
    & ! [U_4910,U_4911,U_4912] :
        ( sP399(U_4910,U_4911,U_4912)
        | ~ class_Rings_Olinordered__idom(U_4910) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP398,sP399])],[f_1508_2]) ).

cnf(f_1508_4,plain,
    ( sP399(U_4910,U_4911,U_4912)
    | ~ class_Rings_Olinordered__idom(U_4910) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_5,plain,
    ( U_4912 != c_Groups_Ozero__class_Ozero(U_4910)
    | U_4911 != c_Groups_Ozero__class_Ozero(U_4910)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4910),c_Groups_Ozero__class_Ozero(U_4910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4911),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4912),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ sP399(U_4910,U_4911,U_4912) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4910),c_Groups_Ozero__class_Ozero(U_4910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4911),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4910),U_4912),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | sP398(U_4910,U_4911,U_4912)
    | ~ sP399(U_4910,U_4911,U_4912) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_7,plain,
    ( U_4911 = c_Groups_Ozero__class_Ozero(U_4910)
    | ~ sP398(U_4910,U_4911,U_4912) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_8,plain,
    ( U_4912 = c_Groups_Ozero__class_Ozero(U_4910)
    | ~ sP398(U_4910,U_4911,U_4912) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

fof(f_1509_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__sum]) ).

fof(f_1509_2,plain,
    ! [U_4915,U_4914,U_4913] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),U_4914),U_4915)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),U_4914),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),U_4915),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4913),hAPP(c_Int_Onumber__class_Onumber__of(U_4913),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4914)),U_4915))
      | ~ class_Int_Onumber__ring(U_4913) ),
    inference(variable_rename,[status(thm)],[f_1509_1]) ).

fof(f_1509_3,plain,
    ! [U_4915,U_4913,U_4914] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),U_4914),U_4915)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),U_4914),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),U_4915),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4913),hAPP(c_Int_Onumber__class_Onumber__of(U_4913),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4914)),U_4915))
      | ~ class_Int_Onumber__ring(U_4913) ),
    inference(definitional_conversion,[status(esa)],[f_1509_2]) ).

cnf(f_1509_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),U_4914),U_4915)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4913),hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),U_4914),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4913),U_4915),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4913),hAPP(c_Int_Onumber__class_Onumber__of(U_4913),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4914)),U_4915))
    | ~ class_Int_Onumber__ring(U_4913) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

fof(f_1510_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H]) ).

fof(f_1510_2,plain,
    ! [U_4918,U_4917,U_4916] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4916),U_4917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4918))))
      | ~ class_Rings_Olinordered__idom(U_4916) ),
    inference(variable_rename,[status(thm)],[f_1510_1]) ).

fof(f_1510_3,plain,
    ! [U_4916,U_4917,U_4918] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4916),U_4917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4918))))
      | ~ class_Rings_Olinordered__idom(U_4916) ),
    inference(definitional_conversion,[status(esa)],[f_1510_2]) ).

cnf(f_1510_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4916),U_4917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4918))))
    | ~ class_Rings_Olinordered__idom(U_4916) ),
    inference(clausify,[status(thm)],[f_1510_3]) ).

fof(f_1511_1,plain,
    ! [V_n,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J]) ).

fof(f_1511_2,plain,
    ! [U_4921,U_4920,U_4919] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4921))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),U_4920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),U_4921)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),U_4921)))
      | ~ class_Rings_Ocomm__semiring__1(U_4919) ),
    inference(variable_rename,[status(thm)],[f_1511_1]) ).

fof(f_1511_3,plain,
    ! [U_4919,U_4920,U_4921] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4921))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),U_4920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),U_4921)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),U_4921)))
      | ~ class_Rings_Ocomm__semiring__1(U_4919) ),
    inference(definitional_conversion,[status(esa)],[f_1511_2]) ).

cnf(f_1511_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4921))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),U_4920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4919),hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),U_4921)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4919),U_4920),U_4921)))
    | ~ class_Rings_Ocomm__semiring__1(U_4919) ),
    inference(clausify,[status(thm)],[f_1511_3]) ).

fof(f_1512_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__odd__eq]) ).

fof(f_1512_2,plain,
    ! [U_4924,U_4923,U_4922] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),U_4923),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4924))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4922),U_4923),hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),U_4923),U_4924)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_4922) ),
    inference(variable_rename,[status(thm)],[f_1512_1]) ).

fof(f_1512_3,plain,
    ! [U_4922,U_4923,U_4924] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),U_4923),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4924))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4922),U_4923),hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),U_4923),U_4924)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_4922) ),
    inference(definitional_conversion,[status(esa)],[f_1512_2]) ).

cnf(f_1512_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),U_4923),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4924))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4922),U_4923),hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),hAPP(hAPP(c_Power_Opower__class_Opower(U_4922),U_4923),U_4924)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(U_4922) ),
    inference(clausify,[status(thm)],[f_1512_3]) ).

fof(f_1513_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus1__even]) ).

fof(f_1513_2,plain,
    ! [U_4926,U_4925] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4925),hAPP(c_Groups_Ouminus__class_Ouminus(U_4925),c_Groups_Oone__class_Oone(U_4925))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4926)) = c_Groups_Oone__class_Oone(U_4925)
      | ~ class_Rings_Oring__1(U_4925) ),
    inference(variable_rename,[status(thm)],[f_1513_1]) ).

fof(f_1513_3,plain,
    ! [U_4925,U_4926] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4925),hAPP(c_Groups_Ouminus__class_Ouminus(U_4925),c_Groups_Oone__class_Oone(U_4925))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4926)) = c_Groups_Oone__class_Oone(U_4925)
      | ~ class_Rings_Oring__1(U_4925) ),
    inference(definitional_conversion,[status(esa)],[f_1513_2]) ).

cnf(f_1513_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4925),hAPP(c_Groups_Ouminus__class_Ouminus(U_4925),c_Groups_Oone__class_Oone(U_4925))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4926)) = c_Groups_Oone__class_Oone(U_4925)
    | ~ class_Rings_Oring__1(U_4925) ),
    inference(clausify,[status(thm)],[f_1513_3]) ).

fof(f_1514_1,plain,
    ! [V_v,V_w] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(f_1514_2,plain,
    ! [U_4928,U_4927] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4928))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4927))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4928)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4928))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4927))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927))) ) ),
    inference(variable_rename,[status(thm)],[f_1514_1]) ).

fof(f_1514_3,plain,
    ( ! [U_4932,U_4930] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4932))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4930))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4932)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4930))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4930))) )
    & ! [U_4931,U_4929] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4931))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4929))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4929))) ) ),
    inference(miniscope,[status(thm)],[f_1514_2]) ).

fof(f_1514_4,plain,
    ( ! [U_4930,U_4932] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4932))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4930))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4932)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4930))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4930))) )
    & ! [U_4931,U_4929] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4931))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4929))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4929))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1514_3]) ).

cnf(f_1514_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4931))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4929))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4929))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4929))) ),
    inference(clausify,[status(thm)],[f_1514_4]) ).

cnf(f_1514_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4932))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4930))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4932)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4930))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4930))) ),
    inference(clausify,[status(thm)],[f_1514_4]) ).

fof(f_1515_1,plain,
    ! [V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod2__gr__0]) ).

fof(f_1515_2,plain,
    ! [U_4933] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4933,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4933,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4933,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4933,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(variable_rename,[status(thm)],[f_1515_1]) ).

fof(f_1515_3,plain,
    ( ! [U_4935] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_4934] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4934,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4934,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(miniscope,[status(thm)],[f_1515_2]) ).

fof(f_1515_4,plain,
    ( ! [U_4935] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_4934] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4934,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4934,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1515_3]) ).

cnf(f_1515_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4934,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4934,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(clausify,[status(thm)],[f_1515_4]) ).

cnf(f_1515_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1515_4]) ).

fof(f_1516_1,plain,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__2__gt__zero]) ).

fof(f_1516_2,plain,
    ! [U_4936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4936),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4936)) ),
    inference(variable_rename,[status(thm)],[f_1516_1]) ).

fof(f_1516_3,plain,
    ! [U_4936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4936),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4936)) ),
    inference(definitional_conversion,[status(esa)],[f_1516_2]) ).

cnf(f_1516_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4936),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4936)) ),
    inference(clausify,[status(thm)],[f_1516_3]) ).

fof(f_1517_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__diff]) ).

fof(f_1517_2,plain,
    ! [U_4939,U_4938,U_4937] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4937),hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),U_4938),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),U_4939),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4937),hAPP(c_Int_Onumber__class_Onumber__of(U_4937),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4938)),U_4939))
      | ~ class_Int_Onumber__ring(U_4937) ),
    inference(variable_rename,[status(thm)],[f_1517_1]) ).

fof(f_1517_3,plain,
    ! [U_4937,U_4938,U_4939] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4937),hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),U_4938),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),U_4939),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4937),hAPP(c_Int_Onumber__class_Onumber__of(U_4937),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4938)),U_4939))
      | ~ class_Int_Onumber__ring(U_4937) ),
    inference(definitional_conversion,[status(esa)],[f_1517_2]) ).

cnf(f_1517_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4937),hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),U_4938),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4937),U_4939),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4937),hAPP(c_Int_Onumber__class_Onumber__of(U_4937),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4938)),U_4939))
    | ~ class_Int_Onumber__ring(U_4937) ),
    inference(clausify,[status(thm)],[f_1517_3]) ).

fof(f_1518_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le]) ).

fof(f_1518_2,plain,
    ! [U_4942,U_4941,U_4940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4940),c_Groups_Ozero__class_Ozero(U_4940)),U_4941))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4940),c_Groups_Ozero__class_Ozero(U_4940)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4940),U_4941),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4942)))))
      | ~ class_Rings_Olinordered__idom(U_4940) ),
    inference(variable_rename,[status(thm)],[f_1518_1]) ).

fof(f_1518_3,plain,
    ! [U_4940,U_4941,U_4942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4940),c_Groups_Ozero__class_Ozero(U_4940)),U_4941))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4940),c_Groups_Ozero__class_Ozero(U_4940)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4940),U_4941),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4942)))))
      | ~ class_Rings_Olinordered__idom(U_4940) ),
    inference(definitional_conversion,[status(esa)],[f_1518_2]) ).

cnf(f_1518_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4940),c_Groups_Ozero__class_Ozero(U_4940)),U_4941))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4940),c_Groups_Ozero__class_Ozero(U_4940)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4940),U_4941),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4942)))))
    | ~ class_Rings_Olinordered__idom(U_4940) ),
    inference(clausify,[status(thm)],[f_1518_3]) ).

fof(f_1519_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero]) ).

fof(f_1519_2,plain,
    ! [U_4945,U_4944,U_4943] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4943),hAPP(hAPP(c_Power_Opower__class_Opower(U_4943),U_4944),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4945)))),c_Groups_Ozero__class_Ozero(U_4943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4943),U_4944),c_Groups_Ozero__class_Ozero(U_4943)))
      | ~ class_Rings_Olinordered__idom(U_4943) ),
    inference(variable_rename,[status(thm)],[f_1519_1]) ).

fof(f_1519_3,plain,
    ! [U_4943,U_4944,U_4945] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4943),hAPP(hAPP(c_Power_Opower__class_Opower(U_4943),U_4944),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4945)))),c_Groups_Ozero__class_Ozero(U_4943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4943),U_4944),c_Groups_Ozero__class_Ozero(U_4943)))
      | ~ class_Rings_Olinordered__idom(U_4943) ),
    inference(definitional_conversion,[status(esa)],[f_1519_2]) ).

cnf(f_1519_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4943),hAPP(hAPP(c_Power_Opower__class_Opower(U_4943),U_4944),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4945)))),c_Groups_Ozero__class_Ozero(U_4943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4943),U_4944),c_Groups_Ozero__class_Ozero(U_4943)))
    | ~ class_Rings_Olinordered__idom(U_4943) ),
    inference(clausify,[status(thm)],[f_1519_3]) ).

fof(f_1520_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus1__odd]) ).

fof(f_1520_2,plain,
    ! [U_4947,U_4946] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4946),hAPP(c_Groups_Ouminus__class_Ouminus(U_4946),c_Groups_Oone__class_Oone(U_4946))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4947))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4946),c_Groups_Oone__class_Oone(U_4946))
      | ~ class_Rings_Oring__1(U_4946) ),
    inference(variable_rename,[status(thm)],[f_1520_1]) ).

fof(f_1520_3,plain,
    ! [U_4946,U_4947] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4946),hAPP(c_Groups_Ouminus__class_Ouminus(U_4946),c_Groups_Oone__class_Oone(U_4946))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4947))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4946),c_Groups_Oone__class_Oone(U_4946))
      | ~ class_Rings_Oring__1(U_4946) ),
    inference(definitional_conversion,[status(esa)],[f_1520_2]) ).

cnf(f_1520_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4946),hAPP(c_Groups_Ouminus__class_Ouminus(U_4946),c_Groups_Oone__class_Oone(U_4946))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4947))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4946),c_Groups_Oone__class_Oone(U_4946))
    | ~ class_Rings_Oring__1(U_4946) ),
    inference(clausify,[status(thm)],[f_1520_3]) ).

fof(f_1521_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__m1__even]) ).

fof(f_1521_2,plain,
    ! [U_4949,U_4948] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4948),hAPP(c_Int_Onumber__class_Onumber__of(U_4948),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4949)) = c_Groups_Oone__class_Oone(U_4948)
      | ~ class_Int_Onumber__ring(U_4948) ),
    inference(variable_rename,[status(thm)],[f_1521_1]) ).

fof(f_1521_3,plain,
    ! [U_4948,U_4949] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4948),hAPP(c_Int_Onumber__class_Onumber__of(U_4948),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4949)) = c_Groups_Oone__class_Oone(U_4948)
      | ~ class_Int_Onumber__ring(U_4948) ),
    inference(definitional_conversion,[status(esa)],[f_1521_2]) ).

cnf(f_1521_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4948),hAPP(c_Int_Onumber__class_Onumber__of(U_4948),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4949)) = c_Groups_Oone__class_Oone(U_4948)
    | ~ class_Int_Onumber__ring(U_4948) ),
    inference(clausify,[status(thm)],[f_1521_3]) ).

fof(f_1522_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__m1__odd]) ).

fof(f_1522_2,plain,
    ! [U_4951,U_4950] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4950),hAPP(c_Int_Onumber__class_Onumber__of(U_4950),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4951))) = hAPP(c_Int_Onumber__class_Onumber__of(U_4950),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4950) ),
    inference(variable_rename,[status(thm)],[f_1522_1]) ).

fof(f_1522_3,plain,
    ! [U_4950,U_4951] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4950),hAPP(c_Int_Onumber__class_Onumber__of(U_4950),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4951))) = hAPP(c_Int_Onumber__class_Onumber__of(U_4950),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4950) ),
    inference(definitional_conversion,[status(esa)],[f_1522_2]) ).

cnf(f_1522_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4950),hAPP(c_Int_Onumber__class_Onumber__of(U_4950),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4951))) = hAPP(c_Int_Onumber__class_Onumber__of(U_4950),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4950) ),
    inference(clausify,[status(thm)],[f_1522_3]) ).

fof(f_1523_1,plain,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero]) ).

fof(f_1523_2,plain,
    ! [U_4952] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4952)) ),
    inference(variable_rename,[status(thm)],[f_1523_1]) ).

fof(f_1523_3,plain,
    ! [U_4952] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4952)) ),
    inference(definitional_conversion,[status(esa)],[f_1523_2]) ).

cnf(f_1523_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4952),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4952)) ),
    inference(clausify,[status(thm)],[f_1523_3]) ).

fof(f_1524_1,plain,
    ! [V_k] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
          & ( hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) )
        | V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__of__code]) ).

fof(f_1524_2,plain,
    ! [U_4953] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_4953) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4953,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
          & ( hAPP(c_Code__Numeral_Oint__of,U_4953) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4953,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) )
        | U_4953 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,U_4953) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_4953 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1524_1]) ).

fof(f_1524_3,plain,
    ( ! [U_4955] :
        ( ( ( hAPP(c_Code__Numeral_Oint__of,U_4955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4955,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
          & ( hAPP(c_Code__Numeral_Oint__of,U_4955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4955,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) )
        | U_4955 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_4954] :
        ( hAPP(c_Code__Numeral_Oint__of,U_4954) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_4954 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1524_2]) ).

fof(f_1524_4,plain,
    ( ! [U_4955] :
        ( hAPP(c_Code__Numeral_Oint__of,U_4955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4955,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | ~ sP400(U_4955) )
    & ! [U_4955] :
        ( hAPP(c_Code__Numeral_Oint__of,U_4955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4955,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | ~ sP400(U_4955) )
    & ! [U_4955] :
        ( sP400(U_4955)
        | U_4955 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_4954] :
        ( hAPP(c_Code__Numeral_Oint__of,U_4954) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_4954 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP400])],[f_1524_3]) ).

cnf(f_1524_5,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_4954) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_4954 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1524_4]) ).

cnf(f_1524_6,plain,
    ( sP400(U_4955)
    | U_4955 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1524_4]) ).

cnf(f_1524_7,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_4955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4955,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | ~ sP400(U_4955) ),
    inference(clausify,[status(thm)],[f_1524_4]) ).

cnf(f_1524_8,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_4955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4955,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | ~ sP400(U_4955) ),
    inference(clausify,[status(thm)],[f_1524_4]) ).

fof(f_1525_1,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_one__code__numeral__code]) ).

fof(f_1525_2,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_1525_1]) ).

cnf(f_1525_3,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1525_2]) ).

fof(f_1526_1,plain,
    ! [V_r_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).

fof(f_1526_2,plain,
    ! [U_4957,U_4956] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4956),U_4957),hAPP(c_Int_Onumber__class_Onumber__of(U_4956),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),U_4957)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),U_4957))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4956),U_4957),hAPP(c_Int_Onumber__class_Onumber__of(U_4956),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(U_4956)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4956) ),
    inference(variable_rename,[status(thm)],[f_1526_1]) ).

fof(f_1526_3,plain,
    ( ! [U_4957,U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4956),U_4957),hAPP(c_Int_Onumber__class_Onumber__of(U_4956),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),U_4957))
        | ~ sP401(U_4957,U_4956) )
    & ! [U_4957,U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),U_4957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4956),U_4957),hAPP(c_Int_Onumber__class_Onumber__of(U_4956),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ sP401(U_4957,U_4956) )
    & ! [U_4957,U_4956] :
        ( sP401(U_4957,U_4956)
        | ~ class_Int_Onumber__ring(U_4956)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_4956) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP401])],[f_1526_2]) ).

cnf(f_1526_4,plain,
    ( sP401(U_4957,U_4956)
    | ~ class_Int_Onumber__ring(U_4956)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4956) ),
    inference(clausify,[status(thm)],[f_1526_3]) ).

cnf(f_1526_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),U_4957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4956),U_4957),hAPP(c_Int_Onumber__class_Onumber__of(U_4956),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ sP401(U_4957,U_4956) ),
    inference(clausify,[status(thm)],[f_1526_3]) ).

cnf(f_1526_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4956),U_4957),hAPP(c_Int_Onumber__class_Onumber__of(U_4956),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),c_Groups_Ozero__class_Ozero(U_4956)),U_4957))
    | ~ sP401(U_4957,U_4956) ),
    inference(clausify,[status(thm)],[f_1526_3]) ).

fof(f_1527_1,plain,
    ! [V_r,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_half__gt__zero]) ).

fof(f_1527_2,plain,
    ! [U_4959,U_4958] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4958),c_Groups_Ozero__class_Ozero(U_4958)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4958),U_4959),hAPP(c_Int_Onumber__class_Onumber__of(U_4958),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4958),c_Groups_Ozero__class_Ozero(U_4958)),U_4959))
      | ~ class_Int_Onumber__ring(U_4958)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4958) ),
    inference(variable_rename,[status(thm)],[f_1527_1]) ).

fof(f_1527_3,plain,
    ! [U_4958,U_4959] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4958),c_Groups_Ozero__class_Ozero(U_4958)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4958),U_4959),hAPP(c_Int_Onumber__class_Onumber__of(U_4958),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4958),c_Groups_Ozero__class_Ozero(U_4958)),U_4959))
      | ~ class_Int_Onumber__ring(U_4958)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4958) ),
    inference(definitional_conversion,[status(esa)],[f_1527_2]) ).

cnf(f_1527_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4958),c_Groups_Ozero__class_Ozero(U_4958)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4958),U_4959),hAPP(c_Int_Onumber__class_Onumber__of(U_4958),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4958),c_Groups_Ozero__class_Ozero(U_4958)),U_4959))
    | ~ class_Int_Onumber__ring(U_4958)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4958) ),
    inference(clausify,[status(thm)],[f_1527_3]) ).

fof(f_1528_1,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J]) ).

fof(f_1528_2,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1528_1]) ).

cnf(f_1528_3,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1528_2]) ).

fof(f_1529_1,plain,
    ! [V_k_2,V_f_2,V_n_2,V_m_2] :
      ( ? [B_i] :
          ( hAPP(V_f_2,B_i) = V_k_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__intermed__int__val]) ).

fof(f_1529_2,plain,
    ! [U_4965,U_4964,U_4963,U_4962] :
      ( ? [U_4961] :
          ( hAPP(U_4964,U_4961) = U_4965
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4961),U_4963))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),U_4961)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4965),hAPP(U_4964,U_4963)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4964,U_4962)),U_4965))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4962),U_4963))
      | ? [U_4960] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4964,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4960),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4964,U_4960)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4960),U_4963))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),U_4960)) ) ),
    inference(variable_rename,[status(thm)],[f_1529_1]) ).

fof(f_1529_3,plain,
    ! [U_4965,U_4964,U_4963,U_4962] :
      ( ? [U_4961] :
          ( hAPP(U_4964,U_4961) = U_4965
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4961),U_4963))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),U_4961)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4965),hAPP(U_4964,U_4963)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4964,U_4962)),U_4965))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4962),U_4963))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4964,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4964,sK83(U_4965,U_4964,U_4963,U_4962))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),U_4963))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK83(U_4965,U_4964,U_4963,U_4962))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_4960,sK83(U_4965,U_4964,U_4963,U_4962))],[f_1529_2]) ).

fof(f_1529_4,plain,
    ! [U_4965,U_4964,U_4963,U_4962] :
      ( ( hAPP(U_4964,sK84(U_4965,U_4964,U_4963,U_4962)) = U_4965
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK84(U_4965,U_4964,U_4963,U_4962)),U_4963))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK84(U_4965,U_4964,U_4963,U_4962))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4965),hAPP(U_4964,U_4963)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4964,U_4962)),U_4965))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4962),U_4963))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4964,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4964,sK83(U_4965,U_4964,U_4963,U_4962))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),U_4963))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK83(U_4965,U_4964,U_4963,U_4962))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_4961,sK84(U_4965,U_4964,U_4963,U_4962))],[f_1529_3]) ).

fof(f_1529_5,plain,
    ( ! [U_4962,U_4963,U_4964,U_4965] :
        ( hAPP(U_4964,sK84(U_4965,U_4964,U_4963,U_4962)) = U_4965
        | ~ sP403(U_4962,U_4963,U_4964,U_4965) )
    & ! [U_4962,U_4963,U_4964,U_4965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK84(U_4965,U_4964,U_4963,U_4962)),U_4963))
        | ~ sP403(U_4962,U_4963,U_4964,U_4965) )
    & ! [U_4962,U_4963,U_4964,U_4965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK84(U_4965,U_4964,U_4963,U_4962)))
        | ~ sP403(U_4962,U_4963,U_4964,U_4965) )
    & ! [U_4962,U_4963,U_4964,U_4965] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4964,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4964,sK83(U_4965,U_4964,U_4963,U_4962))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP402(U_4962,U_4963,U_4964,U_4965) )
    & ! [U_4962,U_4963,U_4964,U_4965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),U_4963))
        | ~ sP402(U_4962,U_4963,U_4964,U_4965) )
    & ! [U_4962,U_4963,U_4964,U_4965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK83(U_4965,U_4964,U_4963,U_4962)))
        | ~ sP402(U_4962,U_4963,U_4964,U_4965) )
    & ! [U_4962,U_4963,U_4964,U_4965] :
        ( sP403(U_4962,U_4963,U_4964,U_4965)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4965),hAPP(U_4964,U_4963)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4964,U_4962)),U_4965))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4962),U_4963))
        | sP402(U_4962,U_4963,U_4964,U_4965) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP402,sP403])],[f_1529_4]) ).

cnf(f_1529_6,plain,
    ( sP403(U_4962,U_4963,U_4964,U_4965)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4965),hAPP(U_4964,U_4963)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4964,U_4962)),U_4965))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4962),U_4963))
    | sP402(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

cnf(f_1529_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK83(U_4965,U_4964,U_4963,U_4962)))
    | ~ sP402(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

cnf(f_1529_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),U_4963))
    | ~ sP402(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

cnf(f_1529_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_4964,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK83(U_4965,U_4964,U_4963,U_4962)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4964,sK83(U_4965,U_4964,U_4963,U_4962))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP402(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

cnf(f_1529_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4962),sK84(U_4965,U_4964,U_4963,U_4962)))
    | ~ sP403(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

cnf(f_1529_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK84(U_4965,U_4964,U_4963,U_4962)),U_4963))
    | ~ sP403(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

cnf(f_1529_12,plain,
    ( hAPP(U_4964,sK84(U_4965,U_4964,U_4963,U_4962)) = U_4965
    | ~ sP403(U_4962,U_4963,U_4964,U_4965) ),
    inference(clausify,[status(thm)],[f_1529_5]) ).

fof(f_1530_1,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_code__numeral__zero__minus__one]) ).

fof(f_1530_2,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1530_1]) ).

cnf(f_1530_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1530_2]) ).

fof(f_1531_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__zero__left]) ).

fof(f_1531_2,plain,
    ! [U_4967,U_4966] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4966),c_Groups_Ozero__class_Ozero(U_4966)),U_4967) = c_Groups_Ozero__class_Ozero(U_4966)
      | ~ class_Rings_Odivision__ring(U_4966) ),
    inference(variable_rename,[status(thm)],[f_1531_1]) ).

fof(f_1531_3,plain,
    ! [U_4966,U_4967] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4966),c_Groups_Ozero__class_Ozero(U_4966)),U_4967) = c_Groups_Ozero__class_Ozero(U_4966)
      | ~ class_Rings_Odivision__ring(U_4966) ),
    inference(definitional_conversion,[status(esa)],[f_1531_2]) ).

cnf(f_1531_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4966),c_Groups_Ozero__class_Ozero(U_4966)),U_4967) = c_Groups_Ozero__class_Ozero(U_4966)
    | ~ class_Rings_Odivision__ring(U_4966) ),
    inference(clausify,[status(thm)],[f_1531_3]) ).

fof(f_1532_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__zero]) ).

fof(f_1532_2,plain,
    ! [U_4969,U_4968] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4968),U_4969),c_Groups_Ozero__class_Ozero(U_4968)) = c_Groups_Ozero__class_Ozero(U_4968)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_4968) ),
    inference(variable_rename,[status(thm)],[f_1532_1]) ).

fof(f_1532_3,plain,
    ! [U_4969,U_4968] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4968),U_4969),c_Groups_Ozero__class_Ozero(U_4968)) = c_Groups_Ozero__class_Ozero(U_4968)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_4968) ),
    inference(definitional_conversion,[status(esa)],[f_1532_2]) ).

cnf(f_1532_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4968),U_4969),c_Groups_Ozero__class_Ozero(U_4968)) = c_Groups_Ozero__class_Ozero(U_4968)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_4968) ),
    inference(clausify,[status(thm)],[f_1532_3]) ).

fof(f_1533_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__divide__distrib]) ).

fof(f_1533_2,plain,
    ! [U_4973,U_4972,U_4971,U_4970] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4970),U_4971),U_4972)),U_4973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),U_4971),U_4973)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),U_4972),U_4973))
      | ~ class_Rings_Odivision__ring(U_4970) ),
    inference(variable_rename,[status(thm)],[f_1533_1]) ).

fof(f_1533_3,plain,
    ! [U_4970,U_4971,U_4972,U_4973] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4970),U_4971),U_4972)),U_4973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),U_4971),U_4973)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),U_4972),U_4973))
      | ~ class_Rings_Odivision__ring(U_4970) ),
    inference(definitional_conversion,[status(esa)],[f_1533_2]) ).

cnf(f_1533_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4970),U_4971),U_4972)),U_4973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),U_4971),U_4973)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4970),U_4972),U_4973))
    | ~ class_Rings_Odivision__ring(U_4970) ),
    inference(clausify,[status(thm)],[f_1533_3]) ).

fof(f_1534_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right]) ).

fof(f_1534_2,plain,
    ! [U_4977,U_4976,U_4975,U_4974] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4974),U_4975),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4974),U_4976),U_4977)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4974),U_4975),U_4976)),U_4977)
      | ~ class_Rings_Odivision__ring(U_4974) ),
    inference(variable_rename,[status(thm)],[f_1534_1]) ).

fof(f_1534_3,plain,
    ! [U_4974,U_4975,U_4976,U_4977] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4974),U_4975),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4974),U_4976),U_4977)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4974),U_4975),U_4976)),U_4977)
      | ~ class_Rings_Odivision__ring(U_4974) ),
    inference(definitional_conversion,[status(esa)],[f_1534_2]) ).

cnf(f_1534_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4974),U_4975),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4974),U_4976),U_4977)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4974),U_4975),U_4976)),U_4977)
    | ~ class_Rings_Odivision__ring(U_4974) ),
    inference(clausify,[status(thm)],[f_1534_3]) ).

fof(f_1535_1,plain,
    ! [V_w,V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w))
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq]) ).

fof(f_1535_2,plain,
    ! [U_4982,U_4981,U_4980,U_4979,U_4978] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),U_4979),U_4980)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),U_4981),U_4982)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),U_4979),U_4981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),U_4980),U_4982))
      | ~ class_Fields_Ofield__inverse__zero(U_4978) ),
    inference(variable_rename,[status(thm)],[f_1535_1]) ).

fof(f_1535_3,plain,
    ! [U_4978,U_4979,U_4980,U_4981,U_4982] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),U_4979),U_4980)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),U_4981),U_4982)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),U_4979),U_4981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),U_4980),U_4982))
      | ~ class_Fields_Ofield__inverse__zero(U_4978) ),
    inference(definitional_conversion,[status(esa)],[f_1535_2]) ).

cnf(f_1535_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),U_4979),U_4980)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),U_4981),U_4982)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),U_4979),U_4981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4978),U_4980),U_4982))
    | ~ class_Fields_Ofield__inverse__zero(U_4978) ),
    inference(clausify,[status(thm)],[f_1535_3]) ).

fof(f_1536_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib]) ).

fof(f_1536_2,plain,
    ! [U_4986,U_4985,U_4984,U_4983] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4983),U_4984),U_4985)),U_4986) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4983),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),U_4984),U_4986)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),U_4985),U_4986))
      | ~ class_Rings_Odivision__ring(U_4983) ),
    inference(variable_rename,[status(thm)],[f_1536_1]) ).

fof(f_1536_3,plain,
    ! [U_4983,U_4984,U_4985,U_4986] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4983),U_4984),U_4985)),U_4986) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4983),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),U_4984),U_4986)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),U_4985),U_4986))
      | ~ class_Rings_Odivision__ring(U_4983) ),
    inference(definitional_conversion,[status(esa)],[f_1536_2]) ).

cnf(f_1536_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4983),U_4984),U_4985)),U_4986) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4983),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),U_4984),U_4986)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4983),U_4985),U_4986))
    | ~ class_Rings_Odivision__ring(U_4983) ),
    inference(clausify,[status(thm)],[f_1536_3]) ).

fof(f_1537_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__1]) ).

fof(f_1537_2,plain,
    ! [U_4988,U_4987] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4987),U_4988),c_Groups_Oone__class_Oone(U_4987)) = U_4988
      | ~ class_Rings_Odivision__ring(U_4987) ),
    inference(variable_rename,[status(thm)],[f_1537_1]) ).

fof(f_1537_3,plain,
    ! [U_4988,U_4987] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4987),U_4988),c_Groups_Oone__class_Oone(U_4987)) = U_4988
      | ~ class_Rings_Odivision__ring(U_4987) ),
    inference(definitional_conversion,[status(esa)],[f_1537_2]) ).

cnf(f_1537_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4987),U_4988),c_Groups_Oone__class_Oone(U_4987)) = U_4988
    | ~ class_Rings_Odivision__ring(U_4987) ),
    inference(clausify,[status(thm)],[f_1537_3]) ).

fof(f_1538_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__divide__left]) ).

fof(f_1538_2,plain,
    ! [U_4991,U_4990,U_4989] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4989),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4989),U_4990),U_4991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4989),hAPP(c_Groups_Ouminus__class_Ouminus(U_4989),U_4990)),U_4991)
      | ~ class_Rings_Odivision__ring(U_4989) ),
    inference(variable_rename,[status(thm)],[f_1538_1]) ).

fof(f_1538_3,plain,
    ! [U_4989,U_4990,U_4991] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4989),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4989),U_4990),U_4991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4989),hAPP(c_Groups_Ouminus__class_Ouminus(U_4989),U_4990)),U_4991)
      | ~ class_Rings_Odivision__ring(U_4989) ),
    inference(definitional_conversion,[status(esa)],[f_1538_2]) ).

cnf(f_1538_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4989),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4989),U_4990),U_4991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4989),hAPP(c_Groups_Ouminus__class_Ouminus(U_4989),U_4990)),U_4991)
    | ~ class_Rings_Odivision__ring(U_4989) ),
    inference(clausify,[status(thm)],[f_1538_3]) ).

fof(f_1539_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__divide__right]) ).

fof(f_1539_2,plain,
    ! [U_4994,U_4993,U_4992] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4992),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4992),U_4993),U_4994)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4992),U_4993),hAPP(c_Groups_Ouminus__class_Ouminus(U_4992),U_4994))
      | ~ class_Fields_Ofield__inverse__zero(U_4992) ),
    inference(variable_rename,[status(thm)],[f_1539_1]) ).

fof(f_1539_3,plain,
    ! [U_4992,U_4993,U_4994] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4992),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4992),U_4993),U_4994)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4992),U_4993),hAPP(c_Groups_Ouminus__class_Ouminus(U_4992),U_4994))
      | ~ class_Fields_Ofield__inverse__zero(U_4992) ),
    inference(definitional_conversion,[status(esa)],[f_1539_2]) ).

cnf(f_1539_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4992),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4992),U_4993),U_4994)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4992),U_4993),hAPP(c_Groups_Ouminus__class_Ouminus(U_4992),U_4994))
    | ~ class_Fields_Ofield__inverse__zero(U_4992) ),
    inference(clausify,[status(thm)],[f_1539_3]) ).

fof(f_1540_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__divide__divide]) ).

fof(f_1540_2,plain,
    ! [U_4997,U_4996,U_4995] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4995),hAPP(c_Groups_Ouminus__class_Ouminus(U_4995),U_4996)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4995),U_4997)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4995),U_4996),U_4997)
      | ~ class_Fields_Ofield__inverse__zero(U_4995) ),
    inference(variable_rename,[status(thm)],[f_1540_1]) ).

fof(f_1540_3,plain,
    ! [U_4995,U_4996,U_4997] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4995),hAPP(c_Groups_Ouminus__class_Ouminus(U_4995),U_4996)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4995),U_4997)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4995),U_4996),U_4997)
      | ~ class_Fields_Ofield__inverse__zero(U_4995) ),
    inference(definitional_conversion,[status(esa)],[f_1540_2]) ).

cnf(f_1540_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4995),hAPP(c_Groups_Ouminus__class_Ouminus(U_4995),U_4996)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4995),U_4997)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4995),U_4996),U_4997)
    | ~ class_Fields_Ofield__inverse__zero(U_4995) ),
    inference(clausify,[status(thm)],[f_1540_3]) ).

fof(f_1541_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__divide]) ).

fof(f_1541_2,plain,
    ! [U_5001,U_5000,U_4999,U_4998] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4998),U_4999),U_5000)),U_5001) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4998),hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),U_4999),U_5001)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),U_5000),U_5001))
      | ~ class_Fields_Ofield__inverse__zero(U_4998) ),
    inference(variable_rename,[status(thm)],[f_1541_1]) ).

fof(f_1541_3,plain,
    ! [U_4998,U_4999,U_5000,U_5001] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4998),U_4999),U_5000)),U_5001) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4998),hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),U_4999),U_5001)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),U_5000),U_5001))
      | ~ class_Fields_Ofield__inverse__zero(U_4998) ),
    inference(definitional_conversion,[status(esa)],[f_1541_2]) ).

cnf(f_1541_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4998),U_4999),U_5000)),U_5001) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4998),hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),U_4999),U_5001)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4998),U_5000),U_5001))
    | ~ class_Fields_Ofield__inverse__zero(U_4998) ),
    inference(clausify,[status(thm)],[f_1541_3]) ).

fof(f_1542_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__divide]) ).

fof(f_1542_2,plain,
    ! [U_5004,U_5003,U_5002] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5002),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5002),U_5003),U_5004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5002),hAPP(c_Groups_Oabs__class_Oabs(U_5002),U_5003)),hAPP(c_Groups_Oabs__class_Oabs(U_5002),U_5004))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5002) ),
    inference(variable_rename,[status(thm)],[f_1542_1]) ).

fof(f_1542_3,plain,
    ! [U_5002,U_5003,U_5004] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5002),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5002),U_5003),U_5004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5002),hAPP(c_Groups_Oabs__class_Oabs(U_5002),U_5003)),hAPP(c_Groups_Oabs__class_Oabs(U_5002),U_5004))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5002) ),
    inference(definitional_conversion,[status(esa)],[f_1542_2]) ).

cnf(f_1542_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5002),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5002),U_5003),U_5004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5002),hAPP(c_Groups_Oabs__class_Oabs(U_5002),U_5003)),hAPP(c_Groups_Oabs__class_Oabs(U_5002),U_5004))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5002) ),
    inference(clausify,[status(thm)],[f_1542_3]) ).

fof(f_1543_1,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]) ).

fof(f_1543_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1543_1]) ).

cnf(f_1543_3,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1543_2]) ).

fof(f_1544_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J]) ).

fof(f_1544_2,plain,
    ! [U_5006,U_5005] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5005),U_5006))
      | ~ c_Nat__Transfer_Ois__nat(U_5006)
      | ~ c_Nat__Transfer_Ois__nat(U_5005) ),
    inference(variable_rename,[status(thm)],[f_1544_1]) ).

fof(f_1544_3,plain,
    ! [U_5005,U_5006] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5005),U_5006))
      | ~ c_Nat__Transfer_Ois__nat(U_5006)
      | ~ c_Nat__Transfer_Ois__nat(U_5005) ),
    inference(definitional_conversion,[status(esa)],[f_1544_2]) ).

cnf(f_1544_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5005),U_5006))
    | ~ c_Nat__Transfer_Ois__nat(U_5006)
    | ~ c_Nat__Transfer_Ois__nat(U_5005) ),
    inference(clausify,[status(thm)],[f_1544_3]) ).

fof(f_1545_1,plain,
    ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).

fof(f_1545_2,plain,
    ! [U_5007] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5007)),
    inference(variable_rename,[status(thm)],[f_1545_1]) ).

fof(f_1545_3,plain,
    ! [U_5007] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5007)),
    inference(definitional_conversion,[status(esa)],[f_1545_2]) ).

cnf(f_1545_4,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5007)),
    inference(clausify,[status(thm)],[f_1545_3]) ).

fof(f_1546_1,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]) ).

fof(f_1546_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1546_1]) ).

cnf(f_1546_3,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1546_2]) ).

fof(f_1547_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J]) ).

fof(f_1547_2,plain,
    ! [U_5009,U_5008] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5008),U_5009))
      | ~ c_Nat__Transfer_Ois__nat(U_5009)
      | ~ c_Nat__Transfer_Ois__nat(U_5008) ),
    inference(variable_rename,[status(thm)],[f_1547_1]) ).

fof(f_1547_3,plain,
    ! [U_5008,U_5009] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5008),U_5009))
      | ~ c_Nat__Transfer_Ois__nat(U_5009)
      | ~ c_Nat__Transfer_Ois__nat(U_5008) ),
    inference(definitional_conversion,[status(esa)],[f_1547_2]) ).

cnf(f_1547_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5008),U_5009))
    | ~ c_Nat__Transfer_Ois__nat(U_5009)
    | ~ c_Nat__Transfer_Ois__nat(U_5008) ),
    inference(clausify,[status(thm)],[f_1547_3]) ).

fof(f_1548_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J]) ).

fof(f_1548_2,plain,
    ! [U_5011,U_5010] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5010,U_5011))
      | ~ c_Nat__Transfer_Ois__nat(U_5011)
      | ~ c_Nat__Transfer_Ois__nat(U_5010) ),
    inference(variable_rename,[status(thm)],[f_1548_1]) ).

fof(f_1548_3,plain,
    ! [U_5011,U_5010] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5010,U_5011))
      | ~ c_Nat__Transfer_Ois__nat(U_5011)
      | ~ c_Nat__Transfer_Ois__nat(U_5010) ),
    inference(definitional_conversion,[status(esa)],[f_1548_2]) ).

cnf(f_1548_4,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5010,U_5011))
    | ~ c_Nat__Transfer_Ois__nat(U_5011)
    | ~ c_Nat__Transfer_Ois__nat(U_5010) ),
    inference(clausify,[status(thm)],[f_1548_3]) ).

fof(f_1549_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J]) ).

fof(f_1549_2,plain,
    ! [U_5013,U_5012] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5012),U_5013))
      | ~ c_Nat__Transfer_Ois__nat(U_5013)
      | ~ c_Nat__Transfer_Ois__nat(U_5012) ),
    inference(variable_rename,[status(thm)],[f_1549_1]) ).

fof(f_1549_3,plain,
    ! [U_5013,U_5012] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5012),U_5013))
      | ~ c_Nat__Transfer_Ois__nat(U_5013)
      | ~ c_Nat__Transfer_Ois__nat(U_5012) ),
    inference(definitional_conversion,[status(esa)],[f_1549_2]) ).

cnf(f_1549_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5012),U_5013))
    | ~ c_Nat__Transfer_Ois__nat(U_5013)
    | ~ c_Nat__Transfer_Ois__nat(U_5012) ),
    inference(clausify,[status(thm)],[f_1549_3]) ).

fof(f_1550_1,plain,
    ! [V_n,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J]) ).

fof(f_1550_2,plain,
    ! [U_5015,U_5014] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5014),U_5015))
      | ~ c_Nat__Transfer_Ois__nat(U_5014) ),
    inference(variable_rename,[status(thm)],[f_1550_1]) ).

fof(f_1550_3,plain,
    ! [U_5014,U_5015] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5014),U_5015))
      | ~ c_Nat__Transfer_Ois__nat(U_5014) ),
    inference(definitional_conversion,[status(esa)],[f_1550_2]) ).

cnf(f_1550_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5014),U_5015))
    | ~ c_Nat__Transfer_Ois__nat(U_5014) ),
    inference(clausify,[status(thm)],[f_1550_3]) ).

fof(f_1551_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg]) ).

fof(f_1551_2,plain,
    ! [U_5019,U_5018,U_5017,U_5016] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5016),U_5018),U_5019)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5016),U_5017),U_5019)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5019),c_Groups_Ozero__class_Ozero(U_5016)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5017),U_5018))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5016) ),
    inference(variable_rename,[status(thm)],[f_1551_1]) ).

fof(f_1551_3,plain,
    ! [U_5016,U_5017,U_5018,U_5019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5016),U_5018),U_5019)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5016),U_5017),U_5019)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5019),c_Groups_Ozero__class_Ozero(U_5016)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5017),U_5018))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5016) ),
    inference(definitional_conversion,[status(esa)],[f_1551_2]) ).

cnf(f_1551_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5016),U_5018),U_5019)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5016),U_5017),U_5019)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5019),c_Groups_Ozero__class_Ozero(U_5016)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5017),U_5018))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5016) ),
    inference(clausify,[status(thm)],[f_1551_3]) ).

fof(f_1552_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__right__mono]) ).

fof(f_1552_2,plain,
    ! [U_5023,U_5022,U_5021,U_5020] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5020),U_5021),U_5023)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5020),U_5022),U_5023)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),c_Groups_Ozero__class_Ozero(U_5020)),U_5023))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),U_5021),U_5022))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5020) ),
    inference(variable_rename,[status(thm)],[f_1552_1]) ).

fof(f_1552_3,plain,
    ! [U_5020,U_5021,U_5022,U_5023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5020),U_5021),U_5023)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5020),U_5022),U_5023)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),c_Groups_Ozero__class_Ozero(U_5020)),U_5023))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),U_5021),U_5022))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5020) ),
    inference(definitional_conversion,[status(esa)],[f_1552_2]) ).

cnf(f_1552_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5020),U_5021),U_5023)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5020),U_5022),U_5023)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),c_Groups_Ozero__class_Ozero(U_5020)),U_5023))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5020),U_5021),U_5022))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5020) ),
    inference(clausify,[status(thm)],[f_1552_3]) ).

fof(f_1553_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).

fof(f_1553_2,plain,
    ! [U_5026,U_5025,U_5024] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5024),U_5025),U_5026)),c_Groups_Ozero__class_Ozero(U_5024)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5026))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5025),c_Groups_Ozero__class_Ozero(U_5024))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5026),c_Groups_Ozero__class_Ozero(U_5024)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5025)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5026))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5025),c_Groups_Ozero__class_Ozero(U_5024))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5026),c_Groups_Ozero__class_Ozero(U_5024)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5025)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5024),U_5025),U_5026)),c_Groups_Ozero__class_Ozero(U_5024))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5024) ),
    inference(variable_rename,[status(thm)],[f_1553_1]) ).

fof(f_1553_3,plain,
    ( ! [U_5024,U_5025,U_5026] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5025),c_Groups_Ozero__class_Ozero(U_5024)))
        | ~ sP406(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5026),c_Groups_Ozero__class_Ozero(U_5024)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5025))
        | ~ sP406(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5026))
        | ~ sP405(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5025),c_Groups_Ozero__class_Ozero(U_5024)))
        | ~ sP405(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5026),c_Groups_Ozero__class_Ozero(U_5024)))
        | ~ sP404(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5025))
        | ~ sP404(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5024),U_5025),U_5026)),c_Groups_Ozero__class_Ozero(U_5024)))
        | sP406(U_5024,U_5025,U_5026)
        | ~ sP407(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( sP405(U_5024,U_5025,U_5026)
        | sP404(U_5024,U_5025,U_5026)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5024),U_5025),U_5026)),c_Groups_Ozero__class_Ozero(U_5024)))
        | ~ sP407(U_5024,U_5025,U_5026) )
    & ! [U_5024,U_5025,U_5026] :
        ( sP407(U_5024,U_5025,U_5026)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5024) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP404,sP405,sP406,sP407])],[f_1553_2]) ).

cnf(f_1553_4,plain,
    ( sP407(U_5024,U_5025,U_5026)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5024) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_5,plain,
    ( sP405(U_5024,U_5025,U_5026)
    | sP404(U_5024,U_5025,U_5026)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5024),U_5025),U_5026)),c_Groups_Ozero__class_Ozero(U_5024)))
    | ~ sP407(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5024),U_5025),U_5026)),c_Groups_Ozero__class_Ozero(U_5024)))
    | sP406(U_5024,U_5025,U_5026)
    | ~ sP407(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5025))
    | ~ sP404(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5026),c_Groups_Ozero__class_Ozero(U_5024)))
    | ~ sP404(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5025),c_Groups_Ozero__class_Ozero(U_5024)))
    | ~ sP405(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5026))
    | ~ sP405(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5026),c_Groups_Ozero__class_Ozero(U_5024)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5025))
    | ~ sP406(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

cnf(f_1553_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),c_Groups_Ozero__class_Ozero(U_5024)),U_5026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5024),U_5025),c_Groups_Ozero__class_Ozero(U_5024)))
    | ~ sP406(U_5024,U_5025,U_5026) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

fof(f_1554_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).

fof(f_1554_2,plain,
    ! [U_5029,U_5028,U_5027] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5027),U_5028),U_5029)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5029),c_Groups_Ozero__class_Ozero(U_5027)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5028),c_Groups_Ozero__class_Ozero(U_5027))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5029))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5028)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5029),c_Groups_Ozero__class_Ozero(U_5027)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5028),c_Groups_Ozero__class_Ozero(U_5027))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5029))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5028)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5027),U_5028),U_5029))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5027) ),
    inference(variable_rename,[status(thm)],[f_1554_1]) ).

fof(f_1554_3,plain,
    ( ! [U_5029,U_5027,U_5028] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5029),c_Groups_Ozero__class_Ozero(U_5027)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5028),c_Groups_Ozero__class_Ozero(U_5027)))
        | ~ sP410(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5029))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5028))
        | ~ sP410(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5029),c_Groups_Ozero__class_Ozero(U_5027)))
        | ~ sP409(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5028),c_Groups_Ozero__class_Ozero(U_5027)))
        | ~ sP409(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5029))
        | ~ sP408(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5028))
        | ~ sP408(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5027),U_5028),U_5029)))
        | sP410(U_5029,U_5027,U_5028)
        | ~ sP411(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( sP409(U_5029,U_5027,U_5028)
        | sP408(U_5029,U_5027,U_5028)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5027),U_5028),U_5029)))
        | ~ sP411(U_5029,U_5027,U_5028) )
    & ! [U_5029,U_5027,U_5028] :
        ( sP411(U_5029,U_5027,U_5028)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5027) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP408,sP409,sP410,sP411])],[f_1554_2]) ).

cnf(f_1554_4,plain,
    ( sP411(U_5029,U_5027,U_5028)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5027) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_5,plain,
    ( sP409(U_5029,U_5027,U_5028)
    | sP408(U_5029,U_5027,U_5028)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5027),U_5028),U_5029)))
    | ~ sP411(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5027),U_5028),U_5029)))
    | sP410(U_5029,U_5027,U_5028)
    | ~ sP411(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5028))
    | ~ sP408(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5029))
    | ~ sP408(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5028),c_Groups_Ozero__class_Ozero(U_5027)))
    | ~ sP409(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5029),c_Groups_Ozero__class_Ozero(U_5027)))
    | ~ sP409(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5029))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),c_Groups_Ozero__class_Ozero(U_5027)),U_5028))
    | ~ sP410(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5029),c_Groups_Ozero__class_Ozero(U_5027)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5027),U_5028),c_Groups_Ozero__class_Ozero(U_5027)))
    | ~ sP410(U_5029,U_5027,U_5028) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

fof(f_1555_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg]) ).

fof(f_1555_2,plain,
    ! [U_5033,U_5032,U_5031,U_5030] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5030),U_5032),U_5033)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5030),U_5031),U_5033)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),U_5033),c_Groups_Ozero__class_Ozero(U_5030)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),U_5031),U_5032))
      | ~ class_Fields_Olinordered__field(U_5030) ),
    inference(variable_rename,[status(thm)],[f_1555_1]) ).

fof(f_1555_3,plain,
    ! [U_5033,U_5031,U_5030,U_5032] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5030),U_5032),U_5033)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5030),U_5031),U_5033)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),U_5033),c_Groups_Ozero__class_Ozero(U_5030)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),U_5031),U_5032))
      | ~ class_Fields_Olinordered__field(U_5030) ),
    inference(definitional_conversion,[status(esa)],[f_1555_2]) ).

cnf(f_1555_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5030),U_5032),U_5033)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5030),U_5031),U_5033)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),U_5033),c_Groups_Ozero__class_Ozero(U_5030)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5030),U_5031),U_5032))
    | ~ class_Fields_Olinordered__field(U_5030) ),
    inference(clausify,[status(thm)],[f_1555_3]) ).

fof(f_1556_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono]) ).

fof(f_1556_2,plain,
    ! [U_5037,U_5036,U_5035,U_5034] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5034),U_5035),U_5037)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5034),U_5036),U_5037)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),c_Groups_Ozero__class_Ozero(U_5034)),U_5037))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),U_5035),U_5036))
      | ~ class_Fields_Olinordered__field(U_5034) ),
    inference(variable_rename,[status(thm)],[f_1556_1]) ).

fof(f_1556_3,plain,
    ! [U_5035,U_5034,U_5036,U_5037] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5034),U_5035),U_5037)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5034),U_5036),U_5037)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),c_Groups_Ozero__class_Ozero(U_5034)),U_5037))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),U_5035),U_5036))
      | ~ class_Fields_Olinordered__field(U_5034) ),
    inference(definitional_conversion,[status(esa)],[f_1556_2]) ).

cnf(f_1556_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5034),U_5035),U_5037)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5034),U_5036),U_5037)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),c_Groups_Ozero__class_Ozero(U_5034)),U_5037))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5034),U_5035),U_5036))
    | ~ class_Fields_Olinordered__field(U_5034) ),
    inference(clausify,[status(thm)],[f_1556_3]) ).

fof(f_1557_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__neg__neg]) ).

fof(f_1557_2,plain,
    ! [U_5040,U_5039,U_5038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),c_Groups_Ozero__class_Ozero(U_5038)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5038),U_5039),U_5040)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),U_5040),c_Groups_Ozero__class_Ozero(U_5038)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),U_5039),c_Groups_Ozero__class_Ozero(U_5038)))
      | ~ class_Fields_Olinordered__field(U_5038) ),
    inference(variable_rename,[status(thm)],[f_1557_1]) ).

fof(f_1557_3,plain,
    ! [U_5039,U_5038,U_5040] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),c_Groups_Ozero__class_Ozero(U_5038)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5038),U_5039),U_5040)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),U_5040),c_Groups_Ozero__class_Ozero(U_5038)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),U_5039),c_Groups_Ozero__class_Ozero(U_5038)))
      | ~ class_Fields_Olinordered__field(U_5038) ),
    inference(definitional_conversion,[status(esa)],[f_1557_2]) ).

cnf(f_1557_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),c_Groups_Ozero__class_Ozero(U_5038)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5038),U_5039),U_5040)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),U_5040),c_Groups_Ozero__class_Ozero(U_5038)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5038),U_5039),c_Groups_Ozero__class_Ozero(U_5038)))
    | ~ class_Fields_Olinordered__field(U_5038) ),
    inference(clausify,[status(thm)],[f_1557_3]) ).

fof(f_1558_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__neg__pos]) ).

fof(f_1558_2,plain,
    ! [U_5043,U_5042,U_5041] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5041),U_5042),U_5043)),c_Groups_Ozero__class_Ozero(U_5041)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),c_Groups_Ozero__class_Ozero(U_5041)),U_5043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),U_5042),c_Groups_Ozero__class_Ozero(U_5041)))
      | ~ class_Fields_Olinordered__field(U_5041) ),
    inference(variable_rename,[status(thm)],[f_1558_1]) ).

fof(f_1558_3,plain,
    ! [U_5041,U_5042,U_5043] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5041),U_5042),U_5043)),c_Groups_Ozero__class_Ozero(U_5041)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),c_Groups_Ozero__class_Ozero(U_5041)),U_5043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),U_5042),c_Groups_Ozero__class_Ozero(U_5041)))
      | ~ class_Fields_Olinordered__field(U_5041) ),
    inference(definitional_conversion,[status(esa)],[f_1558_2]) ).

cnf(f_1558_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5041),U_5042),U_5043)),c_Groups_Ozero__class_Ozero(U_5041)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),c_Groups_Ozero__class_Ozero(U_5041)),U_5043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5041),U_5042),c_Groups_Ozero__class_Ozero(U_5041)))
    | ~ class_Fields_Olinordered__field(U_5041) ),
    inference(clausify,[status(thm)],[f_1558_3]) ).

fof(f_1559_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__pos__neg]) ).

fof(f_1559_2,plain,
    ! [U_5046,U_5045,U_5044] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5044),U_5045),U_5046)),c_Groups_Ozero__class_Ozero(U_5044)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),U_5046),c_Groups_Ozero__class_Ozero(U_5044)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),c_Groups_Ozero__class_Ozero(U_5044)),U_5045))
      | ~ class_Fields_Olinordered__field(U_5044) ),
    inference(variable_rename,[status(thm)],[f_1559_1]) ).

fof(f_1559_3,plain,
    ! [U_5044,U_5045,U_5046] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5044),U_5045),U_5046)),c_Groups_Ozero__class_Ozero(U_5044)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),U_5046),c_Groups_Ozero__class_Ozero(U_5044)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),c_Groups_Ozero__class_Ozero(U_5044)),U_5045))
      | ~ class_Fields_Olinordered__field(U_5044) ),
    inference(definitional_conversion,[status(esa)],[f_1559_2]) ).

cnf(f_1559_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5044),U_5045),U_5046)),c_Groups_Ozero__class_Ozero(U_5044)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),U_5046),c_Groups_Ozero__class_Ozero(U_5044)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5044),c_Groups_Ozero__class_Ozero(U_5044)),U_5045))
    | ~ class_Fields_Olinordered__field(U_5044) ),
    inference(clausify,[status(thm)],[f_1559_3]) ).

fof(f_1560_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__pos__pos]) ).

fof(f_1560_2,plain,
    ! [U_5049,U_5048,U_5047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5047),U_5048),U_5049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),U_5049))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),U_5048))
      | ~ class_Fields_Olinordered__field(U_5047) ),
    inference(variable_rename,[status(thm)],[f_1560_1]) ).

fof(f_1560_3,plain,
    ! [U_5048,U_5047,U_5049] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5047),U_5048),U_5049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),U_5049))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),U_5048))
      | ~ class_Fields_Olinordered__field(U_5047) ),
    inference(definitional_conversion,[status(esa)],[f_1560_2]) ).

cnf(f_1560_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5047),U_5048),U_5049)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),U_5049))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5047),c_Groups_Ozero__class_Ozero(U_5047)),U_5048))
    | ~ class_Fields_Olinordered__field(U_5047) ),
    inference(clausify,[status(thm)],[f_1560_3]) ).

fof(f_1561_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).

fof(f_1561_2,plain,
    ! [U_5052,U_5051,U_5050] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5050),U_5051),U_5052)),c_Groups_Ozero__class_Ozero(U_5050)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5052))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5051),c_Groups_Ozero__class_Ozero(U_5050))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5052),c_Groups_Ozero__class_Ozero(U_5050)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5051)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5052))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5051),c_Groups_Ozero__class_Ozero(U_5050))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5052),c_Groups_Ozero__class_Ozero(U_5050)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5051)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5050),U_5051),U_5052)),c_Groups_Ozero__class_Ozero(U_5050))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5050) ),
    inference(variable_rename,[status(thm)],[f_1561_1]) ).

fof(f_1561_3,plain,
    ( ! [U_5050,U_5051,U_5052] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5051),c_Groups_Ozero__class_Ozero(U_5050)))
        | ~ sP414(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5052),c_Groups_Ozero__class_Ozero(U_5050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5051))
        | ~ sP414(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5052))
        | ~ sP413(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5051),c_Groups_Ozero__class_Ozero(U_5050)))
        | ~ sP413(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5052),c_Groups_Ozero__class_Ozero(U_5050)))
        | ~ sP412(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5051))
        | ~ sP412(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5050),U_5051),U_5052)),c_Groups_Ozero__class_Ozero(U_5050)))
        | sP414(U_5050,U_5051,U_5052)
        | ~ sP415(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( sP413(U_5050,U_5051,U_5052)
        | sP412(U_5050,U_5051,U_5052)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5050),U_5051),U_5052)),c_Groups_Ozero__class_Ozero(U_5050)))
        | ~ sP415(U_5050,U_5051,U_5052) )
    & ! [U_5050,U_5051,U_5052] :
        ( sP415(U_5050,U_5051,U_5052)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5050) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP412,sP413,sP414,sP415])],[f_1561_2]) ).

cnf(f_1561_4,plain,
    ( sP415(U_5050,U_5051,U_5052)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5050) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_5,plain,
    ( sP413(U_5050,U_5051,U_5052)
    | sP412(U_5050,U_5051,U_5052)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5050),U_5051),U_5052)),c_Groups_Ozero__class_Ozero(U_5050)))
    | ~ sP415(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5050),U_5051),U_5052)),c_Groups_Ozero__class_Ozero(U_5050)))
    | sP414(U_5050,U_5051,U_5052)
    | ~ sP415(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5051))
    | ~ sP412(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5052),c_Groups_Ozero__class_Ozero(U_5050)))
    | ~ sP412(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5051),c_Groups_Ozero__class_Ozero(U_5050)))
    | ~ sP413(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5052))
    | ~ sP413(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5052),c_Groups_Ozero__class_Ozero(U_5050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5051))
    | ~ sP414(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),c_Groups_Ozero__class_Ozero(U_5050)),U_5052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5050),U_5051),c_Groups_Ozero__class_Ozero(U_5050)))
    | ~ sP414(U_5050,U_5051,U_5052) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

fof(f_1562_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).

fof(f_1562_2,plain,
    ! [U_5055,U_5054,U_5053] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5053),U_5054),U_5055)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5055),c_Groups_Ozero__class_Ozero(U_5053)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5054),c_Groups_Ozero__class_Ozero(U_5053))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5055))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5054)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5055),c_Groups_Ozero__class_Ozero(U_5053)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5054),c_Groups_Ozero__class_Ozero(U_5053))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5055))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5054)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5053),U_5054),U_5055))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5053) ),
    inference(variable_rename,[status(thm)],[f_1562_1]) ).

fof(f_1562_3,plain,
    ( ! [U_5055,U_5054,U_5053] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5055),c_Groups_Ozero__class_Ozero(U_5053)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5054),c_Groups_Ozero__class_Ozero(U_5053)))
        | ~ sP418(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5055))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5054))
        | ~ sP418(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5055),c_Groups_Ozero__class_Ozero(U_5053)))
        | ~ sP417(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5054),c_Groups_Ozero__class_Ozero(U_5053)))
        | ~ sP417(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5055))
        | ~ sP416(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5054))
        | ~ sP416(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5053),U_5054),U_5055)))
        | sP418(U_5055,U_5054,U_5053)
        | ~ sP419(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( sP417(U_5055,U_5054,U_5053)
        | sP416(U_5055,U_5054,U_5053)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5053),U_5054),U_5055)))
        | ~ sP419(U_5055,U_5054,U_5053) )
    & ! [U_5055,U_5054,U_5053] :
        ( sP419(U_5055,U_5054,U_5053)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5053) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP416,sP417,sP418,sP419])],[f_1562_2]) ).

cnf(f_1562_4,plain,
    ( sP419(U_5055,U_5054,U_5053)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_5,plain,
    ( sP417(U_5055,U_5054,U_5053)
    | sP416(U_5055,U_5054,U_5053)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5053),U_5054),U_5055)))
    | ~ sP419(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5053),U_5054),U_5055)))
    | sP418(U_5055,U_5054,U_5053)
    | ~ sP419(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5054))
    | ~ sP416(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5055))
    | ~ sP416(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5054),c_Groups_Ozero__class_Ozero(U_5053)))
    | ~ sP417(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5055),c_Groups_Ozero__class_Ozero(U_5053)))
    | ~ sP417(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),c_Groups_Ozero__class_Ozero(U_5053)),U_5054))
    | ~ sP418(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5055),c_Groups_Ozero__class_Ozero(U_5053)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5053),U_5054),c_Groups_Ozero__class_Ozero(U_5053)))
    | ~ sP418(U_5055,U_5054,U_5053) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

fof(f_1563_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Rings_Odivision__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).

fof(f_1563_2,plain,
    ! [U_5059,U_5058,U_5057,U_5056] :
      ( ( ( U_5058 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5056),U_5059),U_5057)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5056),U_5058),U_5057) != U_5059 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5056),U_5058),U_5057) = U_5059
          | U_5058 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5056),U_5059),U_5057) ) )
      | U_5057 = c_Groups_Ozero__class_Ozero(U_5056)
      | ~ class_Rings_Odivision__ring(U_5056) ),
    inference(variable_rename,[status(thm)],[f_1563_1]) ).

fof(f_1563_3,plain,
    ( ! [U_5059,U_5056,U_5057,U_5058] :
        ( U_5058 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5056),U_5059),U_5057)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5056),U_5058),U_5057) != U_5059
        | ~ sP420(U_5059,U_5056,U_5057,U_5058) )
    & ! [U_5059,U_5056,U_5057,U_5058] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5056),U_5058),U_5057) = U_5059
        | U_5058 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5056),U_5059),U_5057)
        | ~ sP420(U_5059,U_5056,U_5057,U_5058) )
    & ! [U_5059,U_5056,U_5057,U_5058] :
        ( sP420(U_5059,U_5056,U_5057,U_5058)
        | U_5057 = c_Groups_Ozero__class_Ozero(U_5056)
        | ~ class_Rings_Odivision__ring(U_5056) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP420])],[f_1563_2]) ).

cnf(f_1563_4,plain,
    ( sP420(U_5059,U_5056,U_5057,U_5058)
    | U_5057 = c_Groups_Ozero__class_Ozero(U_5056)
    | ~ class_Rings_Odivision__ring(U_5056) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

cnf(f_1563_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5056),U_5058),U_5057) = U_5059
    | U_5058 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5056),U_5059),U_5057)
    | ~ sP420(U_5059,U_5056,U_5057,U_5058) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

cnf(f_1563_6,plain,
    ( U_5058 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5056),U_5059),U_5057)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5056),U_5058),U_5057) != U_5059
    | ~ sP420(U_5059,U_5056,U_5057,U_5058) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

fof(f_1564_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
          | V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
        & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Rings_Odivision__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).

fof(f_1564_2,plain,
    ! [U_5063,U_5062,U_5061,U_5060] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5060),U_5062),U_5061) = U_5063
          | U_5062 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5060),U_5063),U_5061) )
        & ( U_5062 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5060),U_5063),U_5061)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5060),U_5062),U_5061) != U_5063 ) )
      | U_5061 = c_Groups_Ozero__class_Ozero(U_5060)
      | ~ class_Rings_Odivision__ring(U_5060) ),
    inference(variable_rename,[status(thm)],[f_1564_1]) ).

fof(f_1564_3,plain,
    ( ! [U_5062,U_5061,U_5060,U_5063] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5060),U_5062),U_5061) = U_5063
        | U_5062 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5060),U_5063),U_5061)
        | ~ sP421(U_5062,U_5061,U_5060,U_5063) )
    & ! [U_5062,U_5061,U_5060,U_5063] :
        ( U_5062 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5060),U_5063),U_5061)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5060),U_5062),U_5061) != U_5063
        | ~ sP421(U_5062,U_5061,U_5060,U_5063) )
    & ! [U_5062,U_5061,U_5060,U_5063] :
        ( sP421(U_5062,U_5061,U_5060,U_5063)
        | U_5061 = c_Groups_Ozero__class_Ozero(U_5060)
        | ~ class_Rings_Odivision__ring(U_5060) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP421])],[f_1564_2]) ).

cnf(f_1564_4,plain,
    ( sP421(U_5062,U_5061,U_5060,U_5063)
    | U_5061 = c_Groups_Ozero__class_Ozero(U_5060)
    | ~ class_Rings_Odivision__ring(U_5060) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

cnf(f_1564_5,plain,
    ( U_5062 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5060),U_5063),U_5061)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5060),U_5062),U_5061) != U_5063
    | ~ sP421(U_5062,U_5061,U_5060,U_5063) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

cnf(f_1564_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5060),U_5062),U_5061) = U_5063
    | U_5062 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5060),U_5063),U_5061)
    | ~ sP421(U_5062,U_5061,U_5060,U_5063) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

fof(f_1565_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a
      | V_b != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__imp]) ).

fof(f_1565_2,plain,
    ! [U_5067,U_5066,U_5065,U_5064] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5064),U_5066),U_5065) = U_5067
      | U_5066 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5064),U_5067),U_5065)
      | U_5065 = c_Groups_Ozero__class_Ozero(U_5064)
      | ~ class_Rings_Odivision__ring(U_5064) ),
    inference(variable_rename,[status(thm)],[f_1565_1]) ).

fof(f_1565_3,plain,
    ! [U_5064,U_5066,U_5067,U_5065] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5064),U_5066),U_5065) = U_5067
      | U_5066 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5064),U_5067),U_5065)
      | U_5065 = c_Groups_Ozero__class_Ozero(U_5064)
      | ~ class_Rings_Odivision__ring(U_5064) ),
    inference(definitional_conversion,[status(esa)],[f_1565_2]) ).

cnf(f_1565_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5064),U_5066),U_5065) = U_5067
    | U_5066 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5064),U_5067),U_5065)
    | U_5065 = c_Groups_Ozero__class_Ozero(U_5064)
    | ~ class_Rings_Odivision__ring(U_5064) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

fof(f_1566_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) != V_b
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__imp]) ).

fof(f_1566_2,plain,
    ! [U_5071,U_5070,U_5069,U_5068] :
      ( U_5070 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5068),U_5071),U_5069)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5068),U_5070),U_5069) != U_5071
      | U_5069 = c_Groups_Ozero__class_Ozero(U_5068)
      | ~ class_Rings_Odivision__ring(U_5068) ),
    inference(variable_rename,[status(thm)],[f_1566_1]) ).

fof(f_1566_3,plain,
    ! [U_5068,U_5070,U_5069,U_5071] :
      ( U_5070 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5068),U_5071),U_5069)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5068),U_5070),U_5069) != U_5071
      | U_5069 = c_Groups_Ozero__class_Ozero(U_5068)
      | ~ class_Rings_Odivision__ring(U_5068) ),
    inference(definitional_conversion,[status(esa)],[f_1566_2]) ).

cnf(f_1566_4,plain,
    ( U_5070 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5068),U_5071),U_5069)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5068),U_5070),U_5069) != U_5071
    | U_5069 = c_Groups_Ozero__class_Ozero(U_5068)
    | ~ class_Rings_Odivision__ring(U_5068) ),
    inference(clausify,[status(thm)],[f_1566_3]) ).

fof(f_1567_1,plain,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) ) )
      | V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
      | V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).

fof(f_1567_2,plain,
    ! [U_5076,U_5075,U_5074,U_5073,U_5072] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5075),U_5073) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5076),U_5074)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5075),U_5074) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5076),U_5073) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5075),U_5074) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5076),U_5073)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5075),U_5073) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5076),U_5074) ) )
      | U_5074 = c_Groups_Ozero__class_Ozero(U_5072)
      | U_5073 = c_Groups_Ozero__class_Ozero(U_5072)
      | ~ class_Fields_Ofield(U_5072) ),
    inference(variable_rename,[status(thm)],[f_1567_1]) ).

fof(f_1567_3,plain,
    ( ! [U_5074,U_5072,U_5073,U_5075,U_5076] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5075),U_5073) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5076),U_5074)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5075),U_5074) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5076),U_5073)
        | ~ sP422(U_5074,U_5072,U_5073,U_5075,U_5076) )
    & ! [U_5074,U_5072,U_5073,U_5075,U_5076] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5075),U_5074) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5076),U_5073)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5075),U_5073) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5076),U_5074)
        | ~ sP422(U_5074,U_5072,U_5073,U_5075,U_5076) )
    & ! [U_5074,U_5072,U_5073,U_5075,U_5076] :
        ( sP422(U_5074,U_5072,U_5073,U_5075,U_5076)
        | U_5074 = c_Groups_Ozero__class_Ozero(U_5072)
        | U_5073 = c_Groups_Ozero__class_Ozero(U_5072)
        | ~ class_Fields_Ofield(U_5072) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP422])],[f_1567_2]) ).

cnf(f_1567_4,plain,
    ( sP422(U_5074,U_5072,U_5073,U_5075,U_5076)
    | U_5074 = c_Groups_Ozero__class_Ozero(U_5072)
    | U_5073 = c_Groups_Ozero__class_Ozero(U_5072)
    | ~ class_Fields_Ofield(U_5072) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

cnf(f_1567_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5075),U_5074) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5076),U_5073)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5075),U_5073) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5076),U_5074)
    | ~ sP422(U_5074,U_5072,U_5073,U_5075,U_5076) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

cnf(f_1567_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5075),U_5073) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5072),U_5076),U_5074)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5075),U_5074) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),U_5076),U_5073)
    | ~ sP422(U_5074,U_5072,U_5073,U_5075,U_5076) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

fof(f_1568_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left]) ).

fof(f_1568_2,plain,
    ! [U_5080,U_5079,U_5078,U_5077] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5077),U_5078),U_5079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5077),U_5078),U_5080)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5077),U_5079),U_5080)
      | U_5078 = c_Groups_Ozero__class_Ozero(U_5077)
      | ~ class_Fields_Ofield__inverse__zero(U_5077) ),
    inference(variable_rename,[status(thm)],[f_1568_1]) ).

fof(f_1568_3,plain,
    ! [U_5080,U_5079,U_5078,U_5077] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5077),U_5078),U_5079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5077),U_5078),U_5080)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5077),U_5079),U_5080)
      | U_5078 = c_Groups_Ozero__class_Ozero(U_5077)
      | ~ class_Fields_Ofield__inverse__zero(U_5077) ),
    inference(definitional_conversion,[status(esa)],[f_1568_2]) ).

cnf(f_1568_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5077),U_5078),U_5079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5077),U_5078),U_5080)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5077),U_5079),U_5080)
    | U_5078 = c_Groups_Ozero__class_Ozero(U_5077)
    | ~ class_Fields_Ofield__inverse__zero(U_5077) ),
    inference(clausify,[status(thm)],[f_1568_3]) ).

fof(f_1569_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right]) ).

fof(f_1569_2,plain,
    ! [U_5084,U_5083,U_5082,U_5081] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5083),U_5082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5084),U_5082)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5081),U_5083),U_5084)
      | U_5082 = c_Groups_Ozero__class_Ozero(U_5081)
      | ~ class_Fields_Ofield__inverse__zero(U_5081) ),
    inference(variable_rename,[status(thm)],[f_1569_1]) ).

fof(f_1569_3,plain,
    ! [U_5081,U_5082,U_5083,U_5084] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5083),U_5082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5084),U_5082)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5081),U_5083),U_5084)
      | U_5082 = c_Groups_Ozero__class_Ozero(U_5081)
      | ~ class_Fields_Ofield__inverse__zero(U_5081) ),
    inference(definitional_conversion,[status(esa)],[f_1569_2]) ).

cnf(f_1569_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5083),U_5082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5084),U_5082)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5081),U_5083),U_5084)
    | U_5082 = c_Groups_Ozero__class_Ozero(U_5081)
    | ~ class_Fields_Ofield__inverse__zero(U_5081) ),
    inference(clausify,[status(thm)],[f_1569_3]) ).

fof(f_1570_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).

fof(f_1570_2,plain,
    ! [U_5088,U_5087,U_5086,U_5085] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5085),U_5086),U_5087) = U_5088
          | ( U_5088 != c_Groups_Ozero__class_Ozero(U_5085)
            & U_5087 = c_Groups_Ozero__class_Ozero(U_5085) )
          | ( U_5086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5085),U_5088),U_5087)
            & U_5087 != c_Groups_Ozero__class_Ozero(U_5085) ) )
        & ( ( ( U_5088 = c_Groups_Ozero__class_Ozero(U_5085)
              | U_5087 != c_Groups_Ozero__class_Ozero(U_5085) )
            & ( U_5086 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5085),U_5088),U_5087)
              | U_5087 = c_Groups_Ozero__class_Ozero(U_5085) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5085),U_5086),U_5087) != U_5088 ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5085) ),
    inference(variable_rename,[status(thm)],[f_1570_1]) ).

fof(f_1570_3,plain,
    ( ! [U_5085,U_5087,U_5088] :
        ( U_5088 != c_Groups_Ozero__class_Ozero(U_5085)
        | ~ sP425(U_5085,U_5087,U_5088) )
    & ! [U_5085,U_5087,U_5088] :
        ( U_5087 = c_Groups_Ozero__class_Ozero(U_5085)
        | ~ sP425(U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( U_5086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5085),U_5088),U_5087)
        | ~ sP424(U_5086,U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( U_5087 != c_Groups_Ozero__class_Ozero(U_5085)
        | ~ sP424(U_5086,U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( U_5088 = c_Groups_Ozero__class_Ozero(U_5085)
        | U_5087 != c_Groups_Ozero__class_Ozero(U_5085)
        | ~ sP423(U_5086,U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( U_5086 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5085),U_5088),U_5087)
        | U_5087 = c_Groups_Ozero__class_Ozero(U_5085)
        | ~ sP423(U_5086,U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5085),U_5086),U_5087) = U_5088
        | sP425(U_5085,U_5087,U_5088)
        | sP424(U_5086,U_5085,U_5087,U_5088)
        | ~ sP426(U_5086,U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( sP423(U_5086,U_5085,U_5087,U_5088)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5085),U_5086),U_5087) != U_5088
        | ~ sP426(U_5086,U_5085,U_5087,U_5088) )
    & ! [U_5086,U_5085,U_5087,U_5088] :
        ( sP426(U_5086,U_5085,U_5087,U_5088)
        | ~ class_Fields_Ofield__inverse__zero(U_5085) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP423,sP424,sP425,sP426])],[f_1570_2]) ).

cnf(f_1570_4,plain,
    ( sP426(U_5086,U_5085,U_5087,U_5088)
    | ~ class_Fields_Ofield__inverse__zero(U_5085) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_5,plain,
    ( sP423(U_5086,U_5085,U_5087,U_5088)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5085),U_5086),U_5087) != U_5088
    | ~ sP426(U_5086,U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5085),U_5086),U_5087) = U_5088
    | sP425(U_5085,U_5087,U_5088)
    | sP424(U_5086,U_5085,U_5087,U_5088)
    | ~ sP426(U_5086,U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_7,plain,
    ( U_5086 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5085),U_5088),U_5087)
    | U_5087 = c_Groups_Ozero__class_Ozero(U_5085)
    | ~ sP423(U_5086,U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_8,plain,
    ( U_5088 = c_Groups_Ozero__class_Ozero(U_5085)
    | U_5087 != c_Groups_Ozero__class_Ozero(U_5085)
    | ~ sP423(U_5086,U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_9,plain,
    ( U_5087 != c_Groups_Ozero__class_Ozero(U_5085)
    | ~ sP424(U_5086,U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_10,plain,
    ( U_5086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5085),U_5088),U_5087)
    | ~ sP424(U_5086,U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_11,plain,
    ( U_5087 = c_Groups_Ozero__class_Ozero(U_5085)
    | ~ sP425(U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_12,plain,
    ( U_5088 != c_Groups_Ozero__class_Ozero(U_5085)
    | ~ sP425(U_5085,U_5087,U_5088) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

fof(f_1571_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).

fof(f_1571_2,plain,
    ! [U_5092,U_5091,U_5090,U_5089] :
      ( ( ( U_5090 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5089),U_5091),U_5092)
          | ( U_5090 != c_Groups_Ozero__class_Ozero(U_5089)
            & U_5092 = c_Groups_Ozero__class_Ozero(U_5089) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5089),U_5090),U_5092) != U_5091
            & U_5092 != c_Groups_Ozero__class_Ozero(U_5089) ) )
        & ( ( ( U_5090 = c_Groups_Ozero__class_Ozero(U_5089)
              | U_5092 != c_Groups_Ozero__class_Ozero(U_5089) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5089),U_5090),U_5092) = U_5091
              | U_5092 = c_Groups_Ozero__class_Ozero(U_5089) ) )
          | U_5090 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5089),U_5091),U_5092) ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5089) ),
    inference(variable_rename,[status(thm)],[f_1571_1]) ).

fof(f_1571_3,plain,
    ( ! [U_5089,U_5092,U_5090] :
        ( U_5090 != c_Groups_Ozero__class_Ozero(U_5089)
        | ~ sP429(U_5089,U_5092,U_5090) )
    & ! [U_5089,U_5092,U_5090] :
        ( U_5092 = c_Groups_Ozero__class_Ozero(U_5089)
        | ~ sP429(U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5089),U_5090),U_5092) != U_5091
        | ~ sP428(U_5091,U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( U_5092 != c_Groups_Ozero__class_Ozero(U_5089)
        | ~ sP428(U_5091,U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( U_5090 = c_Groups_Ozero__class_Ozero(U_5089)
        | U_5092 != c_Groups_Ozero__class_Ozero(U_5089)
        | ~ sP427(U_5091,U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5089),U_5090),U_5092) = U_5091
        | U_5092 = c_Groups_Ozero__class_Ozero(U_5089)
        | ~ sP427(U_5091,U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( U_5090 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5089),U_5091),U_5092)
        | sP429(U_5089,U_5092,U_5090)
        | sP428(U_5091,U_5089,U_5092,U_5090)
        | ~ sP430(U_5091,U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( sP427(U_5091,U_5089,U_5092,U_5090)
        | U_5090 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5089),U_5091),U_5092)
        | ~ sP430(U_5091,U_5089,U_5092,U_5090) )
    & ! [U_5091,U_5089,U_5092,U_5090] :
        ( sP430(U_5091,U_5089,U_5092,U_5090)
        | ~ class_Fields_Ofield__inverse__zero(U_5089) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP427,sP428,sP429,sP430])],[f_1571_2]) ).

cnf(f_1571_4,plain,
    ( sP430(U_5091,U_5089,U_5092,U_5090)
    | ~ class_Fields_Ofield__inverse__zero(U_5089) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_5,plain,
    ( sP427(U_5091,U_5089,U_5092,U_5090)
    | U_5090 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5089),U_5091),U_5092)
    | ~ sP430(U_5091,U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_6,plain,
    ( U_5090 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5089),U_5091),U_5092)
    | sP429(U_5089,U_5092,U_5090)
    | sP428(U_5091,U_5089,U_5092,U_5090)
    | ~ sP430(U_5091,U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5089),U_5090),U_5092) = U_5091
    | U_5092 = c_Groups_Ozero__class_Ozero(U_5089)
    | ~ sP427(U_5091,U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_8,plain,
    ( U_5090 = c_Groups_Ozero__class_Ozero(U_5089)
    | U_5092 != c_Groups_Ozero__class_Ozero(U_5089)
    | ~ sP427(U_5091,U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_9,plain,
    ( U_5092 != c_Groups_Ozero__class_Ozero(U_5089)
    | ~ sP428(U_5091,U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5089),U_5090),U_5092) != U_5091
    | ~ sP428(U_5091,U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_11,plain,
    ( U_5092 = c_Groups_Ozero__class_Ozero(U_5089)
    | ~ sP429(U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_12,plain,
    ( U_5090 != c_Groups_Ozero__class_Ozero(U_5089)
    | ~ sP429(U_5089,U_5092,U_5090) ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

fof(f_1572_1,plain,
    ! [V_a,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
          | V_a = c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__self__if]) ).

fof(f_1572_2,plain,
    ! [U_5094,U_5093] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5093),U_5094),U_5094) = c_Groups_Oone__class_Oone(U_5093)
          | U_5094 = c_Groups_Ozero__class_Ozero(U_5093) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5093),U_5094),U_5094) = c_Groups_Ozero__class_Ozero(U_5093)
          | U_5094 != c_Groups_Ozero__class_Ozero(U_5093) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5093) ),
    inference(variable_rename,[status(thm)],[f_1572_1]) ).

fof(f_1572_3,plain,
    ( ! [U_5093,U_5094] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5093),U_5094),U_5094) = c_Groups_Oone__class_Oone(U_5093)
        | U_5094 = c_Groups_Ozero__class_Ozero(U_5093)
        | ~ sP431(U_5093,U_5094) )
    & ! [U_5093,U_5094] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5093),U_5094),U_5094) = c_Groups_Ozero__class_Ozero(U_5093)
        | U_5094 != c_Groups_Ozero__class_Ozero(U_5093)
        | ~ sP431(U_5093,U_5094) )
    & ! [U_5093,U_5094] :
        ( sP431(U_5093,U_5094)
        | ~ class_Rings_Odivision__ring__inverse__zero(U_5093) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP431])],[f_1572_2]) ).

cnf(f_1572_4,plain,
    ( sP431(U_5093,U_5094)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5093) ),
    inference(clausify,[status(thm)],[f_1572_3]) ).

cnf(f_1572_5,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5093),U_5094),U_5094) = c_Groups_Ozero__class_Ozero(U_5093)
    | U_5094 != c_Groups_Ozero__class_Ozero(U_5093)
    | ~ sP431(U_5093,U_5094) ),
    inference(clausify,[status(thm)],[f_1572_3]) ).

cnf(f_1572_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5093),U_5094),U_5094) = c_Groups_Oone__class_Oone(U_5093)
    | U_5094 = c_Groups_Ozero__class_Ozero(U_5093)
    | ~ sP431(U_5093,U_5094) ),
    inference(clausify,[status(thm)],[f_1572_3]) ).

fof(f_1573_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__self]) ).

fof(f_1573_2,plain,
    ! [U_5096,U_5095] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5095),U_5096),U_5096) = c_Groups_Oone__class_Oone(U_5095)
      | U_5096 = c_Groups_Ozero__class_Ozero(U_5095)
      | ~ class_Rings_Odivision__ring(U_5095) ),
    inference(variable_rename,[status(thm)],[f_1573_1]) ).

fof(f_1573_3,plain,
    ! [U_5096,U_5095] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5095),U_5096),U_5096) = c_Groups_Oone__class_Oone(U_5095)
      | U_5096 = c_Groups_Ozero__class_Ozero(U_5095)
      | ~ class_Rings_Odivision__ring(U_5095) ),
    inference(definitional_conversion,[status(esa)],[f_1573_2]) ).

cnf(f_1573_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5095),U_5096),U_5096) = c_Groups_Oone__class_Oone(U_5095)
    | U_5096 = c_Groups_Ozero__class_Ozero(U_5095)
    | ~ class_Rings_Odivision__ring(U_5095) ),
    inference(clausify,[status(thm)],[f_1573_3]) ).

fof(f_1574_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Rings_Odivision__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).

fof(f_1574_2,plain,
    ! [U_5099,U_5098,U_5097] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5097),U_5099),U_5098) = c_Groups_Oone__class_Oone(U_5097)
          | U_5099 != U_5098 )
        & ( U_5099 = U_5098
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5097),U_5099),U_5098) != c_Groups_Oone__class_Oone(U_5097) ) )
      | U_5098 = c_Groups_Ozero__class_Ozero(U_5097)
      | ~ class_Rings_Odivision__ring(U_5097) ),
    inference(variable_rename,[status(thm)],[f_1574_1]) ).

fof(f_1574_3,plain,
    ( ! [U_5098,U_5099,U_5097] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5097),U_5099),U_5098) = c_Groups_Oone__class_Oone(U_5097)
        | U_5099 != U_5098
        | ~ sP432(U_5098,U_5099,U_5097) )
    & ! [U_5098,U_5099,U_5097] :
        ( U_5099 = U_5098
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5097),U_5099),U_5098) != c_Groups_Oone__class_Oone(U_5097)
        | ~ sP432(U_5098,U_5099,U_5097) )
    & ! [U_5098,U_5099,U_5097] :
        ( sP432(U_5098,U_5099,U_5097)
        | U_5098 = c_Groups_Ozero__class_Ozero(U_5097)
        | ~ class_Rings_Odivision__ring(U_5097) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP432])],[f_1574_2]) ).

cnf(f_1574_4,plain,
    ( sP432(U_5098,U_5099,U_5097)
    | U_5098 = c_Groups_Ozero__class_Ozero(U_5097)
    | ~ class_Rings_Odivision__ring(U_5097) ),
    inference(clausify,[status(thm)],[f_1574_3]) ).

cnf(f_1574_5,plain,
    ( U_5099 = U_5098
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5097),U_5099),U_5098) != c_Groups_Oone__class_Oone(U_5097)
    | ~ sP432(U_5098,U_5099,U_5097) ),
    inference(clausify,[status(thm)],[f_1574_3]) ).

cnf(f_1574_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5097),U_5099),U_5098) = c_Groups_Oone__class_Oone(U_5097)
    | U_5099 != U_5098
    | ~ sP432(U_5098,U_5099,U_5097) ),
    inference(clausify,[status(thm)],[f_1574_3]) ).

fof(f_1575_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right]) ).

fof(f_1575_2,plain,
    ! [U_5102,U_5101,U_5100] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5100),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5100),U_5102),U_5101)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5100),U_5102),hAPP(c_Groups_Ouminus__class_Ouminus(U_5100),U_5101))
      | U_5101 = c_Groups_Ozero__class_Ozero(U_5100)
      | ~ class_Rings_Odivision__ring(U_5100) ),
    inference(variable_rename,[status(thm)],[f_1575_1]) ).

fof(f_1575_3,plain,
    ! [U_5102,U_5101,U_5100] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5100),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5100),U_5102),U_5101)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5100),U_5102),hAPP(c_Groups_Ouminus__class_Ouminus(U_5100),U_5101))
      | U_5101 = c_Groups_Ozero__class_Ozero(U_5100)
      | ~ class_Rings_Odivision__ring(U_5100) ),
    inference(definitional_conversion,[status(esa)],[f_1575_2]) ).

cnf(f_1575_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5100),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5100),U_5102),U_5101)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5100),U_5102),hAPP(c_Groups_Ouminus__class_Ouminus(U_5100),U_5101))
    | U_5101 = c_Groups_Ozero__class_Ozero(U_5100)
    | ~ class_Rings_Odivision__ring(U_5100) ),
    inference(clausify,[status(thm)],[f_1575_3]) ).

fof(f_1576_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide]) ).

fof(f_1576_2,plain,
    ! [U_5105,U_5104,U_5103] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5103),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),U_5105)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),U_5104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5103),U_5105),U_5104)
      | U_5104 = c_Groups_Ozero__class_Ozero(U_5103)
      | ~ class_Rings_Odivision__ring(U_5103) ),
    inference(variable_rename,[status(thm)],[f_1576_1]) ).

fof(f_1576_3,plain,
    ! [U_5103,U_5104,U_5105] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5103),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),U_5105)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),U_5104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5103),U_5105),U_5104)
      | U_5104 = c_Groups_Ozero__class_Ozero(U_5103)
      | ~ class_Rings_Odivision__ring(U_5103) ),
    inference(definitional_conversion,[status(esa)],[f_1576_2]) ).

cnf(f_1576_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5103),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),U_5105)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),U_5104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5103),U_5105),U_5104)
    | U_5104 = c_Groups_Ozero__class_Ozero(U_5103)
    | ~ class_Rings_Odivision__ring(U_5103) ),
    inference(clausify,[status(thm)],[f_1576_3]) ).

fof(f_1577_1,plain,
    ! [V_n,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).

fof(f_1577_2,plain,
    ! [U_5109,U_5108,U_5107,U_5106] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5106),U_5108),U_5107)),U_5109) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5106),hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),U_5108),U_5109)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),U_5107),U_5109))
      | U_5107 = c_Groups_Ozero__class_Ozero(U_5106)
      | ~ class_Fields_Ofield(U_5106) ),
    inference(variable_rename,[status(thm)],[f_1577_1]) ).

fof(f_1577_3,plain,
    ! [U_5106,U_5107,U_5108,U_5109] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5106),U_5108),U_5107)),U_5109) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5106),hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),U_5108),U_5109)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),U_5107),U_5109))
      | U_5107 = c_Groups_Ozero__class_Ozero(U_5106)
      | ~ class_Fields_Ofield(U_5106) ),
    inference(definitional_conversion,[status(esa)],[f_1577_2]) ).

cnf(f_1577_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5106),U_5108),U_5107)),U_5109) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5106),hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),U_5108),U_5109)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5106),U_5107),U_5109))
    | U_5107 = c_Groups_Ozero__class_Ozero(U_5106)
    | ~ class_Fields_Ofield(U_5106) ),
    inference(clausify,[status(thm)],[f_1577_3]) ).

fof(f_1578_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide]) ).

fof(f_1578_2,plain,
    ! [U_5112,U_5111,U_5110] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5110),U_5112),U_5111)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5110),hAPP(c_Groups_Oabs__class_Oabs(U_5110),U_5112)),hAPP(c_Groups_Oabs__class_Oabs(U_5110),U_5111))
      | U_5111 = c_Groups_Ozero__class_Ozero(U_5110)
      | ~ class_Fields_Olinordered__field(U_5110) ),
    inference(variable_rename,[status(thm)],[f_1578_1]) ).

fof(f_1578_3,plain,
    ! [U_5110,U_5111,U_5112] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5110),U_5112),U_5111)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5110),hAPP(c_Groups_Oabs__class_Oabs(U_5110),U_5112)),hAPP(c_Groups_Oabs__class_Oabs(U_5110),U_5111))
      | U_5111 = c_Groups_Ozero__class_Ozero(U_5110)
      | ~ class_Fields_Olinordered__field(U_5110) ),
    inference(definitional_conversion,[status(esa)],[f_1578_2]) ).

cnf(f_1578_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5110),U_5112),U_5111)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5110),hAPP(c_Groups_Oabs__class_Oabs(U_5110),U_5112)),hAPP(c_Groups_Oabs__class_Oabs(U_5110),U_5111))
    | U_5111 = c_Groups_Ozero__class_Ozero(U_5110)
    | ~ class_Fields_Olinordered__field(U_5110) ),
    inference(clausify,[status(thm)],[f_1578_3]) ).

fof(f_1579_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one__over]) ).

fof(f_1579_2,plain,
    ! [U_5115,U_5114,U_5113] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5113),c_Groups_Oone__class_Oone(U_5113)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5113),U_5114),U_5115)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5113),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5113),c_Groups_Oone__class_Oone(U_5113)),U_5114)),U_5115)
      | ~ class_Fields_Ofield__inverse__zero(U_5113) ),
    inference(variable_rename,[status(thm)],[f_1579_1]) ).

fof(f_1579_3,plain,
    ! [U_5113,U_5114,U_5115] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5113),c_Groups_Oone__class_Oone(U_5113)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5113),U_5114),U_5115)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5113),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5113),c_Groups_Oone__class_Oone(U_5113)),U_5114)),U_5115)
      | ~ class_Fields_Ofield__inverse__zero(U_5113) ),
    inference(definitional_conversion,[status(esa)],[f_1579_2]) ).

cnf(f_1579_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5113),c_Groups_Oone__class_Oone(U_5113)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5113),U_5114),U_5115)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5113),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5113),c_Groups_Oone__class_Oone(U_5113)),U_5114)),U_5115)
    | ~ class_Fields_Ofield__inverse__zero(U_5113) ),
    inference(clausify,[status(thm)],[f_1579_3]) ).

fof(f_1580_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J]) ).

fof(f_1580_2,plain,
    ! [U_5117,U_5116] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_5116,U_5117))
      | ~ c_Nat__Transfer_Ois__nat(U_5117)
      | ~ c_Nat__Transfer_Ois__nat(U_5116) ),
    inference(variable_rename,[status(thm)],[f_1580_1]) ).

fof(f_1580_3,plain,
    ! [U_5116,U_5117] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_5116,U_5117))
      | ~ c_Nat__Transfer_Ois__nat(U_5117)
      | ~ c_Nat__Transfer_Ois__nat(U_5116) ),
    inference(definitional_conversion,[status(esa)],[f_1580_2]) ).

cnf(f_1580_4,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_5116,U_5117))
    | ~ c_Nat__Transfer_Ois__nat(U_5117)
    | ~ c_Nat__Transfer_Ois__nat(U_5116) ),
    inference(clausify,[status(thm)],[f_1580_3]) ).

fof(f_1581_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg]) ).

fof(f_1581_2,plain,
    ! [U_5120,U_5119,U_5118] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5118),U_5119),U_5120)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5118),U_5120),c_Groups_Ozero__class_Ozero(U_5118)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),U_5119),c_Groups_Ozero__class_Ozero(U_5118)))
      | ~ class_Fields_Olinordered__field(U_5118) ),
    inference(variable_rename,[status(thm)],[f_1581_1]) ).

fof(f_1581_3,plain,
    ! [U_5120,U_5118,U_5119] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5118),U_5119),U_5120)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5118),U_5120),c_Groups_Ozero__class_Ozero(U_5118)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),U_5119),c_Groups_Ozero__class_Ozero(U_5118)))
      | ~ class_Fields_Olinordered__field(U_5118) ),
    inference(definitional_conversion,[status(esa)],[f_1581_2]) ).

cnf(f_1581_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5118),U_5119),U_5120)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5118),U_5120),c_Groups_Ozero__class_Ozero(U_5118)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),U_5119),c_Groups_Ozero__class_Ozero(U_5118)))
    | ~ class_Fields_Olinordered__field(U_5118) ),
    inference(clausify,[status(thm)],[f_1581_3]) ).

fof(f_1582_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos]) ).

fof(f_1582_2,plain,
    ! [U_5123,U_5122,U_5121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121)))
      | ~ class_Fields_Olinordered__field(U_5121) ),
    inference(variable_rename,[status(thm)],[f_1582_1]) ).

fof(f_1582_3,plain,
    ! [U_5121,U_5122,U_5123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121)))
      | ~ class_Fields_Olinordered__field(U_5121) ),
    inference(definitional_conversion,[status(esa)],[f_1582_2]) ).

cnf(f_1582_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Fields_Olinordered__field(U_5121) ),
    inference(clausify,[status(thm)],[f_1582_3]) ).

fof(f_1583_1,plain,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__le]) ).

fof(f_1583_2,plain,
    ! [U_5128,U_5127,U_5126,U_5125,U_5124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5124),U_5125),U_5128)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5124),U_5126),U_5127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5127),U_5128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),U_5126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125))
      | ~ class_Fields_Olinordered__field(U_5124) ),
    inference(variable_rename,[status(thm)],[f_1583_1]) ).

fof(f_1583_3,plain,
    ! [U_5124,U_5125,U_5126,U_5127,U_5128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5124),U_5125),U_5128)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5124),U_5126),U_5127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5127),U_5128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),U_5126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125))
      | ~ class_Fields_Olinordered__field(U_5124) ),
    inference(definitional_conversion,[status(esa)],[f_1583_2]) ).

cnf(f_1583_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5124),U_5125),U_5128)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5124),U_5126),U_5127)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5127),U_5128))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5127))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),U_5126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125))
    | ~ class_Fields_Olinordered__field(U_5124) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

fof(f_1584_1,plain,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__less]) ).

fof(f_1584_2,plain,
    ! [U_5133,U_5132,U_5131,U_5130,U_5129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5129),U_5130),U_5133)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5129),U_5131),U_5132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5132),U_5133))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5132))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5130),U_5131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5130))
      | ~ class_Fields_Olinordered__field(U_5129) ),
    inference(variable_rename,[status(thm)],[f_1584_1]) ).

fof(f_1584_3,plain,
    ! [U_5129,U_5131,U_5130,U_5132,U_5133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5129),U_5130),U_5133)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5129),U_5131),U_5132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5132),U_5133))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5132))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5130),U_5131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5130))
      | ~ class_Fields_Olinordered__field(U_5129) ),
    inference(definitional_conversion,[status(esa)],[f_1584_2]) ).

cnf(f_1584_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5129),U_5130),U_5133)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5129),U_5131),U_5132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5132),U_5133))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5130),U_5131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5130))
    | ~ class_Fields_Olinordered__field(U_5129) ),
    inference(clausify,[status(thm)],[f_1584_3]) ).

fof(f_1585_1,plain,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__less2]) ).

fof(f_1585_2,plain,
    ! [U_5138,U_5137,U_5136,U_5135,U_5134] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5134),U_5135),U_5138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5134),U_5136),U_5137)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),U_5137),U_5138))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),c_Groups_Ozero__class_Ozero(U_5134)),U_5137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5134),U_5135),U_5136))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),c_Groups_Ozero__class_Ozero(U_5134)),U_5135))
      | ~ class_Fields_Olinordered__field(U_5134) ),
    inference(variable_rename,[status(thm)],[f_1585_1]) ).

fof(f_1585_3,plain,
    ! [U_5135,U_5136,U_5134,U_5137,U_5138] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5134),U_5135),U_5138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5134),U_5136),U_5137)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),U_5137),U_5138))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),c_Groups_Ozero__class_Ozero(U_5134)),U_5137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5134),U_5135),U_5136))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),c_Groups_Ozero__class_Ozero(U_5134)),U_5135))
      | ~ class_Fields_Olinordered__field(U_5134) ),
    inference(definitional_conversion,[status(esa)],[f_1585_2]) ).

cnf(f_1585_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5134),U_5135),U_5138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5134),U_5136),U_5137)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),U_5137),U_5138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),c_Groups_Ozero__class_Ozero(U_5134)),U_5137))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5134),U_5135),U_5136))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5134),c_Groups_Ozero__class_Ozero(U_5134)),U_5135))
    | ~ class_Fields_Olinordered__field(U_5134) ),
    inference(clausify,[status(thm)],[f_1585_3]) ).

fof(f_1586_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg]) ).

fof(f_1586_2,plain,
    ! [U_5141,U_5140,U_5139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5139),U_5140),U_5141)),c_Groups_Ozero__class_Ozero(U_5139)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5139),U_5141),c_Groups_Ozero__class_Ozero(U_5139)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5139),c_Groups_Ozero__class_Ozero(U_5139)),U_5140))
      | ~ class_Fields_Olinordered__field(U_5139) ),
    inference(variable_rename,[status(thm)],[f_1586_1]) ).

fof(f_1586_3,plain,
    ! [U_5140,U_5141,U_5139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5139),U_5140),U_5141)),c_Groups_Ozero__class_Ozero(U_5139)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5139),U_5141),c_Groups_Ozero__class_Ozero(U_5139)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5139),c_Groups_Ozero__class_Ozero(U_5139)),U_5140))
      | ~ class_Fields_Olinordered__field(U_5139) ),
    inference(definitional_conversion,[status(esa)],[f_1586_2]) ).

cnf(f_1586_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5139),U_5140),U_5141)),c_Groups_Ozero__class_Ozero(U_5139)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5139),U_5141),c_Groups_Ozero__class_Ozero(U_5139)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5139),c_Groups_Ozero__class_Ozero(U_5139)),U_5140))
    | ~ class_Fields_Olinordered__field(U_5139) ),
    inference(clausify,[status(thm)],[f_1586_3]) ).

fof(f_1587_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos]) ).

fof(f_1587_2,plain,
    ! [U_5144,U_5143,U_5142] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5142),U_5143),U_5144)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),U_5144))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),U_5143))
      | ~ class_Fields_Olinordered__field(U_5142) ),
    inference(variable_rename,[status(thm)],[f_1587_1]) ).

fof(f_1587_3,plain,
    ! [U_5142,U_5143,U_5144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5142),U_5143),U_5144)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),U_5144))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),U_5143))
      | ~ class_Fields_Olinordered__field(U_5142) ),
    inference(definitional_conversion,[status(esa)],[f_1587_2]) ).

cnf(f_1587_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5142),U_5143),U_5144)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),U_5144))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),c_Groups_Ozero__class_Ozero(U_5142)),U_5143))
    | ~ class_Fields_Olinordered__field(U_5142) ),
    inference(clausify,[status(thm)],[f_1587_3]) ).

fof(f_1588_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg]) ).

fof(f_1588_2,plain,
    ! [U_5148,U_5147,U_5146,U_5145] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5145),U_5148),U_5146)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5145),U_5148),U_5147)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),c_Groups_Ozero__class_Ozero(U_5145)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5147))
      | ~ class_Fields_Olinordered__field(U_5145) ),
    inference(variable_rename,[status(thm)],[f_1588_1]) ).

fof(f_1588_3,plain,
    ! [U_5145,U_5146,U_5147,U_5148] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5145),U_5148),U_5146)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5145),U_5148),U_5147)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),c_Groups_Ozero__class_Ozero(U_5145)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5147))
      | ~ class_Fields_Olinordered__field(U_5145) ),
    inference(definitional_conversion,[status(esa)],[f_1588_2]) ).

cnf(f_1588_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5145),U_5148),U_5146)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5145),U_5148),U_5147)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),c_Groups_Ozero__class_Ozero(U_5145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5147))
    | ~ class_Fields_Olinordered__field(U_5145) ),
    inference(clausify,[status(thm)],[f_1588_3]) ).

fof(f_1589_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono]) ).

fof(f_1589_2,plain,
    ! [U_5152,U_5151,U_5150,U_5149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5149),U_5152),U_5151)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5149),U_5152),U_5150)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5151),U_5150)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),U_5151))
      | ~ class_Fields_Olinordered__field(U_5149) ),
    inference(variable_rename,[status(thm)],[f_1589_1]) ).

fof(f_1589_3,plain,
    ! [U_5150,U_5151,U_5149,U_5152] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5149),U_5152),U_5151)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5149),U_5152),U_5150)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5151),U_5150)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),U_5151))
      | ~ class_Fields_Olinordered__field(U_5149) ),
    inference(definitional_conversion,[status(esa)],[f_1589_2]) ).

cnf(f_1589_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5149),U_5152),U_5151)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5149),U_5152),U_5150)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5151),U_5150)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),U_5151))
    | ~ class_Fields_Olinordered__field(U_5149) ),
    inference(clausify,[status(thm)],[f_1589_3]) ).

fof(f_1590_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).

fof(f_1590_2,plain,
    ! [U_5156,U_5155,U_5154,U_5153] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5153),U_5155),U_5154)),U_5156))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5156),U_5154)),U_5155)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5156),U_5154)),U_5155))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5153),U_5155),U_5154)),U_5156)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5154),c_Groups_Ozero__class_Ozero(U_5153)))
      | ~ class_Fields_Olinordered__field(U_5153) ),
    inference(variable_rename,[status(thm)],[f_1590_1]) ).

fof(f_1590_3,plain,
    ( ! [U_5154,U_5155,U_5153,U_5156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5153),U_5155),U_5154)),U_5156))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5156),U_5154)),U_5155))
        | ~ sP433(U_5154,U_5155,U_5153,U_5156) )
    & ! [U_5154,U_5155,U_5153,U_5156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5156),U_5154)),U_5155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5153),U_5155),U_5154)),U_5156))
        | ~ sP433(U_5154,U_5155,U_5153,U_5156) )
    & ! [U_5154,U_5155,U_5153,U_5156] :
        ( sP433(U_5154,U_5155,U_5153,U_5156)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5154),c_Groups_Ozero__class_Ozero(U_5153)))
        | ~ class_Fields_Olinordered__field(U_5153) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP433])],[f_1590_2]) ).

cnf(f_1590_4,plain,
    ( sP433(U_5154,U_5155,U_5153,U_5156)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5154),c_Groups_Ozero__class_Ozero(U_5153)))
    | ~ class_Fields_Olinordered__field(U_5153) ),
    inference(clausify,[status(thm)],[f_1590_3]) ).

cnf(f_1590_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5156),U_5154)),U_5155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5153),U_5155),U_5154)),U_5156))
    | ~ sP433(U_5154,U_5155,U_5153,U_5156) ),
    inference(clausify,[status(thm)],[f_1590_3]) ).

cnf(f_1590_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5153),U_5155),U_5154)),U_5156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5156),U_5154)),U_5155))
    | ~ sP433(U_5154,U_5155,U_5153,U_5156) ),
    inference(clausify,[status(thm)],[f_1590_3]) ).

fof(f_1591_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).

fof(f_1591_2,plain,
    ! [U_5160,U_5159,U_5158,U_5157] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5159),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5157),U_5160),U_5158)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5159),U_5158))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5159),U_5158)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5159),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5157),U_5160),U_5158))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5158),c_Groups_Ozero__class_Ozero(U_5157)))
      | ~ class_Fields_Olinordered__field(U_5157) ),
    inference(variable_rename,[status(thm)],[f_1591_1]) ).

fof(f_1591_3,plain,
    ( ! [U_5159,U_5158,U_5160,U_5157] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5159),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5157),U_5160),U_5158)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5159),U_5158)))
        | ~ sP434(U_5159,U_5158,U_5160,U_5157) )
    & ! [U_5159,U_5158,U_5160,U_5157] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5159),U_5158)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5159),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5157),U_5160),U_5158)))
        | ~ sP434(U_5159,U_5158,U_5160,U_5157) )
    & ! [U_5159,U_5158,U_5160,U_5157] :
        ( sP434(U_5159,U_5158,U_5160,U_5157)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5158),c_Groups_Ozero__class_Ozero(U_5157)))
        | ~ class_Fields_Olinordered__field(U_5157) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP434])],[f_1591_2]) ).

cnf(f_1591_4,plain,
    ( sP434(U_5159,U_5158,U_5160,U_5157)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5158),c_Groups_Ozero__class_Ozero(U_5157)))
    | ~ class_Fields_Olinordered__field(U_5157) ),
    inference(clausify,[status(thm)],[f_1591_3]) ).

cnf(f_1591_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5159),U_5158)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5159),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5157),U_5160),U_5158)))
    | ~ sP434(U_5159,U_5158,U_5160,U_5157) ),
    inference(clausify,[status(thm)],[f_1591_3]) ).

cnf(f_1591_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5159),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5157),U_5160),U_5158)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5159),U_5158)))
    | ~ sP434(U_5159,U_5158,U_5160,U_5157) ),
    inference(clausify,[status(thm)],[f_1591_3]) ).

fof(f_1592_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos]) ).

fof(f_1592_2,plain,
    ! [U_5164,U_5163,U_5162,U_5161] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),U_5163),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5161),U_5164),U_5162)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5161),U_5163),U_5162)),U_5164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),c_Groups_Ozero__class_Ozero(U_5161)),U_5162))
      | ~ class_Fields_Olinordered__field(U_5161) ),
    inference(variable_rename,[status(thm)],[f_1592_1]) ).

fof(f_1592_3,plain,
    ! [U_5161,U_5162,U_5163,U_5164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),U_5163),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5161),U_5164),U_5162)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5161),U_5163),U_5162)),U_5164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),c_Groups_Ozero__class_Ozero(U_5161)),U_5162))
      | ~ class_Fields_Olinordered__field(U_5161) ),
    inference(definitional_conversion,[status(esa)],[f_1592_2]) ).

cnf(f_1592_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),U_5163),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5161),U_5164),U_5162)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5161),U_5163),U_5162)),U_5164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5161),c_Groups_Ozero__class_Ozero(U_5161)),U_5162))
    | ~ class_Fields_Olinordered__field(U_5161) ),
    inference(clausify,[status(thm)],[f_1592_3]) ).

fof(f_1593_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less]) ).

fof(f_1593_2,plain,
    ! [U_5168,U_5167,U_5166,U_5165] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5165),U_5167),U_5166)),U_5168))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),U_5167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5165),U_5168),U_5166)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),U_5166))
      | ~ class_Fields_Olinordered__field(U_5165) ),
    inference(variable_rename,[status(thm)],[f_1593_1]) ).

fof(f_1593_3,plain,
    ! [U_5165,U_5166,U_5167,U_5168] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5165),U_5167),U_5166)),U_5168))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),U_5167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5165),U_5168),U_5166)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),U_5166))
      | ~ class_Fields_Olinordered__field(U_5165) ),
    inference(definitional_conversion,[status(esa)],[f_1593_2]) ).

cnf(f_1593_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5165),U_5167),U_5166)),U_5168))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),U_5167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5165),U_5168),U_5166)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),U_5166))
    | ~ class_Fields_Olinordered__field(U_5165) ),
    inference(clausify,[status(thm)],[f_1593_3]) ).

fof(f_1594_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).

fof(f_1594_2,plain,
    ! [U_5172,U_5171,U_5170,U_5169] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5169),U_5171),U_5170)),U_5172))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),U_5171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5172),U_5170))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),U_5171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5172),U_5170)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5169),U_5171),U_5170)),U_5172)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5170))
      | ~ class_Fields_Olinordered__field(U_5169) ),
    inference(variable_rename,[status(thm)],[f_1594_1]) ).

fof(f_1594_3,plain,
    ( ! [U_5170,U_5169,U_5171,U_5172] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5169),U_5171),U_5170)),U_5172))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),U_5171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5172),U_5170)))
        | ~ sP435(U_5170,U_5169,U_5171,U_5172) )
    & ! [U_5170,U_5169,U_5171,U_5172] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),U_5171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5172),U_5170)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5169),U_5171),U_5170)),U_5172))
        | ~ sP435(U_5170,U_5169,U_5171,U_5172) )
    & ! [U_5170,U_5169,U_5171,U_5172] :
        ( sP435(U_5170,U_5169,U_5171,U_5172)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5170))
        | ~ class_Fields_Olinordered__field(U_5169) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP435])],[f_1594_2]) ).

cnf(f_1594_4,plain,
    ( sP435(U_5170,U_5169,U_5171,U_5172)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5170))
    | ~ class_Fields_Olinordered__field(U_5169) ),
    inference(clausify,[status(thm)],[f_1594_3]) ).

cnf(f_1594_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),U_5171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5172),U_5170)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5169),U_5171),U_5170)),U_5172))
    | ~ sP435(U_5170,U_5169,U_5171,U_5172) ),
    inference(clausify,[status(thm)],[f_1594_3]) ).

cnf(f_1594_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5169),U_5171),U_5170)),U_5172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),U_5171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5172),U_5170)))
    | ~ sP435(U_5170,U_5169,U_5171,U_5172) ),
    inference(clausify,[status(thm)],[f_1594_3]) ).

fof(f_1595_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).

fof(f_1595_2,plain,
    ! [U_5176,U_5175,U_5174,U_5173] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),U_5175),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5173),U_5176),U_5174)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5173),U_5175),U_5174)),U_5176)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5173),U_5175),U_5174)),U_5176))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),U_5175),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5173),U_5176),U_5174))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),c_Groups_Ozero__class_Ozero(U_5173)),U_5174))
      | ~ class_Fields_Olinordered__field(U_5173) ),
    inference(variable_rename,[status(thm)],[f_1595_1]) ).

fof(f_1595_3,plain,
    ( ! [U_5174,U_5173,U_5175,U_5176] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),U_5175),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5173),U_5176),U_5174)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5173),U_5175),U_5174)),U_5176))
        | ~ sP436(U_5174,U_5173,U_5175,U_5176) )
    & ! [U_5174,U_5173,U_5175,U_5176] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5173),U_5175),U_5174)),U_5176))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),U_5175),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5173),U_5176),U_5174)))
        | ~ sP436(U_5174,U_5173,U_5175,U_5176) )
    & ! [U_5174,U_5173,U_5175,U_5176] :
        ( sP436(U_5174,U_5173,U_5175,U_5176)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),c_Groups_Ozero__class_Ozero(U_5173)),U_5174))
        | ~ class_Fields_Olinordered__field(U_5173) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP436])],[f_1595_2]) ).

cnf(f_1595_4,plain,
    ( sP436(U_5174,U_5173,U_5175,U_5176)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),c_Groups_Ozero__class_Ozero(U_5173)),U_5174))
    | ~ class_Fields_Olinordered__field(U_5173) ),
    inference(clausify,[status(thm)],[f_1595_3]) ).

cnf(f_1595_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5173),U_5175),U_5174)),U_5176))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),U_5175),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5173),U_5176),U_5174)))
    | ~ sP436(U_5174,U_5173,U_5175,U_5176) ),
    inference(clausify,[status(thm)],[f_1595_3]) ).

cnf(f_1595_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),U_5175),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5173),U_5176),U_5174)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5173),U_5175),U_5174)),U_5176))
    | ~ sP436(U_5174,U_5173,U_5175,U_5176) ),
    inference(clausify,[status(thm)],[f_1595_3]) ).

fof(f_1596_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).

fof(f_1596_2,plain,
    ! [U_5180,U_5179,U_5178,U_5177] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5177),U_5178),U_5179)),U_5180))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5180))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)),U_5178))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5180))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)),U_5178))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5177),U_5178),U_5179)),U_5180)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5177) ),
    inference(variable_rename,[status(thm)],[f_1596_1]) ).

fof(f_1596_3,plain,
    ( ! [U_5177,U_5179,U_5180] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5180))
        | ~ sP441(U_5177,U_5179,U_5180) )
    & ! [U_5177,U_5179,U_5180] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
        | ~ sP441(U_5177,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)),U_5178))
        | ~ sP440(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
        | ~ sP440(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( sP441(U_5177,U_5179,U_5180)
        | sP440(U_5177,U_5178,U_5179,U_5180)
        | ~ sP442(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
        | ~ sP442(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)))
        | ~ sP439(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
        | ~ sP439(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5180))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
        | ~ sP437(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)),U_5178))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
        | ~ sP437(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( sP437(U_5177,U_5178,U_5179,U_5180)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
        | ~ sP438(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
        | ~ sP438(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5177),U_5178),U_5179)),U_5180))
        | sP442(U_5177,U_5178,U_5179,U_5180)
        | sP439(U_5177,U_5178,U_5179,U_5180)
        | ~ sP443(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( sP438(U_5177,U_5178,U_5179,U_5180)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5177),U_5178),U_5179)),U_5180))
        | ~ sP443(U_5177,U_5178,U_5179,U_5180) )
    & ! [U_5177,U_5178,U_5179,U_5180] :
        ( sP443(U_5177,U_5178,U_5179,U_5180)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5177) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP437,sP438,sP439,sP440,sP441,sP442,sP443])],[f_1596_2]) ).

cnf(f_1596_4,plain,
    ( sP443(U_5177,U_5178,U_5179,U_5180)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5177) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_5,plain,
    ( sP438(U_5177,U_5178,U_5179,U_5180)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5177),U_5178),U_5179)),U_5180))
    | ~ sP443(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5177),U_5178),U_5179)),U_5180))
    | sP442(U_5177,U_5178,U_5179,U_5180)
    | sP439(U_5177,U_5178,U_5179,U_5180)
    | ~ sP443(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
    | ~ sP438(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_8,plain,
    ( sP437(U_5177,U_5178,U_5179,U_5180)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
    | ~ sP438(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)),U_5178))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
    | ~ sP437(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5180))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
    | ~ sP437(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
    | ~ sP439(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)))
    | ~ sP439(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5179))
    | ~ sP442(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_14,plain,
    ( sP441(U_5177,U_5179,U_5180)
    | sP440(U_5177,U_5178,U_5179,U_5180)
    | ~ sP442(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
    | ~ sP440(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5177),U_5180),U_5179)),U_5178))
    | ~ sP440(U_5177,U_5178,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),U_5179),c_Groups_Ozero__class_Ozero(U_5177)))
    | ~ sP441(U_5177,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),c_Groups_Ozero__class_Ozero(U_5177)),U_5180))
    | ~ sP441(U_5177,U_5179,U_5180) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

fof(f_1597_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).

fof(f_1597_2,plain,
    ! [U_5184,U_5183,U_5182,U_5181] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5181),U_5183),U_5184)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),c_Groups_Ozero__class_Ozero(U_5181)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)),U_5183))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),c_Groups_Ozero__class_Ozero(U_5181)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)),U_5183))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5181),U_5183),U_5184))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5181) ),
    inference(variable_rename,[status(thm)],[f_1597_1]) ).

fof(f_1597_3,plain,
    ( ! [U_5184,U_5182,U_5181] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),c_Groups_Ozero__class_Ozero(U_5181)))
        | ~ sP448(U_5184,U_5182,U_5181) )
    & ! [U_5184,U_5182,U_5181] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
        | ~ sP448(U_5184,U_5182,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)))
        | ~ sP447(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
        | ~ sP447(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( sP448(U_5184,U_5182,U_5181)
        | sP447(U_5184,U_5182,U_5183,U_5181)
        | ~ sP449(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
        | ~ sP449(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)),U_5183))
        | ~ sP446(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
        | ~ sP446(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),c_Groups_Ozero__class_Ozero(U_5181)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
        | ~ sP444(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
        | ~ sP444(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( sP444(U_5184,U_5182,U_5183,U_5181)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
        | ~ sP445(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)),U_5183))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
        | ~ sP445(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5181),U_5183),U_5184)))
        | sP449(U_5184,U_5182,U_5183,U_5181)
        | sP446(U_5184,U_5182,U_5183,U_5181)
        | ~ sP450(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( sP445(U_5184,U_5182,U_5183,U_5181)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5181),U_5183),U_5184)))
        | ~ sP450(U_5184,U_5182,U_5183,U_5181) )
    & ! [U_5184,U_5182,U_5183,U_5181] :
        ( sP450(U_5184,U_5182,U_5183,U_5181)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5181) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP444,sP445,sP446,sP447,sP448,sP449,sP450])],[f_1597_2]) ).

cnf(f_1597_4,plain,
    ( sP450(U_5184,U_5182,U_5183,U_5181)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_5,plain,
    ( sP445(U_5184,U_5182,U_5183,U_5181)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5181),U_5183),U_5184)))
    | ~ sP450(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5181),U_5183),U_5184)))
    | sP449(U_5184,U_5182,U_5183,U_5181)
    | sP446(U_5184,U_5182,U_5183,U_5181)
    | ~ sP450(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)),U_5183))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
    | ~ sP445(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_8,plain,
    ( sP444(U_5184,U_5182,U_5183,U_5181)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
    | ~ sP445(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
    | ~ sP444(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),c_Groups_Ozero__class_Ozero(U_5181)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
    | ~ sP444(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
    | ~ sP446(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)),U_5183))
    | ~ sP446(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),c_Groups_Ozero__class_Ozero(U_5181)),U_5184))
    | ~ sP449(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_14,plain,
    ( sP448(U_5184,U_5182,U_5181)
    | sP447(U_5184,U_5182,U_5183,U_5181)
    | ~ sP449(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
    | ~ sP447(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5181),U_5182),U_5184)))
    | ~ sP447(U_5184,U_5182,U_5183,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5184),c_Groups_Ozero__class_Ozero(U_5181)))
    | ~ sP448(U_5184,U_5182,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5181),U_5182),c_Groups_Ozero__class_Ozero(U_5181)))
    | ~ sP448(U_5184,U_5182,U_5181) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

fof(f_1598_1,plain,
    ! [V_x_2] :
      ( ( c_Nat__Transfer_Ois__nat(V_x_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
        | ~ c_Nat__Transfer_Ois__nat(V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_is__nat__def]) ).

fof(f_1598_2,plain,
    ! [U_5185] :
      ( ( c_Nat__Transfer_Ois__nat(U_5185)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5185)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5185))
        | ~ c_Nat__Transfer_Ois__nat(U_5185) ) ),
    inference(variable_rename,[status(thm)],[f_1598_1]) ).

fof(f_1598_3,plain,
    ( ! [U_5187] :
        ( c_Nat__Transfer_Ois__nat(U_5187)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5187)) )
    & ! [U_5186] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5186))
        | ~ c_Nat__Transfer_Ois__nat(U_5186) ) ),
    inference(miniscope,[status(thm)],[f_1598_2]) ).

fof(f_1598_4,plain,
    ( ! [U_5187] :
        ( c_Nat__Transfer_Ois__nat(U_5187)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5187)) )
    & ! [U_5186] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5186))
        | ~ c_Nat__Transfer_Ois__nat(U_5186) ) ),
    inference(definitional_conversion,[status(esa)],[f_1598_3]) ).

cnf(f_1598_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5186))
    | ~ c_Nat__Transfer_Ois__nat(U_5186) ),
    inference(clausify,[status(thm)],[f_1598_4]) ).

cnf(f_1598_6,plain,
    ( c_Nat__Transfer_Ois__nat(U_5187)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5187)) ),
    inference(clausify,[status(thm)],[f_1598_4]) ).

fof(f_1599_1,plain,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__frac__eq]) ).

fof(f_1599_2,plain,
    ! [U_5192,U_5191,U_5190,U_5189,U_5188] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5188),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),U_5191),U_5189)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),U_5192),U_5190)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5191),U_5190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5192),U_5189))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5189),U_5190))
      | U_5190 = c_Groups_Ozero__class_Ozero(U_5188)
      | U_5189 = c_Groups_Ozero__class_Ozero(U_5188)
      | ~ class_Fields_Ofield(U_5188) ),
    inference(variable_rename,[status(thm)],[f_1599_1]) ).

fof(f_1599_3,plain,
    ! [U_5191,U_5188,U_5192,U_5189,U_5190] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5188),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),U_5191),U_5189)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),U_5192),U_5190)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5191),U_5190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5192),U_5189))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5189),U_5190))
      | U_5190 = c_Groups_Ozero__class_Ozero(U_5188)
      | U_5189 = c_Groups_Ozero__class_Ozero(U_5188)
      | ~ class_Fields_Ofield(U_5188) ),
    inference(definitional_conversion,[status(esa)],[f_1599_2]) ).

cnf(f_1599_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5188),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),U_5191),U_5189)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),U_5192),U_5190)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5191),U_5190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5192),U_5189))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5188),U_5189),U_5190))
    | U_5190 = c_Groups_Ozero__class_Ozero(U_5188)
    | U_5189 = c_Groups_Ozero__class_Ozero(U_5188)
    | ~ class_Fields_Ofield(U_5188) ),
    inference(clausify,[status(thm)],[f_1599_3]) ).

fof(f_1600_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff]) ).

fof(f_1600_2,plain,
    ! [U_5196,U_5195,U_5194,U_5193] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5193),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5193),U_5195),U_5194)),U_5196) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5193),U_5195),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5193),U_5194),U_5196))),U_5194)
      | U_5194 = c_Groups_Ozero__class_Ozero(U_5193)
      | ~ class_Fields_Ofield(U_5193) ),
    inference(variable_rename,[status(thm)],[f_1600_1]) ).

fof(f_1600_3,plain,
    ! [U_5196,U_5195,U_5194,U_5193] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5193),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5193),U_5195),U_5194)),U_5196) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5193),U_5195),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5193),U_5194),U_5196))),U_5194)
      | U_5194 = c_Groups_Ozero__class_Ozero(U_5193)
      | ~ class_Fields_Ofield(U_5193) ),
    inference(definitional_conversion,[status(esa)],[f_1600_2]) ).

cnf(f_1600_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5193),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5193),U_5195),U_5194)),U_5196) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5193),U_5195),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5193),U_5194),U_5196))),U_5194)
    | U_5194 = c_Groups_Ozero__class_Ozero(U_5193)
    | ~ class_Fields_Ofield(U_5193) ),
    inference(clausify,[status(thm)],[f_1600_3]) ).

fof(f_1601_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__frac__num]) ).

fof(f_1601_2,plain,
    ! [U_5200,U_5199,U_5198,U_5197] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5197),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5197),U_5199),U_5198)),U_5200) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5197),U_5199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5197),U_5200),U_5198))),U_5198)
      | U_5198 = c_Groups_Ozero__class_Ozero(U_5197)
      | ~ class_Fields_Ofield__inverse__zero(U_5197) ),
    inference(variable_rename,[status(thm)],[f_1601_1]) ).

fof(f_1601_3,plain,
    ! [U_5197,U_5198,U_5199,U_5200] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5197),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5197),U_5199),U_5198)),U_5200) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5197),U_5199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5197),U_5200),U_5198))),U_5198)
      | U_5198 = c_Groups_Ozero__class_Ozero(U_5197)
      | ~ class_Fields_Ofield__inverse__zero(U_5197) ),
    inference(definitional_conversion,[status(esa)],[f_1601_2]) ).

cnf(f_1601_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5197),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5197),U_5199),U_5198)),U_5200) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5197),U_5199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5197),U_5200),U_5198))),U_5198)
    | U_5198 = c_Groups_Ozero__class_Ozero(U_5197)
    | ~ class_Fields_Ofield__inverse__zero(U_5197) ),
    inference(clausify,[status(thm)],[f_1601_3]) ).

fof(f_1602_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff]) ).

fof(f_1602_2,plain,
    ! [U_5204,U_5203,U_5202,U_5201] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5201),U_5203),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5201),U_5204),U_5202)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5201),U_5202),U_5203)),U_5204)),U_5202)
      | U_5202 = c_Groups_Ozero__class_Ozero(U_5201)
      | ~ class_Fields_Ofield(U_5201) ),
    inference(variable_rename,[status(thm)],[f_1602_1]) ).

fof(f_1602_3,plain,
    ! [U_5201,U_5202,U_5203,U_5204] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5201),U_5203),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5201),U_5204),U_5202)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5201),U_5202),U_5203)),U_5204)),U_5202)
      | U_5202 = c_Groups_Ozero__class_Ozero(U_5201)
      | ~ class_Fields_Ofield(U_5201) ),
    inference(definitional_conversion,[status(esa)],[f_1602_2]) ).

cnf(f_1602_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5201),U_5203),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5201),U_5204),U_5202)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5201),U_5202),U_5203)),U_5204)),U_5202)
    | U_5202 = c_Groups_Ozero__class_Ozero(U_5201)
    | ~ class_Fields_Ofield(U_5201) ),
    inference(clausify,[status(thm)],[f_1602_3]) ).

fof(f_1603_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__num__frac]) ).

fof(f_1603_2,plain,
    ! [U_5208,U_5207,U_5206,U_5205] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5205),U_5207),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5205),U_5208),U_5206)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5205),U_5208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5205),U_5207),U_5206))),U_5206)
      | U_5206 = c_Groups_Ozero__class_Ozero(U_5205)
      | ~ class_Fields_Ofield__inverse__zero(U_5205) ),
    inference(variable_rename,[status(thm)],[f_1603_1]) ).

fof(f_1603_3,plain,
    ! [U_5205,U_5206,U_5207,U_5208] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5205),U_5207),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5205),U_5208),U_5206)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5205),U_5208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5205),U_5207),U_5206))),U_5206)
      | U_5206 = c_Groups_Ozero__class_Ozero(U_5205)
      | ~ class_Fields_Ofield__inverse__zero(U_5205) ),
    inference(definitional_conversion,[status(esa)],[f_1603_2]) ).

cnf(f_1603_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5205),U_5207),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5205),U_5208),U_5206)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5205),U_5208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5205),U_5207),U_5206))),U_5206)
    | U_5206 = c_Groups_Ozero__class_Ozero(U_5205)
    | ~ class_Fields_Ofield__inverse__zero(U_5205) ),
    inference(clausify,[status(thm)],[f_1603_3]) ).

fof(f_1604_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff]) ).

fof(f_1604_2,plain,
    ! [U_5212,U_5211,U_5210,U_5209] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5209),U_5211),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5209),U_5212),U_5210)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5209),U_5210),U_5211)),U_5212)),U_5210)
      | U_5210 = c_Groups_Ozero__class_Ozero(U_5209)
      | ~ class_Fields_Ofield(U_5209) ),
    inference(variable_rename,[status(thm)],[f_1604_1]) ).

fof(f_1604_3,plain,
    ! [U_5209,U_5210,U_5211,U_5212] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5209),U_5211),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5209),U_5212),U_5210)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5209),U_5210),U_5211)),U_5212)),U_5210)
      | U_5210 = c_Groups_Ozero__class_Ozero(U_5209)
      | ~ class_Fields_Ofield(U_5209) ),
    inference(definitional_conversion,[status(esa)],[f_1604_2]) ).

cnf(f_1604_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5209),U_5211),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5209),U_5212),U_5210)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5209),U_5210),U_5211)),U_5212)),U_5210)
    | U_5210 = c_Groups_Ozero__class_Ozero(U_5209)
    | ~ class_Fields_Ofield(U_5209) ),
    inference(clausify,[status(thm)],[f_1604_3]) ).

fof(f_1605_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff]) ).

fof(f_1605_2,plain,
    ! [U_5216,U_5215,U_5214,U_5213] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5213),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5213),U_5215),U_5214)),U_5216) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5213),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5213),U_5215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5213),U_5214),U_5216))),U_5214)
      | U_5214 = c_Groups_Ozero__class_Ozero(U_5213)
      | ~ class_Fields_Ofield(U_5213) ),
    inference(variable_rename,[status(thm)],[f_1605_1]) ).

fof(f_1605_3,plain,
    ! [U_5213,U_5214,U_5215,U_5216] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5213),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5213),U_5215),U_5214)),U_5216) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5213),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5213),U_5215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5213),U_5214),U_5216))),U_5214)
      | U_5214 = c_Groups_Ozero__class_Ozero(U_5213)
      | ~ class_Fields_Ofield(U_5213) ),
    inference(definitional_conversion,[status(esa)],[f_1605_2]) ).

cnf(f_1605_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5213),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5213),U_5215),U_5214)),U_5216) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5213),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5213),U_5215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5213),U_5214),U_5216))),U_5214)
    | U_5214 = c_Groups_Ozero__class_Ozero(U_5213)
    | ~ class_Fields_Ofield(U_5213) ),
    inference(clausify,[status(thm)],[f_1605_3]) ).

fof(f_1606_1,plain,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__frac__eq]) ).

fof(f_1606_2,plain,
    ! [U_5221,U_5220,U_5219,U_5218,U_5217] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5217),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),U_5220),U_5218)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),U_5221),U_5219)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5220),U_5219)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5221),U_5218))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5218),U_5219))
      | U_5219 = c_Groups_Ozero__class_Ozero(U_5217)
      | U_5218 = c_Groups_Ozero__class_Ozero(U_5217)
      | ~ class_Fields_Ofield(U_5217) ),
    inference(variable_rename,[status(thm)],[f_1606_1]) ).

fof(f_1606_3,plain,
    ! [U_5217,U_5218,U_5219,U_5220,U_5221] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5217),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),U_5220),U_5218)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),U_5221),U_5219)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5220),U_5219)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5221),U_5218))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5218),U_5219))
      | U_5219 = c_Groups_Ozero__class_Ozero(U_5217)
      | U_5218 = c_Groups_Ozero__class_Ozero(U_5217)
      | ~ class_Fields_Ofield(U_5217) ),
    inference(definitional_conversion,[status(esa)],[f_1606_2]) ).

cnf(f_1606_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5217),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),U_5220),U_5218)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),U_5221),U_5219)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5220),U_5219)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5221),U_5218))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5217),U_5218),U_5219))
    | U_5219 = c_Groups_Ozero__class_Ozero(U_5217)
    | U_5218 = c_Groups_Ozero__class_Ozero(U_5217)
    | ~ class_Fields_Ofield(U_5217) ),
    inference(clausify,[status(thm)],[f_1606_3]) ).

fof(f_1607_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) != V_b_2
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).

fof(f_1607_2,plain,
    ! [U_5225,U_5224,U_5223,U_5222] :
      ( ( ( U_5223 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5224),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225))
          | ( U_5223 != c_Groups_Ozero__class_Ozero(U_5222)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) = c_Groups_Ozero__class_Ozero(U_5222) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5222),U_5223),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) != U_5224
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) != c_Groups_Ozero__class_Ozero(U_5222) ) )
        & ( ( ( U_5223 = c_Groups_Ozero__class_Ozero(U_5222)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) != c_Groups_Ozero__class_Ozero(U_5222) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5222),U_5223),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) = U_5224
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) = c_Groups_Ozero__class_Ozero(U_5222) ) )
          | U_5223 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5224),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) ) )
      | ~ class_Int_Onumber(U_5222)
      | ~ class_Fields_Ofield__inverse__zero(U_5222) ),
    inference(variable_rename,[status(thm)],[f_1607_1]) ).

fof(f_1607_3,plain,
    ( ! [U_5222,U_5223,U_5225] :
        ( U_5223 != c_Groups_Ozero__class_Ozero(U_5222)
        | ~ sP453(U_5222,U_5223,U_5225) )
    & ! [U_5222,U_5223,U_5225] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) = c_Groups_Ozero__class_Ozero(U_5222)
        | ~ sP453(U_5222,U_5223,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5222),U_5223),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) != U_5224
        | ~ sP452(U_5222,U_5223,U_5224,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) != c_Groups_Ozero__class_Ozero(U_5222)
        | ~ sP452(U_5222,U_5223,U_5224,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( U_5223 = c_Groups_Ozero__class_Ozero(U_5222)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) != c_Groups_Ozero__class_Ozero(U_5222)
        | ~ sP451(U_5222,U_5223,U_5224,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5222),U_5223),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) = U_5224
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) = c_Groups_Ozero__class_Ozero(U_5222)
        | ~ sP451(U_5222,U_5223,U_5224,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( U_5223 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5224),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225))
        | sP453(U_5222,U_5223,U_5225)
        | sP452(U_5222,U_5223,U_5224,U_5225)
        | ~ sP454(U_5222,U_5223,U_5224,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( sP451(U_5222,U_5223,U_5224,U_5225)
        | U_5223 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5224),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225))
        | ~ sP454(U_5222,U_5223,U_5224,U_5225) )
    & ! [U_5222,U_5223,U_5224,U_5225] :
        ( sP454(U_5222,U_5223,U_5224,U_5225)
        | ~ class_Int_Onumber(U_5222)
        | ~ class_Fields_Ofield__inverse__zero(U_5222) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP451,sP452,sP453,sP454])],[f_1607_2]) ).

cnf(f_1607_4,plain,
    ( sP454(U_5222,U_5223,U_5224,U_5225)
    | ~ class_Int_Onumber(U_5222)
    | ~ class_Fields_Ofield__inverse__zero(U_5222) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_5,plain,
    ( sP451(U_5222,U_5223,U_5224,U_5225)
    | U_5223 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5224),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225))
    | ~ sP454(U_5222,U_5223,U_5224,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_6,plain,
    ( U_5223 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5222),U_5224),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225))
    | sP453(U_5222,U_5223,U_5225)
    | sP452(U_5222,U_5223,U_5224,U_5225)
    | ~ sP454(U_5222,U_5223,U_5224,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5222),U_5223),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) = U_5224
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) = c_Groups_Ozero__class_Ozero(U_5222)
    | ~ sP451(U_5222,U_5223,U_5224,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_8,plain,
    ( U_5223 = c_Groups_Ozero__class_Ozero(U_5222)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) != c_Groups_Ozero__class_Ozero(U_5222)
    | ~ sP451(U_5222,U_5223,U_5224,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) != c_Groups_Ozero__class_Ozero(U_5222)
    | ~ sP452(U_5222,U_5223,U_5224,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5222),U_5223),hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225)) != U_5224
    | ~ sP452(U_5222,U_5223,U_5224,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_11,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5222),U_5225) = c_Groups_Ozero__class_Ozero(U_5222)
    | ~ sP453(U_5222,U_5223,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

cnf(f_1607_12,plain,
    ( U_5223 != c_Groups_Ozero__class_Ozero(U_5222)
    | ~ sP453(U_5222,U_5223,U_5225) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

fof(f_1608_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) != V_b_2
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).

fof(f_1608_2,plain,
    ! [U_5229,U_5228,U_5227,U_5226] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5226),U_5228),U_5229)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) != c_Groups_Ozero__class_Ozero(U_5226)
            & U_5229 = c_Groups_Ozero__class_Ozero(U_5226) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)),U_5229) != U_5228
            & U_5229 != c_Groups_Ozero__class_Ozero(U_5226) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) = c_Groups_Ozero__class_Ozero(U_5226)
              | U_5229 != c_Groups_Ozero__class_Ozero(U_5226) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)),U_5229) = U_5228
              | U_5229 = c_Groups_Ozero__class_Ozero(U_5226) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5226),U_5228),U_5229) ) )
      | ~ class_Int_Onumber(U_5226)
      | ~ class_Fields_Ofield__inverse__zero(U_5226) ),
    inference(variable_rename,[status(thm)],[f_1608_1]) ).

fof(f_1608_3,plain,
    ( ! [U_5227,U_5226,U_5229] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) != c_Groups_Ozero__class_Ozero(U_5226)
        | ~ sP457(U_5227,U_5226,U_5229) )
    & ! [U_5227,U_5226,U_5229] :
        ( U_5229 = c_Groups_Ozero__class_Ozero(U_5226)
        | ~ sP457(U_5227,U_5226,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)),U_5229) != U_5228
        | ~ sP456(U_5227,U_5226,U_5228,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( U_5229 != c_Groups_Ozero__class_Ozero(U_5226)
        | ~ sP456(U_5227,U_5226,U_5228,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) = c_Groups_Ozero__class_Ozero(U_5226)
        | U_5229 != c_Groups_Ozero__class_Ozero(U_5226)
        | ~ sP455(U_5227,U_5226,U_5228,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)),U_5229) = U_5228
        | U_5229 = c_Groups_Ozero__class_Ozero(U_5226)
        | ~ sP455(U_5227,U_5226,U_5228,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5226),U_5228),U_5229)
        | sP457(U_5227,U_5226,U_5229)
        | sP456(U_5227,U_5226,U_5228,U_5229)
        | ~ sP458(U_5227,U_5226,U_5228,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( sP455(U_5227,U_5226,U_5228,U_5229)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5226),U_5228),U_5229)
        | ~ sP458(U_5227,U_5226,U_5228,U_5229) )
    & ! [U_5227,U_5226,U_5228,U_5229] :
        ( sP458(U_5227,U_5226,U_5228,U_5229)
        | ~ class_Int_Onumber(U_5226)
        | ~ class_Fields_Ofield__inverse__zero(U_5226) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP455,sP456,sP457,sP458])],[f_1608_2]) ).

cnf(f_1608_4,plain,
    ( sP458(U_5227,U_5226,U_5228,U_5229)
    | ~ class_Int_Onumber(U_5226)
    | ~ class_Fields_Ofield__inverse__zero(U_5226) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_5,plain,
    ( sP455(U_5227,U_5226,U_5228,U_5229)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5226),U_5228),U_5229)
    | ~ sP458(U_5227,U_5226,U_5228,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5226),U_5228),U_5229)
    | sP457(U_5227,U_5226,U_5229)
    | sP456(U_5227,U_5226,U_5228,U_5229)
    | ~ sP458(U_5227,U_5226,U_5228,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)),U_5229) = U_5228
    | U_5229 = c_Groups_Ozero__class_Ozero(U_5226)
    | ~ sP455(U_5227,U_5226,U_5228,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) = c_Groups_Ozero__class_Ozero(U_5226)
    | U_5229 != c_Groups_Ozero__class_Ozero(U_5226)
    | ~ sP455(U_5227,U_5226,U_5228,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_9,plain,
    ( U_5229 != c_Groups_Ozero__class_Ozero(U_5226)
    | ~ sP456(U_5227,U_5226,U_5228,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)),U_5229) != U_5228
    | ~ sP456(U_5227,U_5226,U_5228,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_11,plain,
    ( U_5229 = c_Groups_Ozero__class_Ozero(U_5226)
    | ~ sP457(U_5227,U_5226,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_12,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227) != c_Groups_Ozero__class_Ozero(U_5226)
    | ~ sP457(U_5227,U_5226,U_5229) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

fof(f_1609_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).

fof(f_1609_2,plain,
    ! [U_5233,U_5232,U_5231,U_5230] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5230),U_5231),U_5232) = hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) != c_Groups_Ozero__class_Ozero(U_5230)
            & U_5232 = c_Groups_Ozero__class_Ozero(U_5230) )
          | ( U_5231 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)),U_5232)
            & U_5232 != c_Groups_Ozero__class_Ozero(U_5230) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) = c_Groups_Ozero__class_Ozero(U_5230)
              | U_5232 != c_Groups_Ozero__class_Ozero(U_5230) )
            & ( U_5231 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)),U_5232)
              | U_5232 = c_Groups_Ozero__class_Ozero(U_5230) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5230),U_5231),U_5232) != hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) ) )
      | ~ class_Int_Onumber(U_5230)
      | ~ class_Fields_Ofield__inverse__zero(U_5230) ),
    inference(variable_rename,[status(thm)],[f_1609_1]) ).

fof(f_1609_3,plain,
    ( ! [U_5233,U_5232,U_5230] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) != c_Groups_Ozero__class_Ozero(U_5230)
        | ~ sP461(U_5233,U_5232,U_5230) )
    & ! [U_5233,U_5232,U_5230] :
        ( U_5232 = c_Groups_Ozero__class_Ozero(U_5230)
        | ~ sP461(U_5233,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( U_5231 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)),U_5232)
        | ~ sP460(U_5233,U_5231,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( U_5232 != c_Groups_Ozero__class_Ozero(U_5230)
        | ~ sP460(U_5233,U_5231,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) = c_Groups_Ozero__class_Ozero(U_5230)
        | U_5232 != c_Groups_Ozero__class_Ozero(U_5230)
        | ~ sP459(U_5233,U_5231,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( U_5231 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)),U_5232)
        | U_5232 = c_Groups_Ozero__class_Ozero(U_5230)
        | ~ sP459(U_5233,U_5231,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5230),U_5231),U_5232) = hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)
        | sP461(U_5233,U_5232,U_5230)
        | sP460(U_5233,U_5231,U_5232,U_5230)
        | ~ sP462(U_5233,U_5231,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( sP459(U_5233,U_5231,U_5232,U_5230)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5230),U_5231),U_5232) != hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)
        | ~ sP462(U_5233,U_5231,U_5232,U_5230) )
    & ! [U_5233,U_5231,U_5232,U_5230] :
        ( sP462(U_5233,U_5231,U_5232,U_5230)
        | ~ class_Int_Onumber(U_5230)
        | ~ class_Fields_Ofield__inverse__zero(U_5230) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP459,sP460,sP461,sP462])],[f_1609_2]) ).

cnf(f_1609_4,plain,
    ( sP462(U_5233,U_5231,U_5232,U_5230)
    | ~ class_Int_Onumber(U_5230)
    | ~ class_Fields_Ofield__inverse__zero(U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_5,plain,
    ( sP459(U_5233,U_5231,U_5232,U_5230)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5230),U_5231),U_5232) != hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)
    | ~ sP462(U_5233,U_5231,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5230),U_5231),U_5232) = hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)
    | sP461(U_5233,U_5232,U_5230)
    | sP460(U_5233,U_5231,U_5232,U_5230)
    | ~ sP462(U_5233,U_5231,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_7,plain,
    ( U_5231 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)),U_5232)
    | U_5232 = c_Groups_Ozero__class_Ozero(U_5230)
    | ~ sP459(U_5233,U_5231,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) = c_Groups_Ozero__class_Ozero(U_5230)
    | U_5232 != c_Groups_Ozero__class_Ozero(U_5230)
    | ~ sP459(U_5233,U_5231,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_9,plain,
    ( U_5232 != c_Groups_Ozero__class_Ozero(U_5230)
    | ~ sP460(U_5233,U_5231,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_10,plain,
    ( U_5231 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233)),U_5232)
    | ~ sP460(U_5233,U_5231,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_11,plain,
    ( U_5232 = c_Groups_Ozero__class_Ozero(U_5230)
    | ~ sP461(U_5233,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_12,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5230),U_5233) != c_Groups_Ozero__class_Ozero(U_5230)
    | ~ sP461(U_5233,U_5232,U_5230) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

fof(f_1610_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) != V_a_2 ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).

fof(f_1610_2,plain,
    ! [U_5237,U_5236,U_5235,U_5234] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5234),U_5235),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236)) = U_5237
          | ( U_5237 != c_Groups_Ozero__class_Ozero(U_5234)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) = c_Groups_Ozero__class_Ozero(U_5234) )
          | ( U_5235 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5234),U_5237),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236))
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) != c_Groups_Ozero__class_Ozero(U_5234) ) )
        & ( ( ( U_5237 = c_Groups_Ozero__class_Ozero(U_5234)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) != c_Groups_Ozero__class_Ozero(U_5234) )
            & ( U_5235 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5234),U_5237),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236))
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) = c_Groups_Ozero__class_Ozero(U_5234) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5234),U_5235),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236)) != U_5237 ) )
      | ~ class_Int_Onumber(U_5234)
      | ~ class_Fields_Ofield__inverse__zero(U_5234) ),
    inference(variable_rename,[status(thm)],[f_1610_1]) ).

fof(f_1610_3,plain,
    ( ! [U_5234,U_5237,U_5236] :
        ( U_5237 != c_Groups_Ozero__class_Ozero(U_5234)
        | ~ sP465(U_5234,U_5237,U_5236) )
    & ! [U_5234,U_5237,U_5236] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) = c_Groups_Ozero__class_Ozero(U_5234)
        | ~ sP465(U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( U_5235 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5234),U_5237),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236))
        | ~ sP464(U_5235,U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) != c_Groups_Ozero__class_Ozero(U_5234)
        | ~ sP464(U_5235,U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( U_5237 = c_Groups_Ozero__class_Ozero(U_5234)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) != c_Groups_Ozero__class_Ozero(U_5234)
        | ~ sP463(U_5235,U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( U_5235 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5234),U_5237),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) = c_Groups_Ozero__class_Ozero(U_5234)
        | ~ sP463(U_5235,U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5234),U_5235),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236)) = U_5237
        | sP465(U_5234,U_5237,U_5236)
        | sP464(U_5235,U_5234,U_5237,U_5236)
        | ~ sP466(U_5235,U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( sP463(U_5235,U_5234,U_5237,U_5236)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5234),U_5235),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236)) != U_5237
        | ~ sP466(U_5235,U_5234,U_5237,U_5236) )
    & ! [U_5235,U_5234,U_5237,U_5236] :
        ( sP466(U_5235,U_5234,U_5237,U_5236)
        | ~ class_Int_Onumber(U_5234)
        | ~ class_Fields_Ofield__inverse__zero(U_5234) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP463,sP464,sP465,sP466])],[f_1610_2]) ).

cnf(f_1610_4,plain,
    ( sP466(U_5235,U_5234,U_5237,U_5236)
    | ~ class_Int_Onumber(U_5234)
    | ~ class_Fields_Ofield__inverse__zero(U_5234) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_5,plain,
    ( sP463(U_5235,U_5234,U_5237,U_5236)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5234),U_5235),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236)) != U_5237
    | ~ sP466(U_5235,U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5234),U_5235),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236)) = U_5237
    | sP465(U_5234,U_5237,U_5236)
    | sP464(U_5235,U_5234,U_5237,U_5236)
    | ~ sP466(U_5235,U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_7,plain,
    ( U_5235 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5234),U_5237),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) = c_Groups_Ozero__class_Ozero(U_5234)
    | ~ sP463(U_5235,U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_8,plain,
    ( U_5237 = c_Groups_Ozero__class_Ozero(U_5234)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) != c_Groups_Ozero__class_Ozero(U_5234)
    | ~ sP463(U_5235,U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) != c_Groups_Ozero__class_Ozero(U_5234)
    | ~ sP464(U_5235,U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_10,plain,
    ( U_5235 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5234),U_5237),hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236))
    | ~ sP464(U_5235,U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_11,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5234),U_5236) = c_Groups_Ozero__class_Ozero(U_5234)
    | ~ sP465(U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

cnf(f_1610_12,plain,
    ( U_5237 != c_Groups_Ozero__class_Ozero(U_5234)
    | ~ sP465(U_5234,U_5237,U_5236) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

fof(f_1611_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__half__sum]) ).

fof(f_1611_2,plain,
    ! [U_5240,U_5239,U_5238] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5238),U_5239),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5238),U_5239),U_5240)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5238),c_Groups_Oone__class_Oone(U_5238)),c_Groups_Oone__class_Oone(U_5238)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5238),U_5239),U_5240))
      | ~ class_Fields_Olinordered__field(U_5238) ),
    inference(variable_rename,[status(thm)],[f_1611_1]) ).

fof(f_1611_3,plain,
    ! [U_5239,U_5240,U_5238] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5238),U_5239),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5238),U_5239),U_5240)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5238),c_Groups_Oone__class_Oone(U_5238)),c_Groups_Oone__class_Oone(U_5238)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5238),U_5239),U_5240))
      | ~ class_Fields_Olinordered__field(U_5238) ),
    inference(definitional_conversion,[status(esa)],[f_1611_2]) ).

cnf(f_1611_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5238),U_5239),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5238),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5238),U_5239),U_5240)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5238),c_Groups_Oone__class_Oone(U_5238)),c_Groups_Oone__class_Oone(U_5238)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5238),U_5239),U_5240))
    | ~ class_Fields_Olinordered__field(U_5238) ),
    inference(clausify,[status(thm)],[f_1611_3]) ).

fof(f_1612_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_gt__half__sum]) ).

fof(f_1612_2,plain,
    ! [U_5243,U_5242,U_5241] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5241),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),U_5242),U_5243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),c_Groups_Oone__class_Oone(U_5241)),c_Groups_Oone__class_Oone(U_5241)))),U_5243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5241),U_5242),U_5243))
      | ~ class_Fields_Olinordered__field(U_5241) ),
    inference(variable_rename,[status(thm)],[f_1612_1]) ).

fof(f_1612_3,plain,
    ! [U_5242,U_5241,U_5243] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5241),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),U_5242),U_5243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),c_Groups_Oone__class_Oone(U_5241)),c_Groups_Oone__class_Oone(U_5241)))),U_5243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5241),U_5242),U_5243))
      | ~ class_Fields_Olinordered__field(U_5241) ),
    inference(definitional_conversion,[status(esa)],[f_1612_2]) ).

cnf(f_1612_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5241),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),U_5242),U_5243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),c_Groups_Oone__class_Oone(U_5241)),c_Groups_Oone__class_Oone(U_5241)))),U_5243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5241),U_5242),U_5243))
    | ~ class_Fields_Olinordered__field(U_5241) ),
    inference(clausify,[status(thm)],[f_1612_3]) ).

fof(f_1613_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__Numeral0]) ).

fof(f_1613_2,plain,
    ! [U_5245,U_5244] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),U_5245),hAPP(c_Int_Onumber__class_Onumber__of(U_5244),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5244)
      | ~ class_Int_Onumber__ring(U_5244)
      | ~ class_Fields_Ofield__inverse__zero(U_5244) ),
    inference(variable_rename,[status(thm)],[f_1613_1]) ).

fof(f_1613_3,plain,
    ! [U_5244,U_5245] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),U_5245),hAPP(c_Int_Onumber__class_Onumber__of(U_5244),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5244)
      | ~ class_Int_Onumber__ring(U_5244)
      | ~ class_Fields_Ofield__inverse__zero(U_5244) ),
    inference(definitional_conversion,[status(esa)],[f_1613_2]) ).

cnf(f_1613_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),U_5245),hAPP(c_Int_Onumber__class_Onumber__of(U_5244),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5244)
    | ~ class_Int_Onumber__ring(U_5244)
    | ~ class_Fields_Ofield__inverse__zero(U_5244) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

fof(f_1614_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__div__pos]) ).

fof(f_1614_2,plain,
    ! [U_5248,U_5247,U_5246] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5246),hAPP(c_Groups_Oabs__class_Oabs(U_5246),U_5248)),U_5247) = hAPP(c_Groups_Oabs__class_Oabs(U_5246),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5246),U_5248),U_5247))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5246),c_Groups_Ozero__class_Ozero(U_5246)),U_5247))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5246) ),
    inference(variable_rename,[status(thm)],[f_1614_1]) ).

fof(f_1614_3,plain,
    ! [U_5246,U_5247,U_5248] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5246),hAPP(c_Groups_Oabs__class_Oabs(U_5246),U_5248)),U_5247) = hAPP(c_Groups_Oabs__class_Oabs(U_5246),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5246),U_5248),U_5247))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5246),c_Groups_Ozero__class_Ozero(U_5246)),U_5247))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5246) ),
    inference(definitional_conversion,[status(esa)],[f_1614_2]) ).

cnf(f_1614_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5246),hAPP(c_Groups_Oabs__class_Oabs(U_5246),U_5248)),U_5247) = hAPP(c_Groups_Oabs__class_Oabs(U_5246),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5246),U_5248),U_5247))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5246),c_Groups_Ozero__class_Ozero(U_5246)),U_5247))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5246) ),
    inference(clausify,[status(thm)],[f_1614_3]) ).

fof(f_1615_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__Numeral1]) ).

fof(f_1615_2,plain,
    ! [U_5250,U_5249] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5249),U_5250),hAPP(c_Int_Onumber__class_Onumber__of(U_5249),c_Int_OBit1(c_Int_OPls))) = U_5250
      | ~ class_Int_Onumber__ring(U_5249)
      | ~ class_Fields_Ofield(U_5249) ),
    inference(variable_rename,[status(thm)],[f_1615_1]) ).

fof(f_1615_3,plain,
    ! [U_5249,U_5250] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5249),U_5250),hAPP(c_Int_Onumber__class_Onumber__of(U_5249),c_Int_OBit1(c_Int_OPls))) = U_5250
      | ~ class_Int_Onumber__ring(U_5249)
      | ~ class_Fields_Ofield(U_5249) ),
    inference(definitional_conversion,[status(esa)],[f_1615_2]) ).

cnf(f_1615_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5249),U_5250),hAPP(c_Int_Onumber__class_Onumber__of(U_5249),c_Int_OBit1(c_Int_OPls))) = U_5250
    | ~ class_Int_Onumber__ring(U_5249)
    | ~ class_Fields_Ofield(U_5249) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

fof(f_1616_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__numeral__1]) ).

fof(f_1616_2,plain,
    ! [U_5252,U_5251] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5251),U_5252),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),c_Int_OBit1(c_Int_OPls))) = U_5252
      | ~ class_Int_Onumber__ring(U_5251)
      | ~ class_Fields_Ofield(U_5251) ),
    inference(variable_rename,[status(thm)],[f_1616_1]) ).

fof(f_1616_3,plain,
    ! [U_5251,U_5252] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5251),U_5252),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),c_Int_OBit1(c_Int_OPls))) = U_5252
      | ~ class_Int_Onumber__ring(U_5251)
      | ~ class_Fields_Ofield(U_5251) ),
    inference(definitional_conversion,[status(esa)],[f_1616_2]) ).

cnf(f_1616_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5251),U_5252),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),c_Int_OBit1(c_Int_OPls))) = U_5252
    | ~ class_Int_Onumber__ring(U_5251)
    | ~ class_Fields_Ofield(U_5251) ),
    inference(clausify,[status(thm)],[f_1616_3]) ).

fof(f_1617_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__minus1]) ).

fof(f_1617_2,plain,
    ! [U_5254,U_5253] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5253),U_5254),hAPP(c_Int_Onumber__class_Onumber__of(U_5253),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5253),U_5254)
      | ~ class_Int_Onumber__ring(U_5253)
      | ~ class_Fields_Ofield__inverse__zero(U_5253) ),
    inference(variable_rename,[status(thm)],[f_1617_1]) ).

fof(f_1617_3,plain,
    ! [U_5253,U_5254] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5253),U_5254),hAPP(c_Int_Onumber__class_Onumber__of(U_5253),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5253),U_5254)
      | ~ class_Int_Onumber__ring(U_5253)
      | ~ class_Fields_Ofield__inverse__zero(U_5253) ),
    inference(definitional_conversion,[status(esa)],[f_1617_2]) ).

cnf(f_1617_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5253),U_5254),hAPP(c_Int_Onumber__class_Onumber__of(U_5253),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5253),U_5254)
    | ~ class_Int_Onumber__ring(U_5253)
    | ~ class_Fields_Ofield__inverse__zero(U_5253) ),
    inference(clausify,[status(thm)],[f_1617_3]) ).

fof(f_1618_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__code]) ).

fof(f_1618_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1618_1]) ).

cnf(f_1618_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    inference(clausify,[status(thm)],[f_1618_2]) ).

fof(f_1619_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).

fof(f_1619_2,plain,
    ! [U_5258,U_5257,U_5256,U_5255] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5258)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),c_Groups_Ozero__class_Ozero(U_5255)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)),U_5257))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),c_Groups_Ozero__class_Ozero(U_5255)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)),U_5257))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5258))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5255) ),
    inference(variable_rename,[status(thm)],[f_1619_1]) ).

fof(f_1619_3,plain,
    ( ! [U_5255,U_5256,U_5258] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),c_Groups_Ozero__class_Ozero(U_5255)))
        | ~ sP471(U_5255,U_5256,U_5258) )
    & ! [U_5255,U_5256,U_5258] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
        | ~ sP471(U_5255,U_5256,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)))
        | ~ sP470(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
        | ~ sP470(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( sP471(U_5255,U_5256,U_5258)
        | sP470(U_5255,U_5256,U_5257,U_5258)
        | ~ sP472(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
        | ~ sP472(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)),U_5257))
        | ~ sP469(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
        | ~ sP469(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),c_Groups_Ozero__class_Ozero(U_5255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
        | ~ sP467(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
        | ~ sP467(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( sP467(U_5255,U_5256,U_5257,U_5258)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
        | ~ sP468(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)),U_5257))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
        | ~ sP468(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5258)))
        | sP472(U_5255,U_5256,U_5257,U_5258)
        | sP469(U_5255,U_5256,U_5257,U_5258)
        | ~ sP473(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( sP468(U_5255,U_5256,U_5257,U_5258)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5258)))
        | ~ sP473(U_5255,U_5256,U_5257,U_5258) )
    & ! [U_5255,U_5256,U_5257,U_5258] :
        ( sP473(U_5255,U_5256,U_5257,U_5258)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5255) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP467,sP468,sP469,sP470,sP471,sP472,sP473])],[f_1619_2]) ).

cnf(f_1619_4,plain,
    ( sP473(U_5255,U_5256,U_5257,U_5258)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5255) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_5,plain,
    ( sP468(U_5255,U_5256,U_5257,U_5258)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5258)))
    | ~ sP473(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5255),U_5257),U_5258)))
    | sP472(U_5255,U_5256,U_5257,U_5258)
    | sP469(U_5255,U_5256,U_5257,U_5258)
    | ~ sP473(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)),U_5257))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
    | ~ sP468(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_8,plain,
    ( sP467(U_5255,U_5256,U_5257,U_5258)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
    | ~ sP468(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
    | ~ sP467(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),c_Groups_Ozero__class_Ozero(U_5255)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
    | ~ sP467(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
    | ~ sP469(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)),U_5257))
    | ~ sP469(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),c_Groups_Ozero__class_Ozero(U_5255)),U_5258))
    | ~ sP472(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_14,plain,
    ( sP471(U_5255,U_5256,U_5258)
    | sP470(U_5255,U_5256,U_5257,U_5258)
    | ~ sP472(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
    | ~ sP470(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5255),U_5256),U_5258)))
    | ~ sP470(U_5255,U_5256,U_5257,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5255),U_5258),c_Groups_Ozero__class_Ozero(U_5255)))
    | ~ sP471(U_5255,U_5256,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5255),U_5256),c_Groups_Ozero__class_Ozero(U_5255)))
    | ~ sP471(U_5255,U_5256,U_5258) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

fof(f_1620_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).

fof(f_1620_2,plain,
    ! [U_5262,U_5261,U_5260,U_5259] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5260),U_5261)),U_5262))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5262))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)),U_5260))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),U_5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5262))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)),U_5260))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),U_5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5260),U_5261)),U_5262)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5259) ),
    inference(variable_rename,[status(thm)],[f_1620_1]) ).

fof(f_1620_3,plain,
    ( ! [U_5261,U_5262,U_5259] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5262))
        | ~ sP478(U_5261,U_5262,U_5259) )
    & ! [U_5261,U_5262,U_5259] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
        | ~ sP478(U_5261,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)),U_5260))
        | ~ sP477(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
        | ~ sP477(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( sP478(U_5261,U_5262,U_5259)
        | sP477(U_5261,U_5260,U_5262,U_5259)
        | ~ sP479(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
        | ~ sP479(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),U_5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)))
        | ~ sP476(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
        | ~ sP476(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5262))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
        | ~ sP474(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)),U_5260))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
        | ~ sP474(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( sP474(U_5261,U_5260,U_5262,U_5259)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
        | ~ sP475(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),U_5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
        | ~ sP475(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5260),U_5261)),U_5262))
        | sP479(U_5261,U_5260,U_5262,U_5259)
        | sP476(U_5261,U_5260,U_5262,U_5259)
        | ~ sP480(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( sP475(U_5261,U_5260,U_5262,U_5259)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5260),U_5261)),U_5262))
        | ~ sP480(U_5261,U_5260,U_5262,U_5259) )
    & ! [U_5261,U_5260,U_5262,U_5259] :
        ( sP480(U_5261,U_5260,U_5262,U_5259)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5259) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP474,sP475,sP476,sP477,sP478,sP479,sP480])],[f_1620_2]) ).

cnf(f_1620_4,plain,
    ( sP480(U_5261,U_5260,U_5262,U_5259)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_5,plain,
    ( sP475(U_5261,U_5260,U_5262,U_5259)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5260),U_5261)),U_5262))
    | ~ sP480(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5259),U_5260),U_5261)),U_5262))
    | sP479(U_5261,U_5260,U_5262,U_5259)
    | sP476(U_5261,U_5260,U_5262,U_5259)
    | ~ sP480(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),U_5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
    | ~ sP475(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_8,plain,
    ( sP474(U_5261,U_5260,U_5262,U_5259)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
    | ~ sP475(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)),U_5260))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
    | ~ sP474(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5262))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
    | ~ sP474(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
    | ~ sP476(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),U_5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)))
    | ~ sP476(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5261))
    | ~ sP479(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_14,plain,
    ( sP478(U_5261,U_5262,U_5259)
    | sP477(U_5261,U_5260,U_5262,U_5259)
    | ~ sP479(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
    | ~ sP477(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5259),U_5262),U_5261)),U_5260))
    | ~ sP477(U_5261,U_5260,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),U_5261),c_Groups_Ozero__class_Ozero(U_5259)))
    | ~ sP478(U_5261,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),U_5262))
    | ~ sP478(U_5261,U_5262,U_5259) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

fof(f_1621_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).

fof(f_1621_2,plain,
    ! [U_5266,U_5265,U_5264,U_5263] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5266),U_5264)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5264)),U_5266)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5264)),U_5266))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5266),U_5264))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),c_Groups_Ozero__class_Ozero(U_5263)),U_5264))
      | ~ class_Fields_Olinordered__field(U_5263) ),
    inference(variable_rename,[status(thm)],[f_1621_1]) ).

fof(f_1621_3,plain,
    ( ! [U_5266,U_5265,U_5264,U_5263] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5266),U_5264)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5264)),U_5266))
        | ~ sP481(U_5266,U_5265,U_5264,U_5263) )
    & ! [U_5266,U_5265,U_5264,U_5263] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5264)),U_5266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5266),U_5264)))
        | ~ sP481(U_5266,U_5265,U_5264,U_5263) )
    & ! [U_5266,U_5265,U_5264,U_5263] :
        ( sP481(U_5266,U_5265,U_5264,U_5263)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),c_Groups_Ozero__class_Ozero(U_5263)),U_5264))
        | ~ class_Fields_Olinordered__field(U_5263) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP481])],[f_1621_2]) ).

cnf(f_1621_4,plain,
    ( sP481(U_5266,U_5265,U_5264,U_5263)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),c_Groups_Ozero__class_Ozero(U_5263)),U_5264))
    | ~ class_Fields_Olinordered__field(U_5263) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5264)),U_5266))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5266),U_5264)))
    | ~ sP481(U_5266,U_5265,U_5264,U_5263) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5263),U_5266),U_5264)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5264)),U_5266))
    | ~ sP481(U_5266,U_5265,U_5264,U_5263) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

fof(f_1622_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).

fof(f_1622_2,plain,
    ! [U_5270,U_5269,U_5268,U_5267] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5267),U_5269),U_5268)),U_5270))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),U_5269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5267),U_5270),U_5268))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),U_5269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5267),U_5270),U_5268)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5267),U_5269),U_5268)),U_5270)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Ozero__class_Ozero(U_5267)),U_5268))
      | ~ class_Fields_Olinordered__field(U_5267) ),
    inference(variable_rename,[status(thm)],[f_1622_1]) ).

fof(f_1622_3,plain,
    ( ! [U_5268,U_5270,U_5269,U_5267] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5267),U_5269),U_5268)),U_5270))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),U_5269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5267),U_5270),U_5268)))
        | ~ sP482(U_5268,U_5270,U_5269,U_5267) )
    & ! [U_5268,U_5270,U_5269,U_5267] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),U_5269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5267),U_5270),U_5268)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5267),U_5269),U_5268)),U_5270))
        | ~ sP482(U_5268,U_5270,U_5269,U_5267) )
    & ! [U_5268,U_5270,U_5269,U_5267] :
        ( sP482(U_5268,U_5270,U_5269,U_5267)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Ozero__class_Ozero(U_5267)),U_5268))
        | ~ class_Fields_Olinordered__field(U_5267) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP482])],[f_1622_2]) ).

cnf(f_1622_4,plain,
    ( sP482(U_5268,U_5270,U_5269,U_5267)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Ozero__class_Ozero(U_5267)),U_5268))
    | ~ class_Fields_Olinordered__field(U_5267) ),
    inference(clausify,[status(thm)],[f_1622_3]) ).

cnf(f_1622_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),U_5269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5267),U_5270),U_5268)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5267),U_5269),U_5268)),U_5270))
    | ~ sP482(U_5268,U_5270,U_5269,U_5267) ),
    inference(clausify,[status(thm)],[f_1622_3]) ).

cnf(f_1622_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5267),U_5269),U_5268)),U_5270))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5267),U_5269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5267),U_5270),U_5268)))
    | ~ sP482(U_5268,U_5270,U_5269,U_5267) ),
    inference(clausify,[status(thm)],[f_1622_3]) ).

fof(f_1623_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le]) ).

fof(f_1623_2,plain,
    ! [U_5274,U_5273,U_5272,U_5271] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5271),U_5273),U_5272)),U_5274))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),U_5273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5271),U_5274),U_5272)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5271),c_Groups_Ozero__class_Ozero(U_5271)),U_5272))
      | ~ class_Fields_Olinordered__field(U_5271) ),
    inference(variable_rename,[status(thm)],[f_1623_1]) ).

fof(f_1623_3,plain,
    ! [U_5273,U_5272,U_5271,U_5274] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5271),U_5273),U_5272)),U_5274))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),U_5273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5271),U_5274),U_5272)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5271),c_Groups_Ozero__class_Ozero(U_5271)),U_5272))
      | ~ class_Fields_Olinordered__field(U_5271) ),
    inference(definitional_conversion,[status(esa)],[f_1623_2]) ).

cnf(f_1623_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5271),U_5273),U_5272)),U_5274))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),U_5273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5271),U_5274),U_5272)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5271),c_Groups_Ozero__class_Ozero(U_5271)),U_5272))
    | ~ class_Fields_Olinordered__field(U_5271) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

fof(f_1624_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos]) ).

fof(f_1624_2,plain,
    ! [U_5278,U_5277,U_5276,U_5275] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5275),U_5277),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5275),U_5278),U_5276)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5275),U_5277),U_5276)),U_5278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5275),c_Groups_Ozero__class_Ozero(U_5275)),U_5276))
      | ~ class_Fields_Olinordered__field(U_5275) ),
    inference(variable_rename,[status(thm)],[f_1624_1]) ).

fof(f_1624_3,plain,
    ! [U_5276,U_5275,U_5277,U_5278] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5275),U_5277),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5275),U_5278),U_5276)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5275),U_5277),U_5276)),U_5278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5275),c_Groups_Ozero__class_Ozero(U_5275)),U_5276))
      | ~ class_Fields_Olinordered__field(U_5275) ),
    inference(definitional_conversion,[status(esa)],[f_1624_2]) ).

cnf(f_1624_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5275),U_5277),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5275),U_5278),U_5276)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5275),U_5277),U_5276)),U_5278))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5275),c_Groups_Ozero__class_Ozero(U_5275)),U_5276))
    | ~ class_Fields_Olinordered__field(U_5275) ),
    inference(clausify,[status(thm)],[f_1624_3]) ).

fof(f_1625_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).

fof(f_1625_2,plain,
    ! [U_5282,U_5281,U_5280,U_5279] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5279),U_5282),U_5280)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5279),U_5281),U_5280))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5279),U_5281),U_5280)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5279),U_5282),U_5280))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5279),U_5280),c_Groups_Ozero__class_Ozero(U_5279)))
      | ~ class_Fields_Olinordered__field(U_5279) ),
    inference(variable_rename,[status(thm)],[f_1625_1]) ).

fof(f_1625_3,plain,
    ( ! [U_5280,U_5279,U_5281,U_5282] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5279),U_5282),U_5280)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5279),U_5281),U_5280)))
        | ~ sP483(U_5280,U_5279,U_5281,U_5282) )
    & ! [U_5280,U_5279,U_5281,U_5282] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5279),U_5281),U_5280)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5279),U_5282),U_5280)))
        | ~ sP483(U_5280,U_5279,U_5281,U_5282) )
    & ! [U_5280,U_5279,U_5281,U_5282] :
        ( sP483(U_5280,U_5279,U_5281,U_5282)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5279),U_5280),c_Groups_Ozero__class_Ozero(U_5279)))
        | ~ class_Fields_Olinordered__field(U_5279) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP483])],[f_1625_2]) ).

cnf(f_1625_4,plain,
    ( sP483(U_5280,U_5279,U_5281,U_5282)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5279),U_5280),c_Groups_Ozero__class_Ozero(U_5279)))
    | ~ class_Fields_Olinordered__field(U_5279) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

cnf(f_1625_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5279),U_5281),U_5280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5279),U_5282),U_5280)))
    | ~ sP483(U_5280,U_5279,U_5281,U_5282) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

cnf(f_1625_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5279),U_5282),U_5280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5279),U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5279),U_5281),U_5280)))
    | ~ sP483(U_5280,U_5279,U_5281,U_5282) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

fof(f_1626_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).

fof(f_1626_2,plain,
    ! [U_5286,U_5285,U_5284,U_5283] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5283),U_5285),U_5284)),U_5286))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5283),U_5286),U_5284)),U_5285)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5283),U_5286),U_5284)),U_5285))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5283),U_5285),U_5284)),U_5286)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5283),U_5284),c_Groups_Ozero__class_Ozero(U_5283)))
      | ~ class_Fields_Olinordered__field(U_5283) ),
    inference(variable_rename,[status(thm)],[f_1626_1]) ).

fof(f_1626_3,plain,
    ( ! [U_5284,U_5286,U_5285,U_5283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5283),U_5285),U_5284)),U_5286))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5283),U_5286),U_5284)),U_5285))
        | ~ sP484(U_5284,U_5286,U_5285,U_5283) )
    & ! [U_5284,U_5286,U_5285,U_5283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5283),U_5286),U_5284)),U_5285))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5283),U_5285),U_5284)),U_5286))
        | ~ sP484(U_5284,U_5286,U_5285,U_5283) )
    & ! [U_5284,U_5286,U_5285,U_5283] :
        ( sP484(U_5284,U_5286,U_5285,U_5283)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5283),U_5284),c_Groups_Ozero__class_Ozero(U_5283)))
        | ~ class_Fields_Olinordered__field(U_5283) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP484])],[f_1626_2]) ).

cnf(f_1626_4,plain,
    ( sP484(U_5284,U_5286,U_5285,U_5283)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5283),U_5284),c_Groups_Ozero__class_Ozero(U_5283)))
    | ~ class_Fields_Olinordered__field(U_5283) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

cnf(f_1626_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5283),U_5286),U_5284)),U_5285))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5283),U_5285),U_5284)),U_5286))
    | ~ sP484(U_5284,U_5286,U_5285,U_5283) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

cnf(f_1626_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5283),U_5285),U_5284)),U_5286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5283),U_5286),U_5284)),U_5285))
    | ~ sP484(U_5284,U_5286,U_5285,U_5283) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

fof(f_1627_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__left__mono]) ).

fof(f_1627_2,plain,
    ! [U_5290,U_5289,U_5288,U_5287] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5287),U_5290),U_5289)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5287),U_5290),U_5288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5287),c_Groups_Ozero__class_Ozero(U_5287)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5287),U_5289),U_5288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),c_Groups_Ozero__class_Ozero(U_5287)),U_5290))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),U_5288),U_5289))
      | ~ class_Fields_Olinordered__field(U_5287) ),
    inference(variable_rename,[status(thm)],[f_1627_1]) ).

fof(f_1627_3,plain,
    ! [U_5287,U_5288,U_5289,U_5290] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5287),U_5290),U_5289)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5287),U_5290),U_5288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5287),c_Groups_Ozero__class_Ozero(U_5287)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5287),U_5289),U_5288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),c_Groups_Ozero__class_Ozero(U_5287)),U_5290))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),U_5288),U_5289))
      | ~ class_Fields_Olinordered__field(U_5287) ),
    inference(definitional_conversion,[status(esa)],[f_1627_2]) ).

cnf(f_1627_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5287),U_5290),U_5289)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5287),U_5290),U_5288)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5287),c_Groups_Ozero__class_Ozero(U_5287)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5287),U_5289),U_5288)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),c_Groups_Ozero__class_Ozero(U_5287)),U_5290))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5287),U_5288),U_5289))
    | ~ class_Fields_Olinordered__field(U_5287) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

fof(f_1628_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg]) ).

fof(f_1628_2,plain,
    ! [U_5294,U_5293,U_5292,U_5291] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5291),U_5294),U_5292)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5291),U_5294),U_5293)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5291),c_Groups_Ozero__class_Ozero(U_5291)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5291),U_5292),U_5293)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),U_5294),c_Groups_Ozero__class_Ozero(U_5291)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),U_5292),U_5293))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5291) ),
    inference(variable_rename,[status(thm)],[f_1628_1]) ).

fof(f_1628_3,plain,
    ! [U_5291,U_5292,U_5293,U_5294] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5291),U_5294),U_5292)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5291),U_5294),U_5293)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5291),c_Groups_Ozero__class_Ozero(U_5291)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5291),U_5292),U_5293)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),U_5294),c_Groups_Ozero__class_Ozero(U_5291)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),U_5292),U_5293))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5291) ),
    inference(definitional_conversion,[status(esa)],[f_1628_2]) ).

cnf(f_1628_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5291),U_5294),U_5292)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5291),U_5294),U_5293)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5291),c_Groups_Ozero__class_Ozero(U_5291)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5291),U_5292),U_5293)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),U_5294),c_Groups_Ozero__class_Ozero(U_5291)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5291),U_5292),U_5293))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5291) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

fof(f_1629_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(f_1629_2,plain,
    ! [U_5298,U_5297,U_5296,U_5295] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5295),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),c_Groups_Ozero__class_Ozero(U_5295)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))),U_5297))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),c_Groups_Ozero__class_Ozero(U_5295)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))),U_5297))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5295),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))) ) )
      | ~ class_Int_Onumber(U_5295)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5295) ),
    inference(variable_rename,[status(thm)],[f_1629_1]) ).

fof(f_1629_3,plain,
    ( ! [U_5295,U_5296,U_5298] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),c_Groups_Ozero__class_Ozero(U_5295)))
        | ~ sP489(U_5295,U_5296,U_5298) )
    & ! [U_5295,U_5296,U_5298] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
        | ~ sP489(U_5295,U_5296,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
        | ~ sP488(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
        | ~ sP488(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( sP489(U_5295,U_5296,U_5298)
        | sP488(U_5295,U_5296,U_5297,U_5298)
        | ~ sP490(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
        | ~ sP490(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))),U_5297))
        | ~ sP487(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
        | ~ sP487(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),c_Groups_Ozero__class_Ozero(U_5295)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
        | ~ sP485(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
        | ~ sP485(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( sP485(U_5295,U_5296,U_5297,U_5298)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
        | ~ sP486(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))),U_5297))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
        | ~ sP486(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5295),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
        | sP490(U_5295,U_5296,U_5297,U_5298)
        | sP487(U_5295,U_5296,U_5297,U_5298)
        | ~ sP491(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( sP486(U_5295,U_5296,U_5297,U_5298)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5295),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
        | ~ sP491(U_5295,U_5296,U_5297,U_5298) )
    & ! [U_5295,U_5296,U_5297,U_5298] :
        ( sP491(U_5295,U_5296,U_5297,U_5298)
        | ~ class_Int_Onumber(U_5295)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5295) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP485,sP486,sP487,sP488,sP489,sP490,sP491])],[f_1629_2]) ).

cnf(f_1629_4,plain,
    ( sP491(U_5295,U_5296,U_5297,U_5298)
    | ~ class_Int_Onumber(U_5295)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5295) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_5,plain,
    ( sP486(U_5295,U_5296,U_5297,U_5298)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5295),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
    | ~ sP491(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5295),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
    | sP490(U_5295,U_5296,U_5297,U_5298)
    | sP487(U_5295,U_5296,U_5297,U_5298)
    | ~ sP491(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))),U_5297))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
    | ~ sP486(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_8,plain,
    ( sP485(U_5295,U_5296,U_5297,U_5298)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
    | ~ sP486(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
    | ~ sP485(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),c_Groups_Ozero__class_Ozero(U_5295)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
    | ~ sP485(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
    | ~ sP487(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))),U_5297))
    | ~ sP487(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),c_Groups_Ozero__class_Ozero(U_5295)),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)))
    | ~ sP490(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_14,plain,
    ( sP489(U_5295,U_5296,U_5298)
    | sP488(U_5295,U_5296,U_5297,U_5298)
    | ~ sP490(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
    | ~ sP488(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5295),U_5296),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298))))
    | ~ sP488(U_5295,U_5296,U_5297,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(c_Int_Onumber__class_Onumber__of(U_5295),U_5298)),c_Groups_Ozero__class_Ozero(U_5295)))
    | ~ sP489(U_5295,U_5296,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),U_5296),c_Groups_Ozero__class_Ozero(U_5295)))
    | ~ sP489(U_5295,U_5296,U_5298) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

fof(f_1630_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(f_1630_2,plain,
    ! [U_5302,U_5301,U_5300,U_5299] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5299),U_5301),U_5302)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),c_Groups_Ozero__class_Ozero(U_5299)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)),U_5301))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),c_Groups_Ozero__class_Ozero(U_5299)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)),U_5301))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5299),U_5301),U_5302))) ) )
      | ~ class_Int_Onumber(U_5299)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5299) ),
    inference(variable_rename,[status(thm)],[f_1630_1]) ).

fof(f_1630_3,plain,
    ( ! [U_5300,U_5299,U_5302] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),c_Groups_Ozero__class_Ozero(U_5299)))
        | ~ sP496(U_5300,U_5299,U_5302) )
    & ! [U_5300,U_5299,U_5302] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
        | ~ sP496(U_5300,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)))
        | ~ sP495(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
        | ~ sP495(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( sP496(U_5300,U_5299,U_5302)
        | sP495(U_5300,U_5301,U_5299,U_5302)
        | ~ sP497(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
        | ~ sP497(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)),U_5301))
        | ~ sP494(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
        | ~ sP494(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),c_Groups_Ozero__class_Ozero(U_5299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
        | ~ sP492(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
        | ~ sP492(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( sP492(U_5300,U_5301,U_5299,U_5302)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
        | ~ sP493(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)),U_5301))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
        | ~ sP493(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5299),U_5301),U_5302)))
        | sP497(U_5300,U_5301,U_5299,U_5302)
        | sP494(U_5300,U_5301,U_5299,U_5302)
        | ~ sP498(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( sP493(U_5300,U_5301,U_5299,U_5302)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5299),U_5301),U_5302)))
        | ~ sP498(U_5300,U_5301,U_5299,U_5302) )
    & ! [U_5300,U_5301,U_5299,U_5302] :
        ( sP498(U_5300,U_5301,U_5299,U_5302)
        | ~ class_Int_Onumber(U_5299)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5299) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP492,sP493,sP494,sP495,sP496,sP497,sP498])],[f_1630_2]) ).

cnf(f_1630_4,plain,
    ( sP498(U_5300,U_5301,U_5299,U_5302)
    | ~ class_Int_Onumber(U_5299)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5299) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_5,plain,
    ( sP493(U_5300,U_5301,U_5299,U_5302)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5299),U_5301),U_5302)))
    | ~ sP498(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5299),U_5301),U_5302)))
    | sP497(U_5300,U_5301,U_5299,U_5302)
    | sP494(U_5300,U_5301,U_5299,U_5302)
    | ~ sP498(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)),U_5301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
    | ~ sP493(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_8,plain,
    ( sP492(U_5300,U_5301,U_5299,U_5302)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
    | ~ sP493(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
    | ~ sP492(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),c_Groups_Ozero__class_Ozero(U_5299)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
    | ~ sP492(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
    | ~ sP494(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)),U_5301))
    | ~ sP494(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),c_Groups_Ozero__class_Ozero(U_5299)),U_5302))
    | ~ sP497(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_14,plain,
    ( sP496(U_5300,U_5299,U_5302)
    | sP495(U_5300,U_5301,U_5299,U_5302)
    | ~ sP497(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
    | ~ sP495(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),U_5302)))
    | ~ sP495(U_5300,U_5301,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),U_5302),c_Groups_Ozero__class_Ozero(U_5299)))
    | ~ sP496(U_5300,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5299),hAPP(c_Int_Onumber__class_Onumber__of(U_5299),U_5300)),c_Groups_Ozero__class_Ozero(U_5299)))
    | ~ sP496(U_5300,U_5299,U_5302) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

fof(f_1631_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(f_1631_2,plain,
    ! [U_5306,U_5305,U_5304,U_5303] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5303),U_5304),U_5305)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)),U_5304))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)),U_5304))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5303),U_5304),U_5305)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306))) ) )
      | ~ class_Int_Onumber(U_5303)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5303) ),
    inference(variable_rename,[status(thm)],[f_1631_1]) ).

fof(f_1631_3,plain,
    ( ! [U_5306,U_5305,U_5303] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
        | ~ sP503(U_5306,U_5305,U_5303) )
    & ! [U_5306,U_5305,U_5303] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
        | ~ sP503(U_5306,U_5305,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)),U_5304))
        | ~ sP502(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
        | ~ sP502(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( sP503(U_5306,U_5305,U_5303)
        | sP502(U_5306,U_5305,U_5304,U_5303)
        | ~ sP504(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
        | ~ sP504(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)))
        | ~ sP501(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
        | ~ sP501(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
        | ~ sP499(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)),U_5304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
        | ~ sP499(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( sP499(U_5306,U_5305,U_5304,U_5303)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
        | ~ sP500(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
        | ~ sP500(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5303),U_5304),U_5305)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
        | sP504(U_5306,U_5305,U_5304,U_5303)
        | sP501(U_5306,U_5305,U_5304,U_5303)
        | ~ sP505(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( sP500(U_5306,U_5305,U_5304,U_5303)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5303),U_5304),U_5305)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
        | ~ sP505(U_5306,U_5305,U_5304,U_5303) )
    & ! [U_5306,U_5305,U_5304,U_5303] :
        ( sP505(U_5306,U_5305,U_5304,U_5303)
        | ~ class_Int_Onumber(U_5303)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5303) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP499,sP500,sP501,sP502,sP503,sP504,sP505])],[f_1631_2]) ).

cnf(f_1631_4,plain,
    ( sP505(U_5306,U_5305,U_5304,U_5303)
    | ~ class_Int_Onumber(U_5303)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_5,plain,
    ( sP500(U_5306,U_5305,U_5304,U_5303)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5303),U_5304),U_5305)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
    | ~ sP505(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5303),U_5304),U_5305)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
    | sP504(U_5306,U_5305,U_5304,U_5303)
    | sP501(U_5306,U_5305,U_5304,U_5303)
    | ~ sP505(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
    | ~ sP500(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_8,plain,
    ( sP499(U_5306,U_5305,U_5304,U_5303)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
    | ~ sP500(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)),U_5304))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
    | ~ sP499(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
    | ~ sP499(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
    | ~ sP501(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)))
    | ~ sP501(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),U_5305))
    | ~ sP504(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_14,plain,
    ( sP503(U_5306,U_5305,U_5303)
    | sP502(U_5306,U_5305,U_5304,U_5303)
    | ~ sP504(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
    | ~ sP502(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5303),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)),U_5305)),U_5304))
    | ~ sP502(U_5306,U_5305,U_5304,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),U_5305),c_Groups_Ozero__class_Ozero(U_5303)))
    | ~ sP503(U_5306,U_5305,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(c_Int_Onumber__class_Onumber__of(U_5303),U_5306)))
    | ~ sP503(U_5306,U_5305,U_5303) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

fof(f_1632_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(f_1632_2,plain,
    ! [U_5310,U_5309,U_5308,U_5307] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5307),U_5308),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5310))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),U_5310))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5308))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),U_5308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),U_5310))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5308))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),U_5308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5307),U_5308),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5310)) ) )
      | ~ class_Int_Onumber(U_5307)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5307) ),
    inference(variable_rename,[status(thm)],[f_1632_1]) ).

fof(f_1632_3,plain,
    ( ! [U_5310,U_5309,U_5307] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),U_5310))
        | ~ sP510(U_5310,U_5309,U_5307) )
    & ! [U_5310,U_5309,U_5307] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
        | ~ sP510(U_5310,U_5309,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5308))
        | ~ sP509(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
        | ~ sP509(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( sP510(U_5310,U_5309,U_5307)
        | sP509(U_5310,U_5309,U_5308,U_5307)
        | ~ sP511(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
        | ~ sP511(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),U_5308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))))
        | ~ sP508(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
        | ~ sP508(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),U_5310))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
        | ~ sP506(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5308))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
        | ~ sP506(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( sP506(U_5310,U_5309,U_5308,U_5307)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
        | ~ sP507(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),U_5308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
        | ~ sP507(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5307),U_5308),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5310))
        | sP511(U_5310,U_5309,U_5308,U_5307)
        | sP508(U_5310,U_5309,U_5308,U_5307)
        | ~ sP512(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( sP507(U_5310,U_5309,U_5308,U_5307)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5307),U_5308),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5310))
        | ~ sP512(U_5310,U_5309,U_5308,U_5307) )
    & ! [U_5310,U_5309,U_5308,U_5307] :
        ( sP512(U_5310,U_5309,U_5308,U_5307)
        | ~ class_Int_Onumber(U_5307)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5307) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP506,sP507,sP508,sP509,sP510,sP511,sP512])],[f_1632_2]) ).

cnf(f_1632_4,plain,
    ( sP512(U_5310,U_5309,U_5308,U_5307)
    | ~ class_Int_Onumber(U_5307)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_5,plain,
    ( sP507(U_5310,U_5309,U_5308,U_5307)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5307),U_5308),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5310))
    | ~ sP512(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5307),U_5308),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5310))
    | sP511(U_5310,U_5309,U_5308,U_5307)
    | sP508(U_5310,U_5309,U_5308,U_5307)
    | ~ sP512(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),U_5308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
    | ~ sP507(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_8,plain,
    ( sP506(U_5310,U_5309,U_5308,U_5307)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
    | ~ sP507(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5308))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
    | ~ sP506(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),U_5310))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
    | ~ sP506(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
    | ~ sP508(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),U_5308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))))
    | ~ sP508(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)))
    | ~ sP511(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_14,plain,
    ( sP510(U_5310,U_5309,U_5307)
    | sP509(U_5310,U_5309,U_5308,U_5307)
    | ~ sP511(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
    | ~ sP509(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309))),U_5308))
    | ~ sP509(U_5310,U_5309,U_5308,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),hAPP(c_Int_Onumber__class_Onumber__of(U_5307),U_5309)),c_Groups_Ozero__class_Ozero(U_5307)))
    | ~ sP510(U_5310,U_5309,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

cnf(f_1632_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5307),c_Groups_Ozero__class_Ozero(U_5307)),U_5310))
    | ~ sP510(U_5310,U_5309,U_5307) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

fof(f_1633_1,plain,
    ! [V_m,V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__diff]) ).

fof(f_1633_2,plain,
    ! [U_5314,U_5313,U_5312,U_5311] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5314),U_5313)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5311),hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),U_5314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),U_5313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5313),U_5314))
      | U_5312 = c_Groups_Ozero__class_Ozero(U_5311)
      | ~ class_Fields_Ofield(U_5311) ),
    inference(variable_rename,[status(thm)],[f_1633_1]) ).

fof(f_1633_3,plain,
    ! [U_5311,U_5314,U_5312,U_5313] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5314),U_5313)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5311),hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),U_5314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),U_5313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5313),U_5314))
      | U_5312 = c_Groups_Ozero__class_Ozero(U_5311)
      | ~ class_Fields_Ofield(U_5311) ),
    inference(definitional_conversion,[status(esa)],[f_1633_2]) ).

cnf(f_1633_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5314),U_5313)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5311),hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),U_5314)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5311),U_5312),U_5313))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5313),U_5314))
    | U_5312 = c_Groups_Ozero__class_Ozero(U_5311)
    | ~ class_Fields_Ofield(U_5311) ),
    inference(clausify,[status(thm)],[f_1633_3]) ).

fof(f_1634_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x))
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus1__divide]) ).

fof(f_1634_2,plain,
    ! [U_5316,U_5315] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5315),hAPP(c_Int_Onumber__class_Onumber__of(U_5315),c_Int_OMin)),U_5316) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5315),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5315),c_Groups_Oone__class_Oone(U_5315)),U_5316))
      | ~ class_Int_Onumber__ring(U_5315)
      | ~ class_Fields_Ofield__inverse__zero(U_5315) ),
    inference(variable_rename,[status(thm)],[f_1634_1]) ).

fof(f_1634_3,plain,
    ! [U_5316,U_5315] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5315),hAPP(c_Int_Onumber__class_Onumber__of(U_5315),c_Int_OMin)),U_5316) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5315),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5315),c_Groups_Oone__class_Oone(U_5315)),U_5316))
      | ~ class_Int_Onumber__ring(U_5315)
      | ~ class_Fields_Ofield__inverse__zero(U_5315) ),
    inference(definitional_conversion,[status(esa)],[f_1634_2]) ).

cnf(f_1634_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5315),hAPP(c_Int_Onumber__class_Onumber__of(U_5315),c_Int_OMin)),U_5316) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5315),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5315),c_Groups_Oone__class_Oone(U_5315)),U_5316))
    | ~ class_Int_Onumber__ring(U_5315)
    | ~ class_Fields_Ofield__inverse__zero(U_5315) ),
    inference(clausify,[status(thm)],[f_1634_3]) ).

fof(f_1635_1,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J]) ).

fof(f_1635_2,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(definitional_conversion,[status(esa)],[f_1635_1]) ).

cnf(f_1635_3,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1635_2]) ).

fof(f_1636_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(f_1636_2,plain,
    ! [U_5320,U_5319,U_5318,U_5317] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5317),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),c_Groups_Ozero__class_Ozero(U_5317)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))),U_5319))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),c_Groups_Ozero__class_Ozero(U_5317)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))),U_5319))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5317),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))) ) )
      | ~ class_Int_Onumber(U_5317)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5317) ),
    inference(variable_rename,[status(thm)],[f_1636_1]) ).

fof(f_1636_3,plain,
    ( ! [U_5318,U_5317,U_5320] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),c_Groups_Ozero__class_Ozero(U_5317)))
        | ~ sP517(U_5318,U_5317,U_5320) )
    & ! [U_5318,U_5317,U_5320] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
        | ~ sP517(U_5318,U_5317,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
        | ~ sP516(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
        | ~ sP516(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( sP517(U_5318,U_5317,U_5320)
        | sP516(U_5318,U_5317,U_5319,U_5320)
        | ~ sP518(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
        | ~ sP518(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))),U_5319))
        | ~ sP515(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
        | ~ sP515(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),c_Groups_Ozero__class_Ozero(U_5317)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
        | ~ sP513(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
        | ~ sP513(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( sP513(U_5318,U_5317,U_5319,U_5320)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
        | ~ sP514(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))),U_5319))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
        | ~ sP514(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5317),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
        | sP518(U_5318,U_5317,U_5319,U_5320)
        | sP515(U_5318,U_5317,U_5319,U_5320)
        | ~ sP519(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( sP514(U_5318,U_5317,U_5319,U_5320)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5317),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
        | ~ sP519(U_5318,U_5317,U_5319,U_5320) )
    & ! [U_5318,U_5317,U_5319,U_5320] :
        ( sP519(U_5318,U_5317,U_5319,U_5320)
        | ~ class_Int_Onumber(U_5317)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5317) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP513,sP514,sP515,sP516,sP517,sP518,sP519])],[f_1636_2]) ).

cnf(f_1636_4,plain,
    ( sP519(U_5318,U_5317,U_5319,U_5320)
    | ~ class_Int_Onumber(U_5317)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5317) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_5,plain,
    ( sP514(U_5318,U_5317,U_5319,U_5320)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5317),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
    | ~ sP519(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5317),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
    | sP518(U_5318,U_5317,U_5319,U_5320)
    | sP515(U_5318,U_5317,U_5319,U_5320)
    | ~ sP519(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))),U_5319))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
    | ~ sP514(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_8,plain,
    ( sP513(U_5318,U_5317,U_5319,U_5320)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
    | ~ sP514(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
    | ~ sP513(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),c_Groups_Ozero__class_Ozero(U_5317)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
    | ~ sP513(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
    | ~ sP515(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))),U_5319))
    | ~ sP515(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),c_Groups_Ozero__class_Ozero(U_5317)),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)))
    | ~ sP518(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_14,plain,
    ( sP517(U_5318,U_5317,U_5320)
    | sP516(U_5318,U_5317,U_5319,U_5320)
    | ~ sP518(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
    | ~ sP516(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5317),U_5318),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320))))
    | ~ sP516(U_5318,U_5317,U_5319,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5317),hAPP(c_Int_Onumber__class_Onumber__of(U_5317),U_5320)),c_Groups_Ozero__class_Ozero(U_5317)))
    | ~ sP517(U_5318,U_5317,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5317),U_5318),c_Groups_Ozero__class_Ozero(U_5317)))
    | ~ sP517(U_5318,U_5317,U_5320) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

fof(f_1637_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(f_1637_2,plain,
    ! [U_5324,U_5323,U_5322,U_5321] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5321),U_5323),U_5324)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),c_Groups_Ozero__class_Ozero(U_5321)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),U_5323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)),U_5323))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),c_Groups_Ozero__class_Ozero(U_5321)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),U_5323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)),U_5323))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5321),U_5323),U_5324))) ) )
      | ~ class_Int_Onumber(U_5321)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5321) ),
    inference(variable_rename,[status(thm)],[f_1637_1]) ).

fof(f_1637_3,plain,
    ( ! [U_5324,U_5322,U_5321] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),c_Groups_Ozero__class_Ozero(U_5321)))
        | ~ sP524(U_5324,U_5322,U_5321) )
    & ! [U_5324,U_5322,U_5321] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
        | ~ sP524(U_5324,U_5322,U_5321) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),U_5323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)))
        | ~ sP523(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
        | ~ sP523(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( sP524(U_5324,U_5322,U_5321)
        | sP523(U_5324,U_5322,U_5321,U_5323)
        | ~ sP525(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
        | ~ sP525(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)),U_5323))
        | ~ sP522(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
        | ~ sP522(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),c_Groups_Ozero__class_Ozero(U_5321)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
        | ~ sP520(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),U_5323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
        | ~ sP520(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( sP520(U_5324,U_5322,U_5321,U_5323)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
        | ~ sP521(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)),U_5323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
        | ~ sP521(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5321),U_5323),U_5324)))
        | sP525(U_5324,U_5322,U_5321,U_5323)
        | sP522(U_5324,U_5322,U_5321,U_5323)
        | ~ sP526(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( sP521(U_5324,U_5322,U_5321,U_5323)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5321),U_5323),U_5324)))
        | ~ sP526(U_5324,U_5322,U_5321,U_5323) )
    & ! [U_5324,U_5322,U_5321,U_5323] :
        ( sP526(U_5324,U_5322,U_5321,U_5323)
        | ~ class_Int_Onumber(U_5321)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5321) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP520,sP521,sP522,sP523,sP524,sP525,sP526])],[f_1637_2]) ).

cnf(f_1637_4,plain,
    ( sP526(U_5324,U_5322,U_5321,U_5323)
    | ~ class_Int_Onumber(U_5321)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5321) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_5,plain,
    ( sP521(U_5324,U_5322,U_5321,U_5323)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5321),U_5323),U_5324)))
    | ~ sP526(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5321),U_5323),U_5324)))
    | sP525(U_5324,U_5322,U_5321,U_5323)
    | sP522(U_5324,U_5322,U_5321,U_5323)
    | ~ sP526(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)),U_5323))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
    | ~ sP521(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_8,plain,
    ( sP520(U_5324,U_5322,U_5321,U_5323)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
    | ~ sP521(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),U_5323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
    | ~ sP520(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),c_Groups_Ozero__class_Ozero(U_5321)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
    | ~ sP520(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
    | ~ sP522(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)),U_5323))
    | ~ sP522(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),c_Groups_Ozero__class_Ozero(U_5321)),U_5324))
    | ~ sP525(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_14,plain,
    ( sP524(U_5324,U_5322,U_5321)
    | sP523(U_5324,U_5322,U_5321,U_5323)
    | ~ sP525(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
    | ~ sP523(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),U_5323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),U_5324)))
    | ~ sP523(U_5324,U_5322,U_5321,U_5323) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5321),U_5324),c_Groups_Ozero__class_Ozero(U_5321)))
    | ~ sP524(U_5324,U_5322,U_5321) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

cnf(f_1637_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5321),hAPP(c_Int_Onumber__class_Onumber__of(U_5321),U_5322)),c_Groups_Ozero__class_Ozero(U_5321)))
    | ~ sP524(U_5324,U_5322,U_5321) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

fof(f_1638_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(f_1638_2,plain,
    ! [U_5328,U_5327,U_5326,U_5325] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5325),U_5326),U_5327)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)),U_5326))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),U_5326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)),U_5326))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),U_5326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5325),U_5326),U_5327)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328))) ) )
      | ~ class_Int_Onumber(U_5325)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5325) ),
    inference(variable_rename,[status(thm)],[f_1638_1]) ).

fof(f_1638_3,plain,
    ( ! [U_5327,U_5325,U_5328] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
        | ~ sP531(U_5327,U_5325,U_5328) )
    & ! [U_5327,U_5325,U_5328] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
        | ~ sP531(U_5327,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)),U_5326))
        | ~ sP530(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
        | ~ sP530(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( sP531(U_5327,U_5325,U_5328)
        | sP530(U_5327,U_5326,U_5325,U_5328)
        | ~ sP532(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
        | ~ sP532(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),U_5326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)))
        | ~ sP529(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
        | ~ sP529(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
        | ~ sP527(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)),U_5326))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
        | ~ sP527(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( sP527(U_5327,U_5326,U_5325,U_5328)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
        | ~ sP528(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),U_5326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
        | ~ sP528(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5325),U_5326),U_5327)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
        | sP532(U_5327,U_5326,U_5325,U_5328)
        | sP529(U_5327,U_5326,U_5325,U_5328)
        | ~ sP533(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( sP528(U_5327,U_5326,U_5325,U_5328)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5325),U_5326),U_5327)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
        | ~ sP533(U_5327,U_5326,U_5325,U_5328) )
    & ! [U_5327,U_5326,U_5325,U_5328] :
        ( sP533(U_5327,U_5326,U_5325,U_5328)
        | ~ class_Int_Onumber(U_5325)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5325) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP527,sP528,sP529,sP530,sP531,sP532,sP533])],[f_1638_2]) ).

cnf(f_1638_4,plain,
    ( sP533(U_5327,U_5326,U_5325,U_5328)
    | ~ class_Int_Onumber(U_5325)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5325) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_5,plain,
    ( sP528(U_5327,U_5326,U_5325,U_5328)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5325),U_5326),U_5327)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
    | ~ sP533(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5325),U_5326),U_5327)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
    | sP532(U_5327,U_5326,U_5325,U_5328)
    | sP529(U_5327,U_5326,U_5325,U_5328)
    | ~ sP533(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),U_5326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
    | ~ sP528(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_8,plain,
    ( sP527(U_5327,U_5326,U_5325,U_5328)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
    | ~ sP528(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)),U_5326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
    | ~ sP527(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
    | ~ sP527(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
    | ~ sP529(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),U_5326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)))
    | ~ sP529(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
    | ~ sP532(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_14,plain,
    ( sP531(U_5327,U_5325,U_5328)
    | sP530(U_5327,U_5326,U_5325,U_5328)
    | ~ sP532(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
    | ~ sP530(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)),U_5327)),U_5326))
    | ~ sP530(U_5327,U_5326,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5325),U_5327),c_Groups_Ozero__class_Ozero(U_5325)))
    | ~ sP531(U_5327,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),U_5328)))
    | ~ sP531(U_5327,U_5325,U_5328) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

fof(f_1639_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(f_1639_2,plain,
    ! [U_5332,U_5331,U_5330,U_5329] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5329),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5332))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),U_5332))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5330))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),U_5330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),U_5332))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5330))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),U_5330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5329),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5332)) ) )
      | ~ class_Int_Onumber(U_5329)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5329) ),
    inference(variable_rename,[status(thm)],[f_1639_1]) ).

fof(f_1639_3,plain,
    ( ! [U_5331,U_5332,U_5329] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),U_5332))
        | ~ sP538(U_5331,U_5332,U_5329) )
    & ! [U_5331,U_5332,U_5329] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
        | ~ sP538(U_5331,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5330))
        | ~ sP537(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
        | ~ sP537(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( sP538(U_5331,U_5332,U_5329)
        | sP537(U_5331,U_5330,U_5332,U_5329)
        | ~ sP539(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
        | ~ sP539(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),U_5330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))))
        | ~ sP536(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
        | ~ sP536(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),U_5332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
        | ~ sP534(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5330))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
        | ~ sP534(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( sP534(U_5331,U_5330,U_5332,U_5329)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
        | ~ sP535(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),U_5330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
        | ~ sP535(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5329),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5332))
        | sP539(U_5331,U_5330,U_5332,U_5329)
        | sP536(U_5331,U_5330,U_5332,U_5329)
        | ~ sP540(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( sP535(U_5331,U_5330,U_5332,U_5329)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5329),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5332))
        | ~ sP540(U_5331,U_5330,U_5332,U_5329) )
    & ! [U_5331,U_5330,U_5332,U_5329] :
        ( sP540(U_5331,U_5330,U_5332,U_5329)
        | ~ class_Int_Onumber(U_5329)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5329) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP534,sP535,sP536,sP537,sP538,sP539,sP540])],[f_1639_2]) ).

cnf(f_1639_4,plain,
    ( sP540(U_5331,U_5330,U_5332,U_5329)
    | ~ class_Int_Onumber(U_5329)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_5,plain,
    ( sP535(U_5331,U_5330,U_5332,U_5329)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5329),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5332))
    | ~ sP540(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5329),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5332))
    | sP539(U_5331,U_5330,U_5332,U_5329)
    | sP536(U_5331,U_5330,U_5332,U_5329)
    | ~ sP540(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),U_5330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
    | ~ sP535(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_8,plain,
    ( sP534(U_5331,U_5330,U_5332,U_5329)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
    | ~ sP535(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
    | ~ sP534(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),U_5332))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
    | ~ sP534(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
    | ~ sP536(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),U_5330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))))
    | ~ sP536(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)))
    | ~ sP539(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_14,plain,
    ( sP538(U_5331,U_5332,U_5329)
    | sP537(U_5331,U_5330,U_5332,U_5329)
    | ~ sP539(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
    | ~ sP537(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5329),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331))),U_5330))
    | ~ sP537(U_5331,U_5330,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5329),hAPP(c_Int_Onumber__class_Onumber__of(U_5329),U_5331)),c_Groups_Ozero__class_Ozero(U_5329)))
    | ~ sP538(U_5331,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

cnf(f_1639_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5329),c_Groups_Ozero__class_Ozero(U_5329)),U_5332))
    | ~ sP538(U_5331,U_5332,U_5329) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

fof(f_1640_1,plain,
    ! [V_n,V_i] :
      ( ( c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n))
        | V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n
        | V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code]) ).

fof(f_1640_2,plain,
    ! [U_5334,U_5333] :
      ( ( c_Code__Numeral_Onat__of__aux(U_5333,U_5334) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5333),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5334))
        | U_5333 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(U_5333,U_5334) = U_5334
        | U_5333 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1640_1]) ).

fof(f_1640_3,plain,
    ( ! [U_5338,U_5336] :
        ( c_Code__Numeral_Onat__of__aux(U_5336,U_5338) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5336),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5338))
        | U_5336 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5337,U_5335] :
        ( c_Code__Numeral_Onat__of__aux(U_5335,U_5337) = U_5337
        | U_5335 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1640_2]) ).

fof(f_1640_4,plain,
    ( ! [U_5336,U_5338] :
        ( c_Code__Numeral_Onat__of__aux(U_5336,U_5338) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5336),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5338))
        | U_5336 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5337,U_5335] :
        ( c_Code__Numeral_Onat__of__aux(U_5335,U_5337) = U_5337
        | U_5335 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_1640_3]) ).

cnf(f_1640_5,plain,
    ( c_Code__Numeral_Onat__of__aux(U_5335,U_5337) = U_5337
    | U_5335 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1640_4]) ).

cnf(f_1640_6,plain,
    ( c_Code__Numeral_Onat__of__aux(U_5336,U_5338) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5336),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5338))
    | U_5336 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1640_4]) ).

fof(f_1641_1,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I1_J]) ).

fof(f_1641_2,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1641_1]) ).

cnf(f_1641_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1641_2]) ).

fof(f_1642_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I3_J]) ).

fof(f_1642_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1642_1]) ).

cnf(f_1642_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1642_2]) ).

fof(f_1643_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).

fof(f_1643_2,plain,
    ! [U_5341,U_5340,U_5339] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5339,U_5340,U_5341,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5340,
    inference(variable_rename,[status(thm)],[f_1643_1]) ).

fof(f_1643_3,plain,
    ! [U_5341,U_5340,U_5339] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5339,U_5340,U_5341,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5340,
    inference(definitional_conversion,[status(esa)],[f_1643_2]) ).

cnf(f_1643_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5339,U_5340,U_5341,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5340,
    inference(clausify,[status(thm)],[f_1643_3]) ).

fof(f_1644_1,plain,
    ! [V_i,V_b] :
      ( ( c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_log_Osimps]) ).

fof(f_1644_2,plain,
    ! [U_5343,U_5342] :
      ( ( c_Random_Olog(U_5342,U_5343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_5342,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5343),U_5342)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5343),U_5342))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5342),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(U_5342,U_5343) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5343),U_5342))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5342),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(variable_rename,[status(thm)],[f_1644_1]) ).

fof(f_1644_3,plain,
    ( ! [U_5347,U_5345] :
        ( c_Random_Olog(U_5345,U_5347) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_5345,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5347),U_5345)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5347),U_5345))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5345),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_5346,U_5344] :
        ( c_Random_Olog(U_5344,U_5346) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5346),U_5344))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5344),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(miniscope,[status(thm)],[f_1644_2]) ).

fof(f_1644_4,plain,
    ( ! [U_5346,U_5344] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5346),U_5344))
        | ~ sP541(U_5346,U_5344) )
    & ! [U_5346,U_5344] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5344),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | ~ sP541(U_5346,U_5344) )
    & ! [U_5345,U_5347] :
        ( c_Random_Olog(U_5345,U_5347) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_5345,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5347),U_5345)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5347),U_5345))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5345),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_5346,U_5344] :
        ( c_Random_Olog(U_5344,U_5346) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | sP541(U_5346,U_5344) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP541])],[f_1644_3]) ).

cnf(f_1644_5,plain,
    ( c_Random_Olog(U_5344,U_5346) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | sP541(U_5346,U_5344) ),
    inference(clausify,[status(thm)],[f_1644_4]) ).

cnf(f_1644_6,plain,
    ( c_Random_Olog(U_5345,U_5347) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_5345,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5347),U_5345)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5347),U_5345))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5345),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_1644_4]) ).

cnf(f_1644_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5344),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | ~ sP541(U_5346,U_5344) ),
    inference(clausify,[status(thm)],[f_1644_4]) ).

cnf(f_1644_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5346),U_5344))
    | ~ sP541(U_5346,U_5344) ),
    inference(clausify,[status(thm)],[f_1644_4]) ).

fof(f_1645_1,plain,
    ! [V_w] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).

fof(f_1645_2,plain,
    ! [U_5348] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))) ),
    inference(variable_rename,[status(thm)],[f_1645_1]) ).

fof(f_1645_3,plain,
    ( ! [U_5348] :
        ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
        | ~ sP542(U_5348) )
    & ! [U_5348] :
        ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
        | ~ sP542(U_5348) )
    & ! [U_5348] :
        ( sP542(U_5348)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP542])],[f_1645_2]) ).

cnf(f_1645_4,plain,
    ( sP542(U_5348)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))) ),
    inference(clausify,[status(thm)],[f_1645_3]) ).

cnf(f_1645_5,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
    | ~ sP542(U_5348) ),
    inference(clausify,[status(thm)],[f_1645_3]) ).

cnf(f_1645_6,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5348))))
    | ~ sP542(U_5348) ),
    inference(clausify,[status(thm)],[f_1645_3]) ).

fof(f_1646_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod]) ).

fof(f_1646_2,plain,
    ! [U_5350,U_5349] :
      ( c_Divides_OnegDivAlg(U_5349,U_5350) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5349),U_5350)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5349,U_5350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1646_1]) ).

fof(f_1646_3,plain,
    ! [U_5349,U_5350] :
      ( c_Divides_OnegDivAlg(U_5349,U_5350) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5349),U_5350)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5349,U_5350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1646_2]) ).

cnf(f_1646_4,plain,
    ( c_Divides_OnegDivAlg(U_5349,U_5350) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5349),U_5350)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5349,U_5350))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

fof(f_1647_1,plain,
    ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__minus1]) ).

fof(f_1647_2,plain,
    ! [U_5351] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5351) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5351),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1647_1]) ).

fof(f_1647_3,plain,
    ! [U_5351] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5351) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5351),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1647_2]) ).

cnf(f_1647_4,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5351) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5351),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1647_3]) ).

fof(f_1648_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
      & ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps]) ).

fof(f_1648_2,plain,
    ! [U_5353,U_5352] :
      ( ( c_Divides_OnegDivAlg(U_5352,U_5353) = hAPP(c_Divides_Oadjust(U_5353),c_Divides_OnegDivAlg(U_5352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5353)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5352),U_5353))) )
      & ( c_Divides_OnegDivAlg(U_5352,U_5353) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5352),U_5353))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5352),U_5353))) ) ) ),
    inference(variable_rename,[status(thm)],[f_1648_1]) ).

fof(f_1648_3,plain,
    ( ! [U_5357,U_5355] :
        ( c_Divides_OnegDivAlg(U_5355,U_5357) = hAPP(c_Divides_Oadjust(U_5357),c_Divides_OnegDivAlg(U_5355,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5357)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5357),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5355),U_5357))) )
    & ! [U_5356,U_5354] :
        ( c_Divides_OnegDivAlg(U_5354,U_5356) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5354),U_5356))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5356),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5354),U_5356))) ) ) ),
    inference(miniscope,[status(thm)],[f_1648_2]) ).

fof(f_1648_4,plain,
    ( ! [U_5356,U_5354] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5356),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP543(U_5356,U_5354) )
    & ! [U_5356,U_5354] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5354),U_5356)))
        | ~ sP543(U_5356,U_5354) )
    & ! [U_5357,U_5355] :
        ( c_Divides_OnegDivAlg(U_5355,U_5357) = hAPP(c_Divides_Oadjust(U_5357),c_Divides_OnegDivAlg(U_5355,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5357)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5357),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5355),U_5357))) )
    & ! [U_5356,U_5354] :
        ( c_Divides_OnegDivAlg(U_5354,U_5356) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5354),U_5356))
        | sP543(U_5356,U_5354) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP543])],[f_1648_3]) ).

cnf(f_1648_5,plain,
    ( c_Divides_OnegDivAlg(U_5354,U_5356) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5354),U_5356))
    | sP543(U_5356,U_5354) ),
    inference(clausify,[status(thm)],[f_1648_4]) ).

cnf(f_1648_6,plain,
    ( c_Divides_OnegDivAlg(U_5355,U_5357) = hAPP(c_Divides_Oadjust(U_5357),c_Divides_OnegDivAlg(U_5355,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5357)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5357),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5355),U_5357))) ),
    inference(clausify,[status(thm)],[f_1648_4]) ).

cnf(f_1648_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5354),U_5356)))
    | ~ sP543(U_5356,U_5354) ),
    inference(clausify,[status(thm)],[f_1648_4]) ).

cnf(f_1648_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5356),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP543(U_5356,U_5354) ),
    inference(clausify,[status(thm)],[f_1648_4]) ).

fof(f_1649_1,plain,
    ! [V_w,V_v] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).

fof(f_1649_2,plain,
    ! [U_5359,U_5358] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))) ),
    inference(variable_rename,[status(thm)],[f_1649_1]) ).

fof(f_1649_3,plain,
    ( ! [U_5358,U_5359] :
        ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
        | ~ sP544(U_5358,U_5359) )
    & ! [U_5358,U_5359] :
        ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
        | ~ sP544(U_5358,U_5359) )
    & ! [U_5358,U_5359] :
        ( sP544(U_5358,U_5359)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP544])],[f_1649_2]) ).

cnf(f_1649_4,plain,
    ( sP544(U_5358,U_5359)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

cnf(f_1649_5,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
    | ~ sP544(U_5358,U_5359) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

cnf(f_1649_6,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5358))))
    | ~ sP544(U_5358,U_5359) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

fof(f_1650_1,plain,
    ! [V_a,V_b] :
      ( ( ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
        & ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn]) ).

fof(f_1650_2,plain,
    ! [U_5361,U_5360] :
      ( ( ( c_Divides_OnegDivAlg(U_5361,U_5360) = hAPP(c_Divides_Oadjust(U_5360),c_Divides_OnegDivAlg(U_5361,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5360)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360))) )
        & ( c_Divides_OnegDivAlg(U_5361,U_5360) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5360)) ),
    inference(variable_rename,[status(thm)],[f_1650_1]) ).

fof(f_1650_3,plain,
    ( ! [U_5361,U_5360] :
        ( c_Divides_OnegDivAlg(U_5361,U_5360) = hAPP(c_Divides_Oadjust(U_5360),c_Divides_OnegDivAlg(U_5361,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5360)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360)))
        | ~ sP545(U_5361,U_5360) )
    & ! [U_5361,U_5360] :
        ( c_Divides_OnegDivAlg(U_5361,U_5360) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360)))
        | ~ sP545(U_5361,U_5360) )
    & ! [U_5361,U_5360] :
        ( sP545(U_5361,U_5360)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5360)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP545])],[f_1650_2]) ).

cnf(f_1650_4,plain,
    ( sP545(U_5361,U_5360)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5360)) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_5,plain,
    ( c_Divides_OnegDivAlg(U_5361,U_5360) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360)))
    | ~ sP545(U_5361,U_5360) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_6,plain,
    ( c_Divides_OnegDivAlg(U_5361,U_5360) = hAPP(c_Divides_Oadjust(U_5360),c_Divides_OnegDivAlg(U_5361,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5360)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5361),U_5360)))
    | ~ sP545(U_5361,U_5360) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

fof(f_1651_1,plain,
    ! [V_r,V_l,V_k] :
      ( ( c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) )
      & ( c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_minus__shift__def]) ).

fof(f_1651_2,plain,
    ! [U_5364,U_5363,U_5362] :
      ( ( c_Random_Ominus__shift(U_5364,U_5362,U_5363) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5362),U_5363)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5362),U_5363)) )
      & ( c_Random_Ominus__shift(U_5364,U_5362,U_5363) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5364),U_5362)),U_5363)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5362),U_5363)) ) ),
    inference(variable_rename,[status(thm)],[f_1651_1]) ).

fof(f_1651_3,plain,
    ( ! [U_5370,U_5368,U_5366] :
        ( c_Random_Ominus__shift(U_5370,U_5366,U_5368) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5366),U_5368)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5366),U_5368)) )
    & ! [U_5369,U_5367,U_5365] :
        ( c_Random_Ominus__shift(U_5369,U_5365,U_5367) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5369),U_5365)),U_5367)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5365),U_5367)) ) ),
    inference(miniscope,[status(thm)],[f_1651_2]) ).

fof(f_1651_4,plain,
    ( ! [U_5368,U_5366,U_5370] :
        ( c_Random_Ominus__shift(U_5370,U_5366,U_5368) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5366),U_5368)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5366),U_5368)) )
    & ! [U_5369,U_5367,U_5365] :
        ( c_Random_Ominus__shift(U_5369,U_5365,U_5367) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5369),U_5365)),U_5367)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5365),U_5367)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1651_3]) ).

cnf(f_1651_5,plain,
    ( c_Random_Ominus__shift(U_5369,U_5365,U_5367) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5369),U_5365)),U_5367)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5365),U_5367)) ),
    inference(clausify,[status(thm)],[f_1651_4]) ).

cnf(f_1651_6,plain,
    ( c_Random_Ominus__shift(U_5370,U_5366,U_5368) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5366),U_5368)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5366),U_5368)) ),
    inference(clausify,[status(thm)],[f_1651_4]) ).

fof(f_1652_1,plain,
    ! [V_k,V_v] :
      ( ( c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | V_v = V_k )
      & ( c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | V_v != V_k ) ),
    inference(fof_nnf,[status(thm)],[fact_inc__shift__def]) ).

fof(f_1652_2,plain,
    ! [U_5372,U_5371] :
      ( ( c_Random_Oinc__shift(U_5371,U_5372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5372),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_5371 = U_5372 )
      & ( c_Random_Oinc__shift(U_5371,U_5372) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_5371 != U_5372 ) ),
    inference(variable_rename,[status(thm)],[f_1652_1]) ).

fof(f_1652_3,plain,
    ( ! [U_5376,U_5374] :
        ( c_Random_Oinc__shift(U_5374,U_5376) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5376),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_5374 = U_5376 )
    & ! [U_5375,U_5373] :
        ( c_Random_Oinc__shift(U_5373,U_5375) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_5373 != U_5375 ) ),
    inference(miniscope,[status(thm)],[f_1652_2]) ).

fof(f_1652_4,plain,
    ( ! [U_5374,U_5376] :
        ( c_Random_Oinc__shift(U_5374,U_5376) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5376),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_5374 = U_5376 )
    & ! [U_5375,U_5373] :
        ( c_Random_Oinc__shift(U_5373,U_5375) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_5373 != U_5375 ) ),
    inference(definitional_conversion,[status(esa)],[f_1652_3]) ).

cnf(f_1652_5,plain,
    ( c_Random_Oinc__shift(U_5373,U_5375) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | U_5373 != U_5375 ),
    inference(clausify,[status(thm)],[f_1652_4]) ).

cnf(f_1652_6,plain,
    ( c_Random_Oinc__shift(U_5374,U_5376) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5376),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
    | U_5374 = U_5376 ),
    inference(clausify,[status(thm)],[f_1652_4]) ).

fof(f_1653_1,plain,
    ! [V_w] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).

fof(f_1653_2,plain,
    ! [U_5377] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))) ),
    inference(variable_rename,[status(thm)],[f_1653_1]) ).

fof(f_1653_3,plain,
    ( ! [U_5377] :
        ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)))
        | ~ sP546(U_5377) )
    & ! [U_5377] :
        ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)))
        | ~ sP546(U_5377) )
    & ! [U_5377] :
        ( sP546(U_5377)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP546])],[f_1653_2]) ).

cnf(f_1653_4,plain,
    ( sP546(U_5377)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_5,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)))
    | ~ sP546(U_5377) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_6,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5377)))
    | ~ sP546(U_5377) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

fof(f_1654_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
      & ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps]) ).

fof(f_1654_2,plain,
    ! [U_5379,U_5378] :
      ( ( c_Divides_OposDivAlg(U_5378,U_5379) = hAPP(c_Divides_Oadjust(U_5379),c_Divides_OposDivAlg(U_5378,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5379),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5378),U_5379)) )
      & ( c_Divides_OposDivAlg(U_5378,U_5379) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5378)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5379),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5378),U_5379)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1654_1]) ).

fof(f_1654_3,plain,
    ( ! [U_5383,U_5381] :
        ( c_Divides_OposDivAlg(U_5381,U_5383) = hAPP(c_Divides_Oadjust(U_5383),c_Divides_OposDivAlg(U_5381,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5383),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5381),U_5383)) )
    & ! [U_5382,U_5380] :
        ( c_Divides_OposDivAlg(U_5380,U_5382) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5380)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5380),U_5382)) ) ) ),
    inference(miniscope,[status(thm)],[f_1654_2]) ).

fof(f_1654_4,plain,
    ( ! [U_5382,U_5380] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP547(U_5382,U_5380) )
    & ! [U_5382,U_5380] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5380),U_5382))
        | ~ sP547(U_5382,U_5380) )
    & ! [U_5383,U_5381] :
        ( c_Divides_OposDivAlg(U_5381,U_5383) = hAPP(c_Divides_Oadjust(U_5383),c_Divides_OposDivAlg(U_5381,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5383),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5381),U_5383)) )
    & ! [U_5382,U_5380] :
        ( c_Divides_OposDivAlg(U_5380,U_5382) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5380)
        | sP547(U_5382,U_5380) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP547])],[f_1654_3]) ).

cnf(f_1654_5,plain,
    ( c_Divides_OposDivAlg(U_5380,U_5382) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5380)
    | sP547(U_5382,U_5380) ),
    inference(clausify,[status(thm)],[f_1654_4]) ).

cnf(f_1654_6,plain,
    ( c_Divides_OposDivAlg(U_5381,U_5383) = hAPP(c_Divides_Oadjust(U_5383),c_Divides_OposDivAlg(U_5381,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5383)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5383),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5381),U_5383)) ),
    inference(clausify,[status(thm)],[f_1654_4]) ).

cnf(f_1654_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5380),U_5382))
    | ~ sP547(U_5382,U_5380) ),
    inference(clausify,[status(thm)],[f_1654_4]) ).

cnf(f_1654_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP547(U_5382,U_5380) ),
    inference(clausify,[status(thm)],[f_1654_4]) ).

fof(f_1655_1,plain,
    ! [V_w,V_v] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).

fof(f_1655_2,plain,
    ! [U_5385,U_5384] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))) ),
    inference(variable_rename,[status(thm)],[f_1655_1]) ).

fof(f_1655_3,plain,
    ( ! [U_5384,U_5385] :
        ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)))
        | ~ sP548(U_5384,U_5385) )
    & ! [U_5384,U_5385] :
        ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)))
        | ~ sP548(U_5384,U_5385) )
    & ! [U_5384,U_5385] :
        ( sP548(U_5384,U_5385)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP548])],[f_1655_2]) ).

cnf(f_1655_4,plain,
    ( sP548(U_5384,U_5385)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))) ),
    inference(clausify,[status(thm)],[f_1655_3]) ).

cnf(f_1655_5,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)))
    | ~ sP548(U_5384,U_5385) ),
    inference(clausify,[status(thm)],[f_1655_3]) ).

cnf(f_1655_6,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5385)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)))
    | ~ sP548(U_5384,U_5385) ),
    inference(clausify,[status(thm)],[f_1655_3]) ).

fof(f_1656_1,plain,
    ! [V_a,V_b] :
      ( ( ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
        & ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn]) ).

fof(f_1656_2,plain,
    ! [U_5387,U_5386] :
      ( ( ( c_Divides_OposDivAlg(U_5387,U_5386) = hAPP(c_Divides_Oadjust(U_5386),c_Divides_OposDivAlg(U_5387,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5386)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5387),U_5386)) )
        & ( c_Divides_OposDivAlg(U_5387,U_5386) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5387)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5387),U_5386)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5386)) ),
    inference(variable_rename,[status(thm)],[f_1656_1]) ).

fof(f_1656_3,plain,
    ( ! [U_5386,U_5387] :
        ( c_Divides_OposDivAlg(U_5387,U_5386) = hAPP(c_Divides_Oadjust(U_5386),c_Divides_OposDivAlg(U_5387,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5386)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5387),U_5386))
        | ~ sP549(U_5386,U_5387) )
    & ! [U_5386,U_5387] :
        ( c_Divides_OposDivAlg(U_5387,U_5386) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5387)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5387),U_5386))
        | ~ sP549(U_5386,U_5387) )
    & ! [U_5386,U_5387] :
        ( sP549(U_5386,U_5387)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5386)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP549])],[f_1656_2]) ).

cnf(f_1656_4,plain,
    ( sP549(U_5386,U_5387)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5386)) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

cnf(f_1656_5,plain,
    ( c_Divides_OposDivAlg(U_5387,U_5386) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5387)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5387),U_5386))
    | ~ sP549(U_5386,U_5387) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

cnf(f_1656_6,plain,
    ( c_Divides_OposDivAlg(U_5387,U_5386) = hAPP(c_Divides_Oadjust(U_5386),c_Divides_OposDivAlg(U_5387,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5387),U_5386))
    | ~ sP549(U_5386,U_5387) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

fof(f_1657_1,plain,
    ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__0]) ).

fof(f_1657_2,plain,
    ! [U_5388] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5388) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1657_1]) ).

fof(f_1657_3,plain,
    ! [U_5388] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5388) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1657_2]) ).

cnf(f_1657_4,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5388) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1657_3]) ).

fof(f_1658_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod]) ).

fof(f_1658_2,plain,
    ! [U_5390,U_5389] :
      ( c_Divides_OposDivAlg(U_5389,U_5390) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5389),U_5390)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5389,U_5390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5389)) ),
    inference(variable_rename,[status(thm)],[f_1658_1]) ).

fof(f_1658_3,plain,
    ! [U_5389,U_5390] :
      ( c_Divides_OposDivAlg(U_5389,U_5390) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5389),U_5390)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5389,U_5390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5389)) ),
    inference(definitional_conversion,[status(esa)],[f_1658_2]) ).

cnf(f_1658_4,plain,
    ( c_Divides_OposDivAlg(U_5389,U_5390) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5389),U_5390)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5389,U_5390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5389)) ),
    inference(clausify,[status(thm)],[f_1658_3]) ).

fof(f_1659_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
        & ( c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps]) ).

fof(f_1659_2,plain,
    ! [U_5392,U_5391] :
      ( ( ( c_Divides_OnegDivAlg(U_5391,U_5392) = hAPP(c_Divides_Oadjust(U_5392),c_Divides_OnegDivAlg(U_5391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5392)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392))) )
        & ( c_Divides_OnegDivAlg(U_5391,U_5392) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392))) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5391),U_5392))) ),
    inference(variable_rename,[status(thm)],[f_1659_1]) ).

fof(f_1659_3,plain,
    ( ! [U_5391,U_5392] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP550(U_5391,U_5392) )
    & ! [U_5391,U_5392] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392)))
        | ~ sP550(U_5391,U_5392) )
    & ! [U_5391,U_5392] :
        ( c_Divides_OnegDivAlg(U_5391,U_5392) = hAPP(c_Divides_Oadjust(U_5392),c_Divides_OnegDivAlg(U_5391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5392)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392)))
        | ~ sP551(U_5391,U_5392) )
    & ! [U_5391,U_5392] :
        ( c_Divides_OnegDivAlg(U_5391,U_5392) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392))
        | sP550(U_5391,U_5392)
        | ~ sP551(U_5391,U_5392) )
    & ! [U_5391,U_5392] :
        ( sP551(U_5391,U_5392)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5391),U_5392))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP550,sP551])],[f_1659_2]) ).

cnf(f_1659_4,plain,
    ( sP551(U_5391,U_5392)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5391),U_5392))) ),
    inference(clausify,[status(thm)],[f_1659_3]) ).

cnf(f_1659_5,plain,
    ( c_Divides_OnegDivAlg(U_5391,U_5392) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392))
    | sP550(U_5391,U_5392)
    | ~ sP551(U_5391,U_5392) ),
    inference(clausify,[status(thm)],[f_1659_3]) ).

cnf(f_1659_6,plain,
    ( c_Divides_OnegDivAlg(U_5391,U_5392) = hAPP(c_Divides_Oadjust(U_5392),c_Divides_OnegDivAlg(U_5391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392)))
    | ~ sP551(U_5391,U_5392) ),
    inference(clausify,[status(thm)],[f_1659_3]) ).

cnf(f_1659_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5391),U_5392)))
    | ~ sP550(U_5391,U_5392) ),
    inference(clausify,[status(thm)],[f_1659_3]) ).

cnf(f_1659_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP550(U_5391,U_5392) ),
    inference(clausify,[status(thm)],[f_1659_3]) ).

fof(f_1660_1,plain,
    ! [V_k,V_l] :
      ( ( c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))
        | V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k))
        | V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg]) ).

fof(f_1660_2,plain,
    ! [U_5394,U_5393] :
      ( ( c_Divides_Opdivmod(U_5394,U_5393) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5394),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5393))
        | U_5393 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(U_5394,U_5393) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5394))
        | U_5393 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1660_1]) ).

fof(f_1660_3,plain,
    ( ! [U_5398,U_5396] :
        ( c_Divides_Opdivmod(U_5398,U_5396) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5398),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5396))
        | U_5396 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_5397,U_5395] :
        ( c_Divides_Opdivmod(U_5397,U_5395) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5397))
        | U_5395 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1660_2]) ).

fof(f_1660_4,plain,
    ( ! [U_5398,U_5396] :
        ( c_Divides_Opdivmod(U_5398,U_5396) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5398),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5396))
        | U_5396 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_5397,U_5395] :
        ( c_Divides_Opdivmod(U_5397,U_5395) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5397))
        | U_5395 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1660_3]) ).

cnf(f_1660_5,plain,
    ( c_Divides_Opdivmod(U_5397,U_5395) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5397))
    | U_5395 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1660_4]) ).

cnf(f_1660_6,plain,
    ( c_Divides_Opdivmod(U_5398,U_5396) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5398),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5396))
    | U_5396 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1660_4]) ).

fof(f_1661_1,plain,
    ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),
    inference(fof_nnf,[status(thm)],[fact_pdivmod__def]) ).

fof(f_1661_2,plain,
    ! [U_5400,U_5399] : c_Divides_Opdivmod(U_5399,U_5400) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5399)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5400))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5399),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5400))),
    inference(variable_rename,[status(thm)],[f_1661_1]) ).

fof(f_1661_3,plain,
    ! [U_5400,U_5399] : c_Divides_Opdivmod(U_5399,U_5400) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5399)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5400))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5399),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5400))),
    inference(definitional_conversion,[status(esa)],[f_1661_2]) ).

cnf(f_1661_4,plain,
    c_Divides_Opdivmod(U_5399,U_5400) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5399)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5400))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5399),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5400))),
    inference(clausify,[status(thm)],[f_1661_3]) ).

fof(f_1662_1,plain,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma]) ).

fof(f_1662_2,plain,
    ! [U_5405,U_5404,U_5403,U_5402,U_5401] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5401,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5402),U_5405)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5403),U_5405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5402),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5403,U_5405))),U_5404))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5405))
      | U_5402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5401,U_5402),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5403),U_5404))) ),
    inference(variable_rename,[status(thm)],[f_1662_1]) ).

fof(f_1662_3,plain,
    ! [U_5401,U_5402,U_5403,U_5404,U_5405] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5401,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5402),U_5405)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5403),U_5405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5402),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5403,U_5405))),U_5404))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5405))
      | U_5402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5401,U_5402),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5403),U_5404))) ),
    inference(definitional_conversion,[status(esa)],[f_1662_2]) ).

cnf(f_1662_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5401,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5402),U_5405)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5403),U_5405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5402),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5403,U_5405))),U_5404))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5405))
    | U_5402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5401,U_5402),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5403),U_5404))) ),
    inference(clausify,[status(thm)],[f_1662_3]) ).

fof(f_1663_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
        & ( c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps]) ).

fof(f_1663_2,plain,
    ! [U_5407,U_5406] :
      ( ( ( c_Divides_OposDivAlg(U_5406,U_5407) = hAPP(c_Divides_Oadjust(U_5407),c_Divides_OposDivAlg(U_5406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5407)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),U_5407)) )
        & ( c_Divides_OposDivAlg(U_5406,U_5407) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5406)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),U_5407)) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5406),U_5407))) ),
    inference(variable_rename,[status(thm)],[f_1663_1]) ).

fof(f_1663_3,plain,
    ( ! [U_5406,U_5407] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP552(U_5406,U_5407) )
    & ! [U_5406,U_5407] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),U_5407))
        | ~ sP552(U_5406,U_5407) )
    & ! [U_5406,U_5407] :
        ( c_Divides_OposDivAlg(U_5406,U_5407) = hAPP(c_Divides_Oadjust(U_5407),c_Divides_OposDivAlg(U_5406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5407)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),U_5407))
        | ~ sP553(U_5406,U_5407) )
    & ! [U_5406,U_5407] :
        ( c_Divides_OposDivAlg(U_5406,U_5407) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5406)
        | sP552(U_5406,U_5407)
        | ~ sP553(U_5406,U_5407) )
    & ! [U_5406,U_5407] :
        ( sP553(U_5406,U_5407)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5406),U_5407))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP552,sP553])],[f_1663_2]) ).

cnf(f_1663_4,plain,
    ( sP553(U_5406,U_5407)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5406),U_5407))) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

cnf(f_1663_5,plain,
    ( c_Divides_OposDivAlg(U_5406,U_5407) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5406)
    | sP552(U_5406,U_5407)
    | ~ sP553(U_5406,U_5407) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

cnf(f_1663_6,plain,
    ( c_Divides_OposDivAlg(U_5406,U_5407) = hAPP(c_Divides_Oadjust(U_5407),c_Divides_OposDivAlg(U_5406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5407)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),U_5407))
    | ~ sP553(U_5406,U_5407) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

cnf(f_1663_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),U_5407))
    | ~ sP552(U_5406,U_5407) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

cnf(f_1663_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP552(U_5406,U_5407) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

fof(f_1664_1,plain,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c))))
      | V_c = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_zmult1__lemma]) ).

fof(f_1664_2,plain,
    ! [U_5412,U_5411,U_5410,U_5409,U_5408] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5408),U_5409),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5410)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5411)),U_5409))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5411),U_5409))))
      | U_5409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5408,U_5409),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5410),U_5411))) ),
    inference(variable_rename,[status(thm)],[f_1664_1]) ).

fof(f_1664_3,plain,
    ! [U_5411,U_5409,U_5410,U_5408,U_5412] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5408),U_5409),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5410)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5411)),U_5409))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5411),U_5409))))
      | U_5409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5408,U_5409),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5410),U_5411))) ),
    inference(definitional_conversion,[status(esa)],[f_1664_2]) ).

cnf(f_1664_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5408),U_5409),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5410)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5411)),U_5409))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5412),U_5411),U_5409))))
    | U_5409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5408,U_5409),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5410),U_5411))) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

fof(f_1665_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            & hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            | ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp_Osimps]) ).

fof(f_1665_2,plain,
    ! [U_5417,U_5416,U_5415] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5415,U_5416),U_5417))
        | ? [U_5414] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5415,U_5416),U_5414))
            & hBOOL(hAPP(hAPP(U_5416,U_5414),U_5417)) ) )
      & ( ! [U_5413] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5415,U_5416),U_5413))
            | ~ hBOOL(hAPP(hAPP(U_5416,U_5413),U_5417)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5415,U_5416),U_5417)) ) ),
    inference(variable_rename,[status(thm)],[f_1665_1]) ).

fof(f_1665_3,plain,
    ( ! [U_5423,U_5421,U_5419] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),U_5423))
        | ? [U_5414] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),U_5414))
            & hBOOL(hAPP(hAPP(U_5421,U_5414),U_5423)) ) )
    & ! [U_5422,U_5420,U_5418] :
        ( ! [U_5413] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5413))
            | ~ hBOOL(hAPP(hAPP(U_5420,U_5413),U_5422)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5422)) ) ),
    inference(miniscope,[status(thm)],[f_1665_2]) ).

fof(f_1665_4,plain,
    ( ! [U_5423,U_5421,U_5419] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),U_5423))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),sK85(U_5423,U_5421,U_5419)))
          & hBOOL(hAPP(hAPP(U_5421,sK85(U_5423,U_5421,U_5419)),U_5423)) ) )
    & ! [U_5422,U_5420,U_5418] :
        ( ! [U_5413] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5413))
            | ~ hBOOL(hAPP(hAPP(U_5420,U_5413),U_5422)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5422)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_5414,sK85(U_5423,U_5421,U_5419))],[f_1665_3]) ).

fof(f_1665_5,plain,
    ( ! [U_5423,U_5419,U_5421] :
        ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),sK85(U_5423,U_5421,U_5419)))
        | ~ sP554(U_5423,U_5419,U_5421) )
    & ! [U_5423,U_5419,U_5421] :
        ( hBOOL(hAPP(hAPP(U_5421,sK85(U_5423,U_5421,U_5419)),U_5423))
        | ~ sP554(U_5423,U_5419,U_5421) )
    & ! [U_5423,U_5419,U_5421] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),U_5423))
        | sP554(U_5423,U_5419,U_5421) )
    & ! [U_5420,U_5413,U_5418,U_5422] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5413))
        | ~ hBOOL(hAPP(hAPP(U_5420,U_5413),U_5422))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5422)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP554])],[f_1665_4]) ).

cnf(f_1665_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5413))
    | ~ hBOOL(hAPP(hAPP(U_5420,U_5413),U_5422))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5418,U_5420),U_5422)) ),
    inference(clausify,[status(thm)],[f_1665_5]) ).

cnf(f_1665_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),U_5423))
    | sP554(U_5423,U_5419,U_5421) ),
    inference(clausify,[status(thm)],[f_1665_5]) ).

cnf(f_1665_8,plain,
    ( hBOOL(hAPP(hAPP(U_5421,sK85(U_5423,U_5421,U_5419)),U_5423))
    | ~ sP554(U_5423,U_5419,U_5421) ),
    inference(clausify,[status(thm)],[f_1665_5]) ).

cnf(f_1665_9,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5419,U_5421),sK85(U_5423,U_5421,U_5419)))
    | ~ sP554(U_5423,U_5419,U_5421) ),
    inference(clausify,[status(thm)],[f_1665_5]) ).

fof(f_1666_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            & hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            | ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp_Oequations]) ).

fof(f_1666_2,plain,
    ! [U_5428,U_5427,U_5426] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5426,U_5427),U_5428))
        | ? [U_5425] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5426,U_5427),U_5425))
            & hBOOL(hAPP(hAPP(U_5427,U_5425),U_5428)) ) )
      & ( ! [U_5424] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5426,U_5427),U_5424))
            | ~ hBOOL(hAPP(hAPP(U_5427,U_5424),U_5428)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5426,U_5427),U_5428)) ) ),
    inference(variable_rename,[status(thm)],[f_1666_1]) ).

fof(f_1666_3,plain,
    ( ! [U_5434,U_5432,U_5430] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),U_5434))
        | ? [U_5425] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),U_5425))
            & hBOOL(hAPP(hAPP(U_5432,U_5425),U_5434)) ) )
    & ! [U_5433,U_5431,U_5429] :
        ( ! [U_5424] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5424))
            | ~ hBOOL(hAPP(hAPP(U_5431,U_5424),U_5433)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5433)) ) ),
    inference(miniscope,[status(thm)],[f_1666_2]) ).

fof(f_1666_4,plain,
    ( ! [U_5434,U_5432,U_5430] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),U_5434))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),sK86(U_5434,U_5432,U_5430)))
          & hBOOL(hAPP(hAPP(U_5432,sK86(U_5434,U_5432,U_5430)),U_5434)) ) )
    & ! [U_5433,U_5431,U_5429] :
        ( ! [U_5424] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5424))
            | ~ hBOOL(hAPP(hAPP(U_5431,U_5424),U_5433)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5433)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_5425,sK86(U_5434,U_5432,U_5430))],[f_1666_3]) ).

fof(f_1666_5,plain,
    ( ! [U_5432,U_5434,U_5430] :
        ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),sK86(U_5434,U_5432,U_5430)))
        | ~ sP555(U_5432,U_5434,U_5430) )
    & ! [U_5432,U_5434,U_5430] :
        ( hBOOL(hAPP(hAPP(U_5432,sK86(U_5434,U_5432,U_5430)),U_5434))
        | ~ sP555(U_5432,U_5434,U_5430) )
    & ! [U_5432,U_5434,U_5430] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),U_5434))
        | sP555(U_5432,U_5434,U_5430) )
    & ! [U_5433,U_5424,U_5431,U_5429] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5424))
        | ~ hBOOL(hAPP(hAPP(U_5431,U_5424),U_5433))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5433)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP555])],[f_1666_4]) ).

cnf(f_1666_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5424))
    | ~ hBOOL(hAPP(hAPP(U_5431,U_5424),U_5433))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5429,U_5431),U_5433)) ),
    inference(clausify,[status(thm)],[f_1666_5]) ).

cnf(f_1666_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),U_5434))
    | sP555(U_5432,U_5434,U_5430) ),
    inference(clausify,[status(thm)],[f_1666_5]) ).

cnf(f_1666_8,plain,
    ( hBOOL(hAPP(hAPP(U_5432,sK86(U_5434,U_5432,U_5430)),U_5434))
    | ~ sP555(U_5432,U_5434,U_5430) ),
    inference(clausify,[status(thm)],[f_1666_5]) ).

cnf(f_1666_9,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5430,U_5432),sK86(U_5434,U_5432,U_5430)))
    | ~ sP555(U_5432,U_5434,U_5430) ),
    inference(clausify,[status(thm)],[f_1666_5]) ).

fof(f_1667_1,plain,
    ! [V_a_2,V_b_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_accp__downward]) ).

fof(f_1667_2,plain,
    ! [U_5438,U_5437,U_5436,U_5435] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5435,U_5436),U_5438))
      | ~ hBOOL(hAPP(hAPP(U_5436,U_5438),U_5437))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5435,U_5436),U_5437)) ),
    inference(variable_rename,[status(thm)],[f_1667_1]) ).

fof(f_1667_3,plain,
    ! [U_5435,U_5436,U_5438,U_5437] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5435,U_5436),U_5438))
      | ~ hBOOL(hAPP(hAPP(U_5436,U_5438),U_5437))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5435,U_5436),U_5437)) ),
    inference(definitional_conversion,[status(esa)],[f_1667_2]) ).

cnf(f_1667_4,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5435,U_5436),U_5438))
    | ~ hBOOL(hAPP(hAPP(U_5436,U_5438),U_5437))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5435,U_5436),U_5437)) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

fof(f_1668_1,plain,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) ),
    inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).

fof(f_1668_2,plain,
    ! [U_5441,U_5440,U_5439] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5439,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_5439,U_5441)),c_Wellfounded_Oaccp(U_5439,U_5440)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5439,tc_fun(U_5439,tc_HOL_Obool))),U_5440),U_5441)) ),
    inference(variable_rename,[status(thm)],[f_1668_1]) ).

fof(f_1668_3,plain,
    ! [U_5439,U_5440,U_5441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5439,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_5439,U_5441)),c_Wellfounded_Oaccp(U_5439,U_5440)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5439,tc_fun(U_5439,tc_HOL_Obool))),U_5440),U_5441)) ),
    inference(definitional_conversion,[status(esa)],[f_1668_2]) ).

cnf(f_1668_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5439,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_5439,U_5441)),c_Wellfounded_Oaccp(U_5439,U_5440)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5439,tc_fun(U_5439,tc_HOL_Obool))),U_5440),U_5441)) ),
    inference(clausify,[status(thm)],[f_1668_3]) ).

fof(f_1669_1,plain,
    ! [V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__0]) ).

fof(f_1669_2,plain,
    ! [U_5442] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5442),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
      | U_5442 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1669_1]) ).

fof(f_1669_3,plain,
    ! [U_5442] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5442),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
      | U_5442 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1669_2]) ).

cnf(f_1669_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5442),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
    | U_5442 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1669_3]) ).

fof(f_1670_1,plain,
    ! [V_r,V_q,V_a] :
      ( V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_self__remainder]) ).

fof(f_1670_2,plain,
    ! [U_5445,U_5444,U_5443] :
      ( U_5445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_5443 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5443,U_5443),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5444),U_5445))) ),
    inference(variable_rename,[status(thm)],[f_1670_1]) ).

fof(f_1670_3,plain,
    ! [U_5443,U_5444,U_5445] :
      ( U_5445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_5443 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5443,U_5443),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5444),U_5445))) ),
    inference(definitional_conversion,[status(esa)],[f_1670_2]) ).

cnf(f_1670_4,plain,
    ( U_5445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5443 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5443,U_5443),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5444),U_5445))) ),
    inference(clausify,[status(thm)],[f_1670_3]) ).

fof(f_1671_1,plain,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( V_q = V_q_H
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient]) ).

fof(f_1671_2,plain,
    ! [U_5451,U_5450,U_5449,U_5448,U_5447,U_5446] :
      ( U_5448 = U_5450
      | U_5447 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5446,U_5447),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5450),U_5451)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5446,U_5447),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5448),U_5449))) ),
    inference(variable_rename,[status(thm)],[f_1671_1]) ).

fof(f_1671_3,plain,
    ! [U_5451,U_5450,U_5447,U_5446,U_5448,U_5449] :
      ( U_5448 = U_5450
      | U_5447 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5446,U_5447),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5450),U_5451)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5446,U_5447),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5448),U_5449))) ),
    inference(definitional_conversion,[status(esa)],[f_1671_2]) ).

cnf(f_1671_4,plain,
    ( U_5448 = U_5450
    | U_5447 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5446,U_5447),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5450),U_5451)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5446,U_5447),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5448),U_5449))) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

fof(f_1672_1,plain,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( V_r = V_r_H
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__remainder]) ).

fof(f_1672_2,plain,
    ! [U_5457,U_5456,U_5455,U_5454,U_5453,U_5452] :
      ( U_5455 = U_5457
      | U_5453 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5452,U_5453),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5456),U_5457)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5452,U_5453),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5454),U_5455))) ),
    inference(variable_rename,[status(thm)],[f_1672_1]) ).

fof(f_1672_3,plain,
    ! [U_5453,U_5454,U_5452,U_5455,U_5456,U_5457] :
      ( U_5455 = U_5457
      | U_5453 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5452,U_5453),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5456),U_5457)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5452,U_5453),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5454),U_5455))) ),
    inference(definitional_conversion,[status(esa)],[f_1672_2]) ).

cnf(f_1672_4,plain,
    ( U_5455 = U_5457
    | U_5453 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5452,U_5453),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5456),U_5457)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5452,U_5453),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5454),U_5455))) ),
    inference(clausify,[status(thm)],[f_1672_3]) ).

fof(f_1673_1,plain,
    ! [V_r,V_q,V_a] :
      ( V_q = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient]) ).

fof(f_1673_2,plain,
    ! [U_5460,U_5459,U_5458] :
      ( U_5459 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_5458 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5458,U_5458),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5459),U_5460))) ),
    inference(variable_rename,[status(thm)],[f_1673_1]) ).

fof(f_1673_3,plain,
    ! [U_5459,U_5458,U_5460] :
      ( U_5459 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_5458 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5458,U_5458),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5459),U_5460))) ),
    inference(definitional_conversion,[status(esa)],[f_1673_2]) ).

cnf(f_1673_4,plain,
    ( U_5459 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_5458 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5458,U_5458),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5459),U_5460))) ),
    inference(clausify,[status(thm)],[f_1673_3]) ).

fof(f_1674_1,plain,
    ! [V_r,V_q,V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod]) ).

fof(f_1674_2,plain,
    ! [U_5464,U_5463,U_5462,U_5461] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5461,U_5462) = U_5464
      | U_5462 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5461,U_5462),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5463),U_5464))) ),
    inference(variable_rename,[status(thm)],[f_1674_1]) ).

fof(f_1674_3,plain,
    ! [U_5462,U_5461,U_5463,U_5464] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5461,U_5462) = U_5464
      | U_5462 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5461,U_5462),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5463),U_5464))) ),
    inference(definitional_conversion,[status(esa)],[f_1674_2]) ).

cnf(f_1674_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5461,U_5462) = U_5464
    | U_5462 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5461,U_5462),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5463),U_5464))) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

fof(f_1675_1,plain,
    ! [V_r,V_q,V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div]) ).

fof(f_1675_2,plain,
    ! [U_5468,U_5467,U_5466,U_5465] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5465),U_5466) = U_5467
      | U_5466 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5465,U_5466),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5467),U_5468))) ),
    inference(variable_rename,[status(thm)],[f_1675_1]) ).

fof(f_1675_3,plain,
    ! [U_5465,U_5466,U_5467,U_5468] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5465),U_5466) = U_5467
      | U_5466 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5465,U_5466),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5467),U_5468))) ),
    inference(definitional_conversion,[status(esa)],[f_1675_2]) ).

cnf(f_1675_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5465),U_5466) = U_5467
    | U_5466 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5465,U_5466),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5467),U_5468))) ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

fof(f_1676_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct]) ).

fof(f_1676_2,plain,
    ! [U_5470,U_5469] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5469,U_5470),c_Divides_OnegDivAlg(U_5469,U_5470)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1676_1]) ).

fof(f_1676_3,plain,
    ! [U_5469,U_5470] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5469,U_5470),c_Divides_OnegDivAlg(U_5469,U_5470)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1676_2]) ).

cnf(f_1676_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5469,U_5470),c_Divides_OnegDivAlg(U_5469,U_5470)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

fof(f_1677_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod]) ).

fof(f_1677_2,plain,
    ! [U_5472,U_5471] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5472,U_5471),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5472),U_5471)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5472,U_5471))))
      | U_5471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1677_1]) ).

fof(f_1677_3,plain,
    ! [U_5471,U_5472] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5472,U_5471),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5472),U_5471)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5472,U_5471))))
      | U_5471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1677_2]) ).

cnf(f_1677_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5472,U_5471),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5472),U_5471)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5472,U_5471))))
    | U_5471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

fof(f_1678_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct]) ).

fof(f_1678_2,plain,
    ! [U_5474,U_5473] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5473,U_5474),c_Divides_OposDivAlg(U_5473,U_5474)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5473)) ),
    inference(variable_rename,[status(thm)],[f_1678_1]) ).

fof(f_1678_3,plain,
    ! [U_5473,U_5474] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5473,U_5474),c_Divides_OposDivAlg(U_5473,U_5474)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5473)) ),
    inference(definitional_conversion,[status(esa)],[f_1678_2]) ).

cnf(f_1678_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5473,U_5474),c_Divides_OposDivAlg(U_5473,U_5474)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5473)) ),
    inference(clausify,[status(thm)],[f_1678_3]) ).

fof(f_1679_1,plain,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c))))
      | V_c = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) ),
    inference(fof_nnf,[status(thm)],[fact_zadd1__lemma]) ).

fof(f_1679_2,plain,
    ! [U_5481,U_5480,U_5479,U_5478,U_5477,U_5476,U_5475] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5475),U_5479),U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5477),U_5480)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5478),U_5481)),U_5476))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5478),U_5481),U_5476))))
      | U_5476 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5479,U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5480),U_5481)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5475,U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5477),U_5478))) ),
    inference(variable_rename,[status(thm)],[f_1679_1]) ).

fof(f_1679_3,plain,
    ! [U_5475,U_5476,U_5477,U_5478,U_5479,U_5480,U_5481] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5475),U_5479),U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5477),U_5480)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5478),U_5481)),U_5476))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5478),U_5481),U_5476))))
      | U_5476 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5479,U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5480),U_5481)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5475,U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5477),U_5478))) ),
    inference(definitional_conversion,[status(esa)],[f_1679_2]) ).

cnf(f_1679_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5475),U_5479),U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5477),U_5480)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5478),U_5481)),U_5476))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5478),U_5481),U_5476))))
    | U_5476 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5479,U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5480),U_5481)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5475,U_5476),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5477),U_5478))) ),
    inference(clausify,[status(thm)],[f_1679_3]) ).

fof(f_1680_1,plain,
    ! [V_r_2,V_q_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_zminus1__lemma]) ).

fof(f_1680_2,plain,
    ! [U_5485,U_5484,U_5483,U_5482] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5482),U_5483),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_5485),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5484)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5484)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_5485),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5483),U_5485)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5482,U_5483),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5484),U_5485))) ),
    inference(variable_rename,[status(thm)],[f_1680_1]) ).

fof(f_1680_3,plain,
    ! [U_5483,U_5482,U_5484,U_5485] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5482),U_5483),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_5485),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5484)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5484)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_5485),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5483),U_5485)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5482,U_5483),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5484),U_5485))) ),
    inference(definitional_conversion,[status(esa)],[f_1680_2]) ).

cnf(f_1680_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5482),U_5483),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_5485),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5484)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5484)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_5485),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5483),U_5485)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5482,U_5483),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5484),U_5485))) ),
    inference(clausify,[status(thm)],[f_1680_3]) ).

fof(f_1681_1,plain,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
      | V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__relI]) ).

fof(f_1681_2,plain,
    ! [U_5489,U_5488,U_5487,U_5486] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5486,U_5487),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5488),U_5489)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5489),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5487),U_5489)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5487)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5489),U_5487))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5489)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5487)) )
      | U_5486 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5487),U_5488)),U_5489) ),
    inference(variable_rename,[status(thm)],[f_1681_1]) ).

fof(f_1681_3,plain,
    ( ! [U_5487,U_5489] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5489),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5487),U_5489))
        | ~ sP557(U_5487,U_5489) )
    & ! [U_5487,U_5489] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5487))
        | ~ sP557(U_5487,U_5489) )
    & ! [U_5487,U_5489] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5489),U_5487))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5489))
        | ~ sP556(U_5487,U_5489) )
    & ! [U_5487,U_5489] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5487))
        | ~ sP556(U_5487,U_5489) )
    & ! [U_5486,U_5487,U_5488,U_5489] :
        ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5486,U_5487),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5488),U_5489)))
        | sP557(U_5487,U_5489)
        | sP556(U_5487,U_5489)
        | U_5486 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5487),U_5488)),U_5489) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP556,sP557])],[f_1681_2]) ).

cnf(f_1681_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5486,U_5487),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5488),U_5489)))
    | sP557(U_5487,U_5489)
    | sP556(U_5487,U_5489)
    | U_5486 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5487),U_5488)),U_5489) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

cnf(f_1681_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5487))
    | ~ sP556(U_5487,U_5489) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

cnf(f_1681_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5489),U_5487))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5489))
    | ~ sP556(U_5487,U_5489) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

cnf(f_1681_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5487))
    | ~ sP557(U_5487,U_5489) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

cnf(f_1681_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5489),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5487),U_5489))
    | ~ sP557(U_5487,U_5489) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

fof(f_1682_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct]) ).

fof(f_1682_2,plain,
    ! [U_5494,U_5493,U_5492] :
      ( hBOOL(hAPP(hAPP(U_5494,U_5492),U_5493))
      | ? [U_5491,U_5490] :
          ( ~ hBOOL(hAPP(hAPP(U_5494,U_5491),U_5490))
          & ( hBOOL(hAPP(hAPP(U_5494,U_5491),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5490)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5490),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5491),U_5490))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5491),U_5490))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5492),U_5493))) ),
    inference(variable_rename,[status(thm)],[f_1682_1]) ).

fof(f_1682_3,plain,
    ! [U_5494,U_5493,U_5492] :
      ( hBOOL(hAPP(hAPP(U_5494,U_5492),U_5493))
      | ? [U_5490] :
          ( ~ hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),U_5490))
          & ( hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5490)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5490),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),U_5490))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),U_5490))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5492),U_5493))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_5491,sK87(U_5494,U_5493,U_5492))],[f_1682_2]) ).

fof(f_1682_4,plain,
    ! [U_5494,U_5493,U_5492] :
      ( hBOOL(hAPP(hAPP(U_5494,U_5492),U_5493))
      | ( ~ hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492)))
        & ( hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK88(U_5494,U_5493,U_5492))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK88(U_5494,U_5493,U_5492)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492)))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5492),U_5493))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_5490,sK88(U_5494,U_5493,U_5492))],[f_1682_3]) ).

fof(f_1682_5,plain,
    ( ! [U_5492,U_5494,U_5493] :
        ( ~ hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492)))
        | ~ sP558(U_5492,U_5494,U_5493) )
    & ! [U_5492,U_5494,U_5493] :
        ( hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK88(U_5494,U_5493,U_5492))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK88(U_5494,U_5493,U_5492)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492))))
        | ~ sP558(U_5492,U_5494,U_5493) )
    & ! [U_5492,U_5494,U_5493] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492))))
        | ~ sP558(U_5492,U_5494,U_5493) )
    & ! [U_5492,U_5494,U_5493] :
        ( hBOOL(hAPP(hAPP(U_5494,U_5492),U_5493))
        | sP558(U_5492,U_5494,U_5493)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5492),U_5493))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP558])],[f_1682_4]) ).

cnf(f_1682_6,plain,
    ( hBOOL(hAPP(hAPP(U_5494,U_5492),U_5493))
    | sP558(U_5492,U_5494,U_5493)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5492),U_5493))) ),
    inference(clausify,[status(thm)],[f_1682_5]) ).

cnf(f_1682_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492))))
    | ~ sP558(U_5492,U_5494,U_5493) ),
    inference(clausify,[status(thm)],[f_1682_5]) ).

cnf(f_1682_8,plain,
    ( hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK88(U_5494,U_5493,U_5492))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK88(U_5494,U_5493,U_5492)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492))))
    | ~ sP558(U_5492,U_5494,U_5493) ),
    inference(clausify,[status(thm)],[f_1682_5]) ).

cnf(f_1682_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_5494,sK87(U_5494,U_5493,U_5492)),sK88(U_5494,U_5493,U_5492)))
    | ~ sP558(U_5492,U_5494,U_5493) ),
    inference(clausify,[status(thm)],[f_1682_5]) ).

fof(f_1683_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct]) ).

fof(f_1683_2,plain,
    ! [U_5499,U_5498,U_5497] :
      ( hBOOL(hAPP(hAPP(U_5499,U_5497),U_5498))
      | ? [U_5496,U_5495] :
          ( ~ hBOOL(hAPP(hAPP(U_5499,U_5496),U_5495))
          & ( hBOOL(hAPP(hAPP(U_5499,U_5496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5495)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5495),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5496),U_5495)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5496),U_5495))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5497),U_5498))) ),
    inference(variable_rename,[status(thm)],[f_1683_1]) ).

fof(f_1683_3,plain,
    ! [U_5499,U_5498,U_5497] :
      ( hBOOL(hAPP(hAPP(U_5499,U_5497),U_5498))
      | ? [U_5495] :
          ( ~ hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),U_5495))
          & ( hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5495)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5495),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),U_5495)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),U_5495))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5497),U_5498))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_5496,sK89(U_5499,U_5498,U_5497))],[f_1683_2]) ).

fof(f_1683_4,plain,
    ! [U_5499,U_5498,U_5497] :
      ( hBOOL(hAPP(hAPP(U_5499,U_5497),U_5498))
      | ( ~ hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497)))
        & ( hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK90(U_5499,U_5498,U_5497))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK90(U_5499,U_5498,U_5497)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5497),U_5498))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_5495,sK90(U_5499,U_5498,U_5497))],[f_1683_3]) ).

fof(f_1683_5,plain,
    ( ! [U_5499,U_5498,U_5497] :
        ( ~ hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497)))
        | ~ sP559(U_5499,U_5498,U_5497) )
    & ! [U_5499,U_5498,U_5497] :
        ( hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK90(U_5499,U_5498,U_5497))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK90(U_5499,U_5498,U_5497)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497)))
        | ~ sP559(U_5499,U_5498,U_5497) )
    & ! [U_5499,U_5498,U_5497] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497))))
        | ~ sP559(U_5499,U_5498,U_5497) )
    & ! [U_5499,U_5498,U_5497] :
        ( hBOOL(hAPP(hAPP(U_5499,U_5497),U_5498))
        | sP559(U_5499,U_5498,U_5497)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5497),U_5498))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP559])],[f_1683_4]) ).

cnf(f_1683_6,plain,
    ( hBOOL(hAPP(hAPP(U_5499,U_5497),U_5498))
    | sP559(U_5499,U_5498,U_5497)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5497),U_5498))) ),
    inference(clausify,[status(thm)],[f_1683_5]) ).

cnf(f_1683_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497))))
    | ~ sP559(U_5499,U_5498,U_5497) ),
    inference(clausify,[status(thm)],[f_1683_5]) ).

cnf(f_1683_8,plain,
    ( hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK90(U_5499,U_5498,U_5497))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK90(U_5499,U_5498,U_5497)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497)))
    | ~ sP559(U_5499,U_5498,U_5497) ),
    inference(clausify,[status(thm)],[f_1683_5]) ).

cnf(f_1683_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_5499,sK89(U_5499,U_5498,U_5497)),sK90(U_5499,U_5498,U_5497)))
    | ~ sP559(U_5499,U_5498,U_5497) ),
    inference(clausify,[status(thm)],[f_1683_5]) ).

fof(f_1684_1,plain,
    ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I4_J]) ).

fof(f_1684_2,plain,
    ! [U_5500] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_5500)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1684_1]) ).

fof(f_1684_3,plain,
    ! [U_5500] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_5500)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1684_2]) ).

cnf(f_1684_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_5500)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1684_3]) ).

fof(f_1685_1,plain,
    ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I2_J]) ).

fof(f_1685_2,plain,
    ! [U_5501] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_5501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_5501)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1685_1]) ).

fof(f_1685_3,plain,
    ! [U_5501] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_5501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_5501)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1685_2]) ).

cnf(f_1685_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_5501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_5501)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1685_3]) ).

fof(f_1686_1,plain,
    ! [V_b,V_a] :
      ( ( ( ( c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
          & ( c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))
                | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
          & ( c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__def]) ).

fof(f_1686_2,plain,
    ! [U_5503,U_5502] :
      ( ( ( ( c_Divides_Odivmod__int(U_5502,U_5503) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5502),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5503)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5503)) )
          & ( c_Divides_Odivmod__int(U_5502,U_5503) = c_Divides_OnegDivAlg(U_5502,U_5503)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5503)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5502)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(U_5502,U_5503) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5502),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5503)))
                | U_5502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_5502,U_5503) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | U_5502 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5503)) )
          & ( c_Divides_Odivmod__int(U_5502,U_5503) = c_Divides_OposDivAlg(U_5502,U_5503)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5503)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5502)) ) ),
    inference(variable_rename,[status(thm)],[f_1686_1]) ).

fof(f_1686_3,plain,
    ( ! [U_5507,U_5505] :
        ( ( ( c_Divides_Odivmod__int(U_5505,U_5507) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5505),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5507)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5507)) )
          & ( c_Divides_Odivmod__int(U_5505,U_5507) = c_Divides_OnegDivAlg(U_5505,U_5507)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5507)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5505)) )
    & ! [U_5506,U_5504] :
        ( ( ( ( ( c_Divides_Odivmod__int(U_5504,U_5506) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5504),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5506)))
                | U_5504 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_5504,U_5506) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | U_5504 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506)) )
          & ( c_Divides_Odivmod__int(U_5504,U_5506) = c_Divides_OposDivAlg(U_5504,U_5506)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5504)) ) ),
    inference(miniscope,[status(thm)],[f_1686_2]) ).

fof(f_1686_4,plain,
    ( ! [U_5505,U_5507] :
        ( c_Divides_Odivmod__int(U_5505,U_5507) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5505),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5507)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5507))
        | ~ sP562(U_5505,U_5507) )
    & ! [U_5505,U_5507] :
        ( c_Divides_Odivmod__int(U_5505,U_5507) = c_Divides_OnegDivAlg(U_5505,U_5507)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5507))
        | ~ sP562(U_5505,U_5507) )
    & ! [U_5506,U_5504] :
        ( c_Divides_Odivmod__int(U_5504,U_5506) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5504),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5506)))
        | U_5504 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP560(U_5506,U_5504) )
    & ! [U_5506,U_5504] :
        ( c_Divides_Odivmod__int(U_5504,U_5506) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_5504 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP560(U_5506,U_5504) )
    & ! [U_5506,U_5504] :
        ( sP560(U_5506,U_5504)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506))
        | ~ sP561(U_5506,U_5504) )
    & ! [U_5506,U_5504] :
        ( c_Divides_Odivmod__int(U_5504,U_5506) = c_Divides_OposDivAlg(U_5504,U_5506)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506))
        | ~ sP561(U_5506,U_5504) )
    & ! [U_5505,U_5507] :
        ( sP562(U_5505,U_5507)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5505)) )
    & ! [U_5506,U_5504] :
        ( sP561(U_5506,U_5504)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5504)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP560,sP561,sP562])],[f_1686_3]) ).

cnf(f_1686_5,plain,
    ( sP561(U_5506,U_5504)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5504)) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_6,plain,
    ( sP562(U_5505,U_5507)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5505)) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_7,plain,
    ( c_Divides_Odivmod__int(U_5504,U_5506) = c_Divides_OposDivAlg(U_5504,U_5506)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506))
    | ~ sP561(U_5506,U_5504) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_8,plain,
    ( sP560(U_5506,U_5504)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506))
    | ~ sP561(U_5506,U_5504) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_9,plain,
    ( c_Divides_Odivmod__int(U_5504,U_5506) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_5504 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP560(U_5506,U_5504) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_10,plain,
    ( c_Divides_Odivmod__int(U_5504,U_5506) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5504),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5506)))
    | U_5504 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP560(U_5506,U_5504) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_11,plain,
    ( c_Divides_Odivmod__int(U_5505,U_5507) = c_Divides_OnegDivAlg(U_5505,U_5507)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5507))
    | ~ sP562(U_5505,U_5507) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

cnf(f_1686_12,plain,
    ( c_Divides_Odivmod__int(U_5505,U_5507) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5505),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5507)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5507))
    | ~ sP562(U_5505,U_5507) ),
    inference(clausify,[status(thm)],[f_1686_4]) ).

fof(f_1687_1,plain,
    ! [V_w] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of]) ).

fof(f_1687_2,plain,
    ! [U_5508] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508))) ),
    inference(variable_rename,[status(thm)],[f_1687_1]) ).

fof(f_1687_3,plain,
    ! [U_5508] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508))) ),
    inference(definitional_conversion,[status(esa)],[f_1687_2]) ).

cnf(f_1687_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5508))) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

fof(f_1688_1,plain,
    ! [V_code__numeral_H_2,V_code__numeral_2] :
      ( ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
        | V_code__numeral_2 != V_code__numeral_H_2 )
      & ( V_code__numeral_2 = V_code__numeral_H_2
        | c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject]) ).

fof(f_1688_2,plain,
    ! [U_5510,U_5509] :
      ( ( c_Code__Numeral_OSuc__code__numeral(U_5509) = c_Code__Numeral_OSuc__code__numeral(U_5510)
        | U_5509 != U_5510 )
      & ( U_5509 = U_5510
        | c_Code__Numeral_OSuc__code__numeral(U_5509) != c_Code__Numeral_OSuc__code__numeral(U_5510) ) ),
    inference(variable_rename,[status(thm)],[f_1688_1]) ).

fof(f_1688_3,plain,
    ( ! [U_5514,U_5512] :
        ( c_Code__Numeral_OSuc__code__numeral(U_5512) = c_Code__Numeral_OSuc__code__numeral(U_5514)
        | U_5512 != U_5514 )
    & ! [U_5513,U_5511] :
        ( U_5511 = U_5513
        | c_Code__Numeral_OSuc__code__numeral(U_5511) != c_Code__Numeral_OSuc__code__numeral(U_5513) ) ),
    inference(miniscope,[status(thm)],[f_1688_2]) ).

fof(f_1688_4,plain,
    ( ! [U_5514,U_5512] :
        ( c_Code__Numeral_OSuc__code__numeral(U_5512) = c_Code__Numeral_OSuc__code__numeral(U_5514)
        | U_5512 != U_5514 )
    & ! [U_5513,U_5511] :
        ( U_5511 = U_5513
        | c_Code__Numeral_OSuc__code__numeral(U_5511) != c_Code__Numeral_OSuc__code__numeral(U_5513) ) ),
    inference(definitional_conversion,[status(esa)],[f_1688_3]) ).

cnf(f_1688_5,plain,
    ( U_5511 = U_5513
    | c_Code__Numeral_OSuc__code__numeral(U_5511) != c_Code__Numeral_OSuc__code__numeral(U_5513) ),
    inference(clausify,[status(thm)],[f_1688_4]) ).

cnf(f_1688_6,plain,
    ( c_Code__Numeral_OSuc__code__numeral(U_5512) = c_Code__Numeral_OSuc__code__numeral(U_5514)
    | U_5512 != U_5514 ),
    inference(clausify,[status(thm)],[f_1688_4]) ).

fof(f_1689_1,plain,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_mod__int__def]) ).

fof(f_1689_2,plain,
    ! [U_5516,U_5515] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5515,U_5516) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5515,U_5516)),
    inference(variable_rename,[status(thm)],[f_1689_1]) ).

fof(f_1689_3,plain,
    ! [U_5516,U_5515] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5515,U_5516) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5515,U_5516)),
    inference(definitional_conversion,[status(esa)],[f_1689_2]) ).

cnf(f_1689_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5515,U_5516) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5515,U_5516)),
    inference(clausify,[status(thm)],[f_1689_3]) ).

fof(f_1690_1,plain,
    ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).

fof(f_1690_2,plain,
    ! [U_5517] : c_Code__Numeral_OSuc__code__numeral(U_5517) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_1690_1]) ).

fof(f_1690_3,plain,
    ! [U_5517] : c_Code__Numeral_OSuc__code__numeral(U_5517) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1690_2]) ).

cnf(f_1690_4,plain,
    c_Code__Numeral_OSuc__code__numeral(U_5517) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1690_3]) ).

fof(f_1691_1,plain,
    ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).

fof(f_1691_2,plain,
    ! [U_5518] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_5518),
    inference(variable_rename,[status(thm)],[f_1691_1]) ).

fof(f_1691_3,plain,
    ! [U_5518] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_5518),
    inference(definitional_conversion,[status(esa)],[f_1691_2]) ).

cnf(f_1691_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_5518),
    inference(clausify,[status(thm)],[f_1691_3]) ).

fof(f_1692_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__neg]) ).

fof(f_1692_2,plain,
    ! [U_5520,U_5519] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5519,U_5520) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5519),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5520))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5519)) ),
    inference(variable_rename,[status(thm)],[f_1692_1]) ).

fof(f_1692_3,plain,
    ! [U_5519,U_5520] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5519,U_5520) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5519),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5520))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5519)) ),
    inference(definitional_conversion,[status(esa)],[f_1692_2]) ).

cnf(f_1692_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5519,U_5520) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5519),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5520))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5519)) ),
    inference(clausify,[status(thm)],[f_1692_3]) ).

fof(f_1693_1,plain,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).

fof(f_1693_2,plain,
    ! [U_5524,U_5523,U_5522,U_5521] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5521,U_5522,U_5523,c_Code__Numeral_OSuc__code__numeral(U_5524)) = hAPP(U_5523,U_5524),
    inference(variable_rename,[status(thm)],[f_1693_1]) ).

fof(f_1693_3,plain,
    ! [U_5523,U_5522,U_5524,U_5521] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5521,U_5522,U_5523,c_Code__Numeral_OSuc__code__numeral(U_5524)) = hAPP(U_5523,U_5524),
    inference(definitional_conversion,[status(esa)],[f_1693_2]) ).

cnf(f_1693_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5521,U_5522,U_5523,c_Code__Numeral_OSuc__code__numeral(U_5524)) = hAPP(U_5523,U_5524),
    inference(clausify,[status(thm)],[f_1693_3]) ).

fof(f_1694_1,plain,
    ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)),
    inference(fof_nnf,[status(thm)],[fact_negateSnd__eq]) ).

fof(f_1694_2,plain,
    ! [U_5526,U_5525] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5525),U_5526)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5525),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5526)),
    inference(variable_rename,[status(thm)],[f_1694_1]) ).

fof(f_1694_3,plain,
    ! [U_5525,U_5526] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5525),U_5526)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5525),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5526)),
    inference(definitional_conversion,[status(esa)],[f_1694_2]) ).

cnf(f_1694_4,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5525),U_5526)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5525),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5526)),
    inference(clausify,[status(thm)],[f_1694_3]) ).

fof(f_1695_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__neg__neg]) ).

fof(f_1695_2,plain,
    ! [U_5528,U_5527] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5527,U_5528) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5527),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5528))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5528),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1695_1]) ).

fof(f_1695_3,plain,
    ! [U_5527,U_5528] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5527,U_5528) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5527),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5528))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5528),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1695_2]) ).

cnf(f_1695_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5527,U_5528) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5527),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5528))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5528),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

fof(f_1696_1,plain,
    ! [V_qr,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg]) ).

fof(f_1696_2,plain,
    ! [U_5531,U_5530,U_5529] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5529,U_5530),hAPP(c_Divides_OnegateSnd,U_5531)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5529),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5530)),U_5531)) ),
    inference(variable_rename,[status(thm)],[f_1696_1]) ).

fof(f_1696_3,plain,
    ! [U_5530,U_5529,U_5531] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5529,U_5530),hAPP(c_Divides_OnegateSnd,U_5531)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5529),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5530)),U_5531)) ),
    inference(definitional_conversion,[status(esa)],[f_1696_2]) ).

cnf(f_1696_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5529,U_5530),hAPP(c_Divides_OnegateSnd,U_5531)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5529),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5530)),U_5531)) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

fof(f_1697_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).

fof(f_1697_2,plain,
    ! [U_5532] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5532)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_5532,
    inference(variable_rename,[status(thm)],[f_1697_1]) ).

fof(f_1697_3,plain,
    ! [U_5532] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5532)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_5532,
    inference(definitional_conversion,[status(esa)],[f_1697_2]) ).

cnf(f_1697_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5532)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_5532,
    inference(clausify,[status(thm)],[f_1697_3]) ).

fof(f_1698_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__neg__pos]) ).

fof(f_1698_2,plain,
    ! [U_5534,U_5533] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5533,U_5534) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5533,U_5534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5533),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1698_1]) ).

fof(f_1698_3,plain,
    ! [U_5533,U_5534] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5533,U_5534) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5533,U_5534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5533),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1698_2]) ).

cnf(f_1698_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5533,U_5534) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5533,U_5534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5533),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1698_3]) ).

fof(f_1699_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b)))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__correct]) ).

fof(f_1699_2,plain,
    ! [U_5536,U_5535] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5536,U_5535),c_Divides_Odivmod__int(U_5536,U_5535)))
      | U_5535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1699_1]) ).

fof(f_1699_3,plain,
    ! [U_5536,U_5535] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5536,U_5535),c_Divides_Odivmod__int(U_5536,U_5535)))
      | U_5535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1699_2]) ).

cnf(f_1699_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_5536,U_5535),c_Divides_Odivmod__int(U_5536,U_5535)))
    | U_5535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1699_3]) ).

fof(f_1700_1,plain,
    ! [V_w] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of]) ).

fof(f_1700_2,plain,
    ! [U_5537] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1700_1]) ).

fof(f_1700_3,plain,
    ! [U_5537] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1700_2]) ).

cnf(f_1700_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1700_3]) ).

fof(f_1701_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__pos]) ).

fof(f_1701_2,plain,
    ! [U_5539,U_5538] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5538,U_5539) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5538,U_5539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5538)) ),
    inference(variable_rename,[status(thm)],[f_1701_1]) ).

fof(f_1701_3,plain,
    ! [U_5538,U_5539] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5538,U_5539) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5538,U_5539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5538)) ),
    inference(definitional_conversion,[status(esa)],[f_1701_2]) ).

cnf(f_1701_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5538,U_5539) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5538,U_5539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5538)) ),
    inference(clausify,[status(thm)],[f_1701_3]) ).

fof(f_1702_1,plain,
    ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__mod__div]) ).

fof(f_1702_2,plain,
    ! [U_5541,U_5540] : c_Divides_Odivmod__int(U_5540,U_5541) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5540),U_5541)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5541)),
    inference(variable_rename,[status(thm)],[f_1702_1]) ).

fof(f_1702_3,plain,
    ! [U_5540,U_5541] : c_Divides_Odivmod__int(U_5540,U_5541) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5540),U_5541)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5541)),
    inference(definitional_conversion,[status(esa)],[f_1702_2]) ).

cnf(f_1702_4,plain,
    c_Divides_Odivmod__int(U_5540,U_5541) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5540),U_5541)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5541)),
    inference(clausify,[status(thm)],[f_1702_3]) ).

fof(f_1703_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( V_A_2 = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_equalityI]) ).

fof(f_1703_2,plain,
    ! [U_5544,U_5543,U_5542] :
      ( U_5543 = U_5544
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5542,tc_HOL_Obool)),U_5544),U_5543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5542,tc_HOL_Obool)),U_5543),U_5544)) ),
    inference(variable_rename,[status(thm)],[f_1703_1]) ).

fof(f_1703_3,plain,
    ! [U_5542,U_5543,U_5544] :
      ( U_5543 = U_5544
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5542,tc_HOL_Obool)),U_5544),U_5543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5542,tc_HOL_Obool)),U_5543),U_5544)) ),
    inference(definitional_conversion,[status(esa)],[f_1703_2]) ).

cnf(f_1703_4,plain,
    ( U_5543 = U_5544
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5542,tc_HOL_Obool)),U_5544),U_5543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5542,tc_HOL_Obool)),U_5543),U_5544)) ),
    inference(clausify,[status(thm)],[f_1703_3]) ).

fof(f_1704_1,plain,
    ! [V_w] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of]) ).

fof(f_1704_2,plain,
    ! [U_5545] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1704_1]) ).

fof(f_1704_3,plain,
    ! [U_5545] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1704_2]) ).

cnf(f_1704_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5545)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1704_3]) ).

fof(f_1705_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__neg]) ).

fof(f_1705_2,plain,
    ! [U_5547,U_5546] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5546),U_5547) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5547))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5547),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5546),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1705_1]) ).

fof(f_1705_3,plain,
    ! [U_5546,U_5547] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5546),U_5547) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5547))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5547),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5546),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1705_2]) ).

cnf(f_1705_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5546),U_5547) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5547))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5547),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5546),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1705_3]) ).

fof(f_1706_1,plain,
    ! [V_a,V_y,V_x,T_a,T_b] :
      ( V_y = V_a
      | hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) != V_a ),
    inference(fof_nnf,[status(thm)],[fact_snd__eqD]) ).

fof(f_1706_2,plain,
    ! [U_5552,U_5551,U_5550,U_5549,U_5548] :
      ( U_5551 = U_5552
      | hAPP(c_Product__Type_Osnd(U_5548,U_5549),hAPP(hAPP(c_Product__Type_OPair(U_5548,U_5549),U_5550),U_5551)) != U_5552 ),
    inference(variable_rename,[status(thm)],[f_1706_1]) ).

fof(f_1706_3,plain,
    ! [U_5552,U_5551] :
      ( ! [U_5550,U_5549,U_5548] : hAPP(c_Product__Type_Osnd(U_5548,U_5549),hAPP(hAPP(c_Product__Type_OPair(U_5548,U_5549),U_5550),U_5551)) != U_5552
      | U_5551 = U_5552 ),
    inference(miniscope,[status(thm)],[f_1706_2]) ).

fof(f_1706_4,plain,
    ! [U_5548,U_5549,U_5550,U_5551,U_5552] :
      ( hAPP(c_Product__Type_Osnd(U_5548,U_5549),hAPP(hAPP(c_Product__Type_OPair(U_5548,U_5549),U_5550),U_5551)) != U_5552
      | U_5551 = U_5552 ),
    inference(definitional_conversion,[status(esa)],[f_1706_3]) ).

cnf(f_1706_5,plain,
    ( hAPP(c_Product__Type_Osnd(U_5548,U_5549),hAPP(hAPP(c_Product__Type_OPair(U_5548,U_5549),U_5550),U_5551)) != U_5552
    | U_5551 = U_5552 ),
    inference(clausify,[status(thm)],[f_1706_4]) ).

fof(f_1707_1,plain,
    ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b,
    inference(fof_nnf,[status(thm)],[fact_snd__conv]) ).

fof(f_1707_2,plain,
    ! [U_5556,U_5555,U_5554,U_5553] : hAPP(c_Product__Type_Osnd(U_5553,U_5554),hAPP(hAPP(c_Product__Type_OPair(U_5553,U_5554),U_5555),U_5556)) = U_5556,
    inference(variable_rename,[status(thm)],[f_1707_1]) ).

fof(f_1707_3,plain,
    ! [U_5553,U_5554,U_5555,U_5556] : hAPP(c_Product__Type_Osnd(U_5553,U_5554),hAPP(hAPP(c_Product__Type_OPair(U_5553,U_5554),U_5555),U_5556)) = U_5556,
    inference(definitional_conversion,[status(esa)],[f_1707_2]) ).

cnf(f_1707_4,plain,
    hAPP(c_Product__Type_Osnd(U_5553,U_5554),hAPP(hAPP(c_Product__Type_OPair(U_5553,U_5554),U_5555),U_5556)) = U_5556,
    inference(clausify,[status(thm)],[f_1707_3]) ).

fof(f_1708_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__neg]) ).

fof(f_1708_2,plain,
    ! [U_5558,U_5557] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5557),U_5558) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5558))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5558),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5557)) ),
    inference(variable_rename,[status(thm)],[f_1708_1]) ).

fof(f_1708_3,plain,
    ! [U_5557,U_5558] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5557),U_5558) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5558))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5558),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5557)) ),
    inference(definitional_conversion,[status(esa)],[f_1708_2]) ).

cnf(f_1708_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5557),U_5558) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5558))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5558),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5557)) ),
    inference(clausify,[status(thm)],[f_1708_3]) ).

fof(f_1709_1,plain,
    ! [T_c,T_b,V_t_2,V_s_2] :
      ( ( V_s_2 = V_t_2
        | hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
        | hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
      & ( ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
          & hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
        | V_s_2 != V_t_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq]) ).

fof(f_1709_2,plain,
    ! [U_5562,U_5561,U_5560,U_5559] :
      ( ( U_5559 = U_5560
        | hAPP(c_Product__Type_Osnd(U_5561,U_5562),U_5559) != hAPP(c_Product__Type_Osnd(U_5561,U_5562),U_5560)
        | hAPP(c_Product__Type_Ofst(U_5561,U_5562),U_5559) != hAPP(c_Product__Type_Ofst(U_5561,U_5562),U_5560) )
      & ( ( hAPP(c_Product__Type_Osnd(U_5561,U_5562),U_5559) = hAPP(c_Product__Type_Osnd(U_5561,U_5562),U_5560)
          & hAPP(c_Product__Type_Ofst(U_5561,U_5562),U_5559) = hAPP(c_Product__Type_Ofst(U_5561,U_5562),U_5560) )
        | U_5559 != U_5560 ) ),
    inference(variable_rename,[status(thm)],[f_1709_1]) ).

fof(f_1709_3,plain,
    ( ! [U_5570,U_5568,U_5566,U_5564] :
        ( U_5564 = U_5566
        | hAPP(c_Product__Type_Osnd(U_5568,U_5570),U_5564) != hAPP(c_Product__Type_Osnd(U_5568,U_5570),U_5566)
        | hAPP(c_Product__Type_Ofst(U_5568,U_5570),U_5564) != hAPP(c_Product__Type_Ofst(U_5568,U_5570),U_5566) )
    & ! [U_5569,U_5567,U_5565,U_5563] :
        ( ( hAPP(c_Product__Type_Osnd(U_5567,U_5569),U_5563) = hAPP(c_Product__Type_Osnd(U_5567,U_5569),U_5565)
          & hAPP(c_Product__Type_Ofst(U_5567,U_5569),U_5563) = hAPP(c_Product__Type_Ofst(U_5567,U_5569),U_5565) )
        | U_5563 != U_5565 ) ),
    inference(miniscope,[status(thm)],[f_1709_2]) ).

fof(f_1709_4,plain,
    ( ! [U_5565,U_5563,U_5567,U_5569] :
        ( hAPP(c_Product__Type_Osnd(U_5567,U_5569),U_5563) = hAPP(c_Product__Type_Osnd(U_5567,U_5569),U_5565)
        | ~ sP563(U_5565,U_5563,U_5567,U_5569) )
    & ! [U_5565,U_5563,U_5567,U_5569] :
        ( hAPP(c_Product__Type_Ofst(U_5567,U_5569),U_5563) = hAPP(c_Product__Type_Ofst(U_5567,U_5569),U_5565)
        | ~ sP563(U_5565,U_5563,U_5567,U_5569) )
    & ! [U_5566,U_5564,U_5568,U_5570] :
        ( U_5564 = U_5566
        | hAPP(c_Product__Type_Osnd(U_5568,U_5570),U_5564) != hAPP(c_Product__Type_Osnd(U_5568,U_5570),U_5566)
        | hAPP(c_Product__Type_Ofst(U_5568,U_5570),U_5564) != hAPP(c_Product__Type_Ofst(U_5568,U_5570),U_5566) )
    & ! [U_5565,U_5563,U_5567,U_5569] :
        ( sP563(U_5565,U_5563,U_5567,U_5569)
        | U_5563 != U_5565 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP563])],[f_1709_3]) ).

cnf(f_1709_5,plain,
    ( sP563(U_5565,U_5563,U_5567,U_5569)
    | U_5563 != U_5565 ),
    inference(clausify,[status(thm)],[f_1709_4]) ).

cnf(f_1709_6,plain,
    ( U_5564 = U_5566
    | hAPP(c_Product__Type_Osnd(U_5568,U_5570),U_5564) != hAPP(c_Product__Type_Osnd(U_5568,U_5570),U_5566)
    | hAPP(c_Product__Type_Ofst(U_5568,U_5570),U_5564) != hAPP(c_Product__Type_Ofst(U_5568,U_5570),U_5566) ),
    inference(clausify,[status(thm)],[f_1709_4]) ).

cnf(f_1709_7,plain,
    ( hAPP(c_Product__Type_Ofst(U_5567,U_5569),U_5563) = hAPP(c_Product__Type_Ofst(U_5567,U_5569),U_5565)
    | ~ sP563(U_5565,U_5563,U_5567,U_5569) ),
    inference(clausify,[status(thm)],[f_1709_4]) ).

cnf(f_1709_8,plain,
    ( hAPP(c_Product__Type_Osnd(U_5567,U_5569),U_5563) = hAPP(c_Product__Type_Osnd(U_5567,U_5569),U_5565)
    | ~ sP563(U_5565,U_5563,U_5567,U_5569) ),
    inference(clausify,[status(thm)],[f_1709_4]) ).

fof(f_1710_1,plain,
    ! [V_q,V_p,T_b,T_a] :
      ( V_p = V_q
      | hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) != hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
      | hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) != hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) ),
    inference(fof_nnf,[status(thm)],[fact_prod__eqI]) ).

fof(f_1710_2,plain,
    ! [U_5574,U_5573,U_5572,U_5571] :
      ( U_5573 = U_5574
      | hAPP(c_Product__Type_Osnd(U_5571,U_5572),U_5573) != hAPP(c_Product__Type_Osnd(U_5571,U_5572),U_5574)
      | hAPP(c_Product__Type_Ofst(U_5571,U_5572),U_5573) != hAPP(c_Product__Type_Ofst(U_5571,U_5572),U_5574) ),
    inference(variable_rename,[status(thm)],[f_1710_1]) ).

fof(f_1710_3,plain,
    ! [U_5571,U_5572,U_5573,U_5574] :
      ( U_5573 = U_5574
      | hAPP(c_Product__Type_Osnd(U_5571,U_5572),U_5573) != hAPP(c_Product__Type_Osnd(U_5571,U_5572),U_5574)
      | hAPP(c_Product__Type_Ofst(U_5571,U_5572),U_5573) != hAPP(c_Product__Type_Ofst(U_5571,U_5572),U_5574) ),
    inference(definitional_conversion,[status(esa)],[f_1710_2]) ).

cnf(f_1710_4,plain,
    ( U_5573 = U_5574
    | hAPP(c_Product__Type_Osnd(U_5571,U_5572),U_5573) != hAPP(c_Product__Type_Osnd(U_5571,U_5572),U_5574)
    | hAPP(c_Product__Type_Ofst(U_5571,U_5572),U_5573) != hAPP(c_Product__Type_Ofst(U_5571,U_5572),U_5574) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

fof(f_1711_1,plain,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
    inference(fof_nnf,[status(thm)],[fact_fst__conv]) ).

fof(f_1711_2,plain,
    ! [U_5578,U_5577,U_5576,U_5575] : hAPP(c_Product__Type_Ofst(U_5575,U_5576),hAPP(hAPP(c_Product__Type_OPair(U_5575,U_5576),U_5577),U_5578)) = U_5577,
    inference(variable_rename,[status(thm)],[f_1711_1]) ).

fof(f_1711_3,plain,
    ! [U_5575,U_5576,U_5577,U_5578] : hAPP(c_Product__Type_Ofst(U_5575,U_5576),hAPP(hAPP(c_Product__Type_OPair(U_5575,U_5576),U_5577),U_5578)) = U_5577,
    inference(definitional_conversion,[status(esa)],[f_1711_2]) ).

cnf(f_1711_4,plain,
    hAPP(c_Product__Type_Ofst(U_5575,U_5576),hAPP(hAPP(c_Product__Type_OPair(U_5575,U_5576),U_5577),U_5578)) = U_5577,
    inference(clausify,[status(thm)],[f_1711_3]) ).

fof(f_1712_1,plain,
    ! [V_a,V_y,V_x,T_b,T_a] :
      ( V_x = V_a
      | hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) != V_a ),
    inference(fof_nnf,[status(thm)],[fact_fst__eqD]) ).

fof(f_1712_2,plain,
    ! [U_5583,U_5582,U_5581,U_5580,U_5579] :
      ( U_5581 = U_5583
      | hAPP(c_Product__Type_Ofst(U_5579,U_5580),hAPP(hAPP(c_Product__Type_OPair(U_5579,U_5580),U_5581),U_5582)) != U_5583 ),
    inference(variable_rename,[status(thm)],[f_1712_1]) ).

fof(f_1712_3,plain,
    ! [U_5583,U_5582,U_5581] :
      ( ! [U_5580,U_5579] : hAPP(c_Product__Type_Ofst(U_5579,U_5580),hAPP(hAPP(c_Product__Type_OPair(U_5579,U_5580),U_5581),U_5582)) != U_5583
      | U_5581 = U_5583 ),
    inference(miniscope,[status(thm)],[f_1712_2]) ).

fof(f_1712_4,plain,
    ! [U_5579,U_5580,U_5581,U_5582,U_5583] :
      ( hAPP(c_Product__Type_Ofst(U_5579,U_5580),hAPP(hAPP(c_Product__Type_OPair(U_5579,U_5580),U_5581),U_5582)) != U_5583
      | U_5581 = U_5583 ),
    inference(definitional_conversion,[status(esa)],[f_1712_3]) ).

cnf(f_1712_5,plain,
    ( hAPP(c_Product__Type_Ofst(U_5579,U_5580),hAPP(hAPP(c_Product__Type_OPair(U_5579,U_5580),U_5581),U_5582)) != U_5583
    | U_5581 = U_5583 ),
    inference(clausify,[status(thm)],[f_1712_4]) ).

fof(f_1713_1,plain,
    ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
    inference(fof_nnf,[status(thm)],[fact_surjective__pairing]) ).

fof(f_1713_2,plain,
    ! [U_5586,U_5585,U_5584] : U_5584 = hAPP(hAPP(c_Product__Type_OPair(U_5585,U_5586),hAPP(c_Product__Type_Ofst(U_5585,U_5586),U_5584)),hAPP(c_Product__Type_Osnd(U_5585,U_5586),U_5584)),
    inference(variable_rename,[status(thm)],[f_1713_1]) ).

fof(f_1713_3,plain,
    ! [U_5584,U_5585,U_5586] : U_5584 = hAPP(hAPP(c_Product__Type_OPair(U_5585,U_5586),hAPP(c_Product__Type_Ofst(U_5585,U_5586),U_5584)),hAPP(c_Product__Type_Osnd(U_5585,U_5586),U_5584)),
    inference(definitional_conversion,[status(esa)],[f_1713_2]) ).

cnf(f_1713_4,plain,
    U_5584 = hAPP(hAPP(c_Product__Type_OPair(U_5585,U_5586),hAPP(c_Product__Type_Ofst(U_5585,U_5586),U_5584)),hAPP(c_Product__Type_Osnd(U_5585,U_5586),U_5584)),
    inference(clausify,[status(thm)],[f_1713_3]) ).

fof(f_1714_1,plain,
    ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
    inference(fof_nnf,[status(thm)],[fact_pair__collapse]) ).

fof(f_1714_2,plain,
    ! [U_5589,U_5588,U_5587] : hAPP(hAPP(c_Product__Type_OPair(U_5587,U_5588),hAPP(c_Product__Type_Ofst(U_5587,U_5588),U_5589)),hAPP(c_Product__Type_Osnd(U_5587,U_5588),U_5589)) = U_5589,
    inference(variable_rename,[status(thm)],[f_1714_1]) ).

fof(f_1714_3,plain,
    ! [U_5587,U_5588,U_5589] : hAPP(hAPP(c_Product__Type_OPair(U_5587,U_5588),hAPP(c_Product__Type_Ofst(U_5587,U_5588),U_5589)),hAPP(c_Product__Type_Osnd(U_5587,U_5588),U_5589)) = U_5589,
    inference(definitional_conversion,[status(esa)],[f_1714_2]) ).

cnf(f_1714_4,plain,
    hAPP(hAPP(c_Product__Type_OPair(U_5587,U_5588),hAPP(c_Product__Type_Ofst(U_5587,U_5588),U_5589)),hAPP(c_Product__Type_Osnd(U_5587,U_5588),U_5589)) = U_5589,
    inference(clausify,[status(thm)],[f_1714_3]) ).

fof(f_1715_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_div__int__def]) ).

fof(f_1715_2,plain,
    ! [U_5591,U_5590] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5590),U_5591) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5590,U_5591)),
    inference(variable_rename,[status(thm)],[f_1715_1]) ).

fof(f_1715_3,plain,
    ! [U_5590,U_5591] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5590),U_5591) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5590,U_5591)),
    inference(definitional_conversion,[status(esa)],[f_1715_2]) ).

cnf(f_1715_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5590),U_5591) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5590,U_5591)),
    inference(clausify,[status(thm)],[f_1715_3]) ).

fof(f_1716_1,plain,
    ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
      ( ( V_b = V_b_H
        & V_a = V_a_H )
      | hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__inject]) ).

fof(f_1716_2,plain,
    ! [U_5597,U_5596,U_5595,U_5594,U_5593,U_5592] :
      ( ( U_5595 = U_5597
        & U_5594 = U_5596 )
      | hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5594),U_5595) != hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5596),U_5597) ),
    inference(variable_rename,[status(thm)],[f_1716_1]) ).

fof(f_1716_3,plain,
    ! [U_5597,U_5596,U_5595,U_5594] :
      ( ! [U_5593,U_5592] : hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5594),U_5595) != hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5596),U_5597)
      | ( U_5595 = U_5597
        & U_5594 = U_5596 ) ),
    inference(miniscope,[status(thm)],[f_1716_2]) ).

fof(f_1716_4,plain,
    ( ! [U_5594,U_5595,U_5596,U_5597] :
        ( U_5595 = U_5597
        | ~ sP564(U_5594,U_5595,U_5596,U_5597) )
    & ! [U_5594,U_5595,U_5596,U_5597] :
        ( U_5594 = U_5596
        | ~ sP564(U_5594,U_5595,U_5596,U_5597) )
    & ! [U_5592,U_5593,U_5594,U_5595,U_5596,U_5597] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5594),U_5595) != hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5596),U_5597)
        | sP564(U_5594,U_5595,U_5596,U_5597) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP564])],[f_1716_3]) ).

cnf(f_1716_5,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5594),U_5595) != hAPP(hAPP(c_Product__Type_OPair(U_5592,U_5593),U_5596),U_5597)
    | sP564(U_5594,U_5595,U_5596,U_5597) ),
    inference(clausify,[status(thm)],[f_1716_4]) ).

cnf(f_1716_6,plain,
    ( U_5594 = U_5596
    | ~ sP564(U_5594,U_5595,U_5596,U_5597) ),
    inference(clausify,[status(thm)],[f_1716_4]) ).

cnf(f_1716_7,plain,
    ( U_5595 = U_5597
    | ~ sP564(U_5594,U_5595,U_5596,U_5597) ),
    inference(clausify,[status(thm)],[f_1716_4]) ).

fof(f_1717_1,plain,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
        | V_b_2 != V_b_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_b_2 = V_b_H_2
          & V_a_2 = V_a_H_2 )
        | hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).

fof(f_1717_2,plain,
    ! [U_5603,U_5602,U_5601,U_5600,U_5599,U_5598] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(U_5598,U_5599),U_5600),U_5601) = hAPP(hAPP(c_Product__Type_OPair(U_5598,U_5599),U_5602),U_5603)
        | U_5601 != U_5603
        | U_5600 != U_5602 )
      & ( ( U_5601 = U_5603
          & U_5600 = U_5602 )
        | hAPP(hAPP(c_Product__Type_OPair(U_5598,U_5599),U_5600),U_5601) != hAPP(hAPP(c_Product__Type_OPair(U_5598,U_5599),U_5602),U_5603) ) ),
    inference(variable_rename,[status(thm)],[f_1717_1]) ).

fof(f_1717_3,plain,
    ( ! [U_5615,U_5613,U_5611,U_5609] :
        ( ! [U_5607,U_5605] : hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5607),U_5609),U_5611) = hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5607),U_5613),U_5615)
        | U_5611 != U_5615
        | U_5609 != U_5613 )
    & ! [U_5614,U_5612,U_5610,U_5608] :
        ( ! [U_5606,U_5604] : hAPP(hAPP(c_Product__Type_OPair(U_5604,U_5606),U_5608),U_5610) != hAPP(hAPP(c_Product__Type_OPair(U_5604,U_5606),U_5612),U_5614)
        | ( U_5610 = U_5614
          & U_5608 = U_5612 ) ) ),
    inference(miniscope,[status(thm)],[f_1717_2]) ).

fof(f_1717_4,plain,
    ( ! [U_5612,U_5610,U_5608,U_5614] :
        ( U_5610 = U_5614
        | ~ sP565(U_5612,U_5610,U_5608,U_5614) )
    & ! [U_5612,U_5610,U_5608,U_5614] :
        ( U_5608 = U_5612
        | ~ sP565(U_5612,U_5610,U_5608,U_5614) )
    & ! [U_5609,U_5607,U_5611,U_5605,U_5613,U_5615] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5607),U_5609),U_5611) = hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5607),U_5613),U_5615)
        | U_5611 != U_5615
        | U_5609 != U_5613 )
    & ! [U_5612,U_5606,U_5610,U_5604,U_5608,U_5614] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_5604,U_5606),U_5608),U_5610) != hAPP(hAPP(c_Product__Type_OPair(U_5604,U_5606),U_5612),U_5614)
        | sP565(U_5612,U_5610,U_5608,U_5614) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP565])],[f_1717_3]) ).

cnf(f_1717_5,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_5604,U_5606),U_5608),U_5610) != hAPP(hAPP(c_Product__Type_OPair(U_5604,U_5606),U_5612),U_5614)
    | sP565(U_5612,U_5610,U_5608,U_5614) ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

cnf(f_1717_6,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5607),U_5609),U_5611) = hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5607),U_5613),U_5615)
    | U_5611 != U_5615
    | U_5609 != U_5613 ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

cnf(f_1717_7,plain,
    ( U_5608 = U_5612
    | ~ sP565(U_5612,U_5610,U_5608,U_5614) ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

cnf(f_1717_8,plain,
    ( U_5610 = U_5614
    | ~ sP565(U_5612,U_5610,U_5608,U_5614) ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

fof(f_1718_1,plain,
    ! [T_c,T_b,V_P_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_a,B_b] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
      & ( ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).

fof(f_1718_2,plain,
    ! [U_5624,U_5623,U_5622] :
      ( ( ! [U_5621] : hBOOL(hAPP(U_5622,U_5621))
        | ? [U_5620,U_5619] : ~ hBOOL(hAPP(U_5622,hAPP(hAPP(c_Product__Type_OPair(U_5623,U_5624),U_5620),U_5619))) )
      & ( ! [U_5618,U_5617] : hBOOL(hAPP(U_5622,hAPP(hAPP(c_Product__Type_OPair(U_5623,U_5624),U_5618),U_5617)))
        | ? [U_5616] : ~ hBOOL(hAPP(U_5622,U_5616)) ) ),
    inference(variable_rename,[status(thm)],[f_1718_1]) ).

fof(f_1718_3,plain,
    ( ! [U_5630,U_5628,U_5626] :
        ( ! [U_5621] : hBOOL(hAPP(U_5626,U_5621))
        | ? [U_5620,U_5619] : ~ hBOOL(hAPP(U_5626,hAPP(hAPP(c_Product__Type_OPair(U_5628,U_5630),U_5620),U_5619))) )
    & ! [U_5629,U_5627,U_5625] :
        ( ! [U_5618,U_5617] : hBOOL(hAPP(U_5625,hAPP(hAPP(c_Product__Type_OPair(U_5627,U_5629),U_5618),U_5617)))
        | ? [U_5616] : ~ hBOOL(hAPP(U_5625,U_5616)) ) ),
    inference(miniscope,[status(thm)],[f_1718_2]) ).

fof(f_1718_4,plain,
    ( ! [U_5630,U_5628,U_5626] :
        ( ! [U_5621] : hBOOL(hAPP(U_5626,U_5621))
        | ? [U_5620,U_5619] : ~ hBOOL(hAPP(U_5626,hAPP(hAPP(c_Product__Type_OPair(U_5628,U_5630),U_5620),U_5619))) )
    & ! [U_5629,U_5627,U_5625] :
        ( ! [U_5618,U_5617] : hBOOL(hAPP(U_5625,hAPP(hAPP(c_Product__Type_OPair(U_5627,U_5629),U_5618),U_5617)))
        | ~ hBOOL(hAPP(U_5625,sK91(U_5629,U_5627,U_5625))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_5616,sK91(U_5629,U_5627,U_5625))],[f_1718_3]) ).

fof(f_1718_5,plain,
    ( ! [U_5630,U_5628,U_5626] :
        ( ! [U_5621] : hBOOL(hAPP(U_5626,U_5621))
        | ? [U_5619] : ~ hBOOL(hAPP(U_5626,hAPP(hAPP(c_Product__Type_OPair(U_5628,U_5630),sK92(U_5630,U_5628,U_5626)),U_5619))) )
    & ! [U_5629,U_5627,U_5625] :
        ( ! [U_5618,U_5617] : hBOOL(hAPP(U_5625,hAPP(hAPP(c_Product__Type_OPair(U_5627,U_5629),U_5618),U_5617)))
        | ~ hBOOL(hAPP(U_5625,sK91(U_5629,U_5627,U_5625))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_5620,sK92(U_5630,U_5628,U_5626))],[f_1718_4]) ).

fof(f_1718_6,plain,
    ( ! [U_5630,U_5628,U_5626] :
        ( ! [U_5621] : hBOOL(hAPP(U_5626,U_5621))
        | ~ hBOOL(hAPP(U_5626,hAPP(hAPP(c_Product__Type_OPair(U_5628,U_5630),sK92(U_5630,U_5628,U_5626)),sK93(U_5630,U_5628,U_5626)))) )
    & ! [U_5629,U_5627,U_5625] :
        ( ! [U_5618,U_5617] : hBOOL(hAPP(U_5625,hAPP(hAPP(c_Product__Type_OPair(U_5627,U_5629),U_5618),U_5617)))
        | ~ hBOOL(hAPP(U_5625,sK91(U_5629,U_5627,U_5625))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_5619,sK93(U_5630,U_5628,U_5626))],[f_1718_5]) ).

fof(f_1718_7,plain,
    ( ! [U_5621,U_5626,U_5628,U_5630] :
        ( hBOOL(hAPP(U_5626,U_5621))
        | ~ hBOOL(hAPP(U_5626,hAPP(hAPP(c_Product__Type_OPair(U_5628,U_5630),sK92(U_5630,U_5628,U_5626)),sK93(U_5630,U_5628,U_5626)))) )
    & ! [U_5618,U_5617,U_5627,U_5625,U_5629] :
        ( hBOOL(hAPP(U_5625,hAPP(hAPP(c_Product__Type_OPair(U_5627,U_5629),U_5618),U_5617)))
        | ~ hBOOL(hAPP(U_5625,sK91(U_5629,U_5627,U_5625))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1718_6]) ).

cnf(f_1718_8,plain,
    ( hBOOL(hAPP(U_5625,hAPP(hAPP(c_Product__Type_OPair(U_5627,U_5629),U_5618),U_5617)))
    | ~ hBOOL(hAPP(U_5625,sK91(U_5629,U_5627,U_5625))) ),
    inference(clausify,[status(thm)],[f_1718_7]) ).

cnf(f_1718_9,plain,
    ( hBOOL(hAPP(U_5626,U_5621))
    | ~ hBOOL(hAPP(U_5626,hAPP(hAPP(c_Product__Type_OPair(U_5628,U_5630),sK92(U_5630,U_5628,U_5626)),sK93(U_5630,U_5628,U_5626)))) ),
    inference(clausify,[status(thm)],[f_1718_7]) ).

fof(f_1719_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | V_A_2 = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( V_A_2 != V_B_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).

fof(f_1719_2,plain,
    ! [U_5633,U_5632,U_5631] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5631,tc_HOL_Obool)),U_5632),U_5633))
        | U_5632 = U_5633
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5631,tc_HOL_Obool)),U_5632),U_5633)) )
      & ( ( U_5632 != U_5633
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5631,tc_HOL_Obool)),U_5632),U_5633)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5631,tc_HOL_Obool)),U_5632),U_5633)) ) ),
    inference(variable_rename,[status(thm)],[f_1719_1]) ).

fof(f_1719_3,plain,
    ( ! [U_5639,U_5637,U_5635] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5639))
        | U_5637 = U_5639
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5639)) )
    & ! [U_5638,U_5636,U_5634] :
        ( ( U_5636 != U_5638
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5634,tc_HOL_Obool)),U_5636),U_5638)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5634,tc_HOL_Obool)),U_5636),U_5638)) ) ),
    inference(miniscope,[status(thm)],[f_1719_2]) ).

fof(f_1719_4,plain,
    ( ! [U_5636,U_5634,U_5638] :
        ( U_5636 != U_5638
        | ~ sP566(U_5636,U_5634,U_5638) )
    & ! [U_5636,U_5634,U_5638] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5634,tc_HOL_Obool)),U_5636),U_5638))
        | ~ sP566(U_5636,U_5634,U_5638) )
    & ! [U_5637,U_5635,U_5639] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5639))
        | U_5637 = U_5639
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5639)) )
    & ! [U_5636,U_5634,U_5638] :
        ( sP566(U_5636,U_5634,U_5638)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5634,tc_HOL_Obool)),U_5636),U_5638)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP566])],[f_1719_3]) ).

cnf(f_1719_5,plain,
    ( sP566(U_5636,U_5634,U_5638)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5634,tc_HOL_Obool)),U_5636),U_5638)) ),
    inference(clausify,[status(thm)],[f_1719_4]) ).

cnf(f_1719_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5639))
    | U_5637 = U_5639
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5639)) ),
    inference(clausify,[status(thm)],[f_1719_4]) ).

cnf(f_1719_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5634,tc_HOL_Obool)),U_5636),U_5638))
    | ~ sP566(U_5636,U_5634,U_5638) ),
    inference(clausify,[status(thm)],[f_1719_4]) ).

cnf(f_1719_8,plain,
    ( U_5636 != U_5638
    | ~ sP566(U_5636,U_5634,U_5638) ),
    inference(clausify,[status(thm)],[f_1719_4]) ).

fof(f_1720_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ( V_A_2 != V_B_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
      & ( V_A_2 = V_B_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).

fof(f_1720_2,plain,
    ! [U_5642,U_5641,U_5640] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5640,tc_HOL_Obool)),U_5641),U_5642))
        | ( U_5641 != U_5642
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5640,tc_HOL_Obool)),U_5641),U_5642)) ) )
      & ( U_5641 = U_5642
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5640,tc_HOL_Obool)),U_5641),U_5642))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5640,tc_HOL_Obool)),U_5641),U_5642)) ) ),
    inference(variable_rename,[status(thm)],[f_1720_1]) ).

fof(f_1720_3,plain,
    ( ! [U_5648,U_5646,U_5644] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5644,tc_HOL_Obool)),U_5646),U_5648))
        | ( U_5646 != U_5648
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5644,tc_HOL_Obool)),U_5646),U_5648)) ) )
    & ! [U_5647,U_5645,U_5643] :
        ( U_5645 = U_5647
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5643,tc_HOL_Obool)),U_5645),U_5647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5643,tc_HOL_Obool)),U_5645),U_5647)) ) ),
    inference(miniscope,[status(thm)],[f_1720_2]) ).

fof(f_1720_4,plain,
    ( ! [U_5648,U_5644,U_5646] :
        ( U_5646 != U_5648
        | ~ sP567(U_5648,U_5644,U_5646) )
    & ! [U_5648,U_5644,U_5646] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5644,tc_HOL_Obool)),U_5646),U_5648))
        | ~ sP567(U_5648,U_5644,U_5646) )
    & ! [U_5648,U_5644,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5644,tc_HOL_Obool)),U_5646),U_5648))
        | sP567(U_5648,U_5644,U_5646) )
    & ! [U_5643,U_5645,U_5647] :
        ( U_5645 = U_5647
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5643,tc_HOL_Obool)),U_5645),U_5647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5643,tc_HOL_Obool)),U_5645),U_5647)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP567])],[f_1720_3]) ).

cnf(f_1720_5,plain,
    ( U_5645 = U_5647
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5643,tc_HOL_Obool)),U_5645),U_5647))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5643,tc_HOL_Obool)),U_5645),U_5647)) ),
    inference(clausify,[status(thm)],[f_1720_4]) ).

cnf(f_1720_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5644,tc_HOL_Obool)),U_5646),U_5648))
    | sP567(U_5648,U_5644,U_5646) ),
    inference(clausify,[status(thm)],[f_1720_4]) ).

cnf(f_1720_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5644,tc_HOL_Obool)),U_5646),U_5648))
    | ~ sP567(U_5648,U_5644,U_5646) ),
    inference(clausify,[status(thm)],[f_1720_4]) ).

cnf(f_1720_8,plain,
    ( U_5646 != U_5648
    | ~ sP567(U_5648,U_5644,U_5646) ),
    inference(clausify,[status(thm)],[f_1720_4]) ).

fof(f_1721_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).

fof(f_1721_2,plain,
    ! [U_5651,U_5650,U_5649] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) ),
    inference(variable_rename,[status(thm)],[f_1721_1]) ).

fof(f_1721_3,plain,
    ! [U_5649,U_5650,U_5651] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) ),
    inference(definitional_conversion,[status(esa)],[f_1721_2]) ).

cnf(f_1721_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

fof(f_1722_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).

fof(f_1722_2,plain,
    ! [U_5655,U_5654,U_5653,U_5652] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5652,tc_HOL_Obool)),U_5653),U_5655))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5652,tc_HOL_Obool)),U_5654),U_5655))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5652,tc_HOL_Obool)),U_5653),U_5654)) ),
    inference(variable_rename,[status(thm)],[f_1722_1]) ).

fof(f_1722_3,plain,
    ! [U_5652,U_5653,U_5654,U_5655] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5652,tc_HOL_Obool)),U_5653),U_5655))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5652,tc_HOL_Obool)),U_5654),U_5655))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5652,tc_HOL_Obool)),U_5653),U_5654)) ),
    inference(definitional_conversion,[status(esa)],[f_1722_2]) ).

cnf(f_1722_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5652,tc_HOL_Obool)),U_5653),U_5655))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5652,tc_HOL_Obool)),U_5654),U_5655))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5652,tc_HOL_Obool)),U_5653),U_5654)) ),
    inference(clausify,[status(thm)],[f_1722_3]) ).

fof(f_1723_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).

fof(f_1723_2,plain,
    ! [U_5659,U_5658,U_5657,U_5656] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5656,tc_HOL_Obool)),U_5657),U_5659))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5656,tc_HOL_Obool)),U_5658),U_5659))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5656,tc_HOL_Obool)),U_5657),U_5658)) ),
    inference(variable_rename,[status(thm)],[f_1723_1]) ).

fof(f_1723_3,plain,
    ! [U_5656,U_5657,U_5658,U_5659] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5656,tc_HOL_Obool)),U_5657),U_5659))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5656,tc_HOL_Obool)),U_5658),U_5659))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5656,tc_HOL_Obool)),U_5657),U_5658)) ),
    inference(definitional_conversion,[status(esa)],[f_1723_2]) ).

cnf(f_1723_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5656,tc_HOL_Obool)),U_5657),U_5659))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5656,tc_HOL_Obool)),U_5658),U_5659))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5656,tc_HOL_Obool)),U_5657),U_5658)) ),
    inference(clausify,[status(thm)],[f_1723_3]) ).

fof(f_1724_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).

fof(f_1724_2,plain,
    ! [U_5661,U_5660] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5660,tc_HOL_Obool)),U_5661),U_5661)),
    inference(variable_rename,[status(thm)],[f_1724_1]) ).

fof(f_1724_3,plain,
    ! [U_5661,U_5660] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5660,tc_HOL_Obool)),U_5661),U_5661)),
    inference(definitional_conversion,[status(esa)],[f_1724_2]) ).

cnf(f_1724_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5660,tc_HOL_Obool)),U_5661),U_5661)),
    inference(clausify,[status(thm)],[f_1724_3]) ).

fof(f_1725_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( ( V_A_2 = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | V_A_2 != V_B_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_set__eq__subset]) ).

fof(f_1725_2,plain,
    ! [U_5664,U_5663,U_5662] :
      ( ( U_5662 = U_5663
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5664,tc_HOL_Obool)),U_5663),U_5662))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5664,tc_HOL_Obool)),U_5662),U_5663)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5664,tc_HOL_Obool)),U_5663),U_5662))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5664,tc_HOL_Obool)),U_5662),U_5663)) )
        | U_5662 != U_5663 ) ),
    inference(variable_rename,[status(thm)],[f_1725_1]) ).

fof(f_1725_3,plain,
    ( ! [U_5670,U_5668,U_5666] :
        ( U_5666 = U_5668
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5668),U_5666))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5666),U_5668)) )
    & ! [U_5669,U_5667,U_5665] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5669,tc_HOL_Obool)),U_5667),U_5665))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5669,tc_HOL_Obool)),U_5665),U_5667)) )
        | U_5665 != U_5667 ) ),
    inference(miniscope,[status(thm)],[f_1725_2]) ).

fof(f_1725_4,plain,
    ( ! [U_5667,U_5665,U_5669] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5669,tc_HOL_Obool)),U_5667),U_5665))
        | ~ sP568(U_5667,U_5665,U_5669) )
    & ! [U_5667,U_5665,U_5669] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5669,tc_HOL_Obool)),U_5665),U_5667))
        | ~ sP568(U_5667,U_5665,U_5669) )
    & ! [U_5668,U_5666,U_5670] :
        ( U_5666 = U_5668
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5668),U_5666))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5666),U_5668)) )
    & ! [U_5667,U_5665,U_5669] :
        ( sP568(U_5667,U_5665,U_5669)
        | U_5665 != U_5667 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP568])],[f_1725_3]) ).

cnf(f_1725_5,plain,
    ( sP568(U_5667,U_5665,U_5669)
    | U_5665 != U_5667 ),
    inference(clausify,[status(thm)],[f_1725_4]) ).

cnf(f_1725_6,plain,
    ( U_5666 = U_5668
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5668),U_5666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5666),U_5668)) ),
    inference(clausify,[status(thm)],[f_1725_4]) ).

cnf(f_1725_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5669,tc_HOL_Obool)),U_5665),U_5667))
    | ~ sP568(U_5667,U_5665,U_5669) ),
    inference(clausify,[status(thm)],[f_1725_4]) ).

cnf(f_1725_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5669,tc_HOL_Obool)),U_5667),U_5665))
    | ~ sP568(U_5667,U_5665,U_5669) ),
    inference(clausify,[status(thm)],[f_1725_4]) ).

fof(f_1726_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).

fof(f_1726_2,plain,
    ! [U_5673,U_5672,U_5671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5673,tc_HOL_Obool)),U_5671),U_5672))
      | U_5671 != U_5672 ),
    inference(variable_rename,[status(thm)],[f_1726_1]) ).

fof(f_1726_3,plain,
    ! [U_5671,U_5673,U_5672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5673,tc_HOL_Obool)),U_5671),U_5672))
      | U_5671 != U_5672 ),
    inference(definitional_conversion,[status(esa)],[f_1726_2]) ).

cnf(f_1726_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5673,tc_HOL_Obool)),U_5671),U_5672))
    | U_5671 != U_5672 ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

fof(f_1727_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).

fof(f_1727_2,plain,
    ! [U_5676,U_5675,U_5674] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5676,tc_HOL_Obool)),U_5675),U_5674))
      | U_5674 != U_5675 ),
    inference(variable_rename,[status(thm)],[f_1727_1]) ).

fof(f_1727_3,plain,
    ! [U_5674,U_5675,U_5676] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5676,tc_HOL_Obool)),U_5675),U_5674))
      | U_5674 != U_5675 ),
    inference(definitional_conversion,[status(esa)],[f_1727_2]) ).

cnf(f_1727_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5676,tc_HOL_Obool)),U_5675),U_5674))
    | U_5674 != U_5675 ),
    inference(clausify,[status(thm)],[f_1727_3]) ).

fof(f_1728_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).

fof(f_1728_2,plain,
    ! [U_5680,U_5679,U_5678,U_5677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5678),U_5680))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5679),U_5680))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5678),U_5679)) ),
    inference(variable_rename,[status(thm)],[f_1728_1]) ).

fof(f_1728_3,plain,
    ! [U_5677,U_5678,U_5679,U_5680] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5678),U_5680))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5679),U_5680))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5678),U_5679)) ),
    inference(definitional_conversion,[status(esa)],[f_1728_2]) ).

cnf(f_1728_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5678),U_5680))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5679),U_5680))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5677,tc_HOL_Obool)),U_5678),U_5679)) ),
    inference(clausify,[status(thm)],[f_1728_3]) ).

fof(f_1729_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityE]) ).

fof(f_1729_2,plain,
    ! [U_5683,U_5682,U_5681] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5683,tc_HOL_Obool)),U_5682),U_5681))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5683,tc_HOL_Obool)),U_5681),U_5682)) )
      | U_5681 != U_5682 ),
    inference(variable_rename,[status(thm)],[f_1729_1]) ).

fof(f_1729_3,plain,
    ( ! [U_5681,U_5682,U_5683] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5683,tc_HOL_Obool)),U_5682),U_5681))
        | ~ sP569(U_5681,U_5682,U_5683) )
    & ! [U_5681,U_5682,U_5683] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5683,tc_HOL_Obool)),U_5681),U_5682))
        | ~ sP569(U_5681,U_5682,U_5683) )
    & ! [U_5681,U_5682,U_5683] :
        ( sP569(U_5681,U_5682,U_5683)
        | U_5681 != U_5682 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP569])],[f_1729_2]) ).

cnf(f_1729_4,plain,
    ( sP569(U_5681,U_5682,U_5683)
    | U_5681 != U_5682 ),
    inference(clausify,[status(thm)],[f_1729_3]) ).

cnf(f_1729_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5683,tc_HOL_Obool)),U_5681),U_5682))
    | ~ sP569(U_5681,U_5682,U_5683) ),
    inference(clausify,[status(thm)],[f_1729_3]) ).

cnf(f_1729_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5683,tc_HOL_Obool)),U_5682),U_5681))
    | ~ sP569(U_5681,U_5682,U_5683) ),
    inference(clausify,[status(thm)],[f_1729_3]) ).

fof(f_1730_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff]) ).

fof(f_1730_2,plain,
    ! [U_5686,U_5685,U_5684] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5684,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5684,tc_HOL_Obool)),U_5685)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5684,tc_HOL_Obool)),U_5686)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5684,tc_HOL_Obool)),U_5686),U_5685)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5684,tc_HOL_Obool)),U_5686),U_5685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5684,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5684,tc_HOL_Obool)),U_5685)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5684,tc_HOL_Obool)),U_5686))) ) ),
    inference(variable_rename,[status(thm)],[f_1730_1]) ).

fof(f_1730_3,plain,
    ( ! [U_5692,U_5690,U_5688] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5688,tc_HOL_Obool)),U_5690)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5688,tc_HOL_Obool)),U_5692)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),U_5692),U_5690)) )
    & ! [U_5691,U_5689,U_5687] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5687,tc_HOL_Obool)),U_5691),U_5689))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5687,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5687,tc_HOL_Obool)),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5687,tc_HOL_Obool)),U_5691))) ) ),
    inference(miniscope,[status(thm)],[f_1730_2]) ).

fof(f_1730_4,plain,
    ( ! [U_5688,U_5690,U_5692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5688,tc_HOL_Obool)),U_5690)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5688,tc_HOL_Obool)),U_5692)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),U_5692),U_5690)) )
    & ! [U_5689,U_5687,U_5691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5687,tc_HOL_Obool)),U_5691),U_5689))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5687,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5687,tc_HOL_Obool)),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5687,tc_HOL_Obool)),U_5691))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1730_3]) ).

cnf(f_1730_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5687,tc_HOL_Obool)),U_5691),U_5689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5687,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5687,tc_HOL_Obool)),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5687,tc_HOL_Obool)),U_5691))) ),
    inference(clausify,[status(thm)],[f_1730_4]) ).

cnf(f_1730_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5688,tc_HOL_Obool)),U_5690)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5688,tc_HOL_Obool)),U_5692)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),U_5692),U_5690)) ),
    inference(clausify,[status(thm)],[f_1730_4]) ).

fof(f_1731_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono]) ).

fof(f_1731_2,plain,
    ! [U_5695,U_5694,U_5693] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5693,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5693,tc_HOL_Obool)),U_5695)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5693,tc_HOL_Obool)),U_5694)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5693,tc_HOL_Obool)),U_5694),U_5695)) ),
    inference(variable_rename,[status(thm)],[f_1731_1]) ).

fof(f_1731_3,plain,
    ! [U_5693,U_5694,U_5695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5693,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5693,tc_HOL_Obool)),U_5695)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5693,tc_HOL_Obool)),U_5694)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5693,tc_HOL_Obool)),U_5694),U_5695)) ),
    inference(definitional_conversion,[status(esa)],[f_1731_2]) ).

cnf(f_1731_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5693,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5693,tc_HOL_Obool)),U_5695)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5693,tc_HOL_Obool)),U_5694)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5693,tc_HOL_Obool)),U_5694),U_5695)) ),
    inference(clausify,[status(thm)],[f_1731_3]) ).

fof(f_1732_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__subset]) ).

fof(f_1732_2,plain,
    ! [U_5698,U_5697,U_5696] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5696,tc_HOL_Obool)),U_5697),U_5698)),U_5697)),
    inference(variable_rename,[status(thm)],[f_1732_1]) ).

fof(f_1732_3,plain,
    ! [U_5696,U_5697,U_5698] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5696,tc_HOL_Obool)),U_5697),U_5698)),U_5697)),
    inference(definitional_conversion,[status(esa)],[f_1732_2]) ).

cnf(f_1732_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5696,tc_HOL_Obool)),U_5697),U_5698)),U_5697)),
    inference(clausify,[status(thm)],[f_1732_3]) ).

fof(f_1733_1,plain,
    ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__mono]) ).

fof(f_1733_2,plain,
    ! [U_5703,U_5702,U_5701,U_5700,U_5699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5699,tc_HOL_Obool)),U_5700),U_5703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5699,tc_HOL_Obool)),U_5701),U_5702)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),U_5702),U_5703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),U_5700),U_5701)) ),
    inference(variable_rename,[status(thm)],[f_1733_1]) ).

fof(f_1733_3,plain,
    ! [U_5699,U_5700,U_5701,U_5702,U_5703] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5699,tc_HOL_Obool)),U_5700),U_5703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5699,tc_HOL_Obool)),U_5701),U_5702)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),U_5702),U_5703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),U_5700),U_5701)) ),
    inference(definitional_conversion,[status(esa)],[f_1733_2]) ).

cnf(f_1733_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5699,tc_HOL_Obool)),U_5700),U_5703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5699,tc_HOL_Obool)),U_5701),U_5702)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),U_5702),U_5703))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5699,tc_HOL_Obool)),U_5700),U_5701)) ),
    inference(clausify,[status(thm)],[f_1733_3]) ).

fof(f_1734_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_double__diff]) ).

fof(f_1734_2,plain,
    ! [U_5707,U_5706,U_5705,U_5704] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5704,tc_HOL_Obool)),U_5706),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5704,tc_HOL_Obool)),U_5707),U_5705)) = U_5705
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),U_5706),U_5707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),U_5705),U_5706)) ),
    inference(variable_rename,[status(thm)],[f_1734_1]) ).

fof(f_1734_3,plain,
    ! [U_5704,U_5705,U_5706,U_5707] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5704,tc_HOL_Obool)),U_5706),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5704,tc_HOL_Obool)),U_5707),U_5705)) = U_5705
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),U_5706),U_5707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),U_5705),U_5706)) ),
    inference(definitional_conversion,[status(esa)],[f_1734_2]) ).

cnf(f_1734_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5704,tc_HOL_Obool)),U_5706),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5704,tc_HOL_Obool)),U_5707),U_5705)) = U_5705
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),U_5706),U_5707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),U_5705),U_5706)) ),
    inference(clausify,[status(thm)],[f_1734_3]) ).

fof(f_1735_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__pos]) ).

fof(f_1735_2,plain,
    ! [U_5709,U_5708] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5708),U_5709) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5708,U_5709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5708),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1735_1]) ).

fof(f_1735_3,plain,
    ! [U_5708,U_5709] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5708),U_5709) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5708,U_5709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5708),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1735_2]) ).

cnf(f_1735_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5708),U_5709) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5708,U_5709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5708),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1735_3]) ).

fof(f_1736_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos]) ).

fof(f_1736_2,plain,
    ! [U_5711,U_5710] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5710),U_5711) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5710,U_5711))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5711))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5710)) ),
    inference(variable_rename,[status(thm)],[f_1736_1]) ).

fof(f_1736_3,plain,
    ! [U_5710,U_5711] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5710),U_5711) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5710,U_5711))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5711))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5710)) ),
    inference(definitional_conversion,[status(esa)],[f_1736_2]) ).

cnf(f_1736_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5710),U_5711) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5710,U_5711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5710)) ),
    inference(clausify,[status(thm)],[f_1736_3]) ).

fof(f_1737_1,plain,
    ! [V_w] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of]) ).

fof(f_1737_2,plain,
    ! [U_5712] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712))) ),
    inference(variable_rename,[status(thm)],[f_1737_1]) ).

fof(f_1737_3,plain,
    ! [U_5712] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712))) ),
    inference(definitional_conversion,[status(esa)],[f_1737_2]) ).

cnf(f_1737_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5712))) ),
    inference(clausify,[status(thm)],[f_1737_3]) ).

fof(f_1738_1,plain,
    ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_prod__size__simp]) ).

fof(f_1738_2,plain,
    ! [U_5717,U_5716,U_5715,U_5714,U_5713] : c_Product__Type_Oprod_Oprod__size(U_5713,U_5714,U_5715,U_5716,U_5717) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5715,hAPP(c_Product__Type_Ofst(U_5713,U_5714),U_5717))),hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5713,U_5714),U_5717)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1738_1]) ).

fof(f_1738_3,plain,
    ! [U_5713,U_5714,U_5715,U_5716,U_5717] : c_Product__Type_Oprod_Oprod__size(U_5713,U_5714,U_5715,U_5716,U_5717) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5715,hAPP(c_Product__Type_Ofst(U_5713,U_5714),U_5717))),hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5713,U_5714),U_5717)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1738_2]) ).

cnf(f_1738_4,plain,
    c_Product__Type_Oprod_Oprod__size(U_5713,U_5714,U_5715,U_5716,U_5717) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5715,hAPP(c_Product__Type_Ofst(U_5713,U_5714),U_5717))),hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5713,U_5714),U_5717)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1738_3]) ).

fof(f_1739_1,plain,
    ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)),
    inference(fof_nnf,[status(thm)],[fact_div__mod__code__numeral__def]) ).

fof(f_1739_2,plain,
    ! [U_5719,U_5718] : c_Code__Numeral_Odiv__mod__code__numeral(U_5718,U_5719) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5718),U_5719)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5718,U_5719)),
    inference(variable_rename,[status(thm)],[f_1739_1]) ).

fof(f_1739_3,plain,
    ! [U_5718,U_5719] : c_Code__Numeral_Odiv__mod__code__numeral(U_5718,U_5719) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5718),U_5719)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5718,U_5719)),
    inference(definitional_conversion,[status(esa)],[f_1739_2]) ).

cnf(f_1739_4,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(U_5718,U_5719) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5718),U_5719)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5718,U_5719)),
    inference(clausify,[status(thm)],[f_1739_3]) ).

fof(f_1740_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__step]) ).

fof(f_1740_2,plain,
    ! [U_5721,U_5720] :
      ( c_Divides_Odivmod__nat(U_5721,U_5720) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5721),U_5720)),U_5720))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5721),U_5720),U_5720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5720),U_5721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5720)) ),
    inference(variable_rename,[status(thm)],[f_1740_1]) ).

fof(f_1740_3,plain,
    ! [U_5720,U_5721] :
      ( c_Divides_Odivmod__nat(U_5721,U_5720) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5721),U_5720)),U_5720))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5721),U_5720),U_5720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5720),U_5721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5720)) ),
    inference(definitional_conversion,[status(esa)],[f_1740_2]) ).

cnf(f_1740_4,plain,
    ( c_Divides_Odivmod__nat(U_5721,U_5720) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5721),U_5720)),U_5720))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5721),U_5720),U_5720))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5720),U_5721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5720)) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

fof(f_1741_1,plain,
    ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
      ( ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
        & hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) )
      | ~ hBOOL(hAPP(V_Q_2,V_q_2))
      | ~ hBOOL(hAPP(V_P_2,V_p_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).

fof(f_1741_2,plain,
    ! [U_5727,U_5726,U_5725,U_5724,U_5723,U_5722] :
      ( ( hBOOL(hAPP(U_5724,hAPP(c_Product__Type_Osnd(U_5726,U_5727),hAPP(hAPP(c_Product__Type_OPair(U_5726,U_5727),U_5723),U_5725))))
        & hBOOL(hAPP(U_5722,hAPP(c_Product__Type_Ofst(U_5726,U_5727),hAPP(hAPP(c_Product__Type_OPair(U_5726,U_5727),U_5723),U_5725)))) )
      | ~ hBOOL(hAPP(U_5724,U_5725))
      | ~ hBOOL(hAPP(U_5722,U_5723)) ),
    inference(variable_rename,[status(thm)],[f_1741_1]) ).

fof(f_1741_3,plain,
    ( ! [U_5723,U_5722,U_5724,U_5725,U_5726,U_5727] :
        ( hBOOL(hAPP(U_5724,hAPP(c_Product__Type_Osnd(U_5726,U_5727),hAPP(hAPP(c_Product__Type_OPair(U_5726,U_5727),U_5723),U_5725))))
        | ~ sP570(U_5723,U_5722,U_5724,U_5725,U_5726,U_5727) )
    & ! [U_5723,U_5722,U_5724,U_5725,U_5726,U_5727] :
        ( hBOOL(hAPP(U_5722,hAPP(c_Product__Type_Ofst(U_5726,U_5727),hAPP(hAPP(c_Product__Type_OPair(U_5726,U_5727),U_5723),U_5725))))
        | ~ sP570(U_5723,U_5722,U_5724,U_5725,U_5726,U_5727) )
    & ! [U_5723,U_5722,U_5724,U_5725,U_5726,U_5727] :
        ( sP570(U_5723,U_5722,U_5724,U_5725,U_5726,U_5727)
        | ~ hBOOL(hAPP(U_5724,U_5725))
        | ~ hBOOL(hAPP(U_5722,U_5723)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP570])],[f_1741_2]) ).

cnf(f_1741_4,plain,
    ( sP570(U_5723,U_5722,U_5724,U_5725,U_5726,U_5727)
    | ~ hBOOL(hAPP(U_5724,U_5725))
    | ~ hBOOL(hAPP(U_5722,U_5723)) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_5,plain,
    ( hBOOL(hAPP(U_5722,hAPP(c_Product__Type_Ofst(U_5726,U_5727),hAPP(hAPP(c_Product__Type_OPair(U_5726,U_5727),U_5723),U_5725))))
    | ~ sP570(U_5723,U_5722,U_5724,U_5725,U_5726,U_5727) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_6,plain,
    ( hBOOL(hAPP(U_5724,hAPP(c_Product__Type_Osnd(U_5726,U_5727),hAPP(hAPP(c_Product__Type_OPair(U_5726,U_5727),U_5723),U_5725))))
    | ~ sP570(U_5723,U_5722,U_5724,U_5725,U_5726,U_5727) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

fof(f_1742_1,plain,
    ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).

fof(f_1742_2,plain,
    ! [U_5732,U_5731,U_5730,U_5729,U_5728] :
      ( hBOOL(hAPP(hAPP(U_5728,hAPP(c_Product__Type_Osnd(U_5731,U_5732),hAPP(hAPP(c_Product__Type_OPair(U_5731,U_5732),U_5730),U_5729))),hAPP(c_Product__Type_Ofst(U_5731,U_5732),hAPP(hAPP(c_Product__Type_OPair(U_5731,U_5732),U_5730),U_5729))))
      | ~ hBOOL(hAPP(hAPP(U_5728,U_5729),U_5730)) ),
    inference(variable_rename,[status(thm)],[f_1742_1]) ).

fof(f_1742_3,plain,
    ! [U_5728,U_5730,U_5729,U_5731,U_5732] :
      ( hBOOL(hAPP(hAPP(U_5728,hAPP(c_Product__Type_Osnd(U_5731,U_5732),hAPP(hAPP(c_Product__Type_OPair(U_5731,U_5732),U_5730),U_5729))),hAPP(c_Product__Type_Ofst(U_5731,U_5732),hAPP(hAPP(c_Product__Type_OPair(U_5731,U_5732),U_5730),U_5729))))
      | ~ hBOOL(hAPP(hAPP(U_5728,U_5729),U_5730)) ),
    inference(definitional_conversion,[status(esa)],[f_1742_2]) ).

cnf(f_1742_4,plain,
    ( hBOOL(hAPP(hAPP(U_5728,hAPP(c_Product__Type_Osnd(U_5731,U_5732),hAPP(hAPP(c_Product__Type_OPair(U_5731,U_5732),U_5730),U_5729))),hAPP(c_Product__Type_Ofst(U_5731,U_5732),hAPP(hAPP(c_Product__Type_OPair(U_5731,U_5732),U_5730),U_5729))))
    | ~ hBOOL(hAPP(hAPP(U_5728,U_5729),U_5730)) ),
    inference(clausify,[status(thm)],[f_1742_3]) ).

fof(f_1743_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_div__nat__def]) ).

fof(f_1743_2,plain,
    ! [U_5734,U_5733] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5733),U_5734) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5733,U_5734)),
    inference(variable_rename,[status(thm)],[f_1743_1]) ).

fof(f_1743_3,plain,
    ! [U_5734,U_5733] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5733),U_5734) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5733,U_5734)),
    inference(definitional_conversion,[status(esa)],[f_1743_2]) ).

cnf(f_1743_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5733),U_5734) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5733,U_5734)),
    inference(clausify,[status(thm)],[f_1743_3]) ).

fof(f_1744_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_double__complement]) ).

fof(f_1744_2,plain,
    ! [U_5736,U_5735] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5735,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5735,tc_HOL_Obool)),U_5736)) = U_5736,
    inference(variable_rename,[status(thm)],[f_1744_1]) ).

fof(f_1744_3,plain,
    ! [U_5735,U_5736] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5735,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5735,tc_HOL_Obool)),U_5736)) = U_5736,
    inference(definitional_conversion,[status(esa)],[f_1744_2]) ).

cnf(f_1744_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5735,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5735,tc_HOL_Obool)),U_5736)) = U_5736,
    inference(clausify,[status(thm)],[f_1744_3]) ).

fof(f_1745_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
        | V_A_2 != V_B_2 )
      & ( V_A_2 = V_B_2
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff]) ).

fof(f_1745_2,plain,
    ! [U_5739,U_5738,U_5737] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5737,tc_HOL_Obool)),U_5738) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5737,tc_HOL_Obool)),U_5739)
        | U_5738 != U_5739 )
      & ( U_5738 = U_5739
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5737,tc_HOL_Obool)),U_5738) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5737,tc_HOL_Obool)),U_5739) ) ),
    inference(variable_rename,[status(thm)],[f_1745_1]) ).

fof(f_1745_3,plain,
    ( ! [U_5745,U_5743] :
        ( ! [U_5741] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5741,tc_HOL_Obool)),U_5743) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5741,tc_HOL_Obool)),U_5745)
        | U_5743 != U_5745 )
    & ! [U_5744,U_5742] :
        ( ! [U_5740] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5740,tc_HOL_Obool)),U_5742) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5740,tc_HOL_Obool)),U_5744)
        | U_5742 = U_5744 ) ),
    inference(miniscope,[status(thm)],[f_1745_2]) ).

fof(f_1745_4,plain,
    ( ! [U_5745,U_5741,U_5743] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5741,tc_HOL_Obool)),U_5743) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5741,tc_HOL_Obool)),U_5745)
        | U_5743 != U_5745 )
    & ! [U_5740,U_5744,U_5742] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5740,tc_HOL_Obool)),U_5742) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5740,tc_HOL_Obool)),U_5744)
        | U_5742 = U_5744 ) ),
    inference(definitional_conversion,[status(esa)],[f_1745_3]) ).

cnf(f_1745_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5740,tc_HOL_Obool)),U_5742) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5740,tc_HOL_Obool)),U_5744)
    | U_5742 = U_5744 ),
    inference(clausify,[status(thm)],[f_1745_4]) ).

cnf(f_1745_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5741,tc_HOL_Obool)),U_5743) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5741,tc_HOL_Obool)),U_5745)
    | U_5743 != U_5745 ),
    inference(clausify,[status(thm)],[f_1745_4]) ).

fof(f_1746_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).

fof(f_1746_2,plain,
    ! [U_5749,U_5748,U_5747,U_5746] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5747),U_5749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5748),U_5749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5747),U_5748)) ),
    inference(variable_rename,[status(thm)],[f_1746_1]) ).

fof(f_1746_3,plain,
    ! [U_5746,U_5747,U_5748,U_5749] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5747),U_5749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5748),U_5749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5747),U_5748)) ),
    inference(definitional_conversion,[status(esa)],[f_1746_2]) ).

cnf(f_1746_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5747),U_5749))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5748),U_5749))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5746,tc_HOL_Obool)),U_5747),U_5748)) ),
    inference(clausify,[status(thm)],[f_1746_3]) ).

fof(f_1747_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__idemp]) ).

fof(f_1747_2,plain,
    ! [U_5752,U_5751,U_5750] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),U_5751),U_5752)),U_5752) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),U_5751),U_5752),
    inference(variable_rename,[status(thm)],[f_1747_1]) ).

fof(f_1747_3,plain,
    ! [U_5750,U_5751,U_5752] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),U_5751),U_5752)),U_5752) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),U_5751),U_5752),
    inference(definitional_conversion,[status(esa)],[f_1747_2]) ).

cnf(f_1747_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),U_5751),U_5752)),U_5752) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5750,tc_HOL_Obool)),U_5751),U_5752),
    inference(clausify,[status(thm)],[f_1747_3]) ).

fof(f_1748_1,plain,
    ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__zero]) ).

fof(f_1748_2,plain,
    ! [U_5753] : c_Divides_Odivmod__nat(U_5753,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5753),
    inference(variable_rename,[status(thm)],[f_1748_1]) ).

fof(f_1748_3,plain,
    ! [U_5753] : c_Divides_Odivmod__nat(U_5753,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5753),
    inference(definitional_conversion,[status(esa)],[f_1748_2]) ).

cnf(f_1748_4,plain,
    c_Divides_Odivmod__nat(U_5753,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5753),
    inference(clausify,[status(thm)],[f_1748_3]) ).

fof(f_1749_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_mod__nat__def]) ).

fof(f_1749_2,plain,
    ! [U_5755,U_5754] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5754,U_5755) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5754,U_5755)),
    inference(variable_rename,[status(thm)],[f_1749_1]) ).

fof(f_1749_3,plain,
    ! [U_5754,U_5755] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5754,U_5755) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5754,U_5755)),
    inference(definitional_conversion,[status(esa)],[f_1749_2]) ).

cnf(f_1749_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5754,U_5755) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5754,U_5755)),
    inference(clausify,[status(thm)],[f_1749_3]) ).

fof(f_1750_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__base]) ).

fof(f_1750_2,plain,
    ! [U_5757,U_5756] :
      ( c_Divides_Odivmod__nat(U_5756,U_5757) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5756)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5756),U_5757)) ),
    inference(variable_rename,[status(thm)],[f_1750_1]) ).

fof(f_1750_3,plain,
    ! [U_5756,U_5757] :
      ( c_Divides_Odivmod__nat(U_5756,U_5757) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5756)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5756),U_5757)) ),
    inference(definitional_conversion,[status(esa)],[f_1750_2]) ).

cnf(f_1750_4,plain,
    ( c_Divides_Odivmod__nat(U_5756,U_5757) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5756)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5756),U_5757)) ),
    inference(clausify,[status(thm)],[f_1750_3]) ).

fof(f_1751_1,plain,
    ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__div__mod]) ).

fof(f_1751_2,plain,
    ! [U_5759,U_5758] : c_Divides_Odivmod__nat(U_5758,U_5759) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5758),U_5759)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5758,U_5759)),
    inference(variable_rename,[status(thm)],[f_1751_1]) ).

fof(f_1751_3,plain,
    ! [U_5758,U_5759] : c_Divides_Odivmod__nat(U_5758,U_5759) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5758),U_5759)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5758,U_5759)),
    inference(definitional_conversion,[status(esa)],[f_1751_2]) ).

cnf(f_1751_4,plain,
    c_Divides_Odivmod__nat(U_5758,U_5759) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5758),U_5759)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5758,U_5759)),
    inference(clausify,[status(thm)],[f_1751_3]) ).

fof(f_1752_1,plain,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq]) ).

fof(f_1752_2,plain,
    ! [U_5764,U_5763,U_5762,U_5761,U_5760] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5761),U_5764)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5762),U_5764)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5761),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5762,U_5764))),U_5763))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5761))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5760,U_5761),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5762),U_5763))) ),
    inference(variable_rename,[status(thm)],[f_1752_1]) ).

fof(f_1752_3,plain,
    ! [U_5761,U_5760,U_5762,U_5763,U_5764] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5761),U_5764)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5762),U_5764)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5761),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5762,U_5764))),U_5763))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5761))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5760,U_5761),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5762),U_5763))) ),
    inference(definitional_conversion,[status(esa)],[f_1752_2]) ).

cnf(f_1752_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5761),U_5764)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5762),U_5764)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5761),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5762,U_5764))),U_5763))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5764))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5761))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5760,U_5761),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5762),U_5763))) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

fof(f_1753_1,plain,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq]) ).

fof(f_1753_2,plain,
    ! [U_5769,U_5768,U_5767,U_5766,U_5765] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5765),U_5766),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5767)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5768)),U_5766))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5768),U_5766))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5766))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5765,U_5766),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5767),U_5768))) ),
    inference(variable_rename,[status(thm)],[f_1753_1]) ).

fof(f_1753_3,plain,
    ! [U_5766,U_5765,U_5767,U_5768,U_5769] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5765),U_5766),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5767)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5768)),U_5766))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5768),U_5766))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5766))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5765,U_5766),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5767),U_5768))) ),
    inference(definitional_conversion,[status(esa)],[f_1753_2]) ).

cnf(f_1753_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5765),U_5766),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5767)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5768)),U_5766))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5769),U_5768),U_5766))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5766))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5765,U_5766),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5767),U_5768))) ),
    inference(clausify,[status(thm)],[f_1753_3]) ).

fof(f_1754_1,plain,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq]) ).

fof(f_1754_2,plain,
    ! [U_5776,U_5775,U_5774,U_5773,U_5772,U_5771,U_5770] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5770),U_5774),U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5772),U_5775)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5773),U_5776)),U_5771))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5773),U_5776),U_5771))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5771))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5774,U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5775),U_5776)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5770,U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5772),U_5773))) ),
    inference(variable_rename,[status(thm)],[f_1754_1]) ).

fof(f_1754_3,plain,
    ! [U_5771,U_5770,U_5772,U_5773,U_5774,U_5775,U_5776] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5770),U_5774),U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5772),U_5775)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5773),U_5776)),U_5771))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5773),U_5776),U_5771))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5771))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5774,U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5775),U_5776)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5770,U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5772),U_5773))) ),
    inference(definitional_conversion,[status(esa)],[f_1754_2]) ).

cnf(f_1754_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5770),U_5774),U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5772),U_5775)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5773),U_5776)),U_5771))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5773),U_5776),U_5771))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5771))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5774,U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5775),U_5776)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5770,U_5771),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5772),U_5773))) ),
    inference(clausify,[status(thm)],[f_1754_3]) ).

fof(f_1755_1,plain,
    ! [V_s,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_range]) ).

fof(f_1755_2,plain,
    ! [U_5778,U_5777] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_5777),U_5778))),U_5777))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_5777)) ),
    inference(variable_rename,[status(thm)],[f_1755_1]) ).

fof(f_1755_3,plain,
    ! [U_5778,U_5777] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_5777),U_5778))),U_5777))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_5777)) ),
    inference(definitional_conversion,[status(esa)],[f_1755_2]) ).

cnf(f_1755_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_5777),U_5778))),U_5777))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_5777)) ),
    inference(clausify,[status(thm)],[f_1755_3]) ).

fof(f_1756_1,plain,
    ! [V_qr_2,V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) )
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | V_m_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) )
            | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__def]) ).

fof(f_1756_2,plain,
    ! [U_5781,U_5780,U_5779] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5779,U_5780),U_5781))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5780),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5780)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781)),U_5780))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5780)) ) )
          & U_5780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5781) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_5779 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5781)),U_5780)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5780),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5780)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781)),U_5780))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5780)) ) )
            | U_5780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_5780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_5779 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5781)),U_5780)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5781)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5779,U_5780),U_5781)) ) ),
    inference(variable_rename,[status(thm)],[f_1756_1]) ).

fof(f_1756_3,plain,
    ( ! [U_5787,U_5785,U_5783] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5783,U_5785),U_5787))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5785),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5785)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)),U_5785))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5785)) ) )
          & U_5785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5787) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_5783 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5787)),U_5785)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)) )
    & ! [U_5786,U_5784,U_5782] :
        ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5784),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5784)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)),U_5784))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5784)) ) )
            | U_5784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5786) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_5784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_5782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5786)),U_5784)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5782,U_5784),U_5786)) ) ),
    inference(miniscope,[status(thm)],[f_1756_2]) ).

fof(f_1756_4,plain,
    ( ! [U_5787,U_5785] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5785),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)))
        | ~ sP577(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5785))
        | ~ sP577(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)),U_5785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)))
        | ~ sP576(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5785))
        | ~ sP576(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( sP577(U_5787,U_5785)
        | sP576(U_5787,U_5785)
        | ~ sP578(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( U_5785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP578(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5787) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP575(U_5787,U_5785) )
    & ! [U_5787,U_5785] :
        ( U_5785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP575(U_5787,U_5785) )
    & ! [U_5784,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP572(U_5784,U_5786) )
    & ! [U_5784,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5784),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)))
        | ~ sP572(U_5784,U_5786) )
    & ! [U_5784,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)),U_5784))
        | ~ sP571(U_5784,U_5786) )
    & ! [U_5784,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)))
        | ~ sP571(U_5784,U_5786) )
    & ! [U_5784,U_5786] :
        ( sP572(U_5784,U_5786)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5784))
        | ~ sP573(U_5784,U_5786) )
    & ! [U_5784,U_5786] :
        ( sP571(U_5784,U_5786)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5784))
        | ~ sP573(U_5784,U_5786) )
    & ! [U_5784,U_5782,U_5786] :
        ( sP573(U_5784,U_5786)
        | U_5784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP574(U_5784,U_5782,U_5786) )
    & ! [U_5784,U_5782,U_5786] :
        ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5786) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP574(U_5784,U_5782,U_5786) )
    & ! [U_5784,U_5782,U_5786] :
        ( U_5782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5786)),U_5784)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786))
        | ~ sP574(U_5784,U_5782,U_5786) )
    & ! [U_5787,U_5785,U_5783] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5783,U_5785),U_5787))
        | sP578(U_5787,U_5785)
        | sP575(U_5787,U_5785)
        | U_5783 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5787)),U_5785)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)) )
    & ! [U_5784,U_5782,U_5786] :
        ( sP574(U_5784,U_5782,U_5786)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5782,U_5784),U_5786)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP571,sP572,sP573,sP574,sP575,sP576,sP577,sP578])],[f_1756_3]) ).

cnf(f_1756_5,plain,
    ( sP574(U_5784,U_5782,U_5786)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5782,U_5784),U_5786)) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_6,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5783,U_5785),U_5787))
    | sP578(U_5787,U_5785)
    | sP575(U_5787,U_5785)
    | U_5783 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5787)),U_5785)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_7,plain,
    ( U_5782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5786)),U_5784)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786))
    | ~ sP574(U_5784,U_5782,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_8,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5786) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP574(U_5784,U_5782,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_9,plain,
    ( sP573(U_5784,U_5786)
    | U_5784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP574(U_5784,U_5782,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_10,plain,
    ( sP571(U_5784,U_5786)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5784))
    | ~ sP573(U_5784,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_11,plain,
    ( sP572(U_5784,U_5786)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5784))
    | ~ sP573(U_5784,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)))
    | ~ sP571(U_5784,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)),U_5784))
    | ~ sP571(U_5784,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5784),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)))
    | ~ sP572(U_5784,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5786)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP572(U_5784,U_5786) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_16,plain,
    ( U_5785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP575(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_17,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5787) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP575(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_18,plain,
    ( U_5785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP578(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_19,plain,
    ( sP577(U_5787,U_5785)
    | sP576(U_5787,U_5785)
    | ~ sP578(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_20,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5785))
    | ~ sP576(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_21,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)),U_5785))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)))
    | ~ sP576(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_22,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5785))
    | ~ sP577(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

cnf(f_1756_23,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5785),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5787)))
    | ~ sP577(U_5787,U_5785) ),
    inference(clausify,[status(thm)],[f_1756_4]) ).

fof(f_1757_1,plain,
    ! [V_qr_H,V_qr,V_n,V_m] :
      ( V_qr = V_qr_H
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique]) ).

fof(f_1757_2,plain,
    ! [U_5791,U_5790,U_5789,U_5788] :
      ( U_5790 = U_5791
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5788,U_5789),U_5791))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5788,U_5789),U_5790)) ),
    inference(variable_rename,[status(thm)],[f_1757_1]) ).

fof(f_1757_3,plain,
    ! [U_5791,U_5789,U_5788,U_5790] :
      ( U_5790 = U_5791
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5788,U_5789),U_5791))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5788,U_5789),U_5790)) ),
    inference(definitional_conversion,[status(esa)],[f_1757_2]) ).

cnf(f_1757_4,plain,
    ( U_5790 = U_5791
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5788,U_5789),U_5791))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5788,U_5789),U_5790)) ),
    inference(clausify,[status(thm)],[f_1757_3]) ).

fof(f_1758_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).

fof(f_1758_2,plain,
    ! [U_5793,U_5792] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5792,U_5793),c_Divides_Odivmod__nat(U_5792,U_5793))),
    inference(variable_rename,[status(thm)],[f_1758_1]) ).

fof(f_1758_3,plain,
    ! [U_5792,U_5793] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5792,U_5793),c_Divides_Odivmod__nat(U_5792,U_5793))),
    inference(definitional_conversion,[status(esa)],[f_1758_2]) ).

cnf(f_1758_4,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5792,U_5793),c_Divides_Odivmod__nat(U_5792,U_5793))),
    inference(clausify,[status(thm)],[f_1758_3]) ).

fof(f_1759_1,plain,
    ! [V_qr,V_n,V_m] :
      ( c_Divides_Odivmod__nat(V_m,V_n) = V_qr
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq]) ).

fof(f_1759_2,plain,
    ! [U_5796,U_5795,U_5794] :
      ( c_Divides_Odivmod__nat(U_5794,U_5795) = U_5796
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5794,U_5795),U_5796)) ),
    inference(variable_rename,[status(thm)],[f_1759_1]) ).

fof(f_1759_3,plain,
    ! [U_5796,U_5795,U_5794] :
      ( c_Divides_Odivmod__nat(U_5794,U_5795) = U_5796
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5794,U_5795),U_5796)) ),
    inference(definitional_conversion,[status(esa)],[f_1759_2]) ).

cnf(f_1759_4,plain,
    ( c_Divides_Odivmod__nat(U_5794,U_5795) = U_5796
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5794,U_5795),U_5796)) ),
    inference(clausify,[status(thm)],[f_1759_3]) ).

fof(f_1760_1,plain,
    ! [V_r,V_q,V_n,V_m] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__eq]) ).

fof(f_1760_2,plain,
    ! [U_5800,U_5799,U_5798,U_5797] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5797,U_5798) = U_5800
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5797,U_5798),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5799),U_5800))) ),
    inference(variable_rename,[status(thm)],[f_1760_1]) ).

fof(f_1760_3,plain,
    ! [U_5798,U_5799,U_5800,U_5797] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5797,U_5798) = U_5800
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5797,U_5798),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5799),U_5800))) ),
    inference(definitional_conversion,[status(esa)],[f_1760_2]) ).

cnf(f_1760_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5797,U_5798) = U_5800
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5797,U_5798),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5799),U_5800))) ),
    inference(clausify,[status(thm)],[f_1760_3]) ).

fof(f_1761_1,plain,
    ! [V_r,V_q,V_n,V_m] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_div__eq]) ).

fof(f_1761_2,plain,
    ! [U_5804,U_5803,U_5802,U_5801] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5801),U_5802) = U_5803
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5801,U_5802),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5803),U_5804))) ),
    inference(variable_rename,[status(thm)],[f_1761_1]) ).

fof(f_1761_3,plain,
    ! [U_5802,U_5804,U_5801,U_5803] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5801),U_5802) = U_5803
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5801,U_5802),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5803),U_5804))) ),
    inference(definitional_conversion,[status(esa)],[f_1761_2]) ).

cnf(f_1761_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5801),U_5802) = U_5803
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5801,U_5802),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5803),U_5804))) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

fof(f_1762_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel]) ).

fof(f_1762_2,plain,
    ! [U_5806,U_5805] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5805,U_5806),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5805),U_5806)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5805,U_5806)))),
    inference(variable_rename,[status(thm)],[f_1762_1]) ).

fof(f_1762_3,plain,
    ! [U_5805,U_5806] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5805,U_5806),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5805),U_5806)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5805,U_5806)))),
    inference(definitional_conversion,[status(esa)],[f_1762_2]) ).

cnf(f_1762_4,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5805,U_5806),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5805),U_5806)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5805,U_5806)))),
    inference(clausify,[status(thm)],[f_1762_3]) ).

fof(f_1763_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_prod_Orecs]) ).

fof(f_1763_2,plain,
    ! [U_5812,U_5811,U_5810,U_5809,U_5808,U_5807] : c_Product__Type_Oprod_Oprod__rec(U_5807,U_5808,U_5809,U_5810,hAPP(hAPP(c_Product__Type_OPair(U_5807,U_5808),U_5811),U_5812)) = hAPP(hAPP(U_5810,U_5811),U_5812),
    inference(variable_rename,[status(thm)],[f_1763_1]) ).

fof(f_1763_3,plain,
    ! [U_5809,U_5810,U_5812,U_5811,U_5807,U_5808] : c_Product__Type_Oprod_Oprod__rec(U_5807,U_5808,U_5809,U_5810,hAPP(hAPP(c_Product__Type_OPair(U_5807,U_5808),U_5811),U_5812)) = hAPP(hAPP(U_5810,U_5811),U_5812),
    inference(definitional_conversion,[status(esa)],[f_1763_2]) ).

cnf(f_1763_4,plain,
    c_Product__Type_Oprod_Oprod__rec(U_5807,U_5808,U_5809,U_5810,hAPP(hAPP(c_Product__Type_OPair(U_5807,U_5808),U_5811),U_5812)) = hAPP(hAPP(U_5810,U_5811),U_5812),
    inference(clausify,[status(thm)],[f_1763_3]) ).

fof(f_1764_1,plain,
    ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_adjust__eq]) ).

fof(f_1764_2,plain,
    ! [U_5815,U_5814,U_5813] : hAPP(c_Divides_Oadjust(U_5813),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5814),U_5815)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5815),U_5813)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5814)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5814)),U_5815))),
    inference(variable_rename,[status(thm)],[f_1764_1]) ).

fof(f_1764_3,plain,
    ! [U_5815,U_5813,U_5814] : hAPP(c_Divides_Oadjust(U_5813),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5814),U_5815)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5815),U_5813)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5814)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5814)),U_5815))),
    inference(definitional_conversion,[status(esa)],[f_1764_2]) ).

cnf(f_1764_4,plain,
    hAPP(c_Divides_Oadjust(U_5813),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5814),U_5815)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5815),U_5813)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5814)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5814)),U_5815))),
    inference(clausify,[status(thm)],[f_1764_3]) ).

fof(f_1765_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2))
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2)
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_iterate_Osimps]) ).

fof(f_1765_2,plain,
    ! [U_5820,U_5819,U_5818,U_5817,U_5816] :
      ( ( hAPP(c_Random_Oiterate(U_5817,U_5818,U_5816,U_5819),U_5820) = hAPP(hAPP(c_Product__Type_Oscomp(U_5818,U_5817,U_5818,tc_prod(U_5817,U_5818)),hAPP(U_5819,U_5820)),c_Random_Oiterate(U_5817,U_5818,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5816),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5819))
        | U_5816 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(U_5817,U_5818,U_5816,U_5819),U_5820) = hAPP(c_Product__Type_OPair(U_5817,U_5818),U_5820)
        | U_5816 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1765_1]) ).

fof(f_1765_3,plain,
    ( ! [U_5830,U_5828,U_5826,U_5824,U_5822] :
        ( hAPP(c_Random_Oiterate(U_5824,U_5826,U_5822,U_5828),U_5830) = hAPP(hAPP(c_Product__Type_Oscomp(U_5826,U_5824,U_5826,tc_prod(U_5824,U_5826)),hAPP(U_5828,U_5830)),c_Random_Oiterate(U_5824,U_5826,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5822),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5828))
        | U_5822 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5829,U_5827,U_5825,U_5823,U_5821] :
        ( hAPP(c_Random_Oiterate(U_5823,U_5825,U_5821,U_5827),U_5829) = hAPP(c_Product__Type_OPair(U_5823,U_5825),U_5829)
        | U_5821 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1765_2]) ).

fof(f_1765_4,plain,
    ( ! [U_5822,U_5830,U_5824,U_5826,U_5828] :
        ( hAPP(c_Random_Oiterate(U_5824,U_5826,U_5822,U_5828),U_5830) = hAPP(hAPP(c_Product__Type_Oscomp(U_5826,U_5824,U_5826,tc_prod(U_5824,U_5826)),hAPP(U_5828,U_5830)),c_Random_Oiterate(U_5824,U_5826,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5822),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5828))
        | U_5822 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5827,U_5823,U_5821,U_5825,U_5829] :
        ( hAPP(c_Random_Oiterate(U_5823,U_5825,U_5821,U_5827),U_5829) = hAPP(c_Product__Type_OPair(U_5823,U_5825),U_5829)
        | U_5821 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_1765_3]) ).

cnf(f_1765_5,plain,
    ( hAPP(c_Random_Oiterate(U_5823,U_5825,U_5821,U_5827),U_5829) = hAPP(c_Product__Type_OPair(U_5823,U_5825),U_5829)
    | U_5821 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1765_4]) ).

cnf(f_1765_6,plain,
    ( hAPP(c_Random_Oiterate(U_5824,U_5826,U_5822,U_5828),U_5830) = hAPP(hAPP(c_Product__Type_Oscomp(U_5826,U_5824,U_5826,tc_prod(U_5824,U_5826)),hAPP(U_5828,U_5830)),c_Random_Oiterate(U_5824,U_5826,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5822),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5828))
    | U_5822 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1765_4]) ).

fof(f_1766_1,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__def]) ).

fof(f_1766_2,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1766_1]) ).

cnf(f_1766_3,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1766_2]) ).

fof(f_1767_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__code]) ).

fof(f_1767_2,plain,
    ! [U_5832,U_5831] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5831),U_5832) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_5831),U_5832),
    inference(variable_rename,[status(thm)],[f_1767_1]) ).

fof(f_1767_3,plain,
    ! [U_5832,U_5831] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5831),U_5832) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_5831),U_5832),
    inference(definitional_conversion,[status(esa)],[f_1767_2]) ).

cnf(f_1767_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5831),U_5832) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_5831),U_5832),
    inference(clausify,[status(thm)],[f_1767_3]) ).

fof(f_1768_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_scomp__unfold]) ).

fof(f_1768_2,plain,
    ! [U_5839,U_5838,U_5837,U_5836,U_5835,U_5834,U_5833] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5833,U_5834,U_5835,U_5836),U_5837),U_5838),U_5839) = hAPP(hAPP(U_5838,hAPP(c_Product__Type_Ofst(U_5834,U_5835),hAPP(U_5837,U_5839))),hAPP(c_Product__Type_Osnd(U_5834,U_5835),hAPP(U_5837,U_5839))),
    inference(variable_rename,[status(thm)],[f_1768_1]) ).

fof(f_1768_3,plain,
    ! [U_5833,U_5834,U_5835,U_5836,U_5837,U_5838,U_5839] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5833,U_5834,U_5835,U_5836),U_5837),U_5838),U_5839) = hAPP(hAPP(U_5838,hAPP(c_Product__Type_Ofst(U_5834,U_5835),hAPP(U_5837,U_5839))),hAPP(c_Product__Type_Osnd(U_5834,U_5835),hAPP(U_5837,U_5839))),
    inference(definitional_conversion,[status(esa)],[f_1768_2]) ).

cnf(f_1768_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5833,U_5834,U_5835,U_5836),U_5837),U_5838),U_5839) = hAPP(hAPP(U_5838,hAPP(c_Product__Type_Ofst(U_5834,U_5835),hAPP(U_5837,U_5839))),hAPP(c_Product__Type_Osnd(U_5834,U_5835),hAPP(U_5837,U_5839))),
    inference(clausify,[status(thm)],[f_1768_3]) ).

fof(f_1769_1,plain,
    ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__scomp]) ).

fof(f_1769_2,plain,
    ! [U_5848,U_5847,U_5846,U_5845,U_5844,U_5843,U_5842,U_5841,U_5840] : hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5841,U_5842,U_5843),hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5844,U_5845,tc_prod(U_5841,U_5842)),U_5846),U_5847)),U_5848) = hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5844,U_5845,U_5843),U_5846),hAPP(hAPP(c_COMBC(U_5844,tc_fun(U_5841,tc_fun(U_5842,U_5843)),tc_fun(U_5845,U_5843)),hAPP(hAPP(c_COMBB(tc_fun(U_5845,tc_prod(U_5841,U_5842)),tc_fun(tc_fun(U_5841,tc_fun(U_5842,U_5843)),tc_fun(U_5845,U_5843)),U_5844),c_Product__Type_Oscomp(U_5845,U_5841,U_5842,U_5843)),U_5847)),U_5848)),
    inference(variable_rename,[status(thm)],[f_1769_1]) ).

fof(f_1769_3,plain,
    ! [U_5840,U_5841,U_5842,U_5843,U_5844,U_5845,U_5846,U_5847,U_5848] : hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5841,U_5842,U_5843),hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5844,U_5845,tc_prod(U_5841,U_5842)),U_5846),U_5847)),U_5848) = hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5844,U_5845,U_5843),U_5846),hAPP(hAPP(c_COMBC(U_5844,tc_fun(U_5841,tc_fun(U_5842,U_5843)),tc_fun(U_5845,U_5843)),hAPP(hAPP(c_COMBB(tc_fun(U_5845,tc_prod(U_5841,U_5842)),tc_fun(tc_fun(U_5841,tc_fun(U_5842,U_5843)),tc_fun(U_5845,U_5843)),U_5844),c_Product__Type_Oscomp(U_5845,U_5841,U_5842,U_5843)),U_5847)),U_5848)),
    inference(definitional_conversion,[status(esa)],[f_1769_2]) ).

cnf(f_1769_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5841,U_5842,U_5843),hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5844,U_5845,tc_prod(U_5841,U_5842)),U_5846),U_5847)),U_5848) = hAPP(hAPP(c_Product__Type_Oscomp(U_5840,U_5844,U_5845,U_5843),U_5846),hAPP(hAPP(c_COMBC(U_5844,tc_fun(U_5841,tc_fun(U_5842,U_5843)),tc_fun(U_5845,U_5843)),hAPP(hAPP(c_COMBB(tc_fun(U_5845,tc_prod(U_5841,U_5842)),tc_fun(tc_fun(U_5841,tc_fun(U_5842,U_5843)),tc_fun(U_5845,U_5843)),U_5844),c_Product__Type_Oscomp(U_5845,U_5841,U_5842,U_5843)),U_5847)),U_5848)),
    inference(clausify,[status(thm)],[f_1769_3]) ).

fof(f_1770_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))
      | ~ class_Groups_Ouminus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__Compl__def]) ).

fof(f_1770_2,plain,
    ! [U_5852,U_5851,U_5850,U_5849] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5850,U_5849)),U_5851),U_5852) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5849),hAPP(U_5851,U_5852))
      | ~ class_Groups_Ouminus(U_5849) ),
    inference(variable_rename,[status(thm)],[f_1770_1]) ).

fof(f_1770_3,plain,
    ! [U_5851,U_5849,U_5850,U_5852] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5850,U_5849)),U_5851),U_5852) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5849),hAPP(U_5851,U_5852))
      | ~ class_Groups_Ouminus(U_5849) ),
    inference(definitional_conversion,[status(esa)],[f_1770_2]) ).

cnf(f_1770_4,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5850,U_5849)),U_5851),U_5852) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5849),hAPP(U_5851,U_5852))
    | ~ class_Groups_Ouminus(U_5849) ),
    inference(clausify,[status(thm)],[f_1770_3]) ).

fof(f_1771_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
      | ~ class_Groups_Ominus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__diff__def]) ).

fof(f_1771_2,plain,
    ! [U_5857,U_5856,U_5855,U_5854,U_5853] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5854,U_5853)),U_5855),U_5856),U_5857) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5853),hAPP(U_5855,U_5857)),hAPP(U_5856,U_5857))
      | ~ class_Groups_Ominus(U_5853) ),
    inference(variable_rename,[status(thm)],[f_1771_1]) ).

fof(f_1771_3,plain,
    ! [U_5853,U_5854,U_5855,U_5856,U_5857] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5854,U_5853)),U_5855),U_5856),U_5857) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5853),hAPP(U_5855,U_5857)),hAPP(U_5856,U_5857))
      | ~ class_Groups_Ominus(U_5853) ),
    inference(definitional_conversion,[status(esa)],[f_1771_2]) ).

cnf(f_1771_4,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5854,U_5853)),U_5855),U_5856),U_5857) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5853),hAPP(U_5855,U_5857)),hAPP(U_5856,U_5857))
    | ~ class_Groups_Ominus(U_5853) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

fof(f_1772_1,plain,
    ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(f_1772_2,plain,
    ! [U_5858] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5858) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5858)),
    inference(variable_rename,[status(thm)],[f_1772_1]) ).

fof(f_1772_3,plain,
    ! [U_5858] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5858) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5858)),
    inference(definitional_conversion,[status(esa)],[f_1772_2]) ).

cnf(f_1772_4,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5858) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5858)),
    inference(clausify,[status(thm)],[f_1772_3]) ).

fof(f_1773_1,plain,
    ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Bit0]) ).

fof(f_1773_2,plain,
    ! [U_5859] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5859)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5859)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1773_1]) ).

fof(f_1773_3,plain,
    ! [U_5859] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5859)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5859)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1773_2]) ).

cnf(f_1773_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5859)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5859)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1773_3]) ).

fof(f_1774_1,plain,
    ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_scomp__Pair]) ).

fof(f_1774_2,plain,
    ! [U_5863,U_5862,U_5861,U_5860] : hAPP(hAPP(c_Product__Type_Oscomp(U_5860,U_5861,U_5862,tc_prod(U_5861,U_5862)),U_5863),c_Product__Type_OPair(U_5861,U_5862)) = U_5863,
    inference(variable_rename,[status(thm)],[f_1774_1]) ).

fof(f_1774_3,plain,
    ! [U_5860,U_5861,U_5862,U_5863] : hAPP(hAPP(c_Product__Type_Oscomp(U_5860,U_5861,U_5862,tc_prod(U_5861,U_5862)),U_5863),c_Product__Type_OPair(U_5861,U_5862)) = U_5863,
    inference(definitional_conversion,[status(esa)],[f_1774_2]) ).

cnf(f_1774_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_5860,U_5861,U_5862,tc_prod(U_5861,U_5862)),U_5863),c_Product__Type_OPair(U_5861,U_5862)) = U_5863,
    inference(clausify,[status(thm)],[f_1774_3]) ).

fof(f_1775_1,plain,
    ! [V_w_2,V_z_2,T_b] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b)))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__even]) ).

fof(f_1775_2,plain,
    ! [U_5866,U_5865,U_5864] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5864),U_5865),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5866))) = hAPP(hAPP(c_HOL_OLet(U_5864,U_5864),hAPP(hAPP(c_Power_Opower__class_Opower(U_5864),U_5865),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5866))),hAPP(hAPP(c_COMBS(U_5864,U_5864,U_5864),c_Groups_Otimes__class_Otimes(U_5864)),c_COMBI(U_5864)))
      | ~ class_Int_Onumber__ring(U_5864) ),
    inference(variable_rename,[status(thm)],[f_1775_1]) ).

fof(f_1775_3,plain,
    ! [U_5864,U_5865,U_5866] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5864),U_5865),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5866))) = hAPP(hAPP(c_HOL_OLet(U_5864,U_5864),hAPP(hAPP(c_Power_Opower__class_Opower(U_5864),U_5865),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5866))),hAPP(hAPP(c_COMBS(U_5864,U_5864,U_5864),c_Groups_Otimes__class_Otimes(U_5864)),c_COMBI(U_5864)))
      | ~ class_Int_Onumber__ring(U_5864) ),
    inference(definitional_conversion,[status(esa)],[f_1775_2]) ).

cnf(f_1775_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5864),U_5865),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5866))) = hAPP(hAPP(c_HOL_OLet(U_5864,U_5864),hAPP(hAPP(c_Power_Opower__class_Opower(U_5864),U_5865),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5866))),hAPP(hAPP(c_COMBS(U_5864,U_5864,U_5864),c_Groups_Otimes__class_Otimes(U_5864)),c_COMBI(U_5864)))
    | ~ class_Int_Onumber__ring(U_5864) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

fof(f_1776_1,plain,
    ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_zpower__number__of__even]) ).

fof(f_1776_2,plain,
    ! [U_5868,U_5867] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5867),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5868))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5867),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5868))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1776_1]) ).

fof(f_1776_3,plain,
    ! [U_5867,U_5868] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5867),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5868))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5867),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5868))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1776_2]) ).

cnf(f_1776_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5867),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5868))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5867),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5868))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1776_3]) ).

fof(f_1777_1,plain,
    ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_Pair__scomp]) ).

fof(f_1777_2,plain,
    ! [U_5873,U_5872,U_5871,U_5870,U_5869] : hAPP(hAPP(c_Product__Type_Oscomp(U_5869,U_5870,U_5869,U_5871),hAPP(c_Product__Type_OPair(U_5870,U_5869),U_5872)),U_5873) = hAPP(U_5873,U_5872),
    inference(variable_rename,[status(thm)],[f_1777_1]) ).

fof(f_1777_3,plain,
    ! [U_5869,U_5870,U_5871,U_5872,U_5873] : hAPP(hAPP(c_Product__Type_Oscomp(U_5869,U_5870,U_5869,U_5871),hAPP(c_Product__Type_OPair(U_5870,U_5869),U_5872)),U_5873) = hAPP(U_5873,U_5872),
    inference(definitional_conversion,[status(esa)],[f_1777_2]) ).

cnf(f_1777_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_5869,U_5870,U_5869,U_5871),hAPP(c_Product__Type_OPair(U_5870,U_5869),U_5872)),U_5873) = hAPP(U_5873,U_5872),
    inference(clausify,[status(thm)],[f_1777_3]) ).

fof(f_1778_1,plain,
    ! [V_w_2,V_v_2,T_b] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b)))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of]) ).

fof(f_1778_2,plain,
    ! [U_5876,U_5875,U_5874] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5874),hAPP(c_Int_Onumber__class_Onumber__of(U_5874),U_5875)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5876))) = hAPP(hAPP(c_HOL_OLet(U_5874,U_5874),hAPP(hAPP(c_Power_Opower__class_Opower(U_5874),hAPP(c_Int_Onumber__class_Onumber__of(U_5874),U_5875)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5876))),hAPP(hAPP(c_COMBS(U_5874,U_5874,U_5874),c_Groups_Otimes__class_Otimes(U_5874)),c_COMBI(U_5874)))
      | ~ class_Int_Onumber__ring(U_5874) ),
    inference(variable_rename,[status(thm)],[f_1778_1]) ).

fof(f_1778_3,plain,
    ! [U_5874,U_5875,U_5876] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5874),hAPP(c_Int_Onumber__class_Onumber__of(U_5874),U_5875)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5876))) = hAPP(hAPP(c_HOL_OLet(U_5874,U_5874),hAPP(hAPP(c_Power_Opower__class_Opower(U_5874),hAPP(c_Int_Onumber__class_Onumber__of(U_5874),U_5875)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5876))),hAPP(hAPP(c_COMBS(U_5874,U_5874,U_5874),c_Groups_Otimes__class_Otimes(U_5874)),c_COMBI(U_5874)))
      | ~ class_Int_Onumber__ring(U_5874) ),
    inference(definitional_conversion,[status(esa)],[f_1778_2]) ).

cnf(f_1778_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5874),hAPP(c_Int_Onumber__class_Onumber__of(U_5874),U_5875)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5876))) = hAPP(hAPP(c_HOL_OLet(U_5874,U_5874),hAPP(hAPP(c_Power_Opower__class_Opower(U_5874),hAPP(c_Int_Onumber__class_Onumber__of(U_5874),U_5875)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5876))),hAPP(hAPP(c_COMBS(U_5874,U_5874,U_5874),c_Groups_Otimes__class_Otimes(U_5874)),c_COMBI(U_5874)))
    | ~ class_Int_Onumber__ring(U_5874) ),
    inference(clausify,[status(thm)],[f_1778_3]) ).

fof(f_1779_1,plain,
    ! [V_z_2,V_z_H_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__nat__eq__if]) ).

fof(f_1779_2,plain,
    ! [U_5878,U_5877] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5878)),hAPP(c_Int_Onat,U_5877)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5878),U_5877)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5877)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5878)),hAPP(c_Int_Onat,U_5877)) = hAPP(c_Int_Onat,U_5878)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5877)) ) ),
    inference(variable_rename,[status(thm)],[f_1779_1]) ).

fof(f_1779_3,plain,
    ( ! [U_5882,U_5880] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5882)),hAPP(c_Int_Onat,U_5880)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5882),U_5880)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5880)) )
    & ! [U_5881,U_5879] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5881)),hAPP(c_Int_Onat,U_5879)) = hAPP(c_Int_Onat,U_5881)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5879)) ) ),
    inference(miniscope,[status(thm)],[f_1779_2]) ).

fof(f_1779_4,plain,
    ( ! [U_5880,U_5882] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5882)),hAPP(c_Int_Onat,U_5880)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5882),U_5880)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5880)) )
    & ! [U_5879,U_5881] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5881)),hAPP(c_Int_Onat,U_5879)) = hAPP(c_Int_Onat,U_5881)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5879)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1779_3]) ).

cnf(f_1779_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5881)),hAPP(c_Int_Onat,U_5879)) = hAPP(c_Int_Onat,U_5881)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5879)) ),
    inference(clausify,[status(thm)],[f_1779_4]) ).

cnf(f_1779_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5882)),hAPP(c_Int_Onat,U_5880)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5882),U_5880)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5880)) ),
    inference(clausify,[status(thm)],[f_1779_4]) ).

fof(f_1780_1,plain,
    ! [V_n_2,T_b] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code]) ).

fof(f_1780_2,plain,
    ! [U_5884,U_5883] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5883),U_5884) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5883,hAPP(hAPP(c_COMBC(U_5883,U_5883,U_5883),c_Groups_Oplus__class_Oplus(U_5883)),c_Groups_Oone__class_Oone(U_5883)),U_5884,c_Groups_Ozero__class_Ozero(U_5883))
      | ~ class_Rings_Osemiring__1(U_5883) ),
    inference(variable_rename,[status(thm)],[f_1780_1]) ).

fof(f_1780_3,plain,
    ! [U_5883,U_5884] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5883),U_5884) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5883,hAPP(hAPP(c_COMBC(U_5883,U_5883,U_5883),c_Groups_Oplus__class_Oplus(U_5883)),c_Groups_Oone__class_Oone(U_5883)),U_5884,c_Groups_Ozero__class_Ozero(U_5883))
      | ~ class_Rings_Osemiring__1(U_5883) ),
    inference(definitional_conversion,[status(esa)],[f_1780_2]) ).

cnf(f_1780_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5883),U_5884) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5883,hAPP(hAPP(c_COMBC(U_5883,U_5883,U_5883),c_Groups_Oplus__class_Oplus(U_5883)),c_Groups_Oone__class_Oone(U_5883)),U_5884,c_Groups_Ozero__class_Ozero(U_5883))
    | ~ class_Rings_Osemiring__1(U_5883) ),
    inference(clausify,[status(thm)],[f_1780_3]) ).

fof(f_1781_1,plain,
    ! [V_n_2,V_v_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != hAPP(c_Nat_OSuc,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc]) ).

fof(f_1781_2,plain,
    ! [U_5886,U_5885] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5885) = hAPP(c_Nat_OSuc,U_5886)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5885))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5886))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5885))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5886)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5885) != hAPP(c_Nat_OSuc,U_5886) ) ),
    inference(variable_rename,[status(thm)],[f_1781_1]) ).

fof(f_1781_3,plain,
    ( ! [U_5890,U_5888] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5888) = hAPP(c_Nat_OSuc,U_5890)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5888))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5890))))) )
    & ! [U_5889,U_5887] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5887))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5889)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5887) != hAPP(c_Nat_OSuc,U_5889) ) ),
    inference(miniscope,[status(thm)],[f_1781_2]) ).

fof(f_1781_4,plain,
    ( ! [U_5888,U_5890] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5888) = hAPP(c_Nat_OSuc,U_5890)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5888))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5890))))) )
    & ! [U_5889,U_5887] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5887))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5889)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5887) != hAPP(c_Nat_OSuc,U_5889) ) ),
    inference(definitional_conversion,[status(esa)],[f_1781_3]) ).

cnf(f_1781_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5887))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5889)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5887) != hAPP(c_Nat_OSuc,U_5889) ),
    inference(clausify,[status(thm)],[f_1781_4]) ).

cnf(f_1781_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5888) = hAPP(c_Nat_OSuc,U_5890)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5888))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5890))))) ),
    inference(clausify,[status(thm)],[f_1781_4]) ).

fof(f_1782_1,plain,
    ! [V_v_2,V_n_2] :
      ( ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2)))))
        | hAPP(c_Nat_OSuc,V_n_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of]) ).

fof(f_1782_2,plain,
    ! [U_5892,U_5891] :
      ( ( hAPP(c_Nat_OSuc,U_5891) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5892)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5892))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5891))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5892))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5891)))))
        | hAPP(c_Nat_OSuc,U_5891) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5892) ) ),
    inference(variable_rename,[status(thm)],[f_1782_1]) ).

fof(f_1782_3,plain,
    ( ! [U_5896,U_5894] :
        ( hAPP(c_Nat_OSuc,U_5894) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5896)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5896))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5894))))) )
    & ! [U_5895,U_5893] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5895))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5893)))))
        | hAPP(c_Nat_OSuc,U_5893) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5895) ) ),
    inference(miniscope,[status(thm)],[f_1782_2]) ).

fof(f_1782_4,plain,
    ( ! [U_5896,U_5894] :
        ( hAPP(c_Nat_OSuc,U_5894) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5896)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5896))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5894))))) )
    & ! [U_5895,U_5893] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5895))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5893)))))
        | hAPP(c_Nat_OSuc,U_5893) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5895) ) ),
    inference(definitional_conversion,[status(esa)],[f_1782_3]) ).

cnf(f_1782_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5895))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5893)))))
    | hAPP(c_Nat_OSuc,U_5893) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5895) ),
    inference(clausify,[status(thm)],[f_1782_4]) ).

cnf(f_1782_6,plain,
    ( hAPP(c_Nat_OSuc,U_5894) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5896)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5896))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_5894))))) ),
    inference(clausify,[status(thm)],[f_1782_4]) ).

fof(f_1783_1,plain,
    ! [V_w_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Bit1]) ).

fof(f_1783_2,plain,
    ! [U_5897] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5897)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5897)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5897))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5897)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5897))) ) ),
    inference(variable_rename,[status(thm)],[f_1783_1]) ).

fof(f_1783_3,plain,
    ( ! [U_5899] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5899)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5899)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5899))) )
    & ! [U_5898] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5898)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5898))) ) ),
    inference(miniscope,[status(thm)],[f_1783_2]) ).

fof(f_1783_4,plain,
    ( ! [U_5899] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5899)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5899)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5899))) )
    & ! [U_5898] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5898)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5898))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1783_3]) ).

cnf(f_1783_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5898)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5898))) ),
    inference(clausify,[status(thm)],[f_1783_4]) ).

cnf(f_1783_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5899)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5899)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5899))) ),
    inference(clausify,[status(thm)],[f_1783_4]) ).

fof(f_1784_1,plain,
    ! [V_n_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc]) ).

fof(f_1784_2,plain,
    ! [U_5901,U_5900] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5900)),hAPP(c_Nat_OSuc,U_5901)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5900))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5901)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5900))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5901))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5900)),hAPP(c_Nat_OSuc,U_5901))) ) ),
    inference(variable_rename,[status(thm)],[f_1784_1]) ).

fof(f_1784_3,plain,
    ( ! [U_5905,U_5903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5903)),hAPP(c_Nat_OSuc,U_5905)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5903))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5905)))) )
    & ! [U_5904,U_5902] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5902))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5904))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5902)),hAPP(c_Nat_OSuc,U_5904))) ) ),
    inference(miniscope,[status(thm)],[f_1784_2]) ).

fof(f_1784_4,plain,
    ( ! [U_5903,U_5905] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5903)),hAPP(c_Nat_OSuc,U_5905)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5903))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5905)))) )
    & ! [U_5904,U_5902] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5902))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5904))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5902)),hAPP(c_Nat_OSuc,U_5904))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1784_3]) ).

cnf(f_1784_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5902))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5904))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5902)),hAPP(c_Nat_OSuc,U_5904))) ),
    inference(clausify,[status(thm)],[f_1784_4]) ).

cnf(f_1784_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5903)),hAPP(c_Nat_OSuc,U_5905)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5903))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_5905)))) ),
    inference(clausify,[status(thm)],[f_1784_4]) ).

fof(f_1785_1,plain,
    ! [V_v_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of]) ).

fof(f_1785_2,plain,
    ! [U_5907,U_5906] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5906)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5907)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5907))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5906)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5907))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5906)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5906)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5907))) ) ),
    inference(variable_rename,[status(thm)],[f_1785_1]) ).

fof(f_1785_3,plain,
    ( ! [U_5911,U_5909] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5909)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5911)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5911))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5909)),c_Int_Onat))))) )
    & ! [U_5910,U_5908] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5910))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5908)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5908)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5910))) ) ),
    inference(miniscope,[status(thm)],[f_1785_2]) ).

fof(f_1785_4,plain,
    ( ! [U_5909,U_5911] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5909)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5911)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5911))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5909)),c_Int_Onat))))) )
    & ! [U_5910,U_5908] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5910))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5908)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5908)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5910))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1785_3]) ).

cnf(f_1785_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5910))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5908)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5908)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5910))) ),
    inference(clausify,[status(thm)],[f_1785_4]) ).

cnf(f_1785_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5909)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5911)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5911))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5909)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_1785_4]) ).

fof(f_1786_1,plain,
    ! [V_n_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc]) ).

fof(f_1786_2,plain,
    ! [U_5913,U_5912] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5912)),hAPP(c_Nat_OSuc,U_5913)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5912))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5913)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5912))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5913))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5912)),hAPP(c_Nat_OSuc,U_5913))) ) ),
    inference(variable_rename,[status(thm)],[f_1786_1]) ).

fof(f_1786_3,plain,
    ( ! [U_5917,U_5915] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5915)),hAPP(c_Nat_OSuc,U_5917)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5915))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5917)))) )
    & ! [U_5916,U_5914] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5914))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5916))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5914)),hAPP(c_Nat_OSuc,U_5916))) ) ),
    inference(miniscope,[status(thm)],[f_1786_2]) ).

fof(f_1786_4,plain,
    ( ! [U_5917,U_5915] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5915)),hAPP(c_Nat_OSuc,U_5917)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5915))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5917)))) )
    & ! [U_5914,U_5916] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5914))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5916))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5914)),hAPP(c_Nat_OSuc,U_5916))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1786_3]) ).

cnf(f_1786_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5914))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5916))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5914)),hAPP(c_Nat_OSuc,U_5916))) ),
    inference(clausify,[status(thm)],[f_1786_4]) ).

cnf(f_1786_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5915)),hAPP(c_Nat_OSuc,U_5917)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5915))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_5917)))) ),
    inference(clausify,[status(thm)],[f_1786_4]) ).

fof(f_1787_1,plain,
    ! [V_v_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of]) ).

fof(f_1787_2,plain,
    ! [U_5919,U_5918] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5918)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5919)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5919))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5918)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5919))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5918)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5918)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5919))) ) ),
    inference(variable_rename,[status(thm)],[f_1787_1]) ).

fof(f_1787_3,plain,
    ( ! [U_5923,U_5921] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5921)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5923)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5923))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5921)),c_Int_Onat))))) )
    & ! [U_5922,U_5920] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5922))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5920)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5920)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5922))) ) ),
    inference(miniscope,[status(thm)],[f_1787_2]) ).

fof(f_1787_4,plain,
    ( ! [U_5921,U_5923] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5921)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5923)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5923))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5921)),c_Int_Onat))))) )
    & ! [U_5922,U_5920] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5922))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5920)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5920)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5922))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1787_3]) ).

cnf(f_1787_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5922))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5920)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5920)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5922))) ),
    inference(clausify,[status(thm)],[f_1787_4]) ).

cnf(f_1787_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5921)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5923)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5923))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5921)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_1787_4]) ).

fof(f_1788_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__odd]) ).

fof(f_1788_2,plain,
    ! [U_5926,U_5925,U_5924] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5925))) = c_Groups_Oone__class_Oone(U_5924)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5925))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5925))) = hAPP(hAPP(c_HOL_OLet(U_5924,U_5924),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5925))),hAPP(hAPP(c_COMBS(U_5924,U_5924,U_5924),hAPP(hAPP(c_COMBB(U_5924,tc_fun(U_5924,U_5924),U_5924),c_Groups_Otimes__class_Otimes(U_5924)),hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5926))),c_COMBI(U_5924)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5925))) ) )
      | ~ class_Int_Onumber__ring(U_5924) ),
    inference(variable_rename,[status(thm)],[f_1788_1]) ).

fof(f_1788_3,plain,
    ( ! [U_5924,U_5925,U_5926] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5925))) = c_Groups_Oone__class_Oone(U_5924)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5925)))
        | ~ sP579(U_5924,U_5925,U_5926) )
    & ! [U_5924,U_5925,U_5926] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5925))) = hAPP(hAPP(c_HOL_OLet(U_5924,U_5924),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5925))),hAPP(hAPP(c_COMBS(U_5924,U_5924,U_5924),hAPP(hAPP(c_COMBB(U_5924,tc_fun(U_5924,U_5924),U_5924),c_Groups_Otimes__class_Otimes(U_5924)),hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5926))),c_COMBI(U_5924)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5925)))
        | ~ sP579(U_5924,U_5925,U_5926) )
    & ! [U_5924,U_5925,U_5926] :
        ( sP579(U_5924,U_5925,U_5926)
        | ~ class_Int_Onumber__ring(U_5924) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP579])],[f_1788_2]) ).

cnf(f_1788_4,plain,
    ( sP579(U_5924,U_5925,U_5926)
    | ~ class_Int_Onumber__ring(U_5924) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

cnf(f_1788_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5925))) = hAPP(hAPP(c_HOL_OLet(U_5924,U_5924),hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5925))),hAPP(hAPP(c_COMBS(U_5924,U_5924,U_5924),hAPP(hAPP(c_COMBB(U_5924,tc_fun(U_5924,U_5924),U_5924),c_Groups_Otimes__class_Otimes(U_5924)),hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5926))),c_COMBI(U_5924)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5925)))
    | ~ sP579(U_5924,U_5925,U_5926) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

cnf(f_1788_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5924),U_5926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5925))) = c_Groups_Oone__class_Oone(U_5924)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5925)))
    | ~ sP579(U_5924,U_5925,U_5926) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

fof(f_1789_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zpower__number__of__odd]) ).

fof(f_1789_2,plain,
    ! [U_5928,U_5927] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5927))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5927))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5927))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5927))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5928))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5927))) ) ),
    inference(variable_rename,[status(thm)],[f_1789_1]) ).

fof(f_1789_3,plain,
    ( ! [U_5932,U_5930] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5932),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5930))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5930))) )
    & ! [U_5931,U_5929] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5929))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5929))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5931))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5929))) ) ),
    inference(miniscope,[status(thm)],[f_1789_2]) ).

fof(f_1789_4,plain,
    ( ! [U_5930,U_5932] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5932),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5930))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5930))) )
    & ! [U_5929,U_5931] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5929))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5929))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5931))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5929))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1789_3]) ).

cnf(f_1789_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5929))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5929))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5931))),c_COMBI(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5929))) ),
    inference(clausify,[status(thm)],[f_1789_4]) ).

cnf(f_1789_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5932),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5930))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5930))) ),
    inference(clausify,[status(thm)],[f_1789_4]) ).

fof(f_1790_1,plain,
    ! [V_v_2,V_w_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(f_1790_2,plain,
    ! [U_5935,U_5934,U_5933] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5934))) = c_Groups_Oone__class_Oone(U_5933)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5934))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5934))) = hAPP(hAPP(c_HOL_OLet(U_5933,U_5933),hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5934))),hAPP(hAPP(c_COMBS(U_5933,U_5933,U_5933),hAPP(hAPP(c_COMBB(U_5933,tc_fun(U_5933,U_5933),U_5933),c_Groups_Otimes__class_Otimes(U_5933)),hAPP(c_Groups_Otimes__class_Otimes(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)))),c_COMBI(U_5933)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5934))) ) )
      | ~ class_Int_Onumber__ring(U_5933) ),
    inference(variable_rename,[status(thm)],[f_1790_1]) ).

fof(f_1790_3,plain,
    ( ! [U_5934,U_5933,U_5935] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5934))) = c_Groups_Oone__class_Oone(U_5933)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5934)))
        | ~ sP580(U_5934,U_5933,U_5935) )
    & ! [U_5934,U_5933,U_5935] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5934))) = hAPP(hAPP(c_HOL_OLet(U_5933,U_5933),hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5934))),hAPP(hAPP(c_COMBS(U_5933,U_5933,U_5933),hAPP(hAPP(c_COMBB(U_5933,tc_fun(U_5933,U_5933),U_5933),c_Groups_Otimes__class_Otimes(U_5933)),hAPP(c_Groups_Otimes__class_Otimes(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)))),c_COMBI(U_5933)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5934)))
        | ~ sP580(U_5934,U_5933,U_5935) )
    & ! [U_5934,U_5933,U_5935] :
        ( sP580(U_5934,U_5933,U_5935)
        | ~ class_Int_Onumber__ring(U_5933) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP580])],[f_1790_2]) ).

cnf(f_1790_4,plain,
    ( sP580(U_5934,U_5933,U_5935)
    | ~ class_Int_Onumber__ring(U_5933) ),
    inference(clausify,[status(thm)],[f_1790_3]) ).

cnf(f_1790_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5934))) = hAPP(hAPP(c_HOL_OLet(U_5933,U_5933),hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5934))),hAPP(hAPP(c_COMBS(U_5933,U_5933,U_5933),hAPP(hAPP(c_COMBB(U_5933,tc_fun(U_5933,U_5933),U_5933),c_Groups_Otimes__class_Otimes(U_5933)),hAPP(c_Groups_Otimes__class_Otimes(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)))),c_COMBI(U_5933)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5934)))
    | ~ sP580(U_5934,U_5933,U_5935) ),
    inference(clausify,[status(thm)],[f_1790_3]) ).

cnf(f_1790_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5933),hAPP(c_Int_Onumber__class_Onumber__of(U_5933),U_5935)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5934))) = c_Groups_Oone__class_Oone(U_5933)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5934)))
    | ~ sP580(U_5934,U_5933,U_5935) ),
    inference(clausify,[status(thm)],[f_1790_3]) ).

fof(f_1791_1,plain,
    ! [V_v_2,V_v_H_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__nat__number__of]) ).

fof(f_1791_2,plain,
    ! [U_5937,U_5936] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5936)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5936)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5936),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5936)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5937)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5936),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1791_1]) ).

fof(f_1791_3,plain,
    ( ! [U_5941,U_5939] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5939)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5941),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5939)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5939),c_Int_OPls)) )
    & ! [U_5940,U_5938] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5938)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5940)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5938),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1791_2]) ).

fof(f_1791_4,plain,
    ( ! [U_5939,U_5941] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5939)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5941),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5939)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5939),c_Int_OPls)) )
    & ! [U_5938,U_5940] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5938)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5940)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5938),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1791_3]) ).

cnf(f_1791_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5938)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5940)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5938),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5939)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5941),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5939)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5939),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

fof(f_1792_1,plain,
    ! [V_k_2,T_b] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__num]) ).

fof(f_1792_2,plain,
    ! [U_5943,U_5942] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5942),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5942,U_5942)),tc_fun(tc_Int_Oint,U_5942)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5942,U_5942),U_5942),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5942,U_5942)),tc_fun(tc_Int_Oint,U_5942)),tc_Int_Oint),c_COMBB(tc_fun(U_5942,U_5942),U_5942,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5942,tc_fun(tc_fun(U_5942,U_5942),U_5942),tc_Int_Oint),c_HOL_OLet(U_5942,U_5942)),c_Int_Oring__1__class_Oof__int(U_5942)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5942,U_5942),tc_fun(U_5942,U_5942)),hAPP(hAPP(c_COMBB(tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_fun(tc_fun(U_5942,U_5942),tc_fun(U_5942,U_5942)),tc_Int_Oint),c_COMBS(U_5942,U_5942,U_5942)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5942,U_5942),tc_fun(U_5942,tc_fun(U_5942,U_5942))),hAPP(hAPP(c_COMBB(tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_fun(tc_fun(U_5942,U_5942),tc_fun(U_5942,tc_fun(U_5942,U_5942))),tc_Int_Oint),c_COMBB(U_5942,tc_fun(U_5942,U_5942),U_5942)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_Int_Oint),c_If(U_5942)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(U_5942,U_5942,U_5942),c_Groups_Oplus__class_Oplus(U_5942)),c_COMBI(U_5942))))),hAPP(hAPP(c_COMBC(U_5942,U_5942,U_5942),hAPP(hAPP(c_COMBB(U_5942,tc_fun(U_5942,U_5942),U_5942),c_Groups_Oplus__class_Oplus(U_5942)),hAPP(hAPP(c_COMBS(U_5942,U_5942,U_5942),c_Groups_Oplus__class_Oplus(U_5942)),c_COMBI(U_5942)))),c_Groups_Oone__class_Oone(U_5942))))),c_Divides_Odivmod__int(U_5943,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5942),hAPP(c_Int_Oring__1__class_Oof__int(U_5942),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5943)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | U_5943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = c_Groups_Ozero__class_Ozero(U_5942)
          | U_5943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(U_5942) ),
    inference(variable_rename,[status(thm)],[f_1792_1]) ).

fof(f_1792_3,plain,
    ( ! [U_5942,U_5943] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5942),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5942,U_5942)),tc_fun(tc_Int_Oint,U_5942)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5942,U_5942),U_5942),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5942,U_5942)),tc_fun(tc_Int_Oint,U_5942)),tc_Int_Oint),c_COMBB(tc_fun(U_5942,U_5942),U_5942,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5942,tc_fun(tc_fun(U_5942,U_5942),U_5942),tc_Int_Oint),c_HOL_OLet(U_5942,U_5942)),c_Int_Oring__1__class_Oof__int(U_5942)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5942,U_5942),tc_fun(U_5942,U_5942)),hAPP(hAPP(c_COMBB(tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_fun(tc_fun(U_5942,U_5942),tc_fun(U_5942,U_5942)),tc_Int_Oint),c_COMBS(U_5942,U_5942,U_5942)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5942,U_5942),tc_fun(U_5942,tc_fun(U_5942,U_5942))),hAPP(hAPP(c_COMBB(tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_fun(tc_fun(U_5942,U_5942),tc_fun(U_5942,tc_fun(U_5942,U_5942))),tc_Int_Oint),c_COMBB(U_5942,tc_fun(U_5942,U_5942),U_5942)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_Int_Oint),c_If(U_5942)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(U_5942,U_5942,U_5942),c_Groups_Oplus__class_Oplus(U_5942)),c_COMBI(U_5942))))),hAPP(hAPP(c_COMBC(U_5942,U_5942,U_5942),hAPP(hAPP(c_COMBB(U_5942,tc_fun(U_5942,U_5942),U_5942),c_Groups_Oplus__class_Oplus(U_5942)),hAPP(hAPP(c_COMBS(U_5942,U_5942,U_5942),c_Groups_Oplus__class_Oplus(U_5942)),c_COMBI(U_5942)))),c_Groups_Oone__class_Oone(U_5942))))),c_Divides_Odivmod__int(U_5943,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP581(U_5942,U_5943) )
    & ! [U_5942,U_5943] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5942),hAPP(c_Int_Oring__1__class_Oof__int(U_5942),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5943)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP581(U_5942,U_5943) )
    & ! [U_5942,U_5943] :
        ( sP581(U_5942,U_5943)
        | U_5943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP582(U_5942,U_5943) )
    & ! [U_5942,U_5943] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = c_Groups_Ozero__class_Ozero(U_5942)
        | U_5943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP582(U_5942,U_5943) )
    & ! [U_5942,U_5943] :
        ( sP582(U_5942,U_5943)
        | ~ class_Rings_Oring__1(U_5942) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP581,sP582])],[f_1792_2]) ).

cnf(f_1792_4,plain,
    ( sP582(U_5942,U_5943)
    | ~ class_Rings_Oring__1(U_5942) ),
    inference(clausify,[status(thm)],[f_1792_3]) ).

cnf(f_1792_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = c_Groups_Ozero__class_Ozero(U_5942)
    | U_5943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP582(U_5942,U_5943) ),
    inference(clausify,[status(thm)],[f_1792_3]) ).

cnf(f_1792_6,plain,
    ( sP581(U_5942,U_5943)
    | U_5943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP582(U_5942,U_5943) ),
    inference(clausify,[status(thm)],[f_1792_3]) ).

cnf(f_1792_7,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5942),hAPP(c_Int_Oring__1__class_Oof__int(U_5942),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP581(U_5942,U_5943) ),
    inference(clausify,[status(thm)],[f_1792_3]) ).

cnf(f_1792_8,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5942),U_5943) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5942),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5942,U_5942)),tc_fun(tc_Int_Oint,U_5942)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5942,U_5942),U_5942),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5942,U_5942)),tc_fun(tc_Int_Oint,U_5942)),tc_Int_Oint),c_COMBB(tc_fun(U_5942,U_5942),U_5942,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5942,tc_fun(tc_fun(U_5942,U_5942),U_5942),tc_Int_Oint),c_HOL_OLet(U_5942,U_5942)),c_Int_Oring__1__class_Oof__int(U_5942)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5942,U_5942),tc_fun(U_5942,U_5942)),hAPP(hAPP(c_COMBB(tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_fun(tc_fun(U_5942,U_5942),tc_fun(U_5942,U_5942)),tc_Int_Oint),c_COMBS(U_5942,U_5942,U_5942)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5942,U_5942),tc_fun(U_5942,tc_fun(U_5942,U_5942))),hAPP(hAPP(c_COMBB(tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_fun(tc_fun(U_5942,U_5942),tc_fun(U_5942,tc_fun(U_5942,U_5942))),tc_Int_Oint),c_COMBB(U_5942,tc_fun(U_5942,U_5942),U_5942)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5942,tc_fun(U_5942,U_5942)),tc_Int_Oint),c_If(U_5942)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(U_5942,U_5942,U_5942),c_Groups_Oplus__class_Oplus(U_5942)),c_COMBI(U_5942))))),hAPP(hAPP(c_COMBC(U_5942,U_5942,U_5942),hAPP(hAPP(c_COMBB(U_5942,tc_fun(U_5942,U_5942),U_5942),c_Groups_Oplus__class_Oplus(U_5942)),hAPP(hAPP(c_COMBS(U_5942,U_5942,U_5942),c_Groups_Oplus__class_Oplus(U_5942)),c_COMBI(U_5942)))),c_Groups_Oone__class_Oone(U_5942))))),c_Divides_Odivmod__int(U_5943,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP581(U_5942,U_5943) ),
    inference(clausify,[status(thm)],[f_1792_3]) ).

fof(f_1793_1,plain,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    inference(fof_nnf,[status(thm)],[fact_nat__case__add__eq__if]) ).

fof(f_1793_2,plain,
    ! [U_5948,U_5947,U_5946,U_5945,U_5944] : c_Nat_Onat_Onat__case(U_5944,U_5945,U_5946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5947)),U_5948)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5944),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5947))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5944,U_5944),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5944,tc_fun(U_5944,U_5944)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5944,tc_fun(U_5944,U_5944)),tc_Int_Oint),c_If(U_5944)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5944,U_5945,U_5946,U_5948))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5944,tc_Int_Oint),U_5946),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5948)))),
    inference(variable_rename,[status(thm)],[f_1793_1]) ).

fof(f_1793_3,plain,
    ! [U_5944,U_5946,U_5947,U_5945,U_5948] : c_Nat_Onat_Onat__case(U_5944,U_5945,U_5946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5947)),U_5948)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5944),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5947))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5944,U_5944),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5944,tc_fun(U_5944,U_5944)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5944,tc_fun(U_5944,U_5944)),tc_Int_Oint),c_If(U_5944)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5944,U_5945,U_5946,U_5948))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5944,tc_Int_Oint),U_5946),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5948)))),
    inference(definitional_conversion,[status(esa)],[f_1793_2]) ).

cnf(f_1793_4,plain,
    c_Nat_Onat_Onat__case(U_5944,U_5945,U_5946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5947)),U_5948)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5944),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5947))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5944,U_5944),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5944,tc_fun(U_5944,U_5944)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5944,tc_fun(U_5944,U_5944)),tc_Int_Oint),c_If(U_5944)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5944,U_5945,U_5946,U_5948))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5944,tc_Int_Oint),U_5946),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5948)))),
    inference(clausify,[status(thm)],[f_1793_3]) ).

fof(f_1794_1,plain,
    ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(fof_nnf,[status(thm)],[fact_adjust__def]) ).

fof(f_1794_2,plain,
    ! [U_5949] : c_Divides_Oadjust(U_5949) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_5949))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_5949))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(variable_rename,[status(thm)],[f_1794_1]) ).

fof(f_1794_3,plain,
    ! [U_5949] : c_Divides_Oadjust(U_5949) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_5949))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_5949))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(definitional_conversion,[status(esa)],[f_1794_2]) ).

cnf(f_1794_4,plain,
    c_Divides_Oadjust(U_5949) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_5949))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_5949))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(clausify,[status(thm)],[f_1794_3]) ).

fof(f_1795_1,plain,
    ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__case__number__of]) ).

fof(f_1795_2,plain,
    ! [U_5953,U_5952,U_5951,U_5950] : c_Nat_Onat_Onat__case(U_5950,U_5951,U_5952,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5953)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5953))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5950,U_5950),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5950,tc_fun(U_5950,U_5950)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5950,tc_fun(U_5950,U_5950)),tc_Int_Oint),c_If(U_5950)),c_Nat__Numeral_Oneg)),U_5951)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5950,tc_Int_Oint),U_5952),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[f_1795_1]) ).

fof(f_1795_3,plain,
    ! [U_5950,U_5951,U_5952,U_5953] : c_Nat_Onat_Onat__case(U_5950,U_5951,U_5952,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5953)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5953))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5950,U_5950),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5950,tc_fun(U_5950,U_5950)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5950,tc_fun(U_5950,U_5950)),tc_Int_Oint),c_If(U_5950)),c_Nat__Numeral_Oneg)),U_5951)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5950,tc_Int_Oint),U_5952),c_Int_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1795_2]) ).

cnf(f_1795_4,plain,
    c_Nat_Onat_Onat__case(U_5950,U_5951,U_5952,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5953)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5953))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5950,U_5950),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5950,tc_fun(U_5950,U_5950)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5950,tc_fun(U_5950,U_5950)),tc_Int_Oint),c_If(U_5950)),c_Nat__Numeral_Oneg)),U_5951)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5950,tc_Int_Oint),U_5952),c_Int_Onat))),
    inference(clausify,[status(thm)],[f_1795_3]) ).

fof(f_1796_1,plain,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__add__eq__if]) ).

fof(f_1796_2,plain,
    ! [U_5958,U_5957,U_5956,U_5955,U_5954] : hAPP(c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5957)),U_5958)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5954),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5957))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5954,U_5954),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5954,tc_fun(U_5954,U_5954)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5954,tc_fun(U_5954,U_5954)),tc_Int_Oint),c_If(U_5954)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956),U_5958))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5954,U_5954),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5954,U_5954),tc_Int_Oint),U_5956),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5958))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5954,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5958))))),
    inference(variable_rename,[status(thm)],[f_1796_1]) ).

fof(f_1796_3,plain,
    ! [U_5954,U_5955,U_5956,U_5957,U_5958] : hAPP(c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5957)),U_5958)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5954),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5957))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5954,U_5954),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5954,tc_fun(U_5954,U_5954)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5954,tc_fun(U_5954,U_5954)),tc_Int_Oint),c_If(U_5954)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956),U_5958))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5954,U_5954),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5954,U_5954),tc_Int_Oint),U_5956),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5958))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5954,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5958))))),
    inference(definitional_conversion,[status(esa)],[f_1796_2]) ).

cnf(f_1796_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5957)),U_5958)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5954),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5957))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5954,U_5954),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5954,tc_fun(U_5954,U_5954)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5954,tc_fun(U_5954,U_5954)),tc_Int_Oint),c_If(U_5954)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956),U_5958))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5954,U_5954),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5954,U_5954),tc_Int_Oint),U_5956),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5958))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5954,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5954,U_5955,U_5956)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_5958))))),
    inference(clausify,[status(thm)],[f_1796_3]) ).

fof(f_1797_1,plain,
    ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_split__twice]) ).

fof(f_1797_2,plain,
    ! [U_5966,U_5965,U_5964,U_5963,U_5962,U_5961,U_5960,U_5959] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5959,U_5960,U_5961),U_5962),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5963,U_5964,tc_prod(U_5959,U_5960)),U_5965),U_5966)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5963,U_5964,U_5961),hAPP(hAPP(c_COMBB(tc_fun(U_5964,tc_prod(U_5959,U_5960)),tc_fun(U_5964,U_5961),U_5963),hAPP(c_COMBB(tc_prod(U_5959,U_5960),U_5961,U_5964),hAPP(c_Product__Type_Oprod_Oprod__case(U_5959,U_5960,U_5961),U_5962))),U_5965)),U_5966),
    inference(variable_rename,[status(thm)],[f_1797_1]) ).

fof(f_1797_3,plain,
    ! [U_5959,U_5960,U_5961,U_5962,U_5963,U_5964,U_5965,U_5966] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5959,U_5960,U_5961),U_5962),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5963,U_5964,tc_prod(U_5959,U_5960)),U_5965),U_5966)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5963,U_5964,U_5961),hAPP(hAPP(c_COMBB(tc_fun(U_5964,tc_prod(U_5959,U_5960)),tc_fun(U_5964,U_5961),U_5963),hAPP(c_COMBB(tc_prod(U_5959,U_5960),U_5961,U_5964),hAPP(c_Product__Type_Oprod_Oprod__case(U_5959,U_5960,U_5961),U_5962))),U_5965)),U_5966),
    inference(definitional_conversion,[status(esa)],[f_1797_2]) ).

cnf(f_1797_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5959,U_5960,U_5961),U_5962),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5963,U_5964,tc_prod(U_5959,U_5960)),U_5965),U_5966)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5963,U_5964,U_5961),hAPP(hAPP(c_COMBB(tc_fun(U_5964,tc_prod(U_5959,U_5960)),tc_fun(U_5964,U_5961),U_5963),hAPP(c_COMBB(tc_prod(U_5959,U_5960),U_5961,U_5964),hAPP(c_Product__Type_Oprod_Oprod__case(U_5959,U_5960,U_5961),U_5962))),U_5965)),U_5966),
    inference(clausify,[status(thm)],[f_1797_3]) ).

fof(f_1798_1,plain,
    ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2)
      | V_p_2 != V_q_2 ),
    inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).

fof(f_1798_2,plain,
    ! [U_5972,U_5971,U_5970,U_5969,U_5968,U_5967] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5969,U_5970,U_5971),U_5972),U_5967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5969,U_5970,U_5971),U_5972),U_5968)
      | U_5967 != U_5968 ),
    inference(variable_rename,[status(thm)],[f_1798_1]) ).

fof(f_1798_3,plain,
    ! [U_5967,U_5968,U_5969,U_5970,U_5971,U_5972] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5969,U_5970,U_5971),U_5972),U_5967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5969,U_5970,U_5971),U_5972),U_5968)
      | U_5967 != U_5968 ),
    inference(definitional_conversion,[status(esa)],[f_1798_2]) ).

cnf(f_1798_4,plain,
    ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5969,U_5970,U_5971),U_5972),U_5967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5969,U_5970,U_5971),U_5972),U_5968)
    | U_5967 != U_5968 ),
    inference(clausify,[status(thm)],[f_1798_3]) ).

fof(f_1799_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_split__conv]) ).

fof(f_1799_2,plain,
    ! [U_5978,U_5977,U_5976,U_5975,U_5974,U_5973] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5973,U_5974,U_5975),U_5976),hAPP(hAPP(c_Product__Type_OPair(U_5973,U_5974),U_5977),U_5978)) = hAPP(hAPP(U_5976,U_5977),U_5978),
    inference(variable_rename,[status(thm)],[f_1799_1]) ).

fof(f_1799_3,plain,
    ! [U_5974,U_5973,U_5975,U_5976,U_5977,U_5978] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5973,U_5974,U_5975),U_5976),hAPP(hAPP(c_Product__Type_OPair(U_5973,U_5974),U_5977),U_5978)) = hAPP(hAPP(U_5976,U_5977),U_5978),
    inference(definitional_conversion,[status(esa)],[f_1799_2]) ).

cnf(f_1799_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5973,U_5974,U_5975),U_5976),hAPP(hAPP(c_Product__Type_OPair(U_5973,U_5974),U_5977),U_5978)) = hAPP(hAPP(U_5976,U_5977),U_5978),
    inference(clausify,[status(thm)],[f_1799_3]) ).

fof(f_1800_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_prod_Osimps_I2_J]) ).

fof(f_1800_2,plain,
    ! [U_5984,U_5983,U_5982,U_5981,U_5980,U_5979] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5979,U_5980,U_5981),U_5982),hAPP(hAPP(c_Product__Type_OPair(U_5979,U_5980),U_5983),U_5984)) = hAPP(hAPP(U_5982,U_5983),U_5984),
    inference(variable_rename,[status(thm)],[f_1800_1]) ).

fof(f_1800_3,plain,
    ! [U_5979,U_5980,U_5981,U_5982,U_5983,U_5984] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5979,U_5980,U_5981),U_5982),hAPP(hAPP(c_Product__Type_OPair(U_5979,U_5980),U_5983),U_5984)) = hAPP(hAPP(U_5982,U_5983),U_5984),
    inference(definitional_conversion,[status(esa)],[f_1800_2]) ).

cnf(f_1800_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5979,U_5980,U_5981),U_5982),hAPP(hAPP(c_Product__Type_OPair(U_5979,U_5980),U_5983),U_5984)) = hAPP(hAPP(U_5982,U_5983),U_5984),
    inference(clausify,[status(thm)],[f_1800_3]) ).

fof(f_1801_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__apply]) ).

fof(f_1801_2,plain,
    ! [U_5991,U_5990,U_5989,U_5988,U_5987,U_5986,U_5985] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5985,U_5986,U_5987,U_5988),U_5989),U_5990),U_5991) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5990),hAPP(U_5989,U_5991)),
    inference(variable_rename,[status(thm)],[f_1801_1]) ).

fof(f_1801_3,plain,
    ! [U_5985,U_5986,U_5987,U_5988,U_5989,U_5990,U_5991] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5985,U_5986,U_5987,U_5988),U_5989),U_5990),U_5991) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5990),hAPP(U_5989,U_5991)),
    inference(definitional_conversion,[status(esa)],[f_1801_2]) ).

cnf(f_1801_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5985,U_5986,U_5987,U_5988),U_5989),U_5990),U_5991) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5990),hAPP(U_5989,U_5991)),
    inference(clausify,[status(thm)],[f_1801_3]) ).

fof(f_1802_1,plain,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_split__eta]) ).

fof(f_1802_2,plain,
    ! [U_5995,U_5994,U_5993,U_5992] : hAPP(c_Product__Type_Oprod_Oprod__case(U_5992,U_5993,U_5994),hAPP(hAPP(c_COMBB(tc_fun(U_5993,tc_prod(U_5992,U_5993)),tc_fun(U_5993,U_5994),U_5992),hAPP(c_COMBB(tc_prod(U_5992,U_5993),U_5994,U_5993),U_5995)),c_Product__Type_OPair(U_5992,U_5993))) = U_5995,
    inference(variable_rename,[status(thm)],[f_1802_1]) ).

fof(f_1802_3,plain,
    ! [U_5992,U_5993,U_5994,U_5995] : hAPP(c_Product__Type_Oprod_Oprod__case(U_5992,U_5993,U_5994),hAPP(hAPP(c_COMBB(tc_fun(U_5993,tc_prod(U_5992,U_5993)),tc_fun(U_5993,U_5994),U_5992),hAPP(c_COMBB(tc_prod(U_5992,U_5993),U_5994,U_5993),U_5995)),c_Product__Type_OPair(U_5992,U_5993))) = U_5995,
    inference(definitional_conversion,[status(esa)],[f_1802_2]) ).

cnf(f_1802_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_5992,U_5993,U_5994),hAPP(hAPP(c_COMBB(tc_fun(U_5993,tc_prod(U_5992,U_5993)),tc_fun(U_5993,U_5994),U_5992),hAPP(c_COMBB(tc_prod(U_5992,U_5993),U_5994,U_5993),U_5995)),c_Product__Type_OPair(U_5992,U_5993))) = U_5995,
    inference(clausify,[status(thm)],[f_1802_3]) ).

fof(f_1803_1,plain,
    ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_fst__def]) ).

fof(f_1803_2,plain,
    ! [U_5998,U_5997,U_5996] : hAPP(c_Product__Type_Ofst(U_5996,U_5997),U_5998) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5996,U_5997,U_5996),c_COMBK(U_5996,U_5997)),U_5998),
    inference(variable_rename,[status(thm)],[f_1803_1]) ).

fof(f_1803_3,plain,
    ! [U_5996,U_5997,U_5998] : hAPP(c_Product__Type_Ofst(U_5996,U_5997),U_5998) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5996,U_5997,U_5996),c_COMBK(U_5996,U_5997)),U_5998),
    inference(definitional_conversion,[status(esa)],[f_1803_2]) ).

cnf(f_1803_4,plain,
    hAPP(c_Product__Type_Ofst(U_5996,U_5997),U_5998) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5996,U_5997,U_5996),c_COMBK(U_5996,U_5997)),U_5998),
    inference(clausify,[status(thm)],[f_1803_3]) ).

fof(f_1804_1,plain,
    ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_snd__def]) ).

fof(f_1804_2,plain,
    ! [U_6001,U_6000,U_5999] : hAPP(c_Product__Type_Osnd(U_5999,U_6000),U_6001) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5999,U_6000,U_6000),hAPP(c_COMBK(tc_fun(U_6000,U_6000),U_5999),c_COMBI(U_6000))),U_6001),
    inference(variable_rename,[status(thm)],[f_1804_1]) ).

fof(f_1804_3,plain,
    ! [U_5999,U_6000,U_6001] : hAPP(c_Product__Type_Osnd(U_5999,U_6000),U_6001) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5999,U_6000,U_6000),hAPP(c_COMBK(tc_fun(U_6000,U_6000),U_5999),c_COMBI(U_6000))),U_6001),
    inference(definitional_conversion,[status(esa)],[f_1804_2]) ).

cnf(f_1804_4,plain,
    hAPP(c_Product__Type_Osnd(U_5999,U_6000),U_6001) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5999,U_6000,U_6000),hAPP(c_COMBK(tc_fun(U_6000,U_6000),U_5999),c_COMBI(U_6000))),U_6001),
    inference(clausify,[status(thm)],[f_1804_3]) ).

fof(f_1805_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__def]) ).

fof(f_1805_2,plain,
    ! [U_6008,U_6007,U_6006,U_6005,U_6004,U_6003,U_6002] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6002,U_6003,U_6004,U_6005),U_6006),U_6007),U_6008) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6003,U_6004,U_6005),U_6007),hAPP(U_6006,U_6008)),
    inference(variable_rename,[status(thm)],[f_1805_1]) ).

fof(f_1805_3,plain,
    ! [U_6002,U_6003,U_6004,U_6005,U_6006,U_6007,U_6008] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6002,U_6003,U_6004,U_6005),U_6006),U_6007),U_6008) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6003,U_6004,U_6005),U_6007),hAPP(U_6006,U_6008)),
    inference(definitional_conversion,[status(esa)],[f_1805_2]) ).

cnf(f_1805_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6002,U_6003,U_6004,U_6005),U_6006),U_6007),U_6008) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6003,U_6004,U_6005),U_6007),hAPP(U_6006,U_6008)),
    inference(clausify,[status(thm)],[f_1805_3]) ).

fof(f_1806_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_nat__rec__0]) ).

fof(f_1806_2,plain,
    ! [U_6011,U_6010,U_6009] : hAPP(c_Nat_Onat_Onat__rec(U_6009,U_6010,U_6011),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6010,
    inference(variable_rename,[status(thm)],[f_1806_1]) ).

fof(f_1806_3,plain,
    ! [U_6009,U_6011,U_6010] : hAPP(c_Nat_Onat_Onat__rec(U_6009,U_6010,U_6011),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6010,
    inference(definitional_conversion,[status(esa)],[f_1806_2]) ).

cnf(f_1806_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6009,U_6010,U_6011),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6010,
    inference(clausify,[status(thm)],[f_1806_3]) ).

fof(f_1807_1,plain,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__Suc]) ).

fof(f_1807_2,plain,
    ! [U_6015,U_6014,U_6013,U_6012] : hAPP(c_Nat_Onat_Onat__rec(U_6012,U_6013,U_6014),hAPP(c_Nat_OSuc,U_6015)) = hAPP(hAPP(U_6014,U_6015),hAPP(c_Nat_Onat_Onat__rec(U_6012,U_6013,U_6014),U_6015)),
    inference(variable_rename,[status(thm)],[f_1807_1]) ).

fof(f_1807_3,plain,
    ! [U_6012,U_6013,U_6014,U_6015] : hAPP(c_Nat_Onat_Onat__rec(U_6012,U_6013,U_6014),hAPP(c_Nat_OSuc,U_6015)) = hAPP(hAPP(U_6014,U_6015),hAPP(c_Nat_Onat_Onat__rec(U_6012,U_6013,U_6014),U_6015)),
    inference(definitional_conversion,[status(esa)],[f_1807_2]) ).

cnf(f_1807_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6012,U_6013,U_6014),hAPP(c_Nat_OSuc,U_6015)) = hAPP(hAPP(U_6014,U_6015),hAPP(c_Nat_Onat_Onat__rec(U_6012,U_6013,U_6014),U_6015)),
    inference(clausify,[status(thm)],[f_1807_3]) ).

fof(f_1808_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_nat__case__0]) ).

fof(f_1808_2,plain,
    ! [U_6018,U_6017,U_6016] : c_Nat_Onat_Onat__case(U_6016,U_6017,U_6018,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6017,
    inference(variable_rename,[status(thm)],[f_1808_1]) ).

fof(f_1808_3,plain,
    ! [U_6016,U_6018,U_6017] : c_Nat_Onat_Onat__case(U_6016,U_6017,U_6018,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6017,
    inference(definitional_conversion,[status(esa)],[f_1808_2]) ).

cnf(f_1808_4,plain,
    c_Nat_Onat_Onat__case(U_6016,U_6017,U_6018,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6017,
    inference(clausify,[status(thm)],[f_1808_3]) ).

fof(f_1809_1,plain,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
    inference(fof_nnf,[status(thm)],[fact_nat__case__Suc]) ).

fof(f_1809_2,plain,
    ! [U_6022,U_6021,U_6020,U_6019] : c_Nat_Onat_Onat__case(U_6019,U_6020,U_6021,hAPP(c_Nat_OSuc,U_6022)) = hAPP(U_6021,U_6022),
    inference(variable_rename,[status(thm)],[f_1809_1]) ).

fof(f_1809_3,plain,
    ! [U_6019,U_6020,U_6021,U_6022] : c_Nat_Onat_Onat__case(U_6019,U_6020,U_6021,hAPP(c_Nat_OSuc,U_6022)) = hAPP(U_6021,U_6022),
    inference(definitional_conversion,[status(esa)],[f_1809_2]) ).

cnf(f_1809_4,plain,
    c_Nat_Onat_Onat__case(U_6019,U_6020,U_6021,hAPP(c_Nat_OSuc,U_6022)) = hAPP(U_6021,U_6022),
    inference(clausify,[status(thm)],[f_1809_3]) ).

fof(f_1810_1,plain,
    ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_prod__case__beta]) ).

fof(f_1810_2,plain,
    ! [U_6027,U_6026,U_6025,U_6024,U_6023] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6023,U_6024,U_6025),U_6026),U_6027) = hAPP(hAPP(U_6026,hAPP(c_Product__Type_Ofst(U_6023,U_6024),U_6027)),hAPP(c_Product__Type_Osnd(U_6023,U_6024),U_6027)),
    inference(variable_rename,[status(thm)],[f_1810_1]) ).

fof(f_1810_3,plain,
    ! [U_6024,U_6023,U_6025,U_6026,U_6027] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6023,U_6024,U_6025),U_6026),U_6027) = hAPP(hAPP(U_6026,hAPP(c_Product__Type_Ofst(U_6023,U_6024),U_6027)),hAPP(c_Product__Type_Osnd(U_6023,U_6024),U_6027)),
    inference(definitional_conversion,[status(esa)],[f_1810_2]) ).

cnf(f_1810_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6023,U_6024,U_6025),U_6026),U_6027) = hAPP(hAPP(U_6026,hAPP(c_Product__Type_Ofst(U_6023,U_6024),U_6027)),hAPP(c_Product__Type_Osnd(U_6023,U_6024),U_6027)),
    inference(clausify,[status(thm)],[f_1810_3]) ).

fof(f_1811_1,plain,
    ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_split__beta]) ).

fof(f_1811_2,plain,
    ! [U_6032,U_6031,U_6030,U_6029,U_6028] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6028,U_6029,U_6030),U_6031),U_6032) = hAPP(hAPP(U_6031,hAPP(c_Product__Type_Ofst(U_6028,U_6029),U_6032)),hAPP(c_Product__Type_Osnd(U_6028,U_6029),U_6032)),
    inference(variable_rename,[status(thm)],[f_1811_1]) ).

fof(f_1811_3,plain,
    ! [U_6028,U_6029,U_6030,U_6031,U_6032] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6028,U_6029,U_6030),U_6031),U_6032) = hAPP(hAPP(U_6031,hAPP(c_Product__Type_Ofst(U_6028,U_6029),U_6032)),hAPP(c_Product__Type_Osnd(U_6028,U_6029),U_6032)),
    inference(definitional_conversion,[status(esa)],[f_1811_2]) ).

cnf(f_1811_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6028,U_6029,U_6030),U_6031),U_6032) = hAPP(hAPP(U_6031,hAPP(c_Product__Type_Ofst(U_6028,U_6029),U_6032)),hAPP(c_Product__Type_Osnd(U_6028,U_6029),U_6032)),
    inference(clausify,[status(thm)],[f_1811_3]) ).

fof(f_1812_1,plain,
    ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_split__comp__eq]) ).

fof(f_1812_2,plain,
    ! [U_6038,U_6037,U_6036,U_6035,U_6034,U_6033] : hAPP(hAPP(c_COMBS(tc_prod(U_6033,U_6034),U_6034,U_6035),hAPP(hAPP(c_COMBB(U_6036,tc_fun(U_6034,U_6035),tc_prod(U_6033,U_6034)),U_6037),hAPP(hAPP(c_COMBB(U_6033,U_6036,tc_prod(U_6033,U_6034)),U_6038),c_Product__Type_Ofst(U_6033,U_6034)))),c_Product__Type_Osnd(U_6033,U_6034)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6033,U_6034,U_6035),hAPP(hAPP(c_COMBB(U_6036,tc_fun(U_6034,U_6035),U_6033),U_6037),U_6038)),
    inference(variable_rename,[status(thm)],[f_1812_1]) ).

fof(f_1812_3,plain,
    ! [U_6033,U_6034,U_6035,U_6036,U_6037,U_6038] : hAPP(hAPP(c_COMBS(tc_prod(U_6033,U_6034),U_6034,U_6035),hAPP(hAPP(c_COMBB(U_6036,tc_fun(U_6034,U_6035),tc_prod(U_6033,U_6034)),U_6037),hAPP(hAPP(c_COMBB(U_6033,U_6036,tc_prod(U_6033,U_6034)),U_6038),c_Product__Type_Ofst(U_6033,U_6034)))),c_Product__Type_Osnd(U_6033,U_6034)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6033,U_6034,U_6035),hAPP(hAPP(c_COMBB(U_6036,tc_fun(U_6034,U_6035),U_6033),U_6037),U_6038)),
    inference(definitional_conversion,[status(esa)],[f_1812_2]) ).

cnf(f_1812_4,plain,
    hAPP(hAPP(c_COMBS(tc_prod(U_6033,U_6034),U_6034,U_6035),hAPP(hAPP(c_COMBB(U_6036,tc_fun(U_6034,U_6035),tc_prod(U_6033,U_6034)),U_6037),hAPP(hAPP(c_COMBB(U_6033,U_6036,tc_prod(U_6033,U_6034)),U_6038),c_Product__Type_Ofst(U_6033,U_6034)))),c_Product__Type_Osnd(U_6033,U_6034)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6033,U_6034,U_6035),hAPP(hAPP(c_COMBB(U_6036,tc_fun(U_6034,U_6035),U_6033),U_6037),U_6038)),
    inference(clausify,[status(thm)],[f_1812_3]) ).

fof(f_1813_1,plain,
    ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_split__def]) ).

fof(f_1813_2,plain,
    ! [U_6043,U_6042,U_6041,U_6040,U_6039] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6039,U_6040,U_6041),U_6042),U_6043) = hAPP(hAPP(U_6042,hAPP(c_Product__Type_Ofst(U_6039,U_6040),U_6043)),hAPP(c_Product__Type_Osnd(U_6039,U_6040),U_6043)),
    inference(variable_rename,[status(thm)],[f_1813_1]) ).

fof(f_1813_3,plain,
    ! [U_6039,U_6040,U_6041,U_6042,U_6043] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6039,U_6040,U_6041),U_6042),U_6043) = hAPP(hAPP(U_6042,hAPP(c_Product__Type_Ofst(U_6039,U_6040),U_6043)),hAPP(c_Product__Type_Osnd(U_6039,U_6040),U_6043)),
    inference(definitional_conversion,[status(esa)],[f_1813_2]) ).

cnf(f_1813_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6039,U_6040,U_6041),U_6042),U_6043) = hAPP(hAPP(U_6042,hAPP(c_Product__Type_Ofst(U_6039,U_6040),U_6043)),hAPP(c_Product__Type_Osnd(U_6039,U_6040),U_6043)),
    inference(clausify,[status(thm)],[f_1813_3]) ).

fof(f_1814_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J]) ).

fof(f_1814_2,plain,
    ! [U_6045,U_6044] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6044)),U_6045))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6044),U_6045)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6044),U_6045))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6044)),U_6045)) ) ),
    inference(variable_rename,[status(thm)],[f_1814_1]) ).

fof(f_1814_3,plain,
    ( ! [U_6049,U_6047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6047)),U_6049))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6047),U_6049)) )
    & ! [U_6048,U_6046] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6046),U_6048))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6046)),U_6048)) ) ),
    inference(miniscope,[status(thm)],[f_1814_2]) ).

fof(f_1814_4,plain,
    ( ! [U_6049,U_6047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6047)),U_6049))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6047),U_6049)) )
    & ! [U_6048,U_6046] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6046),U_6048))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6046)),U_6048)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1814_3]) ).

cnf(f_1814_5,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6046),U_6048))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6046)),U_6048)) ),
    inference(clausify,[status(thm)],[f_1814_4]) ).

cnf(f_1814_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6047)),U_6049))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6047),U_6049)) ),
    inference(clausify,[status(thm)],[f_1814_4]) ).

fof(f_1815_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc]) ).

fof(f_1815_2,plain,
    ! [U_6051,U_6050] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),hAPP(c_Nat_OSuc,U_6051)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),U_6051)),
    inference(variable_rename,[status(thm)],[f_1815_1]) ).

fof(f_1815_3,plain,
    ! [U_6050,U_6051] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),hAPP(c_Nat_OSuc,U_6051)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),U_6051)),
    inference(definitional_conversion,[status(esa)],[f_1815_2]) ).

cnf(f_1815_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),hAPP(c_Nat_OSuc,U_6051)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),U_6051)),
    inference(clausify,[status(thm)],[f_1815_3]) ).

fof(f_1816_1,plain,
    ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__def]) ).

fof(f_1816_2,plain,
    ! [U_6053,U_6052] : c_Divides_Odivmod__int__rel(U_6052,U_6053) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_6052))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6053)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_6053))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(variable_rename,[status(thm)],[f_1816_1]) ).

fof(f_1816_3,plain,
    ! [U_6052,U_6053] : c_Divides_Odivmod__int__rel(U_6052,U_6053) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_6052))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6053)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_6053))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(definitional_conversion,[status(esa)],[f_1816_2]) ).

cnf(f_1816_4,plain,
    c_Divides_Odivmod__int__rel(U_6052,U_6053) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_6052))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6053)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_6053))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(clausify,[status(thm)],[f_1816_3]) ).

fof(f_1817_1,plain,
    ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__number__of]) ).

fof(f_1817_2,plain,
    ! [U_6057,U_6056,U_6055,U_6054] : hAPP(c_Nat_Onat_Onat__rec(U_6054,U_6055,U_6056),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6054),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6057))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6054,tc_fun(U_6054,U_6054)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6054,tc_fun(U_6054,U_6054)),tc_Int_Oint),c_If(U_6054)),c_Nat__Numeral_Oneg)),U_6055)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6054,U_6054),tc_Int_Oint),U_6056),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6054,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6054,U_6055,U_6056)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1817_1]) ).

fof(f_1817_3,plain,
    ! [U_6054,U_6055,U_6056,U_6057] : hAPP(c_Nat_Onat_Onat__rec(U_6054,U_6055,U_6056),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6054),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6057))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6054,tc_fun(U_6054,U_6054)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6054,tc_fun(U_6054,U_6054)),tc_Int_Oint),c_If(U_6054)),c_Nat__Numeral_Oneg)),U_6055)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6054,U_6054),tc_Int_Oint),U_6056),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6054,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6054,U_6055,U_6056)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1817_2]) ).

cnf(f_1817_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6054,U_6055,U_6056),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6054),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6057))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6054,tc_fun(U_6054,U_6054)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6054,tc_fun(U_6054,U_6054)),tc_Int_Oint),c_If(U_6054)),c_Nat__Numeral_Oneg)),U_6055)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6054,U_6054),tc_Int_Oint),U_6056),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6054,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6054,U_6055,U_6056)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1817_3]) ).

fof(f_1818_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( ( ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2))))
            | V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)
            | V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__pdivmod]) ).

fof(f_1818_2,plain,
    ! [U_6059,U_6058] :
      ( ( ( ( c_Divides_Odivmod__int(U_6058,U_6059) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6059))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6059)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6058,U_6059)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6059))))),c_Divides_Opdivmod(U_6058,U_6059))))
            | U_6059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6058,U_6059) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058)
            | U_6059 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_6058,U_6059) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6058 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1818_1]) ).

fof(f_1818_3,plain,
    ( ! [U_6063,U_6061] :
        ( ( ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6063))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6063)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6061,U_6063)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6063))))),c_Divides_Opdivmod(U_6061,U_6063))))
            | U_6063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)
            | U_6063 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6062,U_6060] :
        ( c_Divides_Odivmod__int(U_6060,U_6062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6060 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1818_2]) ).

fof(f_1818_4,plain,
    ( ! [U_6061,U_6063] :
        ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6063))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6063)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6061,U_6063)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6063))))),c_Divides_Opdivmod(U_6061,U_6063))))
        | U_6063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP583(U_6061,U_6063) )
    & ! [U_6061,U_6063] :
        ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)
        | U_6063 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP583(U_6061,U_6063) )
    & ! [U_6061,U_6063] :
        ( sP583(U_6061,U_6063)
        | U_6061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6062,U_6060] :
        ( c_Divides_Odivmod__int(U_6060,U_6062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6060 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP583])],[f_1818_3]) ).

cnf(f_1818_5,plain,
    ( c_Divides_Odivmod__int(U_6060,U_6062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_6060 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1818_4]) ).

cnf(f_1818_6,plain,
    ( sP583(U_6061,U_6063)
    | U_6061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1818_4]) ).

cnf(f_1818_7,plain,
    ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)
    | U_6063 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP583(U_6061,U_6063) ),
    inference(clausify,[status(thm)],[f_1818_4]) ).

cnf(f_1818_8,plain,
    ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6063))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6063)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6061,U_6063)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6063))))),c_Divides_Opdivmod(U_6061,U_6063))))
    | U_6063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP583(U_6061,U_6063) ),
    inference(clausify,[status(thm)],[f_1818_4]) ).

fof(f_1819_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( ( ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2))))
            | V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)
            | V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__code]) ).

fof(f_1819_2,plain,
    ! [U_6065,U_6064] :
      ( ( ( ( c_Divides_Odivmod__int(U_6064,U_6065) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6065))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6064)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6065))),c_Divides_Opdivmod(U_6064,U_6065)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6065))))),c_Divides_Opdivmod(U_6064,U_6065))))
            | U_6065 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6064,U_6065) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6064)
            | U_6065 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_6064,U_6065) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6064 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1819_1]) ).

fof(f_1819_3,plain,
    ( ! [U_6069,U_6067] :
        ( ( ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6067)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),c_Divides_Opdivmod(U_6067,U_6069)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6069))))),c_Divides_Opdivmod(U_6067,U_6069))))
            | U_6069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
            | U_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6068,U_6066] :
        ( c_Divides_Odivmod__int(U_6066,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6066 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1819_2]) ).

fof(f_1819_4,plain,
    ( ! [U_6067,U_6069] :
        ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6067)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),c_Divides_Opdivmod(U_6067,U_6069)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6069))))),c_Divides_Opdivmod(U_6067,U_6069))))
        | U_6069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP584(U_6067,U_6069) )
    & ! [U_6067,U_6069] :
        ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
        | U_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP584(U_6067,U_6069) )
    & ! [U_6067,U_6069] :
        ( sP584(U_6067,U_6069)
        | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6066,U_6068] :
        ( c_Divides_Odivmod__int(U_6066,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6066 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP584])],[f_1819_3]) ).

cnf(f_1819_5,plain,
    ( c_Divides_Odivmod__int(U_6066,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_6066 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1819_4]) ).

cnf(f_1819_6,plain,
    ( sP584(U_6067,U_6069)
    | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1819_4]) ).

cnf(f_1819_7,plain,
    ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
    | U_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP584(U_6067,U_6069) ),
    inference(clausify,[status(thm)],[f_1819_4]) ).

cnf(f_1819_8,plain,
    ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6067)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),c_Divides_Opdivmod(U_6067,U_6069)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6069))))),c_Divides_Opdivmod(U_6067,U_6069))))
    | U_6069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP584(U_6067,U_6069) ),
    inference(clausify,[status(thm)],[f_1819_4]) ).

fof(f_1820_1,plain,
    ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)),
    inference(fof_nnf,[status(thm)],[fact_MGT__def]) ).

fof(f_1820_2,plain,
    ! [U_6070] : c_Hoare__Mirabelle_OMGT(U_6070) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_6070),c_Natural_Oevalc(U_6070)),
    inference(variable_rename,[status(thm)],[f_1820_1]) ).

fof(f_1820_3,plain,
    ! [U_6070] : c_Hoare__Mirabelle_OMGT(U_6070) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_6070),c_Natural_Oevalc(U_6070)),
    inference(definitional_conversion,[status(esa)],[f_1820_2]) ).

cnf(f_1820_4,plain,
    c_Hoare__Mirabelle_OMGT(U_6070) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_6070),c_Natural_Oevalc(U_6070)),
    inference(clausify,[status(thm)],[f_1820_3]) ).

fof(f_1821_1,plain,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    inference(fof_nnf,[status(thm)],[fact_min__Suc__number__of]) ).

fof(f_1821_2,plain,
    ! [U_6072,U_6071] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6071)),hAPP(c_Nat_OSuc,U_6072)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6071))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),U_6072)))),
    inference(variable_rename,[status(thm)],[f_1821_1]) ).

fof(f_1821_3,plain,
    ! [U_6072,U_6071] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6071)),hAPP(c_Nat_OSuc,U_6072)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6071))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),U_6072)))),
    inference(definitional_conversion,[status(esa)],[f_1821_2]) ).

cnf(f_1821_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6071)),hAPP(c_Nat_OSuc,U_6072)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6071))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),U_6072)))),
    inference(clausify,[status(thm)],[f_1821_3]) ).

fof(f_1822_1,plain,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_min__number__of__Suc]) ).

fof(f_1822_2,plain,
    ! [U_6074,U_6073] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6073)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6074)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6074))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6073)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1822_1]) ).

fof(f_1822_3,plain,
    ! [U_6074,U_6073] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6073)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6074)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6074))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6073)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1822_2]) ).

cnf(f_1822_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6073)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6074)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6074))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6073)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1822_3]) ).

fof(f_1823_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_prod__caseI]) ).

fof(f_1823_2,plain,
    ! [U_6079,U_6078,U_6077,U_6076,U_6075] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6078,U_6079,tc_HOL_Obool),U_6075),hAPP(hAPP(c_Product__Type_OPair(U_6078,U_6079),U_6076),U_6077)))
      | ~ hBOOL(hAPP(hAPP(U_6075,U_6076),U_6077)) ),
    inference(variable_rename,[status(thm)],[f_1823_1]) ).

fof(f_1823_3,plain,
    ! [U_6075,U_6076,U_6077,U_6078,U_6079] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6078,U_6079,tc_HOL_Obool),U_6075),hAPP(hAPP(c_Product__Type_OPair(U_6078,U_6079),U_6076),U_6077)))
      | ~ hBOOL(hAPP(hAPP(U_6075,U_6076),U_6077)) ),
    inference(definitional_conversion,[status(esa)],[f_1823_2]) ).

cnf(f_1823_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6078,U_6079,tc_HOL_Obool),U_6075),hAPP(hAPP(c_Product__Type_OPair(U_6078,U_6079),U_6076),U_6077)))
    | ~ hBOOL(hAPP(hAPP(U_6075,U_6076),U_6077)) ),
    inference(clausify,[status(thm)],[f_1823_3]) ).

fof(f_1824_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_splitI]) ).

fof(f_1824_2,plain,
    ! [U_6084,U_6083,U_6082,U_6081,U_6080] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6083,U_6084,tc_HOL_Obool),U_6080),hAPP(hAPP(c_Product__Type_OPair(U_6083,U_6084),U_6081),U_6082)))
      | ~ hBOOL(hAPP(hAPP(U_6080,U_6081),U_6082)) ),
    inference(variable_rename,[status(thm)],[f_1824_1]) ).

fof(f_1824_3,plain,
    ! [U_6081,U_6080,U_6082,U_6083,U_6084] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6083,U_6084,tc_HOL_Obool),U_6080),hAPP(hAPP(c_Product__Type_OPair(U_6083,U_6084),U_6081),U_6082)))
      | ~ hBOOL(hAPP(hAPP(U_6080,U_6081),U_6082)) ),
    inference(definitional_conversion,[status(esa)],[f_1824_2]) ).

cnf(f_1824_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6083,U_6084,tc_HOL_Obool),U_6080),hAPP(hAPP(c_Product__Type_OPair(U_6083,U_6084),U_6081),U_6082)))
    | ~ hBOOL(hAPP(hAPP(U_6080,U_6081),U_6082)) ),
    inference(clausify,[status(thm)],[f_1824_3]) ).

fof(f_1825_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_splitD]) ).

fof(f_1825_2,plain,
    ! [U_6089,U_6088,U_6087,U_6086,U_6085] :
      ( hBOOL(hAPP(hAPP(U_6087,U_6088),U_6089))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6085,U_6086,tc_HOL_Obool),U_6087),hAPP(hAPP(c_Product__Type_OPair(U_6085,U_6086),U_6088),U_6089))) ),
    inference(variable_rename,[status(thm)],[f_1825_1]) ).

fof(f_1825_3,plain,
    ! [U_6089,U_6088,U_6087] :
      ( ! [U_6086,U_6085] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6085,U_6086,tc_HOL_Obool),U_6087),hAPP(hAPP(c_Product__Type_OPair(U_6085,U_6086),U_6088),U_6089)))
      | hBOOL(hAPP(hAPP(U_6087,U_6088),U_6089)) ),
    inference(miniscope,[status(thm)],[f_1825_2]) ).

fof(f_1825_4,plain,
    ! [U_6085,U_6086,U_6087,U_6088,U_6089] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6085,U_6086,tc_HOL_Obool),U_6087),hAPP(hAPP(c_Product__Type_OPair(U_6085,U_6086),U_6088),U_6089)))
      | hBOOL(hAPP(hAPP(U_6087,U_6088),U_6089)) ),
    inference(definitional_conversion,[status(esa)],[f_1825_3]) ).

cnf(f_1825_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6085,U_6086,tc_HOL_Obool),U_6087),hAPP(hAPP(c_Product__Type_OPair(U_6085,U_6086),U_6088),U_6089)))
    | hBOOL(hAPP(hAPP(U_6087,U_6088),U_6089)) ),
    inference(clausify,[status(thm)],[f_1825_4]) ).

fof(f_1826_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_min__0R]) ).

fof(f_1826_2,plain,
    ! [U_6090] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6090),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1826_1]) ).

fof(f_1826_3,plain,
    ! [U_6090] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6090),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1826_2]) ).

cnf(f_1826_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6090),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1826_3]) ).

fof(f_1827_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_min__0L]) ).

fof(f_1827_2,plain,
    ! [U_6091] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6091) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1827_1]) ).

fof(f_1827_3,plain,
    ! [U_6091] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6091) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1827_2]) ).

cnf(f_1827_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6091) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1827_3]) ).

fof(f_1828_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_min__Suc__Suc]) ).

fof(f_1828_2,plain,
    ! [U_6093,U_6092] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6092)),hAPP(c_Nat_OSuc,U_6093)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6092),U_6093)),
    inference(variable_rename,[status(thm)],[f_1828_1]) ).

fof(f_1828_3,plain,
    ! [U_6092,U_6093] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6092)),hAPP(c_Nat_OSuc,U_6093)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6092),U_6093)),
    inference(definitional_conversion,[status(esa)],[f_1828_2]) ).

cnf(f_1828_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6092)),hAPP(c_Nat_OSuc,U_6093)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6092),U_6093)),
    inference(clausify,[status(thm)],[f_1828_3]) ).

fof(f_1829_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left]) ).

fof(f_1829_2,plain,
    ! [U_6097,U_6096,U_6095,U_6094] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6094),U_6095),U_6096)),U_6097) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6095),U_6097)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6096),U_6097))
      | ~ class_Groups_Oordered__ab__group__add(U_6094) ),
    inference(variable_rename,[status(thm)],[f_1829_1]) ).

fof(f_1829_3,plain,
    ! [U_6094,U_6095,U_6096,U_6097] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6094),U_6095),U_6096)),U_6097) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6095),U_6097)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6096),U_6097))
      | ~ class_Groups_Oordered__ab__group__add(U_6094) ),
    inference(definitional_conversion,[status(esa)],[f_1829_2]) ).

cnf(f_1829_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6094),U_6095),U_6096)),U_6097) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6095),U_6097)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6096),U_6097))
    | ~ class_Groups_Oordered__ab__group__add(U_6094) ),
    inference(clausify,[status(thm)],[f_1829_3]) ).

fof(f_1830_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infE]) ).

fof(f_1830_2,plain,
    ! [U_6101,U_6100,U_6099,U_6098] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),U_6101))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),U_6100)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6098),U_6100),U_6101)))
      | ~ class_Orderings_Olinorder(U_6098) ),
    inference(variable_rename,[status(thm)],[f_1830_1]) ).

fof(f_1830_3,plain,
    ( ! [U_6098,U_6099,U_6100,U_6101] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),U_6101))
        | ~ sP585(U_6098,U_6099,U_6100,U_6101) )
    & ! [U_6098,U_6099,U_6100,U_6101] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),U_6100))
        | ~ sP585(U_6098,U_6099,U_6100,U_6101) )
    & ! [U_6098,U_6099,U_6100,U_6101] :
        ( sP585(U_6098,U_6099,U_6100,U_6101)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6098),U_6100),U_6101)))
        | ~ class_Orderings_Olinorder(U_6098) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP585])],[f_1830_2]) ).

cnf(f_1830_4,plain,
    ( sP585(U_6098,U_6099,U_6100,U_6101)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6098),U_6100),U_6101)))
    | ~ class_Orderings_Olinorder(U_6098) ),
    inference(clausify,[status(thm)],[f_1830_3]) ).

cnf(f_1830_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),U_6100))
    | ~ sP585(U_6098,U_6099,U_6100,U_6101) ),
    inference(clausify,[status(thm)],[f_1830_3]) ).

cnf(f_1830_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6098),U_6099),U_6101))
    | ~ sP585(U_6098,U_6099,U_6100,U_6101) ),
    inference(clausify,[status(thm)],[f_1830_3]) ).

fof(f_1831_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono]) ).

fof(f_1831_2,plain,
    ! [U_6106,U_6105,U_6104,U_6103,U_6102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6102),U_6103),U_6105)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6102),U_6104),U_6106)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),U_6105),U_6106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),U_6103),U_6104))
      | ~ class_Orderings_Olinorder(U_6102) ),
    inference(variable_rename,[status(thm)],[f_1831_1]) ).

fof(f_1831_3,plain,
    ! [U_6103,U_6102,U_6104,U_6105,U_6106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6102),U_6103),U_6105)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6102),U_6104),U_6106)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),U_6105),U_6106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),U_6103),U_6104))
      | ~ class_Orderings_Olinorder(U_6102) ),
    inference(definitional_conversion,[status(esa)],[f_1831_2]) ).

cnf(f_1831_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6102),U_6103),U_6105)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6102),U_6104),U_6106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),U_6105),U_6106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6102),U_6103),U_6104))
    | ~ class_Orderings_Olinorder(U_6102) ),
    inference(clausify,[status(thm)],[f_1831_3]) ).

fof(f_1832_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest]) ).

fof(f_1832_2,plain,
    ! [U_6110,U_6109,U_6108,U_6107] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6107),U_6109),U_6110)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),U_6110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),U_6109))
      | ~ class_Orderings_Olinorder(U_6107) ),
    inference(variable_rename,[status(thm)],[f_1832_1]) ).

fof(f_1832_3,plain,
    ! [U_6107,U_6108,U_6109,U_6110] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6107),U_6109),U_6110)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),U_6110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),U_6109))
      | ~ class_Orderings_Olinorder(U_6107) ),
    inference(definitional_conversion,[status(esa)],[f_1832_2]) ).

cnf(f_1832_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6107),U_6109),U_6110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),U_6110))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6107),U_6108),U_6109))
    | ~ class_Orderings_Olinorder(U_6107) ),
    inference(clausify,[status(thm)],[f_1832_3]) ).

fof(f_1833_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI]) ).

fof(f_1833_2,plain,
    ! [U_6114,U_6113,U_6112,U_6111] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6111),U_6113),U_6114)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),U_6114))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),U_6113))
      | ~ class_Orderings_Olinorder(U_6111) ),
    inference(variable_rename,[status(thm)],[f_1833_1]) ).

fof(f_1833_3,plain,
    ! [U_6111,U_6112,U_6113,U_6114] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6111),U_6113),U_6114)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),U_6114))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),U_6113))
      | ~ class_Orderings_Olinorder(U_6111) ),
    inference(definitional_conversion,[status(esa)],[f_1833_2]) ).

cnf(f_1833_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6111),U_6113),U_6114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),U_6114))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6111),U_6112),U_6113))
    | ~ class_Orderings_Olinorder(U_6111) ),
    inference(clausify,[status(thm)],[f_1833_3]) ).

fof(f_1834_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2]) ).

fof(f_1834_2,plain,
    ! [U_6117,U_6116,U_6115] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6115),U_6117),U_6116) = U_6116
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6115),U_6116),U_6117))
      | ~ class_Orderings_Olinorder(U_6115) ),
    inference(variable_rename,[status(thm)],[f_1834_1]) ).

fof(f_1834_3,plain,
    ! [U_6115,U_6116,U_6117] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6115),U_6117),U_6116) = U_6116
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6115),U_6116),U_6117))
      | ~ class_Orderings_Olinorder(U_6115) ),
    inference(definitional_conversion,[status(esa)],[f_1834_2]) ).

cnf(f_1834_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6115),U_6117),U_6116) = U_6116
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6115),U_6116),U_6117))
    | ~ class_Orderings_Olinorder(U_6115) ),
    inference(clausify,[status(thm)],[f_1834_3]) ).

fof(f_1835_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1]) ).

fof(f_1835_2,plain,
    ! [U_6120,U_6119,U_6118] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6118),U_6119),U_6120) = U_6119
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
      | ~ class_Orderings_Olinorder(U_6118) ),
    inference(variable_rename,[status(thm)],[f_1835_1]) ).

fof(f_1835_3,plain,
    ! [U_6118,U_6119,U_6120] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6118),U_6119),U_6120) = U_6119
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
      | ~ class_Orderings_Olinorder(U_6118) ),
    inference(definitional_conversion,[status(esa)],[f_1835_2]) ).

cnf(f_1835_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6118),U_6119),U_6120) = U_6119
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
    | ~ class_Orderings_Olinorder(U_6118) ),
    inference(clausify,[status(thm)],[f_1835_3]) ).

fof(f_1836_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2]) ).

fof(f_1836_2,plain,
    ! [U_6124,U_6123,U_6122,U_6121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6121),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6121),U_6124),U_6122)),U_6123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6121),U_6122),U_6123))
      | ~ class_Orderings_Olinorder(U_6121) ),
    inference(variable_rename,[status(thm)],[f_1836_1]) ).

fof(f_1836_3,plain,
    ! [U_6121,U_6122,U_6123,U_6124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6121),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6121),U_6124),U_6122)),U_6123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6121),U_6122),U_6123))
      | ~ class_Orderings_Olinorder(U_6121) ),
    inference(definitional_conversion,[status(esa)],[f_1836_2]) ).

cnf(f_1836_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6121),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6121),U_6124),U_6122)),U_6123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6121),U_6122),U_6123))
    | ~ class_Orderings_Olinorder(U_6121) ),
    inference(clausify,[status(thm)],[f_1836_3]) ).

fof(f_1837_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1]) ).

fof(f_1837_2,plain,
    ! [U_6128,U_6127,U_6126,U_6125] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6125),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6125),U_6126),U_6128)),U_6127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6125),U_6126),U_6127))
      | ~ class_Orderings_Olinorder(U_6125) ),
    inference(variable_rename,[status(thm)],[f_1837_1]) ).

fof(f_1837_3,plain,
    ! [U_6125,U_6126,U_6127,U_6128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6125),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6125),U_6126),U_6128)),U_6127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6125),U_6126),U_6127))
      | ~ class_Orderings_Olinorder(U_6125) ),
    inference(definitional_conversion,[status(esa)],[f_1837_2]) ).

cnf(f_1837_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6125),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6125),U_6126),U_6128)),U_6127))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6125),U_6126),U_6127))
    | ~ class_Orderings_Olinorder(U_6125) ),
    inference(clausify,[status(thm)],[f_1837_3]) ).

fof(f_1838_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff]) ).

fof(f_1838_2,plain,
    ! [U_6132,U_6131,U_6130,U_6129] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6129),U_6131),U_6132)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6132))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6131)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6132))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6131)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6129),U_6131),U_6132))) ) )
      | ~ class_Orderings_Olinorder(U_6129) ),
    inference(variable_rename,[status(thm)],[f_1838_1]) ).

fof(f_1838_3,plain,
    ( ! [U_6129,U_6130,U_6131,U_6132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6132))
        | ~ sP586(U_6129,U_6130,U_6131,U_6132) )
    & ! [U_6129,U_6130,U_6131,U_6132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6131))
        | ~ sP586(U_6129,U_6130,U_6131,U_6132) )
    & ! [U_6129,U_6130,U_6131,U_6132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6129),U_6131),U_6132)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6132))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6131))
        | ~ sP587(U_6129,U_6130,U_6131,U_6132) )
    & ! [U_6129,U_6130,U_6131,U_6132] :
        ( sP586(U_6129,U_6130,U_6131,U_6132)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6129),U_6131),U_6132)))
        | ~ sP587(U_6129,U_6130,U_6131,U_6132) )
    & ! [U_6129,U_6130,U_6131,U_6132] :
        ( sP587(U_6129,U_6130,U_6131,U_6132)
        | ~ class_Orderings_Olinorder(U_6129) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP586,sP587])],[f_1838_2]) ).

cnf(f_1838_4,plain,
    ( sP587(U_6129,U_6130,U_6131,U_6132)
    | ~ class_Orderings_Olinorder(U_6129) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_5,plain,
    ( sP586(U_6129,U_6130,U_6131,U_6132)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6129),U_6131),U_6132)))
    | ~ sP587(U_6129,U_6130,U_6131,U_6132) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6129),U_6131),U_6132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6131))
    | ~ sP587(U_6129,U_6130,U_6131,U_6132) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6131))
    | ~ sP586(U_6129,U_6130,U_6131,U_6132) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6130),U_6132))
    | ~ sP586(U_6129,U_6130,U_6131,U_6132) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

fof(f_1839_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) != V_x_2 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf]) ).

fof(f_1839_2,plain,
    ! [U_6135,U_6134,U_6133] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6133),U_6134),U_6135))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6133),U_6134),U_6135) != U_6134 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6133),U_6134),U_6135) = U_6134
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6133),U_6134),U_6135)) ) )
      | ~ class_Orderings_Olinorder(U_6133) ),
    inference(variable_rename,[status(thm)],[f_1839_1]) ).

fof(f_1839_3,plain,
    ( ! [U_6135,U_6134,U_6133] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6133),U_6134),U_6135))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6133),U_6134),U_6135) != U_6134
        | ~ sP588(U_6135,U_6134,U_6133) )
    & ! [U_6135,U_6134,U_6133] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6133),U_6134),U_6135) = U_6134
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6133),U_6134),U_6135))
        | ~ sP588(U_6135,U_6134,U_6133) )
    & ! [U_6135,U_6134,U_6133] :
        ( sP588(U_6135,U_6134,U_6133)
        | ~ class_Orderings_Olinorder(U_6133) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP588])],[f_1839_2]) ).

cnf(f_1839_4,plain,
    ( sP588(U_6135,U_6134,U_6133)
    | ~ class_Orderings_Olinorder(U_6133) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

cnf(f_1839_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6133),U_6134),U_6135) = U_6134
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6133),U_6134),U_6135))
    | ~ sP588(U_6135,U_6134,U_6133) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

cnf(f_1839_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6133),U_6134),U_6135))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6133),U_6134),U_6135) != U_6134
    | ~ sP588(U_6135,U_6134,U_6133) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

fof(f_1840_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2]) ).

fof(f_1840_2,plain,
    ! [U_6138,U_6137,U_6136] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6136),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6136),U_6137),U_6138)),U_6138))
      | ~ class_Orderings_Olinorder(U_6136) ),
    inference(variable_rename,[status(thm)],[f_1840_1]) ).

fof(f_1840_3,plain,
    ! [U_6137,U_6136,U_6138] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6136),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6136),U_6137),U_6138)),U_6138))
      | ~ class_Orderings_Olinorder(U_6136) ),
    inference(definitional_conversion,[status(esa)],[f_1840_2]) ).

cnf(f_1840_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6136),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6136),U_6137),U_6138)),U_6138))
    | ~ class_Orderings_Olinorder(U_6136) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

fof(f_1841_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1]) ).

fof(f_1841_2,plain,
    ! [U_6141,U_6140,U_6139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6139),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6139),U_6140),U_6141)),U_6140))
      | ~ class_Orderings_Olinorder(U_6139) ),
    inference(variable_rename,[status(thm)],[f_1841_1]) ).

fof(f_1841_3,plain,
    ! [U_6139,U_6140,U_6141] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6139),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6139),U_6140),U_6141)),U_6140))
      | ~ class_Orderings_Olinorder(U_6139) ),
    inference(definitional_conversion,[status(esa)],[f_1841_2]) ).

cnf(f_1841_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6139),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6139),U_6140),U_6141)),U_6140))
    | ~ class_Orderings_Olinorder(U_6139) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

fof(f_1842_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj]) ).

fof(f_1842_2,plain,
    ! [U_6145,U_6144,U_6143,U_6142] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6142),U_6143),U_6144)),U_6145))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6144),U_6145))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6143),U_6145)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6144),U_6145))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6143),U_6145))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6142),U_6143),U_6144)),U_6145)) ) )
      | ~ class_Orderings_Olinorder(U_6142) ),
    inference(variable_rename,[status(thm)],[f_1842_1]) ).

fof(f_1842_3,plain,
    ( ! [U_6142,U_6143,U_6144,U_6145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6144),U_6145))
        | ~ sP589(U_6142,U_6143,U_6144,U_6145) )
    & ! [U_6142,U_6143,U_6144,U_6145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6143),U_6145))
        | ~ sP589(U_6142,U_6143,U_6144,U_6145) )
    & ! [U_6142,U_6143,U_6144,U_6145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6142),U_6143),U_6144)),U_6145))
        | sP589(U_6142,U_6143,U_6144,U_6145)
        | ~ sP590(U_6142,U_6143,U_6144,U_6145) )
    & ! [U_6142,U_6143,U_6144,U_6145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6144),U_6145))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6143),U_6145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6142),U_6143),U_6144)),U_6145))
        | ~ sP590(U_6142,U_6143,U_6144,U_6145) )
    & ! [U_6142,U_6143,U_6144,U_6145] :
        ( sP590(U_6142,U_6143,U_6144,U_6145)
        | ~ class_Orderings_Olinorder(U_6142) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP589,sP590])],[f_1842_2]) ).

cnf(f_1842_4,plain,
    ( sP590(U_6142,U_6143,U_6144,U_6145)
    | ~ class_Orderings_Olinorder(U_6142) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

cnf(f_1842_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6144),U_6145))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6143),U_6145))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6142),U_6143),U_6144)),U_6145))
    | ~ sP590(U_6142,U_6143,U_6144,U_6145) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

cnf(f_1842_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6142),U_6143),U_6144)),U_6145))
    | sP589(U_6142,U_6143,U_6144,U_6145)
    | ~ sP590(U_6142,U_6143,U_6144,U_6145) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

cnf(f_1842_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6143),U_6145))
    | ~ sP589(U_6142,U_6143,U_6144,U_6145) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

cnf(f_1842_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6142),U_6144),U_6145))
    | ~ sP589(U_6142,U_6143,U_6144,U_6145) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

fof(f_1843_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc]) ).

fof(f_1843_2,plain,
    ! [U_6149,U_6148,U_6147,U_6146] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6147),U_6148)),U_6149) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6147),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6148),U_6149))
      | ~ class_Orderings_Olinorder(U_6146) ),
    inference(variable_rename,[status(thm)],[f_1843_1]) ).

fof(f_1843_3,plain,
    ! [U_6148,U_6149,U_6146,U_6147] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6147),U_6148)),U_6149) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6147),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6148),U_6149))
      | ~ class_Orderings_Olinorder(U_6146) ),
    inference(definitional_conversion,[status(esa)],[f_1843_2]) ).

cnf(f_1843_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6147),U_6148)),U_6149) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6147),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6146),U_6148),U_6149))
    | ~ class_Orderings_Olinorder(U_6146) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

fof(f_1844_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc]) ).

fof(f_1844_2,plain,
    ! [U_6153,U_6152,U_6151,U_6150] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6151),U_6152)),U_6153) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6151),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6152),U_6153))
      | ~ class_Orderings_Olinorder(U_6150) ),
    inference(variable_rename,[status(thm)],[f_1844_1]) ).

fof(f_1844_3,plain,
    ! [U_6150,U_6151,U_6152,U_6153] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6151),U_6152)),U_6153) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6151),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6152),U_6153))
      | ~ class_Orderings_Olinorder(U_6150) ),
    inference(definitional_conversion,[status(esa)],[f_1844_2]) ).

cnf(f_1844_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6151),U_6152)),U_6153) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6151),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6150),U_6152),U_6153))
    | ~ class_Orderings_Olinorder(U_6150) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

fof(f_1845_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute]) ).

fof(f_1845_2,plain,
    ! [U_6157,U_6156,U_6155,U_6154] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6155),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6156),U_6157)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6156),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6155),U_6157))
      | ~ class_Orderings_Olinorder(U_6154) ),
    inference(variable_rename,[status(thm)],[f_1845_1]) ).

fof(f_1845_3,plain,
    ! [U_6154,U_6155,U_6156,U_6157] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6155),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6156),U_6157)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6156),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6155),U_6157))
      | ~ class_Orderings_Olinorder(U_6154) ),
    inference(definitional_conversion,[status(esa)],[f_1845_2]) ).

cnf(f_1845_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6155),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6156),U_6157)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6156),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6154),U_6155),U_6157))
    | ~ class_Orderings_Olinorder(U_6154) ),
    inference(clausify,[status(thm)],[f_1845_3]) ).

fof(f_1846_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute]) ).

fof(f_1846_2,plain,
    ! [U_6161,U_6160,U_6159,U_6158] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6159),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6160),U_6161)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6160),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6159),U_6161))
      | ~ class_Orderings_Olinorder(U_6158) ),
    inference(variable_rename,[status(thm)],[f_1846_1]) ).

fof(f_1846_3,plain,
    ! [U_6158,U_6159,U_6160,U_6161] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6159),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6160),U_6161)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6160),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6159),U_6161))
      | ~ class_Orderings_Olinorder(U_6158) ),
    inference(definitional_conversion,[status(esa)],[f_1846_2]) ).

cnf(f_1846_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6159),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6160),U_6161)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6160),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6158),U_6159),U_6161))
    | ~ class_Orderings_Olinorder(U_6158) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

fof(f_1847_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem]) ).

fof(f_1847_2,plain,
    ! [U_6164,U_6163,U_6162] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),U_6164)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),U_6164)
      | ~ class_Orderings_Olinorder(U_6162) ),
    inference(variable_rename,[status(thm)],[f_1847_1]) ).

fof(f_1847_3,plain,
    ! [U_6162,U_6163,U_6164] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),U_6164)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),U_6164)
      | ~ class_Orderings_Olinorder(U_6162) ),
    inference(definitional_conversion,[status(esa)],[f_1847_2]) ).

cnf(f_1847_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),U_6164)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6162),U_6163),U_6164)
    | ~ class_Orderings_Olinorder(U_6162) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

fof(f_1848_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem]) ).

fof(f_1848_2,plain,
    ! [U_6167,U_6166,U_6165] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),U_6167)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),U_6167)
      | ~ class_Orderings_Olinorder(U_6165) ),
    inference(variable_rename,[status(thm)],[f_1848_1]) ).

fof(f_1848_3,plain,
    ! [U_6165,U_6166,U_6167] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),U_6167)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),U_6167)
      | ~ class_Orderings_Olinorder(U_6165) ),
    inference(definitional_conversion,[status(esa)],[f_1848_2]) ).

cnf(f_1848_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),U_6167)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6165),U_6166),U_6167)
    | ~ class_Orderings_Olinorder(U_6165) ),
    inference(clausify,[status(thm)],[f_1848_3]) ).

fof(f_1849_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute]) ).

fof(f_1849_2,plain,
    ! [U_6170,U_6169,U_6168] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6168),U_6169),U_6170) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6168),U_6170),U_6169)
      | ~ class_Orderings_Olinorder(U_6168) ),
    inference(variable_rename,[status(thm)],[f_1849_1]) ).

fof(f_1849_3,plain,
    ! [U_6168,U_6169,U_6170] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6168),U_6169),U_6170) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6168),U_6170),U_6169)
      | ~ class_Orderings_Olinorder(U_6168) ),
    inference(definitional_conversion,[status(esa)],[f_1849_2]) ).

cnf(f_1849_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6168),U_6169),U_6170) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6168),U_6170),U_6169)
    | ~ class_Orderings_Olinorder(U_6168) ),
    inference(clausify,[status(thm)],[f_1849_3]) ).

fof(f_1850_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute]) ).

fof(f_1850_2,plain,
    ! [U_6173,U_6172,U_6171] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6171),U_6172),U_6173) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6171),U_6173),U_6172)
      | ~ class_Orderings_Olinorder(U_6171) ),
    inference(variable_rename,[status(thm)],[f_1850_1]) ).

fof(f_1850_3,plain,
    ! [U_6171,U_6172,U_6173] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6171),U_6172),U_6173) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6171),U_6173),U_6172)
      | ~ class_Orderings_Olinorder(U_6171) ),
    inference(definitional_conversion,[status(esa)],[f_1850_2]) ).

cnf(f_1850_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6171),U_6172),U_6173) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6171),U_6173),U_6172)
    | ~ class_Orderings_Olinorder(U_6171) ),
    inference(clausify,[status(thm)],[f_1850_3]) ).

fof(f_1851_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem]) ).

fof(f_1851_2,plain,
    ! [U_6175,U_6174] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),U_6175),U_6175) = U_6175
      | ~ class_Orderings_Olinorder(U_6174) ),
    inference(variable_rename,[status(thm)],[f_1851_1]) ).

fof(f_1851_3,plain,
    ! [U_6174,U_6175] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),U_6175),U_6175) = U_6175
      | ~ class_Orderings_Olinorder(U_6174) ),
    inference(definitional_conversion,[status(esa)],[f_1851_2]) ).

cnf(f_1851_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),U_6175),U_6175) = U_6175
    | ~ class_Orderings_Olinorder(U_6174) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

fof(f_1852_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left]) ).

fof(f_1852_2,plain,
    ! [U_6179,U_6178,U_6177,U_6176] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6176),U_6177),U_6178)),U_6179) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),U_6177),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),U_6178),U_6179))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6176) ),
    inference(variable_rename,[status(thm)],[f_1852_1]) ).

fof(f_1852_3,plain,
    ! [U_6176,U_6177,U_6178,U_6179] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6176),U_6177),U_6178)),U_6179) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),U_6177),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),U_6178),U_6179))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6176) ),
    inference(definitional_conversion,[status(esa)],[f_1852_2]) ).

cnf(f_1852_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6176),U_6177),U_6178)),U_6179) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),U_6177),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),U_6178),U_6179))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6176) ),
    inference(clausify,[status(thm)],[f_1852_3]) ).

fof(f_1853_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1]) ).

fof(f_1853_2,plain,
    ! [U_6183,U_6182,U_6181,U_6180] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6180),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6180),U_6181),U_6183)),U_6182))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6180),U_6181),U_6182))
      | ~ class_Orderings_Olinorder(U_6180) ),
    inference(variable_rename,[status(thm)],[f_1853_1]) ).

fof(f_1853_3,plain,
    ! [U_6180,U_6181,U_6182,U_6183] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6180),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6180),U_6181),U_6183)),U_6182))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6180),U_6181),U_6182))
      | ~ class_Orderings_Olinorder(U_6180) ),
    inference(definitional_conversion,[status(esa)],[f_1853_2]) ).

cnf(f_1853_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6180),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6180),U_6181),U_6183)),U_6182))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6180),U_6181),U_6182))
    | ~ class_Orderings_Olinorder(U_6180) ),
    inference(clausify,[status(thm)],[f_1853_3]) ).

fof(f_1854_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2]) ).

fof(f_1854_2,plain,
    ! [U_6187,U_6186,U_6185,U_6184] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6184),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6184),U_6187),U_6185)),U_6186))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6184),U_6185),U_6186))
      | ~ class_Orderings_Olinorder(U_6184) ),
    inference(variable_rename,[status(thm)],[f_1854_1]) ).

fof(f_1854_3,plain,
    ! [U_6184,U_6185,U_6186,U_6187] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6184),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6184),U_6187),U_6185)),U_6186))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6184),U_6185),U_6186))
      | ~ class_Orderings_Olinorder(U_6184) ),
    inference(definitional_conversion,[status(esa)],[f_1854_2]) ).

cnf(f_1854_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6184),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6184),U_6187),U_6185)),U_6186))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6184),U_6185),U_6186))
    | ~ class_Orderings_Olinorder(U_6184) ),
    inference(clausify,[status(thm)],[f_1854_3]) ).

fof(f_1855_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj]) ).

fof(f_1855_2,plain,
    ! [U_6191,U_6190,U_6189,U_6188] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6188),U_6189),U_6190)),U_6191))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6190),U_6191))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6189),U_6191)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6190),U_6191))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6189),U_6191))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6188),U_6189),U_6190)),U_6191)) ) )
      | ~ class_Orderings_Olinorder(U_6188) ),
    inference(variable_rename,[status(thm)],[f_1855_1]) ).

fof(f_1855_3,plain,
    ( ! [U_6188,U_6189,U_6190,U_6191] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6190),U_6191))
        | ~ sP591(U_6188,U_6189,U_6190,U_6191) )
    & ! [U_6188,U_6189,U_6190,U_6191] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6189),U_6191))
        | ~ sP591(U_6188,U_6189,U_6190,U_6191) )
    & ! [U_6188,U_6189,U_6190,U_6191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6188),U_6189),U_6190)),U_6191))
        | sP591(U_6188,U_6189,U_6190,U_6191)
        | ~ sP592(U_6188,U_6189,U_6190,U_6191) )
    & ! [U_6188,U_6189,U_6190,U_6191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6190),U_6191))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6189),U_6191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6188),U_6189),U_6190)),U_6191))
        | ~ sP592(U_6188,U_6189,U_6190,U_6191) )
    & ! [U_6188,U_6189,U_6190,U_6191] :
        ( sP592(U_6188,U_6189,U_6190,U_6191)
        | ~ class_Orderings_Olinorder(U_6188) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP591,sP592])],[f_1855_2]) ).

cnf(f_1855_4,plain,
    ( sP592(U_6188,U_6189,U_6190,U_6191)
    | ~ class_Orderings_Olinorder(U_6188) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6190),U_6191))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6189),U_6191))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6188),U_6189),U_6190)),U_6191))
    | ~ sP592(U_6188,U_6189,U_6190,U_6191) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6188),U_6189),U_6190)),U_6191))
    | sP591(U_6188,U_6189,U_6190,U_6191)
    | ~ sP592(U_6188,U_6189,U_6190,U_6191) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6189),U_6191))
    | ~ sP591(U_6188,U_6189,U_6190,U_6191) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),U_6190),U_6191))
    | ~ sP591(U_6188,U_6189,U_6190,U_6191) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

fof(f_1856_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj]) ).

fof(f_1856_2,plain,
    ! [U_6195,U_6194,U_6193,U_6192] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6192),U_6194),U_6195)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6195))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6194)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6195))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6194)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6192),U_6194),U_6195))) ) )
      | ~ class_Orderings_Olinorder(U_6192) ),
    inference(variable_rename,[status(thm)],[f_1856_1]) ).

fof(f_1856_3,plain,
    ( ! [U_6194,U_6195,U_6193,U_6192] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6195))
        | ~ sP593(U_6194,U_6195,U_6193,U_6192) )
    & ! [U_6194,U_6195,U_6193,U_6192] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6194))
        | ~ sP593(U_6194,U_6195,U_6193,U_6192) )
    & ! [U_6194,U_6195,U_6193,U_6192] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6192),U_6194),U_6195)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6195))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6194))
        | ~ sP594(U_6194,U_6195,U_6193,U_6192) )
    & ! [U_6194,U_6195,U_6193,U_6192] :
        ( sP593(U_6194,U_6195,U_6193,U_6192)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6192),U_6194),U_6195)))
        | ~ sP594(U_6194,U_6195,U_6193,U_6192) )
    & ! [U_6194,U_6195,U_6193,U_6192] :
        ( sP594(U_6194,U_6195,U_6193,U_6192)
        | ~ class_Orderings_Olinorder(U_6192) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP593,sP594])],[f_1856_2]) ).

cnf(f_1856_4,plain,
    ( sP594(U_6194,U_6195,U_6193,U_6192)
    | ~ class_Orderings_Olinorder(U_6192) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_5,plain,
    ( sP593(U_6194,U_6195,U_6193,U_6192)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6192),U_6194),U_6195)))
    | ~ sP594(U_6194,U_6195,U_6193,U_6192) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6192),U_6194),U_6195)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6194))
    | ~ sP594(U_6194,U_6195,U_6193,U_6192) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6194))
    | ~ sP593(U_6194,U_6195,U_6193,U_6192) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6192),U_6193),U_6195))
    | ~ sP593(U_6194,U_6195,U_6193,U_6192) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

fof(f_1857_1,plain,
    ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i),
    inference(fof_nnf,[status(thm)],[fact_min__diff]) ).

fof(f_1857_2,plain,
    ! [U_6198,U_6197,U_6196] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6196),U_6197)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6198),U_6197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6196),U_6198)),U_6197),
    inference(variable_rename,[status(thm)],[f_1857_1]) ).

fof(f_1857_3,plain,
    ! [U_6198,U_6197,U_6196] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6196),U_6197)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6198),U_6197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6196),U_6198)),U_6197),
    inference(definitional_conversion,[status(esa)],[f_1857_2]) ).

cnf(f_1857_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6196),U_6197)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6198),U_6197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6196),U_6198)),U_6197),
    inference(clausify,[status(thm)],[f_1857_3]) ).

fof(f_1858_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).

fof(f_1858_2,plain,
    ! [U_6205,U_6204,U_6203,U_6202,U_6201,U_6200,U_6199] :
      ( hBOOL(hAPP(hAPP(hAPP(U_6202,U_6203),U_6204),U_6205))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6199,U_6200,tc_fun(U_6201,tc_HOL_Obool)),U_6202),hAPP(hAPP(c_Product__Type_OPair(U_6199,U_6200),U_6203),U_6204)),U_6205)) ),
    inference(variable_rename,[status(thm)],[f_1858_1]) ).

fof(f_1858_3,plain,
    ! [U_6205,U_6204,U_6203,U_6202] :
      ( ! [U_6201,U_6200,U_6199] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6199,U_6200,tc_fun(U_6201,tc_HOL_Obool)),U_6202),hAPP(hAPP(c_Product__Type_OPair(U_6199,U_6200),U_6203),U_6204)),U_6205))
      | hBOOL(hAPP(hAPP(hAPP(U_6202,U_6203),U_6204),U_6205)) ),
    inference(miniscope,[status(thm)],[f_1858_2]) ).

fof(f_1858_4,plain,
    ! [U_6199,U_6200,U_6201,U_6202,U_6203,U_6204,U_6205] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6199,U_6200,tc_fun(U_6201,tc_HOL_Obool)),U_6202),hAPP(hAPP(c_Product__Type_OPair(U_6199,U_6200),U_6203),U_6204)),U_6205))
      | hBOOL(hAPP(hAPP(hAPP(U_6202,U_6203),U_6204),U_6205)) ),
    inference(definitional_conversion,[status(esa)],[f_1858_3]) ).

cnf(f_1858_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6199,U_6200,tc_fun(U_6201,tc_HOL_Obool)),U_6202),hAPP(hAPP(c_Product__Type_OPair(U_6199,U_6200),U_6203),U_6204)),U_6205))
    | hBOOL(hAPP(hAPP(hAPP(U_6202,U_6203),U_6204),U_6205)) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

fof(f_1859_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__conv]) ).

fof(f_1859_2,plain,
    ! [U_6211,U_6210,U_6209,U_6208,U_6207,U_6206] : hAPP(c_Product__Type_Oapsnd(U_6206,U_6207,U_6208,U_6209),hAPP(hAPP(c_Product__Type_OPair(U_6208,U_6206),U_6210),U_6211)) = hAPP(hAPP(c_Product__Type_OPair(U_6208,U_6207),U_6210),hAPP(U_6209,U_6211)),
    inference(variable_rename,[status(thm)],[f_1859_1]) ).

fof(f_1859_3,plain,
    ! [U_6206,U_6207,U_6208,U_6209,U_6210,U_6211] : hAPP(c_Product__Type_Oapsnd(U_6206,U_6207,U_6208,U_6209),hAPP(hAPP(c_Product__Type_OPair(U_6208,U_6206),U_6210),U_6211)) = hAPP(hAPP(c_Product__Type_OPair(U_6208,U_6207),U_6210),hAPP(U_6209,U_6211)),
    inference(definitional_conversion,[status(esa)],[f_1859_2]) ).

cnf(f_1859_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6206,U_6207,U_6208,U_6209),hAPP(hAPP(c_Product__Type_OPair(U_6208,U_6206),U_6210),U_6211)) = hAPP(hAPP(c_Product__Type_OPair(U_6208,U_6207),U_6210),hAPP(U_6209,U_6211)),
    inference(clausify,[status(thm)],[f_1859_3]) ).

fof(f_1860_1,plain,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_fst__apsnd]) ).

fof(f_1860_2,plain,
    ! [U_6216,U_6215,U_6214,U_6213,U_6212] : hAPP(c_Product__Type_Ofst(U_6212,U_6213),hAPP(c_Product__Type_Oapsnd(U_6214,U_6213,U_6212,U_6215),U_6216)) = hAPP(c_Product__Type_Ofst(U_6212,U_6214),U_6216),
    inference(variable_rename,[status(thm)],[f_1860_1]) ).

fof(f_1860_3,plain,
    ! [U_6212,U_6213,U_6214,U_6215,U_6216] : hAPP(c_Product__Type_Ofst(U_6212,U_6213),hAPP(c_Product__Type_Oapsnd(U_6214,U_6213,U_6212,U_6215),U_6216)) = hAPP(c_Product__Type_Ofst(U_6212,U_6214),U_6216),
    inference(definitional_conversion,[status(esa)],[f_1860_2]) ).

cnf(f_1860_4,plain,
    hAPP(c_Product__Type_Ofst(U_6212,U_6213),hAPP(c_Product__Type_Oapsnd(U_6214,U_6213,U_6212,U_6215),U_6216)) = hAPP(c_Product__Type_Ofst(U_6212,U_6214),U_6216),
    inference(clausify,[status(thm)],[f_1860_3]) ).

fof(f_1861_1,plain,
    ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
      ( ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
        | hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) )
      & ( hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2))
        | hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv]) ).

fof(f_1861_2,plain,
    ! [U_6222,U_6221,U_6220,U_6219,U_6218,U_6217] :
      ( ( hAPP(c_Product__Type_Oapsnd(U_6217,U_6218,U_6219,U_6220),U_6221) = hAPP(c_Product__Type_Oapsnd(U_6217,U_6218,U_6219,U_6222),U_6221)
        | hAPP(U_6220,hAPP(c_Product__Type_Osnd(U_6219,U_6217),U_6221)) != hAPP(U_6222,hAPP(c_Product__Type_Osnd(U_6219,U_6217),U_6221)) )
      & ( hAPP(U_6220,hAPP(c_Product__Type_Osnd(U_6219,U_6217),U_6221)) = hAPP(U_6222,hAPP(c_Product__Type_Osnd(U_6219,U_6217),U_6221))
        | hAPP(c_Product__Type_Oapsnd(U_6217,U_6218,U_6219,U_6220),U_6221) != hAPP(c_Product__Type_Oapsnd(U_6217,U_6218,U_6219,U_6222),U_6221) ) ),
    inference(variable_rename,[status(thm)],[f_1861_1]) ).

fof(f_1861_3,plain,
    ( ! [U_6234,U_6232,U_6230,U_6228,U_6226,U_6224] :
        ( hAPP(c_Product__Type_Oapsnd(U_6224,U_6226,U_6228,U_6230),U_6232) = hAPP(c_Product__Type_Oapsnd(U_6224,U_6226,U_6228,U_6234),U_6232)
        | hAPP(U_6230,hAPP(c_Product__Type_Osnd(U_6228,U_6224),U_6232)) != hAPP(U_6234,hAPP(c_Product__Type_Osnd(U_6228,U_6224),U_6232)) )
    & ! [U_6233,U_6231,U_6229,U_6227,U_6225,U_6223] :
        ( hAPP(U_6229,hAPP(c_Product__Type_Osnd(U_6227,U_6223),U_6231)) = hAPP(U_6233,hAPP(c_Product__Type_Osnd(U_6227,U_6223),U_6231))
        | hAPP(c_Product__Type_Oapsnd(U_6223,U_6225,U_6227,U_6229),U_6231) != hAPP(c_Product__Type_Oapsnd(U_6223,U_6225,U_6227,U_6233),U_6231) ) ),
    inference(miniscope,[status(thm)],[f_1861_2]) ).

fof(f_1861_4,plain,
    ( ! [U_6226,U_6224,U_6228,U_6230,U_6232,U_6234] :
        ( hAPP(c_Product__Type_Oapsnd(U_6224,U_6226,U_6228,U_6230),U_6232) = hAPP(c_Product__Type_Oapsnd(U_6224,U_6226,U_6228,U_6234),U_6232)
        | hAPP(U_6230,hAPP(c_Product__Type_Osnd(U_6228,U_6224),U_6232)) != hAPP(U_6234,hAPP(c_Product__Type_Osnd(U_6228,U_6224),U_6232)) )
    & ! [U_6225,U_6229,U_6223,U_6227,U_6233,U_6231] :
        ( hAPP(U_6229,hAPP(c_Product__Type_Osnd(U_6227,U_6223),U_6231)) = hAPP(U_6233,hAPP(c_Product__Type_Osnd(U_6227,U_6223),U_6231))
        | hAPP(c_Product__Type_Oapsnd(U_6223,U_6225,U_6227,U_6229),U_6231) != hAPP(c_Product__Type_Oapsnd(U_6223,U_6225,U_6227,U_6233),U_6231) ) ),
    inference(definitional_conversion,[status(esa)],[f_1861_3]) ).

cnf(f_1861_5,plain,
    ( hAPP(U_6229,hAPP(c_Product__Type_Osnd(U_6227,U_6223),U_6231)) = hAPP(U_6233,hAPP(c_Product__Type_Osnd(U_6227,U_6223),U_6231))
    | hAPP(c_Product__Type_Oapsnd(U_6223,U_6225,U_6227,U_6229),U_6231) != hAPP(c_Product__Type_Oapsnd(U_6223,U_6225,U_6227,U_6233),U_6231) ),
    inference(clausify,[status(thm)],[f_1861_4]) ).

cnf(f_1861_6,plain,
    ( hAPP(c_Product__Type_Oapsnd(U_6224,U_6226,U_6228,U_6230),U_6232) = hAPP(c_Product__Type_Oapsnd(U_6224,U_6226,U_6228,U_6234),U_6232)
    | hAPP(U_6230,hAPP(c_Product__Type_Osnd(U_6228,U_6224),U_6232)) != hAPP(U_6234,hAPP(c_Product__Type_Osnd(U_6228,U_6224),U_6232)) ),
    inference(clausify,[status(thm)],[f_1861_4]) ).

fof(f_1862_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_snd__apsnd]) ).

fof(f_1862_2,plain,
    ! [U_6239,U_6238,U_6237,U_6236,U_6235] : hAPP(c_Product__Type_Osnd(U_6235,U_6236),hAPP(c_Product__Type_Oapsnd(U_6237,U_6236,U_6235,U_6238),U_6239)) = hAPP(U_6238,hAPP(c_Product__Type_Osnd(U_6235,U_6237),U_6239)),
    inference(variable_rename,[status(thm)],[f_1862_1]) ).

fof(f_1862_3,plain,
    ! [U_6236,U_6235,U_6237,U_6238,U_6239] : hAPP(c_Product__Type_Osnd(U_6235,U_6236),hAPP(c_Product__Type_Oapsnd(U_6237,U_6236,U_6235,U_6238),U_6239)) = hAPP(U_6238,hAPP(c_Product__Type_Osnd(U_6235,U_6237),U_6239)),
    inference(definitional_conversion,[status(esa)],[f_1862_2]) ).

cnf(f_1862_4,plain,
    hAPP(c_Product__Type_Osnd(U_6235,U_6236),hAPP(c_Product__Type_Oapsnd(U_6237,U_6236,U_6235,U_6238),U_6239)) = hAPP(U_6238,hAPP(c_Product__Type_Osnd(U_6235,U_6237),U_6239)),
    inference(clausify,[status(thm)],[f_1862_3]) ).

fof(f_1863_1,plain,
    ! [V_v,V_u,T_b] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) )
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__number__of]) ).

fof(f_1863_2,plain,
    ! [U_6242,U_6241,U_6240] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242))) ) )
      | ~ class_Orderings_Oord(U_6240)
      | ~ class_Int_Onumber(U_6240) ),
    inference(variable_rename,[status(thm)],[f_1863_1]) ).

fof(f_1863_3,plain,
    ( ! [U_6240,U_6241,U_6242] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)))
        | ~ sP595(U_6240,U_6241,U_6242) )
    & ! [U_6240,U_6241,U_6242] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)))
        | ~ sP595(U_6240,U_6241,U_6242) )
    & ! [U_6240,U_6241,U_6242] :
        ( sP595(U_6240,U_6241,U_6242)
        | ~ class_Orderings_Oord(U_6240)
        | ~ class_Int_Onumber(U_6240) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP595])],[f_1863_2]) ).

cnf(f_1863_4,plain,
    ( sP595(U_6240,U_6241,U_6242)
    | ~ class_Orderings_Oord(U_6240)
    | ~ class_Int_Onumber(U_6240) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

cnf(f_1863_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)))
    | ~ sP595(U_6240,U_6241,U_6242) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

cnf(f_1863_6,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6240),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6241)),hAPP(c_Int_Onumber__class_Onumber__of(U_6240),U_6242)))
    | ~ sP595(U_6240,U_6241,U_6242) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

fof(f_1864_1,plain,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_min__Suc1]) ).

fof(f_1864_2,plain,
    ! [U_6244,U_6243] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6243)),U_6244) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6243)),U_6244),
    inference(variable_rename,[status(thm)],[f_1864_1]) ).

fof(f_1864_3,plain,
    ! [U_6244,U_6243] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6243)),U_6244) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6243)),U_6244),
    inference(definitional_conversion,[status(esa)],[f_1864_2]) ).

cnf(f_1864_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6243)),U_6244) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6243)),U_6244),
    inference(clausify,[status(thm)],[f_1864_3]) ).

fof(f_1865_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_min__Suc2]) ).

fof(f_1865_2,plain,
    ! [U_6246,U_6245] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6245),hAPP(c_Nat_OSuc,U_6246)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),U_6246)),U_6245),
    inference(variable_rename,[status(thm)],[f_1865_1]) ).

fof(f_1865_3,plain,
    ! [U_6245,U_6246] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6245),hAPP(c_Nat_OSuc,U_6246)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),U_6246)),U_6245),
    inference(definitional_conversion,[status(esa)],[f_1865_2]) ).

cnf(f_1865_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6245),hAPP(c_Nat_OSuc,U_6246)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),U_6246)),U_6245),
    inference(clausify,[status(thm)],[f_1865_3]) ).

fof(f_1866_1,plain,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_negateSnd__def]) ).

fof(f_1866_2,plain,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1866_1]) ).

cnf(f_1866_3,plain,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1866_2]) ).

fof(f_1867_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__if]) ).

fof(f_1867_2,plain,
    ! [U_6248,U_6247] :
      ( ( c_Divides_Odivmod__nat(U_6248,U_6247) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6248),U_6247),U_6247))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6248),U_6247))
        | U_6247 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(U_6248,U_6247) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6248)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6248),U_6247))
          & U_6247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(variable_rename,[status(thm)],[f_1867_1]) ).

fof(f_1867_3,plain,
    ( ! [U_6252,U_6250] :
        ( c_Divides_Odivmod__nat(U_6252,U_6250) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6252),U_6250),U_6250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6252),U_6250))
        | U_6250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6251,U_6249] :
        ( c_Divides_Odivmod__nat(U_6251,U_6249) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6251)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6251),U_6249))
          & U_6249 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(miniscope,[status(thm)],[f_1867_2]) ).

fof(f_1867_4,plain,
    ( ! [U_6251,U_6249] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6251),U_6249))
        | ~ sP596(U_6251,U_6249) )
    & ! [U_6251,U_6249] :
        ( U_6249 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP596(U_6251,U_6249) )
    & ! [U_6250,U_6252] :
        ( c_Divides_Odivmod__nat(U_6252,U_6250) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6252),U_6250),U_6250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6252),U_6250))
        | U_6250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6251,U_6249] :
        ( c_Divides_Odivmod__nat(U_6251,U_6249) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6251)
        | sP596(U_6251,U_6249) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP596])],[f_1867_3]) ).

cnf(f_1867_5,plain,
    ( c_Divides_Odivmod__nat(U_6251,U_6249) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6251)
    | sP596(U_6251,U_6249) ),
    inference(clausify,[status(thm)],[f_1867_4]) ).

cnf(f_1867_6,plain,
    ( c_Divides_Odivmod__nat(U_6252,U_6250) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6252),U_6250),U_6250))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6252),U_6250))
    | U_6250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1867_4]) ).

cnf(f_1867_7,plain,
    ( U_6249 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP596(U_6251,U_6249) ),
    inference(clausify,[status(thm)],[f_1867_4]) ).

cnf(f_1867_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6251),U_6249))
    | ~ sP596(U_6251,U_6249) ),
    inference(clausify,[status(thm)],[f_1867_4]) ).

fof(f_1868_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__ord__min]) ).

fof(f_1868_2,plain,
    ! [U_6253] :
      ( c_Orderings_Oord__class_Omin(U_6253) = c_Orderings_Oord_Omin(U_6253,c_Orderings_Oord__class_Oless__eq(U_6253))
      | ~ class_Orderings_Oord(U_6253) ),
    inference(variable_rename,[status(thm)],[f_1868_1]) ).

fof(f_1868_3,plain,
    ! [U_6253] :
      ( c_Orderings_Oord__class_Omin(U_6253) = c_Orderings_Oord_Omin(U_6253,c_Orderings_Oord__class_Oless__eq(U_6253))
      | ~ class_Orderings_Oord(U_6253) ),
    inference(definitional_conversion,[status(esa)],[f_1868_2]) ).

cnf(f_1868_4,plain,
    ( c_Orderings_Oord__class_Omin(U_6253) = c_Orderings_Oord_Omin(U_6253,c_Orderings_Oord__class_Oless__eq(U_6253))
    | ~ class_Orderings_Oord(U_6253) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

fof(f_1869_1,plain,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_max__number__of__Suc]) ).

fof(f_1869_2,plain,
    ! [U_6255,U_6254] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6254)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6255)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6255))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_6254))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6254)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1869_1]) ).

fof(f_1869_3,plain,
    ! [U_6255,U_6254] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6254)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6255)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6255))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_6254))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6254)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1869_2]) ).

cnf(f_1869_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6254)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6255)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6255))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_6254))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6254)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1869_3]) ).

fof(f_1870_1,plain,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    inference(fof_nnf,[status(thm)],[fact_max__Suc__number__of]) ).

fof(f_1870_2,plain,
    ! [U_6257,U_6256] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6256)),hAPP(c_Nat_OSuc,U_6257)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6256))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_6257))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),U_6257)))),
    inference(variable_rename,[status(thm)],[f_1870_1]) ).

fof(f_1870_3,plain,
    ! [U_6256,U_6257] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6256)),hAPP(c_Nat_OSuc,U_6257)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6256))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_6257))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),U_6257)))),
    inference(definitional_conversion,[status(esa)],[f_1870_2]) ).

cnf(f_1870_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6256)),hAPP(c_Nat_OSuc,U_6257)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6256))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_6257))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),U_6257)))),
    inference(clausify,[status(thm)],[f_1870_3]) ).

fof(f_1871_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_apfst__apsnd]) ).

fof(f_1871_2,plain,
    ! [U_6264,U_6263,U_6262,U_6261,U_6260,U_6259,U_6258] : hAPP(c_Product__Type_Oapfst(U_6258,U_6259,U_6260,U_6261),hAPP(c_Product__Type_Oapsnd(U_6262,U_6260,U_6258,U_6263),U_6264)) = hAPP(hAPP(c_Product__Type_OPair(U_6259,U_6260),hAPP(U_6261,hAPP(c_Product__Type_Ofst(U_6258,U_6262),U_6264))),hAPP(U_6263,hAPP(c_Product__Type_Osnd(U_6258,U_6262),U_6264))),
    inference(variable_rename,[status(thm)],[f_1871_1]) ).

fof(f_1871_3,plain,
    ! [U_6258,U_6259,U_6260,U_6261,U_6262,U_6263,U_6264] : hAPP(c_Product__Type_Oapfst(U_6258,U_6259,U_6260,U_6261),hAPP(c_Product__Type_Oapsnd(U_6262,U_6260,U_6258,U_6263),U_6264)) = hAPP(hAPP(c_Product__Type_OPair(U_6259,U_6260),hAPP(U_6261,hAPP(c_Product__Type_Ofst(U_6258,U_6262),U_6264))),hAPP(U_6263,hAPP(c_Product__Type_Osnd(U_6258,U_6262),U_6264))),
    inference(definitional_conversion,[status(esa)],[f_1871_2]) ).

cnf(f_1871_4,plain,
    hAPP(c_Product__Type_Oapfst(U_6258,U_6259,U_6260,U_6261),hAPP(c_Product__Type_Oapsnd(U_6262,U_6260,U_6258,U_6263),U_6264)) = hAPP(hAPP(c_Product__Type_OPair(U_6259,U_6260),hAPP(U_6261,hAPP(c_Product__Type_Ofst(U_6258,U_6262),U_6264))),hAPP(U_6263,hAPP(c_Product__Type_Osnd(U_6258,U_6262),U_6264))),
    inference(clausify,[status(thm)],[f_1871_3]) ).

fof(f_1872_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_apsnd__apfst]) ).

fof(f_1872_2,plain,
    ! [U_6271,U_6270,U_6269,U_6268,U_6267,U_6266,U_6265] : hAPP(c_Product__Type_Oapsnd(U_6265,U_6266,U_6267,U_6268),hAPP(c_Product__Type_Oapfst(U_6269,U_6267,U_6265,U_6270),U_6271)) = hAPP(hAPP(c_Product__Type_OPair(U_6267,U_6266),hAPP(U_6270,hAPP(c_Product__Type_Ofst(U_6269,U_6265),U_6271))),hAPP(U_6268,hAPP(c_Product__Type_Osnd(U_6269,U_6265),U_6271))),
    inference(variable_rename,[status(thm)],[f_1872_1]) ).

fof(f_1872_3,plain,
    ! [U_6265,U_6266,U_6267,U_6268,U_6269,U_6270,U_6271] : hAPP(c_Product__Type_Oapsnd(U_6265,U_6266,U_6267,U_6268),hAPP(c_Product__Type_Oapfst(U_6269,U_6267,U_6265,U_6270),U_6271)) = hAPP(hAPP(c_Product__Type_OPair(U_6267,U_6266),hAPP(U_6270,hAPP(c_Product__Type_Ofst(U_6269,U_6265),U_6271))),hAPP(U_6268,hAPP(c_Product__Type_Osnd(U_6269,U_6265),U_6271))),
    inference(definitional_conversion,[status(esa)],[f_1872_2]) ).

cnf(f_1872_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6265,U_6266,U_6267,U_6268),hAPP(c_Product__Type_Oapfst(U_6269,U_6267,U_6265,U_6270),U_6271)) = hAPP(hAPP(c_Product__Type_OPair(U_6267,U_6266),hAPP(U_6270,hAPP(c_Product__Type_Ofst(U_6269,U_6265),U_6271))),hAPP(U_6268,hAPP(c_Product__Type_Osnd(U_6269,U_6265),U_6271))),
    inference(clausify,[status(thm)],[f_1872_3]) ).

fof(f_1873_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1]) ).

fof(f_1873_2,plain,
    ! [U_6275,U_6274,U_6273,U_6272] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6272),U_6273),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6272),U_6274),U_6275)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6272),U_6273),U_6274))
      | ~ class_Orderings_Olinorder(U_6272) ),
    inference(variable_rename,[status(thm)],[f_1873_1]) ).

fof(f_1873_3,plain,
    ! [U_6272,U_6274,U_6273,U_6275] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6272),U_6273),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6272),U_6274),U_6275)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6272),U_6273),U_6274))
      | ~ class_Orderings_Olinorder(U_6272) ),
    inference(definitional_conversion,[status(esa)],[f_1873_2]) ).

cnf(f_1873_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6272),U_6273),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6272),U_6274),U_6275)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6272),U_6273),U_6274))
    | ~ class_Orderings_Olinorder(U_6272) ),
    inference(clausify,[status(thm)],[f_1873_3]) ).

fof(f_1874_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2]) ).

fof(f_1874_2,plain,
    ! [U_6279,U_6278,U_6277,U_6276] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6276),U_6279),U_6278)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),U_6278))
      | ~ class_Orderings_Olinorder(U_6276) ),
    inference(variable_rename,[status(thm)],[f_1874_1]) ).

fof(f_1874_3,plain,
    ! [U_6276,U_6277,U_6278,U_6279] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6276),U_6279),U_6278)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),U_6278))
      | ~ class_Orderings_Olinorder(U_6276) ),
    inference(definitional_conversion,[status(esa)],[f_1874_2]) ).

cnf(f_1874_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6276),U_6279),U_6278)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),U_6278))
    | ~ class_Orderings_Olinorder(U_6276) ),
    inference(clausify,[status(thm)],[f_1874_3]) ).

fof(f_1875_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj]) ).

fof(f_1875_2,plain,
    ! [U_6283,U_6282,U_6281,U_6280] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6280),U_6281),U_6282)),U_6283))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6282),U_6283))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6281),U_6283)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6282),U_6283))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6281),U_6283)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6280),U_6281),U_6282)),U_6283)) ) )
      | ~ class_Orderings_Olinorder(U_6280) ),
    inference(variable_rename,[status(thm)],[f_1875_1]) ).

fof(f_1875_3,plain,
    ( ! [U_6280,U_6281,U_6282,U_6283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6282),U_6283))
        | ~ sP597(U_6280,U_6281,U_6282,U_6283) )
    & ! [U_6280,U_6281,U_6282,U_6283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6281),U_6283))
        | ~ sP597(U_6280,U_6281,U_6282,U_6283) )
    & ! [U_6280,U_6281,U_6282,U_6283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6280),U_6281),U_6282)),U_6283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6282),U_6283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6281),U_6283))
        | ~ sP598(U_6280,U_6281,U_6282,U_6283) )
    & ! [U_6280,U_6281,U_6282,U_6283] :
        ( sP597(U_6280,U_6281,U_6282,U_6283)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6280),U_6281),U_6282)),U_6283))
        | ~ sP598(U_6280,U_6281,U_6282,U_6283) )
    & ! [U_6280,U_6281,U_6282,U_6283] :
        ( sP598(U_6280,U_6281,U_6282,U_6283)
        | ~ class_Orderings_Olinorder(U_6280) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP597,sP598])],[f_1875_2]) ).

cnf(f_1875_4,plain,
    ( sP598(U_6280,U_6281,U_6282,U_6283)
    | ~ class_Orderings_Olinorder(U_6280) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

cnf(f_1875_5,plain,
    ( sP597(U_6280,U_6281,U_6282,U_6283)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6280),U_6281),U_6282)),U_6283))
    | ~ sP598(U_6280,U_6281,U_6282,U_6283) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

cnf(f_1875_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6280),U_6281),U_6282)),U_6283))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6282),U_6283))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6281),U_6283))
    | ~ sP598(U_6280,U_6281,U_6282,U_6283) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

cnf(f_1875_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6281),U_6283))
    | ~ sP597(U_6280,U_6281,U_6282,U_6283) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

cnf(f_1875_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6280),U_6282),U_6283))
    | ~ sP597(U_6280,U_6281,U_6282,U_6283) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

fof(f_1876_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj]) ).

fof(f_1876_2,plain,
    ! [U_6287,U_6286,U_6285,U_6284] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6284),U_6286),U_6287)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6287))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6286)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6287))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6286))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6284),U_6286),U_6287))) ) )
      | ~ class_Orderings_Olinorder(U_6284) ),
    inference(variable_rename,[status(thm)],[f_1876_1]) ).

fof(f_1876_3,plain,
    ( ! [U_6287,U_6285,U_6286,U_6284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6287))
        | ~ sP599(U_6287,U_6285,U_6286,U_6284) )
    & ! [U_6287,U_6285,U_6286,U_6284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6286))
        | ~ sP599(U_6287,U_6285,U_6286,U_6284) )
    & ! [U_6287,U_6285,U_6286,U_6284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6284),U_6286),U_6287)))
        | sP599(U_6287,U_6285,U_6286,U_6284)
        | ~ sP600(U_6287,U_6285,U_6286,U_6284) )
    & ! [U_6287,U_6285,U_6286,U_6284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6287))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6286))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6284),U_6286),U_6287)))
        | ~ sP600(U_6287,U_6285,U_6286,U_6284) )
    & ! [U_6287,U_6285,U_6286,U_6284] :
        ( sP600(U_6287,U_6285,U_6286,U_6284)
        | ~ class_Orderings_Olinorder(U_6284) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP599,sP600])],[f_1876_2]) ).

cnf(f_1876_4,plain,
    ( sP600(U_6287,U_6285,U_6286,U_6284)
    | ~ class_Orderings_Olinorder(U_6284) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

cnf(f_1876_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6287))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6284),U_6286),U_6287)))
    | ~ sP600(U_6287,U_6285,U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

cnf(f_1876_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6284),U_6286),U_6287)))
    | sP599(U_6287,U_6285,U_6286,U_6284)
    | ~ sP600(U_6287,U_6285,U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

cnf(f_1876_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6286))
    | ~ sP599(U_6287,U_6285,U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

cnf(f_1876_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),U_6285),U_6287))
    | ~ sP599(U_6287,U_6285,U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

fof(f_1877_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left]) ).

fof(f_1877_2,plain,
    ! [U_6291,U_6290,U_6289,U_6288] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6288),U_6289),U_6290)),U_6291) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6288),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),U_6289),U_6291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),U_6290),U_6291))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6288) ),
    inference(variable_rename,[status(thm)],[f_1877_1]) ).

fof(f_1877_3,plain,
    ! [U_6291,U_6289,U_6290,U_6288] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6288),U_6289),U_6290)),U_6291) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6288),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),U_6289),U_6291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),U_6290),U_6291))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6288) ),
    inference(definitional_conversion,[status(esa)],[f_1877_2]) ).

cnf(f_1877_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6288),U_6289),U_6290)),U_6291) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6288),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),U_6289),U_6291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6288),U_6290),U_6291))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6288) ),
    inference(clausify,[status(thm)],[f_1877_3]) ).

fof(f_1878_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem]) ).

fof(f_1878_2,plain,
    ! [U_6293,U_6292] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6292),U_6293),U_6293) = U_6293
      | ~ class_Orderings_Olinorder(U_6292) ),
    inference(variable_rename,[status(thm)],[f_1878_1]) ).

fof(f_1878_3,plain,
    ! [U_6293,U_6292] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6292),U_6293),U_6293) = U_6293
      | ~ class_Orderings_Olinorder(U_6292) ),
    inference(definitional_conversion,[status(esa)],[f_1878_2]) ).

cnf(f_1878_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6292),U_6293),U_6293) = U_6293
    | ~ class_Orderings_Olinorder(U_6292) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

fof(f_1879_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute]) ).

fof(f_1879_2,plain,
    ! [U_6296,U_6295,U_6294] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6294),U_6295),U_6296) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6294),U_6296),U_6295)
      | ~ class_Orderings_Olinorder(U_6294) ),
    inference(variable_rename,[status(thm)],[f_1879_1]) ).

fof(f_1879_3,plain,
    ! [U_6294,U_6295,U_6296] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6294),U_6295),U_6296) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6294),U_6296),U_6295)
      | ~ class_Orderings_Olinorder(U_6294) ),
    inference(definitional_conversion,[status(esa)],[f_1879_2]) ).

cnf(f_1879_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6294),U_6295),U_6296) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6294),U_6296),U_6295)
    | ~ class_Orderings_Olinorder(U_6294) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

fof(f_1880_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute]) ).

fof(f_1880_2,plain,
    ! [U_6299,U_6298,U_6297] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6297),U_6298),U_6299) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6297),U_6299),U_6298)
      | ~ class_Orderings_Olinorder(U_6297) ),
    inference(variable_rename,[status(thm)],[f_1880_1]) ).

fof(f_1880_3,plain,
    ! [U_6297,U_6298,U_6299] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6297),U_6298),U_6299) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6297),U_6299),U_6298)
      | ~ class_Orderings_Olinorder(U_6297) ),
    inference(definitional_conversion,[status(esa)],[f_1880_2]) ).

cnf(f_1880_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6297),U_6298),U_6299) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6297),U_6299),U_6298)
    | ~ class_Orderings_Olinorder(U_6297) ),
    inference(clausify,[status(thm)],[f_1880_3]) ).

fof(f_1881_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem]) ).

fof(f_1881_2,plain,
    ! [U_6302,U_6301,U_6300] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),U_6302)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),U_6302)
      | ~ class_Orderings_Olinorder(U_6300) ),
    inference(variable_rename,[status(thm)],[f_1881_1]) ).

fof(f_1881_3,plain,
    ! [U_6300,U_6301,U_6302] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),U_6302)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),U_6302)
      | ~ class_Orderings_Olinorder(U_6300) ),
    inference(definitional_conversion,[status(esa)],[f_1881_2]) ).

cnf(f_1881_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),U_6302)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6300),U_6301),U_6302)
    | ~ class_Orderings_Olinorder(U_6300) ),
    inference(clausify,[status(thm)],[f_1881_3]) ).

fof(f_1882_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem]) ).

fof(f_1882_2,plain,
    ! [U_6305,U_6304,U_6303] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),U_6305)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),U_6305)
      | ~ class_Orderings_Olinorder(U_6303) ),
    inference(variable_rename,[status(thm)],[f_1882_1]) ).

fof(f_1882_3,plain,
    ! [U_6303,U_6304,U_6305] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),U_6305)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),U_6305)
      | ~ class_Orderings_Olinorder(U_6303) ),
    inference(definitional_conversion,[status(esa)],[f_1882_2]) ).

cnf(f_1882_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),U_6305)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6303),U_6304),U_6305)
    | ~ class_Orderings_Olinorder(U_6303) ),
    inference(clausify,[status(thm)],[f_1882_3]) ).

fof(f_1883_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute]) ).

fof(f_1883_2,plain,
    ! [U_6309,U_6308,U_6307,U_6306] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6308),U_6309)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6308),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),U_6309))
      | ~ class_Orderings_Olinorder(U_6306) ),
    inference(variable_rename,[status(thm)],[f_1883_1]) ).

fof(f_1883_3,plain,
    ! [U_6306,U_6307,U_6308,U_6309] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6308),U_6309)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6308),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),U_6309))
      | ~ class_Orderings_Olinorder(U_6306) ),
    inference(definitional_conversion,[status(esa)],[f_1883_2]) ).

cnf(f_1883_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6308),U_6309)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6308),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),U_6309))
    | ~ class_Orderings_Olinorder(U_6306) ),
    inference(clausify,[status(thm)],[f_1883_3]) ).

fof(f_1884_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute]) ).

fof(f_1884_2,plain,
    ! [U_6313,U_6312,U_6311,U_6310] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6311),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6312),U_6313)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6312),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6311),U_6313))
      | ~ class_Orderings_Olinorder(U_6310) ),
    inference(variable_rename,[status(thm)],[f_1884_1]) ).

fof(f_1884_3,plain,
    ! [U_6310,U_6311,U_6312,U_6313] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6311),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6312),U_6313)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6312),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6311),U_6313))
      | ~ class_Orderings_Olinorder(U_6310) ),
    inference(definitional_conversion,[status(esa)],[f_1884_2]) ).

cnf(f_1884_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6311),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6312),U_6313)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6312),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6310),U_6311),U_6313))
    | ~ class_Orderings_Olinorder(U_6310) ),
    inference(clausify,[status(thm)],[f_1884_3]) ).

fof(f_1885_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc]) ).

fof(f_1885_2,plain,
    ! [U_6317,U_6316,U_6315,U_6314] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),U_6316)),U_6317) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6316),U_6317))
      | ~ class_Orderings_Olinorder(U_6314) ),
    inference(variable_rename,[status(thm)],[f_1885_1]) ).

fof(f_1885_3,plain,
    ! [U_6314,U_6315,U_6316,U_6317] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),U_6316)),U_6317) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6316),U_6317))
      | ~ class_Orderings_Olinorder(U_6314) ),
    inference(definitional_conversion,[status(esa)],[f_1885_2]) ).

cnf(f_1885_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),U_6316)),U_6317) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6316),U_6317))
    | ~ class_Orderings_Olinorder(U_6314) ),
    inference(clausify,[status(thm)],[f_1885_3]) ).

fof(f_1886_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc]) ).

fof(f_1886_2,plain,
    ! [U_6321,U_6320,U_6319,U_6318] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),U_6320)),U_6321) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6320),U_6321))
      | ~ class_Orderings_Olinorder(U_6318) ),
    inference(variable_rename,[status(thm)],[f_1886_1]) ).

fof(f_1886_3,plain,
    ! [U_6318,U_6319,U_6320,U_6321] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),U_6320)),U_6321) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6320),U_6321))
      | ~ class_Orderings_Olinorder(U_6318) ),
    inference(definitional_conversion,[status(esa)],[f_1886_2]) ).

cnf(f_1886_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),U_6320)),U_6321) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6320),U_6321))
    | ~ class_Orderings_Olinorder(U_6318) ),
    inference(clausify,[status(thm)],[f_1886_3]) ).

fof(f_1887_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj]) ).

fof(f_1887_2,plain,
    ! [U_6325,U_6324,U_6323,U_6322] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6322),U_6324),U_6325)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6325))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6324)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6325))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6324))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6322),U_6324),U_6325))) ) )
      | ~ class_Orderings_Olinorder(U_6322) ),
    inference(variable_rename,[status(thm)],[f_1887_1]) ).

fof(f_1887_3,plain,
    ( ! [U_6322,U_6323,U_6324,U_6325] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6325))
        | ~ sP601(U_6322,U_6323,U_6324,U_6325) )
    & ! [U_6322,U_6323,U_6324,U_6325] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6324))
        | ~ sP601(U_6322,U_6323,U_6324,U_6325) )
    & ! [U_6322,U_6323,U_6324,U_6325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6322),U_6324),U_6325)))
        | sP601(U_6322,U_6323,U_6324,U_6325)
        | ~ sP602(U_6322,U_6323,U_6324,U_6325) )
    & ! [U_6322,U_6323,U_6324,U_6325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6325))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6324))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6322),U_6324),U_6325)))
        | ~ sP602(U_6322,U_6323,U_6324,U_6325) )
    & ! [U_6322,U_6323,U_6324,U_6325] :
        ( sP602(U_6322,U_6323,U_6324,U_6325)
        | ~ class_Orderings_Olinorder(U_6322) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP601,sP602])],[f_1887_2]) ).

cnf(f_1887_4,plain,
    ( sP602(U_6322,U_6323,U_6324,U_6325)
    | ~ class_Orderings_Olinorder(U_6322) ),
    inference(clausify,[status(thm)],[f_1887_3]) ).

cnf(f_1887_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6325))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6322),U_6324),U_6325)))
    | ~ sP602(U_6322,U_6323,U_6324,U_6325) ),
    inference(clausify,[status(thm)],[f_1887_3]) ).

cnf(f_1887_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6322),U_6324),U_6325)))
    | sP601(U_6322,U_6323,U_6324,U_6325)
    | ~ sP602(U_6322,U_6323,U_6324,U_6325) ),
    inference(clausify,[status(thm)],[f_1887_3]) ).

cnf(f_1887_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6324))
    | ~ sP601(U_6322,U_6323,U_6324,U_6325) ),
    inference(clausify,[status(thm)],[f_1887_3]) ).

cnf(f_1887_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6322),U_6323),U_6325))
    | ~ sP601(U_6322,U_6323,U_6324,U_6325) ),
    inference(clausify,[status(thm)],[f_1887_3]) ).

fof(f_1888_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__maxI1]) ).

fof(f_1888_2,plain,
    ! [U_6328,U_6327,U_6326] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6326),U_6327),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6326),U_6327),U_6328)))
      | ~ class_Orderings_Olinorder(U_6326) ),
    inference(variable_rename,[status(thm)],[f_1888_1]) ).

fof(f_1888_3,plain,
    ! [U_6327,U_6326,U_6328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6326),U_6327),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6326),U_6327),U_6328)))
      | ~ class_Orderings_Olinorder(U_6326) ),
    inference(definitional_conversion,[status(esa)],[f_1888_2]) ).

cnf(f_1888_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6326),U_6327),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6326),U_6327),U_6328)))
    | ~ class_Orderings_Olinorder(U_6326) ),
    inference(clausify,[status(thm)],[f_1888_3]) ).

fof(f_1889_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__maxI2]) ).

fof(f_1889_2,plain,
    ! [U_6331,U_6330,U_6329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),U_6330),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6329),U_6331),U_6330)))
      | ~ class_Orderings_Olinorder(U_6329) ),
    inference(variable_rename,[status(thm)],[f_1889_1]) ).

fof(f_1889_3,plain,
    ! [U_6329,U_6330,U_6331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),U_6330),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6329),U_6331),U_6330)))
      | ~ class_Orderings_Olinorder(U_6329) ),
    inference(definitional_conversion,[status(esa)],[f_1889_2]) ).

cnf(f_1889_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),U_6330),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6329),U_6331),U_6330)))
    | ~ class_Orderings_Olinorder(U_6329) ),
    inference(clausify,[status(thm)],[f_1889_3]) ).

fof(f_1890_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) != V_y_2 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup]) ).

fof(f_1890_2,plain,
    ! [U_6334,U_6333,U_6332] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6332),U_6333),U_6334))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6332),U_6333),U_6334) != U_6334 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6332),U_6333),U_6334) = U_6334
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6332),U_6333),U_6334)) ) )
      | ~ class_Orderings_Olinorder(U_6332) ),
    inference(variable_rename,[status(thm)],[f_1890_1]) ).

fof(f_1890_3,plain,
    ( ! [U_6332,U_6333,U_6334] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6332),U_6333),U_6334))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6332),U_6333),U_6334) != U_6334
        | ~ sP603(U_6332,U_6333,U_6334) )
    & ! [U_6332,U_6333,U_6334] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6332),U_6333),U_6334) = U_6334
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6332),U_6333),U_6334))
        | ~ sP603(U_6332,U_6333,U_6334) )
    & ! [U_6332,U_6333,U_6334] :
        ( sP603(U_6332,U_6333,U_6334)
        | ~ class_Orderings_Olinorder(U_6332) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP603])],[f_1890_2]) ).

cnf(f_1890_4,plain,
    ( sP603(U_6332,U_6333,U_6334)
    | ~ class_Orderings_Olinorder(U_6332) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

cnf(f_1890_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6332),U_6333),U_6334) = U_6334
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6332),U_6333),U_6334))
    | ~ sP603(U_6332,U_6333,U_6334) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

cnf(f_1890_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6332),U_6333),U_6334))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6332),U_6333),U_6334) != U_6334
    | ~ sP603(U_6332,U_6333,U_6334) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

fof(f_1891_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff]) ).

fof(f_1891_2,plain,
    ! [U_6338,U_6337,U_6336,U_6335] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6335),U_6336),U_6337)),U_6338))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6337),U_6338))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6336),U_6338)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6337),U_6338))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6336),U_6338)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6335),U_6336),U_6337)),U_6338)) ) )
      | ~ class_Orderings_Olinorder(U_6335) ),
    inference(variable_rename,[status(thm)],[f_1891_1]) ).

fof(f_1891_3,plain,
    ( ! [U_6336,U_6335,U_6337,U_6338] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6337),U_6338))
        | ~ sP604(U_6336,U_6335,U_6337,U_6338) )
    & ! [U_6336,U_6335,U_6337,U_6338] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6336),U_6338))
        | ~ sP604(U_6336,U_6335,U_6337,U_6338) )
    & ! [U_6336,U_6335,U_6337,U_6338] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6335),U_6336),U_6337)),U_6338))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6337),U_6338))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6336),U_6338))
        | ~ sP605(U_6336,U_6335,U_6337,U_6338) )
    & ! [U_6336,U_6335,U_6337,U_6338] :
        ( sP604(U_6336,U_6335,U_6337,U_6338)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6335),U_6336),U_6337)),U_6338))
        | ~ sP605(U_6336,U_6335,U_6337,U_6338) )
    & ! [U_6336,U_6335,U_6337,U_6338] :
        ( sP605(U_6336,U_6335,U_6337,U_6338)
        | ~ class_Orderings_Olinorder(U_6335) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP604,sP605])],[f_1891_2]) ).

cnf(f_1891_4,plain,
    ( sP605(U_6336,U_6335,U_6337,U_6338)
    | ~ class_Orderings_Olinorder(U_6335) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_5,plain,
    ( sP604(U_6336,U_6335,U_6337,U_6338)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6335),U_6336),U_6337)),U_6338))
    | ~ sP605(U_6336,U_6335,U_6337,U_6338) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6335),U_6336),U_6337)),U_6338))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6337),U_6338))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6336),U_6338))
    | ~ sP605(U_6336,U_6335,U_6337,U_6338) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6336),U_6338))
    | ~ sP604(U_6336,U_6335,U_6337,U_6338) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6335),U_6337),U_6338))
    | ~ sP604(U_6336,U_6335,U_6337,U_6338) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

fof(f_1892_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1]) ).

fof(f_1892_2,plain,
    ! [U_6342,U_6341,U_6340,U_6339] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6339),U_6340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6341),U_6342)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6339),U_6340),U_6341))
      | ~ class_Orderings_Olinorder(U_6339) ),
    inference(variable_rename,[status(thm)],[f_1892_1]) ).

fof(f_1892_3,plain,
    ! [U_6341,U_6340,U_6342,U_6339] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6339),U_6340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6341),U_6342)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6339),U_6340),U_6341))
      | ~ class_Orderings_Olinorder(U_6339) ),
    inference(definitional_conversion,[status(esa)],[f_1892_2]) ).

cnf(f_1892_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6339),U_6340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6341),U_6342)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6339),U_6340),U_6341))
    | ~ class_Orderings_Olinorder(U_6339) ),
    inference(clausify,[status(thm)],[f_1892_3]) ).

fof(f_1893_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2]) ).

fof(f_1893_2,plain,
    ! [U_6346,U_6345,U_6344,U_6343] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6343),U_6346),U_6345)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),U_6345))
      | ~ class_Orderings_Olinorder(U_6343) ),
    inference(variable_rename,[status(thm)],[f_1893_1]) ).

fof(f_1893_3,plain,
    ! [U_6343,U_6344,U_6345,U_6346] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6343),U_6346),U_6345)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),U_6345))
      | ~ class_Orderings_Olinorder(U_6343) ),
    inference(definitional_conversion,[status(esa)],[f_1893_2]) ).

cnf(f_1893_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6343),U_6346),U_6345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),U_6345))
    | ~ class_Orderings_Olinorder(U_6343) ),
    inference(clausify,[status(thm)],[f_1893_3]) ).

fof(f_1894_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2]) ).

fof(f_1894_2,plain,
    ! [U_6349,U_6348,U_6347] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6347),U_6348),U_6349) = U_6349
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),U_6349))
      | ~ class_Orderings_Olinorder(U_6347) ),
    inference(variable_rename,[status(thm)],[f_1894_1]) ).

fof(f_1894_3,plain,
    ! [U_6347,U_6348,U_6349] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6347),U_6348),U_6349) = U_6349
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),U_6349))
      | ~ class_Orderings_Olinorder(U_6347) ),
    inference(definitional_conversion,[status(esa)],[f_1894_2]) ).

cnf(f_1894_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6347),U_6348),U_6349) = U_6349
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),U_6349))
    | ~ class_Orderings_Olinorder(U_6347) ),
    inference(clausify,[status(thm)],[f_1894_3]) ).

fof(f_1895_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1]) ).

fof(f_1895_2,plain,
    ! [U_6352,U_6351,U_6350] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6350),U_6352),U_6351) = U_6352
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6350),U_6351),U_6352))
      | ~ class_Orderings_Olinorder(U_6350) ),
    inference(variable_rename,[status(thm)],[f_1895_1]) ).

fof(f_1895_3,plain,
    ! [U_6350,U_6351,U_6352] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6350),U_6352),U_6351) = U_6352
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6350),U_6351),U_6352))
      | ~ class_Orderings_Olinorder(U_6350) ),
    inference(definitional_conversion,[status(esa)],[f_1895_2]) ).

cnf(f_1895_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6350),U_6352),U_6351) = U_6352
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6350),U_6351),U_6352))
    | ~ class_Orderings_Olinorder(U_6350) ),
    inference(clausify,[status(thm)],[f_1895_3]) ).

fof(f_1896_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI]) ).

fof(f_1896_2,plain,
    ! [U_6356,U_6355,U_6354,U_6353] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6353),U_6354),U_6356)),U_6355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),U_6356),U_6355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),U_6354),U_6355))
      | ~ class_Orderings_Olinorder(U_6353) ),
    inference(variable_rename,[status(thm)],[f_1896_1]) ).

fof(f_1896_3,plain,
    ! [U_6353,U_6354,U_6355,U_6356] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6353),U_6354),U_6356)),U_6355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),U_6356),U_6355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),U_6354),U_6355))
      | ~ class_Orderings_Olinorder(U_6353) ),
    inference(definitional_conversion,[status(esa)],[f_1896_2]) ).

cnf(f_1896_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6353),U_6354),U_6356)),U_6355))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),U_6356),U_6355))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6353),U_6354),U_6355))
    | ~ class_Orderings_Olinorder(U_6353) ),
    inference(clausify,[status(thm)],[f_1896_3]) ).

fof(f_1897_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least]) ).

fof(f_1897_2,plain,
    ! [U_6360,U_6359,U_6358,U_6357] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6357),U_6358),U_6360)),U_6359))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),U_6360),U_6359))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),U_6358),U_6359))
      | ~ class_Orderings_Olinorder(U_6357) ),
    inference(variable_rename,[status(thm)],[f_1897_1]) ).

fof(f_1897_3,plain,
    ! [U_6357,U_6358,U_6359,U_6360] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6357),U_6358),U_6360)),U_6359))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),U_6360),U_6359))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),U_6358),U_6359))
      | ~ class_Orderings_Olinorder(U_6357) ),
    inference(definitional_conversion,[status(esa)],[f_1897_2]) ).

cnf(f_1897_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6357),U_6358),U_6360)),U_6359))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),U_6360),U_6359))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6357),U_6358),U_6359))
    | ~ class_Orderings_Olinorder(U_6357) ),
    inference(clausify,[status(thm)],[f_1897_3]) ).

fof(f_1898_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono]) ).

fof(f_1898_2,plain,
    ! [U_6365,U_6364,U_6363,U_6362,U_6361] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6361),U_6362),U_6364)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6361),U_6363),U_6365)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),U_6364),U_6365))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),U_6362),U_6363))
      | ~ class_Orderings_Olinorder(U_6361) ),
    inference(variable_rename,[status(thm)],[f_1898_1]) ).

fof(f_1898_3,plain,
    ! [U_6361,U_6362,U_6363,U_6364,U_6365] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6361),U_6362),U_6364)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6361),U_6363),U_6365)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),U_6364),U_6365))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),U_6362),U_6363))
      | ~ class_Orderings_Olinorder(U_6361) ),
    inference(definitional_conversion,[status(esa)],[f_1898_2]) ).

cnf(f_1898_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6361),U_6362),U_6364)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6361),U_6363),U_6365)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),U_6364),U_6365))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6361),U_6362),U_6363))
    | ~ class_Orderings_Olinorder(U_6361) ),
    inference(clausify,[status(thm)],[f_1898_3]) ).

fof(f_1899_1,plain,
    ! [V_x,V_b,V_a,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supE]) ).

fof(f_1899_2,plain,
    ! [U_6369,U_6368,U_6367,U_6366] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),U_6368),U_6369))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),U_6367),U_6369)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6366),U_6367),U_6368)),U_6369))
      | ~ class_Orderings_Olinorder(U_6366) ),
    inference(variable_rename,[status(thm)],[f_1899_1]) ).

fof(f_1899_3,plain,
    ( ! [U_6367,U_6366,U_6368,U_6369] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),U_6368),U_6369))
        | ~ sP606(U_6367,U_6366,U_6368,U_6369) )
    & ! [U_6367,U_6366,U_6368,U_6369] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),U_6367),U_6369))
        | ~ sP606(U_6367,U_6366,U_6368,U_6369) )
    & ! [U_6367,U_6366,U_6368,U_6369] :
        ( sP606(U_6367,U_6366,U_6368,U_6369)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6366),U_6367),U_6368)),U_6369))
        | ~ class_Orderings_Olinorder(U_6366) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP606])],[f_1899_2]) ).

cnf(f_1899_4,plain,
    ( sP606(U_6367,U_6366,U_6368,U_6369)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6366),U_6367),U_6368)),U_6369))
    | ~ class_Orderings_Olinorder(U_6366) ),
    inference(clausify,[status(thm)],[f_1899_3]) ).

cnf(f_1899_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),U_6367),U_6369))
    | ~ sP606(U_6367,U_6366,U_6368,U_6369) ),
    inference(clausify,[status(thm)],[f_1899_3]) ).

cnf(f_1899_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),U_6368),U_6369))
    | ~ sP606(U_6367,U_6366,U_6368,U_6369) ),
    inference(clausify,[status(thm)],[f_1899_3]) ).

fof(f_1900_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left]) ).

fof(f_1900_2,plain,
    ! [U_6373,U_6372,U_6371,U_6370] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6370),U_6371),U_6372)),U_6373) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),U_6371),U_6373)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),U_6372),U_6373))
      | ~ class_Groups_Oordered__ab__group__add(U_6370) ),
    inference(variable_rename,[status(thm)],[f_1900_1]) ).

fof(f_1900_3,plain,
    ! [U_6371,U_6370,U_6372,U_6373] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6370),U_6371),U_6372)),U_6373) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),U_6371),U_6373)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),U_6372),U_6373))
      | ~ class_Groups_Oordered__ab__group__add(U_6370) ),
    inference(definitional_conversion,[status(esa)],[f_1900_2]) ).

cnf(f_1900_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6370),U_6371),U_6372)),U_6373) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),U_6371),U_6373)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6370),U_6372),U_6373))
    | ~ class_Groups_Oordered__ab__group__add(U_6370) ),
    inference(clausify,[status(thm)],[f_1900_3]) ).

fof(f_1901_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_max__Suc__Suc]) ).

fof(f_1901_2,plain,
    ! [U_6375,U_6374] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6374)),hAPP(c_Nat_OSuc,U_6375)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6374),U_6375)),
    inference(variable_rename,[status(thm)],[f_1901_1]) ).

fof(f_1901_3,plain,
    ! [U_6374,U_6375] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6374)),hAPP(c_Nat_OSuc,U_6375)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6374),U_6375)),
    inference(definitional_conversion,[status(esa)],[f_1901_2]) ).

cnf(f_1901_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6374)),hAPP(c_Nat_OSuc,U_6375)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6374),U_6375)),
    inference(clausify,[status(thm)],[f_1901_3]) ).

fof(f_1902_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_max__0L]) ).

fof(f_1902_2,plain,
    ! [U_6376] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6376) = U_6376,
    inference(variable_rename,[status(thm)],[f_1902_1]) ).

fof(f_1902_3,plain,
    ! [U_6376] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6376) = U_6376,
    inference(definitional_conversion,[status(esa)],[f_1902_2]) ).

cnf(f_1902_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6376) = U_6376,
    inference(clausify,[status(thm)],[f_1902_3]) ).

fof(f_1903_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_max__0R]) ).

fof(f_1903_2,plain,
    ! [U_6377] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6377),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6377,
    inference(variable_rename,[status(thm)],[f_1903_1]) ).

fof(f_1903_3,plain,
    ! [U_6377] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6377),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6377,
    inference(definitional_conversion,[status(esa)],[f_1903_2]) ).

cnf(f_1903_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6377),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6377,
    inference(clausify,[status(thm)],[f_1903_3]) ).

fof(f_1904_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb]) ).

fof(f_1904_2,plain,
    ! [U_6380,U_6379,U_6378] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6378),U_6379),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),U_6380)) = U_6379
      | ~ class_Orderings_Olinorder(U_6378) ),
    inference(variable_rename,[status(thm)],[f_1904_1]) ).

fof(f_1904_3,plain,
    ! [U_6378,U_6379,U_6380] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6378),U_6379),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),U_6380)) = U_6379
      | ~ class_Orderings_Olinorder(U_6378) ),
    inference(definitional_conversion,[status(esa)],[f_1904_2]) ).

cnf(f_1904_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6378),U_6379),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),U_6380)) = U_6379
    | ~ class_Orderings_Olinorder(U_6378) ),
    inference(clausify,[status(thm)],[f_1904_3]) ).

fof(f_1905_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb]) ).

fof(f_1905_2,plain,
    ! [U_6383,U_6382,U_6381] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6381),U_6382),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6381),U_6382),U_6383)) = U_6382
      | ~ class_Orderings_Olinorder(U_6381) ),
    inference(variable_rename,[status(thm)],[f_1905_1]) ).

fof(f_1905_3,plain,
    ! [U_6381,U_6382,U_6383] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6381),U_6382),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6381),U_6382),U_6383)) = U_6382
      | ~ class_Orderings_Olinorder(U_6381) ),
    inference(definitional_conversion,[status(esa)],[f_1905_2]) ).

cnf(f_1905_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6381),U_6382),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6381),U_6382),U_6383)) = U_6382
    | ~ class_Orderings_Olinorder(U_6381) ),
    inference(clausify,[status(thm)],[f_1905_3]) ).

fof(f_1906_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1]) ).

fof(f_1906_2,plain,
    ! [U_6387,U_6386,U_6385,U_6384] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6386),U_6387)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),U_6386)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),U_6387))
      | ~ class_Orderings_Olinorder(U_6384) ),
    inference(variable_rename,[status(thm)],[f_1906_1]) ).

fof(f_1906_3,plain,
    ! [U_6384,U_6385,U_6386,U_6387] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6386),U_6387)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),U_6386)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),U_6387))
      | ~ class_Orderings_Olinorder(U_6384) ),
    inference(definitional_conversion,[status(esa)],[f_1906_2]) ).

cnf(f_1906_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6386),U_6387)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),U_6386)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6384),U_6385),U_6387))
    | ~ class_Orderings_Olinorder(U_6384) ),
    inference(clausify,[status(thm)],[f_1906_3]) ).

fof(f_1907_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1]) ).

fof(f_1907_2,plain,
    ! [U_6391,U_6390,U_6389,U_6388] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6390),U_6391)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6390)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6391))
      | ~ class_Orderings_Olinorder(U_6388) ),
    inference(variable_rename,[status(thm)],[f_1907_1]) ).

fof(f_1907_3,plain,
    ! [U_6388,U_6389,U_6390,U_6391] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6390),U_6391)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6390)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6391))
      | ~ class_Orderings_Olinorder(U_6388) ),
    inference(definitional_conversion,[status(esa)],[f_1907_2]) ).

cnf(f_1907_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6390),U_6391)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6390)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6391))
    | ~ class_Orderings_Olinorder(U_6388) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

fof(f_1908_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2]) ).

fof(f_1908_2,plain,
    ! [U_6395,U_6394,U_6393,U_6392] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6394)),U_6395) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6393),U_6395)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6394),U_6395))
      | ~ class_Orderings_Olinorder(U_6392) ),
    inference(variable_rename,[status(thm)],[f_1908_1]) ).

fof(f_1908_3,plain,
    ! [U_6392,U_6393,U_6394,U_6395] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6394)),U_6395) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6393),U_6395)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6394),U_6395))
      | ~ class_Orderings_Olinorder(U_6392) ),
    inference(definitional_conversion,[status(esa)],[f_1908_2]) ).

cnf(f_1908_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6394)),U_6395) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6393),U_6395)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6394),U_6395))
    | ~ class_Orderings_Olinorder(U_6392) ),
    inference(clausify,[status(thm)],[f_1908_3]) ).

fof(f_1909_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2]) ).

fof(f_1909_2,plain,
    ! [U_6399,U_6398,U_6397,U_6396] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),U_6397),U_6398)),U_6399) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6397),U_6399)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6398),U_6399))
      | ~ class_Orderings_Olinorder(U_6396) ),
    inference(variable_rename,[status(thm)],[f_1909_1]) ).

fof(f_1909_3,plain,
    ! [U_6396,U_6397,U_6398,U_6399] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),U_6397),U_6398)),U_6399) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6397),U_6399)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6398),U_6399))
      | ~ class_Orderings_Olinorder(U_6396) ),
    inference(definitional_conversion,[status(esa)],[f_1909_2]) ).

cnf(f_1909_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),U_6397),U_6398)),U_6399) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6397),U_6399)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6398),U_6399))
    | ~ class_Orderings_Olinorder(U_6396) ),
    inference(clausify,[status(thm)],[f_1909_3]) ).

fof(f_1910_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_apfst__conv]) ).

fof(f_1910_2,plain,
    ! [U_6405,U_6404,U_6403,U_6402,U_6401,U_6400] : hAPP(c_Product__Type_Oapfst(U_6400,U_6401,U_6402,U_6403),hAPP(hAPP(c_Product__Type_OPair(U_6400,U_6402),U_6404),U_6405)) = hAPP(hAPP(c_Product__Type_OPair(U_6401,U_6402),hAPP(U_6403,U_6404)),U_6405),
    inference(variable_rename,[status(thm)],[f_1910_1]) ).

fof(f_1910_3,plain,
    ! [U_6400,U_6401,U_6402,U_6403,U_6404,U_6405] : hAPP(c_Product__Type_Oapfst(U_6400,U_6401,U_6402,U_6403),hAPP(hAPP(c_Product__Type_OPair(U_6400,U_6402),U_6404),U_6405)) = hAPP(hAPP(c_Product__Type_OPair(U_6401,U_6402),hAPP(U_6403,U_6404)),U_6405),
    inference(definitional_conversion,[status(esa)],[f_1910_2]) ).

cnf(f_1910_4,plain,
    hAPP(c_Product__Type_Oapfst(U_6400,U_6401,U_6402,U_6403),hAPP(hAPP(c_Product__Type_OPair(U_6400,U_6402),U_6404),U_6405)) = hAPP(hAPP(c_Product__Type_OPair(U_6401,U_6402),hAPP(U_6403,U_6404)),U_6405),
    inference(clausify,[status(thm)],[f_1910_3]) ).

fof(f_1911_1,plain,
    ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
      ( ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
        | hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) )
      & ( hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))
        | hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv]) ).

fof(f_1911_2,plain,
    ! [U_6411,U_6410,U_6409,U_6408,U_6407,U_6406] :
      ( ( hAPP(c_Product__Type_Oapfst(U_6406,U_6407,U_6408,U_6409),U_6410) = hAPP(c_Product__Type_Oapfst(U_6406,U_6407,U_6408,U_6411),U_6410)
        | hAPP(U_6409,hAPP(c_Product__Type_Ofst(U_6406,U_6408),U_6410)) != hAPP(U_6411,hAPP(c_Product__Type_Ofst(U_6406,U_6408),U_6410)) )
      & ( hAPP(U_6409,hAPP(c_Product__Type_Ofst(U_6406,U_6408),U_6410)) = hAPP(U_6411,hAPP(c_Product__Type_Ofst(U_6406,U_6408),U_6410))
        | hAPP(c_Product__Type_Oapfst(U_6406,U_6407,U_6408,U_6409),U_6410) != hAPP(c_Product__Type_Oapfst(U_6406,U_6407,U_6408,U_6411),U_6410) ) ),
    inference(variable_rename,[status(thm)],[f_1911_1]) ).

fof(f_1911_3,plain,
    ( ! [U_6423,U_6421,U_6419,U_6417,U_6415,U_6413] :
        ( hAPP(c_Product__Type_Oapfst(U_6413,U_6415,U_6417,U_6419),U_6421) = hAPP(c_Product__Type_Oapfst(U_6413,U_6415,U_6417,U_6423),U_6421)
        | hAPP(U_6419,hAPP(c_Product__Type_Ofst(U_6413,U_6417),U_6421)) != hAPP(U_6423,hAPP(c_Product__Type_Ofst(U_6413,U_6417),U_6421)) )
    & ! [U_6422,U_6420,U_6418,U_6416,U_6414,U_6412] :
        ( hAPP(U_6418,hAPP(c_Product__Type_Ofst(U_6412,U_6416),U_6420)) = hAPP(U_6422,hAPP(c_Product__Type_Ofst(U_6412,U_6416),U_6420))
        | hAPP(c_Product__Type_Oapfst(U_6412,U_6414,U_6416,U_6418),U_6420) != hAPP(c_Product__Type_Oapfst(U_6412,U_6414,U_6416,U_6422),U_6420) ) ),
    inference(miniscope,[status(thm)],[f_1911_2]) ).

fof(f_1911_4,plain,
    ( ! [U_6413,U_6415,U_6417,U_6419,U_6421,U_6423] :
        ( hAPP(c_Product__Type_Oapfst(U_6413,U_6415,U_6417,U_6419),U_6421) = hAPP(c_Product__Type_Oapfst(U_6413,U_6415,U_6417,U_6423),U_6421)
        | hAPP(U_6419,hAPP(c_Product__Type_Ofst(U_6413,U_6417),U_6421)) != hAPP(U_6423,hAPP(c_Product__Type_Ofst(U_6413,U_6417),U_6421)) )
    & ! [U_6418,U_6412,U_6414,U_6416,U_6422,U_6420] :
        ( hAPP(U_6418,hAPP(c_Product__Type_Ofst(U_6412,U_6416),U_6420)) = hAPP(U_6422,hAPP(c_Product__Type_Ofst(U_6412,U_6416),U_6420))
        | hAPP(c_Product__Type_Oapfst(U_6412,U_6414,U_6416,U_6418),U_6420) != hAPP(c_Product__Type_Oapfst(U_6412,U_6414,U_6416,U_6422),U_6420) ) ),
    inference(definitional_conversion,[status(esa)],[f_1911_3]) ).

cnf(f_1911_5,plain,
    ( hAPP(U_6418,hAPP(c_Product__Type_Ofst(U_6412,U_6416),U_6420)) = hAPP(U_6422,hAPP(c_Product__Type_Ofst(U_6412,U_6416),U_6420))
    | hAPP(c_Product__Type_Oapfst(U_6412,U_6414,U_6416,U_6418),U_6420) != hAPP(c_Product__Type_Oapfst(U_6412,U_6414,U_6416,U_6422),U_6420) ),
    inference(clausify,[status(thm)],[f_1911_4]) ).

cnf(f_1911_6,plain,
    ( hAPP(c_Product__Type_Oapfst(U_6413,U_6415,U_6417,U_6419),U_6421) = hAPP(c_Product__Type_Oapfst(U_6413,U_6415,U_6417,U_6423),U_6421)
    | hAPP(U_6419,hAPP(c_Product__Type_Ofst(U_6413,U_6417),U_6421)) != hAPP(U_6423,hAPP(c_Product__Type_Ofst(U_6413,U_6417),U_6421)) ),
    inference(clausify,[status(thm)],[f_1911_4]) ).

fof(f_1912_1,plain,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_fst__apfst]) ).

fof(f_1912_2,plain,
    ! [U_6428,U_6427,U_6426,U_6425,U_6424] : hAPP(c_Product__Type_Ofst(U_6424,U_6425),hAPP(c_Product__Type_Oapfst(U_6426,U_6424,U_6425,U_6427),U_6428)) = hAPP(U_6427,hAPP(c_Product__Type_Ofst(U_6426,U_6425),U_6428)),
    inference(variable_rename,[status(thm)],[f_1912_1]) ).

fof(f_1912_3,plain,
    ! [U_6425,U_6424,U_6426,U_6427,U_6428] : hAPP(c_Product__Type_Ofst(U_6424,U_6425),hAPP(c_Product__Type_Oapfst(U_6426,U_6424,U_6425,U_6427),U_6428)) = hAPP(U_6427,hAPP(c_Product__Type_Ofst(U_6426,U_6425),U_6428)),
    inference(definitional_conversion,[status(esa)],[f_1912_2]) ).

cnf(f_1912_4,plain,
    hAPP(c_Product__Type_Ofst(U_6424,U_6425),hAPP(c_Product__Type_Oapfst(U_6426,U_6424,U_6425,U_6427),U_6428)) = hAPP(U_6427,hAPP(c_Product__Type_Ofst(U_6426,U_6425),U_6428)),
    inference(clausify,[status(thm)],[f_1912_3]) ).

fof(f_1913_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_snd__apfst]) ).

fof(f_1913_2,plain,
    ! [U_6433,U_6432,U_6431,U_6430,U_6429] : hAPP(c_Product__Type_Osnd(U_6429,U_6430),hAPP(c_Product__Type_Oapfst(U_6431,U_6429,U_6430,U_6432),U_6433)) = hAPP(c_Product__Type_Osnd(U_6431,U_6430),U_6433),
    inference(variable_rename,[status(thm)],[f_1913_1]) ).

fof(f_1913_3,plain,
    ! [U_6429,U_6430,U_6431,U_6432,U_6433] : hAPP(c_Product__Type_Osnd(U_6429,U_6430),hAPP(c_Product__Type_Oapfst(U_6431,U_6429,U_6430,U_6432),U_6433)) = hAPP(c_Product__Type_Osnd(U_6431,U_6430),U_6433),
    inference(definitional_conversion,[status(esa)],[f_1913_2]) ).

cnf(f_1913_4,plain,
    hAPP(c_Product__Type_Osnd(U_6429,U_6430),hAPP(c_Product__Type_Oapfst(U_6431,U_6429,U_6430,U_6432),U_6433)) = hAPP(c_Product__Type_Osnd(U_6431,U_6430),U_6433),
    inference(clausify,[status(thm)],[f_1913_3]) ).

fof(f_1914_1,plain,
    ! [V_v,V_u,T_b] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) )
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_max__number__of]) ).

fof(f_1914_2,plain,
    ! [U_6436,U_6435,U_6434] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436))) ) )
      | ~ class_Orderings_Oord(U_6434)
      | ~ class_Int_Onumber(U_6434) ),
    inference(variable_rename,[status(thm)],[f_1914_1]) ).

fof(f_1914_3,plain,
    ( ! [U_6434,U_6435,U_6436] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)))
        | ~ sP607(U_6434,U_6435,U_6436) )
    & ! [U_6434,U_6435,U_6436] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)))
        | ~ sP607(U_6434,U_6435,U_6436) )
    & ! [U_6434,U_6435,U_6436] :
        ( sP607(U_6434,U_6435,U_6436)
        | ~ class_Orderings_Oord(U_6434)
        | ~ class_Int_Onumber(U_6434) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP607])],[f_1914_2]) ).

cnf(f_1914_4,plain,
    ( sP607(U_6434,U_6435,U_6436)
    | ~ class_Orderings_Oord(U_6434)
    | ~ class_Int_Onumber(U_6434) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

cnf(f_1914_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)))
    | ~ sP607(U_6434,U_6435,U_6436) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

cnf(f_1914_6,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6435)),hAPP(c_Int_Onumber__class_Onumber__of(U_6434),U_6436)))
    | ~ sP607(U_6434,U_6435,U_6436) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

fof(f_1915_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le]) ).

fof(f_1915_2,plain,
    ! [U_6440,U_6439,U_6438,U_6437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6437),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6437),U_6439),U_6440))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6437),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),U_6439)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),U_6440))))
      | ~ class_Orderings_Olinorder(U_6437) ),
    inference(variable_rename,[status(thm)],[f_1915_1]) ).

fof(f_1915_3,plain,
    ! [U_6438,U_6439,U_6437,U_6440] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6437),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6437),U_6439),U_6440))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6437),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),U_6439)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),U_6440))))
      | ~ class_Orderings_Olinorder(U_6437) ),
    inference(definitional_conversion,[status(esa)],[f_1915_2]) ).

cnf(f_1915_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6437),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6437),U_6439),U_6440))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6437),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),U_6439)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6437),U_6438),U_6440))))
    | ~ class_Orderings_Olinorder(U_6437) ),
    inference(clausify,[status(thm)],[f_1915_3]) ).

fof(f_1916_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le]) ).

fof(f_1916_2,plain,
    ! [U_6444,U_6443,U_6442,U_6441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6441),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6441),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),U_6443)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),U_6444))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6441),U_6443),U_6444))))
      | ~ class_Orderings_Olinorder(U_6441) ),
    inference(variable_rename,[status(thm)],[f_1916_1]) ).

fof(f_1916_3,plain,
    ! [U_6441,U_6442,U_6443,U_6444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6441),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6441),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),U_6443)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),U_6444))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6441),U_6443),U_6444))))
      | ~ class_Orderings_Olinorder(U_6441) ),
    inference(definitional_conversion,[status(esa)],[f_1916_2]) ).

cnf(f_1916_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6441),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6441),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),U_6443)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),U_6444))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6441),U_6442),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6441),U_6443),U_6444))))
    | ~ class_Orderings_Olinorder(U_6441) ),
    inference(clausify,[status(thm)],[f_1916_3]) ).

fof(f_1917_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min]) ).

fof(f_1917_2,plain,
    ! [U_6447,U_6446,U_6445] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6445),U_6446),U_6447)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6445),hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),U_6446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),U_6447))
      | ~ class_Groups_Olinordered__ab__group__add(U_6445) ),
    inference(variable_rename,[status(thm)],[f_1917_1]) ).

fof(f_1917_3,plain,
    ! [U_6445,U_6446,U_6447] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6445),U_6446),U_6447)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6445),hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),U_6446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),U_6447))
      | ~ class_Groups_Olinordered__ab__group__add(U_6445) ),
    inference(definitional_conversion,[status(esa)],[f_1917_2]) ).

cnf(f_1917_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6445),U_6446),U_6447)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6445),hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),U_6446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6445),U_6447))
    | ~ class_Groups_Olinordered__ab__group__add(U_6445) ),
    inference(clausify,[status(thm)],[f_1917_3]) ).

fof(f_1918_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max]) ).

fof(f_1918_2,plain,
    ! [U_6450,U_6449,U_6448] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6448),U_6449),U_6450)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6448),hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),U_6449)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),U_6450))
      | ~ class_Groups_Olinordered__ab__group__add(U_6448) ),
    inference(variable_rename,[status(thm)],[f_1918_1]) ).

fof(f_1918_3,plain,
    ! [U_6448,U_6449,U_6450] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6448),U_6449),U_6450)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6448),hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),U_6449)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),U_6450))
      | ~ class_Groups_Olinordered__ab__group__add(U_6448) ),
    inference(definitional_conversion,[status(esa)],[f_1918_2]) ).

cnf(f_1918_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6448),U_6449),U_6450)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6448),hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),U_6449)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6448),U_6450))
    | ~ class_Groups_Olinordered__ab__group__add(U_6448) ),
    inference(clausify,[status(thm)],[f_1918_3]) ).

fof(f_1919_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__minus__add__max]) ).

fof(f_1919_2,plain,
    ! [U_6452,U_6451] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6451),U_6452)),U_6452) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6451),U_6452),
    inference(variable_rename,[status(thm)],[f_1919_1]) ).

fof(f_1919_3,plain,
    ! [U_6451,U_6452] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6451),U_6452)),U_6452) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6451),U_6452),
    inference(definitional_conversion,[status(esa)],[f_1919_2]) ).

cnf(f_1919_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6451),U_6452)),U_6452) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6451),U_6452),
    inference(clausify,[status(thm)],[f_1919_3]) ).

fof(f_1920_1,plain,
    ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(f_1920_2,plain,
    ! [U_6459,U_6458,U_6457,U_6456,U_6455,U_6454,U_6453] : hAPP(c_Product__Type_Oapsnd(U_6453,U_6454,U_6455,U_6456),hAPP(c_Product__Type_Oapfst(U_6457,U_6455,U_6453,U_6458),U_6459)) = hAPP(c_Product__Type_Oapfst(U_6457,U_6455,U_6454,U_6458),hAPP(c_Product__Type_Oapsnd(U_6453,U_6454,U_6457,U_6456),U_6459)),
    inference(variable_rename,[status(thm)],[f_1920_1]) ).

fof(f_1920_3,plain,
    ! [U_6453,U_6454,U_6455,U_6456,U_6457,U_6458,U_6459] : hAPP(c_Product__Type_Oapsnd(U_6453,U_6454,U_6455,U_6456),hAPP(c_Product__Type_Oapfst(U_6457,U_6455,U_6453,U_6458),U_6459)) = hAPP(c_Product__Type_Oapfst(U_6457,U_6455,U_6454,U_6458),hAPP(c_Product__Type_Oapsnd(U_6453,U_6454,U_6457,U_6456),U_6459)),
    inference(definitional_conversion,[status(esa)],[f_1920_2]) ).

cnf(f_1920_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6453,U_6454,U_6455,U_6456),hAPP(c_Product__Type_Oapfst(U_6457,U_6455,U_6453,U_6458),U_6459)) = hAPP(c_Product__Type_Oapfst(U_6457,U_6455,U_6454,U_6458),hAPP(c_Product__Type_Oapsnd(U_6453,U_6454,U_6457,U_6456),U_6459)),
    inference(clausify,[status(thm)],[f_1920_3]) ).

fof(f_1921_1,plain,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_max__Suc1]) ).

fof(f_1921_2,plain,
    ! [U_6461,U_6460] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6460)),U_6461) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6460),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6460)),U_6461),
    inference(variable_rename,[status(thm)],[f_1921_1]) ).

fof(f_1921_3,plain,
    ! [U_6461,U_6460] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6460)),U_6461) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6460),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6460)),U_6461),
    inference(definitional_conversion,[status(esa)],[f_1921_2]) ).

cnf(f_1921_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6460)),U_6461) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6460),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6460)),U_6461),
    inference(clausify,[status(thm)],[f_1921_3]) ).

fof(f_1922_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_max__Suc2]) ).

fof(f_1922_2,plain,
    ! [U_6463,U_6462] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6462),hAPP(c_Nat_OSuc,U_6463)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6463),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),U_6463)),U_6462),
    inference(variable_rename,[status(thm)],[f_1922_1]) ).

fof(f_1922_3,plain,
    ! [U_6462,U_6463] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6462),hAPP(c_Nat_OSuc,U_6463)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6463),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),U_6463)),U_6462),
    inference(definitional_conversion,[status(esa)],[f_1922_2]) ).

cnf(f_1922_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6462),hAPP(c_Nat_OSuc,U_6463)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6463),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),U_6463)),U_6462),
    inference(clausify,[status(thm)],[f_1922_3]) ).

fof(f_1923_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dual__min]) ).

fof(f_1923_2,plain,
    ! [U_6464] :
      ( c_Orderings_Oord_Omin(U_6464,hAPP(c_COMBC(U_6464,U_6464,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6464))) = c_Orderings_Oord__class_Omax(U_6464)
      | ~ class_Orderings_Olinorder(U_6464) ),
    inference(variable_rename,[status(thm)],[f_1923_1]) ).

fof(f_1923_3,plain,
    ! [U_6464] :
      ( c_Orderings_Oord_Omin(U_6464,hAPP(c_COMBC(U_6464,U_6464,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6464))) = c_Orderings_Oord__class_Omax(U_6464)
      | ~ class_Orderings_Olinorder(U_6464) ),
    inference(definitional_conversion,[status(esa)],[f_1923_2]) ).

cnf(f_1923_4,plain,
    ( c_Orderings_Oord_Omin(U_6464,hAPP(c_COMBC(U_6464,U_6464,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6464))) = c_Orderings_Oord__class_Omax(U_6464)
    | ~ class_Orderings_Olinorder(U_6464) ),
    inference(clausify,[status(thm)],[f_1923_3]) ).

fof(f_1924_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_max__ord__max]) ).

fof(f_1924_2,plain,
    ! [U_6465] :
      ( c_Orderings_Oord__class_Omax(U_6465) = c_Orderings_Oord_Omax(U_6465,c_Orderings_Oord__class_Oless__eq(U_6465))
      | ~ class_Orderings_Oord(U_6465) ),
    inference(variable_rename,[status(thm)],[f_1924_1]) ).

fof(f_1924_3,plain,
    ! [U_6465] :
      ( c_Orderings_Oord__class_Omax(U_6465) = c_Orderings_Oord_Omax(U_6465,c_Orderings_Oord__class_Oless__eq(U_6465))
      | ~ class_Orderings_Oord(U_6465) ),
    inference(definitional_conversion,[status(esa)],[f_1924_2]) ).

cnf(f_1924_4,plain,
    ( c_Orderings_Oord__class_Omax(U_6465) = c_Orderings_Oord_Omax(U_6465,c_Orderings_Oord__class_Oless__eq(U_6465))
    | ~ class_Orderings_Oord(U_6465) ),
    inference(clausify,[status(thm)],[f_1924_3]) ).

fof(f_1925_1,plain,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_OFrac__def]) ).

fof(f_1925_2,plain,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_1925_1]) ).

cnf(f_1925_3,plain,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_1925_2]) ).

fof(f_1926_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2)))
            | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | ( V_b_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & V_a_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Osimps]) ).

fof(f_1926_2,plain,
    ! [U_6467,U_6466] :
      ( ( ( ( c_Nitpick_Onorm__frac(U_6467,U_6466) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6467),U_6466)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6467))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6466)))
            | U_6466 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_6467 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_6467,U_6466) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | ( U_6466 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_6467 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6466),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(U_6467,U_6466) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6467),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6466))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6466),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1926_1]) ).

fof(f_1926_3,plain,
    ( ! [U_6471,U_6469] :
        ( ( ( c_Nitpick_Onorm__frac(U_6471,U_6469) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6471),U_6469)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6471))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6469)))
            | U_6469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_6471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_6471,U_6469) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | ( U_6469 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_6471 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6469),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6470,U_6468] :
        ( c_Nitpick_Onorm__frac(U_6470,U_6468) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6468))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1926_2]) ).

fof(f_1926_4,plain,
    ( ! [U_6471,U_6469] :
        ( U_6469 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP608(U_6471,U_6469) )
    & ! [U_6471,U_6469] :
        ( U_6471 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP608(U_6471,U_6469) )
    & ! [U_6471,U_6469] :
        ( c_Nitpick_Onorm__frac(U_6471,U_6469) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6471),U_6469)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6471))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6469)))
        | U_6469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP609(U_6471,U_6469) )
    & ! [U_6471,U_6469] :
        ( c_Nitpick_Onorm__frac(U_6471,U_6469) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | sP608(U_6471,U_6469)
        | ~ sP609(U_6471,U_6469) )
    & ! [U_6471,U_6469] :
        ( sP609(U_6471,U_6469)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6469),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6470,U_6468] :
        ( c_Nitpick_Onorm__frac(U_6470,U_6468) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6468))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP608,sP609])],[f_1926_3]) ).

cnf(f_1926_5,plain,
    ( c_Nitpick_Onorm__frac(U_6470,U_6468) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6468))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1926_4]) ).

cnf(f_1926_6,plain,
    ( sP609(U_6471,U_6469)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6469),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1926_4]) ).

cnf(f_1926_7,plain,
    ( c_Nitpick_Onorm__frac(U_6471,U_6469) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | sP608(U_6471,U_6469)
    | ~ sP609(U_6471,U_6469) ),
    inference(clausify,[status(thm)],[f_1926_4]) ).

cnf(f_1926_8,plain,
    ( c_Nitpick_Onorm__frac(U_6471,U_6469) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6471),U_6469)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6471))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6469)))
    | U_6469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP609(U_6471,U_6469) ),
    inference(clausify,[status(thm)],[f_1926_4]) ).

cnf(f_1926_9,plain,
    ( U_6471 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP608(U_6471,U_6469) ),
    inference(clausify,[status(thm)],[f_1926_4]) ).

cnf(f_1926_10,plain,
    ( U_6469 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP608(U_6471,U_6469) ),
    inference(clausify,[status(thm)],[f_1926_4]) ).

fof(f_1927_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2)))
              | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
              | ( V_b_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & V_a_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Opsimps]) ).

fof(f_1927_2,plain,
    ! [U_6473,U_6472] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(U_6472,U_6473) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6472),U_6473)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6472))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6473)))
              | U_6473 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | U_6472 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(U_6472,U_6473) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
              | ( U_6473 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & U_6472 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(U_6472,U_6473) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6472),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6473))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6472),U_6473))) ),
    inference(variable_rename,[status(thm)],[f_1927_1]) ).

fof(f_1927_3,plain,
    ( ! [U_6473,U_6472] :
        ( U_6473 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP610(U_6473,U_6472) )
    & ! [U_6473,U_6472] :
        ( U_6472 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP610(U_6473,U_6472) )
    & ! [U_6473,U_6472] :
        ( c_Nitpick_Onorm__frac(U_6472,U_6473) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6472),U_6473)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6472))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6473)))
        | U_6473 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6472 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP611(U_6473,U_6472) )
    & ! [U_6473,U_6472] :
        ( c_Nitpick_Onorm__frac(U_6472,U_6473) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | sP610(U_6473,U_6472)
        | ~ sP611(U_6473,U_6472) )
    & ! [U_6473,U_6472] :
        ( sP611(U_6473,U_6472)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6473),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP612(U_6473,U_6472) )
    & ! [U_6473,U_6472] :
        ( c_Nitpick_Onorm__frac(U_6472,U_6473) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6472),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6473))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6473),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP612(U_6473,U_6472) )
    & ! [U_6473,U_6472] :
        ( sP612(U_6473,U_6472)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6472),U_6473))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP610,sP611,sP612])],[f_1927_2]) ).

cnf(f_1927_4,plain,
    ( sP612(U_6473,U_6472)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6472),U_6473))) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_5,plain,
    ( c_Nitpick_Onorm__frac(U_6472,U_6473) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6472),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6473))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6473),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP612(U_6473,U_6472) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_6,plain,
    ( sP611(U_6473,U_6472)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6473),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP612(U_6473,U_6472) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_7,plain,
    ( c_Nitpick_Onorm__frac(U_6472,U_6473) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | sP610(U_6473,U_6472)
    | ~ sP611(U_6473,U_6472) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_8,plain,
    ( c_Nitpick_Onorm__frac(U_6472,U_6473) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6472),U_6473)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6472))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6473)))
    | U_6473 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6472 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP611(U_6473,U_6472) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_9,plain,
    ( U_6472 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP610(U_6473,U_6472) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_10,plain,
    ( U_6473 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP610(U_6473,U_6472) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

fof(f_1928_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oidem]) ).

fof(f_1928_2,plain,
    ! [U_6475,U_6474] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6474),U_6475),U_6475) = U_6475
      | ~ class_Orderings_Olinorder(U_6474) ),
    inference(variable_rename,[status(thm)],[f_1928_1]) ).

fof(f_1928_3,plain,
    ! [U_6475,U_6474] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6474),U_6475),U_6475) = U_6475
      | ~ class_Orderings_Olinorder(U_6474) ),
    inference(definitional_conversion,[status(esa)],[f_1928_2]) ).

cnf(f_1928_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6474),U_6475),U_6475) = U_6475
    | ~ class_Orderings_Olinorder(U_6474) ),
    inference(clausify,[status(thm)],[f_1928_3]) ).

fof(f_1929_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oidem]) ).

fof(f_1929_2,plain,
    ! [U_6477,U_6476] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6476),U_6477),U_6477) = U_6477
      | ~ class_Orderings_Olinorder(U_6476) ),
    inference(variable_rename,[status(thm)],[f_1929_1]) ).

fof(f_1929_3,plain,
    ! [U_6476,U_6477] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6476),U_6477),U_6477) = U_6477
      | ~ class_Orderings_Olinorder(U_6476) ),
    inference(definitional_conversion,[status(esa)],[f_1929_2]) ).

cnf(f_1929_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6476),U_6477),U_6477) = U_6477
    | ~ class_Orderings_Olinorder(U_6476) ),
    inference(clausify,[status(thm)],[f_1929_3]) ).

fof(f_1930_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dual__max]) ).

fof(f_1930_2,plain,
    ! [U_6478] :
      ( c_Orderings_Oord_Omax(U_6478,hAPP(c_COMBC(U_6478,U_6478,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6478))) = c_Orderings_Oord__class_Omin(U_6478)
      | ~ class_Orderings_Olinorder(U_6478) ),
    inference(variable_rename,[status(thm)],[f_1930_1]) ).

fof(f_1930_3,plain,
    ! [U_6478] :
      ( c_Orderings_Oord_Omax(U_6478,hAPP(c_COMBC(U_6478,U_6478,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6478))) = c_Orderings_Oord__class_Omin(U_6478)
      | ~ class_Orderings_Olinorder(U_6478) ),
    inference(definitional_conversion,[status(esa)],[f_1930_2]) ).

cnf(f_1930_4,plain,
    ( c_Orderings_Oord_Omax(U_6478,hAPP(c_COMBC(U_6478,U_6478,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6478))) = c_Orderings_Oord__class_Omin(U_6478)
    | ~ class_Orderings_Olinorder(U_6478) ),
    inference(clausify,[status(thm)],[f_1930_3]) ).

fof(f_1931_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).

fof(f_1931_2,plain,
    ! [U_6480,U_6479] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_6479),U_6480) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6479)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6480)))),
    inference(variable_rename,[status(thm)],[f_1931_1]) ).

fof(f_1931_3,plain,
    ! [U_6479,U_6480] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_6479),U_6480) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6479)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6480)))),
    inference(definitional_conversion,[status(esa)],[f_1931_2]) ).

cnf(f_1931_4,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,U_6479),U_6480) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6479)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6480)))),
    inference(clausify,[status(thm)],[f_1931_3]) ).

fof(f_1932_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct]) ).

fof(f_1932_2,plain,
    ! [U_6485,U_6484,U_6483] :
      ( hBOOL(hAPP(hAPP(U_6485,U_6483),U_6484))
      | ? [U_6482,U_6481] :
          ( ~ hBOOL(hAPP(hAPP(U_6485,U_6482),U_6481))
          & ( hBOOL(hAPP(hAPP(U_6485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6482)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6481)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6481),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6482),U_6481))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6483),U_6484))) ),
    inference(variable_rename,[status(thm)],[f_1932_1]) ).

fof(f_1932_3,plain,
    ! [U_6485,U_6484,U_6483] :
      ( hBOOL(hAPP(hAPP(U_6485,U_6483),U_6484))
      | ? [U_6481] :
          ( ~ hBOOL(hAPP(hAPP(U_6485,sK94(U_6485,U_6484,U_6483)),U_6481))
          & ( hBOOL(hAPP(hAPP(U_6485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK94(U_6485,U_6484,U_6483))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6481)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6481),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK94(U_6485,U_6484,U_6483)),U_6481))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6483),U_6484))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_6482,sK94(U_6485,U_6484,U_6483))],[f_1932_2]) ).

fof(f_1932_4,plain,
    ! [U_6485,U_6484,U_6483] :
      ( hBOOL(hAPP(hAPP(U_6485,U_6483),U_6484))
      | ( ~ hBOOL(hAPP(hAPP(U_6485,sK94(U_6485,U_6484,U_6483)),sK95(U_6485,U_6484,U_6483)))
        & ( hBOOL(hAPP(hAPP(U_6485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK94(U_6485,U_6484,U_6483))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK95(U_6485,U_6484,U_6483))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK95(U_6485,U_6484,U_6483)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK94(U_6485,U_6484,U_6483)),sK95(U_6485,U_6484,U_6483)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6483),U_6484))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_6481,sK95(U_6485,U_6484,U_6483))],[f_1932_3]) ).

fof(f_1932_5,plain,
    ( ! [U_6483,U_6484,U_6485] :
        ( ~ hBOOL(hAPP(hAPP(U_6485,sK94(U_6485,U_6484,U_6483)),sK95(U_6485,U_6484,U_6483)))
        | ~ sP613(U_6483,U_6484,U_6485) )
    & ! [U_6483,U_6484,U_6485] :
        ( hBOOL(hAPP(hAPP(U_6485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK94(U_6485,U_6484,U_6483))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK95(U_6485,U_6484,U_6483))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK95(U_6485,U_6484,U_6483)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP613(U_6483,U_6484,U_6485) )
    & ! [U_6483,U_6484,U_6485] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK94(U_6485,U_6484,U_6483)),sK95(U_6485,U_6484,U_6483))))
        | ~ sP613(U_6483,U_6484,U_6485) )
    & ! [U_6483,U_6484,U_6485] :
        ( hBOOL(hAPP(hAPP(U_6485,U_6483),U_6484))
        | sP613(U_6483,U_6484,U_6485)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6483),U_6484))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP613])],[f_1932_4]) ).

cnf(f_1932_6,plain,
    ( hBOOL(hAPP(hAPP(U_6485,U_6483),U_6484))
    | sP613(U_6483,U_6484,U_6485)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6483),U_6484))) ),
    inference(clausify,[status(thm)],[f_1932_5]) ).

cnf(f_1932_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK94(U_6485,U_6484,U_6483)),sK95(U_6485,U_6484,U_6483))))
    | ~ sP613(U_6483,U_6484,U_6485) ),
    inference(clausify,[status(thm)],[f_1932_5]) ).

cnf(f_1932_8,plain,
    ( hBOOL(hAPP(hAPP(U_6485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK94(U_6485,U_6484,U_6483))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK95(U_6485,U_6484,U_6483))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK95(U_6485,U_6484,U_6483)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP613(U_6483,U_6484,U_6485) ),
    inference(clausify,[status(thm)],[f_1932_5]) ).

cnf(f_1932_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6485,sK94(U_6485,U_6484,U_6483)),sK95(U_6485,U_6484,U_6483)))
    | ~ sP613(U_6483,U_6484,U_6485) ),
    inference(clausify,[status(thm)],[f_1932_5]) ).

fof(f_1933_1,plain,
    ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).

fof(f_1933_2,plain,
    ! [U_6487,U_6486] : c_Nitpick_Oint__lcm(U_6486,U_6487) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6486)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6487)))),
    inference(variable_rename,[status(thm)],[f_1933_1]) ).

fof(f_1933_3,plain,
    ! [U_6486,U_6487] : c_Nitpick_Oint__lcm(U_6486,U_6487) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6486)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6487)))),
    inference(definitional_conversion,[status(esa)],[f_1933_2]) ).

cnf(f_1933_4,plain,
    c_Nitpick_Oint__lcm(U_6486,U_6487) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6486)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6487)))),
    inference(clausify,[status(thm)],[f_1933_3]) ).

fof(f_1934_1,plain,
    ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ozero__frac__def]) ).

fof(f_1934_2,plain,
    ! [U_6488] : c_Nitpick_Ozero__frac(U_6488) = c_Nitpick_OAbs__Frac(U_6488,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1934_1]) ).

fof(f_1934_3,plain,
    ! [U_6488] : c_Nitpick_Ozero__frac(U_6488) = c_Nitpick_OAbs__Frac(U_6488,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1934_2]) ).

cnf(f_1934_4,plain,
    c_Nitpick_Ozero__frac(U_6488) = c_Nitpick_OAbs__Frac(U_6488,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1934_3]) ).

fof(f_1935_1,plain,
    ! [V_x,V_y] :
      ( ( c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y))
        | V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(V_x,V_y) = V_x
        | V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps]) ).

fof(f_1935_2,plain,
    ! [U_6490,U_6489] :
      ( ( c_Nitpick_Onat__gcd(U_6490,U_6489) = c_Nitpick_Onat__gcd(U_6489,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6490,U_6489))
        | U_6489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(U_6490,U_6489) = U_6490
        | U_6489 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1935_1]) ).

fof(f_1935_3,plain,
    ( ! [U_6494,U_6492] :
        ( c_Nitpick_Onat__gcd(U_6494,U_6492) = c_Nitpick_Onat__gcd(U_6492,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6494,U_6492))
        | U_6492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6493,U_6491] :
        ( c_Nitpick_Onat__gcd(U_6493,U_6491) = U_6493
        | U_6491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1935_2]) ).

fof(f_1935_4,plain,
    ( ! [U_6494,U_6492] :
        ( c_Nitpick_Onat__gcd(U_6494,U_6492) = c_Nitpick_Onat__gcd(U_6492,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6494,U_6492))
        | U_6492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6493,U_6491] :
        ( c_Nitpick_Onat__gcd(U_6493,U_6491) = U_6493
        | U_6491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1935_3]) ).

cnf(f_1935_5,plain,
    ( c_Nitpick_Onat__gcd(U_6493,U_6491) = U_6493
    | U_6491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1935_4]) ).

cnf(f_1935_6,plain,
    ( c_Nitpick_Onat__gcd(U_6494,U_6492) = c_Nitpick_Onat__gcd(U_6492,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6494,U_6492))
    | U_6492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1935_4]) ).

fof(f_1936_1,plain,
    ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).

fof(f_1936_2,plain,
    ! [U_6496,U_6495] : c_Nitpick_Onat__lcm(U_6495,U_6496) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6495),U_6496)),c_Nitpick_Onat__gcd(U_6495,U_6496)),
    inference(variable_rename,[status(thm)],[f_1936_1]) ).

fof(f_1936_3,plain,
    ! [U_6495,U_6496] : c_Nitpick_Onat__lcm(U_6495,U_6496) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6495),U_6496)),c_Nitpick_Onat__gcd(U_6495,U_6496)),
    inference(definitional_conversion,[status(esa)],[f_1936_2]) ).

cnf(f_1936_4,plain,
    c_Nitpick_Onat__lcm(U_6495,U_6496) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6495),U_6496)),c_Nitpick_Onat__gcd(U_6495,U_6496)),
    inference(clausify,[status(thm)],[f_1936_3]) ).

fof(f_1937_1,plain,
    ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oone__frac__def]) ).

fof(f_1937_2,plain,
    ! [U_6497] : c_Nitpick_Oone__frac(U_6497) = c_Nitpick_OAbs__Frac(U_6497,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1937_1]) ).

fof(f_1937_3,plain,
    ! [U_6497] : c_Nitpick_Oone__frac(U_6497) = c_Nitpick_OAbs__Frac(U_6497,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1937_2]) ).

cnf(f_1937_4,plain,
    c_Nitpick_Oone__frac(U_6497) = c_Nitpick_OAbs__Frac(U_6497,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1937_3]) ).

fof(f_1938_1,plain,
    ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onumber__of__frac__def]) ).

fof(f_1938_2,plain,
    ! [U_6499,U_6498] : c_Nitpick_Onumber__of__frac(U_6498,U_6499) = c_Nitpick_OAbs__Frac(U_6498,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6499),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1938_1]) ).

fof(f_1938_3,plain,
    ! [U_6498,U_6499] : c_Nitpick_Onumber__of__frac(U_6498,U_6499) = c_Nitpick_OAbs__Frac(U_6498,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6499),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1938_2]) ).

cnf(f_1938_4,plain,
    c_Nitpick_Onumber__of__frac(U_6498,U_6499) = c_Nitpick_OAbs__Frac(U_6498,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6499),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1938_3]) ).

fof(f_1939_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2))
          | V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2
          | V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps]) ).

fof(f_1939_2,plain,
    ! [U_6501,U_6500] :
      ( ( ( c_Nitpick_Onat__gcd(U_6500,U_6501) = c_Nitpick_Onat__gcd(U_6501,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6500,U_6501))
          | U_6501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(U_6500,U_6501) = U_6500
          | U_6501 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6500),U_6501))) ),
    inference(variable_rename,[status(thm)],[f_1939_1]) ).

fof(f_1939_3,plain,
    ( ! [U_6500,U_6501] :
        ( c_Nitpick_Onat__gcd(U_6500,U_6501) = c_Nitpick_Onat__gcd(U_6501,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6500,U_6501))
        | U_6501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP614(U_6500,U_6501) )
    & ! [U_6500,U_6501] :
        ( c_Nitpick_Onat__gcd(U_6500,U_6501) = U_6500
        | U_6501 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP614(U_6500,U_6501) )
    & ! [U_6500,U_6501] :
        ( sP614(U_6500,U_6501)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6500),U_6501))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP614])],[f_1939_2]) ).

cnf(f_1939_4,plain,
    ( sP614(U_6500,U_6501)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6500),U_6501))) ),
    inference(clausify,[status(thm)],[f_1939_3]) ).

cnf(f_1939_5,plain,
    ( c_Nitpick_Onat__gcd(U_6500,U_6501) = U_6500
    | U_6501 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP614(U_6500,U_6501) ),
    inference(clausify,[status(thm)],[f_1939_3]) ).

cnf(f_1939_6,plain,
    ( c_Nitpick_Onat__gcd(U_6500,U_6501) = c_Nitpick_Onat__gcd(U_6501,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6500,U_6501))
    | U_6501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP614(U_6500,U_6501) ),
    inference(clausify,[status(thm)],[f_1939_3]) ).

fof(f_1940_1,plain,
    ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ofrac__def]) ).

fof(f_1940_2,plain,
    ! [U_6504,U_6503,U_6502] : hAPP(hAPP(c_Nitpick_Ofrac(U_6502),U_6503),U_6504) = c_Nitpick_OAbs__Frac(U_6502,c_Nitpick_Onorm__frac(U_6503,U_6504)),
    inference(variable_rename,[status(thm)],[f_1940_1]) ).

fof(f_1940_3,plain,
    ! [U_6503,U_6504,U_6502] : hAPP(hAPP(c_Nitpick_Ofrac(U_6502),U_6503),U_6504) = c_Nitpick_OAbs__Frac(U_6502,c_Nitpick_Onorm__frac(U_6503,U_6504)),
    inference(definitional_conversion,[status(esa)],[f_1940_2]) ).

cnf(f_1940_4,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(U_6502),U_6503),U_6504) = c_Nitpick_OAbs__Frac(U_6502,c_Nitpick_Onorm__frac(U_6503,U_6504)),
    inference(clausify,[status(thm)],[f_1940_3]) ).

fof(f_1941_1,plain,
    ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
    inference(fof_nnf,[status(thm)],[fact_internal__split__def]) ).

fof(f_1941_2,plain,
    ! [U_6507,U_6506,U_6505] : c_Product__Type_Ointernal__split(U_6505,U_6506,U_6507) = c_Product__Type_Oprod_Oprod__case(U_6505,U_6506,U_6507),
    inference(variable_rename,[status(thm)],[f_1941_1]) ).

fof(f_1941_3,plain,
    ! [U_6505,U_6506,U_6507] : c_Product__Type_Ointernal__split(U_6505,U_6506,U_6507) = c_Product__Type_Oprod_Oprod__case(U_6505,U_6506,U_6507),
    inference(definitional_conversion,[status(esa)],[f_1941_2]) ).

cnf(f_1941_4,plain,
    c_Product__Type_Ointernal__split(U_6505,U_6506,U_6507) = c_Product__Type_Oprod_Oprod__case(U_6505,U_6506,U_6507),
    inference(clausify,[status(thm)],[f_1941_3]) ).

fof(f_1942_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_internal__split__conv]) ).

fof(f_1942_2,plain,
    ! [U_6513,U_6512,U_6511,U_6510,U_6509,U_6508] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_6508,U_6509,U_6510),U_6511),hAPP(hAPP(c_Product__Type_OPair(U_6508,U_6509),U_6512),U_6513)) = hAPP(hAPP(U_6511,U_6512),U_6513),
    inference(variable_rename,[status(thm)],[f_1942_1]) ).

fof(f_1942_3,plain,
    ! [U_6508,U_6509,U_6510,U_6511,U_6512,U_6513] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_6508,U_6509,U_6510),U_6511),hAPP(hAPP(c_Product__Type_OPair(U_6508,U_6509),U_6512),U_6513)) = hAPP(hAPP(U_6511,U_6512),U_6513),
    inference(definitional_conversion,[status(esa)],[f_1942_2]) ).

cnf(f_1942_4,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(U_6508,U_6509,U_6510),U_6511),hAPP(hAPP(c_Product__Type_OPair(U_6508,U_6509),U_6512),U_6513)) = hAPP(hAPP(U_6511,U_6512),U_6513),
    inference(clausify,[status(thm)],[f_1942_3]) ).

fof(f_1943_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_x),B_y))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))
            | B_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct]) ).

fof(f_1943_2,plain,
    ! [U_6518,U_6517,U_6516] :
      ( hBOOL(hAPP(hAPP(U_6518,U_6516),U_6517))
      | ? [U_6515,U_6514] :
          ( ~ hBOOL(hAPP(hAPP(U_6518,U_6515),U_6514))
          & ( hBOOL(hAPP(hAPP(U_6518,U_6514),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6515,U_6514)))
            | U_6514 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6515),U_6514))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6516),U_6517))) ),
    inference(variable_rename,[status(thm)],[f_1943_1]) ).

fof(f_1943_3,plain,
    ! [U_6518,U_6517,U_6516] :
      ( hBOOL(hAPP(hAPP(U_6518,U_6516),U_6517))
      | ? [U_6514] :
          ( ~ hBOOL(hAPP(hAPP(U_6518,sK96(U_6518,U_6517,U_6516)),U_6514))
          & ( hBOOL(hAPP(hAPP(U_6518,U_6514),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK96(U_6518,U_6517,U_6516),U_6514)))
            | U_6514 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK96(U_6518,U_6517,U_6516)),U_6514))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6516),U_6517))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_6515,sK96(U_6518,U_6517,U_6516))],[f_1943_2]) ).

fof(f_1943_4,plain,
    ! [U_6518,U_6517,U_6516] :
      ( hBOOL(hAPP(hAPP(U_6518,U_6516),U_6517))
      | ( ~ hBOOL(hAPP(hAPP(U_6518,sK96(U_6518,U_6517,U_6516)),sK97(U_6518,U_6517,U_6516)))
        & ( hBOOL(hAPP(hAPP(U_6518,sK97(U_6518,U_6517,U_6516)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK96(U_6518,U_6517,U_6516),sK97(U_6518,U_6517,U_6516))))
          | sK97(U_6518,U_6517,U_6516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK96(U_6518,U_6517,U_6516)),sK97(U_6518,U_6517,U_6516)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6516),U_6517))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_6514,sK97(U_6518,U_6517,U_6516))],[f_1943_3]) ).

fof(f_1943_5,plain,
    ( ! [U_6516,U_6517,U_6518] :
        ( ~ hBOOL(hAPP(hAPP(U_6518,sK96(U_6518,U_6517,U_6516)),sK97(U_6518,U_6517,U_6516)))
        | ~ sP615(U_6516,U_6517,U_6518) )
    & ! [U_6516,U_6517,U_6518] :
        ( hBOOL(hAPP(hAPP(U_6518,sK97(U_6518,U_6517,U_6516)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK96(U_6518,U_6517,U_6516),sK97(U_6518,U_6517,U_6516))))
        | sK97(U_6518,U_6517,U_6516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP615(U_6516,U_6517,U_6518) )
    & ! [U_6516,U_6517,U_6518] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK96(U_6518,U_6517,U_6516)),sK97(U_6518,U_6517,U_6516))))
        | ~ sP615(U_6516,U_6517,U_6518) )
    & ! [U_6516,U_6517,U_6518] :
        ( hBOOL(hAPP(hAPP(U_6518,U_6516),U_6517))
        | sP615(U_6516,U_6517,U_6518)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6516),U_6517))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP615])],[f_1943_4]) ).

cnf(f_1943_6,plain,
    ( hBOOL(hAPP(hAPP(U_6518,U_6516),U_6517))
    | sP615(U_6516,U_6517,U_6518)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6516),U_6517))) ),
    inference(clausify,[status(thm)],[f_1943_5]) ).

cnf(f_1943_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK96(U_6518,U_6517,U_6516)),sK97(U_6518,U_6517,U_6516))))
    | ~ sP615(U_6516,U_6517,U_6518) ),
    inference(clausify,[status(thm)],[f_1943_5]) ).

cnf(f_1943_8,plain,
    ( hBOOL(hAPP(hAPP(U_6518,sK97(U_6518,U_6517,U_6516)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK96(U_6518,U_6517,U_6516),sK97(U_6518,U_6517,U_6516))))
    | sK97(U_6518,U_6517,U_6516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP615(U_6516,U_6517,U_6518) ),
    inference(clausify,[status(thm)],[f_1943_5]) ).

cnf(f_1943_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6518,sK96(U_6518,U_6517,U_6516)),sK97(U_6518,U_6517,U_6516)))
    | ~ sP615(U_6516,U_6517,U_6518) ),
    inference(clausify,[status(thm)],[f_1943_5]) ).

fof(f_1944_1,plain,
    ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(f_1944_2,plain,
    ! [U_6521,U_6520,U_6519] : c_Nitpick_Oplus__frac(U_6519,U_6520,U_6521) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6519),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6519),U_6520),hAPP(c_Nitpick_Odenom(U_6519),U_6521))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6519),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6519),tc_Int_Oint),c_Nitpick_Ofrac(U_6519)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6519),U_6520))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_6519),U_6520))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6519),U_6521))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_6519),U_6521)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1944_1]) ).

fof(f_1944_3,plain,
    ! [U_6519,U_6520,U_6521] : c_Nitpick_Oplus__frac(U_6519,U_6520,U_6521) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6519),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6519),U_6520),hAPP(c_Nitpick_Odenom(U_6519),U_6521))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6519),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6519),tc_Int_Oint),c_Nitpick_Ofrac(U_6519)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6519),U_6520))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_6519),U_6520))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6519),U_6521))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_6519),U_6521)))))),c_COMBI(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1944_2]) ).

cnf(f_1944_4,plain,
    c_Nitpick_Oplus__frac(U_6519,U_6520,U_6521) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6519),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6519),U_6520),hAPP(c_Nitpick_Odenom(U_6519),U_6521))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6519),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6519),tc_Int_Oint),c_Nitpick_Ofrac(U_6519)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6519),U_6520))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_6519),U_6520))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6519),U_6521))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_6519),U_6521)))))),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1944_3]) ).

fof(f_1945_1,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    inference(fof_nnf,[status(thm)],[fact_transfer__morphism__int__nat]) ).

fof(f_1945_2,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    inference(definitional_conversion,[status(esa)],[f_1945_1]) ).

cnf(f_1945_3,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    inference(clausify,[status(thm)],[f_1945_2]) ).

fof(f_1946_1,plain,
    ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I1_J]) ).

fof(f_1946_2,plain,
    ! [U_6527,U_6526,U_6525,U_6524,U_6523,U_6522] : c_Nitpick_Opair__box_Opair__box__size(U_6522,U_6523,U_6524,U_6525,c_Nitpick_Opair__box_OPairBox(U_6522,U_6523,U_6526,U_6527)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6524,U_6526)),hAPP(U_6525,U_6527))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1946_1]) ).

fof(f_1946_3,plain,
    ! [U_6523,U_6522,U_6524,U_6525,U_6526,U_6527] : c_Nitpick_Opair__box_Opair__box__size(U_6522,U_6523,U_6524,U_6525,c_Nitpick_Opair__box_OPairBox(U_6522,U_6523,U_6526,U_6527)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6524,U_6526)),hAPP(U_6525,U_6527))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1946_2]) ).

cnf(f_1946_4,plain,
    c_Nitpick_Opair__box_Opair__box__size(U_6522,U_6523,U_6524,U_6525,c_Nitpick_Opair__box_OPairBox(U_6522,U_6523,U_6526,U_6527)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6524,U_6526)),hAPP(U_6525,U_6527))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1946_3]) ).

fof(f_1947_1,plain,
    ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).

fof(f_1947_2,plain,
    ! [U_6533,U_6532,U_6531,U_6530,U_6529,U_6528] :
      ( hBOOL(hAPP(hAPP(U_6533,U_6529),U_6530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6531,tc_fun(U_6532,tc_HOL_Obool))),U_6528),U_6533))
      | ~ hBOOL(hAPP(hAPP(U_6528,U_6529),U_6530)) ),
    inference(variable_rename,[status(thm)],[f_1947_1]) ).

fof(f_1947_3,plain,
    ! [U_6528,U_6529,U_6530,U_6531,U_6532,U_6533] :
      ( hBOOL(hAPP(hAPP(U_6533,U_6529),U_6530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6531,tc_fun(U_6532,tc_HOL_Obool))),U_6528),U_6533))
      | ~ hBOOL(hAPP(hAPP(U_6528,U_6529),U_6530)) ),
    inference(definitional_conversion,[status(esa)],[f_1947_2]) ).

cnf(f_1947_4,plain,
    ( hBOOL(hAPP(hAPP(U_6533,U_6529),U_6530))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6531,tc_fun(U_6532,tc_HOL_Obool))),U_6528),U_6533))
    | ~ hBOOL(hAPP(hAPP(U_6528,U_6529),U_6530)) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

fof(f_1948_1,plain,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
        | V_b_2 != V_b_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_b_2 = V_b_H_2
          & V_a_2 = V_a_H_2 )
        | c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) != c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject]) ).

fof(f_1948_2,plain,
    ! [U_6539,U_6538,U_6537,U_6536,U_6535,U_6534] :
      ( ( c_Nitpick_Opair__box_OPairBox(U_6534,U_6535,U_6536,U_6537) = c_Nitpick_Opair__box_OPairBox(U_6534,U_6535,U_6538,U_6539)
        | U_6537 != U_6539
        | U_6536 != U_6538 )
      & ( ( U_6537 = U_6539
          & U_6536 = U_6538 )
        | c_Nitpick_Opair__box_OPairBox(U_6534,U_6535,U_6536,U_6537) != c_Nitpick_Opair__box_OPairBox(U_6534,U_6535,U_6538,U_6539) ) ),
    inference(variable_rename,[status(thm)],[f_1948_1]) ).

fof(f_1948_3,plain,
    ( ! [U_6551,U_6549,U_6547,U_6545] :
        ( ! [U_6543,U_6541] : c_Nitpick_Opair__box_OPairBox(U_6541,U_6543,U_6545,U_6547) = c_Nitpick_Opair__box_OPairBox(U_6541,U_6543,U_6549,U_6551)
        | U_6547 != U_6551
        | U_6545 != U_6549 )
    & ! [U_6550,U_6548,U_6546,U_6544] :
        ( ! [U_6542,U_6540] : c_Nitpick_Opair__box_OPairBox(U_6540,U_6542,U_6544,U_6546) != c_Nitpick_Opair__box_OPairBox(U_6540,U_6542,U_6548,U_6550)
        | ( U_6546 = U_6550
          & U_6544 = U_6548 ) ) ),
    inference(miniscope,[status(thm)],[f_1948_2]) ).

fof(f_1948_4,plain,
    ( ! [U_6544,U_6548,U_6550,U_6546] :
        ( U_6546 = U_6550
        | ~ sP616(U_6544,U_6548,U_6550,U_6546) )
    & ! [U_6544,U_6548,U_6550,U_6546] :
        ( U_6544 = U_6548
        | ~ sP616(U_6544,U_6548,U_6550,U_6546) )
    & ! [U_6551,U_6549,U_6547,U_6545,U_6541,U_6543] :
        ( c_Nitpick_Opair__box_OPairBox(U_6541,U_6543,U_6545,U_6547) = c_Nitpick_Opair__box_OPairBox(U_6541,U_6543,U_6549,U_6551)
        | U_6547 != U_6551
        | U_6545 != U_6549 )
    & ! [U_6544,U_6548,U_6550,U_6540,U_6542,U_6546] :
        ( c_Nitpick_Opair__box_OPairBox(U_6540,U_6542,U_6544,U_6546) != c_Nitpick_Opair__box_OPairBox(U_6540,U_6542,U_6548,U_6550)
        | sP616(U_6544,U_6548,U_6550,U_6546) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP616])],[f_1948_3]) ).

cnf(f_1948_5,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_6540,U_6542,U_6544,U_6546) != c_Nitpick_Opair__box_OPairBox(U_6540,U_6542,U_6548,U_6550)
    | sP616(U_6544,U_6548,U_6550,U_6546) ),
    inference(clausify,[status(thm)],[f_1948_4]) ).

cnf(f_1948_6,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_6541,U_6543,U_6545,U_6547) = c_Nitpick_Opair__box_OPairBox(U_6541,U_6543,U_6549,U_6551)
    | U_6547 != U_6551
    | U_6545 != U_6549 ),
    inference(clausify,[status(thm)],[f_1948_4]) ).

cnf(f_1948_7,plain,
    ( U_6544 = U_6548
    | ~ sP616(U_6544,U_6548,U_6550,U_6546) ),
    inference(clausify,[status(thm)],[f_1948_4]) ).

cnf(f_1948_8,plain,
    ( U_6546 = U_6550
    | ~ sP616(U_6544,U_6548,U_6550,U_6546) ),
    inference(clausify,[status(thm)],[f_1948_4]) ).

fof(f_1949_1,plain,
    ! [V_Q_2,T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_Q_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).

fof(f_1949_2,plain,
    ! [U_6555,U_6554,U_6553,U_6552] :
      ( hBOOL(hAPP(U_6555,U_6553))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6554,tc_HOL_Obool)),U_6552),U_6555))
      | ~ hBOOL(hAPP(U_6552,U_6553)) ),
    inference(variable_rename,[status(thm)],[f_1949_1]) ).

fof(f_1949_3,plain,
    ! [U_6554,U_6555,U_6552,U_6553] :
      ( hBOOL(hAPP(U_6555,U_6553))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6554,tc_HOL_Obool)),U_6552),U_6555))
      | ~ hBOOL(hAPP(U_6552,U_6553)) ),
    inference(definitional_conversion,[status(esa)],[f_1949_2]) ).

cnf(f_1949_4,plain,
    ( hBOOL(hAPP(U_6555,U_6553))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6554,tc_HOL_Obool)),U_6552),U_6555))
    | ~ hBOOL(hAPP(U_6552,U_6553)) ),
    inference(clausify,[status(thm)],[f_1949_3]) ).

fof(f_1950_1,plain,
    ! [V_x_2,V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(V_Q_2,V_x_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).

fof(f_1950_2,plain,
    ! [U_6559,U_6558,U_6557,U_6556] :
      ( hBOOL(hAPP(U_6558,U_6559))
      | ~ hBOOL(hAPP(U_6557,U_6559))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6556,tc_HOL_Obool)),U_6557),U_6558)) ),
    inference(variable_rename,[status(thm)],[f_1950_1]) ).

fof(f_1950_3,plain,
    ! [U_6559,U_6558,U_6557] :
      ( ! [U_6556] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6556,tc_HOL_Obool)),U_6557),U_6558))
      | hBOOL(hAPP(U_6558,U_6559))
      | ~ hBOOL(hAPP(U_6557,U_6559)) ),
    inference(miniscope,[status(thm)],[f_1950_2]) ).

fof(f_1950_4,plain,
    ! [U_6559,U_6556,U_6557,U_6558] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6556,tc_HOL_Obool)),U_6557),U_6558))
      | hBOOL(hAPP(U_6558,U_6559))
      | ~ hBOOL(hAPP(U_6557,U_6559)) ),
    inference(definitional_conversion,[status(esa)],[f_1950_3]) ).

cnf(f_1950_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6556,tc_HOL_Obool)),U_6557),U_6558))
    | hBOOL(hAPP(U_6558,U_6559))
    | ~ hBOOL(hAPP(U_6557,U_6559)) ),
    inference(clausify,[status(thm)],[f_1950_4]) ).

fof(f_1951_1,plain,
    ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).

fof(f_1951_2,plain,
    ! [U_6565,U_6564,U_6563,U_6562,U_6561,U_6560] :
      ( hBOOL(hAPP(hAPP(U_6563,U_6564),U_6565))
      | ~ hBOOL(hAPP(hAPP(U_6562,U_6564),U_6565))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6560,tc_fun(U_6561,tc_HOL_Obool))),U_6562),U_6563)) ),
    inference(variable_rename,[status(thm)],[f_1951_1]) ).

fof(f_1951_3,plain,
    ! [U_6565,U_6564,U_6563,U_6562] :
      ( ! [U_6561,U_6560] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6560,tc_fun(U_6561,tc_HOL_Obool))),U_6562),U_6563))
      | hBOOL(hAPP(hAPP(U_6563,U_6564),U_6565))
      | ~ hBOOL(hAPP(hAPP(U_6562,U_6564),U_6565)) ),
    inference(miniscope,[status(thm)],[f_1951_2]) ).

fof(f_1951_4,plain,
    ! [U_6560,U_6561,U_6562,U_6563,U_6564,U_6565] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6560,tc_fun(U_6561,tc_HOL_Obool))),U_6562),U_6563))
      | hBOOL(hAPP(hAPP(U_6563,U_6564),U_6565))
      | ~ hBOOL(hAPP(hAPP(U_6562,U_6564),U_6565)) ),
    inference(definitional_conversion,[status(esa)],[f_1951_3]) ).

cnf(f_1951_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6560,tc_fun(U_6561,tc_HOL_Obool))),U_6562),U_6563))
    | hBOOL(hAPP(hAPP(U_6563,U_6564),U_6565))
    | ~ hBOOL(hAPP(hAPP(U_6562,U_6564),U_6565)) ),
    inference(clausify,[status(thm)],[f_1951_4]) ).

fof(f_1952_1,plain,
    ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).

fof(f_1952_2,plain,
    ! [U_6568,U_6567,U_6566] : c_Nitpick_Otimes__frac(U_6566,U_6567,U_6568) = hAPP(hAPP(c_Nitpick_Ofrac(U_6566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6566),U_6567)),hAPP(c_Nitpick_Onum(U_6566),U_6568))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_6566),U_6567)),hAPP(c_Nitpick_Odenom(U_6566),U_6568))),
    inference(variable_rename,[status(thm)],[f_1952_1]) ).

fof(f_1952_3,plain,
    ! [U_6566,U_6567,U_6568] : c_Nitpick_Otimes__frac(U_6566,U_6567,U_6568) = hAPP(hAPP(c_Nitpick_Ofrac(U_6566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6566),U_6567)),hAPP(c_Nitpick_Onum(U_6566),U_6568))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_6566),U_6567)),hAPP(c_Nitpick_Odenom(U_6566),U_6568))),
    inference(definitional_conversion,[status(esa)],[f_1952_2]) ).

cnf(f_1952_4,plain,
    c_Nitpick_Otimes__frac(U_6566,U_6567,U_6568) = hAPP(hAPP(c_Nitpick_Ofrac(U_6566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6566),U_6567)),hAPP(c_Nitpick_Onum(U_6566),U_6568))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_6566),U_6567)),hAPP(c_Nitpick_Odenom(U_6566),U_6568))),
    inference(clausify,[status(thm)],[f_1952_3]) ).

fof(f_1953_1,plain,
    ! [V_q,T_a,T_b] :
      ( c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q)))
      | ~ class_Rings_Oring__1(T_b)
      | ~ class_Rings_Oinverse(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def]) ).

fof(f_1953_2,plain,
    ! [U_6571,U_6570,U_6569] :
      ( c_Nitpick_Oof__frac(U_6570,U_6569,U_6571) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6569),hAPP(c_Int_Oring__1__class_Oof__int(U_6569),hAPP(c_Nitpick_Onum(U_6570),U_6571))),hAPP(c_Int_Oring__1__class_Oof__int(U_6569),hAPP(c_Nitpick_Odenom(U_6570),U_6571)))
      | ~ class_Rings_Oring__1(U_6569)
      | ~ class_Rings_Oinverse(U_6569) ),
    inference(variable_rename,[status(thm)],[f_1953_1]) ).

fof(f_1953_3,plain,
    ! [U_6569,U_6570,U_6571] :
      ( c_Nitpick_Oof__frac(U_6570,U_6569,U_6571) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6569),hAPP(c_Int_Oring__1__class_Oof__int(U_6569),hAPP(c_Nitpick_Onum(U_6570),U_6571))),hAPP(c_Int_Oring__1__class_Oof__int(U_6569),hAPP(c_Nitpick_Odenom(U_6570),U_6571)))
      | ~ class_Rings_Oring__1(U_6569)
      | ~ class_Rings_Oinverse(U_6569) ),
    inference(definitional_conversion,[status(esa)],[f_1953_2]) ).

cnf(f_1953_4,plain,
    ( c_Nitpick_Oof__frac(U_6570,U_6569,U_6571) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6569),hAPP(c_Int_Oring__1__class_Oof__int(U_6569),hAPP(c_Nitpick_Onum(U_6570),U_6571))),hAPP(c_Int_Oring__1__class_Oof__int(U_6569),hAPP(c_Nitpick_Odenom(U_6570),U_6571)))
    | ~ class_Rings_Oring__1(U_6569)
    | ~ class_Rings_Oinverse(U_6569) ),
    inference(clausify,[status(thm)],[f_1953_3]) ).

fof(f_1954_1,plain,
    ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oinverse__frac__def]) ).

fof(f_1954_2,plain,
    ! [U_6573,U_6572] : c_Nitpick_Oinverse__frac(U_6572,U_6573) = hAPP(hAPP(c_Nitpick_Ofrac(U_6572),hAPP(c_Nitpick_Odenom(U_6572),U_6573)),hAPP(c_Nitpick_Onum(U_6572),U_6573)),
    inference(variable_rename,[status(thm)],[f_1954_1]) ).

fof(f_1954_3,plain,
    ! [U_6572,U_6573] : c_Nitpick_Oinverse__frac(U_6572,U_6573) = hAPP(hAPP(c_Nitpick_Ofrac(U_6572),hAPP(c_Nitpick_Odenom(U_6572),U_6573)),hAPP(c_Nitpick_Onum(U_6572),U_6573)),
    inference(definitional_conversion,[status(esa)],[f_1954_2]) ).

cnf(f_1954_4,plain,
    c_Nitpick_Oinverse__frac(U_6572,U_6573) = hAPP(hAPP(c_Nitpick_Ofrac(U_6572),hAPP(c_Nitpick_Odenom(U_6572),U_6573)),hAPP(c_Nitpick_Onum(U_6572),U_6573)),
    inference(clausify,[status(thm)],[f_1954_3]) ).

fof(f_1955_1,plain,
    ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).

fof(f_1955_2,plain,
    ! [U_6575,U_6574] : c_Nitpick_Ouminus__frac(U_6574,U_6575) = c_Nitpick_OAbs__Frac(U_6574,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6574),U_6575))),hAPP(c_Nitpick_Odenom(U_6574),U_6575))),
    inference(variable_rename,[status(thm)],[f_1955_1]) ).

fof(f_1955_3,plain,
    ! [U_6574,U_6575] : c_Nitpick_Ouminus__frac(U_6574,U_6575) = c_Nitpick_OAbs__Frac(U_6574,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6574),U_6575))),hAPP(c_Nitpick_Odenom(U_6574),U_6575))),
    inference(definitional_conversion,[status(esa)],[f_1955_2]) ).

cnf(f_1955_4,plain,
    c_Nitpick_Ouminus__frac(U_6574,U_6575) = c_Nitpick_OAbs__Frac(U_6574,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6574),U_6575))),hAPP(c_Nitpick_Odenom(U_6574),U_6575))),
    inference(clausify,[status(thm)],[f_1955_3]) ).

fof(f_1956_1,plain,
    ! [V_r_2,V_q_2,T_b] :
      ( ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def]) ).

fof(f_1956_2,plain,
    ! [U_6578,U_6577,U_6576] :
      ( ( c_Nitpick_Oless__frac(U_6576,U_6577,U_6578)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6576),c_Nitpick_Oplus__frac(U_6576,U_6577,c_Nitpick_Ouminus__frac(U_6576,U_6578)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6576),c_Nitpick_Oplus__frac(U_6576,U_6577,c_Nitpick_Ouminus__frac(U_6576,U_6578)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_6576,U_6577,U_6578) ) ),
    inference(variable_rename,[status(thm)],[f_1956_1]) ).

fof(f_1956_3,plain,
    ( ! [U_6584,U_6582,U_6580] :
        ( c_Nitpick_Oless__frac(U_6580,U_6582,U_6584)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6580),c_Nitpick_Oplus__frac(U_6580,U_6582,c_Nitpick_Ouminus__frac(U_6580,U_6584)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6583,U_6581,U_6579] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6579),c_Nitpick_Oplus__frac(U_6579,U_6581,c_Nitpick_Ouminus__frac(U_6579,U_6583)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_6579,U_6581,U_6583) ) ),
    inference(miniscope,[status(thm)],[f_1956_2]) ).

fof(f_1956_4,plain,
    ( ! [U_6580,U_6582,U_6584] :
        ( c_Nitpick_Oless__frac(U_6580,U_6582,U_6584)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6580),c_Nitpick_Oplus__frac(U_6580,U_6582,c_Nitpick_Ouminus__frac(U_6580,U_6584)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6581,U_6583,U_6579] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6579),c_Nitpick_Oplus__frac(U_6579,U_6581,c_Nitpick_Ouminus__frac(U_6579,U_6583)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_6579,U_6581,U_6583) ) ),
    inference(definitional_conversion,[status(esa)],[f_1956_3]) ).

cnf(f_1956_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6579),c_Nitpick_Oplus__frac(U_6579,U_6581,c_Nitpick_Ouminus__frac(U_6579,U_6583)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(U_6579,U_6581,U_6583) ),
    inference(clausify,[status(thm)],[f_1956_4]) ).

cnf(f_1956_6,plain,
    ( c_Nitpick_Oless__frac(U_6580,U_6582,U_6584)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6580),c_Nitpick_Oplus__frac(U_6580,U_6582,c_Nitpick_Ouminus__frac(U_6580,U_6584)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1956_4]) ).

fof(f_1957_1,plain,
    ! [V_r_2,V_q_2,T_b] :
      ( ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def]) ).

fof(f_1957_2,plain,
    ! [U_6587,U_6586,U_6585] :
      ( ( c_Nitpick_Oless__eq__frac(U_6585,U_6586,U_6587)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6585),c_Nitpick_Oplus__frac(U_6585,U_6586,c_Nitpick_Ouminus__frac(U_6585,U_6587)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6585),c_Nitpick_Oplus__frac(U_6585,U_6586,c_Nitpick_Ouminus__frac(U_6585,U_6587)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_6585,U_6586,U_6587) ) ),
    inference(variable_rename,[status(thm)],[f_1957_1]) ).

fof(f_1957_3,plain,
    ( ! [U_6593,U_6591,U_6589] :
        ( c_Nitpick_Oless__eq__frac(U_6589,U_6591,U_6593)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6589),c_Nitpick_Oplus__frac(U_6589,U_6591,c_Nitpick_Ouminus__frac(U_6589,U_6593)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6592,U_6590,U_6588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6588),c_Nitpick_Oplus__frac(U_6588,U_6590,c_Nitpick_Ouminus__frac(U_6588,U_6592)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_6588,U_6590,U_6592) ) ),
    inference(miniscope,[status(thm)],[f_1957_2]) ).

fof(f_1957_4,plain,
    ( ! [U_6589,U_6591,U_6593] :
        ( c_Nitpick_Oless__eq__frac(U_6589,U_6591,U_6593)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6589),c_Nitpick_Oplus__frac(U_6589,U_6591,c_Nitpick_Ouminus__frac(U_6589,U_6593)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6590,U_6588,U_6592] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6588),c_Nitpick_Oplus__frac(U_6588,U_6590,c_Nitpick_Ouminus__frac(U_6588,U_6592)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_6588,U_6590,U_6592) ) ),
    inference(definitional_conversion,[status(esa)],[f_1957_3]) ).

cnf(f_1957_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6588),c_Nitpick_Oplus__frac(U_6588,U_6590,c_Nitpick_Ouminus__frac(U_6588,U_6592)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(U_6588,U_6590,U_6592) ),
    inference(clausify,[status(thm)],[f_1957_4]) ).

cnf(f_1957_6,plain,
    ( c_Nitpick_Oless__eq__frac(U_6589,U_6591,U_6593)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6589),c_Nitpick_Oplus__frac(U_6589,U_6591,c_Nitpick_Ouminus__frac(U_6589,U_6593)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1957_4]) ).

fof(f_1958_1,plain,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I2_J]) ).

fof(f_1958_2,plain,
    ! [U_6597,U_6596,U_6595,U_6594] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_6594,U_6595)),c_Nitpick_Opair__box_OPairBox(U_6594,U_6595,U_6596,U_6597)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1958_1]) ).

fof(f_1958_3,plain,
    ! [U_6594,U_6596,U_6595,U_6597] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_6594,U_6595)),c_Nitpick_Opair__box_OPairBox(U_6594,U_6595,U_6596,U_6597)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1958_2]) ).

cnf(f_1958_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_6594,U_6595)),c_Nitpick_Opair__box_OPairBox(U_6594,U_6595,U_6596,U_6597)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1958_3]) ).

fof(f_1959_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).

fof(f_1959_2,plain,
    ! [U_6603,U_6602,U_6601,U_6600,U_6599,U_6598] : c_Nitpick_Opair__box_Opair__box__case(U_6598,U_6599,U_6600,U_6601,c_Nitpick_Opair__box_OPairBox(U_6598,U_6599,U_6602,U_6603)) = hAPP(hAPP(U_6601,U_6602),U_6603),
    inference(variable_rename,[status(thm)],[f_1959_1]) ).

fof(f_1959_3,plain,
    ! [U_6598,U_6599,U_6600,U_6601,U_6602,U_6603] : c_Nitpick_Opair__box_Opair__box__case(U_6598,U_6599,U_6600,U_6601,c_Nitpick_Opair__box_OPairBox(U_6598,U_6599,U_6602,U_6603)) = hAPP(hAPP(U_6601,U_6602),U_6603),
    inference(definitional_conversion,[status(esa)],[f_1959_2]) ).

cnf(f_1959_4,plain,
    c_Nitpick_Opair__box_Opair__box__case(U_6598,U_6599,U_6600,U_6601,c_Nitpick_Opair__box_OPairBox(U_6598,U_6599,U_6602,U_6603)) = hAPP(hAPP(U_6601,U_6602),U_6603),
    inference(clausify,[status(thm)],[f_1959_3]) ).

fof(f_1960_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Orecs]) ).

fof(f_1960_2,plain,
    ! [U_6609,U_6608,U_6607,U_6606,U_6605,U_6604] : c_Nitpick_Opair__box_Opair__box__rec(U_6604,U_6605,U_6606,U_6607,c_Nitpick_Opair__box_OPairBox(U_6604,U_6605,U_6608,U_6609)) = hAPP(hAPP(U_6607,U_6608),U_6609),
    inference(variable_rename,[status(thm)],[f_1960_1]) ).

fof(f_1960_3,plain,
    ! [U_6605,U_6604,U_6606,U_6607,U_6608,U_6609] : c_Nitpick_Opair__box_Opair__box__rec(U_6604,U_6605,U_6606,U_6607,c_Nitpick_Opair__box_OPairBox(U_6604,U_6605,U_6608,U_6609)) = hAPP(hAPP(U_6607,U_6608),U_6609),
    inference(definitional_conversion,[status(esa)],[f_1960_2]) ).

cnf(f_1960_4,plain,
    c_Nitpick_Opair__box_Opair__box__rec(U_6604,U_6605,U_6606,U_6607,c_Nitpick_Opair__box_OPairBox(U_6604,U_6605,U_6608,U_6609)) = hAPP(hAPP(U_6607,U_6608),U_6609),
    inference(clausify,[status(thm)],[f_1960_3]) ).

fof(f_1961_1,plain,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    inference(fof_nnf,[status(thm)],[fact_The__split]) ).

fof(f_1961_2,plain,
    ! [U_6612,U_6611,U_6610] : c_HOL_OThe(tc_prod(U_6610,U_6611),hAPP(c_Product__Type_Oprod_Oprod__case(U_6610,U_6611,tc_HOL_Obool),U_6612)) = c_HOL_OThe(tc_prod(U_6610,U_6611),hAPP(hAPP(c_COMBS(tc_prod(U_6610,U_6611),U_6611,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_6610,tc_fun(U_6611,tc_HOL_Obool),tc_prod(U_6610,U_6611)),U_6612),c_Product__Type_Ofst(U_6610,U_6611))),c_Product__Type_Osnd(U_6610,U_6611))),
    inference(variable_rename,[status(thm)],[f_1961_1]) ).

fof(f_1961_3,plain,
    ! [U_6610,U_6611,U_6612] : c_HOL_OThe(tc_prod(U_6610,U_6611),hAPP(c_Product__Type_Oprod_Oprod__case(U_6610,U_6611,tc_HOL_Obool),U_6612)) = c_HOL_OThe(tc_prod(U_6610,U_6611),hAPP(hAPP(c_COMBS(tc_prod(U_6610,U_6611),U_6611,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_6610,tc_fun(U_6611,tc_HOL_Obool),tc_prod(U_6610,U_6611)),U_6612),c_Product__Type_Ofst(U_6610,U_6611))),c_Product__Type_Osnd(U_6610,U_6611))),
    inference(definitional_conversion,[status(esa)],[f_1961_2]) ).

cnf(f_1961_4,plain,
    c_HOL_OThe(tc_prod(U_6610,U_6611),hAPP(c_Product__Type_Oprod_Oprod__case(U_6610,U_6611,tc_HOL_Obool),U_6612)) = c_HOL_OThe(tc_prod(U_6610,U_6611),hAPP(hAPP(c_COMBS(tc_prod(U_6610,U_6611),U_6611,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_6610,tc_fun(U_6611,tc_HOL_Obool),tc_prod(U_6610,U_6611)),U_6612),c_Product__Type_Ofst(U_6610,U_6611))),c_Product__Type_Osnd(U_6610,U_6611))),
    inference(clausify,[status(thm)],[f_1961_3]) ).

fof(f_1962_1,plain,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).

fof(f_1962_2,plain,
    ! [U_6615,U_6614,U_6613] : c_HOL_OThe(tc_prod(U_6613,U_6614),U_6615) = c_HOL_OThe(tc_prod(U_6613,U_6614),hAPP(c_Product__Type_Oprod_Oprod__case(U_6613,U_6614,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_6614,tc_prod(U_6613,U_6614)),tc_fun(U_6614,tc_HOL_Obool),U_6613),hAPP(c_COMBB(tc_prod(U_6613,U_6614),tc_HOL_Obool,U_6614),U_6615)),c_Product__Type_OPair(U_6613,U_6614)))),
    inference(variable_rename,[status(thm)],[f_1962_1]) ).

fof(f_1962_3,plain,
    ! [U_6613,U_6614,U_6615] : c_HOL_OThe(tc_prod(U_6613,U_6614),U_6615) = c_HOL_OThe(tc_prod(U_6613,U_6614),hAPP(c_Product__Type_Oprod_Oprod__case(U_6613,U_6614,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_6614,tc_prod(U_6613,U_6614)),tc_fun(U_6614,tc_HOL_Obool),U_6613),hAPP(c_COMBB(tc_prod(U_6613,U_6614),tc_HOL_Obool,U_6614),U_6615)),c_Product__Type_OPair(U_6613,U_6614)))),
    inference(definitional_conversion,[status(esa)],[f_1962_2]) ).

cnf(f_1962_4,plain,
    c_HOL_OThe(tc_prod(U_6613,U_6614),U_6615) = c_HOL_OThe(tc_prod(U_6613,U_6614),hAPP(c_Product__Type_Oprod_Oprod__case(U_6613,U_6614,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_6614,tc_prod(U_6613,U_6614)),tc_fun(U_6614,tc_HOL_Obool),U_6613),hAPP(c_COMBB(tc_prod(U_6613,U_6614),tc_HOL_Obool,U_6614),U_6615)),c_Product__Type_OPair(U_6613,U_6614)))),
    inference(clausify,[status(thm)],[f_1962_3]) ).

fof(f_1963_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_The__split__eq]) ).

fof(f_1963_2,plain,
    ! [U_6619,U_6618,U_6617,U_6616] : c_HOL_OThe(tc_prod(U_6616,U_6617),hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_6616,tc_fun(U_6617,tc_HOL_Obool),tc_fun(U_6617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_6617,tc_HOL_Obool),tc_fun(U_6617,tc_HOL_Obool)),U_6616),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_6617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_6616),c_fconj),hAPP(c_fequal,U_6618)))),hAPP(c_fequal,U_6619)))) = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),U_6618),U_6619),
    inference(variable_rename,[status(thm)],[f_1963_1]) ).

fof(f_1963_3,plain,
    ! [U_6616,U_6617,U_6618,U_6619] : c_HOL_OThe(tc_prod(U_6616,U_6617),hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_6616,tc_fun(U_6617,tc_HOL_Obool),tc_fun(U_6617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_6617,tc_HOL_Obool),tc_fun(U_6617,tc_HOL_Obool)),U_6616),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_6617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_6616),c_fconj),hAPP(c_fequal,U_6618)))),hAPP(c_fequal,U_6619)))) = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),U_6618),U_6619),
    inference(definitional_conversion,[status(esa)],[f_1963_2]) ).

cnf(f_1963_4,plain,
    c_HOL_OThe(tc_prod(U_6616,U_6617),hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_6616,tc_fun(U_6617,tc_HOL_Obool),tc_fun(U_6617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_6617,tc_HOL_Obool),tc_fun(U_6617,tc_HOL_Obool)),U_6616),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_6617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_6616),c_fconj),hAPP(c_fequal,U_6618)))),hAPP(c_fequal,U_6619)))) = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),U_6618),U_6619),
    inference(clausify,[status(thm)],[f_1963_3]) ).

fof(f_1964_1,plain,
    ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__def]) ).

fof(f_1964_2,plain,
    ! [U_6621,U_6620] : c_Divides_Odivmod__nat(U_6620,U_6621) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_6620,U_6621)),
    inference(variable_rename,[status(thm)],[f_1964_1]) ).

fof(f_1964_3,plain,
    ! [U_6620,U_6621] : c_Divides_Odivmod__nat(U_6620,U_6621) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_6620,U_6621)),
    inference(definitional_conversion,[status(esa)],[f_1964_2]) ).

cnf(f_1964_4,plain,
    c_Divides_Odivmod__nat(U_6620,U_6621) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_6620,U_6621)),
    inference(clausify,[status(thm)],[f_1964_3]) ).

fof(f_1965_1,plain,
    ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_the__eq__trivial]) ).

fof(f_1965_2,plain,
    ! [U_6623,U_6622] : c_HOL_OThe(U_6622,hAPP(hAPP(c_COMBC(U_6622,U_6622,tc_HOL_Obool),c_fequal),U_6623)) = U_6623,
    inference(variable_rename,[status(thm)],[f_1965_1]) ).

fof(f_1965_3,plain,
    ! [U_6622,U_6623] : c_HOL_OThe(U_6622,hAPP(hAPP(c_COMBC(U_6622,U_6622,tc_HOL_Obool),c_fequal),U_6623)) = U_6623,
    inference(definitional_conversion,[status(esa)],[f_1965_2]) ).

cnf(f_1965_4,plain,
    c_HOL_OThe(U_6622,hAPP(hAPP(c_COMBC(U_6622,U_6622,tc_HOL_Obool),c_fequal),U_6623)) = U_6623,
    inference(clausify,[status(thm)],[f_1965_3]) ).

fof(f_1966_1,plain,
    ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(f_1966_2,plain,
    ! [U_6625,U_6624] : c_HOL_OThe(U_6624,hAPP(c_fequal,U_6625)) = U_6625,
    inference(variable_rename,[status(thm)],[f_1966_1]) ).

fof(f_1966_3,plain,
    ! [U_6624,U_6625] : c_HOL_OThe(U_6624,hAPP(c_fequal,U_6625)) = U_6625,
    inference(definitional_conversion,[status(esa)],[f_1966_2]) ).

cnf(f_1966_4,plain,
    c_HOL_OThe(U_6624,hAPP(c_fequal,U_6625)) = U_6625,
    inference(clausify,[status(thm)],[f_1966_3]) ).

fof(f_1967_1,plain,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).

fof(f_1967_2,plain,
    ! [U_6629,U_6628,U_6627,U_6626] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6626,U_6627,U_6628,c_Code__Numeral_OSuc__code__numeral(U_6629)) = hAPP(hAPP(U_6628,U_6629),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6626,U_6627,U_6628,U_6629)),
    inference(variable_rename,[status(thm)],[f_1967_1]) ).

fof(f_1967_3,plain,
    ! [U_6627,U_6626,U_6628,U_6629] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6626,U_6627,U_6628,c_Code__Numeral_OSuc__code__numeral(U_6629)) = hAPP(hAPP(U_6628,U_6629),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6626,U_6627,U_6628,U_6629)),
    inference(definitional_conversion,[status(esa)],[f_1967_2]) ).

cnf(f_1967_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6626,U_6627,U_6628,c_Code__Numeral_OSuc__code__numeral(U_6629)) = hAPP(hAPP(U_6628,U_6629),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6626,U_6627,U_6628,U_6629)),
    inference(clausify,[status(thm)],[f_1967_3]) ).

fof(f_1968_1,plain,
    ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
      ( ( c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Random_Osimps]) ).

fof(f_1968_2,plain,
    ! [U_6633,U_6632,U_6631,U_6630] :
      ( ( c_Random__Sequence_ORandom(U_6631,U_6632,U_6630,U_6633) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6631,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6632,U_6633)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6631,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6631,U_6632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6630),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6633))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6631,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631))))),tc_prod(U_6631,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6631)),hAPP(hAPP(c_COMBB(U_6631,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(U_6631,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6631)),c_Product__Type_Ofst(U_6631,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6630),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(U_6631,U_6632,U_6630,U_6633) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6631)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6631))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6630),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(variable_rename,[status(thm)],[f_1968_1]) ).

fof(f_1968_3,plain,
    ( ! [U_6641,U_6639,U_6637,U_6635] :
        ( c_Random__Sequence_ORandom(U_6637,U_6639,U_6635,U_6641) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6639,U_6641)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6637,U_6639,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6635),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6641))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6637)),hAPP(hAPP(c_COMBB(U_6637,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6637)),c_Product__Type_Ofst(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6635),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_6640,U_6638,U_6636,U_6634] :
        ( c_Random__Sequence_ORandom(U_6636,U_6638,U_6634,U_6640) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6636)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6636))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6634),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(miniscope,[status(thm)],[f_1968_2]) ).

fof(f_1968_4,plain,
    ( ! [U_6639,U_6635,U_6641,U_6637] :
        ( c_Random__Sequence_ORandom(U_6637,U_6639,U_6635,U_6641) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6639,U_6641)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6637,U_6639,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6635),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6641))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6637)),hAPP(hAPP(c_COMBB(U_6637,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6637)),c_Product__Type_Ofst(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6635),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_6636,U_6634,U_6638,U_6640] :
        ( c_Random__Sequence_ORandom(U_6636,U_6638,U_6634,U_6640) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6636)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6636))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6634),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1968_3]) ).

cnf(f_1968_5,plain,
    ( c_Random__Sequence_ORandom(U_6636,U_6638,U_6634,U_6640) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6636)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6636))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6634),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_1968_4]) ).

cnf(f_1968_6,plain,
    ( c_Random__Sequence_ORandom(U_6637,U_6639,U_6635,U_6641) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6639,U_6641)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6637,U_6639,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6635),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6641))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637))))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6637)),hAPP(hAPP(c_COMBB(U_6637,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6637)))),tc_prod(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6637)),c_Product__Type_Ofst(U_6637,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6635),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_1968_4]) ).

fof(f_1969_1,plain,
    ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
      ( hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2)))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y)))
          & hBOOL(hAPP(hAPP(V_P_2,B_y),B_x)) )
      | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) ),
    inference(fof_nnf,[status(thm)],[fact_exE__realizer]) ).

fof(f_1969_2,plain,
    ! [U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644] :
      ( hBOOL(hAPP(U_6648,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6645,U_6646,U_6650),U_6649),U_6647)))
      | ? [U_6643,U_6642] :
          ( ~ hBOOL(hAPP(U_6648,hAPP(hAPP(U_6649,U_6643),U_6642)))
          & hBOOL(hAPP(hAPP(U_6644,U_6642),U_6643)) )
      | ~ hBOOL(hAPP(hAPP(U_6644,hAPP(c_Product__Type_Osnd(U_6645,U_6646),U_6647)),hAPP(c_Product__Type_Ofst(U_6645,U_6646),U_6647))) ),
    inference(variable_rename,[status(thm)],[f_1969_1]) ).

fof(f_1969_3,plain,
    ! [U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644] :
      ( hBOOL(hAPP(U_6648,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6645,U_6646,U_6650),U_6649),U_6647)))
      | ? [U_6642] :
          ( ~ hBOOL(hAPP(U_6648,hAPP(hAPP(U_6649,sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),U_6642)))
          & hBOOL(hAPP(hAPP(U_6644,U_6642),sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))) )
      | ~ hBOOL(hAPP(hAPP(U_6644,hAPP(c_Product__Type_Osnd(U_6645,U_6646),U_6647)),hAPP(c_Product__Type_Ofst(U_6645,U_6646),U_6647))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_6643,sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))],[f_1969_2]) ).

fof(f_1969_4,plain,
    ! [U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644] :
      ( hBOOL(hAPP(U_6648,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6645,U_6646,U_6650),U_6649),U_6647)))
      | ( ~ hBOOL(hAPP(U_6648,hAPP(hAPP(U_6649,sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))))
        & hBOOL(hAPP(hAPP(U_6644,sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))) )
      | ~ hBOOL(hAPP(hAPP(U_6644,hAPP(c_Product__Type_Osnd(U_6645,U_6646),U_6647)),hAPP(c_Product__Type_Ofst(U_6645,U_6646),U_6647))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_6642,sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))],[f_1969_3]) ).

fof(f_1969_5,plain,
    ( ! [U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650] :
        ( ~ hBOOL(hAPP(U_6648,hAPP(hAPP(U_6649,sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))))
        | ~ sP617(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650) )
    & ! [U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650] :
        ( hBOOL(hAPP(hAPP(U_6644,sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)))
        | ~ sP617(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650) )
    & ! [U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650] :
        ( hBOOL(hAPP(U_6648,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6645,U_6646,U_6650),U_6649),U_6647)))
        | sP617(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650)
        | ~ hBOOL(hAPP(hAPP(U_6644,hAPP(c_Product__Type_Osnd(U_6645,U_6646),U_6647)),hAPP(c_Product__Type_Ofst(U_6645,U_6646),U_6647))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP617])],[f_1969_4]) ).

cnf(f_1969_6,plain,
    ( hBOOL(hAPP(U_6648,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6645,U_6646,U_6650),U_6649),U_6647)))
    | sP617(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650)
    | ~ hBOOL(hAPP(hAPP(U_6644,hAPP(c_Product__Type_Osnd(U_6645,U_6646),U_6647)),hAPP(c_Product__Type_Ofst(U_6645,U_6646),U_6647))) ),
    inference(clausify,[status(thm)],[f_1969_5]) ).

cnf(f_1969_7,plain,
    ( hBOOL(hAPP(hAPP(U_6644,sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)))
    | ~ sP617(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650) ),
    inference(clausify,[status(thm)],[f_1969_5]) ).

cnf(f_1969_8,plain,
    ( ~ hBOOL(hAPP(U_6648,hAPP(hAPP(U_6649,sK98(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644)),sK99(U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644))))
    | ~ sP617(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649,U_6650) ),
    inference(clausify,[status(thm)],[f_1969_5]) ).

fof(f_1970_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).

fof(f_1970_2,plain,
    ! [U_6653,U_6652,U_6651] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6651,U_6652,U_6653,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6652,
    inference(variable_rename,[status(thm)],[f_1970_1]) ).

fof(f_1970_3,plain,
    ! [U_6651,U_6653,U_6652] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6651,U_6652,U_6653,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6652,
    inference(definitional_conversion,[status(esa)],[f_1970_2]) ).

cnf(f_1970_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6651,U_6652,U_6653,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6652,
    inference(clausify,[status(thm)],[f_1970_3]) ).

fof(f_1971_1,plain,
    ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).

fof(f_1971_2,plain,
    ! [U_6656,U_6655,U_6654] : c_Random__Sequence_Oempty(U_6654,U_6655,U_6656) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6654)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6654)),
    inference(variable_rename,[status(thm)],[f_1971_1]) ).

fof(f_1971_3,plain,
    ! [U_6654,U_6656,U_6655] : c_Random__Sequence_Oempty(U_6654,U_6655,U_6656) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6654)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6654)),
    inference(definitional_conversion,[status(esa)],[f_1971_2]) ).

cnf(f_1971_4,plain,
    c_Random__Sequence_Oempty(U_6654,U_6655,U_6656) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6654)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6654)),
    inference(clausify,[status(thm)],[f_1971_3]) ).

fof(f_1972_1,plain,
    ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).

fof(f_1972_2,plain,
    ! [U_6660,U_6659,U_6658,U_6657] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_6657),U_6658),U_6659),U_6660) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6657)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_6657),U_6658)),
    inference(variable_rename,[status(thm)],[f_1972_1]) ).

fof(f_1972_3,plain,
    ! [U_6657,U_6658,U_6659,U_6660] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_6657),U_6658),U_6659),U_6660) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6657)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_6657),U_6658)),
    inference(definitional_conversion,[status(esa)],[f_1972_2]) ).

cnf(f_1972_4,plain,
    hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_6657),U_6658),U_6659),U_6660) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6657)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_6657),U_6658)),
    inference(clausify,[status(thm)],[f_1972_3]) ).

fof(f_1973_1,plain,
    ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).

fof(f_1973_2,plain,
    ! [U_6662,U_6661] : hAPP(c_New__DSequence_Opos__not__seq(U_6661),U_6662) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_6662))),
    inference(variable_rename,[status(thm)],[f_1973_1]) ).

fof(f_1973_3,plain,
    ! [U_6661,U_6662] : hAPP(c_New__DSequence_Opos__not__seq(U_6661),U_6662) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_6662))),
    inference(definitional_conversion,[status(esa)],[f_1973_2]) ).

cnf(f_1973_4,plain,
    hAPP(c_New__DSequence_Opos__not__seq(U_6661),U_6662) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_6662))),
    inference(clausify,[status(thm)],[f_1973_3]) ).

fof(f_1974_1,plain,
    ! [V_i_2] :
      ( ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2))
        | V_i_2 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero]) ).

fof(f_1974_2,plain,
    ! [U_6663] :
      ( ( U_6663 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6663)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6663))
        | U_6663 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1974_1]) ).

fof(f_1974_3,plain,
    ( ! [U_6665] :
        ( U_6665 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6665)) )
    & ! [U_6664] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6664))
        | U_6664 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1974_2]) ).

fof(f_1974_4,plain,
    ( ! [U_6665] :
        ( U_6665 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6665)) )
    & ! [U_6664] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6664))
        | U_6664 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1974_3]) ).

cnf(f_1974_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6664))
    | U_6664 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1974_4]) ).

cnf(f_1974_6,plain,
    ( U_6665 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6665)) ),
    inference(clausify,[status(thm)],[f_1974_4]) ).

fof(f_1975_1,plain,
    ! [V_l,V_k] :
      ( ( c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) )
      & ( c_Quickcheck_Obeyond(V_k,V_l) = V_l
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_beyond__def]) ).

fof(f_1975_2,plain,
    ! [U_6667,U_6666] :
      ( ( c_Quickcheck_Obeyond(U_6666,U_6667) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6666),U_6667)) )
      & ( c_Quickcheck_Obeyond(U_6666,U_6667) = U_6667
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6666),U_6667)) ) ),
    inference(variable_rename,[status(thm)],[f_1975_1]) ).

fof(f_1975_3,plain,
    ( ! [U_6671,U_6669] :
        ( c_Quickcheck_Obeyond(U_6669,U_6671) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6669),U_6671)) )
    & ! [U_6670,U_6668] :
        ( c_Quickcheck_Obeyond(U_6668,U_6670) = U_6670
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6668),U_6670)) ) ),
    inference(miniscope,[status(thm)],[f_1975_2]) ).

fof(f_1975_4,plain,
    ( ! [U_6669,U_6671] :
        ( c_Quickcheck_Obeyond(U_6669,U_6671) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6669),U_6671)) )
    & ! [U_6668,U_6670] :
        ( c_Quickcheck_Obeyond(U_6668,U_6670) = U_6670
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6668),U_6670)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1975_3]) ).

cnf(f_1975_5,plain,
    ( c_Quickcheck_Obeyond(U_6668,U_6670) = U_6670
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6668),U_6670)) ),
    inference(clausify,[status(thm)],[f_1975_4]) ).

cnf(f_1975_6,plain,
    ( c_Quickcheck_Obeyond(U_6669,U_6671) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6669),U_6671)) ),
    inference(clausify,[status(thm)],[f_1975_4]) ).

fof(f_1976_1,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__code]) ).

fof(f_1976_2,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1976_1]) ).

cnf(f_1976_3,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1976_2]) ).

fof(f_1977_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
        | V_n_2 != V_m_2 )
      & ( V_n_2 = V_m_2
        | hAPP(c_Code__Numeral_Oof__nat,V_n_2) != hAPP(c_Code__Numeral_Oof__nat,V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject]) ).

fof(f_1977_2,plain,
    ! [U_6673,U_6672] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,U_6672) = hAPP(c_Code__Numeral_Oof__nat,U_6673)
        | U_6672 != U_6673 )
      & ( U_6672 = U_6673
        | hAPP(c_Code__Numeral_Oof__nat,U_6672) != hAPP(c_Code__Numeral_Oof__nat,U_6673) ) ),
    inference(variable_rename,[status(thm)],[f_1977_1]) ).

fof(f_1977_3,plain,
    ( ! [U_6677,U_6675] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_6675) = hAPP(c_Code__Numeral_Oof__nat,U_6677)
        | U_6675 != U_6677 )
    & ! [U_6676,U_6674] :
        ( U_6674 = U_6676
        | hAPP(c_Code__Numeral_Oof__nat,U_6674) != hAPP(c_Code__Numeral_Oof__nat,U_6676) ) ),
    inference(miniscope,[status(thm)],[f_1977_2]) ).

fof(f_1977_4,plain,
    ( ! [U_6675,U_6677] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_6675) = hAPP(c_Code__Numeral_Oof__nat,U_6677)
        | U_6675 != U_6677 )
    & ! [U_6676,U_6674] :
        ( U_6674 = U_6676
        | hAPP(c_Code__Numeral_Oof__nat,U_6674) != hAPP(c_Code__Numeral_Oof__nat,U_6676) ) ),
    inference(definitional_conversion,[status(esa)],[f_1977_3]) ).

cnf(f_1977_5,plain,
    ( U_6674 = U_6676
    | hAPP(c_Code__Numeral_Oof__nat,U_6674) != hAPP(c_Code__Numeral_Oof__nat,U_6676) ),
    inference(clausify,[status(thm)],[f_1977_4]) ).

cnf(f_1977_6,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_6675) = hAPP(c_Code__Numeral_Oof__nat,U_6677)
    | U_6675 != U_6677 ),
    inference(clausify,[status(thm)],[f_1977_4]) ).

fof(f_1978_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),
    inference(fof_nnf,[status(thm)],[fact_times__code__numeral__code]) ).

fof(f_1978_2,plain,
    ! [U_6679,U_6678] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6678)),hAPP(c_Code__Numeral_Oof__nat,U_6679)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6678),U_6679)),
    inference(variable_rename,[status(thm)],[f_1978_1]) ).

fof(f_1978_3,plain,
    ! [U_6678,U_6679] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6678)),hAPP(c_Code__Numeral_Oof__nat,U_6679)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6678),U_6679)),
    inference(definitional_conversion,[status(esa)],[f_1978_2]) ).

cnf(f_1978_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6678)),hAPP(c_Code__Numeral_Oof__nat,U_6679)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6678),U_6679)),
    inference(clausify,[status(thm)],[f_1978_3]) ).

fof(f_1979_1,plain,
    ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_beyond__zero]) ).

fof(f_1979_2,plain,
    ! [U_6680] : c_Quickcheck_Obeyond(U_6680,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_1979_1]) ).

fof(f_1979_3,plain,
    ! [U_6680] : c_Quickcheck_Obeyond(U_6680,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1979_2]) ).

cnf(f_1979_4,plain,
    c_Quickcheck_Obeyond(U_6680,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1979_3]) ).

fof(f_1980_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__def]) ).

fof(f_1980_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1980_1]) ).

cnf(f_1980_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1980_2]) ).

fof(f_1981_1,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_one__code__numeral__def]) ).

fof(f_1981_2,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1981_1]) ).

cnf(f_1981_3,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1981_2]) ).

fof(f_1982_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code]) ).

fof(f_1982_2,plain,
    ! [U_6682,U_6681] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6681)),hAPP(c_Code__Numeral_Oof__nat,U_6682)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6681),U_6682)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6681),U_6682))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6681)),hAPP(c_Code__Numeral_Oof__nat,U_6682))) ) ),
    inference(variable_rename,[status(thm)],[f_1982_1]) ).

fof(f_1982_3,plain,
    ( ! [U_6686,U_6684] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6684)),hAPP(c_Code__Numeral_Oof__nat,U_6686)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6684),U_6686)) )
    & ! [U_6685,U_6683] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6683),U_6685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6683)),hAPP(c_Code__Numeral_Oof__nat,U_6685))) ) ),
    inference(miniscope,[status(thm)],[f_1982_2]) ).

fof(f_1982_4,plain,
    ( ! [U_6684,U_6686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6684)),hAPP(c_Code__Numeral_Oof__nat,U_6686)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6684),U_6686)) )
    & ! [U_6685,U_6683] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6683),U_6685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6683)),hAPP(c_Code__Numeral_Oof__nat,U_6685))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1982_3]) ).

cnf(f_1982_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6683),U_6685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6683)),hAPP(c_Code__Numeral_Oof__nat,U_6685))) ),
    inference(clausify,[status(thm)],[f_1982_4]) ).

cnf(f_1982_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6684)),hAPP(c_Code__Numeral_Oof__nat,U_6686)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6684),U_6686)) ),
    inference(clausify,[status(thm)],[f_1982_4]) ).

fof(f_1983_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),
    inference(fof_nnf,[status(thm)],[fact_plus__code__numeral__code]) ).

fof(f_1983_2,plain,
    ! [U_6688,U_6687] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6687)),hAPP(c_Code__Numeral_Oof__nat,U_6688)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6687),U_6688)),
    inference(variable_rename,[status(thm)],[f_1983_1]) ).

fof(f_1983_3,plain,
    ! [U_6688,U_6687] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6687)),hAPP(c_Code__Numeral_Oof__nat,U_6688)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6687),U_6688)),
    inference(definitional_conversion,[status(esa)],[f_1983_2]) ).

cnf(f_1983_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6687)),hAPP(c_Code__Numeral_Oof__nat,U_6688)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6687),U_6688)),
    inference(clausify,[status(thm)],[f_1983_3]) ).

fof(f_1984_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code]) ).

fof(f_1984_2,plain,
    ! [U_6690,U_6689] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6689)),hAPP(c_Code__Numeral_Oof__nat,U_6690)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6689),U_6690)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6689),U_6690))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6689)),hAPP(c_Code__Numeral_Oof__nat,U_6690))) ) ),
    inference(variable_rename,[status(thm)],[f_1984_1]) ).

fof(f_1984_3,plain,
    ( ! [U_6694,U_6692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6692)),hAPP(c_Code__Numeral_Oof__nat,U_6694)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6692),U_6694)) )
    & ! [U_6693,U_6691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6691),U_6693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6691)),hAPP(c_Code__Numeral_Oof__nat,U_6693))) ) ),
    inference(miniscope,[status(thm)],[f_1984_2]) ).

fof(f_1984_4,plain,
    ( ! [U_6692,U_6694] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6692)),hAPP(c_Code__Numeral_Oof__nat,U_6694)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6692),U_6694)) )
    & ! [U_6693,U_6691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6691),U_6693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6691)),hAPP(c_Code__Numeral_Oof__nat,U_6693))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1984_3]) ).

cnf(f_1984_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6691),U_6693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6691)),hAPP(c_Code__Numeral_Oof__nat,U_6693))) ),
    inference(clausify,[status(thm)],[f_1984_4]) ).

cnf(f_1984_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_6692)),hAPP(c_Code__Numeral_Oof__nat,U_6694)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6692),U_6694)) ),
    inference(clausify,[status(thm)],[f_1984_4]) ).

fof(f_1985_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
    inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__code]) ).

fof(f_1985_2,plain,
    ! [U_6696,U_6695] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_6695)),hAPP(c_Code__Numeral_Oof__nat,U_6696)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6695),U_6696)),
    inference(variable_rename,[status(thm)],[f_1985_1]) ).

fof(f_1985_3,plain,
    ! [U_6696,U_6695] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_6695)),hAPP(c_Code__Numeral_Oof__nat,U_6696)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6695),U_6696)),
    inference(definitional_conversion,[status(esa)],[f_1985_2]) ).

cnf(f_1985_4,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_6695)),hAPP(c_Code__Numeral_Oof__nat,U_6696)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6695),U_6696)),
    inference(clausify,[status(thm)],[f_1985_3]) ).

fof(f_1986_1,plain,
    ! [V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k)))
      | V_k = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral__decr]) ).

fof(f_1986_2,plain,
    ! [U_6697] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6697)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_6697)))
      | U_6697 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[f_1986_1]) ).

fof(f_1986_3,plain,
    ! [U_6697] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6697)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_6697)))
      | U_6697 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(definitional_conversion,[status(esa)],[f_1986_2]) ).

cnf(f_1986_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6697)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_6697)))
    | U_6697 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1986_3]) ).

fof(f_1987_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__not__random__dseq__def]) ).

fof(f_1987_2,plain,
    ! [U_6701,U_6700,U_6699,U_6698] : c_New__Random__Sequence_Opos__not__random__dseq(U_6698,U_6699,U_6700,U_6701) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_6698,U_6699),U_6700),U_6701)),
    inference(variable_rename,[status(thm)],[f_1987_1]) ).

fof(f_1987_3,plain,
    ! [U_6698,U_6699,U_6700,U_6701] : c_New__Random__Sequence_Opos__not__random__dseq(U_6698,U_6699,U_6700,U_6701) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_6698,U_6699),U_6700),U_6701)),
    inference(definitional_conversion,[status(esa)],[f_1987_2]) ).

cnf(f_1987_4,plain,
    c_New__Random__Sequence_Opos__not__random__dseq(U_6698,U_6699,U_6700,U_6701) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_6698,U_6699),U_6700),U_6701)),
    inference(clausify,[status(thm)],[f_1987_3]) ).

fof(f_1988_1,plain,
    ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_mod__code__numeral__def]) ).

fof(f_1988_2,plain,
    ! [U_6703,U_6702] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6702,U_6703) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_6702),hAPP(c_Code__Numeral_Onat__of,U_6703))),
    inference(variable_rename,[status(thm)],[f_1988_1]) ).

fof(f_1988_3,plain,
    ! [U_6702,U_6703] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6702,U_6703) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_6702),hAPP(c_Code__Numeral_Onat__of,U_6703))),
    inference(definitional_conversion,[status(esa)],[f_1988_2]) ).

cnf(f_1988_4,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6702,U_6703) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_6702),hAPP(c_Code__Numeral_Onat__of,U_6703))),
    inference(clausify,[status(thm)],[f_1988_3]) ).

fof(f_1989_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_times__code__numeral__def]) ).

fof(f_1989_2,plain,
    ! [U_6705,U_6704] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_6704),U_6705) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6704)),hAPP(c_Code__Numeral_Onat__of,U_6705))),
    inference(variable_rename,[status(thm)],[f_1989_1]) ).

fof(f_1989_3,plain,
    ! [U_6704,U_6705] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_6704),U_6705) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6704)),hAPP(c_Code__Numeral_Onat__of,U_6705))),
    inference(definitional_conversion,[status(esa)],[f_1989_2]) ).

cnf(f_1989_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_6704),U_6705) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6704)),hAPP(c_Code__Numeral_Onat__of,U_6705))),
    inference(clausify,[status(thm)],[f_1989_3]) ).

fof(f_1990_1,plain,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2))
        | V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b)
        | V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def]) ).

fof(f_1990_2,plain,
    ! [U_6710,U_6709,U_6708,U_6707,U_6706] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(U_6707,U_6708,U_6709,U_6710),U_6706) = c_Lazy__Sequence_Obind(U_6707,U_6708,hAPP(U_6709,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6706),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6707,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6708)),U_6710),U_6706))
        | U_6706 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(U_6707,U_6708,U_6709,U_6710),U_6706) = c_Lazy__Sequence_Oempty(U_6708)
        | U_6706 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1990_1]) ).

fof(f_1990_3,plain,
    ( ! [U_6720,U_6718,U_6716,U_6714,U_6712] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_6714,U_6716,U_6718,U_6720),U_6712) = c_Lazy__Sequence_Obind(U_6714,U_6716,hAPP(U_6718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6712),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6714,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6716)),U_6720),U_6712))
        | U_6712 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6719,U_6717,U_6715,U_6713,U_6711] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_6713,U_6715,U_6717,U_6719),U_6711) = c_Lazy__Sequence_Oempty(U_6715)
        | U_6711 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1990_2]) ).

fof(f_1990_4,plain,
    ( ! [U_6718,U_6712,U_6714,U_6716,U_6720] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_6714,U_6716,U_6718,U_6720),U_6712) = c_Lazy__Sequence_Obind(U_6714,U_6716,hAPP(U_6718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6712),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6714,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6716)),U_6720),U_6712))
        | U_6712 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6711,U_6713,U_6715,U_6717,U_6719] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_6713,U_6715,U_6717,U_6719),U_6711) = c_Lazy__Sequence_Oempty(U_6715)
        | U_6711 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_1990_3]) ).

cnf(f_1990_5,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_6713,U_6715,U_6717,U_6719),U_6711) = c_Lazy__Sequence_Oempty(U_6715)
    | U_6711 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1990_4]) ).

cnf(f_1990_6,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_6714,U_6716,U_6718,U_6720),U_6712) = c_Lazy__Sequence_Obind(U_6714,U_6716,hAPP(U_6718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6712),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6714,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6716)),U_6720),U_6712))
    | U_6712 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1990_4]) ).

fof(f_1991_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Code__Numeral_Onat__of,V_x_2) != hAPP(c_Code__Numeral_Onat__of,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject]) ).

fof(f_1991_2,plain,
    ! [U_6722,U_6721] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_6721) = hAPP(c_Code__Numeral_Onat__of,U_6722)
        | U_6721 != U_6722 )
      & ( U_6721 = U_6722
        | hAPP(c_Code__Numeral_Onat__of,U_6721) != hAPP(c_Code__Numeral_Onat__of,U_6722) ) ),
    inference(variable_rename,[status(thm)],[f_1991_1]) ).

fof(f_1991_3,plain,
    ( ! [U_6726,U_6724] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6724) = hAPP(c_Code__Numeral_Onat__of,U_6726)
        | U_6724 != U_6726 )
    & ! [U_6725,U_6723] :
        ( U_6723 = U_6725
        | hAPP(c_Code__Numeral_Onat__of,U_6723) != hAPP(c_Code__Numeral_Onat__of,U_6725) ) ),
    inference(miniscope,[status(thm)],[f_1991_2]) ).

fof(f_1991_4,plain,
    ( ! [U_6724,U_6726] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6724) = hAPP(c_Code__Numeral_Onat__of,U_6726)
        | U_6724 != U_6726 )
    & ! [U_6725,U_6723] :
        ( U_6723 = U_6725
        | hAPP(c_Code__Numeral_Onat__of,U_6723) != hAPP(c_Code__Numeral_Onat__of,U_6725) ) ),
    inference(definitional_conversion,[status(esa)],[f_1991_3]) ).

cnf(f_1991_5,plain,
    ( U_6723 = U_6725
    | hAPP(c_Code__Numeral_Onat__of,U_6723) != hAPP(c_Code__Numeral_Onat__of,U_6725) ),
    inference(clausify,[status(thm)],[f_1991_4]) ).

cnf(f_1991_6,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_6724) = hAPP(c_Code__Numeral_Onat__of,U_6726)
    | U_6724 != U_6726 ),
    inference(clausify,[status(thm)],[f_1991_4]) ).

fof(f_1992_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
        | V_k_2 != V_l_2 )
      & ( V_k_2 = V_l_2
        | hAPP(c_Code__Numeral_Onat__of,V_k_2) != hAPP(c_Code__Numeral_Onat__of,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject]) ).

fof(f_1992_2,plain,
    ! [U_6728,U_6727] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_6727) = hAPP(c_Code__Numeral_Onat__of,U_6728)
        | U_6727 != U_6728 )
      & ( U_6727 = U_6728
        | hAPP(c_Code__Numeral_Onat__of,U_6727) != hAPP(c_Code__Numeral_Onat__of,U_6728) ) ),
    inference(variable_rename,[status(thm)],[f_1992_1]) ).

fof(f_1992_3,plain,
    ( ! [U_6732,U_6730] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6730) = hAPP(c_Code__Numeral_Onat__of,U_6732)
        | U_6730 != U_6732 )
    & ! [U_6731,U_6729] :
        ( U_6729 = U_6731
        | hAPP(c_Code__Numeral_Onat__of,U_6729) != hAPP(c_Code__Numeral_Onat__of,U_6731) ) ),
    inference(miniscope,[status(thm)],[f_1992_2]) ).

fof(f_1992_4,plain,
    ( ! [U_6730,U_6732] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6730) = hAPP(c_Code__Numeral_Onat__of,U_6732)
        | U_6730 != U_6732 )
    & ! [U_6731,U_6729] :
        ( U_6729 = U_6731
        | hAPP(c_Code__Numeral_Onat__of,U_6729) != hAPP(c_Code__Numeral_Onat__of,U_6731) ) ),
    inference(definitional_conversion,[status(esa)],[f_1992_3]) ).

cnf(f_1992_5,plain,
    ( U_6729 = U_6731
    | hAPP(c_Code__Numeral_Onat__of,U_6729) != hAPP(c_Code__Numeral_Onat__of,U_6731) ),
    inference(clausify,[status(thm)],[f_1992_4]) ).

cnf(f_1992_6,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_6730) = hAPP(c_Code__Numeral_Onat__of,U_6732)
    | U_6730 != U_6732 ),
    inference(clausify,[status(thm)],[f_1992_4]) ).

fof(f_1993_1,plain,
    ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_nat__of__inverse]) ).

fof(f_1993_2,plain,
    ! [U_6733] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6733)) = U_6733,
    inference(variable_rename,[status(thm)],[f_1993_1]) ).

fof(f_1993_3,plain,
    ! [U_6733] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6733)) = U_6733,
    inference(definitional_conversion,[status(esa)],[f_1993_2]) ).

cnf(f_1993_4,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6733)) = U_6733,
    inference(clausify,[status(thm)],[f_1993_3]) ).

fof(f_1994_1,plain,
    ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
    inference(fof_nnf,[status(thm)],[fact_of__nat__nat__of]) ).

fof(f_1994_2,plain,
    ! [U_6734] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6734)) = U_6734,
    inference(variable_rename,[status(thm)],[f_1994_1]) ).

fof(f_1994_3,plain,
    ! [U_6734] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6734)) = U_6734,
    inference(definitional_conversion,[status(esa)],[f_1994_2]) ).

cnf(f_1994_4,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6734)) = U_6734,
    inference(clausify,[status(thm)],[f_1994_3]) ).

fof(f_1995_1,plain,
    ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__of__of__nat]) ).

fof(f_1995_2,plain,
    ! [U_6735] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_6735)) = U_6735,
    inference(variable_rename,[status(thm)],[f_1995_1]) ).

fof(f_1995_3,plain,
    ! [U_6735] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_6735)) = U_6735,
    inference(definitional_conversion,[status(esa)],[f_1995_2]) ).

cnf(f_1995_4,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_6735)) = U_6735,
    inference(clausify,[status(thm)],[f_1995_3]) ).

fof(f_1996_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def]) ).

fof(f_1996_2,plain,
    ! [U_6737,U_6736] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6736),U_6737))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6736)),hAPP(c_Code__Numeral_Onat__of,U_6737))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6736)),hAPP(c_Code__Numeral_Onat__of,U_6737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6736),U_6737)) ) ),
    inference(variable_rename,[status(thm)],[f_1996_1]) ).

fof(f_1996_3,plain,
    ( ! [U_6741,U_6739] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6739),U_6741))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6739)),hAPP(c_Code__Numeral_Onat__of,U_6741))) )
    & ! [U_6740,U_6738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6738)),hAPP(c_Code__Numeral_Onat__of,U_6740)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6738),U_6740)) ) ),
    inference(miniscope,[status(thm)],[f_1996_2]) ).

fof(f_1996_4,plain,
    ( ! [U_6739,U_6741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6739),U_6741))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6739)),hAPP(c_Code__Numeral_Onat__of,U_6741))) )
    & ! [U_6740,U_6738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6738)),hAPP(c_Code__Numeral_Onat__of,U_6740)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6738),U_6740)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1996_3]) ).

cnf(f_1996_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6738)),hAPP(c_Code__Numeral_Onat__of,U_6740)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6738),U_6740)) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6739),U_6741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6739)),hAPP(c_Code__Numeral_Onat__of,U_6741))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

fof(f_1997_1,plain,
    ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k),
    inference(fof_nnf,[status(thm)],[fact_nat__of__number]) ).

fof(f_1997_2,plain,
    ! [U_6742] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_6742)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6742),
    inference(variable_rename,[status(thm)],[f_1997_1]) ).

fof(f_1997_3,plain,
    ! [U_6742] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_6742)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6742),
    inference(definitional_conversion,[status(esa)],[f_1997_2]) ).

cnf(f_1997_4,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_6742)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6742),
    inference(clausify,[status(thm)],[f_1997_3]) ).

fof(f_1998_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def]) ).

fof(f_1998_2,plain,
    ! [U_6744,U_6743] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6743),U_6744))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6743)),hAPP(c_Code__Numeral_Onat__of,U_6744))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6743)),hAPP(c_Code__Numeral_Onat__of,U_6744)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6743),U_6744)) ) ),
    inference(variable_rename,[status(thm)],[f_1998_1]) ).

fof(f_1998_3,plain,
    ( ! [U_6748,U_6746] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6746),U_6748))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6746)),hAPP(c_Code__Numeral_Onat__of,U_6748))) )
    & ! [U_6747,U_6745] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6745)),hAPP(c_Code__Numeral_Onat__of,U_6747)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6745),U_6747)) ) ),
    inference(miniscope,[status(thm)],[f_1998_2]) ).

fof(f_1998_4,plain,
    ( ! [U_6746,U_6748] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6746),U_6748))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6746)),hAPP(c_Code__Numeral_Onat__of,U_6748))) )
    & ! [U_6747,U_6745] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6745)),hAPP(c_Code__Numeral_Onat__of,U_6747)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6745),U_6747)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1998_3]) ).

cnf(f_1998_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6745)),hAPP(c_Code__Numeral_Onat__of,U_6747)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6745),U_6747)) ),
    inference(clausify,[status(thm)],[f_1998_4]) ).

cnf(f_1998_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6746),U_6748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6746)),hAPP(c_Code__Numeral_Onat__of,U_6748))) ),
    inference(clausify,[status(thm)],[f_1998_4]) ).

fof(f_1999_1,plain,
    ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_nat__of__code]) ).

fof(f_1999_2,plain,
    ! [U_6749] : hAPP(c_Code__Numeral_Onat__of,U_6749) = c_Code__Numeral_Onat__of__aux(U_6749,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1999_1]) ).

fof(f_1999_3,plain,
    ! [U_6749] : hAPP(c_Code__Numeral_Onat__of,U_6749) = c_Code__Numeral_Onat__of__aux(U_6749,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1999_2]) ).

cnf(f_1999_4,plain,
    hAPP(c_Code__Numeral_Onat__of,U_6749) = c_Code__Numeral_Onat__of__aux(U_6749,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1999_3]) ).

fof(f_2000_1,plain,
    ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n),
    inference(fof_nnf,[status(thm)],[fact_nat__of__aux__def]) ).

fof(f_2000_2,plain,
    ! [U_6751,U_6750] : c_Code__Numeral_Onat__of__aux(U_6750,U_6751) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6750)),U_6751),
    inference(variable_rename,[status(thm)],[f_2000_1]) ).

fof(f_2000_3,plain,
    ! [U_6750,U_6751] : c_Code__Numeral_Onat__of__aux(U_6750,U_6751) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6750)),U_6751),
    inference(definitional_conversion,[status(esa)],[f_2000_2]) ).

cnf(f_2000_4,plain,
    c_Code__Numeral_Onat__of__aux(U_6750,U_6751) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6750)),U_6751),
    inference(clausify,[status(thm)],[f_2000_3]) ).

fof(f_2001_1,plain,
    ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))),
    inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__def]) ).

fof(f_2001_2,plain,
    ! [U_6752] : c_Code__Numeral_OSuc__code__numeral(U_6752) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_6752))),
    inference(variable_rename,[status(thm)],[f_2001_1]) ).

fof(f_2001_3,plain,
    ! [U_6752] : c_Code__Numeral_OSuc__code__numeral(U_6752) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_6752))),
    inference(definitional_conversion,[status(esa)],[f_2001_2]) ).

cnf(f_2001_4,plain,
    c_Code__Numeral_OSuc__code__numeral(U_6752) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_6752))),
    inference(clausify,[status(thm)],[f_2001_3]) ).

fof(f_2002_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__def]) ).

fof(f_2002_2,plain,
    ! [U_6754,U_6753] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6753),U_6754) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6753)),hAPP(c_Code__Numeral_Onat__of,U_6754))),
    inference(variable_rename,[status(thm)],[f_2002_1]) ).

fof(f_2002_3,plain,
    ! [U_6753,U_6754] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6753),U_6754) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6753)),hAPP(c_Code__Numeral_Onat__of,U_6754))),
    inference(definitional_conversion,[status(esa)],[f_2002_2]) ).

cnf(f_2002_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6753),U_6754) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6753)),hAPP(c_Code__Numeral_Onat__of,U_6754))),
    inference(clausify,[status(thm)],[f_2002_3]) ).

fof(f_2003_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_plus__code__numeral__def]) ).

fof(f_2003_2,plain,
    ! [U_6756,U_6755] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6755),U_6756) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6755)),hAPP(c_Code__Numeral_Onat__of,U_6756))),
    inference(variable_rename,[status(thm)],[f_2003_1]) ).

fof(f_2003_3,plain,
    ! [U_6755,U_6756] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6755),U_6756) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6755)),hAPP(c_Code__Numeral_Onat__of,U_6756))),
    inference(definitional_conversion,[status(esa)],[f_2003_2]) ).

cnf(f_2003_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6755),U_6756) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6755)),hAPP(c_Code__Numeral_Onat__of,U_6756))),
    inference(clausify,[status(thm)],[f_2003_3]) ).

fof(f_2004_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_div__code__numeral__def]) ).

fof(f_2004_2,plain,
    ! [U_6758,U_6757] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6757),U_6758) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6757)),hAPP(c_Code__Numeral_Onat__of,U_6758))),
    inference(variable_rename,[status(thm)],[f_2004_1]) ).

fof(f_2004_3,plain,
    ! [U_6757,U_6758] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6757),U_6758) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6757)),hAPP(c_Code__Numeral_Onat__of,U_6758))),
    inference(definitional_conversion,[status(esa)],[f_2004_2]) ).

cnf(f_2004_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6757),U_6758) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6757)),hAPP(c_Code__Numeral_Onat__of,U_6758))),
    inference(clausify,[status(thm)],[f_2004_3]) ).

fof(f_2005_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).

fof(f_2005_2,plain,
    ! [U_6765,U_6764,U_6763,U_6762,U_6761,U_6760,U_6759] : c_New__Random__Sequence_Opos__decr__bind(U_6759,U_6760,U_6761,U_6762,U_6763,U_6764,U_6765) = c_New__DSequence_Opos__decr__bind(U_6759,U_6760,hAPP(hAPP(hAPP(U_6761,U_6763),U_6764),U_6765),hAPP(hAPP(c_COMBC(U_6759,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760))),hAPP(hAPP(c_COMBC(U_6759,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760)))),hAPP(hAPP(c_COMBC(U_6759,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760))))),U_6762),U_6763)),U_6764)),U_6765)),
    inference(variable_rename,[status(thm)],[f_2005_1]) ).

fof(f_2005_3,plain,
    ! [U_6759,U_6760,U_6761,U_6762,U_6763,U_6764,U_6765] : c_New__Random__Sequence_Opos__decr__bind(U_6759,U_6760,U_6761,U_6762,U_6763,U_6764,U_6765) = c_New__DSequence_Opos__decr__bind(U_6759,U_6760,hAPP(hAPP(hAPP(U_6761,U_6763),U_6764),U_6765),hAPP(hAPP(c_COMBC(U_6759,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760))),hAPP(hAPP(c_COMBC(U_6759,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760)))),hAPP(hAPP(c_COMBC(U_6759,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760))))),U_6762),U_6763)),U_6764)),U_6765)),
    inference(definitional_conversion,[status(esa)],[f_2005_2]) ).

cnf(f_2005_4,plain,
    c_New__Random__Sequence_Opos__decr__bind(U_6759,U_6760,U_6761,U_6762,U_6763,U_6764,U_6765) = c_New__DSequence_Opos__decr__bind(U_6759,U_6760,hAPP(hAPP(hAPP(U_6761,U_6763),U_6764),U_6765),hAPP(hAPP(c_COMBC(U_6759,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760))),hAPP(hAPP(c_COMBC(U_6759,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760)))),hAPP(hAPP(c_COMBC(U_6759,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6760))))),U_6762),U_6763)),U_6764)),U_6765)),
    inference(clausify,[status(thm)],[f_2005_3]) ).

fof(f_2006_1,plain,
    ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).

fof(f_2006_2,plain,
    ! [U_6767,U_6766] : hAPP(c_New__DSequence_Opos__empty(U_6766),U_6767) = c_Lazy__Sequence_Oempty(U_6766),
    inference(variable_rename,[status(thm)],[f_2006_1]) ).

fof(f_2006_3,plain,
    ! [U_6766,U_6767] : hAPP(c_New__DSequence_Opos__empty(U_6766),U_6767) = c_Lazy__Sequence_Oempty(U_6766),
    inference(definitional_conversion,[status(esa)],[f_2006_2]) ).

cnf(f_2006_4,plain,
    hAPP(c_New__DSequence_Opos__empty(U_6766),U_6767) = c_Lazy__Sequence_Oempty(U_6766),
    inference(clausify,[status(thm)],[f_2006_3]) ).

fof(f_2007_1,plain,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(f_2007_2,plain,
    ! [U_6772,U_6771,U_6770,U_6769,U_6768] : hAPP(c_New__DSequence_Opos__bind(U_6768,U_6769,U_6770,U_6771),U_6772) = c_Lazy__Sequence_Obind(U_6768,U_6769,hAPP(U_6770,U_6772),hAPP(hAPP(c_COMBC(U_6768,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6769)),U_6771),U_6772)),
    inference(variable_rename,[status(thm)],[f_2007_1]) ).

fof(f_2007_3,plain,
    ! [U_6769,U_6768,U_6770,U_6771,U_6772] : hAPP(c_New__DSequence_Opos__bind(U_6768,U_6769,U_6770,U_6771),U_6772) = c_Lazy__Sequence_Obind(U_6768,U_6769,hAPP(U_6770,U_6772),hAPP(hAPP(c_COMBC(U_6768,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6769)),U_6771),U_6772)),
    inference(definitional_conversion,[status(esa)],[f_2007_2]) ).

cnf(f_2007_4,plain,
    hAPP(c_New__DSequence_Opos__bind(U_6768,U_6769,U_6770,U_6771),U_6772) = c_Lazy__Sequence_Obind(U_6768,U_6769,hAPP(U_6770,U_6772),hAPP(hAPP(c_COMBC(U_6768,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6769)),U_6771),U_6772)),
    inference(clausify,[status(thm)],[f_2007_3]) ).

fof(f_2008_1,plain,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2))
        | V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b)
        | V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def]) ).

fof(f_2008_2,plain,
    ! [U_6777,U_6776,U_6775,U_6774,U_6773] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6774,U_6775,U_6776,U_6777),U_6773) = c_Lazy__Sequence_Ohb__bind(U_6774,U_6775,hAPP(U_6776,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6773),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6774,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6775))),U_6777),U_6773))
        | U_6773 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6774,U_6775,U_6776,U_6777),U_6773) = c_Lazy__Sequence_Ohit__bound(U_6775)
        | U_6773 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2008_1]) ).

fof(f_2008_3,plain,
    ( ! [U_6787,U_6785,U_6783,U_6781,U_6779] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6781,U_6783,U_6785,U_6787),U_6779) = c_Lazy__Sequence_Ohb__bind(U_6781,U_6783,hAPP(U_6785,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6779),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6781,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6783))),U_6787),U_6779))
        | U_6779 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6786,U_6784,U_6782,U_6780,U_6778] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6780,U_6782,U_6784,U_6786),U_6778) = c_Lazy__Sequence_Ohit__bound(U_6782)
        | U_6778 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2008_2]) ).

fof(f_2008_4,plain,
    ( ! [U_6785,U_6779,U_6781,U_6783,U_6787] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6781,U_6783,U_6785,U_6787),U_6779) = c_Lazy__Sequence_Ohb__bind(U_6781,U_6783,hAPP(U_6785,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6779),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6781,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6783))),U_6787),U_6779))
        | U_6779 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6778,U_6780,U_6782,U_6784,U_6786] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6780,U_6782,U_6784,U_6786),U_6778) = c_Lazy__Sequence_Ohit__bound(U_6782)
        | U_6778 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_2008_3]) ).

cnf(f_2008_5,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6780,U_6782,U_6784,U_6786),U_6778) = c_Lazy__Sequence_Ohit__bound(U_6782)
    | U_6778 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2008_4]) ).

cnf(f_2008_6,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_6781,U_6783,U_6785,U_6787),U_6779) = c_Lazy__Sequence_Ohb__bind(U_6781,U_6783,hAPP(U_6785,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6779),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_6781,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6783))),U_6787),U_6779))
    | U_6779 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2008_4]) ).

fof(f_2009_1,plain,
    ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_curry__def]) ).

fof(f_2009_2,plain,
    ! [U_6793,U_6792,U_6791,U_6790,U_6789,U_6788] : hAPP(hAPP(c_Product__Type_Ocurry(U_6788,U_6789,U_6790,U_6791),U_6792),U_6793) = hAPP(U_6791,hAPP(hAPP(c_Product__Type_OPair(U_6788,U_6789),U_6792),U_6793)),
    inference(variable_rename,[status(thm)],[f_2009_1]) ).

fof(f_2009_3,plain,
    ! [U_6788,U_6791,U_6789,U_6790,U_6792,U_6793] : hAPP(hAPP(c_Product__Type_Ocurry(U_6788,U_6789,U_6790,U_6791),U_6792),U_6793) = hAPP(U_6791,hAPP(hAPP(c_Product__Type_OPair(U_6788,U_6789),U_6792),U_6793)),
    inference(definitional_conversion,[status(esa)],[f_2009_2]) ).

cnf(f_2009_4,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_6788,U_6789,U_6790,U_6791),U_6792),U_6793) = hAPP(U_6791,hAPP(hAPP(c_Product__Type_OPair(U_6788,U_6789),U_6792),U_6793)),
    inference(clausify,[status(thm)],[f_2009_3]) ).

fof(f_2010_1,plain,
    ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
      | ~ hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_curryI]) ).

fof(f_2010_2,plain,
    ! [U_6798,U_6797,U_6796,U_6795,U_6794] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6795,U_6796,tc_HOL_Obool,U_6794),U_6797),U_6798))
      | ~ hBOOL(hAPP(U_6794,hAPP(hAPP(c_Product__Type_OPair(U_6795,U_6796),U_6797),U_6798))) ),
    inference(variable_rename,[status(thm)],[f_2010_1]) ).

fof(f_2010_3,plain,
    ! [U_6795,U_6794,U_6796,U_6797,U_6798] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6795,U_6796,tc_HOL_Obool,U_6794),U_6797),U_6798))
      | ~ hBOOL(hAPP(U_6794,hAPP(hAPP(c_Product__Type_OPair(U_6795,U_6796),U_6797),U_6798))) ),
    inference(definitional_conversion,[status(esa)],[f_2010_2]) ).

cnf(f_2010_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6795,U_6796,tc_HOL_Obool,U_6794),U_6797),U_6798))
    | ~ hBOOL(hAPP(U_6794,hAPP(hAPP(c_Product__Type_OPair(U_6795,U_6796),U_6797),U_6798))) ),
    inference(clausify,[status(thm)],[f_2010_3]) ).

fof(f_2011_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_curryD]) ).

fof(f_2011_2,plain,
    ! [U_6803,U_6802,U_6801,U_6800,U_6799] :
      ( hBOOL(hAPP(U_6801,hAPP(hAPP(c_Product__Type_OPair(U_6799,U_6800),U_6802),U_6803)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6799,U_6800,tc_HOL_Obool,U_6801),U_6802),U_6803)) ),
    inference(variable_rename,[status(thm)],[f_2011_1]) ).

fof(f_2011_3,plain,
    ! [U_6799,U_6800,U_6801,U_6802,U_6803] :
      ( hBOOL(hAPP(U_6801,hAPP(hAPP(c_Product__Type_OPair(U_6799,U_6800),U_6802),U_6803)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6799,U_6800,tc_HOL_Obool,U_6801),U_6802),U_6803)) ),
    inference(definitional_conversion,[status(esa)],[f_2011_2]) ).

cnf(f_2011_4,plain,
    ( hBOOL(hAPP(U_6801,hAPP(hAPP(c_Product__Type_OPair(U_6799,U_6800),U_6802),U_6803)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6799,U_6800,tc_HOL_Obool,U_6801),U_6802),U_6803)) ),
    inference(clausify,[status(thm)],[f_2011_3]) ).

fof(f_2012_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_curryE]) ).

fof(f_2012_2,plain,
    ! [U_6808,U_6807,U_6806,U_6805,U_6804] :
      ( hBOOL(hAPP(U_6806,hAPP(hAPP(c_Product__Type_OPair(U_6804,U_6805),U_6807),U_6808)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6804,U_6805,tc_HOL_Obool,U_6806),U_6807),U_6808)) ),
    inference(variable_rename,[status(thm)],[f_2012_1]) ).

fof(f_2012_3,plain,
    ! [U_6804,U_6805,U_6806,U_6807,U_6808] :
      ( hBOOL(hAPP(U_6806,hAPP(hAPP(c_Product__Type_OPair(U_6804,U_6805),U_6807),U_6808)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6804,U_6805,tc_HOL_Obool,U_6806),U_6807),U_6808)) ),
    inference(definitional_conversion,[status(esa)],[f_2012_2]) ).

cnf(f_2012_4,plain,
    ( hBOOL(hAPP(U_6806,hAPP(hAPP(c_Product__Type_OPair(U_6804,U_6805),U_6807),U_6808)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6804,U_6805,tc_HOL_Obool,U_6806),U_6807),U_6808)) ),
    inference(clausify,[status(thm)],[f_2012_3]) ).

fof(f_2013_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),
    inference(fof_nnf,[status(thm)],[fact_curry__conv]) ).

fof(f_2013_2,plain,
    ! [U_6814,U_6813,U_6812,U_6811,U_6810,U_6809] : hAPP(hAPP(c_Product__Type_Ocurry(U_6809,U_6810,U_6811,U_6812),U_6813),U_6814) = hAPP(U_6812,hAPP(hAPP(c_Product__Type_OPair(U_6809,U_6810),U_6813),U_6814)),
    inference(variable_rename,[status(thm)],[f_2013_1]) ).

fof(f_2013_3,plain,
    ! [U_6809,U_6810,U_6811,U_6812,U_6813,U_6814] : hAPP(hAPP(c_Product__Type_Ocurry(U_6809,U_6810,U_6811,U_6812),U_6813),U_6814) = hAPP(U_6812,hAPP(hAPP(c_Product__Type_OPair(U_6809,U_6810),U_6813),U_6814)),
    inference(definitional_conversion,[status(esa)],[f_2013_2]) ).

cnf(f_2013_4,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_6809,U_6810,U_6811,U_6812),U_6813),U_6814) = hAPP(U_6812,hAPP(hAPP(c_Product__Type_OPair(U_6809,U_6810),U_6813),U_6814)),
    inference(clausify,[status(thm)],[f_2013_3]) ).

fof(f_2014_1,plain,
    ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_curry__split]) ).

fof(f_2014_2,plain,
    ! [U_6818,U_6817,U_6816,U_6815] : c_Product__Type_Ocurry(U_6815,U_6816,U_6817,hAPP(c_Product__Type_Oprod_Oprod__case(U_6815,U_6816,U_6817),U_6818)) = U_6818,
    inference(variable_rename,[status(thm)],[f_2014_1]) ).

fof(f_2014_3,plain,
    ! [U_6815,U_6817,U_6816,U_6818] : c_Product__Type_Ocurry(U_6815,U_6816,U_6817,hAPP(c_Product__Type_Oprod_Oprod__case(U_6815,U_6816,U_6817),U_6818)) = U_6818,
    inference(definitional_conversion,[status(esa)],[f_2014_2]) ).

cnf(f_2014_4,plain,
    c_Product__Type_Ocurry(U_6815,U_6816,U_6817,hAPP(c_Product__Type_Oprod_Oprod__case(U_6815,U_6816,U_6817),U_6818)) = U_6818,
    inference(clausify,[status(thm)],[f_2014_3]) ).

fof(f_2015_1,plain,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_split__curry]) ).

fof(f_2015_2,plain,
    ! [U_6822,U_6821,U_6820,U_6819] : hAPP(c_Product__Type_Oprod_Oprod__case(U_6819,U_6820,U_6821),c_Product__Type_Ocurry(U_6819,U_6820,U_6821,U_6822)) = U_6822,
    inference(variable_rename,[status(thm)],[f_2015_1]) ).

fof(f_2015_3,plain,
    ! [U_6819,U_6820,U_6821,U_6822] : hAPP(c_Product__Type_Oprod_Oprod__case(U_6819,U_6820,U_6821),c_Product__Type_Ocurry(U_6819,U_6820,U_6821,U_6822)) = U_6822,
    inference(definitional_conversion,[status(esa)],[f_2015_2]) ).

cnf(f_2015_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_6819,U_6820,U_6821),c_Product__Type_Ocurry(U_6819,U_6820,U_6821,U_6822)) = U_6822,
    inference(clausify,[status(thm)],[f_2015_3]) ).

fof(f_2016_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
    inference(fof_nnf,[status(thm)],[fact_pos__empty__def]) ).

fof(f_2016_2,plain,
    ! [U_6826,U_6825,U_6824,U_6823] : c_New__Random__Sequence_Opos__empty(U_6823,U_6824,U_6825,U_6826) = c_New__DSequence_Opos__empty(U_6823),
    inference(variable_rename,[status(thm)],[f_2016_1]) ).

fof(f_2016_3,plain,
    ! [U_6824,U_6823,U_6825,U_6826] : c_New__Random__Sequence_Opos__empty(U_6823,U_6824,U_6825,U_6826) = c_New__DSequence_Opos__empty(U_6823),
    inference(definitional_conversion,[status(esa)],[f_2016_2]) ).

cnf(f_2016_4,plain,
    c_New__Random__Sequence_Opos__empty(U_6823,U_6824,U_6825,U_6826) = c_New__DSequence_Opos__empty(U_6823),
    inference(clausify,[status(thm)],[f_2016_3]) ).

fof(f_2017_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).

fof(f_2017_2,plain,
    ! [U_6833,U_6832,U_6831,U_6830,U_6829,U_6828,U_6827] : c_New__Random__Sequence_Oneg__decr__bind(U_6827,U_6828,U_6829,U_6830,U_6831,U_6832,U_6833) = c_New__DSequence_Oneg__decr__bind(U_6827,U_6828,hAPP(hAPP(hAPP(U_6829,U_6831),U_6832),U_6833),hAPP(hAPP(c_COMBC(U_6827,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828)))),hAPP(hAPP(c_COMBC(U_6827,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828))))),hAPP(hAPP(c_COMBC(U_6827,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828)))))),U_6830),U_6831)),U_6832)),U_6833)),
    inference(variable_rename,[status(thm)],[f_2017_1]) ).

fof(f_2017_3,plain,
    ! [U_6828,U_6827,U_6829,U_6830,U_6831,U_6832,U_6833] : c_New__Random__Sequence_Oneg__decr__bind(U_6827,U_6828,U_6829,U_6830,U_6831,U_6832,U_6833) = c_New__DSequence_Oneg__decr__bind(U_6827,U_6828,hAPP(hAPP(hAPP(U_6829,U_6831),U_6832),U_6833),hAPP(hAPP(c_COMBC(U_6827,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828)))),hAPP(hAPP(c_COMBC(U_6827,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828))))),hAPP(hAPP(c_COMBC(U_6827,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828)))))),U_6830),U_6831)),U_6832)),U_6833)),
    inference(definitional_conversion,[status(esa)],[f_2017_2]) ).

cnf(f_2017_4,plain,
    c_New__Random__Sequence_Oneg__decr__bind(U_6827,U_6828,U_6829,U_6830,U_6831,U_6832,U_6833) = c_New__DSequence_Oneg__decr__bind(U_6827,U_6828,hAPP(hAPP(hAPP(U_6829,U_6831),U_6832),U_6833),hAPP(hAPP(c_COMBC(U_6827,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828)))),hAPP(hAPP(c_COMBC(U_6827,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828))))),hAPP(hAPP(c_COMBC(U_6827,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6828)))))),U_6830),U_6831)),U_6832)),U_6833)),
    inference(clausify,[status(thm)],[f_2017_3]) ).

fof(f_2018_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__bind__def]) ).

fof(f_2018_2,plain,
    ! [U_6840,U_6839,U_6838,U_6837,U_6836,U_6835,U_6834] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_6834,U_6835,U_6836,U_6837),U_6838),U_6839),U_6840) = c_New__DSequence_Opos__bind(U_6834,U_6835,hAPP(hAPP(hAPP(U_6836,U_6838),U_6839),U_6840),hAPP(hAPP(c_COMBC(U_6834,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835))),hAPP(hAPP(c_COMBC(U_6834,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835)))),hAPP(hAPP(c_COMBC(U_6834,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835))))),U_6837),U_6838)),U_6839)),U_6840)),
    inference(variable_rename,[status(thm)],[f_2018_1]) ).

fof(f_2018_3,plain,
    ! [U_6834,U_6835,U_6836,U_6837,U_6838,U_6839,U_6840] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_6834,U_6835,U_6836,U_6837),U_6838),U_6839),U_6840) = c_New__DSequence_Opos__bind(U_6834,U_6835,hAPP(hAPP(hAPP(U_6836,U_6838),U_6839),U_6840),hAPP(hAPP(c_COMBC(U_6834,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835))),hAPP(hAPP(c_COMBC(U_6834,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835)))),hAPP(hAPP(c_COMBC(U_6834,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835))))),U_6837),U_6838)),U_6839)),U_6840)),
    inference(definitional_conversion,[status(esa)],[f_2018_2]) ).

cnf(f_2018_4,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_6834,U_6835,U_6836,U_6837),U_6838),U_6839),U_6840) = c_New__DSequence_Opos__bind(U_6834,U_6835,hAPP(hAPP(hAPP(U_6836,U_6838),U_6839),U_6840),hAPP(hAPP(c_COMBC(U_6834,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835))),hAPP(hAPP(c_COMBC(U_6834,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835)))),hAPP(hAPP(c_COMBC(U_6834,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_6835))))),U_6837),U_6838)),U_6839)),U_6840)),
    inference(clausify,[status(thm)],[f_2018_3]) ).

fof(f_2019_1,plain,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(f_2019_2,plain,
    ! [U_6845,U_6844,U_6843,U_6842,U_6841] : hAPP(c_New__DSequence_Oneg__bind(U_6841,U_6842,U_6843,U_6844),U_6845) = c_Lazy__Sequence_Ohb__bind(U_6841,U_6842,hAPP(U_6843,U_6845),hAPP(hAPP(c_COMBC(U_6841,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6842))),U_6844),U_6845)),
    inference(variable_rename,[status(thm)],[f_2019_1]) ).

fof(f_2019_3,plain,
    ! [U_6842,U_6841,U_6843,U_6844,U_6845] : hAPP(c_New__DSequence_Oneg__bind(U_6841,U_6842,U_6843,U_6844),U_6845) = c_Lazy__Sequence_Ohb__bind(U_6841,U_6842,hAPP(U_6843,U_6845),hAPP(hAPP(c_COMBC(U_6841,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6842))),U_6844),U_6845)),
    inference(definitional_conversion,[status(esa)],[f_2019_2]) ).

cnf(f_2019_4,plain,
    hAPP(c_New__DSequence_Oneg__bind(U_6841,U_6842,U_6843,U_6844),U_6845) = c_Lazy__Sequence_Ohb__bind(U_6841,U_6842,hAPP(U_6843,U_6845),hAPP(hAPP(c_COMBC(U_6841,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_6842))),U_6844),U_6845)),
    inference(clausify,[status(thm)],[f_2019_3]) ).

fof(f_2020_1,plain,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le]) ).

fof(f_2020_2,plain,
    ! [U_6848,U_6847,U_6846] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6847),U_6848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6846))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6846),U_6847)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6846),U_6848))) ),
    inference(variable_rename,[status(thm)],[f_2020_1]) ).

fof(f_2020_3,plain,
    ! [U_6846,U_6847,U_6848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6847),U_6848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6846))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6846),U_6847)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6846),U_6848))) ),
    inference(definitional_conversion,[status(esa)],[f_2020_2]) ).

cnf(f_2020_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6847),U_6848))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6846))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6846),U_6847)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6846),U_6848))) ),
    inference(clausify,[status(thm)],[f_2020_3]) ).

fof(f_2021_1,plain,
    ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__refl]) ).

fof(f_2021_2,plain,
    ! [U_6849] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6849),U_6849)),
    inference(variable_rename,[status(thm)],[f_2021_1]) ).

fof(f_2021_3,plain,
    ! [U_6849] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6849),U_6849)),
    inference(definitional_conversion,[status(esa)],[f_2021_2]) ).

cnf(f_2021_4,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6849),U_6849)),
    inference(clausify,[status(thm)],[f_2021_3]) ).

fof(f_2022_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__0__right]) ).

fof(f_2022_2,plain,
    ! [U_6851,U_6850] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6850),U_6851),c_Groups_Ozero__class_Ozero(U_6850)))
      | ~ class_Rings_Ocomm__semiring__1(U_6850) ),
    inference(variable_rename,[status(thm)],[f_2022_1]) ).

fof(f_2022_3,plain,
    ! [U_6850,U_6851] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6850),U_6851),c_Groups_Ozero__class_Ozero(U_6850)))
      | ~ class_Rings_Ocomm__semiring__1(U_6850) ),
    inference(definitional_conversion,[status(esa)],[f_2022_2]) ).

cnf(f_2022_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6850),U_6851),c_Groups_Ozero__class_Ozero(U_6850)))
    | ~ class_Rings_Ocomm__semiring__1(U_6850) ),
    inference(clausify,[status(thm)],[f_2022_3]) ).

fof(f_2023_1,plain,
    ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
    inference(fof_nnf,[status(thm)],[fact_dvd__1__left]) ).

fof(f_2023_2,plain,
    ! [U_6852] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6852)),
    inference(variable_rename,[status(thm)],[f_2023_1]) ).

fof(f_2023_3,plain,
    ! [U_6852] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6852)),
    inference(definitional_conversion,[status(esa)],[f_2023_2]) ).

cnf(f_2023_4,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6852)),
    inference(clausify,[status(thm)],[f_2023_3]) ).

fof(f_2024_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__right]) ).

fof(f_2024_2,plain,
    ! [U_6856,U_6855,U_6854,U_6853] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6853),U_6855),U_6856))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6853),U_6854),U_6855)),U_6856))
      | ~ class_Rings_Ocomm__semiring__1(U_6853) ),
    inference(variable_rename,[status(thm)],[f_2024_1]) ).

fof(f_2024_3,plain,
    ! [U_6853,U_6854,U_6855,U_6856] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6853),U_6855),U_6856))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6853),U_6854),U_6855)),U_6856))
      | ~ class_Rings_Ocomm__semiring__1(U_6853) ),
    inference(definitional_conversion,[status(esa)],[f_2024_2]) ).

cnf(f_2024_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6853),U_6855),U_6856))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6853),U_6854),U_6855)),U_6856))
    | ~ class_Rings_Ocomm__semiring__1(U_6853) ),
    inference(clausify,[status(thm)],[f_2024_3]) ).

fof(f_2025_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__left]) ).

fof(f_2025_2,plain,
    ! [U_6860,U_6859,U_6858,U_6857] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6857),U_6858),U_6860))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6857),U_6858),U_6859)),U_6860))
      | ~ class_Rings_Ocomm__semiring__1(U_6857) ),
    inference(variable_rename,[status(thm)],[f_2025_1]) ).

fof(f_2025_3,plain,
    ! [U_6857,U_6858,U_6859,U_6860] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6857),U_6858),U_6860))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6857),U_6858),U_6859)),U_6860))
      | ~ class_Rings_Ocomm__semiring__1(U_6857) ),
    inference(definitional_conversion,[status(esa)],[f_2025_2]) ).

cnf(f_2025_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6857),U_6858),U_6860))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6857),U_6858),U_6859)),U_6860))
    | ~ class_Rings_Ocomm__semiring__1(U_6857) ),
    inference(clausify,[status(thm)],[f_2025_3]) ).

fof(f_2026_1,plain,
    ! [V_k,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a))
      | V_a != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
      | ~ class_Rings_Odvd(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvdI]) ).

fof(f_2026_2,plain,
    ! [U_6864,U_6863,U_6862,U_6861] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6861),U_6863),U_6862))
      | U_6862 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),U_6863),U_6864)
      | ~ class_Rings_Odvd(U_6861) ),
    inference(variable_rename,[status(thm)],[f_2026_1]) ).

fof(f_2026_3,plain,
    ! [U_6861,U_6862,U_6863,U_6864] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6861),U_6863),U_6862))
      | U_6862 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),U_6863),U_6864)
      | ~ class_Rings_Odvd(U_6861) ),
    inference(definitional_conversion,[status(esa)],[f_2026_2]) ).

cnf(f_2026_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6861),U_6863),U_6862))
    | U_6862 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),U_6863),U_6864)
    | ~ class_Rings_Odvd(U_6861) ),
    inference(clausify,[status(thm)],[f_2026_3]) ).

fof(f_2027_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono]) ).

fof(f_2027_2,plain,
    ! [U_6869,U_6868,U_6867,U_6866,U_6865] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6865),U_6866),U_6868)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6865),U_6867),U_6869)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),U_6868),U_6869))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),U_6866),U_6867))
      | ~ class_Rings_Ocomm__semiring__1(U_6865) ),
    inference(variable_rename,[status(thm)],[f_2027_1]) ).

fof(f_2027_3,plain,
    ! [U_6865,U_6866,U_6867,U_6868,U_6869] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6865),U_6866),U_6868)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6865),U_6867),U_6869)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),U_6868),U_6869))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),U_6866),U_6867))
      | ~ class_Rings_Ocomm__semiring__1(U_6865) ),
    inference(definitional_conversion,[status(esa)],[f_2027_2]) ).

cnf(f_2027_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6865),U_6866),U_6868)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6865),U_6867),U_6869)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),U_6868),U_6869))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6865),U_6866),U_6867))
    | ~ class_Rings_Ocomm__semiring__1(U_6865) ),
    inference(clausify,[status(thm)],[f_2027_3]) ).

fof(f_2028_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult]) ).

fof(f_2028_2,plain,
    ! [U_6873,U_6872,U_6871,U_6870] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6870),U_6871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6870),U_6873),U_6872)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6870),U_6871),U_6872))
      | ~ class_Rings_Ocomm__semiring__1(U_6870) ),
    inference(variable_rename,[status(thm)],[f_2028_1]) ).

fof(f_2028_3,plain,
    ! [U_6871,U_6870,U_6872,U_6873] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6870),U_6871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6870),U_6873),U_6872)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6870),U_6871),U_6872))
      | ~ class_Rings_Ocomm__semiring__1(U_6870) ),
    inference(definitional_conversion,[status(esa)],[f_2028_2]) ).

cnf(f_2028_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6870),U_6871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6870),U_6873),U_6872)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6870),U_6871),U_6872))
    | ~ class_Rings_Ocomm__semiring__1(U_6870) ),
    inference(clausify,[status(thm)],[f_2028_3]) ).

fof(f_2029_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult2]) ).

fof(f_2029_2,plain,
    ! [U_6877,U_6876,U_6875,U_6874] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6874),U_6875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6874),U_6876),U_6877)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6874),U_6875),U_6876))
      | ~ class_Rings_Ocomm__semiring__1(U_6874) ),
    inference(variable_rename,[status(thm)],[f_2029_1]) ).

fof(f_2029_3,plain,
    ! [U_6874,U_6875,U_6876,U_6877] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6874),U_6875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6874),U_6876),U_6877)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6874),U_6875),U_6876))
      | ~ class_Rings_Ocomm__semiring__1(U_6874) ),
    inference(definitional_conversion,[status(esa)],[f_2029_2]) ).

cnf(f_2029_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6874),U_6875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6874),U_6876),U_6877)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6874),U_6875),U_6876))
    | ~ class_Rings_Ocomm__semiring__1(U_6874) ),
    inference(clausify,[status(thm)],[f_2029_3]) ).

fof(f_2030_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__triv__right]) ).

fof(f_2030_2,plain,
    ! [U_6880,U_6879,U_6878] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6878),U_6879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6878),U_6880),U_6879)))
      | ~ class_Rings_Ocomm__semiring__1(U_6878) ),
    inference(variable_rename,[status(thm)],[f_2030_1]) ).

fof(f_2030_3,plain,
    ! [U_6878,U_6879,U_6880] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6878),U_6879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6878),U_6880),U_6879)))
      | ~ class_Rings_Ocomm__semiring__1(U_6878) ),
    inference(definitional_conversion,[status(esa)],[f_2030_2]) ).

cnf(f_2030_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6878),U_6879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6878),U_6880),U_6879)))
    | ~ class_Rings_Ocomm__semiring__1(U_6878) ),
    inference(clausify,[status(thm)],[f_2030_3]) ).

fof(f_2031_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__triv__left]) ).

fof(f_2031_2,plain,
    ! [U_6883,U_6882,U_6881] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6881),U_6882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6881),U_6882),U_6883)))
      | ~ class_Rings_Ocomm__semiring__1(U_6881) ),
    inference(variable_rename,[status(thm)],[f_2031_1]) ).

fof(f_2031_3,plain,
    ! [U_6881,U_6882,U_6883] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6881),U_6882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6881),U_6882),U_6883)))
      | ~ class_Rings_Ocomm__semiring__1(U_6881) ),
    inference(definitional_conversion,[status(esa)],[f_2031_2]) ).

cnf(f_2031_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6881),U_6882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6881),U_6882),U_6883)))
    | ~ class_Rings_Ocomm__semiring__1(U_6881) ),
    inference(clausify,[status(thm)],[f_2031_3]) ).

fof(f_2032_1,plain,
    ! [V_n,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power__same]) ).

fof(f_2032_2,plain,
    ! [U_6887,U_6886,U_6885,U_6884] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6884),hAPP(hAPP(c_Power_Opower__class_Opower(U_6884),U_6885),U_6887)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6884),U_6886),U_6887)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6884),U_6885),U_6886))
      | ~ class_Rings_Ocomm__semiring__1(U_6884) ),
    inference(variable_rename,[status(thm)],[f_2032_1]) ).

fof(f_2032_3,plain,
    ! [U_6884,U_6885,U_6886,U_6887] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6884),hAPP(hAPP(c_Power_Opower__class_Opower(U_6884),U_6885),U_6887)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6884),U_6886),U_6887)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6884),U_6885),U_6886))
      | ~ class_Rings_Ocomm__semiring__1(U_6884) ),
    inference(definitional_conversion,[status(esa)],[f_2032_2]) ).

cnf(f_2032_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6884),hAPP(hAPP(c_Power_Opower__class_Opower(U_6884),U_6885),U_6887)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6884),U_6886),U_6887)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6884),U_6885),U_6886))
    | ~ class_Rings_Ocomm__semiring__1(U_6884) ),
    inference(clausify,[status(thm)],[f_2032_3]) ).

fof(f_2033_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_div__dvd__div]) ).

fof(f_2033_2,plain,
    ! [U_6891,U_6890,U_6889,U_6888] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6890),U_6889)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6891),U_6889)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6890),U_6891)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6890),U_6891))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6890),U_6889)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6891),U_6889))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6889),U_6891))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6889),U_6890))
      | ~ class_Divides_Osemiring__div(U_6888) ),
    inference(variable_rename,[status(thm)],[f_2033_1]) ).

fof(f_2033_3,plain,
    ( ! [U_6888,U_6889,U_6890,U_6891] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6890),U_6889)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6891),U_6889)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6890),U_6891))
        | ~ sP618(U_6888,U_6889,U_6890,U_6891) )
    & ! [U_6888,U_6889,U_6890,U_6891] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6890),U_6891))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6890),U_6889)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6891),U_6889)))
        | ~ sP618(U_6888,U_6889,U_6890,U_6891) )
    & ! [U_6888,U_6889,U_6890,U_6891] :
        ( sP618(U_6888,U_6889,U_6890,U_6891)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6889),U_6891))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6889),U_6890))
        | ~ class_Divides_Osemiring__div(U_6888) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP618])],[f_2033_2]) ).

cnf(f_2033_4,plain,
    ( sP618(U_6888,U_6889,U_6890,U_6891)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6889),U_6891))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6889),U_6890))
    | ~ class_Divides_Osemiring__div(U_6888) ),
    inference(clausify,[status(thm)],[f_2033_3]) ).

cnf(f_2033_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6890),U_6891))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6890),U_6889)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6891),U_6889)))
    | ~ sP618(U_6888,U_6889,U_6890,U_6891) ),
    inference(clausify,[status(thm)],[f_2033_3]) ).

cnf(f_2033_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6890),U_6889)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6888),U_6891),U_6889)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6888),U_6890),U_6891))
    | ~ sP618(U_6888,U_6889,U_6890,U_6891) ),
    inference(clausify,[status(thm)],[f_2033_3]) ).

fof(f_2034_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__dvd]) ).

fof(f_2034_2,plain,
    ! [U_6893,U_6892] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6892),c_Groups_Oone__class_Oone(U_6892)),U_6893))
      | ~ class_Rings_Ocomm__semiring__1(U_6892) ),
    inference(variable_rename,[status(thm)],[f_2034_1]) ).

fof(f_2034_3,plain,
    ! [U_6892,U_6893] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6892),c_Groups_Oone__class_Oone(U_6892)),U_6893))
      | ~ class_Rings_Ocomm__semiring__1(U_6892) ),
    inference(definitional_conversion,[status(esa)],[f_2034_2]) ).

cnf(f_2034_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6892),c_Groups_Oone__class_Oone(U_6892)),U_6893))
    | ~ class_Rings_Ocomm__semiring__1(U_6892) ),
    inference(clausify,[status(thm)],[f_2034_3]) ).

fof(f_2035_1,plain,
    ! [V_a,T_a] :
      ( V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__0__left]) ).

fof(f_2035_2,plain,
    ! [U_6895,U_6894] :
      ( U_6895 = c_Groups_Ozero__class_Ozero(U_6894)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6894),c_Groups_Ozero__class_Ozero(U_6894)),U_6895))
      | ~ class_Rings_Ocomm__semiring__1(U_6894) ),
    inference(variable_rename,[status(thm)],[f_2035_1]) ).

fof(f_2035_3,plain,
    ! [U_6895,U_6894] :
      ( U_6895 = c_Groups_Ozero__class_Ozero(U_6894)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6894),c_Groups_Ozero__class_Ozero(U_6894)),U_6895))
      | ~ class_Rings_Ocomm__semiring__1(U_6894) ),
    inference(definitional_conversion,[status(esa)],[f_2035_2]) ).

cnf(f_2035_4,plain,
    ( U_6895 = c_Groups_Ozero__class_Ozero(U_6894)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6894),c_Groups_Ozero__class_Ozero(U_6894)),U_6895))
    | ~ class_Rings_Ocomm__semiring__1(U_6894) ),
    inference(clausify,[status(thm)],[f_2035_3]) ).

fof(f_2036_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__trans]) ).

fof(f_2036_2,plain,
    ! [U_6899,U_6898,U_6897,U_6896] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6897),U_6899))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6898),U_6899))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6897),U_6898))
      | ~ class_Rings_Ocomm__semiring__1(U_6896) ),
    inference(variable_rename,[status(thm)],[f_2036_1]) ).

fof(f_2036_3,plain,
    ! [U_6896,U_6899,U_6898,U_6897] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6897),U_6899))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6898),U_6899))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6897),U_6898))
      | ~ class_Rings_Ocomm__semiring__1(U_6896) ),
    inference(definitional_conversion,[status(esa)],[f_2036_2]) ).

cnf(f_2036_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6897),U_6899))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6898),U_6899))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6896),U_6897),U_6898))
    | ~ class_Rings_Ocomm__semiring__1(U_6896) ),
    inference(clausify,[status(thm)],[f_2036_3]) ).

fof(f_2037_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__refl]) ).

fof(f_2037_2,plain,
    ! [U_6901,U_6900] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6900),U_6901),U_6901))
      | ~ class_Rings_Ocomm__semiring__1(U_6900) ),
    inference(variable_rename,[status(thm)],[f_2037_1]) ).

fof(f_2037_3,plain,
    ! [U_6900,U_6901] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6900),U_6901),U_6901))
      | ~ class_Rings_Ocomm__semiring__1(U_6900) ),
    inference(definitional_conversion,[status(esa)],[f_2037_2]) ).

cnf(f_2037_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6900),U_6901),U_6901))
    | ~ class_Rings_Ocomm__semiring__1(U_6900) ),
    inference(clausify,[status(thm)],[f_2037_3]) ).

fof(f_2038_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym]) ).

fof(f_2038_2,plain,
    ! [U_6903,U_6902] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6903))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6902))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6902))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6903)) ),
    inference(variable_rename,[status(thm)],[f_2038_1]) ).

fof(f_2038_3,plain,
    ! [U_6902,U_6903] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6903))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6902))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6902))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6903)) ),
    inference(definitional_conversion,[status(esa)],[f_2038_2]) ).

cnf(f_2038_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6903))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6902))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6902))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6903)) ),
    inference(clausify,[status(thm)],[f_2038_3]) ).

fof(f_2039_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__trans]) ).

fof(f_2039_2,plain,
    ! [U_6906,U_6905,U_6904] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6904))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6905))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6906))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6904))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6905)) ),
    inference(variable_rename,[status(thm)],[f_2039_1]) ).

fof(f_2039_3,plain,
    ( ! [U_6904,U_6906] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6904))
        | ~ sP619(U_6904,U_6906) )
    & ! [U_6904,U_6906] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906))
        | ~ sP619(U_6904,U_6906) )
    & ! [U_6905,U_6904,U_6906] :
        ( sP619(U_6904,U_6906)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6905))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6906))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6904))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6905)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP619])],[f_2039_2]) ).

cnf(f_2039_4,plain,
    ( sP619(U_6904,U_6906)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6905))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6906))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6904))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6905)) ),
    inference(clausify,[status(thm)],[f_2039_3]) ).

cnf(f_2039_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906))
    | ~ sP619(U_6904,U_6906) ),
    inference(clausify,[status(thm)],[f_2039_3]) ).

cnf(f_2039_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6904))
    | ~ sP619(U_6904,U_6906) ),
    inference(clausify,[status(thm)],[f_2039_3]) ).

fof(f_2040_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym_H]) ).

fof(f_2040_2,plain,
    ! [U_6908,U_6907] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6907),U_6908))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6908),U_6907))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6908),U_6907))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6907),U_6908)) ),
    inference(variable_rename,[status(thm)],[f_2040_1]) ).

fof(f_2040_3,plain,
    ! [U_6908,U_6907] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6907),U_6908))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6908),U_6907))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6908),U_6907))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6907),U_6908)) ),
    inference(definitional_conversion,[status(esa)],[f_2040_2]) ).

cnf(f_2040_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6907),U_6908))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6908),U_6907))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6908),U_6907))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6907),U_6908)) ),
    inference(clausify,[status(thm)],[f_2040_3]) ).

fof(f_2041_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le__trans]) ).

fof(f_2041_2,plain,
    ! [U_6911,U_6910,U_6909] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6911),U_6909))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6909),U_6911)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6910),U_6911))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6910),U_6909))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6909),U_6910)) ),
    inference(variable_rename,[status(thm)],[f_2041_1]) ).

fof(f_2041_3,plain,
    ( ! [U_6909,U_6911] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6911),U_6909))
        | ~ sP620(U_6909,U_6911) )
    & ! [U_6909,U_6911] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6909),U_6911))
        | ~ sP620(U_6909,U_6911) )
    & ! [U_6909,U_6910,U_6911] :
        ( sP620(U_6909,U_6911)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6910),U_6911))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6910),U_6909))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6909),U_6910)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP620])],[f_2041_2]) ).

cnf(f_2041_4,plain,
    ( sP620(U_6909,U_6911)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6910),U_6911))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6910),U_6909))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6909),U_6910)) ),
    inference(clausify,[status(thm)],[f_2041_3]) ).

cnf(f_2041_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6909),U_6911))
    | ~ sP620(U_6909,U_6911) ),
    inference(clausify,[status(thm)],[f_2041_3]) ).

cnf(f_2041_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6911),U_6909))
    | ~ sP620(U_6909,U_6911) ),
    inference(clausify,[status(thm)],[f_2041_3]) ).

fof(f_2042_1,plain,
    ! [V_c,V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
      | V_b != V_c
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__less__eq__trans]) ).

fof(f_2042_2,plain,
    ! [U_6914,U_6913,U_6912] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6914),U_6912))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6912),U_6914)) )
      | U_6913 != U_6914
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6913),U_6912))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6912),U_6913)) ),
    inference(variable_rename,[status(thm)],[f_2042_1]) ).

fof(f_2042_3,plain,
    ( ! [U_6912,U_6914] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6914),U_6912))
        | ~ sP621(U_6912,U_6914) )
    & ! [U_6912,U_6914] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6912),U_6914))
        | ~ sP621(U_6912,U_6914) )
    & ! [U_6913,U_6912,U_6914] :
        ( sP621(U_6912,U_6914)
        | U_6913 != U_6914
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6913),U_6912))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6912),U_6913)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP621])],[f_2042_2]) ).

cnf(f_2042_4,plain,
    ( sP621(U_6912,U_6914)
    | U_6913 != U_6914
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6913),U_6912))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6912),U_6913)) ),
    inference(clausify,[status(thm)],[f_2042_3]) ).

cnf(f_2042_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6912),U_6914))
    | ~ sP621(U_6912,U_6914) ),
    inference(clausify,[status(thm)],[f_2042_3]) ).

cnf(f_2042_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6914),U_6912))
    | ~ sP621(U_6912,U_6914) ),
    inference(clausify,[status(thm)],[f_2042_3]) ).

fof(f_2043_1,plain,
    ! [V_y,V_x] :
      ( V_y != V_x
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq2]) ).

fof(f_2043_2,plain,
    ! [U_6916,U_6915] :
      ( U_6916 != U_6915
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6916),U_6915))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6915),U_6916)) ),
    inference(variable_rename,[status(thm)],[f_2043_1]) ).

fof(f_2043_3,plain,
    ! [U_6916,U_6915] :
      ( U_6916 != U_6915
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6916),U_6915))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6915),U_6916)) ),
    inference(definitional_conversion,[status(esa)],[f_2043_2]) ).

cnf(f_2043_4,plain,
    ( U_6916 != U_6915
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6916),U_6915))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6915),U_6916)) ),
    inference(clausify,[status(thm)],[f_2043_3]) ).

fof(f_2044_1,plain,
    ! [V_y,V_x] :
      ( V_x != V_y
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq]) ).

fof(f_2044_2,plain,
    ! [U_6918,U_6917] :
      ( U_6917 != U_6918
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6918),U_6917))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6917),U_6918)) ),
    inference(variable_rename,[status(thm)],[f_2044_1]) ).

fof(f_2044_3,plain,
    ! [U_6918,U_6917] :
      ( U_6917 != U_6918
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6918),U_6917))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6917),U_6918)) ),
    inference(definitional_conversion,[status(esa)],[f_2044_2]) ).

cnf(f_2044_4,plain,
    ( U_6917 != U_6918
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6918),U_6917))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6917),U_6918)) ),
    inference(clausify,[status(thm)],[f_2044_3]) ).

fof(f_2045_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__less]) ).

fof(f_2045_2,plain,
    ! [U_6920,U_6919] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6919),U_6920))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6920),U_6919))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6920),U_6919))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6919),U_6920)) ),
    inference(variable_rename,[status(thm)],[f_2045_1]) ).

fof(f_2045_3,plain,
    ! [U_6920,U_6919] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6919),U_6920))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6920),U_6919))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6920),U_6919))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6919),U_6920)) ),
    inference(definitional_conversion,[status(esa)],[f_2045_2]) ).

cnf(f_2045_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6919),U_6920))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6920),U_6919))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6920),U_6919))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6919),U_6920)) ),
    inference(clausify,[status(thm)],[f_2045_3]) ).

fof(f_2046_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__le]) ).

fof(f_2046_2,plain,
    ! [U_6922,U_6921] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6921),U_6922))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6922),U_6921))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6921),U_6922)) ),
    inference(variable_rename,[status(thm)],[f_2046_1]) ).

fof(f_2046_3,plain,
    ! [U_6921,U_6922] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6921),U_6922))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6922),U_6921))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6921),U_6922)) ),
    inference(definitional_conversion,[status(esa)],[f_2046_2]) ).

cnf(f_2046_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6921),U_6922))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6922),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6921),U_6922)) ),
    inference(clausify,[status(thm)],[f_2046_3]) ).

fof(f_2047_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__not__sym]) ).

fof(f_2047_2,plain,
    ! [U_6924,U_6923] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6923),U_6924))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6924),U_6923))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6924),U_6923))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6923),U_6924)) ),
    inference(variable_rename,[status(thm)],[f_2047_1]) ).

fof(f_2047_3,plain,
    ! [U_6923,U_6924] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6923),U_6924))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6924),U_6923))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6924),U_6923))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6923),U_6924)) ),
    inference(definitional_conversion,[status(esa)],[f_2047_2]) ).

cnf(f_2047_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6923),U_6924))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6924),U_6923))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6924),U_6923))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6923),U_6924)) ),
    inference(clausify,[status(thm)],[f_2047_3]) ).

fof(f_2048_1,plain,
    ! [V_y,V_x] :
      ( V_x != V_y
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__neq]) ).

fof(f_2048_2,plain,
    ! [U_6926,U_6925] :
      ( U_6925 != U_6926
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6926),U_6925))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6925),U_6926)) ),
    inference(variable_rename,[status(thm)],[f_2048_1]) ).

fof(f_2048_3,plain,
    ! [U_6925,U_6926] :
      ( U_6925 != U_6926
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6926),U_6925))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6925),U_6926)) ),
    inference(definitional_conversion,[status(esa)],[f_2048_2]) ).

cnf(f_2048_4,plain,
    ( U_6925 != U_6926
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6926),U_6925))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6925),U_6926)) ),
    inference(clausify,[status(thm)],[f_2048_3]) ).

fof(f_2049_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less__trans]) ).

fof(f_2049_2,plain,
    ! [U_6929,U_6928,U_6927] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6929),U_6927))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6927),U_6929)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6929),U_6928))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6928),U_6929))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6927),U_6928)) ),
    inference(variable_rename,[status(thm)],[f_2049_1]) ).

fof(f_2049_3,plain,
    ( ! [U_6927,U_6929] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6929),U_6927))
        | ~ sP622(U_6927,U_6929) )
    & ! [U_6927,U_6929] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6927),U_6929))
        | ~ sP622(U_6927,U_6929) )
    & ! [U_6927,U_6928,U_6929] :
        ( sP622(U_6927,U_6929)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6929),U_6928))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6928),U_6929))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6927),U_6928)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP622])],[f_2049_2]) ).

cnf(f_2049_4,plain,
    ( sP622(U_6927,U_6929)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6929),U_6928))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6928),U_6929))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6927),U_6928)) ),
    inference(clausify,[status(thm)],[f_2049_3]) ).

cnf(f_2049_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6927),U_6929))
    | ~ sP622(U_6927,U_6929) ),
    inference(clausify,[status(thm)],[f_2049_3]) ).

cnf(f_2049_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6929),U_6927))
    | ~ sP622(U_6927,U_6929) ),
    inference(clausify,[status(thm)],[f_2049_3]) ).

fof(f_2050_1,plain,
    ! [V_c,V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
      | V_a != V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__less__trans]) ).

fof(f_2050_2,plain,
    ! [U_6932,U_6931,U_6930] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6932),U_6930))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6930),U_6932)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6932),U_6931))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6931),U_6932))
      | U_6930 != U_6931 ),
    inference(variable_rename,[status(thm)],[f_2050_1]) ).

fof(f_2050_3,plain,
    ( ! [U_6930,U_6932] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6932),U_6930))
        | ~ sP623(U_6930,U_6932) )
    & ! [U_6930,U_6932] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6930),U_6932))
        | ~ sP623(U_6930,U_6932) )
    & ! [U_6931,U_6930,U_6932] :
        ( sP623(U_6930,U_6932)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6932),U_6931))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6931),U_6932))
        | U_6930 != U_6931 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP623])],[f_2050_2]) ).

cnf(f_2050_4,plain,
    ( sP623(U_6930,U_6932)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6932),U_6931))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6931),U_6932))
    | U_6930 != U_6931 ),
    inference(clausify,[status(thm)],[f_2050_3]) ).

cnf(f_2050_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6930),U_6932))
    | ~ sP623(U_6930,U_6932) ),
    inference(clausify,[status(thm)],[f_2050_3]) ).

cnf(f_2050_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6932),U_6930))
    | ~ sP623(U_6930,U_6932) ),
    inference(clausify,[status(thm)],[f_2050_3]) ).

fof(f_2051_1,plain,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans]) ).

fof(f_2051_2,plain,
    ! [U_6935,U_6934,U_6933] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6933),U_6935))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6934),U_6935))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6933),U_6934)) ),
    inference(variable_rename,[status(thm)],[f_2051_1]) ).

fof(f_2051_3,plain,
    ! [U_6935,U_6933,U_6934] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6933),U_6935))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6934),U_6935))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6933),U_6934)) ),
    inference(definitional_conversion,[status(esa)],[f_2051_2]) ).

cnf(f_2051_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6933),U_6935))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6934),U_6935))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6933),U_6934)) ),
    inference(clausify,[status(thm)],[f_2051_3]) ).

fof(f_2052_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym]) ).

fof(f_2052_2,plain,
    ! [U_6937,U_6936] :
      ( U_6936 = U_6937
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6937),U_6936))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6936),U_6937)) ),
    inference(variable_rename,[status(thm)],[f_2052_1]) ).

fof(f_2052_3,plain,
    ! [U_6936,U_6937] :
      ( U_6936 = U_6937
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6937),U_6936))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6936),U_6937)) ),
    inference(definitional_conversion,[status(esa)],[f_2052_2]) ).

cnf(f_2052_4,plain,
    ( U_6936 = U_6937
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6937),U_6936))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6936),U_6937)) ),
    inference(clausify,[status(thm)],[f_2052_3]) ).

fof(f_2053_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__antisym]) ).

fof(f_2053_2,plain,
    ! [U_6939,U_6938] :
      ( U_6938 = U_6939
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6939),U_6938))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6938),U_6939)) ),
    inference(variable_rename,[status(thm)],[f_2053_1]) ).

fof(f_2053_3,plain,
    ! [U_6938,U_6939] :
      ( U_6938 = U_6939
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6939),U_6938))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6938),U_6939)) ),
    inference(definitional_conversion,[status(esa)],[f_2053_2]) ).

cnf(f_2053_4,plain,
    ( U_6938 = U_6939
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6939),U_6938))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6938),U_6939)) ),
    inference(clausify,[status(thm)],[f_2053_3]) ).

fof(f_2054_1,plain,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__le__eq__trans]) ).

fof(f_2054_2,plain,
    ! [U_6942,U_6941,U_6940] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6940),U_6942))
      | U_6941 != U_6942
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6940),U_6941)) ),
    inference(variable_rename,[status(thm)],[f_2054_1]) ).

fof(f_2054_3,plain,
    ! [U_6940,U_6941,U_6942] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6940),U_6942))
      | U_6941 != U_6942
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6940),U_6941)) ),
    inference(definitional_conversion,[status(esa)],[f_2054_2]) ).

cnf(f_2054_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6940),U_6942))
    | U_6941 != U_6942
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6940),U_6941)) ),
    inference(clausify,[status(thm)],[f_2054_3]) ).

fof(f_2055_1,plain,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
      | V_a != V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__le__trans]) ).

fof(f_2055_2,plain,
    ! [U_6945,U_6944,U_6943] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6943),U_6945))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6944),U_6945))
      | U_6943 != U_6944 ),
    inference(variable_rename,[status(thm)],[f_2055_1]) ).

fof(f_2055_3,plain,
    ! [U_6943,U_6944,U_6945] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6943),U_6945))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6944),U_6945))
      | U_6943 != U_6944 ),
    inference(definitional_conversion,[status(esa)],[f_2055_2]) ).

cnf(f_2055_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6943),U_6945))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6944),U_6945))
    | U_6943 != U_6944 ),
    inference(clausify,[status(thm)],[f_2055_3]) ).

fof(f_2056_1,plain,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
      | V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__neq__trans]) ).

fof(f_2056_2,plain,
    ! [U_6947,U_6946] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6947),U_6946))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6946),U_6947)) )
      | U_6946 = U_6947
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6946),U_6947)) ),
    inference(variable_rename,[status(thm)],[f_2056_1]) ).

fof(f_2056_3,plain,
    ( ! [U_6946,U_6947] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6947),U_6946))
        | ~ sP624(U_6946,U_6947) )
    & ! [U_6946,U_6947] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6946),U_6947))
        | ~ sP624(U_6946,U_6947) )
    & ! [U_6946,U_6947] :
        ( sP624(U_6946,U_6947)
        | U_6946 = U_6947
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6946),U_6947)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP624])],[f_2056_2]) ).

cnf(f_2056_4,plain,
    ( sP624(U_6946,U_6947)
    | U_6946 = U_6947
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6946),U_6947)) ),
    inference(clausify,[status(thm)],[f_2056_3]) ).

cnf(f_2056_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6946),U_6947))
    | ~ sP624(U_6946,U_6947) ),
    inference(clausify,[status(thm)],[f_2056_3]) ).

cnf(f_2056_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6947),U_6946))
    | ~ sP624(U_6946,U_6947) ),
    inference(clausify,[status(thm)],[f_2056_3]) ).

fof(f_2057_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).

fof(f_2057_2,plain,
    ! [U_6949,U_6948] :
      ( U_6948 = U_6949
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6949),U_6948))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6948),U_6949)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6948),U_6949)) ),
    inference(variable_rename,[status(thm)],[f_2057_1]) ).

fof(f_2057_3,plain,
    ( ! [U_6949,U_6948] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6949),U_6948))
        | ~ sP625(U_6949,U_6948) )
    & ! [U_6949,U_6948] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6948),U_6949))
        | ~ sP625(U_6949,U_6948) )
    & ! [U_6949,U_6948] :
        ( U_6948 = U_6949
        | sP625(U_6949,U_6948)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6948),U_6949)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP625])],[f_2057_2]) ).

cnf(f_2057_4,plain,
    ( U_6948 = U_6949
    | sP625(U_6949,U_6948)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6948),U_6949)) ),
    inference(clausify,[status(thm)],[f_2057_3]) ).

cnf(f_2057_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6948),U_6949))
    | ~ sP625(U_6949,U_6948) ),
    inference(clausify,[status(thm)],[f_2057_3]) ).

cnf(f_2057_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6949),U_6948))
    | ~ sP625(U_6949,U_6948) ),
    inference(clausify,[status(thm)],[f_2057_3]) ).

fof(f_2058_1,plain,
    ! [V_x_2,V_y_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv]) ).

fof(f_2058_2,plain,
    ! [U_6951,U_6950] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6951),U_6950))
          | U_6951 != U_6950 )
        & ( U_6951 = U_6950
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6951),U_6950)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6950),U_6951)) ),
    inference(variable_rename,[status(thm)],[f_2058_1]) ).

fof(f_2058_3,plain,
    ( ! [U_6950,U_6951] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6951),U_6950))
        | U_6951 != U_6950
        | ~ sP626(U_6950,U_6951) )
    & ! [U_6950,U_6951] :
        ( U_6951 = U_6950
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6951),U_6950))
        | ~ sP626(U_6950,U_6951) )
    & ! [U_6950,U_6951] :
        ( sP626(U_6950,U_6951)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6950),U_6951)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP626])],[f_2058_2]) ).

cnf(f_2058_4,plain,
    ( sP626(U_6950,U_6951)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6950),U_6951)) ),
    inference(clausify,[status(thm)],[f_2058_3]) ).

cnf(f_2058_5,plain,
    ( U_6951 = U_6950
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6951),U_6950))
    | ~ sP626(U_6950,U_6951) ),
    inference(clausify,[status(thm)],[f_2058_3]) ).

cnf(f_2058_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6951),U_6950))
    | U_6951 != U_6950
    | ~ sP626(U_6950,U_6951) ),
    inference(clausify,[status(thm)],[f_2058_3]) ).

fof(f_2059_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | V_x != V_y ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl]) ).

fof(f_2059_2,plain,
    ! [U_6953,U_6952] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6952),U_6953))
      | U_6952 != U_6953 ),
    inference(variable_rename,[status(thm)],[f_2059_1]) ).

fof(f_2059_3,plain,
    ! [U_6953,U_6952] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6952),U_6953))
      | U_6952 != U_6953 ),
    inference(definitional_conversion,[status(esa)],[f_2059_2]) ).

cnf(f_2059_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6952),U_6953))
    | U_6952 != U_6953 ),
    inference(clausify,[status(thm)],[f_2059_3]) ).

fof(f_2060_1,plain,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
      | V_a = V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oneq__le__trans]) ).

fof(f_2060_2,plain,
    ! [U_6955,U_6954] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6955),U_6954))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6954),U_6955)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6954),U_6955))
      | U_6954 = U_6955 ),
    inference(variable_rename,[status(thm)],[f_2060_1]) ).

fof(f_2060_3,plain,
    ( ! [U_6954,U_6955] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6955),U_6954))
        | ~ sP627(U_6954,U_6955) )
    & ! [U_6954,U_6955] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6954),U_6955))
        | ~ sP627(U_6954,U_6955) )
    & ! [U_6954,U_6955] :
        ( sP627(U_6954,U_6955)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6954),U_6955))
        | U_6954 = U_6955 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP627])],[f_2060_2]) ).

cnf(f_2060_4,plain,
    ( sP627(U_6954,U_6955)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6954),U_6955))
    | U_6954 = U_6955 ),
    inference(clausify,[status(thm)],[f_2060_3]) ).

cnf(f_2060_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6954),U_6955))
    | ~ sP627(U_6954,U_6955) ),
    inference(clausify,[status(thm)],[f_2060_3]) ).

cnf(f_2060_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6955),U_6954))
    | ~ sP627(U_6954,U_6955) ),
    inference(clausify,[status(thm)],[f_2060_3]) ).

fof(f_2061_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( ( V_x_2 != V_y_2
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le]) ).

fof(f_2061_2,plain,
    ! [U_6957,U_6956] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6957),U_6956))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6956),U_6957)) )
        | U_6956 = U_6957
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6956),U_6957)) )
      & ( ( U_6956 != U_6957
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6956),U_6957)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6957),U_6956))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6956),U_6957)) ) ),
    inference(variable_rename,[status(thm)],[f_2061_1]) ).

fof(f_2061_3,plain,
    ( ! [U_6961,U_6959] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6961),U_6959))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6959),U_6961)) )
        | U_6959 = U_6961
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6959),U_6961)) )
    & ! [U_6960,U_6958] :
        ( ( U_6958 != U_6960
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6958),U_6960)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6960),U_6958))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6958),U_6960)) ) ),
    inference(miniscope,[status(thm)],[f_2061_2]) ).

fof(f_2061_4,plain,
    ( ! [U_6961,U_6959] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6961),U_6959))
        | ~ sP629(U_6961,U_6959) )
    & ! [U_6961,U_6959] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6959),U_6961))
        | ~ sP629(U_6961,U_6959) )
    & ! [U_6958,U_6960] :
        ( U_6958 != U_6960
        | ~ sP628(U_6958,U_6960) )
    & ! [U_6958,U_6960] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6958),U_6960))
        | ~ sP628(U_6958,U_6960) )
    & ! [U_6961,U_6959] :
        ( sP629(U_6961,U_6959)
        | U_6959 = U_6961
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6959),U_6961)) )
    & ! [U_6958,U_6960] :
        ( sP628(U_6958,U_6960)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6960),U_6958))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6958),U_6960)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP628,sP629])],[f_2061_3]) ).

cnf(f_2061_5,plain,
    ( sP628(U_6958,U_6960)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6960),U_6958))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6958),U_6960)) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

cnf(f_2061_6,plain,
    ( sP629(U_6961,U_6959)
    | U_6959 = U_6961
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6959),U_6961)) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

cnf(f_2061_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6958),U_6960))
    | ~ sP628(U_6958,U_6960) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

cnf(f_2061_8,plain,
    ( U_6958 != U_6960
    | ~ sP628(U_6958,U_6960) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

cnf(f_2061_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6959),U_6961))
    | ~ sP629(U_6961,U_6959) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

cnf(f_2061_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6961),U_6959))
    | ~ sP629(U_6961,U_6959) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

fof(f_2062_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
        | ( V_x_2 != V_y_2
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) )
      & ( V_x_2 = V_y_2
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less]) ).

fof(f_2062_2,plain,
    ! [U_6963,U_6962] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6962),U_6963))
        | ( U_6962 != U_6963
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6963),U_6962))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6962),U_6963)) ) ) )
      & ( U_6962 = U_6963
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6963),U_6962))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6962),U_6963)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6962),U_6963)) ) ),
    inference(variable_rename,[status(thm)],[f_2062_1]) ).

fof(f_2062_3,plain,
    ( ! [U_6967,U_6965] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6965),U_6967))
        | ( U_6965 != U_6967
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6967),U_6965))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6965),U_6967)) ) ) )
    & ! [U_6966,U_6964] :
        ( U_6964 = U_6966
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6966),U_6964))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6964),U_6966)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6964),U_6966)) ) ),
    inference(miniscope,[status(thm)],[f_2062_2]) ).

fof(f_2062_4,plain,
    ( ! [U_6967,U_6965] :
        ( U_6965 != U_6967
        | ~ sP631(U_6967,U_6965) )
    & ! [U_6967,U_6965] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6967),U_6965))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6965),U_6967))
        | ~ sP631(U_6967,U_6965) )
    & ! [U_6964,U_6966] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6966),U_6964))
        | ~ sP630(U_6964,U_6966) )
    & ! [U_6964,U_6966] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6964),U_6966))
        | ~ sP630(U_6964,U_6966) )
    & ! [U_6967,U_6965] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6965),U_6967))
        | sP631(U_6967,U_6965) )
    & ! [U_6964,U_6966] :
        ( U_6964 = U_6966
        | sP630(U_6964,U_6966)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6964),U_6966)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP630,sP631])],[f_2062_3]) ).

cnf(f_2062_5,plain,
    ( U_6964 = U_6966
    | sP630(U_6964,U_6966)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6964),U_6966)) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

cnf(f_2062_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6965),U_6967))
    | sP631(U_6967,U_6965) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

cnf(f_2062_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6964),U_6966))
    | ~ sP630(U_6964,U_6966) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

cnf(f_2062_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6966),U_6964))
    | ~ sP630(U_6964,U_6966) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

cnf(f_2062_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6967),U_6965))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6965),U_6967))
    | ~ sP631(U_6967,U_6965) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

cnf(f_2062_10,plain,
    ( U_6965 != U_6967
    | ~ sP631(U_6967,U_6965) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

fof(f_2063_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | V_x_2 != V_y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff]) ).

fof(f_2063_2,plain,
    ! [U_6969,U_6968] :
      ( ( U_6968 = U_6969
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6969),U_6968))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6968),U_6969)) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6969),U_6968))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6968),U_6969)) )
        | U_6968 != U_6969 ) ),
    inference(variable_rename,[status(thm)],[f_2063_1]) ).

fof(f_2063_3,plain,
    ( ! [U_6973,U_6971] :
        ( U_6971 = U_6973
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6973),U_6971))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6971),U_6973)) )
    & ! [U_6972,U_6970] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6972),U_6970))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6970),U_6972)) )
        | U_6970 != U_6972 ) ),
    inference(miniscope,[status(thm)],[f_2063_2]) ).

fof(f_2063_4,plain,
    ( ! [U_6970,U_6972] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6972),U_6970))
        | ~ sP632(U_6970,U_6972) )
    & ! [U_6970,U_6972] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6970),U_6972))
        | ~ sP632(U_6970,U_6972) )
    & ! [U_6971,U_6973] :
        ( U_6971 = U_6973
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6973),U_6971))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6971),U_6973)) )
    & ! [U_6970,U_6972] :
        ( sP632(U_6970,U_6972)
        | U_6970 != U_6972 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP632])],[f_2063_3]) ).

cnf(f_2063_5,plain,
    ( sP632(U_6970,U_6972)
    | U_6970 != U_6972 ),
    inference(clausify,[status(thm)],[f_2063_4]) ).

cnf(f_2063_6,plain,
    ( U_6971 = U_6973
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6973),U_6971))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6971),U_6973)) ),
    inference(clausify,[status(thm)],[f_2063_4]) ).

cnf(f_2063_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6970),U_6972))
    | ~ sP632(U_6970,U_6972) ),
    inference(clausify,[status(thm)],[f_2063_4]) ).

cnf(f_2063_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6972),U_6970))
    | ~ sP632(U_6970,U_6972) ),
    inference(clausify,[status(thm)],[f_2063_4]) ).

fof(f_2064_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__add]) ).

fof(f_2064_2,plain,
    ! [U_6977,U_6976,U_6975,U_6974] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6974),U_6976),U_6977)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),U_6977))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),U_6976))
      | ~ class_Rings_Ocomm__semiring__1(U_6974) ),
    inference(variable_rename,[status(thm)],[f_2064_1]) ).

fof(f_2064_3,plain,
    ! [U_6976,U_6974,U_6975,U_6977] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6974),U_6976),U_6977)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),U_6977))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),U_6976))
      | ~ class_Rings_Ocomm__semiring__1(U_6974) ),
    inference(definitional_conversion,[status(esa)],[f_2064_2]) ).

cnf(f_2064_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6974),U_6976),U_6977)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),U_6977))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6974),U_6975),U_6976))
    | ~ class_Rings_Ocomm__semiring__1(U_6974) ),
    inference(clausify,[status(thm)],[f_2064_3]) ).

fof(f_2065_1,plain,
    ! [V_m_2,V_n_2,V_k_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff]) ).

fof(f_2065_2,plain,
    ! [U_6981,U_6980,U_6979,U_6978] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),c_Divides_Odiv__class_Omod(U_6978,U_6981,U_6980)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6981)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6981))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),c_Divides_Odiv__class_Omod(U_6978,U_6981,U_6980))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6980))
      | ~ class_Divides_Osemiring__div(U_6978) ),
    inference(variable_rename,[status(thm)],[f_2065_1]) ).

fof(f_2065_3,plain,
    ( ! [U_6978,U_6979,U_6980,U_6981] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),c_Divides_Odiv__class_Omod(U_6978,U_6981,U_6980)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6981))
        | ~ sP633(U_6978,U_6979,U_6980,U_6981) )
    & ! [U_6978,U_6979,U_6980,U_6981] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6981))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),c_Divides_Odiv__class_Omod(U_6978,U_6981,U_6980)))
        | ~ sP633(U_6978,U_6979,U_6980,U_6981) )
    & ! [U_6978,U_6979,U_6980,U_6981] :
        ( sP633(U_6978,U_6979,U_6980,U_6981)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6980))
        | ~ class_Divides_Osemiring__div(U_6978) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP633])],[f_2065_2]) ).

cnf(f_2065_4,plain,
    ( sP633(U_6978,U_6979,U_6980,U_6981)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6980))
    | ~ class_Divides_Osemiring__div(U_6978) ),
    inference(clausify,[status(thm)],[f_2065_3]) ).

cnf(f_2065_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6981))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),c_Divides_Odiv__class_Omod(U_6978,U_6981,U_6980)))
    | ~ sP633(U_6978,U_6979,U_6980,U_6981) ),
    inference(clausify,[status(thm)],[f_2065_3]) ).

cnf(f_2065_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),c_Divides_Odiv__class_Omod(U_6978,U_6981,U_6980)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6978),U_6979),U_6981))
    | ~ sP633(U_6978,U_6979,U_6980,U_6981) ),
    inference(clausify,[status(thm)],[f_2065_3]) ).

fof(f_2066_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel]) ).

fof(f_2066_2,plain,
    ! [U_6985,U_6984,U_6983,U_6982] :
      ( c_Divides_Odiv__class_Omod(U_6982,c_Divides_Odiv__class_Omod(U_6982,U_6985,U_6984),U_6983) = c_Divides_Odiv__class_Omod(U_6982,U_6985,U_6983)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6982),U_6983),U_6984))
      | ~ class_Divides_Osemiring__div(U_6982) ),
    inference(variable_rename,[status(thm)],[f_2066_1]) ).

fof(f_2066_3,plain,
    ! [U_6985,U_6982,U_6983,U_6984] :
      ( c_Divides_Odiv__class_Omod(U_6982,c_Divides_Odiv__class_Omod(U_6982,U_6985,U_6984),U_6983) = c_Divides_Odiv__class_Omod(U_6982,U_6985,U_6983)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6982),U_6983),U_6984))
      | ~ class_Divides_Osemiring__div(U_6982) ),
    inference(definitional_conversion,[status(esa)],[f_2066_2]) ).

cnf(f_2066_4,plain,
    ( c_Divides_Odiv__class_Omod(U_6982,c_Divides_Odiv__class_Omod(U_6982,U_6985,U_6984),U_6983) = c_Divides_Odiv__class_Omod(U_6982,U_6985,U_6983)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6982),U_6983),U_6984))
    | ~ class_Divides_Osemiring__div(U_6982) ),
    inference(clausify,[status(thm)],[f_2066_3]) ).

fof(f_2067_1,plain,
    ! [V_n,V_m,V_k,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mod]) ).

fof(f_2067_2,plain,
    ! [U_6989,U_6988,U_6987,U_6986] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),c_Divides_Odiv__class_Omod(U_6986,U_6988,U_6989)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),U_6989))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),U_6988))
      | ~ class_Divides_Osemiring__div(U_6986) ),
    inference(variable_rename,[status(thm)],[f_2067_1]) ).

fof(f_2067_3,plain,
    ! [U_6986,U_6987,U_6988,U_6989] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),c_Divides_Odiv__class_Omod(U_6986,U_6988,U_6989)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),U_6989))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),U_6988))
      | ~ class_Divides_Osemiring__div(U_6986) ),
    inference(definitional_conversion,[status(esa)],[f_2067_2]) ).

cnf(f_2067_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),c_Divides_Odiv__class_Omod(U_6986,U_6988,U_6989)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),U_6989))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6986),U_6987),U_6988))
    | ~ class_Divides_Osemiring__div(U_6986) ),
    inference(clausify,[status(thm)],[f_2067_3]) ).

fof(f_2068_1,plain,
    ! [V_n,V_m,V_k,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd]) ).

fof(f_2068_2,plain,
    ! [U_6993,U_6992,U_6991,U_6990] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),U_6992))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),U_6993))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),c_Divides_Odiv__class_Omod(U_6990,U_6992,U_6993)))
      | ~ class_Divides_Osemiring__div(U_6990) ),
    inference(variable_rename,[status(thm)],[f_2068_1]) ).

fof(f_2068_3,plain,
    ! [U_6991,U_6990,U_6992,U_6993] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),U_6992))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),U_6993))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),c_Divides_Odiv__class_Omod(U_6990,U_6992,U_6993)))
      | ~ class_Divides_Osemiring__div(U_6990) ),
    inference(definitional_conversion,[status(esa)],[f_2068_2]) ).

cnf(f_2068_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),U_6992))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),U_6993))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6990),U_6991),c_Divides_Odiv__class_Omod(U_6990,U_6992,U_6993)))
    | ~ class_Divides_Osemiring__div(U_6990) ),
    inference(clausify,[status(thm)],[f_2068_3]) ).

fof(f_2069_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) ) )
      | ~ class_Rings_Ocomm__ring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff]) ).

fof(f_2069_2,plain,
    ! [U_6996,U_6995,U_6994] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),hAPP(c_Groups_Ouminus__class_Ouminus(U_6994),U_6996)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),U_6996)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),U_6996))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),hAPP(c_Groups_Ouminus__class_Ouminus(U_6994),U_6996))) ) )
      | ~ class_Rings_Ocomm__ring__1(U_6994) ),
    inference(variable_rename,[status(thm)],[f_2069_1]) ).

fof(f_2069_3,plain,
    ( ! [U_6994,U_6995,U_6996] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),hAPP(c_Groups_Ouminus__class_Ouminus(U_6994),U_6996)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),U_6996))
        | ~ sP634(U_6994,U_6995,U_6996) )
    & ! [U_6994,U_6995,U_6996] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),U_6996))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),hAPP(c_Groups_Ouminus__class_Ouminus(U_6994),U_6996)))
        | ~ sP634(U_6994,U_6995,U_6996) )
    & ! [U_6994,U_6995,U_6996] :
        ( sP634(U_6994,U_6995,U_6996)
        | ~ class_Rings_Ocomm__ring__1(U_6994) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP634])],[f_2069_2]) ).

cnf(f_2069_4,plain,
    ( sP634(U_6994,U_6995,U_6996)
    | ~ class_Rings_Ocomm__ring__1(U_6994) ),
    inference(clausify,[status(thm)],[f_2069_3]) ).

cnf(f_2069_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),U_6996))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),hAPP(c_Groups_Ouminus__class_Ouminus(U_6994),U_6996)))
    | ~ sP634(U_6994,U_6995,U_6996) ),
    inference(clausify,[status(thm)],[f_2069_3]) ).

cnf(f_2069_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),hAPP(c_Groups_Ouminus__class_Ouminus(U_6994),U_6996)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6994),U_6995),U_6996))
    | ~ sP634(U_6994,U_6995,U_6996) ),
    inference(clausify,[status(thm)],[f_2069_3]) ).

fof(f_2070_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) ) )
      | ~ class_Rings_Ocomm__ring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff]) ).

fof(f_2070_2,plain,
    ! [U_6999,U_6998,U_6997] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),hAPP(c_Groups_Ouminus__class_Ouminus(U_6997),U_6998)),U_6999))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),U_6998),U_6999)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),U_6998),U_6999))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),hAPP(c_Groups_Ouminus__class_Ouminus(U_6997),U_6998)),U_6999)) ) )
      | ~ class_Rings_Ocomm__ring__1(U_6997) ),
    inference(variable_rename,[status(thm)],[f_2070_1]) ).

fof(f_2070_3,plain,
    ( ! [U_6997,U_6998,U_6999] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),hAPP(c_Groups_Ouminus__class_Ouminus(U_6997),U_6998)),U_6999))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),U_6998),U_6999))
        | ~ sP635(U_6997,U_6998,U_6999) )
    & ! [U_6997,U_6998,U_6999] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),U_6998),U_6999))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),hAPP(c_Groups_Ouminus__class_Ouminus(U_6997),U_6998)),U_6999))
        | ~ sP635(U_6997,U_6998,U_6999) )
    & ! [U_6997,U_6998,U_6999] :
        ( sP635(U_6997,U_6998,U_6999)
        | ~ class_Rings_Ocomm__ring__1(U_6997) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP635])],[f_2070_2]) ).

cnf(f_2070_4,plain,
    ( sP635(U_6997,U_6998,U_6999)
    | ~ class_Rings_Ocomm__ring__1(U_6997) ),
    inference(clausify,[status(thm)],[f_2070_3]) ).

cnf(f_2070_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),U_6998),U_6999))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),hAPP(c_Groups_Ouminus__class_Ouminus(U_6997),U_6998)),U_6999))
    | ~ sP635(U_6997,U_6998,U_6999) ),
    inference(clausify,[status(thm)],[f_2070_3]) ).

cnf(f_2070_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),hAPP(c_Groups_Ouminus__class_Ouminus(U_6997),U_6998)),U_6999))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6997),U_6998),U_6999))
    | ~ sP635(U_6997,U_6998,U_6999) ),
    inference(clausify,[status(thm)],[f_2070_3]) ).

fof(f_2071_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diff]) ).

fof(f_2071_2,plain,
    ! [U_7003,U_7002,U_7001,U_7000] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7000),U_7002),U_7003)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),U_7003))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),U_7002))
      | ~ class_Rings_Ocomm__ring__1(U_7000) ),
    inference(variable_rename,[status(thm)],[f_2071_1]) ).

fof(f_2071_3,plain,
    ! [U_7001,U_7000,U_7002,U_7003] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7000),U_7002),U_7003)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),U_7003))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),U_7002))
      | ~ class_Rings_Ocomm__ring__1(U_7000) ),
    inference(definitional_conversion,[status(esa)],[f_2071_2]) ).

cnf(f_2071_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7000),U_7002),U_7003)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),U_7003))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7000),U_7001),U_7002))
    | ~ class_Rings_Ocomm__ring__1(U_7000) ),
    inference(clausify,[status(thm)],[f_2071_3]) ).

fof(f_2072_1,plain,
    ! [V_k_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff]) ).

fof(f_2072_2,plain,
    ! [U_7006,U_7005,U_7004] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),hAPP(c_Groups_Oabs__class_Oabs(U_7004),U_7006)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),U_7006)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),U_7006))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),hAPP(c_Groups_Oabs__class_Oabs(U_7004),U_7006))) ) )
      | ~ class_Rings_Olinordered__idom(U_7004) ),
    inference(variable_rename,[status(thm)],[f_2072_1]) ).

fof(f_2072_3,plain,
    ( ! [U_7005,U_7004,U_7006] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),hAPP(c_Groups_Oabs__class_Oabs(U_7004),U_7006)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),U_7006))
        | ~ sP636(U_7005,U_7004,U_7006) )
    & ! [U_7005,U_7004,U_7006] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),U_7006))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),hAPP(c_Groups_Oabs__class_Oabs(U_7004),U_7006)))
        | ~ sP636(U_7005,U_7004,U_7006) )
    & ! [U_7005,U_7004,U_7006] :
        ( sP636(U_7005,U_7004,U_7006)
        | ~ class_Rings_Olinordered__idom(U_7004) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP636])],[f_2072_2]) ).

cnf(f_2072_4,plain,
    ( sP636(U_7005,U_7004,U_7006)
    | ~ class_Rings_Olinordered__idom(U_7004) ),
    inference(clausify,[status(thm)],[f_2072_3]) ).

cnf(f_2072_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),U_7006))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),hAPP(c_Groups_Oabs__class_Oabs(U_7004),U_7006)))
    | ~ sP636(U_7005,U_7004,U_7006) ),
    inference(clausify,[status(thm)],[f_2072_3]) ).

cnf(f_2072_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),hAPP(c_Groups_Oabs__class_Oabs(U_7004),U_7006)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7004),U_7005),U_7006))
    | ~ sP636(U_7005,U_7004,U_7006) ),
    inference(clausify,[status(thm)],[f_2072_3]) ).

fof(f_2073_1,plain,
    ! [V_k_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff]) ).

fof(f_2073_2,plain,
    ! [U_7009,U_7008,U_7007] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),hAPP(c_Groups_Oabs__class_Oabs(U_7007),U_7008)),U_7009))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),U_7008),U_7009)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),U_7008),U_7009))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),hAPP(c_Groups_Oabs__class_Oabs(U_7007),U_7008)),U_7009)) ) )
      | ~ class_Rings_Olinordered__idom(U_7007) ),
    inference(variable_rename,[status(thm)],[f_2073_1]) ).

fof(f_2073_3,plain,
    ( ! [U_7009,U_7007,U_7008] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),hAPP(c_Groups_Oabs__class_Oabs(U_7007),U_7008)),U_7009))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),U_7008),U_7009))
        | ~ sP637(U_7009,U_7007,U_7008) )
    & ! [U_7009,U_7007,U_7008] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),U_7008),U_7009))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),hAPP(c_Groups_Oabs__class_Oabs(U_7007),U_7008)),U_7009))
        | ~ sP637(U_7009,U_7007,U_7008) )
    & ! [U_7009,U_7007,U_7008] :
        ( sP637(U_7009,U_7007,U_7008)
        | ~ class_Rings_Olinordered__idom(U_7007) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP637])],[f_2073_2]) ).

cnf(f_2073_4,plain,
    ( sP637(U_7009,U_7007,U_7008)
    | ~ class_Rings_Olinordered__idom(U_7007) ),
    inference(clausify,[status(thm)],[f_2073_3]) ).

cnf(f_2073_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),U_7008),U_7009))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),hAPP(c_Groups_Oabs__class_Oabs(U_7007),U_7008)),U_7009))
    | ~ sP637(U_7009,U_7007,U_7008) ),
    inference(clausify,[status(thm)],[f_2073_3]) ).

cnf(f_2073_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),hAPP(c_Groups_Oabs__class_Oabs(U_7007),U_7008)),U_7009))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7007),U_7008),U_7009))
    | ~ sP637(U_7009,U_7007,U_7008) ),
    inference(clausify,[status(thm)],[f_2073_3]) ).

fof(f_2074_1,plain,
    ! [V_k,V_l,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k))
      | hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) != hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq]) ).

fof(f_2074_2,plain,
    ! [U_7012,U_7011,U_7010] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7010),U_7011),U_7012))
      | hAPP(c_Groups_Oabs__class_Oabs(U_7010),U_7011) != hAPP(c_Groups_Oabs__class_Oabs(U_7010),U_7012)
      | ~ class_Rings_Olinordered__idom(U_7010) ),
    inference(variable_rename,[status(thm)],[f_2074_1]) ).

fof(f_2074_3,plain,
    ! [U_7011,U_7010,U_7012] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7010),U_7011),U_7012))
      | hAPP(c_Groups_Oabs__class_Oabs(U_7010),U_7011) != hAPP(c_Groups_Oabs__class_Oabs(U_7010),U_7012)
      | ~ class_Rings_Olinordered__idom(U_7010) ),
    inference(definitional_conversion,[status(esa)],[f_2074_2]) ).

cnf(f_2074_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7010),U_7011),U_7012))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7010),U_7011) != hAPP(c_Groups_Oabs__class_Oabs(U_7010),U_7012)
    | ~ class_Rings_Olinordered__idom(U_7010) ),
    inference(clausify,[status(thm)],[f_2074_3]) ).

fof(f_2075_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat]) ).

fof(f_2075_2,plain,
    ! [U_7015,U_7014,U_7013] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7014),U_7015)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),U_7015))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),U_7014)) ),
    inference(variable_rename,[status(thm)],[f_2075_1]) ).

fof(f_2075_3,plain,
    ! [U_7013,U_7014,U_7015] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7014),U_7015)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),U_7015))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),U_7014)) ),
    inference(definitional_conversion,[status(esa)],[f_2075_2]) ).

cnf(f_2075_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7014),U_7015)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),U_7015))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7013),U_7014)) ),
    inference(clausify,[status(thm)],[f_2075_3]) ).

fof(f_2076_1,plain,
    ! [V_n_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__reduce]) ).

fof(f_2076_2,plain,
    ! [U_7017,U_7016] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7016),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7017),U_7016)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7016),U_7017)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7016),U_7017))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7016),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7017),U_7016))) ) ),
    inference(variable_rename,[status(thm)],[f_2076_1]) ).

fof(f_2076_3,plain,
    ( ! [U_7021,U_7019] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7021),U_7019)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7019),U_7021)) )
    & ! [U_7020,U_7018] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7018),U_7020))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7018),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7020),U_7018))) ) ),
    inference(miniscope,[status(thm)],[f_2076_2]) ).

fof(f_2076_4,plain,
    ( ! [U_7019,U_7021] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7021),U_7019)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7019),U_7021)) )
    & ! [U_7020,U_7018] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7018),U_7020))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7018),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7020),U_7018))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2076_3]) ).

cnf(f_2076_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7018),U_7020))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7018),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7020),U_7018))) ),
    inference(clausify,[status(thm)],[f_2076_4]) ).

cnf(f_2076_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7021),U_7019)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7019),U_7021)) ),
    inference(clausify,[status(thm)],[f_2076_4]) ).

fof(f_2077_1,plain,
    ! [V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1]) ).

fof(f_2077_2,plain,
    ! [U_7022] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7022),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7022 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( U_7022 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7022),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_2077_1]) ).

fof(f_2077_3,plain,
    ( ! [U_7024] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7024),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7024 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_7023] :
        ( U_7023 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7023),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_2077_2]) ).

fof(f_2077_4,plain,
    ( ! [U_7024] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7024),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7024 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_7023] :
        ( U_7023 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7023),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2077_3]) ).

cnf(f_2077_5,plain,
    ( U_7023 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7023),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_2077_4]) ).

cnf(f_2077_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7024),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_7024 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2077_4]) ).

fof(f_2078_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
          | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Rings_Oidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right]) ).

fof(f_2078_2,plain,
    ! [U_7028,U_7027,U_7026,U_7025] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7026),U_7027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7028),U_7027)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),U_7026),U_7028))
            & U_7027 != c_Groups_Ozero__class_Ozero(U_7025) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),U_7026),U_7028))
          | U_7027 = c_Groups_Ozero__class_Ozero(U_7025)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7026),U_7027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7028),U_7027))) ) )
      | ~ class_Rings_Oidom(U_7025) ),
    inference(variable_rename,[status(thm)],[f_2078_1]) ).

fof(f_2078_3,plain,
    ( ! [U_7025,U_7026,U_7027,U_7028] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),U_7026),U_7028))
        | ~ sP638(U_7025,U_7026,U_7027,U_7028) )
    & ! [U_7025,U_7026,U_7027,U_7028] :
        ( U_7027 != c_Groups_Ozero__class_Ozero(U_7025)
        | ~ sP638(U_7025,U_7026,U_7027,U_7028) )
    & ! [U_7025,U_7026,U_7027,U_7028] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7026),U_7027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7028),U_7027)))
        | sP638(U_7025,U_7026,U_7027,U_7028)
        | ~ sP639(U_7025,U_7026,U_7027,U_7028) )
    & ! [U_7025,U_7026,U_7027,U_7028] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),U_7026),U_7028))
        | U_7027 = c_Groups_Ozero__class_Ozero(U_7025)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7026),U_7027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7028),U_7027)))
        | ~ sP639(U_7025,U_7026,U_7027,U_7028) )
    & ! [U_7025,U_7026,U_7027,U_7028] :
        ( sP639(U_7025,U_7026,U_7027,U_7028)
        | ~ class_Rings_Oidom(U_7025) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP638,sP639])],[f_2078_2]) ).

cnf(f_2078_4,plain,
    ( sP639(U_7025,U_7026,U_7027,U_7028)
    | ~ class_Rings_Oidom(U_7025) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

cnf(f_2078_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),U_7026),U_7028))
    | U_7027 = c_Groups_Ozero__class_Ozero(U_7025)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7026),U_7027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7028),U_7027)))
    | ~ sP639(U_7025,U_7026,U_7027,U_7028) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

cnf(f_2078_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7026),U_7027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7025),U_7028),U_7027)))
    | sP638(U_7025,U_7026,U_7027,U_7028)
    | ~ sP639(U_7025,U_7026,U_7027,U_7028) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

cnf(f_2078_7,plain,
    ( U_7027 != c_Groups_Ozero__class_Ozero(U_7025)
    | ~ sP638(U_7025,U_7026,U_7027,U_7028) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

cnf(f_2078_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7025),U_7026),U_7028))
    | ~ sP638(U_7025,U_7026,U_7027,U_7028) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

fof(f_2079_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
          | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Rings_Oidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left]) ).

fof(f_2079_2,plain,
    ! [U_7032,U_7031,U_7030,U_7029] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7032)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),U_7031),U_7032))
            & U_7030 != c_Groups_Ozero__class_Ozero(U_7029) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),U_7031),U_7032))
          | U_7030 = c_Groups_Ozero__class_Ozero(U_7029)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7032))) ) )
      | ~ class_Rings_Oidom(U_7029) ),
    inference(variable_rename,[status(thm)],[f_2079_1]) ).

fof(f_2079_3,plain,
    ( ! [U_7030,U_7032,U_7031,U_7029] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),U_7031),U_7032))
        | ~ sP640(U_7030,U_7032,U_7031,U_7029) )
    & ! [U_7030,U_7032,U_7031,U_7029] :
        ( U_7030 != c_Groups_Ozero__class_Ozero(U_7029)
        | ~ sP640(U_7030,U_7032,U_7031,U_7029) )
    & ! [U_7030,U_7032,U_7031,U_7029] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7032)))
        | sP640(U_7030,U_7032,U_7031,U_7029)
        | ~ sP641(U_7030,U_7032,U_7031,U_7029) )
    & ! [U_7030,U_7032,U_7031,U_7029] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),U_7031),U_7032))
        | U_7030 = c_Groups_Ozero__class_Ozero(U_7029)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7032)))
        | ~ sP641(U_7030,U_7032,U_7031,U_7029) )
    & ! [U_7030,U_7032,U_7031,U_7029] :
        ( sP641(U_7030,U_7032,U_7031,U_7029)
        | ~ class_Rings_Oidom(U_7029) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP640,sP641])],[f_2079_2]) ).

cnf(f_2079_4,plain,
    ( sP641(U_7030,U_7032,U_7031,U_7029)
    | ~ class_Rings_Oidom(U_7029) ),
    inference(clausify,[status(thm)],[f_2079_3]) ).

cnf(f_2079_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),U_7031),U_7032))
    | U_7030 = c_Groups_Ozero__class_Ozero(U_7029)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7032)))
    | ~ sP641(U_7030,U_7032,U_7031,U_7029) ),
    inference(clausify,[status(thm)],[f_2079_3]) ).

cnf(f_2079_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7029),U_7030),U_7032)))
    | sP640(U_7030,U_7032,U_7031,U_7029)
    | ~ sP641(U_7030,U_7032,U_7031,U_7029) ),
    inference(clausify,[status(thm)],[f_2079_3]) ).

cnf(f_2079_7,plain,
    ( U_7030 != c_Groups_Ozero__class_Ozero(U_7029)
    | ~ sP640(U_7030,U_7032,U_7031,U_7029) ),
    inference(clausify,[status(thm)],[f_2079_3]) ).

cnf(f_2079_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7029),U_7031),U_7032))
    | ~ sP640(U_7030,U_7032,U_7031,U_7029) ),
    inference(clausify,[status(thm)],[f_2079_3]) ).

fof(f_2080_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
          | c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) )
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0]) ).

fof(f_2080_2,plain,
    ! [U_7035,U_7034,U_7033] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7033),U_7034),U_7035))
          | c_Divides_Odiv__class_Omod(U_7033,U_7035,U_7034) != c_Groups_Ozero__class_Ozero(U_7033) )
        & ( c_Divides_Odiv__class_Omod(U_7033,U_7035,U_7034) = c_Groups_Ozero__class_Ozero(U_7033)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7033),U_7034),U_7035)) ) )
      | ~ class_Divides_Osemiring__div(U_7033) ),
    inference(variable_rename,[status(thm)],[f_2080_1]) ).

fof(f_2080_3,plain,
    ( ! [U_7034,U_7035,U_7033] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7033),U_7034),U_7035))
        | c_Divides_Odiv__class_Omod(U_7033,U_7035,U_7034) != c_Groups_Ozero__class_Ozero(U_7033)
        | ~ sP642(U_7034,U_7035,U_7033) )
    & ! [U_7034,U_7035,U_7033] :
        ( c_Divides_Odiv__class_Omod(U_7033,U_7035,U_7034) = c_Groups_Ozero__class_Ozero(U_7033)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7033),U_7034),U_7035))
        | ~ sP642(U_7034,U_7035,U_7033) )
    & ! [U_7034,U_7035,U_7033] :
        ( sP642(U_7034,U_7035,U_7033)
        | ~ class_Divides_Osemiring__div(U_7033) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP642])],[f_2080_2]) ).

cnf(f_2080_4,plain,
    ( sP642(U_7034,U_7035,U_7033)
    | ~ class_Divides_Osemiring__div(U_7033) ),
    inference(clausify,[status(thm)],[f_2080_3]) ).

cnf(f_2080_5,plain,
    ( c_Divides_Odiv__class_Omod(U_7033,U_7035,U_7034) = c_Groups_Ozero__class_Ozero(U_7033)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7033),U_7034),U_7035))
    | ~ sP642(U_7034,U_7035,U_7033) ),
    inference(clausify,[status(thm)],[f_2080_3]) ).

cnf(f_2080_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7033),U_7034),U_7035))
    | c_Divides_Odiv__class_Omod(U_7033,U_7035,U_7034) != c_Groups_Ozero__class_Ozero(U_7033)
    | ~ sP642(U_7034,U_7035,U_7033) ),
    inference(clausify,[status(thm)],[f_2080_3]) ).

fof(f_2081_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0]) ).

fof(f_2081_2,plain,
    ! [U_7038,U_7037,U_7036] :
      ( c_Divides_Odiv__class_Omod(U_7036,U_7038,U_7037) = c_Groups_Ozero__class_Ozero(U_7036)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7036),U_7037),U_7038))
      | ~ class_Divides_Osemiring__div(U_7036) ),
    inference(variable_rename,[status(thm)],[f_2081_1]) ).

fof(f_2081_3,plain,
    ! [U_7038,U_7037,U_7036] :
      ( c_Divides_Odiv__class_Omod(U_7036,U_7038,U_7037) = c_Groups_Ozero__class_Ozero(U_7036)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7036),U_7037),U_7038))
      | ~ class_Divides_Osemiring__div(U_7036) ),
    inference(definitional_conversion,[status(esa)],[f_2081_2]) ).

cnf(f_2081_4,plain,
    ( c_Divides_Odiv__class_Omod(U_7036,U_7038,U_7037) = c_Groups_Ozero__class_Ozero(U_7036)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7036),U_7037),U_7038))
    | ~ class_Divides_Osemiring__div(U_7036) ),
    inference(clausify,[status(thm)],[f_2081_3]) ).

fof(f_2082_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add]) ).

fof(f_2082_2,plain,
    ! [U_7042,U_7041,U_7040,U_7039] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7039),U_7041),U_7042)),U_7040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7039),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),U_7041),U_7040)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),U_7042),U_7040))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7039),U_7040),U_7042))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7039),U_7040),U_7041))
      | ~ class_Divides_Osemiring__div(U_7039) ),
    inference(variable_rename,[status(thm)],[f_2082_1]) ).

fof(f_2082_3,plain,
    ! [U_7039,U_7040,U_7041,U_7042] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7039),U_7041),U_7042)),U_7040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7039),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),U_7041),U_7040)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),U_7042),U_7040))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7039),U_7040),U_7042))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7039),U_7040),U_7041))
      | ~ class_Divides_Osemiring__div(U_7039) ),
    inference(definitional_conversion,[status(esa)],[f_2082_2]) ).

cnf(f_2082_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7039),U_7041),U_7042)),U_7040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7039),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),U_7041),U_7040)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7039),U_7042),U_7040))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7039),U_7040),U_7042))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7039),U_7040),U_7041))
    | ~ class_Divides_Osemiring__div(U_7039) ),
    inference(clausify,[status(thm)],[f_2082_3]) ).

fof(f_2083_1,plain,
    ! [V_w,V_z,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd]) ).

fof(f_2083_2,plain,
    ! [U_7047,U_7046,U_7045,U_7044,U_7043] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),U_7045),U_7044)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),U_7047),U_7046)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),U_7045),U_7047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),U_7044),U_7046))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7043),U_7046),U_7047))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7043),U_7044),U_7045))
      | ~ class_Divides_Osemiring__div(U_7043) ),
    inference(variable_rename,[status(thm)],[f_2083_1]) ).

fof(f_2083_3,plain,
    ! [U_7043,U_7044,U_7045,U_7046,U_7047] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),U_7045),U_7044)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),U_7047),U_7046)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),U_7045),U_7047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),U_7044),U_7046))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7043),U_7046),U_7047))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7043),U_7044),U_7045))
      | ~ class_Divides_Osemiring__div(U_7043) ),
    inference(definitional_conversion,[status(esa)],[f_2083_2]) ).

cnf(f_2083_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),U_7045),U_7044)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),U_7047),U_7046)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),U_7045),U_7047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7043),U_7044),U_7046))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7043),U_7046),U_7047))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7043),U_7044),U_7045))
    | ~ class_Divides_Osemiring__div(U_7043) ),
    inference(clausify,[status(thm)],[f_2083_3]) ).

fof(f_2084_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__mult]) ).

fof(f_2084_2,plain,
    ! [U_7051,U_7050,U_7049,U_7048] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7048),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7048),U_7050),U_7049)),U_7051) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7048),U_7050),U_7051)),U_7049)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7048),U_7049),U_7050))
      | ~ class_Divides_Osemiring__div(U_7048) ),
    inference(variable_rename,[status(thm)],[f_2084_1]) ).

fof(f_2084_3,plain,
    ! [U_7048,U_7049,U_7050,U_7051] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7048),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7048),U_7050),U_7049)),U_7051) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7048),U_7050),U_7051)),U_7049)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7048),U_7049),U_7050))
      | ~ class_Divides_Osemiring__div(U_7048) ),
    inference(definitional_conversion,[status(esa)],[f_2084_2]) ).

cnf(f_2084_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7048),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7048),U_7050),U_7049)),U_7051) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7048),U_7050),U_7051)),U_7049)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7048),U_7049),U_7050))
    | ~ class_Divides_Osemiring__div(U_7048) ),
    inference(clausify,[status(thm)],[f_2084_3]) ).

fof(f_2085_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self]) ).

fof(f_2085_2,plain,
    ! [U_7054,U_7053,U_7052] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7052),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7052),U_7054),U_7053)),U_7053) = U_7054
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7052),U_7053),U_7054))
      | ~ class_Divides_Osemiring__div(U_7052) ),
    inference(variable_rename,[status(thm)],[f_2085_1]) ).

fof(f_2085_3,plain,
    ! [U_7052,U_7053,U_7054] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7052),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7052),U_7054),U_7053)),U_7053) = U_7054
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7052),U_7053),U_7054))
      | ~ class_Divides_Osemiring__div(U_7052) ),
    inference(definitional_conversion,[status(esa)],[f_2085_2]) ).

cnf(f_2085_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7052),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7052),U_7054),U_7053)),U_7053) = U_7054
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7052),U_7053),U_7054))
    | ~ class_Divides_Osemiring__div(U_7052) ),
    inference(clausify,[status(thm)],[f_2085_3]) ).

fof(f_2086_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__swap]) ).

fof(f_2086_2,plain,
    ! [U_7058,U_7057,U_7056,U_7055] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7058),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7055),U_7057),U_7056)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7058),U_7057)),U_7056)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7055),U_7056),U_7057))
      | ~ class_Divides_Osemiring__div(U_7055) ),
    inference(variable_rename,[status(thm)],[f_2086_1]) ).

fof(f_2086_3,plain,
    ! [U_7055,U_7056,U_7057,U_7058] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7058),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7055),U_7057),U_7056)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7058),U_7057)),U_7056)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7055),U_7056),U_7057))
      | ~ class_Divides_Osemiring__div(U_7055) ),
    inference(definitional_conversion,[status(esa)],[f_2086_2]) ).

cnf(f_2086_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7058),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7055),U_7057),U_7056)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7058),U_7057)),U_7056)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7055),U_7056),U_7057))
    | ~ class_Divides_Osemiring__div(U_7055) ),
    inference(clausify,[status(thm)],[f_2086_3]) ).

fof(f_2087_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel]) ).

fof(f_2087_2,plain,
    ! [U_7061,U_7060,U_7059] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7059),U_7060),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7059),U_7061),U_7060)) = U_7061
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7059),U_7060),U_7061))
      | ~ class_Divides_Osemiring__div(U_7059) ),
    inference(variable_rename,[status(thm)],[f_2087_1]) ).

fof(f_2087_3,plain,
    ! [U_7059,U_7060,U_7061] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7059),U_7060),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7059),U_7061),U_7060)) = U_7061
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7059),U_7060),U_7061))
      | ~ class_Divides_Osemiring__div(U_7059) ),
    inference(definitional_conversion,[status(esa)],[f_2087_2]) ).

cnf(f_2087_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7059),U_7060),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7059),U_7061),U_7060)) = U_7061
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7059),U_7060),U_7061))
    | ~ class_Divides_Osemiring__div(U_7059) ),
    inference(clausify,[status(thm)],[f_2087_3]) ).

fof(f_2088_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__neg__div]) ).

fof(f_2088_2,plain,
    ! [U_7064,U_7063,U_7062] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7062),hAPP(c_Groups_Ouminus__class_Ouminus(U_7062),U_7064)),U_7063) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7062),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7062),U_7064),U_7063))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7062),U_7063),U_7064))
      | ~ class_Divides_Oring__div(U_7062) ),
    inference(variable_rename,[status(thm)],[f_2088_1]) ).

fof(f_2088_3,plain,
    ! [U_7062,U_7063,U_7064] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7062),hAPP(c_Groups_Ouminus__class_Ouminus(U_7062),U_7064)),U_7063) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7062),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7062),U_7064),U_7063))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7062),U_7063),U_7064))
      | ~ class_Divides_Oring__div(U_7062) ),
    inference(definitional_conversion,[status(esa)],[f_2088_2]) ).

cnf(f_2088_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7062),hAPP(c_Groups_Ouminus__class_Ouminus(U_7062),U_7064)),U_7063) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7062),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7062),U_7064),U_7063))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7062),U_7063),U_7064))
    | ~ class_Divides_Oring__div(U_7062) ),
    inference(clausify,[status(thm)],[f_2088_3]) ).

fof(f_2089_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__neg]) ).

fof(f_2089_2,plain,
    ! [U_7067,U_7066,U_7065] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7065),U_7067),hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),U_7066)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7065),U_7067),U_7066))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7065),U_7066),U_7067))
      | ~ class_Divides_Oring__div(U_7065) ),
    inference(variable_rename,[status(thm)],[f_2089_1]) ).

fof(f_2089_3,plain,
    ! [U_7065,U_7066,U_7067] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7065),U_7067),hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),U_7066)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7065),U_7067),U_7066))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7065),U_7066),U_7067))
      | ~ class_Divides_Oring__div(U_7065) ),
    inference(definitional_conversion,[status(esa)],[f_2089_2]) ).

cnf(f_2089_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7065),U_7067),hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),U_7066)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7065),U_7067),U_7066))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7065),U_7066),U_7067))
    | ~ class_Divides_Oring__div(U_7065) ),
    inference(clausify,[status(thm)],[f_2089_3]) ).

fof(f_2090_1,plain,
    ! [V_a,V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd]) ).

fof(f_2090_2,plain,
    ! [U_7071,U_7070,U_7069,U_7068] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7068),hAPP(hAPP(c_Power_Opower__class_Opower(U_7068),U_7071),U_7069)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7068),U_7071),U_7070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7069),U_7070))
      | ~ class_Rings_Ocomm__semiring__1(U_7068) ),
    inference(variable_rename,[status(thm)],[f_2090_1]) ).

fof(f_2090_3,plain,
    ! [U_7068,U_7069,U_7070,U_7071] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7068),hAPP(hAPP(c_Power_Opower__class_Opower(U_7068),U_7071),U_7069)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7068),U_7071),U_7070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7069),U_7070))
      | ~ class_Rings_Ocomm__semiring__1(U_7068) ),
    inference(definitional_conversion,[status(esa)],[f_2090_2]) ).

cnf(f_2090_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7068),hAPP(hAPP(c_Power_Opower__class_Opower(U_7068),U_7071),U_7069)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7068),U_7071),U_7070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7069),U_7070))
    | ~ class_Rings_Ocomm__semiring__1(U_7068) ),
    inference(clausify,[status(thm)],[f_2090_3]) ).

fof(f_2091_1,plain,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power__le]) ).

fof(f_2091_2,plain,
    ! [U_7076,U_7075,U_7074,U_7073,U_7072] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7072),hAPP(hAPP(c_Power_Opower__class_Opower(U_7072),U_7073),U_7075)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7072),U_7074),U_7076)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7075),U_7076))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7072),U_7073),U_7074))
      | ~ class_Rings_Ocomm__semiring__1(U_7072) ),
    inference(variable_rename,[status(thm)],[f_2091_1]) ).

fof(f_2091_3,plain,
    ! [U_7072,U_7073,U_7074,U_7075,U_7076] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7072),hAPP(hAPP(c_Power_Opower__class_Opower(U_7072),U_7073),U_7075)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7072),U_7074),U_7076)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7075),U_7076))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7072),U_7073),U_7074))
      | ~ class_Rings_Ocomm__semiring__1(U_7072) ),
    inference(definitional_conversion,[status(esa)],[f_2091_2]) ).

cnf(f_2091_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7072),hAPP(hAPP(c_Power_Opower__class_Opower(U_7072),U_7073),U_7075)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7072),U_7074),U_7076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7075),U_7076))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7072),U_7073),U_7074))
    | ~ class_Rings_Ocomm__semiring__1(U_7072) ),
    inference(clausify,[status(thm)],[f_2091_3]) ).

fof(f_2092_1,plain,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__dvd]) ).

fof(f_2092_2,plain,
    ! [U_7081,U_7080,U_7079,U_7078,U_7077] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7077),hAPP(hAPP(c_Power_Opower__class_Opower(U_7077),U_7078),U_7081)),U_7080))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7081),U_7079))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7077),hAPP(hAPP(c_Power_Opower__class_Opower(U_7077),U_7078),U_7079)),U_7080))
      | ~ class_Rings_Ocomm__semiring__1(U_7077) ),
    inference(variable_rename,[status(thm)],[f_2092_1]) ).

fof(f_2092_3,plain,
    ! [U_7078,U_7077,U_7079,U_7080,U_7081] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7077),hAPP(hAPP(c_Power_Opower__class_Opower(U_7077),U_7078),U_7081)),U_7080))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7081),U_7079))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7077),hAPP(hAPP(c_Power_Opower__class_Opower(U_7077),U_7078),U_7079)),U_7080))
      | ~ class_Rings_Ocomm__semiring__1(U_7077) ),
    inference(definitional_conversion,[status(esa)],[f_2092_2]) ).

cnf(f_2092_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7077),hAPP(hAPP(c_Power_Opower__class_Opower(U_7077),U_7078),U_7081)),U_7080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7081),U_7079))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7077),hAPP(hAPP(c_Power_Opower__class_Opower(U_7077),U_7078),U_7079)),U_7080))
    | ~ class_Rings_Ocomm__semiring__1(U_7077) ),
    inference(clausify,[status(thm)],[f_2092_3]) ).

fof(f_2093_1,plain,
    ! [V_n,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__power]) ).

fof(f_2093_2,plain,
    ! [U_7085,U_7084,U_7083,U_7082] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7082),U_7084),U_7083)),U_7085) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7082),hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),U_7084),U_7085)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),U_7083),U_7085))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7082),U_7083),U_7084))
      | ~ class_Divides_Osemiring__div(U_7082) ),
    inference(variable_rename,[status(thm)],[f_2093_1]) ).

fof(f_2093_3,plain,
    ! [U_7082,U_7083,U_7084,U_7085] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7082),U_7084),U_7083)),U_7085) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7082),hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),U_7084),U_7085)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),U_7083),U_7085))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7082),U_7083),U_7084))
      | ~ class_Divides_Osemiring__div(U_7082) ),
    inference(definitional_conversion,[status(esa)],[f_2093_2]) ).

cnf(f_2093_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7082),U_7084),U_7083)),U_7085) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7082),hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),U_7084),U_7085)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7082),U_7083),U_7085))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7082),U_7083),U_7084))
    | ~ class_Divides_Osemiring__div(U_7082) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

fof(f_2094_1,plain,
    ! [V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1]) ).

fof(f_2094_2,plain,
    ! [U_7086] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7086),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7086 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( U_7086 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7086),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_2094_1]) ).

fof(f_2094_3,plain,
    ( ! [U_7088] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7088),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7088 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_7087] :
        ( U_7087 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7087),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_2094_2]) ).

fof(f_2094_4,plain,
    ( ! [U_7088] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7088),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7088 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_7087] :
        ( U_7087 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7087),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2094_3]) ).

cnf(f_2094_5,plain,
    ( U_7087 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7087),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_2094_4]) ).

cnf(f_2094_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7088),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_7088 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2094_4]) ).

fof(f_2095_1,plain,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__not__less]) ).

fof(f_2095_2,plain,
    ! [U_7090,U_7089] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7090),U_7089))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7089),U_7090))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7089)) ),
    inference(variable_rename,[status(thm)],[f_2095_1]) ).

fof(f_2095_3,plain,
    ! [U_7089,U_7090] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7090),U_7089))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7089),U_7090))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7089)) ),
    inference(definitional_conversion,[status(esa)],[f_2095_2]) ).

cnf(f_2095_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7090),U_7089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7089),U_7090))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7089)) ),
    inference(clausify,[status(thm)],[f_2095_3]) ).

fof(f_2096_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj]) ).

fof(f_2096_2,plain,
    ! [U_7093,U_7092,U_7091] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7091),U_7092)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7091),U_7093)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7092),U_7093))
          & U_7091 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7092),U_7093))
        | U_7091 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7091),U_7092)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7091),U_7093))) ) ),
    inference(variable_rename,[status(thm)],[f_2096_1]) ).

fof(f_2096_3,plain,
    ( ! [U_7099,U_7097,U_7095] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7095),U_7097)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7095),U_7099)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7097),U_7099))
          & U_7095 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_7098,U_7096,U_7094] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7096),U_7098))
        | U_7094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7094),U_7096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7094),U_7098))) ) ),
    inference(miniscope,[status(thm)],[f_2096_2]) ).

fof(f_2096_4,plain,
    ( ! [U_7099,U_7097,U_7095] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7097),U_7099))
        | ~ sP643(U_7099,U_7097,U_7095) )
    & ! [U_7099,U_7097,U_7095] :
        ( U_7095 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP643(U_7099,U_7097,U_7095) )
    & ! [U_7099,U_7097,U_7095] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7095),U_7097)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7095),U_7099)))
        | sP643(U_7099,U_7097,U_7095) )
    & ! [U_7096,U_7094,U_7098] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7096),U_7098))
        | U_7094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7094),U_7096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7094),U_7098))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP643])],[f_2096_3]) ).

cnf(f_2096_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7096),U_7098))
    | U_7094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7094),U_7096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7094),U_7098))) ),
    inference(clausify,[status(thm)],[f_2096_4]) ).

cnf(f_2096_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7095),U_7097)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7095),U_7099)))
    | sP643(U_7099,U_7097,U_7095) ),
    inference(clausify,[status(thm)],[f_2096_4]) ).

cnf(f_2096_7,plain,
    ( U_7095 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP643(U_7099,U_7097,U_7095) ),
    inference(clausify,[status(thm)],[f_2096_4]) ).

cnf(f_2096_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7097),U_7099))
    | ~ sP643(U_7099,U_7097,U_7095) ),
    inference(clausify,[status(thm)],[f_2096_4]) ).

fof(f_2097_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diffD]) ).

fof(f_2097_2,plain,
    ! [U_7102,U_7101,U_7100] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),U_7101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7102),U_7101))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),U_7102))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7101),U_7102))) ),
    inference(variable_rename,[status(thm)],[f_2097_1]) ).

fof(f_2097_3,plain,
    ! [U_7100,U_7101,U_7102] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),U_7101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7102),U_7101))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),U_7102))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7101),U_7102))) ),
    inference(definitional_conversion,[status(esa)],[f_2097_2]) ).

cnf(f_2097_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),U_7101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7102),U_7101))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),U_7102))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7101),U_7102))) ),
    inference(clausify,[status(thm)],[f_2097_3]) ).

fof(f_2098_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diffD1]) ).

fof(f_2098_2,plain,
    ! [U_7105,U_7104,U_7103] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),U_7105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7105),U_7104))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),U_7104))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7104),U_7105))) ),
    inference(variable_rename,[status(thm)],[f_2098_1]) ).

fof(f_2098_3,plain,
    ! [U_7103,U_7104,U_7105] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),U_7105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7105),U_7104))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),U_7104))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7104),U_7105))) ),
    inference(definitional_conversion,[status(esa)],[f_2098_2]) ).

cnf(f_2098_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),U_7105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7105),U_7104))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),U_7104))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7104),U_7105))) ),
    inference(clausify,[status(thm)],[f_2098_3]) ).

fof(f_2099_1,plain,
    ! [V_l_2,V_P_2,T_b] :
      ( ( ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) )
          | ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) ) )
      | ~ class_Rings_Osemiring__0(T_b)
      | ~ class_Rings_Odvd(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex]) ).

fof(f_2099_2,plain,
    ! [U_7112,U_7111,U_7110] :
      ( ( ( ? [U_7109] : hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7109)))
          | ! [U_7108] :
              ( ~ hBOOL(hAPP(U_7111,U_7108))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),U_7108),c_Groups_Ozero__class_Ozero(U_7110)))) ) )
        & ( ? [U_7107] :
              ( hBOOL(hAPP(U_7111,U_7107))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),U_7107),c_Groups_Ozero__class_Ozero(U_7110)))) )
          | ! [U_7106] : ~ hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7106))) ) )
      | ~ class_Rings_Osemiring__0(U_7110)
      | ~ class_Rings_Odvd(U_7110) ),
    inference(variable_rename,[status(thm)],[f_2099_1]) ).

fof(f_2099_3,plain,
    ! [U_7112,U_7111,U_7110] :
      ( ( ( ? [U_7109] : hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7109)))
          | ! [U_7108] :
              ( ~ hBOOL(hAPP(U_7111,U_7108))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),U_7108),c_Groups_Ozero__class_Ozero(U_7110)))) ) )
        & ( ( hBOOL(hAPP(U_7111,sK100(U_7112,U_7111,U_7110)))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),sK100(U_7112,U_7111,U_7110)),c_Groups_Ozero__class_Ozero(U_7110)))) )
          | ! [U_7106] : ~ hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7106))) ) )
      | ~ class_Rings_Osemiring__0(U_7110)
      | ~ class_Rings_Odvd(U_7110) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_7107,sK100(U_7112,U_7111,U_7110))],[f_2099_2]) ).

fof(f_2099_4,plain,
    ! [U_7112,U_7111,U_7110] :
      ( ( ( hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),sK101(U_7112,U_7111,U_7110))))
          | ! [U_7108] :
              ( ~ hBOOL(hAPP(U_7111,U_7108))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),U_7108),c_Groups_Ozero__class_Ozero(U_7110)))) ) )
        & ( ( hBOOL(hAPP(U_7111,sK100(U_7112,U_7111,U_7110)))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),sK100(U_7112,U_7111,U_7110)),c_Groups_Ozero__class_Ozero(U_7110)))) )
          | ! [U_7106] : ~ hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7106))) ) )
      | ~ class_Rings_Osemiring__0(U_7110)
      | ~ class_Rings_Odvd(U_7110) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_7109,sK101(U_7112,U_7111,U_7110))],[f_2099_3]) ).

fof(f_2099_5,plain,
    ( ! [U_7110,U_7111,U_7112] :
        ( hBOOL(hAPP(U_7111,sK100(U_7112,U_7111,U_7110)))
        | ~ sP644(U_7110,U_7111,U_7112) )
    & ! [U_7110,U_7111,U_7112] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),sK100(U_7112,U_7111,U_7110)),c_Groups_Ozero__class_Ozero(U_7110))))
        | ~ sP644(U_7110,U_7111,U_7112) )
    & ! [U_7106,U_7108,U_7110,U_7111,U_7112] :
        ( hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),sK101(U_7112,U_7111,U_7110))))
        | ~ hBOOL(hAPP(U_7111,U_7108))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),U_7108),c_Groups_Ozero__class_Ozero(U_7110))))
        | ~ sP645(U_7106,U_7108,U_7110,U_7111,U_7112) )
    & ! [U_7106,U_7108,U_7110,U_7111,U_7112] :
        ( sP644(U_7110,U_7111,U_7112)
        | ~ hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7106)))
        | ~ sP645(U_7106,U_7108,U_7110,U_7111,U_7112) )
    & ! [U_7106,U_7108,U_7110,U_7111,U_7112] :
        ( sP645(U_7106,U_7108,U_7110,U_7111,U_7112)
        | ~ class_Rings_Osemiring__0(U_7110)
        | ~ class_Rings_Odvd(U_7110) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP644,sP645])],[f_2099_4]) ).

cnf(f_2099_6,plain,
    ( sP645(U_7106,U_7108,U_7110,U_7111,U_7112)
    | ~ class_Rings_Osemiring__0(U_7110)
    | ~ class_Rings_Odvd(U_7110) ),
    inference(clausify,[status(thm)],[f_2099_5]) ).

cnf(f_2099_7,plain,
    ( sP644(U_7110,U_7111,U_7112)
    | ~ hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),U_7106)))
    | ~ sP645(U_7106,U_7108,U_7110,U_7111,U_7112) ),
    inference(clausify,[status(thm)],[f_2099_5]) ).

cnf(f_2099_8,plain,
    ( hBOOL(hAPP(U_7111,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7110),U_7112),sK101(U_7112,U_7111,U_7110))))
    | ~ hBOOL(hAPP(U_7111,U_7108))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),U_7108),c_Groups_Ozero__class_Ozero(U_7110))))
    | ~ sP645(U_7106,U_7108,U_7110,U_7111,U_7112) ),
    inference(clausify,[status(thm)],[f_2099_5]) ).

cnf(f_2099_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7110),U_7112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7110),sK100(U_7112,U_7111,U_7110)),c_Groups_Ozero__class_Ozero(U_7110))))
    | ~ sP644(U_7110,U_7111,U_7112) ),
    inference(clausify,[status(thm)],[f_2099_5]) ).

cnf(f_2099_10,plain,
    ( hBOOL(hAPP(U_7111,sK100(U_7112,U_7111,U_7110)))
    | ~ sP644(U_7110,U_7111,U_7112) ),
    inference(clausify,[status(thm)],[f_2099_5]) ).

fof(f_2100_1,plain,
    ! [V_t_2,V_D_2,V_d_2,T_b] :
      ( ! [B_x,B_k] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
      | ~ class_Rings_Odvd(T_b)
      | ~ class_Rings_Ocomm__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J]) ).

fof(f_2100_2,plain,
    ! [U_7118,U_7117,U_7116,U_7115] :
      ( ! [U_7114,U_7113] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7114),U_7118)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7113),U_7117))),U_7118))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7113),U_7117))),U_7118)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7114),U_7118))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),U_7117))
      | ~ class_Rings_Odvd(U_7115)
      | ~ class_Rings_Ocomm__ring(U_7115) ),
    inference(variable_rename,[status(thm)],[f_2100_1]) ).

fof(f_2100_3,plain,
    ! [U_7118,U_7117,U_7116,U_7115] :
      ( ( ! [U_7122] :
            ( ! [U_7120] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7120),U_7117))),U_7118)))
            | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7122),U_7118))) )
        & ! [U_7121] :
            ( ! [U_7119] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7119),U_7117))),U_7118)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7121),U_7118))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),U_7117))
      | ~ class_Rings_Odvd(U_7115)
      | ~ class_Rings_Ocomm__ring(U_7115) ),
    inference(miniscope,[status(thm)],[f_2100_2]) ).

fof(f_2100_4,plain,
    ( ! [U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7120),U_7117))),U_7118)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7122),U_7118)))
        | ~ sP646(U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122) )
    & ! [U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7119),U_7117))),U_7118)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7121),U_7118)))
        | ~ sP646(U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122) )
    & ! [U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122] :
        ( sP646(U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),U_7117))
        | ~ class_Rings_Odvd(U_7115)
        | ~ class_Rings_Ocomm__ring(U_7115) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP646])],[f_2100_3]) ).

cnf(f_2100_5,plain,
    ( sP646(U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),U_7117))
    | ~ class_Rings_Odvd(U_7115)
    | ~ class_Rings_Ocomm__ring(U_7115) ),
    inference(clausify,[status(thm)],[f_2100_4]) ).

cnf(f_2100_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7119),U_7117))),U_7118)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7121),U_7118)))
    | ~ sP646(U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122) ),
    inference(clausify,[status(thm)],[f_2100_4]) ).

cnf(f_2100_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7115),U_7122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7115),U_7120),U_7117))),U_7118)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7115),U_7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7115),U_7122),U_7118)))
    | ~ sP646(U_7115,U_7116,U_7117,U_7118,U_7121,U_7119,U_7120,U_7122) ),
    inference(clausify,[status(thm)],[f_2100_4]) ).

fof(f_2101_1,plain,
    ! [V_t_2,V_D_2,V_d_2,T_b] :
      ( ! [B_x,B_k] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
      | ~ class_Rings_Odvd(T_b)
      | ~ class_Rings_Ocomm__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J]) ).

fof(f_2101_2,plain,
    ! [U_7128,U_7127,U_7126,U_7125] :
      ( ! [U_7124,U_7123] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7124),U_7128)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7123),U_7127))),U_7128))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7123),U_7127))),U_7128)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7124),U_7128))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),U_7127))
      | ~ class_Rings_Odvd(U_7125)
      | ~ class_Rings_Ocomm__ring(U_7125) ),
    inference(variable_rename,[status(thm)],[f_2101_1]) ).

fof(f_2101_3,plain,
    ! [U_7128,U_7127,U_7126,U_7125] :
      ( ( ! [U_7132] :
            ( ! [U_7130] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7130),U_7127))),U_7128)))
            | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7132),U_7128))) )
        & ! [U_7131] :
            ( ! [U_7129] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7129),U_7127))),U_7128)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7131),U_7128))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),U_7127))
      | ~ class_Rings_Odvd(U_7125)
      | ~ class_Rings_Ocomm__ring(U_7125) ),
    inference(miniscope,[status(thm)],[f_2101_2]) ).

fof(f_2101_4,plain,
    ( ! [U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7130),U_7127))),U_7128)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7132),U_7128)))
        | ~ sP647(U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132) )
    & ! [U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7129),U_7127))),U_7128)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7131),U_7128)))
        | ~ sP647(U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132) )
    & ! [U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132] :
        ( sP647(U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),U_7127))
        | ~ class_Rings_Odvd(U_7125)
        | ~ class_Rings_Ocomm__ring(U_7125) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP647])],[f_2101_3]) ).

cnf(f_2101_5,plain,
    ( sP647(U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),U_7127))
    | ~ class_Rings_Odvd(U_7125)
    | ~ class_Rings_Ocomm__ring(U_7125) ),
    inference(clausify,[status(thm)],[f_2101_4]) ).

cnf(f_2101_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7129),U_7127))),U_7128)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7131),U_7128)))
    | ~ sP647(U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132) ),
    inference(clausify,[status(thm)],[f_2101_4]) ).

cnf(f_2101_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7125),U_7132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7125),U_7130),U_7127))),U_7128)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7125),U_7126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7125),U_7132),U_7128)))
    | ~ sP647(U_7126,U_7130,U_7127,U_7129,U_7128,U_7131,U_7125,U_7132) ),
    inference(clausify,[status(thm)],[f_2101_4]) ).

fof(f_2102_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0__number__of]) ).

fof(f_2102_2,plain,
    ! [U_7135,U_7134,U_7133] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7133),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135)))
          | c_Divides_Odiv__class_Omod(U_7133,hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)) != c_Groups_Ozero__class_Ozero(U_7133) )
        & ( c_Divides_Odiv__class_Omod(U_7133,hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)) = c_Groups_Ozero__class_Ozero(U_7133)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7133),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135))) ) )
      | ~ class_Int_Onumber(U_7133)
      | ~ class_Divides_Osemiring__div(U_7133) ),
    inference(variable_rename,[status(thm)],[f_2102_1]) ).

fof(f_2102_3,plain,
    ( ! [U_7133,U_7134,U_7135] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7133),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135)))
        | c_Divides_Odiv__class_Omod(U_7133,hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)) != c_Groups_Ozero__class_Ozero(U_7133)
        | ~ sP648(U_7133,U_7134,U_7135) )
    & ! [U_7133,U_7134,U_7135] :
        ( c_Divides_Odiv__class_Omod(U_7133,hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)) = c_Groups_Ozero__class_Ozero(U_7133)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7133),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135)))
        | ~ sP648(U_7133,U_7134,U_7135) )
    & ! [U_7133,U_7134,U_7135] :
        ( sP648(U_7133,U_7134,U_7135)
        | ~ class_Int_Onumber(U_7133)
        | ~ class_Divides_Osemiring__div(U_7133) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP648])],[f_2102_2]) ).

cnf(f_2102_4,plain,
    ( sP648(U_7133,U_7134,U_7135)
    | ~ class_Int_Onumber(U_7133)
    | ~ class_Divides_Osemiring__div(U_7133) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

cnf(f_2102_5,plain,
    ( c_Divides_Odiv__class_Omod(U_7133,hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)) = c_Groups_Ozero__class_Ozero(U_7133)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7133),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135)))
    | ~ sP648(U_7133,U_7134,U_7135) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

cnf(f_2102_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7133),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135)))
    | c_Divides_Odiv__class_Omod(U_7133,hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7135),hAPP(c_Int_Onumber__class_Onumber__of(U_7133),U_7134)) != c_Groups_Ozero__class_Ozero(U_7133)
    | ~ sP648(U_7133,U_7134,U_7135) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

fof(f_2103_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
          | V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) )
        & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) != V_c_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
      | V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult]) ).

fof(f_2103_2,plain,
    ! [U_7139,U_7138,U_7137,U_7136] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7136),U_7138),U_7137) = U_7139
          | U_7138 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7136),U_7139),U_7137) )
        & ( U_7138 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7136),U_7139),U_7137)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7136),U_7138),U_7137) != U_7139 ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7136),U_7137),U_7138))
      | U_7137 = c_Groups_Ozero__class_Ozero(U_7136)
      | ~ class_Divides_Osemiring__div(U_7136) ),
    inference(variable_rename,[status(thm)],[f_2103_1]) ).

fof(f_2103_3,plain,
    ( ! [U_7137,U_7139,U_7138,U_7136] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7136),U_7138),U_7137) = U_7139
        | U_7138 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7136),U_7139),U_7137)
        | ~ sP649(U_7137,U_7139,U_7138,U_7136) )
    & ! [U_7137,U_7139,U_7138,U_7136] :
        ( U_7138 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7136),U_7139),U_7137)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7136),U_7138),U_7137) != U_7139
        | ~ sP649(U_7137,U_7139,U_7138,U_7136) )
    & ! [U_7137,U_7139,U_7138,U_7136] :
        ( sP649(U_7137,U_7139,U_7138,U_7136)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7136),U_7137),U_7138))
        | U_7137 = c_Groups_Ozero__class_Ozero(U_7136)
        | ~ class_Divides_Osemiring__div(U_7136) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP649])],[f_2103_2]) ).

cnf(f_2103_4,plain,
    ( sP649(U_7137,U_7139,U_7138,U_7136)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7136),U_7137),U_7138))
    | U_7137 = c_Groups_Ozero__class_Ozero(U_7136)
    | ~ class_Divides_Osemiring__div(U_7136) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

cnf(f_2103_5,plain,
    ( U_7138 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7136),U_7139),U_7137)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7136),U_7138),U_7137) != U_7139
    | ~ sP649(U_7137,U_7139,U_7138,U_7136) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

cnf(f_2103_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7136),U_7138),U_7137) = U_7139
    | U_7138 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7136),U_7139),U_7137)
    | ~ sP649(U_7137,U_7139,U_7138,U_7136) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

fof(f_2104_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
      | V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult]) ).

fof(f_2104_2,plain,
    ! [U_7144,U_7143,U_7142,U_7141,U_7140] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7143),U_7141) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7144),U_7142)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7143),U_7142) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7141),U_7144) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7143),U_7142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7141),U_7144)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7143),U_7141) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7144),U_7142) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7140),U_7142),U_7144))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7140),U_7141),U_7143))
      | U_7142 = c_Groups_Ozero__class_Ozero(U_7140)
      | U_7141 = c_Groups_Ozero__class_Ozero(U_7140)
      | ~ class_Divides_Osemiring__div(U_7140) ),
    inference(variable_rename,[status(thm)],[f_2104_1]) ).

fof(f_2104_3,plain,
    ( ! [U_7141,U_7144,U_7142,U_7143,U_7140] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7143),U_7141) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7144),U_7142)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7143),U_7142) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7141),U_7144)
        | ~ sP650(U_7141,U_7144,U_7142,U_7143,U_7140) )
    & ! [U_7141,U_7144,U_7142,U_7143,U_7140] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7143),U_7142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7141),U_7144)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7143),U_7141) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7144),U_7142)
        | ~ sP650(U_7141,U_7144,U_7142,U_7143,U_7140) )
    & ! [U_7141,U_7144,U_7142,U_7143,U_7140] :
        ( sP650(U_7141,U_7144,U_7142,U_7143,U_7140)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7140),U_7142),U_7144))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7140),U_7141),U_7143))
        | U_7142 = c_Groups_Ozero__class_Ozero(U_7140)
        | U_7141 = c_Groups_Ozero__class_Ozero(U_7140)
        | ~ class_Divides_Osemiring__div(U_7140) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP650])],[f_2104_2]) ).

cnf(f_2104_4,plain,
    ( sP650(U_7141,U_7144,U_7142,U_7143,U_7140)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7140),U_7142),U_7144))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7140),U_7141),U_7143))
    | U_7142 = c_Groups_Ozero__class_Ozero(U_7140)
    | U_7141 = c_Groups_Ozero__class_Ozero(U_7140)
    | ~ class_Divides_Osemiring__div(U_7140) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

cnf(f_2104_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7143),U_7142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7141),U_7144)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7143),U_7141) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7144),U_7142)
    | ~ sP650(U_7141,U_7144,U_7142,U_7143,U_7140) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

cnf(f_2104_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7143),U_7141) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7140),U_7144),U_7142)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7143),U_7142) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7140),U_7141),U_7144)
    | ~ sP650(U_7141,U_7144,U_7142,U_7143,U_7140) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

fof(f_2105_1,plain,
    ! [V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__imp__le]) ).

fof(f_2105_2,plain,
    ! [U_7146,U_7145] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7145),U_7146))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7146))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7145),U_7146)) ),
    inference(variable_rename,[status(thm)],[f_2105_1]) ).

fof(f_2105_3,plain,
    ! [U_7146,U_7145] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7145),U_7146))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7146))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7145),U_7146)) ),
    inference(definitional_conversion,[status(esa)],[f_2105_2]) ).

cnf(f_2105_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7145),U_7146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7146))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7145),U_7146)) ),
    inference(clausify,[status(thm)],[f_2105_3]) ).

fof(f_2106_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1]) ).

fof(f_2106_2,plain,
    ! [U_7149,U_7148,U_7147] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7149)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7148),U_7149)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7148),U_7149))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7149))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7147)) ),
    inference(variable_rename,[status(thm)],[f_2106_1]) ).

fof(f_2106_3,plain,
    ( ! [U_7148,U_7149,U_7147] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7149)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7148),U_7149))
        | ~ sP651(U_7148,U_7149,U_7147) )
    & ! [U_7148,U_7149,U_7147] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7148),U_7149))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7149)))
        | ~ sP651(U_7148,U_7149,U_7147) )
    & ! [U_7148,U_7149,U_7147] :
        ( sP651(U_7148,U_7149,U_7147)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7147)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP651])],[f_2106_2]) ).

cnf(f_2106_4,plain,
    ( sP651(U_7148,U_7149,U_7147)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7147)) ),
    inference(clausify,[status(thm)],[f_2106_3]) ).

cnf(f_2106_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7148),U_7149))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7149)))
    | ~ sP651(U_7148,U_7149,U_7147) ),
    inference(clausify,[status(thm)],[f_2106_3]) ).

cnf(f_2106_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7147),U_7149)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7148),U_7149))
    | ~ sP651(U_7148,U_7149,U_7147) ),
    inference(clausify,[status(thm)],[f_2106_3]) ).

fof(f_2107_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel]) ).

fof(f_2107_2,plain,
    ! [U_7152,U_7151,U_7150] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7151),U_7152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7150))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7150),U_7151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7150),U_7152))) ),
    inference(variable_rename,[status(thm)],[f_2107_1]) ).

fof(f_2107_3,plain,
    ! [U_7152,U_7150,U_7151] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7151),U_7152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7150))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7150),U_7151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7150),U_7152))) ),
    inference(definitional_conversion,[status(esa)],[f_2107_2]) ).

cnf(f_2107_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7151),U_7152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7150))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7150),U_7151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7150),U_7152))) ),
    inference(clausify,[status(thm)],[f_2107_3]) ).

fof(f_2108_1,plain,
    ! [V_x,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))
      | ( V_x != c_Groups_Oone__class_Oone(T_a)
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) )
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power]) ).

fof(f_2108_2,plain,
    ! [U_7155,U_7154,U_7153] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7153),U_7155),hAPP(hAPP(c_Power_Opower__class_Opower(U_7153),U_7155),U_7154)))
      | ( U_7155 != c_Groups_Oone__class_Oone(U_7153)
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7154)) )
      | ~ class_Rings_Ocomm__semiring__1(U_7153) ),
    inference(variable_rename,[status(thm)],[f_2108_1]) ).

fof(f_2108_3,plain,
    ( ! [U_7155,U_7153,U_7154] :
        ( U_7155 != c_Groups_Oone__class_Oone(U_7153)
        | ~ sP652(U_7155,U_7153,U_7154) )
    & ! [U_7155,U_7153,U_7154] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7154))
        | ~ sP652(U_7155,U_7153,U_7154) )
    & ! [U_7155,U_7153,U_7154] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7153),U_7155),hAPP(hAPP(c_Power_Opower__class_Opower(U_7153),U_7155),U_7154)))
        | sP652(U_7155,U_7153,U_7154)
        | ~ class_Rings_Ocomm__semiring__1(U_7153) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP652])],[f_2108_2]) ).

cnf(f_2108_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7153),U_7155),hAPP(hAPP(c_Power_Opower__class_Opower(U_7153),U_7155),U_7154)))
    | sP652(U_7155,U_7153,U_7154)
    | ~ class_Rings_Ocomm__semiring__1(U_7153) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

cnf(f_2108_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7154))
    | ~ sP652(U_7155,U_7153,U_7154) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

cnf(f_2108_6,plain,
    ( U_7155 != c_Groups_Oone__class_Oone(U_7153)
    | ~ sP652(U_7155,U_7153,U_7154) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

fof(f_2109_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2]) ).

fof(f_2109_2,plain,
    ! [U_7157,U_7156] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7157),U_7156)),U_7156))
          | U_7157 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_7157 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7157),U_7156)),U_7156)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7156)) ),
    inference(variable_rename,[status(thm)],[f_2109_1]) ).

fof(f_2109_3,plain,
    ( ! [U_7156,U_7157] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7157),U_7156)),U_7156))
        | U_7157 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP653(U_7156,U_7157) )
    & ! [U_7156,U_7157] :
        ( U_7157 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7157),U_7156)),U_7156))
        | ~ sP653(U_7156,U_7157) )
    & ! [U_7156,U_7157] :
        ( sP653(U_7156,U_7157)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7156)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP653])],[f_2109_2]) ).

cnf(f_2109_4,plain,
    ( sP653(U_7156,U_7157)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7156)) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

cnf(f_2109_5,plain,
    ( U_7157 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7157),U_7156)),U_7156))
    | ~ sP653(U_7156,U_7157) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

cnf(f_2109_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7157),U_7156)),U_7156))
    | U_7157 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP653(U_7156,U_7157) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

fof(f_2110_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1]) ).

fof(f_2110_2,plain,
    ! [U_7159,U_7158] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7158),U_7159)),U_7158))
          | U_7159 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_7159 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7158),U_7159)),U_7158)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7158)) ),
    inference(variable_rename,[status(thm)],[f_2110_1]) ).

fof(f_2110_3,plain,
    ( ! [U_7158,U_7159] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7158),U_7159)),U_7158))
        | U_7159 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP654(U_7158,U_7159) )
    & ! [U_7158,U_7159] :
        ( U_7159 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7158),U_7159)),U_7158))
        | ~ sP654(U_7158,U_7159) )
    & ! [U_7158,U_7159] :
        ( sP654(U_7158,U_7159)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7158)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP654])],[f_2110_2]) ).

cnf(f_2110_4,plain,
    ( sP654(U_7158,U_7159)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7158)) ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

cnf(f_2110_5,plain,
    ( U_7159 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7158),U_7159)),U_7158))
    | ~ sP654(U_7158,U_7159) ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

cnf(f_2110_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7158),U_7159)),U_7158))
    | U_7159 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP654(U_7158,U_7159) ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

fof(f_2111_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_neg__bind__def]) ).

fof(f_2111_2,plain,
    ! [U_7166,U_7165,U_7164,U_7163,U_7162,U_7161,U_7160] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7160,U_7161,U_7162,U_7163),U_7164),U_7165),U_7166) = c_New__DSequence_Oneg__bind(U_7160,U_7161,hAPP(hAPP(hAPP(U_7162,U_7164),U_7165),U_7166),hAPP(hAPP(c_COMBC(U_7160,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161)))),hAPP(hAPP(c_COMBC(U_7160,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161))))),hAPP(hAPP(c_COMBC(U_7160,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161)))))),U_7163),U_7164)),U_7165)),U_7166)),
    inference(variable_rename,[status(thm)],[f_2111_1]) ).

fof(f_2111_3,plain,
    ! [U_7161,U_7160,U_7162,U_7163,U_7164,U_7165,U_7166] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7160,U_7161,U_7162,U_7163),U_7164),U_7165),U_7166) = c_New__DSequence_Oneg__bind(U_7160,U_7161,hAPP(hAPP(hAPP(U_7162,U_7164),U_7165),U_7166),hAPP(hAPP(c_COMBC(U_7160,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161)))),hAPP(hAPP(c_COMBC(U_7160,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161))))),hAPP(hAPP(c_COMBC(U_7160,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161)))))),U_7163),U_7164)),U_7165)),U_7166)),
    inference(definitional_conversion,[status(esa)],[f_2111_2]) ).

cnf(f_2111_4,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7160,U_7161,U_7162,U_7163),U_7164),U_7165),U_7166) = c_New__DSequence_Oneg__bind(U_7160,U_7161,hAPP(hAPP(hAPP(U_7162,U_7164),U_7165),U_7166),hAPP(hAPP(c_COMBC(U_7160,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161)))),hAPP(hAPP(c_COMBC(U_7160,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161))))),hAPP(hAPP(c_COMBC(U_7160,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7161)))))),U_7163),U_7164)),U_7165)),U_7166)),
    inference(clausify,[status(thm)],[f_2111_3]) ).

fof(f_2112_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__monoD]) ).

fof(f_2112_2,plain,
    ! [U_7170,U_7169,U_7168,U_7167] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7167),hAPP(U_7168,U_7169)),hAPP(U_7168,U_7170)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7170),U_7169))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7169),U_7170))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7167,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7168)
      | ~ class_Orderings_Oorder(U_7167) ),
    inference(variable_rename,[status(thm)],[f_2112_1]) ).

fof(f_2112_3,plain,
    ! [U_7168,U_7167,U_7169,U_7170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7167),hAPP(U_7168,U_7169)),hAPP(U_7168,U_7170)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7170),U_7169))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7169),U_7170))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7167,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7168)
      | ~ class_Orderings_Oorder(U_7167) ),
    inference(definitional_conversion,[status(esa)],[f_2112_2]) ).

cnf(f_2112_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7167),hAPP(U_7168,U_7169)),hAPP(U_7168,U_7170)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7170),U_7169))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7169),U_7170))
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7167,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7168)
    | ~ class_Orderings_Oorder(U_7167) ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

fof(f_2113_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OmonoD]) ).

fof(f_2113_2,plain,
    ! [U_7174,U_7173,U_7172,U_7171] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7171),hAPP(U_7172,U_7173)),hAPP(U_7172,U_7174)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7173),U_7174))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7171,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7172)
      | ~ class_Orderings_Oorder(U_7171) ),
    inference(variable_rename,[status(thm)],[f_2113_1]) ).

fof(f_2113_3,plain,
    ! [U_7171,U_7172,U_7174,U_7173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7171),hAPP(U_7172,U_7173)),hAPP(U_7172,U_7174)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7173),U_7174))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7171,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7172)
      | ~ class_Orderings_Oorder(U_7171) ),
    inference(definitional_conversion,[status(esa)],[f_2113_2]) ).

cnf(f_2113_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7171),hAPP(U_7172,U_7173)),hAPP(U_7172,U_7174)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7173),U_7174))
    | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7171,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7172)
    | ~ class_Orderings_Oorder(U_7171) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

fof(f_2114_1,plain,
    ! [V_m_2,V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
        | ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) )
      & ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__iff]) ).

fof(f_2114_2,plain,
    ! [U_7176,U_7175] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7175)),U_7176))
        | ( U_7176 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7175)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7175),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7176)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7175)) ) )
      & ( ( ( U_7176 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7175)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7175),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7176)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7175)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7175)),U_7176)) ) ),
    inference(variable_rename,[status(thm)],[f_2114_1]) ).

fof(f_2114_3,plain,
    ( ! [U_7180,U_7178] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7178)),U_7180))
        | ( U_7180 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7178),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7180)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178)) ) )
    & ! [U_7179,U_7177] :
        ( ( ( U_7179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7179)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7177)),U_7179)) ) ),
    inference(miniscope,[status(thm)],[f_2114_2]) ).

fof(f_2114_4,plain,
    ( ! [U_7180,U_7178] :
        ( U_7180 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP657(U_7180,U_7178) )
    & ! [U_7180,U_7178] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178))
        | ~ sP657(U_7180,U_7178) )
    & ! [U_7180,U_7178] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7178),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7180)))
        | ~ sP656(U_7180,U_7178) )
    & ! [U_7180,U_7178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178))
        | ~ sP656(U_7180,U_7178) )
    & ! [U_7177,U_7179] :
        ( U_7179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177))
        | ~ sP655(U_7177,U_7179) )
    & ! [U_7177,U_7179] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7179)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177))
        | ~ sP655(U_7177,U_7179) )
    & ! [U_7180,U_7178] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7178)),U_7180))
        | sP657(U_7180,U_7178)
        | sP656(U_7180,U_7178) )
    & ! [U_7177,U_7179] :
        ( sP655(U_7177,U_7179)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7177)),U_7179)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP655,sP656,sP657])],[f_2114_3]) ).

cnf(f_2114_5,plain,
    ( sP655(U_7177,U_7179)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7177)),U_7179)) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7178)),U_7180))
    | sP657(U_7180,U_7178)
    | sP656(U_7180,U_7178) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7179)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177))
    | ~ sP655(U_7177,U_7179) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_8,plain,
    ( U_7179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177))
    | ~ sP655(U_7177,U_7179) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178))
    | ~ sP656(U_7180,U_7178) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7178),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7180)))
    | ~ sP656(U_7180,U_7178) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178))
    | ~ sP657(U_7180,U_7178) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_12,plain,
    ( U_7180 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP657(U_7180,U_7178) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

fof(f_2115_1,plain,
    ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),V_a_2)))),c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,V_s_H_2)))),V_X_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OCall]) ).

fof(f_2115_2,plain,
    ! [U_7188,U_7187,U_7186,U_7185,U_7184,U_7183,U_7182,U_7181] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7181,U_7182,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7181)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7181),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7181),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,U_7186)))),hAPP(hAPP(c_COMBC(U_7181,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7181),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7183)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),U_7188)))),c_Com_Ocom_OCall(U_7187,U_7184,U_7188)),U_7185)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7181),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7181,U_7182,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7181)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7181),U_7183),hAPP(c_Com_Ocom_OBODY,U_7184)),hAPP(hAPP(c_COMBC(U_7181,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7181),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7185)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,U_7186)))),U_7187)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7181),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2115_1]) ).

fof(f_2115_3,plain,
    ! [U_7184,U_7181,U_7182,U_7185,U_7183,U_7187,U_7186,U_7188] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7181,U_7182,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7181)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7181),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7181),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,U_7186)))),hAPP(hAPP(c_COMBC(U_7181,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7181),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7183)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),U_7188)))),c_Com_Ocom_OCall(U_7187,U_7184,U_7188)),U_7185)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7181),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7181,U_7182,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7181)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7181),U_7183),hAPP(c_Com_Ocom_OBODY,U_7184)),hAPP(hAPP(c_COMBC(U_7181,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7181),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7185)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,U_7186)))),U_7187)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7181),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2115_2]) ).

cnf(f_2115_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7181,U_7182,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7181)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7181),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7181),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,U_7186)))),hAPP(hAPP(c_COMBC(U_7181,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7181),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7183)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),U_7188)))),c_Com_Ocom_OCall(U_7187,U_7184,U_7188)),U_7185)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7181),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7181,U_7182,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7181)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7181),U_7183),hAPP(c_Com_Ocom_OBODY,U_7184)),hAPP(hAPP(c_COMBC(U_7181,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7181),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7185)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,U_7186)))),U_7187)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7181),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2115_3]) ).

fof(f_2116_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_empty__subsetI]) ).

fof(f_2116_2,plain,
    ! [U_7190,U_7189] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7189,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7189,tc_HOL_Obool))),U_7190)),
    inference(variable_rename,[status(thm)],[f_2116_1]) ).

fof(f_2116_3,plain,
    ! [U_7190,U_7189] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7189,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7189,tc_HOL_Obool))),U_7190)),
    inference(definitional_conversion,[status(esa)],[f_2116_2]) ).

cnf(f_2116_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7189,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7189,tc_HOL_Obool))),U_7190)),
    inference(clausify,[status(thm)],[f_2116_3]) ).

fof(f_2117_1,plain,
    ! [V_n,V_m,V_f] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__zmod]) ).

fof(f_2117_2,plain,
    ! [U_7193,U_7192,U_7191] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7192,U_7193)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),U_7193))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),U_7192)) ),
    inference(variable_rename,[status(thm)],[f_2117_1]) ).

fof(f_2117_3,plain,
    ! [U_7192,U_7193,U_7191] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7192,U_7193)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),U_7193))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),U_7192)) ),
    inference(definitional_conversion,[status(esa)],[f_2117_2]) ).

cnf(f_2117_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7192,U_7193)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),U_7193))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7191),U_7192)) ),
    inference(clausify,[status(thm)],[f_2117_3]) ).

fof(f_2118_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__zmod__imp__zdvd]) ).

fof(f_2118_2,plain,
    ! [U_7196,U_7195,U_7194] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),U_7195))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),U_7196))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7195,U_7196))) ),
    inference(variable_rename,[status(thm)],[f_2118_1]) ).

fof(f_2118_3,plain,
    ! [U_7194,U_7195,U_7196] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),U_7195))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),U_7196))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7195,U_7196))) ),
    inference(definitional_conversion,[status(esa)],[f_2118_2]) ).

cnf(f_2118_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),U_7195))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),U_7196))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7194),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7195,U_7196))) ),
    inference(clausify,[status(thm)],[f_2118_3]) ).

fof(f_2119_1,plain,
    ! [V_t_2,V_d_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J]) ).

fof(f_2119_2,plain,
    ! [U_7198,U_7197] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7197),U_7198))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7197)),U_7198)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7197)),U_7198))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7197),U_7198)) ) ),
    inference(variable_rename,[status(thm)],[f_2119_1]) ).

fof(f_2119_3,plain,
    ( ! [U_7202,U_7200] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7200),U_7202))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7200)),U_7202)) )
    & ! [U_7201,U_7199] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7199)),U_7201))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7199),U_7201)) ) ),
    inference(miniscope,[status(thm)],[f_2119_2]) ).

fof(f_2119_4,plain,
    ( ! [U_7200,U_7202] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7200),U_7202))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7200)),U_7202)) )
    & ! [U_7201,U_7199] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7199)),U_7201))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7199),U_7201)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2119_3]) ).

cnf(f_2119_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7199)),U_7201))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7199),U_7201)) ),
    inference(clausify,[status(thm)],[f_2119_4]) ).

cnf(f_2119_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7200),U_7202))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7200)),U_7202)) ),
    inference(clausify,[status(thm)],[f_2119_4]) ).

fof(f_2120_1,plain,
    ! [V_t_2,V_d_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J]) ).

fof(f_2120_2,plain,
    ! [U_7204,U_7203] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7203),U_7204))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7203),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7204))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7203),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7204)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7203),U_7204)) ) ),
    inference(variable_rename,[status(thm)],[f_2120_1]) ).

fof(f_2120_3,plain,
    ( ! [U_7208,U_7206] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7206),U_7208))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7206),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7208))) )
    & ! [U_7207,U_7205] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7205),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7207)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7205),U_7207)) ) ),
    inference(miniscope,[status(thm)],[f_2120_2]) ).

fof(f_2120_4,plain,
    ( ! [U_7206,U_7208] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7206),U_7208))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7206),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7208))) )
    & ! [U_7207,U_7205] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7205),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7207)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7205),U_7207)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2120_3]) ).

cnf(f_2120_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7205),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7207)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7205),U_7207)) ),
    inference(clausify,[status(thm)],[f_2120_4]) ).

cnf(f_2120_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7206),U_7208))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7206),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7208))) ),
    inference(clausify,[status(thm)],[f_2120_4]) ).

fof(f_2121_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD]) ).

fof(f_2121_2,plain,
    ! [U_7211,U_7210,U_7209] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),U_7210))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),U_7211))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7210),U_7211))) ),
    inference(variable_rename,[status(thm)],[f_2121_1]) ).

fof(f_2121_3,plain,
    ! [U_7210,U_7209,U_7211] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),U_7210))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),U_7211))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7210),U_7211))) ),
    inference(definitional_conversion,[status(esa)],[f_2121_2]) ).

cnf(f_2121_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),U_7210))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),U_7211))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7210),U_7211))) ),
    inference(clausify,[status(thm)],[f_2121_3]) ).

fof(f_2122_1,plain,
    ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).

fof(f_2122_2,plain,
    ! [U_7214,U_7213,U_7212] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7212,tc_HOL_Obool)),U_7213),hAPP(hAPP(c_Set_Oinsert(U_7212),U_7214),U_7213))),
    inference(variable_rename,[status(thm)],[f_2122_1]) ).

fof(f_2122_3,plain,
    ! [U_7212,U_7213,U_7214] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7212,tc_HOL_Obool)),U_7213),hAPP(hAPP(c_Set_Oinsert(U_7212),U_7214),U_7213))),
    inference(definitional_conversion,[status(esa)],[f_2122_2]) ).

cnf(f_2122_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7212,tc_HOL_Obool)),U_7213),hAPP(hAPP(c_Set_Oinsert(U_7212),U_7214),U_7213))),
    inference(clausify,[status(thm)],[f_2122_3]) ).

fof(f_2123_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).

fof(f_2123_2,plain,
    ! [U_7218,U_7217,U_7216,U_7215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7215,tc_HOL_Obool)),U_7216),hAPP(hAPP(c_Set_Oinsert(U_7215),U_7218),U_7217)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7215,tc_HOL_Obool)),U_7216),U_7217)) ),
    inference(variable_rename,[status(thm)],[f_2123_1]) ).

fof(f_2123_3,plain,
    ! [U_7215,U_7216,U_7217,U_7218] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7215,tc_HOL_Obool)),U_7216),hAPP(hAPP(c_Set_Oinsert(U_7215),U_7218),U_7217)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7215,tc_HOL_Obool)),U_7216),U_7217)) ),
    inference(definitional_conversion,[status(esa)],[f_2123_2]) ).

cnf(f_2123_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7215,tc_HOL_Obool)),U_7216),hAPP(hAPP(c_Set_Oinsert(U_7215),U_7218),U_7217)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7215,tc_HOL_Obool)),U_7216),U_7217)) ),
    inference(clausify,[status(thm)],[f_2123_3]) ).

fof(f_2124_1,plain,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).

fof(f_2124_2,plain,
    ! [U_7222,U_7221,U_7220,U_7219] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7219),U_7222),U_7220)),hAPP(hAPP(c_Set_Oinsert(U_7219),U_7222),U_7221)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7219,tc_HOL_Obool)),U_7220),U_7221)) ),
    inference(variable_rename,[status(thm)],[f_2124_1]) ).

fof(f_2124_3,plain,
    ! [U_7219,U_7220,U_7221,U_7222] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7219),U_7222),U_7220)),hAPP(hAPP(c_Set_Oinsert(U_7219),U_7222),U_7221)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7219,tc_HOL_Obool)),U_7220),U_7221)) ),
    inference(definitional_conversion,[status(esa)],[f_2124_2]) ).

cnf(f_2124_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7219),U_7222),U_7220)),hAPP(hAPP(c_Set_Oinsert(U_7219),U_7222),U_7221)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7219,tc_HOL_Obool)),U_7220),U_7221)) ),
    inference(clausify,[status(thm)],[f_2124_3]) ).

fof(f_2125_1,plain,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_LoopF]) ).

fof(f_2125_2,plain,
    ! [U_7227,U_7226,U_7225,U_7224,U_7223] : c_Hoare__Mirabelle_Ohoare__derivs(U_7223,U_7224,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7223)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7223),hAPP(hAPP(c_COMBC(U_7223,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7223),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_7223),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_7225))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_7226))),c_Com_Ocom_OWhile(U_7226,U_7227)),U_7225)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7223),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2125_1]) ).

fof(f_2125_3,plain,
    ! [U_7223,U_7224,U_7225,U_7226,U_7227] : c_Hoare__Mirabelle_Ohoare__derivs(U_7223,U_7224,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7223)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7223),hAPP(hAPP(c_COMBC(U_7223,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7223),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_7223),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_7225))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_7226))),c_Com_Ocom_OWhile(U_7226,U_7227)),U_7225)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7223),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2125_2]) ).

cnf(f_2125_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7223,U_7224,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7223)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7223),hAPP(hAPP(c_COMBC(U_7223,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7223),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_7223),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_7225))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_7226))),c_Com_Ocom_OWhile(U_7226,U_7227)),U_7225)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7223),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2125_3]) ).

fof(f_2126_1,plain,
    ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Comp]) ).

fof(f_2126_2,plain,
    ! [U_7234,U_7233,U_7232,U_7231,U_7230,U_7229,U_7228] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7230),c_Com_Ocom_OSemi(U_7231,U_7233)),U_7234)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7232),U_7233),U_7234)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7230),U_7231),U_7232)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2126_1]) ).

fof(f_2126_3,plain,
    ! [U_7228,U_7229,U_7230,U_7231,U_7232,U_7233,U_7234] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7230),c_Com_Ocom_OSemi(U_7231,U_7233)),U_7234)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7232),U_7233),U_7234)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7230),U_7231),U_7232)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2126_2]) ).

cnf(f_2126_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7230),c_Com_Ocom_OSemi(U_7231,U_7233)),U_7234)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7232),U_7233),U_7234)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7228,U_7229,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7228)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7228),U_7230),U_7231),U_7232)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7228),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2126_3]) ).

fof(f_2127_1,plain,
    ! [V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OSkip]) ).

fof(f_2127_2,plain,
    ! [U_7237,U_7236,U_7235] : c_Hoare__Mirabelle_Ohoare__derivs(U_7235,U_7236,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7235),U_7237),c_Com_Ocom_OSKIP),U_7237)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7235),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2127_1]) ).

fof(f_2127_3,plain,
    ! [U_7236,U_7237,U_7235] : c_Hoare__Mirabelle_Ohoare__derivs(U_7235,U_7236,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7235),U_7237),c_Com_Ocom_OSKIP),U_7237)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7235),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2127_2]) ).

cnf(f_2127_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7235,U_7236,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7235),U_7237),c_Com_Ocom_OSKIP),U_7237)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7235),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2127_3]) ).

fof(f_2128_1,plain,
    ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).

fof(f_2128_2,plain,
    ! [U_7240,U_7239,U_7238] : c_Hoare__Mirabelle_Ohoare__derivs(U_7238,U_7239,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7238)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7238),U_7240),c_Com_Ocom_OSKIP),U_7240)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7238),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2128_1]) ).

fof(f_2128_3,plain,
    ! [U_7238,U_7239,U_7240] : c_Hoare__Mirabelle_Ohoare__derivs(U_7238,U_7239,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7238)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7238),U_7240),c_Com_Ocom_OSKIP),U_7240)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7238),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2128_2]) ).

cnf(f_2128_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7238,U_7239,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7238)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7238),U_7240),c_Com_Ocom_OSKIP),U_7240)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7238),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2128_3]) ).

fof(f_2129_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert]) ).

fof(f_2129_2,plain,
    ! [U_7244,U_7243,U_7242,U_7241] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),U_7242),hAPP(hAPP(c_Set_Oinsert(U_7241),U_7243),U_7244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),U_7242),U_7244)),hAPP(hAPP(c_Set_Oinsert(U_7241),U_7243),c_Orderings_Obot__class_Obot(tc_fun(U_7241,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2129_1]) ).

fof(f_2129_3,plain,
    ! [U_7241,U_7242,U_7243,U_7244] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),U_7242),hAPP(hAPP(c_Set_Oinsert(U_7241),U_7243),U_7244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),U_7242),U_7244)),hAPP(hAPP(c_Set_Oinsert(U_7241),U_7243),c_Orderings_Obot__class_Obot(tc_fun(U_7241,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2129_2]) ).

cnf(f_2129_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),U_7242),hAPP(hAPP(c_Set_Oinsert(U_7241),U_7243),U_7244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7241,tc_HOL_Obool)),U_7242),U_7244)),hAPP(hAPP(c_Set_Oinsert(U_7241),U_7243),c_Orderings_Obot__class_Obot(tc_fun(U_7241,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2129_3]) ).

fof(f_2130_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert2]) ).

fof(f_2130_2,plain,
    ! [U_7248,U_7247,U_7246,U_7245] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),U_7246),hAPP(hAPP(c_Set_Oinsert(U_7245),U_7247),U_7248)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),U_7246),hAPP(hAPP(c_Set_Oinsert(U_7245),U_7247),c_Orderings_Obot__class_Obot(tc_fun(U_7245,tc_HOL_Obool))))),U_7248),
    inference(variable_rename,[status(thm)],[f_2130_1]) ).

fof(f_2130_3,plain,
    ! [U_7245,U_7246,U_7247,U_7248] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),U_7246),hAPP(hAPP(c_Set_Oinsert(U_7245),U_7247),U_7248)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),U_7246),hAPP(hAPP(c_Set_Oinsert(U_7245),U_7247),c_Orderings_Obot__class_Obot(tc_fun(U_7245,tc_HOL_Obool))))),U_7248),
    inference(definitional_conversion,[status(esa)],[f_2130_2]) ).

cnf(f_2130_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),U_7246),hAPP(hAPP(c_Set_Oinsert(U_7245),U_7247),U_7248)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7245,tc_HOL_Obool)),U_7246),hAPP(hAPP(c_Set_Oinsert(U_7245),U_7247),c_Orderings_Obot__class_Obot(tc_fun(U_7245,tc_HOL_Obool))))),U_7248),
    inference(clausify,[status(thm)],[f_2130_3]) ).

fof(f_2131_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff__single]) ).

fof(f_2131_2,plain,
    ! [U_7251,U_7250,U_7249] : hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7249,tc_HOL_Obool)),U_7251),hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),c_Orderings_Obot__class_Obot(tc_fun(U_7249,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),U_7251),
    inference(variable_rename,[status(thm)],[f_2131_1]) ).

fof(f_2131_3,plain,
    ! [U_7249,U_7250,U_7251] : hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7249,tc_HOL_Obool)),U_7251),hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),c_Orderings_Obot__class_Obot(tc_fun(U_7249,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),U_7251),
    inference(definitional_conversion,[status(esa)],[f_2131_2]) ).

cnf(f_2131_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7249,tc_HOL_Obool)),U_7251),hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),c_Orderings_Obot__class_Obot(tc_fun(U_7249,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7249),U_7250),U_7251),
    inference(clausify,[status(thm)],[f_2131_3]) ).

fof(f_2132_1,plain,
    ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2) ),
    inference(fof_nnf,[status(thm)],[fact_thin]) ).

fof(f_2132_2,plain,
    ! [U_7255,U_7254,U_7253,U_7252] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7252,U_7255,U_7254)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7252),tc_HOL_Obool)),U_7253),U_7255))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7252,U_7253,U_7254) ),
    inference(variable_rename,[status(thm)],[f_2132_1]) ).

fof(f_2132_3,plain,
    ! [U_7252,U_7253,U_7254,U_7255] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7252,U_7255,U_7254)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7252),tc_HOL_Obool)),U_7253),U_7255))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7252,U_7253,U_7254) ),
    inference(definitional_conversion,[status(esa)],[f_2132_2]) ).

cnf(f_2132_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7252,U_7255,U_7254)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7252),tc_HOL_Obool)),U_7253),U_7255))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7252,U_7253,U_7254) ),
    inference(clausify,[status(thm)],[f_2132_3]) ).

fof(f_2133_1,plain,
    ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_weaken]) ).

fof(f_2133_2,plain,
    ! [U_7259,U_7258,U_7257,U_7256] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7256,U_7257,U_7259)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7256),tc_HOL_Obool)),U_7259),U_7258))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7256,U_7257,U_7258) ),
    inference(variable_rename,[status(thm)],[f_2133_1]) ).

fof(f_2133_3,plain,
    ! [U_7256,U_7257,U_7258,U_7259] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7256,U_7257,U_7259)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7256),tc_HOL_Obool)),U_7259),U_7258))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7256,U_7257,U_7258) ),
    inference(definitional_conversion,[status(esa)],[f_2133_2]) ).

cnf(f_2133_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7256,U_7257,U_7259)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7256),tc_HOL_Obool)),U_7259),U_7258))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7256,U_7257,U_7258) ),
    inference(clausify,[status(thm)],[f_2133_3]) ).

fof(f_2134_1,plain,
    ! [V_Ga_2,V_tsa_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2)) ),
    inference(fof_nnf,[status(thm)],[fact_asm]) ).

fof(f_2134_2,plain,
    ! [U_7262,U_7261,U_7260] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7260,U_7262,U_7261)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7260),tc_HOL_Obool)),U_7261),U_7262)) ),
    inference(variable_rename,[status(thm)],[f_2134_1]) ).

fof(f_2134_3,plain,
    ! [U_7261,U_7260,U_7262] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7260,U_7262,U_7261)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7260),tc_HOL_Obool)),U_7261),U_7262)) ),
    inference(definitional_conversion,[status(esa)],[f_2134_2]) ).

cnf(f_2134_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7260,U_7262,U_7261)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7260),tc_HOL_Obool)),U_7261),U_7262)) ),
    inference(clausify,[status(thm)],[f_2134_3]) ).

fof(f_2135_1,plain,
    ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
        & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_derivs__insertD]) ).

fof(f_2135_2,plain,
    ! [U_7266,U_7265,U_7264,U_7263] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,U_7266)
        & c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7263)),U_7265),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7263),tc_HOL_Obool)))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7263)),U_7265),U_7266)) ),
    inference(variable_rename,[status(thm)],[f_2135_1]) ).

fof(f_2135_3,plain,
    ( ! [U_7263,U_7264,U_7265,U_7266] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,U_7266)
        | ~ sP658(U_7263,U_7264,U_7265,U_7266) )
    & ! [U_7263,U_7264,U_7265,U_7266] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7263)),U_7265),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7263),tc_HOL_Obool))))
        | ~ sP658(U_7263,U_7264,U_7265,U_7266) )
    & ! [U_7263,U_7264,U_7265,U_7266] :
        ( sP658(U_7263,U_7264,U_7265,U_7266)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7263)),U_7265),U_7266)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP658])],[f_2135_2]) ).

cnf(f_2135_4,plain,
    ( sP658(U_7263,U_7264,U_7265,U_7266)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7263)),U_7265),U_7266)) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

cnf(f_2135_5,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7263)),U_7265),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7263),tc_HOL_Obool))))
    | ~ sP658(U_7263,U_7264,U_7265,U_7266) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

cnf(f_2135_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7263,U_7264,U_7266)
    | ~ sP658(U_7263,U_7264,U_7265,U_7266) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

fof(f_2136_1,plain,
    ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert]) ).

fof(f_2136_2,plain,
    ! [U_7270,U_7269,U_7268,U_7267] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7267)),U_7269),U_7270))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,U_7270)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7267)),U_7269),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7267),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2136_1]) ).

fof(f_2136_3,plain,
    ! [U_7267,U_7268,U_7269,U_7270] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7267)),U_7269),U_7270))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,U_7270)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7267)),U_7269),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7267),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2136_2]) ).

cnf(f_2136_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7267)),U_7269),U_7270))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,U_7270)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7267,U_7268,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7267)),U_7269),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7267),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2136_3]) ).

fof(f_2137_1,plain,
    ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2) ),
    inference(fof_nnf,[status(thm)],[fact_cut]) ).

fof(f_2137_2,plain,
    ! [U_7274,U_7273,U_7272,U_7271] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7274,U_7273)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7274,U_7272)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7272,U_7273) ),
    inference(variable_rename,[status(thm)],[f_2137_1]) ).

fof(f_2137_3,plain,
    ! [U_7273,U_7271,U_7274,U_7272] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7274,U_7273)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7274,U_7272)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7272,U_7273) ),
    inference(definitional_conversion,[status(esa)],[f_2137_2]) ).

cnf(f_2137_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7274,U_7273)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7274,U_7272)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7271,U_7272,U_7273) ),
    inference(clausify,[status(thm)],[f_2137_3]) ).

fof(f_2138_1,plain,
    ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).

fof(f_2138_2,plain,
    ! [U_7276,U_7275] : c_Hoare__Mirabelle_Ohoare__derivs(U_7275,U_7276,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7275),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2138_1]) ).

fof(f_2138_3,plain,
    ! [U_7276,U_7275] : c_Hoare__Mirabelle_Ohoare__derivs(U_7275,U_7276,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7275),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2138_2]) ).

cnf(f_2138_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7275,U_7276,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7275),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2138_3]) ).

fof(f_2139_1,plain,
    ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_empty]) ).

fof(f_2139_2,plain,
    ! [U_7278,U_7277] : c_Hoare__Mirabelle_Ohoare__derivs(U_7277,U_7278,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7277),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2139_1]) ).

fof(f_2139_3,plain,
    ! [U_7277,U_7278] : c_Hoare__Mirabelle_Ohoare__derivs(U_7277,U_7278,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7277),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2139_2]) ).

cnf(f_2139_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7277,U_7278,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7277),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2139_3]) ).

fof(f_2140_1,plain,
    ! [V_x_2,T_c,T_b] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Orderings_Obot(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_bot__apply]) ).

fof(f_2140_2,plain,
    ! [U_7281,U_7280,U_7279] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7280,U_7279)),U_7281) = c_Orderings_Obot__class_Obot(U_7279)
      | ~ class_Orderings_Obot(U_7279) ),
    inference(variable_rename,[status(thm)],[f_2140_1]) ).

fof(f_2140_3,plain,
    ! [U_7279,U_7280,U_7281] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7280,U_7279)),U_7281) = c_Orderings_Obot__class_Obot(U_7279)
      | ~ class_Orderings_Obot(U_7279) ),
    inference(definitional_conversion,[status(esa)],[f_2140_2]) ).

cnf(f_2140_4,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7280,U_7279)),U_7281) = c_Orderings_Obot__class_Obot(U_7279)
    | ~ class_Orderings_Obot(U_7279) ),
    inference(clausify,[status(thm)],[f_2140_3]) ).

fof(f_2141_1,plain,
    ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_empty__not__insert]) ).

fof(f_2141_2,plain,
    ! [U_7284,U_7283,U_7282] : c_Orderings_Obot__class_Obot(tc_fun(U_7282,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7282),U_7283),U_7284),
    inference(variable_rename,[status(thm)],[f_2141_1]) ).

fof(f_2141_3,plain,
    ! [U_7282,U_7283,U_7284] : c_Orderings_Obot__class_Obot(tc_fun(U_7282,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7282),U_7283),U_7284),
    inference(definitional_conversion,[status(esa)],[f_2141_2]) ).

cnf(f_2141_4,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_7282,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7282),U_7283),U_7284),
    inference(clausify,[status(thm)],[f_2141_3]) ).

fof(f_2142_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_insert__not__empty]) ).

fof(f_2142_2,plain,
    ! [U_7287,U_7286,U_7285] : hAPP(hAPP(c_Set_Oinsert(U_7285),U_7286),U_7287) != c_Orderings_Obot__class_Obot(tc_fun(U_7285,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2142_1]) ).

fof(f_2142_3,plain,
    ! [U_7285,U_7286,U_7287] : hAPP(hAPP(c_Set_Oinsert(U_7285),U_7286),U_7287) != c_Orderings_Obot__class_Obot(tc_fun(U_7285,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2142_2]) ).

cnf(f_2142_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7285),U_7286),U_7287) != c_Orderings_Obot__class_Obot(tc_fun(U_7285,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2142_3]) ).

fof(f_2143_1,plain,
    ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).

fof(f_2143_2,plain,
    ! [U_7290,U_7289,U_7288] : hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),U_7290)) = hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),U_7290),
    inference(variable_rename,[status(thm)],[f_2143_1]) ).

fof(f_2143_3,plain,
    ! [U_7288,U_7289,U_7290] : hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),U_7290)) = hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),U_7290),
    inference(definitional_conversion,[status(esa)],[f_2143_2]) ).

cnf(f_2143_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),U_7290)) = hAPP(hAPP(c_Set_Oinsert(U_7288),U_7289),U_7290),
    inference(clausify,[status(thm)],[f_2143_3]) ).

fof(f_2144_1,plain,
    ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).

fof(f_2144_2,plain,
    ! [U_7294,U_7293,U_7292,U_7291] : hAPP(hAPP(c_Set_Oinsert(U_7291),U_7292),hAPP(hAPP(c_Set_Oinsert(U_7291),U_7293),U_7294)) = hAPP(hAPP(c_Set_Oinsert(U_7291),U_7293),hAPP(hAPP(c_Set_Oinsert(U_7291),U_7292),U_7294)),
    inference(variable_rename,[status(thm)],[f_2144_1]) ).

fof(f_2144_3,plain,
    ! [U_7293,U_7291,U_7292,U_7294] : hAPP(hAPP(c_Set_Oinsert(U_7291),U_7292),hAPP(hAPP(c_Set_Oinsert(U_7291),U_7293),U_7294)) = hAPP(hAPP(c_Set_Oinsert(U_7291),U_7293),hAPP(hAPP(c_Set_Oinsert(U_7291),U_7292),U_7294)),
    inference(definitional_conversion,[status(esa)],[f_2144_2]) ).

cnf(f_2144_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7291),U_7292),hAPP(hAPP(c_Set_Oinsert(U_7291),U_7293),U_7294)) = hAPP(hAPP(c_Set_Oinsert(U_7291),U_7293),hAPP(hAPP(c_Set_Oinsert(U_7291),U_7292),U_7294)),
    inference(clausify,[status(thm)],[f_2144_3]) ).

fof(f_2145_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
        | ( ( V_b_2 != V_c_2
            | V_a_2 != V_d_2 )
          & ( V_b_2 != V_d_2
            | V_a_2 != V_c_2 ) ) )
      & ( ( V_b_2 = V_c_2
          & V_a_2 = V_d_2 )
        | ( V_b_2 = V_d_2
          & V_a_2 = V_c_2 )
        | hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).

fof(f_2145_2,plain,
    ! [U_7299,U_7298,U_7297,U_7296,U_7295] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_7295),U_7296),hAPP(hAPP(c_Set_Oinsert(U_7295),U_7297),c_Orderings_Obot__class_Obot(tc_fun(U_7295,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7295),U_7298),hAPP(hAPP(c_Set_Oinsert(U_7295),U_7299),c_Orderings_Obot__class_Obot(tc_fun(U_7295,tc_HOL_Obool))))
        | ( ( U_7297 != U_7298
            | U_7296 != U_7299 )
          & ( U_7297 != U_7299
            | U_7296 != U_7298 ) ) )
      & ( ( U_7297 = U_7298
          & U_7296 = U_7299 )
        | ( U_7297 = U_7299
          & U_7296 = U_7298 )
        | hAPP(hAPP(c_Set_Oinsert(U_7295),U_7296),hAPP(hAPP(c_Set_Oinsert(U_7295),U_7297),c_Orderings_Obot__class_Obot(tc_fun(U_7295,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7295),U_7298),hAPP(hAPP(c_Set_Oinsert(U_7295),U_7299),c_Orderings_Obot__class_Obot(tc_fun(U_7295,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2145_1]) ).

fof(f_2145_3,plain,
    ( ! [U_7309,U_7307,U_7305,U_7303] :
        ( ! [U_7301] : hAPP(hAPP(c_Set_Oinsert(U_7301),U_7303),hAPP(hAPP(c_Set_Oinsert(U_7301),U_7305),c_Orderings_Obot__class_Obot(tc_fun(U_7301,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7301),U_7307),hAPP(hAPP(c_Set_Oinsert(U_7301),U_7309),c_Orderings_Obot__class_Obot(tc_fun(U_7301,tc_HOL_Obool))))
        | ( ( U_7305 != U_7307
            | U_7303 != U_7309 )
          & ( U_7305 != U_7309
            | U_7303 != U_7307 ) ) )
    & ! [U_7308,U_7306,U_7304,U_7302] :
        ( ! [U_7300] : hAPP(hAPP(c_Set_Oinsert(U_7300),U_7302),hAPP(hAPP(c_Set_Oinsert(U_7300),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7300,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7300),U_7306),hAPP(hAPP(c_Set_Oinsert(U_7300),U_7308),c_Orderings_Obot__class_Obot(tc_fun(U_7300,tc_HOL_Obool))))
        | ( U_7304 = U_7306
          & U_7302 = U_7308 )
        | ( U_7304 = U_7308
          & U_7302 = U_7306 ) ) ),
    inference(miniscope,[status(thm)],[f_2145_2]) ).

fof(f_2145_4,plain,
    ( ! [U_7303,U_7305,U_7307,U_7309] :
        ( U_7305 != U_7307
        | U_7303 != U_7309
        | ~ sP661(U_7303,U_7305,U_7307,U_7309) )
    & ! [U_7303,U_7305,U_7307,U_7309] :
        ( U_7305 != U_7309
        | U_7303 != U_7307
        | ~ sP661(U_7303,U_7305,U_7307,U_7309) )
    & ! [U_7302,U_7304,U_7306,U_7308] :
        ( U_7304 = U_7306
        | ~ sP660(U_7302,U_7304,U_7306,U_7308) )
    & ! [U_7302,U_7304,U_7306,U_7308] :
        ( U_7302 = U_7308
        | ~ sP660(U_7302,U_7304,U_7306,U_7308) )
    & ! [U_7302,U_7304,U_7306,U_7308] :
        ( U_7304 = U_7308
        | ~ sP659(U_7302,U_7304,U_7306,U_7308) )
    & ! [U_7302,U_7304,U_7306,U_7308] :
        ( U_7302 = U_7306
        | ~ sP659(U_7302,U_7304,U_7306,U_7308) )
    & ! [U_7301,U_7303,U_7305,U_7307,U_7309] :
        ( hAPP(hAPP(c_Set_Oinsert(U_7301),U_7303),hAPP(hAPP(c_Set_Oinsert(U_7301),U_7305),c_Orderings_Obot__class_Obot(tc_fun(U_7301,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7301),U_7307),hAPP(hAPP(c_Set_Oinsert(U_7301),U_7309),c_Orderings_Obot__class_Obot(tc_fun(U_7301,tc_HOL_Obool))))
        | sP661(U_7303,U_7305,U_7307,U_7309) )
    & ! [U_7302,U_7300,U_7304,U_7306,U_7308] :
        ( hAPP(hAPP(c_Set_Oinsert(U_7300),U_7302),hAPP(hAPP(c_Set_Oinsert(U_7300),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7300,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7300),U_7306),hAPP(hAPP(c_Set_Oinsert(U_7300),U_7308),c_Orderings_Obot__class_Obot(tc_fun(U_7300,tc_HOL_Obool))))
        | sP660(U_7302,U_7304,U_7306,U_7308)
        | sP659(U_7302,U_7304,U_7306,U_7308) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP659,sP660,sP661])],[f_2145_3]) ).

cnf(f_2145_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7300),U_7302),hAPP(hAPP(c_Set_Oinsert(U_7300),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7300,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7300),U_7306),hAPP(hAPP(c_Set_Oinsert(U_7300),U_7308),c_Orderings_Obot__class_Obot(tc_fun(U_7300,tc_HOL_Obool))))
    | sP660(U_7302,U_7304,U_7306,U_7308)
    | sP659(U_7302,U_7304,U_7306,U_7308) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7301),U_7303),hAPP(hAPP(c_Set_Oinsert(U_7301),U_7305),c_Orderings_Obot__class_Obot(tc_fun(U_7301,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7301),U_7307),hAPP(hAPP(c_Set_Oinsert(U_7301),U_7309),c_Orderings_Obot__class_Obot(tc_fun(U_7301,tc_HOL_Obool))))
    | sP661(U_7303,U_7305,U_7307,U_7309) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_7,plain,
    ( U_7302 = U_7306
    | ~ sP659(U_7302,U_7304,U_7306,U_7308) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_8,plain,
    ( U_7304 = U_7308
    | ~ sP659(U_7302,U_7304,U_7306,U_7308) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_9,plain,
    ( U_7302 = U_7308
    | ~ sP660(U_7302,U_7304,U_7306,U_7308) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_10,plain,
    ( U_7304 = U_7306
    | ~ sP660(U_7302,U_7304,U_7306,U_7308) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_11,plain,
    ( U_7305 != U_7309
    | U_7303 != U_7307
    | ~ sP661(U_7303,U_7305,U_7307,U_7309) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

cnf(f_2145_12,plain,
    ( U_7305 != U_7307
    | U_7303 != U_7309
    | ~ sP661(U_7303,U_7305,U_7307,U_7309) ),
    inference(clausify,[status(thm)],[f_2145_4]) ).

fof(f_2146_1,plain,
    ! [V_x_2,V_A_2,V_y_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
        | ( ~ hBOOL(hAPP(V_A_2,V_x_2))
          & V_y_2 != V_x_2 ) )
      & ( hBOOL(hAPP(V_A_2,V_x_2))
        | V_y_2 = V_x_2
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__code]) ).

fof(f_2146_2,plain,
    ! [U_7313,U_7312,U_7311,U_7310] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7310),U_7311),U_7312),U_7313))
        | ( ~ hBOOL(hAPP(U_7312,U_7313))
          & U_7311 != U_7313 ) )
      & ( hBOOL(hAPP(U_7312,U_7313))
        | U_7311 = U_7313
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7310),U_7311),U_7312),U_7313)) ) ),
    inference(variable_rename,[status(thm)],[f_2146_1]) ).

fof(f_2146_3,plain,
    ( ! [U_7321,U_7319,U_7317] :
        ( ! [U_7315] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7315),U_7317),U_7319),U_7321))
        | ( ~ hBOOL(hAPP(U_7319,U_7321))
          & U_7317 != U_7321 ) )
    & ! [U_7320,U_7318,U_7316] :
        ( ! [U_7314] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7314),U_7316),U_7318),U_7320))
        | hBOOL(hAPP(U_7318,U_7320))
        | U_7316 = U_7320 ) ),
    inference(miniscope,[status(thm)],[f_2146_2]) ).

fof(f_2146_4,plain,
    ( ! [U_7319,U_7317,U_7321] :
        ( ~ hBOOL(hAPP(U_7319,U_7321))
        | ~ sP662(U_7319,U_7317,U_7321) )
    & ! [U_7319,U_7317,U_7321] :
        ( U_7317 != U_7321
        | ~ sP662(U_7319,U_7317,U_7321) )
    & ! [U_7319,U_7315,U_7317,U_7321] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7315),U_7317),U_7319),U_7321))
        | sP662(U_7319,U_7317,U_7321) )
    & ! [U_7314,U_7320,U_7318,U_7316] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7314),U_7316),U_7318),U_7320))
        | hBOOL(hAPP(U_7318,U_7320))
        | U_7316 = U_7320 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP662])],[f_2146_3]) ).

cnf(f_2146_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7314),U_7316),U_7318),U_7320))
    | hBOOL(hAPP(U_7318,U_7320))
    | U_7316 = U_7320 ),
    inference(clausify,[status(thm)],[f_2146_4]) ).

cnf(f_2146_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7315),U_7317),U_7319),U_7321))
    | sP662(U_7319,U_7317,U_7321) ),
    inference(clausify,[status(thm)],[f_2146_4]) ).

cnf(f_2146_7,plain,
    ( U_7317 != U_7321
    | ~ sP662(U_7319,U_7317,U_7321) ),
    inference(clausify,[status(thm)],[f_2146_4]) ).

cnf(f_2146_8,plain,
    ( ~ hBOOL(hAPP(U_7319,U_7321))
    | ~ sP662(U_7319,U_7317,U_7321) ),
    inference(clausify,[status(thm)],[f_2146_4]) ).

fof(f_2147_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( V_a_2 = V_b_2
      | hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__inject]) ).

fof(f_2147_2,plain,
    ! [U_7324,U_7323,U_7322] :
      ( U_7323 = U_7324
      | hAPP(hAPP(c_Set_Oinsert(U_7322),U_7323),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7322),U_7324),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_2147_1]) ).

fof(f_2147_3,plain,
    ! [U_7324,U_7323] :
      ( ! [U_7322] : hAPP(hAPP(c_Set_Oinsert(U_7322),U_7323),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7322),U_7324),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool)))
      | U_7323 = U_7324 ),
    inference(miniscope,[status(thm)],[f_2147_2]) ).

fof(f_2147_4,plain,
    ! [U_7323,U_7324,U_7322] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7322),U_7323),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7322),U_7324),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool)))
      | U_7323 = U_7324 ),
    inference(definitional_conversion,[status(esa)],[f_2147_3]) ).

cnf(f_2147_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7322),U_7323),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7322),U_7324),c_Orderings_Obot__class_Obot(tc_fun(U_7322,tc_HOL_Obool)))
    | U_7323 = U_7324 ),
    inference(clausify,[status(thm)],[f_2147_4]) ).

fof(f_2148_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_subset__singletonD]) ).

fof(f_2148_2,plain,
    ! [U_7327,U_7326,U_7325] :
      ( U_7326 = hAPP(hAPP(c_Set_Oinsert(U_7325),U_7327),c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool)))
      | U_7326 = c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7325,tc_HOL_Obool)),U_7326),hAPP(hAPP(c_Set_Oinsert(U_7325),U_7327),c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2148_1]) ).

fof(f_2148_3,plain,
    ! [U_7325,U_7326,U_7327] :
      ( U_7326 = hAPP(hAPP(c_Set_Oinsert(U_7325),U_7327),c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool)))
      | U_7326 = c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7325,tc_HOL_Obool)),U_7326),hAPP(hAPP(c_Set_Oinsert(U_7325),U_7327),c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_2148_2]) ).

cnf(f_2148_4,plain,
    ( U_7326 = hAPP(hAPP(c_Set_Oinsert(U_7325),U_7327),c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool)))
    | U_7326 = c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7325,tc_HOL_Obool)),U_7326),hAPP(hAPP(c_Set_Oinsert(U_7325),U_7327),c_Orderings_Obot__class_Obot(tc_fun(U_7325,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2148_3]) ).

fof(f_2149_1,plain,
    ! [V_x_2,T_c,T_b] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Orderings_Obot(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_bot__fun__def]) ).

fof(f_2149_2,plain,
    ! [U_7330,U_7329,U_7328] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7329,U_7328)),U_7330) = c_Orderings_Obot__class_Obot(U_7328)
      | ~ class_Orderings_Obot(U_7328) ),
    inference(variable_rename,[status(thm)],[f_2149_1]) ).

fof(f_2149_3,plain,
    ! [U_7328,U_7329,U_7330] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7329,U_7328)),U_7330) = c_Orderings_Obot__class_Obot(U_7328)
      | ~ class_Orderings_Obot(U_7328) ),
    inference(definitional_conversion,[status(esa)],[f_2149_2]) ).

cnf(f_2149_4,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7329,U_7328)),U_7330) = c_Orderings_Obot__class_Obot(U_7328)
    | ~ class_Orderings_Obot(U_7328) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

fof(f_2150_1,plain,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I8_J]) ).

fof(f_2150_2,plain,
    ! [U_7335,U_7334,U_7333,U_7332,U_7331] : c_Hoare__Mirabelle_Ohoare__derivs(U_7331,U_7332,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7331)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7331),hAPP(hAPP(c_COMBC(U_7331,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7331),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7333)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),U_7334)),U_7335))),c_Com_Ocom_OAss(U_7334,U_7335)),U_7333)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7331),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2150_1]) ).

fof(f_2150_3,plain,
    ! [U_7332,U_7333,U_7331,U_7334,U_7335] : c_Hoare__Mirabelle_Ohoare__derivs(U_7331,U_7332,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7331)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7331),hAPP(hAPP(c_COMBC(U_7331,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7331),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7333)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),U_7334)),U_7335))),c_Com_Ocom_OAss(U_7334,U_7335)),U_7333)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7331),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2150_2]) ).

cnf(f_2150_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7331,U_7332,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7331)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7331),hAPP(hAPP(c_COMBC(U_7331,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7331),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7333)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),U_7334)),U_7335))),c_Com_Ocom_OAss(U_7334,U_7335)),U_7333)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7331),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2150_3]) ).

fof(f_2151_1,plain,
    ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Ass]) ).

fof(f_2151_2,plain,
    ! [U_7340,U_7339,U_7338,U_7337,U_7336] : c_Hoare__Mirabelle_Ohoare__derivs(U_7336,U_7337,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7336)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7336),hAPP(hAPP(c_COMBC(U_7336,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7336),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7338)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),U_7339)),U_7340))),c_Com_Ocom_OAss(U_7339,U_7340)),U_7338)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7336),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2151_1]) ).

fof(f_2151_3,plain,
    ! [U_7336,U_7337,U_7338,U_7339,U_7340] : c_Hoare__Mirabelle_Ohoare__derivs(U_7336,U_7337,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7336)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7336),hAPP(hAPP(c_COMBC(U_7336,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7336),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7338)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),U_7339)),U_7340))),c_Com_Ocom_OAss(U_7339,U_7340)),U_7338)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7336),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2151_2]) ).

cnf(f_2151_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7336,U_7337,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7336)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7336),hAPP(hAPP(c_COMBC(U_7336,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7336),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7338)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),U_7339)),U_7340))),c_Com_Ocom_OAss(U_7339,U_7340)),U_7338)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7336),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2151_3]) ).

fof(f_2152_1,plain,
    ! [V_b,V_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__abs]) ).

fof(f_2152_2,plain,
    ! [U_7342,U_7341] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7341) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7342)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7342),U_7341))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7341),U_7342)) ),
    inference(variable_rename,[status(thm)],[f_2152_1]) ).

fof(f_2152_3,plain,
    ! [U_7341,U_7342] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7341) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7342)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7342),U_7341))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7341),U_7342)) ),
    inference(definitional_conversion,[status(esa)],[f_2152_2]) ).

cnf(f_2152_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7341) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7342)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7342),U_7341))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7341),U_7342)) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

fof(f_2153_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__empty]) ).

fof(f_2153_2,plain,
    ! [U_7344,U_7343] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7343,tc_HOL_Obool)),U_7344),c_Orderings_Obot__class_Obot(tc_fun(U_7343,tc_HOL_Obool))))
        | U_7344 != c_Orderings_Obot__class_Obot(tc_fun(U_7343,tc_HOL_Obool)) )
      & ( U_7344 = c_Orderings_Obot__class_Obot(tc_fun(U_7343,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7343,tc_HOL_Obool)),U_7344),c_Orderings_Obot__class_Obot(tc_fun(U_7343,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2153_1]) ).

fof(f_2153_3,plain,
    ( ! [U_7348,U_7346] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7346,tc_HOL_Obool)),U_7348),c_Orderings_Obot__class_Obot(tc_fun(U_7346,tc_HOL_Obool))))
        | U_7348 != c_Orderings_Obot__class_Obot(tc_fun(U_7346,tc_HOL_Obool)) )
    & ! [U_7347,U_7345] :
        ( U_7347 = c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7345,tc_HOL_Obool)),U_7347),c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2153_2]) ).

fof(f_2153_4,plain,
    ( ! [U_7346,U_7348] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7346,tc_HOL_Obool)),U_7348),c_Orderings_Obot__class_Obot(tc_fun(U_7346,tc_HOL_Obool))))
        | U_7348 != c_Orderings_Obot__class_Obot(tc_fun(U_7346,tc_HOL_Obool)) )
    & ! [U_7347,U_7345] :
        ( U_7347 = c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7345,tc_HOL_Obool)),U_7347),c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2153_3]) ).

cnf(f_2153_5,plain,
    ( U_7347 = c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7345,tc_HOL_Obool)),U_7347),c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2153_4]) ).

cnf(f_2153_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7346,tc_HOL_Obool)),U_7348),c_Orderings_Obot__class_Obot(tc_fun(U_7346,tc_HOL_Obool))))
    | U_7348 != c_Orderings_Obot__class_Obot(tc_fun(U_7346,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2153_4]) ).

fof(f_2154_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__cancel]) ).

fof(f_2154_2,plain,
    ! [U_7350,U_7349] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7349,tc_HOL_Obool)),U_7350),U_7350) = c_Orderings_Obot__class_Obot(tc_fun(U_7349,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2154_1]) ).

fof(f_2154_3,plain,
    ! [U_7349,U_7350] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7349,tc_HOL_Obool)),U_7350),U_7350) = c_Orderings_Obot__class_Obot(tc_fun(U_7349,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2154_2]) ).

cnf(f_2154_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7349,tc_HOL_Obool)),U_7350),U_7350) = c_Orderings_Obot__class_Obot(tc_fun(U_7349,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2154_3]) ).

fof(f_2155_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Diff__empty]) ).

fof(f_2155_2,plain,
    ! [U_7352,U_7351] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7351,tc_HOL_Obool)),U_7352),c_Orderings_Obot__class_Obot(tc_fun(U_7351,tc_HOL_Obool))) = U_7352,
    inference(variable_rename,[status(thm)],[f_2155_1]) ).

fof(f_2155_3,plain,
    ! [U_7351,U_7352] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7351,tc_HOL_Obool)),U_7352),c_Orderings_Obot__class_Obot(tc_fun(U_7351,tc_HOL_Obool))) = U_7352,
    inference(definitional_conversion,[status(esa)],[f_2155_2]) ).

cnf(f_2155_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7351,tc_HOL_Obool)),U_7352),c_Orderings_Obot__class_Obot(tc_fun(U_7351,tc_HOL_Obool))) = U_7352,
    inference(clausify,[status(thm)],[f_2155_3]) ).

fof(f_2156_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_empty__Diff]) ).

fof(f_2156_2,plain,
    ! [U_7354,U_7353] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7353,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7353,tc_HOL_Obool))),U_7354) = c_Orderings_Obot__class_Obot(tc_fun(U_7353,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2156_1]) ).

fof(f_2156_3,plain,
    ! [U_7353,U_7354] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7353,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7353,tc_HOL_Obool))),U_7354) = c_Orderings_Obot__class_Obot(tc_fun(U_7353,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2156_2]) ).

cnf(f_2156_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7353,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7353,tc_HOL_Obool))),U_7354) = c_Orderings_Obot__class_Obot(tc_fun(U_7353,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2156_3]) ).

fof(f_2157_1,plain,
    ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_not__psubset__empty]) ).

fof(f_2157_2,plain,
    ! [U_7356,U_7355] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7355,tc_HOL_Obool)),U_7356),c_Orderings_Obot__class_Obot(tc_fun(U_7355,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2157_1]) ).

fof(f_2157_3,plain,
    ! [U_7355,U_7356] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7355,tc_HOL_Obool)),U_7356),c_Orderings_Obot__class_Obot(tc_fun(U_7355,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2157_2]) ).

cnf(f_2157_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7355,tc_HOL_Obool)),U_7356),c_Orderings_Obot__class_Obot(tc_fun(U_7355,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2157_3]) ).

fof(f_2158_1,plain,
    ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_weak__Body]) ).

fof(f_2158_2,plain,
    ! [U_7361,U_7360,U_7359,U_7358,U_7357] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7357,U_7358,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7357)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7357),U_7359),hAPP(c_Com_Ocom_OBODY,U_7360)),U_7361)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7357),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7357,U_7358,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7357)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7357),U_7359),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7360))),U_7361)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7357),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2158_1]) ).

fof(f_2158_3,plain,
    ! [U_7357,U_7358,U_7359,U_7360,U_7361] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7357,U_7358,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7357)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7357),U_7359),hAPP(c_Com_Ocom_OBODY,U_7360)),U_7361)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7357),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7357,U_7358,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7357)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7357),U_7359),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7360))),U_7361)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7357),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2158_2]) ).

cnf(f_2158_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7357,U_7358,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7357)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7357),U_7359),hAPP(c_Com_Ocom_OBODY,U_7360)),U_7361)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7357),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7357,U_7358,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7357)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7357),U_7359),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7360))),U_7361)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7357),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

fof(f_2159_1,plain,
    ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_BodyN]) ).

fof(f_2159_2,plain,
    ! [U_7366,U_7365,U_7364,U_7363,U_7362] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7362,U_7366,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Com_Ocom_OBODY,U_7364)),U_7365)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7362),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7362,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Com_Ocom_OBODY,U_7364)),U_7365)),U_7366),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7364))),U_7365)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7362),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2159_1]) ).

fof(f_2159_3,plain,
    ! [U_7362,U_7363,U_7364,U_7365,U_7366] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7362,U_7366,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Com_Ocom_OBODY,U_7364)),U_7365)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7362),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7362,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Com_Ocom_OBODY,U_7364)),U_7365)),U_7366),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7364))),U_7365)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7362),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2159_2]) ).

cnf(f_2159_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7362,U_7366,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Com_Ocom_OBODY,U_7364)),U_7365)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7362),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7362,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Com_Ocom_OBODY,U_7364)),U_7365)),U_7366),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7362)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7362),U_7363),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7364))),U_7365)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7362),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2159_3]) ).

fof(f_2160_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x))
      | ~ class_Orderings_Obot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_bot__least]) ).

fof(f_2160_2,plain,
    ! [U_7368,U_7367] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7367),c_Orderings_Obot__class_Obot(U_7367)),U_7368))
      | ~ class_Orderings_Obot(U_7367) ),
    inference(variable_rename,[status(thm)],[f_2160_1]) ).

fof(f_2160_3,plain,
    ! [U_7367,U_7368] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7367),c_Orderings_Obot__class_Obot(U_7367)),U_7368))
      | ~ class_Orderings_Obot(U_7367) ),
    inference(definitional_conversion,[status(esa)],[f_2160_2]) ).

cnf(f_2160_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7367),c_Orderings_Obot__class_Obot(U_7367)),U_7368))
    | ~ class_Orderings_Obot(U_7367) ),
    inference(clausify,[status(thm)],[f_2160_3]) ).

fof(f_2161_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg]) ).

fof(f_2161_2,plain,
    ! [U_7370,U_7369] :
      ( U_7369 = U_7370
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7370),U_7369))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7369),U_7370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7369)) ),
    inference(variable_rename,[status(thm)],[f_2161_1]) ).

fof(f_2161_3,plain,
    ! [U_7369,U_7370] :
      ( U_7369 = U_7370
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7370),U_7369))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7369),U_7370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7369)) ),
    inference(definitional_conversion,[status(esa)],[f_2161_2]) ).

cnf(f_2161_4,plain,
    ( U_7369 = U_7370
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7370),U_7369))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7369),U_7370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7369)) ),
    inference(clausify,[status(thm)],[f_2161_3]) ).

fof(f_2162_1,plain,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__not__zless]) ).

fof(f_2162_2,plain,
    ! [U_7372,U_7371] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7372),U_7371))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7371),U_7372))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7371)) ),
    inference(variable_rename,[status(thm)],[f_2162_1]) ).

fof(f_2162_3,plain,
    ! [U_7372,U_7371] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7372),U_7371))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7371),U_7372))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7371)) ),
    inference(definitional_conversion,[status(esa)],[f_2162_2]) ).

cnf(f_2162_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7372),U_7371))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7371),U_7372))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7371)) ),
    inference(clausify,[status(thm)],[f_2162_3]) ).

fof(f_2163_1,plain,
    ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_c_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),hAPP(hAPP(c_Natural_Ogetlocs,V_s_H_2),V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OLocal]) ).

fof(f_2163_2,plain,
    ! [U_7380,U_7379,U_7378,U_7377,U_7376,U_7375,U_7374,U_7373] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7373,U_7374,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7373)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7373),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7373),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,U_7379)))),hAPP(hAPP(c_COMBC(U_7373,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7373),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7375)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(U_7378))),U_7380)))),c_Com_Ocom_OLocal(U_7378,U_7380,U_7376)),U_7377)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7373),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7373,U_7374,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7373)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7373),U_7375),U_7376),hAPP(hAPP(c_COMBC(U_7373,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7373),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7377)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(U_7378))),hAPP(hAPP(c_Natural_Ogetlocs,U_7379),U_7378))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7373),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2163_1]) ).

fof(f_2163_3,plain,
    ! [U_7373,U_7374,U_7375,U_7376,U_7377,U_7378,U_7379,U_7380] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7373,U_7374,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7373)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7373),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7373),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,U_7379)))),hAPP(hAPP(c_COMBC(U_7373,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7373),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7375)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(U_7378))),U_7380)))),c_Com_Ocom_OLocal(U_7378,U_7380,U_7376)),U_7377)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7373),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7373,U_7374,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7373)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7373),U_7375),U_7376),hAPP(hAPP(c_COMBC(U_7373,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7373),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7377)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(U_7378))),hAPP(hAPP(c_Natural_Ogetlocs,U_7379),U_7378))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7373),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2163_2]) ).

cnf(f_2163_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7373,U_7374,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7373)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7373),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7373),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,U_7379)))),hAPP(hAPP(c_COMBC(U_7373,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7373),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7375)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(U_7378))),U_7380)))),c_Com_Ocom_OLocal(U_7378,U_7380,U_7376)),U_7377)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7373),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7373,U_7374,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7373)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7373),U_7375),U_7376),hAPP(hAPP(c_COMBC(U_7373,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_7373),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7377)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(U_7378))),hAPP(hAPP(c_Natural_Ogetlocs,U_7379),U_7378))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7373),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2163_3]) ).

fof(f_2164_1,plain,
    ! [V_t_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) ) )
      | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mono]) ).

fof(f_2164_2,plain,
    ! [U_7383,U_7382,U_7381] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7382),U_7383))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7383))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7383)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7382),U_7383)) ) )
      | U_7381 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2164_1]) ).

fof(f_2164_3,plain,
    ( ! [U_7382,U_7381,U_7383] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7382),U_7383))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7383)))
        | ~ sP663(U_7382,U_7381,U_7383) )
    & ! [U_7382,U_7381,U_7383] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7383)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7382),U_7383))
        | ~ sP663(U_7382,U_7381,U_7383) )
    & ! [U_7382,U_7381,U_7383] :
        ( sP663(U_7382,U_7381,U_7383)
        | U_7381 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP663])],[f_2164_2]) ).

cnf(f_2164_4,plain,
    ( sP663(U_7382,U_7381,U_7383)
    | U_7381 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2164_3]) ).

cnf(f_2164_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7383)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7382),U_7383))
    | ~ sP663(U_7382,U_7381,U_7383) ),
    inference(clausify,[status(thm)],[f_2164_3]) ).

cnf(f_2164_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7382),U_7383))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7381),U_7383)))
    | ~ sP663(U_7382,U_7381,U_7383) ),
    inference(clausify,[status(thm)],[f_2164_3]) ).

fof(f_2165_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
      | V_k = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel]) ).

fof(f_2165_2,plain,
    ! [U_7386,U_7385,U_7384] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7385),U_7386))
      | U_7384 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7384),U_7385)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7384),U_7386))) ),
    inference(variable_rename,[status(thm)],[f_2165_1]) ).

fof(f_2165_3,plain,
    ! [U_7385,U_7384,U_7386] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7385),U_7386))
      | U_7384 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7384),U_7385)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7384),U_7386))) ),
    inference(definitional_conversion,[status(esa)],[f_2165_2]) ).

cnf(f_2165_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7385),U_7386))
    | U_7384 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7384),U_7385)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7384),U_7386))) ),
    inference(clausify,[status(thm)],[f_2165_3]) ).

fof(f_2166_1,plain,
    ! [V_m_2,V_n_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__reduce]) ).

fof(f_2166_2,plain,
    ! [U_7389,U_7388,U_7387] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7387),U_7389))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7387),U_7388)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7387),U_7388))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7387),U_7389)))) ) ),
    inference(variable_rename,[status(thm)],[f_2166_1]) ).

fof(f_2166_3,plain,
    ( ! [U_7395,U_7393,U_7391] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7391),U_7395))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7391),U_7393)) )
    & ! [U_7394,U_7392,U_7390] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7390),U_7392))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7390),U_7394)))) ) ),
    inference(miniscope,[status(thm)],[f_2166_2]) ).

fof(f_2166_4,plain,
    ( ! [U_7391,U_7393,U_7395] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7391),U_7395))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7391),U_7393)) )
    & ! [U_7392,U_7390,U_7394] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7390),U_7392))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7390),U_7394)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2166_3]) ).

cnf(f_2166_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7390),U_7392))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7390),U_7394)))) ),
    inference(clausify,[status(thm)],[f_2166_4]) ).

cnf(f_2166_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7391),U_7395))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7391),U_7393)) ),
    inference(clausify,[status(thm)],[f_2166_4]) ).

fof(f_2167_1,plain,
    ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__period]) ).

fof(f_2167_2,plain,
    ! [U_7400,U_7399,U_7398,U_7397,U_7396] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),U_7399)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7400),U_7397))),U_7399))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7400),U_7397))),U_7399)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),U_7399))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),U_7397)) ),
    inference(variable_rename,[status(thm)],[f_2167_1]) ).

fof(f_2167_3,plain,
    ( ! [U_7397,U_7396,U_7398,U_7399,U_7400] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),U_7399)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7400),U_7397))),U_7399)))
        | ~ sP664(U_7397,U_7396,U_7398,U_7399,U_7400) )
    & ! [U_7397,U_7396,U_7398,U_7399,U_7400] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7400),U_7397))),U_7399)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),U_7399)))
        | ~ sP664(U_7397,U_7396,U_7398,U_7399,U_7400) )
    & ! [U_7397,U_7396,U_7398,U_7399,U_7400] :
        ( sP664(U_7397,U_7396,U_7398,U_7399,U_7400)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),U_7397)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP664])],[f_2167_2]) ).

cnf(f_2167_4,plain,
    ( sP664(U_7397,U_7396,U_7398,U_7399,U_7400)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),U_7397)) ),
    inference(clausify,[status(thm)],[f_2167_3]) ).

cnf(f_2167_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7400),U_7397))),U_7399)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),U_7399)))
    | ~ sP664(U_7397,U_7396,U_7398,U_7399,U_7400) ),
    inference(clausify,[status(thm)],[f_2167_3]) ).

cnf(f_2167_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),U_7399)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7400),U_7397))),U_7399)))
    | ~ sP664(U_7397,U_7396,U_7398,U_7399,U_7400) ),
    inference(clausify,[status(thm)],[f_2167_3]) ).

fof(f_2168_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__int]) ).

fof(f_2168_2,plain,
    ! [U_7402,U_7401] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7401),U_7402))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7401)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7402))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7401)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7402)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7401),U_7402)) ) ),
    inference(variable_rename,[status(thm)],[f_2168_1]) ).

fof(f_2168_3,plain,
    ( ! [U_7406,U_7404] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7406))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7404)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7406))) )
    & ! [U_7405,U_7403] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7403)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7405)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7405)) ) ),
    inference(miniscope,[status(thm)],[f_2168_2]) ).

fof(f_2168_4,plain,
    ( ! [U_7404,U_7406] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7406))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7404)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7406))) )
    & ! [U_7403,U_7405] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7403)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7405)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7405)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2168_3]) ).

cnf(f_2168_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7403)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7405)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7405)) ),
    inference(clausify,[status(thm)],[f_2168_4]) ).

cnf(f_2168_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7406))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7404)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7406))) ),
    inference(clausify,[status(thm)],[f_2168_4]) ).

fof(f_2169_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I4_J]) ).

fof(f_2169_2,plain,
    ! [U_7408,U_7407] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7407)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7408)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7407),U_7408)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7407),U_7408))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7407)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7408))) ) ),
    inference(variable_rename,[status(thm)],[f_2169_1]) ).

fof(f_2169_3,plain,
    ( ! [U_7412,U_7410] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7410)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7412)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7410),U_7412)) )
    & ! [U_7411,U_7409] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7409),U_7411))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7409)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7411))) ) ),
    inference(miniscope,[status(thm)],[f_2169_2]) ).

fof(f_2169_4,plain,
    ( ! [U_7410,U_7412] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7410)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7412)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7410),U_7412)) )
    & ! [U_7411,U_7409] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7409),U_7411))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7409)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7411))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2169_3]) ).

cnf(f_2169_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7409),U_7411))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7409)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7411))) ),
    inference(clausify,[status(thm)],[f_2169_4]) ).

cnf(f_2169_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7410)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7412)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7410),U_7412)) ),
    inference(clausify,[status(thm)],[f_2169_4]) ).

fof(f_2170_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel]) ).

fof(f_2170_2,plain,
    ! [U_7414,U_7413] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7413),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7414),U_7413)) = U_7414
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7413),U_7414)) ),
    inference(variable_rename,[status(thm)],[f_2170_1]) ).

fof(f_2170_3,plain,
    ! [U_7413,U_7414] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7413),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7414),U_7413)) = U_7414
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7413),U_7414)) ),
    inference(definitional_conversion,[status(esa)],[f_2170_2]) ).

cnf(f_2170_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7413),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7414),U_7413)) = U_7414
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7413),U_7414)) ),
    inference(clausify,[status(thm)],[f_2170_3]) ).

fof(f_2171_1,plain,
    ! [V_y_2,V_n_2,V_x_2] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) != c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__eq__dvd__iff]) ).

fof(f_2171_2,plain,
    ! [U_7417,U_7416,U_7415] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7415,U_7416) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7417,U_7416)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7416),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7415),U_7417))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7416),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7415),U_7417)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7415,U_7416) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7417,U_7416) ) ),
    inference(variable_rename,[status(thm)],[f_2171_1]) ).

fof(f_2171_3,plain,
    ( ! [U_7423,U_7421,U_7419] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7419,U_7421) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7423,U_7421)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7419),U_7423))) )
    & ! [U_7422,U_7420,U_7418] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7418),U_7422)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7418,U_7420) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7422,U_7420) ) ),
    inference(miniscope,[status(thm)],[f_2171_2]) ).

fof(f_2171_4,plain,
    ( ! [U_7419,U_7421,U_7423] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7419,U_7421) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7423,U_7421)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7419),U_7423))) )
    & ! [U_7418,U_7420,U_7422] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7418),U_7422)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7418,U_7420) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7422,U_7420) ) ),
    inference(definitional_conversion,[status(esa)],[f_2171_3]) ).

cnf(f_2171_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7418),U_7422)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7418,U_7420) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7422,U_7420) ),
    inference(clausify,[status(thm)],[f_2171_4]) ).

cnf(f_2171_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7419,U_7421) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7423,U_7421)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7419),U_7423))) ),
    inference(clausify,[status(thm)],[f_2171_4]) ).

fof(f_2172_1,plain,
    ! [V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd1__eq]) ).

fof(f_2172_2,plain,
    ! [U_7424] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7424),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7424) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7424) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7424),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2172_1]) ).

fof(f_2172_3,plain,
    ( ! [U_7426] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7426),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7426) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
    & ! [U_7425] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7425) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2172_2]) ).

fof(f_2172_4,plain,
    ( ! [U_7426] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7426),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7426) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
    & ! [U_7425] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7425) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2172_3]) ).

cnf(f_2172_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7425) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2172_4]) ).

cnf(f_2172_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7426),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7426) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2172_4]) ).

fof(f_2173_1,plain,
    ! [V_x,V_y] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_abs__div]) ).

fof(f_2173_2,plain,
    ! [U_7428,U_7427] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7428),U_7427)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7428)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7427))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7427),U_7428)) ),
    inference(variable_rename,[status(thm)],[f_2173_1]) ).

fof(f_2173_3,plain,
    ! [U_7428,U_7427] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7428),U_7427)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7428)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7427))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7427),U_7428)) ),
    inference(definitional_conversion,[status(esa)],[f_2173_2]) ).

cnf(f_2173_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7428),U_7427)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7428)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7427))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7427),U_7428)) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

fof(f_2174_1,plain,
    ! [V_f_2,T_b] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__mono__mono]) ).

fof(f_2174_2,plain,
    ! [U_7430,U_7429] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7429,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7430)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7429,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7430)
      | ~ class_Orderings_Oorder(U_7429) ),
    inference(variable_rename,[status(thm)],[f_2174_1]) ).

fof(f_2174_3,plain,
    ! [U_7430,U_7429] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7429,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7430)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7429,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7430)
      | ~ class_Orderings_Oorder(U_7429) ),
    inference(definitional_conversion,[status(esa)],[f_2174_2]) ).

cnf(f_2174_4,plain,
    ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7429,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7430)
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7429,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7430)
    | ~ class_Orderings_Oorder(U_7429) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

fof(f_2175_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq]) ).

fof(f_2175_2,plain,
    ! [U_7432,U_7431] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7431,tc_HOL_Obool)),U_7432),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7431,tc_HOL_Obool)),U_7432)))
        | U_7432 != c_Orderings_Obot__class_Obot(tc_fun(U_7431,tc_HOL_Obool)) )
      & ( U_7432 = c_Orderings_Obot__class_Obot(tc_fun(U_7431,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7431,tc_HOL_Obool)),U_7432),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7431,tc_HOL_Obool)),U_7432))) ) ),
    inference(variable_rename,[status(thm)],[f_2175_1]) ).

fof(f_2175_3,plain,
    ( ! [U_7436,U_7434] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7434,tc_HOL_Obool)),U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7434,tc_HOL_Obool)),U_7436)))
        | U_7436 != c_Orderings_Obot__class_Obot(tc_fun(U_7434,tc_HOL_Obool)) )
    & ! [U_7435,U_7433] :
        ( U_7435 = c_Orderings_Obot__class_Obot(tc_fun(U_7433,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7433,tc_HOL_Obool)),U_7435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7433,tc_HOL_Obool)),U_7435))) ) ),
    inference(miniscope,[status(thm)],[f_2175_2]) ).

fof(f_2175_4,plain,
    ( ! [U_7434,U_7436] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7434,tc_HOL_Obool)),U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7434,tc_HOL_Obool)),U_7436)))
        | U_7436 != c_Orderings_Obot__class_Obot(tc_fun(U_7434,tc_HOL_Obool)) )
    & ! [U_7433,U_7435] :
        ( U_7435 = c_Orderings_Obot__class_Obot(tc_fun(U_7433,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7433,tc_HOL_Obool)),U_7435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7433,tc_HOL_Obool)),U_7435))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2175_3]) ).

cnf(f_2175_5,plain,
    ( U_7435 = c_Orderings_Obot__class_Obot(tc_fun(U_7433,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7433,tc_HOL_Obool)),U_7435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7433,tc_HOL_Obool)),U_7435))) ),
    inference(clausify,[status(thm)],[f_2175_4]) ).

cnf(f_2175_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7434,tc_HOL_Obool)),U_7436),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7434,tc_HOL_Obool)),U_7436)))
    | U_7436 != c_Orderings_Obot__class_Obot(tc_fun(U_7434,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2175_4]) ).

fof(f_2176_1,plain,
    ! [V_n,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le]) ).

fof(f_2176_2,plain,
    ! [U_7438,U_7437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7437),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7437),U_7438)) ),
    inference(variable_rename,[status(thm)],[f_2176_1]) ).

fof(f_2176_3,plain,
    ! [U_7437,U_7438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7437),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7437),U_7438)) ),
    inference(definitional_conversion,[status(esa)],[f_2176_2]) ).

cnf(f_2176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7437),U_7438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7438))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7437),U_7438)) ),
    inference(clausify,[status(thm)],[f_2176_3]) ).

fof(f_2177_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__iff__zmod__eq__0__number__of]) ).

fof(f_2177_2,plain,
    ! [U_7440,U_7439] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7439)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7440)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7440),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7439)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7440),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7439)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7439)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7440))) ) ),
    inference(variable_rename,[status(thm)],[f_2177_1]) ).

fof(f_2177_3,plain,
    ( ! [U_7444,U_7442] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7444)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7444),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7442)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7443,U_7441] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7443),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7441)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7441)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7443))) ) ),
    inference(miniscope,[status(thm)],[f_2177_2]) ).

fof(f_2177_4,plain,
    ( ! [U_7442,U_7444] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7444)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7444),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7442)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7441,U_7443] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7443),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7441)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7441)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7443))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2177_3]) ).

cnf(f_2177_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7443),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7441)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7441)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7443))) ),
    inference(clausify,[status(thm)],[f_2177_4]) ).

cnf(f_2177_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7444)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7444),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7442)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2177_4]) ).

fof(f_2178_1,plain,
    ! [V_d,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
      | V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__imp__le__int]) ).

fof(f_2178_2,plain,
    ! [U_7446,U_7445] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7446)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7445)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7446),U_7445))
      | U_7445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2178_1]) ).

fof(f_2178_3,plain,
    ! [U_7446,U_7445] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7446)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7445)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7446),U_7445))
      | U_7445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_2178_2]) ).

cnf(f_2178_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7446)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7445)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7446),U_7445))
    | U_7445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2178_3]) ).

fof(f_2179_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I4_J]) ).

fof(f_2179_2,plain,
    ! [U_7448,U_7447] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7447)),hAPP(c_Int_Onat,U_7448)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7447),U_7448)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7447),U_7448))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7447)),hAPP(c_Int_Onat,U_7448))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7448))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7447)) ),
    inference(variable_rename,[status(thm)],[f_2179_1]) ).

fof(f_2179_3,plain,
    ( ! [U_7447,U_7448] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7447)),hAPP(c_Int_Onat,U_7448)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7447),U_7448))
        | ~ sP665(U_7447,U_7448) )
    & ! [U_7447,U_7448] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7447),U_7448))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7447)),hAPP(c_Int_Onat,U_7448)))
        | ~ sP665(U_7447,U_7448) )
    & ! [U_7447,U_7448] :
        ( sP665(U_7447,U_7448)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7448))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7447)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP665])],[f_2179_2]) ).

cnf(f_2179_4,plain,
    ( sP665(U_7447,U_7448)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7448))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7447)) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

cnf(f_2179_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7447),U_7448))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7447)),hAPP(c_Int_Onat,U_7448)))
    | ~ sP665(U_7447,U_7448) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

cnf(f_2179_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7447)),hAPP(c_Int_Onat,U_7448)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7447),U_7448))
    | ~ sP665(U_7447,U_7448) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

fof(f_2180_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2))
          | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2)) ) )
      | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel1]) ).

fof(f_2180_2,plain,
    ! [U_7450,U_7449] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7449),U_7450)),U_7449))
          | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7449),U_7450)),U_7449)) ) )
      | U_7449 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2180_1]) ).

fof(f_2180_3,plain,
    ( ! [U_7449,U_7450] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7449),U_7450)),U_7449))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP666(U_7449,U_7450) )
    & ! [U_7449,U_7450] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7449),U_7450)),U_7449))
        | ~ sP666(U_7449,U_7450) )
    & ! [U_7449,U_7450] :
        ( sP666(U_7449,U_7450)
        | U_7449 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP666])],[f_2180_2]) ).

cnf(f_2180_4,plain,
    ( sP666(U_7449,U_7450)
    | U_7449 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

cnf(f_2180_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7449),U_7450)),U_7449))
    | ~ sP666(U_7449,U_7450) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

cnf(f_2180_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7449),U_7450)),U_7449))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7450) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP666(U_7449,U_7450) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

fof(f_2181_1,plain,
    ! [V_z_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__dvd__iff]) ).

fof(f_2181_2,plain,
    ! [U_7452,U_7451] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7451)),U_7452))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7451),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7452)))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7451),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7452))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7451)),U_7452)) ) ),
    inference(variable_rename,[status(thm)],[f_2181_1]) ).

fof(f_2181_3,plain,
    ( ! [U_7456,U_7454] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7454)),U_7456))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7454),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7456)))) )
    & ! [U_7455,U_7453] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7453),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7455))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7453)),U_7455)) ) ),
    inference(miniscope,[status(thm)],[f_2181_2]) ).

fof(f_2181_4,plain,
    ( ! [U_7454,U_7456] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7454)),U_7456))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7454),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7456)))) )
    & ! [U_7453,U_7455] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7453),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7455))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7453)),U_7455)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2181_3]) ).

cnf(f_2181_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7453),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7455))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7453)),U_7455)) ),
    inference(clausify,[status(thm)],[f_2181_4]) ).

cnf(f_2181_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7454)),U_7456))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7454),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7456)))) ),
    inference(clausify,[status(thm)],[f_2181_4]) ).

fof(f_2182_1,plain,
    ! [V_m_2,V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__int__iff]) ).

fof(f_2182_2,plain,
    ! [U_7458,U_7457] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7457),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7458)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7457))),U_7458)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7457))),U_7458))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7457),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7458))) ) ),
    inference(variable_rename,[status(thm)],[f_2182_1]) ).

fof(f_2182_3,plain,
    ( ! [U_7462,U_7460] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7462)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7460))),U_7462)) )
    & ! [U_7461,U_7459] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7459))),U_7461))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7459),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7461))) ) ),
    inference(miniscope,[status(thm)],[f_2182_2]) ).

fof(f_2182_4,plain,
    ( ! [U_7460,U_7462] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7462)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7460))),U_7462)) )
    & ! [U_7461,U_7459] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7459))),U_7461))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7459),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7461))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2182_3]) ).

cnf(f_2182_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7459))),U_7461))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7459),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7461))) ),
    inference(clausify,[status(thm)],[f_2182_4]) ).

cnf(f_2182_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7462)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7460))),U_7462)) ),
    inference(clausify,[status(thm)],[f_2182_4]) ).

fof(f_2183_1,plain,
    ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_the__elem__def]) ).

fof(f_2183_2,plain,
    ! [U_7464,U_7463] : c_Set_Othe__elem(U_7463,U_7464) = c_HOL_OThe(U_7463,hAPP(hAPP(c_COMBB(tc_fun(U_7463,tc_HOL_Obool),tc_HOL_Obool,U_7463),hAPP(c_fequal,U_7464)),hAPP(hAPP(c_COMBC(U_7463,tc_fun(U_7463,tc_HOL_Obool),tc_fun(U_7463,tc_HOL_Obool)),c_Set_Oinsert(U_7463)),c_Orderings_Obot__class_Obot(tc_fun(U_7463,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2183_1]) ).

fof(f_2183_3,plain,
    ! [U_7463,U_7464] : c_Set_Othe__elem(U_7463,U_7464) = c_HOL_OThe(U_7463,hAPP(hAPP(c_COMBB(tc_fun(U_7463,tc_HOL_Obool),tc_HOL_Obool,U_7463),hAPP(c_fequal,U_7464)),hAPP(hAPP(c_COMBC(U_7463,tc_fun(U_7463,tc_HOL_Obool),tc_fun(U_7463,tc_HOL_Obool)),c_Set_Oinsert(U_7463)),c_Orderings_Obot__class_Obot(tc_fun(U_7463,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2183_2]) ).

cnf(f_2183_4,plain,
    c_Set_Othe__elem(U_7463,U_7464) = c_HOL_OThe(U_7463,hAPP(hAPP(c_COMBB(tc_fun(U_7463,tc_HOL_Obool),tc_HOL_Obool,U_7463),hAPP(c_fequal,U_7464)),hAPP(hAPP(c_COMBC(U_7463,tc_fun(U_7463,tc_HOL_Obool),tc_fun(U_7463,tc_HOL_Obool)),c_Set_Oinsert(U_7463)),c_Orderings_Obot__class_Obot(tc_fun(U_7463,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2183_3]) ).

fof(f_2184_1,plain,
    ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_the__elem__eq]) ).

fof(f_2184_2,plain,
    ! [U_7466,U_7465] : c_Set_Othe__elem(U_7465,hAPP(hAPP(c_Set_Oinsert(U_7465),U_7466),c_Orderings_Obot__class_Obot(tc_fun(U_7465,tc_HOL_Obool)))) = U_7466,
    inference(variable_rename,[status(thm)],[f_2184_1]) ).

fof(f_2184_3,plain,
    ! [U_7465,U_7466] : c_Set_Othe__elem(U_7465,hAPP(hAPP(c_Set_Oinsert(U_7465),U_7466),c_Orderings_Obot__class_Obot(tc_fun(U_7465,tc_HOL_Obool)))) = U_7466,
    inference(definitional_conversion,[status(esa)],[f_2184_2]) ).

cnf(f_2184_4,plain,
    c_Set_Othe__elem(U_7465,hAPP(hAPP(c_Set_Oinsert(U_7465),U_7466),c_Orderings_Obot__class_Obot(tc_fun(U_7465,tc_HOL_Obool)))) = U_7466,
    inference(clausify,[status(thm)],[f_2184_3]) ).

fof(f_2185_1,plain,
    ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Option_Oset_Osimps_I2_J]) ).

fof(f_2185_2,plain,
    ! [U_7468,U_7467] : c_Option_Oset(U_7467,hAPP(c_Option_Ooption_OSome(U_7467),U_7468)) = hAPP(hAPP(c_Set_Oinsert(U_7467),U_7468),c_Orderings_Obot__class_Obot(tc_fun(U_7467,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2185_1]) ).

fof(f_2185_3,plain,
    ! [U_7467,U_7468] : c_Option_Oset(U_7467,hAPP(c_Option_Ooption_OSome(U_7467),U_7468)) = hAPP(hAPP(c_Set_Oinsert(U_7467),U_7468),c_Orderings_Obot__class_Obot(tc_fun(U_7467,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2185_2]) ).

cnf(f_2185_4,plain,
    c_Option_Oset(U_7467,hAPP(c_Option_Ooption_OSome(U_7467),U_7468)) = hAPP(hAPP(c_Set_Oinsert(U_7467),U_7468),c_Orderings_Obot__class_Obot(tc_fun(U_7467,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2185_3]) ).

fof(f_2186_1,plain,
    ! [V_Q_2,V_c_2,V_Ga_2,T_b,V_P_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ? [B_Z,B_s] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) ) ),
    inference(fof_nnf,[status(thm)],[fact_escape]) ).

fof(f_2186_2,plain,
    ! [U_7475,U_7474,U_7473,U_7472,U_7471] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),U_7471),U_7474),U_7475)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
      | ? [U_7470,U_7469] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_7469))),U_7474),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(U_7475,U_7470)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_7471,U_7470),U_7469)) ) ),
    inference(variable_rename,[status(thm)],[f_2186_1]) ).

fof(f_2186_3,plain,
    ! [U_7475,U_7474,U_7473,U_7472,U_7471] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),U_7471),U_7474),U_7475)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
      | ? [U_7469] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_7469))),U_7474),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(U_7475,sK102(U_7475,U_7474,U_7473,U_7472,U_7471))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_7471,sK102(U_7475,U_7474,U_7473,U_7472,U_7471)),U_7469)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_7470,sK102(U_7475,U_7474,U_7473,U_7472,U_7471))],[f_2186_2]) ).

fof(f_2186_4,plain,
    ! [U_7475,U_7474,U_7473,U_7472,U_7471] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),U_7471),U_7474),U_7475)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK103(U_7475,U_7474,U_7473,U_7472,U_7471)))),U_7474),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(U_7475,sK102(U_7475,U_7474,U_7473,U_7472,U_7471))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
        & hBOOL(hAPP(hAPP(U_7471,sK102(U_7475,U_7474,U_7473,U_7472,U_7471)),sK103(U_7475,U_7474,U_7473,U_7472,U_7471))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_7469,sK103(U_7475,U_7474,U_7473,U_7472,U_7471))],[f_2186_3]) ).

fof(f_2186_5,plain,
    ( ! [U_7471,U_7472,U_7473,U_7474,U_7475] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK103(U_7475,U_7474,U_7473,U_7472,U_7471)))),U_7474),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(U_7475,sK102(U_7475,U_7474,U_7473,U_7472,U_7471))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
        | ~ sP667(U_7471,U_7472,U_7473,U_7474,U_7475) )
    & ! [U_7471,U_7472,U_7473,U_7474,U_7475] :
        ( hBOOL(hAPP(hAPP(U_7471,sK102(U_7475,U_7474,U_7473,U_7472,U_7471)),sK103(U_7475,U_7474,U_7473,U_7472,U_7471)))
        | ~ sP667(U_7471,U_7472,U_7473,U_7474,U_7475) )
    & ! [U_7471,U_7472,U_7473,U_7474,U_7475] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),U_7471),U_7474),U_7475)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
        | sP667(U_7471,U_7472,U_7473,U_7474,U_7475) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP667])],[f_2186_4]) ).

cnf(f_2186_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),U_7471),U_7474),U_7475)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
    | sP667(U_7471,U_7472,U_7473,U_7474,U_7475) ),
    inference(clausify,[status(thm)],[f_2186_5]) ).

cnf(f_2186_7,plain,
    ( hBOOL(hAPP(hAPP(U_7471,sK102(U_7475,U_7474,U_7473,U_7472,U_7471)),sK103(U_7475,U_7474,U_7473,U_7472,U_7471)))
    | ~ sP667(U_7471,U_7472,U_7473,U_7474,U_7475) ),
    inference(clausify,[status(thm)],[f_2186_5]) ).

cnf(f_2186_8,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7472,U_7473,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7472)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7472),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK103(U_7475,U_7474,U_7473,U_7472,U_7471)))),U_7474),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7472),hAPP(U_7475,sK102(U_7475,U_7474,U_7473,U_7472,U_7471))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7472),tc_HOL_Obool))))
    | ~ sP667(U_7471,U_7472,U_7473,U_7474,U_7475) ),
    inference(clausify,[status(thm)],[f_2186_5]) ).

fof(f_2187_1,plain,
    ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ? [B_Z,B_s] :
          ( ~ hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s))
          & hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_conseq1]) ).

fof(f_2187_2,plain,
    ! [U_7483,U_7482,U_7481,U_7480,U_7479,U_7478] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7483),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool))))
      | ? [U_7477,U_7476] :
          ( ~ hBOOL(hAPP(hAPP(U_7480,U_7477),U_7476))
          & hBOOL(hAPP(hAPP(U_7483,U_7477),U_7476)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7480),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2187_1]) ).

fof(f_2187_3,plain,
    ! [U_7483,U_7482,U_7481,U_7480,U_7479,U_7478] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7483),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool))))
      | ? [U_7476] :
          ( ~ hBOOL(hAPP(hAPP(U_7480,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),U_7476))
          & hBOOL(hAPP(hAPP(U_7483,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),U_7476)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7480),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_7477,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478))],[f_2187_2]) ).

fof(f_2187_4,plain,
    ! [U_7483,U_7482,U_7481,U_7480,U_7479,U_7478] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7483),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_7480,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)))
        & hBOOL(hAPP(hAPP(U_7483,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7480),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_7476,sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478))],[f_2187_3]) ).

fof(f_2187_5,plain,
    ( ! [U_7478,U_7479,U_7480,U_7481,U_7482,U_7483] :
        ( ~ hBOOL(hAPP(hAPP(U_7480,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)))
        | ~ sP668(U_7478,U_7479,U_7480,U_7481,U_7482,U_7483) )
    & ! [U_7478,U_7479,U_7480,U_7481,U_7482,U_7483] :
        ( hBOOL(hAPP(hAPP(U_7483,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)))
        | ~ sP668(U_7478,U_7479,U_7480,U_7481,U_7482,U_7483) )
    & ! [U_7478,U_7479,U_7480,U_7481,U_7482,U_7483] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7483),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool))))
        | sP668(U_7478,U_7479,U_7480,U_7481,U_7482,U_7483)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7480),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP668])],[f_2187_4]) ).

cnf(f_2187_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7483),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool))))
    | sP668(U_7478,U_7479,U_7480,U_7481,U_7482,U_7483)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7478,U_7479,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7478)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7478),U_7480),U_7481),U_7482)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7478),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2187_5]) ).

cnf(f_2187_7,plain,
    ( hBOOL(hAPP(hAPP(U_7483,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)))
    | ~ sP668(U_7478,U_7479,U_7480,U_7481,U_7482,U_7483) ),
    inference(clausify,[status(thm)],[f_2187_5]) ).

cnf(f_2187_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_7480,sK104(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)),sK105(U_7483,U_7482,U_7481,U_7480,U_7479,U_7478)))
    | ~ sP668(U_7478,U_7479,U_7480,U_7481,U_7482,U_7483) ),
    inference(clausify,[status(thm)],[f_2187_5]) ).

fof(f_2188_1,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bot__nat__def]) ).

fof(f_2188_2,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2188_1]) ).

cnf(f_2188_3,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2188_2]) ).

fof(f_2189_1,plain,
    ! [V_xo_2,T_b] :
      ( ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_xo_2 != c_Option_Ooption_ONone(T_b) )
      & ( V_xo_2 = c_Option_Ooption_ONone(T_b)
        | c_Option_Oset(T_b,V_xo_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty__eq]) ).

fof(f_2189_2,plain,
    ! [U_7485,U_7484] :
      ( ( c_Option_Oset(U_7484,U_7485) = c_Orderings_Obot__class_Obot(tc_fun(U_7484,tc_HOL_Obool))
        | U_7485 != c_Option_Ooption_ONone(U_7484) )
      & ( U_7485 = c_Option_Ooption_ONone(U_7484)
        | c_Option_Oset(U_7484,U_7485) != c_Orderings_Obot__class_Obot(tc_fun(U_7484,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2189_1]) ).

fof(f_2189_3,plain,
    ( ! [U_7489,U_7487] :
        ( c_Option_Oset(U_7487,U_7489) = c_Orderings_Obot__class_Obot(tc_fun(U_7487,tc_HOL_Obool))
        | U_7489 != c_Option_Ooption_ONone(U_7487) )
    & ! [U_7488,U_7486] :
        ( U_7488 = c_Option_Ooption_ONone(U_7486)
        | c_Option_Oset(U_7486,U_7488) != c_Orderings_Obot__class_Obot(tc_fun(U_7486,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2189_2]) ).

fof(f_2189_4,plain,
    ( ! [U_7489,U_7487] :
        ( c_Option_Oset(U_7487,U_7489) = c_Orderings_Obot__class_Obot(tc_fun(U_7487,tc_HOL_Obool))
        | U_7489 != c_Option_Ooption_ONone(U_7487) )
    & ! [U_7486,U_7488] :
        ( U_7488 = c_Option_Ooption_ONone(U_7486)
        | c_Option_Oset(U_7486,U_7488) != c_Orderings_Obot__class_Obot(tc_fun(U_7486,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2189_3]) ).

cnf(f_2189_5,plain,
    ( U_7488 = c_Option_Ooption_ONone(U_7486)
    | c_Option_Oset(U_7486,U_7488) != c_Orderings_Obot__class_Obot(tc_fun(U_7486,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2189_4]) ).

cnf(f_2189_6,plain,
    ( c_Option_Oset(U_7487,U_7489) = c_Orderings_Obot__class_Obot(tc_fun(U_7487,tc_HOL_Obool))
    | U_7489 != c_Option_Ooption_ONone(U_7487) ),
    inference(clausify,[status(thm)],[f_2189_4]) ).

fof(f_2190_1,plain,
    ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Option_Oset_Osimps_I1_J]) ).

fof(f_2190_2,plain,
    ! [U_7490] : c_Option_Oset(U_7490,c_Option_Ooption_ONone(U_7490)) = c_Orderings_Obot__class_Obot(tc_fun(U_7490,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2190_1]) ).

fof(f_2190_3,plain,
    ! [U_7490] : c_Option_Oset(U_7490,c_Option_Ooption_ONone(U_7490)) = c_Orderings_Obot__class_Obot(tc_fun(U_7490,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2190_2]) ).

cnf(f_2190_4,plain,
    c_Option_Oset(U_7490,c_Option_Ooption_ONone(U_7490)) = c_Orderings_Obot__class_Obot(tc_fun(U_7490,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2190_3]) ).

fof(f_2191_1,plain,
    ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ? [B_Z,B_s] :
          ( ~ hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s))
          & hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_conseq2]) ).

fof(f_2191_2,plain,
    ! [U_7498,U_7497,U_7496,U_7495,U_7494,U_7493] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7498)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool))))
      | ? [U_7492,U_7491] :
          ( ~ hBOOL(hAPP(hAPP(U_7498,U_7492),U_7491))
          & hBOOL(hAPP(hAPP(U_7497,U_7492),U_7491)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7497)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2191_1]) ).

fof(f_2191_3,plain,
    ! [U_7498,U_7497,U_7496,U_7495,U_7494,U_7493] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7498)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool))))
      | ? [U_7491] :
          ( ~ hBOOL(hAPP(hAPP(U_7498,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),U_7491))
          & hBOOL(hAPP(hAPP(U_7497,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),U_7491)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7497)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_7492,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493))],[f_2191_2]) ).

fof(f_2191_4,plain,
    ! [U_7498,U_7497,U_7496,U_7495,U_7494,U_7493] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7498)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_7498,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)))
        & hBOOL(hAPP(hAPP(U_7497,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7497)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_7491,sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493))],[f_2191_3]) ).

fof(f_2191_5,plain,
    ( ! [U_7493,U_7494,U_7495,U_7496,U_7497,U_7498] :
        ( ~ hBOOL(hAPP(hAPP(U_7498,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)))
        | ~ sP669(U_7493,U_7494,U_7495,U_7496,U_7497,U_7498) )
    & ! [U_7493,U_7494,U_7495,U_7496,U_7497,U_7498] :
        ( hBOOL(hAPP(hAPP(U_7497,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)))
        | ~ sP669(U_7493,U_7494,U_7495,U_7496,U_7497,U_7498) )
    & ! [U_7493,U_7494,U_7495,U_7496,U_7497,U_7498] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7498)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool))))
        | sP669(U_7493,U_7494,U_7495,U_7496,U_7497,U_7498)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7497)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP669])],[f_2191_4]) ).

cnf(f_2191_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7498)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool))))
    | sP669(U_7493,U_7494,U_7495,U_7496,U_7497,U_7498)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7493,U_7494,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7493)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7493),U_7495),U_7496),U_7497)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7493),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2191_5]) ).

cnf(f_2191_7,plain,
    ( hBOOL(hAPP(hAPP(U_7497,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)))
    | ~ sP669(U_7493,U_7494,U_7495,U_7496,U_7497,U_7498) ),
    inference(clausify,[status(thm)],[f_2191_5]) ).

cnf(f_2191_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_7498,sK106(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)),sK107(U_7498,U_7497,U_7496,U_7495,U_7494,U_7493)))
    | ~ sP669(U_7493,U_7494,U_7495,U_7496,U_7497,U_7498) ),
    inference(clausify,[status(thm)],[f_2191_5]) ).

fof(f_2192_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
              & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
                | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
            | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__insert__iff]) ).

fof(f_2192_2,plain,
    ! [U_7502,U_7501,U_7500,U_7499] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7499,tc_HOL_Obool)),U_7500),hAPP(hAPP(c_Set_Oinsert(U_7499),U_7501),U_7502)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7499,tc_HOL_Obool)),U_7500),U_7502))
              & ~ hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7500)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7499,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7499,tc_HOL_Obool)),U_7500),hAPP(hAPP(c_Set_Oinsert(U_7499),U_7501),c_Orderings_Obot__class_Obot(tc_fun(U_7499,tc_HOL_Obool))))),U_7502))
              & hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7500)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7502)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7499,tc_HOL_Obool)),U_7500),U_7502))
          & hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7502)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7499,tc_HOL_Obool)),U_7500),U_7502))
                | hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7500)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7499,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7499,tc_HOL_Obool)),U_7500),hAPP(hAPP(c_Set_Oinsert(U_7499),U_7501),c_Orderings_Obot__class_Obot(tc_fun(U_7499,tc_HOL_Obool))))),U_7502))
                | ~ hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7500)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7502)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7499,tc_HOL_Obool)),U_7500),U_7502))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7499),U_7501),U_7502)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7499,tc_HOL_Obool)),U_7500),hAPP(hAPP(c_Set_Oinsert(U_7499),U_7501),U_7502))) ) ),
    inference(variable_rename,[status(thm)],[f_2192_1]) ).

fof(f_2192_3,plain,
    ( ! [U_7510,U_7508,U_7506,U_7504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7504),U_7508),U_7510)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7504,tc_HOL_Obool)),U_7506),U_7510))
              & ~ hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7506)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7504,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7504),U_7508),c_Orderings_Obot__class_Obot(tc_fun(U_7504,tc_HOL_Obool))))),U_7510))
              & hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7506)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7510)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),U_7506),U_7510))
          & hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7510)) ) )
    & ! [U_7509,U_7507,U_7505,U_7503] :
        ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7503,tc_HOL_Obool)),U_7505),U_7509))
                | hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7505)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7503,tc_HOL_Obool)),U_7505),hAPP(hAPP(c_Set_Oinsert(U_7503),U_7507),c_Orderings_Obot__class_Obot(tc_fun(U_7503,tc_HOL_Obool))))),U_7509))
                | ~ hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7505)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7509)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),U_7505),U_7509))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7509)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),U_7505),hAPP(hAPP(c_Set_Oinsert(U_7503),U_7507),U_7509))) ) ),
    inference(miniscope,[status(thm)],[f_2192_2]) ).

fof(f_2192_4,plain,
    ( ! [U_7510,U_7504,U_7506,U_7508] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7504,tc_HOL_Obool)),U_7506),U_7510))
        | ~ sP674(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7506))
        | ~ sP674(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7504,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7504),U_7508),c_Orderings_Obot__class_Obot(tc_fun(U_7504,tc_HOL_Obool))))),U_7510))
        | ~ sP673(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7506))
        | ~ sP673(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( sP674(U_7510,U_7504,U_7506,U_7508)
        | sP673(U_7510,U_7504,U_7506,U_7508)
        | ~ sP675(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7510))
        | ~ sP675(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),U_7506),U_7510))
        | ~ sP672(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7510))
        | ~ sP672(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7503,U_7505,U_7507,U_7509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7503,tc_HOL_Obool)),U_7505),U_7509))
        | hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7505))
        | ~ sP670(U_7503,U_7505,U_7507,U_7509) )
    & ! [U_7503,U_7505,U_7507,U_7509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7503,tc_HOL_Obool)),U_7505),hAPP(hAPP(c_Set_Oinsert(U_7503),U_7507),c_Orderings_Obot__class_Obot(tc_fun(U_7503,tc_HOL_Obool))))),U_7509))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7505))
        | ~ sP670(U_7503,U_7505,U_7507,U_7509) )
    & ! [U_7503,U_7505,U_7507,U_7509] :
        ( sP670(U_7503,U_7505,U_7507,U_7509)
        | hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7509))
        | ~ sP671(U_7503,U_7505,U_7507,U_7509) )
    & ! [U_7503,U_7505,U_7507,U_7509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),U_7505),U_7509))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7509))
        | ~ sP671(U_7503,U_7505,U_7507,U_7509) )
    & ! [U_7510,U_7504,U_7506,U_7508] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7504),U_7508),U_7510)))
        | sP675(U_7510,U_7504,U_7506,U_7508)
        | sP672(U_7510,U_7504,U_7506,U_7508) )
    & ! [U_7503,U_7505,U_7507,U_7509] :
        ( sP671(U_7503,U_7505,U_7507,U_7509)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),U_7505),hAPP(hAPP(c_Set_Oinsert(U_7503),U_7507),U_7509))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP670,sP671,sP672,sP673,sP674,sP675])],[f_2192_3]) ).

cnf(f_2192_5,plain,
    ( sP671(U_7503,U_7505,U_7507,U_7509)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),U_7505),hAPP(hAPP(c_Set_Oinsert(U_7503),U_7507),U_7509))) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7504),U_7508),U_7510)))
    | sP675(U_7510,U_7504,U_7506,U_7508)
    | sP672(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),U_7505),U_7509))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7509))
    | ~ sP671(U_7503,U_7505,U_7507,U_7509) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_8,plain,
    ( sP670(U_7503,U_7505,U_7507,U_7509)
    | hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7509))
    | ~ sP671(U_7503,U_7505,U_7507,U_7509) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7503,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7503,tc_HOL_Obool)),U_7505),hAPP(hAPP(c_Set_Oinsert(U_7503),U_7507),c_Orderings_Obot__class_Obot(tc_fun(U_7503,tc_HOL_Obool))))),U_7509))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7505))
    | ~ sP670(U_7503,U_7505,U_7507,U_7509) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7503,tc_HOL_Obool)),U_7505),U_7509))
    | hBOOL(hAPP(hAPP(c_member(U_7503),U_7507),U_7505))
    | ~ sP670(U_7503,U_7505,U_7507,U_7509) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7510))
    | ~ sP672(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),U_7506),U_7510))
    | ~ sP672(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7510))
    | ~ sP675(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_14,plain,
    ( sP674(U_7510,U_7504,U_7506,U_7508)
    | sP673(U_7510,U_7504,U_7506,U_7508)
    | ~ sP675(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7506))
    | ~ sP673(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7504,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7504,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7504),U_7508),c_Orderings_Obot__class_Obot(tc_fun(U_7504,tc_HOL_Obool))))),U_7510))
    | ~ sP673(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7504),U_7508),U_7506))
    | ~ sP674(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

cnf(f_2192_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7504,tc_HOL_Obool)),U_7506),U_7510))
    | ~ sP674(U_7510,U_7504,U_7506,U_7508) ),
    inference(clausify,[status(thm)],[f_2192_4]) ).

fof(f_2193_1,plain,
    ! [V_f_2,T_b] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__monoI]) ).

fof(f_2193_2,plain,
    ! [U_7514,U_7513] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7513,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7514)
      | ? [U_7512,U_7511] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7513),hAPP(U_7514,U_7512)),hAPP(U_7514,U_7511)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7511),U_7512))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7512),U_7511)) )
      | ~ class_Orderings_Oorder(U_7513) ),
    inference(variable_rename,[status(thm)],[f_2193_1]) ).

fof(f_2193_3,plain,
    ! [U_7514,U_7513] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7513,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7514)
      | ? [U_7511] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7513),hAPP(U_7514,sK108(U_7514,U_7513))),hAPP(U_7514,U_7511)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7511),sK108(U_7514,U_7513)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7514,U_7513)),U_7511)) )
      | ~ class_Orderings_Oorder(U_7513) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_7512,sK108(U_7514,U_7513))],[f_2193_2]) ).

fof(f_2193_4,plain,
    ! [U_7514,U_7513] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7513,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7514)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7513),hAPP(U_7514,sK108(U_7514,U_7513))),hAPP(U_7514,sK109(U_7514,U_7513))))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7514,U_7513)),sK108(U_7514,U_7513)))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7514,U_7513)),sK109(U_7514,U_7513))) )
      | ~ class_Orderings_Oorder(U_7513) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_7511,sK109(U_7514,U_7513))],[f_2193_3]) ).

fof(f_2193_5,plain,
    ( ! [U_7513,U_7514] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7513),hAPP(U_7514,sK108(U_7514,U_7513))),hAPP(U_7514,sK109(U_7514,U_7513))))
        | ~ sP676(U_7513,U_7514) )
    & ! [U_7513,U_7514] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7514,U_7513)),sK108(U_7514,U_7513)))
        | ~ sP676(U_7513,U_7514) )
    & ! [U_7513,U_7514] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7514,U_7513)),sK109(U_7514,U_7513)))
        | ~ sP676(U_7513,U_7514) )
    & ! [U_7513,U_7514] :
        ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7513,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7514)
        | sP676(U_7513,U_7514)
        | ~ class_Orderings_Oorder(U_7513) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP676])],[f_2193_4]) ).

cnf(f_2193_6,plain,
    ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7513,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_7514)
    | sP676(U_7513,U_7514)
    | ~ class_Orderings_Oorder(U_7513) ),
    inference(clausify,[status(thm)],[f_2193_5]) ).

cnf(f_2193_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7514,U_7513)),sK109(U_7514,U_7513)))
    | ~ sP676(U_7513,U_7514) ),
    inference(clausify,[status(thm)],[f_2193_5]) ).

cnf(f_2193_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7514,U_7513)),sK108(U_7514,U_7513)))
    | ~ sP676(U_7513,U_7514) ),
    inference(clausify,[status(thm)],[f_2193_5]) ).

cnf(f_2193_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7513),hAPP(U_7514,sK108(U_7514,U_7513))),hAPP(U_7514,sK109(U_7514,U_7513))))
    | ~ sP676(U_7513,U_7514) ),
    inference(clausify,[status(thm)],[f_2193_5]) ).

fof(f_2194_1,plain,
    ! [V_f_2,T_b] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OmonoI]) ).

fof(f_2194_2,plain,
    ! [U_7518,U_7517] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7517,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7518)
      | ? [U_7516,U_7515] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7517),hAPP(U_7518,U_7516)),hAPP(U_7518,U_7515)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7516),U_7515)) )
      | ~ class_Orderings_Oorder(U_7517) ),
    inference(variable_rename,[status(thm)],[f_2194_1]) ).

fof(f_2194_3,plain,
    ! [U_7518,U_7517] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7517,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7518)
      | ? [U_7515] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7517),hAPP(U_7518,sK110(U_7518,U_7517))),hAPP(U_7518,U_7515)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK110(U_7518,U_7517)),U_7515)) )
      | ~ class_Orderings_Oorder(U_7517) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_7516,sK110(U_7518,U_7517))],[f_2194_2]) ).

fof(f_2194_4,plain,
    ! [U_7518,U_7517] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7517,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7518)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7517),hAPP(U_7518,sK110(U_7518,U_7517))),hAPP(U_7518,sK111(U_7518,U_7517))))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK110(U_7518,U_7517)),sK111(U_7518,U_7517))) )
      | ~ class_Orderings_Oorder(U_7517) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_7515,sK111(U_7518,U_7517))],[f_2194_3]) ).

fof(f_2194_5,plain,
    ( ! [U_7518,U_7517] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7517),hAPP(U_7518,sK110(U_7518,U_7517))),hAPP(U_7518,sK111(U_7518,U_7517))))
        | ~ sP677(U_7518,U_7517) )
    & ! [U_7518,U_7517] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK110(U_7518,U_7517)),sK111(U_7518,U_7517)))
        | ~ sP677(U_7518,U_7517) )
    & ! [U_7518,U_7517] :
        ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7517,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7518)
        | sP677(U_7518,U_7517)
        | ~ class_Orderings_Oorder(U_7517) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP677])],[f_2194_4]) ).

cnf(f_2194_6,plain,
    ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7517,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7518)
    | sP677(U_7518,U_7517)
    | ~ class_Orderings_Oorder(U_7517) ),
    inference(clausify,[status(thm)],[f_2194_5]) ).

cnf(f_2194_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK110(U_7518,U_7517)),sK111(U_7518,U_7517)))
    | ~ sP677(U_7518,U_7517) ),
    inference(clausify,[status(thm)],[f_2194_5]) ).

cnf(f_2194_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7517),hAPP(U_7518,sK110(U_7518,U_7517))),hAPP(U_7518,sK111(U_7518,U_7517))))
    | ~ sP677(U_7518,U_7517) ),
    inference(clausify,[status(thm)],[f_2194_5]) ).

fof(f_2195_1,plain,
    ! [V_c_2,T_b,V_B_2,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).

fof(f_2195_2,plain,
    ! [U_7522,U_7521,U_7520,U_7519] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7520))
        & ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7519)) )
      | ( hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7520))
        & hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7519)) )
      | U_7519 != U_7520 ),
    inference(variable_rename,[status(thm)],[f_2195_1]) ).

fof(f_2195_3,plain,
    ( ! [U_7519,U_7520,U_7521,U_7522] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7520))
        | ~ sP679(U_7519,U_7520,U_7521,U_7522) )
    & ! [U_7519,U_7520,U_7521,U_7522] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7519))
        | ~ sP679(U_7519,U_7520,U_7521,U_7522) )
    & ! [U_7519,U_7520,U_7521,U_7522] :
        ( hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7520))
        | ~ sP678(U_7519,U_7520,U_7521,U_7522) )
    & ! [U_7519,U_7520,U_7521,U_7522] :
        ( hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7519))
        | ~ sP678(U_7519,U_7520,U_7521,U_7522) )
    & ! [U_7519,U_7520,U_7521,U_7522] :
        ( sP679(U_7519,U_7520,U_7521,U_7522)
        | sP678(U_7519,U_7520,U_7521,U_7522)
        | U_7519 != U_7520 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP678,sP679])],[f_2195_2]) ).

cnf(f_2195_4,plain,
    ( sP679(U_7519,U_7520,U_7521,U_7522)
    | sP678(U_7519,U_7520,U_7521,U_7522)
    | U_7519 != U_7520 ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

cnf(f_2195_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7519))
    | ~ sP678(U_7519,U_7520,U_7521,U_7522) ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

cnf(f_2195_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7520))
    | ~ sP678(U_7519,U_7520,U_7521,U_7522) ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

cnf(f_2195_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7519))
    | ~ sP679(U_7519,U_7520,U_7521,U_7522) ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

cnf(f_2195_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7522),U_7520))
    | ~ sP679(U_7519,U_7520,U_7521,U_7522) ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

fof(f_2196_1,plain,
    ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_emptyE]) ).

fof(f_2196_2,plain,
    ! [U_7524,U_7523] : ~ hBOOL(hAPP(hAPP(c_member(U_7523),U_7524),c_Orderings_Obot__class_Obot(tc_fun(U_7523,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2196_1]) ).

fof(f_2196_3,plain,
    ! [U_7523,U_7524] : ~ hBOOL(hAPP(hAPP(c_member(U_7523),U_7524),c_Orderings_Obot__class_Obot(tc_fun(U_7523,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2196_2]) ).

cnf(f_2196_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_7523),U_7524),c_Orderings_Obot__class_Obot(tc_fun(U_7523,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2196_3]) ).

fof(f_2197_1,plain,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_insertE]) ).

fof(f_2197_2,plain,
    ! [U_7528,U_7527,U_7526,U_7525] :
      ( hBOOL(hAPP(hAPP(c_member(U_7525),U_7526),U_7528))
      | U_7526 = U_7527
      | ~ hBOOL(hAPP(hAPP(c_member(U_7525),U_7526),hAPP(hAPP(c_Set_Oinsert(U_7525),U_7527),U_7528))) ),
    inference(variable_rename,[status(thm)],[f_2197_1]) ).

fof(f_2197_3,plain,
    ! [U_7525,U_7526,U_7527,U_7528] :
      ( hBOOL(hAPP(hAPP(c_member(U_7525),U_7526),U_7528))
      | U_7526 = U_7527
      | ~ hBOOL(hAPP(hAPP(c_member(U_7525),U_7526),hAPP(hAPP(c_Set_Oinsert(U_7525),U_7527),U_7528))) ),
    inference(definitional_conversion,[status(esa)],[f_2197_2]) ).

cnf(f_2197_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7525),U_7526),U_7528))
    | U_7526 = U_7527
    | ~ hBOOL(hAPP(hAPP(c_member(U_7525),U_7526),hAPP(hAPP(c_Set_Oinsert(U_7525),U_7527),U_7528))) ),
    inference(clausify,[status(thm)],[f_2197_3]) ).

fof(f_2198_1,plain,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
      | ( V_a_2 != V_b_2
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insertCI]) ).

fof(f_2198_2,plain,
    ! [U_7532,U_7531,U_7530,U_7529] :
      ( hBOOL(hAPP(hAPP(c_member(U_7529),U_7530),hAPP(hAPP(c_Set_Oinsert(U_7529),U_7532),U_7531)))
      | ( U_7530 != U_7532
        & ~ hBOOL(hAPP(hAPP(c_member(U_7529),U_7530),U_7531)) ) ),
    inference(variable_rename,[status(thm)],[f_2198_1]) ).

fof(f_2198_3,plain,
    ( ! [U_7529,U_7530,U_7531,U_7532] :
        ( U_7530 != U_7532
        | ~ sP680(U_7529,U_7530,U_7531,U_7532) )
    & ! [U_7529,U_7530,U_7531,U_7532] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7529),U_7530),U_7531))
        | ~ sP680(U_7529,U_7530,U_7531,U_7532) )
    & ! [U_7529,U_7530,U_7531,U_7532] :
        ( hBOOL(hAPP(hAPP(c_member(U_7529),U_7530),hAPP(hAPP(c_Set_Oinsert(U_7529),U_7532),U_7531)))
        | sP680(U_7529,U_7530,U_7531,U_7532) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP680])],[f_2198_2]) ).

cnf(f_2198_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7529),U_7530),hAPP(hAPP(c_Set_Oinsert(U_7529),U_7532),U_7531)))
    | sP680(U_7529,U_7530,U_7531,U_7532) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7529),U_7530),U_7531))
    | ~ sP680(U_7529,U_7530,U_7531,U_7532) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_6,plain,
    ( U_7530 != U_7532
    | ~ sP680(U_7529,U_7530,U_7531,U_7532) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

fof(f_2199_1,plain,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subsetD]) ).

fof(f_2199_2,plain,
    ! [U_7536,U_7535,U_7534,U_7533] :
      ( hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),U_7535))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),U_7534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7533,tc_HOL_Obool)),U_7534),U_7535)) ),
    inference(variable_rename,[status(thm)],[f_2199_1]) ).

fof(f_2199_3,plain,
    ! [U_7533,U_7534,U_7535,U_7536] :
      ( hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),U_7535))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),U_7534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7533,tc_HOL_Obool)),U_7534),U_7535)) ),
    inference(definitional_conversion,[status(esa)],[f_2199_2]) ).

cnf(f_2199_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),U_7535))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),U_7534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7533,tc_HOL_Obool)),U_7534),U_7535)) ),
    inference(clausify,[status(thm)],[f_2199_3]) ).

fof(f_2200_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffE]) ).

fof(f_2200_2,plain,
    ! [U_7540,U_7539,U_7538,U_7537] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),U_7540))
        & hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),U_7539)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7537,tc_HOL_Obool)),U_7539),U_7540))) ),
    inference(variable_rename,[status(thm)],[f_2200_1]) ).

fof(f_2200_3,plain,
    ( ! [U_7537,U_7538,U_7539,U_7540] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),U_7540))
        | ~ sP681(U_7537,U_7538,U_7539,U_7540) )
    & ! [U_7537,U_7538,U_7539,U_7540] :
        ( hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),U_7539))
        | ~ sP681(U_7537,U_7538,U_7539,U_7540) )
    & ! [U_7537,U_7538,U_7539,U_7540] :
        ( sP681(U_7537,U_7538,U_7539,U_7540)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7537,tc_HOL_Obool)),U_7539),U_7540))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP681])],[f_2200_2]) ).

cnf(f_2200_4,plain,
    ( sP681(U_7537,U_7538,U_7539,U_7540)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7537,tc_HOL_Obool)),U_7539),U_7540))) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

cnf(f_2200_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),U_7539))
    | ~ sP681(U_7537,U_7538,U_7539,U_7540) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

cnf(f_2200_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7537),U_7538),U_7540))
    | ~ sP681(U_7537,U_7538,U_7539,U_7540) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

fof(f_2201_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DiffI]) ).

fof(f_2201_2,plain,
    ! [U_7544,U_7543,U_7542,U_7541] :
      ( hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7541,tc_HOL_Obool)),U_7543),U_7544)))
      | hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),U_7544))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),U_7543)) ),
    inference(variable_rename,[status(thm)],[f_2201_1]) ).

fof(f_2201_3,plain,
    ! [U_7541,U_7542,U_7543,U_7544] :
      ( hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7541,tc_HOL_Obool)),U_7543),U_7544)))
      | hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),U_7544))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),U_7543)) ),
    inference(definitional_conversion,[status(esa)],[f_2201_2]) ).

cnf(f_2201_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7541,tc_HOL_Obool)),U_7543),U_7544)))
    | hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),U_7544))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7541),U_7542),U_7543)) ),
    inference(clausify,[status(thm)],[f_2201_3]) ).

fof(f_2202_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ComplI]) ).

fof(f_2202_2,plain,
    ! [U_7547,U_7546,U_7545] :
      ( hBOOL(hAPP(hAPP(c_member(U_7545),U_7546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7545,tc_HOL_Obool)),U_7547)))
      | hBOOL(hAPP(hAPP(c_member(U_7545),U_7546),U_7547)) ),
    inference(variable_rename,[status(thm)],[f_2202_1]) ).

fof(f_2202_3,plain,
    ! [U_7545,U_7546,U_7547] :
      ( hBOOL(hAPP(hAPP(c_member(U_7545),U_7546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7545,tc_HOL_Obool)),U_7547)))
      | hBOOL(hAPP(hAPP(c_member(U_7545),U_7546),U_7547)) ),
    inference(definitional_conversion,[status(esa)],[f_2202_2]) ).

cnf(f_2202_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7545),U_7546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7545,tc_HOL_Obool)),U_7547)))
    | hBOOL(hAPP(hAPP(c_member(U_7545),U_7546),U_7547)) ),
    inference(clausify,[status(thm)],[f_2202_3]) ).

fof(f_2203_1,plain,
    ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).

fof(f_2203_2,plain,
    ! [U_7554,U_7553,U_7552,U_7551,U_7550,U_7549,U_7548] :
      ( hBOOL(hAPP(hAPP(c_member(U_7548),U_7549),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7553,U_7554,tc_fun(U_7548,tc_HOL_Obool)),U_7550),hAPP(hAPP(c_Product__Type_OPair(U_7553,U_7554),U_7551),U_7552))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7548),U_7549),hAPP(hAPP(U_7550,U_7551),U_7552))) ),
    inference(variable_rename,[status(thm)],[f_2203_1]) ).

fof(f_2203_3,plain,
    ! [U_7548,U_7549,U_7550,U_7551,U_7552,U_7553,U_7554] :
      ( hBOOL(hAPP(hAPP(c_member(U_7548),U_7549),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7553,U_7554,tc_fun(U_7548,tc_HOL_Obool)),U_7550),hAPP(hAPP(c_Product__Type_OPair(U_7553,U_7554),U_7551),U_7552))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7548),U_7549),hAPP(hAPP(U_7550,U_7551),U_7552))) ),
    inference(definitional_conversion,[status(esa)],[f_2203_2]) ).

cnf(f_2203_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7548),U_7549),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7553,U_7554,tc_fun(U_7548,tc_HOL_Obool)),U_7550),hAPP(hAPP(c_Product__Type_OPair(U_7553,U_7554),U_7551),U_7552))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7548),U_7549),hAPP(hAPP(U_7550,U_7551),U_7552))) ),
    inference(clausify,[status(thm)],[f_2203_3]) ).

fof(f_2204_1,plain,
    ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insertI1]) ).

fof(f_2204_2,plain,
    ! [U_7557,U_7556,U_7555] : hBOOL(hAPP(hAPP(c_member(U_7555),U_7556),hAPP(hAPP(c_Set_Oinsert(U_7555),U_7556),U_7557))),
    inference(variable_rename,[status(thm)],[f_2204_1]) ).

fof(f_2204_3,plain,
    ! [U_7557,U_7556,U_7555] : hBOOL(hAPP(hAPP(c_member(U_7555),U_7556),hAPP(hAPP(c_Set_Oinsert(U_7555),U_7556),U_7557))),
    inference(definitional_conversion,[status(esa)],[f_2204_2]) ).

cnf(f_2204_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_7555),U_7556),hAPP(hAPP(c_Set_Oinsert(U_7555),U_7556),U_7557))),
    inference(clausify,[status(thm)],[f_2204_3]) ).

fof(f_2205_1,plain,
    ! [V_A_2,T_b] :
      ( ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__not__in__conv]) ).

fof(f_2205_2,plain,
    ! [U_7561,U_7560] :
      ( ( ! [U_7559] : ~ hBOOL(hAPP(hAPP(c_member(U_7560),U_7559),U_7561))
        | U_7561 != c_Orderings_Obot__class_Obot(tc_fun(U_7560,tc_HOL_Obool)) )
      & ( U_7561 = c_Orderings_Obot__class_Obot(tc_fun(U_7560,tc_HOL_Obool))
        | ? [U_7558] : hBOOL(hAPP(hAPP(c_member(U_7560),U_7558),U_7561)) ) ),
    inference(variable_rename,[status(thm)],[f_2205_1]) ).

fof(f_2205_3,plain,
    ( ! [U_7565,U_7563] :
        ( ! [U_7559] : ~ hBOOL(hAPP(hAPP(c_member(U_7563),U_7559),U_7565))
        | U_7565 != c_Orderings_Obot__class_Obot(tc_fun(U_7563,tc_HOL_Obool)) )
    & ! [U_7564,U_7562] :
        ( U_7564 = c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool))
        | ? [U_7558] : hBOOL(hAPP(hAPP(c_member(U_7562),U_7558),U_7564)) ) ),
    inference(miniscope,[status(thm)],[f_2205_2]) ).

fof(f_2205_4,plain,
    ( ! [U_7565,U_7563] :
        ( ! [U_7559] : ~ hBOOL(hAPP(hAPP(c_member(U_7563),U_7559),U_7565))
        | U_7565 != c_Orderings_Obot__class_Obot(tc_fun(U_7563,tc_HOL_Obool)) )
    & ! [U_7564,U_7562] :
        ( U_7564 = c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_7562),sK112(U_7564,U_7562)),U_7564)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_7558,sK112(U_7564,U_7562))],[f_2205_3]) ).

fof(f_2205_5,plain,
    ( ! [U_7559,U_7563,U_7565] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7563),U_7559),U_7565))
        | U_7565 != c_Orderings_Obot__class_Obot(tc_fun(U_7563,tc_HOL_Obool)) )
    & ! [U_7564,U_7562] :
        ( U_7564 = c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_7562),sK112(U_7564,U_7562)),U_7564)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2205_4]) ).

cnf(f_2205_6,plain,
    ( U_7564 = c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_7562),sK112(U_7564,U_7562)),U_7564)) ),
    inference(clausify,[status(thm)],[f_2205_5]) ).

cnf(f_2205_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7563),U_7559),U_7565))
    | U_7565 != c_Orderings_Obot__class_Obot(tc_fun(U_7563,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2205_5]) ).

fof(f_2206_1,plain,
    ! [V_A_2,T_b] :
      ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__in__conv]) ).

fof(f_2206_2,plain,
    ! [U_7569,U_7568] :
      ( ( ? [U_7567] : hBOOL(hAPP(hAPP(c_member(U_7568),U_7567),U_7569))
        | U_7569 = c_Orderings_Obot__class_Obot(tc_fun(U_7568,tc_HOL_Obool)) )
      & ( U_7569 != c_Orderings_Obot__class_Obot(tc_fun(U_7568,tc_HOL_Obool))
        | ! [U_7566] : ~ hBOOL(hAPP(hAPP(c_member(U_7568),U_7566),U_7569)) ) ),
    inference(variable_rename,[status(thm)],[f_2206_1]) ).

fof(f_2206_3,plain,
    ( ! [U_7573,U_7571] :
        ( ? [U_7567] : hBOOL(hAPP(hAPP(c_member(U_7571),U_7567),U_7573))
        | U_7573 = c_Orderings_Obot__class_Obot(tc_fun(U_7571,tc_HOL_Obool)) )
    & ! [U_7572,U_7570] :
        ( U_7572 != c_Orderings_Obot__class_Obot(tc_fun(U_7570,tc_HOL_Obool))
        | ! [U_7566] : ~ hBOOL(hAPP(hAPP(c_member(U_7570),U_7566),U_7572)) ) ),
    inference(miniscope,[status(thm)],[f_2206_2]) ).

fof(f_2206_4,plain,
    ( ! [U_7573,U_7571] :
        ( hBOOL(hAPP(hAPP(c_member(U_7571),sK113(U_7573,U_7571)),U_7573))
        | U_7573 = c_Orderings_Obot__class_Obot(tc_fun(U_7571,tc_HOL_Obool)) )
    & ! [U_7572,U_7570] :
        ( U_7572 != c_Orderings_Obot__class_Obot(tc_fun(U_7570,tc_HOL_Obool))
        | ! [U_7566] : ~ hBOOL(hAPP(hAPP(c_member(U_7570),U_7566),U_7572)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_7567,sK113(U_7573,U_7571))],[f_2206_3]) ).

fof(f_2206_5,plain,
    ( ! [U_7571,U_7573] :
        ( hBOOL(hAPP(hAPP(c_member(U_7571),sK113(U_7573,U_7571)),U_7573))
        | U_7573 = c_Orderings_Obot__class_Obot(tc_fun(U_7571,tc_HOL_Obool)) )
    & ! [U_7566,U_7572,U_7570] :
        ( U_7572 != c_Orderings_Obot__class_Obot(tc_fun(U_7570,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7570),U_7566),U_7572)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2206_4]) ).

cnf(f_2206_6,plain,
    ( U_7572 != c_Orderings_Obot__class_Obot(tc_fun(U_7570,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7570),U_7566),U_7572)) ),
    inference(clausify,[status(thm)],[f_2206_5]) ).

cnf(f_2206_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7571),sK113(U_7573,U_7571)),U_7573))
    | U_7573 = c_Orderings_Obot__class_Obot(tc_fun(U_7571,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2206_5]) ).

fof(f_2207_1,plain,
    ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).

fof(f_2207_2,plain,
    ! [U_7575,U_7574] : ~ hBOOL(hAPP(hAPP(c_member(U_7574),U_7575),c_Orderings_Obot__class_Obot(tc_fun(U_7574,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2207_1]) ).

fof(f_2207_3,plain,
    ! [U_7574,U_7575] : ~ hBOOL(hAPP(hAPP(c_member(U_7574),U_7575),c_Orderings_Obot__class_Obot(tc_fun(U_7574,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2207_2]) ).

cnf(f_2207_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_7574),U_7575),c_Orderings_Obot__class_Obot(tc_fun(U_7574,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2207_3]) ).

fof(f_2208_1,plain,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
          & V_a_2 != V_b_2 ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
        | V_a_2 = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).

fof(f_2208_2,plain,
    ! [U_7579,U_7578,U_7577,U_7576] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7576),U_7577),hAPP(hAPP(c_Set_Oinsert(U_7576),U_7578),U_7579)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_7576),U_7577),U_7579))
          & U_7577 != U_7578 ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7576),U_7577),U_7579))
        | U_7577 = U_7578
        | ~ hBOOL(hAPP(hAPP(c_member(U_7576),U_7577),hAPP(hAPP(c_Set_Oinsert(U_7576),U_7578),U_7579))) ) ),
    inference(variable_rename,[status(thm)],[f_2208_1]) ).

fof(f_2208_3,plain,
    ( ! [U_7587,U_7585,U_7583,U_7581] :
        ( hBOOL(hAPP(hAPP(c_member(U_7581),U_7583),hAPP(hAPP(c_Set_Oinsert(U_7581),U_7585),U_7587)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_7581),U_7583),U_7587))
          & U_7583 != U_7585 ) )
    & ! [U_7586,U_7584,U_7582,U_7580] :
        ( hBOOL(hAPP(hAPP(c_member(U_7580),U_7582),U_7586))
        | U_7582 = U_7584
        | ~ hBOOL(hAPP(hAPP(c_member(U_7580),U_7582),hAPP(hAPP(c_Set_Oinsert(U_7580),U_7584),U_7586))) ) ),
    inference(miniscope,[status(thm)],[f_2208_2]) ).

fof(f_2208_4,plain,
    ( ! [U_7585,U_7583,U_7587,U_7581] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7581),U_7583),U_7587))
        | ~ sP682(U_7585,U_7583,U_7587,U_7581) )
    & ! [U_7585,U_7583,U_7587,U_7581] :
        ( U_7583 != U_7585
        | ~ sP682(U_7585,U_7583,U_7587,U_7581) )
    & ! [U_7585,U_7583,U_7587,U_7581] :
        ( hBOOL(hAPP(hAPP(c_member(U_7581),U_7583),hAPP(hAPP(c_Set_Oinsert(U_7581),U_7585),U_7587)))
        | sP682(U_7585,U_7583,U_7587,U_7581) )
    & ! [U_7582,U_7580,U_7584,U_7586] :
        ( hBOOL(hAPP(hAPP(c_member(U_7580),U_7582),U_7586))
        | U_7582 = U_7584
        | ~ hBOOL(hAPP(hAPP(c_member(U_7580),U_7582),hAPP(hAPP(c_Set_Oinsert(U_7580),U_7584),U_7586))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP682])],[f_2208_3]) ).

cnf(f_2208_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7580),U_7582),U_7586))
    | U_7582 = U_7584
    | ~ hBOOL(hAPP(hAPP(c_member(U_7580),U_7582),hAPP(hAPP(c_Set_Oinsert(U_7580),U_7584),U_7586))) ),
    inference(clausify,[status(thm)],[f_2208_4]) ).

cnf(f_2208_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7581),U_7583),hAPP(hAPP(c_Set_Oinsert(U_7581),U_7585),U_7587)))
    | sP682(U_7585,U_7583,U_7587,U_7581) ),
    inference(clausify,[status(thm)],[f_2208_4]) ).

cnf(f_2208_7,plain,
    ( U_7583 != U_7585
    | ~ sP682(U_7585,U_7583,U_7587,U_7581) ),
    inference(clausify,[status(thm)],[f_2208_4]) ).

cnf(f_2208_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7581),U_7583),U_7587))
    | ~ sP682(U_7585,U_7583,U_7587,U_7581) ),
    inference(clausify,[status(thm)],[f_2208_4]) ).

fof(f_2209_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) ) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).

fof(f_2209_2,plain,
    ! [U_7591,U_7590,U_7589,U_7588] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7590) = hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7591)
          | U_7590 != U_7591 )
        & ( U_7590 = U_7591
          | hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7590) != hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7591) ) )
      | hBOOL(hAPP(hAPP(c_member(U_7588),U_7589),U_7591))
      | hBOOL(hAPP(hAPP(c_member(U_7588),U_7589),U_7590)) ),
    inference(variable_rename,[status(thm)],[f_2209_1]) ).

fof(f_2209_3,plain,
    ( ! [U_7588,U_7589,U_7590,U_7591] :
        ( hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7590) = hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7591)
        | U_7590 != U_7591
        | ~ sP683(U_7588,U_7589,U_7590,U_7591) )
    & ! [U_7588,U_7589,U_7590,U_7591] :
        ( U_7590 = U_7591
        | hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7590) != hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7591)
        | ~ sP683(U_7588,U_7589,U_7590,U_7591) )
    & ! [U_7588,U_7589,U_7590,U_7591] :
        ( sP683(U_7588,U_7589,U_7590,U_7591)
        | hBOOL(hAPP(hAPP(c_member(U_7588),U_7589),U_7591))
        | hBOOL(hAPP(hAPP(c_member(U_7588),U_7589),U_7590)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP683])],[f_2209_2]) ).

cnf(f_2209_4,plain,
    ( sP683(U_7588,U_7589,U_7590,U_7591)
    | hBOOL(hAPP(hAPP(c_member(U_7588),U_7589),U_7591))
    | hBOOL(hAPP(hAPP(c_member(U_7588),U_7589),U_7590)) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

cnf(f_2209_5,plain,
    ( U_7590 = U_7591
    | hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7590) != hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7591)
    | ~ sP683(U_7588,U_7589,U_7590,U_7591) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

cnf(f_2209_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7590) = hAPP(hAPP(c_Set_Oinsert(U_7588),U_7589),U_7591)
    | U_7590 != U_7591
    | ~ sP683(U_7588,U_7589,U_7590,U_7591) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

fof(f_2210_1,plain,
    ! [V_a_2,T_b,V_A_2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_equals0D]) ).

fof(f_2210_2,plain,
    ! [U_7594,U_7593,U_7592] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7594),U_7592))
      | U_7592 != c_Orderings_Obot__class_Obot(tc_fun(U_7593,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2210_1]) ).

fof(f_2210_3,plain,
    ! [U_7592,U_7594,U_7593] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7594),U_7592))
      | U_7592 != c_Orderings_Obot__class_Obot(tc_fun(U_7593,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2210_2]) ).

cnf(f_2210_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7593),U_7594),U_7592))
    | U_7592 != c_Orderings_Obot__class_Obot(tc_fun(U_7593,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

fof(f_2211_1,plain,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insertI2]) ).

fof(f_2211_2,plain,
    ! [U_7598,U_7597,U_7596,U_7595] :
      ( hBOOL(hAPP(hAPP(c_member(U_7595),U_7596),hAPP(hAPP(c_Set_Oinsert(U_7595),U_7598),U_7597)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7595),U_7596),U_7597)) ),
    inference(variable_rename,[status(thm)],[f_2211_1]) ).

fof(f_2211_3,plain,
    ! [U_7595,U_7596,U_7597,U_7598] :
      ( hBOOL(hAPP(hAPP(c_member(U_7595),U_7596),hAPP(hAPP(c_Set_Oinsert(U_7595),U_7598),U_7597)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7595),U_7596),U_7597)) ),
    inference(definitional_conversion,[status(esa)],[f_2211_2]) ).

cnf(f_2211_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7595),U_7596),hAPP(hAPP(c_Set_Oinsert(U_7595),U_7598),U_7597)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7595),U_7596),U_7597)) ),
    inference(clausify,[status(thm)],[f_2211_3]) ).

fof(f_2212_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).

fof(f_2212_2,plain,
    ! [U_7601,U_7600,U_7599] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7599),U_7600),U_7601) = U_7601
      | ~ hBOOL(hAPP(hAPP(c_member(U_7599),U_7600),U_7601)) ),
    inference(variable_rename,[status(thm)],[f_2212_1]) ).

fof(f_2212_3,plain,
    ! [U_7599,U_7600,U_7601] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7599),U_7600),U_7601) = U_7601
      | ~ hBOOL(hAPP(hAPP(c_member(U_7599),U_7600),U_7601)) ),
    inference(definitional_conversion,[status(esa)],[f_2212_2]) ).

cnf(f_2212_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7599),U_7600),U_7601) = U_7601
    | ~ hBOOL(hAPP(hAPP(c_member(U_7599),U_7600),U_7601)) ),
    inference(clausify,[status(thm)],[f_2212_3]) ).

fof(f_2213_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__mp]) ).

fof(f_2213_2,plain,
    ! [U_7605,U_7604,U_7603,U_7602] :
      ( hBOOL(hAPP(hAPP(c_member(U_7602),U_7605),U_7604))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7602),U_7605),U_7603))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7602,tc_HOL_Obool)),U_7603),U_7604)) ),
    inference(variable_rename,[status(thm)],[f_2213_1]) ).

fof(f_2213_3,plain,
    ! [U_7602,U_7603,U_7604,U_7605] :
      ( hBOOL(hAPP(hAPP(c_member(U_7602),U_7605),U_7604))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7602),U_7605),U_7603))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7602,tc_HOL_Obool)),U_7603),U_7604)) ),
    inference(definitional_conversion,[status(esa)],[f_2213_2]) ).

cnf(f_2213_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7602),U_7605),U_7604))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7602),U_7605),U_7603))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7602,tc_HOL_Obool)),U_7603),U_7604)) ),
    inference(clausify,[status(thm)],[f_2213_3]) ).

fof(f_2214_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).

fof(f_2214_2,plain,
    ! [U_7609,U_7608,U_7607,U_7606] :
      ( hBOOL(hAPP(hAPP(c_member(U_7606),U_7607),U_7609))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7606,tc_HOL_Obool)),U_7608),U_7609))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7606),U_7607),U_7608)) ),
    inference(variable_rename,[status(thm)],[f_2214_1]) ).

fof(f_2214_3,plain,
    ! [U_7606,U_7607,U_7608,U_7609] :
      ( hBOOL(hAPP(hAPP(c_member(U_7606),U_7607),U_7609))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7606,tc_HOL_Obool)),U_7608),U_7609))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7606),U_7607),U_7608)) ),
    inference(definitional_conversion,[status(esa)],[f_2214_2]) ).

cnf(f_2214_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7606),U_7607),U_7609))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7606,tc_HOL_Obool)),U_7608),U_7609))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7606),U_7607),U_7608)) ),
    inference(clausify,[status(thm)],[f_2214_3]) ).

fof(f_2215_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_in__mono]) ).

fof(f_2215_2,plain,
    ! [U_7613,U_7612,U_7611,U_7610] :
      ( hBOOL(hAPP(hAPP(c_member(U_7610),U_7613),U_7612))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7610),U_7613),U_7611))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7610,tc_HOL_Obool)),U_7611),U_7612)) ),
    inference(variable_rename,[status(thm)],[f_2215_1]) ).

fof(f_2215_3,plain,
    ! [U_7610,U_7611,U_7612,U_7613] :
      ( hBOOL(hAPP(hAPP(c_member(U_7610),U_7613),U_7612))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7610),U_7613),U_7611))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7610,tc_HOL_Obool)),U_7611),U_7612)) ),
    inference(definitional_conversion,[status(esa)],[f_2215_2]) ).

cnf(f_2215_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7610),U_7613),U_7612))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7610),U_7613),U_7611))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7610,tc_HOL_Obool)),U_7611),U_7612)) ),
    inference(clausify,[status(thm)],[f_2215_3]) ).

fof(f_2216_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).

fof(f_2216_2,plain,
    ! [U_7616,U_7615,U_7614] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7614),U_7615),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7614,tc_HOL_Obool)),U_7616)))
        | hBOOL(hAPP(hAPP(c_member(U_7614),U_7615),U_7616)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_7614),U_7615),U_7616))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7614),U_7615),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7614,tc_HOL_Obool)),U_7616))) ) ),
    inference(variable_rename,[status(thm)],[f_2216_1]) ).

fof(f_2216_3,plain,
    ( ! [U_7622,U_7620,U_7618] :
        ( hBOOL(hAPP(hAPP(c_member(U_7618),U_7620),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7618,tc_HOL_Obool)),U_7622)))
        | hBOOL(hAPP(hAPP(c_member(U_7618),U_7620),U_7622)) )
    & ! [U_7621,U_7619,U_7617] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7619),U_7621))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7617,tc_HOL_Obool)),U_7621))) ) ),
    inference(miniscope,[status(thm)],[f_2216_2]) ).

fof(f_2216_4,plain,
    ( ! [U_7618,U_7620,U_7622] :
        ( hBOOL(hAPP(hAPP(c_member(U_7618),U_7620),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7618,tc_HOL_Obool)),U_7622)))
        | hBOOL(hAPP(hAPP(c_member(U_7618),U_7620),U_7622)) )
    & ! [U_7621,U_7619,U_7617] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7619),U_7621))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7617,tc_HOL_Obool)),U_7621))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2216_3]) ).

cnf(f_2216_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7619),U_7621))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7617,tc_HOL_Obool)),U_7621))) ),
    inference(clausify,[status(thm)],[f_2216_4]) ).

cnf(f_2216_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7618),U_7620),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7618,tc_HOL_Obool)),U_7622)))
    | hBOOL(hAPP(hAPP(c_member(U_7618),U_7620),U_7622)) ),
    inference(clausify,[status(thm)],[f_2216_4]) ).

fof(f_2217_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ComplD]) ).

fof(f_2217_2,plain,
    ! [U_7625,U_7624,U_7623] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7624),U_7625))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7624),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7623,tc_HOL_Obool)),U_7625))) ),
    inference(variable_rename,[status(thm)],[f_2217_1]) ).

fof(f_2217_3,plain,
    ! [U_7623,U_7624,U_7625] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7624),U_7625))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7624),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7623,tc_HOL_Obool)),U_7625))) ),
    inference(definitional_conversion,[status(esa)],[f_2217_2]) ).

cnf(f_2217_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7624),U_7625))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7624),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7623,tc_HOL_Obool)),U_7625))) ),
    inference(clausify,[status(thm)],[f_2217_3]) ).

fof(f_2218_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ComplE]) ).

fof(f_2218_2,plain,
    ! [U_7628,U_7627,U_7626] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7626),U_7627),U_7628))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7626),U_7627),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7626,tc_HOL_Obool)),U_7628))) ),
    inference(variable_rename,[status(thm)],[f_2218_1]) ).

fof(f_2218_3,plain,
    ! [U_7626,U_7627,U_7628] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7626),U_7627),U_7628))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7626),U_7627),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7626,tc_HOL_Obool)),U_7628))) ),
    inference(definitional_conversion,[status(esa)],[f_2218_2]) ).

cnf(f_2218_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7626),U_7627),U_7628))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7626),U_7627),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7626,tc_HOL_Obool)),U_7628))) ),
    inference(clausify,[status(thm)],[f_2218_3]) ).

fof(f_2219_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__iff]) ).

fof(f_2219_2,plain,
    ! [U_7632,U_7631,U_7630,U_7629] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7629),U_7630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7629,tc_HOL_Obool)),U_7631),U_7632)))
        | hBOOL(hAPP(hAPP(c_member(U_7629),U_7630),U_7632))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7629),U_7630),U_7631)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7629),U_7630),U_7632))
          & hBOOL(hAPP(hAPP(c_member(U_7629),U_7630),U_7631)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_7629),U_7630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7629,tc_HOL_Obool)),U_7631),U_7632))) ) ),
    inference(variable_rename,[status(thm)],[f_2219_1]) ).

fof(f_2219_3,plain,
    ( ! [U_7640,U_7638,U_7636,U_7634] :
        ( hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7634,tc_HOL_Obool)),U_7638),U_7640)))
        | hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),U_7640))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),U_7638)) )
    & ! [U_7639,U_7637,U_7635,U_7633] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),U_7639))
          & hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),U_7637)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7633,tc_HOL_Obool)),U_7637),U_7639))) ) ),
    inference(miniscope,[status(thm)],[f_2219_2]) ).

fof(f_2219_4,plain,
    ( ! [U_7633,U_7635,U_7639,U_7637] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),U_7639))
        | ~ sP684(U_7633,U_7635,U_7639,U_7637) )
    & ! [U_7633,U_7635,U_7639,U_7637] :
        ( hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),U_7637))
        | ~ sP684(U_7633,U_7635,U_7639,U_7637) )
    & ! [U_7636,U_7634,U_7640,U_7638] :
        ( hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7634,tc_HOL_Obool)),U_7638),U_7640)))
        | hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),U_7640))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),U_7638)) )
    & ! [U_7633,U_7635,U_7639,U_7637] :
        ( sP684(U_7633,U_7635,U_7639,U_7637)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7633,tc_HOL_Obool)),U_7637),U_7639))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP684])],[f_2219_3]) ).

cnf(f_2219_5,plain,
    ( sP684(U_7633,U_7635,U_7639,U_7637)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7633,tc_HOL_Obool)),U_7637),U_7639))) ),
    inference(clausify,[status(thm)],[f_2219_4]) ).

cnf(f_2219_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7634,tc_HOL_Obool)),U_7638),U_7640)))
    | hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),U_7640))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7634),U_7636),U_7638)) ),
    inference(clausify,[status(thm)],[f_2219_4]) ).

cnf(f_2219_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),U_7637))
    | ~ sP684(U_7633,U_7635,U_7639,U_7637) ),
    inference(clausify,[status(thm)],[f_2219_4]) ).

cnf(f_2219_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7633),U_7635),U_7639))
    | ~ sP684(U_7633,U_7635,U_7639,U_7637) ),
    inference(clausify,[status(thm)],[f_2219_4]) ).

fof(f_2220_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffD1]) ).

fof(f_2220_2,plain,
    ! [U_7644,U_7643,U_7642,U_7641] :
      ( hBOOL(hAPP(hAPP(c_member(U_7641),U_7642),U_7643))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7641),U_7642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7641,tc_HOL_Obool)),U_7643),U_7644))) ),
    inference(variable_rename,[status(thm)],[f_2220_1]) ).

fof(f_2220_3,plain,
    ! [U_7642,U_7644,U_7641,U_7643] :
      ( hBOOL(hAPP(hAPP(c_member(U_7641),U_7642),U_7643))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7641),U_7642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7641,tc_HOL_Obool)),U_7643),U_7644))) ),
    inference(definitional_conversion,[status(esa)],[f_2220_2]) ).

cnf(f_2220_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7641),U_7642),U_7643))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7641),U_7642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7641,tc_HOL_Obool)),U_7643),U_7644))) ),
    inference(clausify,[status(thm)],[f_2220_3]) ).

fof(f_2221_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffD2]) ).

fof(f_2221_2,plain,
    ! [U_7648,U_7647,U_7646,U_7645] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7646),U_7648))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7645,tc_HOL_Obool)),U_7647),U_7648))) ),
    inference(variable_rename,[status(thm)],[f_2221_1]) ).

fof(f_2221_3,plain,
    ! [U_7645,U_7646,U_7647,U_7648] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7646),U_7648))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7645,tc_HOL_Obool)),U_7647),U_7648))) ),
    inference(definitional_conversion,[status(esa)],[f_2221_2]) ).

cnf(f_2221_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7646),U_7648))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7645,tc_HOL_Obool)),U_7647),U_7648))) ),
    inference(clausify,[status(thm)],[f_2221_3]) ).

fof(f_2222_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | ~ hBOOL(hAPP(V_A_2,V_x_2)) )
      & ( hBOOL(hAPP(V_A_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__def]) ).

fof(f_2222_2,plain,
    ! [U_7651,U_7650,U_7649] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7649),U_7650),U_7651))
        | ~ hBOOL(hAPP(U_7651,U_7650)) )
      & ( hBOOL(hAPP(U_7651,U_7650))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7649),U_7650),U_7651)) ) ),
    inference(variable_rename,[status(thm)],[f_2222_1]) ).

fof(f_2222_3,plain,
    ( ! [U_7657,U_7655] :
        ( ! [U_7653] : hBOOL(hAPP(hAPP(c_member(U_7653),U_7655),U_7657))
        | ~ hBOOL(hAPP(U_7657,U_7655)) )
    & ! [U_7656,U_7654] :
        ( ! [U_7652] : ~ hBOOL(hAPP(hAPP(c_member(U_7652),U_7654),U_7656))
        | hBOOL(hAPP(U_7656,U_7654)) ) ),
    inference(miniscope,[status(thm)],[f_2222_2]) ).

fof(f_2222_4,plain,
    ( ! [U_7657,U_7653,U_7655] :
        ( hBOOL(hAPP(hAPP(c_member(U_7653),U_7655),U_7657))
        | ~ hBOOL(hAPP(U_7657,U_7655)) )
    & ! [U_7656,U_7654,U_7652] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7652),U_7654),U_7656))
        | hBOOL(hAPP(U_7656,U_7654)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2222_3]) ).

cnf(f_2222_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7652),U_7654),U_7656))
    | hBOOL(hAPP(U_7656,U_7654)) ),
    inference(clausify,[status(thm)],[f_2222_4]) ).

cnf(f_2222_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7653),U_7655),U_7657))
    | ~ hBOOL(hAPP(U_7657,U_7655)) ),
    inference(clausify,[status(thm)],[f_2222_4]) ).

fof(f_2223_1,plain,
    ! [V_x_2,T_b,V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).

fof(f_2223_2,plain,
    ! [U_7661,U_7660,U_7659,U_7658] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7658))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7659)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7659))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7658)) ) )
      | U_7658 != U_7659 ),
    inference(variable_rename,[status(thm)],[f_2223_1]) ).

fof(f_2223_3,plain,
    ( ! [U_7658,U_7659,U_7660,U_7661] :
        ( hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7658))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7659))
        | ~ sP685(U_7658,U_7659,U_7660,U_7661) )
    & ! [U_7658,U_7659,U_7660,U_7661] :
        ( hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7659))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7658))
        | ~ sP685(U_7658,U_7659,U_7660,U_7661) )
    & ! [U_7658,U_7659,U_7660,U_7661] :
        ( sP685(U_7658,U_7659,U_7660,U_7661)
        | U_7658 != U_7659 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP685])],[f_2223_2]) ).

cnf(f_2223_4,plain,
    ( sP685(U_7658,U_7659,U_7660,U_7661)
    | U_7658 != U_7659 ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

cnf(f_2223_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7659))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7658))
    | ~ sP685(U_7658,U_7659,U_7660,U_7661) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

cnf(f_2223_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7658))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7660),U_7661),U_7659))
    | ~ sP685(U_7658,U_7659,U_7660,U_7661) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

fof(f_2224_1,plain,
    ! [V_A_2,T_b,V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | V_x_2 != V_y_2 ),
    inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).

fof(f_2224_2,plain,
    ! [U_7665,U_7664,U_7663,U_7662] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7664),U_7662),U_7665))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7664),U_7663),U_7665)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_7664),U_7663),U_7665))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7664),U_7662),U_7665)) ) )
      | U_7662 != U_7663 ),
    inference(variable_rename,[status(thm)],[f_2224_1]) ).

fof(f_2224_3,plain,
    ( ! [U_7665,U_7663,U_7662,U_7664] :
        ( hBOOL(hAPP(hAPP(c_member(U_7664),U_7662),U_7665))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7664),U_7663),U_7665))
        | ~ sP686(U_7665,U_7663,U_7662,U_7664) )
    & ! [U_7665,U_7663,U_7662,U_7664] :
        ( hBOOL(hAPP(hAPP(c_member(U_7664),U_7663),U_7665))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7664),U_7662),U_7665))
        | ~ sP686(U_7665,U_7663,U_7662,U_7664) )
    & ! [U_7665,U_7663,U_7662,U_7664] :
        ( sP686(U_7665,U_7663,U_7662,U_7664)
        | U_7662 != U_7663 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP686])],[f_2224_2]) ).

cnf(f_2224_4,plain,
    ( sP686(U_7665,U_7663,U_7662,U_7664)
    | U_7662 != U_7663 ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

cnf(f_2224_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7664),U_7663),U_7665))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7664),U_7662),U_7665))
    | ~ sP686(U_7665,U_7663,U_7662,U_7664) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

cnf(f_2224_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7664),U_7662),U_7665))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7664),U_7663),U_7665))
    | ~ sP686(U_7665,U_7663,U_7662,U_7664) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

fof(f_2225_1,plain,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).

fof(f_2225_2,plain,
    ! [U_7669,U_7668,U_7667,U_7666] :
      ( hBOOL(hAPP(hAPP(c_member(U_7668),U_7666),U_7669))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7668),U_7667),U_7669))
      | U_7666 != U_7667 ),
    inference(variable_rename,[status(thm)],[f_2225_1]) ).

fof(f_2225_3,plain,
    ! [U_7667,U_7666,U_7668,U_7669] :
      ( hBOOL(hAPP(hAPP(c_member(U_7668),U_7666),U_7669))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7668),U_7667),U_7669))
      | U_7666 != U_7667 ),
    inference(definitional_conversion,[status(esa)],[f_2225_2]) ).

cnf(f_2225_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7668),U_7666),U_7669))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7668),U_7667),U_7669))
    | U_7666 != U_7667 ),
    inference(clausify,[status(thm)],[f_2225_3]) ).

fof(f_2226_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
        | V_R_2 != V_S_2 )
      & ( V_R_2 = V_S_2
        | hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) != hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).

fof(f_2226_2,plain,
    ! [U_7672,U_7671,U_7670] :
      ( ( hAPP(hAPP(c_COMBC(U_7670,tc_fun(U_7670,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7670)),U_7671) = hAPP(hAPP(c_COMBC(U_7670,tc_fun(U_7670,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7670)),U_7672)
        | U_7671 != U_7672 )
      & ( U_7671 = U_7672
        | hAPP(hAPP(c_COMBC(U_7670,tc_fun(U_7670,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7670)),U_7671) != hAPP(hAPP(c_COMBC(U_7670,tc_fun(U_7670,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7670)),U_7672) ) ),
    inference(variable_rename,[status(thm)],[f_2226_1]) ).

fof(f_2226_3,plain,
    ( ! [U_7678,U_7676] :
        ( ! [U_7674] : hAPP(hAPP(c_COMBC(U_7674,tc_fun(U_7674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7674)),U_7676) = hAPP(hAPP(c_COMBC(U_7674,tc_fun(U_7674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7674)),U_7678)
        | U_7676 != U_7678 )
    & ! [U_7677,U_7675] :
        ( ! [U_7673] : hAPP(hAPP(c_COMBC(U_7673,tc_fun(U_7673,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7673)),U_7675) != hAPP(hAPP(c_COMBC(U_7673,tc_fun(U_7673,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7673)),U_7677)
        | U_7675 = U_7677 ) ),
    inference(miniscope,[status(thm)],[f_2226_2]) ).

fof(f_2226_4,plain,
    ( ! [U_7674,U_7678,U_7676] :
        ( hAPP(hAPP(c_COMBC(U_7674,tc_fun(U_7674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7674)),U_7676) = hAPP(hAPP(c_COMBC(U_7674,tc_fun(U_7674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7674)),U_7678)
        | U_7676 != U_7678 )
    & ! [U_7675,U_7673,U_7677] :
        ( hAPP(hAPP(c_COMBC(U_7673,tc_fun(U_7673,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7673)),U_7675) != hAPP(hAPP(c_COMBC(U_7673,tc_fun(U_7673,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7673)),U_7677)
        | U_7675 = U_7677 ) ),
    inference(definitional_conversion,[status(esa)],[f_2226_3]) ).

cnf(f_2226_5,plain,
    ( hAPP(hAPP(c_COMBC(U_7673,tc_fun(U_7673,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7673)),U_7675) != hAPP(hAPP(c_COMBC(U_7673,tc_fun(U_7673,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7673)),U_7677)
    | U_7675 = U_7677 ),
    inference(clausify,[status(thm)],[f_2226_4]) ).

cnf(f_2226_6,plain,
    ( hAPP(hAPP(c_COMBC(U_7674,tc_fun(U_7674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7674)),U_7676) = hAPP(hAPP(c_COMBC(U_7674,tc_fun(U_7674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7674)),U_7678)
    | U_7676 != U_7678 ),
    inference(clausify,[status(thm)],[f_2226_4]) ).

fof(f_2227_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).

fof(f_2227_2,plain,
    ! [U_7681,U_7680,U_7679] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7679),U_7680),hAPP(c_fequal,U_7681)))
        | U_7680 != U_7681 )
      & ( U_7680 = U_7681
        | ~ hBOOL(hAPP(hAPP(c_member(U_7679),U_7680),hAPP(c_fequal,U_7681))) ) ),
    inference(variable_rename,[status(thm)],[f_2227_1]) ).

fof(f_2227_3,plain,
    ( ! [U_7687,U_7685] :
        ( ! [U_7683] : hBOOL(hAPP(hAPP(c_member(U_7683),U_7685),hAPP(c_fequal,U_7687)))
        | U_7685 != U_7687 )
    & ! [U_7686,U_7684] :
        ( ! [U_7682] : ~ hBOOL(hAPP(hAPP(c_member(U_7682),U_7684),hAPP(c_fequal,U_7686)))
        | U_7684 = U_7686 ) ),
    inference(miniscope,[status(thm)],[f_2227_2]) ).

fof(f_2227_4,plain,
    ( ! [U_7687,U_7683,U_7685] :
        ( hBOOL(hAPP(hAPP(c_member(U_7683),U_7685),hAPP(c_fequal,U_7687)))
        | U_7685 != U_7687 )
    & ! [U_7686,U_7682,U_7684] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7682),U_7684),hAPP(c_fequal,U_7686)))
        | U_7684 = U_7686 ) ),
    inference(definitional_conversion,[status(esa)],[f_2227_3]) ).

cnf(f_2227_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7682),U_7684),hAPP(c_fequal,U_7686)))
    | U_7684 = U_7686 ),
    inference(clausify,[status(thm)],[f_2227_4]) ).

cnf(f_2227_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7683),U_7685),hAPP(c_fequal,U_7687)))
    | U_7685 != U_7687 ),
    inference(clausify,[status(thm)],[f_2227_4]) ).

fof(f_2228_1,plain,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).

fof(f_2228_2,plain,
    ! [U_7691,U_7690,U_7689,U_7688] :
      ( hBOOL(hAPP(hAPP(c_member(U_7688),U_7691),U_7690))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7688),U_7691),U_7689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7688,tc_HOL_Obool)),U_7689),U_7690)) ),
    inference(variable_rename,[status(thm)],[f_2228_1]) ).

fof(f_2228_3,plain,
    ! [U_7688,U_7689,U_7690,U_7691] :
      ( hBOOL(hAPP(hAPP(c_member(U_7688),U_7691),U_7690))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7688),U_7691),U_7689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7688,tc_HOL_Obool)),U_7689),U_7690)) ),
    inference(definitional_conversion,[status(esa)],[f_2228_2]) ).

cnf(f_2228_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7688),U_7691),U_7690))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7688),U_7691),U_7689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7688,tc_HOL_Obool)),U_7689),U_7690)) ),
    inference(clausify,[status(thm)],[f_2228_3]) ).

fof(f_2229_1,plain,
    ! [V_x_2,T_b] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_bot__empty__eq]) ).

fof(f_2229_2,plain,
    ! [U_7693,U_7692] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7692,tc_HOL_Obool)),U_7693))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7692),U_7693),c_Orderings_Obot__class_Obot(tc_fun(U_7692,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7692),U_7693),c_Orderings_Obot__class_Obot(tc_fun(U_7692,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7692,tc_HOL_Obool)),U_7693)) ) ),
    inference(variable_rename,[status(thm)],[f_2229_1]) ).

fof(f_2229_3,plain,
    ( ! [U_7697,U_7695] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7695,tc_HOL_Obool)),U_7697))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7695),U_7697),c_Orderings_Obot__class_Obot(tc_fun(U_7695,tc_HOL_Obool)))) )
    & ! [U_7696,U_7694] :
        ( hBOOL(hAPP(hAPP(c_member(U_7694),U_7696),c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool)),U_7696)) ) ),
    inference(miniscope,[status(thm)],[f_2229_2]) ).

fof(f_2229_4,plain,
    ( ! [U_7695,U_7697] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7695,tc_HOL_Obool)),U_7697))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7695),U_7697),c_Orderings_Obot__class_Obot(tc_fun(U_7695,tc_HOL_Obool)))) )
    & ! [U_7696,U_7694] :
        ( hBOOL(hAPP(hAPP(c_member(U_7694),U_7696),c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool)),U_7696)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2229_3]) ).

cnf(f_2229_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7694),U_7696),c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool)),U_7696)) ),
    inference(clausify,[status(thm)],[f_2229_4]) ).

cnf(f_2229_6,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7695,tc_HOL_Obool)),U_7697))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7695),U_7697),c_Orderings_Obot__class_Obot(tc_fun(U_7695,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2229_4]) ).

fof(f_2230_1,plain,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
        | V_R_2 != V_S_2 )
      & ( V_R_2 = V_S_2
        | hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) != hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).

fof(f_2230_2,plain,
    ! [U_7701,U_7700,U_7699,U_7698] :
      ( ( hAPP(hAPP(c_COMBC(U_7698,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),U_7698),c_COMBC(U_7699,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_prod(U_7698,U_7699)),tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),U_7698),hAPP(c_COMBB(tc_prod(U_7698,U_7699),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool),U_7699),c_member(tc_prod(U_7698,U_7699)))),c_Product__Type_OPair(U_7698,U_7699)))),U_7700) = hAPP(hAPP(c_COMBC(U_7698,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),U_7698),c_COMBC(U_7699,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_prod(U_7698,U_7699)),tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),U_7698),hAPP(c_COMBB(tc_prod(U_7698,U_7699),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool),U_7699),c_member(tc_prod(U_7698,U_7699)))),c_Product__Type_OPair(U_7698,U_7699)))),U_7701)
        | U_7700 != U_7701 )
      & ( U_7700 = U_7701
        | hAPP(hAPP(c_COMBC(U_7698,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),U_7698),c_COMBC(U_7699,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_prod(U_7698,U_7699)),tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),U_7698),hAPP(c_COMBB(tc_prod(U_7698,U_7699),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool),U_7699),c_member(tc_prod(U_7698,U_7699)))),c_Product__Type_OPair(U_7698,U_7699)))),U_7700) != hAPP(hAPP(c_COMBC(U_7698,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_fun(U_7699,tc_HOL_Obool)),U_7698),c_COMBC(U_7699,tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7699,tc_prod(U_7698,U_7699)),tc_fun(U_7699,tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool)),U_7698),hAPP(c_COMBB(tc_prod(U_7698,U_7699),tc_fun(tc_fun(tc_prod(U_7698,U_7699),tc_HOL_Obool),tc_HOL_Obool),U_7699),c_member(tc_prod(U_7698,U_7699)))),c_Product__Type_OPair(U_7698,U_7699)))),U_7701) ) ),
    inference(variable_rename,[status(thm)],[f_2230_1]) ).

fof(f_2230_3,plain,
    ( ! [U_7709,U_7707] :
        ( ! [U_7705,U_7703] : hAPP(hAPP(c_COMBC(U_7703,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),U_7703),c_COMBC(U_7705,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_prod(U_7703,U_7705)),tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),U_7703),hAPP(c_COMBB(tc_prod(U_7703,U_7705),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool),U_7705),c_member(tc_prod(U_7703,U_7705)))),c_Product__Type_OPair(U_7703,U_7705)))),U_7707) = hAPP(hAPP(c_COMBC(U_7703,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),U_7703),c_COMBC(U_7705,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_prod(U_7703,U_7705)),tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),U_7703),hAPP(c_COMBB(tc_prod(U_7703,U_7705),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool),U_7705),c_member(tc_prod(U_7703,U_7705)))),c_Product__Type_OPair(U_7703,U_7705)))),U_7709)
        | U_7707 != U_7709 )
    & ! [U_7708,U_7706] :
        ( ! [U_7704,U_7702] : hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),U_7702),c_COMBC(U_7704,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_prod(U_7702,U_7704)),tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7702,U_7704),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool),U_7704),c_member(tc_prod(U_7702,U_7704)))),c_Product__Type_OPair(U_7702,U_7704)))),U_7706) != hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),U_7702),c_COMBC(U_7704,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_prod(U_7702,U_7704)),tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7702,U_7704),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool),U_7704),c_member(tc_prod(U_7702,U_7704)))),c_Product__Type_OPair(U_7702,U_7704)))),U_7708)
        | U_7706 = U_7708 ) ),
    inference(miniscope,[status(thm)],[f_2230_2]) ).

fof(f_2230_4,plain,
    ( ! [U_7707,U_7709,U_7703,U_7705] :
        ( hAPP(hAPP(c_COMBC(U_7703,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),U_7703),c_COMBC(U_7705,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_prod(U_7703,U_7705)),tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),U_7703),hAPP(c_COMBB(tc_prod(U_7703,U_7705),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool),U_7705),c_member(tc_prod(U_7703,U_7705)))),c_Product__Type_OPair(U_7703,U_7705)))),U_7707) = hAPP(hAPP(c_COMBC(U_7703,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),U_7703),c_COMBC(U_7705,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_prod(U_7703,U_7705)),tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),U_7703),hAPP(c_COMBB(tc_prod(U_7703,U_7705),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool),U_7705),c_member(tc_prod(U_7703,U_7705)))),c_Product__Type_OPair(U_7703,U_7705)))),U_7709)
        | U_7707 != U_7709 )
    & ! [U_7706,U_7704,U_7702,U_7708] :
        ( hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),U_7702),c_COMBC(U_7704,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_prod(U_7702,U_7704)),tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7702,U_7704),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool),U_7704),c_member(tc_prod(U_7702,U_7704)))),c_Product__Type_OPair(U_7702,U_7704)))),U_7706) != hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),U_7702),c_COMBC(U_7704,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_prod(U_7702,U_7704)),tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7702,U_7704),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool),U_7704),c_member(tc_prod(U_7702,U_7704)))),c_Product__Type_OPair(U_7702,U_7704)))),U_7708)
        | U_7706 = U_7708 ) ),
    inference(definitional_conversion,[status(esa)],[f_2230_3]) ).

cnf(f_2230_5,plain,
    ( hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),U_7702),c_COMBC(U_7704,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_prod(U_7702,U_7704)),tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7702,U_7704),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool),U_7704),c_member(tc_prod(U_7702,U_7704)))),c_Product__Type_OPair(U_7702,U_7704)))),U_7706) != hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_fun(U_7704,tc_HOL_Obool)),U_7702),c_COMBC(U_7704,tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7704,tc_prod(U_7702,U_7704)),tc_fun(U_7704,tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7702,U_7704),tc_fun(tc_fun(tc_prod(U_7702,U_7704),tc_HOL_Obool),tc_HOL_Obool),U_7704),c_member(tc_prod(U_7702,U_7704)))),c_Product__Type_OPair(U_7702,U_7704)))),U_7708)
    | U_7706 = U_7708 ),
    inference(clausify,[status(thm)],[f_2230_4]) ).

cnf(f_2230_6,plain,
    ( hAPP(hAPP(c_COMBC(U_7703,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),U_7703),c_COMBC(U_7705,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_prod(U_7703,U_7705)),tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),U_7703),hAPP(c_COMBB(tc_prod(U_7703,U_7705),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool),U_7705),c_member(tc_prod(U_7703,U_7705)))),c_Product__Type_OPair(U_7703,U_7705)))),U_7707) = hAPP(hAPP(c_COMBC(U_7703,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_fun(U_7705,tc_HOL_Obool)),U_7703),c_COMBC(U_7705,tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7705,tc_prod(U_7703,U_7705)),tc_fun(U_7705,tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool)),U_7703),hAPP(c_COMBB(tc_prod(U_7703,U_7705),tc_fun(tc_fun(tc_prod(U_7703,U_7705),tc_HOL_Obool),tc_HOL_Obool),U_7705),c_member(tc_prod(U_7703,U_7705)))),c_Product__Type_OPair(U_7703,U_7705)))),U_7709)
    | U_7707 != U_7709 ),
    inference(clausify,[status(thm)],[f_2230_4]) ).

fof(f_2231_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2]) ).

fof(f_2231_2,plain,
    ! [U_7713,U_7712,U_7711,U_7710] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7710,tc_fun(U_7711,tc_HOL_Obool))),U_7712),U_7713))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7710,U_7711)),hAPP(hAPP(c_Product__Type_OPair(U_7710,U_7711),U_7712),U_7713)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7710,U_7711),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7710,U_7711)),hAPP(hAPP(c_Product__Type_OPair(U_7710,U_7711),U_7712),U_7713)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7710,U_7711),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7710,tc_fun(U_7711,tc_HOL_Obool))),U_7712),U_7713)) ) ),
    inference(variable_rename,[status(thm)],[f_2231_1]) ).

fof(f_2231_3,plain,
    ( ! [U_7721,U_7719,U_7717,U_7715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7715,tc_fun(U_7717,tc_HOL_Obool))),U_7719),U_7721))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7715,U_7717)),hAPP(hAPP(c_Product__Type_OPair(U_7715,U_7717),U_7719),U_7721)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7715,U_7717),tc_HOL_Obool)))) )
    & ! [U_7720,U_7718,U_7716,U_7714] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7714,U_7716)),hAPP(hAPP(c_Product__Type_OPair(U_7714,U_7716),U_7718),U_7720)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7714,U_7716),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7714,tc_fun(U_7716,tc_HOL_Obool))),U_7718),U_7720)) ) ),
    inference(miniscope,[status(thm)],[f_2231_2]) ).

fof(f_2231_4,plain,
    ( ! [U_7715,U_7717,U_7719,U_7721] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7715,tc_fun(U_7717,tc_HOL_Obool))),U_7719),U_7721))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7715,U_7717)),hAPP(hAPP(c_Product__Type_OPair(U_7715,U_7717),U_7719),U_7721)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7715,U_7717),tc_HOL_Obool)))) )
    & ! [U_7718,U_7716,U_7720,U_7714] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7714,U_7716)),hAPP(hAPP(c_Product__Type_OPair(U_7714,U_7716),U_7718),U_7720)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7714,U_7716),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7714,tc_fun(U_7716,tc_HOL_Obool))),U_7718),U_7720)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2231_3]) ).

cnf(f_2231_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7714,U_7716)),hAPP(hAPP(c_Product__Type_OPair(U_7714,U_7716),U_7718),U_7720)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7714,U_7716),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7714,tc_fun(U_7716,tc_HOL_Obool))),U_7718),U_7720)) ),
    inference(clausify,[status(thm)],[f_2231_4]) ).

cnf(f_2231_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7715,tc_fun(U_7717,tc_HOL_Obool))),U_7719),U_7721))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7715,U_7717)),hAPP(hAPP(c_Product__Type_OPair(U_7715,U_7717),U_7719),U_7721)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7715,U_7717),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2231_4]) ).

fof(f_2232_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).

fof(f_2232_2,plain,
    ! [U_7724,U_7723,U_7722] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7722,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7722,tc_fun(U_7722,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7722)),U_7723)),hAPP(hAPP(c_COMBC(U_7722,tc_fun(U_7722,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7722)),U_7724)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7722,tc_HOL_Obool)),U_7723),U_7724)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7722,tc_HOL_Obool)),U_7723),U_7724))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7722,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7722,tc_fun(U_7722,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7722)),U_7723)),hAPP(hAPP(c_COMBC(U_7722,tc_fun(U_7722,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7722)),U_7724))) ) ),
    inference(variable_rename,[status(thm)],[f_2232_1]) ).

fof(f_2232_3,plain,
    ( ! [U_7730,U_7728,U_7726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7726,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7726,tc_fun(U_7726,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7726)),U_7728)),hAPP(hAPP(c_COMBC(U_7726,tc_fun(U_7726,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7726)),U_7730)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7726,tc_HOL_Obool)),U_7728),U_7730)) )
    & ! [U_7729,U_7727,U_7725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7725,tc_HOL_Obool)),U_7727),U_7729))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7725,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7725,tc_fun(U_7725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7725)),U_7727)),hAPP(hAPP(c_COMBC(U_7725,tc_fun(U_7725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7725)),U_7729))) ) ),
    inference(miniscope,[status(thm)],[f_2232_2]) ).

fof(f_2232_4,plain,
    ( ! [U_7726,U_7728,U_7730] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7726,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7726,tc_fun(U_7726,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7726)),U_7728)),hAPP(hAPP(c_COMBC(U_7726,tc_fun(U_7726,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7726)),U_7730)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7726,tc_HOL_Obool)),U_7728),U_7730)) )
    & ! [U_7727,U_7729,U_7725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7725,tc_HOL_Obool)),U_7727),U_7729))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7725,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7725,tc_fun(U_7725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7725)),U_7727)),hAPP(hAPP(c_COMBC(U_7725,tc_fun(U_7725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7725)),U_7729))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2232_3]) ).

cnf(f_2232_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7725,tc_HOL_Obool)),U_7727),U_7729))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7725,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7725,tc_fun(U_7725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7725)),U_7727)),hAPP(hAPP(c_COMBC(U_7725,tc_fun(U_7725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7725)),U_7729))) ),
    inference(clausify,[status(thm)],[f_2232_4]) ).

cnf(f_2232_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7726,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7726,tc_fun(U_7726,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7726)),U_7728)),hAPP(hAPP(c_COMBC(U_7726,tc_fun(U_7726,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7726)),U_7730)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7726,tc_HOL_Obool)),U_7728),U_7730)) ),
    inference(clausify,[status(thm)],[f_2232_4]) ).

fof(f_2233_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
        | V_b_2 != V_a_2 )
      & ( V_b_2 = V_a_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__iff]) ).

fof(f_2233_2,plain,
    ! [U_7733,U_7732,U_7731] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7731),U_7732),hAPP(hAPP(c_Set_Oinsert(U_7731),U_7733),c_Orderings_Obot__class_Obot(tc_fun(U_7731,tc_HOL_Obool)))))
        | U_7732 != U_7733 )
      & ( U_7732 = U_7733
        | ~ hBOOL(hAPP(hAPP(c_member(U_7731),U_7732),hAPP(hAPP(c_Set_Oinsert(U_7731),U_7733),c_Orderings_Obot__class_Obot(tc_fun(U_7731,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_2233_1]) ).

fof(f_2233_3,plain,
    ( ! [U_7739,U_7737] :
        ( ! [U_7735] : hBOOL(hAPP(hAPP(c_member(U_7735),U_7737),hAPP(hAPP(c_Set_Oinsert(U_7735),U_7739),c_Orderings_Obot__class_Obot(tc_fun(U_7735,tc_HOL_Obool)))))
        | U_7737 != U_7739 )
    & ! [U_7738,U_7736] :
        ( ! [U_7734] : ~ hBOOL(hAPP(hAPP(c_member(U_7734),U_7736),hAPP(hAPP(c_Set_Oinsert(U_7734),U_7738),c_Orderings_Obot__class_Obot(tc_fun(U_7734,tc_HOL_Obool)))))
        | U_7736 = U_7738 ) ),
    inference(miniscope,[status(thm)],[f_2233_2]) ).

fof(f_2233_4,plain,
    ( ! [U_7735,U_7737,U_7739] :
        ( hBOOL(hAPP(hAPP(c_member(U_7735),U_7737),hAPP(hAPP(c_Set_Oinsert(U_7735),U_7739),c_Orderings_Obot__class_Obot(tc_fun(U_7735,tc_HOL_Obool)))))
        | U_7737 != U_7739 )
    & ! [U_7738,U_7734,U_7736] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7734),U_7736),hAPP(hAPP(c_Set_Oinsert(U_7734),U_7738),c_Orderings_Obot__class_Obot(tc_fun(U_7734,tc_HOL_Obool)))))
        | U_7736 = U_7738 ) ),
    inference(definitional_conversion,[status(esa)],[f_2233_3]) ).

cnf(f_2233_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7734),U_7736),hAPP(hAPP(c_Set_Oinsert(U_7734),U_7738),c_Orderings_Obot__class_Obot(tc_fun(U_7734,tc_HOL_Obool)))))
    | U_7736 = U_7738 ),
    inference(clausify,[status(thm)],[f_2233_4]) ).

cnf(f_2233_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7735),U_7737),hAPP(hAPP(c_Set_Oinsert(U_7735),U_7739),c_Orderings_Obot__class_Obot(tc_fun(U_7735,tc_HOL_Obool)))))
    | U_7737 != U_7739 ),
    inference(clausify,[status(thm)],[f_2233_4]) ).

fof(f_2234_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( V_b_2 = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_singletonE]) ).

fof(f_2234_2,plain,
    ! [U_7742,U_7741,U_7740] :
      ( U_7741 = U_7742
      | ~ hBOOL(hAPP(hAPP(c_member(U_7740),U_7741),hAPP(hAPP(c_Set_Oinsert(U_7740),U_7742),c_Orderings_Obot__class_Obot(tc_fun(U_7740,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2234_1]) ).

fof(f_2234_3,plain,
    ! [U_7742,U_7741] :
      ( ! [U_7740] : ~ hBOOL(hAPP(hAPP(c_member(U_7740),U_7741),hAPP(hAPP(c_Set_Oinsert(U_7740),U_7742),c_Orderings_Obot__class_Obot(tc_fun(U_7740,tc_HOL_Obool)))))
      | U_7741 = U_7742 ),
    inference(miniscope,[status(thm)],[f_2234_2]) ).

fof(f_2234_4,plain,
    ! [U_7740,U_7741,U_7742] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7740),U_7741),hAPP(hAPP(c_Set_Oinsert(U_7740),U_7742),c_Orderings_Obot__class_Obot(tc_fun(U_7740,tc_HOL_Obool)))))
      | U_7741 = U_7742 ),
    inference(definitional_conversion,[status(esa)],[f_2234_3]) ).

cnf(f_2234_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7740),U_7741),hAPP(hAPP(c_Set_Oinsert(U_7740),U_7742),c_Orderings_Obot__class_Obot(tc_fun(U_7740,tc_HOL_Obool)))))
    | U_7741 = U_7742 ),
    inference(clausify,[status(thm)],[f_2234_4]) ).

fof(f_2235_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).

fof(f_2235_2,plain,
    ! [U_7746,U_7745,U_7744,U_7743] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7743,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7743),U_7744),U_7745)),U_7746))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7743,tc_HOL_Obool)),U_7745),U_7746))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7743),U_7744),U_7746)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7743,tc_HOL_Obool)),U_7745),U_7746))
          & hBOOL(hAPP(hAPP(c_member(U_7743),U_7744),U_7746)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7743,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7743),U_7744),U_7745)),U_7746)) ) ),
    inference(variable_rename,[status(thm)],[f_2235_1]) ).

fof(f_2235_3,plain,
    ( ! [U_7754,U_7752,U_7750,U_7748] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7748,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7748),U_7750),U_7752)),U_7754))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7748,tc_HOL_Obool)),U_7752),U_7754))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7748),U_7750),U_7754)) )
    & ! [U_7753,U_7751,U_7749,U_7747] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7747,tc_HOL_Obool)),U_7751),U_7753))
          & hBOOL(hAPP(hAPP(c_member(U_7747),U_7749),U_7753)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7747,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7747),U_7749),U_7751)),U_7753)) ) ),
    inference(miniscope,[status(thm)],[f_2235_2]) ).

fof(f_2235_4,plain,
    ( ! [U_7749,U_7747,U_7751,U_7753] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7747,tc_HOL_Obool)),U_7751),U_7753))
        | ~ sP687(U_7749,U_7747,U_7751,U_7753) )
    & ! [U_7749,U_7747,U_7751,U_7753] :
        ( hBOOL(hAPP(hAPP(c_member(U_7747),U_7749),U_7753))
        | ~ sP687(U_7749,U_7747,U_7751,U_7753) )
    & ! [U_7752,U_7748,U_7754,U_7750] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7748,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7748),U_7750),U_7752)),U_7754))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7748,tc_HOL_Obool)),U_7752),U_7754))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7748),U_7750),U_7754)) )
    & ! [U_7749,U_7747,U_7751,U_7753] :
        ( sP687(U_7749,U_7747,U_7751,U_7753)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7747,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7747),U_7749),U_7751)),U_7753)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP687])],[f_2235_3]) ).

cnf(f_2235_5,plain,
    ( sP687(U_7749,U_7747,U_7751,U_7753)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7747,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7747),U_7749),U_7751)),U_7753)) ),
    inference(clausify,[status(thm)],[f_2235_4]) ).

cnf(f_2235_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7748,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7748),U_7750),U_7752)),U_7754))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7748,tc_HOL_Obool)),U_7752),U_7754))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7748),U_7750),U_7754)) ),
    inference(clausify,[status(thm)],[f_2235_4]) ).

cnf(f_2235_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7747),U_7749),U_7753))
    | ~ sP687(U_7749,U_7747,U_7751,U_7753) ),
    inference(clausify,[status(thm)],[f_2235_4]) ).

cnf(f_2235_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7747,tc_HOL_Obool)),U_7751),U_7753))
    | ~ sP687(U_7749,U_7747,U_7751,U_7753) ),
    inference(clausify,[status(thm)],[f_2235_4]) ).

fof(f_2236_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).

fof(f_2236_2,plain,
    ! [U_7758,U_7757,U_7756,U_7755] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),hAPP(hAPP(c_Set_Oinsert(U_7755),U_7756),U_7758)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),U_7758)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),U_7758))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),hAPP(hAPP(c_Set_Oinsert(U_7755),U_7756),U_7758))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_7755),U_7756),U_7757)) ),
    inference(variable_rename,[status(thm)],[f_2236_1]) ).

fof(f_2236_3,plain,
    ( ! [U_7755,U_7756,U_7757,U_7758] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),hAPP(hAPP(c_Set_Oinsert(U_7755),U_7756),U_7758)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),U_7758))
        | ~ sP688(U_7755,U_7756,U_7757,U_7758) )
    & ! [U_7755,U_7756,U_7757,U_7758] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),U_7758))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),hAPP(hAPP(c_Set_Oinsert(U_7755),U_7756),U_7758)))
        | ~ sP688(U_7755,U_7756,U_7757,U_7758) )
    & ! [U_7755,U_7756,U_7757,U_7758] :
        ( sP688(U_7755,U_7756,U_7757,U_7758)
        | hBOOL(hAPP(hAPP(c_member(U_7755),U_7756),U_7757)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP688])],[f_2236_2]) ).

cnf(f_2236_4,plain,
    ( sP688(U_7755,U_7756,U_7757,U_7758)
    | hBOOL(hAPP(hAPP(c_member(U_7755),U_7756),U_7757)) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

cnf(f_2236_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),U_7758))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),hAPP(hAPP(c_Set_Oinsert(U_7755),U_7756),U_7758)))
    | ~ sP688(U_7755,U_7756,U_7757,U_7758) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

cnf(f_2236_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),hAPP(hAPP(c_Set_Oinsert(U_7755),U_7756),U_7758)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7755,tc_HOL_Obool)),U_7757),U_7758))
    | ~ sP688(U_7755,U_7756,U_7757,U_7758) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

fof(f_2237_1,plain,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff__if]) ).

fof(f_2237_2,plain,
    ! [U_7762,U_7761,U_7760,U_7759] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7759,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7759),U_7760),U_7762)),U_7761) = hAPP(hAPP(c_Set_Oinsert(U_7759),U_7760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7759,tc_HOL_Obool)),U_7762),U_7761))
        | hBOOL(hAPP(hAPP(c_member(U_7759),U_7760),U_7761)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7759,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7759),U_7760),U_7762)),U_7761) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7759,tc_HOL_Obool)),U_7762),U_7761)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7759),U_7760),U_7761)) ) ),
    inference(variable_rename,[status(thm)],[f_2237_1]) ).

fof(f_2237_3,plain,
    ( ! [U_7770,U_7768,U_7766,U_7764] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7764,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7764),U_7766),U_7770)),U_7768) = hAPP(hAPP(c_Set_Oinsert(U_7764),U_7766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7764,tc_HOL_Obool)),U_7770),U_7768))
        | hBOOL(hAPP(hAPP(c_member(U_7764),U_7766),U_7768)) )
    & ! [U_7769,U_7767,U_7765,U_7763] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7763,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7763),U_7765),U_7769)),U_7767) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7763,tc_HOL_Obool)),U_7769),U_7767)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7763),U_7765),U_7767)) ) ),
    inference(miniscope,[status(thm)],[f_2237_2]) ).

fof(f_2237_4,plain,
    ( ! [U_7764,U_7766,U_7768,U_7770] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7764,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7764),U_7766),U_7770)),U_7768) = hAPP(hAPP(c_Set_Oinsert(U_7764),U_7766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7764,tc_HOL_Obool)),U_7770),U_7768))
        | hBOOL(hAPP(hAPP(c_member(U_7764),U_7766),U_7768)) )
    & ! [U_7765,U_7767,U_7769,U_7763] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7763,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7763),U_7765),U_7769)),U_7767) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7763,tc_HOL_Obool)),U_7769),U_7767)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7763),U_7765),U_7767)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2237_3]) ).

cnf(f_2237_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7763,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7763),U_7765),U_7769)),U_7767) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7763,tc_HOL_Obool)),U_7769),U_7767)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7763),U_7765),U_7767)) ),
    inference(clausify,[status(thm)],[f_2237_4]) ).

cnf(f_2237_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7764,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7764),U_7766),U_7770)),U_7768) = hAPP(hAPP(c_Set_Oinsert(U_7764),U_7766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7764,tc_HOL_Obool)),U_7770),U_7768))
    | hBOOL(hAPP(hAPP(c_member(U_7764),U_7766),U_7768)) ),
    inference(clausify,[status(thm)],[f_2237_4]) ).

fof(f_2238_1,plain,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff1]) ).

fof(f_2238_2,plain,
    ! [U_7774,U_7773,U_7772,U_7771] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7771,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7771),U_7772),U_7774)),U_7773) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7771,tc_HOL_Obool)),U_7774),U_7773)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7771),U_7772),U_7773)) ),
    inference(variable_rename,[status(thm)],[f_2238_1]) ).

fof(f_2238_3,plain,
    ! [U_7771,U_7772,U_7773,U_7774] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7771,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7771),U_7772),U_7774)),U_7773) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7771,tc_HOL_Obool)),U_7774),U_7773)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7771),U_7772),U_7773)) ),
    inference(definitional_conversion,[status(esa)],[f_2238_2]) ).

cnf(f_2238_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7771,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7771),U_7772),U_7774)),U_7773) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7771,tc_HOL_Obool)),U_7774),U_7773)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7771),U_7772),U_7773)) ),
    inference(clausify,[status(thm)],[f_2238_3]) ).

fof(f_2239_1,plain,
    ! [V_xo_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
        | V_xo_2 != hAPP(c_Option_Ooption_OSome(T_b),V_x_2) )
      & ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_elem__set]) ).

fof(f_2239_2,plain,
    ! [U_7777,U_7776,U_7775] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7775),U_7776),c_Option_Oset(U_7775,U_7777)))
        | U_7777 != hAPP(c_Option_Ooption_OSome(U_7775),U_7776) )
      & ( U_7777 = hAPP(c_Option_Ooption_OSome(U_7775),U_7776)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7775),U_7776),c_Option_Oset(U_7775,U_7777))) ) ),
    inference(variable_rename,[status(thm)],[f_2239_1]) ).

fof(f_2239_3,plain,
    ( ! [U_7783,U_7781,U_7779] :
        ( hBOOL(hAPP(hAPP(c_member(U_7779),U_7781),c_Option_Oset(U_7779,U_7783)))
        | U_7783 != hAPP(c_Option_Ooption_OSome(U_7779),U_7781) )
    & ! [U_7782,U_7780,U_7778] :
        ( U_7782 = hAPP(c_Option_Ooption_OSome(U_7778),U_7780)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7778),U_7780),c_Option_Oset(U_7778,U_7782))) ) ),
    inference(miniscope,[status(thm)],[f_2239_2]) ).

fof(f_2239_4,plain,
    ( ! [U_7779,U_7781,U_7783] :
        ( hBOOL(hAPP(hAPP(c_member(U_7779),U_7781),c_Option_Oset(U_7779,U_7783)))
        | U_7783 != hAPP(c_Option_Ooption_OSome(U_7779),U_7781) )
    & ! [U_7780,U_7778,U_7782] :
        ( U_7782 = hAPP(c_Option_Ooption_OSome(U_7778),U_7780)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7778),U_7780),c_Option_Oset(U_7778,U_7782))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2239_3]) ).

cnf(f_2239_5,plain,
    ( U_7782 = hAPP(c_Option_Ooption_OSome(U_7778),U_7780)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7778),U_7780),c_Option_Oset(U_7778,U_7782))) ),
    inference(clausify,[status(thm)],[f_2239_4]) ).

cnf(f_2239_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7779),U_7781),c_Option_Oset(U_7779,U_7783)))
    | U_7783 != hAPP(c_Option_Ooption_OSome(U_7779),U_7781) ),
    inference(clausify,[status(thm)],[f_2239_4]) ).

fof(f_2240_1,plain,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).

fof(f_2240_2,plain,
    ! [U_7787,U_7786,U_7785,U_7784] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7784,tc_fun(U_7785,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7784,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),U_7784),c_COMBC(U_7785,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_prod(U_7784,U_7785)),tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),U_7784),hAPP(c_COMBB(tc_prod(U_7784,U_7785),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool),U_7785),c_member(tc_prod(U_7784,U_7785)))),c_Product__Type_OPair(U_7784,U_7785)))),U_7786)),hAPP(hAPP(c_COMBC(U_7784,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),U_7784),c_COMBC(U_7785,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_prod(U_7784,U_7785)),tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),U_7784),hAPP(c_COMBB(tc_prod(U_7784,U_7785),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool),U_7785),c_member(tc_prod(U_7784,U_7785)))),c_Product__Type_OPair(U_7784,U_7785)))),U_7787)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool)),U_7786),U_7787)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool)),U_7786),U_7787))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7784,tc_fun(U_7785,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7784,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),U_7784),c_COMBC(U_7785,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_prod(U_7784,U_7785)),tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),U_7784),hAPP(c_COMBB(tc_prod(U_7784,U_7785),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool),U_7785),c_member(tc_prod(U_7784,U_7785)))),c_Product__Type_OPair(U_7784,U_7785)))),U_7786)),hAPP(hAPP(c_COMBC(U_7784,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_fun(U_7785,tc_HOL_Obool)),U_7784),c_COMBC(U_7785,tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7785,tc_prod(U_7784,U_7785)),tc_fun(U_7785,tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool)),U_7784),hAPP(c_COMBB(tc_prod(U_7784,U_7785),tc_fun(tc_fun(tc_prod(U_7784,U_7785),tc_HOL_Obool),tc_HOL_Obool),U_7785),c_member(tc_prod(U_7784,U_7785)))),c_Product__Type_OPair(U_7784,U_7785)))),U_7787))) ) ),
    inference(variable_rename,[status(thm)],[f_2240_1]) ).

fof(f_2240_3,plain,
    ( ! [U_7795,U_7793,U_7791,U_7789] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7789,tc_fun(U_7791,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7789,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),U_7789),c_COMBC(U_7791,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_prod(U_7789,U_7791)),tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),U_7789),hAPP(c_COMBB(tc_prod(U_7789,U_7791),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool),U_7791),c_member(tc_prod(U_7789,U_7791)))),c_Product__Type_OPair(U_7789,U_7791)))),U_7793)),hAPP(hAPP(c_COMBC(U_7789,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),U_7789),c_COMBC(U_7791,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_prod(U_7789,U_7791)),tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),U_7789),hAPP(c_COMBB(tc_prod(U_7789,U_7791),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool),U_7791),c_member(tc_prod(U_7789,U_7791)))),c_Product__Type_OPair(U_7789,U_7791)))),U_7795)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool)),U_7793),U_7795)) )
    & ! [U_7794,U_7792,U_7790,U_7788] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool)),U_7792),U_7794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7788,tc_fun(U_7790,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7788,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),U_7788),c_COMBC(U_7790,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_prod(U_7788,U_7790)),tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),U_7788),hAPP(c_COMBB(tc_prod(U_7788,U_7790),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool),U_7790),c_member(tc_prod(U_7788,U_7790)))),c_Product__Type_OPair(U_7788,U_7790)))),U_7792)),hAPP(hAPP(c_COMBC(U_7788,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),U_7788),c_COMBC(U_7790,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_prod(U_7788,U_7790)),tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),U_7788),hAPP(c_COMBB(tc_prod(U_7788,U_7790),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool),U_7790),c_member(tc_prod(U_7788,U_7790)))),c_Product__Type_OPair(U_7788,U_7790)))),U_7794))) ) ),
    inference(miniscope,[status(thm)],[f_2240_2]) ).

fof(f_2240_4,plain,
    ( ! [U_7789,U_7791,U_7793,U_7795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7789,tc_fun(U_7791,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7789,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),U_7789),c_COMBC(U_7791,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_prod(U_7789,U_7791)),tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),U_7789),hAPP(c_COMBB(tc_prod(U_7789,U_7791),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool),U_7791),c_member(tc_prod(U_7789,U_7791)))),c_Product__Type_OPair(U_7789,U_7791)))),U_7793)),hAPP(hAPP(c_COMBC(U_7789,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),U_7789),c_COMBC(U_7791,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_prod(U_7789,U_7791)),tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),U_7789),hAPP(c_COMBB(tc_prod(U_7789,U_7791),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool),U_7791),c_member(tc_prod(U_7789,U_7791)))),c_Product__Type_OPair(U_7789,U_7791)))),U_7795)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool)),U_7793),U_7795)) )
    & ! [U_7790,U_7794,U_7792,U_7788] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool)),U_7792),U_7794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7788,tc_fun(U_7790,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7788,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),U_7788),c_COMBC(U_7790,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_prod(U_7788,U_7790)),tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),U_7788),hAPP(c_COMBB(tc_prod(U_7788,U_7790),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool),U_7790),c_member(tc_prod(U_7788,U_7790)))),c_Product__Type_OPair(U_7788,U_7790)))),U_7792)),hAPP(hAPP(c_COMBC(U_7788,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),U_7788),c_COMBC(U_7790,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_prod(U_7788,U_7790)),tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),U_7788),hAPP(c_COMBB(tc_prod(U_7788,U_7790),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool),U_7790),c_member(tc_prod(U_7788,U_7790)))),c_Product__Type_OPair(U_7788,U_7790)))),U_7794))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2240_3]) ).

cnf(f_2240_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool)),U_7792),U_7794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7788,tc_fun(U_7790,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7788,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),U_7788),c_COMBC(U_7790,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_prod(U_7788,U_7790)),tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),U_7788),hAPP(c_COMBB(tc_prod(U_7788,U_7790),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool),U_7790),c_member(tc_prod(U_7788,U_7790)))),c_Product__Type_OPair(U_7788,U_7790)))),U_7792)),hAPP(hAPP(c_COMBC(U_7788,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_fun(U_7790,tc_HOL_Obool)),U_7788),c_COMBC(U_7790,tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7790,tc_prod(U_7788,U_7790)),tc_fun(U_7790,tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool)),U_7788),hAPP(c_COMBB(tc_prod(U_7788,U_7790),tc_fun(tc_fun(tc_prod(U_7788,U_7790),tc_HOL_Obool),tc_HOL_Obool),U_7790),c_member(tc_prod(U_7788,U_7790)))),c_Product__Type_OPair(U_7788,U_7790)))),U_7794))) ),
    inference(clausify,[status(thm)],[f_2240_4]) ).

cnf(f_2240_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7789,tc_fun(U_7791,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7789,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),U_7789),c_COMBC(U_7791,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_prod(U_7789,U_7791)),tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),U_7789),hAPP(c_COMBB(tc_prod(U_7789,U_7791),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool),U_7791),c_member(tc_prod(U_7789,U_7791)))),c_Product__Type_OPair(U_7789,U_7791)))),U_7793)),hAPP(hAPP(c_COMBC(U_7789,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_fun(U_7791,tc_HOL_Obool)),U_7789),c_COMBC(U_7791,tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7791,tc_prod(U_7789,U_7791)),tc_fun(U_7791,tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool)),U_7789),hAPP(c_COMBB(tc_prod(U_7789,U_7791),tc_fun(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool),tc_HOL_Obool),U_7791),c_member(tc_prod(U_7789,U_7791)))),c_Product__Type_OPair(U_7789,U_7791)))),U_7795)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7789,U_7791),tc_HOL_Obool)),U_7793),U_7795)) ),
    inference(clausify,[status(thm)],[f_2240_4]) ).

fof(f_2241_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(f_2241_2,plain,
    ! [U_7798,U_7797,U_7796] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7796,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7796),U_7797),U_7798)),hAPP(hAPP(c_Set_Oinsert(U_7796),U_7797),c_Orderings_Obot__class_Obot(tc_fun(U_7796,tc_HOL_Obool)))) = U_7798
      | hBOOL(hAPP(hAPP(c_member(U_7796),U_7797),U_7798)) ),
    inference(variable_rename,[status(thm)],[f_2241_1]) ).

fof(f_2241_3,plain,
    ! [U_7796,U_7797,U_7798] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7796,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7796),U_7797),U_7798)),hAPP(hAPP(c_Set_Oinsert(U_7796),U_7797),c_Orderings_Obot__class_Obot(tc_fun(U_7796,tc_HOL_Obool)))) = U_7798
      | hBOOL(hAPP(hAPP(c_member(U_7796),U_7797),U_7798)) ),
    inference(definitional_conversion,[status(esa)],[f_2241_2]) ).

cnf(f_2241_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7796,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7796),U_7797),U_7798)),hAPP(hAPP(c_Set_Oinsert(U_7796),U_7797),c_Orderings_Obot__class_Obot(tc_fun(U_7796,tc_HOL_Obool)))) = U_7798
    | hBOOL(hAPP(hAPP(c_member(U_7796),U_7797),U_7798)) ),
    inference(clausify,[status(thm)],[f_2241_3]) ).

fof(f_2242_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff]) ).

fof(f_2242_2,plain,
    ! [U_7801,U_7800,U_7799] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7799),U_7800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7799,tc_HOL_Obool)),U_7801),hAPP(hAPP(c_Set_Oinsert(U_7799),U_7800),c_Orderings_Obot__class_Obot(tc_fun(U_7799,tc_HOL_Obool))))) = U_7801
      | ~ hBOOL(hAPP(hAPP(c_member(U_7799),U_7800),U_7801)) ),
    inference(variable_rename,[status(thm)],[f_2242_1]) ).

fof(f_2242_3,plain,
    ! [U_7799,U_7800,U_7801] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7799),U_7800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7799,tc_HOL_Obool)),U_7801),hAPP(hAPP(c_Set_Oinsert(U_7799),U_7800),c_Orderings_Obot__class_Obot(tc_fun(U_7799,tc_HOL_Obool))))) = U_7801
      | ~ hBOOL(hAPP(hAPP(c_member(U_7799),U_7800),U_7801)) ),
    inference(definitional_conversion,[status(esa)],[f_2242_2]) ).

cnf(f_2242_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7799),U_7800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7799,tc_HOL_Obool)),U_7801),hAPP(hAPP(c_Set_Oinsert(U_7799),U_7800),c_Orderings_Obot__class_Obot(tc_fun(U_7799,tc_HOL_Obool))))) = U_7801
    | ~ hBOOL(hAPP(hAPP(c_member(U_7799),U_7800),U_7801)) ),
    inference(clausify,[status(thm)],[f_2242_3]) ).

fof(f_2243_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__single__insert]) ).

fof(f_2243_2,plain,
    ! [U_7805,U_7804,U_7803,U_7802] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7802,tc_HOL_Obool)),U_7803),hAPP(hAPP(c_Set_Oinsert(U_7802),U_7804),U_7805)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7802),U_7804),U_7803))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7802,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7802,tc_HOL_Obool)),U_7803),hAPP(hAPP(c_Set_Oinsert(U_7802),U_7804),c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool))))),U_7805)) ),
    inference(variable_rename,[status(thm)],[f_2243_1]) ).

fof(f_2243_3,plain,
    ! [U_7802,U_7803,U_7804,U_7805] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7802,tc_HOL_Obool)),U_7803),hAPP(hAPP(c_Set_Oinsert(U_7802),U_7804),U_7805)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7802),U_7804),U_7803))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7802,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7802,tc_HOL_Obool)),U_7803),hAPP(hAPP(c_Set_Oinsert(U_7802),U_7804),c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool))))),U_7805)) ),
    inference(definitional_conversion,[status(esa)],[f_2243_2]) ).

cnf(f_2243_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7802,tc_HOL_Obool)),U_7803),hAPP(hAPP(c_Set_Oinsert(U_7802),U_7804),U_7805)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7802),U_7804),U_7803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7802,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7802,tc_HOL_Obool)),U_7803),hAPP(hAPP(c_Set_Oinsert(U_7802),U_7804),c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool))))),U_7805)) ),
    inference(clausify,[status(thm)],[f_2243_3]) ).

fof(f_2244_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
            | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insert__iff]) ).

fof(f_2244_2,plain,
    ! [U_7809,U_7808,U_7807,U_7806] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7806,tc_HOL_Obool)),U_7807),hAPP(hAPP(c_Set_Oinsert(U_7806),U_7808),U_7809)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7806,tc_HOL_Obool)),U_7807),U_7809))
          & ~ hBOOL(hAPP(hAPP(c_member(U_7806),U_7808),U_7807)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7806,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7806,tc_HOL_Obool)),U_7807),hAPP(hAPP(c_Set_Oinsert(U_7806),U_7808),c_Orderings_Obot__class_Obot(tc_fun(U_7806,tc_HOL_Obool))))),U_7809))
          & hBOOL(hAPP(hAPP(c_member(U_7806),U_7808),U_7807)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7806,tc_HOL_Obool)),U_7807),U_7809))
            | hBOOL(hAPP(hAPP(c_member(U_7806),U_7808),U_7807)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7806,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7806,tc_HOL_Obool)),U_7807),hAPP(hAPP(c_Set_Oinsert(U_7806),U_7808),c_Orderings_Obot__class_Obot(tc_fun(U_7806,tc_HOL_Obool))))),U_7809))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7806),U_7808),U_7807)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7806,tc_HOL_Obool)),U_7807),hAPP(hAPP(c_Set_Oinsert(U_7806),U_7808),U_7809))) ) ),
    inference(variable_rename,[status(thm)],[f_2244_1]) ).

fof(f_2244_3,plain,
    ( ! [U_7817,U_7815,U_7813,U_7811] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),hAPP(hAPP(c_Set_Oinsert(U_7811),U_7815),U_7817)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),U_7817))
          & ~ hBOOL(hAPP(hAPP(c_member(U_7811),U_7815),U_7813)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7811,tc_HOL_Obool)),U_7813),hAPP(hAPP(c_Set_Oinsert(U_7811),U_7815),c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool))))),U_7817))
          & hBOOL(hAPP(hAPP(c_member(U_7811),U_7815),U_7813)) ) )
    & ! [U_7816,U_7814,U_7812,U_7810] :
        ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),U_7812),U_7816))
            | hBOOL(hAPP(hAPP(c_member(U_7810),U_7814),U_7812)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7810,tc_HOL_Obool)),U_7812),hAPP(hAPP(c_Set_Oinsert(U_7810),U_7814),c_Orderings_Obot__class_Obot(tc_fun(U_7810,tc_HOL_Obool))))),U_7816))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7810),U_7814),U_7812)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),U_7812),hAPP(hAPP(c_Set_Oinsert(U_7810),U_7814),U_7816))) ) ),
    inference(miniscope,[status(thm)],[f_2244_2]) ).

fof(f_2244_4,plain,
    ( ! [U_7811,U_7817,U_7815,U_7813] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),U_7817))
        | ~ sP691(U_7811,U_7817,U_7815,U_7813) )
    & ! [U_7811,U_7817,U_7815,U_7813] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7811),U_7815),U_7813))
        | ~ sP691(U_7811,U_7817,U_7815,U_7813) )
    & ! [U_7811,U_7817,U_7815,U_7813] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7811,tc_HOL_Obool)),U_7813),hAPP(hAPP(c_Set_Oinsert(U_7811),U_7815),c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool))))),U_7817))
        | ~ sP690(U_7811,U_7817,U_7815,U_7813) )
    & ! [U_7811,U_7817,U_7815,U_7813] :
        ( hBOOL(hAPP(hAPP(c_member(U_7811),U_7815),U_7813))
        | ~ sP690(U_7811,U_7817,U_7815,U_7813) )
    & ! [U_7810,U_7812,U_7814,U_7816] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),U_7812),U_7816))
        | hBOOL(hAPP(hAPP(c_member(U_7810),U_7814),U_7812))
        | ~ sP689(U_7810,U_7812,U_7814,U_7816) )
    & ! [U_7810,U_7812,U_7814,U_7816] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7810,tc_HOL_Obool)),U_7812),hAPP(hAPP(c_Set_Oinsert(U_7810),U_7814),c_Orderings_Obot__class_Obot(tc_fun(U_7810,tc_HOL_Obool))))),U_7816))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7810),U_7814),U_7812))
        | ~ sP689(U_7810,U_7812,U_7814,U_7816) )
    & ! [U_7811,U_7817,U_7815,U_7813] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),hAPP(hAPP(c_Set_Oinsert(U_7811),U_7815),U_7817)))
        | sP691(U_7811,U_7817,U_7815,U_7813)
        | sP690(U_7811,U_7817,U_7815,U_7813) )
    & ! [U_7810,U_7812,U_7814,U_7816] :
        ( sP689(U_7810,U_7812,U_7814,U_7816)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),U_7812),hAPP(hAPP(c_Set_Oinsert(U_7810),U_7814),U_7816))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP689,sP690,sP691])],[f_2244_3]) ).

cnf(f_2244_5,plain,
    ( sP689(U_7810,U_7812,U_7814,U_7816)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),U_7812),hAPP(hAPP(c_Set_Oinsert(U_7810),U_7814),U_7816))) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),hAPP(hAPP(c_Set_Oinsert(U_7811),U_7815),U_7817)))
    | sP691(U_7811,U_7817,U_7815,U_7813)
    | sP690(U_7811,U_7817,U_7815,U_7813) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7810,tc_HOL_Obool)),U_7812),hAPP(hAPP(c_Set_Oinsert(U_7810),U_7814),c_Orderings_Obot__class_Obot(tc_fun(U_7810,tc_HOL_Obool))))),U_7816))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7810),U_7814),U_7812))
    | ~ sP689(U_7810,U_7812,U_7814,U_7816) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7810,tc_HOL_Obool)),U_7812),U_7816))
    | hBOOL(hAPP(hAPP(c_member(U_7810),U_7814),U_7812))
    | ~ sP689(U_7810,U_7812,U_7814,U_7816) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7811),U_7815),U_7813))
    | ~ sP690(U_7811,U_7817,U_7815,U_7813) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7811,tc_HOL_Obool)),U_7813),hAPP(hAPP(c_Set_Oinsert(U_7811),U_7815),c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool))))),U_7817))
    | ~ sP690(U_7811,U_7817,U_7815,U_7813) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7811),U_7815),U_7813))
    | ~ sP691(U_7811,U_7817,U_7815,U_7813) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

cnf(f_2244_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),U_7817))
    | ~ sP691(U_7811,U_7817,U_7815,U_7813) ),
    inference(clausify,[status(thm)],[f_2244_4]) ).

fof(f_2245_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).

fof(f_2245_2,plain,
    ! [U_7822,U_7821,U_7820,U_7819,U_7818] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7818,U_7819,U_7820),U_7821),U_7822))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7818,U_7819)),hAPP(hAPP(c_Product__Type_OPair(U_7818,U_7819),U_7821),U_7822)),U_7820)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7818,U_7819)),hAPP(hAPP(c_Product__Type_OPair(U_7818,U_7819),U_7821),U_7822)),U_7820))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7818,U_7819,U_7820),U_7821),U_7822)) ) ),
    inference(variable_rename,[status(thm)],[f_2245_1]) ).

fof(f_2245_3,plain,
    ( ! [U_7832,U_7830,U_7828,U_7826,U_7824] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7824,U_7826,U_7828),U_7830),U_7832))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7824,U_7826)),hAPP(hAPP(c_Product__Type_OPair(U_7824,U_7826),U_7830),U_7832)),U_7828)) )
    & ! [U_7831,U_7829,U_7827,U_7825,U_7823] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7823,U_7825)),hAPP(hAPP(c_Product__Type_OPair(U_7823,U_7825),U_7829),U_7831)),U_7827))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7823,U_7825,U_7827),U_7829),U_7831)) ) ),
    inference(miniscope,[status(thm)],[f_2245_2]) ).

fof(f_2245_4,plain,
    ( ! [U_7826,U_7824,U_7828,U_7830,U_7832] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7824,U_7826,U_7828),U_7830),U_7832))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7824,U_7826)),hAPP(hAPP(c_Product__Type_OPair(U_7824,U_7826),U_7830),U_7832)),U_7828)) )
    & ! [U_7829,U_7825,U_7823,U_7827,U_7831] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7823,U_7825)),hAPP(hAPP(c_Product__Type_OPair(U_7823,U_7825),U_7829),U_7831)),U_7827))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7823,U_7825,U_7827),U_7829),U_7831)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2245_3]) ).

cnf(f_2245_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7823,U_7825)),hAPP(hAPP(c_Product__Type_OPair(U_7823,U_7825),U_7829),U_7831)),U_7827))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7823,U_7825,U_7827),U_7829),U_7831)) ),
    inference(clausify,[status(thm)],[f_2245_4]) ).

cnf(f_2245_6,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7824,U_7826,U_7828),U_7830),U_7832))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7824,U_7826)),hAPP(hAPP(c_Product__Type_OPair(U_7824,U_7826),U_7830),U_7832)),U_7828)) ),
    inference(clausify,[status(thm)],[f_2245_4]) ).

fof(f_2246_1,plain,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2))
      | ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J]) ).

fof(f_2246_2,plain,
    ! [U_7839,U_7838,U_7837,U_7836,U_7835,U_7834,U_7833] :
      ( c_Nitpick_Ofold__graph_H(U_7833,U_7836,U_7837,U_7838,U_7835,hAPP(hAPP(U_7837,U_7834),U_7839))
      | ~ c_Nitpick_Ofold__graph_H(U_7833,U_7836,U_7837,U_7838,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7833,tc_HOL_Obool)),U_7835),hAPP(hAPP(c_Set_Oinsert(U_7833),U_7834),c_Orderings_Obot__class_Obot(tc_fun(U_7833,tc_HOL_Obool)))),U_7839)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7833),U_7834),U_7835)) ),
    inference(variable_rename,[status(thm)],[f_2246_1]) ).

fof(f_2246_3,plain,
    ! [U_7833,U_7834,U_7835,U_7836,U_7837,U_7838,U_7839] :
      ( c_Nitpick_Ofold__graph_H(U_7833,U_7836,U_7837,U_7838,U_7835,hAPP(hAPP(U_7837,U_7834),U_7839))
      | ~ c_Nitpick_Ofold__graph_H(U_7833,U_7836,U_7837,U_7838,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7833,tc_HOL_Obool)),U_7835),hAPP(hAPP(c_Set_Oinsert(U_7833),U_7834),c_Orderings_Obot__class_Obot(tc_fun(U_7833,tc_HOL_Obool)))),U_7839)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7833),U_7834),U_7835)) ),
    inference(definitional_conversion,[status(esa)],[f_2246_2]) ).

cnf(f_2246_4,plain,
    ( c_Nitpick_Ofold__graph_H(U_7833,U_7836,U_7837,U_7838,U_7835,hAPP(hAPP(U_7837,U_7834),U_7839))
    | ~ c_Nitpick_Ofold__graph_H(U_7833,U_7836,U_7837,U_7838,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7833,tc_HOL_Obool)),U_7835),hAPP(hAPP(c_Set_Oinsert(U_7833),U_7834),c_Orderings_Obot__class_Obot(tc_fun(U_7833,tc_HOL_Obool)))),U_7839)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7833),U_7834),U_7835)) ),
    inference(clausify,[status(thm)],[f_2246_3]) ).

fof(f_2247_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Nitpick_Orefl_H(T_b,V_r_2)
        | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
      & ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
        | ~ c_Nitpick_Orefl_H(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).

fof(f_2247_2,plain,
    ! [U_7843,U_7842] :
      ( ( c_Nitpick_Orefl_H(U_7842,U_7843)
        | ? [U_7841] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7842,U_7842)),hAPP(hAPP(c_Product__Type_OPair(U_7842,U_7842),U_7841),U_7841)),U_7843)) )
      & ( ! [U_7840] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7842,U_7842)),hAPP(hAPP(c_Product__Type_OPair(U_7842,U_7842),U_7840),U_7840)),U_7843))
        | ~ c_Nitpick_Orefl_H(U_7842,U_7843) ) ),
    inference(variable_rename,[status(thm)],[f_2247_1]) ).

fof(f_2247_3,plain,
    ( ! [U_7847,U_7845] :
        ( c_Nitpick_Orefl_H(U_7845,U_7847)
        | ? [U_7841] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7845,U_7845)),hAPP(hAPP(c_Product__Type_OPair(U_7845,U_7845),U_7841),U_7841)),U_7847)) )
    & ! [U_7846,U_7844] :
        ( ! [U_7840] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7844,U_7844)),hAPP(hAPP(c_Product__Type_OPair(U_7844,U_7844),U_7840),U_7840)),U_7846))
        | ~ c_Nitpick_Orefl_H(U_7844,U_7846) ) ),
    inference(miniscope,[status(thm)],[f_2247_2]) ).

fof(f_2247_4,plain,
    ( ! [U_7847,U_7845] :
        ( c_Nitpick_Orefl_H(U_7845,U_7847)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7845,U_7845)),hAPP(hAPP(c_Product__Type_OPair(U_7845,U_7845),sK114(U_7847,U_7845)),sK114(U_7847,U_7845))),U_7847)) )
    & ! [U_7846,U_7844] :
        ( ! [U_7840] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7844,U_7844)),hAPP(hAPP(c_Product__Type_OPair(U_7844,U_7844),U_7840),U_7840)),U_7846))
        | ~ c_Nitpick_Orefl_H(U_7844,U_7846) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_7841,sK114(U_7847,U_7845))],[f_2247_3]) ).

fof(f_2247_5,plain,
    ( ! [U_7847,U_7845] :
        ( c_Nitpick_Orefl_H(U_7845,U_7847)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7845,U_7845)),hAPP(hAPP(c_Product__Type_OPair(U_7845,U_7845),sK114(U_7847,U_7845)),sK114(U_7847,U_7845))),U_7847)) )
    & ! [U_7846,U_7840,U_7844] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7844,U_7844)),hAPP(hAPP(c_Product__Type_OPair(U_7844,U_7844),U_7840),U_7840)),U_7846))
        | ~ c_Nitpick_Orefl_H(U_7844,U_7846) ) ),
    inference(definitional_conversion,[status(esa)],[f_2247_4]) ).

cnf(f_2247_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7844,U_7844)),hAPP(hAPP(c_Product__Type_OPair(U_7844,U_7844),U_7840),U_7840)),U_7846))
    | ~ c_Nitpick_Orefl_H(U_7844,U_7846) ),
    inference(clausify,[status(thm)],[f_2247_5]) ).

cnf(f_2247_7,plain,
    ( c_Nitpick_Orefl_H(U_7845,U_7847)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7845,U_7845)),hAPP(hAPP(c_Product__Type_OPair(U_7845,U_7845),sK114(U_7847,U_7845)),sK114(U_7847,U_7845))),U_7847)) ),
    inference(clausify,[status(thm)],[f_2247_5]) ).

fof(f_2248_1,plain,
    ! [V_b_2,V_A_2,T_b] :
      ( ( c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_flat__lub__def]) ).

fof(f_2248_2,plain,
    ! [U_7850,U_7849,U_7848] :
      ( ( c_Partial__Function_Oflat__lub(U_7848,U_7850,U_7849) = c_HOL_OThe(U_7848,hAPP(hAPP(c_COMBC(U_7848,tc_fun(U_7848,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7848)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7848,tc_HOL_Obool)),U_7849),hAPP(hAPP(c_Set_Oinsert(U_7848),U_7850),c_Orderings_Obot__class_Obot(tc_fun(U_7848,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7848,tc_HOL_Obool)),U_7849),hAPP(hAPP(c_Set_Oinsert(U_7848),U_7850),c_Orderings_Obot__class_Obot(tc_fun(U_7848,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(U_7848,U_7850,U_7849) = U_7850
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7848,tc_HOL_Obool)),U_7849),hAPP(hAPP(c_Set_Oinsert(U_7848),U_7850),c_Orderings_Obot__class_Obot(tc_fun(U_7848,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_2248_1]) ).

fof(f_2248_3,plain,
    ( ! [U_7856,U_7854,U_7852] :
        ( c_Partial__Function_Oflat__lub(U_7852,U_7856,U_7854) = c_HOL_OThe(U_7852,hAPP(hAPP(c_COMBC(U_7852,tc_fun(U_7852,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7852,tc_HOL_Obool)),U_7854),hAPP(hAPP(c_Set_Oinsert(U_7852),U_7856),c_Orderings_Obot__class_Obot(tc_fun(U_7852,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7852,tc_HOL_Obool)),U_7854),hAPP(hAPP(c_Set_Oinsert(U_7852),U_7856),c_Orderings_Obot__class_Obot(tc_fun(U_7852,tc_HOL_Obool))))) )
    & ! [U_7855,U_7853,U_7851] :
        ( c_Partial__Function_Oflat__lub(U_7851,U_7855,U_7853) = U_7855
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7851,tc_HOL_Obool)),U_7853),hAPP(hAPP(c_Set_Oinsert(U_7851),U_7855),c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool))))) ) ),
    inference(miniscope,[status(thm)],[f_2248_2]) ).

fof(f_2248_4,plain,
    ( ! [U_7852,U_7854,U_7856] :
        ( c_Partial__Function_Oflat__lub(U_7852,U_7856,U_7854) = c_HOL_OThe(U_7852,hAPP(hAPP(c_COMBC(U_7852,tc_fun(U_7852,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7852,tc_HOL_Obool)),U_7854),hAPP(hAPP(c_Set_Oinsert(U_7852),U_7856),c_Orderings_Obot__class_Obot(tc_fun(U_7852,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7852,tc_HOL_Obool)),U_7854),hAPP(hAPP(c_Set_Oinsert(U_7852),U_7856),c_Orderings_Obot__class_Obot(tc_fun(U_7852,tc_HOL_Obool))))) )
    & ! [U_7853,U_7851,U_7855] :
        ( c_Partial__Function_Oflat__lub(U_7851,U_7855,U_7853) = U_7855
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7851,tc_HOL_Obool)),U_7853),hAPP(hAPP(c_Set_Oinsert(U_7851),U_7855),c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2248_3]) ).

cnf(f_2248_5,plain,
    ( c_Partial__Function_Oflat__lub(U_7851,U_7855,U_7853) = U_7855
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7851,tc_HOL_Obool)),U_7853),hAPP(hAPP(c_Set_Oinsert(U_7851),U_7855),c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2248_4]) ).

cnf(f_2248_6,plain,
    ( c_Partial__Function_Oflat__lub(U_7852,U_7856,U_7854) = c_HOL_OThe(U_7852,hAPP(hAPP(c_COMBC(U_7852,tc_fun(U_7852,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7852,tc_HOL_Obool)),U_7854),hAPP(hAPP(c_Set_Oinsert(U_7852),U_7856),c_Orderings_Obot__class_Obot(tc_fun(U_7852,tc_HOL_Obool))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7852,tc_HOL_Obool)),U_7854),hAPP(hAPP(c_Set_Oinsert(U_7852),U_7856),c_Orderings_Obot__class_Obot(tc_fun(U_7852,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2248_4]) ).

fof(f_2249_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_bot2E]) ).

fof(f_2249_2,plain,
    ! [U_7860,U_7859,U_7858,U_7857] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7857,tc_fun(U_7858,tc_HOL_Obool))),U_7859),U_7860)),
    inference(variable_rename,[status(thm)],[f_2249_1]) ).

fof(f_2249_3,plain,
    ! [U_7857,U_7858,U_7860,U_7859] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7857,tc_fun(U_7858,tc_HOL_Obool))),U_7859),U_7860)),
    inference(definitional_conversion,[status(esa)],[f_2249_2]) ).

cnf(f_2249_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7857,tc_fun(U_7858,tc_HOL_Obool))),U_7859),U_7860)),
    inference(clausify,[status(thm)],[f_2249_3]) ).

fof(f_2250_1,plain,
    ! [V_B_2,T_b,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_less__by__empty]) ).

fof(f_2250_2,plain,
    ! [U_7863,U_7862,U_7861] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7862,U_7862),tc_HOL_Obool)),U_7861),U_7863))
      | U_7861 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7862,U_7862),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2250_1]) ).

fof(f_2250_3,plain,
    ! [U_7861,U_7862,U_7863] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7862,U_7862),tc_HOL_Obool)),U_7861),U_7863))
      | U_7861 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7862,U_7862),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2250_2]) ).

cnf(f_2250_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7862,U_7862),tc_HOL_Obool)),U_7861),U_7863))
    | U_7861 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7862,U_7862),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2250_3]) ).

fof(f_2251_1,plain,
    ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(f_2251_2,plain,
    ! [U_7867,U_7866,U_7865,U_7864] : c_Nitpick_Ofold__graph_H(U_7864,U_7865,U_7866,U_7867,c_Orderings_Obot__class_Obot(tc_fun(U_7864,tc_HOL_Obool)),U_7867),
    inference(variable_rename,[status(thm)],[f_2251_1]) ).

fof(f_2251_3,plain,
    ! [U_7867,U_7864,U_7865,U_7866] : c_Nitpick_Ofold__graph_H(U_7864,U_7865,U_7866,U_7867,c_Orderings_Obot__class_Obot(tc_fun(U_7864,tc_HOL_Obool)),U_7867),
    inference(definitional_conversion,[status(esa)],[f_2251_2]) ).

cnf(f_2251_4,plain,
    c_Nitpick_Ofold__graph_H(U_7864,U_7865,U_7866,U_7867,c_Orderings_Obot__class_Obot(tc_fun(U_7864,tc_HOL_Obool)),U_7867),
    inference(clausify,[status(thm)],[f_2251_3]) ).

fof(f_2252_1,plain,
    ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(f_2252_2,plain,
    ! [U_7871,U_7870,U_7869,U_7868] : c_Nitpick_Ofold__graph_H(U_7868,U_7869,U_7870,U_7871,c_Orderings_Obot__class_Obot(tc_fun(U_7868,tc_HOL_Obool)),U_7871),
    inference(variable_rename,[status(thm)],[f_2252_1]) ).

fof(f_2252_3,plain,
    ! [U_7868,U_7869,U_7870,U_7871] : c_Nitpick_Ofold__graph_H(U_7868,U_7869,U_7870,U_7871,c_Orderings_Obot__class_Obot(tc_fun(U_7868,tc_HOL_Obool)),U_7871),
    inference(definitional_conversion,[status(esa)],[f_2252_2]) ).

cnf(f_2252_4,plain,
    c_Nitpick_Ofold__graph_H(U_7868,U_7869,U_7870,U_7871,c_Orderings_Obot__class_Obot(tc_fun(U_7868,tc_HOL_Obool)),U_7871),
    inference(clausify,[status(thm)],[f_2252_3]) ).

fof(f_2253_1,plain,
    ! [V_f_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__measure]) ).

fof(f_2253_2,plain,
    ! [U_7875,U_7874,U_7873,U_7872] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7872,U_7872)),hAPP(hAPP(c_Product__Type_OPair(U_7872,U_7872),U_7873),U_7874)),hAPP(c_Wellfounded_Omeasure(U_7872),U_7875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7875,U_7873)),hAPP(U_7875,U_7874))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7875,U_7873)),hAPP(U_7875,U_7874)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7872,U_7872)),hAPP(hAPP(c_Product__Type_OPair(U_7872,U_7872),U_7873),U_7874)),hAPP(c_Wellfounded_Omeasure(U_7872),U_7875))) ) ),
    inference(variable_rename,[status(thm)],[f_2253_1]) ).

fof(f_2253_3,plain,
    ( ! [U_7883,U_7881,U_7879] :
        ( ! [U_7877] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7877,U_7877)),hAPP(hAPP(c_Product__Type_OPair(U_7877,U_7877),U_7879),U_7881)),hAPP(c_Wellfounded_Omeasure(U_7877),U_7883)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7883,U_7879)),hAPP(U_7883,U_7881))) )
    & ! [U_7882,U_7880,U_7878] :
        ( ! [U_7876] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7876,U_7876)),hAPP(hAPP(c_Product__Type_OPair(U_7876,U_7876),U_7878),U_7880)),hAPP(c_Wellfounded_Omeasure(U_7876),U_7882)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7882,U_7878)),hAPP(U_7882,U_7880))) ) ),
    inference(miniscope,[status(thm)],[f_2253_2]) ).

fof(f_2253_4,plain,
    ( ! [U_7877,U_7879,U_7881,U_7883] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7877,U_7877)),hAPP(hAPP(c_Product__Type_OPair(U_7877,U_7877),U_7879),U_7881)),hAPP(c_Wellfounded_Omeasure(U_7877),U_7883)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7883,U_7879)),hAPP(U_7883,U_7881))) )
    & ! [U_7876,U_7878,U_7882,U_7880] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7876,U_7876)),hAPP(hAPP(c_Product__Type_OPair(U_7876,U_7876),U_7878),U_7880)),hAPP(c_Wellfounded_Omeasure(U_7876),U_7882)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7882,U_7878)),hAPP(U_7882,U_7880))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2253_3]) ).

cnf(f_2253_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7876,U_7876)),hAPP(hAPP(c_Product__Type_OPair(U_7876,U_7876),U_7878),U_7880)),hAPP(c_Wellfounded_Omeasure(U_7876),U_7882)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7882,U_7878)),hAPP(U_7882,U_7880))) ),
    inference(clausify,[status(thm)],[f_2253_4]) ).

cnf(f_2253_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7877,U_7877)),hAPP(hAPP(c_Product__Type_OPair(U_7877,U_7877),U_7879),U_7881)),hAPP(c_Wellfounded_Omeasure(U_7877),U_7883)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7883,U_7879)),hAPP(U_7883,U_7881))) ),
    inference(clausify,[status(thm)],[f_2253_4]) ).

fof(f_2254_1,plain,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mlex__leq]) ).

fof(f_2254_2,plain,
    ! [U_7888,U_7887,U_7886,U_7885,U_7884] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7887,U_7887)),hAPP(hAPP(c_Product__Type_OPair(U_7887,U_7887),U_7885),U_7886)),c_Wellfounded_Omlex__prod(U_7887,U_7884,U_7888)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7887,U_7887)),hAPP(hAPP(c_Product__Type_OPair(U_7887,U_7887),U_7885),U_7886)),U_7888))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_7884,U_7885)),hAPP(U_7884,U_7886))) ),
    inference(variable_rename,[status(thm)],[f_2254_1]) ).

fof(f_2254_3,plain,
    ! [U_7884,U_7886,U_7887,U_7888,U_7885] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7887,U_7887)),hAPP(hAPP(c_Product__Type_OPair(U_7887,U_7887),U_7885),U_7886)),c_Wellfounded_Omlex__prod(U_7887,U_7884,U_7888)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7887,U_7887)),hAPP(hAPP(c_Product__Type_OPair(U_7887,U_7887),U_7885),U_7886)),U_7888))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_7884,U_7885)),hAPP(U_7884,U_7886))) ),
    inference(definitional_conversion,[status(esa)],[f_2254_2]) ).

cnf(f_2254_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7887,U_7887)),hAPP(hAPP(c_Product__Type_OPair(U_7887,U_7887),U_7885),U_7886)),c_Wellfounded_Omlex__prod(U_7887,U_7884,U_7888)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7887,U_7887)),hAPP(hAPP(c_Product__Type_OPair(U_7887,U_7887),U_7885),U_7886)),U_7888))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_7884,U_7885)),hAPP(U_7884,U_7886))) ),
    inference(clausify,[status(thm)],[f_2254_3]) ).

fof(f_2255_1,plain,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mlex__less]) ).

fof(f_2255_2,plain,
    ! [U_7893,U_7892,U_7891,U_7890,U_7889] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7892,U_7892)),hAPP(hAPP(c_Product__Type_OPair(U_7892,U_7892),U_7890),U_7891)),c_Wellfounded_Omlex__prod(U_7892,U_7889,U_7893)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7889,U_7890)),hAPP(U_7889,U_7891))) ),
    inference(variable_rename,[status(thm)],[f_2255_1]) ).

fof(f_2255_3,plain,
    ! [U_7889,U_7890,U_7891,U_7892,U_7893] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7892,U_7892)),hAPP(hAPP(c_Product__Type_OPair(U_7892,U_7892),U_7890),U_7891)),c_Wellfounded_Omlex__prod(U_7892,U_7889,U_7893)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7889,U_7890)),hAPP(U_7889,U_7891))) ),
    inference(definitional_conversion,[status(esa)],[f_2255_2]) ).

cnf(f_2255_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7892,U_7892)),hAPP(hAPP(c_Product__Type_OPair(U_7892,U_7892),U_7890),U_7891)),c_Wellfounded_Omlex__prod(U_7892,U_7889,U_7893)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_7889,U_7890)),hAPP(U_7889,U_7891))) ),
    inference(clausify,[status(thm)],[f_2255_3]) ).

fof(f_2256_1,plain,
    ! [V_w_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__number__of]) ).

fof(f_2256_2,plain,
    ! [U_7895,U_7894] :
      ( hBOOL(hAPP(hAPP(c_member(U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7894),U_7895)),c_Nat_Osemiring__1__class_ONats(U_7894)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7895))
      | ~ class_Int_Onumber__ring(U_7894) ),
    inference(variable_rename,[status(thm)],[f_2256_1]) ).

fof(f_2256_3,plain,
    ! [U_7894,U_7895] :
      ( hBOOL(hAPP(hAPP(c_member(U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7894),U_7895)),c_Nat_Osemiring__1__class_ONats(U_7894)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7895))
      | ~ class_Int_Onumber__ring(U_7894) ),
    inference(definitional_conversion,[status(esa)],[f_2256_2]) ).

cnf(f_2256_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7894),U_7895)),c_Nat_Osemiring__1__class_ONats(U_7894)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7895))
    | ~ class_Int_Onumber__ring(U_7894) ),
    inference(clausify,[status(thm)],[f_2256_3]) ).

fof(f_2257_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__0]) ).

fof(f_2257_2,plain,
    ! [U_7896] :
      ( hBOOL(hAPP(hAPP(c_member(U_7896),c_Groups_Ozero__class_Ozero(U_7896)),c_Nat_Osemiring__1__class_ONats(U_7896)))
      | ~ class_Rings_Osemiring__1(U_7896) ),
    inference(variable_rename,[status(thm)],[f_2257_1]) ).

fof(f_2257_3,plain,
    ! [U_7896] :
      ( hBOOL(hAPP(hAPP(c_member(U_7896),c_Groups_Ozero__class_Ozero(U_7896)),c_Nat_Osemiring__1__class_ONats(U_7896)))
      | ~ class_Rings_Osemiring__1(U_7896) ),
    inference(definitional_conversion,[status(esa)],[f_2257_2]) ).

cnf(f_2257_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7896),c_Groups_Ozero__class_Ozero(U_7896)),c_Nat_Osemiring__1__class_ONats(U_7896)))
    | ~ class_Rings_Osemiring__1(U_7896) ),
    inference(clausify,[status(thm)],[f_2257_3]) ).

fof(f_2258_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__add]) ).

fof(f_2258_2,plain,
    ! [U_7899,U_7898,U_7897] :
      ( hBOOL(hAPP(hAPP(c_member(U_7897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7897),U_7898),U_7899)),c_Nat_Osemiring__1__class_ONats(U_7897)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7897),U_7899),c_Nat_Osemiring__1__class_ONats(U_7897)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7897),U_7898),c_Nat_Osemiring__1__class_ONats(U_7897)))
      | ~ class_Rings_Osemiring__1(U_7897) ),
    inference(variable_rename,[status(thm)],[f_2258_1]) ).

fof(f_2258_3,plain,
    ! [U_7897,U_7898,U_7899] :
      ( hBOOL(hAPP(hAPP(c_member(U_7897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7897),U_7898),U_7899)),c_Nat_Osemiring__1__class_ONats(U_7897)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7897),U_7899),c_Nat_Osemiring__1__class_ONats(U_7897)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7897),U_7898),c_Nat_Osemiring__1__class_ONats(U_7897)))
      | ~ class_Rings_Osemiring__1(U_7897) ),
    inference(definitional_conversion,[status(esa)],[f_2258_2]) ).

cnf(f_2258_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7897),U_7898),U_7899)),c_Nat_Osemiring__1__class_ONats(U_7897)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7897),U_7899),c_Nat_Osemiring__1__class_ONats(U_7897)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7897),U_7898),c_Nat_Osemiring__1__class_ONats(U_7897)))
    | ~ class_Rings_Osemiring__1(U_7897) ),
    inference(clausify,[status(thm)],[f_2258_3]) ).

fof(f_2259_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__mult]) ).

fof(f_2259_2,plain,
    ! [U_7902,U_7901,U_7900] :
      ( hBOOL(hAPP(hAPP(c_member(U_7900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7900),U_7901),U_7902)),c_Nat_Osemiring__1__class_ONats(U_7900)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7900),U_7902),c_Nat_Osemiring__1__class_ONats(U_7900)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7900),U_7901),c_Nat_Osemiring__1__class_ONats(U_7900)))
      | ~ class_Rings_Osemiring__1(U_7900) ),
    inference(variable_rename,[status(thm)],[f_2259_1]) ).

fof(f_2259_3,plain,
    ! [U_7902,U_7900,U_7901] :
      ( hBOOL(hAPP(hAPP(c_member(U_7900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7900),U_7901),U_7902)),c_Nat_Osemiring__1__class_ONats(U_7900)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7900),U_7902),c_Nat_Osemiring__1__class_ONats(U_7900)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7900),U_7901),c_Nat_Osemiring__1__class_ONats(U_7900)))
      | ~ class_Rings_Osemiring__1(U_7900) ),
    inference(definitional_conversion,[status(esa)],[f_2259_2]) ).

cnf(f_2259_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7900),U_7901),U_7902)),c_Nat_Osemiring__1__class_ONats(U_7900)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7900),U_7902),c_Nat_Osemiring__1__class_ONats(U_7900)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7900),U_7901),c_Nat_Osemiring__1__class_ONats(U_7900)))
    | ~ class_Rings_Osemiring__1(U_7900) ),
    inference(clausify,[status(thm)],[f_2259_3]) ).

fof(f_2260_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__1]) ).

fof(f_2260_2,plain,
    ! [U_7903] :
      ( hBOOL(hAPP(hAPP(c_member(U_7903),c_Groups_Oone__class_Oone(U_7903)),c_Nat_Osemiring__1__class_ONats(U_7903)))
      | ~ class_Rings_Osemiring__1(U_7903) ),
    inference(variable_rename,[status(thm)],[f_2260_1]) ).

fof(f_2260_3,plain,
    ! [U_7903] :
      ( hBOOL(hAPP(hAPP(c_member(U_7903),c_Groups_Oone__class_Oone(U_7903)),c_Nat_Osemiring__1__class_ONats(U_7903)))
      | ~ class_Rings_Osemiring__1(U_7903) ),
    inference(definitional_conversion,[status(esa)],[f_2260_2]) ).

cnf(f_2260_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7903),c_Groups_Oone__class_Oone(U_7903)),c_Nat_Osemiring__1__class_ONats(U_7903)))
    | ~ class_Rings_Osemiring__1(U_7903) ),
    inference(clausify,[status(thm)],[f_2260_3]) ).

fof(f_2261_1,plain,
    ! [V_n_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats]) ).

fof(f_2261_2,plain,
    ! [U_7905,U_7904] :
      ( hBOOL(hAPP(hAPP(c_member(U_7904),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7904),U_7905)),c_Nat_Osemiring__1__class_ONats(U_7904)))
      | ~ class_Rings_Osemiring__1(U_7904) ),
    inference(variable_rename,[status(thm)],[f_2261_1]) ).

fof(f_2261_3,plain,
    ! [U_7904,U_7905] :
      ( hBOOL(hAPP(hAPP(c_member(U_7904),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7904),U_7905)),c_Nat_Osemiring__1__class_ONats(U_7904)))
      | ~ class_Rings_Osemiring__1(U_7904) ),
    inference(definitional_conversion,[status(esa)],[f_2261_2]) ).

cnf(f_2261_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7904),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7904),U_7905)),c_Nat_Osemiring__1__class_ONats(U_7904)))
    | ~ class_Rings_Osemiring__1(U_7904) ),
    inference(clausify,[status(thm)],[f_2261_3]) ).

fof(f_2262_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0]) ).

fof(f_2262_2,plain,
    ! [U_7907,U_7906] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),c_Groups_Oone__class_Oone(U_7906)),U_7907)),U_7907)),c_Groups_Ozero__class_Ozero(U_7906)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),U_7907),c_Groups_Ozero__class_Ozero(U_7906))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),U_7907),c_Groups_Ozero__class_Ozero(U_7906)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),c_Groups_Oone__class_Oone(U_7906)),U_7907)),U_7907)),c_Groups_Ozero__class_Ozero(U_7906))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_7906),U_7907),c_Int_Oring__1__class_OInts(U_7906)))
      | ~ class_Rings_Olinordered__idom(U_7906) ),
    inference(variable_rename,[status(thm)],[f_2262_1]) ).

fof(f_2262_3,plain,
    ( ! [U_7906,U_7907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),c_Groups_Oone__class_Oone(U_7906)),U_7907)),U_7907)),c_Groups_Ozero__class_Ozero(U_7906)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),U_7907),c_Groups_Ozero__class_Ozero(U_7906)))
        | ~ sP692(U_7906,U_7907) )
    & ! [U_7906,U_7907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),U_7907),c_Groups_Ozero__class_Ozero(U_7906)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),c_Groups_Oone__class_Oone(U_7906)),U_7907)),U_7907)),c_Groups_Ozero__class_Ozero(U_7906)))
        | ~ sP692(U_7906,U_7907) )
    & ! [U_7906,U_7907] :
        ( sP692(U_7906,U_7907)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7906),U_7907),c_Int_Oring__1__class_OInts(U_7906)))
        | ~ class_Rings_Olinordered__idom(U_7906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP692])],[f_2262_2]) ).

cnf(f_2262_4,plain,
    ( sP692(U_7906,U_7907)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7906),U_7907),c_Int_Oring__1__class_OInts(U_7906)))
    | ~ class_Rings_Olinordered__idom(U_7906) ),
    inference(clausify,[status(thm)],[f_2262_3]) ).

cnf(f_2262_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),U_7907),c_Groups_Ozero__class_Ozero(U_7906)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),c_Groups_Oone__class_Oone(U_7906)),U_7907)),U_7907)),c_Groups_Ozero__class_Ozero(U_7906)))
    | ~ sP692(U_7906,U_7907) ),
    inference(clausify,[status(thm)],[f_2262_3]) ).

cnf(f_2262_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7906),c_Groups_Oone__class_Oone(U_7906)),U_7907)),U_7907)),c_Groups_Ozero__class_Ozero(U_7906)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7906),U_7907),c_Groups_Ozero__class_Ozero(U_7906)))
    | ~ sP692(U_7906,U_7907) ),
    inference(clausify,[status(thm)],[f_2262_3]) ).

fof(f_2263_1,plain,
    ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
      ( ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
        | ( ! [B_x,B_y] :
              ( ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
              | hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != hAPP(hAPP(V_a3_2,B_x),B_y) )
          & ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != V_a4_2
            | V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
      & ( ? [B_x,B_y] :
            ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
            & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
        | ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
          & V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J]) ).

fof(f_2263_2,plain,
    ! [U_7918,U_7917,U_7916,U_7915,U_7914,U_7913,U_7912] :
      ( ( c_Nitpick_Ofold__graph_H(U_7912,U_7913,U_7914,U_7915,U_7916,hAPP(hAPP(U_7914,U_7917),U_7918))
        | ( ! [U_7911,U_7910] :
              ( ~ c_Nitpick_Ofold__graph_H(U_7912,U_7913,U_7914,U_7915,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7912,tc_HOL_Obool)),U_7916),hAPP(hAPP(c_Set_Oinsert(U_7912),U_7911),c_Orderings_Obot__class_Obot(tc_fun(U_7912,tc_HOL_Obool)))),U_7910)
              | ~ hBOOL(hAPP(hAPP(c_member(U_7912),U_7911),U_7916))
              | hAPP(hAPP(U_7914,U_7917),U_7918) != hAPP(hAPP(U_7914,U_7911),U_7910) )
          & ( hAPP(hAPP(U_7914,U_7917),U_7918) != U_7915
            | U_7916 != c_Orderings_Obot__class_Obot(tc_fun(U_7912,tc_HOL_Obool)) ) ) )
      & ( ? [U_7909,U_7908] :
            ( c_Nitpick_Ofold__graph_H(U_7912,U_7913,U_7914,U_7915,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7912,tc_HOL_Obool)),U_7916),hAPP(hAPP(c_Set_Oinsert(U_7912),U_7909),c_Orderings_Obot__class_Obot(tc_fun(U_7912,tc_HOL_Obool)))),U_7908)
            & hBOOL(hAPP(hAPP(c_member(U_7912),U_7909),U_7916))
            & hAPP(hAPP(U_7914,U_7917),U_7918) = hAPP(hAPP(U_7914,U_7909),U_7908) )
        | ( hAPP(hAPP(U_7914,U_7917),U_7918) = U_7915
          & U_7916 = c_Orderings_Obot__class_Obot(tc_fun(U_7912,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7912,U_7913,U_7914,U_7915,U_7916,hAPP(hAPP(U_7914,U_7917),U_7918)) ) ),
    inference(variable_rename,[status(thm)],[f_2263_1]) ).

fof(f_2263_3,plain,
    ( ! [U_7932,U_7930,U_7928,U_7926,U_7924,U_7922,U_7920] :
        ( c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,U_7928,hAPP(hAPP(U_7924,U_7930),U_7932))
        | ( ! [U_7911] :
              ( ! [U_7910] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7920,tc_HOL_Obool)),U_7928),hAPP(hAPP(c_Set_Oinsert(U_7920),U_7911),c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)))),U_7910)
                  | hAPP(hAPP(U_7924,U_7930),U_7932) != hAPP(hAPP(U_7924,U_7911),U_7910) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_7920),U_7911),U_7928)) )
          & ( hAPP(hAPP(U_7924,U_7930),U_7932) != U_7926
            | U_7928 != c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)) ) ) )
    & ! [U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919] :
        ( ? [U_7909] :
            ( ? [U_7908] :
                ( c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7927),hAPP(hAPP(c_Set_Oinsert(U_7919),U_7909),c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)))),U_7908)
                & hAPP(hAPP(U_7923,U_7929),U_7931) = hAPP(hAPP(U_7923,U_7909),U_7908) )
            & hBOOL(hAPP(hAPP(c_member(U_7919),U_7909),U_7927)) )
        | ( hAPP(hAPP(U_7923,U_7929),U_7931) = U_7925
          & U_7927 = c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,U_7927,hAPP(hAPP(U_7923,U_7929),U_7931)) ) ),
    inference(miniscope,[status(thm)],[f_2263_2]) ).

fof(f_2263_4,plain,
    ( ! [U_7932,U_7930,U_7928,U_7926,U_7924,U_7922,U_7920] :
        ( c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,U_7928,hAPP(hAPP(U_7924,U_7930),U_7932))
        | ( ! [U_7911] :
              ( ! [U_7910] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7920,tc_HOL_Obool)),U_7928),hAPP(hAPP(c_Set_Oinsert(U_7920),U_7911),c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)))),U_7910)
                  | hAPP(hAPP(U_7924,U_7930),U_7932) != hAPP(hAPP(U_7924,U_7911),U_7910) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_7920),U_7911),U_7928)) )
          & ( hAPP(hAPP(U_7924,U_7930),U_7932) != U_7926
            | U_7928 != c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)) ) ) )
    & ! [U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919] :
        ( ( ? [U_7908] :
              ( c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7927),hAPP(hAPP(c_Set_Oinsert(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)))),U_7908)
              & hAPP(hAPP(U_7923,U_7929),U_7931) = hAPP(hAPP(U_7923,sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),U_7908) )
          & hBOOL(hAPP(hAPP(c_member(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),U_7927)) )
        | ( hAPP(hAPP(U_7923,U_7929),U_7931) = U_7925
          & U_7927 = c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,U_7927,hAPP(hAPP(U_7923,U_7929),U_7931)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_7909,sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))],[f_2263_3]) ).

fof(f_2263_5,plain,
    ( ! [U_7932,U_7930,U_7928,U_7926,U_7924,U_7922,U_7920] :
        ( c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,U_7928,hAPP(hAPP(U_7924,U_7930),U_7932))
        | ( ! [U_7911] :
              ( ! [U_7910] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7920,tc_HOL_Obool)),U_7928),hAPP(hAPP(c_Set_Oinsert(U_7920),U_7911),c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)))),U_7910)
                  | hAPP(hAPP(U_7924,U_7930),U_7932) != hAPP(hAPP(U_7924,U_7911),U_7910) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_7920),U_7911),U_7928)) )
          & ( hAPP(hAPP(U_7924,U_7930),U_7932) != U_7926
            | U_7928 != c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)) ) ) )
    & ! [U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919] :
        ( ( c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7927),hAPP(hAPP(c_Set_Oinsert(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)))),sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))
          & hAPP(hAPP(U_7923,U_7929),U_7931) = hAPP(hAPP(U_7923,sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))
          & hBOOL(hAPP(hAPP(c_member(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),U_7927)) )
        | ( hAPP(hAPP(U_7923,U_7929),U_7931) = U_7925
          & U_7927 = c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,U_7927,hAPP(hAPP(U_7923,U_7929),U_7931)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_7908,sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))],[f_2263_4]) ).

fof(f_2263_6,plain,
    ( ! [U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922] :
        ( ~ c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7920,tc_HOL_Obool)),U_7928),hAPP(hAPP(c_Set_Oinsert(U_7920),U_7911),c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)))),U_7910)
        | hAPP(hAPP(U_7924,U_7930),U_7932) != hAPP(hAPP(U_7924,U_7911),U_7910)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7920),U_7911),U_7928))
        | ~ sP695(U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922) )
    & ! [U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922] :
        ( hAPP(hAPP(U_7924,U_7930),U_7932) != U_7926
        | U_7928 != c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool))
        | ~ sP695(U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922) )
    & ! [U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931] :
        ( c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7927),hAPP(hAPP(c_Set_Oinsert(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)))),sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))
        | ~ sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931) )
    & ! [U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931] :
        ( hAPP(hAPP(U_7923,U_7929),U_7931) = hAPP(hAPP(U_7923,sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))
        | ~ sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931) )
    & ! [U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931] :
        ( hBOOL(hAPP(hAPP(c_member(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),U_7927))
        | ~ sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931) )
    & ! [U_7929,U_7923,U_7919,U_7925,U_7927,U_7931] :
        ( hAPP(hAPP(U_7923,U_7929),U_7931) = U_7925
        | ~ sP693(U_7929,U_7923,U_7919,U_7925,U_7927,U_7931) )
    & ! [U_7929,U_7923,U_7919,U_7925,U_7927,U_7931] :
        ( U_7927 = c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool))
        | ~ sP693(U_7929,U_7923,U_7919,U_7925,U_7927,U_7931) )
    & ! [U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922] :
        ( c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,U_7928,hAPP(hAPP(U_7924,U_7930),U_7932))
        | sP695(U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922) )
    & ! [U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931] :
        ( sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931)
        | sP693(U_7929,U_7923,U_7919,U_7925,U_7927,U_7931)
        | ~ c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,U_7927,hAPP(hAPP(U_7923,U_7929),U_7931)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP693,sP694,sP695])],[f_2263_5]) ).

cnf(f_2263_7,plain,
    ( sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931)
    | sP693(U_7929,U_7923,U_7919,U_7925,U_7927,U_7931)
    | ~ c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,U_7927,hAPP(hAPP(U_7923,U_7929),U_7931)) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_8,plain,
    ( c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,U_7928,hAPP(hAPP(U_7924,U_7930),U_7932))
    | sP695(U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_9,plain,
    ( U_7927 = c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool))
    | ~ sP693(U_7929,U_7923,U_7919,U_7925,U_7927,U_7931) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_10,plain,
    ( hAPP(hAPP(U_7923,U_7929),U_7931) = U_7925
    | ~ sP693(U_7929,U_7923,U_7919,U_7925,U_7927,U_7931) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),U_7927))
    | ~ sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_12,plain,
    ( hAPP(hAPP(U_7923,U_7929),U_7931) = hAPP(hAPP(U_7923,sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))
    | ~ sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_13,plain,
    ( c_Nitpick_Ofold__graph_H(U_7919,U_7921,U_7923,U_7925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7927),hAPP(hAPP(c_Set_Oinsert(U_7919),sK115(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919)),c_Orderings_Obot__class_Obot(tc_fun(U_7919,tc_HOL_Obool)))),sK116(U_7931,U_7929,U_7927,U_7925,U_7923,U_7921,U_7919))
    | ~ sP694(U_7929,U_7923,U_7921,U_7919,U_7925,U_7927,U_7931) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_14,plain,
    ( hAPP(hAPP(U_7924,U_7930),U_7932) != U_7926
    | U_7928 != c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool))
    | ~ sP695(U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

cnf(f_2263_15,plain,
    ( ~ c_Nitpick_Ofold__graph_H(U_7920,U_7922,U_7924,U_7926,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7920,tc_HOL_Obool)),U_7928),hAPP(hAPP(c_Set_Oinsert(U_7920),U_7911),c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool)))),U_7910)
    | hAPP(hAPP(U_7924,U_7930),U_7932) != hAPP(hAPP(U_7924,U_7911),U_7910)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7920),U_7911),U_7928))
    | ~ sP695(U_7920,U_7930,U_7932,U_7911,U_7924,U_7928,U_7910,U_7926,U_7922) ),
    inference(clausify,[status(thm)],[f_2263_6]) ).

fof(f_2264_1,plain,
    ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
            | V_a_2 != V_a_H_2 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
          & V_a_2 = V_a_H_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__lex__prod]) ).

fof(f_2264_2,plain,
    ! [U_7940,U_7939,U_7938,U_7937,U_7936,U_7935,U_7934,U_7933] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7933,U_7934),tc_prod(U_7933,U_7934))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7933,U_7934),tc_prod(U_7933,U_7934)),hAPP(hAPP(c_Product__Type_OPair(U_7933,U_7934),U_7935),U_7936)),hAPP(hAPP(c_Product__Type_OPair(U_7933,U_7934),U_7937),U_7938))),c_Wellfounded_Olex__prod(U_7933,U_7934,U_7939,U_7940)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7934,U_7934)),hAPP(hAPP(c_Product__Type_OPair(U_7934,U_7934),U_7936),U_7938)),U_7940))
            | U_7935 != U_7937 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7933,U_7933)),hAPP(hAPP(c_Product__Type_OPair(U_7933,U_7933),U_7935),U_7937)),U_7939)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7934,U_7934)),hAPP(hAPP(c_Product__Type_OPair(U_7934,U_7934),U_7936),U_7938)),U_7940))
          & U_7935 = U_7937 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7933,U_7933)),hAPP(hAPP(c_Product__Type_OPair(U_7933,U_7933),U_7935),U_7937)),U_7939))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7933,U_7934),tc_prod(U_7933,U_7934))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7933,U_7934),tc_prod(U_7933,U_7934)),hAPP(hAPP(c_Product__Type_OPair(U_7933,U_7934),U_7935),U_7936)),hAPP(hAPP(c_Product__Type_OPair(U_7933,U_7934),U_7937),U_7938))),c_Wellfounded_Olex__prod(U_7933,U_7934,U_7939,U_7940))) ) ),
    inference(variable_rename,[status(thm)],[f_2264_1]) ).

fof(f_2264_3,plain,
    ( ! [U_7956,U_7954,U_7952,U_7950,U_7948,U_7946,U_7944,U_7942] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7942,U_7944),tc_prod(U_7942,U_7944))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7942,U_7944),tc_prod(U_7942,U_7944)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7944),U_7946),U_7948)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7944),U_7950),U_7952))),c_Wellfounded_Olex__prod(U_7942,U_7944,U_7954,U_7956)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7944,U_7944)),hAPP(hAPP(c_Product__Type_OPair(U_7944,U_7944),U_7948),U_7952)),U_7956))
            | U_7946 != U_7950 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7942,U_7942)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7942),U_7946),U_7950)),U_7954)) ) )
    & ! [U_7955,U_7953,U_7951,U_7949,U_7947,U_7945,U_7943,U_7941] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7943,U_7943)),hAPP(hAPP(c_Product__Type_OPair(U_7943,U_7943),U_7947),U_7951)),U_7955))
          & U_7945 = U_7949 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7941,U_7941)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7941),U_7945),U_7949)),U_7953))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7941,U_7943),tc_prod(U_7941,U_7943))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7941,U_7943),tc_prod(U_7941,U_7943)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7943),U_7945),U_7947)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7943),U_7949),U_7951))),c_Wellfounded_Olex__prod(U_7941,U_7943,U_7953,U_7955))) ) ),
    inference(miniscope,[status(thm)],[f_2264_2]) ).

fof(f_2264_4,plain,
    ( ! [U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7944,U_7944)),hAPP(hAPP(c_Product__Type_OPair(U_7944,U_7944),U_7948),U_7952)),U_7956))
        | U_7946 != U_7950
        | ~ sP697(U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956) )
    & ! [U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7942,U_7942)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7942),U_7946),U_7950)),U_7954))
        | ~ sP697(U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956) )
    & ! [U_7943,U_7945,U_7947,U_7949,U_7951,U_7955] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7943,U_7943)),hAPP(hAPP(c_Product__Type_OPair(U_7943,U_7943),U_7947),U_7951)),U_7955))
        | ~ sP696(U_7943,U_7945,U_7947,U_7949,U_7951,U_7955) )
    & ! [U_7943,U_7945,U_7947,U_7949,U_7951,U_7955] :
        ( U_7945 = U_7949
        | ~ sP696(U_7943,U_7945,U_7947,U_7949,U_7951,U_7955) )
    & ! [U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7942,U_7944),tc_prod(U_7942,U_7944))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7942,U_7944),tc_prod(U_7942,U_7944)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7944),U_7946),U_7948)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7944),U_7950),U_7952))),c_Wellfounded_Olex__prod(U_7942,U_7944,U_7954,U_7956)))
        | sP697(U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956) )
    & ! [U_7941,U_7943,U_7945,U_7947,U_7949,U_7951,U_7955,U_7953] :
        ( sP696(U_7943,U_7945,U_7947,U_7949,U_7951,U_7955)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7941,U_7941)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7941),U_7945),U_7949)),U_7953))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7941,U_7943),tc_prod(U_7941,U_7943))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7941,U_7943),tc_prod(U_7941,U_7943)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7943),U_7945),U_7947)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7943),U_7949),U_7951))),c_Wellfounded_Olex__prod(U_7941,U_7943,U_7953,U_7955))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP696,sP697])],[f_2264_3]) ).

cnf(f_2264_5,plain,
    ( sP696(U_7943,U_7945,U_7947,U_7949,U_7951,U_7955)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7941,U_7941)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7941),U_7945),U_7949)),U_7953))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7941,U_7943),tc_prod(U_7941,U_7943))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7941,U_7943),tc_prod(U_7941,U_7943)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7943),U_7945),U_7947)),hAPP(hAPP(c_Product__Type_OPair(U_7941,U_7943),U_7949),U_7951))),c_Wellfounded_Olex__prod(U_7941,U_7943,U_7953,U_7955))) ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

cnf(f_2264_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7942,U_7944),tc_prod(U_7942,U_7944))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7942,U_7944),tc_prod(U_7942,U_7944)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7944),U_7946),U_7948)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7944),U_7950),U_7952))),c_Wellfounded_Olex__prod(U_7942,U_7944,U_7954,U_7956)))
    | sP697(U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956) ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

cnf(f_2264_7,plain,
    ( U_7945 = U_7949
    | ~ sP696(U_7943,U_7945,U_7947,U_7949,U_7951,U_7955) ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

cnf(f_2264_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7943,U_7943)),hAPP(hAPP(c_Product__Type_OPair(U_7943,U_7943),U_7947),U_7951)),U_7955))
    | ~ sP696(U_7943,U_7945,U_7947,U_7949,U_7951,U_7955) ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

cnf(f_2264_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7942,U_7942)),hAPP(hAPP(c_Product__Type_OPair(U_7942,U_7942),U_7946),U_7950)),U_7954))
    | ~ sP697(U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956) ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

cnf(f_2264_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7944,U_7944)),hAPP(hAPP(c_Product__Type_OPair(U_7944,U_7944),U_7948),U_7952)),U_7956))
    | U_7946 != U_7950
    | ~ sP697(U_7942,U_7944,U_7950,U_7946,U_7948,U_7952,U_7954,U_7956) ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

fof(f_2265_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__lessI2]) ).

fof(f_2265_2,plain,
    ! [U_7960,U_7959,U_7958,U_7957] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7957),U_7959)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7958),U_7960))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7959),U_7960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7957),U_7958)) ),
    inference(variable_rename,[status(thm)],[f_2265_1]) ).

fof(f_2265_3,plain,
    ! [U_7958,U_7957,U_7959,U_7960] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7957),U_7959)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7958),U_7960))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7959),U_7960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7957),U_7958)) ),
    inference(definitional_conversion,[status(esa)],[f_2265_2]) ).

cnf(f_2265_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7957),U_7959)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7958),U_7960))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7959),U_7960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7957),U_7958)) ),
    inference(clausify,[status(thm)],[f_2265_3]) ).

fof(f_2266_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__0]) ).

fof(f_2266_2,plain,
    ! [U_7961] :
      ( hBOOL(hAPP(hAPP(c_member(U_7961),c_Groups_Ozero__class_Ozero(U_7961)),c_Int_Oring__1__class_OInts(U_7961)))
      | ~ class_Rings_Oring__1(U_7961) ),
    inference(variable_rename,[status(thm)],[f_2266_1]) ).

fof(f_2266_3,plain,
    ! [U_7961] :
      ( hBOOL(hAPP(hAPP(c_member(U_7961),c_Groups_Ozero__class_Ozero(U_7961)),c_Int_Oring__1__class_OInts(U_7961)))
      | ~ class_Rings_Oring__1(U_7961) ),
    inference(definitional_conversion,[status(esa)],[f_2266_2]) ).

cnf(f_2266_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7961),c_Groups_Ozero__class_Ozero(U_7961)),c_Int_Oring__1__class_OInts(U_7961)))
    | ~ class_Rings_Oring__1(U_7961) ),
    inference(clausify,[status(thm)],[f_2266_3]) ).

fof(f_2267_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__add]) ).

fof(f_2267_2,plain,
    ! [U_7964,U_7963,U_7962] :
      ( hBOOL(hAPP(hAPP(c_member(U_7962),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7962),U_7963),U_7964)),c_Int_Oring__1__class_OInts(U_7962)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7964),c_Int_Oring__1__class_OInts(U_7962)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7963),c_Int_Oring__1__class_OInts(U_7962)))
      | ~ class_Rings_Oring__1(U_7962) ),
    inference(variable_rename,[status(thm)],[f_2267_1]) ).

fof(f_2267_3,plain,
    ! [U_7962,U_7963,U_7964] :
      ( hBOOL(hAPP(hAPP(c_member(U_7962),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7962),U_7963),U_7964)),c_Int_Oring__1__class_OInts(U_7962)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7964),c_Int_Oring__1__class_OInts(U_7962)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7963),c_Int_Oring__1__class_OInts(U_7962)))
      | ~ class_Rings_Oring__1(U_7962) ),
    inference(definitional_conversion,[status(esa)],[f_2267_2]) ).

cnf(f_2267_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7962),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7962),U_7963),U_7964)),c_Int_Oring__1__class_OInts(U_7962)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7964),c_Int_Oring__1__class_OInts(U_7962)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7963),c_Int_Oring__1__class_OInts(U_7962)))
    | ~ class_Rings_Oring__1(U_7962) ),
    inference(clausify,[status(thm)],[f_2267_3]) ).

fof(f_2268_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__mult]) ).

fof(f_2268_2,plain,
    ! [U_7967,U_7966,U_7965] :
      ( hBOOL(hAPP(hAPP(c_member(U_7965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7965),U_7966),U_7967)),c_Int_Oring__1__class_OInts(U_7965)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7967),c_Int_Oring__1__class_OInts(U_7965)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),c_Int_Oring__1__class_OInts(U_7965)))
      | ~ class_Rings_Oring__1(U_7965) ),
    inference(variable_rename,[status(thm)],[f_2268_1]) ).

fof(f_2268_3,plain,
    ! [U_7965,U_7966,U_7967] :
      ( hBOOL(hAPP(hAPP(c_member(U_7965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7965),U_7966),U_7967)),c_Int_Oring__1__class_OInts(U_7965)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7967),c_Int_Oring__1__class_OInts(U_7965)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),c_Int_Oring__1__class_OInts(U_7965)))
      | ~ class_Rings_Oring__1(U_7965) ),
    inference(definitional_conversion,[status(esa)],[f_2268_2]) ).

cnf(f_2268_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7965),U_7966),U_7967)),c_Int_Oring__1__class_OInts(U_7965)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7967),c_Int_Oring__1__class_OInts(U_7965)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),c_Int_Oring__1__class_OInts(U_7965)))
    | ~ class_Rings_Oring__1(U_7965) ),
    inference(clausify,[status(thm)],[f_2268_3]) ).

fof(f_2269_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__diff]) ).

fof(f_2269_2,plain,
    ! [U_7970,U_7969,U_7968] :
      ( hBOOL(hAPP(hAPP(c_member(U_7968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7968),U_7969),U_7970)),c_Int_Oring__1__class_OInts(U_7968)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7970),c_Int_Oring__1__class_OInts(U_7968)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7969),c_Int_Oring__1__class_OInts(U_7968)))
      | ~ class_Rings_Oring__1(U_7968) ),
    inference(variable_rename,[status(thm)],[f_2269_1]) ).

fof(f_2269_3,plain,
    ! [U_7968,U_7969,U_7970] :
      ( hBOOL(hAPP(hAPP(c_member(U_7968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7968),U_7969),U_7970)),c_Int_Oring__1__class_OInts(U_7968)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7970),c_Int_Oring__1__class_OInts(U_7968)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7969),c_Int_Oring__1__class_OInts(U_7968)))
      | ~ class_Rings_Oring__1(U_7968) ),
    inference(definitional_conversion,[status(esa)],[f_2269_2]) ).

cnf(f_2269_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7968),U_7969),U_7970)),c_Int_Oring__1__class_OInts(U_7968)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7970),c_Int_Oring__1__class_OInts(U_7968)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7969),c_Int_Oring__1__class_OInts(U_7968)))
    | ~ class_Rings_Oring__1(U_7968) ),
    inference(clausify,[status(thm)],[f_2269_3]) ).

fof(f_2270_1,plain,
    ! [V_w_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__number__of]) ).

fof(f_2270_2,plain,
    ! [U_7972,U_7971] :
      ( hBOOL(hAPP(hAPP(c_member(U_7971),hAPP(c_Int_Onumber__class_Onumber__of(U_7971),U_7972)),c_Int_Oring__1__class_OInts(U_7971)))
      | ~ class_Int_Onumber__ring(U_7971) ),
    inference(variable_rename,[status(thm)],[f_2270_1]) ).

fof(f_2270_3,plain,
    ! [U_7972,U_7971] :
      ( hBOOL(hAPP(hAPP(c_member(U_7971),hAPP(c_Int_Onumber__class_Onumber__of(U_7971),U_7972)),c_Int_Oring__1__class_OInts(U_7971)))
      | ~ class_Int_Onumber__ring(U_7971) ),
    inference(definitional_conversion,[status(esa)],[f_2270_2]) ).

cnf(f_2270_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7971),hAPP(c_Int_Onumber__class_Onumber__of(U_7971),U_7972)),c_Int_Oring__1__class_OInts(U_7971)))
    | ~ class_Int_Onumber__ring(U_7971) ),
    inference(clausify,[status(thm)],[f_2270_3]) ).

fof(f_2271_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__1]) ).

fof(f_2271_2,plain,
    ! [U_7973] :
      ( hBOOL(hAPP(hAPP(c_member(U_7973),c_Groups_Oone__class_Oone(U_7973)),c_Int_Oring__1__class_OInts(U_7973)))
      | ~ class_Rings_Oring__1(U_7973) ),
    inference(variable_rename,[status(thm)],[f_2271_1]) ).

fof(f_2271_3,plain,
    ! [U_7973] :
      ( hBOOL(hAPP(hAPP(c_member(U_7973),c_Groups_Oone__class_Oone(U_7973)),c_Int_Oring__1__class_OInts(U_7973)))
      | ~ class_Rings_Oring__1(U_7973) ),
    inference(definitional_conversion,[status(esa)],[f_2271_2]) ).

cnf(f_2271_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7973),c_Groups_Oone__class_Oone(U_7973)),c_Int_Oring__1__class_OInts(U_7973)))
    | ~ class_Rings_Oring__1(U_7973) ),
    inference(clausify,[status(thm)],[f_2271_3]) ).

fof(f_2272_1,plain,
    ! [V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__minus]) ).

fof(f_2272_2,plain,
    ! [U_7975,U_7974] :
      ( hBOOL(hAPP(hAPP(c_member(U_7974),hAPP(c_Groups_Ouminus__class_Ouminus(U_7974),U_7975)),c_Int_Oring__1__class_OInts(U_7974)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7974),U_7975),c_Int_Oring__1__class_OInts(U_7974)))
      | ~ class_Rings_Oring__1(U_7974) ),
    inference(variable_rename,[status(thm)],[f_2272_1]) ).

fof(f_2272_3,plain,
    ! [U_7974,U_7975] :
      ( hBOOL(hAPP(hAPP(c_member(U_7974),hAPP(c_Groups_Ouminus__class_Ouminus(U_7974),U_7975)),c_Int_Oring__1__class_OInts(U_7974)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7974),U_7975),c_Int_Oring__1__class_OInts(U_7974)))
      | ~ class_Rings_Oring__1(U_7974) ),
    inference(definitional_conversion,[status(esa)],[f_2272_2]) ).

cnf(f_2272_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7974),hAPP(c_Groups_Ouminus__class_Ouminus(U_7974),U_7975)),c_Int_Oring__1__class_OInts(U_7974)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7974),U_7975),c_Int_Oring__1__class_OInts(U_7974)))
    | ~ class_Rings_Oring__1(U_7974) ),
    inference(clausify,[status(thm)],[f_2272_3]) ).

fof(f_2273_1,plain,
    ! [V_n_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__power]) ).

fof(f_2273_2,plain,
    ! [U_7978,U_7977,U_7976] :
      ( hBOOL(hAPP(hAPP(c_member(U_7976),hAPP(hAPP(c_Power_Opower__class_Opower(U_7976),U_7977),U_7978)),c_Int_Oring__1__class_OInts(U_7976)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),c_Int_Oring__1__class_OInts(U_7976)))
      | ~ class_Rings_Oring__1(U_7976) ),
    inference(variable_rename,[status(thm)],[f_2273_1]) ).

fof(f_2273_3,plain,
    ! [U_7976,U_7977,U_7978] :
      ( hBOOL(hAPP(hAPP(c_member(U_7976),hAPP(hAPP(c_Power_Opower__class_Opower(U_7976),U_7977),U_7978)),c_Int_Oring__1__class_OInts(U_7976)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),c_Int_Oring__1__class_OInts(U_7976)))
      | ~ class_Rings_Oring__1(U_7976) ),
    inference(definitional_conversion,[status(esa)],[f_2273_2]) ).

cnf(f_2273_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7976),hAPP(hAPP(c_Power_Opower__class_Opower(U_7976),U_7977),U_7978)),c_Int_Oring__1__class_OInts(U_7976)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),c_Int_Oring__1__class_OInts(U_7976)))
    | ~ class_Rings_Oring__1(U_7976) ),
    inference(clausify,[status(thm)],[f_2273_3]) ).

fof(f_2274_1,plain,
    ! [V_n_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__of__nat]) ).

fof(f_2274_2,plain,
    ! [U_7980,U_7979] :
      ( hBOOL(hAPP(hAPP(c_member(U_7979),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7979),U_7980)),c_Int_Oring__1__class_OInts(U_7979)))
      | ~ class_Rings_Oring__1(U_7979) ),
    inference(variable_rename,[status(thm)],[f_2274_1]) ).

fof(f_2274_3,plain,
    ! [U_7979,U_7980] :
      ( hBOOL(hAPP(hAPP(c_member(U_7979),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7979),U_7980)),c_Int_Oring__1__class_OInts(U_7979)))
      | ~ class_Rings_Oring__1(U_7979) ),
    inference(definitional_conversion,[status(esa)],[f_2274_2]) ).

cnf(f_2274_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7979),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7979),U_7980)),c_Int_Oring__1__class_OInts(U_7979)))
    | ~ class_Rings_Oring__1(U_7979) ),
    inference(clausify,[status(thm)],[f_2274_3]) ).

fof(f_2275_1,plain,
    ! [V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__of__int]) ).

fof(f_2275_2,plain,
    ! [U_7982,U_7981] :
      ( hBOOL(hAPP(hAPP(c_member(U_7981),hAPP(c_Int_Oring__1__class_Oof__int(U_7981),U_7982)),c_Int_Oring__1__class_OInts(U_7981)))
      | ~ class_Rings_Oring__1(U_7981) ),
    inference(variable_rename,[status(thm)],[f_2275_1]) ).

fof(f_2275_3,plain,
    ! [U_7981,U_7982] :
      ( hBOOL(hAPP(hAPP(c_member(U_7981),hAPP(c_Int_Oring__1__class_Oof__int(U_7981),U_7982)),c_Int_Oring__1__class_OInts(U_7981)))
      | ~ class_Rings_Oring__1(U_7981) ),
    inference(definitional_conversion,[status(esa)],[f_2275_2]) ).

cnf(f_2275_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7981),hAPP(c_Int_Oring__1__class_Oof__int(U_7981),U_7982)),c_Int_Oring__1__class_OInts(U_7981)))
    | ~ class_Rings_Oring__1(U_7981) ),
    inference(clausify,[status(thm)],[f_2275_3]) ).

fof(f_2276_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff]) ).

fof(f_2276_2,plain,
    ! [U_7984,U_7983] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7983),U_7984),U_7984) = c_Groups_Ozero__class_Ozero(U_7983)
          | U_7984 != c_Groups_Ozero__class_Ozero(U_7983) )
        & ( U_7984 = c_Groups_Ozero__class_Ozero(U_7983)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7983),U_7984),U_7984) != c_Groups_Ozero__class_Ozero(U_7983) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_7983),U_7984),c_Int_Oring__1__class_OInts(U_7983)))
      | ~ class_Int_Oring__char__0(U_7983) ),
    inference(variable_rename,[status(thm)],[f_2276_1]) ).

fof(f_2276_3,plain,
    ( ! [U_7983,U_7984] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7983),U_7984),U_7984) = c_Groups_Ozero__class_Ozero(U_7983)
        | U_7984 != c_Groups_Ozero__class_Ozero(U_7983)
        | ~ sP698(U_7983,U_7984) )
    & ! [U_7983,U_7984] :
        ( U_7984 = c_Groups_Ozero__class_Ozero(U_7983)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7983),U_7984),U_7984) != c_Groups_Ozero__class_Ozero(U_7983)
        | ~ sP698(U_7983,U_7984) )
    & ! [U_7983,U_7984] :
        ( sP698(U_7983,U_7984)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7983),U_7984),c_Int_Oring__1__class_OInts(U_7983)))
        | ~ class_Int_Oring__char__0(U_7983) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP698])],[f_2276_2]) ).

cnf(f_2276_4,plain,
    ( sP698(U_7983,U_7984)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7983),U_7984),c_Int_Oring__1__class_OInts(U_7983)))
    | ~ class_Int_Oring__char__0(U_7983) ),
    inference(clausify,[status(thm)],[f_2276_3]) ).

cnf(f_2276_5,plain,
    ( U_7984 = c_Groups_Ozero__class_Ozero(U_7983)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7983),U_7984),U_7984) != c_Groups_Ozero__class_Ozero(U_7983)
    | ~ sP698(U_7983,U_7984) ),
    inference(clausify,[status(thm)],[f_2276_3]) ).

cnf(f_2276_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7983),U_7984),U_7984) = c_Groups_Ozero__class_Ozero(U_7983)
    | U_7984 != c_Groups_Ozero__class_Ozero(U_7983)
    | ~ sP698(U_7983,U_7984) ),
    inference(clausify,[status(thm)],[f_2276_3]) ).

fof(f_2277_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__lessI1]) ).

fof(f_2277_2,plain,
    ! [U_7988,U_7987,U_7986,U_7985] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7985),U_7987)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7986),U_7988))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7985),U_7986)) ),
    inference(variable_rename,[status(thm)],[f_2277_1]) ).

fof(f_2277_3,plain,
    ! [U_7986,U_7985,U_7987,U_7988] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7985),U_7987)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7986),U_7988))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7985),U_7986)) ),
    inference(definitional_conversion,[status(esa)],[f_2277_2]) ).

cnf(f_2277_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7985),U_7987)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7986),U_7988))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7985),U_7986)) ),
    inference(clausify,[status(thm)],[f_2277_3]) ).

fof(f_2278_1,plain,
    ! [V_a_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero]) ).

fof(f_2278_2,plain,
    ! [U_7990,U_7989] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7989),c_Groups_Oone__class_Oone(U_7989)),U_7990)),U_7990) != c_Groups_Ozero__class_Ozero(U_7989)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7989),U_7990),c_Int_Oring__1__class_OInts(U_7989)))
      | ~ class_Int_Oring__char__0(U_7989) ),
    inference(variable_rename,[status(thm)],[f_2278_1]) ).

fof(f_2278_3,plain,
    ! [U_7989,U_7990] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7989),c_Groups_Oone__class_Oone(U_7989)),U_7990)),U_7990) != c_Groups_Ozero__class_Ozero(U_7989)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7989),U_7990),c_Int_Oring__1__class_OInts(U_7989)))
      | ~ class_Int_Oring__char__0(U_7989) ),
    inference(definitional_conversion,[status(esa)],[f_2278_2]) ).

cnf(f_2278_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7989),c_Groups_Oone__class_Oone(U_7989)),U_7990)),U_7990) != c_Groups_Ozero__class_Ozero(U_7989)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7989),U_7990),c_Int_Oring__1__class_OInts(U_7989)))
    | ~ class_Int_Oring__char__0(U_7989) ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

fof(f_2279_1,plain,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).

fof(f_2279_2,plain,
    ! [U_7997,U_7996,U_7995,U_7994,U_7993,U_7992,U_7991] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7997,U_7993),tc_prod(U_7997,U_7993))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7997,U_7993),tc_prod(U_7997,U_7993)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7993),U_7992),U_7994)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7993),U_7992),U_7995))),c_Recdef_Osame__fst(U_7997,U_7993,U_7991,U_7996)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7993,U_7993)),hAPP(hAPP(c_Product__Type_OPair(U_7993,U_7993),U_7994),U_7995)),hAPP(U_7996,U_7992)))
      | ~ hBOOL(hAPP(U_7991,U_7992)) ),
    inference(variable_rename,[status(thm)],[f_2279_1]) ).

fof(f_2279_3,plain,
    ! [U_7991,U_7992,U_7993,U_7994,U_7995,U_7996,U_7997] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7997,U_7993),tc_prod(U_7997,U_7993))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7997,U_7993),tc_prod(U_7997,U_7993)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7993),U_7992),U_7994)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7993),U_7992),U_7995))),c_Recdef_Osame__fst(U_7997,U_7993,U_7991,U_7996)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7993,U_7993)),hAPP(hAPP(c_Product__Type_OPair(U_7993,U_7993),U_7994),U_7995)),hAPP(U_7996,U_7992)))
      | ~ hBOOL(hAPP(U_7991,U_7992)) ),
    inference(definitional_conversion,[status(esa)],[f_2279_2]) ).

cnf(f_2279_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_7997,U_7993),tc_prod(U_7997,U_7993))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_7997,U_7993),tc_prod(U_7997,U_7993)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7993),U_7992),U_7994)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7993),U_7992),U_7995))),c_Recdef_Osame__fst(U_7997,U_7993,U_7991,U_7996)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7993,U_7993)),hAPP(hAPP(c_Product__Type_OPair(U_7993,U_7993),U_7994),U_7995)),hAPP(U_7996,U_7992)))
    | ~ hBOOL(hAPP(U_7991,U_7992)) ),
    inference(clausify,[status(thm)],[f_2279_3]) ).

fof(f_2280_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__leqI2]) ).

fof(f_2280_2,plain,
    ! [U_8001,U_8000,U_7999,U_7998] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7998),U_8000)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7999),U_8001))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8000),U_8001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7998),U_7999)) ),
    inference(variable_rename,[status(thm)],[f_2280_1]) ).

fof(f_2280_3,plain,
    ! [U_7998,U_7999,U_8000,U_8001] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7998),U_8000)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7999),U_8001))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8000),U_8001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7998),U_7999)) ),
    inference(definitional_conversion,[status(esa)],[f_2280_2]) ).

cnf(f_2280_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7998),U_8000)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_7999),U_8001))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8000),U_8001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7998),U_7999)) ),
    inference(clausify,[status(thm)],[f_2280_3]) ).

fof(f_2281_1,plain,
    ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_smax__insertI]) ).

fof(f_2281_2,plain,
    ! [U_8005,U_8004,U_8003,U_8002] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8004),U_8005)),U_8003)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8005),U_8003)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8004),U_8002)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8002),U_8003)) ),
    inference(variable_rename,[status(thm)],[f_2281_1]) ).

fof(f_2281_3,plain,
    ! [U_8003,U_8004,U_8002,U_8005] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8004),U_8005)),U_8003)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8005),U_8003)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8004),U_8002)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8002),U_8003)) ),
    inference(definitional_conversion,[status(esa)],[f_2281_2]) ).

cnf(f_2281_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8004),U_8005)),U_8003)),c_FunDef_Omax__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8005),U_8003)),c_FunDef_Omax__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8004),U_8002)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8002),U_8003)) ),
    inference(clausify,[status(thm)],[f_2281_3]) ).

fof(f_2282_1,plain,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
    inference(fof_nnf,[status(thm)],[fact_smin__insertI]) ).

fof(f_2282_2,plain,
    ! [U_8009,U_8008,U_8007,U_8006] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8007),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8008),U_8009))),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8007),U_8009)),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8006),U_8008)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8006),U_8007)) ),
    inference(variable_rename,[status(thm)],[f_2282_1]) ).

fof(f_2282_3,plain,
    ! [U_8007,U_8008,U_8006,U_8009] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8007),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8008),U_8009))),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8007),U_8009)),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8006),U_8008)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8006),U_8007)) ),
    inference(definitional_conversion,[status(esa)],[f_2282_2]) ).

cnf(f_2282_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8007),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8008),U_8009))),c_FunDef_Omin__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8007),U_8009)),c_FunDef_Omin__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8006),U_8008)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8006),U_8007)) ),
    inference(clausify,[status(thm)],[f_2282_3]) ).

fof(f_2283_1,plain,
    ! [V_X_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | V_X_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_smin__emptyI]) ).

fof(f_2283_2,plain,
    ! [U_8010] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8010),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_8010 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2283_1]) ).

fof(f_2283_3,plain,
    ! [U_8010] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8010),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_8010 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2283_2]) ).

cnf(f_2283_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8010),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
    | U_8010 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2283_3]) ).

fof(f_2284_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__leqI1]) ).

fof(f_2284_2,plain,
    ! [U_8014,U_8013,U_8012,U_8011] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8011),U_8013)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8012),U_8014))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8011),U_8012)) ),
    inference(variable_rename,[status(thm)],[f_2284_1]) ).

fof(f_2284_3,plain,
    ! [U_8012,U_8013,U_8011,U_8014] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8011),U_8013)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8012),U_8014))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8011),U_8012)) ),
    inference(definitional_conversion,[status(esa)],[f_2284_2]) ).

cnf(f_2284_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8011),U_8013)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8012),U_8014))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8011),U_8012)) ),
    inference(clausify,[status(thm)],[f_2284_3]) ).

fof(f_2285_1,plain,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wmin__insertI]) ).

fof(f_2285_2,plain,
    ! [U_8018,U_8017,U_8016,U_8015] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8016),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8017),U_8018))),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8016),U_8018)),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8015),U_8017)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8015),U_8016)) ),
    inference(variable_rename,[status(thm)],[f_2285_1]) ).

fof(f_2285_3,plain,
    ! [U_8015,U_8016,U_8017,U_8018] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8016),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8017),U_8018))),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8016),U_8018)),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8015),U_8017)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8015),U_8016)) ),
    inference(definitional_conversion,[status(esa)],[f_2285_2]) ).

cnf(f_2285_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8016),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8017),U_8018))),c_FunDef_Omin__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8016),U_8018)),c_FunDef_Omin__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8015),U_8017)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8015),U_8016)) ),
    inference(clausify,[status(thm)],[f_2285_3]) ).

fof(f_2286_1,plain,
    ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wmax__insertI]) ).

fof(f_2286_2,plain,
    ! [U_8022,U_8021,U_8020,U_8019] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8021),U_8022)),U_8020)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8022),U_8020)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8021),U_8019)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8019),U_8020)) ),
    inference(variable_rename,[status(thm)],[f_2286_1]) ).

fof(f_2286_3,plain,
    ! [U_8021,U_8020,U_8019,U_8022] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8021),U_8022)),U_8020)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8022),U_8020)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8021),U_8019)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8019),U_8020)) ),
    inference(definitional_conversion,[status(esa)],[f_2286_2]) ).

cnf(f_2286_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8021),U_8022)),U_8020)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8022),U_8020)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8021),U_8019)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8019),U_8020)) ),
    inference(clausify,[status(thm)],[f_2286_3]) ).

fof(f_2287_1,plain,
    ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(fof_nnf,[status(thm)],[fact_wmin__emptyI]) ).

fof(f_2287_2,plain,
    ! [U_8023] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8023),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(variable_rename,[status(thm)],[f_2287_1]) ).

fof(f_2287_3,plain,
    ! [U_8023] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8023),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(definitional_conversion,[status(esa)],[f_2287_2]) ).

cnf(f_2287_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_8023),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(clausify,[status(thm)],[f_2287_3]) ).

fof(f_2288_1,plain,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(fof_nnf,[status(thm)],[fact_min__strict__def]) ).

fof(f_2288_2,plain,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(definitional_conversion,[status(esa)],[f_2288_1]) ).

cnf(f_2288_3,plain,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_2288_2]) ).

fof(f_2289_1,plain,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_min__weak__def]) ).

fof(f_2289_2,plain,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2289_1]) ).

cnf(f_2289_3,plain,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2289_2]) ).

fof(f_2290_1,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    inference(fof_nnf,[status(thm)],[fact_max__rpair__set]) ).

fof(f_2290_2,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    inference(definitional_conversion,[status(esa)],[f_2290_1]) ).

cnf(f_2290_3,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    inference(clausify,[status(thm)],[f_2290_2]) ).

fof(f_2291_1,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    inference(fof_nnf,[status(thm)],[fact_min__rpair__set]) ).

fof(f_2291_2,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    inference(definitional_conversion,[status(esa)],[f_2291_1]) ).

cnf(f_2291_3,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    inference(clausify,[status(thm)],[f_2291_2]) ).

fof(f_2292_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__than__iff]) ).

fof(f_2292_2,plain,
    ! [U_8025,U_8024] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8024),U_8025)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8024),U_8025)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8024),U_8025))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8024),U_8025)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[f_2292_1]) ).

fof(f_2292_3,plain,
    ( ! [U_8029,U_8027] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8027),U_8029)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8027),U_8029)) )
    & ! [U_8028,U_8026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8026),U_8028))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8026),U_8028)),c_Wellfounded_Oless__than)) ) ),
    inference(miniscope,[status(thm)],[f_2292_2]) ).

fof(f_2292_4,plain,
    ( ! [U_8027,U_8029] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8027),U_8029)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8027),U_8029)) )
    & ! [U_8028,U_8026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8026),U_8028))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8026),U_8028)),c_Wellfounded_Oless__than)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2292_3]) ).

cnf(f_2292_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8026),U_8028))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8026),U_8028)),c_Wellfounded_Oless__than)) ),
    inference(clausify,[status(thm)],[f_2292_4]) ).

cnf(f_2292_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8027),U_8029)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8027),U_8029)) ),
    inference(clausify,[status(thm)],[f_2292_4]) ).

fof(f_2293_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
      | hBOOL(hAPP(V_A_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1E]) ).

fof(f_2293_2,plain,
    ! [U_8033,U_8032,U_8031,U_8030] :
      ( hBOOL(hAPP(U_8032,U_8033))
      | hBOOL(hAPP(U_8031,U_8033))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8030,tc_HOL_Obool)),U_8031),U_8032),U_8033)) ),
    inference(variable_rename,[status(thm)],[f_2293_1]) ).

fof(f_2293_3,plain,
    ! [U_8033,U_8032,U_8031] :
      ( ! [U_8030] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8030,tc_HOL_Obool)),U_8031),U_8032),U_8033))
      | hBOOL(hAPP(U_8032,U_8033))
      | hBOOL(hAPP(U_8031,U_8033)) ),
    inference(miniscope,[status(thm)],[f_2293_2]) ).

fof(f_2293_4,plain,
    ! [U_8031,U_8030,U_8032,U_8033] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8030,tc_HOL_Obool)),U_8031),U_8032),U_8033))
      | hBOOL(hAPP(U_8032,U_8033))
      | hBOOL(hAPP(U_8031,U_8033)) ),
    inference(definitional_conversion,[status(esa)],[f_2293_3]) ).

cnf(f_2293_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8030,tc_HOL_Obool)),U_8031),U_8032),U_8033))
    | hBOOL(hAPP(U_8032,U_8033))
    | hBOOL(hAPP(U_8031,U_8033)) ),
    inference(clausify,[status(thm)],[f_2293_4]) ).

fof(f_2294_1,plain,
    ! [T_b,V_A_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ( ~ hBOOL(hAPP(V_A_2,V_x_2))
        & ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup1CI]) ).

fof(f_2294_2,plain,
    ! [U_8037,U_8036,U_8035,U_8034] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8037,tc_HOL_Obool)),U_8036),U_8034),U_8035))
      | ( ~ hBOOL(hAPP(U_8036,U_8035))
        & ~ hBOOL(hAPP(U_8034,U_8035)) ) ),
    inference(variable_rename,[status(thm)],[f_2294_1]) ).

fof(f_2294_3,plain,
    ( ! [U_8034,U_8035,U_8036] :
        ( ~ hBOOL(hAPP(U_8036,U_8035))
        | ~ sP699(U_8034,U_8035,U_8036) )
    & ! [U_8034,U_8035,U_8036] :
        ( ~ hBOOL(hAPP(U_8034,U_8035))
        | ~ sP699(U_8034,U_8035,U_8036) )
    & ! [U_8034,U_8035,U_8036,U_8037] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8037,tc_HOL_Obool)),U_8036),U_8034),U_8035))
        | sP699(U_8034,U_8035,U_8036) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP699])],[f_2294_2]) ).

cnf(f_2294_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8037,tc_HOL_Obool)),U_8036),U_8034),U_8035))
    | sP699(U_8034,U_8035,U_8036) ),
    inference(clausify,[status(thm)],[f_2294_3]) ).

cnf(f_2294_5,plain,
    ( ~ hBOOL(hAPP(U_8034,U_8035))
    | ~ sP699(U_8034,U_8035,U_8036) ),
    inference(clausify,[status(thm)],[f_2294_3]) ).

cnf(f_2294_6,plain,
    ( ~ hBOOL(hAPP(U_8036,U_8035))
    | ~ sP699(U_8034,U_8035,U_8036) ),
    inference(clausify,[status(thm)],[f_2294_3]) ).

fof(f_2295_1,plain,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UnCI]) ).

fof(f_2295_2,plain,
    ! [U_8041,U_8040,U_8039,U_8038] :
      ( hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8038,tc_HOL_Obool)),U_8041),U_8040)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),U_8041))
        & ~ hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),U_8040)) ) ),
    inference(variable_rename,[status(thm)],[f_2295_1]) ).

fof(f_2295_3,plain,
    ( ! [U_8038,U_8039,U_8040,U_8041] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),U_8041))
        | ~ sP700(U_8038,U_8039,U_8040,U_8041) )
    & ! [U_8038,U_8039,U_8040,U_8041] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),U_8040))
        | ~ sP700(U_8038,U_8039,U_8040,U_8041) )
    & ! [U_8038,U_8039,U_8040,U_8041] :
        ( hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8038,tc_HOL_Obool)),U_8041),U_8040)))
        | sP700(U_8038,U_8039,U_8040,U_8041) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP700])],[f_2295_2]) ).

cnf(f_2295_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8038,tc_HOL_Obool)),U_8041),U_8040)))
    | sP700(U_8038,U_8039,U_8040,U_8041) ),
    inference(clausify,[status(thm)],[f_2295_3]) ).

cnf(f_2295_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),U_8040))
    | ~ sP700(U_8038,U_8039,U_8040,U_8041) ),
    inference(clausify,[status(thm)],[f_2295_3]) ).

cnf(f_2295_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8038),U_8039),U_8041))
    | ~ sP700(U_8038,U_8039,U_8040,U_8041) ),
    inference(clausify,[status(thm)],[f_2295_3]) ).

fof(f_2296_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UnE]) ).

fof(f_2296_2,plain,
    ! [U_8045,U_8044,U_8043,U_8042] :
      ( hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),U_8045))
      | hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),U_8044))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8042,tc_HOL_Obool)),U_8044),U_8045))) ),
    inference(variable_rename,[status(thm)],[f_2296_1]) ).

fof(f_2296_3,plain,
    ! [U_8042,U_8043,U_8044,U_8045] :
      ( hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),U_8045))
      | hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),U_8044))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8042,tc_HOL_Obool)),U_8044),U_8045))) ),
    inference(definitional_conversion,[status(esa)],[f_2296_2]) ).

cnf(f_2296_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),U_8045))
    | hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),U_8044))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8042),U_8043),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8042,tc_HOL_Obool)),U_8044),U_8045))) ),
    inference(clausify,[status(thm)],[f_2296_3]) ).

fof(f_2297_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__empty]) ).

fof(f_2297_2,plain,
    ! [U_8048,U_8047,U_8046] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8046,tc_HOL_Obool)),U_8047),U_8048) = c_Orderings_Obot__class_Obot(tc_fun(U_8046,tc_HOL_Obool))
        | U_8048 != c_Orderings_Obot__class_Obot(tc_fun(U_8046,tc_HOL_Obool))
        | U_8047 != c_Orderings_Obot__class_Obot(tc_fun(U_8046,tc_HOL_Obool)) )
      & ( ( U_8048 = c_Orderings_Obot__class_Obot(tc_fun(U_8046,tc_HOL_Obool))
          & U_8047 = c_Orderings_Obot__class_Obot(tc_fun(U_8046,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8046,tc_HOL_Obool)),U_8047),U_8048) != c_Orderings_Obot__class_Obot(tc_fun(U_8046,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2297_1]) ).

fof(f_2297_3,plain,
    ( ! [U_8054,U_8052,U_8050] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8050,tc_HOL_Obool)),U_8052),U_8054) = c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool))
        | U_8054 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool))
        | U_8052 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool)) )
    & ! [U_8053,U_8051,U_8049] :
        ( ( U_8053 = c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool))
          & U_8051 = c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8049,tc_HOL_Obool)),U_8051),U_8053) != c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2297_2]) ).

fof(f_2297_4,plain,
    ( ! [U_8051,U_8049,U_8053] :
        ( U_8053 = c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool))
        | ~ sP701(U_8051,U_8049,U_8053) )
    & ! [U_8051,U_8049,U_8053] :
        ( U_8051 = c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool))
        | ~ sP701(U_8051,U_8049,U_8053) )
    & ! [U_8054,U_8052,U_8050] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8050,tc_HOL_Obool)),U_8052),U_8054) = c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool))
        | U_8054 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool))
        | U_8052 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool)) )
    & ! [U_8051,U_8049,U_8053] :
        ( sP701(U_8051,U_8049,U_8053)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8049,tc_HOL_Obool)),U_8051),U_8053) != c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP701])],[f_2297_3]) ).

cnf(f_2297_5,plain,
    ( sP701(U_8051,U_8049,U_8053)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8049,tc_HOL_Obool)),U_8051),U_8053) != c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

cnf(f_2297_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8050,tc_HOL_Obool)),U_8052),U_8054) = c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool))
    | U_8054 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool))
    | U_8052 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

cnf(f_2297_7,plain,
    ( U_8051 = c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool))
    | ~ sP701(U_8051,U_8049,U_8053) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

cnf(f_2297_8,plain,
    ( U_8053 = c_Orderings_Obot__class_Obot(tc_fun(U_8049,tc_HOL_Obool))
    | ~ sP701(U_8051,U_8049,U_8053) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

fof(f_2298_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__empty__right]) ).

fof(f_2298_2,plain,
    ! [U_8056,U_8055] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8055,tc_HOL_Obool)),U_8056),c_Orderings_Obot__class_Obot(tc_fun(U_8055,tc_HOL_Obool))) = U_8056,
    inference(variable_rename,[status(thm)],[f_2298_1]) ).

fof(f_2298_3,plain,
    ! [U_8055,U_8056] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8055,tc_HOL_Obool)),U_8056),c_Orderings_Obot__class_Obot(tc_fun(U_8055,tc_HOL_Obool))) = U_8056,
    inference(definitional_conversion,[status(esa)],[f_2298_2]) ).

cnf(f_2298_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8055,tc_HOL_Obool)),U_8056),c_Orderings_Obot__class_Obot(tc_fun(U_8055,tc_HOL_Obool))) = U_8056,
    inference(clausify,[status(thm)],[f_2298_3]) ).

fof(f_2299_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    inference(fof_nnf,[status(thm)],[fact_Un__empty__left]) ).

fof(f_2299_2,plain,
    ! [U_8058,U_8057] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8057,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8057,tc_HOL_Obool))),U_8058) = U_8058,
    inference(variable_rename,[status(thm)],[f_2299_1]) ).

fof(f_2299_3,plain,
    ! [U_8057,U_8058] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8057,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8057,tc_HOL_Obool))),U_8058) = U_8058,
    inference(definitional_conversion,[status(esa)],[f_2299_2]) ).

cnf(f_2299_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8057,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8057,tc_HOL_Obool))),U_8058) = U_8058,
    inference(clausify,[status(thm)],[f_2299_3]) ).

fof(f_2300_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
          | V_y_2 != c_Orderings_Obot__class_Obot(T_b)
          | V_x_2 != c_Orderings_Obot__class_Obot(T_b) )
        & ( ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
            & V_x_2 = c_Orderings_Obot__class_Obot(T_b) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != c_Orderings_Obot__class_Obot(T_b) ) )
      | ~ class_Lattices_Obounded__lattice__bot(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff]) ).

fof(f_2300_2,plain,
    ! [U_8061,U_8060,U_8059] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8059),U_8060),U_8061) = c_Orderings_Obot__class_Obot(U_8059)
          | U_8061 != c_Orderings_Obot__class_Obot(U_8059)
          | U_8060 != c_Orderings_Obot__class_Obot(U_8059) )
        & ( ( U_8061 = c_Orderings_Obot__class_Obot(U_8059)
            & U_8060 = c_Orderings_Obot__class_Obot(U_8059) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8059),U_8060),U_8061) != c_Orderings_Obot__class_Obot(U_8059) ) )
      | ~ class_Lattices_Obounded__lattice__bot(U_8059) ),
    inference(variable_rename,[status(thm)],[f_2300_1]) ).

fof(f_2300_3,plain,
    ( ! [U_8059,U_8060,U_8061] :
        ( U_8061 = c_Orderings_Obot__class_Obot(U_8059)
        | ~ sP702(U_8059,U_8060,U_8061) )
    & ! [U_8059,U_8060,U_8061] :
        ( U_8060 = c_Orderings_Obot__class_Obot(U_8059)
        | ~ sP702(U_8059,U_8060,U_8061) )
    & ! [U_8059,U_8060,U_8061] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8059),U_8060),U_8061) = c_Orderings_Obot__class_Obot(U_8059)
        | U_8061 != c_Orderings_Obot__class_Obot(U_8059)
        | U_8060 != c_Orderings_Obot__class_Obot(U_8059)
        | ~ sP703(U_8059,U_8060,U_8061) )
    & ! [U_8059,U_8060,U_8061] :
        ( sP702(U_8059,U_8060,U_8061)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8059),U_8060),U_8061) != c_Orderings_Obot__class_Obot(U_8059)
        | ~ sP703(U_8059,U_8060,U_8061) )
    & ! [U_8059,U_8060,U_8061] :
        ( sP703(U_8059,U_8060,U_8061)
        | ~ class_Lattices_Obounded__lattice__bot(U_8059) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP702,sP703])],[f_2300_2]) ).

cnf(f_2300_4,plain,
    ( sP703(U_8059,U_8060,U_8061)
    | ~ class_Lattices_Obounded__lattice__bot(U_8059) ),
    inference(clausify,[status(thm)],[f_2300_3]) ).

cnf(f_2300_5,plain,
    ( sP702(U_8059,U_8060,U_8061)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8059),U_8060),U_8061) != c_Orderings_Obot__class_Obot(U_8059)
    | ~ sP703(U_8059,U_8060,U_8061) ),
    inference(clausify,[status(thm)],[f_2300_3]) ).

cnf(f_2300_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8059),U_8060),U_8061) = c_Orderings_Obot__class_Obot(U_8059)
    | U_8061 != c_Orderings_Obot__class_Obot(U_8059)
    | U_8060 != c_Orderings_Obot__class_Obot(U_8059)
    | ~ sP703(U_8059,U_8060,U_8061) ),
    inference(clausify,[status(thm)],[f_2300_3]) ).

cnf(f_2300_7,plain,
    ( U_8060 = c_Orderings_Obot__class_Obot(U_8059)
    | ~ sP702(U_8059,U_8060,U_8061) ),
    inference(clausify,[status(thm)],[f_2300_3]) ).

cnf(f_2300_8,plain,
    ( U_8061 = c_Orderings_Obot__class_Obot(U_8059)
    | ~ sP702(U_8059,U_8060,U_8061) ),
    inference(clausify,[status(thm)],[f_2300_3]) ).

fof(f_2301_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__bot__right]) ).

fof(f_2301_2,plain,
    ! [U_8063,U_8062] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8062),U_8063),c_Orderings_Obot__class_Obot(U_8062)) = U_8063
      | ~ class_Lattices_Obounded__lattice__bot(U_8062) ),
    inference(variable_rename,[status(thm)],[f_2301_1]) ).

fof(f_2301_3,plain,
    ! [U_8062,U_8063] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8062),U_8063),c_Orderings_Obot__class_Obot(U_8062)) = U_8063
      | ~ class_Lattices_Obounded__lattice__bot(U_8062) ),
    inference(definitional_conversion,[status(esa)],[f_2301_2]) ).

cnf(f_2301_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8062),U_8063),c_Orderings_Obot__class_Obot(U_8062)) = U_8063
    | ~ class_Lattices_Obounded__lattice__bot(U_8062) ),
    inference(clausify,[status(thm)],[f_2301_3]) ).

fof(f_2302_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__bot__left]) ).

fof(f_2302_2,plain,
    ! [U_8065,U_8064] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8064),c_Orderings_Obot__class_Obot(U_8064)),U_8065) = U_8065
      | ~ class_Lattices_Obounded__lattice__bot(U_8064) ),
    inference(variable_rename,[status(thm)],[f_2302_1]) ).

fof(f_2302_3,plain,
    ! [U_8065,U_8064] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8064),c_Orderings_Obot__class_Obot(U_8064)),U_8065) = U_8065
      | ~ class_Lattices_Obounded__lattice__bot(U_8064) ),
    inference(definitional_conversion,[status(esa)],[f_2302_2]) ).

cnf(f_2302_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8064),c_Orderings_Obot__class_Obot(U_8064)),U_8065) = U_8065
    | ~ class_Lattices_Obounded__lattice__bot(U_8064) ),
    inference(clausify,[status(thm)],[f_2302_3]) ).

fof(f_2303_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__upper1]) ).

fof(f_2303_2,plain,
    ! [U_8068,U_8067,U_8066] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8066,tc_HOL_Obool)),U_8067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8066,tc_HOL_Obool)),U_8067),U_8068))),
    inference(variable_rename,[status(thm)],[f_2303_1]) ).

fof(f_2303_3,plain,
    ! [U_8066,U_8067,U_8068] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8066,tc_HOL_Obool)),U_8067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8066,tc_HOL_Obool)),U_8067),U_8068))),
    inference(definitional_conversion,[status(esa)],[f_2303_2]) ).

cnf(f_2303_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8066,tc_HOL_Obool)),U_8067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8066,tc_HOL_Obool)),U_8067),U_8068))),
    inference(clausify,[status(thm)],[f_2303_3]) ).

fof(f_2304_1,plain,
    ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__upper2]) ).

fof(f_2304_2,plain,
    ! [U_8071,U_8070,U_8069] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8069,tc_HOL_Obool)),U_8070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8069,tc_HOL_Obool)),U_8071),U_8070))),
    inference(variable_rename,[status(thm)],[f_2304_1]) ).

fof(f_2304_3,plain,
    ! [U_8069,U_8070,U_8071] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8069,tc_HOL_Obool)),U_8070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8069,tc_HOL_Obool)),U_8071),U_8070))),
    inference(definitional_conversion,[status(esa)],[f_2304_2]) ).

cnf(f_2304_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8069,tc_HOL_Obool)),U_8070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8069,tc_HOL_Obool)),U_8071),U_8070))),
    inference(clausify,[status(thm)],[f_2304_3]) ).

fof(f_2305_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__Un__eq]) ).

fof(f_2305_2,plain,
    ! [U_8074,U_8073,U_8072] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8072,tc_HOL_Obool)),U_8073),U_8074))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8072,tc_HOL_Obool)),U_8073),U_8074) != U_8074 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8072,tc_HOL_Obool)),U_8073),U_8074) = U_8074
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8072,tc_HOL_Obool)),U_8073),U_8074)) ) ),
    inference(variable_rename,[status(thm)],[f_2305_1]) ).

fof(f_2305_3,plain,
    ( ! [U_8080,U_8078,U_8076] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8076,tc_HOL_Obool)),U_8078),U_8080))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8076,tc_HOL_Obool)),U_8078),U_8080) != U_8080 )
    & ! [U_8079,U_8077,U_8075] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8075,tc_HOL_Obool)),U_8077),U_8079) = U_8079
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8075,tc_HOL_Obool)),U_8077),U_8079)) ) ),
    inference(miniscope,[status(thm)],[f_2305_2]) ).

fof(f_2305_4,plain,
    ( ! [U_8076,U_8078,U_8080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8076,tc_HOL_Obool)),U_8078),U_8080))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8076,tc_HOL_Obool)),U_8078),U_8080) != U_8080 )
    & ! [U_8079,U_8077,U_8075] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8075,tc_HOL_Obool)),U_8077),U_8079) = U_8079
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8075,tc_HOL_Obool)),U_8077),U_8079)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2305_3]) ).

cnf(f_2305_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8075,tc_HOL_Obool)),U_8077),U_8079) = U_8079
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8075,tc_HOL_Obool)),U_8077),U_8079)) ),
    inference(clausify,[status(thm)],[f_2305_4]) ).

cnf(f_2305_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8076,tc_HOL_Obool)),U_8078),U_8080))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8076,tc_HOL_Obool)),U_8078),U_8080) != U_8080 ),
    inference(clausify,[status(thm)],[f_2305_4]) ).

fof(f_2306_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__absorb1]) ).

fof(f_2306_2,plain,
    ! [U_8083,U_8082,U_8081] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8081,tc_HOL_Obool)),U_8082),U_8083) = U_8083
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8081,tc_HOL_Obool)),U_8082),U_8083)) ),
    inference(variable_rename,[status(thm)],[f_2306_1]) ).

fof(f_2306_3,plain,
    ! [U_8081,U_8082,U_8083] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8081,tc_HOL_Obool)),U_8082),U_8083) = U_8083
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8081,tc_HOL_Obool)),U_8082),U_8083)) ),
    inference(definitional_conversion,[status(esa)],[f_2306_2]) ).

cnf(f_2306_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8081,tc_HOL_Obool)),U_8082),U_8083) = U_8083
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8081,tc_HOL_Obool)),U_8082),U_8083)) ),
    inference(clausify,[status(thm)],[f_2306_3]) ).

fof(f_2307_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__absorb2]) ).

fof(f_2307_2,plain,
    ! [U_8086,U_8085,U_8084] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8084,tc_HOL_Obool)),U_8086),U_8085) = U_8086
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8084,tc_HOL_Obool)),U_8085),U_8086)) ),
    inference(variable_rename,[status(thm)],[f_2307_1]) ).

fof(f_2307_3,plain,
    ! [U_8084,U_8085,U_8086] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8084,tc_HOL_Obool)),U_8086),U_8085) = U_8086
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8084,tc_HOL_Obool)),U_8085),U_8086)) ),
    inference(definitional_conversion,[status(esa)],[f_2307_2]) ).

cnf(f_2307_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8084,tc_HOL_Obool)),U_8086),U_8085) = U_8086
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8084,tc_HOL_Obool)),U_8085),U_8086)) ),
    inference(clausify,[status(thm)],[f_2307_3]) ).

fof(f_2308_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__least]) ).

fof(f_2308_2,plain,
    ! [U_8090,U_8089,U_8088,U_8087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8087,tc_HOL_Obool)),U_8088),U_8090)),U_8089))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),U_8090),U_8089))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),U_8088),U_8089)) ),
    inference(variable_rename,[status(thm)],[f_2308_1]) ).

fof(f_2308_3,plain,
    ! [U_8087,U_8088,U_8089,U_8090] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8087,tc_HOL_Obool)),U_8088),U_8090)),U_8089))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),U_8090),U_8089))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),U_8088),U_8089)) ),
    inference(definitional_conversion,[status(esa)],[f_2308_2]) ).

cnf(f_2308_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8087,tc_HOL_Obool)),U_8088),U_8090)),U_8089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),U_8090),U_8089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8087,tc_HOL_Obool)),U_8088),U_8089)) ),
    inference(clausify,[status(thm)],[f_2308_3]) ).

fof(f_2309_1,plain,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__mono]) ).

fof(f_2309_2,plain,
    ! [U_8095,U_8094,U_8093,U_8092,U_8091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8091,tc_HOL_Obool)),U_8092),U_8094)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8091,tc_HOL_Obool)),U_8093),U_8095)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),U_8094),U_8095))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),U_8092),U_8093)) ),
    inference(variable_rename,[status(thm)],[f_2309_1]) ).

fof(f_2309_3,plain,
    ! [U_8091,U_8092,U_8093,U_8094,U_8095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8091,tc_HOL_Obool)),U_8092),U_8094)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8091,tc_HOL_Obool)),U_8093),U_8095)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),U_8094),U_8095))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),U_8092),U_8093)) ),
    inference(definitional_conversion,[status(esa)],[f_2309_2]) ).

cnf(f_2309_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8091,tc_HOL_Obool)),U_8092),U_8094)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8091,tc_HOL_Obool)),U_8093),U_8095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),U_8094),U_8095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8091,tc_HOL_Obool)),U_8092),U_8093)) ),
    inference(clausify,[status(thm)],[f_2309_3]) ).

fof(f_2310_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J]) ).

fof(f_2310_2,plain,
    ! [U_8098,U_8097,U_8096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8096),U_8097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8096),U_8097),U_8098)))
      | ~ class_Lattices_Olattice(U_8096) ),
    inference(variable_rename,[status(thm)],[f_2310_1]) ).

fof(f_2310_3,plain,
    ! [U_8097,U_8098,U_8096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8096),U_8097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8096),U_8097),U_8098)))
      | ~ class_Lattices_Olattice(U_8096) ),
    inference(definitional_conversion,[status(esa)],[f_2310_2]) ).

cnf(f_2310_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8096),U_8097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8096),U_8097),U_8098)))
    | ~ class_Lattices_Olattice(U_8096) ),
    inference(clausify,[status(thm)],[f_2310_3]) ).

fof(f_2311_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__ge1]) ).

fof(f_2311_2,plain,
    ! [U_8101,U_8100,U_8099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8099),U_8100),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8099),U_8100),U_8101)))
      | ~ class_Lattices_Osemilattice__sup(U_8099) ),
    inference(variable_rename,[status(thm)],[f_2311_1]) ).

fof(f_2311_3,plain,
    ! [U_8099,U_8100,U_8101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8099),U_8100),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8099),U_8100),U_8101)))
      | ~ class_Lattices_Osemilattice__sup(U_8099) ),
    inference(definitional_conversion,[status(esa)],[f_2311_2]) ).

cnf(f_2311_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8099),U_8100),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8099),U_8100),U_8101)))
    | ~ class_Lattices_Osemilattice__sup(U_8099) ),
    inference(clausify,[status(thm)],[f_2311_3]) ).

fof(f_2312_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J]) ).

fof(f_2312_2,plain,
    ! [U_8104,U_8103,U_8102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8102),U_8103),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8102),U_8104),U_8103)))
      | ~ class_Lattices_Olattice(U_8102) ),
    inference(variable_rename,[status(thm)],[f_2312_1]) ).

fof(f_2312_3,plain,
    ! [U_8102,U_8103,U_8104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8102),U_8103),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8102),U_8104),U_8103)))
      | ~ class_Lattices_Olattice(U_8102) ),
    inference(definitional_conversion,[status(esa)],[f_2312_2]) ).

cnf(f_2312_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8102),U_8103),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8102),U_8104),U_8103)))
    | ~ class_Lattices_Olattice(U_8102) ),
    inference(clausify,[status(thm)],[f_2312_3]) ).

fof(f_2313_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__ge2]) ).

fof(f_2313_2,plain,
    ! [U_8107,U_8106,U_8105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8105),U_8106),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8105),U_8107),U_8106)))
      | ~ class_Lattices_Osemilattice__sup(U_8105) ),
    inference(variable_rename,[status(thm)],[f_2313_1]) ).

fof(f_2313_3,plain,
    ! [U_8105,U_8106,U_8107] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8105),U_8106),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8105),U_8107),U_8106)))
      | ~ class_Lattices_Osemilattice__sup(U_8105) ),
    inference(definitional_conversion,[status(esa)],[f_2313_2]) ).

cnf(f_2313_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8105),U_8106),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8105),U_8107),U_8106)))
    | ~ class_Lattices_Osemilattice__sup(U_8105) ),
    inference(clausify,[status(thm)],[f_2313_3]) ).

fof(f_2314_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != V_y_2 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__sup]) ).

fof(f_2314_2,plain,
    ! [U_8110,U_8109,U_8108] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8108),U_8109),U_8110))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8108),U_8109),U_8110) != U_8110 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8108),U_8109),U_8110) = U_8110
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8108),U_8109),U_8110)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_8108) ),
    inference(variable_rename,[status(thm)],[f_2314_1]) ).

fof(f_2314_3,plain,
    ( ! [U_8108,U_8109,U_8110] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8108),U_8109),U_8110))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8108),U_8109),U_8110) != U_8110
        | ~ sP704(U_8108,U_8109,U_8110) )
    & ! [U_8108,U_8109,U_8110] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8108),U_8109),U_8110) = U_8110
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8108),U_8109),U_8110))
        | ~ sP704(U_8108,U_8109,U_8110) )
    & ! [U_8108,U_8109,U_8110] :
        ( sP704(U_8108,U_8109,U_8110)
        | ~ class_Lattices_Osemilattice__sup(U_8108) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP704])],[f_2314_2]) ).

cnf(f_2314_4,plain,
    ( sP704(U_8108,U_8109,U_8110)
    | ~ class_Lattices_Osemilattice__sup(U_8108) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

cnf(f_2314_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8108),U_8109),U_8110) = U_8110
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8108),U_8109),U_8110))
    | ~ sP704(U_8108,U_8109,U_8110) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

cnf(f_2314_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8108),U_8109),U_8110))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8108),U_8109),U_8110) != U_8110
    | ~ sP704(U_8108,U_8109,U_8110) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

fof(f_2315_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__sup__iff]) ).

fof(f_2315_2,plain,
    ! [U_8114,U_8113,U_8112,U_8111] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8111),U_8112),U_8113)),U_8114))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8113),U_8114))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8112),U_8114)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8113),U_8114))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8112),U_8114)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8111),U_8112),U_8113)),U_8114)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_8111) ),
    inference(variable_rename,[status(thm)],[f_2315_1]) ).

fof(f_2315_3,plain,
    ( ! [U_8111,U_8112,U_8113,U_8114] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8113),U_8114))
        | ~ sP705(U_8111,U_8112,U_8113,U_8114) )
    & ! [U_8111,U_8112,U_8113,U_8114] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8112),U_8114))
        | ~ sP705(U_8111,U_8112,U_8113,U_8114) )
    & ! [U_8111,U_8112,U_8113,U_8114] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8111),U_8112),U_8113)),U_8114))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8113),U_8114))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8112),U_8114))
        | ~ sP706(U_8111,U_8112,U_8113,U_8114) )
    & ! [U_8111,U_8112,U_8113,U_8114] :
        ( sP705(U_8111,U_8112,U_8113,U_8114)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8111),U_8112),U_8113)),U_8114))
        | ~ sP706(U_8111,U_8112,U_8113,U_8114) )
    & ! [U_8111,U_8112,U_8113,U_8114] :
        ( sP706(U_8111,U_8112,U_8113,U_8114)
        | ~ class_Lattices_Osemilattice__sup(U_8111) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP705,sP706])],[f_2315_2]) ).

cnf(f_2315_4,plain,
    ( sP706(U_8111,U_8112,U_8113,U_8114)
    | ~ class_Lattices_Osemilattice__sup(U_8111) ),
    inference(clausify,[status(thm)],[f_2315_3]) ).

cnf(f_2315_5,plain,
    ( sP705(U_8111,U_8112,U_8113,U_8114)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8111),U_8112),U_8113)),U_8114))
    | ~ sP706(U_8111,U_8112,U_8113,U_8114) ),
    inference(clausify,[status(thm)],[f_2315_3]) ).

cnf(f_2315_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8111),U_8112),U_8113)),U_8114))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8113),U_8114))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8112),U_8114))
    | ~ sP706(U_8111,U_8112,U_8113,U_8114) ),
    inference(clausify,[status(thm)],[f_2315_3]) ).

cnf(f_2315_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8112),U_8114))
    | ~ sP705(U_8111,U_8112,U_8113,U_8114) ),
    inference(clausify,[status(thm)],[f_2315_3]) ).

cnf(f_2315_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8111),U_8113),U_8114))
    | ~ sP705(U_8111,U_8112,U_8113,U_8114) ),
    inference(clausify,[status(thm)],[f_2315_3]) ).

fof(f_2316_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supI1]) ).

fof(f_2316_2,plain,
    ! [U_8118,U_8117,U_8116,U_8115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8115),U_8116),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8115),U_8117),U_8118)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8115),U_8116),U_8117))
      | ~ class_Lattices_Osemilattice__sup(U_8115) ),
    inference(variable_rename,[status(thm)],[f_2316_1]) ).

fof(f_2316_3,plain,
    ! [U_8118,U_8117,U_8116,U_8115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8115),U_8116),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8115),U_8117),U_8118)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8115),U_8116),U_8117))
      | ~ class_Lattices_Osemilattice__sup(U_8115) ),
    inference(definitional_conversion,[status(esa)],[f_2316_2]) ).

cnf(f_2316_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8115),U_8116),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8115),U_8117),U_8118)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8115),U_8116),U_8117))
    | ~ class_Lattices_Osemilattice__sup(U_8115) ),
    inference(clausify,[status(thm)],[f_2316_3]) ).

fof(f_2317_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supI2]) ).

fof(f_2317_2,plain,
    ! [U_8122,U_8121,U_8120,U_8119] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8119),U_8120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8119),U_8122),U_8121)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8119),U_8120),U_8121))
      | ~ class_Lattices_Osemilattice__sup(U_8119) ),
    inference(variable_rename,[status(thm)],[f_2317_1]) ).

fof(f_2317_3,plain,
    ! [U_8119,U_8120,U_8121,U_8122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8119),U_8120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8119),U_8122),U_8121)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8119),U_8120),U_8121))
      | ~ class_Lattices_Osemilattice__sup(U_8119) ),
    inference(definitional_conversion,[status(esa)],[f_2317_2]) ).

cnf(f_2317_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8119),U_8120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8119),U_8122),U_8121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8119),U_8120),U_8121))
    | ~ class_Lattices_Osemilattice__sup(U_8119) ),
    inference(clausify,[status(thm)],[f_2317_3]) ).

fof(f_2318_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__absorb2]) ).

fof(f_2318_2,plain,
    ! [U_8125,U_8124,U_8123] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8123),U_8124),U_8125) = U_8125
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8123),U_8124),U_8125))
      | ~ class_Lattices_Osemilattice__sup(U_8123) ),
    inference(variable_rename,[status(thm)],[f_2318_1]) ).

fof(f_2318_3,plain,
    ! [U_8123,U_8124,U_8125] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8123),U_8124),U_8125) = U_8125
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8123),U_8124),U_8125))
      | ~ class_Lattices_Osemilattice__sup(U_8123) ),
    inference(definitional_conversion,[status(esa)],[f_2318_2]) ).

cnf(f_2318_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8123),U_8124),U_8125) = U_8125
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8123),U_8124),U_8125))
    | ~ class_Lattices_Osemilattice__sup(U_8123) ),
    inference(clausify,[status(thm)],[f_2318_3]) ).

fof(f_2319_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__absorb1]) ).

fof(f_2319_2,plain,
    ! [U_8128,U_8127,U_8126] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8126),U_8128),U_8127) = U_8128
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8126),U_8127),U_8128))
      | ~ class_Lattices_Osemilattice__sup(U_8126) ),
    inference(variable_rename,[status(thm)],[f_2319_1]) ).

fof(f_2319_3,plain,
    ! [U_8126,U_8127,U_8128] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8126),U_8128),U_8127) = U_8128
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8126),U_8127),U_8128))
      | ~ class_Lattices_Osemilattice__sup(U_8126) ),
    inference(definitional_conversion,[status(esa)],[f_2319_2]) ).

cnf(f_2319_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8126),U_8128),U_8127) = U_8128
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8126),U_8127),U_8128))
    | ~ class_Lattices_Osemilattice__sup(U_8126) ),
    inference(clausify,[status(thm)],[f_2319_3]) ).

fof(f_2320_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supI]) ).

fof(f_2320_2,plain,
    ! [U_8132,U_8131,U_8130,U_8129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8129),U_8130),U_8132)),U_8131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8132),U_8131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8130),U_8131))
      | ~ class_Lattices_Osemilattice__sup(U_8129) ),
    inference(variable_rename,[status(thm)],[f_2320_1]) ).

fof(f_2320_3,plain,
    ! [U_8129,U_8130,U_8131,U_8132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8129),U_8130),U_8132)),U_8131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8132),U_8131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8130),U_8131))
      | ~ class_Lattices_Osemilattice__sup(U_8129) ),
    inference(definitional_conversion,[status(esa)],[f_2320_2]) ).

cnf(f_2320_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8129),U_8130),U_8132)),U_8131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8132),U_8131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8130),U_8131))
    | ~ class_Lattices_Osemilattice__sup(U_8129) ),
    inference(clausify,[status(thm)],[f_2320_3]) ).

fof(f_2321_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__least]) ).

fof(f_2321_2,plain,
    ! [U_8136,U_8135,U_8134,U_8133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8133),U_8134),U_8136)),U_8135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),U_8136),U_8135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),U_8134),U_8135))
      | ~ class_Lattices_Osemilattice__sup(U_8133) ),
    inference(variable_rename,[status(thm)],[f_2321_1]) ).

fof(f_2321_3,plain,
    ! [U_8133,U_8134,U_8135,U_8136] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8133),U_8134),U_8136)),U_8135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),U_8136),U_8135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),U_8134),U_8135))
      | ~ class_Lattices_Osemilattice__sup(U_8133) ),
    inference(definitional_conversion,[status(esa)],[f_2321_2]) ).

cnf(f_2321_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8133),U_8134),U_8136)),U_8135))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),U_8136),U_8135))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),U_8134),U_8135))
    | ~ class_Lattices_Osemilattice__sup(U_8133) ),
    inference(clausify,[status(thm)],[f_2321_3]) ).

fof(f_2322_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__mono]) ).

fof(f_2322_2,plain,
    ! [U_8141,U_8140,U_8139,U_8138,U_8137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8137),U_8138),U_8140)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8137),U_8139),U_8141)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),U_8141))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8138),U_8139))
      | ~ class_Lattices_Osemilattice__sup(U_8137) ),
    inference(variable_rename,[status(thm)],[f_2322_1]) ).

fof(f_2322_3,plain,
    ! [U_8137,U_8138,U_8139,U_8140,U_8141] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8137),U_8138),U_8140)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8137),U_8139),U_8141)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),U_8141))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8138),U_8139))
      | ~ class_Lattices_Osemilattice__sup(U_8137) ),
    inference(definitional_conversion,[status(esa)],[f_2322_2]) ).

cnf(f_2322_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8137),U_8138),U_8140)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8137),U_8139),U_8141)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),U_8141))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8138),U_8139))
    | ~ class_Lattices_Osemilattice__sup(U_8137) ),
    inference(clausify,[status(thm)],[f_2322_3]) ).

fof(f_2323_1,plain,
    ! [V_x,V_b,V_a,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supE]) ).

fof(f_2323_2,plain,
    ! [U_8145,U_8144,U_8143,U_8142] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),U_8144),U_8145))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),U_8143),U_8145)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8142),U_8143),U_8144)),U_8145))
      | ~ class_Lattices_Osemilattice__sup(U_8142) ),
    inference(variable_rename,[status(thm)],[f_2323_1]) ).

fof(f_2323_3,plain,
    ( ! [U_8142,U_8143,U_8144,U_8145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),U_8144),U_8145))
        | ~ sP707(U_8142,U_8143,U_8144,U_8145) )
    & ! [U_8142,U_8143,U_8144,U_8145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),U_8143),U_8145))
        | ~ sP707(U_8142,U_8143,U_8144,U_8145) )
    & ! [U_8142,U_8143,U_8144,U_8145] :
        ( sP707(U_8142,U_8143,U_8144,U_8145)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8142),U_8143),U_8144)),U_8145))
        | ~ class_Lattices_Osemilattice__sup(U_8142) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP707])],[f_2323_2]) ).

cnf(f_2323_4,plain,
    ( sP707(U_8142,U_8143,U_8144,U_8145)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8142),U_8143),U_8144)),U_8145))
    | ~ class_Lattices_Osemilattice__sup(U_8142) ),
    inference(clausify,[status(thm)],[f_2323_3]) ).

cnf(f_2323_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),U_8143),U_8145))
    | ~ sP707(U_8142,U_8143,U_8144,U_8145) ),
    inference(clausify,[status(thm)],[f_2323_3]) ).

cnf(f_2323_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8142),U_8144),U_8145))
    | ~ sP707(U_8142,U_8143,U_8144,U_8145) ),
    inference(clausify,[status(thm)],[f_2323_3]) ).

fof(f_2324_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(f_2324_2,plain,
    ! [U_8148,U_8147,U_8146] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8146,tc_HOL_Obool)),U_8147),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8146,tc_HOL_Obool)),U_8148),U_8147)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8146,tc_HOL_Obool)),U_8147),U_8148),
    inference(variable_rename,[status(thm)],[f_2324_1]) ).

fof(f_2324_3,plain,
    ! [U_8147,U_8146,U_8148] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8146,tc_HOL_Obool)),U_8147),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8146,tc_HOL_Obool)),U_8148),U_8147)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8146,tc_HOL_Obool)),U_8147),U_8148),
    inference(definitional_conversion,[status(esa)],[f_2324_2]) ).

cnf(f_2324_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8146,tc_HOL_Obool)),U_8147),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8146,tc_HOL_Obool)),U_8148),U_8147)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8146,tc_HOL_Obool)),U_8147),U_8148),
    inference(clausify,[status(thm)],[f_2324_3]) ).

fof(f_2325_1,plain,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel2]) ).

fof(f_2325_2,plain,
    ! [U_8151,U_8150,U_8149] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151)),U_8151) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151),
    inference(variable_rename,[status(thm)],[f_2325_1]) ).

fof(f_2325_3,plain,
    ! [U_8149,U_8150,U_8151] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151)),U_8151) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151),
    inference(definitional_conversion,[status(esa)],[f_2325_2]) ).

cnf(f_2325_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151)),U_8151) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151),
    inference(clausify,[status(thm)],[f_2325_3]) ).

fof(f_2326_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff]) ).

fof(f_2326_2,plain,
    ! [U_8155,U_8154,U_8153,U_8152] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8154)),U_8155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8152,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),U_8154),U_8155)),
    inference(variable_rename,[status(thm)],[f_2326_1]) ).

fof(f_2326_3,plain,
    ! [U_8152,U_8153,U_8154,U_8155] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8154)),U_8155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8152,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),U_8154),U_8155)),
    inference(definitional_conversion,[status(esa)],[f_2326_2]) ).

cnf(f_2326_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8154)),U_8155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8152,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8152,tc_HOL_Obool)),U_8154),U_8155)),
    inference(clausify,[status(thm)],[f_2326_3]) ).

fof(f_2327_1,plain,
    ! [T_b] :
      ( c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__max]) ).

fof(f_2327_2,plain,
    ! [U_8156] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8156) = c_Orderings_Oord__class_Omax(U_8156)
      | ~ class_Orderings_Olinorder(U_8156)
      | ~ class_Lattices_Osemilattice__sup(U_8156) ),
    inference(variable_rename,[status(thm)],[f_2327_1]) ).

fof(f_2327_3,plain,
    ! [U_8156] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8156) = c_Orderings_Oord__class_Omax(U_8156)
      | ~ class_Orderings_Olinorder(U_8156)
      | ~ class_Lattices_Osemilattice__sup(U_8156) ),
    inference(definitional_conversion,[status(esa)],[f_2327_2]) ).

cnf(f_2327_4,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(U_8156) = c_Orderings_Oord__class_Omax(U_8156)
    | ~ class_Orderings_Olinorder(U_8156)
    | ~ class_Lattices_Osemilattice__sup(U_8156) ),
    inference(clausify,[status(thm)],[f_2327_3]) ).

fof(f_2328_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem]) ).

fof(f_2328_2,plain,
    ! [U_8158,U_8157] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8157),U_8158),U_8158) = U_8158
      | ~ class_Lattices_Olattice(U_8157) ),
    inference(variable_rename,[status(thm)],[f_2328_1]) ).

fof(f_2328_3,plain,
    ! [U_8157,U_8158] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8157),U_8158),U_8158) = U_8158
      | ~ class_Lattices_Olattice(U_8157) ),
    inference(definitional_conversion,[status(esa)],[f_2328_2]) ).

cnf(f_2328_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8157),U_8158),U_8158) = U_8158
    | ~ class_Lattices_Olattice(U_8157) ),
    inference(clausify,[status(thm)],[f_2328_3]) ).

fof(f_2329_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__supI1]) ).

fof(f_2329_2,plain,
    ! [U_8162,U_8161,U_8160,U_8159] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),U_8160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8159),U_8161),U_8162)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),U_8160),U_8161))
      | ~ class_Lattices_Osemilattice__sup(U_8159) ),
    inference(variable_rename,[status(thm)],[f_2329_1]) ).

fof(f_2329_3,plain,
    ! [U_8159,U_8160,U_8161,U_8162] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),U_8160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8159),U_8161),U_8162)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),U_8160),U_8161))
      | ~ class_Lattices_Osemilattice__sup(U_8159) ),
    inference(definitional_conversion,[status(esa)],[f_2329_2]) ).

cnf(f_2329_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),U_8160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8159),U_8161),U_8162)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8159),U_8160),U_8161))
    | ~ class_Lattices_Osemilattice__sup(U_8159) ),
    inference(clausify,[status(thm)],[f_2329_3]) ).

fof(f_2330_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__supI2]) ).

fof(f_2330_2,plain,
    ! [U_8166,U_8165,U_8164,U_8163] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8163),U_8164),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8163),U_8166),U_8165)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8163),U_8164),U_8165))
      | ~ class_Lattices_Osemilattice__sup(U_8163) ),
    inference(variable_rename,[status(thm)],[f_2330_1]) ).

fof(f_2330_3,plain,
    ! [U_8163,U_8164,U_8165,U_8166] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8163),U_8164),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8163),U_8166),U_8165)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8163),U_8164),U_8165))
      | ~ class_Lattices_Osemilattice__sup(U_8163) ),
    inference(definitional_conversion,[status(esa)],[f_2330_2]) ).

cnf(f_2330_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8163),U_8164),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8163),U_8166),U_8165)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8163),U_8164),U_8165))
    | ~ class_Lattices_Osemilattice__sup(U_8163) ),
    inference(clausify,[status(thm)],[f_2330_3]) ).

fof(f_2331_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oidem]) ).

fof(f_2331_2,plain,
    ! [U_8168,U_8167] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8167),U_8168),U_8168) = U_8168
      | ~ class_Lattices_Osemilattice__sup(U_8167) ),
    inference(variable_rename,[status(thm)],[f_2331_1]) ).

fof(f_2331_3,plain,
    ! [U_8168,U_8167] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8167),U_8168),U_8168) = U_8168
      | ~ class_Lattices_Osemilattice__sup(U_8167) ),
    inference(definitional_conversion,[status(esa)],[f_2331_2]) ).

cnf(f_2331_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8167),U_8168),U_8168) = U_8168
    | ~ class_Lattices_Osemilattice__sup(U_8167) ),
    inference(clausify,[status(thm)],[f_2331_3]) ).

fof(f_2332_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__idem]) ).

fof(f_2332_2,plain,
    ! [U_8170,U_8169] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8169),U_8170),U_8170) = U_8170
      | ~ class_Lattices_Osemilattice__sup(U_8169) ),
    inference(variable_rename,[status(thm)],[f_2332_1]) ).

fof(f_2332_3,plain,
    ! [U_8169,U_8170] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8169),U_8170),U_8170) = U_8170
      | ~ class_Lattices_Osemilattice__sup(U_8169) ),
    inference(definitional_conversion,[status(esa)],[f_2332_2]) ).

cnf(f_2332_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8169),U_8170),U_8170) = U_8170
    | ~ class_Lattices_Osemilattice__sup(U_8169) ),
    inference(clausify,[status(thm)],[f_2332_3]) ).

fof(f_2333_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Ocommute]) ).

fof(f_2333_2,plain,
    ! [U_8173,U_8172,U_8171] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8171),U_8172),U_8173) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8171),U_8173),U_8172)
      | ~ class_Lattices_Osemilattice__sup(U_8171) ),
    inference(variable_rename,[status(thm)],[f_2333_1]) ).

fof(f_2333_3,plain,
    ! [U_8171,U_8172,U_8173] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8171),U_8172),U_8173) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8171),U_8173),U_8172)
      | ~ class_Lattices_Osemilattice__sup(U_8171) ),
    inference(definitional_conversion,[status(esa)],[f_2333_2]) ).

cnf(f_2333_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8171),U_8172),U_8173) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8171),U_8173),U_8172)
    | ~ class_Lattices_Osemilattice__sup(U_8171) ),
    inference(clausify,[status(thm)],[f_2333_3]) ).

fof(f_2334_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J]) ).

fof(f_2334_2,plain,
    ! [U_8176,U_8175,U_8174] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8174),U_8175),U_8176) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8174),U_8176),U_8175)
      | ~ class_Lattices_Olattice(U_8174) ),
    inference(variable_rename,[status(thm)],[f_2334_1]) ).

fof(f_2334_3,plain,
    ! [U_8174,U_8175,U_8176] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8174),U_8175),U_8176) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8174),U_8176),U_8175)
      | ~ class_Lattices_Olattice(U_8174) ),
    inference(definitional_conversion,[status(esa)],[f_2334_2]) ).

cnf(f_2334_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8174),U_8175),U_8176) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8174),U_8176),U_8175)
    | ~ class_Lattices_Olattice(U_8174) ),
    inference(clausify,[status(thm)],[f_2334_3]) ).

fof(f_2335_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__commute]) ).

fof(f_2335_2,plain,
    ! [U_8179,U_8178,U_8177] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8177),U_8178),U_8179) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8177),U_8179),U_8178)
      | ~ class_Lattices_Osemilattice__sup(U_8177) ),
    inference(variable_rename,[status(thm)],[f_2335_1]) ).

fof(f_2335_3,plain,
    ! [U_8177,U_8178,U_8179] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8177),U_8178),U_8179) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8177),U_8179),U_8178)
      | ~ class_Lattices_Osemilattice__sup(U_8177) ),
    inference(definitional_conversion,[status(esa)],[f_2335_2]) ).

cnf(f_2335_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8177),U_8178),U_8179) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8177),U_8179),U_8178)
    | ~ class_Lattices_Osemilattice__sup(U_8177) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

fof(f_2336_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem]) ).

fof(f_2336_2,plain,
    ! [U_8182,U_8181,U_8180] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),U_8182)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),U_8182)
      | ~ class_Lattices_Osemilattice__sup(U_8180) ),
    inference(variable_rename,[status(thm)],[f_2336_1]) ).

fof(f_2336_3,plain,
    ! [U_8180,U_8181,U_8182] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),U_8182)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),U_8182)
      | ~ class_Lattices_Osemilattice__sup(U_8180) ),
    inference(definitional_conversion,[status(esa)],[f_2336_2]) ).

cnf(f_2336_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),U_8182)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8180),U_8181),U_8182)
    | ~ class_Lattices_Osemilattice__sup(U_8180) ),
    inference(clausify,[status(thm)],[f_2336_3]) ).

fof(f_2337_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J]) ).

fof(f_2337_2,plain,
    ! [U_8185,U_8184,U_8183] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),U_8185)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),U_8185)
      | ~ class_Lattices_Olattice(U_8183) ),
    inference(variable_rename,[status(thm)],[f_2337_1]) ).

fof(f_2337_3,plain,
    ! [U_8183,U_8184,U_8185] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),U_8185)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),U_8185)
      | ~ class_Lattices_Olattice(U_8183) ),
    inference(definitional_conversion,[status(esa)],[f_2337_2]) ).

cnf(f_2337_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),U_8185)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8183),U_8184),U_8185)
    | ~ class_Lattices_Olattice(U_8183) ),
    inference(clausify,[status(thm)],[f_2337_3]) ).

fof(f_2338_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__left__idem]) ).

fof(f_2338_2,plain,
    ! [U_8188,U_8187,U_8186] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),U_8188)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),U_8188)
      | ~ class_Lattices_Osemilattice__sup(U_8186) ),
    inference(variable_rename,[status(thm)],[f_2338_1]) ).

fof(f_2338_3,plain,
    ! [U_8186,U_8187,U_8188] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),U_8188)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),U_8188)
      | ~ class_Lattices_Osemilattice__sup(U_8186) ),
    inference(definitional_conversion,[status(esa)],[f_2338_2]) ).

cnf(f_2338_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),U_8188)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8186),U_8187),U_8188)
    | ~ class_Lattices_Osemilattice__sup(U_8186) ),
    inference(clausify,[status(thm)],[f_2338_3]) ).

fof(f_2339_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute]) ).

fof(f_2339_2,plain,
    ! [U_8192,U_8191,U_8190,U_8189] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8190),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8191),U_8192)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8191),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8190),U_8192))
      | ~ class_Lattices_Osemilattice__sup(U_8189) ),
    inference(variable_rename,[status(thm)],[f_2339_1]) ).

fof(f_2339_3,plain,
    ! [U_8189,U_8190,U_8191,U_8192] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8190),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8191),U_8192)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8191),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8190),U_8192))
      | ~ class_Lattices_Osemilattice__sup(U_8189) ),
    inference(definitional_conversion,[status(esa)],[f_2339_2]) ).

cnf(f_2339_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8190),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8191),U_8192)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8191),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8189),U_8190),U_8192))
    | ~ class_Lattices_Osemilattice__sup(U_8189) ),
    inference(clausify,[status(thm)],[f_2339_3]) ).

fof(f_2340_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J]) ).

fof(f_2340_2,plain,
    ! [U_8196,U_8195,U_8194,U_8193] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8195),U_8196)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8195),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8194),U_8196))
      | ~ class_Lattices_Olattice(U_8193) ),
    inference(variable_rename,[status(thm)],[f_2340_1]) ).

fof(f_2340_3,plain,
    ! [U_8193,U_8194,U_8195,U_8196] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8195),U_8196)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8195),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8194),U_8196))
      | ~ class_Lattices_Olattice(U_8193) ),
    inference(definitional_conversion,[status(esa)],[f_2340_2]) ).

cnf(f_2340_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8195),U_8196)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8195),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8193),U_8194),U_8196))
    | ~ class_Lattices_Olattice(U_8193) ),
    inference(clausify,[status(thm)],[f_2340_3]) ).

fof(f_2341_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__left__commute]) ).

fof(f_2341_2,plain,
    ! [U_8200,U_8199,U_8198,U_8197] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8199),U_8200)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8198),U_8200))
      | ~ class_Lattices_Osemilattice__sup(U_8197) ),
    inference(variable_rename,[status(thm)],[f_2341_1]) ).

fof(f_2341_3,plain,
    ! [U_8197,U_8198,U_8199,U_8200] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8199),U_8200)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8198),U_8200))
      | ~ class_Lattices_Osemilattice__sup(U_8197) ),
    inference(definitional_conversion,[status(esa)],[f_2341_2]) ).

cnf(f_2341_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8199),U_8200)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8197),U_8198),U_8200))
    | ~ class_Lattices_Osemilattice__sup(U_8197) ),
    inference(clausify,[status(thm)],[f_2341_3]) ).

fof(f_2342_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oassoc]) ).

fof(f_2342_2,plain,
    ! [U_8204,U_8203,U_8202,U_8201] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8202),U_8203)),U_8204) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8202),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8203),U_8204))
      | ~ class_Lattices_Osemilattice__sup(U_8201) ),
    inference(variable_rename,[status(thm)],[f_2342_1]) ).

fof(f_2342_3,plain,
    ! [U_8201,U_8202,U_8203,U_8204] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8202),U_8203)),U_8204) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8202),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8203),U_8204))
      | ~ class_Lattices_Osemilattice__sup(U_8201) ),
    inference(definitional_conversion,[status(esa)],[f_2342_2]) ).

cnf(f_2342_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8202),U_8203)),U_8204) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8202),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8201),U_8203),U_8204))
    | ~ class_Lattices_Osemilattice__sup(U_8201) ),
    inference(clausify,[status(thm)],[f_2342_3]) ).

fof(f_2343_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J]) ).

fof(f_2343_2,plain,
    ! [U_8208,U_8207,U_8206,U_8205] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8206),U_8207)),U_8208) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8207),U_8208))
      | ~ class_Lattices_Olattice(U_8205) ),
    inference(variable_rename,[status(thm)],[f_2343_1]) ).

fof(f_2343_3,plain,
    ! [U_8205,U_8206,U_8207,U_8208] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8206),U_8207)),U_8208) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8207),U_8208))
      | ~ class_Lattices_Olattice(U_8205) ),
    inference(definitional_conversion,[status(esa)],[f_2343_2]) ).

cnf(f_2343_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8206),U_8207)),U_8208) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8205),U_8207),U_8208))
    | ~ class_Lattices_Olattice(U_8205) ),
    inference(clausify,[status(thm)],[f_2343_3]) ).

fof(f_2344_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__assoc]) ).

fof(f_2344_2,plain,
    ! [U_8212,U_8211,U_8210,U_8209] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8210),U_8211)),U_8212) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8210),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8211),U_8212))
      | ~ class_Lattices_Osemilattice__sup(U_8209) ),
    inference(variable_rename,[status(thm)],[f_2344_1]) ).

fof(f_2344_3,plain,
    ! [U_8209,U_8210,U_8211,U_8212] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8210),U_8211)),U_8212) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8210),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8211),U_8212))
      | ~ class_Lattices_Osemilattice__sup(U_8209) ),
    inference(definitional_conversion,[status(esa)],[f_2344_2]) ).

cnf(f_2344_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8210),U_8211)),U_8212) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8210),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8209),U_8211),U_8212))
    | ~ class_Lattices_Osemilattice__sup(U_8209) ),
    inference(clausify,[status(thm)],[f_2344_3]) ).

fof(f_2345_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__apply]) ).

fof(f_2345_2,plain,
    ! [U_8217,U_8216,U_8215,U_8214,U_8213] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8214,U_8213)),U_8215),U_8216),U_8217) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8213),hAPP(U_8215,U_8217)),hAPP(U_8216,U_8217))
      | ~ class_Lattices_Olattice(U_8213) ),
    inference(variable_rename,[status(thm)],[f_2345_1]) ).

fof(f_2345_3,plain,
    ! [U_8213,U_8214,U_8215,U_8216,U_8217] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8214,U_8213)),U_8215),U_8216),U_8217) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8213),hAPP(U_8215,U_8217)),hAPP(U_8216,U_8217))
      | ~ class_Lattices_Olattice(U_8213) ),
    inference(definitional_conversion,[status(esa)],[f_2345_2]) ).

cnf(f_2345_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8214,U_8213)),U_8215),U_8216),U_8217) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8213),hAPP(U_8215,U_8217)),hAPP(U_8216,U_8217))
    | ~ class_Lattices_Olattice(U_8213) ),
    inference(clausify,[status(thm)],[f_2345_3]) ).

fof(f_2346_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__absorb]) ).

fof(f_2346_2,plain,
    ! [U_8219,U_8218] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8218,tc_HOL_Obool)),U_8219),U_8219) = U_8219,
    inference(variable_rename,[status(thm)],[f_2346_1]) ).

fof(f_2346_3,plain,
    ! [U_8219,U_8218] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8218,tc_HOL_Obool)),U_8219),U_8219) = U_8219,
    inference(definitional_conversion,[status(esa)],[f_2346_2]) ).

cnf(f_2346_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8218,tc_HOL_Obool)),U_8219),U_8219) = U_8219,
    inference(clausify,[status(thm)],[f_2346_3]) ).

fof(f_2347_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Un__commute]) ).

fof(f_2347_2,plain,
    ! [U_8222,U_8221,U_8220] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),U_8221),U_8222) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),U_8222),U_8221),
    inference(variable_rename,[status(thm)],[f_2347_1]) ).

fof(f_2347_3,plain,
    ! [U_8220,U_8221,U_8222] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),U_8221),U_8222) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),U_8222),U_8221),
    inference(definitional_conversion,[status(esa)],[f_2347_2]) ).

cnf(f_2347_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),U_8221),U_8222) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),U_8222),U_8221),
    inference(clausify,[status(thm)],[f_2347_3]) ).

fof(f_2348_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Un__left__absorb]) ).

fof(f_2348_2,plain,
    ! [U_8225,U_8224,U_8223] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),U_8225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),U_8225),
    inference(variable_rename,[status(thm)],[f_2348_1]) ).

fof(f_2348_3,plain,
    ! [U_8223,U_8224,U_8225] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),U_8225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),U_8225),
    inference(definitional_conversion,[status(esa)],[f_2348_2]) ).

cnf(f_2348_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),U_8225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),U_8224),U_8225),
    inference(clausify,[status(thm)],[f_2348_3]) ).

fof(f_2349_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__left__commute]) ).

fof(f_2349_2,plain,
    ! [U_8229,U_8228,U_8227,U_8226] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8227),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8228),U_8229)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8228),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8227),U_8229)),
    inference(variable_rename,[status(thm)],[f_2349_1]) ).

fof(f_2349_3,plain,
    ! [U_8226,U_8227,U_8228,U_8229] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8227),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8228),U_8229)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8228),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8227),U_8229)),
    inference(definitional_conversion,[status(esa)],[f_2349_2]) ).

cnf(f_2349_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8227),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8228),U_8229)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8228),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),U_8227),U_8229)),
    inference(clausify,[status(thm)],[f_2349_3]) ).

fof(f_2350_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__assoc]) ).

fof(f_2350_2,plain,
    ! [U_8233,U_8232,U_8231,U_8230] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8231),U_8232)),U_8233) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8231),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8232),U_8233)),
    inference(variable_rename,[status(thm)],[f_2350_1]) ).

fof(f_2350_3,plain,
    ! [U_8230,U_8231,U_8232,U_8233] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8231),U_8232)),U_8233) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8231),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8232),U_8233)),
    inference(definitional_conversion,[status(esa)],[f_2350_2]) ).

cnf(f_2350_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8231),U_8232)),U_8233) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8231),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8230,tc_HOL_Obool)),U_8232),U_8233)),
    inference(clausify,[status(thm)],[f_2350_3]) ).

fof(f_2351_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ( ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).

fof(f_2351_2,plain,
    ! [U_8243,U_8242,U_8241,U_8240] :
      ( ( ? [U_8239] :
            ( hBOOL(hAPP(U_8243,U_8239))
            & hBOOL(hAPP(hAPP(c_member(U_8240),U_8239),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8240,tc_HOL_Obool)),U_8241),U_8242))) )
        | ( ! [U_8238] :
              ( ~ hBOOL(hAPP(U_8243,U_8238))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8240),U_8238),U_8242)) )
          & ! [U_8237] :
              ( ~ hBOOL(hAPP(U_8243,U_8237))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8240),U_8237),U_8241)) ) ) )
      & ( ? [U_8236] :
            ( hBOOL(hAPP(U_8243,U_8236))
            & hBOOL(hAPP(hAPP(c_member(U_8240),U_8236),U_8242)) )
        | ? [U_8235] :
            ( hBOOL(hAPP(U_8243,U_8235))
            & hBOOL(hAPP(hAPP(c_member(U_8240),U_8235),U_8241)) )
        | ! [U_8234] :
            ( ~ hBOOL(hAPP(U_8243,U_8234))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8240),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8240,tc_HOL_Obool)),U_8241),U_8242))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2351_1]) ).

fof(f_2351_3,plain,
    ( ! [U_8251,U_8249,U_8247,U_8245] :
        ( ? [U_8239] :
            ( hBOOL(hAPP(U_8251,U_8239))
            & hBOOL(hAPP(hAPP(c_member(U_8245),U_8239),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8245,tc_HOL_Obool)),U_8247),U_8249))) )
        | ( ! [U_8238] :
              ( ~ hBOOL(hAPP(U_8251,U_8238))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8238),U_8249)) )
          & ! [U_8237] :
              ( ~ hBOOL(hAPP(U_8251,U_8237))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8237),U_8247)) ) ) )
    & ! [U_8250,U_8248,U_8246,U_8244] :
        ( ? [U_8236] :
            ( hBOOL(hAPP(U_8250,U_8236))
            & hBOOL(hAPP(hAPP(c_member(U_8244),U_8236),U_8248)) )
        | ? [U_8235] :
            ( hBOOL(hAPP(U_8250,U_8235))
            & hBOOL(hAPP(hAPP(c_member(U_8244),U_8235),U_8246)) )
        | ! [U_8234] :
            ( ~ hBOOL(hAPP(U_8250,U_8234))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8244),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8244,tc_HOL_Obool)),U_8246),U_8248))) ) ) ),
    inference(miniscope,[status(thm)],[f_2351_2]) ).

fof(f_2351_4,plain,
    ( ! [U_8251,U_8249,U_8247,U_8245] :
        ( ? [U_8239] :
            ( hBOOL(hAPP(U_8251,U_8239))
            & hBOOL(hAPP(hAPP(c_member(U_8245),U_8239),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8245,tc_HOL_Obool)),U_8247),U_8249))) )
        | ( ! [U_8238] :
              ( ~ hBOOL(hAPP(U_8251,U_8238))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8238),U_8249)) )
          & ! [U_8237] :
              ( ~ hBOOL(hAPP(U_8251,U_8237))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8237),U_8247)) ) ) )
    & ! [U_8250,U_8248,U_8246,U_8244] :
        ( ? [U_8236] :
            ( hBOOL(hAPP(U_8250,U_8236))
            & hBOOL(hAPP(hAPP(c_member(U_8244),U_8236),U_8248)) )
        | ( hBOOL(hAPP(U_8250,sK117(U_8250,U_8248,U_8246,U_8244)))
          & hBOOL(hAPP(hAPP(c_member(U_8244),sK117(U_8250,U_8248,U_8246,U_8244)),U_8246)) )
        | ! [U_8234] :
            ( ~ hBOOL(hAPP(U_8250,U_8234))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8244),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8244,tc_HOL_Obool)),U_8246),U_8248))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_8235,sK117(U_8250,U_8248,U_8246,U_8244))],[f_2351_3]) ).

fof(f_2351_5,plain,
    ( ! [U_8251,U_8249,U_8247,U_8245] :
        ( ? [U_8239] :
            ( hBOOL(hAPP(U_8251,U_8239))
            & hBOOL(hAPP(hAPP(c_member(U_8245),U_8239),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8245,tc_HOL_Obool)),U_8247),U_8249))) )
        | ( ! [U_8238] :
              ( ~ hBOOL(hAPP(U_8251,U_8238))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8238),U_8249)) )
          & ! [U_8237] :
              ( ~ hBOOL(hAPP(U_8251,U_8237))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8237),U_8247)) ) ) )
    & ! [U_8250,U_8248,U_8246,U_8244] :
        ( ( hBOOL(hAPP(U_8250,sK118(U_8250,U_8248,U_8246,U_8244)))
          & hBOOL(hAPP(hAPP(c_member(U_8244),sK118(U_8250,U_8248,U_8246,U_8244)),U_8248)) )
        | ( hBOOL(hAPP(U_8250,sK117(U_8250,U_8248,U_8246,U_8244)))
          & hBOOL(hAPP(hAPP(c_member(U_8244),sK117(U_8250,U_8248,U_8246,U_8244)),U_8246)) )
        | ! [U_8234] :
            ( ~ hBOOL(hAPP(U_8250,U_8234))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8244),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8244,tc_HOL_Obool)),U_8246),U_8248))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_8236,sK118(U_8250,U_8248,U_8246,U_8244))],[f_2351_4]) ).

fof(f_2351_6,plain,
    ( ! [U_8251,U_8249,U_8247,U_8245] :
        ( ( hBOOL(hAPP(U_8251,sK119(U_8251,U_8249,U_8247,U_8245)))
          & hBOOL(hAPP(hAPP(c_member(U_8245),sK119(U_8251,U_8249,U_8247,U_8245)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8245,tc_HOL_Obool)),U_8247),U_8249))) )
        | ( ! [U_8238] :
              ( ~ hBOOL(hAPP(U_8251,U_8238))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8238),U_8249)) )
          & ! [U_8237] :
              ( ~ hBOOL(hAPP(U_8251,U_8237))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8237),U_8247)) ) ) )
    & ! [U_8250,U_8248,U_8246,U_8244] :
        ( ( hBOOL(hAPP(U_8250,sK118(U_8250,U_8248,U_8246,U_8244)))
          & hBOOL(hAPP(hAPP(c_member(U_8244),sK118(U_8250,U_8248,U_8246,U_8244)),U_8248)) )
        | ( hBOOL(hAPP(U_8250,sK117(U_8250,U_8248,U_8246,U_8244)))
          & hBOOL(hAPP(hAPP(c_member(U_8244),sK117(U_8250,U_8248,U_8246,U_8244)),U_8246)) )
        | ! [U_8234] :
            ( ~ hBOOL(hAPP(U_8250,U_8234))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8244),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8244,tc_HOL_Obool)),U_8246),U_8248))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_8239,sK119(U_8251,U_8249,U_8247,U_8245))],[f_2351_5]) ).

fof(f_2351_7,plain,
    ( ! [U_8245,U_8251,U_8249,U_8247] :
        ( hBOOL(hAPP(U_8251,sK119(U_8251,U_8249,U_8247,U_8245)))
        | ~ sP711(U_8245,U_8251,U_8249,U_8247) )
    & ! [U_8245,U_8251,U_8249,U_8247] :
        ( hBOOL(hAPP(hAPP(c_member(U_8245),sK119(U_8251,U_8249,U_8247,U_8245)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8245,tc_HOL_Obool)),U_8247),U_8249)))
        | ~ sP711(U_8245,U_8251,U_8249,U_8247) )
    & ! [U_8245,U_8251,U_8249,U_8237,U_8238,U_8247] :
        ( ~ hBOOL(hAPP(U_8251,U_8238))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8238),U_8249))
        | ~ sP710(U_8245,U_8251,U_8249,U_8237,U_8238,U_8247) )
    & ! [U_8245,U_8251,U_8249,U_8237,U_8238,U_8247] :
        ( ~ hBOOL(hAPP(U_8251,U_8237))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8237),U_8247))
        | ~ sP710(U_8245,U_8251,U_8249,U_8237,U_8238,U_8247) )
    & ! [U_8246,U_8248,U_8244,U_8250] :
        ( hBOOL(hAPP(U_8250,sK118(U_8250,U_8248,U_8246,U_8244)))
        | ~ sP709(U_8246,U_8248,U_8244,U_8250) )
    & ! [U_8246,U_8248,U_8244,U_8250] :
        ( hBOOL(hAPP(hAPP(c_member(U_8244),sK118(U_8250,U_8248,U_8246,U_8244)),U_8248))
        | ~ sP709(U_8246,U_8248,U_8244,U_8250) )
    & ! [U_8246,U_8248,U_8244,U_8250] :
        ( hBOOL(hAPP(U_8250,sK117(U_8250,U_8248,U_8246,U_8244)))
        | ~ sP708(U_8246,U_8248,U_8244,U_8250) )
    & ! [U_8246,U_8248,U_8244,U_8250] :
        ( hBOOL(hAPP(hAPP(c_member(U_8244),sK117(U_8250,U_8248,U_8246,U_8244)),U_8246))
        | ~ sP708(U_8246,U_8248,U_8244,U_8250) )
    & ! [U_8245,U_8251,U_8249,U_8237,U_8238,U_8247] :
        ( sP711(U_8245,U_8251,U_8249,U_8247)
        | sP710(U_8245,U_8251,U_8249,U_8237,U_8238,U_8247) )
    & ! [U_8234,U_8246,U_8248,U_8244,U_8250] :
        ( sP709(U_8246,U_8248,U_8244,U_8250)
        | sP708(U_8246,U_8248,U_8244,U_8250)
        | ~ hBOOL(hAPP(U_8250,U_8234))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8244),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8244,tc_HOL_Obool)),U_8246),U_8248))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP708,sP709,sP710,sP711])],[f_2351_6]) ).

cnf(f_2351_8,plain,
    ( sP709(U_8246,U_8248,U_8244,U_8250)
    | sP708(U_8246,U_8248,U_8244,U_8250)
    | ~ hBOOL(hAPP(U_8250,U_8234))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8244),U_8234),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8244,tc_HOL_Obool)),U_8246),U_8248))) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_9,plain,
    ( sP711(U_8245,U_8251,U_8249,U_8247)
    | sP710(U_8245,U_8251,U_8249,U_8237,U_8238,U_8247) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8244),sK117(U_8250,U_8248,U_8246,U_8244)),U_8246))
    | ~ sP708(U_8246,U_8248,U_8244,U_8250) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_11,plain,
    ( hBOOL(hAPP(U_8250,sK117(U_8250,U_8248,U_8246,U_8244)))
    | ~ sP708(U_8246,U_8248,U_8244,U_8250) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8244),sK118(U_8250,U_8248,U_8246,U_8244)),U_8248))
    | ~ sP709(U_8246,U_8248,U_8244,U_8250) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_13,plain,
    ( hBOOL(hAPP(U_8250,sK118(U_8250,U_8248,U_8246,U_8244)))
    | ~ sP709(U_8246,U_8248,U_8244,U_8250) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_14,plain,
    ( ~ hBOOL(hAPP(U_8251,U_8237))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8237),U_8247))
    | ~ sP710(U_8245,U_8251,U_8249,U_8237,U_8238,U_8247) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_15,plain,
    ( ~ hBOOL(hAPP(U_8251,U_8238))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8245),U_8238),U_8249))
    | ~ sP710(U_8245,U_8251,U_8249,U_8237,U_8238,U_8247) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8245),sK119(U_8251,U_8249,U_8247,U_8245)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8245,tc_HOL_Obool)),U_8247),U_8249)))
    | ~ sP711(U_8245,U_8251,U_8249,U_8247) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

cnf(f_2351_17,plain,
    ( hBOOL(hAPP(U_8251,sK119(U_8251,U_8249,U_8247,U_8245)))
    | ~ sP711(U_8245,U_8251,U_8249,U_8247) ),
    inference(clausify,[status(thm)],[f_2351_7]) ).

fof(f_2352_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).

fof(f_2352_2,plain,
    ! [U_8261,U_8260,U_8259,U_8258] :
      ( ( ! [U_8257] :
            ( hBOOL(hAPP(U_8261,U_8257))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8258),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8258,tc_HOL_Obool)),U_8259),U_8260))) )
        | ? [U_8256] :
            ( ~ hBOOL(hAPP(U_8261,U_8256))
            & hBOOL(hAPP(hAPP(c_member(U_8258),U_8256),U_8260)) )
        | ? [U_8255] :
            ( ~ hBOOL(hAPP(U_8261,U_8255))
            & hBOOL(hAPP(hAPP(c_member(U_8258),U_8255),U_8259)) ) )
      & ( ( ! [U_8254] :
              ( hBOOL(hAPP(U_8261,U_8254))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8258),U_8254),U_8260)) )
          & ! [U_8253] :
              ( hBOOL(hAPP(U_8261,U_8253))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8258),U_8253),U_8259)) ) )
        | ? [U_8252] :
            ( ~ hBOOL(hAPP(U_8261,U_8252))
            & hBOOL(hAPP(hAPP(c_member(U_8258),U_8252),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8258,tc_HOL_Obool)),U_8259),U_8260))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2352_1]) ).

fof(f_2352_3,plain,
    ( ! [U_8269,U_8267,U_8265,U_8263] :
        ( ! [U_8257] :
            ( hBOOL(hAPP(U_8269,U_8257))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8263,tc_HOL_Obool)),U_8265),U_8267))) )
        | ? [U_8256] :
            ( ~ hBOOL(hAPP(U_8269,U_8256))
            & hBOOL(hAPP(hAPP(c_member(U_8263),U_8256),U_8267)) )
        | ? [U_8255] :
            ( ~ hBOOL(hAPP(U_8269,U_8255))
            & hBOOL(hAPP(hAPP(c_member(U_8263),U_8255),U_8265)) ) )
    & ! [U_8268,U_8266,U_8264,U_8262] :
        ( ( ! [U_8254] :
              ( hBOOL(hAPP(U_8268,U_8254))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8254),U_8266)) )
          & ! [U_8253] :
              ( hBOOL(hAPP(U_8268,U_8253))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8253),U_8264)) ) )
        | ? [U_8252] :
            ( ~ hBOOL(hAPP(U_8268,U_8252))
            & hBOOL(hAPP(hAPP(c_member(U_8262),U_8252),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8262,tc_HOL_Obool)),U_8264),U_8266))) ) ) ),
    inference(miniscope,[status(thm)],[f_2352_2]) ).

fof(f_2352_4,plain,
    ( ! [U_8269,U_8267,U_8265,U_8263] :
        ( ! [U_8257] :
            ( hBOOL(hAPP(U_8269,U_8257))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8263,tc_HOL_Obool)),U_8265),U_8267))) )
        | ? [U_8256] :
            ( ~ hBOOL(hAPP(U_8269,U_8256))
            & hBOOL(hAPP(hAPP(c_member(U_8263),U_8256),U_8267)) )
        | ? [U_8255] :
            ( ~ hBOOL(hAPP(U_8269,U_8255))
            & hBOOL(hAPP(hAPP(c_member(U_8263),U_8255),U_8265)) ) )
    & ! [U_8268,U_8266,U_8264,U_8262] :
        ( ( ! [U_8254] :
              ( hBOOL(hAPP(U_8268,U_8254))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8254),U_8266)) )
          & ! [U_8253] :
              ( hBOOL(hAPP(U_8268,U_8253))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8253),U_8264)) ) )
        | ( ~ hBOOL(hAPP(U_8268,sK120(U_8268,U_8266,U_8264,U_8262)))
          & hBOOL(hAPP(hAPP(c_member(U_8262),sK120(U_8268,U_8266,U_8264,U_8262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8262,tc_HOL_Obool)),U_8264),U_8266))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_8252,sK120(U_8268,U_8266,U_8264,U_8262))],[f_2352_3]) ).

fof(f_2352_5,plain,
    ( ! [U_8269,U_8267,U_8265,U_8263] :
        ( ! [U_8257] :
            ( hBOOL(hAPP(U_8269,U_8257))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8263,tc_HOL_Obool)),U_8265),U_8267))) )
        | ? [U_8256] :
            ( ~ hBOOL(hAPP(U_8269,U_8256))
            & hBOOL(hAPP(hAPP(c_member(U_8263),U_8256),U_8267)) )
        | ( ~ hBOOL(hAPP(U_8269,sK121(U_8269,U_8267,U_8265,U_8263)))
          & hBOOL(hAPP(hAPP(c_member(U_8263),sK121(U_8269,U_8267,U_8265,U_8263)),U_8265)) ) )
    & ! [U_8268,U_8266,U_8264,U_8262] :
        ( ( ! [U_8254] :
              ( hBOOL(hAPP(U_8268,U_8254))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8254),U_8266)) )
          & ! [U_8253] :
              ( hBOOL(hAPP(U_8268,U_8253))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8253),U_8264)) ) )
        | ( ~ hBOOL(hAPP(U_8268,sK120(U_8268,U_8266,U_8264,U_8262)))
          & hBOOL(hAPP(hAPP(c_member(U_8262),sK120(U_8268,U_8266,U_8264,U_8262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8262,tc_HOL_Obool)),U_8264),U_8266))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_8255,sK121(U_8269,U_8267,U_8265,U_8263))],[f_2352_4]) ).

fof(f_2352_6,plain,
    ( ! [U_8269,U_8267,U_8265,U_8263] :
        ( ! [U_8257] :
            ( hBOOL(hAPP(U_8269,U_8257))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8263,tc_HOL_Obool)),U_8265),U_8267))) )
        | ( ~ hBOOL(hAPP(U_8269,sK122(U_8269,U_8267,U_8265,U_8263)))
          & hBOOL(hAPP(hAPP(c_member(U_8263),sK122(U_8269,U_8267,U_8265,U_8263)),U_8267)) )
        | ( ~ hBOOL(hAPP(U_8269,sK121(U_8269,U_8267,U_8265,U_8263)))
          & hBOOL(hAPP(hAPP(c_member(U_8263),sK121(U_8269,U_8267,U_8265,U_8263)),U_8265)) ) )
    & ! [U_8268,U_8266,U_8264,U_8262] :
        ( ( ! [U_8254] :
              ( hBOOL(hAPP(U_8268,U_8254))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8254),U_8266)) )
          & ! [U_8253] :
              ( hBOOL(hAPP(U_8268,U_8253))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8253),U_8264)) ) )
        | ( ~ hBOOL(hAPP(U_8268,sK120(U_8268,U_8266,U_8264,U_8262)))
          & hBOOL(hAPP(hAPP(c_member(U_8262),sK120(U_8268,U_8266,U_8264,U_8262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8262,tc_HOL_Obool)),U_8264),U_8266))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_8256,sK122(U_8269,U_8267,U_8265,U_8263))],[f_2352_5]) ).

fof(f_2352_7,plain,
    ( ! [U_8265,U_8269,U_8263,U_8267] :
        ( ~ hBOOL(hAPP(U_8269,sK122(U_8269,U_8267,U_8265,U_8263)))
        | ~ sP715(U_8265,U_8269,U_8263,U_8267) )
    & ! [U_8265,U_8269,U_8263,U_8267] :
        ( hBOOL(hAPP(hAPP(c_member(U_8263),sK122(U_8269,U_8267,U_8265,U_8263)),U_8267))
        | ~ sP715(U_8265,U_8269,U_8263,U_8267) )
    & ! [U_8265,U_8269,U_8263,U_8267] :
        ( ~ hBOOL(hAPP(U_8269,sK121(U_8269,U_8267,U_8265,U_8263)))
        | ~ sP714(U_8265,U_8269,U_8263,U_8267) )
    & ! [U_8265,U_8269,U_8263,U_8267] :
        ( hBOOL(hAPP(hAPP(c_member(U_8263),sK121(U_8269,U_8267,U_8265,U_8263)),U_8265))
        | ~ sP714(U_8265,U_8269,U_8263,U_8267) )
    & ! [U_8253,U_8254,U_8264,U_8266,U_8262,U_8268] :
        ( hBOOL(hAPP(U_8268,U_8254))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8254),U_8266))
        | ~ sP713(U_8253,U_8254,U_8264,U_8266,U_8262,U_8268) )
    & ! [U_8253,U_8254,U_8264,U_8266,U_8262,U_8268] :
        ( hBOOL(hAPP(U_8268,U_8253))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8253),U_8264))
        | ~ sP713(U_8253,U_8254,U_8264,U_8266,U_8262,U_8268) )
    & ! [U_8264,U_8266,U_8262,U_8268] :
        ( ~ hBOOL(hAPP(U_8268,sK120(U_8268,U_8266,U_8264,U_8262)))
        | ~ sP712(U_8264,U_8266,U_8262,U_8268) )
    & ! [U_8264,U_8266,U_8262,U_8268] :
        ( hBOOL(hAPP(hAPP(c_member(U_8262),sK120(U_8268,U_8266,U_8264,U_8262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8262,tc_HOL_Obool)),U_8264),U_8266)))
        | ~ sP712(U_8264,U_8266,U_8262,U_8268) )
    & ! [U_8257,U_8265,U_8269,U_8263,U_8267] :
        ( hBOOL(hAPP(U_8269,U_8257))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8263,tc_HOL_Obool)),U_8265),U_8267)))
        | sP715(U_8265,U_8269,U_8263,U_8267)
        | sP714(U_8265,U_8269,U_8263,U_8267) )
    & ! [U_8253,U_8254,U_8264,U_8266,U_8262,U_8268] :
        ( sP713(U_8253,U_8254,U_8264,U_8266,U_8262,U_8268)
        | sP712(U_8264,U_8266,U_8262,U_8268) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP712,sP713,sP714,sP715])],[f_2352_6]) ).

cnf(f_2352_8,plain,
    ( sP713(U_8253,U_8254,U_8264,U_8266,U_8262,U_8268)
    | sP712(U_8264,U_8266,U_8262,U_8268) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_9,plain,
    ( hBOOL(hAPP(U_8269,U_8257))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8263,tc_HOL_Obool)),U_8265),U_8267)))
    | sP715(U_8265,U_8269,U_8263,U_8267)
    | sP714(U_8265,U_8269,U_8263,U_8267) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8262),sK120(U_8268,U_8266,U_8264,U_8262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8262,tc_HOL_Obool)),U_8264),U_8266)))
    | ~ sP712(U_8264,U_8266,U_8262,U_8268) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_11,plain,
    ( ~ hBOOL(hAPP(U_8268,sK120(U_8268,U_8266,U_8264,U_8262)))
    | ~ sP712(U_8264,U_8266,U_8262,U_8268) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_12,plain,
    ( hBOOL(hAPP(U_8268,U_8253))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8253),U_8264))
    | ~ sP713(U_8253,U_8254,U_8264,U_8266,U_8262,U_8268) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_13,plain,
    ( hBOOL(hAPP(U_8268,U_8254))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8262),U_8254),U_8266))
    | ~ sP713(U_8253,U_8254,U_8264,U_8266,U_8262,U_8268) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8263),sK121(U_8269,U_8267,U_8265,U_8263)),U_8265))
    | ~ sP714(U_8265,U_8269,U_8263,U_8267) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_15,plain,
    ( ~ hBOOL(hAPP(U_8269,sK121(U_8269,U_8267,U_8265,U_8263)))
    | ~ sP714(U_8265,U_8269,U_8263,U_8267) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8263),sK122(U_8269,U_8267,U_8265,U_8263)),U_8267))
    | ~ sP715(U_8265,U_8269,U_8263,U_8267) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

cnf(f_2352_17,plain,
    ( ~ hBOOL(hAPP(U_8269,sK122(U_8269,U_8267,U_8265,U_8263)))
    | ~ sP715(U_8265,U_8269,U_8263,U_8267) ),
    inference(clausify,[status(thm)],[f_2352_7]) ).

fof(f_2353_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__fun__def]) ).

fof(f_2353_2,plain,
    ! [U_8274,U_8273,U_8272,U_8271,U_8270] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8271,U_8270)),U_8272),U_8273),U_8274) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8270),hAPP(U_8272,U_8274)),hAPP(U_8273,U_8274))
      | ~ class_Lattices_Olattice(U_8270) ),
    inference(variable_rename,[status(thm)],[f_2353_1]) ).

fof(f_2353_3,plain,
    ! [U_8271,U_8272,U_8270,U_8273,U_8274] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8271,U_8270)),U_8272),U_8273),U_8274) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8270),hAPP(U_8272,U_8274)),hAPP(U_8273,U_8274))
      | ~ class_Lattices_Olattice(U_8270) ),
    inference(definitional_conversion,[status(esa)],[f_2353_2]) ).

cnf(f_2353_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8271,U_8270)),U_8272),U_8273),U_8274) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8270),hAPP(U_8272,U_8274)),hAPP(U_8273,U_8274))
    | ~ class_Lattices_Olattice(U_8270) ),
    inference(clausify,[status(thm)],[f_2353_3]) ).

fof(f_2354_1,plain,
    ! [V_B_2,T_b,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1I1]) ).

fof(f_2354_2,plain,
    ! [U_8278,U_8277,U_8276,U_8275] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8277,tc_HOL_Obool)),U_8275),U_8278),U_8276))
      | ~ hBOOL(hAPP(U_8275,U_8276)) ),
    inference(variable_rename,[status(thm)],[f_2354_1]) ).

fof(f_2354_3,plain,
    ! [U_8275,U_8277,U_8276,U_8278] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8277,tc_HOL_Obool)),U_8275),U_8278),U_8276))
      | ~ hBOOL(hAPP(U_8275,U_8276)) ),
    inference(definitional_conversion,[status(esa)],[f_2354_2]) ).

cnf(f_2354_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8277,tc_HOL_Obool)),U_8275),U_8278),U_8276))
    | ~ hBOOL(hAPP(U_8275,U_8276)) ),
    inference(clausify,[status(thm)],[f_2354_3]) ).

fof(f_2355_1,plain,
    ! [V_A_2,T_b,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ~ hBOOL(hAPP(V_B_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1I2]) ).

fof(f_2355_2,plain,
    ! [U_8282,U_8281,U_8280,U_8279] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8281,tc_HOL_Obool)),U_8282),U_8279),U_8280))
      | ~ hBOOL(hAPP(U_8279,U_8280)) ),
    inference(variable_rename,[status(thm)],[f_2355_1]) ).

fof(f_2355_3,plain,
    ! [U_8279,U_8280,U_8281,U_8282] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8281,tc_HOL_Obool)),U_8282),U_8279),U_8280))
      | ~ hBOOL(hAPP(U_8279,U_8280)) ),
    inference(definitional_conversion,[status(esa)],[f_2355_2]) ).

cnf(f_2355_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8281,tc_HOL_Obool)),U_8282),U_8279),U_8280))
    | ~ hBOOL(hAPP(U_8279,U_8280)) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

fof(f_2356_1,plain,
    ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__insert__left]) ).

fof(f_2356_2,plain,
    ! [U_8286,U_8285,U_8284,U_8283] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8283),U_8284),U_8285)),U_8286) = hAPP(hAPP(c_Set_Oinsert(U_8283),U_8284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8283,tc_HOL_Obool)),U_8285),U_8286)),
    inference(variable_rename,[status(thm)],[f_2356_1]) ).

fof(f_2356_3,plain,
    ! [U_8283,U_8284,U_8285,U_8286] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8283),U_8284),U_8285)),U_8286) = hAPP(hAPP(c_Set_Oinsert(U_8283),U_8284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8283,tc_HOL_Obool)),U_8285),U_8286)),
    inference(definitional_conversion,[status(esa)],[f_2356_2]) ).

cnf(f_2356_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8283),U_8284),U_8285)),U_8286) = hAPP(hAPP(c_Set_Oinsert(U_8283),U_8284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8283,tc_HOL_Obool)),U_8285),U_8286)),
    inference(clausify,[status(thm)],[f_2356_3]) ).

fof(f_2357_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__insert__right]) ).

fof(f_2357_2,plain,
    ! [U_8290,U_8289,U_8288,U_8287] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8287,tc_HOL_Obool)),U_8288),hAPP(hAPP(c_Set_Oinsert(U_8287),U_8289),U_8290)) = hAPP(hAPP(c_Set_Oinsert(U_8287),U_8289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8287,tc_HOL_Obool)),U_8288),U_8290)),
    inference(variable_rename,[status(thm)],[f_2357_1]) ).

fof(f_2357_3,plain,
    ! [U_8287,U_8288,U_8289,U_8290] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8287,tc_HOL_Obool)),U_8288),hAPP(hAPP(c_Set_Oinsert(U_8287),U_8289),U_8290)) = hAPP(hAPP(c_Set_Oinsert(U_8287),U_8289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8287,tc_HOL_Obool)),U_8288),U_8290)),
    inference(definitional_conversion,[status(esa)],[f_2357_2]) ).

cnf(f_2357_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8287,tc_HOL_Obool)),U_8288),hAPP(hAPP(c_Set_Oinsert(U_8287),U_8289),U_8290)) = hAPP(hAPP(c_Set_Oinsert(U_8287),U_8289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8287,tc_HOL_Obool)),U_8288),U_8290)),
    inference(clausify,[status(thm)],[f_2357_3]) ).

fof(f_2358_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).

fof(f_2358_2,plain,
    ! [U_8294,U_8293,U_8292,U_8291] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8291),U_8292),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8291,tc_HOL_Obool)),U_8293),U_8294)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8291),U_8292),U_8294))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8291),U_8292),U_8293)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8291),U_8292),U_8294))
        | hBOOL(hAPP(hAPP(c_member(U_8291),U_8292),U_8293))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8291),U_8292),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8291,tc_HOL_Obool)),U_8293),U_8294))) ) ),
    inference(variable_rename,[status(thm)],[f_2358_1]) ).

fof(f_2358_3,plain,
    ( ! [U_8302,U_8300,U_8298,U_8296] :
        ( hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8296,tc_HOL_Obool)),U_8300),U_8302)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8302))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8300)) ) )
    & ! [U_8301,U_8299,U_8297,U_8295] :
        ( hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),U_8301))
        | hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),U_8299))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8295,tc_HOL_Obool)),U_8299),U_8301))) ) ),
    inference(miniscope,[status(thm)],[f_2358_2]) ).

fof(f_2358_4,plain,
    ( ! [U_8298,U_8296,U_8302,U_8300] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8302))
        | ~ sP716(U_8298,U_8296,U_8302,U_8300) )
    & ! [U_8298,U_8296,U_8302,U_8300] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8300))
        | ~ sP716(U_8298,U_8296,U_8302,U_8300) )
    & ! [U_8298,U_8296,U_8302,U_8300] :
        ( hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8296,tc_HOL_Obool)),U_8300),U_8302)))
        | sP716(U_8298,U_8296,U_8302,U_8300) )
    & ! [U_8301,U_8297,U_8295,U_8299] :
        ( hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),U_8301))
        | hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),U_8299))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8295,tc_HOL_Obool)),U_8299),U_8301))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP716])],[f_2358_3]) ).

cnf(f_2358_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),U_8301))
    | hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),U_8299))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8295),U_8297),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8295,tc_HOL_Obool)),U_8299),U_8301))) ),
    inference(clausify,[status(thm)],[f_2358_4]) ).

cnf(f_2358_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8296,tc_HOL_Obool)),U_8300),U_8302)))
    | sP716(U_8298,U_8296,U_8302,U_8300) ),
    inference(clausify,[status(thm)],[f_2358_4]) ).

cnf(f_2358_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8300))
    | ~ sP716(U_8298,U_8296,U_8302,U_8300) ),
    inference(clausify,[status(thm)],[f_2358_4]) ).

cnf(f_2358_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8302))
    | ~ sP716(U_8298,U_8296,U_8302,U_8300) ),
    inference(clausify,[status(thm)],[f_2358_4]) ).

fof(f_2359_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI1]) ).

fof(f_2359_2,plain,
    ! [U_8306,U_8305,U_8304,U_8303] :
      ( hBOOL(hAPP(hAPP(c_member(U_8303),U_8304),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8303,tc_HOL_Obool)),U_8305),U_8306)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8303),U_8304),U_8305)) ),
    inference(variable_rename,[status(thm)],[f_2359_1]) ).

fof(f_2359_3,plain,
    ! [U_8304,U_8303,U_8305,U_8306] :
      ( hBOOL(hAPP(hAPP(c_member(U_8303),U_8304),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8303,tc_HOL_Obool)),U_8305),U_8306)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8303),U_8304),U_8305)) ),
    inference(definitional_conversion,[status(esa)],[f_2359_2]) ).

cnf(f_2359_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8303),U_8304),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8303,tc_HOL_Obool)),U_8305),U_8306)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8303),U_8304),U_8305)) ),
    inference(clausify,[status(thm)],[f_2359_3]) ).

fof(f_2360_1,plain,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI2]) ).

fof(f_2360_2,plain,
    ! [U_8310,U_8309,U_8308,U_8307] :
      ( hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8307,tc_HOL_Obool)),U_8310),U_8309)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8309)) ),
    inference(variable_rename,[status(thm)],[f_2360_1]) ).

fof(f_2360_3,plain,
    ! [U_8307,U_8308,U_8309,U_8310] :
      ( hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8307,tc_HOL_Obool)),U_8310),U_8309)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8309)) ),
    inference(definitional_conversion,[status(esa)],[f_2360_2]) ).

cnf(f_2360_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8307,tc_HOL_Obool)),U_8310),U_8309)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8309)) ),
    inference(clausify,[status(thm)],[f_2360_3]) ).

fof(f_2361_1,plain,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Un__eq]) ).

fof(f_2361_2,plain,
    ! [U_8314,U_8313,U_8312,U_8311] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8311,tc_fun(U_8311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8311)),U_8312)),hAPP(hAPP(c_COMBC(U_8311,tc_fun(U_8311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8311)),U_8313)),U_8314))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8314),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),U_8312),U_8313))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8311),U_8314),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),U_8312),U_8313)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8311,tc_fun(U_8311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8311)),U_8312)),hAPP(hAPP(c_COMBC(U_8311,tc_fun(U_8311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8311)),U_8313)),U_8314)) ) ),
    inference(variable_rename,[status(thm)],[f_2361_1]) ).

fof(f_2361_3,plain,
    ( ! [U_8322,U_8320,U_8318,U_8316] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8316,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8318)),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8320)),U_8322))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8316,tc_HOL_Obool)),U_8318),U_8320))) )
    & ! [U_8321,U_8319,U_8317,U_8315] :
        ( hBOOL(hAPP(hAPP(c_member(U_8315),U_8321),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8315,tc_HOL_Obool)),U_8317),U_8319)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8315,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8315,tc_fun(U_8315,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8315)),U_8317)),hAPP(hAPP(c_COMBC(U_8315,tc_fun(U_8315,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8315)),U_8319)),U_8321)) ) ),
    inference(miniscope,[status(thm)],[f_2361_2]) ).

fof(f_2361_4,plain,
    ( ! [U_8316,U_8318,U_8320,U_8322] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8316,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8318)),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8320)),U_8322))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8316,tc_HOL_Obool)),U_8318),U_8320))) )
    & ! [U_8317,U_8319,U_8321,U_8315] :
        ( hBOOL(hAPP(hAPP(c_member(U_8315),U_8321),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8315,tc_HOL_Obool)),U_8317),U_8319)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8315,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8315,tc_fun(U_8315,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8315)),U_8317)),hAPP(hAPP(c_COMBC(U_8315,tc_fun(U_8315,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8315)),U_8319)),U_8321)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2361_3]) ).

cnf(f_2361_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8315),U_8321),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8315,tc_HOL_Obool)),U_8317),U_8319)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8315,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8315,tc_fun(U_8315,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8315)),U_8317)),hAPP(hAPP(c_COMBC(U_8315,tc_fun(U_8315,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8315)),U_8319)),U_8321)) ),
    inference(clausify,[status(thm)],[f_2361_4]) ).

cnf(f_2361_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8316,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8318)),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8320)),U_8322))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8316),U_8322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8316,tc_HOL_Obool)),U_8318),U_8320))) ),
    inference(clausify,[status(thm)],[f_2361_4]) ).

fof(f_2362_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__is__Un]) ).

fof(f_2362_2,plain,
    ! [U_8325,U_8324,U_8323] : hAPP(hAPP(c_Set_Oinsert(U_8323),U_8324),U_8325) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8324),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))),U_8325),
    inference(variable_rename,[status(thm)],[f_2362_1]) ).

fof(f_2362_3,plain,
    ! [U_8323,U_8325,U_8324] : hAPP(hAPP(c_Set_Oinsert(U_8323),U_8324),U_8325) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8324),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))),U_8325),
    inference(definitional_conversion,[status(esa)],[f_2362_2]) ).

cnf(f_2362_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8323),U_8324),U_8325) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8323),U_8324),c_Orderings_Obot__class_Obot(tc_fun(U_8323,tc_HOL_Obool)))),U_8325),
    inference(clausify,[status(thm)],[f_2362_3]) ).

fof(f_2363_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__partition]) ).

fof(f_2363_2,plain,
    ! [U_8328,U_8327,U_8326] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8326,tc_HOL_Obool)),U_8327),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8326,tc_HOL_Obool)),U_8328),U_8327)) = U_8328
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8326,tc_HOL_Obool)),U_8327),U_8328)) ),
    inference(variable_rename,[status(thm)],[f_2363_1]) ).

fof(f_2363_3,plain,
    ! [U_8326,U_8327,U_8328] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8326,tc_HOL_Obool)),U_8327),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8326,tc_HOL_Obool)),U_8328),U_8327)) = U_8328
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8326,tc_HOL_Obool)),U_8327),U_8328)) ),
    inference(definitional_conversion,[status(esa)],[f_2363_2]) ).

cnf(f_2363_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8326,tc_HOL_Obool)),U_8327),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8326,tc_HOL_Obool)),U_8328),U_8327)) = U_8328
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8326,tc_HOL_Obool)),U_8327),U_8328)) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

fof(f_2364_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv]) ).

fof(f_2364_2,plain,
    ! [U_8332,U_8331,U_8330,U_8329] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8329,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8329,tc_HOL_Obool)),U_8330),U_8331)),U_8332))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8329,tc_HOL_Obool)),U_8330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8329,tc_HOL_Obool)),U_8331),U_8332))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8329,tc_HOL_Obool)),U_8330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8329,tc_HOL_Obool)),U_8331),U_8332)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8329,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8329,tc_HOL_Obool)),U_8330),U_8331)),U_8332)) ) ),
    inference(variable_rename,[status(thm)],[f_2364_1]) ).

fof(f_2364_3,plain,
    ( ! [U_8340,U_8338,U_8336,U_8334] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8334,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8334,tc_HOL_Obool)),U_8336),U_8338)),U_8340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8334,tc_HOL_Obool)),U_8336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8334,tc_HOL_Obool)),U_8338),U_8340))) )
    & ! [U_8339,U_8337,U_8335,U_8333] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8333,tc_HOL_Obool)),U_8335),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8333,tc_HOL_Obool)),U_8337),U_8339)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8333,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8333,tc_HOL_Obool)),U_8335),U_8337)),U_8339)) ) ),
    inference(miniscope,[status(thm)],[f_2364_2]) ).

fof(f_2364_4,plain,
    ( ! [U_8334,U_8336,U_8338,U_8340] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8334,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8334,tc_HOL_Obool)),U_8336),U_8338)),U_8340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8334,tc_HOL_Obool)),U_8336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8334,tc_HOL_Obool)),U_8338),U_8340))) )
    & ! [U_8339,U_8335,U_8333,U_8337] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8333,tc_HOL_Obool)),U_8335),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8333,tc_HOL_Obool)),U_8337),U_8339)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8333,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8333,tc_HOL_Obool)),U_8335),U_8337)),U_8339)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2364_3]) ).

cnf(f_2364_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8333,tc_HOL_Obool)),U_8335),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8333,tc_HOL_Obool)),U_8337),U_8339)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8333,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8333,tc_HOL_Obool)),U_8335),U_8337)),U_8339)) ),
    inference(clausify,[status(thm)],[f_2364_4]) ).

cnf(f_2364_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8334,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8334,tc_HOL_Obool)),U_8336),U_8338)),U_8340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8334,tc_HOL_Obool)),U_8336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8334,tc_HOL_Obool)),U_8338),U_8340))) ),
    inference(clausify,[status(thm)],[f_2364_4]) ).

fof(f_2365_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Compl__Diff__eq]) ).

fof(f_2365_2,plain,
    ! [U_8343,U_8342,U_8341] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8341,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8341,tc_HOL_Obool)),U_8342),U_8343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8341,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8341,tc_HOL_Obool)),U_8342)),U_8343),
    inference(variable_rename,[status(thm)],[f_2365_1]) ).

fof(f_2365_3,plain,
    ! [U_8341,U_8342,U_8343] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8341,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8341,tc_HOL_Obool)),U_8342),U_8343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8341,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8341,tc_HOL_Obool)),U_8342)),U_8343),
    inference(definitional_conversion,[status(esa)],[f_2365_2]) ).

cnf(f_2365_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8341,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8341,tc_HOL_Obool)),U_8342),U_8343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8341,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8341,tc_HOL_Obool)),U_8342)),U_8343),
    inference(clausify,[status(thm)],[f_2365_3]) ).

fof(f_2366_1,plain,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_pair__less__def]) ).

fof(f_2366_2,plain,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_2366_1]) ).

cnf(f_2366_3,plain,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_2366_2]) ).

fof(f_2367_1,plain,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_max__weak__def]) ).

fof(f_2367_2,plain,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2367_1]) ).

cnf(f_2367_3,plain,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2367_2]) ).

fof(f_2368_1,plain,
    ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
    inference(fof_nnf,[status(thm)],[fact_mlex__prod__def]) ).

fof(f_2368_2,plain,
    ! [U_8346,U_8345,U_8344] : c_Wellfounded_Omlex__prod(U_8344,U_8345,U_8346) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_8344),U_8344),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_8344,c_Wellfounded_Oless__than,U_8346)),hAPP(hAPP(c_COMBS(U_8344,U_8344,tc_prod(tc_Nat_Onat,U_8344)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8344,tc_prod(tc_Nat_Onat,U_8344)),U_8344),c_Product__Type_OPair(tc_Nat_Onat,U_8344)),U_8345)),c_COMBI(U_8344))),
    inference(variable_rename,[status(thm)],[f_2368_1]) ).

fof(f_2368_3,plain,
    ! [U_8344,U_8345,U_8346] : c_Wellfounded_Omlex__prod(U_8344,U_8345,U_8346) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_8344),U_8344),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_8344,c_Wellfounded_Oless__than,U_8346)),hAPP(hAPP(c_COMBS(U_8344,U_8344,tc_prod(tc_Nat_Onat,U_8344)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8344,tc_prod(tc_Nat_Onat,U_8344)),U_8344),c_Product__Type_OPair(tc_Nat_Onat,U_8344)),U_8345)),c_COMBI(U_8344))),
    inference(definitional_conversion,[status(esa)],[f_2368_2]) ).

cnf(f_2368_4,plain,
    c_Wellfounded_Omlex__prod(U_8344,U_8345,U_8346) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_8344),U_8344),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_8344,c_Wellfounded_Oless__than,U_8346)),hAPP(hAPP(c_COMBS(U_8344,U_8344,tc_prod(tc_Nat_Onat,U_8344)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8344,tc_prod(tc_Nat_Onat,U_8344)),U_8344),c_Product__Type_OPair(tc_Nat_Onat,U_8344)),U_8345)),c_COMBI(U_8344))),
    inference(clausify,[status(thm)],[f_2368_3]) ).

fof(f_2369_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) ) ),
    inference(fof_nnf,[status(thm)],[fact_intrel__iff]) ).

fof(f_2369_2,plain,
    ! [U_8350,U_8349,U_8348,U_8347] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8347),U_8348)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8349),U_8350))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8347),U_8350) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8349),U_8348) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8347),U_8350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8349),U_8348)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8347),U_8348)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8349),U_8350))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[f_2369_1]) ).

fof(f_2369_3,plain,
    ( ! [U_8358,U_8356,U_8354,U_8352] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8352),U_8354)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8356),U_8358))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8352),U_8358) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8356),U_8354) )
    & ! [U_8357,U_8355,U_8353,U_8351] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8351),U_8357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8355),U_8353)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8351),U_8353)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8355),U_8357))),c_Int_Ointrel)) ) ),
    inference(miniscope,[status(thm)],[f_2369_2]) ).

fof(f_2369_4,plain,
    ( ! [U_8352,U_8354,U_8356,U_8358] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8352),U_8354)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8356),U_8358))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8352),U_8358) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8356),U_8354) )
    & ! [U_8357,U_8353,U_8351,U_8355] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8351),U_8357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8355),U_8353)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8351),U_8353)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8355),U_8357))),c_Int_Ointrel)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2369_3]) ).

cnf(f_2369_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8351),U_8357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8355),U_8353)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8351),U_8353)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8355),U_8357))),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_2369_4]) ).

cnf(f_2369_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8352),U_8354)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8356),U_8358))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8352),U_8358) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8356),U_8354) ),
    inference(clausify,[status(thm)],[f_2369_4]) ).

fof(f_2370_1,plain,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2))
      | ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).

fof(f_2370_2,plain,
    ! [U_8362,U_8361,U_8360,U_8359] :
      ( c_FunDef_Oreduction__pair(U_8361,hAPP(hAPP(c_FunDef_Orp__inv__image(U_8359,U_8361),U_8360),U_8362))
      | ~ c_FunDef_Oreduction__pair(U_8359,U_8360) ),
    inference(variable_rename,[status(thm)],[f_2370_1]) ).

fof(f_2370_3,plain,
    ! [U_8359,U_8361,U_8360,U_8362] :
      ( c_FunDef_Oreduction__pair(U_8361,hAPP(hAPP(c_FunDef_Orp__inv__image(U_8359,U_8361),U_8360),U_8362))
      | ~ c_FunDef_Oreduction__pair(U_8359,U_8360) ),
    inference(definitional_conversion,[status(esa)],[f_2370_2]) ).

cnf(f_2370_4,plain,
    ( c_FunDef_Oreduction__pair(U_8361,hAPP(hAPP(c_FunDef_Orp__inv__image(U_8359,U_8361),U_8360),U_8362))
    | ~ c_FunDef_Oreduction__pair(U_8359,U_8360) ),
    inference(clausify,[status(thm)],[f_2370_3]) ).

fof(f_2371_1,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_sup__nat__def]) ).

fof(f_2371_2,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2371_1]) ).

cnf(f_2371_3,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2371_2]) ).

fof(f_2372_1,plain,
    ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__def]) ).

fof(f_2372_2,plain,
    ! [U_8364,U_8363] : c_FunDef_Orp__inv__image(U_8363,U_8364) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),c_COMBS(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(U_8364,U_8363)),c_Product__Type_OPair(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),c_Relation_Oinv__image(U_8363,U_8364))))),c_Relation_Oinv__image(U_8363,U_8364))),
    inference(variable_rename,[status(thm)],[f_2372_1]) ).

fof(f_2372_3,plain,
    ! [U_8363,U_8364] : c_FunDef_Orp__inv__image(U_8363,U_8364) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),c_COMBS(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(U_8364,U_8363)),c_Product__Type_OPair(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),c_Relation_Oinv__image(U_8363,U_8364))))),c_Relation_Oinv__image(U_8363,U_8364))),
    inference(definitional_conversion,[status(esa)],[f_2372_2]) ).

cnf(f_2372_4,plain,
    c_FunDef_Orp__inv__image(U_8363,U_8364) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),c_COMBS(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)),tc_fun(tc_fun(U_8364,U_8363),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),tc_fun(tc_prod(U_8363,U_8363),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool))),tc_fun(U_8364,U_8363)),c_Product__Type_OPair(tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool),tc_fun(tc_prod(U_8364,U_8364),tc_HOL_Obool)))),c_Relation_Oinv__image(U_8363,U_8364))))),c_Relation_Oinv__image(U_8363,U_8364))),
    inference(clausify,[status(thm)],[f_2372_3]) ).

fof(f_2373_1,plain,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2]) ).

fof(f_2373_2,plain,
    ! [U_8370,U_8369,U_8368,U_8367,U_8366,U_8365] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8365,tc_fun(U_8366,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8365,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),U_8365),c_COMBC(U_8366,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_prod(U_8365,U_8366)),tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),U_8365),hAPP(c_COMBB(tc_prod(U_8365,U_8366),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool),U_8366),c_member(tc_prod(U_8365,U_8366)))),c_Product__Type_OPair(U_8365,U_8366)))),U_8367)),hAPP(hAPP(c_COMBC(U_8365,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),U_8365),c_COMBC(U_8366,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_prod(U_8365,U_8366)),tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),U_8365),hAPP(c_COMBB(tc_prod(U_8365,U_8366),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool),U_8366),c_member(tc_prod(U_8365,U_8366)))),c_Product__Type_OPair(U_8365,U_8366)))),U_8368)),U_8369),U_8370))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8365,U_8366)),hAPP(hAPP(c_Product__Type_OPair(U_8365,U_8366),U_8369),U_8370)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool)),U_8367),U_8368))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8365,U_8366)),hAPP(hAPP(c_Product__Type_OPair(U_8365,U_8366),U_8369),U_8370)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool)),U_8367),U_8368)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8365,tc_fun(U_8366,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8365,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),U_8365),c_COMBC(U_8366,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_prod(U_8365,U_8366)),tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),U_8365),hAPP(c_COMBB(tc_prod(U_8365,U_8366),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool),U_8366),c_member(tc_prod(U_8365,U_8366)))),c_Product__Type_OPair(U_8365,U_8366)))),U_8367)),hAPP(hAPP(c_COMBC(U_8365,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_fun(U_8366,tc_HOL_Obool)),U_8365),c_COMBC(U_8366,tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8366,tc_prod(U_8365,U_8366)),tc_fun(U_8366,tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool)),U_8365),hAPP(c_COMBB(tc_prod(U_8365,U_8366),tc_fun(tc_fun(tc_prod(U_8365,U_8366),tc_HOL_Obool),tc_HOL_Obool),U_8366),c_member(tc_prod(U_8365,U_8366)))),c_Product__Type_OPair(U_8365,U_8366)))),U_8368)),U_8369),U_8370)) ) ),
    inference(variable_rename,[status(thm)],[f_2373_1]) ).

fof(f_2373_3,plain,
    ( ! [U_8382,U_8380,U_8378,U_8376,U_8374,U_8372] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8372,tc_fun(U_8374,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8372,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),U_8372),c_COMBC(U_8374,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_prod(U_8372,U_8374)),tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),U_8372),hAPP(c_COMBB(tc_prod(U_8372,U_8374),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool),U_8374),c_member(tc_prod(U_8372,U_8374)))),c_Product__Type_OPair(U_8372,U_8374)))),U_8376)),hAPP(hAPP(c_COMBC(U_8372,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),U_8372),c_COMBC(U_8374,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_prod(U_8372,U_8374)),tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),U_8372),hAPP(c_COMBB(tc_prod(U_8372,U_8374),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool),U_8374),c_member(tc_prod(U_8372,U_8374)))),c_Product__Type_OPair(U_8372,U_8374)))),U_8378)),U_8380),U_8382))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8372,U_8374)),hAPP(hAPP(c_Product__Type_OPair(U_8372,U_8374),U_8380),U_8382)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool)),U_8376),U_8378))) )
    & ! [U_8381,U_8379,U_8377,U_8375,U_8373,U_8371] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8371,U_8373)),hAPP(hAPP(c_Product__Type_OPair(U_8371,U_8373),U_8379),U_8381)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool)),U_8375),U_8377)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8371,tc_fun(U_8373,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8371,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),U_8371),c_COMBC(U_8373,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_prod(U_8371,U_8373)),tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),U_8371),hAPP(c_COMBB(tc_prod(U_8371,U_8373),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool),U_8373),c_member(tc_prod(U_8371,U_8373)))),c_Product__Type_OPair(U_8371,U_8373)))),U_8375)),hAPP(hAPP(c_COMBC(U_8371,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),U_8371),c_COMBC(U_8373,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_prod(U_8371,U_8373)),tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),U_8371),hAPP(c_COMBB(tc_prod(U_8371,U_8373),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool),U_8373),c_member(tc_prod(U_8371,U_8373)))),c_Product__Type_OPair(U_8371,U_8373)))),U_8377)),U_8379),U_8381)) ) ),
    inference(miniscope,[status(thm)],[f_2373_2]) ).

fof(f_2373_4,plain,
    ( ! [U_8372,U_8374,U_8376,U_8378,U_8380,U_8382] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8372,tc_fun(U_8374,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8372,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),U_8372),c_COMBC(U_8374,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_prod(U_8372,U_8374)),tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),U_8372),hAPP(c_COMBB(tc_prod(U_8372,U_8374),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool),U_8374),c_member(tc_prod(U_8372,U_8374)))),c_Product__Type_OPair(U_8372,U_8374)))),U_8376)),hAPP(hAPP(c_COMBC(U_8372,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),U_8372),c_COMBC(U_8374,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_prod(U_8372,U_8374)),tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),U_8372),hAPP(c_COMBB(tc_prod(U_8372,U_8374),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool),U_8374),c_member(tc_prod(U_8372,U_8374)))),c_Product__Type_OPair(U_8372,U_8374)))),U_8378)),U_8380),U_8382))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8372,U_8374)),hAPP(hAPP(c_Product__Type_OPair(U_8372,U_8374),U_8380),U_8382)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool)),U_8376),U_8378))) )
    & ! [U_8377,U_8373,U_8371,U_8375,U_8379,U_8381] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8371,U_8373)),hAPP(hAPP(c_Product__Type_OPair(U_8371,U_8373),U_8379),U_8381)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool)),U_8375),U_8377)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8371,tc_fun(U_8373,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8371,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),U_8371),c_COMBC(U_8373,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_prod(U_8371,U_8373)),tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),U_8371),hAPP(c_COMBB(tc_prod(U_8371,U_8373),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool),U_8373),c_member(tc_prod(U_8371,U_8373)))),c_Product__Type_OPair(U_8371,U_8373)))),U_8375)),hAPP(hAPP(c_COMBC(U_8371,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),U_8371),c_COMBC(U_8373,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_prod(U_8371,U_8373)),tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),U_8371),hAPP(c_COMBB(tc_prod(U_8371,U_8373),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool),U_8373),c_member(tc_prod(U_8371,U_8373)))),c_Product__Type_OPair(U_8371,U_8373)))),U_8377)),U_8379),U_8381)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2373_3]) ).

cnf(f_2373_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8371,U_8373)),hAPP(hAPP(c_Product__Type_OPair(U_8371,U_8373),U_8379),U_8381)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool)),U_8375),U_8377)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8371,tc_fun(U_8373,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8371,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),U_8371),c_COMBC(U_8373,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_prod(U_8371,U_8373)),tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),U_8371),hAPP(c_COMBB(tc_prod(U_8371,U_8373),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool),U_8373),c_member(tc_prod(U_8371,U_8373)))),c_Product__Type_OPair(U_8371,U_8373)))),U_8375)),hAPP(hAPP(c_COMBC(U_8371,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_fun(U_8373,tc_HOL_Obool)),U_8371),c_COMBC(U_8373,tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8373,tc_prod(U_8371,U_8373)),tc_fun(U_8373,tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool)),U_8371),hAPP(c_COMBB(tc_prod(U_8371,U_8373),tc_fun(tc_fun(tc_prod(U_8371,U_8373),tc_HOL_Obool),tc_HOL_Obool),U_8373),c_member(tc_prod(U_8371,U_8373)))),c_Product__Type_OPair(U_8371,U_8373)))),U_8377)),U_8379),U_8381)) ),
    inference(clausify,[status(thm)],[f_2373_4]) ).

cnf(f_2373_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8372,tc_fun(U_8374,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8372,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),U_8372),c_COMBC(U_8374,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_prod(U_8372,U_8374)),tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),U_8372),hAPP(c_COMBB(tc_prod(U_8372,U_8374),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool),U_8374),c_member(tc_prod(U_8372,U_8374)))),c_Product__Type_OPair(U_8372,U_8374)))),U_8376)),hAPP(hAPP(c_COMBC(U_8372,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_fun(U_8374,tc_HOL_Obool)),U_8372),c_COMBC(U_8374,tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8374,tc_prod(U_8372,U_8374)),tc_fun(U_8374,tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool)),U_8372),hAPP(c_COMBB(tc_prod(U_8372,U_8374),tc_fun(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool),tc_HOL_Obool),U_8374),c_member(tc_prod(U_8372,U_8374)))),c_Product__Type_OPair(U_8372,U_8374)))),U_8378)),U_8380),U_8382))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8372,U_8374)),hAPP(hAPP(c_Product__Type_OPair(U_8372,U_8374),U_8380),U_8382)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8372,U_8374),tc_HOL_Obool)),U_8376),U_8378))) ),
    inference(clausify,[status(thm)],[f_2373_4]) ).

fof(f_2374_1,plain,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(fof_nnf,[status(thm)],[fact_max__strict__def]) ).

fof(f_2374_2,plain,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(definitional_conversion,[status(esa)],[f_2374_1]) ).

cnf(f_2374_3,plain,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_2374_2]) ).

fof(f_2375_1,plain,
    ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__additive]) ).

fof(f_2375_2,plain,
    ! [U_8388,U_8387,U_8386,U_8385,U_8384,U_8383] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8383,tc_HOL_Obool)),U_8384),U_8387)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8383,tc_HOL_Obool)),U_8385),U_8388))),c_Wellfounded_Omax__ext(U_8383,U_8386)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),U_8387),U_8388)),c_Wellfounded_Omax__ext(U_8383,U_8386)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),U_8384),U_8385)),c_Wellfounded_Omax__ext(U_8383,U_8386))) ),
    inference(variable_rename,[status(thm)],[f_2375_1]) ).

fof(f_2375_3,plain,
    ! [U_8383,U_8385,U_8386,U_8387,U_8384,U_8388] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8383,tc_HOL_Obool)),U_8384),U_8387)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8383,tc_HOL_Obool)),U_8385),U_8388))),c_Wellfounded_Omax__ext(U_8383,U_8386)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),U_8387),U_8388)),c_Wellfounded_Omax__ext(U_8383,U_8386)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),U_8384),U_8385)),c_Wellfounded_Omax__ext(U_8383,U_8386))) ),
    inference(definitional_conversion,[status(esa)],[f_2375_2]) ).

cnf(f_2375_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8383,tc_HOL_Obool)),U_8384),U_8387)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8383,tc_HOL_Obool)),U_8385),U_8388))),c_Wellfounded_Omax__ext(U_8383,U_8386)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),U_8387),U_8388)),c_Wellfounded_Omax__ext(U_8383,U_8386)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8383,tc_HOL_Obool),tc_fun(U_8383,tc_HOL_Obool)),U_8384),U_8385)),c_Wellfounded_Omax__ext(U_8383,U_8386))) ),
    inference(clausify,[status(thm)],[f_2375_3]) ).

fof(f_2376_1,plain,
    ! [V_xa_2,V_x_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
        | ~ c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq]) ).

fof(f_2376_2,plain,
    ! [U_8392,U_8391,U_8390,U_8389] :
      ( ( c_Wellfounded_Omax__extp(U_8389,hAPP(hAPP(c_COMBC(U_8389,tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8389,tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool)),U_8389),c_COMBC(U_8389,tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8389,tc_prod(U_8389,U_8389)),tc_fun(U_8389,tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool)),U_8389),hAPP(c_COMBB(tc_prod(U_8389,U_8389),tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool),U_8389),c_member(tc_prod(U_8389,U_8389)))),c_Product__Type_OPair(U_8389,U_8389)))),U_8390),U_8391,U_8392)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8389,tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8389,tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool)),U_8391),U_8392)),c_Wellfounded_Omax__ext(U_8389,U_8390))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8389,tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8389,tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool)),U_8391),U_8392)),c_Wellfounded_Omax__ext(U_8389,U_8390)))
        | ~ c_Wellfounded_Omax__extp(U_8389,hAPP(hAPP(c_COMBC(U_8389,tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8389,tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_fun(U_8389,tc_HOL_Obool)),U_8389),c_COMBC(U_8389,tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8389,tc_prod(U_8389,U_8389)),tc_fun(U_8389,tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool)),U_8389),hAPP(c_COMBB(tc_prod(U_8389,U_8389),tc_fun(tc_fun(tc_prod(U_8389,U_8389),tc_HOL_Obool),tc_HOL_Obool),U_8389),c_member(tc_prod(U_8389,U_8389)))),c_Product__Type_OPair(U_8389,U_8389)))),U_8390),U_8391,U_8392) ) ),
    inference(variable_rename,[status(thm)],[f_2376_1]) ).

fof(f_2376_3,plain,
    ( ! [U_8400,U_8398,U_8396,U_8394] :
        ( c_Wellfounded_Omax__extp(U_8394,hAPP(hAPP(c_COMBC(U_8394,tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8394,tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),U_8394),c_COMBC(U_8394,tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8394,tc_prod(U_8394,U_8394)),tc_fun(U_8394,tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),U_8394),hAPP(c_COMBB(tc_prod(U_8394,U_8394),tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool),U_8394),c_member(tc_prod(U_8394,U_8394)))),c_Product__Type_OPair(U_8394,U_8394)))),U_8396),U_8398,U_8400)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8394,tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8394,tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),U_8398),U_8400)),c_Wellfounded_Omax__ext(U_8394,U_8396))) )
    & ! [U_8399,U_8397,U_8395,U_8393] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8393,tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8393,tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),U_8397),U_8399)),c_Wellfounded_Omax__ext(U_8393,U_8395)))
        | ~ c_Wellfounded_Omax__extp(U_8393,hAPP(hAPP(c_COMBC(U_8393,tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8393,tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),U_8393),c_COMBC(U_8393,tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8393,tc_prod(U_8393,U_8393)),tc_fun(U_8393,tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),U_8393),hAPP(c_COMBB(tc_prod(U_8393,U_8393),tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool),U_8393),c_member(tc_prod(U_8393,U_8393)))),c_Product__Type_OPair(U_8393,U_8393)))),U_8395),U_8397,U_8399) ) ),
    inference(miniscope,[status(thm)],[f_2376_2]) ).

fof(f_2376_4,plain,
    ( ! [U_8396,U_8394,U_8398,U_8400] :
        ( c_Wellfounded_Omax__extp(U_8394,hAPP(hAPP(c_COMBC(U_8394,tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8394,tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),U_8394),c_COMBC(U_8394,tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8394,tc_prod(U_8394,U_8394)),tc_fun(U_8394,tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),U_8394),hAPP(c_COMBB(tc_prod(U_8394,U_8394),tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool),U_8394),c_member(tc_prod(U_8394,U_8394)))),c_Product__Type_OPair(U_8394,U_8394)))),U_8396),U_8398,U_8400)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8394,tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8394,tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),U_8398),U_8400)),c_Wellfounded_Omax__ext(U_8394,U_8396))) )
    & ! [U_8395,U_8393,U_8397,U_8399] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8393,tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8393,tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),U_8397),U_8399)),c_Wellfounded_Omax__ext(U_8393,U_8395)))
        | ~ c_Wellfounded_Omax__extp(U_8393,hAPP(hAPP(c_COMBC(U_8393,tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8393,tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),U_8393),c_COMBC(U_8393,tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8393,tc_prod(U_8393,U_8393)),tc_fun(U_8393,tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),U_8393),hAPP(c_COMBB(tc_prod(U_8393,U_8393),tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool),U_8393),c_member(tc_prod(U_8393,U_8393)))),c_Product__Type_OPair(U_8393,U_8393)))),U_8395),U_8397,U_8399) ) ),
    inference(definitional_conversion,[status(esa)],[f_2376_3]) ).

cnf(f_2376_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8393,tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8393,tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),U_8397),U_8399)),c_Wellfounded_Omax__ext(U_8393,U_8395)))
    | ~ c_Wellfounded_Omax__extp(U_8393,hAPP(hAPP(c_COMBC(U_8393,tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8393,tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_fun(U_8393,tc_HOL_Obool)),U_8393),c_COMBC(U_8393,tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8393,tc_prod(U_8393,U_8393)),tc_fun(U_8393,tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool)),U_8393),hAPP(c_COMBB(tc_prod(U_8393,U_8393),tc_fun(tc_fun(tc_prod(U_8393,U_8393),tc_HOL_Obool),tc_HOL_Obool),U_8393),c_member(tc_prod(U_8393,U_8393)))),c_Product__Type_OPair(U_8393,U_8393)))),U_8395),U_8397,U_8399) ),
    inference(clausify,[status(thm)],[f_2376_4]) ).

cnf(f_2376_6,plain,
    ( c_Wellfounded_Omax__extp(U_8394,hAPP(hAPP(c_COMBC(U_8394,tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8394,tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),U_8394),c_COMBC(U_8394,tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8394,tc_prod(U_8394,U_8394)),tc_fun(U_8394,tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool)),U_8394),hAPP(c_COMBB(tc_prod(U_8394,U_8394),tc_fun(tc_fun(tc_prod(U_8394,U_8394),tc_HOL_Obool),tc_HOL_Obool),U_8394),c_member(tc_prod(U_8394,U_8394)))),c_Product__Type_OPair(U_8394,U_8394)))),U_8396),U_8398,U_8400)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8394,tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8394,tc_HOL_Obool),tc_fun(U_8394,tc_HOL_Obool)),U_8398),U_8400)),c_Wellfounded_Omax__ext(U_8394,U_8396))) ),
    inference(clausify,[status(thm)],[f_2376_4]) ).

fof(f_2377_1,plain,
    ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__inv__image]) ).

fof(f_2377_2,plain,
    ! [U_8406,U_8405,U_8404,U_8403,U_8402,U_8401] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8401,U_8401)),hAPP(hAPP(c_Product__Type_OPair(U_8401,U_8401),U_8402),U_8403)),hAPP(hAPP(c_Relation_Oinv__image(U_8404,U_8401),U_8405),U_8406)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8404,U_8404)),hAPP(hAPP(c_Product__Type_OPair(U_8404,U_8404),hAPP(U_8406,U_8402)),hAPP(U_8406,U_8403))),U_8405)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8404,U_8404)),hAPP(hAPP(c_Product__Type_OPair(U_8404,U_8404),hAPP(U_8406,U_8402)),hAPP(U_8406,U_8403))),U_8405))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8401,U_8401)),hAPP(hAPP(c_Product__Type_OPair(U_8401,U_8401),U_8402),U_8403)),hAPP(hAPP(c_Relation_Oinv__image(U_8404,U_8401),U_8405),U_8406))) ) ),
    inference(variable_rename,[status(thm)],[f_2377_1]) ).

fof(f_2377_3,plain,
    ( ! [U_8418,U_8416,U_8414,U_8412,U_8410] :
        ( ! [U_8408] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8408,U_8408)),hAPP(hAPP(c_Product__Type_OPair(U_8408,U_8408),U_8410),U_8412)),hAPP(hAPP(c_Relation_Oinv__image(U_8414,U_8408),U_8416),U_8418)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8414,U_8414)),hAPP(hAPP(c_Product__Type_OPair(U_8414,U_8414),hAPP(U_8418,U_8410)),hAPP(U_8418,U_8412))),U_8416)) )
    & ! [U_8417,U_8415,U_8413,U_8411,U_8409] :
        ( ! [U_8407] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8407,U_8407)),hAPP(hAPP(c_Product__Type_OPair(U_8407,U_8407),U_8409),U_8411)),hAPP(hAPP(c_Relation_Oinv__image(U_8413,U_8407),U_8415),U_8417)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8413,U_8413)),hAPP(hAPP(c_Product__Type_OPair(U_8413,U_8413),hAPP(U_8417,U_8409)),hAPP(U_8417,U_8411))),U_8415)) ) ),
    inference(miniscope,[status(thm)],[f_2377_2]) ).

fof(f_2377_4,plain,
    ( ! [U_8408,U_8410,U_8412,U_8414,U_8416,U_8418] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8408,U_8408)),hAPP(hAPP(c_Product__Type_OPair(U_8408,U_8408),U_8410),U_8412)),hAPP(hAPP(c_Relation_Oinv__image(U_8414,U_8408),U_8416),U_8418)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8414,U_8414)),hAPP(hAPP(c_Product__Type_OPair(U_8414,U_8414),hAPP(U_8418,U_8410)),hAPP(U_8418,U_8412))),U_8416)) )
    & ! [U_8413,U_8409,U_8407,U_8411,U_8415,U_8417] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8407,U_8407)),hAPP(hAPP(c_Product__Type_OPair(U_8407,U_8407),U_8409),U_8411)),hAPP(hAPP(c_Relation_Oinv__image(U_8413,U_8407),U_8415),U_8417)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8413,U_8413)),hAPP(hAPP(c_Product__Type_OPair(U_8413,U_8413),hAPP(U_8417,U_8409)),hAPP(U_8417,U_8411))),U_8415)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2377_3]) ).

cnf(f_2377_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8407,U_8407)),hAPP(hAPP(c_Product__Type_OPair(U_8407,U_8407),U_8409),U_8411)),hAPP(hAPP(c_Relation_Oinv__image(U_8413,U_8407),U_8415),U_8417)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8413,U_8413)),hAPP(hAPP(c_Product__Type_OPair(U_8413,U_8413),hAPP(U_8417,U_8409)),hAPP(U_8417,U_8411))),U_8415)) ),
    inference(clausify,[status(thm)],[f_2377_4]) ).

cnf(f_2377_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8408,U_8408)),hAPP(hAPP(c_Product__Type_OPair(U_8408,U_8408),U_8410),U_8412)),hAPP(hAPP(c_Relation_Oinv__image(U_8414,U_8408),U_8416),U_8418)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8414,U_8414)),hAPP(hAPP(c_Product__Type_OPair(U_8414,U_8414),hAPP(U_8418,U_8410)),hAPP(U_8418,U_8412))),U_8416)) ),
    inference(clausify,[status(thm)],[f_2377_4]) ).

fof(f_2378_1,plain,
    ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Body1]) ).

fof(f_2378_2,plain,
    ! [U_8424,U_8423,U_8422,U_8421,U_8420,U_8419] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8419,U_8420,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8419),hAPP(U_8421,U_8424)),hAPP(c_Com_Ocom_OBODY,U_8424)),hAPP(U_8422,U_8424))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8419),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8424),U_8423))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8419,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8419),tc_HOL_Obool)),U_8420),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8419),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),hAPP(hAPP(c_COMBB(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8419)),U_8421)),c_Com_Ocom_OBODY)),U_8422)),U_8423)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8419),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),hAPP(hAPP(c_COMBB(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8419)),U_8421)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8422)),U_8423)) ),
    inference(variable_rename,[status(thm)],[f_2378_1]) ).

fof(f_2378_3,plain,
    ! [U_8419,U_8420,U_8421,U_8422,U_8423,U_8424] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8419,U_8420,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8419),hAPP(U_8421,U_8424)),hAPP(c_Com_Ocom_OBODY,U_8424)),hAPP(U_8422,U_8424))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8419),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8424),U_8423))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8419,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8419),tc_HOL_Obool)),U_8420),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8419),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),hAPP(hAPP(c_COMBB(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8419)),U_8421)),c_Com_Ocom_OBODY)),U_8422)),U_8423)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8419),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),hAPP(hAPP(c_COMBB(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8419)),U_8421)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8422)),U_8423)) ),
    inference(definitional_conversion,[status(esa)],[f_2378_2]) ).

cnf(f_2378_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8419,U_8420,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8419),hAPP(U_8421,U_8424)),hAPP(c_Com_Ocom_OBODY,U_8424)),hAPP(U_8422,U_8424))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8419),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8424),U_8423))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8419,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8419),tc_HOL_Obool)),U_8420),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8419),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),hAPP(hAPP(c_COMBB(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8419)),U_8421)),c_Com_Ocom_OBODY)),U_8422)),U_8423)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8419),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),hAPP(hAPP(c_COMBB(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8419,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8419))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8419)),U_8421)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8422)),U_8423)) ),
    inference(clausify,[status(thm)],[f_2378_3]) ).

fof(f_2379_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff]) ).

fof(f_2379_2,plain,
    ! [U_8426,U_8425] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8425),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8426),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8425),U_8426)),c_Int_Ointrel)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8425),U_8426)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8425),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8426),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2379_1]) ).

fof(f_2379_3,plain,
    ( ! [U_8430,U_8428] :
        ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8428),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8430),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8428),U_8430)),c_Int_Ointrel)) )
    & ! [U_8429,U_8427] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8427),U_8429)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8427),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8429),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2379_2]) ).

fof(f_2379_4,plain,
    ( ! [U_8428,U_8430] :
        ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8428),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8430),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8428),U_8430)),c_Int_Ointrel)) )
    & ! [U_8427,U_8429] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8427),U_8429)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8427),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8429),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2379_3]) ).

cnf(f_2379_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8427),U_8429)),c_Int_Ointrel))
    | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8427),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8429),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2379_4]) ).

cnf(f_2379_6,plain,
    ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8428),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8430),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8428),U_8430)),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_2379_4]) ).

fof(f_2380_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
      | hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2E]) ).

fof(f_2380_2,plain,
    ! [U_8436,U_8435,U_8434,U_8433,U_8432,U_8431] :
      ( hBOOL(hAPP(hAPP(U_8434,U_8435),U_8436))
      | hBOOL(hAPP(hAPP(U_8433,U_8435),U_8436))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8431,tc_fun(U_8432,tc_HOL_Obool))),U_8433),U_8434),U_8435),U_8436)) ),
    inference(variable_rename,[status(thm)],[f_2380_1]) ).

fof(f_2380_3,plain,
    ! [U_8436,U_8435,U_8434,U_8433] :
      ( ! [U_8432,U_8431] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8431,tc_fun(U_8432,tc_HOL_Obool))),U_8433),U_8434),U_8435),U_8436))
      | hBOOL(hAPP(hAPP(U_8434,U_8435),U_8436))
      | hBOOL(hAPP(hAPP(U_8433,U_8435),U_8436)) ),
    inference(miniscope,[status(thm)],[f_2380_2]) ).

fof(f_2380_4,plain,
    ! [U_8431,U_8432,U_8433,U_8434,U_8435,U_8436] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8431,tc_fun(U_8432,tc_HOL_Obool))),U_8433),U_8434),U_8435),U_8436))
      | hBOOL(hAPP(hAPP(U_8434,U_8435),U_8436))
      | hBOOL(hAPP(hAPP(U_8433,U_8435),U_8436)) ),
    inference(definitional_conversion,[status(esa)],[f_2380_3]) ).

cnf(f_2380_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8431,tc_fun(U_8432,tc_HOL_Obool))),U_8433),U_8434),U_8435),U_8436))
    | hBOOL(hAPP(hAPP(U_8434,U_8435),U_8436))
    | hBOOL(hAPP(hAPP(U_8433,U_8435),U_8436)) ),
    inference(clausify,[status(thm)],[f_2380_4]) ).

fof(f_2381_1,plain,
    ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
        & ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup2CI]) ).

fof(f_2381_2,plain,
    ! [U_8442,U_8441,U_8440,U_8439,U_8438,U_8437] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8441,tc_fun(U_8442,tc_HOL_Obool))),U_8440),U_8437),U_8438),U_8439))
      | ( ~ hBOOL(hAPP(hAPP(U_8440,U_8438),U_8439))
        & ~ hBOOL(hAPP(hAPP(U_8437,U_8438),U_8439)) ) ),
    inference(variable_rename,[status(thm)],[f_2381_1]) ).

fof(f_2381_3,plain,
    ( ! [U_8437,U_8438,U_8439,U_8440] :
        ( ~ hBOOL(hAPP(hAPP(U_8440,U_8438),U_8439))
        | ~ sP717(U_8437,U_8438,U_8439,U_8440) )
    & ! [U_8437,U_8438,U_8439,U_8440] :
        ( ~ hBOOL(hAPP(hAPP(U_8437,U_8438),U_8439))
        | ~ sP717(U_8437,U_8438,U_8439,U_8440) )
    & ! [U_8437,U_8438,U_8439,U_8440,U_8441,U_8442] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8441,tc_fun(U_8442,tc_HOL_Obool))),U_8440),U_8437),U_8438),U_8439))
        | sP717(U_8437,U_8438,U_8439,U_8440) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP717])],[f_2381_2]) ).

cnf(f_2381_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8441,tc_fun(U_8442,tc_HOL_Obool))),U_8440),U_8437),U_8438),U_8439))
    | sP717(U_8437,U_8438,U_8439,U_8440) ),
    inference(clausify,[status(thm)],[f_2381_3]) ).

cnf(f_2381_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8437,U_8438),U_8439))
    | ~ sP717(U_8437,U_8438,U_8439,U_8440) ),
    inference(clausify,[status(thm)],[f_2381_3]) ).

cnf(f_2381_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8440,U_8438),U_8439))
    | ~ sP717(U_8437,U_8438,U_8439,U_8440) ),
    inference(clausify,[status(thm)],[f_2381_3]) ).

fof(f_2382_1,plain,
    ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | V_b_2 != hAPP(V_f_2,V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_image__eqI]) ).

fof(f_2382_2,plain,
    ! [U_8448,U_8447,U_8446,U_8445,U_8444,U_8443] :
      ( hBOOL(hAPP(hAPP(c_member(U_8448),U_8443),hAPP(c_Set_Oimage(U_8446,U_8448,U_8444),U_8447)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8445),U_8447))
      | U_8443 != hAPP(U_8444,U_8445) ),
    inference(variable_rename,[status(thm)],[f_2382_1]) ).

fof(f_2382_3,plain,
    ! [U_8444,U_8443,U_8446,U_8445,U_8447,U_8448] :
      ( hBOOL(hAPP(hAPP(c_member(U_8448),U_8443),hAPP(c_Set_Oimage(U_8446,U_8448,U_8444),U_8447)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8445),U_8447))
      | U_8443 != hAPP(U_8444,U_8445) ),
    inference(definitional_conversion,[status(esa)],[f_2382_2]) ).

cnf(f_2382_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8448),U_8443),hAPP(c_Set_Oimage(U_8446,U_8448,U_8444),U_8447)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8445),U_8447))
    | U_8443 != hAPP(U_8444,U_8445) ),
    inference(clausify,[status(thm)],[f_2382_3]) ).

fof(f_2383_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__Un]) ).

fof(f_2383_2,plain,
    ! [U_8453,U_8452,U_8451,U_8450,U_8449] : hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8449,tc_HOL_Obool)),U_8452),U_8453)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8450,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),U_8452)),hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),U_8453)),
    inference(variable_rename,[status(thm)],[f_2383_1]) ).

fof(f_2383_3,plain,
    ! [U_8449,U_8450,U_8451,U_8452,U_8453] : hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8449,tc_HOL_Obool)),U_8452),U_8453)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8450,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),U_8452)),hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),U_8453)),
    inference(definitional_conversion,[status(esa)],[f_2383_2]) ).

cnf(f_2383_4,plain,
    hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8449,tc_HOL_Obool)),U_8452),U_8453)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8450,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),U_8452)),hAPP(c_Relation_OImage(U_8449,U_8450,U_8451),U_8453)),
    inference(clausify,[status(thm)],[f_2383_3]) ).

fof(f_2384_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Un]) ).

fof(f_2384_2,plain,
    ! [U_8458,U_8457,U_8456,U_8455,U_8454] : hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8457),U_8458)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),U_8457)),hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),U_8458)),
    inference(variable_rename,[status(thm)],[f_2384_1]) ).

fof(f_2384_3,plain,
    ! [U_8454,U_8455,U_8456,U_8457,U_8458] : hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8457),U_8458)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),U_8457)),hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),U_8458)),
    inference(definitional_conversion,[status(esa)],[f_2384_2]) ).

cnf(f_2384_4,plain,
    hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8457),U_8458)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),U_8457)),hAPP(c_Set_Oimage(U_8454,U_8455,U_8456),U_8458)),
    inference(clausify,[status(thm)],[f_2384_3]) ).

fof(f_2385_1,plain,
    ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2I1]) ).

fof(f_2385_2,plain,
    ! [U_8464,U_8463,U_8462,U_8461,U_8460,U_8459] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8462,tc_fun(U_8463,tc_HOL_Obool))),U_8459),U_8464),U_8460),U_8461))
      | ~ hBOOL(hAPP(hAPP(U_8459,U_8460),U_8461)) ),
    inference(variable_rename,[status(thm)],[f_2385_1]) ).

fof(f_2385_3,plain,
    ! [U_8459,U_8460,U_8461,U_8462,U_8463,U_8464] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8462,tc_fun(U_8463,tc_HOL_Obool))),U_8459),U_8464),U_8460),U_8461))
      | ~ hBOOL(hAPP(hAPP(U_8459,U_8460),U_8461)) ),
    inference(definitional_conversion,[status(esa)],[f_2385_2]) ).

cnf(f_2385_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8462,tc_fun(U_8463,tc_HOL_Obool))),U_8459),U_8464),U_8460),U_8461))
    | ~ hBOOL(hAPP(hAPP(U_8459,U_8460),U_8461)) ),
    inference(clausify,[status(thm)],[f_2385_3]) ).

fof(f_2386_1,plain,
    ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2I2]) ).

fof(f_2386_2,plain,
    ! [U_8470,U_8469,U_8468,U_8467,U_8466,U_8465] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8468,tc_fun(U_8469,tc_HOL_Obool))),U_8470),U_8465),U_8466),U_8467))
      | ~ hBOOL(hAPP(hAPP(U_8465,U_8466),U_8467)) ),
    inference(variable_rename,[status(thm)],[f_2386_1]) ).

fof(f_2386_3,plain,
    ! [U_8466,U_8465,U_8467,U_8468,U_8469,U_8470] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8468,tc_fun(U_8469,tc_HOL_Obool))),U_8470),U_8465),U_8466),U_8467))
      | ~ hBOOL(hAPP(hAPP(U_8465,U_8466),U_8467)) ),
    inference(definitional_conversion,[status(esa)],[f_2386_2]) ).

cnf(f_2386_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8468,tc_fun(U_8469,tc_HOL_Obool))),U_8470),U_8465),U_8466),U_8467))
    | ~ hBOOL(hAPP(hAPP(U_8465,U_8466),U_8467)) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

fof(f_2387_1,plain,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
        | ! [B_AA] :
            ( V_B_2 != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) )
      & ( ? [B_AA] :
            ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__image__iff]) ).

fof(f_2387_2,plain,
    ! [U_8477,U_8476,U_8475,U_8474,U_8473] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8473,tc_HOL_Obool)),U_8474),hAPP(c_Set_Oimage(U_8475,U_8473,U_8476),U_8477)))
        | ! [U_8472] :
            ( U_8474 != hAPP(c_Set_Oimage(U_8475,U_8473,U_8476),U_8472)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8475,tc_HOL_Obool)),U_8472),U_8477)) ) )
      & ( ? [U_8471] :
            ( U_8474 = hAPP(c_Set_Oimage(U_8475,U_8473,U_8476),U_8471)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8475,tc_HOL_Obool)),U_8471),U_8477)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8473,tc_HOL_Obool)),U_8474),hAPP(c_Set_Oimage(U_8475,U_8473,U_8476),U_8477))) ) ),
    inference(variable_rename,[status(thm)],[f_2387_1]) ).

fof(f_2387_3,plain,
    ( ! [U_8487,U_8485,U_8483,U_8481,U_8479] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8479,tc_HOL_Obool)),U_8481),hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8487)))
        | ! [U_8472] :
            ( U_8481 != hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8472)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8483,tc_HOL_Obool)),U_8472),U_8487)) ) )
    & ! [U_8486,U_8484,U_8482,U_8480,U_8478] :
        ( ? [U_8471] :
            ( U_8480 = hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),U_8471)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8482,tc_HOL_Obool)),U_8471),U_8486)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8478,tc_HOL_Obool)),U_8480),hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),U_8486))) ) ),
    inference(miniscope,[status(thm)],[f_2387_2]) ).

fof(f_2387_4,plain,
    ( ! [U_8487,U_8485,U_8483,U_8481,U_8479] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8479,tc_HOL_Obool)),U_8481),hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8487)))
        | ! [U_8472] :
            ( U_8481 != hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8472)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8483,tc_HOL_Obool)),U_8472),U_8487)) ) )
    & ! [U_8486,U_8484,U_8482,U_8480,U_8478] :
        ( ( U_8480 = hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),sK123(U_8486,U_8484,U_8482,U_8480,U_8478))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8482,tc_HOL_Obool)),sK123(U_8486,U_8484,U_8482,U_8480,U_8478)),U_8486)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8478,tc_HOL_Obool)),U_8480),hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),U_8486))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_8471,sK123(U_8486,U_8484,U_8482,U_8480,U_8478))],[f_2387_3]) ).

fof(f_2387_5,plain,
    ( ! [U_8480,U_8478,U_8482,U_8486,U_8484] :
        ( U_8480 = hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),sK123(U_8486,U_8484,U_8482,U_8480,U_8478))
        | ~ sP718(U_8480,U_8478,U_8482,U_8486,U_8484) )
    & ! [U_8480,U_8478,U_8482,U_8486,U_8484] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8482,tc_HOL_Obool)),sK123(U_8486,U_8484,U_8482,U_8480,U_8478)),U_8486))
        | ~ sP718(U_8480,U_8478,U_8482,U_8486,U_8484) )
    & ! [U_8472,U_8481,U_8479,U_8485,U_8487,U_8483] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8479,tc_HOL_Obool)),U_8481),hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8487)))
        | U_8481 != hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8472)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8483,tc_HOL_Obool)),U_8472),U_8487)) )
    & ! [U_8480,U_8478,U_8482,U_8486,U_8484] :
        ( sP718(U_8480,U_8478,U_8482,U_8486,U_8484)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8478,tc_HOL_Obool)),U_8480),hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),U_8486))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP718])],[f_2387_4]) ).

cnf(f_2387_6,plain,
    ( sP718(U_8480,U_8478,U_8482,U_8486,U_8484)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8478,tc_HOL_Obool)),U_8480),hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),U_8486))) ),
    inference(clausify,[status(thm)],[f_2387_5]) ).

cnf(f_2387_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8479,tc_HOL_Obool)),U_8481),hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8487)))
    | U_8481 != hAPP(c_Set_Oimage(U_8483,U_8479,U_8485),U_8472)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8483,tc_HOL_Obool)),U_8472),U_8487)) ),
    inference(clausify,[status(thm)],[f_2387_5]) ).

cnf(f_2387_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8482,tc_HOL_Obool)),sK123(U_8486,U_8484,U_8482,U_8480,U_8478)),U_8486))
    | ~ sP718(U_8480,U_8478,U_8482,U_8486,U_8484) ),
    inference(clausify,[status(thm)],[f_2387_5]) ).

cnf(f_2387_9,plain,
    ( U_8480 = hAPP(c_Set_Oimage(U_8482,U_8478,U_8484),sK123(U_8486,U_8484,U_8482,U_8480,U_8478))
    | ~ sP718(U_8480,U_8478,U_8482,U_8486,U_8484) ),
    inference(clausify,[status(thm)],[f_2387_5]) ).

fof(f_2388_1,plain,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__mono]) ).

fof(f_2388_2,plain,
    ! [U_8492,U_8491,U_8490,U_8489,U_8488] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8488,U_8491,U_8492),U_8489)),hAPP(c_Set_Oimage(U_8488,U_8491,U_8492),U_8490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8488,tc_HOL_Obool)),U_8489),U_8490)) ),
    inference(variable_rename,[status(thm)],[f_2388_1]) ).

fof(f_2388_3,plain,
    ! [U_8488,U_8489,U_8490,U_8491,U_8492] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8488,U_8491,U_8492),U_8489)),hAPP(c_Set_Oimage(U_8488,U_8491,U_8492),U_8490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8488,tc_HOL_Obool)),U_8489),U_8490)) ),
    inference(definitional_conversion,[status(esa)],[f_2388_2]) ).

cnf(f_2388_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8488,U_8491,U_8492),U_8489)),hAPP(c_Set_Oimage(U_8488,U_8491,U_8492),U_8490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8488,tc_HOL_Obool)),U_8489),U_8490)) ),
    inference(clausify,[status(thm)],[f_2388_3]) ).

fof(f_2389_1,plain,
    ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_image__image]) ).

fof(f_2389_2,plain,
    ! [U_8498,U_8497,U_8496,U_8495,U_8494,U_8493] : hAPP(c_Set_Oimage(U_8493,U_8494,U_8495),hAPP(c_Set_Oimage(U_8496,U_8493,U_8497),U_8498)) = hAPP(c_Set_Oimage(U_8496,U_8494,hAPP(hAPP(c_COMBB(U_8493,U_8494,U_8496),U_8495),U_8497)),U_8498),
    inference(variable_rename,[status(thm)],[f_2389_1]) ).

fof(f_2389_3,plain,
    ! [U_8493,U_8494,U_8495,U_8496,U_8497,U_8498] : hAPP(c_Set_Oimage(U_8493,U_8494,U_8495),hAPP(c_Set_Oimage(U_8496,U_8493,U_8497),U_8498)) = hAPP(c_Set_Oimage(U_8496,U_8494,hAPP(hAPP(c_COMBB(U_8493,U_8494,U_8496),U_8495),U_8497)),U_8498),
    inference(definitional_conversion,[status(esa)],[f_2389_2]) ).

cnf(f_2389_4,plain,
    hAPP(c_Set_Oimage(U_8493,U_8494,U_8495),hAPP(c_Set_Oimage(U_8496,U_8493,U_8497),U_8498)) = hAPP(c_Set_Oimage(U_8496,U_8494,hAPP(hAPP(c_COMBB(U_8493,U_8494,U_8496),U_8495),U_8497)),U_8498),
    inference(clausify,[status(thm)],[f_2389_3]) ).

fof(f_2390_1,plain,
    ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
        | ! [B_x] :
            ( V_z_2 != hAPP(V_f_2,B_x)
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( V_z_2 = hAPP(V_f_2,B_x)
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__iff]) ).

fof(f_2390_2,plain,
    ! [U_8505,U_8504,U_8503,U_8502,U_8501] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8501),U_8502),hAPP(c_Set_Oimage(U_8503,U_8501,U_8504),U_8505)))
        | ! [U_8500] :
            ( U_8502 != hAPP(U_8504,U_8500)
            | ~ hBOOL(hAPP(hAPP(c_member(U_8503),U_8500),U_8505)) ) )
      & ( ? [U_8499] :
            ( U_8502 = hAPP(U_8504,U_8499)
            & hBOOL(hAPP(hAPP(c_member(U_8503),U_8499),U_8505)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8501),U_8502),hAPP(c_Set_Oimage(U_8503,U_8501,U_8504),U_8505))) ) ),
    inference(variable_rename,[status(thm)],[f_2390_1]) ).

fof(f_2390_3,plain,
    ( ! [U_8515,U_8513,U_8511,U_8509] :
        ( ! [U_8507] : hBOOL(hAPP(hAPP(c_member(U_8507),U_8509),hAPP(c_Set_Oimage(U_8511,U_8507,U_8513),U_8515)))
        | ! [U_8500] :
            ( U_8509 != hAPP(U_8513,U_8500)
            | ~ hBOOL(hAPP(hAPP(c_member(U_8511),U_8500),U_8515)) ) )
    & ! [U_8514,U_8512,U_8510,U_8508] :
        ( ! [U_8506] : ~ hBOOL(hAPP(hAPP(c_member(U_8506),U_8508),hAPP(c_Set_Oimage(U_8510,U_8506,U_8512),U_8514)))
        | ? [U_8499] :
            ( U_8508 = hAPP(U_8512,U_8499)
            & hBOOL(hAPP(hAPP(c_member(U_8510),U_8499),U_8514)) ) ) ),
    inference(miniscope,[status(thm)],[f_2390_2]) ).

fof(f_2390_4,plain,
    ( ! [U_8515,U_8513,U_8511,U_8509] :
        ( ! [U_8507] : hBOOL(hAPP(hAPP(c_member(U_8507),U_8509),hAPP(c_Set_Oimage(U_8511,U_8507,U_8513),U_8515)))
        | ! [U_8500] :
            ( U_8509 != hAPP(U_8513,U_8500)
            | ~ hBOOL(hAPP(hAPP(c_member(U_8511),U_8500),U_8515)) ) )
    & ! [U_8514,U_8512,U_8510,U_8508] :
        ( ! [U_8506] : ~ hBOOL(hAPP(hAPP(c_member(U_8506),U_8508),hAPP(c_Set_Oimage(U_8510,U_8506,U_8512),U_8514)))
        | ( U_8508 = hAPP(U_8512,sK124(U_8514,U_8512,U_8510,U_8508))
          & hBOOL(hAPP(hAPP(c_member(U_8510),sK124(U_8514,U_8512,U_8510,U_8508)),U_8514)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_8499,sK124(U_8514,U_8512,U_8510,U_8508))],[f_2390_3]) ).

fof(f_2390_5,plain,
    ( ! [U_8510,U_8512,U_8508,U_8514] :
        ( U_8508 = hAPP(U_8512,sK124(U_8514,U_8512,U_8510,U_8508))
        | ~ sP719(U_8510,U_8512,U_8508,U_8514) )
    & ! [U_8510,U_8512,U_8508,U_8514] :
        ( hBOOL(hAPP(hAPP(c_member(U_8510),sK124(U_8514,U_8512,U_8510,U_8508)),U_8514))
        | ~ sP719(U_8510,U_8512,U_8508,U_8514) )
    & ! [U_8500,U_8515,U_8509,U_8507,U_8513,U_8511] :
        ( hBOOL(hAPP(hAPP(c_member(U_8507),U_8509),hAPP(c_Set_Oimage(U_8511,U_8507,U_8513),U_8515)))
        | U_8509 != hAPP(U_8513,U_8500)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8511),U_8500),U_8515)) )
    & ! [U_8510,U_8512,U_8506,U_8508,U_8514] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8506),U_8508),hAPP(c_Set_Oimage(U_8510,U_8506,U_8512),U_8514)))
        | sP719(U_8510,U_8512,U_8508,U_8514) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP719])],[f_2390_4]) ).

cnf(f_2390_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8506),U_8508),hAPP(c_Set_Oimage(U_8510,U_8506,U_8512),U_8514)))
    | sP719(U_8510,U_8512,U_8508,U_8514) ),
    inference(clausify,[status(thm)],[f_2390_5]) ).

cnf(f_2390_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8507),U_8509),hAPP(c_Set_Oimage(U_8511,U_8507,U_8513),U_8515)))
    | U_8509 != hAPP(U_8513,U_8500)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8511),U_8500),U_8515)) ),
    inference(clausify,[status(thm)],[f_2390_5]) ).

cnf(f_2390_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8510),sK124(U_8514,U_8512,U_8510,U_8508)),U_8514))
    | ~ sP719(U_8510,U_8512,U_8508,U_8514) ),
    inference(clausify,[status(thm)],[f_2390_5]) ).

cnf(f_2390_9,plain,
    ( U_8508 = hAPP(U_8512,sK124(U_8514,U_8512,U_8510,U_8508))
    | ~ sP719(U_8510,U_8512,U_8508,U_8514) ),
    inference(clausify,[status(thm)],[f_2390_5]) ).

fof(f_2391_1,plain,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_imageI]) ).

fof(f_2391_2,plain,
    ! [U_8520,U_8519,U_8518,U_8517,U_8516] :
      ( hBOOL(hAPP(hAPP(c_member(U_8519),hAPP(U_8520,U_8517)),hAPP(c_Set_Oimage(U_8516,U_8519,U_8520),U_8518)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8516),U_8517),U_8518)) ),
    inference(variable_rename,[status(thm)],[f_2391_1]) ).

fof(f_2391_3,plain,
    ! [U_8516,U_8517,U_8519,U_8518,U_8520] :
      ( hBOOL(hAPP(hAPP(c_member(U_8519),hAPP(U_8520,U_8517)),hAPP(c_Set_Oimage(U_8516,U_8519,U_8520),U_8518)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8516),U_8517),U_8518)) ),
    inference(definitional_conversion,[status(esa)],[f_2391_2]) ).

cnf(f_2391_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8519),hAPP(U_8520,U_8517)),hAPP(c_Set_Oimage(U_8516,U_8519,U_8520),U_8518)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8516),U_8517),U_8518)) ),
    inference(clausify,[status(thm)],[f_2391_3]) ).

fof(f_2392_1,plain,
    ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | V_b_2 != hAPP(V_f_2,V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__image__eqI]) ).

fof(f_2392_2,plain,
    ! [U_8526,U_8525,U_8524,U_8523,U_8522,U_8521] :
      ( hBOOL(hAPP(hAPP(c_member(U_8526),U_8524),hAPP(c_Set_Oimage(U_8521,U_8526,U_8525),U_8523)))
      | U_8524 != hAPP(U_8525,U_8522)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8521),U_8522),U_8523)) ),
    inference(variable_rename,[status(thm)],[f_2392_1]) ).

fof(f_2392_3,plain,
    ! [U_8521,U_8522,U_8523,U_8524,U_8525,U_8526] :
      ( hBOOL(hAPP(hAPP(c_member(U_8526),U_8524),hAPP(c_Set_Oimage(U_8521,U_8526,U_8525),U_8523)))
      | U_8524 != hAPP(U_8525,U_8522)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8521),U_8522),U_8523)) ),
    inference(definitional_conversion,[status(esa)],[f_2392_2]) ).

cnf(f_2392_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8526),U_8524),hAPP(c_Set_Oimage(U_8521,U_8526,U_8525),U_8523)))
    | U_8524 != hAPP(U_8525,U_8522)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8521),U_8522),U_8523)) ),
    inference(clausify,[status(thm)],[f_2392_3]) ).

fof(f_2393_1,plain,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__insert]) ).

fof(f_2393_2,plain,
    ! [U_8531,U_8530,U_8529,U_8528,U_8527] : hAPP(c_Set_Oimage(U_8527,U_8528,U_8529),hAPP(hAPP(c_Set_Oinsert(U_8527),U_8530),U_8531)) = hAPP(hAPP(c_Set_Oinsert(U_8528),hAPP(U_8529,U_8530)),hAPP(c_Set_Oimage(U_8527,U_8528,U_8529),U_8531)),
    inference(variable_rename,[status(thm)],[f_2393_1]) ).

fof(f_2393_3,plain,
    ! [U_8527,U_8528,U_8529,U_8530,U_8531] : hAPP(c_Set_Oimage(U_8527,U_8528,U_8529),hAPP(hAPP(c_Set_Oinsert(U_8527),U_8530),U_8531)) = hAPP(hAPP(c_Set_Oinsert(U_8528),hAPP(U_8529,U_8530)),hAPP(c_Set_Oimage(U_8527,U_8528,U_8529),U_8531)),
    inference(definitional_conversion,[status(esa)],[f_2393_2]) ).

cnf(f_2393_4,plain,
    hAPP(c_Set_Oimage(U_8527,U_8528,U_8529),hAPP(hAPP(c_Set_Oinsert(U_8527),U_8530),U_8531)) = hAPP(hAPP(c_Set_Oinsert(U_8528),hAPP(U_8529,U_8530)),hAPP(c_Set_Oimage(U_8527,U_8528,U_8529),U_8531)),
    inference(clausify,[status(thm)],[f_2393_3]) ).

fof(f_2394_1,plain,
    ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Image__empty]) ).

fof(f_2394_2,plain,
    ! [U_8534,U_8533,U_8532] : hAPP(c_Relation_OImage(U_8532,U_8533,U_8534),c_Orderings_Obot__class_Obot(tc_fun(U_8532,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8533,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2394_1]) ).

fof(f_2394_3,plain,
    ! [U_8533,U_8532,U_8534] : hAPP(c_Relation_OImage(U_8532,U_8533,U_8534),c_Orderings_Obot__class_Obot(tc_fun(U_8532,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8533,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2394_2]) ).

cnf(f_2394_4,plain,
    hAPP(c_Relation_OImage(U_8532,U_8533,U_8534),c_Orderings_Obot__class_Obot(tc_fun(U_8532,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8533,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2394_3]) ).

fof(f_2395_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__is__image]) ).

fof(f_2395_2,plain,
    ! [U_8538,U_8537,U_8536,U_8535] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_8535,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8536,U_8535,U_8537),U_8538)
        | U_8538 != c_Orderings_Obot__class_Obot(tc_fun(U_8536,tc_HOL_Obool)) )
      & ( U_8538 = c_Orderings_Obot__class_Obot(tc_fun(U_8536,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(U_8535,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8536,U_8535,U_8537),U_8538) ) ),
    inference(variable_rename,[status(thm)],[f_2395_1]) ).

fof(f_2395_3,plain,
    ( ! [U_8546,U_8544,U_8542] :
        ( ! [U_8540] : c_Orderings_Obot__class_Obot(tc_fun(U_8540,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8542,U_8540,U_8544),U_8546)
        | U_8546 != c_Orderings_Obot__class_Obot(tc_fun(U_8542,tc_HOL_Obool)) )
    & ! [U_8545,U_8543,U_8541] :
        ( ! [U_8539] : c_Orderings_Obot__class_Obot(tc_fun(U_8539,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8541,U_8539,U_8543),U_8545)
        | U_8545 = c_Orderings_Obot__class_Obot(tc_fun(U_8541,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2395_2]) ).

fof(f_2395_4,plain,
    ( ! [U_8544,U_8546,U_8540,U_8542] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_8540,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8542,U_8540,U_8544),U_8546)
        | U_8546 != c_Orderings_Obot__class_Obot(tc_fun(U_8542,tc_HOL_Obool)) )
    & ! [U_8541,U_8545,U_8543,U_8539] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_8539,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8541,U_8539,U_8543),U_8545)
        | U_8545 = c_Orderings_Obot__class_Obot(tc_fun(U_8541,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2395_3]) ).

cnf(f_2395_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8539,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8541,U_8539,U_8543),U_8545)
    | U_8545 = c_Orderings_Obot__class_Obot(tc_fun(U_8541,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2395_4]) ).

cnf(f_2395_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8540,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8542,U_8540,U_8544),U_8546)
    | U_8546 != c_Orderings_Obot__class_Obot(tc_fun(U_8542,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2395_4]) ).

fof(f_2396_1,plain,
    ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_image__empty]) ).

fof(f_2396_2,plain,
    ! [U_8549,U_8548,U_8547] : hAPP(c_Set_Oimage(U_8547,U_8548,U_8549),c_Orderings_Obot__class_Obot(tc_fun(U_8547,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8548,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2396_1]) ).

fof(f_2396_3,plain,
    ! [U_8547,U_8548,U_8549] : hAPP(c_Set_Oimage(U_8547,U_8548,U_8549),c_Orderings_Obot__class_Obot(tc_fun(U_8547,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8548,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2396_2]) ).

cnf(f_2396_4,plain,
    hAPP(c_Set_Oimage(U_8547,U_8548,U_8549),c_Orderings_Obot__class_Obot(tc_fun(U_8547,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8548,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2396_3]) ).

fof(f_2397_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__is__empty]) ).

fof(f_2397_2,plain,
    ! [U_8553,U_8552,U_8551,U_8550] :
      ( ( hAPP(c_Set_Oimage(U_8550,U_8551,U_8552),U_8553) = c_Orderings_Obot__class_Obot(tc_fun(U_8551,tc_HOL_Obool))
        | U_8553 != c_Orderings_Obot__class_Obot(tc_fun(U_8550,tc_HOL_Obool)) )
      & ( U_8553 = c_Orderings_Obot__class_Obot(tc_fun(U_8550,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8550,U_8551,U_8552),U_8553) != c_Orderings_Obot__class_Obot(tc_fun(U_8551,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2397_1]) ).

fof(f_2397_3,plain,
    ( ! [U_8561,U_8559,U_8557,U_8555] :
        ( hAPP(c_Set_Oimage(U_8555,U_8557,U_8559),U_8561) = c_Orderings_Obot__class_Obot(tc_fun(U_8557,tc_HOL_Obool))
        | U_8561 != c_Orderings_Obot__class_Obot(tc_fun(U_8555,tc_HOL_Obool)) )
    & ! [U_8560,U_8558,U_8556,U_8554] :
        ( U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8554,U_8556,U_8558),U_8560) != c_Orderings_Obot__class_Obot(tc_fun(U_8556,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2397_2]) ).

fof(f_2397_4,plain,
    ( ! [U_8555,U_8561,U_8557,U_8559] :
        ( hAPP(c_Set_Oimage(U_8555,U_8557,U_8559),U_8561) = c_Orderings_Obot__class_Obot(tc_fun(U_8557,tc_HOL_Obool))
        | U_8561 != c_Orderings_Obot__class_Obot(tc_fun(U_8555,tc_HOL_Obool)) )
    & ! [U_8556,U_8558,U_8560,U_8554] :
        ( U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8554,U_8556,U_8558),U_8560) != c_Orderings_Obot__class_Obot(tc_fun(U_8556,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2397_3]) ).

cnf(f_2397_5,plain,
    ( U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_8554,U_8556,U_8558),U_8560) != c_Orderings_Obot__class_Obot(tc_fun(U_8556,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2397_4]) ).

cnf(f_2397_6,plain,
    ( hAPP(c_Set_Oimage(U_8555,U_8557,U_8559),U_8561) = c_Orderings_Obot__class_Obot(tc_fun(U_8557,tc_HOL_Obool))
    | U_8561 != c_Orderings_Obot__class_Obot(tc_fun(U_8555,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2397_4]) ).

fof(f_2398_1,plain,
    ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__mono]) ).

fof(f_2398_2,plain,
    ! [U_8567,U_8566,U_8565,U_8564,U_8563,U_8562] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8563,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8562,U_8563,U_8564),U_8566)),hAPP(c_Relation_OImage(U_8562,U_8563,U_8565),U_8567)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8562,tc_HOL_Obool)),U_8566),U_8567))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8562,U_8563),tc_HOL_Obool)),U_8564),U_8565)) ),
    inference(variable_rename,[status(thm)],[f_2398_1]) ).

fof(f_2398_3,plain,
    ! [U_8562,U_8563,U_8564,U_8565,U_8566,U_8567] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8563,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8562,U_8563,U_8564),U_8566)),hAPP(c_Relation_OImage(U_8562,U_8563,U_8565),U_8567)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8562,tc_HOL_Obool)),U_8566),U_8567))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8562,U_8563),tc_HOL_Obool)),U_8564),U_8565)) ),
    inference(definitional_conversion,[status(esa)],[f_2398_2]) ).

cnf(f_2398_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8563,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8562,U_8563,U_8564),U_8566)),hAPP(c_Relation_OImage(U_8562,U_8563,U_8565),U_8567)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8562,tc_HOL_Obool)),U_8566),U_8567))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8562,U_8563),tc_HOL_Obool)),U_8564),U_8565)) ),
    inference(clausify,[status(thm)],[f_2398_3]) ).

fof(f_2399_1,plain,
    ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Image]) ).

fof(f_2399_2,plain,
    ! [U_8572,U_8571,U_8570,U_8569,U_8568] : hAPP(c_Relation_OImage(U_8568,U_8569,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8568,U_8569),tc_HOL_Obool)),U_8570),U_8571)),U_8572) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8569,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8568,U_8569,U_8570),U_8572)),hAPP(c_Relation_OImage(U_8568,U_8569,U_8571),U_8572)),
    inference(variable_rename,[status(thm)],[f_2399_1]) ).

fof(f_2399_3,plain,
    ! [U_8571,U_8572,U_8568,U_8569,U_8570] : hAPP(c_Relation_OImage(U_8568,U_8569,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8568,U_8569),tc_HOL_Obool)),U_8570),U_8571)),U_8572) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8569,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8568,U_8569,U_8570),U_8572)),hAPP(c_Relation_OImage(U_8568,U_8569,U_8571),U_8572)),
    inference(definitional_conversion,[status(esa)],[f_2399_2]) ).

cnf(f_2399_4,plain,
    hAPP(c_Relation_OImage(U_8568,U_8569,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8568,U_8569),tc_HOL_Obool)),U_8570),U_8571)),U_8572) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8569,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8568,U_8569,U_8570),U_8572)),hAPP(c_Relation_OImage(U_8568,U_8569,U_8571),U_8572)),
    inference(clausify,[status(thm)],[f_2399_3]) ).

fof(f_2400_1,plain,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__image]) ).

fof(f_2400_2,plain,
    ! [U_8577,U_8576,U_8575,U_8574,U_8573] :
      ( hAPP(hAPP(c_Set_Oinsert(U_8576),hAPP(U_8577,U_8574)),hAPP(c_Set_Oimage(U_8573,U_8576,U_8577),U_8575)) = hAPP(c_Set_Oimage(U_8573,U_8576,U_8577),U_8575)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8574),U_8575)) ),
    inference(variable_rename,[status(thm)],[f_2400_1]) ).

fof(f_2400_3,plain,
    ! [U_8573,U_8574,U_8575,U_8576,U_8577] :
      ( hAPP(hAPP(c_Set_Oinsert(U_8576),hAPP(U_8577,U_8574)),hAPP(c_Set_Oimage(U_8573,U_8576,U_8577),U_8575)) = hAPP(c_Set_Oimage(U_8573,U_8576,U_8577),U_8575)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8574),U_8575)) ),
    inference(definitional_conversion,[status(esa)],[f_2400_2]) ).

cnf(f_2400_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_8576),hAPP(U_8577,U_8574)),hAPP(c_Set_Oimage(U_8573,U_8576,U_8577),U_8575)) = hAPP(c_Set_Oimage(U_8573,U_8576,U_8577),U_8575)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8574),U_8575)) ),
    inference(clausify,[status(thm)],[f_2400_3]) ).

fof(f_2401_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_image__diff__subset]) ).

fof(f_2401_2,plain,
    ! [U_8582,U_8581,U_8580,U_8579,U_8578] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8578,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8578,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),U_8581)),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),U_8582))),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8582)))),
    inference(variable_rename,[status(thm)],[f_2401_1]) ).

fof(f_2401_3,plain,
    ! [U_8578,U_8579,U_8580,U_8581,U_8582] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8578,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8578,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),U_8581)),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),U_8582))),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8582)))),
    inference(definitional_conversion,[status(esa)],[f_2401_2]) ).

cnf(f_2401_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8578,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8578,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),U_8581)),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),U_8582))),hAPP(c_Set_Oimage(U_8579,U_8578,U_8580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8582)))),
    inference(clausify,[status(thm)],[f_2401_3]) ).

fof(f_2402_1,plain,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__iff]) ).

fof(f_2402_2,plain,
    ! [U_8589,U_8588,U_8587,U_8586,U_8585] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8585),U_8586),hAPP(c_Relation_OImage(U_8587,U_8585,U_8588),U_8589)))
        | ! [U_8584] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8587,U_8585)),hAPP(hAPP(c_Product__Type_OPair(U_8587,U_8585),U_8584),U_8586)),U_8588))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8587),U_8584),U_8589)) ) )
      & ( ? [U_8583] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8587,U_8585)),hAPP(hAPP(c_Product__Type_OPair(U_8587,U_8585),U_8583),U_8586)),U_8588))
            & hBOOL(hAPP(hAPP(c_member(U_8587),U_8583),U_8589)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8585),U_8586),hAPP(c_Relation_OImage(U_8587,U_8585,U_8588),U_8589))) ) ),
    inference(variable_rename,[status(thm)],[f_2402_1]) ).

fof(f_2402_3,plain,
    ( ! [U_8599,U_8597,U_8595,U_8593,U_8591] :
        ( hBOOL(hAPP(hAPP(c_member(U_8591),U_8593),hAPP(c_Relation_OImage(U_8595,U_8591,U_8597),U_8599)))
        | ! [U_8584] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8595,U_8591)),hAPP(hAPP(c_Product__Type_OPair(U_8595,U_8591),U_8584),U_8593)),U_8597))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8584),U_8599)) ) )
    & ! [U_8598,U_8596,U_8594,U_8592,U_8590] :
        ( ? [U_8583] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8594,U_8590)),hAPP(hAPP(c_Product__Type_OPair(U_8594,U_8590),U_8583),U_8592)),U_8596))
            & hBOOL(hAPP(hAPP(c_member(U_8594),U_8583),U_8598)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8592),hAPP(c_Relation_OImage(U_8594,U_8590,U_8596),U_8598))) ) ),
    inference(miniscope,[status(thm)],[f_2402_2]) ).

fof(f_2402_4,plain,
    ( ! [U_8599,U_8597,U_8595,U_8593,U_8591] :
        ( hBOOL(hAPP(hAPP(c_member(U_8591),U_8593),hAPP(c_Relation_OImage(U_8595,U_8591,U_8597),U_8599)))
        | ! [U_8584] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8595,U_8591)),hAPP(hAPP(c_Product__Type_OPair(U_8595,U_8591),U_8584),U_8593)),U_8597))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8584),U_8599)) ) )
    & ! [U_8598,U_8596,U_8594,U_8592,U_8590] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8594,U_8590)),hAPP(hAPP(c_Product__Type_OPair(U_8594,U_8590),sK125(U_8598,U_8596,U_8594,U_8592,U_8590)),U_8592)),U_8596))
          & hBOOL(hAPP(hAPP(c_member(U_8594),sK125(U_8598,U_8596,U_8594,U_8592,U_8590)),U_8598)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8592),hAPP(c_Relation_OImage(U_8594,U_8590,U_8596),U_8598))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_8583,sK125(U_8598,U_8596,U_8594,U_8592,U_8590))],[f_2402_3]) ).

fof(f_2402_5,plain,
    ( ! [U_8590,U_8594,U_8598,U_8596,U_8592] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8594,U_8590)),hAPP(hAPP(c_Product__Type_OPair(U_8594,U_8590),sK125(U_8598,U_8596,U_8594,U_8592,U_8590)),U_8592)),U_8596))
        | ~ sP720(U_8590,U_8594,U_8598,U_8596,U_8592) )
    & ! [U_8590,U_8594,U_8598,U_8596,U_8592] :
        ( hBOOL(hAPP(hAPP(c_member(U_8594),sK125(U_8598,U_8596,U_8594,U_8592,U_8590)),U_8598))
        | ~ sP720(U_8590,U_8594,U_8598,U_8596,U_8592) )
    & ! [U_8584,U_8591,U_8599,U_8597,U_8595,U_8593] :
        ( hBOOL(hAPP(hAPP(c_member(U_8591),U_8593),hAPP(c_Relation_OImage(U_8595,U_8591,U_8597),U_8599)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8595,U_8591)),hAPP(hAPP(c_Product__Type_OPair(U_8595,U_8591),U_8584),U_8593)),U_8597))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8584),U_8599)) )
    & ! [U_8590,U_8594,U_8598,U_8596,U_8592] :
        ( sP720(U_8590,U_8594,U_8598,U_8596,U_8592)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8592),hAPP(c_Relation_OImage(U_8594,U_8590,U_8596),U_8598))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP720])],[f_2402_4]) ).

cnf(f_2402_6,plain,
    ( sP720(U_8590,U_8594,U_8598,U_8596,U_8592)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8592),hAPP(c_Relation_OImage(U_8594,U_8590,U_8596),U_8598))) ),
    inference(clausify,[status(thm)],[f_2402_5]) ).

cnf(f_2402_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8591),U_8593),hAPP(c_Relation_OImage(U_8595,U_8591,U_8597),U_8599)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8595,U_8591)),hAPP(hAPP(c_Product__Type_OPair(U_8595,U_8591),U_8584),U_8593)),U_8597))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8584),U_8599)) ),
    inference(clausify,[status(thm)],[f_2402_5]) ).

cnf(f_2402_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8594),sK125(U_8598,U_8596,U_8594,U_8592,U_8590)),U_8598))
    | ~ sP720(U_8590,U_8594,U_8598,U_8596,U_8592) ),
    inference(clausify,[status(thm)],[f_2402_5]) ).

cnf(f_2402_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8594,U_8590)),hAPP(hAPP(c_Product__Type_OPair(U_8594,U_8590),sK125(U_8598,U_8596,U_8594,U_8592,U_8590)),U_8592)),U_8596))
    | ~ sP720(U_8590,U_8594,U_8598,U_8596,U_8592) ),
    inference(clausify,[status(thm)],[f_2402_5]) ).

fof(f_2403_1,plain,
    ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__ImageI]) ).

fof(f_2403_2,plain,
    ! [U_8605,U_8604,U_8603,U_8602,U_8601,U_8600] :
      ( hBOOL(hAPP(hAPP(c_member(U_8603),U_8604),hAPP(c_Relation_OImage(U_8600,U_8603,U_8605),U_8602)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8600,U_8603)),hAPP(hAPP(c_Product__Type_OPair(U_8600,U_8603),U_8601),U_8604)),U_8605))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8600),U_8601),U_8602)) ),
    inference(variable_rename,[status(thm)],[f_2403_1]) ).

fof(f_2403_3,plain,
    ! [U_8600,U_8602,U_8603,U_8601,U_8604,U_8605] :
      ( hBOOL(hAPP(hAPP(c_member(U_8603),U_8604),hAPP(c_Relation_OImage(U_8600,U_8603,U_8605),U_8602)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8600,U_8603)),hAPP(hAPP(c_Product__Type_OPair(U_8600,U_8603),U_8601),U_8604)),U_8605))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8600),U_8601),U_8602)) ),
    inference(definitional_conversion,[status(esa)],[f_2403_2]) ).

cnf(f_2403_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8603),U_8604),hAPP(c_Relation_OImage(U_8600,U_8603,U_8605),U_8602)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8600,U_8603)),hAPP(hAPP(c_Product__Type_OPair(U_8600,U_8603),U_8601),U_8604)),U_8605))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8600),U_8601),U_8602)) ),
    inference(clausify,[status(thm)],[f_2403_3]) ).

fof(f_2404_1,plain,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).

fof(f_2404_2,plain,
    ! [U_8609,U_8608,U_8607,U_8606] :
      ( ( hAPP(c_Set_Oimage(U_8607,U_8608,hAPP(c_COMBK(U_8608,U_8607),U_8609)),U_8606) = hAPP(hAPP(c_Set_Oinsert(U_8608),U_8609),c_Orderings_Obot__class_Obot(tc_fun(U_8608,tc_HOL_Obool)))
        | U_8606 = c_Orderings_Obot__class_Obot(tc_fun(U_8607,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(U_8607,U_8608,hAPP(c_COMBK(U_8608,U_8607),U_8609)),U_8606) = c_Orderings_Obot__class_Obot(tc_fun(U_8608,tc_HOL_Obool))
        | U_8606 != c_Orderings_Obot__class_Obot(tc_fun(U_8607,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2404_1]) ).

fof(f_2404_3,plain,
    ( ! [U_8617,U_8615,U_8613,U_8611] :
        ( hAPP(c_Set_Oimage(U_8613,U_8615,hAPP(c_COMBK(U_8615,U_8613),U_8617)),U_8611) = hAPP(hAPP(c_Set_Oinsert(U_8615),U_8617),c_Orderings_Obot__class_Obot(tc_fun(U_8615,tc_HOL_Obool)))
        | U_8611 = c_Orderings_Obot__class_Obot(tc_fun(U_8613,tc_HOL_Obool)) )
    & ! [U_8616,U_8614,U_8612,U_8610] :
        ( hAPP(c_Set_Oimage(U_8612,U_8614,hAPP(c_COMBK(U_8614,U_8612),U_8616)),U_8610) = c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool))
        | U_8610 != c_Orderings_Obot__class_Obot(tc_fun(U_8612,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2404_2]) ).

fof(f_2404_4,plain,
    ( ! [U_8617,U_8611,U_8613,U_8615] :
        ( hAPP(c_Set_Oimage(U_8613,U_8615,hAPP(c_COMBK(U_8615,U_8613),U_8617)),U_8611) = hAPP(hAPP(c_Set_Oinsert(U_8615),U_8617),c_Orderings_Obot__class_Obot(tc_fun(U_8615,tc_HOL_Obool)))
        | U_8611 = c_Orderings_Obot__class_Obot(tc_fun(U_8613,tc_HOL_Obool)) )
    & ! [U_8614,U_8616,U_8610,U_8612] :
        ( hAPP(c_Set_Oimage(U_8612,U_8614,hAPP(c_COMBK(U_8614,U_8612),U_8616)),U_8610) = c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool))
        | U_8610 != c_Orderings_Obot__class_Obot(tc_fun(U_8612,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2404_3]) ).

cnf(f_2404_5,plain,
    ( hAPP(c_Set_Oimage(U_8612,U_8614,hAPP(c_COMBK(U_8614,U_8612),U_8616)),U_8610) = c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool))
    | U_8610 != c_Orderings_Obot__class_Obot(tc_fun(U_8612,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2404_4]) ).

cnf(f_2404_6,plain,
    ( hAPP(c_Set_Oimage(U_8613,U_8615,hAPP(c_COMBK(U_8615,U_8613),U_8617)),U_8611) = hAPP(hAPP(c_Set_Oinsert(U_8615),U_8617),c_Orderings_Obot__class_Obot(tc_fun(U_8615,tc_HOL_Obool)))
    | U_8611 = c_Orderings_Obot__class_Obot(tc_fun(U_8613,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2404_4]) ).

fof(f_2405_1,plain,
    ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__constant]) ).

fof(f_2405_2,plain,
    ! [U_8622,U_8621,U_8620,U_8619,U_8618] :
      ( hAPP(c_Set_Oimage(U_8618,U_8621,hAPP(c_COMBK(U_8621,U_8618),U_8622)),U_8620) = hAPP(hAPP(c_Set_Oinsert(U_8621),U_8622),c_Orderings_Obot__class_Obot(tc_fun(U_8621,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8618),U_8619),U_8620)) ),
    inference(variable_rename,[status(thm)],[f_2405_1]) ).

fof(f_2405_3,plain,
    ! [U_8618,U_8619,U_8620,U_8621,U_8622] :
      ( hAPP(c_Set_Oimage(U_8618,U_8621,hAPP(c_COMBK(U_8621,U_8618),U_8622)),U_8620) = hAPP(hAPP(c_Set_Oinsert(U_8621),U_8622),c_Orderings_Obot__class_Obot(tc_fun(U_8621,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8618),U_8619),U_8620)) ),
    inference(definitional_conversion,[status(esa)],[f_2405_2]) ).

cnf(f_2405_4,plain,
    ( hAPP(c_Set_Oimage(U_8618,U_8621,hAPP(c_COMBK(U_8621,U_8618),U_8622)),U_8620) = hAPP(hAPP(c_Set_Oinsert(U_8621),U_8622),c_Orderings_Obot__class_Obot(tc_fun(U_8621,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8618),U_8619),U_8620)) ),
    inference(clausify,[status(thm)],[f_2405_3]) ).

fof(f_2406_1,plain,
    ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff]) ).

fof(f_2406_2,plain,
    ! [U_8627,U_8626,U_8625,U_8624,U_8623] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_Relation_OImage(U_8625,U_8623,U_8626),hAPP(hAPP(c_Set_Oinsert(U_8625),U_8627),c_Orderings_Obot__class_Obot(tc_fun(U_8625,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8625,U_8623)),hAPP(hAPP(c_Product__Type_OPair(U_8625,U_8623),U_8627),U_8624)),U_8626)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8625,U_8623)),hAPP(hAPP(c_Product__Type_OPair(U_8625,U_8623),U_8627),U_8624)),U_8626))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_Relation_OImage(U_8625,U_8623,U_8626),hAPP(hAPP(c_Set_Oinsert(U_8625),U_8627),c_Orderings_Obot__class_Obot(tc_fun(U_8625,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_2406_1]) ).

fof(f_2406_3,plain,
    ( ! [U_8637,U_8635,U_8633,U_8631,U_8629] :
        ( hBOOL(hAPP(hAPP(c_member(U_8629),U_8631),hAPP(c_Relation_OImage(U_8633,U_8629,U_8635),hAPP(hAPP(c_Set_Oinsert(U_8633),U_8637),c_Orderings_Obot__class_Obot(tc_fun(U_8633,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8633,U_8629)),hAPP(hAPP(c_Product__Type_OPair(U_8633,U_8629),U_8637),U_8631)),U_8635)) )
    & ! [U_8636,U_8634,U_8632,U_8630,U_8628] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8632,U_8628)),hAPP(hAPP(c_Product__Type_OPair(U_8632,U_8628),U_8636),U_8630)),U_8634))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8628),U_8630),hAPP(c_Relation_OImage(U_8632,U_8628,U_8634),hAPP(hAPP(c_Set_Oinsert(U_8632),U_8636),c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_HOL_Obool)))))) ) ),
    inference(miniscope,[status(thm)],[f_2406_2]) ).

fof(f_2406_4,plain,
    ( ! [U_8629,U_8631,U_8633,U_8635,U_8637] :
        ( hBOOL(hAPP(hAPP(c_member(U_8629),U_8631),hAPP(c_Relation_OImage(U_8633,U_8629,U_8635),hAPP(hAPP(c_Set_Oinsert(U_8633),U_8637),c_Orderings_Obot__class_Obot(tc_fun(U_8633,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8633,U_8629)),hAPP(hAPP(c_Product__Type_OPair(U_8633,U_8629),U_8637),U_8631)),U_8635)) )
    & ! [U_8634,U_8630,U_8628,U_8632,U_8636] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8632,U_8628)),hAPP(hAPP(c_Product__Type_OPair(U_8632,U_8628),U_8636),U_8630)),U_8634))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8628),U_8630),hAPP(c_Relation_OImage(U_8632,U_8628,U_8634),hAPP(hAPP(c_Set_Oinsert(U_8632),U_8636),c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_HOL_Obool)))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2406_3]) ).

cnf(f_2406_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8632,U_8628)),hAPP(hAPP(c_Product__Type_OPair(U_8632,U_8628),U_8636),U_8630)),U_8634))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8628),U_8630),hAPP(c_Relation_OImage(U_8632,U_8628,U_8634),hAPP(hAPP(c_Set_Oinsert(U_8632),U_8636),c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_HOL_Obool)))))) ),
    inference(clausify,[status(thm)],[f_2406_4]) ).

cnf(f_2406_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8629),U_8631),hAPP(c_Relation_OImage(U_8633,U_8629,U_8635),hAPP(hAPP(c_Set_Oinsert(U_8633),U_8637),c_Orderings_Obot__class_Obot(tc_fun(U_8633,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8633,U_8629)),hAPP(hAPP(c_Product__Type_OPair(U_8633,U_8629),U_8637),U_8631)),U_8635)) ),
    inference(clausify,[status(thm)],[f_2406_4]) ).

fof(f_2407_1,plain,
    ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_measure__def]) ).

fof(f_2407_2,plain,
    ! [U_8638] : c_Wellfounded_Omeasure(U_8638) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_8638),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[f_2407_1]) ).

fof(f_2407_3,plain,
    ! [U_8638] : c_Wellfounded_Omeasure(U_8638) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_8638),c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_2407_2]) ).

cnf(f_2407_4,plain,
    c_Wellfounded_Omeasure(U_8638) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_8638),c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_2407_3]) ).

fof(f_2408_1,plain,
    ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OBody]) ).

fof(f_2408_2,plain,
    ! [U_8643,U_8642,U_8641,U_8640,U_8639] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8639,U_8640,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),c_Com_Ocom_OBODY)),U_8642)),U_8643))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8639),tc_HOL_Obool)),U_8640),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),c_Com_Ocom_OBODY)),U_8642)),U_8643)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8642)),U_8643)) ),
    inference(variable_rename,[status(thm)],[f_2408_1]) ).

fof(f_2408_3,plain,
    ! [U_8639,U_8640,U_8641,U_8642,U_8643] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8639,U_8640,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),c_Com_Ocom_OBODY)),U_8642)),U_8643))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8639),tc_HOL_Obool)),U_8640),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),c_Com_Ocom_OBODY)),U_8642)),U_8643)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8642)),U_8643)) ),
    inference(definitional_conversion,[status(esa)],[f_2408_2]) ).

cnf(f_2408_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8639,U_8640,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),c_Com_Ocom_OBODY)),U_8642)),U_8643))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8639),tc_HOL_Obool)),U_8640),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),c_Com_Ocom_OBODY)),U_8642)),U_8643)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8639),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),hAPP(hAPP(c_COMBB(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8639,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8639))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8639)),U_8641)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8642)),U_8643)) ),
    inference(clausify,[status(thm)],[f_2408_3]) ).

fof(f_2409_1,plain,
    ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Body__sound__lemma]) ).

fof(f_2409_2,plain,
    ! [U_8648,U_8647,U_8646,U_8645,U_8644] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_8644,U_8645,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),c_Com_Ocom_OBODY)),U_8647)),U_8648))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_8644,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8644),tc_HOL_Obool)),U_8645),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),c_Com_Ocom_OBODY)),U_8647)),U_8648)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8647)),U_8648)) ),
    inference(variable_rename,[status(thm)],[f_2409_1]) ).

fof(f_2409_3,plain,
    ! [U_8644,U_8645,U_8646,U_8647,U_8648] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_8644,U_8645,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),c_Com_Ocom_OBODY)),U_8647)),U_8648))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_8644,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8644),tc_HOL_Obool)),U_8645),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),c_Com_Ocom_OBODY)),U_8647)),U_8648)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8647)),U_8648)) ),
    inference(definitional_conversion,[status(esa)],[f_2409_2]) ).

cnf(f_2409_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_8644,U_8645,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),c_Com_Ocom_OBODY)),U_8647)),U_8648))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_8644,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8644),tc_HOL_Obool)),U_8645),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),c_Com_Ocom_OBODY)),U_8647)),U_8648)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),hAPP(hAPP(c_COMBB(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8644)),U_8646)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),U_8647)),U_8648)) ),
    inference(clausify,[status(thm)],[f_2409_3]) ).

fof(f_2410_1,plain,
    ! [V_j_2,V_i_2,T_b] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int]) ).

fof(f_2410_2,plain,
    ! [U_8651,U_8650,U_8649] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8649),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8650),U_8651)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8649),U_8650)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8649),U_8651))
      | ~ class_Rings_Oring__1(U_8649) ),
    inference(variable_rename,[status(thm)],[f_2410_1]) ).

fof(f_2410_3,plain,
    ! [U_8649,U_8651,U_8650] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8649),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8650),U_8651)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8649),U_8650)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8649),U_8651))
      | ~ class_Rings_Oring__1(U_8649) ),
    inference(definitional_conversion,[status(esa)],[f_2410_2]) ).

cnf(f_2410_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8649),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8650),U_8651)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8649),U_8650)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8649),U_8651))
    | ~ class_Rings_Oring__1(U_8649) ),
    inference(clausify,[status(thm)],[f_2410_3]) ).

fof(f_2411_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_One__int__def]) ).

fof(f_2411_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2411_1]) ).

cnf(f_2411_3,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2411_2]) ).

fof(f_2412_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_mult]) ).

fof(f_2412_2,plain,
    ! [U_8655,U_8654,U_8653,U_8652] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8652),U_8653)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8654),U_8655)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8652),U_8654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8653),U_8655))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8652),U_8655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8653),U_8654)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2412_1]) ).

fof(f_2412_3,plain,
    ! [U_8652,U_8653,U_8654,U_8655] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8652),U_8653)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8654),U_8655)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8652),U_8654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8653),U_8655))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8652),U_8655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8653),U_8654)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2412_2]) ).

cnf(f_2412_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8652),U_8653)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8654),U_8655)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8652),U_8654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8653),U_8655))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8652),U_8655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8653),U_8654)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2412_3]) ).

fof(f_2413_1,plain,
    ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__imageI]) ).

fof(f_2413_2,plain,
    ! [U_8662,U_8661,U_8660,U_8659,U_8658,U_8657,U_8656] :
      ( hBOOL(hAPP(hAPP(c_member(U_8661),hAPP(hAPP(U_8662,U_8658),U_8659)),hAPP(c_Set_Oimage(tc_prod(U_8656,U_8657),U_8661,hAPP(c_Product__Type_Oprod_Oprod__case(U_8656,U_8657,U_8661),U_8662)),U_8660)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8656,U_8657)),hAPP(hAPP(c_Product__Type_OPair(U_8656,U_8657),U_8658),U_8659)),U_8660)) ),
    inference(variable_rename,[status(thm)],[f_2413_1]) ).

fof(f_2413_3,plain,
    ! [U_8656,U_8657,U_8658,U_8659,U_8660,U_8661,U_8662] :
      ( hBOOL(hAPP(hAPP(c_member(U_8661),hAPP(hAPP(U_8662,U_8658),U_8659)),hAPP(c_Set_Oimage(tc_prod(U_8656,U_8657),U_8661,hAPP(c_Product__Type_Oprod_Oprod__case(U_8656,U_8657,U_8661),U_8662)),U_8660)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8656,U_8657)),hAPP(hAPP(c_Product__Type_OPair(U_8656,U_8657),U_8658),U_8659)),U_8660)) ),
    inference(definitional_conversion,[status(esa)],[f_2413_2]) ).

cnf(f_2413_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8661),hAPP(hAPP(U_8662,U_8658),U_8659)),hAPP(c_Set_Oimage(tc_prod(U_8656,U_8657),U_8661,hAPP(c_Product__Type_Oprod_Oprod__case(U_8656,U_8657,U_8661),U_8662)),U_8660)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8656,U_8657)),hAPP(hAPP(c_Product__Type_OPair(U_8656,U_8657),U_8658),U_8659)),U_8660)) ),
    inference(clausify,[status(thm)],[f_2413_3]) ).

fof(f_2414_1,plain,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).

fof(f_2414_2,plain,
    ! [U_8664,U_8663] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8663),U_8664) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8663)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8664))),
    inference(variable_rename,[status(thm)],[f_2414_1]) ).

fof(f_2414_3,plain,
    ! [U_8664,U_8663] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8663),U_8664) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8663)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8664))),
    inference(definitional_conversion,[status(esa)],[f_2414_2]) ).

cnf(f_2414_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8663),U_8664) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8663)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8664))),
    inference(clausify,[status(thm)],[f_2414_3]) ).

fof(f_2415_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J]) ).

fof(f_2415_2,plain,
    ! [U_8666,U_8665] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8665),U_8666))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8665)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8666))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8665)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8666)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8665),U_8666)) ) ),
    inference(variable_rename,[status(thm)],[f_2415_1]) ).

fof(f_2415_3,plain,
    ( ! [U_8670,U_8668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8668),U_8670))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8668)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8670))) )
    & ! [U_8669,U_8667] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8667)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8669)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8667),U_8669)) ) ),
    inference(miniscope,[status(thm)],[f_2415_2]) ).

fof(f_2415_4,plain,
    ( ! [U_8668,U_8670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8668),U_8670))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8668)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8670))) )
    & ! [U_8669,U_8667] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8667)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8669)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8667),U_8669)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2415_3]) ).

cnf(f_2415_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8667)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8669)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8667),U_8669)) ),
    inference(clausify,[status(thm)],[f_2415_4]) ).

cnf(f_2415_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8668),U_8670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8668)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8670))) ),
    inference(clausify,[status(thm)],[f_2415_4]) ).

fof(f_2416_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J]) ).

fof(f_2416_2,plain,
    ! [U_8672,U_8671] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8671),U_8672))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8671)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8672))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8671)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8672)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8671),U_8672)) ) ),
    inference(variable_rename,[status(thm)],[f_2416_1]) ).

fof(f_2416_3,plain,
    ( ! [U_8676,U_8674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8674),U_8676))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8674)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8676))) )
    & ! [U_8675,U_8673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8673)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8675)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8673),U_8675)) ) ),
    inference(miniscope,[status(thm)],[f_2416_2]) ).

fof(f_2416_4,plain,
    ( ! [U_8676,U_8674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8674),U_8676))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8674)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8676))) )
    & ! [U_8673,U_8675] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8673)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8675)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8673),U_8675)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2416_3]) ).

cnf(f_2416_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8673)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8675)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8673),U_8675)) ),
    inference(clausify,[status(thm)],[f_2416_4]) ).

cnf(f_2416_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8674),U_8676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8674)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8676))) ),
    inference(clausify,[status(thm)],[f_2416_4]) ).

fof(f_2417_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( V_A_2 = V_B_2
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)
        | V_A_2 != V_B_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J]) ).

fof(f_2417_2,plain,
    ! [U_8678,U_8677] :
      ( ( U_8677 = U_8678
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8677) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8678) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8677) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8678)
        | U_8677 != U_8678 ) ),
    inference(variable_rename,[status(thm)],[f_2417_1]) ).

fof(f_2417_3,plain,
    ( ! [U_8682,U_8680] :
        ( U_8680 = U_8682
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8680) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8682) )
    & ! [U_8681,U_8679] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8679) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8681)
        | U_8679 != U_8681 ) ),
    inference(miniscope,[status(thm)],[f_2417_2]) ).

fof(f_2417_4,plain,
    ( ! [U_8680,U_8682] :
        ( U_8680 = U_8682
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8680) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8682) )
    & ! [U_8679,U_8681] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8679) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8681)
        | U_8679 != U_8681 ) ),
    inference(definitional_conversion,[status(esa)],[f_2417_3]) ).

cnf(f_2417_5,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8679) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8681)
    | U_8679 != U_8681 ),
    inference(clausify,[status(thm)],[f_2417_4]) ).

cnf(f_2417_6,plain,
    ( U_8680 = U_8682
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8680) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8682) ),
    inference(clausify,[status(thm)],[f_2417_4]) ).

fof(f_2418_1,plain,
    ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).

fof(f_2418_2,plain,
    ! [U_8683] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8683)) = U_8683,
    inference(variable_rename,[status(thm)],[f_2418_1]) ).

fof(f_2418_3,plain,
    ! [U_8683] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8683)) = U_8683,
    inference(definitional_conversion,[status(esa)],[f_2418_2]) ).

cnf(f_2418_4,plain,
    hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8683)) = U_8683,
    inference(clausify,[status(thm)],[f_2418_3]) ).

fof(f_2419_1,plain,
    ! [V_A_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J]) ).

fof(f_2419_2,plain,
    ! [U_8685,U_8684] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8684),U_8685))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8684)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8685))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8684)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8685)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8684),U_8685)) ) ),
    inference(variable_rename,[status(thm)],[f_2419_1]) ).

fof(f_2419_3,plain,
    ( ! [U_8689,U_8687] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8687),U_8689))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8687)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8689))) )
    & ! [U_8688,U_8686] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8686)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8688)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8686),U_8688)) ) ),
    inference(miniscope,[status(thm)],[f_2419_2]) ).

fof(f_2419_4,plain,
    ( ! [U_8689,U_8687] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8687),U_8689))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8687)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8689))) )
    & ! [U_8688,U_8686] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8686)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8688)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8686),U_8688)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2419_3]) ).

cnf(f_2419_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8686)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8688)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8686),U_8688)) ),
    inference(clausify,[status(thm)],[f_2419_4]) ).

cnf(f_2419_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8687),U_8689))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8687)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8689))) ),
    inference(clausify,[status(thm)],[f_2419_4]) ).

fof(f_2420_1,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]) ).

fof(f_2420_2,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2420_1]) ).

cnf(f_2420_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2420_2]) ).

fof(f_2421_1,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J]) ).

fof(f_2421_2,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2421_1]) ).

cnf(f_2421_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2421_2]) ).

fof(f_2422_1,plain,
    ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_minus]) ).

fof(f_2422_2,plain,
    ! [U_8691,U_8690] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8690),U_8691)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8691),U_8690)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2422_1]) ).

fof(f_2422_3,plain,
    ! [U_8690,U_8691] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8690),U_8691)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8691),U_8690)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2422_2]) ).

cnf(f_2422_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8690),U_8691)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8691),U_8690)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2422_3]) ).

fof(f_2423_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Zero__int__def]) ).

fof(f_2423_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2423_1]) ).

cnf(f_2423_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2423_2]) ).

fof(f_2424_1,plain,
    ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_int__def]) ).

fof(f_2424_2,plain,
    ! [U_8692] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8692) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8692),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2424_1]) ).

fof(f_2424_3,plain,
    ! [U_8692] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8692) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8692),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2424_2]) ).

cnf(f_2424_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8692) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8692),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2424_3]) ).

fof(f_2425_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_add]) ).

fof(f_2425_2,plain,
    ! [U_8696,U_8695,U_8694,U_8693] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8693),U_8694)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8695),U_8696)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8693),U_8695)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8694),U_8696))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2425_1]) ).

fof(f_2425_3,plain,
    ! [U_8695,U_8693,U_8694,U_8696] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8693),U_8694)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8695),U_8696)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8693),U_8695)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8694),U_8696))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2425_2]) ).

cnf(f_2425_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8693),U_8694)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8695),U_8696)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8693),U_8695)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8694),U_8696))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2425_3]) ).

fof(f_2426_1,plain,
    ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_nat]) ).

fof(f_2426_2,plain,
    ! [U_8698,U_8697] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8697),U_8698)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8697),U_8698),
    inference(variable_rename,[status(thm)],[f_2426_1]) ).

fof(f_2426_3,plain,
    ! [U_8697,U_8698] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8697),U_8698)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8697),U_8698),
    inference(definitional_conversion,[status(esa)],[f_2426_2]) ).

cnf(f_2426_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8697),U_8698)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8697),U_8698),
    inference(clausify,[status(thm)],[f_2426_3]) ).

fof(f_2427_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less]) ).

fof(f_2427_2,plain,
    ! [U_8702,U_8701,U_8700,U_8699] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8699),U_8700)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8701),U_8702)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8699),U_8702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8701),U_8700))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8699),U_8702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8701),U_8700)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8699),U_8700)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8701),U_8702)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_2427_1]) ).

fof(f_2427_3,plain,
    ( ! [U_8710,U_8708,U_8706,U_8704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8704),U_8706)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8708),U_8710)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8704),U_8710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8708),U_8706))) )
    & ! [U_8709,U_8707,U_8705,U_8703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8703),U_8709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8707),U_8705)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8703),U_8705)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8707),U_8709)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_2427_2]) ).

fof(f_2427_4,plain,
    ( ! [U_8704,U_8706,U_8708,U_8710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8704),U_8706)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8708),U_8710)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8704),U_8710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8708),U_8706))) )
    & ! [U_8705,U_8709,U_8703,U_8707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8703),U_8709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8707),U_8705)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8703),U_8705)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8707),U_8709)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2427_3]) ).

cnf(f_2427_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8703),U_8709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8707),U_8705)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8703),U_8705)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8707),U_8709)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_2427_4]) ).

cnf(f_2427_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8704),U_8706)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8708),U_8710)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8704),U_8710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8708),U_8706))) ),
    inference(clausify,[status(thm)],[f_2427_4]) ).

fof(f_2428_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le]) ).

fof(f_2428_2,plain,
    ! [U_8714,U_8713,U_8712,U_8711] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8711),U_8712)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8713),U_8714)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8711),U_8714)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8713),U_8712))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8711),U_8714)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8713),U_8712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8711),U_8712)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8713),U_8714)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_2428_1]) ).

fof(f_2428_3,plain,
    ( ! [U_8722,U_8720,U_8718,U_8716] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8716),U_8718)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8720),U_8722)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8716),U_8722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8720),U_8718))) )
    & ! [U_8721,U_8719,U_8717,U_8715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8715),U_8721)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8719),U_8717)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8715),U_8717)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8719),U_8721)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_2428_2]) ).

fof(f_2428_4,plain,
    ( ! [U_8716,U_8718,U_8720,U_8722] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8716),U_8718)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8720),U_8722)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8716),U_8722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8720),U_8718))) )
    & ! [U_8717,U_8721,U_8715,U_8719] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8715),U_8721)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8719),U_8717)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8715),U_8717)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8719),U_8721)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2428_3]) ).

cnf(f_2428_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8715),U_8721)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8719),U_8717)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8715),U_8717)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8719),U_8721)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_2428_4]) ).

cnf(f_2428_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8716),U_8718)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8720),U_8722)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8716),U_8722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8720),U_8718))) ),
    inference(clausify,[status(thm)],[f_2428_4]) ).

fof(f_2429_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Oirrefl(T_b,V_r_2)
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
        | ~ c_Relation_Oirrefl(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_irrefl__def]) ).

fof(f_2429_2,plain,
    ! [U_8726,U_8725] :
      ( ( c_Relation_Oirrefl(U_8725,U_8726)
        | ? [U_8724] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8725,U_8725)),hAPP(hAPP(c_Product__Type_OPair(U_8725,U_8725),U_8724),U_8724)),U_8726)) )
      & ( ! [U_8723] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8725,U_8725)),hAPP(hAPP(c_Product__Type_OPair(U_8725,U_8725),U_8723),U_8723)),U_8726))
        | ~ c_Relation_Oirrefl(U_8725,U_8726) ) ),
    inference(variable_rename,[status(thm)],[f_2429_1]) ).

fof(f_2429_3,plain,
    ( ! [U_8730,U_8728] :
        ( c_Relation_Oirrefl(U_8728,U_8730)
        | ? [U_8724] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8728,U_8728)),hAPP(hAPP(c_Product__Type_OPair(U_8728,U_8728),U_8724),U_8724)),U_8730)) )
    & ! [U_8729,U_8727] :
        ( ! [U_8723] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8727,U_8727)),hAPP(hAPP(c_Product__Type_OPair(U_8727,U_8727),U_8723),U_8723)),U_8729))
        | ~ c_Relation_Oirrefl(U_8727,U_8729) ) ),
    inference(miniscope,[status(thm)],[f_2429_2]) ).

fof(f_2429_4,plain,
    ( ! [U_8730,U_8728] :
        ( c_Relation_Oirrefl(U_8728,U_8730)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8728,U_8728)),hAPP(hAPP(c_Product__Type_OPair(U_8728,U_8728),sK126(U_8730,U_8728)),sK126(U_8730,U_8728))),U_8730)) )
    & ! [U_8729,U_8727] :
        ( ! [U_8723] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8727,U_8727)),hAPP(hAPP(c_Product__Type_OPair(U_8727,U_8727),U_8723),U_8723)),U_8729))
        | ~ c_Relation_Oirrefl(U_8727,U_8729) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_8724,sK126(U_8730,U_8728))],[f_2429_3]) ).

fof(f_2429_5,plain,
    ( ! [U_8730,U_8728] :
        ( c_Relation_Oirrefl(U_8728,U_8730)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8728,U_8728)),hAPP(hAPP(c_Product__Type_OPair(U_8728,U_8728),sK126(U_8730,U_8728)),sK126(U_8730,U_8728))),U_8730)) )
    & ! [U_8723,U_8729,U_8727] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8727,U_8727)),hAPP(hAPP(c_Product__Type_OPair(U_8727,U_8727),U_8723),U_8723)),U_8729))
        | ~ c_Relation_Oirrefl(U_8727,U_8729) ) ),
    inference(definitional_conversion,[status(esa)],[f_2429_4]) ).

cnf(f_2429_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8727,U_8727)),hAPP(hAPP(c_Product__Type_OPair(U_8727,U_8727),U_8723),U_8723)),U_8729))
    | ~ c_Relation_Oirrefl(U_8727,U_8729) ),
    inference(clausify,[status(thm)],[f_2429_5]) ).

cnf(f_2429_7,plain,
    ( c_Relation_Oirrefl(U_8728,U_8730)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8728,U_8728)),hAPP(hAPP(c_Product__Type_OPair(U_8728,U_8728),sK126(U_8730,U_8728)),sK126(U_8730,U_8728))),U_8730)) ),
    inference(clausify,[status(thm)],[f_2429_5]) ).

fof(f_2430_1,plain,
    ! [V_z_2] :
    ? [B_x,B_y] : V_z_2 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ]) ).

fof(f_2430_2,plain,
    ! [U_8733] :
    ? [U_8732,U_8731] : U_8733 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8732),U_8731)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2430_1]) ).

fof(f_2430_3,plain,
    ! [U_8733] :
    ? [U_8731] : U_8733 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK127(U_8733)),U_8731)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_8732,sK127(U_8733))],[f_2430_2]) ).

fof(f_2430_4,plain,
    ! [U_8733] : U_8733 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK127(U_8733)),sK128(U_8733))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_8731,sK128(U_8733))],[f_2430_3]) ).

fof(f_2430_5,plain,
    ! [U_8733] : U_8733 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK127(U_8733)),sK128(U_8733))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2430_4]) ).

cnf(f_2430_6,plain,
    U_8733 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK127(U_8733)),sK128(U_8733))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2430_5]) ).

fof(f_2431_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__insert]) ).

fof(f_2431_2,plain,
    ! [U_8737,U_8736,U_8735,U_8734] : hAPP(c_Relation_OField(U_8734),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8734,U_8734)),hAPP(hAPP(c_Product__Type_OPair(U_8734,U_8734),U_8735),U_8736)),U_8737)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8734),U_8735),hAPP(hAPP(c_Set_Oinsert(U_8734),U_8736),c_Orderings_Obot__class_Obot(tc_fun(U_8734,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8734),U_8737)),
    inference(variable_rename,[status(thm)],[f_2431_1]) ).

fof(f_2431_3,plain,
    ! [U_8734,U_8735,U_8736,U_8737] : hAPP(c_Relation_OField(U_8734),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8734,U_8734)),hAPP(hAPP(c_Product__Type_OPair(U_8734,U_8734),U_8735),U_8736)),U_8737)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8734),U_8735),hAPP(hAPP(c_Set_Oinsert(U_8734),U_8736),c_Orderings_Obot__class_Obot(tc_fun(U_8734,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8734),U_8737)),
    inference(definitional_conversion,[status(esa)],[f_2431_2]) ).

cnf(f_2431_4,plain,
    hAPP(c_Relation_OField(U_8734),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8734,U_8734)),hAPP(hAPP(c_Product__Type_OPair(U_8734,U_8734),U_8735),U_8736)),U_8737)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8734),U_8735),hAPP(hAPP(c_Set_Oinsert(U_8734),U_8736),c_Orderings_Obot__class_Obot(tc_fun(U_8734,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8734),U_8737)),
    inference(clausify,[status(thm)],[f_2431_3]) ).

fof(f_2432_1,plain,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ImageE]) ).

fof(f_2432_2,plain,
    ! [U_8743,U_8742,U_8741,U_8740,U_8739] :
      ( ? [U_8738] :
          ( hBOOL(hAPP(hAPP(c_member(U_8741),U_8738),U_8743))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8739)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8739),U_8738),U_8740)),U_8742)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8739),U_8740),hAPP(c_Relation_OImage(U_8741,U_8739,U_8742),U_8743))) ),
    inference(variable_rename,[status(thm)],[f_2432_1]) ).

fof(f_2432_3,plain,
    ! [U_8743,U_8742,U_8741,U_8740,U_8739] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8741),sK129(U_8743,U_8742,U_8741,U_8740,U_8739)),U_8743))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8739)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8739),sK129(U_8743,U_8742,U_8741,U_8740,U_8739)),U_8740)),U_8742)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8739),U_8740),hAPP(c_Relation_OImage(U_8741,U_8739,U_8742),U_8743))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_8738,sK129(U_8743,U_8742,U_8741,U_8740,U_8739))],[f_2432_2]) ).

fof(f_2432_4,plain,
    ( ! [U_8739,U_8740,U_8741,U_8742,U_8743] :
        ( hBOOL(hAPP(hAPP(c_member(U_8741),sK129(U_8743,U_8742,U_8741,U_8740,U_8739)),U_8743))
        | ~ sP721(U_8739,U_8740,U_8741,U_8742,U_8743) )
    & ! [U_8739,U_8740,U_8741,U_8742,U_8743] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8739)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8739),sK129(U_8743,U_8742,U_8741,U_8740,U_8739)),U_8740)),U_8742))
        | ~ sP721(U_8739,U_8740,U_8741,U_8742,U_8743) )
    & ! [U_8739,U_8740,U_8741,U_8742,U_8743] :
        ( sP721(U_8739,U_8740,U_8741,U_8742,U_8743)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8739),U_8740),hAPP(c_Relation_OImage(U_8741,U_8739,U_8742),U_8743))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP721])],[f_2432_3]) ).

cnf(f_2432_5,plain,
    ( sP721(U_8739,U_8740,U_8741,U_8742,U_8743)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8739),U_8740),hAPP(c_Relation_OImage(U_8741,U_8739,U_8742),U_8743))) ),
    inference(clausify,[status(thm)],[f_2432_4]) ).

cnf(f_2432_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8739)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8739),sK129(U_8743,U_8742,U_8741,U_8740,U_8739)),U_8740)),U_8742))
    | ~ sP721(U_8739,U_8740,U_8741,U_8742,U_8743) ),
    inference(clausify,[status(thm)],[f_2432_4]) ).

cnf(f_2432_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8741),sK129(U_8743,U_8742,U_8741,U_8740,U_8739)),U_8743))
    | ~ sP721(U_8739,U_8740,U_8741,U_8742,U_8743) ),
    inference(clausify,[status(thm)],[f_2432_4]) ).

fof(f_2433_1,plain,
    ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Field__empty]) ).

fof(f_2433_2,plain,
    ! [U_8744] : hAPP(c_Relation_OField(U_8744),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8744,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2433_1]) ).

fof(f_2433_3,plain,
    ! [U_8744] : hAPP(c_Relation_OField(U_8744),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8744,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2433_2]) ).

cnf(f_2433_4,plain,
    hAPP(c_Relation_OField(U_8744),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8744,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2433_3]) ).

fof(f_2434_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_mono__Field]) ).

fof(f_2434_2,plain,
    ! [U_8747,U_8746,U_8745] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8745,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8745),U_8746)),hAPP(c_Relation_OField(U_8745),U_8747)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8745,U_8745),tc_HOL_Obool)),U_8746),U_8747)) ),
    inference(variable_rename,[status(thm)],[f_2434_1]) ).

fof(f_2434_3,plain,
    ! [U_8745,U_8746,U_8747] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8745,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8745),U_8746)),hAPP(c_Relation_OField(U_8745),U_8747)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8745,U_8745),tc_HOL_Obool)),U_8746),U_8747)) ),
    inference(definitional_conversion,[status(esa)],[f_2434_2]) ).

cnf(f_2434_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8745,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8745),U_8746)),hAPP(c_Relation_OField(U_8745),U_8747)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8745,U_8745),tc_HOL_Obool)),U_8746),U_8747)) ),
    inference(clausify,[status(thm)],[f_2434_3]) ).

fof(f_2435_1,plain,
    ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__Un]) ).

fof(f_2435_2,plain,
    ! [U_8750,U_8749,U_8748] : hAPP(c_Relation_OField(U_8748),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool)),U_8749),U_8750)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8748,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8748),U_8749)),hAPP(c_Relation_OField(U_8748),U_8750)),
    inference(variable_rename,[status(thm)],[f_2435_1]) ).

fof(f_2435_3,plain,
    ! [U_8748,U_8749,U_8750] : hAPP(c_Relation_OField(U_8748),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool)),U_8749),U_8750)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8748,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8748),U_8749)),hAPP(c_Relation_OField(U_8748),U_8750)),
    inference(definitional_conversion,[status(esa)],[f_2435_2]) ).

cnf(f_2435_4,plain,
    hAPP(c_Relation_OField(U_8748),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool)),U_8749),U_8750)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8748,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8748),U_8749)),hAPP(c_Relation_OField(U_8748),U_8750)),
    inference(clausify,[status(thm)],[f_2435_3]) ).

fof(f_2436_1,plain,
    ! [V_B_2,V_A_2] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J]) ).

fof(f_2436_2,plain,
    ! [U_8752,U_8751] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8751),U_8752) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8751)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8752)))
      | ~ c_Nat__Transfer_Onat__set(U_8752)
      | ~ c_Nat__Transfer_Onat__set(U_8751) ),
    inference(variable_rename,[status(thm)],[f_2436_1]) ).

fof(f_2436_3,plain,
    ! [U_8751,U_8752] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8751),U_8752) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8751)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8752)))
      | ~ c_Nat__Transfer_Onat__set(U_8752)
      | ~ c_Nat__Transfer_Onat__set(U_8751) ),
    inference(definitional_conversion,[status(esa)],[f_2436_2]) ).

cnf(f_2436_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8751),U_8752) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8751)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8752)))
    | ~ c_Nat__Transfer_Onat__set(U_8752)
    | ~ c_Nat__Transfer_Onat__set(U_8751) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

fof(f_2437_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I4_J]) ).

fof(f_2437_2,plain,
    ! [U_8754,U_8753] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8753),U_8754))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8753)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8754))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8753)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8754)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8753),U_8754)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8754)
      | ~ c_Nat__Transfer_Onat__set(U_8753) ),
    inference(variable_rename,[status(thm)],[f_2437_1]) ).

fof(f_2437_3,plain,
    ( ! [U_8753,U_8754] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8753),U_8754))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8753)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8754)))
        | ~ sP722(U_8753,U_8754) )
    & ! [U_8753,U_8754] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8753)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8754)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8753),U_8754))
        | ~ sP722(U_8753,U_8754) )
    & ! [U_8753,U_8754] :
        ( sP722(U_8753,U_8754)
        | ~ c_Nat__Transfer_Onat__set(U_8754)
        | ~ c_Nat__Transfer_Onat__set(U_8753) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP722])],[f_2437_2]) ).

cnf(f_2437_4,plain,
    ( sP722(U_8753,U_8754)
    | ~ c_Nat__Transfer_Onat__set(U_8754)
    | ~ c_Nat__Transfer_Onat__set(U_8753) ),
    inference(clausify,[status(thm)],[f_2437_3]) ).

cnf(f_2437_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8753)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8754)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8753),U_8754))
    | ~ sP722(U_8753,U_8754) ),
    inference(clausify,[status(thm)],[f_2437_3]) ).

cnf(f_2437_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8753),U_8754))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8753)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8754)))
    | ~ sP722(U_8753,U_8754) ),
    inference(clausify,[status(thm)],[f_2437_3]) ).

fof(f_2438_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J]) ).

fof(f_2438_2,plain,
    ! [U_8756,U_8755] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8755),U_8756))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8755)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8756))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8755)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8756)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8755),U_8756)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8756)
      | ~ c_Nat__Transfer_Onat__set(U_8755) ),
    inference(variable_rename,[status(thm)],[f_2438_1]) ).

fof(f_2438_3,plain,
    ( ! [U_8755,U_8756] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8755),U_8756))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8755)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8756)))
        | ~ sP723(U_8755,U_8756) )
    & ! [U_8755,U_8756] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8755)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8755),U_8756))
        | ~ sP723(U_8755,U_8756) )
    & ! [U_8755,U_8756] :
        ( sP723(U_8755,U_8756)
        | ~ c_Nat__Transfer_Onat__set(U_8756)
        | ~ c_Nat__Transfer_Onat__set(U_8755) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP723])],[f_2438_2]) ).

cnf(f_2438_4,plain,
    ( sP723(U_8755,U_8756)
    | ~ c_Nat__Transfer_Onat__set(U_8756)
    | ~ c_Nat__Transfer_Onat__set(U_8755) ),
    inference(clausify,[status(thm)],[f_2438_3]) ).

cnf(f_2438_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8755)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8756)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8755),U_8756))
    | ~ sP723(U_8755,U_8756) ),
    inference(clausify,[status(thm)],[f_2438_3]) ).

cnf(f_2438_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8755),U_8756))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8755)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8756)))
    | ~ sP723(U_8755,U_8756) ),
    inference(clausify,[status(thm)],[f_2438_3]) ).

fof(f_2439_1,plain,
    ! [V_A_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_A_2)
      | ~ c_Nat__Transfer_Ois__nat(V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J]) ).

fof(f_2439_2,plain,
    ! [U_8758,U_8757] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),U_8758))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8757)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8758))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8757)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8758)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),U_8758)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8758)
      | ~ c_Nat__Transfer_Ois__nat(U_8757) ),
    inference(variable_rename,[status(thm)],[f_2439_1]) ).

fof(f_2439_3,plain,
    ( ! [U_8758,U_8757] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),U_8758))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8757)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8758)))
        | ~ sP724(U_8758,U_8757) )
    & ! [U_8758,U_8757] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8757)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8758)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),U_8758))
        | ~ sP724(U_8758,U_8757) )
    & ! [U_8758,U_8757] :
        ( sP724(U_8758,U_8757)
        | ~ c_Nat__Transfer_Onat__set(U_8758)
        | ~ c_Nat__Transfer_Ois__nat(U_8757) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP724])],[f_2439_2]) ).

cnf(f_2439_4,plain,
    ( sP724(U_8758,U_8757)
    | ~ c_Nat__Transfer_Onat__set(U_8758)
    | ~ c_Nat__Transfer_Ois__nat(U_8757) ),
    inference(clausify,[status(thm)],[f_2439_3]) ).

cnf(f_2439_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8757)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8758)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),U_8758))
    | ~ sP724(U_8758,U_8757) ),
    inference(clausify,[status(thm)],[f_2439_3]) ).

cnf(f_2439_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),U_8758))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8757)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8758)))
    | ~ sP724(U_8758,U_8757) ),
    inference(clausify,[status(thm)],[f_2439_3]) ).

fof(f_2440_1,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]) ).

fof(f_2440_2,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2440_1]) ).

cnf(f_2440_3,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2440_2]) ).

fof(f_2441_1,plain,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J]) ).

fof(f_2441_2,plain,
    ! [U_8760,U_8759] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8759),U_8760))
      | ~ c_Nat__Transfer_Onat__set(U_8760)
      | ~ c_Nat__Transfer_Onat__set(U_8759) ),
    inference(variable_rename,[status(thm)],[f_2441_1]) ).

fof(f_2441_3,plain,
    ! [U_8760,U_8759] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8759),U_8760))
      | ~ c_Nat__Transfer_Onat__set(U_8760)
      | ~ c_Nat__Transfer_Onat__set(U_8759) ),
    inference(definitional_conversion,[status(esa)],[f_2441_2]) ).

cnf(f_2441_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8759),U_8760))
    | ~ c_Nat__Transfer_Onat__set(U_8760)
    | ~ c_Nat__Transfer_Onat__set(U_8759) ),
    inference(clausify,[status(thm)],[f_2441_3]) ).

fof(f_2442_1,plain,
    ! [V_S_2] :
      ( ( c_Nat__Transfer_Onat__set(V_S_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) )
        | ~ c_Nat__Transfer_Onat__set(V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__set__def]) ).

fof(f_2442_2,plain,
    ! [U_8763] :
      ( ( c_Nat__Transfer_Onat__set(U_8763)
        | ? [U_8762] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8762))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8762),U_8763)) ) )
      & ( ! [U_8761] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8761))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8761),U_8763)) )
        | ~ c_Nat__Transfer_Onat__set(U_8763) ) ),
    inference(variable_rename,[status(thm)],[f_2442_1]) ).

fof(f_2442_3,plain,
    ( ! [U_8765] :
        ( c_Nat__Transfer_Onat__set(U_8765)
        | ? [U_8762] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8762))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8762),U_8765)) ) )
    & ! [U_8764] :
        ( ! [U_8761] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8761))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8761),U_8764)) )
        | ~ c_Nat__Transfer_Onat__set(U_8764) ) ),
    inference(miniscope,[status(thm)],[f_2442_2]) ).

fof(f_2442_4,plain,
    ( ! [U_8765] :
        ( c_Nat__Transfer_Onat__set(U_8765)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK130(U_8765)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK130(U_8765)),U_8765)) ) )
    & ! [U_8764] :
        ( ! [U_8761] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8761))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8761),U_8764)) )
        | ~ c_Nat__Transfer_Onat__set(U_8764) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_8762,sK130(U_8765))],[f_2442_3]) ).

fof(f_2442_5,plain,
    ( ! [U_8765] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK130(U_8765)))
        | ~ sP725(U_8765) )
    & ! [U_8765] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK130(U_8765)),U_8765))
        | ~ sP725(U_8765) )
    & ! [U_8765] :
        ( c_Nat__Transfer_Onat__set(U_8765)
        | sP725(U_8765) )
    & ! [U_8761,U_8764] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8761))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8761),U_8764))
        | ~ c_Nat__Transfer_Onat__set(U_8764) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP725])],[f_2442_4]) ).

cnf(f_2442_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8761))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8761),U_8764))
    | ~ c_Nat__Transfer_Onat__set(U_8764) ),
    inference(clausify,[status(thm)],[f_2442_5]) ).

cnf(f_2442_7,plain,
    ( c_Nat__Transfer_Onat__set(U_8765)
    | sP725(U_8765) ),
    inference(clausify,[status(thm)],[f_2442_5]) ).

cnf(f_2442_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK130(U_8765)),U_8765))
    | ~ sP725(U_8765) ),
    inference(clausify,[status(thm)],[f_2442_5]) ).

cnf(f_2442_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK130(U_8765)))
    | ~ sP725(U_8765) ),
    inference(clausify,[status(thm)],[f_2442_5]) ).

fof(f_2443_1,plain,
    ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).

fof(f_2443_2,plain,
    ! [U_8766] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8766)),
    inference(variable_rename,[status(thm)],[f_2443_1]) ).

fof(f_2443_3,plain,
    ! [U_8766] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8766)),
    inference(definitional_conversion,[status(esa)],[f_2443_2]) ).

cnf(f_2443_4,plain,
    c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8766)),
    inference(clausify,[status(thm)],[f_2443_3]) ).

fof(f_2444_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)
          | V_A_2 != V_B_2 ) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J]) ).

fof(f_2444_2,plain,
    ! [U_8768,U_8767] :
      ( ( ( U_8767 = U_8768
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8767) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8768) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8767) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8768)
          | U_8767 != U_8768 ) )
      | ~ c_Nat__Transfer_Onat__set(U_8768)
      | ~ c_Nat__Transfer_Onat__set(U_8767) ),
    inference(variable_rename,[status(thm)],[f_2444_1]) ).

fof(f_2444_3,plain,
    ( ! [U_8767,U_8768] :
        ( U_8767 = U_8768
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8767) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8768)
        | ~ sP726(U_8767,U_8768) )
    & ! [U_8767,U_8768] :
        ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8767) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8768)
        | U_8767 != U_8768
        | ~ sP726(U_8767,U_8768) )
    & ! [U_8767,U_8768] :
        ( sP726(U_8767,U_8768)
        | ~ c_Nat__Transfer_Onat__set(U_8768)
        | ~ c_Nat__Transfer_Onat__set(U_8767) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP726])],[f_2444_2]) ).

cnf(f_2444_4,plain,
    ( sP726(U_8767,U_8768)
    | ~ c_Nat__Transfer_Onat__set(U_8768)
    | ~ c_Nat__Transfer_Onat__set(U_8767) ),
    inference(clausify,[status(thm)],[f_2444_3]) ).

cnf(f_2444_5,plain,
    ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8767) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8768)
    | U_8767 != U_8768
    | ~ sP726(U_8767,U_8768) ),
    inference(clausify,[status(thm)],[f_2444_3]) ).

cnf(f_2444_6,plain,
    ( U_8767 = U_8768
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8767) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8768)
    | ~ sP726(U_8767,U_8768) ),
    inference(clausify,[status(thm)],[f_2444_3]) ).

fof(f_2445_1,plain,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J]) ).

fof(f_2445_2,plain,
    ! [U_8770,U_8769] :
      ( c_Nat__Transfer_Ois__nat(U_8770)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8770),U_8769))
      | ~ c_Nat__Transfer_Onat__set(U_8769) ),
    inference(variable_rename,[status(thm)],[f_2445_1]) ).

fof(f_2445_3,plain,
    ! [U_8770,U_8769] :
      ( c_Nat__Transfer_Ois__nat(U_8770)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8770),U_8769))
      | ~ c_Nat__Transfer_Onat__set(U_8769) ),
    inference(definitional_conversion,[status(esa)],[f_2445_2]) ).

cnf(f_2445_4,plain,
    ( c_Nat__Transfer_Ois__nat(U_8770)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8770),U_8769))
    | ~ c_Nat__Transfer_Onat__set(U_8769) ),
    inference(clausify,[status(thm)],[f_2445_3]) ).

fof(f_2446_1,plain,
    ! [V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J]) ).

fof(f_2446_2,plain,
    ! [U_8772,U_8771] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8772))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8772),U_8771))
      | ~ c_Nat__Transfer_Onat__set(U_8771) ),
    inference(variable_rename,[status(thm)],[f_2446_1]) ).

fof(f_2446_3,plain,
    ! [U_8771,U_8772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8772))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8772),U_8771))
      | ~ c_Nat__Transfer_Onat__set(U_8771) ),
    inference(definitional_conversion,[status(esa)],[f_2446_2]) ).

cnf(f_2446_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8772))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8772),U_8771))
    | ~ c_Nat__Transfer_Onat__set(U_8771) ),
    inference(clausify,[status(thm)],[f_2446_3]) ).

fof(f_2447_1,plain,
    ! [V_A_2] :
      ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed]) ).

fof(f_2447_2,plain,
    ! [U_8773] :
      ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8773)) = U_8773
      | ~ c_Nat__Transfer_Onat__set(U_8773) ),
    inference(variable_rename,[status(thm)],[f_2447_1]) ).

fof(f_2447_3,plain,
    ! [U_8773] :
      ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8773)) = U_8773
      | ~ c_Nat__Transfer_Onat__set(U_8773) ),
    inference(definitional_conversion,[status(esa)],[f_2447_2]) ).

cnf(f_2447_4,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8773)) = U_8773
    | ~ c_Nat__Transfer_Onat__set(U_8773) ),
    inference(clausify,[status(thm)],[f_2447_3]) ).

fof(f_2448_1,plain,
    ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_subset__equiv__class]) ).

fof(f_2448_2,plain,
    ! [U_8778,U_8777,U_8776,U_8775,U_8774] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8774,U_8774)),hAPP(hAPP(c_Product__Type_OPair(U_8774,U_8774),U_8778),U_8777)),U_8776))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8774),U_8777),U_8775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8774,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8774,U_8774,U_8776),hAPP(hAPP(c_Set_Oinsert(U_8774),U_8777),c_Orderings_Obot__class_Obot(tc_fun(U_8774,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8774,U_8774,U_8776),hAPP(hAPP(c_Set_Oinsert(U_8774),U_8778),c_Orderings_Obot__class_Obot(tc_fun(U_8774,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_8774,U_8775,U_8776) ),
    inference(variable_rename,[status(thm)],[f_2448_1]) ).

fof(f_2448_3,plain,
    ! [U_8774,U_8775,U_8776,U_8777,U_8778] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8774,U_8774)),hAPP(hAPP(c_Product__Type_OPair(U_8774,U_8774),U_8778),U_8777)),U_8776))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8774),U_8777),U_8775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8774,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8774,U_8774,U_8776),hAPP(hAPP(c_Set_Oinsert(U_8774),U_8777),c_Orderings_Obot__class_Obot(tc_fun(U_8774,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8774,U_8774,U_8776),hAPP(hAPP(c_Set_Oinsert(U_8774),U_8778),c_Orderings_Obot__class_Obot(tc_fun(U_8774,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_8774,U_8775,U_8776) ),
    inference(definitional_conversion,[status(esa)],[f_2448_2]) ).

cnf(f_2448_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8774,U_8774)),hAPP(hAPP(c_Product__Type_OPair(U_8774,U_8774),U_8778),U_8777)),U_8776))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8774),U_8777),U_8775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8774,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8774,U_8774,U_8776),hAPP(hAPP(c_Set_Oinsert(U_8774),U_8777),c_Orderings_Obot__class_Obot(tc_fun(U_8774,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8774,U_8774,U_8776),hAPP(hAPP(c_Set_Oinsert(U_8774),U_8778),c_Orderings_Obot__class_Obot(tc_fun(U_8774,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(U_8774,U_8775,U_8776) ),
    inference(clausify,[status(thm)],[f_2448_3]) ).

fof(f_2449_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp__acc__eq]) ).

fof(f_2449_2,plain,
    ! [U_8781,U_8780,U_8779] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8779,hAPP(hAPP(c_COMBC(U_8779,tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_fun(U_8779,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8779,tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_fun(U_8779,tc_HOL_Obool)),U_8779),c_COMBC(U_8779,tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8779,tc_prod(U_8779,U_8779)),tc_fun(U_8779,tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool)),U_8779),hAPP(c_COMBB(tc_prod(U_8779,U_8779),tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool),U_8779),c_member(tc_prod(U_8779,U_8779)))),c_Product__Type_OPair(U_8779,U_8779)))),U_8780)),U_8781))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8779),U_8781),c_Wellfounded_Oacc(U_8779,U_8780))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8779),U_8781),c_Wellfounded_Oacc(U_8779,U_8780)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8779,hAPP(hAPP(c_COMBC(U_8779,tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_fun(U_8779,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8779,tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_fun(U_8779,tc_HOL_Obool)),U_8779),c_COMBC(U_8779,tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8779,tc_prod(U_8779,U_8779)),tc_fun(U_8779,tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool)),U_8779),hAPP(c_COMBB(tc_prod(U_8779,U_8779),tc_fun(tc_fun(tc_prod(U_8779,U_8779),tc_HOL_Obool),tc_HOL_Obool),U_8779),c_member(tc_prod(U_8779,U_8779)))),c_Product__Type_OPair(U_8779,U_8779)))),U_8780)),U_8781)) ) ),
    inference(variable_rename,[status(thm)],[f_2449_1]) ).

fof(f_2449_3,plain,
    ( ! [U_8787,U_8785,U_8783] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8783,hAPP(hAPP(c_COMBC(U_8783,tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_fun(U_8783,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8783,tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_fun(U_8783,tc_HOL_Obool)),U_8783),c_COMBC(U_8783,tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8783,tc_prod(U_8783,U_8783)),tc_fun(U_8783,tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),U_8783),hAPP(c_COMBB(tc_prod(U_8783,U_8783),tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool),U_8783),c_member(tc_prod(U_8783,U_8783)))),c_Product__Type_OPair(U_8783,U_8783)))),U_8785)),U_8787))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8783),U_8787),c_Wellfounded_Oacc(U_8783,U_8785))) )
    & ! [U_8786,U_8784,U_8782] :
        ( hBOOL(hAPP(hAPP(c_member(U_8782),U_8786),c_Wellfounded_Oacc(U_8782,U_8784)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8782,hAPP(hAPP(c_COMBC(U_8782,tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_fun(U_8782,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8782,tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_fun(U_8782,tc_HOL_Obool)),U_8782),c_COMBC(U_8782,tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8782,tc_prod(U_8782,U_8782)),tc_fun(U_8782,tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),U_8782),hAPP(c_COMBB(tc_prod(U_8782,U_8782),tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool),U_8782),c_member(tc_prod(U_8782,U_8782)))),c_Product__Type_OPair(U_8782,U_8782)))),U_8784)),U_8786)) ) ),
    inference(miniscope,[status(thm)],[f_2449_2]) ).

fof(f_2449_4,plain,
    ( ! [U_8783,U_8785,U_8787] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8783,hAPP(hAPP(c_COMBC(U_8783,tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_fun(U_8783,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8783,tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_fun(U_8783,tc_HOL_Obool)),U_8783),c_COMBC(U_8783,tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8783,tc_prod(U_8783,U_8783)),tc_fun(U_8783,tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),U_8783),hAPP(c_COMBB(tc_prod(U_8783,U_8783),tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool),U_8783),c_member(tc_prod(U_8783,U_8783)))),c_Product__Type_OPair(U_8783,U_8783)))),U_8785)),U_8787))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8783),U_8787),c_Wellfounded_Oacc(U_8783,U_8785))) )
    & ! [U_8784,U_8782,U_8786] :
        ( hBOOL(hAPP(hAPP(c_member(U_8782),U_8786),c_Wellfounded_Oacc(U_8782,U_8784)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8782,hAPP(hAPP(c_COMBC(U_8782,tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_fun(U_8782,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8782,tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_fun(U_8782,tc_HOL_Obool)),U_8782),c_COMBC(U_8782,tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8782,tc_prod(U_8782,U_8782)),tc_fun(U_8782,tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),U_8782),hAPP(c_COMBB(tc_prod(U_8782,U_8782),tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool),U_8782),c_member(tc_prod(U_8782,U_8782)))),c_Product__Type_OPair(U_8782,U_8782)))),U_8784)),U_8786)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2449_3]) ).

cnf(f_2449_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8782),U_8786),c_Wellfounded_Oacc(U_8782,U_8784)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8782,hAPP(hAPP(c_COMBC(U_8782,tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_fun(U_8782,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8782,tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_fun(U_8782,tc_HOL_Obool)),U_8782),c_COMBC(U_8782,tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8782,tc_prod(U_8782,U_8782)),tc_fun(U_8782,tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool)),U_8782),hAPP(c_COMBB(tc_prod(U_8782,U_8782),tc_fun(tc_fun(tc_prod(U_8782,U_8782),tc_HOL_Obool),tc_HOL_Obool),U_8782),c_member(tc_prod(U_8782,U_8782)))),c_Product__Type_OPair(U_8782,U_8782)))),U_8784)),U_8786)) ),
    inference(clausify,[status(thm)],[f_2449_4]) ).

cnf(f_2449_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8783,hAPP(hAPP(c_COMBC(U_8783,tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_fun(U_8783,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8783,tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_fun(U_8783,tc_HOL_Obool)),U_8783),c_COMBC(U_8783,tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8783,tc_prod(U_8783,U_8783)),tc_fun(U_8783,tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool)),U_8783),hAPP(c_COMBB(tc_prod(U_8783,U_8783),tc_fun(tc_fun(tc_prod(U_8783,U_8783),tc_HOL_Obool),tc_HOL_Obool),U_8783),c_member(tc_prod(U_8783,U_8783)))),c_Product__Type_OPair(U_8783,U_8783)))),U_8785)),U_8787))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8783),U_8787),c_Wellfounded_Oacc(U_8783,U_8785))) ),
    inference(clausify,[status(thm)],[f_2449_4]) ).

fof(f_2450_1,plain,
    ! [V_X_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wmax__emptyI]) ).

fof(f_2450_2,plain,
    ! [U_8788] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_8788)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8788)) ),
    inference(variable_rename,[status(thm)],[f_2450_1]) ).

fof(f_2450_3,plain,
    ! [U_8788] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_8788)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8788)) ),
    inference(definitional_conversion,[status(esa)],[f_2450_2]) ).

cnf(f_2450_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_8788)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8788)) ),
    inference(clausify,[status(thm)],[f_2450_3]) ).

fof(f_2451_1,plain,
    ! [V_Y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict))
      | V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_smax__emptyI]) ).

fof(f_2451_2,plain,
    ! [U_8789] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_8789)),c_FunDef_Omax__strict))
      | U_8789 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8789)) ),
    inference(variable_rename,[status(thm)],[f_2451_1]) ).

fof(f_2451_3,plain,
    ! [U_8789] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_8789)),c_FunDef_Omax__strict))
      | U_8789 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8789)) ),
    inference(definitional_conversion,[status(esa)],[f_2451_2]) ).

cnf(f_2451_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_8789)),c_FunDef_Omax__strict))
    | U_8789 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8789)) ),
    inference(clausify,[status(thm)],[f_2451_3]) ).

fof(f_2452_1,plain,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Field]) ).

fof(f_2452_2,plain,
    ! [U_8791,U_8790] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8790),hAPP(c_Relation_OField(U_8790),U_8791)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_8790,U_8790)),U_8791)) ),
    inference(variable_rename,[status(thm)],[f_2452_1]) ).

fof(f_2452_3,plain,
    ! [U_8790,U_8791] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8790),hAPP(c_Relation_OField(U_8790),U_8791)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_8790,U_8790)),U_8791)) ),
    inference(definitional_conversion,[status(esa)],[f_2452_2]) ).

cnf(f_2452_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8790),hAPP(c_Relation_OField(U_8790),U_8791)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_8790,U_8790)),U_8791)) ),
    inference(clausify,[status(thm)],[f_2452_3]) ).

fof(f_2453_1,plain,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) ),
    inference(fof_nnf,[status(thm)],[fact_acc__subset]) ).

fof(f_2453_2,plain,
    ! [U_8794,U_8793,U_8792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8792,tc_HOL_Obool)),c_Wellfounded_Oacc(U_8792,U_8794)),c_Wellfounded_Oacc(U_8792,U_8793)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8792,U_8792),tc_HOL_Obool)),U_8793),U_8794)) ),
    inference(variable_rename,[status(thm)],[f_2453_1]) ).

fof(f_2453_3,plain,
    ! [U_8792,U_8793,U_8794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8792,tc_HOL_Obool)),c_Wellfounded_Oacc(U_8792,U_8794)),c_Wellfounded_Oacc(U_8792,U_8793)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8792,U_8792),tc_HOL_Obool)),U_8793),U_8794)) ),
    inference(definitional_conversion,[status(esa)],[f_2453_2]) ).

cnf(f_2453_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8792,tc_HOL_Obool)),c_Wellfounded_Oacc(U_8792,U_8794)),c_Wellfounded_Oacc(U_8792,U_8793)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8792,U_8792),tc_HOL_Obool)),U_8793),U_8794)) ),
    inference(clausify,[status(thm)],[f_2453_3]) ).

fof(f_2454_1,plain,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__self]) ).

fof(f_2454_2,plain,
    ! [U_8798,U_8797,U_8796,U_8795] :
      ( hBOOL(hAPP(hAPP(c_member(U_8795),U_8798),hAPP(c_Relation_OImage(U_8795,U_8795,U_8797),hAPP(hAPP(c_Set_Oinsert(U_8795),U_8798),c_Orderings_Obot__class_Obot(tc_fun(U_8795,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8795),U_8798),U_8796))
      | ~ c_Equiv__Relations_Oequiv(U_8795,U_8796,U_8797) ),
    inference(variable_rename,[status(thm)],[f_2454_1]) ).

fof(f_2454_3,plain,
    ! [U_8795,U_8796,U_8797,U_8798] :
      ( hBOOL(hAPP(hAPP(c_member(U_8795),U_8798),hAPP(c_Relation_OImage(U_8795,U_8795,U_8797),hAPP(hAPP(c_Set_Oinsert(U_8795),U_8798),c_Orderings_Obot__class_Obot(tc_fun(U_8795,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8795),U_8798),U_8796))
      | ~ c_Equiv__Relations_Oequiv(U_8795,U_8796,U_8797) ),
    inference(definitional_conversion,[status(esa)],[f_2454_2]) ).

cnf(f_2454_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8795),U_8798),hAPP(c_Relation_OImage(U_8795,U_8795,U_8797),hAPP(hAPP(c_Set_Oinsert(U_8795),U_8798),c_Orderings_Obot__class_Obot(tc_fun(U_8795,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8795),U_8798),U_8796))
    | ~ c_Equiv__Relations_Oequiv(U_8795,U_8796,U_8797) ),
    inference(clausify,[status(thm)],[f_2454_3]) ).

fof(f_2455_1,plain,
    ! [V_r_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_acc_Osimps]) ).

fof(f_2455_2,plain,
    ! [U_8803,U_8802,U_8801] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8801),U_8802),c_Wellfounded_Oacc(U_8801,U_8803)))
        | ? [U_8800] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_8801),U_8800),c_Wellfounded_Oacc(U_8801,U_8803)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8801,U_8801)),hAPP(hAPP(c_Product__Type_OPair(U_8801,U_8801),U_8800),U_8802)),U_8803)) ) )
      & ( ! [U_8799] :
            ( hBOOL(hAPP(hAPP(c_member(U_8801),U_8799),c_Wellfounded_Oacc(U_8801,U_8803)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8801,U_8801)),hAPP(hAPP(c_Product__Type_OPair(U_8801,U_8801),U_8799),U_8802)),U_8803)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8801),U_8802),c_Wellfounded_Oacc(U_8801,U_8803))) ) ),
    inference(variable_rename,[status(thm)],[f_2455_1]) ).

fof(f_2455_3,plain,
    ( ! [U_8809,U_8807,U_8805] :
        ( hBOOL(hAPP(hAPP(c_member(U_8805),U_8807),c_Wellfounded_Oacc(U_8805,U_8809)))
        | ? [U_8800] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_8805),U_8800),c_Wellfounded_Oacc(U_8805,U_8809)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8805,U_8805)),hAPP(hAPP(c_Product__Type_OPair(U_8805,U_8805),U_8800),U_8807)),U_8809)) ) )
    & ! [U_8808,U_8806,U_8804] :
        ( ! [U_8799] :
            ( hBOOL(hAPP(hAPP(c_member(U_8804),U_8799),c_Wellfounded_Oacc(U_8804,U_8808)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8804,U_8804)),hAPP(hAPP(c_Product__Type_OPair(U_8804,U_8804),U_8799),U_8806)),U_8808)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8804),U_8806),c_Wellfounded_Oacc(U_8804,U_8808))) ) ),
    inference(miniscope,[status(thm)],[f_2455_2]) ).

fof(f_2455_4,plain,
    ( ! [U_8809,U_8807,U_8805] :
        ( hBOOL(hAPP(hAPP(c_member(U_8805),U_8807),c_Wellfounded_Oacc(U_8805,U_8809)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8805),sK131(U_8809,U_8807,U_8805)),c_Wellfounded_Oacc(U_8805,U_8809)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8805,U_8805)),hAPP(hAPP(c_Product__Type_OPair(U_8805,U_8805),sK131(U_8809,U_8807,U_8805)),U_8807)),U_8809)) ) )
    & ! [U_8808,U_8806,U_8804] :
        ( ! [U_8799] :
            ( hBOOL(hAPP(hAPP(c_member(U_8804),U_8799),c_Wellfounded_Oacc(U_8804,U_8808)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8804,U_8804)),hAPP(hAPP(c_Product__Type_OPair(U_8804,U_8804),U_8799),U_8806)),U_8808)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8804),U_8806),c_Wellfounded_Oacc(U_8804,U_8808))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_8800,sK131(U_8809,U_8807,U_8805))],[f_2455_3]) ).

fof(f_2455_5,plain,
    ( ! [U_8809,U_8805,U_8807] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8805),sK131(U_8809,U_8807,U_8805)),c_Wellfounded_Oacc(U_8805,U_8809)))
        | ~ sP727(U_8809,U_8805,U_8807) )
    & ! [U_8809,U_8805,U_8807] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8805,U_8805)),hAPP(hAPP(c_Product__Type_OPair(U_8805,U_8805),sK131(U_8809,U_8807,U_8805)),U_8807)),U_8809))
        | ~ sP727(U_8809,U_8805,U_8807) )
    & ! [U_8809,U_8805,U_8807] :
        ( hBOOL(hAPP(hAPP(c_member(U_8805),U_8807),c_Wellfounded_Oacc(U_8805,U_8809)))
        | sP727(U_8809,U_8805,U_8807) )
    & ! [U_8806,U_8808,U_8799,U_8804] :
        ( hBOOL(hAPP(hAPP(c_member(U_8804),U_8799),c_Wellfounded_Oacc(U_8804,U_8808)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8804,U_8804)),hAPP(hAPP(c_Product__Type_OPair(U_8804,U_8804),U_8799),U_8806)),U_8808))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8804),U_8806),c_Wellfounded_Oacc(U_8804,U_8808))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP727])],[f_2455_4]) ).

cnf(f_2455_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8804),U_8799),c_Wellfounded_Oacc(U_8804,U_8808)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8804,U_8804)),hAPP(hAPP(c_Product__Type_OPair(U_8804,U_8804),U_8799),U_8806)),U_8808))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8804),U_8806),c_Wellfounded_Oacc(U_8804,U_8808))) ),
    inference(clausify,[status(thm)],[f_2455_5]) ).

cnf(f_2455_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8805),U_8807),c_Wellfounded_Oacc(U_8805,U_8809)))
    | sP727(U_8809,U_8805,U_8807) ),
    inference(clausify,[status(thm)],[f_2455_5]) ).

cnf(f_2455_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8805,U_8805)),hAPP(hAPP(c_Product__Type_OPair(U_8805,U_8805),sK131(U_8809,U_8807,U_8805)),U_8807)),U_8809))
    | ~ sP727(U_8809,U_8805,U_8807) ),
    inference(clausify,[status(thm)],[f_2455_5]) ).

cnf(f_2455_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8805),sK131(U_8809,U_8807,U_8805)),c_Wellfounded_Oacc(U_8805,U_8809)))
    | ~ sP727(U_8809,U_8805,U_8807) ),
    inference(clausify,[status(thm)],[f_2455_5]) ).

fof(f_2456_1,plain,
    ! [V_a_2,V_r_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downward]) ).

fof(f_2456_2,plain,
    ! [U_8813,U_8812,U_8811,U_8810] :
      ( hBOOL(hAPP(hAPP(c_member(U_8810),U_8813),c_Wellfounded_Oacc(U_8810,U_8812)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8810,U_8810)),hAPP(hAPP(c_Product__Type_OPair(U_8810,U_8810),U_8813),U_8811)),U_8812))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8810),U_8811),c_Wellfounded_Oacc(U_8810,U_8812))) ),
    inference(variable_rename,[status(thm)],[f_2456_1]) ).

fof(f_2456_3,plain,
    ! [U_8810,U_8811,U_8812,U_8813] :
      ( hBOOL(hAPP(hAPP(c_member(U_8810),U_8813),c_Wellfounded_Oacc(U_8810,U_8812)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8810,U_8810)),hAPP(hAPP(c_Product__Type_OPair(U_8810,U_8810),U_8813),U_8811)),U_8812))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8810),U_8811),c_Wellfounded_Oacc(U_8810,U_8812))) ),
    inference(definitional_conversion,[status(esa)],[f_2456_2]) ).

cnf(f_2456_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8810),U_8813),c_Wellfounded_Oacc(U_8810,U_8812)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8810,U_8810)),hAPP(hAPP(c_Product__Type_OPair(U_8810,U_8810),U_8813),U_8811)),U_8812))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8810),U_8811),c_Wellfounded_Oacc(U_8810,U_8812))) ),
    inference(clausify,[status(thm)],[f_2456_3]) ).

fof(f_2457_1,plain,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__eq]) ).

fof(f_2457_2,plain,
    ! [U_8818,U_8817,U_8816,U_8815,U_8814] :
      ( hAPP(c_Relation_OImage(U_8814,U_8814,U_8816),hAPP(hAPP(c_Set_Oinsert(U_8814),U_8817),c_Orderings_Obot__class_Obot(tc_fun(U_8814,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8814,U_8814,U_8816),hAPP(hAPP(c_Set_Oinsert(U_8814),U_8818),c_Orderings_Obot__class_Obot(tc_fun(U_8814,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8814,U_8814)),hAPP(hAPP(c_Product__Type_OPair(U_8814,U_8814),U_8817),U_8818)),U_8816))
      | ~ c_Equiv__Relations_Oequiv(U_8814,U_8815,U_8816) ),
    inference(variable_rename,[status(thm)],[f_2457_1]) ).

fof(f_2457_3,plain,
    ! [U_8814,U_8815,U_8816,U_8817,U_8818] :
      ( hAPP(c_Relation_OImage(U_8814,U_8814,U_8816),hAPP(hAPP(c_Set_Oinsert(U_8814),U_8817),c_Orderings_Obot__class_Obot(tc_fun(U_8814,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8814,U_8814,U_8816),hAPP(hAPP(c_Set_Oinsert(U_8814),U_8818),c_Orderings_Obot__class_Obot(tc_fun(U_8814,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8814,U_8814)),hAPP(hAPP(c_Product__Type_OPair(U_8814,U_8814),U_8817),U_8818)),U_8816))
      | ~ c_Equiv__Relations_Oequiv(U_8814,U_8815,U_8816) ),
    inference(definitional_conversion,[status(esa)],[f_2457_2]) ).

cnf(f_2457_4,plain,
    ( hAPP(c_Relation_OImage(U_8814,U_8814,U_8816),hAPP(hAPP(c_Set_Oinsert(U_8814),U_8817),c_Orderings_Obot__class_Obot(tc_fun(U_8814,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8814,U_8814,U_8816),hAPP(hAPP(c_Set_Oinsert(U_8814),U_8818),c_Orderings_Obot__class_Obot(tc_fun(U_8814,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8814,U_8814)),hAPP(hAPP(c_Product__Type_OPair(U_8814,U_8814),U_8817),U_8818)),U_8816))
    | ~ c_Equiv__Relations_Oequiv(U_8814,U_8815,U_8816) ),
    inference(clausify,[status(thm)],[f_2457_3]) ).

fof(f_2458_1,plain,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
      | hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class]) ).

fof(f_2458_2,plain,
    ! [U_8823,U_8822,U_8821,U_8820,U_8819] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8821),U_8822)),U_8820))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8819),U_8822),U_8823))
      | ~ c_Equiv__Relations_Oequiv(U_8819,U_8823,U_8820)
      | hAPP(c_Relation_OImage(U_8819,U_8819,U_8820),hAPP(hAPP(c_Set_Oinsert(U_8819),U_8821),c_Orderings_Obot__class_Obot(tc_fun(U_8819,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8819,U_8819,U_8820),hAPP(hAPP(c_Set_Oinsert(U_8819),U_8822),c_Orderings_Obot__class_Obot(tc_fun(U_8819,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2458_1]) ).

fof(f_2458_3,plain,
    ! [U_8819,U_8820,U_8821,U_8822,U_8823] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8821),U_8822)),U_8820))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8819),U_8822),U_8823))
      | ~ c_Equiv__Relations_Oequiv(U_8819,U_8823,U_8820)
      | hAPP(c_Relation_OImage(U_8819,U_8819,U_8820),hAPP(hAPP(c_Set_Oinsert(U_8819),U_8821),c_Orderings_Obot__class_Obot(tc_fun(U_8819,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8819,U_8819,U_8820),hAPP(hAPP(c_Set_Oinsert(U_8819),U_8822),c_Orderings_Obot__class_Obot(tc_fun(U_8819,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2458_2]) ).

cnf(f_2458_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8821),U_8822)),U_8820))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8819),U_8822),U_8823))
    | ~ c_Equiv__Relations_Oequiv(U_8819,U_8823,U_8820)
    | hAPP(c_Relation_OImage(U_8819,U_8819,U_8820),hAPP(hAPP(c_Set_Oinsert(U_8819),U_8821),c_Orderings_Obot__class_Obot(tc_fun(U_8819,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8819,U_8819,U_8820),hAPP(hAPP(c_Set_Oinsert(U_8819),U_8822),c_Orderings_Obot__class_Obot(tc_fun(U_8819,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2458_3]) ).

fof(f_2459_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( ( ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff]) ).

fof(f_2459_2,plain,
    ! [U_8828,U_8827,U_8826,U_8825,U_8824] :
      ( ( ( hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8827),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8828),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8827),U_8828)),U_8826)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8827),U_8828)),U_8826))
          | hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8827),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8828),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8824),U_8828),U_8825))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8824),U_8827),U_8825))
      | ~ c_Equiv__Relations_Oequiv(U_8824,U_8825,U_8826) ),
    inference(variable_rename,[status(thm)],[f_2459_1]) ).

fof(f_2459_3,plain,
    ( ! [U_8824,U_8826,U_8827,U_8828] :
        ( hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8827),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8828),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8827),U_8828)),U_8826))
        | ~ sP728(U_8824,U_8826,U_8827,U_8828) )
    & ! [U_8824,U_8826,U_8827,U_8828] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8827),U_8828)),U_8826))
        | hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8827),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8828),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool))))
        | ~ sP728(U_8824,U_8826,U_8827,U_8828) )
    & ! [U_8824,U_8825,U_8826,U_8827,U_8828] :
        ( sP728(U_8824,U_8826,U_8827,U_8828)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8824),U_8828),U_8825))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8824),U_8827),U_8825))
        | ~ c_Equiv__Relations_Oequiv(U_8824,U_8825,U_8826) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP728])],[f_2459_2]) ).

cnf(f_2459_4,plain,
    ( sP728(U_8824,U_8826,U_8827,U_8828)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8824),U_8828),U_8825))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8824),U_8827),U_8825))
    | ~ c_Equiv__Relations_Oequiv(U_8824,U_8825,U_8826) ),
    inference(clausify,[status(thm)],[f_2459_3]) ).

cnf(f_2459_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8827),U_8828)),U_8826))
    | hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8827),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8828),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool))))
    | ~ sP728(U_8824,U_8826,U_8827,U_8828) ),
    inference(clausify,[status(thm)],[f_2459_3]) ).

cnf(f_2459_6,plain,
    ( hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8827),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8824,U_8824,U_8826),hAPP(hAPP(c_Set_Oinsert(U_8824),U_8828),c_Orderings_Obot__class_Obot(tc_fun(U_8824,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8827),U_8828)),U_8826))
    | ~ sP728(U_8824,U_8826,U_8827,U_8828) ),
    inference(clausify,[status(thm)],[f_2459_3]) ).

fof(f_2460_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          | hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
            & hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) )
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff]) ).

fof(f_2460_2,plain,
    ! [U_8833,U_8832,U_8831,U_8830,U_8829] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8832),U_8833)),U_8831))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8829),U_8833),U_8830))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8829),U_8832),U_8830))
          | hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8832),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8833),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(U_8829),U_8833),U_8830))
            & hBOOL(hAPP(hAPP(c_member(U_8829),U_8832),U_8830))
            & hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8832),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8833),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8832),U_8833)),U_8831)) ) )
      | ~ c_Equiv__Relations_Oequiv(U_8829,U_8830,U_8831) ),
    inference(variable_rename,[status(thm)],[f_2460_1]) ).

fof(f_2460_3,plain,
    ( ! [U_8830,U_8832,U_8831,U_8833,U_8829] :
        ( hBOOL(hAPP(hAPP(c_member(U_8829),U_8833),U_8830))
        | ~ sP729(U_8830,U_8832,U_8831,U_8833,U_8829) )
    & ! [U_8830,U_8832,U_8831,U_8833,U_8829] :
        ( hBOOL(hAPP(hAPP(c_member(U_8829),U_8832),U_8830))
        | ~ sP729(U_8830,U_8832,U_8831,U_8833,U_8829) )
    & ! [U_8830,U_8832,U_8831,U_8833,U_8829] :
        ( hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8832),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8833),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool))))
        | ~ sP729(U_8830,U_8832,U_8831,U_8833,U_8829) )
    & ! [U_8830,U_8832,U_8831,U_8833,U_8829] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8832),U_8833)),U_8831))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8829),U_8833),U_8830))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8829),U_8832),U_8830))
        | hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8832),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8833),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool))))
        | ~ sP730(U_8830,U_8832,U_8831,U_8833,U_8829) )
    & ! [U_8830,U_8832,U_8831,U_8833,U_8829] :
        ( sP729(U_8830,U_8832,U_8831,U_8833,U_8829)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8832),U_8833)),U_8831))
        | ~ sP730(U_8830,U_8832,U_8831,U_8833,U_8829) )
    & ! [U_8830,U_8832,U_8831,U_8833,U_8829] :
        ( sP730(U_8830,U_8832,U_8831,U_8833,U_8829)
        | ~ c_Equiv__Relations_Oequiv(U_8829,U_8830,U_8831) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP729,sP730])],[f_2460_2]) ).

cnf(f_2460_4,plain,
    ( sP730(U_8830,U_8832,U_8831,U_8833,U_8829)
    | ~ c_Equiv__Relations_Oequiv(U_8829,U_8830,U_8831) ),
    inference(clausify,[status(thm)],[f_2460_3]) ).

cnf(f_2460_5,plain,
    ( sP729(U_8830,U_8832,U_8831,U_8833,U_8829)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8832),U_8833)),U_8831))
    | ~ sP730(U_8830,U_8832,U_8831,U_8833,U_8829) ),
    inference(clausify,[status(thm)],[f_2460_3]) ).

cnf(f_2460_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8832),U_8833)),U_8831))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8829),U_8833),U_8830))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8829),U_8832),U_8830))
    | hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8832),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8833),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool))))
    | ~ sP730(U_8830,U_8832,U_8831,U_8833,U_8829) ),
    inference(clausify,[status(thm)],[f_2460_3]) ).

cnf(f_2460_7,plain,
    ( hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8832),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_8829,U_8829,U_8831),hAPP(hAPP(c_Set_Oinsert(U_8829),U_8833),c_Orderings_Obot__class_Obot(tc_fun(U_8829,tc_HOL_Obool))))
    | ~ sP729(U_8830,U_8832,U_8831,U_8833,U_8829) ),
    inference(clausify,[status(thm)],[f_2460_3]) ).

cnf(f_2460_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8829),U_8832),U_8830))
    | ~ sP729(U_8830,U_8832,U_8831,U_8833,U_8829) ),
    inference(clausify,[status(thm)],[f_2460_3]) ).

cnf(f_2460_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8829),U_8833),U_8830))
    | ~ sP729(U_8830,U_8832,U_8831,U_8833,U_8829) ),
    inference(clausify,[status(thm)],[f_2460_3]) ).

fof(f_2461_1,plain,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__subset]) ).

fof(f_2461_2,plain,
    ! [U_8838,U_8837,U_8836,U_8835,U_8834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8834,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8834,U_8834,U_8836),hAPP(hAPP(c_Set_Oinsert(U_8834),U_8837),c_Orderings_Obot__class_Obot(tc_fun(U_8834,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8834,U_8834,U_8836),hAPP(hAPP(c_Set_Oinsert(U_8834),U_8838),c_Orderings_Obot__class_Obot(tc_fun(U_8834,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8837),U_8838)),U_8836))
      | ~ c_Equiv__Relations_Oequiv(U_8834,U_8835,U_8836) ),
    inference(variable_rename,[status(thm)],[f_2461_1]) ).

fof(f_2461_3,plain,
    ! [U_8835,U_8836,U_8834,U_8837,U_8838] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8834,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8834,U_8834,U_8836),hAPP(hAPP(c_Set_Oinsert(U_8834),U_8837),c_Orderings_Obot__class_Obot(tc_fun(U_8834,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8834,U_8834,U_8836),hAPP(hAPP(c_Set_Oinsert(U_8834),U_8838),c_Orderings_Obot__class_Obot(tc_fun(U_8834,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8837),U_8838)),U_8836))
      | ~ c_Equiv__Relations_Oequiv(U_8834,U_8835,U_8836) ),
    inference(definitional_conversion,[status(esa)],[f_2461_2]) ).

cnf(f_2461_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8834,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8834,U_8834,U_8836),hAPP(hAPP(c_Set_Oinsert(U_8834),U_8837),c_Orderings_Obot__class_Obot(tc_fun(U_8834,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8834,U_8834,U_8836),hAPP(hAPP(c_Set_Oinsert(U_8834),U_8838),c_Orderings_Obot__class_Obot(tc_fun(U_8834,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8837),U_8838)),U_8836))
    | ~ c_Equiv__Relations_Oequiv(U_8834,U_8835,U_8836) ),
    inference(clausify,[status(thm)],[f_2461_3]) ).

fof(f_2462_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff]) ).

fof(f_2462_2,plain,
    ! [U_8841,U_8840,U_8839] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8839),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8839,tc_HOL_Obool)),U_8840),U_8841)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8839),U_8840)) ),
    inference(variable_rename,[status(thm)],[f_2462_1]) ).

fof(f_2462_3,plain,
    ! [U_8840,U_8839,U_8841] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8839),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8839,tc_HOL_Obool)),U_8840),U_8841)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8839),U_8840)) ),
    inference(definitional_conversion,[status(esa)],[f_2462_2]) ).

cnf(f_2462_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8839),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8839,tc_HOL_Obool)),U_8840),U_8841)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8839),U_8840)) ),
    inference(clausify,[status(thm)],[f_2462_3]) ).

fof(f_2463_1,plain,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__imageI]) ).

fof(f_2463_2,plain,
    ! [U_8845,U_8844,U_8843,U_8842] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8844),hAPP(c_Set_Oimage(U_8842,U_8844,U_8845),U_8843)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8842),U_8843)) ),
    inference(variable_rename,[status(thm)],[f_2463_1]) ).

fof(f_2463_3,plain,
    ! [U_8842,U_8843,U_8844,U_8845] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8844),hAPP(c_Set_Oimage(U_8842,U_8844,U_8845),U_8843)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8842),U_8843)) ),
    inference(definitional_conversion,[status(esa)],[f_2463_2]) ).

cnf(f_2463_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8844),hAPP(c_Set_Oimage(U_8842,U_8844,U_8845),U_8843)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8842),U_8843)) ),
    inference(clausify,[status(thm)],[f_2463_3]) ).

fof(f_2464_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite_OinsertI]) ).

fof(f_2464_2,plain,
    ! [U_8848,U_8847,U_8846] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8846),hAPP(hAPP(c_Set_Oinsert(U_8846),U_8848),U_8847)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8846),U_8847)) ),
    inference(variable_rename,[status(thm)],[f_2464_1]) ).

fof(f_2464_3,plain,
    ! [U_8846,U_8847,U_8848] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8846),hAPP(hAPP(c_Set_Oinsert(U_8846),U_8848),U_8847)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8846),U_8847)) ),
    inference(definitional_conversion,[status(esa)],[f_2464_2]) ).

cnf(f_2464_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8846),hAPP(hAPP(c_Set_Oinsert(U_8846),U_8848),U_8847)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8846),U_8847)) ),
    inference(clausify,[status(thm)],[f_2464_3]) ).

fof(f_2465_1,plain,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_finite_OemptyI]) ).

fof(f_2465_2,plain,
    ! [U_8849] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_8849),c_Orderings_Obot__class_Obot(tc_fun(U_8849,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2465_1]) ).

fof(f_2465_3,plain,
    ! [U_8849] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_8849),c_Orderings_Obot__class_Obot(tc_fun(U_8849,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2465_2]) ).

cnf(f_2465_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_8849),c_Orderings_Obot__class_Obot(tc_fun(U_8849,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2465_3]) ).

fof(f_2466_1,plain,
    ! [V_A_2] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J]) ).

fof(f_2466_2,plain,
    ! [U_8850] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8850))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8850))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8850)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8850)) ) ),
    inference(variable_rename,[status(thm)],[f_2466_1]) ).

fof(f_2466_3,plain,
    ( ! [U_8852] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8852))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8852))) )
    & ! [U_8851] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8851)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8851)) ) ),
    inference(miniscope,[status(thm)],[f_2466_2]) ).

fof(f_2466_4,plain,
    ( ! [U_8852] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8852))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8852))) )
    & ! [U_8851] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8851)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8851)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2466_3]) ).

cnf(f_2466_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8851)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8851)) ),
    inference(clausify,[status(thm)],[f_2466_4]) ).

cnf(f_2466_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8852))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8852))) ),
    inference(clausify,[status(thm)],[f_2466_4]) ).

fof(f_2467_1,plain,
    ! [V_A_2] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J]) ).

fof(f_2467_2,plain,
    ! [U_8853] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8853))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8853))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8853)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8853)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8853) ),
    inference(variable_rename,[status(thm)],[f_2467_1]) ).

fof(f_2467_3,plain,
    ( ! [U_8853] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8853))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8853)))
        | ~ sP731(U_8853) )
    & ! [U_8853] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8853)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8853))
        | ~ sP731(U_8853) )
    & ! [U_8853] :
        ( sP731(U_8853)
        | ~ c_Nat__Transfer_Onat__set(U_8853) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP731])],[f_2467_2]) ).

cnf(f_2467_4,plain,
    ( sP731(U_8853)
    | ~ c_Nat__Transfer_Onat__set(U_8853) ),
    inference(clausify,[status(thm)],[f_2467_3]) ).

cnf(f_2467_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8853)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8853))
    | ~ sP731(U_8853) ),
    inference(clausify,[status(thm)],[f_2467_3]) ).

cnf(f_2467_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8853))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8853)))
    | ~ sP731(U_8853) ),
    inference(clausify,[status(thm)],[f_2467_3]) ).

fof(f_2468_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Finite__Set_Ofinite(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite]) ).

fof(f_2468_2,plain,
    ! [U_8855,U_8854] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8854),U_8855))
      | ~ class_Finite__Set_Ofinite(U_8854) ),
    inference(variable_rename,[status(thm)],[f_2468_1]) ).

fof(f_2468_3,plain,
    ! [U_8855,U_8854] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8854),U_8855))
      | ~ class_Finite__Set_Ofinite(U_8854) ),
    inference(definitional_conversion,[status(esa)],[f_2468_2]) ).

cnf(f_2468_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8854),U_8855))
    | ~ class_Finite__Set_Ofinite(U_8854) ),
    inference(clausify,[status(thm)],[f_2468_3]) ).

fof(f_2469_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Finite__Set_Ofinite(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite__code]) ).

fof(f_2469_2,plain,
    ! [U_8857,U_8856] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8856),U_8857))
      | ~ class_Finite__Set_Ofinite(U_8856) ),
    inference(variable_rename,[status(thm)],[f_2469_1]) ).

fof(f_2469_3,plain,
    ! [U_8856,U_8857] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8856),U_8857))
      | ~ class_Finite__Set_Ofinite(U_8856) ),
    inference(definitional_conversion,[status(esa)],[f_2469_2]) ).

cnf(f_2469_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8856),U_8857))
    | ~ class_Finite__Set_Ofinite(U_8856) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

fof(f_2470_1,plain,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(f_2470_2,plain,
    ! [U_8858] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_8858),c_Orderings_Obot__class_Obot(tc_fun(U_8858,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2470_1]) ).

fof(f_2470_3,plain,
    ! [U_8858] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_8858),c_Orderings_Obot__class_Obot(tc_fun(U_8858,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2470_2]) ).

cnf(f_2470_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_8858),c_Orderings_Obot__class_Obot(tc_fun(U_8858,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2470_3]) ).

fof(f_2471_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__insert]) ).

fof(f_2471_2,plain,
    ! [U_8861,U_8860,U_8859] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8859),hAPP(hAPP(c_Set_Oinsert(U_8859),U_8860),U_8861)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8859),U_8861)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8859),U_8861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8859),hAPP(hAPP(c_Set_Oinsert(U_8859),U_8860),U_8861))) ) ),
    inference(variable_rename,[status(thm)],[f_2471_1]) ).

fof(f_2471_3,plain,
    ( ! [U_8867,U_8865,U_8863] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8863),hAPP(hAPP(c_Set_Oinsert(U_8863),U_8865),U_8867)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8863),U_8867)) )
    & ! [U_8866,U_8864,U_8862] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8862),U_8866))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8862),hAPP(hAPP(c_Set_Oinsert(U_8862),U_8864),U_8866))) ) ),
    inference(miniscope,[status(thm)],[f_2471_2]) ).

fof(f_2471_4,plain,
    ( ! [U_8863,U_8865,U_8867] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8863),hAPP(hAPP(c_Set_Oinsert(U_8863),U_8865),U_8867)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8863),U_8867)) )
    & ! [U_8864,U_8866,U_8862] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8862),U_8866))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8862),hAPP(hAPP(c_Set_Oinsert(U_8862),U_8864),U_8866))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2471_3]) ).

cnf(f_2471_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8862),U_8866))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8862),hAPP(hAPP(c_Set_Oinsert(U_8862),U_8864),U_8866))) ),
    inference(clausify,[status(thm)],[f_2471_4]) ).

cnf(f_2471_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8863),hAPP(hAPP(c_Set_Oinsert(U_8863),U_8865),U_8867)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8863),U_8867)) ),
    inference(clausify,[status(thm)],[f_2471_4]) ).

fof(f_2472_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__subset]) ).

fof(f_2472_2,plain,
    ! [U_8870,U_8869,U_8868] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8868),U_8869))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8868),U_8870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8868,tc_HOL_Obool)),U_8869),U_8870)) ),
    inference(variable_rename,[status(thm)],[f_2472_1]) ).

fof(f_2472_3,plain,
    ! [U_8869,U_8868,U_8870] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8868),U_8869))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8868),U_8870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8868,tc_HOL_Obool)),U_8869),U_8870)) ),
    inference(definitional_conversion,[status(esa)],[f_2472_2]) ).

cnf(f_2472_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8868),U_8869))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8868),U_8870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8868,tc_HOL_Obool)),U_8869),U_8870)) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

fof(f_2473_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__finite__subset]) ).

fof(f_2473_2,plain,
    ! [U_8873,U_8872,U_8871] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8871),U_8873))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8871,tc_HOL_Obool)),U_8873),U_8872))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8871),U_8872)) ),
    inference(variable_rename,[status(thm)],[f_2473_1]) ).

fof(f_2473_3,plain,
    ! [U_8871,U_8872,U_8873] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8871),U_8873))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8871,tc_HOL_Obool)),U_8873),U_8872))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8871),U_8872)) ),
    inference(definitional_conversion,[status(esa)],[f_2473_2]) ).

cnf(f_2473_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8871),U_8873))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8871,tc_HOL_Obool)),U_8873),U_8872))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8871),U_8872)) ),
    inference(clausify,[status(thm)],[f_2473_3]) ).

fof(f_2474_1,plain,
    ! [V_Ga_2,V_F_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).

fof(f_2474_2,plain,
    ! [U_8876,U_8875,U_8874] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8874,tc_HOL_Obool)),U_8875),U_8876)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8876))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8876))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8874,tc_HOL_Obool)),U_8875),U_8876))) ) ),
    inference(variable_rename,[status(thm)],[f_2474_1]) ).

fof(f_2474_3,plain,
    ( ! [U_8882,U_8880,U_8878] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8878,tc_HOL_Obool)),U_8880),U_8882)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8882))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8880)) )
    & ! [U_8881,U_8879,U_8877] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),U_8881))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),U_8879)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8877,tc_HOL_Obool)),U_8879),U_8881))) ) ),
    inference(miniscope,[status(thm)],[f_2474_2]) ).

fof(f_2474_4,plain,
    ( ! [U_8879,U_8877,U_8881] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),U_8881))
        | ~ sP732(U_8879,U_8877,U_8881) )
    & ! [U_8879,U_8877,U_8881] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),U_8879))
        | ~ sP732(U_8879,U_8877,U_8881) )
    & ! [U_8880,U_8882,U_8878] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8878,tc_HOL_Obool)),U_8880),U_8882)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8882))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8880)) )
    & ! [U_8879,U_8877,U_8881] :
        ( sP732(U_8879,U_8877,U_8881)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8877,tc_HOL_Obool)),U_8879),U_8881))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP732])],[f_2474_3]) ).

cnf(f_2474_5,plain,
    ( sP732(U_8879,U_8877,U_8881)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8877,tc_HOL_Obool)),U_8879),U_8881))) ),
    inference(clausify,[status(thm)],[f_2474_4]) ).

cnf(f_2474_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8878,tc_HOL_Obool)),U_8880),U_8882)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8882))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8880)) ),
    inference(clausify,[status(thm)],[f_2474_4]) ).

cnf(f_2474_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),U_8879))
    | ~ sP732(U_8879,U_8877,U_8881) ),
    inference(clausify,[status(thm)],[f_2474_4]) ).

cnf(f_2474_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8877),U_8881))
    | ~ sP732(U_8879,U_8877,U_8881) ),
    inference(clausify,[status(thm)],[f_2474_4]) ).

fof(f_2475_1,plain,
    ! [V_Ga_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).

fof(f_2475_2,plain,
    ! [U_8885,U_8884,U_8883] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8883,tc_HOL_Obool)),U_8884),U_8885)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),U_8885))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),U_8884)) ),
    inference(variable_rename,[status(thm)],[f_2475_1]) ).

fof(f_2475_3,plain,
    ! [U_8883,U_8884,U_8885] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8883,tc_HOL_Obool)),U_8884),U_8885)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),U_8885))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),U_8884)) ),
    inference(definitional_conversion,[status(esa)],[f_2475_2]) ).

cnf(f_2475_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8883,tc_HOL_Obool)),U_8884),U_8885)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),U_8885))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8883),U_8884)) ),
    inference(clausify,[status(thm)],[f_2475_3]) ).

fof(f_2476_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff2]) ).

fof(f_2476_2,plain,
    ! [U_8888,U_8887,U_8886] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8886,tc_HOL_Obool)),U_8888),U_8887)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8888)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8888))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8886,tc_HOL_Obool)),U_8888),U_8887))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8887)) ),
    inference(variable_rename,[status(thm)],[f_2476_1]) ).

fof(f_2476_3,plain,
    ( ! [U_8886,U_8887,U_8888] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8886,tc_HOL_Obool)),U_8888),U_8887)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8888))
        | ~ sP733(U_8886,U_8887,U_8888) )
    & ! [U_8886,U_8887,U_8888] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8888))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8886,tc_HOL_Obool)),U_8888),U_8887)))
        | ~ sP733(U_8886,U_8887,U_8888) )
    & ! [U_8886,U_8887,U_8888] :
        ( sP733(U_8886,U_8887,U_8888)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8887)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP733])],[f_2476_2]) ).

cnf(f_2476_4,plain,
    ( sP733(U_8886,U_8887,U_8888)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8887)) ),
    inference(clausify,[status(thm)],[f_2476_3]) ).

cnf(f_2476_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8888))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8886,tc_HOL_Obool)),U_8888),U_8887)))
    | ~ sP733(U_8886,U_8887,U_8888) ),
    inference(clausify,[status(thm)],[f_2476_3]) ).

cnf(f_2476_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8886,tc_HOL_Obool)),U_8888),U_8887)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8888))
    | ~ sP733(U_8886,U_8887,U_8888) ),
    inference(clausify,[status(thm)],[f_2476_3]) ).

fof(f_2477_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__surj]) ).

fof(f_2477_2,plain,
    ! [U_8893,U_8892,U_8891,U_8890,U_8889] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8891),U_8892))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8891,tc_HOL_Obool)),U_8892),hAPP(c_Set_Oimage(U_8889,U_8891,U_8893),U_8890)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8889),U_8890)) ),
    inference(variable_rename,[status(thm)],[f_2477_1]) ).

fof(f_2477_3,plain,
    ! [U_8890,U_8891,U_8889,U_8892,U_8893] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8891),U_8892))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8891,tc_HOL_Obool)),U_8892),hAPP(c_Set_Oimage(U_8889,U_8891,U_8893),U_8890)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8889),U_8890)) ),
    inference(definitional_conversion,[status(esa)],[f_2477_2]) ).

cnf(f_2477_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8891),U_8892))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8891,tc_HOL_Obool)),U_8892),hAPP(c_Set_Oimage(U_8889,U_8891,U_8893),U_8890)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8889),U_8890)) ),
    inference(clausify,[status(thm)],[f_2477_3]) ).

fof(f_2478_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert]) ).

fof(f_2478_2,plain,
    ! [U_8897,U_8896,U_8895,U_8894] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8894),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8894,tc_HOL_Obool)),U_8895),hAPP(hAPP(c_Set_Oinsert(U_8894),U_8896),U_8897))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8894),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8894,tc_HOL_Obool)),U_8895),U_8897))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8894),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8894,tc_HOL_Obool)),U_8895),U_8897)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8894),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8894,tc_HOL_Obool)),U_8895),hAPP(hAPP(c_Set_Oinsert(U_8894),U_8896),U_8897)))) ) ),
    inference(variable_rename,[status(thm)],[f_2478_1]) ).

fof(f_2478_3,plain,
    ( ! [U_8905,U_8903,U_8901,U_8899] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),U_8905))) )
    & ! [U_8904,U_8902,U_8900,U_8898] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),U_8904)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),U_8904)))) ) ),
    inference(miniscope,[status(thm)],[f_2478_2]) ).

fof(f_2478_4,plain,
    ( ! [U_8901,U_8899,U_8903,U_8905] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),U_8905))) )
    & ! [U_8900,U_8902,U_8904,U_8898] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),U_8904)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),U_8904)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2478_3]) ).

cnf(f_2478_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),U_8904)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),U_8904)))) ),
    inference(clausify,[status(thm)],[f_2478_4]) ).

cnf(f_2478_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),U_8905))) ),
    inference(clausify,[status(thm)],[f_2478_4]) ).

fof(f_2479_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__finite__psubset]) ).

fof(f_2479_2,plain,
    ! [U_8908,U_8907,U_8906] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8906,tc_HOL_Obool),tc_fun(U_8906,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8906,tc_HOL_Obool),tc_fun(U_8906,tc_HOL_Obool)),U_8907),U_8908)),c_Wellfounded_Ofinite__psubset(U_8906)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8906),U_8908))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8906,tc_HOL_Obool)),U_8907),U_8908)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8906),U_8908))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8906,tc_HOL_Obool)),U_8907),U_8908)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8906,tc_HOL_Obool),tc_fun(U_8906,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8906,tc_HOL_Obool),tc_fun(U_8906,tc_HOL_Obool)),U_8907),U_8908)),c_Wellfounded_Ofinite__psubset(U_8906))) ) ),
    inference(variable_rename,[status(thm)],[f_2479_1]) ).

fof(f_2479_3,plain,
    ( ! [U_8914,U_8912,U_8910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8910,tc_HOL_Obool),tc_fun(U_8910,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8910,tc_HOL_Obool),tc_fun(U_8910,tc_HOL_Obool)),U_8912),U_8914)),c_Wellfounded_Ofinite__psubset(U_8910)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8910),U_8914))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8910,tc_HOL_Obool)),U_8912),U_8914)) )
    & ! [U_8913,U_8911,U_8909] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8909),U_8913))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8909,tc_HOL_Obool)),U_8911),U_8913)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8909,tc_HOL_Obool),tc_fun(U_8909,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8909,tc_HOL_Obool),tc_fun(U_8909,tc_HOL_Obool)),U_8911),U_8913)),c_Wellfounded_Ofinite__psubset(U_8909))) ) ),
    inference(miniscope,[status(thm)],[f_2479_2]) ).

fof(f_2479_4,plain,
    ( ! [U_8911,U_8913,U_8909] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8909),U_8913))
        | ~ sP734(U_8911,U_8913,U_8909) )
    & ! [U_8911,U_8913,U_8909] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8909,tc_HOL_Obool)),U_8911),U_8913))
        | ~ sP734(U_8911,U_8913,U_8909) )
    & ! [U_8914,U_8912,U_8910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8910,tc_HOL_Obool),tc_fun(U_8910,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8910,tc_HOL_Obool),tc_fun(U_8910,tc_HOL_Obool)),U_8912),U_8914)),c_Wellfounded_Ofinite__psubset(U_8910)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8910),U_8914))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8910,tc_HOL_Obool)),U_8912),U_8914)) )
    & ! [U_8911,U_8913,U_8909] :
        ( sP734(U_8911,U_8913,U_8909)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8909,tc_HOL_Obool),tc_fun(U_8909,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8909,tc_HOL_Obool),tc_fun(U_8909,tc_HOL_Obool)),U_8911),U_8913)),c_Wellfounded_Ofinite__psubset(U_8909))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP734])],[f_2479_3]) ).

cnf(f_2479_5,plain,
    ( sP734(U_8911,U_8913,U_8909)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8909,tc_HOL_Obool),tc_fun(U_8909,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8909,tc_HOL_Obool),tc_fun(U_8909,tc_HOL_Obool)),U_8911),U_8913)),c_Wellfounded_Ofinite__psubset(U_8909))) ),
    inference(clausify,[status(thm)],[f_2479_4]) ).

cnf(f_2479_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8910,tc_HOL_Obool),tc_fun(U_8910,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8910,tc_HOL_Obool),tc_fun(U_8910,tc_HOL_Obool)),U_8912),U_8914)),c_Wellfounded_Ofinite__psubset(U_8910)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8910),U_8914))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8910,tc_HOL_Obool)),U_8912),U_8914)) ),
    inference(clausify,[status(thm)],[f_2479_4]) ).

cnf(f_2479_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8909,tc_HOL_Obool)),U_8911),U_8913))
    | ~ sP734(U_8911,U_8913,U_8909) ),
    inference(clausify,[status(thm)],[f_2479_4]) ).

cnf(f_2479_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8909),U_8913))
    | ~ sP734(U_8911,U_8913,U_8909) ),
    inference(clausify,[status(thm)],[f_2479_4]) ).

fof(f_2480_1,plain,
    ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
      | ? [B_p] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
          & c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__pointwise]) ).

fof(f_2480_2,plain,
    ! [U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8923)),U_8921)),U_8924)),U_8917))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8920)),U_8921)),U_8922)),U_8917))
      | ? [U_8915] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8923,U_8915)),hAPP(U_8921,U_8915)),hAPP(U_8924,U_8915))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool))))
          & c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8920,U_8915)),hAPP(U_8921,U_8915)),hAPP(U_8922,U_8915))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8916),U_8917)) ),
    inference(variable_rename,[status(thm)],[f_2480_1]) ).

fof(f_2480_3,plain,
    ! [U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8923)),U_8921)),U_8924)),U_8917))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8920)),U_8921)),U_8922)),U_8917))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8923,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8921,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8924,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8920,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8921,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8922,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8916),U_8917)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_8915,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))],[f_2480_2]) ).

fof(f_2480_4,plain,
    ( ! [U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8923,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8921,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8924,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool))))
        | ~ sP735(U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924) )
    & ! [U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8920,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8921,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8922,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool))))
        | ~ sP735(U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924) )
    & ! [U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8923)),U_8921)),U_8924)),U_8917))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8920)),U_8921)),U_8922)),U_8917))
        | sP735(U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8916),U_8917)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP735])],[f_2480_3]) ).

cnf(f_2480_5,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8923)),U_8921)),U_8924)),U_8917))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(c_Set_Oimage(U_8916,tc_Hoare__Mirabelle_Otriple(U_8918),hAPP(hAPP(c_COMBS(U_8916,tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(c_COMBS(U_8916,tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),hAPP(hAPP(c_COMBB(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8918,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8918))),U_8916),c_Hoare__Mirabelle_Otriple_Otriple(U_8918)),U_8920)),U_8921)),U_8922)),U_8917))
    | sP735(U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8916),U_8917)) ),
    inference(clausify,[status(thm)],[f_2480_4]) ).

cnf(f_2480_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8920,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8921,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8922,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool))))
    | ~ sP735(U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924) ),
    inference(clausify,[status(thm)],[f_2480_4]) ).

cnf(f_2480_7,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8918,U_8919,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8918)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8918),hAPP(U_8923,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8921,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916))),hAPP(U_8924,sK132(U_8924,U_8923,U_8922,U_8921,U_8920,U_8919,U_8918,U_8917,U_8916)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8918),tc_HOL_Obool))))
    | ~ sP735(U_8916,U_8917,U_8918,U_8919,U_8920,U_8921,U_8922,U_8923,U_8924) ),
    inference(clausify,[status(thm)],[f_2480_4]) ).

fof(f_2481_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( ( ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( hAPP(V_F_2,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove]) ).

fof(f_2481_2,plain,
    ! [U_8929,U_8928,U_8927,U_8926,U_8925] :
      ( ( ( hAPP(U_8927,U_8928) = hAPP(hAPP(U_8926,U_8929),hAPP(U_8927,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)) )
        & ( hAPP(U_8927,U_8928) = U_8929
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8925),U_8929),U_8928))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8925),U_8928))
      | ~ c_Finite__Set_Ofolding__one(U_8925,U_8926,U_8927) ),
    inference(variable_rename,[status(thm)],[f_2481_1]) ).

fof(f_2481_3,plain,
    ( ! [U_8925,U_8926,U_8927,U_8928,U_8929] :
        ( hAPP(U_8927,U_8928) = hAPP(hAPP(U_8926,U_8929),hAPP(U_8927,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))
        | ~ sP736(U_8925,U_8926,U_8927,U_8928,U_8929) )
    & ! [U_8925,U_8926,U_8927,U_8928,U_8929] :
        ( hAPP(U_8927,U_8928) = U_8929
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))
        | ~ sP736(U_8925,U_8926,U_8927,U_8928,U_8929) )
    & ! [U_8925,U_8926,U_8927,U_8928,U_8929] :
        ( sP736(U_8925,U_8926,U_8927,U_8928,U_8929)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8925),U_8929),U_8928))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8925),U_8928))
        | ~ c_Finite__Set_Ofolding__one(U_8925,U_8926,U_8927) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP736])],[f_2481_2]) ).

cnf(f_2481_4,plain,
    ( sP736(U_8925,U_8926,U_8927,U_8928,U_8929)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8925),U_8929),U_8928))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8925),U_8928))
    | ~ c_Finite__Set_Ofolding__one(U_8925,U_8926,U_8927) ),
    inference(clausify,[status(thm)],[f_2481_3]) ).

cnf(f_2481_5,plain,
    ( hAPP(U_8927,U_8928) = U_8929
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))
    | ~ sP736(U_8925,U_8926,U_8927,U_8928,U_8929) ),
    inference(clausify,[status(thm)],[f_2481_3]) ).

cnf(f_2481_6,plain,
    ( hAPP(U_8927,U_8928) = hAPP(hAPP(U_8926,U_8929),hAPP(U_8927,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8925,tc_HOL_Obool)),U_8928),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8929),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool))
    | ~ sP736(U_8925,U_8926,U_8927,U_8928,U_8929) ),
    inference(clausify,[status(thm)],[f_2481_3]) ).

fof(f_2482_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove]) ).

fof(f_2482_2,plain,
    ! [U_8937,U_8936,U_8935,U_8934,U_8933,U_8932,U_8931,U_8930] :
      ( hAPP(U_8935,U_8936) = hAPP(hAPP(U_8932,hAPP(U_8934,U_8937)),hAPP(U_8935,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8931,tc_HOL_Obool)),U_8936),hAPP(hAPP(c_Set_Oinsert(U_8931),U_8937),c_Orderings_Obot__class_Obot(tc_fun(U_8931,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8931),U_8937),U_8936))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8931),U_8936))
      | ~ c_Finite__Set_Ofolding__image__simple(U_8930,U_8931,U_8932,U_8933,U_8934,U_8935) ),
    inference(variable_rename,[status(thm)],[f_2482_1]) ).

fof(f_2482_3,plain,
    ! [U_8937,U_8936,U_8935,U_8934,U_8933,U_8932,U_8931] :
      ( ! [U_8930] : ~ c_Finite__Set_Ofolding__image__simple(U_8930,U_8931,U_8932,U_8933,U_8934,U_8935)
      | hAPP(U_8935,U_8936) = hAPP(hAPP(U_8932,hAPP(U_8934,U_8937)),hAPP(U_8935,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8931,tc_HOL_Obool)),U_8936),hAPP(hAPP(c_Set_Oinsert(U_8931),U_8937),c_Orderings_Obot__class_Obot(tc_fun(U_8931,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8931),U_8937),U_8936))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8931),U_8936)) ),
    inference(miniscope,[status(thm)],[f_2482_2]) ).

fof(f_2482_4,plain,
    ! [U_8935,U_8931,U_8932,U_8934,U_8933,U_8937,U_8936,U_8930] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_8930,U_8931,U_8932,U_8933,U_8934,U_8935)
      | hAPP(U_8935,U_8936) = hAPP(hAPP(U_8932,hAPP(U_8934,U_8937)),hAPP(U_8935,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8931,tc_HOL_Obool)),U_8936),hAPP(hAPP(c_Set_Oinsert(U_8931),U_8937),c_Orderings_Obot__class_Obot(tc_fun(U_8931,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8931),U_8937),U_8936))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8931),U_8936)) ),
    inference(definitional_conversion,[status(esa)],[f_2482_3]) ).

cnf(f_2482_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_8930,U_8931,U_8932,U_8933,U_8934,U_8935)
    | hAPP(U_8935,U_8936) = hAPP(hAPP(U_8932,hAPP(U_8934,U_8937)),hAPP(U_8935,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8931,tc_HOL_Obool)),U_8936),hAPP(hAPP(c_Set_Oinsert(U_8931),U_8937),c_Orderings_Obot__class_Obot(tc_fun(U_8931,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8931),U_8937),U_8936))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8931),U_8936)) ),
    inference(clausify,[status(thm)],[f_2482_4]) ).

fof(f_2483_1,plain,
    ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty]) ).

fof(f_2483_2,plain,
    ! [U_8943,U_8942,U_8941,U_8940,U_8939,U_8938] :
      ( hAPP(U_8943,c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))) = U_8941
      | ~ c_Finite__Set_Ofolding__image__simple(U_8938,U_8939,U_8940,U_8941,U_8942,U_8943) ),
    inference(variable_rename,[status(thm)],[f_2483_1]) ).

fof(f_2483_3,plain,
    ! [U_8943,U_8942,U_8941,U_8940,U_8939] :
      ( ! [U_8938] : ~ c_Finite__Set_Ofolding__image__simple(U_8938,U_8939,U_8940,U_8941,U_8942,U_8943)
      | hAPP(U_8943,c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))) = U_8941 ),
    inference(miniscope,[status(thm)],[f_2483_2]) ).

fof(f_2483_4,plain,
    ! [U_8943,U_8941,U_8942,U_8939,U_8938,U_8940] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_8938,U_8939,U_8940,U_8941,U_8942,U_8943)
      | hAPP(U_8943,c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))) = U_8941 ),
    inference(definitional_conversion,[status(esa)],[f_2483_3]) ).

cnf(f_2483_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_8938,U_8939,U_8940,U_8941,U_8942,U_8943)
    | hAPP(U_8943,c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))) = U_8941 ),
    inference(clausify,[status(thm)],[f_2483_4]) ).

fof(f_2484_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton]) ).

fof(f_2484_2,plain,
    ! [U_8947,U_8946,U_8945,U_8944] :
      ( hAPP(U_8946,hAPP(hAPP(c_Set_Oinsert(U_8944),U_8947),c_Orderings_Obot__class_Obot(tc_fun(U_8944,tc_HOL_Obool)))) = U_8947
      | ~ c_Finite__Set_Ofolding__one(U_8944,U_8945,U_8946) ),
    inference(variable_rename,[status(thm)],[f_2484_1]) ).

fof(f_2484_3,plain,
    ! [U_8944,U_8945,U_8946,U_8947] :
      ( hAPP(U_8946,hAPP(hAPP(c_Set_Oinsert(U_8944),U_8947),c_Orderings_Obot__class_Obot(tc_fun(U_8944,tc_HOL_Obool)))) = U_8947
      | ~ c_Finite__Set_Ofolding__one(U_8944,U_8945,U_8946) ),
    inference(definitional_conversion,[status(esa)],[f_2484_2]) ).

cnf(f_2484_4,plain,
    ( hAPP(U_8946,hAPP(hAPP(c_Set_Oinsert(U_8944),U_8947),c_Orderings_Obot__class_Obot(tc_fun(U_8944,tc_HOL_Obool)))) = U_8947
    | ~ c_Finite__Set_Ofolding__one(U_8944,U_8945,U_8946) ),
    inference(clausify,[status(thm)],[f_2484_3]) ).

fof(f_2485_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(f_2485_2,plain,
    ! [U_8955,U_8954,U_8953,U_8952,U_8951,U_8950,U_8949,U_8948] :
      ( hAPP(U_8953,hAPP(hAPP(c_Set_Oinsert(U_8949),U_8955),U_8954)) = hAPP(hAPP(U_8950,hAPP(U_8952,U_8955)),hAPP(U_8953,U_8954))
      | hBOOL(hAPP(hAPP(c_member(U_8949),U_8955),U_8954))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8949),U_8954))
      | ~ c_Finite__Set_Ofolding__image__simple(U_8948,U_8949,U_8950,U_8951,U_8952,U_8953) ),
    inference(variable_rename,[status(thm)],[f_2485_1]) ).

fof(f_2485_3,plain,
    ! [U_8955,U_8954,U_8953,U_8952,U_8951,U_8950,U_8949] :
      ( ! [U_8948] : ~ c_Finite__Set_Ofolding__image__simple(U_8948,U_8949,U_8950,U_8951,U_8952,U_8953)
      | hAPP(U_8953,hAPP(hAPP(c_Set_Oinsert(U_8949),U_8955),U_8954)) = hAPP(hAPP(U_8950,hAPP(U_8952,U_8955)),hAPP(U_8953,U_8954))
      | hBOOL(hAPP(hAPP(c_member(U_8949),U_8955),U_8954))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8949),U_8954)) ),
    inference(miniscope,[status(thm)],[f_2485_2]) ).

fof(f_2485_4,plain,
    ! [U_8948,U_8949,U_8950,U_8951,U_8952,U_8953,U_8954,U_8955] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_8948,U_8949,U_8950,U_8951,U_8952,U_8953)
      | hAPP(U_8953,hAPP(hAPP(c_Set_Oinsert(U_8949),U_8955),U_8954)) = hAPP(hAPP(U_8950,hAPP(U_8952,U_8955)),hAPP(U_8953,U_8954))
      | hBOOL(hAPP(hAPP(c_member(U_8949),U_8955),U_8954))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8949),U_8954)) ),
    inference(definitional_conversion,[status(esa)],[f_2485_3]) ).

cnf(f_2485_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_8948,U_8949,U_8950,U_8951,U_8952,U_8953)
    | hAPP(U_8953,hAPP(hAPP(c_Set_Oinsert(U_8949),U_8955),U_8954)) = hAPP(hAPP(U_8950,hAPP(U_8952,U_8955)),hAPP(U_8953,U_8954))
    | hBOOL(hAPP(hAPP(c_member(U_8949),U_8955),U_8954))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8949),U_8954)) ),
    inference(clausify,[status(thm)],[f_2485_4]) ).

fof(f_2486_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(f_2486_2,plain,
    ! [U_8960,U_8959,U_8958,U_8957,U_8956] :
      ( hAPP(U_8958,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8960),U_8959)) = hAPP(hAPP(U_8957,U_8960),hAPP(U_8958,U_8959))
      | U_8959 = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_8956),U_8960),U_8959))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8956),U_8959))
      | ~ c_Finite__Set_Ofolding__one(U_8956,U_8957,U_8958) ),
    inference(variable_rename,[status(thm)],[f_2486_1]) ).

fof(f_2486_3,plain,
    ! [U_8956,U_8957,U_8958,U_8959,U_8960] :
      ( hAPP(U_8958,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8960),U_8959)) = hAPP(hAPP(U_8957,U_8960),hAPP(U_8958,U_8959))
      | U_8959 = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_8956),U_8960),U_8959))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8956),U_8959))
      | ~ c_Finite__Set_Ofolding__one(U_8956,U_8957,U_8958) ),
    inference(definitional_conversion,[status(esa)],[f_2486_2]) ).

cnf(f_2486_4,plain,
    ( hAPP(U_8958,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8960),U_8959)) = hAPP(hAPP(U_8957,U_8960),hAPP(U_8958,U_8959))
    | U_8959 = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_8956),U_8960),U_8959))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8956),U_8959))
    | ~ c_Finite__Set_Ofolding__one(U_8956,U_8957,U_8958) ),
    inference(clausify,[status(thm)],[f_2486_3]) ).

fof(f_2487_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( ( ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove]) ).

fof(f_2487_2,plain,
    ! [U_8965,U_8964,U_8963,U_8962,U_8961] :
      ( ( ( hAPP(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),U_8964)) = hAPP(hAPP(U_8962,U_8965),hAPP(U_8963,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)) )
        & ( hAPP(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),U_8964)) = U_8965
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8961),U_8964))
      | ~ c_Finite__Set_Ofolding__one(U_8961,U_8962,U_8963) ),
    inference(variable_rename,[status(thm)],[f_2487_1]) ).

fof(f_2487_3,plain,
    ( ! [U_8961,U_8962,U_8963,U_8964,U_8965] :
        ( hAPP(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),U_8964)) = hAPP(hAPP(U_8962,U_8965),hAPP(U_8963,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))
        | ~ sP737(U_8961,U_8962,U_8963,U_8964,U_8965) )
    & ! [U_8961,U_8962,U_8963,U_8964,U_8965] :
        ( hAPP(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),U_8964)) = U_8965
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))
        | ~ sP737(U_8961,U_8962,U_8963,U_8964,U_8965) )
    & ! [U_8961,U_8962,U_8963,U_8964,U_8965] :
        ( sP737(U_8961,U_8962,U_8963,U_8964,U_8965)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8961),U_8964))
        | ~ c_Finite__Set_Ofolding__one(U_8961,U_8962,U_8963) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP737])],[f_2487_2]) ).

cnf(f_2487_4,plain,
    ( sP737(U_8961,U_8962,U_8963,U_8964,U_8965)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8961),U_8964))
    | ~ c_Finite__Set_Ofolding__one(U_8961,U_8962,U_8963) ),
    inference(clausify,[status(thm)],[f_2487_3]) ).

cnf(f_2487_5,plain,
    ( hAPP(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),U_8964)) = U_8965
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))
    | ~ sP737(U_8961,U_8962,U_8963,U_8964,U_8965) ),
    inference(clausify,[status(thm)],[f_2487_3]) ).

cnf(f_2487_6,plain,
    ( hAPP(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),U_8964)) = hAPP(hAPP(U_8962,U_8965),hAPP(U_8963,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8961,tc_HOL_Obool)),U_8964),hAPP(hAPP(c_Set_Oinsert(U_8961),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8961,tc_HOL_Obool))
    | ~ sP737(U_8961,U_8962,U_8963,U_8964,U_8965) ),
    inference(clausify,[status(thm)],[f_2487_3]) ).

fof(f_2488_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove]) ).

fof(f_2488_2,plain,
    ! [U_8973,U_8972,U_8971,U_8970,U_8969,U_8968,U_8967,U_8966] :
      ( hAPP(U_8971,hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),U_8972)) = hAPP(hAPP(U_8968,hAPP(U_8970,U_8973)),hAPP(U_8971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8967,tc_HOL_Obool)),U_8972),hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),c_Orderings_Obot__class_Obot(tc_fun(U_8967,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8967),U_8972))
      | ~ c_Finite__Set_Ofolding__image__simple(U_8966,U_8967,U_8968,U_8969,U_8970,U_8971) ),
    inference(variable_rename,[status(thm)],[f_2488_1]) ).

fof(f_2488_3,plain,
    ! [U_8973,U_8972,U_8971,U_8970,U_8969,U_8968,U_8967] :
      ( ! [U_8966] : ~ c_Finite__Set_Ofolding__image__simple(U_8966,U_8967,U_8968,U_8969,U_8970,U_8971)
      | hAPP(U_8971,hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),U_8972)) = hAPP(hAPP(U_8968,hAPP(U_8970,U_8973)),hAPP(U_8971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8967,tc_HOL_Obool)),U_8972),hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),c_Orderings_Obot__class_Obot(tc_fun(U_8967,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8967),U_8972)) ),
    inference(miniscope,[status(thm)],[f_2488_2]) ).

fof(f_2488_4,plain,
    ! [U_8972,U_8971,U_8973,U_8970,U_8969,U_8966,U_8967,U_8968] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_8966,U_8967,U_8968,U_8969,U_8970,U_8971)
      | hAPP(U_8971,hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),U_8972)) = hAPP(hAPP(U_8968,hAPP(U_8970,U_8973)),hAPP(U_8971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8967,tc_HOL_Obool)),U_8972),hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),c_Orderings_Obot__class_Obot(tc_fun(U_8967,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8967),U_8972)) ),
    inference(definitional_conversion,[status(esa)],[f_2488_3]) ).

cnf(f_2488_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_8966,U_8967,U_8968,U_8969,U_8970,U_8971)
    | hAPP(U_8971,hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),U_8972)) = hAPP(hAPP(U_8968,hAPP(U_8970,U_8973)),hAPP(U_8971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8967,tc_HOL_Obool)),U_8972),hAPP(hAPP(c_Set_Oinsert(U_8967),U_8973),c_Orderings_Obot__class_Obot(tc_fun(U_8967,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8967),U_8972)) ),
    inference(clausify,[status(thm)],[f_2488_4]) ).

fof(f_2489_1,plain,
    ! [V_N_2] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
        | ! [B_m] :
          ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) )
      & ( ? [B_m] :
          ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded__le]) ).

fof(f_2489_2,plain,
    ! [U_8978] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8978))
        | ! [U_8977] :
          ? [U_8976] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8976),U_8977))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8976),U_8978)) ) )
      & ( ? [U_8975] :
          ! [U_8974] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8974),U_8975))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8974),U_8978)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8978)) ) ),
    inference(variable_rename,[status(thm)],[f_2489_1]) ).

fof(f_2489_3,plain,
    ( ! [U_8980] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8980))
        | ! [U_8977] :
          ? [U_8976] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8976),U_8977))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8976),U_8980)) ) )
    & ! [U_8979] :
        ( ? [U_8975] :
          ! [U_8974] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8974),U_8975))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8974),U_8979)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8979)) ) ),
    inference(miniscope,[status(thm)],[f_2489_2]) ).

fof(f_2489_4,plain,
    ( ! [U_8980] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8980))
        | ! [U_8977] :
          ? [U_8976] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8976),U_8977))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8976),U_8980)) ) )
    & ! [U_8979] :
        ( ! [U_8974] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8974),sK133(U_8979)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8974),U_8979)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8979)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_8975,sK133(U_8979))],[f_2489_3]) ).

fof(f_2489_5,plain,
    ( ! [U_8980] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8980))
        | ! [U_8977] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK134(U_8980,U_8977)),U_8977))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK134(U_8980,U_8977)),U_8980)) ) )
    & ! [U_8979] :
        ( ! [U_8974] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8974),sK133(U_8979)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8974),U_8979)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8979)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_8976,sK134(U_8980,U_8977))],[f_2489_4]) ).

fof(f_2489_6,plain,
    ( ! [U_8977,U_8980] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK134(U_8980,U_8977)),U_8977))
        | ~ sP738(U_8977,U_8980) )
    & ! [U_8977,U_8980] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK134(U_8980,U_8977)),U_8980))
        | ~ sP738(U_8977,U_8980) )
    & ! [U_8977,U_8980] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8980))
        | sP738(U_8977,U_8980) )
    & ! [U_8974,U_8979] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8974),sK133(U_8979)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8974),U_8979))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8979)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP738])],[f_2489_5]) ).

cnf(f_2489_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8974),sK133(U_8979)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8974),U_8979))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8979)) ),
    inference(clausify,[status(thm)],[f_2489_6]) ).

cnf(f_2489_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8980))
    | sP738(U_8977,U_8980) ),
    inference(clausify,[status(thm)],[f_2489_6]) ).

cnf(f_2489_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK134(U_8980,U_8977)),U_8980))
    | ~ sP738(U_8977,U_8980) ),
    inference(clausify,[status(thm)],[f_2489_6]) ).

cnf(f_2489_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK134(U_8980,U_8977)),U_8977))
    | ~ sP738(U_8977,U_8980) ),
    inference(clausify,[status(thm)],[f_2489_6]) ).

fof(f_2490_1,plain,
    ! [V_N_2] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
        | ! [B_m] :
          ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) )
      & ( ? [B_m] :
          ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded]) ).

fof(f_2490_2,plain,
    ! [U_8985] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8985))
        | ! [U_8984] :
          ? [U_8983] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8983),U_8984))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8983),U_8985)) ) )
      & ( ? [U_8982] :
          ! [U_8981] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8981),U_8982))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8981),U_8985)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8985)) ) ),
    inference(variable_rename,[status(thm)],[f_2490_1]) ).

fof(f_2490_3,plain,
    ( ! [U_8987] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8987))
        | ! [U_8984] :
          ? [U_8983] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8983),U_8984))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8983),U_8987)) ) )
    & ! [U_8986] :
        ( ? [U_8982] :
          ! [U_8981] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8981),U_8982))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8981),U_8986)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8986)) ) ),
    inference(miniscope,[status(thm)],[f_2490_2]) ).

fof(f_2490_4,plain,
    ( ! [U_8987] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8987))
        | ! [U_8984] :
          ? [U_8983] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8983),U_8984))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8983),U_8987)) ) )
    & ! [U_8986] :
        ( ! [U_8981] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8981),sK135(U_8986)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8981),U_8986)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8986)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_8982,sK135(U_8986))],[f_2490_3]) ).

fof(f_2490_5,plain,
    ( ! [U_8987] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8987))
        | ! [U_8984] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK136(U_8987,U_8984)),U_8984))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK136(U_8987,U_8984)),U_8987)) ) )
    & ! [U_8986] :
        ( ! [U_8981] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8981),sK135(U_8986)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8981),U_8986)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8986)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_8983,sK136(U_8987,U_8984))],[f_2490_4]) ).

fof(f_2490_6,plain,
    ( ! [U_8984,U_8987] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK136(U_8987,U_8984)),U_8984))
        | ~ sP739(U_8984,U_8987) )
    & ! [U_8984,U_8987] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK136(U_8987,U_8984)),U_8987))
        | ~ sP739(U_8984,U_8987) )
    & ! [U_8984,U_8987] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8987))
        | sP739(U_8984,U_8987) )
    & ! [U_8981,U_8986] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8981),sK135(U_8986)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8981),U_8986))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8986)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP739])],[f_2490_5]) ).

cnf(f_2490_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8981),sK135(U_8986)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8981),U_8986))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8986)) ),
    inference(clausify,[status(thm)],[f_2490_6]) ).

cnf(f_2490_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8987))
    | sP739(U_8984,U_8987) ),
    inference(clausify,[status(thm)],[f_2490_6]) ).

cnf(f_2490_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK136(U_8987,U_8984)),U_8987))
    | ~ sP739(U_8984,U_8987) ),
    inference(clausify,[status(thm)],[f_2490_6]) ).

cnf(f_2490_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK136(U_8987,U_8984)),U_8984))
    | ~ sP739(U_8984,U_8987) ),
    inference(clausify,[status(thm)],[f_2490_6]) ).

fof(f_2491_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2]) ).

fof(f_2491_2,plain,
    ! [U_8992,U_8991,U_8990,U_8989,U_8988] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8991),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8992),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8988,U_8988)),hAPP(hAPP(c_Product__Type_OPair(U_8988,U_8988),U_8991),U_8992)),U_8990)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8988,U_8988)),hAPP(hAPP(c_Product__Type_OPair(U_8988,U_8988),U_8991),U_8992)),U_8990))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8991),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8992),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8988),U_8992),U_8989))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8988),U_8991),U_8989))
      | ~ c_Equiv__Relations_Oequiv(U_8988,U_8989,U_8990) ),
    inference(variable_rename,[status(thm)],[f_2491_1]) ).

fof(f_2491_3,plain,
    ( ! [U_8988,U_8991,U_8990,U_8992] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8991),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8992),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8988,U_8988)),hAPP(hAPP(c_Product__Type_OPair(U_8988,U_8988),U_8991),U_8992)),U_8990))
        | ~ sP740(U_8988,U_8991,U_8990,U_8992) )
    & ! [U_8988,U_8991,U_8990,U_8992] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8988,U_8988)),hAPP(hAPP(c_Product__Type_OPair(U_8988,U_8988),U_8991),U_8992)),U_8990))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8991),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8992),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990)
        | ~ sP740(U_8988,U_8991,U_8990,U_8992) )
    & ! [U_8988,U_8991,U_8989,U_8990,U_8992] :
        ( sP740(U_8988,U_8991,U_8990,U_8992)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8988),U_8992),U_8989))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8988),U_8991),U_8989))
        | ~ c_Equiv__Relations_Oequiv(U_8988,U_8989,U_8990) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP740])],[f_2491_2]) ).

cnf(f_2491_4,plain,
    ( sP740(U_8988,U_8991,U_8990,U_8992)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8988),U_8992),U_8989))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8988),U_8991),U_8989))
    | ~ c_Equiv__Relations_Oequiv(U_8988,U_8989,U_8990) ),
    inference(clausify,[status(thm)],[f_2491_3]) ).

cnf(f_2491_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8988,U_8988)),hAPP(hAPP(c_Product__Type_OPair(U_8988,U_8988),U_8991),U_8992)),U_8990))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8991),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8992),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990)
    | ~ sP740(U_8988,U_8991,U_8990,U_8992) ),
    inference(clausify,[status(thm)],[f_2491_3]) ).

cnf(f_2491_6,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8991),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_8988),hAPP(hAPP(c_Set_Oinsert(U_8988),U_8992),c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)))),U_8990)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8988,U_8988)),hAPP(hAPP(c_Product__Type_OPair(U_8988,U_8988),U_8991),U_8992)),U_8990))
    | ~ sP740(U_8988,U_8991,U_8990,U_8992) ),
    inference(clausify,[status(thm)],[f_2491_3]) ).

fof(f_2492_1,plain,
    ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint]) ).

fof(f_2492_2,plain,
    ! [U_8998,U_8997,U_8996,U_8995,U_8994,U_8993] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8993,U_8993)),hAPP(hAPP(c_Product__Type_OPair(U_8993,U_8993),U_8997),U_8998)),U_8995))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8993),U_8996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8993,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8993,U_8993,U_8995),hAPP(hAPP(c_Set_Oinsert(U_8993),U_8997),c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8993,U_8993,U_8995),hAPP(hAPP(c_Set_Oinsert(U_8993),U_8998),c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_8993,U_8994,U_8995) ),
    inference(variable_rename,[status(thm)],[f_2492_1]) ).

fof(f_2492_3,plain,
    ! [U_8997,U_8993,U_8994,U_8996,U_8995,U_8998] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8993,U_8993)),hAPP(hAPP(c_Product__Type_OPair(U_8993,U_8993),U_8997),U_8998)),U_8995))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8993),U_8996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8993,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8993,U_8993,U_8995),hAPP(hAPP(c_Set_Oinsert(U_8993),U_8997),c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8993,U_8993,U_8995),hAPP(hAPP(c_Set_Oinsert(U_8993),U_8998),c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_8993,U_8994,U_8995) ),
    inference(definitional_conversion,[status(esa)],[f_2492_2]) ).

cnf(f_2492_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8993,U_8993)),hAPP(hAPP(c_Product__Type_OPair(U_8993,U_8993),U_8997),U_8998)),U_8995))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8993),U_8996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8993,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8993,U_8993,U_8995),hAPP(hAPP(c_Set_Oinsert(U_8993),U_8997),c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_8993,U_8993,U_8995),hAPP(hAPP(c_Set_Oinsert(U_8993),U_8998),c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool)))))))
    | ~ c_Equiv__Relations_Oequiv(U_8993,U_8994,U_8995) ),
    inference(clausify,[status(thm)],[f_2492_3]) ).

fof(f_2493_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(V_B_2,V_x_2))
        & hBOOL(hAPP(V_A_2,V_x_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1E]) ).

fof(f_2493_2,plain,
    ! [U_9002,U_9001,U_9000,U_8999] :
      ( ( hBOOL(hAPP(U_9001,U_9002))
        & hBOOL(hAPP(U_9000,U_9002)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8999,tc_HOL_Obool)),U_9000),U_9001),U_9002)) ),
    inference(variable_rename,[status(thm)],[f_2493_1]) ).

fof(f_2493_3,plain,
    ! [U_9002,U_9001,U_9000] :
      ( ! [U_8999] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8999,tc_HOL_Obool)),U_9000),U_9001),U_9002))
      | ( hBOOL(hAPP(U_9001,U_9002))
        & hBOOL(hAPP(U_9000,U_9002)) ) ),
    inference(miniscope,[status(thm)],[f_2493_2]) ).

fof(f_2493_4,plain,
    ( ! [U_9000,U_9001,U_9002] :
        ( hBOOL(hAPP(U_9001,U_9002))
        | ~ sP741(U_9000,U_9001,U_9002) )
    & ! [U_9000,U_9001,U_9002] :
        ( hBOOL(hAPP(U_9000,U_9002))
        | ~ sP741(U_9000,U_9001,U_9002) )
    & ! [U_8999,U_9000,U_9001,U_9002] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8999,tc_HOL_Obool)),U_9000),U_9001),U_9002))
        | sP741(U_9000,U_9001,U_9002) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP741])],[f_2493_3]) ).

cnf(f_2493_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8999,tc_HOL_Obool)),U_9000),U_9001),U_9002))
    | sP741(U_9000,U_9001,U_9002) ),
    inference(clausify,[status(thm)],[f_2493_4]) ).

cnf(f_2493_6,plain,
    ( hBOOL(hAPP(U_9000,U_9002))
    | ~ sP741(U_9000,U_9001,U_9002) ),
    inference(clausify,[status(thm)],[f_2493_4]) ).

cnf(f_2493_7,plain,
    ( hBOOL(hAPP(U_9001,U_9002))
    | ~ sP741(U_9000,U_9001,U_9002) ),
    inference(clausify,[status(thm)],[f_2493_4]) ).

fof(f_2494_1,plain,
    ! [T_b,V_B_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ~ hBOOL(hAPP(V_B_2,V_x_2))
      | ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1I]) ).

fof(f_2494_2,plain,
    ! [U_9006,U_9005,U_9004,U_9003] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9006,tc_HOL_Obool)),U_9003),U_9005),U_9004))
      | ~ hBOOL(hAPP(U_9005,U_9004))
      | ~ hBOOL(hAPP(U_9003,U_9004)) ),
    inference(variable_rename,[status(thm)],[f_2494_1]) ).

fof(f_2494_3,plain,
    ! [U_9004,U_9003,U_9005,U_9006] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9006,tc_HOL_Obool)),U_9003),U_9005),U_9004))
      | ~ hBOOL(hAPP(U_9005,U_9004))
      | ~ hBOOL(hAPP(U_9003,U_9004)) ),
    inference(definitional_conversion,[status(esa)],[f_2494_2]) ).

cnf(f_2494_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9006,tc_HOL_Obool)),U_9003),U_9005),U_9004))
    | ~ hBOOL(hAPP(U_9005,U_9004))
    | ~ hBOOL(hAPP(U_9003,U_9004)) ),
    inference(clausify,[status(thm)],[f_2494_3]) ).

fof(f_2495_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_IntI]) ).

fof(f_2495_2,plain,
    ! [U_9010,U_9009,U_9008,U_9007] :
      ( hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9007,tc_HOL_Obool)),U_9009),U_9010)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),U_9010))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),U_9009)) ),
    inference(variable_rename,[status(thm)],[f_2495_1]) ).

fof(f_2495_3,plain,
    ! [U_9007,U_9008,U_9009,U_9010] :
      ( hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9007,tc_HOL_Obool)),U_9009),U_9010)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),U_9010))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),U_9009)) ),
    inference(definitional_conversion,[status(esa)],[f_2495_2]) ).

cnf(f_2495_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9007,tc_HOL_Obool)),U_9009),U_9010)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),U_9010))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9007),U_9008),U_9009)) ),
    inference(clausify,[status(thm)],[f_2495_3]) ).

fof(f_2496_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntE]) ).

fof(f_2496_2,plain,
    ! [U_9014,U_9013,U_9012,U_9011] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),U_9014))
        & hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),U_9013)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9011,tc_HOL_Obool)),U_9013),U_9014))) ),
    inference(variable_rename,[status(thm)],[f_2496_1]) ).

fof(f_2496_3,plain,
    ( ! [U_9011,U_9012,U_9013,U_9014] :
        ( hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),U_9014))
        | ~ sP742(U_9011,U_9012,U_9013,U_9014) )
    & ! [U_9011,U_9012,U_9013,U_9014] :
        ( hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),U_9013))
        | ~ sP742(U_9011,U_9012,U_9013,U_9014) )
    & ! [U_9011,U_9012,U_9013,U_9014] :
        ( sP742(U_9011,U_9012,U_9013,U_9014)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9011,tc_HOL_Obool)),U_9013),U_9014))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP742])],[f_2496_2]) ).

cnf(f_2496_4,plain,
    ( sP742(U_9011,U_9012,U_9013,U_9014)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9011,tc_HOL_Obool)),U_9013),U_9014))) ),
    inference(clausify,[status(thm)],[f_2496_3]) ).

cnf(f_2496_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),U_9013))
    | ~ sP742(U_9011,U_9012,U_9013,U_9014) ),
    inference(clausify,[status(thm)],[f_2496_3]) ).

cnf(f_2496_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9011),U_9012),U_9014))
    | ~ sP742(U_9011,U_9012,U_9013,U_9014) ),
    inference(clausify,[status(thm)],[f_2496_3]) ).

fof(f_2497_1,plain,
    ! [V_Ga_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).

fof(f_2497_2,plain,
    ! [U_9017,U_9016,U_9015] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9015,tc_HOL_Obool)),U_9016),U_9017)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),U_9017))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),U_9016)) ) ),
    inference(variable_rename,[status(thm)],[f_2497_1]) ).

fof(f_2497_3,plain,
    ( ! [U_9015,U_9016,U_9017] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),U_9017))
        | ~ sP743(U_9015,U_9016,U_9017) )
    & ! [U_9015,U_9016,U_9017] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),U_9016))
        | ~ sP743(U_9015,U_9016,U_9017) )
    & ! [U_9015,U_9016,U_9017] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9015,tc_HOL_Obool)),U_9016),U_9017)))
        | sP743(U_9015,U_9016,U_9017) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP743])],[f_2497_2]) ).

cnf(f_2497_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9015,tc_HOL_Obool)),U_9016),U_9017)))
    | sP743(U_9015,U_9016,U_9017) ),
    inference(clausify,[status(thm)],[f_2497_3]) ).

cnf(f_2497_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),U_9016))
    | ~ sP743(U_9015,U_9016,U_9017) ),
    inference(clausify,[status(thm)],[f_2497_3]) ).

cnf(f_2497_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9015),U_9017))
    | ~ sP743(U_9015,U_9016,U_9017) ),
    inference(clausify,[status(thm)],[f_2497_3]) ).

fof(f_2498_1,plain,
    ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_X_2 = V_Y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__disj]) ).

fof(f_2498_2,plain,
    ! [U_9022,U_9021,U_9020,U_9019,U_9018] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9018,tc_HOL_Obool)),U_9021),U_9022) = c_Orderings_Obot__class_Obot(tc_fun(U_9018,tc_HOL_Obool))
      | U_9021 = U_9022
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9018,tc_HOL_Obool)),U_9022),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9018),U_9019),U_9020)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9018,tc_HOL_Obool)),U_9021),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9018),U_9019),U_9020)))
      | ~ c_Equiv__Relations_Oequiv(U_9018,U_9019,U_9020) ),
    inference(variable_rename,[status(thm)],[f_2498_1]) ).

fof(f_2498_3,plain,
    ! [U_9018,U_9019,U_9020,U_9021,U_9022] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9018,tc_HOL_Obool)),U_9021),U_9022) = c_Orderings_Obot__class_Obot(tc_fun(U_9018,tc_HOL_Obool))
      | U_9021 = U_9022
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9018,tc_HOL_Obool)),U_9022),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9018),U_9019),U_9020)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9018,tc_HOL_Obool)),U_9021),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9018),U_9019),U_9020)))
      | ~ c_Equiv__Relations_Oequiv(U_9018,U_9019,U_9020) ),
    inference(definitional_conversion,[status(esa)],[f_2498_2]) ).

cnf(f_2498_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9018,tc_HOL_Obool)),U_9021),U_9022) = c_Orderings_Obot__class_Obot(tc_fun(U_9018,tc_HOL_Obool))
    | U_9021 = U_9022
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9018,tc_HOL_Obool)),U_9022),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9018),U_9019),U_9020)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9018,tc_HOL_Obool)),U_9021),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9018),U_9019),U_9020)))
    | ~ c_Equiv__Relations_Oequiv(U_9018,U_9019,U_9020) ),
    inference(clausify,[status(thm)],[f_2498_3]) ).

fof(f_2499_1,plain,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_quotient__empty]) ).

fof(f_2499_2,plain,
    ! [U_9024,U_9023] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9023),c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool))),U_9024) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9023,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2499_1]) ).

fof(f_2499_3,plain,
    ! [U_9024,U_9023] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9023),c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool))),U_9024) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9023,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2499_2]) ).

cnf(f_2499_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9023),c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool))),U_9024) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9023,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2499_3]) ).

fof(f_2500_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2]) ).

fof(f_2500_2,plain,
    ! [U_9027,U_9026,U_9025] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9025,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9025),U_9026),U_9027)
        | U_9026 != c_Orderings_Obot__class_Obot(tc_fun(U_9025,tc_HOL_Obool)) )
      & ( U_9026 = c_Orderings_Obot__class_Obot(tc_fun(U_9025,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9025,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9025),U_9026),U_9027) ) ),
    inference(variable_rename,[status(thm)],[f_2500_1]) ).

fof(f_2500_3,plain,
    ( ! [U_9033,U_9031,U_9029] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9029,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9029),U_9031),U_9033)
        | U_9031 != c_Orderings_Obot__class_Obot(tc_fun(U_9029,tc_HOL_Obool)) )
    & ! [U_9032,U_9030,U_9028] :
        ( U_9030 = c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9028,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9028),U_9030),U_9032) ) ),
    inference(miniscope,[status(thm)],[f_2500_2]) ).

fof(f_2500_4,plain,
    ( ! [U_9031,U_9033,U_9029] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9029,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9029),U_9031),U_9033)
        | U_9031 != c_Orderings_Obot__class_Obot(tc_fun(U_9029,tc_HOL_Obool)) )
    & ! [U_9032,U_9030,U_9028] :
        ( U_9030 = c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9028,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9028),U_9030),U_9032) ) ),
    inference(definitional_conversion,[status(esa)],[f_2500_3]) ).

cnf(f_2500_5,plain,
    ( U_9030 = c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9028,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9028),U_9030),U_9032) ),
    inference(clausify,[status(thm)],[f_2500_4]) ).

cnf(f_2500_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9029,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9029),U_9031),U_9033)
    | U_9031 != c_Orderings_Obot__class_Obot(tc_fun(U_9029,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2500_4]) ).

fof(f_2501_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__is__empty]) ).

fof(f_2501_2,plain,
    ! [U_9036,U_9035,U_9034] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9034),U_9035),U_9036) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9034,tc_HOL_Obool),tc_HOL_Obool))
        | U_9035 != c_Orderings_Obot__class_Obot(tc_fun(U_9034,tc_HOL_Obool)) )
      & ( U_9035 = c_Orderings_Obot__class_Obot(tc_fun(U_9034,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9034),U_9035),U_9036) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9034,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2501_1]) ).

fof(f_2501_3,plain,
    ( ! [U_9042,U_9040,U_9038] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9038),U_9040),U_9042) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9038,tc_HOL_Obool),tc_HOL_Obool))
        | U_9040 != c_Orderings_Obot__class_Obot(tc_fun(U_9038,tc_HOL_Obool)) )
    & ! [U_9041,U_9039,U_9037] :
        ( U_9039 = c_Orderings_Obot__class_Obot(tc_fun(U_9037,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9037),U_9039),U_9041) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2501_2]) ).

fof(f_2501_4,plain,
    ( ! [U_9038,U_9040,U_9042] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9038),U_9040),U_9042) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9038,tc_HOL_Obool),tc_HOL_Obool))
        | U_9040 != c_Orderings_Obot__class_Obot(tc_fun(U_9038,tc_HOL_Obool)) )
    & ! [U_9039,U_9041,U_9037] :
        ( U_9039 = c_Orderings_Obot__class_Obot(tc_fun(U_9037,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9037),U_9039),U_9041) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2501_3]) ).

cnf(f_2501_5,plain,
    ( U_9039 = c_Orderings_Obot__class_Obot(tc_fun(U_9037,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9037),U_9039),U_9041) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9037,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2501_4]) ).

cnf(f_2501_6,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9038),U_9040),U_9042) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9038,tc_HOL_Obool),tc_HOL_Obool))
    | U_9040 != c_Orderings_Obot__class_Obot(tc_fun(U_9038,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2501_4]) ).

fof(f_2502_1,plain,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).

fof(f_2502_2,plain,
    ! [U_9046,U_9045,U_9044,U_9043] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9043,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9043,tc_fun(U_9043,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9043)),U_9044)),hAPP(hAPP(c_COMBC(U_9043,tc_fun(U_9043,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9043)),U_9045)),U_9046))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9043),U_9046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9043,tc_HOL_Obool)),U_9044),U_9045))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9043),U_9046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9043,tc_HOL_Obool)),U_9044),U_9045)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9043,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9043,tc_fun(U_9043,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9043)),U_9044)),hAPP(hAPP(c_COMBC(U_9043,tc_fun(U_9043,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9043)),U_9045)),U_9046)) ) ),
    inference(variable_rename,[status(thm)],[f_2502_1]) ).

fof(f_2502_3,plain,
    ( ! [U_9054,U_9052,U_9050,U_9048] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9048,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9048,tc_fun(U_9048,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9048)),U_9050)),hAPP(hAPP(c_COMBC(U_9048,tc_fun(U_9048,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9048)),U_9052)),U_9054))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9048),U_9054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9048,tc_HOL_Obool)),U_9050),U_9052))) )
    & ! [U_9053,U_9051,U_9049,U_9047] :
        ( hBOOL(hAPP(hAPP(c_member(U_9047),U_9053),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9047,tc_HOL_Obool)),U_9049),U_9051)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9047,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9047,tc_fun(U_9047,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9047)),U_9049)),hAPP(hAPP(c_COMBC(U_9047,tc_fun(U_9047,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9047)),U_9051)),U_9053)) ) ),
    inference(miniscope,[status(thm)],[f_2502_2]) ).

fof(f_2502_4,plain,
    ( ! [U_9050,U_9048,U_9052,U_9054] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9048,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9048,tc_fun(U_9048,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9048)),U_9050)),hAPP(hAPP(c_COMBC(U_9048,tc_fun(U_9048,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9048)),U_9052)),U_9054))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9048),U_9054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9048,tc_HOL_Obool)),U_9050),U_9052))) )
    & ! [U_9049,U_9053,U_9051,U_9047] :
        ( hBOOL(hAPP(hAPP(c_member(U_9047),U_9053),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9047,tc_HOL_Obool)),U_9049),U_9051)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9047,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9047,tc_fun(U_9047,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9047)),U_9049)),hAPP(hAPP(c_COMBC(U_9047,tc_fun(U_9047,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9047)),U_9051)),U_9053)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2502_3]) ).

cnf(f_2502_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9047),U_9053),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9047,tc_HOL_Obool)),U_9049),U_9051)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9047,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9047,tc_fun(U_9047,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9047)),U_9049)),hAPP(hAPP(c_COMBC(U_9047,tc_fun(U_9047,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9047)),U_9051)),U_9053)) ),
    inference(clausify,[status(thm)],[f_2502_4]) ).

cnf(f_2502_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9048,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9048,tc_fun(U_9048,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9048)),U_9050)),hAPP(hAPP(c_COMBC(U_9048,tc_fun(U_9048,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9048)),U_9052)),U_9054))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9048),U_9054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9048,tc_HOL_Obool)),U_9050),U_9052))) ),
    inference(clausify,[status(thm)],[f_2502_4]) ).

fof(f_2503_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).

fof(f_2503_2,plain,
    ! [U_9057,U_9056,U_9055] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9055,tc_HOL_Obool)),U_9056),U_9057)),U_9056)),
    inference(variable_rename,[status(thm)],[f_2503_1]) ).

fof(f_2503_3,plain,
    ! [U_9056,U_9055,U_9057] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9055,tc_HOL_Obool)),U_9056),U_9057)),U_9056)),
    inference(definitional_conversion,[status(esa)],[f_2503_2]) ).

cnf(f_2503_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9055,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9055,tc_HOL_Obool)),U_9056),U_9057)),U_9056)),
    inference(clausify,[status(thm)],[f_2503_3]) ).

fof(f_2504_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).

fof(f_2504_2,plain,
    ! [U_9060,U_9059,U_9058] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9058,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9058,tc_HOL_Obool)),U_9059),U_9060)),U_9060)),
    inference(variable_rename,[status(thm)],[f_2504_1]) ).

fof(f_2504_3,plain,
    ! [U_9058,U_9059,U_9060] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9058,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9058,tc_HOL_Obool)),U_9059),U_9060)),U_9060)),
    inference(definitional_conversion,[status(esa)],[f_2504_2]) ).

cnf(f_2504_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9058,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9058,tc_HOL_Obool)),U_9059),U_9060)),U_9060)),
    inference(clausify,[status(thm)],[f_2504_3]) ).

fof(f_2505_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).

fof(f_2505_2,plain,
    ! [U_9063,U_9062,U_9061] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9061,tc_HOL_Obool)),U_9062),U_9063) = U_9062
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9061,tc_HOL_Obool)),U_9062),U_9063)) ),
    inference(variable_rename,[status(thm)],[f_2505_1]) ).

fof(f_2505_3,plain,
    ! [U_9061,U_9062,U_9063] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9061,tc_HOL_Obool)),U_9062),U_9063) = U_9062
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9061,tc_HOL_Obool)),U_9062),U_9063)) ),
    inference(definitional_conversion,[status(esa)],[f_2505_2]) ).

cnf(f_2505_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9061,tc_HOL_Obool)),U_9062),U_9063) = U_9062
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9061,tc_HOL_Obool)),U_9062),U_9063)) ),
    inference(clausify,[status(thm)],[f_2505_3]) ).

fof(f_2506_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).

fof(f_2506_2,plain,
    ! [U_9066,U_9065,U_9064] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9064,tc_HOL_Obool)),U_9066),U_9065) = U_9065
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9064,tc_HOL_Obool)),U_9065),U_9066)) ),
    inference(variable_rename,[status(thm)],[f_2506_1]) ).

fof(f_2506_3,plain,
    ! [U_9064,U_9065,U_9066] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9064,tc_HOL_Obool)),U_9066),U_9065) = U_9065
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9064,tc_HOL_Obool)),U_9065),U_9066)) ),
    inference(definitional_conversion,[status(esa)],[f_2506_2]) ).

cnf(f_2506_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9064,tc_HOL_Obool)),U_9066),U_9065) = U_9065
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9064,tc_HOL_Obool)),U_9065),U_9066)) ),
    inference(clausify,[status(thm)],[f_2506_3]) ).

fof(f_2507_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).

fof(f_2507_2,plain,
    ! [U_9070,U_9069,U_9068,U_9067] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9067,tc_HOL_Obool)),U_9069),U_9070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),U_9070))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),U_9069)) ),
    inference(variable_rename,[status(thm)],[f_2507_1]) ).

fof(f_2507_3,plain,
    ! [U_9067,U_9068,U_9069,U_9070] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9067,tc_HOL_Obool)),U_9069),U_9070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),U_9070))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),U_9069)) ),
    inference(definitional_conversion,[status(esa)],[f_2507_2]) ).

cnf(f_2507_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9067,tc_HOL_Obool)),U_9069),U_9070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),U_9070))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9067,tc_HOL_Obool)),U_9068),U_9069)) ),
    inference(clausify,[status(thm)],[f_2507_3]) ).

fof(f_2508_1,plain,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).

fof(f_2508_2,plain,
    ! [U_9075,U_9074,U_9073,U_9072,U_9071] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9074)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9073),U_9075)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9074),U_9075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9073)) ),
    inference(variable_rename,[status(thm)],[f_2508_1]) ).

fof(f_2508_3,plain,
    ! [U_9071,U_9072,U_9073,U_9074,U_9075] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9074)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9073),U_9075)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9074),U_9075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9073)) ),
    inference(definitional_conversion,[status(esa)],[f_2508_2]) ).

cnf(f_2508_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9074)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9073),U_9075)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9074),U_9075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9073)) ),
    inference(clausify,[status(thm)],[f_2508_3]) ).

fof(f_2509_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J]) ).

fof(f_2509_2,plain,
    ! [U_9078,U_9077,U_9076] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9076),U_9077),U_9078)),U_9077))
      | ~ class_Lattices_Olattice(U_9076) ),
    inference(variable_rename,[status(thm)],[f_2509_1]) ).

fof(f_2509_3,plain,
    ! [U_9076,U_9077,U_9078] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9076),U_9077),U_9078)),U_9077))
      | ~ class_Lattices_Olattice(U_9076) ),
    inference(definitional_conversion,[status(esa)],[f_2509_2]) ).

cnf(f_2509_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9076),U_9077),U_9078)),U_9077))
    | ~ class_Lattices_Olattice(U_9076) ),
    inference(clausify,[status(thm)],[f_2509_3]) ).

fof(f_2510_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le1]) ).

fof(f_2510_2,plain,
    ! [U_9081,U_9080,U_9079] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9079),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9079),U_9080),U_9081)),U_9080))
      | ~ class_Lattices_Osemilattice__inf(U_9079) ),
    inference(variable_rename,[status(thm)],[f_2510_1]) ).

fof(f_2510_3,plain,
    ! [U_9079,U_9080,U_9081] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9079),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9079),U_9080),U_9081)),U_9080))
      | ~ class_Lattices_Osemilattice__inf(U_9079) ),
    inference(definitional_conversion,[status(esa)],[f_2510_2]) ).

cnf(f_2510_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9079),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9079),U_9080),U_9081)),U_9080))
    | ~ class_Lattices_Osemilattice__inf(U_9079) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

fof(f_2511_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J]) ).

fof(f_2511_2,plain,
    ! [U_9084,U_9083,U_9082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9082),U_9083),U_9084)),U_9084))
      | ~ class_Lattices_Olattice(U_9082) ),
    inference(variable_rename,[status(thm)],[f_2511_1]) ).

fof(f_2511_3,plain,
    ! [U_9082,U_9083,U_9084] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9082),U_9083),U_9084)),U_9084))
      | ~ class_Lattices_Olattice(U_9082) ),
    inference(definitional_conversion,[status(esa)],[f_2511_2]) ).

cnf(f_2511_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9082),U_9083),U_9084)),U_9084))
    | ~ class_Lattices_Olattice(U_9082) ),
    inference(clausify,[status(thm)],[f_2511_3]) ).

fof(f_2512_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le2]) ).

fof(f_2512_2,plain,
    ! [U_9087,U_9086,U_9085] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9085),U_9086),U_9087)),U_9087))
      | ~ class_Lattices_Osemilattice__inf(U_9085) ),
    inference(variable_rename,[status(thm)],[f_2512_1]) ).

fof(f_2512_3,plain,
    ! [U_9085,U_9086,U_9087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9085),U_9086),U_9087)),U_9087))
      | ~ class_Lattices_Osemilattice__inf(U_9085) ),
    inference(definitional_conversion,[status(esa)],[f_2512_2]) ).

cnf(f_2512_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9085),U_9086),U_9087)),U_9087))
    | ~ class_Lattices_Osemilattice__inf(U_9085) ),
    inference(clausify,[status(thm)],[f_2512_3]) ).

fof(f_2513_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != V_x_2 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).

fof(f_2513_2,plain,
    ! [U_9090,U_9089,U_9088] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9088),U_9089),U_9090))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9088),U_9089),U_9090) != U_9089 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9088),U_9089),U_9090) = U_9089
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9088),U_9089),U_9090)) ) )
      | ~ class_Lattices_Osemilattice__inf(U_9088) ),
    inference(variable_rename,[status(thm)],[f_2513_1]) ).

fof(f_2513_3,plain,
    ( ! [U_9088,U_9089,U_9090] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9088),U_9089),U_9090))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9088),U_9089),U_9090) != U_9089
        | ~ sP744(U_9088,U_9089,U_9090) )
    & ! [U_9088,U_9089,U_9090] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9088),U_9089),U_9090) = U_9089
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9088),U_9089),U_9090))
        | ~ sP744(U_9088,U_9089,U_9090) )
    & ! [U_9088,U_9089,U_9090] :
        ( sP744(U_9088,U_9089,U_9090)
        | ~ class_Lattices_Osemilattice__inf(U_9088) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP744])],[f_2513_2]) ).

cnf(f_2513_4,plain,
    ( sP744(U_9088,U_9089,U_9090)
    | ~ class_Lattices_Osemilattice__inf(U_9088) ),
    inference(clausify,[status(thm)],[f_2513_3]) ).

cnf(f_2513_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9088),U_9089),U_9090) = U_9089
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9088),U_9089),U_9090))
    | ~ sP744(U_9088,U_9089,U_9090) ),
    inference(clausify,[status(thm)],[f_2513_3]) ).

cnf(f_2513_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9088),U_9089),U_9090))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9088),U_9089),U_9090) != U_9089
    | ~ sP744(U_9088,U_9089,U_9090) ),
    inference(clausify,[status(thm)],[f_2513_3]) ).

fof(f_2514_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) ) )
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).

fof(f_2514_2,plain,
    ! [U_9094,U_9093,U_9092,U_9091] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9091),U_9093),U_9094)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9094))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9093)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9094))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9093)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9091),U_9093),U_9094))) ) )
      | ~ class_Lattices_Osemilattice__inf(U_9091) ),
    inference(variable_rename,[status(thm)],[f_2514_1]) ).

fof(f_2514_3,plain,
    ( ! [U_9091,U_9092,U_9093,U_9094] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9094))
        | ~ sP745(U_9091,U_9092,U_9093,U_9094) )
    & ! [U_9091,U_9092,U_9093,U_9094] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9093))
        | ~ sP745(U_9091,U_9092,U_9093,U_9094) )
    & ! [U_9091,U_9092,U_9093,U_9094] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9091),U_9093),U_9094)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9094))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9093))
        | ~ sP746(U_9091,U_9092,U_9093,U_9094) )
    & ! [U_9091,U_9092,U_9093,U_9094] :
        ( sP745(U_9091,U_9092,U_9093,U_9094)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9091),U_9093),U_9094)))
        | ~ sP746(U_9091,U_9092,U_9093,U_9094) )
    & ! [U_9091,U_9092,U_9093,U_9094] :
        ( sP746(U_9091,U_9092,U_9093,U_9094)
        | ~ class_Lattices_Osemilattice__inf(U_9091) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP745,sP746])],[f_2514_2]) ).

cnf(f_2514_4,plain,
    ( sP746(U_9091,U_9092,U_9093,U_9094)
    | ~ class_Lattices_Osemilattice__inf(U_9091) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_5,plain,
    ( sP745(U_9091,U_9092,U_9093,U_9094)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9091),U_9093),U_9094)))
    | ~ sP746(U_9091,U_9092,U_9093,U_9094) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9091),U_9093),U_9094)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9093))
    | ~ sP746(U_9091,U_9092,U_9093,U_9094) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9093))
    | ~ sP745(U_9091,U_9092,U_9093,U_9094) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9091),U_9092),U_9094))
    | ~ sP745(U_9091,U_9092,U_9093,U_9094) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

fof(f_2515_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infI1]) ).

fof(f_2515_2,plain,
    ! [U_9098,U_9097,U_9096,U_9095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9095),U_9096),U_9098)),U_9097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9095),U_9096),U_9097))
      | ~ class_Lattices_Osemilattice__inf(U_9095) ),
    inference(variable_rename,[status(thm)],[f_2515_1]) ).

fof(f_2515_3,plain,
    ! [U_9097,U_9098,U_9096,U_9095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9095),U_9096),U_9098)),U_9097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9095),U_9096),U_9097))
      | ~ class_Lattices_Osemilattice__inf(U_9095) ),
    inference(definitional_conversion,[status(esa)],[f_2515_2]) ).

cnf(f_2515_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9095),U_9096),U_9098)),U_9097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9095),U_9096),U_9097))
    | ~ class_Lattices_Osemilattice__inf(U_9095) ),
    inference(clausify,[status(thm)],[f_2515_3]) ).

fof(f_2516_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infI2]) ).

fof(f_2516_2,plain,
    ! [U_9102,U_9101,U_9100,U_9099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9099),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9099),U_9102),U_9100)),U_9101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9099),U_9100),U_9101))
      | ~ class_Lattices_Osemilattice__inf(U_9099) ),
    inference(variable_rename,[status(thm)],[f_2516_1]) ).

fof(f_2516_3,plain,
    ! [U_9102,U_9099,U_9100,U_9101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9099),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9099),U_9102),U_9100)),U_9101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9099),U_9100),U_9101))
      | ~ class_Lattices_Osemilattice__inf(U_9099) ),
    inference(definitional_conversion,[status(esa)],[f_2516_2]) ).

cnf(f_2516_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9099),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9099),U_9102),U_9100)),U_9101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9099),U_9100),U_9101))
    | ~ class_Lattices_Osemilattice__inf(U_9099) ),
    inference(clausify,[status(thm)],[f_2516_3]) ).

fof(f_2517_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__absorb1]) ).

fof(f_2517_2,plain,
    ! [U_9105,U_9104,U_9103] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9103),U_9104),U_9105) = U_9104
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9103),U_9104),U_9105))
      | ~ class_Lattices_Osemilattice__inf(U_9103) ),
    inference(variable_rename,[status(thm)],[f_2517_1]) ).

fof(f_2517_3,plain,
    ! [U_9103,U_9104,U_9105] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9103),U_9104),U_9105) = U_9104
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9103),U_9104),U_9105))
      | ~ class_Lattices_Osemilattice__inf(U_9103) ),
    inference(definitional_conversion,[status(esa)],[f_2517_2]) ).

cnf(f_2517_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9103),U_9104),U_9105) = U_9104
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9103),U_9104),U_9105))
    | ~ class_Lattices_Osemilattice__inf(U_9103) ),
    inference(clausify,[status(thm)],[f_2517_3]) ).

fof(f_2518_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__absorb2]) ).

fof(f_2518_2,plain,
    ! [U_9108,U_9107,U_9106] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9106),U_9108),U_9107) = U_9107
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9106),U_9107),U_9108))
      | ~ class_Lattices_Osemilattice__inf(U_9106) ),
    inference(variable_rename,[status(thm)],[f_2518_1]) ).

fof(f_2518_3,plain,
    ! [U_9106,U_9107,U_9108] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9106),U_9108),U_9107) = U_9107
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9106),U_9107),U_9108))
      | ~ class_Lattices_Osemilattice__inf(U_9106) ),
    inference(definitional_conversion,[status(esa)],[f_2518_2]) ).

cnf(f_2518_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9106),U_9108),U_9107) = U_9107
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9106),U_9107),U_9108))
    | ~ class_Lattices_Osemilattice__inf(U_9106) ),
    inference(clausify,[status(thm)],[f_2518_3]) ).

fof(f_2519_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infI]) ).

fof(f_2519_2,plain,
    ! [U_9112,U_9111,U_9110,U_9109] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9109),U_9111),U_9112)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),U_9112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),U_9111))
      | ~ class_Lattices_Osemilattice__inf(U_9109) ),
    inference(variable_rename,[status(thm)],[f_2519_1]) ).

fof(f_2519_3,plain,
    ! [U_9109,U_9110,U_9111,U_9112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9109),U_9111),U_9112)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),U_9112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),U_9111))
      | ~ class_Lattices_Osemilattice__inf(U_9109) ),
    inference(definitional_conversion,[status(esa)],[f_2519_2]) ).

cnf(f_2519_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9109),U_9111),U_9112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),U_9112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9109),U_9110),U_9111))
    | ~ class_Lattices_Osemilattice__inf(U_9109) ),
    inference(clausify,[status(thm)],[f_2519_3]) ).

fof(f_2520_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__greatest]) ).

fof(f_2520_2,plain,
    ! [U_9116,U_9115,U_9114,U_9113] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9113),U_9115),U_9116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),U_9116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),U_9115))
      | ~ class_Lattices_Osemilattice__inf(U_9113) ),
    inference(variable_rename,[status(thm)],[f_2520_1]) ).

fof(f_2520_3,plain,
    ! [U_9113,U_9114,U_9115,U_9116] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9113),U_9115),U_9116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),U_9116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),U_9115))
      | ~ class_Lattices_Osemilattice__inf(U_9113) ),
    inference(definitional_conversion,[status(esa)],[f_2520_2]) ).

cnf(f_2520_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9113),U_9115),U_9116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),U_9116))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9113),U_9114),U_9115))
    | ~ class_Lattices_Osemilattice__inf(U_9113) ),
    inference(clausify,[status(thm)],[f_2520_3]) ).

fof(f_2521_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__mono]) ).

fof(f_2521_2,plain,
    ! [U_9121,U_9120,U_9119,U_9118,U_9117] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9117),U_9118),U_9120)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9117),U_9119),U_9121)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),U_9120),U_9121))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),U_9118),U_9119))
      | ~ class_Lattices_Osemilattice__inf(U_9117) ),
    inference(variable_rename,[status(thm)],[f_2521_1]) ).

fof(f_2521_3,plain,
    ! [U_9117,U_9118,U_9119,U_9120,U_9121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9117),U_9118),U_9120)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9117),U_9119),U_9121)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),U_9120),U_9121))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),U_9118),U_9119))
      | ~ class_Lattices_Osemilattice__inf(U_9117) ),
    inference(definitional_conversion,[status(esa)],[f_2521_2]) ).

cnf(f_2521_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9117),U_9118),U_9120)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9117),U_9119),U_9121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),U_9120),U_9121))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9117),U_9118),U_9119))
    | ~ class_Lattices_Osemilattice__inf(U_9117) ),
    inference(clausify,[status(thm)],[f_2521_3]) ).

fof(f_2522_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infE]) ).

fof(f_2522_2,plain,
    ! [U_9125,U_9124,U_9123,U_9122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),U_9125))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),U_9124)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9122),U_9124),U_9125)))
      | ~ class_Lattices_Osemilattice__inf(U_9122) ),
    inference(variable_rename,[status(thm)],[f_2522_1]) ).

fof(f_2522_3,plain,
    ( ! [U_9122,U_9123,U_9124,U_9125] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),U_9125))
        | ~ sP747(U_9122,U_9123,U_9124,U_9125) )
    & ! [U_9122,U_9123,U_9124,U_9125] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),U_9124))
        | ~ sP747(U_9122,U_9123,U_9124,U_9125) )
    & ! [U_9122,U_9123,U_9124,U_9125] :
        ( sP747(U_9122,U_9123,U_9124,U_9125)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9122),U_9124),U_9125)))
        | ~ class_Lattices_Osemilattice__inf(U_9122) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP747])],[f_2522_2]) ).

cnf(f_2522_4,plain,
    ( sP747(U_9122,U_9123,U_9124,U_9125)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9122),U_9124),U_9125)))
    | ~ class_Lattices_Osemilattice__inf(U_9122) ),
    inference(clausify,[status(thm)],[f_2522_3]) ).

cnf(f_2522_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),U_9124))
    | ~ sP747(U_9122,U_9123,U_9124,U_9125) ),
    inference(clausify,[status(thm)],[f_2522_3]) ).

cnf(f_2522_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9122),U_9123),U_9125))
    | ~ sP747(U_9122,U_9123,U_9124,U_9125) ),
    inference(clausify,[status(thm)],[f_2522_3]) ).

fof(f_2523_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__infI1]) ).

fof(f_2523_2,plain,
    ! [U_9129,U_9128,U_9127,U_9126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9126),U_9127),U_9129)),U_9128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9126),U_9127),U_9128))
      | ~ class_Lattices_Osemilattice__inf(U_9126) ),
    inference(variable_rename,[status(thm)],[f_2523_1]) ).

fof(f_2523_3,plain,
    ! [U_9126,U_9127,U_9128,U_9129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9126),U_9127),U_9129)),U_9128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9126),U_9127),U_9128))
      | ~ class_Lattices_Osemilattice__inf(U_9126) ),
    inference(definitional_conversion,[status(esa)],[f_2523_2]) ).

cnf(f_2523_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9126),U_9127),U_9129)),U_9128))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9126),U_9127),U_9128))
    | ~ class_Lattices_Osemilattice__inf(U_9126) ),
    inference(clausify,[status(thm)],[f_2523_3]) ).

fof(f_2524_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__infI2]) ).

fof(f_2524_2,plain,
    ! [U_9133,U_9132,U_9131,U_9130] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9130),U_9133),U_9131)),U_9132))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9130),U_9131),U_9132))
      | ~ class_Lattices_Osemilattice__inf(U_9130) ),
    inference(variable_rename,[status(thm)],[f_2524_1]) ).

fof(f_2524_3,plain,
    ! [U_9130,U_9131,U_9132,U_9133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9130),U_9133),U_9131)),U_9132))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9130),U_9131),U_9132))
      | ~ class_Lattices_Osemilattice__inf(U_9130) ),
    inference(definitional_conversion,[status(esa)],[f_2524_2]) ).

cnf(f_2524_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9130),U_9133),U_9131)),U_9132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9130),U_9131),U_9132))
    | ~ class_Lattices_Osemilattice__inf(U_9130) ),
    inference(clausify,[status(thm)],[f_2524_3]) ).

fof(f_2525_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).

fof(f_2525_2,plain,
    ! [U_9137,U_9136,U_9135,U_9134] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),U_9136)),hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),U_9137)) = hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136),U_9137)),
    inference(variable_rename,[status(thm)],[f_2525_1]) ).

fof(f_2525_3,plain,
    ! [U_9134,U_9135,U_9136,U_9137] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),U_9136)),hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),U_9137)) = hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136),U_9137)),
    inference(definitional_conversion,[status(esa)],[f_2525_2]) ).

cnf(f_2525_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),U_9136)),hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),U_9137)) = hAPP(hAPP(c_Set_Oinsert(U_9134),U_9135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136),U_9137)),
    inference(clausify,[status(thm)],[f_2525_3]) ).

fof(f_2526_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__bot__left]) ).

fof(f_2526_2,plain,
    ! [U_9139,U_9138] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9138),c_Orderings_Obot__class_Obot(U_9138)),U_9139) = c_Orderings_Obot__class_Obot(U_9138)
      | ~ class_Lattices_Obounded__lattice__bot(U_9138) ),
    inference(variable_rename,[status(thm)],[f_2526_1]) ).

fof(f_2526_3,plain,
    ! [U_9138,U_9139] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9138),c_Orderings_Obot__class_Obot(U_9138)),U_9139) = c_Orderings_Obot__class_Obot(U_9138)
      | ~ class_Lattices_Obounded__lattice__bot(U_9138) ),
    inference(definitional_conversion,[status(esa)],[f_2526_2]) ).

cnf(f_2526_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9138),c_Orderings_Obot__class_Obot(U_9138)),U_9139) = c_Orderings_Obot__class_Obot(U_9138)
    | ~ class_Lattices_Obounded__lattice__bot(U_9138) ),
    inference(clausify,[status(thm)],[f_2526_3]) ).

fof(f_2527_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__bot__right]) ).

fof(f_2527_2,plain,
    ! [U_9141,U_9140] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9140),U_9141),c_Orderings_Obot__class_Obot(U_9140)) = c_Orderings_Obot__class_Obot(U_9140)
      | ~ class_Lattices_Obounded__lattice__bot(U_9140) ),
    inference(variable_rename,[status(thm)],[f_2527_1]) ).

fof(f_2527_3,plain,
    ! [U_9140,U_9141] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9140),U_9141),c_Orderings_Obot__class_Obot(U_9140)) = c_Orderings_Obot__class_Obot(U_9140)
      | ~ class_Lattices_Obounded__lattice__bot(U_9140) ),
    inference(definitional_conversion,[status(esa)],[f_2527_2]) ).

cnf(f_2527_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9140),U_9141),c_Orderings_Obot__class_Obot(U_9140)) = c_Orderings_Obot__class_Obot(U_9140)
    | ~ class_Lattices_Obounded__lattice__bot(U_9140) ),
    inference(clausify,[status(thm)],[f_2527_3]) ).

fof(f_2528_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Int__empty__left]) ).

fof(f_2528_2,plain,
    ! [U_9143,U_9142] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9142,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9142,tc_HOL_Obool))),U_9143) = c_Orderings_Obot__class_Obot(tc_fun(U_9142,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2528_1]) ).

fof(f_2528_3,plain,
    ! [U_9142,U_9143] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9142,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9142,tc_HOL_Obool))),U_9143) = c_Orderings_Obot__class_Obot(tc_fun(U_9142,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2528_2]) ).

cnf(f_2528_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9142,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9142,tc_HOL_Obool))),U_9143) = c_Orderings_Obot__class_Obot(tc_fun(U_9142,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2528_3]) ).

fof(f_2529_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Int__empty__right]) ).

fof(f_2529_2,plain,
    ! [U_9145,U_9144] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9144,tc_HOL_Obool)),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9144,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9144,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2529_1]) ).

fof(f_2529_3,plain,
    ! [U_9144,U_9145] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9144,tc_HOL_Obool)),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9144,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9144,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2529_2]) ).

cnf(f_2529_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9144,tc_HOL_Obool)),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9144,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9144,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2529_3]) ).

fof(f_2530_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( ? [B_xa] :
                ( B_x = B_xa
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( B_x != B_xa
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal]) ).

fof(f_2530_2,plain,
    ! [U_9152,U_9151,U_9150] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9150,tc_HOL_Obool)),U_9151),U_9152) = c_Orderings_Obot__class_Obot(tc_fun(U_9150,tc_HOL_Obool))
        | ? [U_9149] :
            ( ? [U_9148] :
                ( U_9149 = U_9148
                & hBOOL(hAPP(hAPP(c_member(U_9150),U_9148),U_9152)) )
            & hBOOL(hAPP(hAPP(c_member(U_9150),U_9149),U_9151)) ) )
      & ( ! [U_9147] :
            ( ! [U_9146] :
                ( U_9147 != U_9146
                | ~ hBOOL(hAPP(hAPP(c_member(U_9150),U_9146),U_9152)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9150),U_9147),U_9151)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9150,tc_HOL_Obool)),U_9151),U_9152) != c_Orderings_Obot__class_Obot(tc_fun(U_9150,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2530_1]) ).

fof(f_2530_3,plain,
    ( ! [U_9158,U_9156,U_9154] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,tc_HOL_Obool)),U_9156),U_9158) = c_Orderings_Obot__class_Obot(tc_fun(U_9154,tc_HOL_Obool))
        | ? [U_9149] :
            ( ? [U_9148] :
                ( U_9149 = U_9148
                & hBOOL(hAPP(hAPP(c_member(U_9154),U_9148),U_9158)) )
            & hBOOL(hAPP(hAPP(c_member(U_9154),U_9149),U_9156)) ) )
    & ! [U_9157,U_9155,U_9153] :
        ( ! [U_9147] :
            ( ! [U_9146] :
                ( U_9147 != U_9146
                | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9146),U_9157)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9147),U_9155)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9153,tc_HOL_Obool)),U_9155),U_9157) != c_Orderings_Obot__class_Obot(tc_fun(U_9153,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2530_2]) ).

fof(f_2530_4,plain,
    ( ! [U_9158,U_9156,U_9154] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,tc_HOL_Obool)),U_9156),U_9158) = c_Orderings_Obot__class_Obot(tc_fun(U_9154,tc_HOL_Obool))
        | ( ? [U_9148] :
              ( sK137(U_9158,U_9156,U_9154) = U_9148
              & hBOOL(hAPP(hAPP(c_member(U_9154),U_9148),U_9158)) )
          & hBOOL(hAPP(hAPP(c_member(U_9154),sK137(U_9158,U_9156,U_9154)),U_9156)) ) )
    & ! [U_9157,U_9155,U_9153] :
        ( ! [U_9147] :
            ( ! [U_9146] :
                ( U_9147 != U_9146
                | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9146),U_9157)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9147),U_9155)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9153,tc_HOL_Obool)),U_9155),U_9157) != c_Orderings_Obot__class_Obot(tc_fun(U_9153,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_9149,sK137(U_9158,U_9156,U_9154))],[f_2530_3]) ).

fof(f_2530_5,plain,
    ( ! [U_9158,U_9156,U_9154] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,tc_HOL_Obool)),U_9156),U_9158) = c_Orderings_Obot__class_Obot(tc_fun(U_9154,tc_HOL_Obool))
        | ( sK137(U_9158,U_9156,U_9154) = sK138(U_9158,U_9156,U_9154)
          & hBOOL(hAPP(hAPP(c_member(U_9154),sK138(U_9158,U_9156,U_9154)),U_9158))
          & hBOOL(hAPP(hAPP(c_member(U_9154),sK137(U_9158,U_9156,U_9154)),U_9156)) ) )
    & ! [U_9157,U_9155,U_9153] :
        ( ! [U_9147] :
            ( ! [U_9146] :
                ( U_9147 != U_9146
                | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9146),U_9157)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9147),U_9155)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9153,tc_HOL_Obool)),U_9155),U_9157) != c_Orderings_Obot__class_Obot(tc_fun(U_9153,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_9148,sK138(U_9158,U_9156,U_9154))],[f_2530_4]) ).

fof(f_2530_6,plain,
    ( ! [U_9158,U_9154,U_9156] :
        ( sK137(U_9158,U_9156,U_9154) = sK138(U_9158,U_9156,U_9154)
        | ~ sP748(U_9158,U_9154,U_9156) )
    & ! [U_9158,U_9154,U_9156] :
        ( hBOOL(hAPP(hAPP(c_member(U_9154),sK138(U_9158,U_9156,U_9154)),U_9158))
        | ~ sP748(U_9158,U_9154,U_9156) )
    & ! [U_9158,U_9154,U_9156] :
        ( hBOOL(hAPP(hAPP(c_member(U_9154),sK137(U_9158,U_9156,U_9154)),U_9156))
        | ~ sP748(U_9158,U_9154,U_9156) )
    & ! [U_9158,U_9154,U_9156] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,tc_HOL_Obool)),U_9156),U_9158) = c_Orderings_Obot__class_Obot(tc_fun(U_9154,tc_HOL_Obool))
        | sP748(U_9158,U_9154,U_9156) )
    & ! [U_9157,U_9146,U_9147,U_9153,U_9155] :
        ( U_9147 != U_9146
        | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9146),U_9157))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9147),U_9155))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9153,tc_HOL_Obool)),U_9155),U_9157) != c_Orderings_Obot__class_Obot(tc_fun(U_9153,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP748])],[f_2530_5]) ).

cnf(f_2530_7,plain,
    ( U_9147 != U_9146
    | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9146),U_9157))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9153),U_9147),U_9155))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9153,tc_HOL_Obool)),U_9155),U_9157) != c_Orderings_Obot__class_Obot(tc_fun(U_9153,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2530_6]) ).

cnf(f_2530_8,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9154,tc_HOL_Obool)),U_9156),U_9158) = c_Orderings_Obot__class_Obot(tc_fun(U_9154,tc_HOL_Obool))
    | sP748(U_9158,U_9154,U_9156) ),
    inference(clausify,[status(thm)],[f_2530_6]) ).

cnf(f_2530_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9154),sK137(U_9158,U_9156,U_9154)),U_9156))
    | ~ sP748(U_9158,U_9154,U_9156) ),
    inference(clausify,[status(thm)],[f_2530_6]) ).

cnf(f_2530_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9154),sK138(U_9158,U_9156,U_9154)),U_9158))
    | ~ sP748(U_9158,U_9154,U_9156) ),
    inference(clausify,[status(thm)],[f_2530_6]) ).

cnf(f_2530_11,plain,
    ( sK137(U_9158,U_9156,U_9154) = sK138(U_9158,U_9156,U_9154)
    | ~ sP748(U_9158,U_9154,U_9156) ),
    inference(clausify,[status(thm)],[f_2530_6]) ).

fof(f_2531_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntD2]) ).

fof(f_2531_2,plain,
    ! [U_9162,U_9161,U_9160,U_9159] :
      ( hBOOL(hAPP(hAPP(c_member(U_9159),U_9160),U_9162))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9159),U_9160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9159,tc_HOL_Obool)),U_9161),U_9162))) ),
    inference(variable_rename,[status(thm)],[f_2531_1]) ).

fof(f_2531_3,plain,
    ! [U_9160,U_9162,U_9161,U_9159] :
      ( hBOOL(hAPP(hAPP(c_member(U_9159),U_9160),U_9162))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9159),U_9160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9159,tc_HOL_Obool)),U_9161),U_9162))) ),
    inference(definitional_conversion,[status(esa)],[f_2531_2]) ).

cnf(f_2531_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9159),U_9160),U_9162))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9159),U_9160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9159,tc_HOL_Obool)),U_9161),U_9162))) ),
    inference(clausify,[status(thm)],[f_2531_3]) ).

fof(f_2532_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntD1]) ).

fof(f_2532_2,plain,
    ! [U_9166,U_9165,U_9164,U_9163] :
      ( hBOOL(hAPP(hAPP(c_member(U_9163),U_9164),U_9165))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9163),U_9164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9163,tc_HOL_Obool)),U_9165),U_9166))) ),
    inference(variable_rename,[status(thm)],[f_2532_1]) ).

fof(f_2532_3,plain,
    ! [U_9163,U_9164,U_9165,U_9166] :
      ( hBOOL(hAPP(hAPP(c_member(U_9163),U_9164),U_9165))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9163),U_9164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9163,tc_HOL_Obool)),U_9165),U_9166))) ),
    inference(definitional_conversion,[status(esa)],[f_2532_2]) ).

cnf(f_2532_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9163),U_9164),U_9165))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9163),U_9164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9163,tc_HOL_Obool)),U_9165),U_9166))) ),
    inference(clausify,[status(thm)],[f_2532_3]) ).

fof(f_2533_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).

fof(f_2533_2,plain,
    ! [U_9170,U_9169,U_9168,U_9167] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9167),U_9168),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9167,tc_HOL_Obool)),U_9169),U_9170)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9167),U_9168),U_9170))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9167),U_9168),U_9169)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_9167),U_9168),U_9170))
          & hBOOL(hAPP(hAPP(c_member(U_9167),U_9168),U_9169)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9167),U_9168),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9167,tc_HOL_Obool)),U_9169),U_9170))) ) ),
    inference(variable_rename,[status(thm)],[f_2533_1]) ).

fof(f_2533_3,plain,
    ( ! [U_9178,U_9176,U_9174,U_9172] :
        ( hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9172,tc_HOL_Obool)),U_9176),U_9178)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9178))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9176)) )
    & ! [U_9177,U_9175,U_9173,U_9171] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),U_9177))
          & hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),U_9175)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9171,tc_HOL_Obool)),U_9175),U_9177))) ) ),
    inference(miniscope,[status(thm)],[f_2533_2]) ).

fof(f_2533_4,plain,
    ( ! [U_9173,U_9177,U_9171,U_9175] :
        ( hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),U_9177))
        | ~ sP749(U_9173,U_9177,U_9171,U_9175) )
    & ! [U_9173,U_9177,U_9171,U_9175] :
        ( hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),U_9175))
        | ~ sP749(U_9173,U_9177,U_9171,U_9175) )
    & ! [U_9174,U_9172,U_9178,U_9176] :
        ( hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9172,tc_HOL_Obool)),U_9176),U_9178)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9178))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9176)) )
    & ! [U_9173,U_9177,U_9171,U_9175] :
        ( sP749(U_9173,U_9177,U_9171,U_9175)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9171,tc_HOL_Obool)),U_9175),U_9177))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP749])],[f_2533_3]) ).

cnf(f_2533_5,plain,
    ( sP749(U_9173,U_9177,U_9171,U_9175)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9171,tc_HOL_Obool)),U_9175),U_9177))) ),
    inference(clausify,[status(thm)],[f_2533_4]) ).

cnf(f_2533_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9172,tc_HOL_Obool)),U_9176),U_9178)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9178))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9176)) ),
    inference(clausify,[status(thm)],[f_2533_4]) ).

cnf(f_2533_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),U_9175))
    | ~ sP749(U_9173,U_9177,U_9171,U_9175) ),
    inference(clausify,[status(thm)],[f_2533_4]) ).

cnf(f_2533_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9171),U_9173),U_9177))
    | ~ sP749(U_9173,U_9177,U_9171,U_9175) ),
    inference(clausify,[status(thm)],[f_2533_4]) ).

fof(f_2534_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__crazy]) ).

fof(f_2534_2,plain,
    ! [U_9182,U_9181,U_9180,U_9179] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9180),U_9181)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9181),U_9182))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9182),U_9180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9180),U_9181)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9181),U_9182))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9182),U_9180)),
    inference(variable_rename,[status(thm)],[f_2534_1]) ).

fof(f_2534_3,plain,
    ! [U_9179,U_9180,U_9181,U_9182] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9180),U_9181)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9181),U_9182))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9182),U_9180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9180),U_9181)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9181),U_9182))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9182),U_9180)),
    inference(definitional_conversion,[status(esa)],[f_2534_2]) ).

cnf(f_2534_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9180),U_9181)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9181),U_9182))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),U_9182),U_9180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9179,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9180),U_9181)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9181),U_9182))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9179,tc_HOL_Obool)),U_9182),U_9180)),
    inference(clausify,[status(thm)],[f_2534_3]) ).

fof(f_2535_1,plain,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(f_2535_2,plain,
    ! [U_9186,U_9185,U_9184,U_9183] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9183,tc_HOL_Obool)),U_9184),U_9185)),U_9186) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),U_9184),U_9186)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),U_9185),U_9186)),
    inference(variable_rename,[status(thm)],[f_2535_1]) ).

fof(f_2535_3,plain,
    ! [U_9184,U_9185,U_9183,U_9186] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9183,tc_HOL_Obool)),U_9184),U_9185)),U_9186) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),U_9184),U_9186)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),U_9185),U_9186)),
    inference(definitional_conversion,[status(esa)],[f_2535_2]) ).

cnf(f_2535_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9183,tc_HOL_Obool)),U_9184),U_9185)),U_9186) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9183,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),U_9184),U_9186)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9183,tc_HOL_Obool)),U_9185),U_9186)),
    inference(clausify,[status(thm)],[f_2535_3]) ).

fof(f_2536_1,plain,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(f_2536_2,plain,
    ! [U_9190,U_9189,U_9188,U_9187] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9187,tc_HOL_Obool)),U_9188),U_9189)),U_9190) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9187,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),U_9188),U_9190)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),U_9189),U_9190)),
    inference(variable_rename,[status(thm)],[f_2536_1]) ).

fof(f_2536_3,plain,
    ! [U_9187,U_9188,U_9189,U_9190] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9187,tc_HOL_Obool)),U_9188),U_9189)),U_9190) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9187,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),U_9188),U_9190)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),U_9189),U_9190)),
    inference(definitional_conversion,[status(esa)],[f_2536_2]) ).

cnf(f_2536_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9187,tc_HOL_Obool)),U_9188),U_9189)),U_9190) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9187,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),U_9188),U_9190)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9187,tc_HOL_Obool)),U_9189),U_9190)),
    inference(clausify,[status(thm)],[f_2536_3]) ).

fof(f_2537_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib]) ).

fof(f_2537_2,plain,
    ! [U_9194,U_9193,U_9192,U_9191] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9191,tc_HOL_Obool)),U_9193),U_9194)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9191,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),U_9193)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),U_9194)),
    inference(variable_rename,[status(thm)],[f_2537_1]) ).

fof(f_2537_3,plain,
    ! [U_9191,U_9192,U_9193,U_9194] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9191,tc_HOL_Obool)),U_9193),U_9194)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9191,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),U_9193)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),U_9194)),
    inference(definitional_conversion,[status(esa)],[f_2537_2]) ).

cnf(f_2537_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9191,tc_HOL_Obool)),U_9193),U_9194)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9191,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),U_9193)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9191,tc_HOL_Obool)),U_9192),U_9194)),
    inference(clausify,[status(thm)],[f_2537_3]) ).

fof(f_2538_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib]) ).

fof(f_2538_2,plain,
    ! [U_9198,U_9197,U_9196,U_9195] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9195,tc_HOL_Obool)),U_9197),U_9198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9195,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9197)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9198)),
    inference(variable_rename,[status(thm)],[f_2538_1]) ).

fof(f_2538_3,plain,
    ! [U_9195,U_9196,U_9197,U_9198] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9195,tc_HOL_Obool)),U_9197),U_9198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9195,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9197)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9198)),
    inference(definitional_conversion,[status(esa)],[f_2538_2]) ).

cnf(f_2538_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9195,tc_HOL_Obool)),U_9197),U_9198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9195,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9197)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9198)),
    inference(clausify,[status(thm)],[f_2538_3]) ).

fof(f_2539_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2]) ).

fof(f_2539_2,plain,
    ! [U_9202,U_9201,U_9200,U_9199] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9199),U_9200),U_9201)),U_9202) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),U_9200),U_9202)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),U_9201),U_9202))
      | ~ class_Lattices_Odistrib__lattice(U_9199) ),
    inference(variable_rename,[status(thm)],[f_2539_1]) ).

fof(f_2539_3,plain,
    ! [U_9199,U_9200,U_9201,U_9202] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9199),U_9200),U_9201)),U_9202) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),U_9200),U_9202)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),U_9201),U_9202))
      | ~ class_Lattices_Odistrib__lattice(U_9199) ),
    inference(definitional_conversion,[status(esa)],[f_2539_2]) ).

cnf(f_2539_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9199),U_9200),U_9201)),U_9202) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),U_9200),U_9202)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9199),U_9201),U_9202))
    | ~ class_Lattices_Odistrib__lattice(U_9199) ),
    inference(clausify,[status(thm)],[f_2539_3]) ).

fof(f_2540_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2]) ).

fof(f_2540_2,plain,
    ! [U_9206,U_9205,U_9204,U_9203] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9203),U_9204),U_9205)),U_9206) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),U_9204),U_9206)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),U_9205),U_9206))
      | ~ class_Lattices_Odistrib__lattice(U_9203) ),
    inference(variable_rename,[status(thm)],[f_2540_1]) ).

fof(f_2540_3,plain,
    ! [U_9203,U_9204,U_9205,U_9206] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9203),U_9204),U_9205)),U_9206) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),U_9204),U_9206)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),U_9205),U_9206))
      | ~ class_Lattices_Odistrib__lattice(U_9203) ),
    inference(definitional_conversion,[status(esa)],[f_2540_2]) ).

cnf(f_2540_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9203),U_9204),U_9205)),U_9206) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),U_9204),U_9206)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9203),U_9205),U_9206))
    | ~ class_Lattices_Odistrib__lattice(U_9203) ),
    inference(clausify,[status(thm)],[f_2540_3]) ).

fof(f_2541_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1]) ).

fof(f_2541_2,plain,
    ! [U_9210,U_9209,U_9208,U_9207] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9207),U_9209),U_9210)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9207),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),U_9209)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),U_9210))
      | ~ class_Lattices_Odistrib__lattice(U_9207) ),
    inference(variable_rename,[status(thm)],[f_2541_1]) ).

fof(f_2541_3,plain,
    ! [U_9207,U_9208,U_9209,U_9210] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9207),U_9209),U_9210)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9207),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),U_9209)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),U_9210))
      | ~ class_Lattices_Odistrib__lattice(U_9207) ),
    inference(definitional_conversion,[status(esa)],[f_2541_2]) ).

cnf(f_2541_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9207),U_9209),U_9210)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9207),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),U_9209)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9207),U_9208),U_9210))
    | ~ class_Lattices_Odistrib__lattice(U_9207) ),
    inference(clausify,[status(thm)],[f_2541_3]) ).

fof(f_2542_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1]) ).

fof(f_2542_2,plain,
    ! [U_9214,U_9213,U_9212,U_9211] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9211),U_9213),U_9214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),U_9213)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),U_9214))
      | ~ class_Lattices_Odistrib__lattice(U_9211) ),
    inference(variable_rename,[status(thm)],[f_2542_1]) ).

fof(f_2542_3,plain,
    ! [U_9211,U_9212,U_9213,U_9214] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9211),U_9213),U_9214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),U_9213)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),U_9214))
      | ~ class_Lattices_Odistrib__lattice(U_9211) ),
    inference(definitional_conversion,[status(esa)],[f_2542_2]) ).

cnf(f_2542_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9211),U_9213),U_9214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),U_9213)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9211),U_9212),U_9214))
    | ~ class_Lattices_Odistrib__lattice(U_9211) ),
    inference(clausify,[status(thm)],[f_2542_3]) ).

fof(f_2543_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb]) ).

fof(f_2543_2,plain,
    ! [U_9217,U_9216,U_9215] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9215),U_9216),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9215),U_9216),U_9217)) = U_9216
      | ~ class_Lattices_Olattice(U_9215) ),
    inference(variable_rename,[status(thm)],[f_2543_1]) ).

fof(f_2543_3,plain,
    ! [U_9215,U_9216,U_9217] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9215),U_9216),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9215),U_9216),U_9217)) = U_9216
      | ~ class_Lattices_Olattice(U_9215) ),
    inference(definitional_conversion,[status(esa)],[f_2543_2]) ).

cnf(f_2543_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9215),U_9216),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9215),U_9216),U_9217)) = U_9216
    | ~ class_Lattices_Olattice(U_9215) ),
    inference(clausify,[status(thm)],[f_2543_3]) ).

fof(f_2544_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb]) ).

fof(f_2544_2,plain,
    ! [U_9220,U_9219,U_9218] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9218),U_9219),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9218),U_9219),U_9220)) = U_9219
      | ~ class_Lattices_Olattice(U_9218) ),
    inference(variable_rename,[status(thm)],[f_2544_1]) ).

fof(f_2544_3,plain,
    ! [U_9218,U_9219,U_9220] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9218),U_9219),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9218),U_9219),U_9220)) = U_9219
      | ~ class_Lattices_Olattice(U_9218) ),
    inference(definitional_conversion,[status(esa)],[f_2544_2]) ).

cnf(f_2544_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9218),U_9219),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9218),U_9219),U_9220)) = U_9219
    | ~ class_Lattices_Olattice(U_9218) ),
    inference(clausify,[status(thm)],[f_2544_3]) ).

fof(f_2545_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).

fof(f_2545_2,plain,
    ! [U_9224,U_9223,U_9222,U_9221] :
      ( hBOOL(hAPP(U_9223,U_9224))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9221,tc_HOL_Obool)),U_9222),U_9223),U_9224)) ),
    inference(variable_rename,[status(thm)],[f_2545_1]) ).

fof(f_2545_3,plain,
    ! [U_9224,U_9223] :
      ( ! [U_9222,U_9221] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9221,tc_HOL_Obool)),U_9222),U_9223),U_9224))
      | hBOOL(hAPP(U_9223,U_9224)) ),
    inference(miniscope,[status(thm)],[f_2545_2]) ).

fof(f_2545_4,plain,
    ! [U_9221,U_9222,U_9223,U_9224] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9221,tc_HOL_Obool)),U_9222),U_9223),U_9224))
      | hBOOL(hAPP(U_9223,U_9224)) ),
    inference(definitional_conversion,[status(esa)],[f_2545_3]) ).

cnf(f_2545_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9221,tc_HOL_Obool)),U_9222),U_9223),U_9224))
    | hBOOL(hAPP(U_9223,U_9224)) ),
    inference(clausify,[status(thm)],[f_2545_4]) ).

fof(f_2546_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).

fof(f_2546_2,plain,
    ! [U_9228,U_9227,U_9226,U_9225] :
      ( hBOOL(hAPP(U_9226,U_9228))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9225,tc_HOL_Obool)),U_9226),U_9227),U_9228)) ),
    inference(variable_rename,[status(thm)],[f_2546_1]) ).

fof(f_2546_3,plain,
    ! [U_9228,U_9227,U_9226] :
      ( ! [U_9225] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9225,tc_HOL_Obool)),U_9226),U_9227),U_9228))
      | hBOOL(hAPP(U_9226,U_9228)) ),
    inference(miniscope,[status(thm)],[f_2546_2]) ).

fof(f_2546_4,plain,
    ! [U_9225,U_9226,U_9227,U_9228] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9225,tc_HOL_Obool)),U_9226),U_9227),U_9228))
      | hBOOL(hAPP(U_9226,U_9228)) ),
    inference(definitional_conversion,[status(esa)],[f_2546_3]) ).

cnf(f_2546_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9225,tc_HOL_Obool)),U_9226),U_9227),U_9228))
    | hBOOL(hAPP(U_9226,U_9228)) ),
    inference(clausify,[status(thm)],[f_2546_4]) ).

fof(f_2547_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int2]) ).

fof(f_2547_2,plain,
    ! [U_9232,U_9231,U_9230,U_9229] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9229,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9230),U_9231)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9232),U_9231)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9229,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9230),U_9231)),U_9232),
    inference(variable_rename,[status(thm)],[f_2547_1]) ).

fof(f_2547_3,plain,
    ! [U_9229,U_9230,U_9231,U_9232] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9229,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9230),U_9231)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9232),U_9231)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9229,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9230),U_9231)),U_9232),
    inference(definitional_conversion,[status(esa)],[f_2547_2]) ).

cnf(f_2547_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9229,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9230),U_9231)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9232),U_9231)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9229,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9229,tc_HOL_Obool)),U_9230),U_9231)),U_9232),
    inference(clausify,[status(thm)],[f_2547_3]) ).

fof(f_2548_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(f_2548_2,plain,
    ! [U_9236,U_9235,U_9234,U_9233] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9233,tc_HOL_Obool)),U_9234),U_9235)),U_9236) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9233,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),U_9234),U_9236)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),U_9235),U_9236)),
    inference(variable_rename,[status(thm)],[f_2548_1]) ).

fof(f_2548_3,plain,
    ! [U_9233,U_9234,U_9235,U_9236] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9233,tc_HOL_Obool)),U_9234),U_9235)),U_9236) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9233,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),U_9234),U_9236)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),U_9235),U_9236)),
    inference(definitional_conversion,[status(esa)],[f_2548_2]) ).

cnf(f_2548_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9233,tc_HOL_Obool)),U_9234),U_9235)),U_9236) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9233,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),U_9234),U_9236)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9233,tc_HOL_Obool)),U_9235),U_9236)),
    inference(clausify,[status(thm)],[f_2548_3]) ).

fof(f_2549_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Diff]) ).

fof(f_2549_2,plain,
    ! [U_9240,U_9239,U_9238,U_9237] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9237,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9237,tc_HOL_Obool)),U_9238),U_9239)),U_9240) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9237,tc_HOL_Obool)),U_9239),U_9240)),
    inference(variable_rename,[status(thm)],[f_2549_1]) ).

fof(f_2549_3,plain,
    ! [U_9237,U_9238,U_9239,U_9240] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9237,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9237,tc_HOL_Obool)),U_9238),U_9239)),U_9240) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9237,tc_HOL_Obool)),U_9239),U_9240)),
    inference(definitional_conversion,[status(esa)],[f_2549_2]) ).

cnf(f_2549_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9237,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9237,tc_HOL_Obool)),U_9238),U_9239)),U_9240) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9237,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9237,tc_HOL_Obool)),U_9239),U_9240)),
    inference(clausify,[status(thm)],[f_2549_3]) ).

fof(f_2550_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(f_2550_2,plain,
    ! [U_9244,U_9243,U_9242,U_9241] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9241,tc_HOL_Obool)),U_9243),U_9244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9241,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9243)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9244)),
    inference(variable_rename,[status(thm)],[f_2550_1]) ).

fof(f_2550_3,plain,
    ! [U_9241,U_9242,U_9243,U_9244] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9241,tc_HOL_Obool)),U_9243),U_9244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9241,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9243)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9244)),
    inference(definitional_conversion,[status(esa)],[f_2550_2]) ).

cnf(f_2550_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9241,tc_HOL_Obool)),U_9243),U_9244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9241,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9243)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9244)),
    inference(clausify,[status(thm)],[f_2550_3]) ).

fof(f_2551_1,plain,
    ! [T_b] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__min]) ).

fof(f_2551_2,plain,
    ! [U_9245] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_9245) = c_Orderings_Oord__class_Omin(U_9245)
      | ~ class_Orderings_Olinorder(U_9245)
      | ~ class_Lattices_Osemilattice__inf(U_9245) ),
    inference(variable_rename,[status(thm)],[f_2551_1]) ).

fof(f_2551_3,plain,
    ! [U_9245] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_9245) = c_Orderings_Oord__class_Omin(U_9245)
      | ~ class_Orderings_Olinorder(U_9245)
      | ~ class_Lattices_Osemilattice__inf(U_9245) ),
    inference(definitional_conversion,[status(esa)],[f_2551_2]) ).

cnf(f_2551_4,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(U_9245) = c_Orderings_Oord__class_Omin(U_9245)
    | ~ class_Orderings_Olinorder(U_9245)
    | ~ class_Lattices_Osemilattice__inf(U_9245) ),
    inference(clausify,[status(thm)],[f_2551_3]) ).

fof(f_2552_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).

fof(f_2552_2,plain,
    ! [U_9250,U_9249,U_9248,U_9247,U_9246] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9247,U_9246)),U_9248),U_9249),U_9250) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9246),hAPP(U_9248,U_9250)),hAPP(U_9249,U_9250))
      | ~ class_Lattices_Olattice(U_9246) ),
    inference(variable_rename,[status(thm)],[f_2552_1]) ).

fof(f_2552_3,plain,
    ! [U_9246,U_9247,U_9248,U_9249,U_9250] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9247,U_9246)),U_9248),U_9249),U_9250) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9246),hAPP(U_9248,U_9250)),hAPP(U_9249,U_9250))
      | ~ class_Lattices_Olattice(U_9246) ),
    inference(definitional_conversion,[status(esa)],[f_2552_2]) ).

cnf(f_2552_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9247,U_9246)),U_9248),U_9249),U_9250) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9246),hAPP(U_9248,U_9250)),hAPP(U_9249,U_9250))
    | ~ class_Lattices_Olattice(U_9246) ),
    inference(clausify,[status(thm)],[f_2552_3]) ).

fof(f_2553_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).

fof(f_2553_2,plain,
    ! [U_9254,U_9253,U_9252,U_9251] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9252),U_9253)),U_9254) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9253),U_9254)),
    inference(variable_rename,[status(thm)],[f_2553_1]) ).

fof(f_2553_3,plain,
    ! [U_9251,U_9252,U_9253,U_9254] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9252),U_9253)),U_9254) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9253),U_9254)),
    inference(definitional_conversion,[status(esa)],[f_2553_2]) ).

cnf(f_2553_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9252),U_9253)),U_9254) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9251,tc_HOL_Obool)),U_9253),U_9254)),
    inference(clausify,[status(thm)],[f_2553_3]) ).

fof(f_2554_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).

fof(f_2554_2,plain,
    ! [U_9258,U_9257,U_9256,U_9255] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9257),U_9258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9258)),
    inference(variable_rename,[status(thm)],[f_2554_1]) ).

fof(f_2554_3,plain,
    ! [U_9255,U_9256,U_9257,U_9258] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9257),U_9258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9258)),
    inference(definitional_conversion,[status(esa)],[f_2554_2]) ).

cnf(f_2554_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9257),U_9258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9258)),
    inference(clausify,[status(thm)],[f_2554_3]) ).

fof(f_2555_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).

fof(f_2555_2,plain,
    ! [U_9261,U_9260,U_9259] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),U_9261)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),U_9261),
    inference(variable_rename,[status(thm)],[f_2555_1]) ).

fof(f_2555_3,plain,
    ! [U_9259,U_9260,U_9261] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),U_9261)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),U_9261),
    inference(definitional_conversion,[status(esa)],[f_2555_2]) ).

cnf(f_2555_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),U_9261)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9259,tc_HOL_Obool)),U_9260),U_9261),
    inference(clausify,[status(thm)],[f_2555_3]) ).

fof(f_2556_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).

fof(f_2556_2,plain,
    ! [U_9264,U_9263,U_9262] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9262,tc_HOL_Obool)),U_9263),U_9264) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9262,tc_HOL_Obool)),U_9264),U_9263),
    inference(variable_rename,[status(thm)],[f_2556_1]) ).

fof(f_2556_3,plain,
    ! [U_9262,U_9263,U_9264] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9262,tc_HOL_Obool)),U_9263),U_9264) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9262,tc_HOL_Obool)),U_9264),U_9263),
    inference(definitional_conversion,[status(esa)],[f_2556_2]) ).

cnf(f_2556_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9262,tc_HOL_Obool)),U_9263),U_9264) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9262,tc_HOL_Obool)),U_9264),U_9263),
    inference(clausify,[status(thm)],[f_2556_3]) ).

fof(f_2557_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).

fof(f_2557_2,plain,
    ! [U_9266,U_9265] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9265,tc_HOL_Obool)),U_9266),U_9266) = U_9266,
    inference(variable_rename,[status(thm)],[f_2557_1]) ).

fof(f_2557_3,plain,
    ! [U_9265,U_9266] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9265,tc_HOL_Obool)),U_9266),U_9266) = U_9266,
    inference(definitional_conversion,[status(esa)],[f_2557_2]) ).

cnf(f_2557_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9265,tc_HOL_Obool)),U_9266),U_9266) = U_9266,
    inference(clausify,[status(thm)],[f_2557_3]) ).

fof(f_2558_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).

fof(f_2558_2,plain,
    ! [U_9271,U_9270,U_9269,U_9268,U_9267] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9268,U_9267)),U_9269),U_9270),U_9271) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9267),hAPP(U_9269,U_9271)),hAPP(U_9270,U_9271))
      | ~ class_Lattices_Olattice(U_9267) ),
    inference(variable_rename,[status(thm)],[f_2558_1]) ).

fof(f_2558_3,plain,
    ! [U_9267,U_9268,U_9269,U_9270,U_9271] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9268,U_9267)),U_9269),U_9270),U_9271) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9267),hAPP(U_9269,U_9271)),hAPP(U_9270,U_9271))
      | ~ class_Lattices_Olattice(U_9267) ),
    inference(definitional_conversion,[status(esa)],[f_2558_2]) ).

cnf(f_2558_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9268,U_9267)),U_9269),U_9270),U_9271) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9267),hAPP(U_9269,U_9271)),hAPP(U_9270,U_9271))
    | ~ class_Lattices_Olattice(U_9267) ),
    inference(clausify,[status(thm)],[f_2558_3]) ).

fof(f_2559_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__assoc]) ).

fof(f_2559_2,plain,
    ! [U_9275,U_9274,U_9273,U_9272] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9273),U_9274)),U_9275) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9273),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9274),U_9275))
      | ~ class_Lattices_Osemilattice__inf(U_9272) ),
    inference(variable_rename,[status(thm)],[f_2559_1]) ).

fof(f_2559_3,plain,
    ! [U_9272,U_9273,U_9274,U_9275] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9273),U_9274)),U_9275) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9273),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9274),U_9275))
      | ~ class_Lattices_Osemilattice__inf(U_9272) ),
    inference(definitional_conversion,[status(esa)],[f_2559_2]) ).

cnf(f_2559_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9273),U_9274)),U_9275) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9273),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9272),U_9274),U_9275))
    | ~ class_Lattices_Osemilattice__inf(U_9272) ),
    inference(clausify,[status(thm)],[f_2559_3]) ).

fof(f_2560_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J]) ).

fof(f_2560_2,plain,
    ! [U_9279,U_9278,U_9277,U_9276] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9277),U_9278)),U_9279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9278),U_9279))
      | ~ class_Lattices_Olattice(U_9276) ),
    inference(variable_rename,[status(thm)],[f_2560_1]) ).

fof(f_2560_3,plain,
    ! [U_9276,U_9277,U_9278,U_9279] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9277),U_9278)),U_9279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9278),U_9279))
      | ~ class_Lattices_Olattice(U_9276) ),
    inference(definitional_conversion,[status(esa)],[f_2560_2]) ).

cnf(f_2560_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9277),U_9278)),U_9279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9276),U_9278),U_9279))
    | ~ class_Lattices_Olattice(U_9276) ),
    inference(clausify,[status(thm)],[f_2560_3]) ).

fof(f_2561_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oassoc]) ).

fof(f_2561_2,plain,
    ! [U_9283,U_9282,U_9281,U_9280] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9281),U_9282)),U_9283) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9281),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9282),U_9283))
      | ~ class_Lattices_Osemilattice__inf(U_9280) ),
    inference(variable_rename,[status(thm)],[f_2561_1]) ).

fof(f_2561_3,plain,
    ! [U_9280,U_9281,U_9282,U_9283] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9281),U_9282)),U_9283) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9281),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9282),U_9283))
      | ~ class_Lattices_Osemilattice__inf(U_9280) ),
    inference(definitional_conversion,[status(esa)],[f_2561_2]) ).

cnf(f_2561_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9281),U_9282)),U_9283) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9281),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9280),U_9282),U_9283))
    | ~ class_Lattices_Osemilattice__inf(U_9280) ),
    inference(clausify,[status(thm)],[f_2561_3]) ).

fof(f_2562_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__left__commute]) ).

fof(f_2562_2,plain,
    ! [U_9287,U_9286,U_9285,U_9284] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9285),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9286),U_9287)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9286),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9285),U_9287))
      | ~ class_Lattices_Osemilattice__inf(U_9284) ),
    inference(variable_rename,[status(thm)],[f_2562_1]) ).

fof(f_2562_3,plain,
    ! [U_9284,U_9285,U_9286,U_9287] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9285),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9286),U_9287)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9286),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9285),U_9287))
      | ~ class_Lattices_Osemilattice__inf(U_9284) ),
    inference(definitional_conversion,[status(esa)],[f_2562_2]) ).

cnf(f_2562_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9285),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9286),U_9287)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9286),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9284),U_9285),U_9287))
    | ~ class_Lattices_Osemilattice__inf(U_9284) ),
    inference(clausify,[status(thm)],[f_2562_3]) ).

fof(f_2563_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J]) ).

fof(f_2563_2,plain,
    ! [U_9291,U_9290,U_9289,U_9288] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9289),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9290),U_9291)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9290),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9289),U_9291))
      | ~ class_Lattices_Olattice(U_9288) ),
    inference(variable_rename,[status(thm)],[f_2563_1]) ).

fof(f_2563_3,plain,
    ! [U_9288,U_9289,U_9290,U_9291] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9289),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9290),U_9291)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9290),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9289),U_9291))
      | ~ class_Lattices_Olattice(U_9288) ),
    inference(definitional_conversion,[status(esa)],[f_2563_2]) ).

cnf(f_2563_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9289),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9290),U_9291)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9290),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9288),U_9289),U_9291))
    | ~ class_Lattices_Olattice(U_9288) ),
    inference(clausify,[status(thm)],[f_2563_3]) ).

fof(f_2564_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute]) ).

fof(f_2564_2,plain,
    ! [U_9295,U_9294,U_9293,U_9292] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9293),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9294),U_9295)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9293),U_9295))
      | ~ class_Lattices_Osemilattice__inf(U_9292) ),
    inference(variable_rename,[status(thm)],[f_2564_1]) ).

fof(f_2564_3,plain,
    ! [U_9292,U_9293,U_9294,U_9295] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9293),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9294),U_9295)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9293),U_9295))
      | ~ class_Lattices_Osemilattice__inf(U_9292) ),
    inference(definitional_conversion,[status(esa)],[f_2564_2]) ).

cnf(f_2564_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9293),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9294),U_9295)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9292),U_9293),U_9295))
    | ~ class_Lattices_Osemilattice__inf(U_9292) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

fof(f_2565_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__left__idem]) ).

fof(f_2565_2,plain,
    ! [U_9298,U_9297,U_9296] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),U_9298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),U_9298)
      | ~ class_Lattices_Osemilattice__inf(U_9296) ),
    inference(variable_rename,[status(thm)],[f_2565_1]) ).

fof(f_2565_3,plain,
    ! [U_9297,U_9296,U_9298] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),U_9298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),U_9298)
      | ~ class_Lattices_Osemilattice__inf(U_9296) ),
    inference(definitional_conversion,[status(esa)],[f_2565_2]) ).

cnf(f_2565_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),U_9298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9296),U_9297),U_9298)
    | ~ class_Lattices_Osemilattice__inf(U_9296) ),
    inference(clausify,[status(thm)],[f_2565_3]) ).

fof(f_2566_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J]) ).

fof(f_2566_2,plain,
    ! [U_9301,U_9300,U_9299] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),U_9301)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),U_9301)
      | ~ class_Lattices_Olattice(U_9299) ),
    inference(variable_rename,[status(thm)],[f_2566_1]) ).

fof(f_2566_3,plain,
    ! [U_9299,U_9300,U_9301] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),U_9301)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),U_9301)
      | ~ class_Lattices_Olattice(U_9299) ),
    inference(definitional_conversion,[status(esa)],[f_2566_2]) ).

cnf(f_2566_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),U_9301)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9299),U_9300),U_9301)
    | ~ class_Lattices_Olattice(U_9299) ),
    inference(clausify,[status(thm)],[f_2566_3]) ).

fof(f_2567_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem]) ).

fof(f_2567_2,plain,
    ! [U_9304,U_9303,U_9302] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),U_9304)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),U_9304)
      | ~ class_Lattices_Osemilattice__inf(U_9302) ),
    inference(variable_rename,[status(thm)],[f_2567_1]) ).

fof(f_2567_3,plain,
    ! [U_9302,U_9303,U_9304] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),U_9304)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),U_9304)
      | ~ class_Lattices_Osemilattice__inf(U_9302) ),
    inference(definitional_conversion,[status(esa)],[f_2567_2]) ).

cnf(f_2567_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),U_9304)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9302),U_9303),U_9304)
    | ~ class_Lattices_Osemilattice__inf(U_9302) ),
    inference(clausify,[status(thm)],[f_2567_3]) ).

fof(f_2568_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__commute]) ).

fof(f_2568_2,plain,
    ! [U_9307,U_9306,U_9305] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9305),U_9306),U_9307) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9305),U_9307),U_9306)
      | ~ class_Lattices_Osemilattice__inf(U_9305) ),
    inference(variable_rename,[status(thm)],[f_2568_1]) ).

fof(f_2568_3,plain,
    ! [U_9305,U_9306,U_9307] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9305),U_9306),U_9307) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9305),U_9307),U_9306)
      | ~ class_Lattices_Osemilattice__inf(U_9305) ),
    inference(definitional_conversion,[status(esa)],[f_2568_2]) ).

cnf(f_2568_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9305),U_9306),U_9307) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9305),U_9307),U_9306)
    | ~ class_Lattices_Osemilattice__inf(U_9305) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

fof(f_2569_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J]) ).

fof(f_2569_2,plain,
    ! [U_9310,U_9309,U_9308] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9308),U_9309),U_9310) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9308),U_9310),U_9309)
      | ~ class_Lattices_Olattice(U_9308) ),
    inference(variable_rename,[status(thm)],[f_2569_1]) ).

fof(f_2569_3,plain,
    ! [U_9308,U_9309,U_9310] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9308),U_9309),U_9310) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9308),U_9310),U_9309)
      | ~ class_Lattices_Olattice(U_9308) ),
    inference(definitional_conversion,[status(esa)],[f_2569_2]) ).

cnf(f_2569_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9308),U_9309),U_9310) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9308),U_9310),U_9309)
    | ~ class_Lattices_Olattice(U_9308) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

fof(f_2570_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Ocommute]) ).

fof(f_2570_2,plain,
    ! [U_9313,U_9312,U_9311] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9311),U_9312),U_9313) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9311),U_9313),U_9312)
      | ~ class_Lattices_Osemilattice__inf(U_9311) ),
    inference(variable_rename,[status(thm)],[f_2570_1]) ).

fof(f_2570_3,plain,
    ! [U_9311,U_9312,U_9313] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9311),U_9312),U_9313) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9311),U_9313),U_9312)
      | ~ class_Lattices_Osemilattice__inf(U_9311) ),
    inference(definitional_conversion,[status(esa)],[f_2570_2]) ).

cnf(f_2570_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9311),U_9312),U_9313) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9311),U_9313),U_9312)
    | ~ class_Lattices_Osemilattice__inf(U_9311) ),
    inference(clausify,[status(thm)],[f_2570_3]) ).

fof(f_2571_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__idem]) ).

fof(f_2571_2,plain,
    ! [U_9315,U_9314] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9314),U_9315),U_9315) = U_9315
      | ~ class_Lattices_Osemilattice__inf(U_9314) ),
    inference(variable_rename,[status(thm)],[f_2571_1]) ).

fof(f_2571_3,plain,
    ! [U_9314,U_9315] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9314),U_9315),U_9315) = U_9315
      | ~ class_Lattices_Osemilattice__inf(U_9314) ),
    inference(definitional_conversion,[status(esa)],[f_2571_2]) ).

cnf(f_2571_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9314),U_9315),U_9315) = U_9315
    | ~ class_Lattices_Osemilattice__inf(U_9314) ),
    inference(clausify,[status(thm)],[f_2571_3]) ).

fof(f_2572_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oidem]) ).

fof(f_2572_2,plain,
    ! [U_9317,U_9316] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9316),U_9317),U_9317) = U_9317
      | ~ class_Lattices_Osemilattice__inf(U_9316) ),
    inference(variable_rename,[status(thm)],[f_2572_1]) ).

fof(f_2572_3,plain,
    ! [U_9316,U_9317] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9316),U_9317),U_9317) = U_9317
      | ~ class_Lattices_Osemilattice__inf(U_9316) ),
    inference(definitional_conversion,[status(esa)],[f_2572_2]) ).

cnf(f_2572_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9316),U_9317),U_9317) = U_9317
    | ~ class_Lattices_Osemilattice__inf(U_9316) ),
    inference(clausify,[status(thm)],[f_2572_3]) ).

fof(f_2573_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem]) ).

fof(f_2573_2,plain,
    ! [U_9319,U_9318] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9318),U_9319),U_9319) = U_9319
      | ~ class_Lattices_Olattice(U_9318) ),
    inference(variable_rename,[status(thm)],[f_2573_1]) ).

fof(f_2573_3,plain,
    ! [U_9318,U_9319] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9318),U_9319),U_9319) = U_9319
      | ~ class_Lattices_Olattice(U_9318) ),
    inference(definitional_conversion,[status(esa)],[f_2573_2]) ).

cnf(f_2573_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9318),U_9319),U_9319) = U_9319
    | ~ class_Lattices_Olattice(U_9318) ),
    inference(clausify,[status(thm)],[f_2573_3]) ).

fof(f_2574_1,plain,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J]) ).

fof(f_2574_2,plain,
    ! [U_9321,U_9320] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9320),U_9321))
      | ~ c_Nat__Transfer_Onat__set(U_9321)
      | ~ c_Nat__Transfer_Onat__set(U_9320) ),
    inference(variable_rename,[status(thm)],[f_2574_1]) ).

fof(f_2574_3,plain,
    ! [U_9320,U_9321] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9320),U_9321))
      | ~ c_Nat__Transfer_Onat__set(U_9321)
      | ~ c_Nat__Transfer_Onat__set(U_9320) ),
    inference(definitional_conversion,[status(esa)],[f_2574_2]) ).

cnf(f_2574_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9320),U_9321))
    | ~ c_Nat__Transfer_Onat__set(U_9321)
    | ~ c_Nat__Transfer_Onat__set(U_9320) ),
    inference(clausify,[status(thm)],[f_2574_3]) ).

fof(f_2575_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distrib__inf__le]) ).

fof(f_2575_2,plain,
    ! [U_9325,U_9324,U_9323,U_9322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9322),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),U_9324)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),U_9325))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9322),U_9324),U_9325))))
      | ~ class_Lattices_Olattice(U_9322) ),
    inference(variable_rename,[status(thm)],[f_2575_1]) ).

fof(f_2575_3,plain,
    ! [U_9322,U_9323,U_9324,U_9325] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9322),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),U_9324)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),U_9325))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9322),U_9324),U_9325))))
      | ~ class_Lattices_Olattice(U_9322) ),
    inference(definitional_conversion,[status(esa)],[f_2575_2]) ).

cnf(f_2575_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9322),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),U_9324)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),U_9325))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9322),U_9323),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9322),U_9324),U_9325))))
    | ~ class_Lattices_Olattice(U_9322) ),
    inference(clausify,[status(thm)],[f_2575_3]) ).

fof(f_2576_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distrib__sup__le]) ).

fof(f_2576_2,plain,
    ! [U_9329,U_9328,U_9327,U_9326] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9326),U_9328),U_9329))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),U_9328)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),U_9329))))
      | ~ class_Lattices_Olattice(U_9326) ),
    inference(variable_rename,[status(thm)],[f_2576_1]) ).

fof(f_2576_3,plain,
    ! [U_9326,U_9327,U_9328,U_9329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9326),U_9328),U_9329))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),U_9328)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),U_9329))))
      | ~ class_Lattices_Olattice(U_9326) ),
    inference(definitional_conversion,[status(esa)],[f_2576_2]) ).

cnf(f_2576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9326),U_9328),U_9329))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),U_9328)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9326),U_9327),U_9329))))
    | ~ class_Lattices_Olattice(U_9326) ),
    inference(clausify,[status(thm)],[f_2576_3]) ).

fof(f_2577_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__inf__bot]) ).

fof(f_2577_2,plain,
    ! [U_9331,U_9330] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9330),hAPP(c_Groups_Ouminus__class_Ouminus(U_9330),U_9331)),U_9331) = c_Orderings_Obot__class_Obot(U_9330)
      | ~ class_Lattices_Oboolean__algebra(U_9330) ),
    inference(variable_rename,[status(thm)],[f_2577_1]) ).

fof(f_2577_3,plain,
    ! [U_9330,U_9331] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9330),hAPP(c_Groups_Ouminus__class_Ouminus(U_9330),U_9331)),U_9331) = c_Orderings_Obot__class_Obot(U_9330)
      | ~ class_Lattices_Oboolean__algebra(U_9330) ),
    inference(definitional_conversion,[status(esa)],[f_2577_2]) ).

cnf(f_2577_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9330),hAPP(c_Groups_Ouminus__class_Ouminus(U_9330),U_9331)),U_9331) = c_Orderings_Obot__class_Obot(U_9330)
    | ~ class_Lattices_Oboolean__algebra(U_9330) ),
    inference(clausify,[status(thm)],[f_2577_3]) ).

fof(f_2578_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__compl__bot]) ).

fof(f_2578_2,plain,
    ! [U_9333,U_9332] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9332),U_9333),hAPP(c_Groups_Ouminus__class_Ouminus(U_9332),U_9333)) = c_Orderings_Obot__class_Obot(U_9332)
      | ~ class_Lattices_Oboolean__algebra(U_9332) ),
    inference(variable_rename,[status(thm)],[f_2578_1]) ).

fof(f_2578_3,plain,
    ! [U_9332,U_9333] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9332),U_9333),hAPP(c_Groups_Ouminus__class_Ouminus(U_9332),U_9333)) = c_Orderings_Obot__class_Obot(U_9332)
      | ~ class_Lattices_Oboolean__algebra(U_9332) ),
    inference(definitional_conversion,[status(esa)],[f_2578_2]) ).

cnf(f_2578_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9332),U_9333),hAPP(c_Groups_Ouminus__class_Ouminus(U_9332),U_9333)) = c_Orderings_Obot__class_Obot(U_9332)
    | ~ class_Lattices_Oboolean__algebra(U_9332) ),
    inference(clausify,[status(thm)],[f_2578_3]) ).

fof(f_2579_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq]) ).

fof(f_2579_2,plain,
    ! [U_9336,U_9335,U_9334] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9334),U_9335),U_9336) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9334),U_9335),hAPP(c_Groups_Ouminus__class_Ouminus(U_9334),U_9336))
      | ~ class_Lattices_Oboolean__algebra(U_9334) ),
    inference(variable_rename,[status(thm)],[f_2579_1]) ).

fof(f_2579_3,plain,
    ! [U_9334,U_9335,U_9336] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9334),U_9335),U_9336) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9334),U_9335),hAPP(c_Groups_Ouminus__class_Ouminus(U_9334),U_9336))
      | ~ class_Lattices_Oboolean__algebra(U_9334) ),
    inference(definitional_conversion,[status(esa)],[f_2579_2]) ).

cnf(f_2579_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9334),U_9335),U_9336) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9334),U_9335),hAPP(c_Groups_Ouminus__class_Ouminus(U_9334),U_9336))
    | ~ class_Lattices_Oboolean__algebra(U_9334) ),
    inference(clausify,[status(thm)],[f_2579_3]) ).

fof(f_2580_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__sup]) ).

fof(f_2580_2,plain,
    ! [U_9339,U_9338,U_9337] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9337),U_9338),U_9339)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9337),hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),U_9338)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),U_9339))
      | ~ class_Lattices_Oboolean__algebra(U_9337) ),
    inference(variable_rename,[status(thm)],[f_2580_1]) ).

fof(f_2580_3,plain,
    ! [U_9337,U_9338,U_9339] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9337),U_9338),U_9339)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9337),hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),U_9338)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),U_9339))
      | ~ class_Lattices_Oboolean__algebra(U_9337) ),
    inference(definitional_conversion,[status(esa)],[f_2580_2]) ).

cnf(f_2580_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9337),U_9338),U_9339)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9337),hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),U_9338)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9337),U_9339))
    | ~ class_Lattices_Oboolean__algebra(U_9337) ),
    inference(clausify,[status(thm)],[f_2580_3]) ).

fof(f_2581_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__inf]) ).

fof(f_2581_2,plain,
    ! [U_9342,U_9341,U_9340] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9340),U_9341),U_9342)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9340),hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),U_9341)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),U_9342))
      | ~ class_Lattices_Oboolean__algebra(U_9340) ),
    inference(variable_rename,[status(thm)],[f_2581_1]) ).

fof(f_2581_3,plain,
    ! [U_9340,U_9341,U_9342] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9340),U_9341),U_9342)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9340),hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),U_9341)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),U_9342))
      | ~ class_Lattices_Oboolean__algebra(U_9340) ),
    inference(definitional_conversion,[status(esa)],[f_2581_2]) ).

cnf(f_2581_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9340),U_9341),U_9342)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9340),hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),U_9341)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9340),U_9342))
    | ~ class_Lattices_Oboolean__algebra(U_9340) ),
    inference(clausify,[status(thm)],[f_2581_3]) ).

fof(f_2582_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).

fof(f_2582_2,plain,
    ! [U_9346,U_9345,U_9344,U_9343] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9343),U_9344),U_9346)),U_9345) = hAPP(hAPP(c_Set_Oinsert(U_9343),U_9344),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),U_9346),U_9345))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9343),U_9344),U_9345)) ),
    inference(variable_rename,[status(thm)],[f_2582_1]) ).

fof(f_2582_3,plain,
    ! [U_9343,U_9344,U_9345,U_9346] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9343),U_9344),U_9346)),U_9345) = hAPP(hAPP(c_Set_Oinsert(U_9343),U_9344),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),U_9346),U_9345))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9343),U_9344),U_9345)) ),
    inference(definitional_conversion,[status(esa)],[f_2582_2]) ).

cnf(f_2582_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9343),U_9344),U_9346)),U_9345) = hAPP(hAPP(c_Set_Oinsert(U_9343),U_9344),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),U_9346),U_9345))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9343),U_9344),U_9345)) ),
    inference(clausify,[status(thm)],[f_2582_3]) ).

fof(f_2583_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).

fof(f_2583_2,plain,
    ! [U_9350,U_9349,U_9348,U_9347] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9347,tc_HOL_Obool)),U_9349),hAPP(hAPP(c_Set_Oinsert(U_9347),U_9348),U_9350)) = hAPP(hAPP(c_Set_Oinsert(U_9347),U_9348),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9347,tc_HOL_Obool)),U_9349),U_9350))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9347),U_9348),U_9349)) ),
    inference(variable_rename,[status(thm)],[f_2583_1]) ).

fof(f_2583_3,plain,
    ! [U_9347,U_9348,U_9349,U_9350] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9347,tc_HOL_Obool)),U_9349),hAPP(hAPP(c_Set_Oinsert(U_9347),U_9348),U_9350)) = hAPP(hAPP(c_Set_Oinsert(U_9347),U_9348),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9347,tc_HOL_Obool)),U_9349),U_9350))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9347),U_9348),U_9349)) ),
    inference(definitional_conversion,[status(esa)],[f_2583_2]) ).

cnf(f_2583_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9347,tc_HOL_Obool)),U_9349),hAPP(hAPP(c_Set_Oinsert(U_9347),U_9348),U_9350)) = hAPP(hAPP(c_Set_Oinsert(U_9347),U_9348),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9347,tc_HOL_Obool)),U_9349),U_9350))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9347),U_9348),U_9349)) ),
    inference(clausify,[status(thm)],[f_2583_3]) ).

fof(f_2584_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(f_2584_2,plain,
    ! [U_9354,U_9353,U_9352,U_9351] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9351),U_9352),U_9354)),U_9353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),U_9354),U_9353)
      | hBOOL(hAPP(hAPP(c_member(U_9351),U_9352),U_9353)) ),
    inference(variable_rename,[status(thm)],[f_2584_1]) ).

fof(f_2584_3,plain,
    ! [U_9351,U_9352,U_9353,U_9354] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9351),U_9352),U_9354)),U_9353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),U_9354),U_9353)
      | hBOOL(hAPP(hAPP(c_member(U_9351),U_9352),U_9353)) ),
    inference(definitional_conversion,[status(esa)],[f_2584_2]) ).

cnf(f_2584_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9351),U_9352),U_9354)),U_9353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),U_9354),U_9353)
    | hBOOL(hAPP(hAPP(c_member(U_9351),U_9352),U_9353)) ),
    inference(clausify,[status(thm)],[f_2584_3]) ).

fof(f_2585_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(f_2585_2,plain,
    ! [U_9358,U_9357,U_9356,U_9355] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9355,tc_HOL_Obool)),U_9357),hAPP(hAPP(c_Set_Oinsert(U_9355),U_9356),U_9358)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9355,tc_HOL_Obool)),U_9357),U_9358)
      | hBOOL(hAPP(hAPP(c_member(U_9355),U_9356),U_9357)) ),
    inference(variable_rename,[status(thm)],[f_2585_1]) ).

fof(f_2585_3,plain,
    ! [U_9355,U_9356,U_9357,U_9358] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9355,tc_HOL_Obool)),U_9357),hAPP(hAPP(c_Set_Oinsert(U_9355),U_9356),U_9358)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9355,tc_HOL_Obool)),U_9357),U_9358)
      | hBOOL(hAPP(hAPP(c_member(U_9355),U_9356),U_9357)) ),
    inference(definitional_conversion,[status(esa)],[f_2585_2]) ).

cnf(f_2585_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9355,tc_HOL_Obool)),U_9357),hAPP(hAPP(c_Set_Oinsert(U_9355),U_9356),U_9358)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9355,tc_HOL_Obool)),U_9357),U_9358)
    | hBOOL(hAPP(hAPP(c_member(U_9355),U_9356),U_9357)) ),
    inference(clausify,[status(thm)],[f_2585_3]) ).

fof(f_2586_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).

fof(f_2586_2,plain,
    ! [U_9362,U_9361,U_9360,U_9359] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9359),U_9360),U_9362)),U_9361) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool)),U_9362),U_9361)
        | hBOOL(hAPP(hAPP(c_member(U_9359),U_9360),U_9361)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9359),U_9360),U_9362)),U_9361) = hAPP(hAPP(c_Set_Oinsert(U_9359),U_9360),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool)),U_9362),U_9361))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9359),U_9360),U_9361)) ) ),
    inference(variable_rename,[status(thm)],[f_2586_1]) ).

fof(f_2586_3,plain,
    ( ! [U_9370,U_9368,U_9366,U_9364] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9364,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9364),U_9366),U_9370)),U_9368) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9364,tc_HOL_Obool)),U_9370),U_9368)
        | hBOOL(hAPP(hAPP(c_member(U_9364),U_9366),U_9368)) )
    & ! [U_9369,U_9367,U_9365,U_9363] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9365),U_9369)),U_9367) = hAPP(hAPP(c_Set_Oinsert(U_9363),U_9365),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),U_9369),U_9367))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9365),U_9367)) ) ),
    inference(miniscope,[status(thm)],[f_2586_2]) ).

fof(f_2586_4,plain,
    ( ! [U_9364,U_9366,U_9368,U_9370] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9364,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9364),U_9366),U_9370)),U_9368) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9364,tc_HOL_Obool)),U_9370),U_9368)
        | hBOOL(hAPP(hAPP(c_member(U_9364),U_9366),U_9368)) )
    & ! [U_9367,U_9369,U_9365,U_9363] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9365),U_9369)),U_9367) = hAPP(hAPP(c_Set_Oinsert(U_9363),U_9365),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),U_9369),U_9367))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9365),U_9367)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2586_3]) ).

cnf(f_2586_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9365),U_9369)),U_9367) = hAPP(hAPP(c_Set_Oinsert(U_9363),U_9365),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),U_9369),U_9367))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9365),U_9367)) ),
    inference(clausify,[status(thm)],[f_2586_4]) ).

cnf(f_2586_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9364,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9364),U_9366),U_9370)),U_9368) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9364,tc_HOL_Obool)),U_9370),U_9368)
    | hBOOL(hAPP(hAPP(c_member(U_9364),U_9366),U_9368)) ),
    inference(clausify,[status(thm)],[f_2586_4]) ).

fof(f_2587_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).

fof(f_2587_2,plain,
    ! [U_9374,U_9373,U_9372,U_9371] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9371,tc_HOL_Obool)),U_9373),hAPP(hAPP(c_Set_Oinsert(U_9371),U_9372),U_9374)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9371,tc_HOL_Obool)),U_9373),U_9374)
        | hBOOL(hAPP(hAPP(c_member(U_9371),U_9372),U_9373)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9371,tc_HOL_Obool)),U_9373),hAPP(hAPP(c_Set_Oinsert(U_9371),U_9372),U_9374)) = hAPP(hAPP(c_Set_Oinsert(U_9371),U_9372),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9371,tc_HOL_Obool)),U_9373),U_9374))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9371),U_9372),U_9373)) ) ),
    inference(variable_rename,[status(thm)],[f_2587_1]) ).

fof(f_2587_3,plain,
    ( ! [U_9382,U_9380,U_9378,U_9376] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_Set_Oinsert(U_9376),U_9378),U_9382)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9380),U_9382)
        | hBOOL(hAPP(hAPP(c_member(U_9376),U_9378),U_9380)) )
    & ! [U_9381,U_9379,U_9377,U_9375] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9375,tc_HOL_Obool)),U_9379),hAPP(hAPP(c_Set_Oinsert(U_9375),U_9377),U_9381)) = hAPP(hAPP(c_Set_Oinsert(U_9375),U_9377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9375,tc_HOL_Obool)),U_9379),U_9381))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9375),U_9377),U_9379)) ) ),
    inference(miniscope,[status(thm)],[f_2587_2]) ).

fof(f_2587_4,plain,
    ( ! [U_9378,U_9376,U_9380,U_9382] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_Set_Oinsert(U_9376),U_9378),U_9382)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9380),U_9382)
        | hBOOL(hAPP(hAPP(c_member(U_9376),U_9378),U_9380)) )
    & ! [U_9381,U_9377,U_9379,U_9375] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9375,tc_HOL_Obool)),U_9379),hAPP(hAPP(c_Set_Oinsert(U_9375),U_9377),U_9381)) = hAPP(hAPP(c_Set_Oinsert(U_9375),U_9377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9375,tc_HOL_Obool)),U_9379),U_9381))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9375),U_9377),U_9379)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2587_3]) ).

cnf(f_2587_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9375,tc_HOL_Obool)),U_9379),hAPP(hAPP(c_Set_Oinsert(U_9375),U_9377),U_9381)) = hAPP(hAPP(c_Set_Oinsert(U_9375),U_9377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9375,tc_HOL_Obool)),U_9379),U_9381))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9375),U_9377),U_9379)) ),
    inference(clausify,[status(thm)],[f_2587_4]) ).

cnf(f_2587_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_Set_Oinsert(U_9376),U_9378),U_9382)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9380),U_9382)
    | hBOOL(hAPP(hAPP(c_member(U_9376),U_9378),U_9380)) ),
    inference(clausify,[status(thm)],[f_2587_4]) ).

fof(f_2588_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_image__Int__subset]) ).

fof(f_2588_2,plain,
    ! [U_9387,U_9386,U_9385,U_9384,U_9383] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9384,tc_HOL_Obool)),U_9386),U_9387))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),U_9386)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),U_9387)))),
    inference(variable_rename,[status(thm)],[f_2588_1]) ).

fof(f_2588_3,plain,
    ! [U_9383,U_9384,U_9385,U_9386,U_9387] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9384,tc_HOL_Obool)),U_9386),U_9387))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),U_9386)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),U_9387)))),
    inference(definitional_conversion,[status(esa)],[f_2588_2]) ).

cnf(f_2588_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9384,tc_HOL_Obool)),U_9386),U_9387))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),U_9386)),hAPP(c_Set_Oimage(U_9384,U_9383,U_9385),U_9387)))),
    inference(clausify,[status(thm)],[f_2588_3]) ).

fof(f_2589_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__triv]) ).

fof(f_2589_2,plain,
    ! [U_9390,U_9389,U_9388] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9388,tc_HOL_Obool)),U_9389),U_9390) = U_9389
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9388,tc_HOL_Obool)),U_9389),U_9390) != c_Orderings_Obot__class_Obot(tc_fun(U_9388,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2589_1]) ).

fof(f_2589_3,plain,
    ! [U_9388,U_9389,U_9390] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9388,tc_HOL_Obool)),U_9389),U_9390) = U_9389
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9388,tc_HOL_Obool)),U_9389),U_9390) != c_Orderings_Obot__class_Obot(tc_fun(U_9388,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2589_2]) ).

cnf(f_2589_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9388,tc_HOL_Obool)),U_9389),U_9390) = U_9389
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9388,tc_HOL_Obool)),U_9389),U_9390) != c_Orderings_Obot__class_Obot(tc_fun(U_9388,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2589_3]) ).

fof(f_2590_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__disjoint]) ).

fof(f_2590_2,plain,
    ! [U_9393,U_9392,U_9391] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9391,tc_HOL_Obool)),U_9392),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9391,tc_HOL_Obool)),U_9393),U_9392)) = c_Orderings_Obot__class_Obot(tc_fun(U_9391,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2590_1]) ).

fof(f_2590_3,plain,
    ! [U_9391,U_9392,U_9393] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9391,tc_HOL_Obool)),U_9392),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9391,tc_HOL_Obool)),U_9393),U_9392)) = c_Orderings_Obot__class_Obot(tc_fun(U_9391,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2590_2]) ).

cnf(f_2590_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9391,tc_HOL_Obool)),U_9392),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9391,tc_HOL_Obool)),U_9393),U_9392)) = c_Orderings_Obot__class_Obot(tc_fun(U_9391,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2590_3]) ).

fof(f_2591_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq]) ).

fof(f_2591_2,plain,
    ! [U_9397,U_9396,U_9395,U_9394] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9394,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9394,tc_HOL_Obool)),U_9395),U_9396)),U_9397) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9394,tc_HOL_Obool)),U_9395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9394,tc_HOL_Obool)),U_9396),U_9397))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9394,tc_HOL_Obool)),U_9397),U_9395)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9394,tc_HOL_Obool)),U_9397),U_9395))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9394,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9394,tc_HOL_Obool)),U_9395),U_9396)),U_9397) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9394,tc_HOL_Obool)),U_9395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9394,tc_HOL_Obool)),U_9396),U_9397)) ) ),
    inference(variable_rename,[status(thm)],[f_2591_1]) ).

fof(f_2591_3,plain,
    ( ! [U_9405,U_9403,U_9401,U_9399] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9399,tc_HOL_Obool)),U_9401),U_9403)),U_9405) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9399,tc_HOL_Obool)),U_9401),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9399,tc_HOL_Obool)),U_9403),U_9405))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9399,tc_HOL_Obool)),U_9405),U_9401)) )
    & ! [U_9404,U_9402,U_9400,U_9398] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9398,tc_HOL_Obool)),U_9404),U_9400))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9398,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9398,tc_HOL_Obool)),U_9400),U_9402)),U_9404) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9398,tc_HOL_Obool)),U_9400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9398,tc_HOL_Obool)),U_9402),U_9404)) ) ),
    inference(miniscope,[status(thm)],[f_2591_2]) ).

fof(f_2591_4,plain,
    ( ! [U_9399,U_9401,U_9403,U_9405] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9399,tc_HOL_Obool)),U_9401),U_9403)),U_9405) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9399,tc_HOL_Obool)),U_9401),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9399,tc_HOL_Obool)),U_9403),U_9405))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9399,tc_HOL_Obool)),U_9405),U_9401)) )
    & ! [U_9400,U_9402,U_9404,U_9398] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9398,tc_HOL_Obool)),U_9404),U_9400))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9398,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9398,tc_HOL_Obool)),U_9400),U_9402)),U_9404) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9398,tc_HOL_Obool)),U_9400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9398,tc_HOL_Obool)),U_9402),U_9404)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2591_3]) ).

cnf(f_2591_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9398,tc_HOL_Obool)),U_9404),U_9400))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9398,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9398,tc_HOL_Obool)),U_9400),U_9402)),U_9404) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9398,tc_HOL_Obool)),U_9400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9398,tc_HOL_Obool)),U_9402),U_9404)) ),
    inference(clausify,[status(thm)],[f_2591_4]) ).

cnf(f_2591_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9399,tc_HOL_Obool)),U_9401),U_9403)),U_9405) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9399,tc_HOL_Obool)),U_9401),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9399,tc_HOL_Obool)),U_9403),U_9405))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9399,tc_HOL_Obool)),U_9405),U_9401)) ),
    inference(clausify,[status(thm)],[f_2591_4]) ).

fof(f_2592_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__Int]) ).

fof(f_2592_2,plain,
    ! [U_9408,U_9407,U_9406] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9406,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9406,tc_HOL_Obool)),U_9407),U_9408)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9406,tc_HOL_Obool)),U_9407),U_9408)) = U_9407,
    inference(variable_rename,[status(thm)],[f_2592_1]) ).

fof(f_2592_3,plain,
    ! [U_9406,U_9407,U_9408] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9406,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9406,tc_HOL_Obool)),U_9407),U_9408)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9406,tc_HOL_Obool)),U_9407),U_9408)) = U_9407,
    inference(definitional_conversion,[status(esa)],[f_2592_2]) ).

cnf(f_2592_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9406,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9406,tc_HOL_Obool)),U_9407),U_9408)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9406,tc_HOL_Obool)),U_9407),U_9408)) = U_9407,
    inference(clausify,[status(thm)],[f_2592_3]) ).

fof(f_2593_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Un]) ).

fof(f_2593_2,plain,
    ! [U_9412,U_9411,U_9410,U_9409] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9409,tc_HOL_Obool)),U_9411),U_9412)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9409,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),U_9411)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),U_9412)),
    inference(variable_rename,[status(thm)],[f_2593_1]) ).

fof(f_2593_3,plain,
    ! [U_9409,U_9410,U_9411,U_9412] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9409,tc_HOL_Obool)),U_9411),U_9412)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9409,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),U_9411)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),U_9412)),
    inference(definitional_conversion,[status(esa)],[f_2593_2]) ).

cnf(f_2593_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9409,tc_HOL_Obool)),U_9411),U_9412)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9409,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),U_9411)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9409,tc_HOL_Obool)),U_9410),U_9412)),
    inference(clausify,[status(thm)],[f_2593_3]) ).

fof(f_2594_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int]) ).

fof(f_2594_2,plain,
    ! [U_9416,U_9415,U_9414,U_9413] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),U_9415),U_9416)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9413,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9415)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9416)),
    inference(variable_rename,[status(thm)],[f_2594_1]) ).

fof(f_2594_3,plain,
    ! [U_9413,U_9414,U_9415,U_9416] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),U_9415),U_9416)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9413,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9415)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9416)),
    inference(definitional_conversion,[status(esa)],[f_2594_2]) ).

cnf(f_2594_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),U_9415),U_9416)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9413,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9415)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9416)),
    inference(clausify,[status(thm)],[f_2594_3]) ).

fof(f_2595_1,plain,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).

fof(f_2595_2,plain,
    ! [U_9418,U_9417] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9417),U_9418) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9417)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9418))),
    inference(variable_rename,[status(thm)],[f_2595_1]) ).

fof(f_2595_3,plain,
    ! [U_9417,U_9418] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9417),U_9418) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9417)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9418))),
    inference(definitional_conversion,[status(esa)],[f_2595_2]) ).

cnf(f_2595_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9417),U_9418) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9417)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9418))),
    inference(clausify,[status(thm)],[f_2595_3]) ).

fof(f_2596_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__disjoint2]) ).

fof(f_2596_2,plain,
    ! [U_9420,U_9419] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9419,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9419,tc_HOL_Obool)),U_9420)),U_9420) = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2596_1]) ).

fof(f_2596_3,plain,
    ! [U_9419,U_9420] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9419,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9419,tc_HOL_Obool)),U_9420)),U_9420) = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2596_2]) ).

cnf(f_2596_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9419,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9419,tc_HOL_Obool)),U_9420)),U_9420) = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2596_3]) ).

fof(f_2597_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__disjoint]) ).

fof(f_2597_2,plain,
    ! [U_9422,U_9421] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9421,tc_HOL_Obool)),U_9422),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9421,tc_HOL_Obool)),U_9422)) = c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2597_1]) ).

fof(f_2597_3,plain,
    ! [U_9421,U_9422] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9421,tc_HOL_Obool)),U_9422),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9421,tc_HOL_Obool)),U_9422)) = c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2597_2]) ).

cnf(f_2597_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9421,tc_HOL_Obool)),U_9422),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9421,tc_HOL_Obool)),U_9422)) = c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2597_3]) ).

fof(f_2598_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__Int__subset]) ).

fof(f_2598_2,plain,
    ! [U_9427,U_9426,U_9425,U_9424,U_9423] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426),U_9427))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),U_9426)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),U_9427)))),
    inference(variable_rename,[status(thm)],[f_2598_1]) ).

fof(f_2598_3,plain,
    ! [U_9423,U_9424,U_9425,U_9426,U_9427] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426),U_9427))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),U_9426)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),U_9427)))),
    inference(definitional_conversion,[status(esa)],[f_2598_2]) ).

cnf(f_2598_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426),U_9427))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),U_9426)),hAPP(c_Relation_OImage(U_9424,U_9423,U_9425),U_9427)))),
    inference(clausify,[status(thm)],[f_2598_3]) ).

fof(f_2599_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__Un]) ).

fof(f_2599_2,plain,
    ! [U_9430,U_9429,U_9428] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9428,tc_HOL_Obool)),U_9429),U_9430)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9428,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),U_9429)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),U_9430)),
    inference(variable_rename,[status(thm)],[f_2599_1]) ).

fof(f_2599_3,plain,
    ! [U_9428,U_9429,U_9430] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9428,tc_HOL_Obool)),U_9429),U_9430)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9428,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),U_9429)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),U_9430)),
    inference(definitional_conversion,[status(esa)],[f_2599_2]) ).

cnf(f_2599_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9428,tc_HOL_Obool)),U_9429),U_9430)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9428,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),U_9429)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9428,tc_HOL_Obool)),U_9430)),
    inference(clausify,[status(thm)],[f_2599_3]) ).

fof(f_2600_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__Int]) ).

fof(f_2600_2,plain,
    ! [U_9433,U_9432,U_9431] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9431,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),U_9432)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),U_9433)),
    inference(variable_rename,[status(thm)],[f_2600_1]) ).

fof(f_2600_3,plain,
    ! [U_9431,U_9432,U_9433] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9431,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),U_9432)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),U_9433)),
    inference(definitional_conversion,[status(esa)],[f_2600_2]) ).

cnf(f_2600_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9431,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),U_9432)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9431,tc_HOL_Obool)),U_9433)),
    inference(clausify,[status(thm)],[f_2600_3]) ).

fof(f_2601_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__Compl]) ).

fof(f_2601_2,plain,
    ! [U_9436,U_9435,U_9434] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9434,tc_HOL_Obool)),U_9435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9434,tc_HOL_Obool)),U_9436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436),
    inference(variable_rename,[status(thm)],[f_2601_1]) ).

fof(f_2601_3,plain,
    ! [U_9434,U_9435,U_9436] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9434,tc_HOL_Obool)),U_9435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9434,tc_HOL_Obool)),U_9436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436),
    inference(definitional_conversion,[status(esa)],[f_2601_2]) ).

cnf(f_2601_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9434,tc_HOL_Obool)),U_9435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9434,tc_HOL_Obool)),U_9436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436),
    inference(clausify,[status(thm)],[f_2601_3]) ).

fof(f_2602_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__eq]) ).

fof(f_2602_2,plain,
    ! [U_9439,U_9438,U_9437] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9437,tc_HOL_Obool)),U_9438),U_9439) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9437,tc_HOL_Obool)),U_9438),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9437,tc_HOL_Obool)),U_9439)),
    inference(variable_rename,[status(thm)],[f_2602_1]) ).

fof(f_2602_3,plain,
    ! [U_9437,U_9438,U_9439] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9437,tc_HOL_Obool)),U_9438),U_9439) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9437,tc_HOL_Obool)),U_9438),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9437,tc_HOL_Obool)),U_9439)),
    inference(definitional_conversion,[status(esa)],[f_2602_2]) ).

cnf(f_2602_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9437,tc_HOL_Obool)),U_9438),U_9439) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9437,tc_HOL_Obool)),U_9438),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9437,tc_HOL_Obool)),U_9439)),
    inference(clausify,[status(thm)],[f_2602_3]) ).

fof(f_2603_1,plain,
    ! [V_B_2,V_A_2] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J]) ).

fof(f_2603_2,plain,
    ! [U_9441,U_9440] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9440),U_9441) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9440)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9441)))
      | ~ c_Nat__Transfer_Onat__set(U_9441)
      | ~ c_Nat__Transfer_Onat__set(U_9440) ),
    inference(variable_rename,[status(thm)],[f_2603_1]) ).

fof(f_2603_3,plain,
    ! [U_9440,U_9441] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9440),U_9441) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9440)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9441)))
      | ~ c_Nat__Transfer_Onat__set(U_9441)
      | ~ c_Nat__Transfer_Onat__set(U_9440) ),
    inference(definitional_conversion,[status(esa)],[f_2603_2]) ).

cnf(f_2603_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9440),U_9441) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9440)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9441)))
    | ~ c_Nat__Transfer_Onat__set(U_9441)
    | ~ c_Nat__Transfer_Onat__set(U_9440) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

fof(f_2604_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl]) ).

fof(f_2604_2,plain,
    ! [U_9444,U_9443,U_9442] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9442,tc_HOL_Obool)),U_9443),U_9444) = c_Orderings_Obot__class_Obot(tc_fun(U_9442,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9442,tc_HOL_Obool)),U_9443),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9442,tc_HOL_Obool)),U_9444))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9442,tc_HOL_Obool)),U_9443),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9442,tc_HOL_Obool)),U_9444)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9442,tc_HOL_Obool)),U_9443),U_9444) != c_Orderings_Obot__class_Obot(tc_fun(U_9442,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2604_1]) ).

fof(f_2604_3,plain,
    ( ! [U_9450,U_9448,U_9446] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9446,tc_HOL_Obool)),U_9448),U_9450) = c_Orderings_Obot__class_Obot(tc_fun(U_9446,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9446,tc_HOL_Obool)),U_9448),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9446,tc_HOL_Obool)),U_9450))) )
    & ! [U_9449,U_9447,U_9445] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9445,tc_HOL_Obool)),U_9447),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9445,tc_HOL_Obool)),U_9449)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9445,tc_HOL_Obool)),U_9447),U_9449) != c_Orderings_Obot__class_Obot(tc_fun(U_9445,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2604_2]) ).

fof(f_2604_4,plain,
    ( ! [U_9446,U_9448,U_9450] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9446,tc_HOL_Obool)),U_9448),U_9450) = c_Orderings_Obot__class_Obot(tc_fun(U_9446,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9446,tc_HOL_Obool)),U_9448),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9446,tc_HOL_Obool)),U_9450))) )
    & ! [U_9447,U_9445,U_9449] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9445,tc_HOL_Obool)),U_9447),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9445,tc_HOL_Obool)),U_9449)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9445,tc_HOL_Obool)),U_9447),U_9449) != c_Orderings_Obot__class_Obot(tc_fun(U_9445,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2604_3]) ).

cnf(f_2604_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9445,tc_HOL_Obool)),U_9447),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9445,tc_HOL_Obool)),U_9449)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9445,tc_HOL_Obool)),U_9447),U_9449) != c_Orderings_Obot__class_Obot(tc_fun(U_9445,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2604_4]) ).

cnf(f_2604_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9446,tc_HOL_Obool)),U_9448),U_9450) = c_Orderings_Obot__class_Obot(tc_fun(U_9446,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9446,tc_HOL_Obool)),U_9448),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9446,tc_HOL_Obool)),U_9450))) ),
    inference(clausify,[status(thm)],[f_2604_4]) ).

fof(f_2605_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter]) ).

fof(f_2605_2,plain,
    ! [U_9458,U_9457,U_9456,U_9455,U_9454,U_9453,U_9452,U_9451] :
      ( hAPP(hAPP(U_9453,hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))),hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))) = hAPP(hAPP(U_9453,hAPP(U_9456,U_9457)),hAPP(U_9456,U_9458))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9458))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9457))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9451,U_9452,U_9453,U_9454,U_9455,U_9456) ),
    inference(variable_rename,[status(thm)],[f_2605_1]) ).

fof(f_2605_3,plain,
    ! [U_9458,U_9457,U_9456,U_9455,U_9454,U_9453,U_9452] :
      ( ! [U_9451] : ~ c_Finite__Set_Ofolding__image__simple(U_9451,U_9452,U_9453,U_9454,U_9455,U_9456)
      | hAPP(hAPP(U_9453,hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))),hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))) = hAPP(hAPP(U_9453,hAPP(U_9456,U_9457)),hAPP(U_9456,U_9458))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9458))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9457)) ),
    inference(miniscope,[status(thm)],[f_2605_2]) ).

fof(f_2605_4,plain,
    ! [U_9451,U_9452,U_9453,U_9454,U_9455,U_9456,U_9457,U_9458] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9451,U_9452,U_9453,U_9454,U_9455,U_9456)
      | hAPP(hAPP(U_9453,hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))),hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))) = hAPP(hAPP(U_9453,hAPP(U_9456,U_9457)),hAPP(U_9456,U_9458))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9458))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9457)) ),
    inference(definitional_conversion,[status(esa)],[f_2605_3]) ).

cnf(f_2605_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9451,U_9452,U_9453,U_9454,U_9455,U_9456)
    | hAPP(hAPP(U_9453,hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))),hAPP(U_9456,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9452,tc_HOL_Obool)),U_9457),U_9458))) = hAPP(hAPP(U_9453,hAPP(U_9456,U_9457)),hAPP(U_9456,U_9458))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9458))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9452),U_9457)) ),
    inference(clausify,[status(thm)],[f_2605_4]) ).

fof(f_2606_1,plain,
    ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__quotient]) ).

fof(f_2606_2,plain,
    ! [U_9461,U_9460,U_9459] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9459),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool)))),U_9461) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9459,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9459,U_9459,U_9461),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9459,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2606_1]) ).

fof(f_2606_3,plain,
    ! [U_9459,U_9461,U_9460] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9459),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool)))),U_9461) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9459,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9459,U_9459,U_9461),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9459,tc_HOL_Obool),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2606_2]) ).

cnf(f_2606_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9459),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool)))),U_9461) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9459,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9459,U_9459,U_9461),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9459,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2606_3]) ).

fof(f_2607_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter]) ).

fof(f_2607_2,plain,
    ! [U_9466,U_9465,U_9464,U_9463,U_9462] :
      ( hAPP(hAPP(U_9463,hAPP(U_9464,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466))),hAPP(U_9464,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466))) = hAPP(hAPP(U_9463,hAPP(U_9464,U_9465)),hAPP(U_9464,U_9466))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466) = c_Orderings_Obot__class_Obot(tc_fun(U_9462,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9462),U_9466))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9462),U_9465))
      | ~ c_Finite__Set_Ofolding__one(U_9462,U_9463,U_9464) ),
    inference(variable_rename,[status(thm)],[f_2607_1]) ).

fof(f_2607_3,plain,
    ! [U_9462,U_9463,U_9464,U_9465,U_9466] :
      ( hAPP(hAPP(U_9463,hAPP(U_9464,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466))),hAPP(U_9464,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466))) = hAPP(hAPP(U_9463,hAPP(U_9464,U_9465)),hAPP(U_9464,U_9466))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466) = c_Orderings_Obot__class_Obot(tc_fun(U_9462,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9462),U_9466))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9462),U_9465))
      | ~ c_Finite__Set_Ofolding__one(U_9462,U_9463,U_9464) ),
    inference(definitional_conversion,[status(esa)],[f_2607_2]) ).

cnf(f_2607_4,plain,
    ( hAPP(hAPP(U_9463,hAPP(U_9464,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466))),hAPP(U_9464,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466))) = hAPP(hAPP(U_9463,hAPP(U_9464,U_9465)),hAPP(U_9464,U_9466))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9462,tc_HOL_Obool)),U_9465),U_9466) = c_Orderings_Obot__class_Obot(tc_fun(U_9462,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9462),U_9466))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9462),U_9465))
    | ~ c_Finite__Set_Ofolding__one(U_9462,U_9463,U_9464) ),
    inference(clausify,[status(thm)],[f_2607_3]) ).

fof(f_2608_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint]) ).

fof(f_2608_2,plain,
    ! [U_9471,U_9470,U_9469,U_9468,U_9467] :
      ( hAPP(U_9469,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9467,tc_HOL_Obool)),U_9470),U_9471)) = hAPP(hAPP(U_9468,hAPP(U_9469,U_9470)),hAPP(U_9469,U_9471))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9467,tc_HOL_Obool)),U_9470),U_9471) != c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
      | U_9471 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9467),U_9471))
      | U_9470 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9467),U_9470))
      | ~ c_Finite__Set_Ofolding__one(U_9467,U_9468,U_9469) ),
    inference(variable_rename,[status(thm)],[f_2608_1]) ).

fof(f_2608_3,plain,
    ! [U_9467,U_9468,U_9469,U_9470,U_9471] :
      ( hAPP(U_9469,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9467,tc_HOL_Obool)),U_9470),U_9471)) = hAPP(hAPP(U_9468,hAPP(U_9469,U_9470)),hAPP(U_9469,U_9471))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9467,tc_HOL_Obool)),U_9470),U_9471) != c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
      | U_9471 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9467),U_9471))
      | U_9470 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9467),U_9470))
      | ~ c_Finite__Set_Ofolding__one(U_9467,U_9468,U_9469) ),
    inference(definitional_conversion,[status(esa)],[f_2608_2]) ).

cnf(f_2608_4,plain,
    ( hAPP(U_9469,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9467,tc_HOL_Obool)),U_9470),U_9471)) = hAPP(hAPP(U_9468,hAPP(U_9469,U_9470)),hAPP(U_9469,U_9471))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9467,tc_HOL_Obool)),U_9470),U_9471) != c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
    | U_9471 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9467),U_9471))
    | U_9470 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9467),U_9470))
    | ~ c_Finite__Set_Ofolding__one(U_9467,U_9468,U_9469) ),
    inference(clausify,[status(thm)],[f_2608_3]) ).

fof(f_2609_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint]) ).

fof(f_2609_2,plain,
    ! [U_9479,U_9478,U_9477,U_9476,U_9475,U_9474,U_9473,U_9472] :
      ( hAPP(U_9477,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479)) = hAPP(hAPP(U_9474,hAPP(U_9477,U_9478)),hAPP(U_9477,U_9479))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479) != c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9479))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9478))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9472,U_9473,U_9474,U_9475,U_9476,U_9477) ),
    inference(variable_rename,[status(thm)],[f_2609_1]) ).

fof(f_2609_3,plain,
    ! [U_9479,U_9478,U_9477,U_9476,U_9475,U_9474,U_9473] :
      ( ! [U_9472] : ~ c_Finite__Set_Ofolding__image__simple(U_9472,U_9473,U_9474,U_9475,U_9476,U_9477)
      | hAPP(U_9477,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479)) = hAPP(hAPP(U_9474,hAPP(U_9477,U_9478)),hAPP(U_9477,U_9479))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479) != c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9479))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9478)) ),
    inference(miniscope,[status(thm)],[f_2609_2]) ).

fof(f_2609_4,plain,
    ! [U_9475,U_9478,U_9476,U_9477,U_9474,U_9473,U_9472,U_9479] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9472,U_9473,U_9474,U_9475,U_9476,U_9477)
      | hAPP(U_9477,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479)) = hAPP(hAPP(U_9474,hAPP(U_9477,U_9478)),hAPP(U_9477,U_9479))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479) != c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9479))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9478)) ),
    inference(definitional_conversion,[status(esa)],[f_2609_3]) ).

cnf(f_2609_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9472,U_9473,U_9474,U_9475,U_9476,U_9477)
    | hAPP(U_9477,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479)) = hAPP(hAPP(U_9474,hAPP(U_9477,U_9478)),hAPP(U_9477,U_9479))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9473,tc_HOL_Obool)),U_9478),U_9479) != c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9479))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9473),U_9478)) ),
    inference(clausify,[status(thm)],[f_2609_4]) ).

fof(f_2610_1,plain,
    ! [V_r_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_quotientI]) ).

fof(f_2610_2,plain,
    ! [U_9483,U_9482,U_9481,U_9480] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9480,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9480,U_9480,U_9483),hAPP(hAPP(c_Set_Oinsert(U_9480),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9480),U_9482),U_9483)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9480),U_9481),U_9482)) ),
    inference(variable_rename,[status(thm)],[f_2610_1]) ).

fof(f_2610_3,plain,
    ! [U_9481,U_9480,U_9482,U_9483] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9480,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9480,U_9480,U_9483),hAPP(hAPP(c_Set_Oinsert(U_9480),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9480),U_9482),U_9483)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9480),U_9481),U_9482)) ),
    inference(definitional_conversion,[status(esa)],[f_2610_2]) ).

cnf(f_2610_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9480,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9480,U_9480,U_9483),hAPP(hAPP(c_Set_Oinsert(U_9480),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9480),U_9482),U_9483)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9480),U_9481),U_9482)) ),
    inference(clausify,[status(thm)],[f_2610_3]) ).

fof(f_2611_1,plain,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( ( ( V_X_2 = V_Y_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | V_X_2 != V_Y_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff]) ).

fof(f_2611_2,plain,
    ! [U_9490,U_9489,U_9488,U_9487,U_9486,U_9485,U_9484] :
      ( ( ( U_9487 = U_9488
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9484,U_9484)),hAPP(hAPP(c_Product__Type_OPair(U_9484,U_9484),U_9489),U_9490)),U_9486)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9484,U_9484)),hAPP(hAPP(c_Product__Type_OPair(U_9484,U_9484),U_9489),U_9490)),U_9486))
          | U_9487 != U_9488 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9484),U_9490),U_9488))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9484),U_9489),U_9487))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9484,tc_HOL_Obool)),U_9488),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9484),U_9485),U_9486)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9484,tc_HOL_Obool)),U_9487),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9484),U_9485),U_9486)))
      | ~ c_Equiv__Relations_Oequiv(U_9484,U_9485,U_9486) ),
    inference(variable_rename,[status(thm)],[f_2611_1]) ).

fof(f_2611_3,plain,
    ( ! [U_9484,U_9486,U_9487,U_9488,U_9489,U_9490] :
        ( U_9487 = U_9488
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9484,U_9484)),hAPP(hAPP(c_Product__Type_OPair(U_9484,U_9484),U_9489),U_9490)),U_9486))
        | ~ sP750(U_9484,U_9486,U_9487,U_9488,U_9489,U_9490) )
    & ! [U_9484,U_9486,U_9487,U_9488,U_9489,U_9490] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9484,U_9484)),hAPP(hAPP(c_Product__Type_OPair(U_9484,U_9484),U_9489),U_9490)),U_9486))
        | U_9487 != U_9488
        | ~ sP750(U_9484,U_9486,U_9487,U_9488,U_9489,U_9490) )
    & ! [U_9484,U_9485,U_9486,U_9487,U_9488,U_9489,U_9490] :
        ( sP750(U_9484,U_9486,U_9487,U_9488,U_9489,U_9490)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9484),U_9490),U_9488))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9484),U_9489),U_9487))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9484,tc_HOL_Obool)),U_9488),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9484),U_9485),U_9486)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9484,tc_HOL_Obool)),U_9487),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9484),U_9485),U_9486)))
        | ~ c_Equiv__Relations_Oequiv(U_9484,U_9485,U_9486) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP750])],[f_2611_2]) ).

cnf(f_2611_4,plain,
    ( sP750(U_9484,U_9486,U_9487,U_9488,U_9489,U_9490)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9484),U_9490),U_9488))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9484),U_9489),U_9487))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9484,tc_HOL_Obool)),U_9488),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9484),U_9485),U_9486)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9484,tc_HOL_Obool)),U_9487),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9484),U_9485),U_9486)))
    | ~ c_Equiv__Relations_Oequiv(U_9484,U_9485,U_9486) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

cnf(f_2611_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9484,U_9484)),hAPP(hAPP(c_Product__Type_OPair(U_9484,U_9484),U_9489),U_9490)),U_9486))
    | U_9487 != U_9488
    | ~ sP750(U_9484,U_9486,U_9487,U_9488,U_9489,U_9490) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

cnf(f_2611_6,plain,
    ( U_9487 = U_9488
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9484,U_9484)),hAPP(hAPP(c_Product__Type_OPair(U_9484,U_9484),U_9489),U_9490)),U_9486))
    | ~ sP750(U_9484,U_9486,U_9487,U_9488,U_9489,U_9490) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

fof(f_2612_1,plain,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( V_X_2 = V_Y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__eqI]) ).

fof(f_2612_2,plain,
    ! [U_9497,U_9496,U_9495,U_9494,U_9493,U_9492,U_9491] :
      ( U_9494 = U_9495
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9491,U_9491)),hAPP(hAPP(c_Product__Type_OPair(U_9491,U_9491),U_9496),U_9497)),U_9493))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9491),U_9497),U_9495))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9491),U_9496),U_9494))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9491,tc_HOL_Obool)),U_9495),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9491),U_9492),U_9493)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9491,tc_HOL_Obool)),U_9494),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9491),U_9492),U_9493)))
      | ~ c_Equiv__Relations_Oequiv(U_9491,U_9492,U_9493) ),
    inference(variable_rename,[status(thm)],[f_2612_1]) ).

fof(f_2612_3,plain,
    ! [U_9496,U_9494,U_9495,U_9492,U_9497,U_9493,U_9491] :
      ( U_9494 = U_9495
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9491,U_9491)),hAPP(hAPP(c_Product__Type_OPair(U_9491,U_9491),U_9496),U_9497)),U_9493))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9491),U_9497),U_9495))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9491),U_9496),U_9494))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9491,tc_HOL_Obool)),U_9495),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9491),U_9492),U_9493)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9491,tc_HOL_Obool)),U_9494),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9491),U_9492),U_9493)))
      | ~ c_Equiv__Relations_Oequiv(U_9491,U_9492,U_9493) ),
    inference(definitional_conversion,[status(esa)],[f_2612_2]) ).

cnf(f_2612_4,plain,
    ( U_9494 = U_9495
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9491,U_9491)),hAPP(hAPP(c_Product__Type_OPair(U_9491,U_9491),U_9496),U_9497)),U_9493))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9491),U_9497),U_9495))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9491),U_9496),U_9494))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9491,tc_HOL_Obool)),U_9495),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9491),U_9492),U_9493)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9491,tc_HOL_Obool)),U_9494),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9491),U_9492),U_9493)))
    | ~ c_Equiv__Relations_Oequiv(U_9491,U_9492,U_9493) ),
    inference(clausify,[status(thm)],[f_2612_3]) ).

fof(f_2613_1,plain,
    ! [V_k_2,V_l_2] :
      ( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty]) ).

fof(f_2613_2,plain,
    ! [U_9499,U_9498] :
      ( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9499,U_9498) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9498),U_9499)) ),
    inference(variable_rename,[status(thm)],[f_2613_1]) ).

fof(f_2613_3,plain,
    ! [U_9499,U_9498] :
      ( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9499,U_9498) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9498),U_9499)) ),
    inference(definitional_conversion,[status(esa)],[f_2613_2]) ).

cnf(f_2613_4,plain,
    ( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9499,U_9498) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9498),U_9499)) ),
    inference(clausify,[status(thm)],[f_2613_3]) ).

fof(f_2614_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OlessThan__iff]) ).

fof(f_2614_2,plain,
    ! [U_9501,U_9500] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9500),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9501)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9501),U_9500))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9500),U_9501)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9501),U_9500))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9500),U_9501)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9500),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9501))) ) ),
    inference(variable_rename,[status(thm)],[f_2614_1]) ).

fof(f_2614_3,plain,
    ( ! [U_9505,U_9503] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9503),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9505)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9505),U_9503))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9503),U_9505)) )
    & ! [U_9504,U_9502] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9504),U_9502))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9502),U_9504)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9502),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9504))) ) ),
    inference(miniscope,[status(thm)],[f_2614_2]) ).

fof(f_2614_4,plain,
    ( ! [U_9504,U_9502] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9504),U_9502))
        | ~ sP751(U_9504,U_9502) )
    & ! [U_9504,U_9502] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9502),U_9504))
        | ~ sP751(U_9504,U_9502) )
    & ! [U_9505,U_9503] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9503),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9505)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9505),U_9503))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9503),U_9505)) )
    & ! [U_9504,U_9502] :
        ( sP751(U_9504,U_9502)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9502),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9504))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP751])],[f_2614_3]) ).

cnf(f_2614_5,plain,
    ( sP751(U_9504,U_9502)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9502),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9504))) ),
    inference(clausify,[status(thm)],[f_2614_4]) ).

cnf(f_2614_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9503),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9505)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9505),U_9503))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9503),U_9505)) ),
    inference(clausify,[status(thm)],[f_2614_4]) ).

cnf(f_2614_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9502),U_9504))
    | ~ sP751(U_9504,U_9502) ),
    inference(clausify,[status(thm)],[f_2614_4]) ).

cnf(f_2614_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9504),U_9502))
    | ~ sP751(U_9504,U_9502) ),
    inference(clausify,[status(thm)],[f_2614_4]) ).

fof(f_2615_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThan__iff]) ).

fof(f_2615_2,plain,
    ! [U_9507,U_9506] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9506),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9507)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9506),U_9507))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9507),U_9506)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9506),U_9507))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9507),U_9506)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9506),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9507))) ) ),
    inference(variable_rename,[status(thm)],[f_2615_1]) ).

fof(f_2615_3,plain,
    ( ! [U_9511,U_9509] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9509),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9511)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9509),U_9511))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9511),U_9509)) )
    & ! [U_9510,U_9508] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9508),U_9510))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9510),U_9508)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9508),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9510))) ) ),
    inference(miniscope,[status(thm)],[f_2615_2]) ).

fof(f_2615_4,plain,
    ( ! [U_9508,U_9510] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9508),U_9510))
        | ~ sP752(U_9508,U_9510) )
    & ! [U_9508,U_9510] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9510),U_9508))
        | ~ sP752(U_9508,U_9510) )
    & ! [U_9511,U_9509] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9509),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9511)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9509),U_9511))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9511),U_9509)) )
    & ! [U_9508,U_9510] :
        ( sP752(U_9508,U_9510)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9508),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9510))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP752])],[f_2615_3]) ).

cnf(f_2615_5,plain,
    ( sP752(U_9508,U_9510)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9508),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9510))) ),
    inference(clausify,[status(thm)],[f_2615_4]) ).

cnf(f_2615_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9509),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9511)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9509),U_9511))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9511),U_9509)) ),
    inference(clausify,[status(thm)],[f_2615_4]) ).

cnf(f_2615_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9510),U_9508))
    | ~ sP752(U_9508,U_9510) ),
    inference(clausify,[status(thm)],[f_2615_4]) ).

cnf(f_2615_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9508),U_9510))
    | ~ sP752(U_9508,U_9510) ),
    inference(clausify,[status(thm)],[f_2615_4]) ).

fof(f_2616_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatMost__iff]) ).

fof(f_2616_2,plain,
    ! [U_9513,U_9512] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9512),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9513)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9512),U_9513)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9512),U_9513))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9512),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9513))) ) ),
    inference(variable_rename,[status(thm)],[f_2616_1]) ).

fof(f_2616_3,plain,
    ( ! [U_9517,U_9515] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9515),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9517)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9515),U_9517)) )
    & ! [U_9516,U_9514] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9514),U_9516))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9514),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9516))) ) ),
    inference(miniscope,[status(thm)],[f_2616_2]) ).

fof(f_2616_4,plain,
    ( ! [U_9517,U_9515] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9515),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9517)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9515),U_9517)) )
    & ! [U_9514,U_9516] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9514),U_9516))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9514),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9516))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2616_3]) ).

cnf(f_2616_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9514),U_9516))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9514),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9516))) ),
    inference(clausify,[status(thm)],[f_2616_4]) ).

cnf(f_2616_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9515),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9517)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9515),U_9517)) ),
    inference(clausify,[status(thm)],[f_2616_4]) ).

fof(f_2617_1,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_inf__nat__def]) ).

fof(f_2617_2,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2617_1]) ).

cnf(f_2617_3,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2617_2]) ).

fof(f_2618_1,plain,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).

fof(f_2618_2,plain,
    ! [U_9523,U_9522,U_9521,U_9520,U_9519,U_9518] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9518,tc_fun(U_9519,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9518,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),U_9518),c_COMBC(U_9519,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_prod(U_9518,U_9519)),tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),U_9518),hAPP(c_COMBB(tc_prod(U_9518,U_9519),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool),U_9519),c_member(tc_prod(U_9518,U_9519)))),c_Product__Type_OPair(U_9518,U_9519)))),U_9520)),hAPP(hAPP(c_COMBC(U_9518,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),U_9518),c_COMBC(U_9519,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_prod(U_9518,U_9519)),tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),U_9518),hAPP(c_COMBB(tc_prod(U_9518,U_9519),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool),U_9519),c_member(tc_prod(U_9518,U_9519)))),c_Product__Type_OPair(U_9518,U_9519)))),U_9521)),U_9522),U_9523))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9518,U_9519)),hAPP(hAPP(c_Product__Type_OPair(U_9518,U_9519),U_9522),U_9523)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool)),U_9520),U_9521))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9518,U_9519)),hAPP(hAPP(c_Product__Type_OPair(U_9518,U_9519),U_9522),U_9523)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool)),U_9520),U_9521)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9518,tc_fun(U_9519,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9518,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),U_9518),c_COMBC(U_9519,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_prod(U_9518,U_9519)),tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),U_9518),hAPP(c_COMBB(tc_prod(U_9518,U_9519),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool),U_9519),c_member(tc_prod(U_9518,U_9519)))),c_Product__Type_OPair(U_9518,U_9519)))),U_9520)),hAPP(hAPP(c_COMBC(U_9518,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_fun(U_9519,tc_HOL_Obool)),U_9518),c_COMBC(U_9519,tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9519,tc_prod(U_9518,U_9519)),tc_fun(U_9519,tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool)),U_9518),hAPP(c_COMBB(tc_prod(U_9518,U_9519),tc_fun(tc_fun(tc_prod(U_9518,U_9519),tc_HOL_Obool),tc_HOL_Obool),U_9519),c_member(tc_prod(U_9518,U_9519)))),c_Product__Type_OPair(U_9518,U_9519)))),U_9521)),U_9522),U_9523)) ) ),
    inference(variable_rename,[status(thm)],[f_2618_1]) ).

fof(f_2618_3,plain,
    ( ! [U_9535,U_9533,U_9531,U_9529,U_9527,U_9525] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9525,tc_fun(U_9527,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9525,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),U_9525),c_COMBC(U_9527,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_prod(U_9525,U_9527)),tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),U_9525),hAPP(c_COMBB(tc_prod(U_9525,U_9527),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool),U_9527),c_member(tc_prod(U_9525,U_9527)))),c_Product__Type_OPair(U_9525,U_9527)))),U_9529)),hAPP(hAPP(c_COMBC(U_9525,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),U_9525),c_COMBC(U_9527,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_prod(U_9525,U_9527)),tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),U_9525),hAPP(c_COMBB(tc_prod(U_9525,U_9527),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool),U_9527),c_member(tc_prod(U_9525,U_9527)))),c_Product__Type_OPair(U_9525,U_9527)))),U_9531)),U_9533),U_9535))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9525,U_9527)),hAPP(hAPP(c_Product__Type_OPair(U_9525,U_9527),U_9533),U_9535)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool)),U_9529),U_9531))) )
    & ! [U_9534,U_9532,U_9530,U_9528,U_9526,U_9524] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9524,U_9526)),hAPP(hAPP(c_Product__Type_OPair(U_9524,U_9526),U_9532),U_9534)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool)),U_9528),U_9530)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9524,tc_fun(U_9526,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9524,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),U_9524),c_COMBC(U_9526,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_prod(U_9524,U_9526)),tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),U_9524),hAPP(c_COMBB(tc_prod(U_9524,U_9526),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool),U_9526),c_member(tc_prod(U_9524,U_9526)))),c_Product__Type_OPair(U_9524,U_9526)))),U_9528)),hAPP(hAPP(c_COMBC(U_9524,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),U_9524),c_COMBC(U_9526,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_prod(U_9524,U_9526)),tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),U_9524),hAPP(c_COMBB(tc_prod(U_9524,U_9526),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool),U_9526),c_member(tc_prod(U_9524,U_9526)))),c_Product__Type_OPair(U_9524,U_9526)))),U_9530)),U_9532),U_9534)) ) ),
    inference(miniscope,[status(thm)],[f_2618_2]) ).

fof(f_2618_4,plain,
    ( ! [U_9525,U_9527,U_9529,U_9531,U_9533,U_9535] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9525,tc_fun(U_9527,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9525,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),U_9525),c_COMBC(U_9527,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_prod(U_9525,U_9527)),tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),U_9525),hAPP(c_COMBB(tc_prod(U_9525,U_9527),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool),U_9527),c_member(tc_prod(U_9525,U_9527)))),c_Product__Type_OPair(U_9525,U_9527)))),U_9529)),hAPP(hAPP(c_COMBC(U_9525,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),U_9525),c_COMBC(U_9527,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_prod(U_9525,U_9527)),tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),U_9525),hAPP(c_COMBB(tc_prod(U_9525,U_9527),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool),U_9527),c_member(tc_prod(U_9525,U_9527)))),c_Product__Type_OPair(U_9525,U_9527)))),U_9531)),U_9533),U_9535))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9525,U_9527)),hAPP(hAPP(c_Product__Type_OPair(U_9525,U_9527),U_9533),U_9535)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool)),U_9529),U_9531))) )
    & ! [U_9526,U_9530,U_9528,U_9524,U_9532,U_9534] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9524,U_9526)),hAPP(hAPP(c_Product__Type_OPair(U_9524,U_9526),U_9532),U_9534)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool)),U_9528),U_9530)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9524,tc_fun(U_9526,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9524,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),U_9524),c_COMBC(U_9526,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_prod(U_9524,U_9526)),tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),U_9524),hAPP(c_COMBB(tc_prod(U_9524,U_9526),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool),U_9526),c_member(tc_prod(U_9524,U_9526)))),c_Product__Type_OPair(U_9524,U_9526)))),U_9528)),hAPP(hAPP(c_COMBC(U_9524,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),U_9524),c_COMBC(U_9526,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_prod(U_9524,U_9526)),tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),U_9524),hAPP(c_COMBB(tc_prod(U_9524,U_9526),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool),U_9526),c_member(tc_prod(U_9524,U_9526)))),c_Product__Type_OPair(U_9524,U_9526)))),U_9530)),U_9532),U_9534)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2618_3]) ).

cnf(f_2618_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9524,U_9526)),hAPP(hAPP(c_Product__Type_OPair(U_9524,U_9526),U_9532),U_9534)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool)),U_9528),U_9530)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9524,tc_fun(U_9526,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9524,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),U_9524),c_COMBC(U_9526,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_prod(U_9524,U_9526)),tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),U_9524),hAPP(c_COMBB(tc_prod(U_9524,U_9526),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool),U_9526),c_member(tc_prod(U_9524,U_9526)))),c_Product__Type_OPair(U_9524,U_9526)))),U_9528)),hAPP(hAPP(c_COMBC(U_9524,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_fun(U_9526,tc_HOL_Obool)),U_9524),c_COMBC(U_9526,tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9526,tc_prod(U_9524,U_9526)),tc_fun(U_9526,tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool)),U_9524),hAPP(c_COMBB(tc_prod(U_9524,U_9526),tc_fun(tc_fun(tc_prod(U_9524,U_9526),tc_HOL_Obool),tc_HOL_Obool),U_9526),c_member(tc_prod(U_9524,U_9526)))),c_Product__Type_OPair(U_9524,U_9526)))),U_9530)),U_9532),U_9534)) ),
    inference(clausify,[status(thm)],[f_2618_4]) ).

cnf(f_2618_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9525,tc_fun(U_9527,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9525,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),U_9525),c_COMBC(U_9527,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_prod(U_9525,U_9527)),tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),U_9525),hAPP(c_COMBB(tc_prod(U_9525,U_9527),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool),U_9527),c_member(tc_prod(U_9525,U_9527)))),c_Product__Type_OPair(U_9525,U_9527)))),U_9529)),hAPP(hAPP(c_COMBC(U_9525,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_fun(U_9527,tc_HOL_Obool)),U_9525),c_COMBC(U_9527,tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9527,tc_prod(U_9525,U_9527)),tc_fun(U_9527,tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool)),U_9525),hAPP(c_COMBB(tc_prod(U_9525,U_9527),tc_fun(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool),tc_HOL_Obool),U_9527),c_member(tc_prod(U_9525,U_9527)))),c_Product__Type_OPair(U_9525,U_9527)))),U_9531)),U_9533),U_9535))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9525,U_9527)),hAPP(hAPP(c_Product__Type_OPair(U_9525,U_9527),U_9533),U_9535)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9525,U_9527),tc_HOL_Obool)),U_9529),U_9531))) ),
    inference(clausify,[status(thm)],[f_2618_4]) ).

fof(f_2619_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff]) ).

fof(f_2619_2,plain,
    ! [U_9540,U_9539,U_9538,U_9537,U_9536] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9536),U_9537),c_SetInterval_Oord_OgreaterThanLessThan(U_9536,U_9538,U_9539,U_9540)))
        | ~ hBOOL(hAPP(hAPP(U_9538,U_9537),U_9540))
        | ~ hBOOL(hAPP(hAPP(U_9538,U_9539),U_9537)) )
      & ( ( hBOOL(hAPP(hAPP(U_9538,U_9537),U_9540))
          & hBOOL(hAPP(hAPP(U_9538,U_9539),U_9537)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9536),U_9537),c_SetInterval_Oord_OgreaterThanLessThan(U_9536,U_9538,U_9539,U_9540))) ) ),
    inference(variable_rename,[status(thm)],[f_2619_1]) ).

fof(f_2619_3,plain,
    ( ! [U_9550,U_9548,U_9546,U_9544] :
        ( ! [U_9542] : hBOOL(hAPP(hAPP(c_member(U_9542),U_9544),c_SetInterval_Oord_OgreaterThanLessThan(U_9542,U_9546,U_9548,U_9550)))
        | ~ hBOOL(hAPP(hAPP(U_9546,U_9544),U_9550))
        | ~ hBOOL(hAPP(hAPP(U_9546,U_9548),U_9544)) )
    & ! [U_9549,U_9547,U_9545,U_9543] :
        ( ! [U_9541] : ~ hBOOL(hAPP(hAPP(c_member(U_9541),U_9543),c_SetInterval_Oord_OgreaterThanLessThan(U_9541,U_9545,U_9547,U_9549)))
        | ( hBOOL(hAPP(hAPP(U_9545,U_9543),U_9549))
          & hBOOL(hAPP(hAPP(U_9545,U_9547),U_9543)) ) ) ),
    inference(miniscope,[status(thm)],[f_2619_2]) ).

fof(f_2619_4,plain,
    ( ! [U_9543,U_9545,U_9547,U_9549] :
        ( hBOOL(hAPP(hAPP(U_9545,U_9543),U_9549))
        | ~ sP753(U_9543,U_9545,U_9547,U_9549) )
    & ! [U_9543,U_9545,U_9547,U_9549] :
        ( hBOOL(hAPP(hAPP(U_9545,U_9547),U_9543))
        | ~ sP753(U_9543,U_9545,U_9547,U_9549) )
    & ! [U_9546,U_9544,U_9542,U_9548,U_9550] :
        ( hBOOL(hAPP(hAPP(c_member(U_9542),U_9544),c_SetInterval_Oord_OgreaterThanLessThan(U_9542,U_9546,U_9548,U_9550)))
        | ~ hBOOL(hAPP(hAPP(U_9546,U_9544),U_9550))
        | ~ hBOOL(hAPP(hAPP(U_9546,U_9548),U_9544)) )
    & ! [U_9541,U_9543,U_9545,U_9547,U_9549] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9541),U_9543),c_SetInterval_Oord_OgreaterThanLessThan(U_9541,U_9545,U_9547,U_9549)))
        | sP753(U_9543,U_9545,U_9547,U_9549) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP753])],[f_2619_3]) ).

cnf(f_2619_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9541),U_9543),c_SetInterval_Oord_OgreaterThanLessThan(U_9541,U_9545,U_9547,U_9549)))
    | sP753(U_9543,U_9545,U_9547,U_9549) ),
    inference(clausify,[status(thm)],[f_2619_4]) ).

cnf(f_2619_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9542),U_9544),c_SetInterval_Oord_OgreaterThanLessThan(U_9542,U_9546,U_9548,U_9550)))
    | ~ hBOOL(hAPP(hAPP(U_9546,U_9544),U_9550))
    | ~ hBOOL(hAPP(hAPP(U_9546,U_9548),U_9544)) ),
    inference(clausify,[status(thm)],[f_2619_4]) ).

cnf(f_2619_7,plain,
    ( hBOOL(hAPP(hAPP(U_9545,U_9547),U_9543))
    | ~ sP753(U_9543,U_9545,U_9547,U_9549) ),
    inference(clausify,[status(thm)],[f_2619_4]) ).

cnf(f_2619_8,plain,
    ( hBOOL(hAPP(hAPP(U_9545,U_9543),U_9549))
    | ~ sP753(U_9543,U_9545,U_9547,U_9549) ),
    inference(clausify,[status(thm)],[f_2619_4]) ).

fof(f_2620_1,plain,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff]) ).

fof(f_2620_2,plain,
    ! [U_9554,U_9553,U_9552,U_9551] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9551),U_9552),c_SetInterval_Oord_OgreaterThan(U_9551,U_9553,U_9554)))
        | ~ hBOOL(hAPP(hAPP(U_9553,U_9554),U_9552)) )
      & ( hBOOL(hAPP(hAPP(U_9553,U_9554),U_9552))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9551),U_9552),c_SetInterval_Oord_OgreaterThan(U_9551,U_9553,U_9554))) ) ),
    inference(variable_rename,[status(thm)],[f_2620_1]) ).

fof(f_2620_3,plain,
    ( ! [U_9562,U_9560,U_9558] :
        ( ! [U_9556] : hBOOL(hAPP(hAPP(c_member(U_9556),U_9558),c_SetInterval_Oord_OgreaterThan(U_9556,U_9560,U_9562)))
        | ~ hBOOL(hAPP(hAPP(U_9560,U_9562),U_9558)) )
    & ! [U_9561,U_9559,U_9557] :
        ( ! [U_9555] : ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9557),c_SetInterval_Oord_OgreaterThan(U_9555,U_9559,U_9561)))
        | hBOOL(hAPP(hAPP(U_9559,U_9561),U_9557)) ) ),
    inference(miniscope,[status(thm)],[f_2620_2]) ).

fof(f_2620_4,plain,
    ( ! [U_9556,U_9558,U_9560,U_9562] :
        ( hBOOL(hAPP(hAPP(c_member(U_9556),U_9558),c_SetInterval_Oord_OgreaterThan(U_9556,U_9560,U_9562)))
        | ~ hBOOL(hAPP(hAPP(U_9560,U_9562),U_9558)) )
    & ! [U_9557,U_9559,U_9561,U_9555] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9557),c_SetInterval_Oord_OgreaterThan(U_9555,U_9559,U_9561)))
        | hBOOL(hAPP(hAPP(U_9559,U_9561),U_9557)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2620_3]) ).

cnf(f_2620_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9555),U_9557),c_SetInterval_Oord_OgreaterThan(U_9555,U_9559,U_9561)))
    | hBOOL(hAPP(hAPP(U_9559,U_9561),U_9557)) ),
    inference(clausify,[status(thm)],[f_2620_4]) ).

cnf(f_2620_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9556),U_9558),c_SetInterval_Oord_OgreaterThan(U_9556,U_9560,U_9562)))
    | ~ hBOOL(hAPP(hAPP(U_9560,U_9562),U_9558)) ),
    inference(clausify,[status(thm)],[f_2620_4]) ).

fof(f_2621_1,plain,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff]) ).

fof(f_2621_2,plain,
    ! [U_9566,U_9565,U_9564,U_9563] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9563),U_9564),c_SetInterval_Oord_OlessThan(U_9563,U_9565,U_9566)))
        | ~ hBOOL(hAPP(hAPP(U_9565,U_9564),U_9566)) )
      & ( hBOOL(hAPP(hAPP(U_9565,U_9564),U_9566))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9563),U_9564),c_SetInterval_Oord_OlessThan(U_9563,U_9565,U_9566))) ) ),
    inference(variable_rename,[status(thm)],[f_2621_1]) ).

fof(f_2621_3,plain,
    ( ! [U_9574,U_9572,U_9570] :
        ( ! [U_9568] : hBOOL(hAPP(hAPP(c_member(U_9568),U_9570),c_SetInterval_Oord_OlessThan(U_9568,U_9572,U_9574)))
        | ~ hBOOL(hAPP(hAPP(U_9572,U_9570),U_9574)) )
    & ! [U_9573,U_9571,U_9569] :
        ( ! [U_9567] : ~ hBOOL(hAPP(hAPP(c_member(U_9567),U_9569),c_SetInterval_Oord_OlessThan(U_9567,U_9571,U_9573)))
        | hBOOL(hAPP(hAPP(U_9571,U_9569),U_9573)) ) ),
    inference(miniscope,[status(thm)],[f_2621_2]) ).

fof(f_2621_4,plain,
    ( ! [U_9574,U_9568,U_9570,U_9572] :
        ( hBOOL(hAPP(hAPP(c_member(U_9568),U_9570),c_SetInterval_Oord_OlessThan(U_9568,U_9572,U_9574)))
        | ~ hBOOL(hAPP(hAPP(U_9572,U_9570),U_9574)) )
    & ! [U_9571,U_9569,U_9567,U_9573] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9567),U_9569),c_SetInterval_Oord_OlessThan(U_9567,U_9571,U_9573)))
        | hBOOL(hAPP(hAPP(U_9571,U_9569),U_9573)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2621_3]) ).

cnf(f_2621_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9567),U_9569),c_SetInterval_Oord_OlessThan(U_9567,U_9571,U_9573)))
    | hBOOL(hAPP(hAPP(U_9571,U_9569),U_9573)) ),
    inference(clausify,[status(thm)],[f_2621_4]) ).

cnf(f_2621_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9568),U_9570),c_SetInterval_Oord_OlessThan(U_9568,U_9572,U_9574)))
    | ~ hBOOL(hAPP(hAPP(U_9572,U_9570),U_9574)) ),
    inference(clausify,[status(thm)],[f_2621_4]) ).

fof(f_2622_1,plain,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff]) ).

fof(f_2622_2,plain,
    ! [U_9578,U_9577,U_9576,U_9575] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9575),U_9576),c_SetInterval_Oord_OatMost(U_9575,U_9577,U_9578)))
        | ~ hBOOL(hAPP(hAPP(U_9577,U_9576),U_9578)) )
      & ( hBOOL(hAPP(hAPP(U_9577,U_9576),U_9578))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9575),U_9576),c_SetInterval_Oord_OatMost(U_9575,U_9577,U_9578))) ) ),
    inference(variable_rename,[status(thm)],[f_2622_1]) ).

fof(f_2622_3,plain,
    ( ! [U_9586,U_9584,U_9582] :
        ( ! [U_9580] : hBOOL(hAPP(hAPP(c_member(U_9580),U_9582),c_SetInterval_Oord_OatMost(U_9580,U_9584,U_9586)))
        | ~ hBOOL(hAPP(hAPP(U_9584,U_9582),U_9586)) )
    & ! [U_9585,U_9583,U_9581] :
        ( ! [U_9579] : ~ hBOOL(hAPP(hAPP(c_member(U_9579),U_9581),c_SetInterval_Oord_OatMost(U_9579,U_9583,U_9585)))
        | hBOOL(hAPP(hAPP(U_9583,U_9581),U_9585)) ) ),
    inference(miniscope,[status(thm)],[f_2622_2]) ).

fof(f_2622_4,plain,
    ( ! [U_9586,U_9580,U_9582,U_9584] :
        ( hBOOL(hAPP(hAPP(c_member(U_9580),U_9582),c_SetInterval_Oord_OatMost(U_9580,U_9584,U_9586)))
        | ~ hBOOL(hAPP(hAPP(U_9584,U_9582),U_9586)) )
    & ! [U_9583,U_9581,U_9579,U_9585] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9579),U_9581),c_SetInterval_Oord_OatMost(U_9579,U_9583,U_9585)))
        | hBOOL(hAPP(hAPP(U_9583,U_9581),U_9585)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2622_3]) ).

cnf(f_2622_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9579),U_9581),c_SetInterval_Oord_OatMost(U_9579,U_9583,U_9585)))
    | hBOOL(hAPP(hAPP(U_9583,U_9581),U_9585)) ),
    inference(clausify,[status(thm)],[f_2622_4]) ).

cnf(f_2622_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9580),U_9582),c_SetInterval_Oord_OatMost(U_9580,U_9584,U_9586)))
    | ~ hBOOL(hAPP(hAPP(U_9584,U_9582),U_9586)) ),
    inference(clausify,[status(thm)],[f_2622_4]) ).

fof(f_2623_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeast__iff]) ).

fof(f_2623_2,plain,
    ! [U_9588,U_9587] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9587),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9588)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9588),U_9587)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9588),U_9587))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9587),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9588))) ) ),
    inference(variable_rename,[status(thm)],[f_2623_1]) ).

fof(f_2623_3,plain,
    ( ! [U_9592,U_9590] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9590),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9592)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9592),U_9590)) )
    & ! [U_9591,U_9589] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9591),U_9589))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9589),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9591))) ) ),
    inference(miniscope,[status(thm)],[f_2623_2]) ).

fof(f_2623_4,plain,
    ( ! [U_9590,U_9592] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9590),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9592)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9592),U_9590)) )
    & ! [U_9591,U_9589] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9591),U_9589))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9589),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9591))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2623_3]) ).

cnf(f_2623_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9591),U_9589))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9589),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9591))) ),
    inference(clausify,[status(thm)],[f_2623_4]) ).

cnf(f_2623_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9590),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9592)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9592),U_9590)) ),
    inference(clausify,[status(thm)],[f_2623_4]) ).

fof(f_2624_1,plain,
    ! [V_r_2,V_A_2,V_X_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
          & V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_quotientE]) ).

fof(f_2624_2,plain,
    ! [U_9597,U_9596,U_9595,U_9594] :
      ( ? [U_9593] :
          ( hBOOL(hAPP(hAPP(c_member(U_9594),U_9593),U_9596))
          & U_9595 = hAPP(c_Relation_OImage(U_9594,U_9594,U_9597),hAPP(hAPP(c_Set_Oinsert(U_9594),U_9593),c_Orderings_Obot__class_Obot(tc_fun(U_9594,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9594,tc_HOL_Obool)),U_9595),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9594),U_9596),U_9597))) ),
    inference(variable_rename,[status(thm)],[f_2624_1]) ).

fof(f_2624_3,plain,
    ! [U_9597,U_9596,U_9595,U_9594] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9594),sK139(U_9597,U_9596,U_9595,U_9594)),U_9596))
        & U_9595 = hAPP(c_Relation_OImage(U_9594,U_9594,U_9597),hAPP(hAPP(c_Set_Oinsert(U_9594),sK139(U_9597,U_9596,U_9595,U_9594)),c_Orderings_Obot__class_Obot(tc_fun(U_9594,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9594,tc_HOL_Obool)),U_9595),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9594),U_9596),U_9597))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_9593,sK139(U_9597,U_9596,U_9595,U_9594))],[f_2624_2]) ).

fof(f_2624_4,plain,
    ( ! [U_9594,U_9595,U_9596,U_9597] :
        ( hBOOL(hAPP(hAPP(c_member(U_9594),sK139(U_9597,U_9596,U_9595,U_9594)),U_9596))
        | ~ sP754(U_9594,U_9595,U_9596,U_9597) )
    & ! [U_9594,U_9595,U_9596,U_9597] :
        ( U_9595 = hAPP(c_Relation_OImage(U_9594,U_9594,U_9597),hAPP(hAPP(c_Set_Oinsert(U_9594),sK139(U_9597,U_9596,U_9595,U_9594)),c_Orderings_Obot__class_Obot(tc_fun(U_9594,tc_HOL_Obool))))
        | ~ sP754(U_9594,U_9595,U_9596,U_9597) )
    & ! [U_9594,U_9595,U_9596,U_9597] :
        ( sP754(U_9594,U_9595,U_9596,U_9597)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9594,tc_HOL_Obool)),U_9595),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9594),U_9596),U_9597))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP754])],[f_2624_3]) ).

cnf(f_2624_5,plain,
    ( sP754(U_9594,U_9595,U_9596,U_9597)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9594,tc_HOL_Obool)),U_9595),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9594),U_9596),U_9597))) ),
    inference(clausify,[status(thm)],[f_2624_4]) ).

cnf(f_2624_6,plain,
    ( U_9595 = hAPP(c_Relation_OImage(U_9594,U_9594,U_9597),hAPP(hAPP(c_Set_Oinsert(U_9594),sK139(U_9597,U_9596,U_9595,U_9594)),c_Orderings_Obot__class_Obot(tc_fun(U_9594,tc_HOL_Obool))))
    | ~ sP754(U_9594,U_9595,U_9596,U_9597) ),
    inference(clausify,[status(thm)],[f_2624_4]) ).

cnf(f_2624_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9594),sK139(U_9597,U_9596,U_9595,U_9594)),U_9596))
    | ~ sP754(U_9594,U_9595,U_9596,U_9597) ),
    inference(clausify,[status(thm)],[f_2624_4]) ).

fof(f_2625_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff]) ).

fof(f_2625_2,plain,
    ! [U_9603,U_9602,U_9601,U_9600,U_9599,U_9598] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9598),U_9599),c_SetInterval_Oord_OgreaterThanAtMost(U_9598,U_9600,U_9601,U_9602,U_9603)))
        | ~ hBOOL(hAPP(hAPP(U_9600,U_9599),U_9603))
        | ~ hBOOL(hAPP(hAPP(U_9601,U_9602),U_9599)) )
      & ( ( hBOOL(hAPP(hAPP(U_9600,U_9599),U_9603))
          & hBOOL(hAPP(hAPP(U_9601,U_9602),U_9599)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9598),U_9599),c_SetInterval_Oord_OgreaterThanAtMost(U_9598,U_9600,U_9601,U_9602,U_9603))) ) ),
    inference(variable_rename,[status(thm)],[f_2625_1]) ).

fof(f_2625_3,plain,
    ( ! [U_9615,U_9613,U_9611,U_9609,U_9607] :
        ( ! [U_9605] : hBOOL(hAPP(hAPP(c_member(U_9605),U_9607),c_SetInterval_Oord_OgreaterThanAtMost(U_9605,U_9609,U_9611,U_9613,U_9615)))
        | ~ hBOOL(hAPP(hAPP(U_9609,U_9607),U_9615))
        | ~ hBOOL(hAPP(hAPP(U_9611,U_9613),U_9607)) )
    & ! [U_9614,U_9612,U_9610,U_9608,U_9606] :
        ( ! [U_9604] : ~ hBOOL(hAPP(hAPP(c_member(U_9604),U_9606),c_SetInterval_Oord_OgreaterThanAtMost(U_9604,U_9608,U_9610,U_9612,U_9614)))
        | ( hBOOL(hAPP(hAPP(U_9608,U_9606),U_9614))
          & hBOOL(hAPP(hAPP(U_9610,U_9612),U_9606)) ) ) ),
    inference(miniscope,[status(thm)],[f_2625_2]) ).

fof(f_2625_4,plain,
    ( ! [U_9608,U_9606,U_9610,U_9612,U_9614] :
        ( hBOOL(hAPP(hAPP(U_9608,U_9606),U_9614))
        | ~ sP755(U_9608,U_9606,U_9610,U_9612,U_9614) )
    & ! [U_9608,U_9606,U_9610,U_9612,U_9614] :
        ( hBOOL(hAPP(hAPP(U_9610,U_9612),U_9606))
        | ~ sP755(U_9608,U_9606,U_9610,U_9612,U_9614) )
    & ! [U_9609,U_9607,U_9605,U_9611,U_9615,U_9613] :
        ( hBOOL(hAPP(hAPP(c_member(U_9605),U_9607),c_SetInterval_Oord_OgreaterThanAtMost(U_9605,U_9609,U_9611,U_9613,U_9615)))
        | ~ hBOOL(hAPP(hAPP(U_9609,U_9607),U_9615))
        | ~ hBOOL(hAPP(hAPP(U_9611,U_9613),U_9607)) )
    & ! [U_9608,U_9606,U_9610,U_9604,U_9612,U_9614] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9604),U_9606),c_SetInterval_Oord_OgreaterThanAtMost(U_9604,U_9608,U_9610,U_9612,U_9614)))
        | sP755(U_9608,U_9606,U_9610,U_9612,U_9614) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP755])],[f_2625_3]) ).

cnf(f_2625_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9604),U_9606),c_SetInterval_Oord_OgreaterThanAtMost(U_9604,U_9608,U_9610,U_9612,U_9614)))
    | sP755(U_9608,U_9606,U_9610,U_9612,U_9614) ),
    inference(clausify,[status(thm)],[f_2625_4]) ).

cnf(f_2625_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9605),U_9607),c_SetInterval_Oord_OgreaterThanAtMost(U_9605,U_9609,U_9611,U_9613,U_9615)))
    | ~ hBOOL(hAPP(hAPP(U_9609,U_9607),U_9615))
    | ~ hBOOL(hAPP(hAPP(U_9611,U_9613),U_9607)) ),
    inference(clausify,[status(thm)],[f_2625_4]) ).

cnf(f_2625_7,plain,
    ( hBOOL(hAPP(hAPP(U_9610,U_9612),U_9606))
    | ~ sP755(U_9608,U_9606,U_9610,U_9612,U_9614) ),
    inference(clausify,[status(thm)],[f_2625_4]) ).

cnf(f_2625_8,plain,
    ( hBOOL(hAPP(hAPP(U_9608,U_9606),U_9614))
    | ~ sP755(U_9608,U_9606,U_9610,U_9612,U_9614) ),
    inference(clausify,[status(thm)],[f_2625_4]) ).

fof(f_2626_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff]) ).

fof(f_2626_2,plain,
    ! [U_9621,U_9620,U_9619,U_9618,U_9617,U_9616] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9616),U_9617),c_SetInterval_Oord_OatLeastLessThan(U_9616,U_9618,U_9619,U_9620,U_9621)))
        | ~ hBOOL(hAPP(hAPP(U_9619,U_9617),U_9621))
        | ~ hBOOL(hAPP(hAPP(U_9618,U_9620),U_9617)) )
      & ( ( hBOOL(hAPP(hAPP(U_9619,U_9617),U_9621))
          & hBOOL(hAPP(hAPP(U_9618,U_9620),U_9617)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9616),U_9617),c_SetInterval_Oord_OatLeastLessThan(U_9616,U_9618,U_9619,U_9620,U_9621))) ) ),
    inference(variable_rename,[status(thm)],[f_2626_1]) ).

fof(f_2626_3,plain,
    ( ! [U_9633,U_9631,U_9629,U_9627,U_9625] :
        ( ! [U_9623] : hBOOL(hAPP(hAPP(c_member(U_9623),U_9625),c_SetInterval_Oord_OatLeastLessThan(U_9623,U_9627,U_9629,U_9631,U_9633)))
        | ~ hBOOL(hAPP(hAPP(U_9629,U_9625),U_9633))
        | ~ hBOOL(hAPP(hAPP(U_9627,U_9631),U_9625)) )
    & ! [U_9632,U_9630,U_9628,U_9626,U_9624] :
        ( ! [U_9622] : ~ hBOOL(hAPP(hAPP(c_member(U_9622),U_9624),c_SetInterval_Oord_OatLeastLessThan(U_9622,U_9626,U_9628,U_9630,U_9632)))
        | ( hBOOL(hAPP(hAPP(U_9628,U_9624),U_9632))
          & hBOOL(hAPP(hAPP(U_9626,U_9630),U_9624)) ) ) ),
    inference(miniscope,[status(thm)],[f_2626_2]) ).

fof(f_2626_4,plain,
    ( ! [U_9628,U_9624,U_9626,U_9630,U_9632] :
        ( hBOOL(hAPP(hAPP(U_9628,U_9624),U_9632))
        | ~ sP756(U_9628,U_9624,U_9626,U_9630,U_9632) )
    & ! [U_9628,U_9624,U_9626,U_9630,U_9632] :
        ( hBOOL(hAPP(hAPP(U_9626,U_9630),U_9624))
        | ~ sP756(U_9628,U_9624,U_9626,U_9630,U_9632) )
    & ! [U_9627,U_9623,U_9629,U_9625,U_9633,U_9631] :
        ( hBOOL(hAPP(hAPP(c_member(U_9623),U_9625),c_SetInterval_Oord_OatLeastLessThan(U_9623,U_9627,U_9629,U_9631,U_9633)))
        | ~ hBOOL(hAPP(hAPP(U_9629,U_9625),U_9633))
        | ~ hBOOL(hAPP(hAPP(U_9627,U_9631),U_9625)) )
    & ! [U_9628,U_9622,U_9624,U_9626,U_9630,U_9632] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9622),U_9624),c_SetInterval_Oord_OatLeastLessThan(U_9622,U_9626,U_9628,U_9630,U_9632)))
        | sP756(U_9628,U_9624,U_9626,U_9630,U_9632) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP756])],[f_2626_3]) ).

cnf(f_2626_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9622),U_9624),c_SetInterval_Oord_OatLeastLessThan(U_9622,U_9626,U_9628,U_9630,U_9632)))
    | sP756(U_9628,U_9624,U_9626,U_9630,U_9632) ),
    inference(clausify,[status(thm)],[f_2626_4]) ).

cnf(f_2626_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9623),U_9625),c_SetInterval_Oord_OatLeastLessThan(U_9623,U_9627,U_9629,U_9631,U_9633)))
    | ~ hBOOL(hAPP(hAPP(U_9629,U_9625),U_9633))
    | ~ hBOOL(hAPP(hAPP(U_9627,U_9631),U_9625)) ),
    inference(clausify,[status(thm)],[f_2626_4]) ).

cnf(f_2626_7,plain,
    ( hBOOL(hAPP(hAPP(U_9626,U_9630),U_9624))
    | ~ sP756(U_9628,U_9624,U_9626,U_9630,U_9632) ),
    inference(clausify,[status(thm)],[f_2626_4]) ).

cnf(f_2626_8,plain,
    ( hBOOL(hAPP(hAPP(U_9628,U_9624),U_9632))
    | ~ sP756(U_9628,U_9624,U_9626,U_9630,U_9632) ),
    inference(clausify,[status(thm)],[f_2626_4]) ).

fof(f_2627_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
        & hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2E]) ).

fof(f_2627_2,plain,
    ! [U_9639,U_9638,U_9637,U_9636,U_9635,U_9634] :
      ( ( hBOOL(hAPP(hAPP(U_9637,U_9638),U_9639))
        & hBOOL(hAPP(hAPP(U_9636,U_9638),U_9639)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9634,tc_fun(U_9635,tc_HOL_Obool))),U_9636),U_9637),U_9638),U_9639)) ),
    inference(variable_rename,[status(thm)],[f_2627_1]) ).

fof(f_2627_3,plain,
    ! [U_9639,U_9638,U_9637,U_9636] :
      ( ! [U_9635,U_9634] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9634,tc_fun(U_9635,tc_HOL_Obool))),U_9636),U_9637),U_9638),U_9639))
      | ( hBOOL(hAPP(hAPP(U_9637,U_9638),U_9639))
        & hBOOL(hAPP(hAPP(U_9636,U_9638),U_9639)) ) ),
    inference(miniscope,[status(thm)],[f_2627_2]) ).

fof(f_2627_4,plain,
    ( ! [U_9636,U_9637,U_9638,U_9639] :
        ( hBOOL(hAPP(hAPP(U_9637,U_9638),U_9639))
        | ~ sP757(U_9636,U_9637,U_9638,U_9639) )
    & ! [U_9636,U_9637,U_9638,U_9639] :
        ( hBOOL(hAPP(hAPP(U_9636,U_9638),U_9639))
        | ~ sP757(U_9636,U_9637,U_9638,U_9639) )
    & ! [U_9636,U_9634,U_9635,U_9637,U_9638,U_9639] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9634,tc_fun(U_9635,tc_HOL_Obool))),U_9636),U_9637),U_9638),U_9639))
        | sP757(U_9636,U_9637,U_9638,U_9639) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP757])],[f_2627_3]) ).

cnf(f_2627_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9634,tc_fun(U_9635,tc_HOL_Obool))),U_9636),U_9637),U_9638),U_9639))
    | sP757(U_9636,U_9637,U_9638,U_9639) ),
    inference(clausify,[status(thm)],[f_2627_4]) ).

cnf(f_2627_6,plain,
    ( hBOOL(hAPP(hAPP(U_9636,U_9638),U_9639))
    | ~ sP757(U_9636,U_9637,U_9638,U_9639) ),
    inference(clausify,[status(thm)],[f_2627_4]) ).

cnf(f_2627_7,plain,
    ( hBOOL(hAPP(hAPP(U_9637,U_9638),U_9639))
    | ~ sP757(U_9636,U_9637,U_9638,U_9639) ),
    inference(clausify,[status(thm)],[f_2627_4]) ).

fof(f_2628_1,plain,
    ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2I]) ).

fof(f_2628_2,plain,
    ! [U_9645,U_9644,U_9643,U_9642,U_9641,U_9640] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9644,tc_fun(U_9645,tc_HOL_Obool))),U_9640),U_9643),U_9641),U_9642))
      | ~ hBOOL(hAPP(hAPP(U_9643,U_9641),U_9642))
      | ~ hBOOL(hAPP(hAPP(U_9640,U_9641),U_9642)) ),
    inference(variable_rename,[status(thm)],[f_2628_1]) ).

fof(f_2628_3,plain,
    ! [U_9640,U_9641,U_9642,U_9643,U_9644,U_9645] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9644,tc_fun(U_9645,tc_HOL_Obool))),U_9640),U_9643),U_9641),U_9642))
      | ~ hBOOL(hAPP(hAPP(U_9643,U_9641),U_9642))
      | ~ hBOOL(hAPP(hAPP(U_9640,U_9641),U_9642)) ),
    inference(definitional_conversion,[status(esa)],[f_2628_2]) ).

cnf(f_2628_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9644,tc_fun(U_9645,tc_HOL_Obool))),U_9640),U_9643),U_9641),U_9642))
    | ~ hBOOL(hAPP(hAPP(U_9643,U_9641),U_9642))
    | ~ hBOOL(hAPP(hAPP(U_9640,U_9641),U_9642)) ),
    inference(clausify,[status(thm)],[f_2628_3]) ).

fof(f_2629_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).

fof(f_2629_2,plain,
    ! [U_9651,U_9650,U_9649,U_9648,U_9647,U_9646] :
      ( hBOOL(hAPP(hAPP(U_9649,U_9650),U_9651))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9646,tc_fun(U_9647,tc_HOL_Obool))),U_9648),U_9649),U_9650),U_9651)) ),
    inference(variable_rename,[status(thm)],[f_2629_1]) ).

fof(f_2629_3,plain,
    ! [U_9651,U_9650,U_9649] :
      ( ! [U_9648,U_9647,U_9646] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9646,tc_fun(U_9647,tc_HOL_Obool))),U_9648),U_9649),U_9650),U_9651))
      | hBOOL(hAPP(hAPP(U_9649,U_9650),U_9651)) ),
    inference(miniscope,[status(thm)],[f_2629_2]) ).

fof(f_2629_4,plain,
    ! [U_9647,U_9646,U_9648,U_9649,U_9650,U_9651] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9646,tc_fun(U_9647,tc_HOL_Obool))),U_9648),U_9649),U_9650),U_9651))
      | hBOOL(hAPP(hAPP(U_9649,U_9650),U_9651)) ),
    inference(definitional_conversion,[status(esa)],[f_2629_3]) ).

cnf(f_2629_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9646,tc_fun(U_9647,tc_HOL_Obool))),U_9648),U_9649),U_9650),U_9651))
    | hBOOL(hAPP(hAPP(U_9649,U_9650),U_9651)) ),
    inference(clausify,[status(thm)],[f_2629_4]) ).

fof(f_2630_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).

fof(f_2630_2,plain,
    ! [U_9657,U_9656,U_9655,U_9654,U_9653,U_9652] :
      ( hBOOL(hAPP(hAPP(U_9654,U_9656),U_9657))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9652,tc_fun(U_9653,tc_HOL_Obool))),U_9654),U_9655),U_9656),U_9657)) ),
    inference(variable_rename,[status(thm)],[f_2630_1]) ).

fof(f_2630_3,plain,
    ! [U_9657,U_9656,U_9655,U_9654] :
      ( ! [U_9653,U_9652] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9652,tc_fun(U_9653,tc_HOL_Obool))),U_9654),U_9655),U_9656),U_9657))
      | hBOOL(hAPP(hAPP(U_9654,U_9656),U_9657)) ),
    inference(miniscope,[status(thm)],[f_2630_2]) ).

fof(f_2630_4,plain,
    ! [U_9652,U_9653,U_9654,U_9655,U_9656,U_9657] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9652,tc_fun(U_9653,tc_HOL_Obool))),U_9654),U_9655),U_9656),U_9657))
      | hBOOL(hAPP(hAPP(U_9654,U_9656),U_9657)) ),
    inference(definitional_conversion,[status(esa)],[f_2630_3]) ).

cnf(f_2630_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9652,tc_fun(U_9653,tc_HOL_Obool))),U_9654),U_9655),U_9656),U_9657))
    | hBOOL(hAPP(hAPP(U_9654,U_9656),U_9657)) ),
    inference(clausify,[status(thm)],[f_2630_4]) ).

fof(f_2631_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).

fof(f_2631_2,plain,
    ! [U_9659,U_9658] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9658,U_9659)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9659),U_9658))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9658),U_9659)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9659),U_9658))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9658),U_9659))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9658,U_9659) ) ),
    inference(variable_rename,[status(thm)],[f_2631_1]) ).

fof(f_2631_3,plain,
    ( ! [U_9663,U_9661] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9661,U_9663)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9663),U_9661))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9661),U_9663)) ) )
    & ! [U_9662,U_9660] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9662),U_9660))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9660),U_9662))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9660,U_9662) ) ),
    inference(miniscope,[status(thm)],[f_2631_2]) ).

fof(f_2631_4,plain,
    ( ! [U_9663,U_9661] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9663),U_9661))
        | ~ sP758(U_9663,U_9661) )
    & ! [U_9663,U_9661] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9661),U_9663))
        | ~ sP758(U_9663,U_9661) )
    & ! [U_9663,U_9661] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9661,U_9663)
        | sP758(U_9663,U_9661) )
    & ! [U_9660,U_9662] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9662),U_9660))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9660),U_9662))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9660,U_9662) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP758])],[f_2631_3]) ).

cnf(f_2631_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9662),U_9660))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9660),U_9662))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9660,U_9662) ),
    inference(clausify,[status(thm)],[f_2631_4]) ).

cnf(f_2631_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9661,U_9663)
    | sP758(U_9663,U_9661) ),
    inference(clausify,[status(thm)],[f_2631_4]) ).

cnf(f_2631_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9661),U_9663))
    | ~ sP758(U_9663,U_9661) ),
    inference(clausify,[status(thm)],[f_2631_4]) ).

cnf(f_2631_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9663),U_9661))
    | ~ sP758(U_9663,U_9661) ),
    inference(clausify,[status(thm)],[f_2631_4]) ).

fof(f_2632_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).

fof(f_2632_2,plain,
    ! [U_9665,U_9664] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9664,U_9665)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9665),U_9664))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9664),U_9665)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9665),U_9664))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9664),U_9665))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9664,U_9665) ) ),
    inference(variable_rename,[status(thm)],[f_2632_1]) ).

fof(f_2632_3,plain,
    ( ! [U_9669,U_9667] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9667,U_9669)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9669),U_9667))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9667),U_9669)) ) )
    & ! [U_9668,U_9666] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9668),U_9666))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9666),U_9668))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9666,U_9668) ) ),
    inference(miniscope,[status(thm)],[f_2632_2]) ).

fof(f_2632_4,plain,
    ( ! [U_9667,U_9669] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9669),U_9667))
        | ~ sP759(U_9667,U_9669) )
    & ! [U_9667,U_9669] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9667),U_9669))
        | ~ sP759(U_9667,U_9669) )
    & ! [U_9667,U_9669] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9667,U_9669)
        | sP759(U_9667,U_9669) )
    & ! [U_9666,U_9668] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9668),U_9666))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9666),U_9668))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9666,U_9668) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP759])],[f_2632_3]) ).

cnf(f_2632_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9668),U_9666))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9666),U_9668))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9666,U_9668) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

cnf(f_2632_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9667,U_9669)
    | sP759(U_9667,U_9669) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

cnf(f_2632_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9667),U_9669))
    | ~ sP759(U_9667,U_9669) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

cnf(f_2632_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9669),U_9667))
    | ~ sP759(U_9667,U_9669) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

fof(f_2633_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).

fof(f_2633_2,plain,
    ! [U_9671,U_9670] :
      ( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9670,U_9671) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9671),U_9670))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9670),U_9671)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9671),U_9670))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9670),U_9671))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9670,U_9671) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2633_1]) ).

fof(f_2633_3,plain,
    ( ! [U_9675,U_9673] :
        ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9673,U_9675) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9675),U_9673))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9673),U_9675)) ) )
    & ! [U_9674,U_9672] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9674),U_9672))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9672),U_9674))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9672,U_9674) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2633_2]) ).

fof(f_2633_4,plain,
    ( ! [U_9675,U_9673] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9675),U_9673))
        | ~ sP760(U_9675,U_9673) )
    & ! [U_9675,U_9673] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9673),U_9675))
        | ~ sP760(U_9675,U_9673) )
    & ! [U_9675,U_9673] :
        ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9673,U_9675) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | sP760(U_9675,U_9673) )
    & ! [U_9672,U_9674] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9674),U_9672))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9672),U_9674))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9672,U_9674) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP760])],[f_2633_3]) ).

cnf(f_2633_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9674),U_9672))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9672),U_9674))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9672,U_9674) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2633_4]) ).

cnf(f_2633_6,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9673,U_9675) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | sP760(U_9675,U_9673) ),
    inference(clausify,[status(thm)],[f_2633_4]) ).

cnf(f_2633_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9673),U_9675))
    | ~ sP760(U_9675,U_9673) ),
    inference(clausify,[status(thm)],[f_2633_4]) ).

cnf(f_2633_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9675),U_9673))
    | ~ sP760(U_9675,U_9673) ),
    inference(clausify,[status(thm)],[f_2633_4]) ).

fof(f_2634_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).

fof(f_2634_2,plain,
    ! [U_9677,U_9676] :
      ( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9676,U_9677) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9677),U_9676))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9676),U_9677)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9677),U_9676))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9676),U_9677))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9676,U_9677) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2634_1]) ).

fof(f_2634_3,plain,
    ( ! [U_9681,U_9679] :
        ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9679,U_9681) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9681),U_9679))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9679),U_9681)) ) )
    & ! [U_9680,U_9678] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9680),U_9678))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9678),U_9680))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9678,U_9680) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2634_2]) ).

fof(f_2634_4,plain,
    ( ! [U_9681,U_9679] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9681),U_9679))
        | ~ sP761(U_9681,U_9679) )
    & ! [U_9681,U_9679] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9679),U_9681))
        | ~ sP761(U_9681,U_9679) )
    & ! [U_9681,U_9679] :
        ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9679,U_9681) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | sP761(U_9681,U_9679) )
    & ! [U_9678,U_9680] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9680),U_9678))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9678),U_9680))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9678,U_9680) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP761])],[f_2634_3]) ).

cnf(f_2634_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9680),U_9678))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9678),U_9680))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9678,U_9680) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2634_4]) ).

cnf(f_2634_6,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9679,U_9681) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | sP761(U_9681,U_9679) ),
    inference(clausify,[status(thm)],[f_2634_4]) ).

cnf(f_2634_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9679),U_9681))
    | ~ sP761(U_9681,U_9679) ),
    inference(clausify,[status(thm)],[f_2634_4]) ).

cnf(f_2634_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9681),U_9679))
    | ~ sP761(U_9681,U_9679) ),
    inference(clausify,[status(thm)],[f_2634_4]) ).

fof(f_2635_1,plain,
    ! [V_a_2,V_b_2] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty]) ).

fof(f_2635_2,plain,
    ! [U_9683,U_9682] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9683,U_9682) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9682),U_9683)) ),
    inference(variable_rename,[status(thm)],[f_2635_1]) ).

fof(f_2635_3,plain,
    ! [U_9683,U_9682] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9683,U_9682) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9682),U_9683)) ),
    inference(definitional_conversion,[status(esa)],[f_2635_2]) ).

cnf(f_2635_4,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9683,U_9682) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9682),U_9683)) ),
    inference(clausify,[status(thm)],[f_2635_3]) ).

fof(f_2636_1,plain,
    ! [V_k_2,V_l_2] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty]) ).

fof(f_2636_2,plain,
    ! [U_9685,U_9684] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9685,U_9684) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9684),U_9685)) ),
    inference(variable_rename,[status(thm)],[f_2636_1]) ).

fof(f_2636_3,plain,
    ! [U_9684,U_9685] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9685,U_9684) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9684),U_9685)) ),
    inference(definitional_conversion,[status(esa)],[f_2636_2]) ).

cnf(f_2636_4,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9685,U_9684) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9684),U_9685)) ),
    inference(clausify,[status(thm)],[f_2636_3]) ).

fof(f_2637_1,plain,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff]) ).

fof(f_2637_2,plain,
    ! [U_9689,U_9688,U_9687,U_9686] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9686),U_9687),c_SetInterval_Oord_OatLeast(U_9686,U_9688,U_9689)))
        | ~ hBOOL(hAPP(hAPP(U_9688,U_9689),U_9687)) )
      & ( hBOOL(hAPP(hAPP(U_9688,U_9689),U_9687))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9686),U_9687),c_SetInterval_Oord_OatLeast(U_9686,U_9688,U_9689))) ) ),
    inference(variable_rename,[status(thm)],[f_2637_1]) ).

fof(f_2637_3,plain,
    ( ! [U_9697,U_9695,U_9693] :
        ( ! [U_9691] : hBOOL(hAPP(hAPP(c_member(U_9691),U_9693),c_SetInterval_Oord_OatLeast(U_9691,U_9695,U_9697)))
        | ~ hBOOL(hAPP(hAPP(U_9695,U_9697),U_9693)) )
    & ! [U_9696,U_9694,U_9692] :
        ( ! [U_9690] : ~ hBOOL(hAPP(hAPP(c_member(U_9690),U_9692),c_SetInterval_Oord_OatLeast(U_9690,U_9694,U_9696)))
        | hBOOL(hAPP(hAPP(U_9694,U_9696),U_9692)) ) ),
    inference(miniscope,[status(thm)],[f_2637_2]) ).

fof(f_2637_4,plain,
    ( ! [U_9691,U_9693,U_9695,U_9697] :
        ( hBOOL(hAPP(hAPP(c_member(U_9691),U_9693),c_SetInterval_Oord_OatLeast(U_9691,U_9695,U_9697)))
        | ~ hBOOL(hAPP(hAPP(U_9695,U_9697),U_9693)) )
    & ! [U_9696,U_9692,U_9690,U_9694] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9690),U_9692),c_SetInterval_Oord_OatLeast(U_9690,U_9694,U_9696)))
        | hBOOL(hAPP(hAPP(U_9694,U_9696),U_9692)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2637_3]) ).

cnf(f_2637_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9690),U_9692),c_SetInterval_Oord_OatLeast(U_9690,U_9694,U_9696)))
    | hBOOL(hAPP(hAPP(U_9694,U_9696),U_9692)) ),
    inference(clausify,[status(thm)],[f_2637_4]) ).

cnf(f_2637_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9691),U_9693),c_SetInterval_Oord_OatLeast(U_9691,U_9695,U_9697)))
    | ~ hBOOL(hAPP(hAPP(U_9695,U_9697),U_9693)) ),
    inference(clausify,[status(thm)],[f_2637_4]) ).

fof(f_2638_1,plain,
    ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff]) ).

fof(f_2638_2,plain,
    ! [U_9702,U_9701,U_9700,U_9699,U_9698] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9698),U_9699),c_SetInterval_Oord_OatLeastAtMost(U_9698,U_9700,U_9701,U_9702)))
        | ~ hBOOL(hAPP(hAPP(U_9700,U_9699),U_9702))
        | ~ hBOOL(hAPP(hAPP(U_9700,U_9701),U_9699)) )
      & ( ( hBOOL(hAPP(hAPP(U_9700,U_9699),U_9702))
          & hBOOL(hAPP(hAPP(U_9700,U_9701),U_9699)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9698),U_9699),c_SetInterval_Oord_OatLeastAtMost(U_9698,U_9700,U_9701,U_9702))) ) ),
    inference(variable_rename,[status(thm)],[f_2638_1]) ).

fof(f_2638_3,plain,
    ( ! [U_9712,U_9710,U_9708,U_9706] :
        ( ! [U_9704] : hBOOL(hAPP(hAPP(c_member(U_9704),U_9706),c_SetInterval_Oord_OatLeastAtMost(U_9704,U_9708,U_9710,U_9712)))
        | ~ hBOOL(hAPP(hAPP(U_9708,U_9706),U_9712))
        | ~ hBOOL(hAPP(hAPP(U_9708,U_9710),U_9706)) )
    & ! [U_9711,U_9709,U_9707,U_9705] :
        ( ! [U_9703] : ~ hBOOL(hAPP(hAPP(c_member(U_9703),U_9705),c_SetInterval_Oord_OatLeastAtMost(U_9703,U_9707,U_9709,U_9711)))
        | ( hBOOL(hAPP(hAPP(U_9707,U_9705),U_9711))
          & hBOOL(hAPP(hAPP(U_9707,U_9709),U_9705)) ) ) ),
    inference(miniscope,[status(thm)],[f_2638_2]) ).

fof(f_2638_4,plain,
    ( ! [U_9705,U_9707,U_9709,U_9711] :
        ( hBOOL(hAPP(hAPP(U_9707,U_9705),U_9711))
        | ~ sP762(U_9705,U_9707,U_9709,U_9711) )
    & ! [U_9705,U_9707,U_9709,U_9711] :
        ( hBOOL(hAPP(hAPP(U_9707,U_9709),U_9705))
        | ~ sP762(U_9705,U_9707,U_9709,U_9711) )
    & ! [U_9708,U_9710,U_9704,U_9706,U_9712] :
        ( hBOOL(hAPP(hAPP(c_member(U_9704),U_9706),c_SetInterval_Oord_OatLeastAtMost(U_9704,U_9708,U_9710,U_9712)))
        | ~ hBOOL(hAPP(hAPP(U_9708,U_9706),U_9712))
        | ~ hBOOL(hAPP(hAPP(U_9708,U_9710),U_9706)) )
    & ! [U_9703,U_9705,U_9707,U_9709,U_9711] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9703),U_9705),c_SetInterval_Oord_OatLeastAtMost(U_9703,U_9707,U_9709,U_9711)))
        | sP762(U_9705,U_9707,U_9709,U_9711) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP762])],[f_2638_3]) ).

cnf(f_2638_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9703),U_9705),c_SetInterval_Oord_OatLeastAtMost(U_9703,U_9707,U_9709,U_9711)))
    | sP762(U_9705,U_9707,U_9709,U_9711) ),
    inference(clausify,[status(thm)],[f_2638_4]) ).

cnf(f_2638_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9704),U_9706),c_SetInterval_Oord_OatLeastAtMost(U_9704,U_9708,U_9710,U_9712)))
    | ~ hBOOL(hAPP(hAPP(U_9708,U_9706),U_9712))
    | ~ hBOOL(hAPP(hAPP(U_9708,U_9710),U_9706)) ),
    inference(clausify,[status(thm)],[f_2638_4]) ).

cnf(f_2638_7,plain,
    ( hBOOL(hAPP(hAPP(U_9707,U_9709),U_9705))
    | ~ sP762(U_9705,U_9707,U_9709,U_9711) ),
    inference(clausify,[status(thm)],[f_2638_4]) ).

cnf(f_2638_8,plain,
    ( hBOOL(hAPP(hAPP(U_9707,U_9705),U_9711))
    | ~ sP762(U_9705,U_9707,U_9709,U_9711) ),
    inference(clausify,[status(thm)],[f_2638_4]) ).

fof(f_2639_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove]) ).

fof(f_2639_2,plain,
    ! [U_9715,U_9714,U_9713] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_9713,U_9714) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9713),U_9715),c_Big__Operators_Olattice__class_OInf__fin(U_9713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_9713,U_9714) = U_9715
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9713),U_9715),U_9714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9713),U_9714))
      | ~ class_Lattices_Olattice(U_9713) ),
    inference(variable_rename,[status(thm)],[f_2639_1]) ).

fof(f_2639_3,plain,
    ( ! [U_9713,U_9714,U_9715] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_9713,U_9714) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9713),U_9715),c_Big__Operators_Olattice__class_OInf__fin(U_9713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))
        | ~ sP763(U_9713,U_9714,U_9715) )
    & ! [U_9713,U_9714,U_9715] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_9713,U_9714) = U_9715
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))
        | ~ sP763(U_9713,U_9714,U_9715) )
    & ! [U_9713,U_9714,U_9715] :
        ( sP763(U_9713,U_9714,U_9715)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9713),U_9715),U_9714))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9713),U_9714))
        | ~ class_Lattices_Olattice(U_9713) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP763])],[f_2639_2]) ).

cnf(f_2639_4,plain,
    ( sP763(U_9713,U_9714,U_9715)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9713),U_9715),U_9714))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9713),U_9714))
    | ~ class_Lattices_Olattice(U_9713) ),
    inference(clausify,[status(thm)],[f_2639_3]) ).

cnf(f_2639_5,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9713,U_9714) = U_9715
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))
    | ~ sP763(U_9713,U_9714,U_9715) ),
    inference(clausify,[status(thm)],[f_2639_3]) ).

cnf(f_2639_6,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9713,U_9714) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9713),U_9715),c_Big__Operators_Olattice__class_OInf__fin(U_9713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9713,tc_HOL_Obool)),U_9714),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9715),c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9713,tc_HOL_Obool))
    | ~ sP763(U_9713,U_9714,U_9715) ),
    inference(clausify,[status(thm)],[f_2639_3]) ).

fof(f_2640_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove]) ).

fof(f_2640_2,plain,
    ! [U_9718,U_9717,U_9716] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_9716,U_9717) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9716),U_9718),c_Big__Operators_Olattice__class_OSup__fin(U_9716,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_9716,U_9717) = U_9718
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9716),U_9718),U_9717))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9716),U_9717))
      | ~ class_Lattices_Olattice(U_9716) ),
    inference(variable_rename,[status(thm)],[f_2640_1]) ).

fof(f_2640_3,plain,
    ( ! [U_9718,U_9717,U_9716] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_9716,U_9717) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9716),U_9718),c_Big__Operators_Olattice__class_OSup__fin(U_9716,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))
        | ~ sP764(U_9718,U_9717,U_9716) )
    & ! [U_9718,U_9717,U_9716] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_9716,U_9717) = U_9718
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))
        | ~ sP764(U_9718,U_9717,U_9716) )
    & ! [U_9718,U_9717,U_9716] :
        ( sP764(U_9718,U_9717,U_9716)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9716),U_9718),U_9717))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9716),U_9717))
        | ~ class_Lattices_Olattice(U_9716) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP764])],[f_2640_2]) ).

cnf(f_2640_4,plain,
    ( sP764(U_9718,U_9717,U_9716)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9716),U_9718),U_9717))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9716),U_9717))
    | ~ class_Lattices_Olattice(U_9716) ),
    inference(clausify,[status(thm)],[f_2640_3]) ).

cnf(f_2640_5,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9716,U_9717) = U_9718
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))
    | ~ sP764(U_9718,U_9717,U_9716) ),
    inference(clausify,[status(thm)],[f_2640_3]) ).

cnf(f_2640_6,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9716,U_9717) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9716),U_9718),c_Big__Operators_Olattice__class_OSup__fin(U_9716,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9716,tc_HOL_Obool)),U_9717),hAPP(hAPP(c_Set_Oinsert(U_9716),U_9718),c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9716,tc_HOL_Obool))
    | ~ sP764(U_9718,U_9717,U_9716) ),
    inference(clausify,[status(thm)],[f_2640_3]) ).

fof(f_2641_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oremove]) ).

fof(f_2641_2,plain,
    ! [U_9721,U_9720,U_9719] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_9719,U_9720) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9719),U_9721),c_Big__Operators_Olinorder__class_OMax(U_9719,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_9719,U_9720) = U_9721
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9719),U_9721),U_9720))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9719),U_9720))
      | ~ class_Orderings_Olinorder(U_9719) ),
    inference(variable_rename,[status(thm)],[f_2641_1]) ).

fof(f_2641_3,plain,
    ( ! [U_9719,U_9721,U_9720] :
        ( c_Big__Operators_Olinorder__class_OMax(U_9719,U_9720) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9719),U_9721),c_Big__Operators_Olinorder__class_OMax(U_9719,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))
        | ~ sP765(U_9719,U_9721,U_9720) )
    & ! [U_9719,U_9721,U_9720] :
        ( c_Big__Operators_Olinorder__class_OMax(U_9719,U_9720) = U_9721
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))
        | ~ sP765(U_9719,U_9721,U_9720) )
    & ! [U_9719,U_9721,U_9720] :
        ( sP765(U_9719,U_9721,U_9720)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9719),U_9721),U_9720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9719),U_9720))
        | ~ class_Orderings_Olinorder(U_9719) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP765])],[f_2641_2]) ).

cnf(f_2641_4,plain,
    ( sP765(U_9719,U_9721,U_9720)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9719),U_9721),U_9720))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9719),U_9720))
    | ~ class_Orderings_Olinorder(U_9719) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

cnf(f_2641_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9719,U_9720) = U_9721
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))
    | ~ sP765(U_9719,U_9721,U_9720) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

cnf(f_2641_6,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9719,U_9720) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9719),U_9721),c_Big__Operators_Olinorder__class_OMax(U_9719,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9719,tc_HOL_Obool)),U_9720),hAPP(hAPP(c_Set_Oinsert(U_9719),U_9721),c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9719,tc_HOL_Obool))
    | ~ sP765(U_9719,U_9721,U_9720) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

fof(f_2642_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup]) ).

fof(f_2642_2,plain,
    ! [U_9723,U_9722] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),c_Big__Operators_Olattice__class_OInf__fin(U_9722,U_9723)),c_Big__Operators_Olattice__class_OSup__fin(U_9722,U_9723)))
      | U_9723 = c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9722),U_9723))
      | ~ class_Lattices_Olattice(U_9722) ),
    inference(variable_rename,[status(thm)],[f_2642_1]) ).

fof(f_2642_3,plain,
    ! [U_9723,U_9722] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),c_Big__Operators_Olattice__class_OInf__fin(U_9722,U_9723)),c_Big__Operators_Olattice__class_OSup__fin(U_9722,U_9723)))
      | U_9723 = c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9722),U_9723))
      | ~ class_Lattices_Olattice(U_9722) ),
    inference(definitional_conversion,[status(esa)],[f_2642_2]) ).

cnf(f_2642_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),c_Big__Operators_Olattice__class_OInf__fin(U_9722,U_9723)),c_Big__Operators_Olattice__class_OSup__fin(U_9722,U_9723)))
    | U_9723 = c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9722),U_9723))
    | ~ class_Lattices_Olattice(U_9722) ),
    inference(clausify,[status(thm)],[f_2642_3]) ).

fof(f_2643_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Osingleton]) ).

fof(f_2643_2,plain,
    ! [U_9725,U_9724] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9724,hAPP(hAPP(c_Set_Oinsert(U_9724),U_9725),c_Orderings_Obot__class_Obot(tc_fun(U_9724,tc_HOL_Obool)))) = U_9725
      | ~ class_Orderings_Olinorder(U_9724) ),
    inference(variable_rename,[status(thm)],[f_2643_1]) ).

fof(f_2643_3,plain,
    ! [U_9725,U_9724] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9724,hAPP(hAPP(c_Set_Oinsert(U_9724),U_9725),c_Orderings_Obot__class_Obot(tc_fun(U_9724,tc_HOL_Obool)))) = U_9725
      | ~ class_Orderings_Olinorder(U_9724) ),
    inference(definitional_conversion,[status(esa)],[f_2643_2]) ).

cnf(f_2643_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9724,hAPP(hAPP(c_Set_Oinsert(U_9724),U_9725),c_Orderings_Obot__class_Obot(tc_fun(U_9724,tc_HOL_Obool)))) = U_9725
    | ~ class_Orderings_Olinorder(U_9724) ),
    inference(clausify,[status(thm)],[f_2643_3]) ).

fof(f_2644_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton]) ).

fof(f_2644_2,plain,
    ! [U_9727,U_9726] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9726,hAPP(hAPP(c_Set_Oinsert(U_9726),U_9727),c_Orderings_Obot__class_Obot(tc_fun(U_9726,tc_HOL_Obool)))) = U_9727
      | ~ class_Lattices_Olattice(U_9726) ),
    inference(variable_rename,[status(thm)],[f_2644_1]) ).

fof(f_2644_3,plain,
    ! [U_9726,U_9727] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9726,hAPP(hAPP(c_Set_Oinsert(U_9726),U_9727),c_Orderings_Obot__class_Obot(tc_fun(U_9726,tc_HOL_Obool)))) = U_9727
      | ~ class_Lattices_Olattice(U_9726) ),
    inference(definitional_conversion,[status(esa)],[f_2644_2]) ).

cnf(f_2644_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9726,hAPP(hAPP(c_Set_Oinsert(U_9726),U_9727),c_Orderings_Obot__class_Obot(tc_fun(U_9726,tc_HOL_Obool)))) = U_9727
    | ~ class_Lattices_Olattice(U_9726) ),
    inference(clausify,[status(thm)],[f_2644_3]) ).

fof(f_2645_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton]) ).

fof(f_2645_2,plain,
    ! [U_9729,U_9728] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9728,hAPP(hAPP(c_Set_Oinsert(U_9728),U_9729),c_Orderings_Obot__class_Obot(tc_fun(U_9728,tc_HOL_Obool)))) = U_9729
      | ~ class_Lattices_Olattice(U_9728) ),
    inference(variable_rename,[status(thm)],[f_2645_1]) ).

fof(f_2645_3,plain,
    ! [U_9728,U_9729] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9728,hAPP(hAPP(c_Set_Oinsert(U_9728),U_9729),c_Orderings_Obot__class_Obot(tc_fun(U_9728,tc_HOL_Obool)))) = U_9729
      | ~ class_Lattices_Olattice(U_9728) ),
    inference(definitional_conversion,[status(esa)],[f_2645_2]) ).

cnf(f_2645_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9728,hAPP(hAPP(c_Set_Oinsert(U_9728),U_9729),c_Orderings_Obot__class_Obot(tc_fun(U_9728,tc_HOL_Obool)))) = U_9729
    | ~ class_Lattices_Olattice(U_9728) ),
    inference(clausify,[status(thm)],[f_2645_3]) ).

fof(f_2646_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__ge]) ).

fof(f_2646_2,plain,
    ! [U_9732,U_9731,U_9730] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9730),U_9732),c_Big__Operators_Olinorder__class_OMax(U_9730,U_9731)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9730),U_9732),U_9731))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9730),U_9731))
      | ~ class_Orderings_Olinorder(U_9730) ),
    inference(variable_rename,[status(thm)],[f_2646_1]) ).

fof(f_2646_3,plain,
    ! [U_9730,U_9731,U_9732] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9730),U_9732),c_Big__Operators_Olinorder__class_OMax(U_9730,U_9731)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9730),U_9732),U_9731))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9730),U_9731))
      | ~ class_Orderings_Olinorder(U_9730) ),
    inference(definitional_conversion,[status(esa)],[f_2646_2]) ).

cnf(f_2646_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9730),U_9732),c_Big__Operators_Olinorder__class_OMax(U_9730,U_9731)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9730),U_9732),U_9731))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9730),U_9731))
    | ~ class_Orderings_Olinorder(U_9730) ),
    inference(clausify,[status(thm)],[f_2646_3]) ).

fof(f_2647_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__in]) ).

fof(f_2647_2,plain,
    ! [U_9734,U_9733] :
      ( hBOOL(hAPP(hAPP(c_member(U_9733),c_Big__Operators_Olinorder__class_OMax(U_9733,U_9734)),U_9734))
      | U_9734 = c_Orderings_Obot__class_Obot(tc_fun(U_9733,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9733),U_9734))
      | ~ class_Orderings_Olinorder(U_9733) ),
    inference(variable_rename,[status(thm)],[f_2647_1]) ).

fof(f_2647_3,plain,
    ! [U_9734,U_9733] :
      ( hBOOL(hAPP(hAPP(c_member(U_9733),c_Big__Operators_Olinorder__class_OMax(U_9733,U_9734)),U_9734))
      | U_9734 = c_Orderings_Obot__class_Obot(tc_fun(U_9733,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9733),U_9734))
      | ~ class_Orderings_Olinorder(U_9733) ),
    inference(definitional_conversion,[status(esa)],[f_2647_2]) ).

cnf(f_2647_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9733),c_Big__Operators_Olinorder__class_OMax(U_9733,U_9734)),U_9734))
    | U_9734 = c_Orderings_Obot__class_Obot(tc_fun(U_9733,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9733),U_9734))
    | ~ class_Orderings_Olinorder(U_9733) ),
    inference(clausify,[status(thm)],[f_2647_3]) ).

fof(f_2648_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb]) ).

fof(f_2648_2,plain,
    ! [U_9737,U_9736,U_9735] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9735),U_9737),c_Big__Operators_Olattice__class_OInf__fin(U_9735,U_9736)) = U_9737
      | ~ hBOOL(hAPP(hAPP(c_member(U_9735),U_9737),U_9736))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),U_9736))
      | ~ class_Lattices_Olattice(U_9735) ),
    inference(variable_rename,[status(thm)],[f_2648_1]) ).

fof(f_2648_3,plain,
    ! [U_9736,U_9735,U_9737] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9735),U_9737),c_Big__Operators_Olattice__class_OInf__fin(U_9735,U_9736)) = U_9737
      | ~ hBOOL(hAPP(hAPP(c_member(U_9735),U_9737),U_9736))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),U_9736))
      | ~ class_Lattices_Olattice(U_9735) ),
    inference(definitional_conversion,[status(esa)],[f_2648_2]) ).

cnf(f_2648_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9735),U_9737),c_Big__Operators_Olattice__class_OInf__fin(U_9735,U_9736)) = U_9737
    | ~ hBOOL(hAPP(hAPP(c_member(U_9735),U_9737),U_9736))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),U_9736))
    | ~ class_Lattices_Olattice(U_9735) ),
    inference(clausify,[status(thm)],[f_2648_3]) ).

fof(f_2649_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem]) ).

fof(f_2649_2,plain,
    ! [U_9740,U_9739,U_9738] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9738),U_9740),c_Big__Operators_Olattice__class_OSup__fin(U_9738,U_9739)) = c_Big__Operators_Olattice__class_OSup__fin(U_9738,U_9739)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9738),U_9740),U_9739))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9738),U_9739))
      | ~ class_Lattices_Olattice(U_9738) ),
    inference(variable_rename,[status(thm)],[f_2649_1]) ).

fof(f_2649_3,plain,
    ! [U_9739,U_9738,U_9740] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9738),U_9740),c_Big__Operators_Olattice__class_OSup__fin(U_9738,U_9739)) = c_Big__Operators_Olattice__class_OSup__fin(U_9738,U_9739)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9738),U_9740),U_9739))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9738),U_9739))
      | ~ class_Lattices_Olattice(U_9738) ),
    inference(definitional_conversion,[status(esa)],[f_2649_2]) ).

cnf(f_2649_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9738),U_9740),c_Big__Operators_Olattice__class_OSup__fin(U_9738,U_9739)) = c_Big__Operators_Olattice__class_OSup__fin(U_9738,U_9739)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9738),U_9740),U_9739))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9738),U_9739))
    | ~ class_Lattices_Olattice(U_9738) ),
    inference(clausify,[status(thm)],[f_2649_3]) ).

fof(f_2650_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem]) ).

fof(f_2650_2,plain,
    ! [U_9743,U_9742,U_9741] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9741),U_9743),c_Big__Operators_Olattice__class_OInf__fin(U_9741,U_9742)) = c_Big__Operators_Olattice__class_OInf__fin(U_9741,U_9742)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9741),U_9743),U_9742))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9741),U_9742))
      | ~ class_Lattices_Olattice(U_9741) ),
    inference(variable_rename,[status(thm)],[f_2650_1]) ).

fof(f_2650_3,plain,
    ! [U_9742,U_9741,U_9743] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9741),U_9743),c_Big__Operators_Olattice__class_OInf__fin(U_9741,U_9742)) = c_Big__Operators_Olattice__class_OInf__fin(U_9741,U_9742)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9741),U_9743),U_9742))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9741),U_9742))
      | ~ class_Lattices_Olattice(U_9741) ),
    inference(definitional_conversion,[status(esa)],[f_2650_2]) ).

cnf(f_2650_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9741),U_9743),c_Big__Operators_Olattice__class_OInf__fin(U_9741,U_9742)) = c_Big__Operators_Olattice__class_OInf__fin(U_9741,U_9742)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9741),U_9743),U_9742))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9741),U_9742))
    | ~ class_Lattices_Olattice(U_9741) ),
    inference(clausify,[status(thm)],[f_2650_3]) ).

fof(f_2651_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb]) ).

fof(f_2651_2,plain,
    ! [U_9746,U_9745,U_9744] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9744),U_9746),c_Big__Operators_Olattice__class_OSup__fin(U_9744,U_9745)) = U_9746
      | ~ hBOOL(hAPP(hAPP(c_member(U_9744),U_9746),U_9745))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9744),U_9745))
      | ~ class_Lattices_Olattice(U_9744) ),
    inference(variable_rename,[status(thm)],[f_2651_1]) ).

fof(f_2651_3,plain,
    ! [U_9745,U_9744,U_9746] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9744),U_9746),c_Big__Operators_Olattice__class_OSup__fin(U_9744,U_9745)) = U_9746
      | ~ hBOOL(hAPP(hAPP(c_member(U_9744),U_9746),U_9745))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9744),U_9745))
      | ~ class_Lattices_Olattice(U_9744) ),
    inference(definitional_conversion,[status(esa)],[f_2651_2]) ).

cnf(f_2651_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9744),U_9746),c_Big__Operators_Olattice__class_OSup__fin(U_9744,U_9745)) = U_9746
    | ~ hBOOL(hAPP(hAPP(c_member(U_9744),U_9746),U_9745))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9744),U_9745))
    | ~ class_Lattices_Olattice(U_9744) ),
    inference(clausify,[status(thm)],[f_2651_3]) ).

fof(f_2652_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem]) ).

fof(f_2652_2,plain,
    ! [U_9749,U_9748,U_9747] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9747),U_9749),c_Big__Operators_Olinorder__class_OMax(U_9747,U_9748)) = c_Big__Operators_Olinorder__class_OMax(U_9747,U_9748)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9747),U_9749),U_9748))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),U_9748))
      | ~ class_Orderings_Olinorder(U_9747) ),
    inference(variable_rename,[status(thm)],[f_2652_1]) ).

fof(f_2652_3,plain,
    ! [U_9748,U_9747,U_9749] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9747),U_9749),c_Big__Operators_Olinorder__class_OMax(U_9747,U_9748)) = c_Big__Operators_Olinorder__class_OMax(U_9747,U_9748)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9747),U_9749),U_9748))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),U_9748))
      | ~ class_Orderings_Olinorder(U_9747) ),
    inference(definitional_conversion,[status(esa)],[f_2652_2]) ).

cnf(f_2652_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9747),U_9749),c_Big__Operators_Olinorder__class_OMax(U_9747,U_9748)) = c_Big__Operators_Olinorder__class_OMax(U_9747,U_9748)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9747),U_9749),U_9748))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),U_9748))
    | ~ class_Orderings_Olinorder(U_9747) ),
    inference(clausify,[status(thm)],[f_2652_3]) ).

fof(f_2653_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).

fof(f_2653_2,plain,
    ! [U_9751,U_9750] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9750,U_9751)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9750),U_9751)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9750),U_9751))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9750,U_9751) ) ),
    inference(variable_rename,[status(thm)],[f_2653_1]) ).

fof(f_2653_3,plain,
    ( ! [U_9755,U_9753] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9753,U_9755)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9753),U_9755)) )
    & ! [U_9754,U_9752] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9752),U_9754))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9752,U_9754) ) ),
    inference(miniscope,[status(thm)],[f_2653_2]) ).

fof(f_2653_4,plain,
    ( ! [U_9755,U_9753] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9753,U_9755)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9753),U_9755)) )
    & ! [U_9752,U_9754] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9752),U_9754))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9752,U_9754) ) ),
    inference(definitional_conversion,[status(esa)],[f_2653_3]) ).

cnf(f_2653_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9752),U_9754))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9752,U_9754) ),
    inference(clausify,[status(thm)],[f_2653_4]) ).

cnf(f_2653_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9753,U_9755)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9753),U_9755)) ),
    inference(clausify,[status(thm)],[f_2653_4]) ).

fof(f_2654_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).

fof(f_2654_2,plain,
    ! [U_9757,U_9756] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9756,U_9757) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9756),U_9757)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9756),U_9757))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9756,U_9757) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2654_1]) ).

fof(f_2654_3,plain,
    ( ! [U_9761,U_9759] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9759,U_9761) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9759),U_9761)) )
    & ! [U_9760,U_9758] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9758),U_9760))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9758,U_9760) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2654_2]) ).

fof(f_2654_4,plain,
    ( ! [U_9761,U_9759] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9759,U_9761) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9759),U_9761)) )
    & ! [U_9758,U_9760] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9758),U_9760))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9758,U_9760) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2654_3]) ).

cnf(f_2654_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9758),U_9760))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9758,U_9760) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2654_4]) ).

cnf(f_2654_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9759,U_9761) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9759),U_9761)) ),
    inference(clausify,[status(thm)],[f_2654_4]) ).

fof(f_2655_1,plain,
    ! [V_a_2,V_b_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty]) ).

fof(f_2655_2,plain,
    ! [U_9763,U_9762] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9763,U_9762) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9763),U_9762))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9762),U_9763)) ),
    inference(variable_rename,[status(thm)],[f_2655_1]) ).

fof(f_2655_3,plain,
    ! [U_9763,U_9762] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9763,U_9762) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9763),U_9762))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9762),U_9763)) ),
    inference(definitional_conversion,[status(esa)],[f_2655_2]) ).

cnf(f_2655_4,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9763,U_9762) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9763),U_9762))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9762),U_9763)) ),
    inference(clausify,[status(thm)],[f_2655_3]) ).

fof(f_2656_1,plain,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton_H]) ).

fof(f_2656_2,plain,
    ! [U_9765,U_9764] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9764,U_9765) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9764),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_9764 != U_9765 ),
    inference(variable_rename,[status(thm)],[f_2656_1]) ).

fof(f_2656_3,plain,
    ! [U_9764,U_9765] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9764,U_9765) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9764),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_9764 != U_9765 ),
    inference(definitional_conversion,[status(esa)],[f_2656_2]) ).

cnf(f_2656_4,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9764,U_9765) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9764),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_9764 != U_9765 ),
    inference(clausify,[status(thm)],[f_2656_3]) ).

fof(f_2657_1,plain,
    ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton]) ).

fof(f_2657_2,plain,
    ! [U_9766] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9766,U_9766) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9766),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2657_1]) ).

fof(f_2657_3,plain,
    ! [U_9766] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9766,U_9766) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9766),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2657_2]) ).

cnf(f_2657_4,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9766,U_9766) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9766),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2657_3]) ).

fof(f_2658_1,plain,
    ! [V_c_2,V_b_2,V_a_2] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | V_b_2 != V_c_2
        | V_a_2 != V_b_2 )
      & ( ( V_b_2 = V_c_2
          & V_a_2 = V_b_2 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff]) ).

fof(f_2658_2,plain,
    ! [U_9769,U_9768,U_9767] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9767,U_9768) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9769),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_9768 != U_9769
        | U_9767 != U_9768 )
      & ( ( U_9768 = U_9769
          & U_9767 = U_9768 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9767,U_9768) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9769),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_2658_1]) ).

fof(f_2658_3,plain,
    ( ! [U_9775,U_9773,U_9771] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9771,U_9773) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9775),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_9773 != U_9775
        | U_9771 != U_9773 )
    & ! [U_9774,U_9772,U_9770] :
        ( ( U_9772 = U_9774
          & U_9770 = U_9772 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9770,U_9772) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9774),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_2658_2]) ).

fof(f_2658_4,plain,
    ( ! [U_9774,U_9770,U_9772] :
        ( U_9772 = U_9774
        | ~ sP766(U_9774,U_9770,U_9772) )
    & ! [U_9774,U_9770,U_9772] :
        ( U_9770 = U_9772
        | ~ sP766(U_9774,U_9770,U_9772) )
    & ! [U_9775,U_9773,U_9771] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9771,U_9773) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9775),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_9773 != U_9775
        | U_9771 != U_9773 )
    & ! [U_9774,U_9770,U_9772] :
        ( sP766(U_9774,U_9770,U_9772)
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9770,U_9772) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9774),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP766])],[f_2658_3]) ).

cnf(f_2658_5,plain,
    ( sP766(U_9774,U_9770,U_9772)
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9770,U_9772) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9774),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_2658_4]) ).

cnf(f_2658_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9771,U_9773) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9775),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_9773 != U_9775
    | U_9771 != U_9773 ),
    inference(clausify,[status(thm)],[f_2658_4]) ).

cnf(f_2658_7,plain,
    ( U_9770 = U_9772
    | ~ sP766(U_9774,U_9770,U_9772) ),
    inference(clausify,[status(thm)],[f_2658_4]) ).

cnf(f_2658_8,plain,
    ( U_9772 = U_9774
    | ~ sP766(U_9774,U_9770,U_9772) ),
    inference(clausify,[status(thm)],[f_2658_4]) ).

fof(f_2659_1,plain,
    ! [V_N_2,V_M_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__mono]) ).

fof(f_2659_2,plain,
    ! [U_9778,U_9777,U_9776] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),c_Big__Operators_Olinorder__class_OMax(U_9776,U_9777)),c_Big__Operators_Olinorder__class_OMax(U_9776,U_9778)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9776),U_9778))
      | U_9777 = c_Orderings_Obot__class_Obot(tc_fun(U_9776,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778))
      | ~ class_Orderings_Olinorder(U_9776) ),
    inference(variable_rename,[status(thm)],[f_2659_1]) ).

fof(f_2659_3,plain,
    ! [U_9776,U_9777,U_9778] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),c_Big__Operators_Olinorder__class_OMax(U_9776,U_9777)),c_Big__Operators_Olinorder__class_OMax(U_9776,U_9778)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9776),U_9778))
      | U_9777 = c_Orderings_Obot__class_Obot(tc_fun(U_9776,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778))
      | ~ class_Orderings_Olinorder(U_9776) ),
    inference(definitional_conversion,[status(esa)],[f_2659_2]) ).

cnf(f_2659_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),c_Big__Operators_Olinorder__class_OMax(U_9776,U_9777)),c_Big__Operators_Olinorder__class_OMax(U_9776,U_9778)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9776),U_9778))
    | U_9777 = c_Orderings_Obot__class_Obot(tc_fun(U_9776,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778))
    | ~ class_Orderings_Olinorder(U_9776) ),
    inference(clausify,[status(thm)],[f_2659_3]) ).

fof(f_2660_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem]) ).

fof(f_2660_2,plain,
    ! [U_9781,U_9780,U_9779] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9779,hAPP(hAPP(c_Set_Oinsert(U_9779),U_9781),U_9780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9779),U_9781),c_Big__Operators_Olattice__class_OSup__fin(U_9779,U_9780))
      | U_9780 = c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9779),U_9780))
      | ~ class_Lattices_Olattice(U_9779) ),
    inference(variable_rename,[status(thm)],[f_2660_1]) ).

fof(f_2660_3,plain,
    ! [U_9779,U_9780,U_9781] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9779,hAPP(hAPP(c_Set_Oinsert(U_9779),U_9781),U_9780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9779),U_9781),c_Big__Operators_Olattice__class_OSup__fin(U_9779,U_9780))
      | U_9780 = c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9779),U_9780))
      | ~ class_Lattices_Olattice(U_9779) ),
    inference(definitional_conversion,[status(esa)],[f_2660_2]) ).

cnf(f_2660_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9779,hAPP(hAPP(c_Set_Oinsert(U_9779),U_9781),U_9780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9779),U_9781),c_Big__Operators_Olattice__class_OSup__fin(U_9779,U_9780))
    | U_9780 = c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9779),U_9780))
    | ~ class_Lattices_Olattice(U_9779) ),
    inference(clausify,[status(thm)],[f_2660_3]) ).

fof(f_2661_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem]) ).

fof(f_2661_2,plain,
    ! [U_9784,U_9783,U_9782] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9782,hAPP(hAPP(c_Set_Oinsert(U_9782),U_9784),U_9783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9782),U_9784),c_Big__Operators_Olattice__class_OInf__fin(U_9782,U_9783))
      | U_9783 = c_Orderings_Obot__class_Obot(tc_fun(U_9782,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9782),U_9783))
      | ~ class_Lattices_Olattice(U_9782) ),
    inference(variable_rename,[status(thm)],[f_2661_1]) ).

fof(f_2661_3,plain,
    ! [U_9782,U_9783,U_9784] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9782,hAPP(hAPP(c_Set_Oinsert(U_9782),U_9784),U_9783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9782),U_9784),c_Big__Operators_Olattice__class_OInf__fin(U_9782,U_9783))
      | U_9783 = c_Orderings_Obot__class_Obot(tc_fun(U_9782,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9782),U_9783))
      | ~ class_Lattices_Olattice(U_9782) ),
    inference(definitional_conversion,[status(esa)],[f_2661_2]) ).

cnf(f_2661_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9782,hAPP(hAPP(c_Set_Oinsert(U_9782),U_9784),U_9783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9782),U_9784),c_Big__Operators_Olattice__class_OInf__fin(U_9782,U_9783))
    | U_9783 = c_Orderings_Obot__class_Obot(tc_fun(U_9782,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9782),U_9783))
    | ~ class_Lattices_Olattice(U_9782) ),
    inference(clausify,[status(thm)],[f_2661_3]) ).

fof(f_2662_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__insert]) ).

fof(f_2662_2,plain,
    ! [U_9787,U_9786,U_9785] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9785,hAPP(hAPP(c_Set_Oinsert(U_9785),U_9787),U_9786)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9785),U_9787),c_Big__Operators_Olinorder__class_OMax(U_9785,U_9786))
      | U_9786 = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9785),U_9786))
      | ~ class_Orderings_Olinorder(U_9785) ),
    inference(variable_rename,[status(thm)],[f_2662_1]) ).

fof(f_2662_3,plain,
    ! [U_9785,U_9786,U_9787] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9785,hAPP(hAPP(c_Set_Oinsert(U_9785),U_9787),U_9786)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9785),U_9787),c_Big__Operators_Olinorder__class_OMax(U_9785,U_9786))
      | U_9786 = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9785),U_9786))
      | ~ class_Orderings_Olinorder(U_9785) ),
    inference(definitional_conversion,[status(esa)],[f_2662_2]) ).

cnf(f_2662_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9785,hAPP(hAPP(c_Set_Oinsert(U_9785),U_9787),U_9786)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9785),U_9787),c_Big__Operators_Olinorder__class_OMax(U_9785,U_9786))
    | U_9786 = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9785),U_9786))
    | ~ class_Orderings_Olinorder(U_9785) ),
    inference(clausify,[status(thm)],[f_2662_3]) ).

fof(f_2663_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem]) ).

fof(f_2663_2,plain,
    ! [U_9790,U_9789,U_9788] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9788),c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9790)),c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9789)) = c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9789)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9788,tc_HOL_Obool)),U_9790),U_9789))
      | U_9790 = c_Orderings_Obot__class_Obot(tc_fun(U_9788,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9788),U_9789))
      | ~ class_Lattices_Olattice(U_9788) ),
    inference(variable_rename,[status(thm)],[f_2663_1]) ).

fof(f_2663_3,plain,
    ! [U_9788,U_9789,U_9790] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9788),c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9790)),c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9789)) = c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9789)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9788,tc_HOL_Obool)),U_9790),U_9789))
      | U_9790 = c_Orderings_Obot__class_Obot(tc_fun(U_9788,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9788),U_9789))
      | ~ class_Lattices_Olattice(U_9788) ),
    inference(definitional_conversion,[status(esa)],[f_2663_2]) ).

cnf(f_2663_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9788),c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9790)),c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9789)) = c_Big__Operators_Olattice__class_OSup__fin(U_9788,U_9789)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9788,tc_HOL_Obool)),U_9790),U_9789))
    | U_9790 = c_Orderings_Obot__class_Obot(tc_fun(U_9788,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9788),U_9789))
    | ~ class_Lattices_Olattice(U_9788) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

fof(f_2664_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem]) ).

fof(f_2664_2,plain,
    ! [U_9793,U_9792,U_9791] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9791),c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9793)),c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9792)) = c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9792)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9791,tc_HOL_Obool)),U_9793),U_9792))
      | U_9793 = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9791),U_9792))
      | ~ class_Lattices_Olattice(U_9791) ),
    inference(variable_rename,[status(thm)],[f_2664_1]) ).

fof(f_2664_3,plain,
    ! [U_9791,U_9792,U_9793] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9791),c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9793)),c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9792)) = c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9792)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9791,tc_HOL_Obool)),U_9793),U_9792))
      | U_9793 = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9791),U_9792))
      | ~ class_Lattices_Olattice(U_9791) ),
    inference(definitional_conversion,[status(esa)],[f_2664_2]) ).

cnf(f_2664_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9791),c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9793)),c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9792)) = c_Big__Operators_Olattice__class_OInf__fin(U_9791,U_9792)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9791,tc_HOL_Obool)),U_9793),U_9792))
    | U_9793 = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9791),U_9792))
    | ~ class_Lattices_Olattice(U_9791) ),
    inference(clausify,[status(thm)],[f_2664_3]) ).

fof(f_2665_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem]) ).

fof(f_2665_2,plain,
    ! [U_9796,U_9795,U_9794] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9794,tc_HOL_Obool)),U_9795),U_9796)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9794),c_Big__Operators_Olattice__class_OSup__fin(U_9794,U_9795)),c_Big__Operators_Olattice__class_OSup__fin(U_9794,U_9796))
      | U_9796 = c_Orderings_Obot__class_Obot(tc_fun(U_9794,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9796))
      | U_9795 = c_Orderings_Obot__class_Obot(tc_fun(U_9794,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9795))
      | ~ class_Lattices_Olattice(U_9794) ),
    inference(variable_rename,[status(thm)],[f_2665_1]) ).

fof(f_2665_3,plain,
    ! [U_9794,U_9795,U_9796] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9794,tc_HOL_Obool)),U_9795),U_9796)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9794),c_Big__Operators_Olattice__class_OSup__fin(U_9794,U_9795)),c_Big__Operators_Olattice__class_OSup__fin(U_9794,U_9796))
      | U_9796 = c_Orderings_Obot__class_Obot(tc_fun(U_9794,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9796))
      | U_9795 = c_Orderings_Obot__class_Obot(tc_fun(U_9794,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9795))
      | ~ class_Lattices_Olattice(U_9794) ),
    inference(definitional_conversion,[status(esa)],[f_2665_2]) ).

cnf(f_2665_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9794,tc_HOL_Obool)),U_9795),U_9796)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9794),c_Big__Operators_Olattice__class_OSup__fin(U_9794,U_9795)),c_Big__Operators_Olattice__class_OSup__fin(U_9794,U_9796))
    | U_9796 = c_Orderings_Obot__class_Obot(tc_fun(U_9794,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9796))
    | U_9795 = c_Orderings_Obot__class_Obot(tc_fun(U_9794,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9795))
    | ~ class_Lattices_Olattice(U_9794) ),
    inference(clausify,[status(thm)],[f_2665_3]) ).

fof(f_2666_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem]) ).

fof(f_2666_2,plain,
    ! [U_9799,U_9798,U_9797] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9797),c_Big__Operators_Olinorder__class_OMax(U_9797,U_9799)),c_Big__Operators_Olinorder__class_OMax(U_9797,U_9798)) = c_Big__Operators_Olinorder__class_OMax(U_9797,U_9798)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9797,tc_HOL_Obool)),U_9799),U_9798))
      | U_9799 = c_Orderings_Obot__class_Obot(tc_fun(U_9797,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9797),U_9798))
      | ~ class_Orderings_Olinorder(U_9797) ),
    inference(variable_rename,[status(thm)],[f_2666_1]) ).

fof(f_2666_3,plain,
    ! [U_9798,U_9799,U_9797] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9797),c_Big__Operators_Olinorder__class_OMax(U_9797,U_9799)),c_Big__Operators_Olinorder__class_OMax(U_9797,U_9798)) = c_Big__Operators_Olinorder__class_OMax(U_9797,U_9798)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9797,tc_HOL_Obool)),U_9799),U_9798))
      | U_9799 = c_Orderings_Obot__class_Obot(tc_fun(U_9797,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9797),U_9798))
      | ~ class_Orderings_Olinorder(U_9797) ),
    inference(definitional_conversion,[status(esa)],[f_2666_2]) ).

cnf(f_2666_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9797),c_Big__Operators_Olinorder__class_OMax(U_9797,U_9799)),c_Big__Operators_Olinorder__class_OMax(U_9797,U_9798)) = c_Big__Operators_Olinorder__class_OMax(U_9797,U_9798)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9797,tc_HOL_Obool)),U_9799),U_9798))
    | U_9799 = c_Orderings_Obot__class_Obot(tc_fun(U_9797,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9797),U_9798))
    | ~ class_Orderings_Olinorder(U_9797) ),
    inference(clausify,[status(thm)],[f_2666_3]) ).

fof(f_2667_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem]) ).

fof(f_2667_2,plain,
    ! [U_9802,U_9801,U_9800] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9800,tc_HOL_Obool)),U_9801),U_9802)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9800),c_Big__Operators_Olattice__class_OInf__fin(U_9800,U_9801)),c_Big__Operators_Olattice__class_OInf__fin(U_9800,U_9802))
      | U_9802 = c_Orderings_Obot__class_Obot(tc_fun(U_9800,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9802))
      | U_9801 = c_Orderings_Obot__class_Obot(tc_fun(U_9800,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9801))
      | ~ class_Lattices_Olattice(U_9800) ),
    inference(variable_rename,[status(thm)],[f_2667_1]) ).

fof(f_2667_3,plain,
    ! [U_9800,U_9801,U_9802] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9800,tc_HOL_Obool)),U_9801),U_9802)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9800),c_Big__Operators_Olattice__class_OInf__fin(U_9800,U_9801)),c_Big__Operators_Olattice__class_OInf__fin(U_9800,U_9802))
      | U_9802 = c_Orderings_Obot__class_Obot(tc_fun(U_9800,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9802))
      | U_9801 = c_Orderings_Obot__class_Obot(tc_fun(U_9800,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9801))
      | ~ class_Lattices_Olattice(U_9800) ),
    inference(definitional_conversion,[status(esa)],[f_2667_2]) ).

cnf(f_2667_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9800,tc_HOL_Obool)),U_9801),U_9802)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9800),c_Big__Operators_Olattice__class_OInf__fin(U_9800,U_9801)),c_Big__Operators_Olattice__class_OInf__fin(U_9800,U_9802))
    | U_9802 = c_Orderings_Obot__class_Obot(tc_fun(U_9800,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9802))
    | U_9801 = c_Orderings_Obot__class_Obot(tc_fun(U_9800,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9801))
    | ~ class_Lattices_Olattice(U_9800) ),
    inference(clausify,[status(thm)],[f_2667_3]) ).

fof(f_2668_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__Un]) ).

fof(f_2668_2,plain,
    ! [U_9805,U_9804,U_9803] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9803,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9803,tc_HOL_Obool)),U_9804),U_9805)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9803),c_Big__Operators_Olinorder__class_OMax(U_9803,U_9804)),c_Big__Operators_Olinorder__class_OMax(U_9803,U_9805))
      | U_9805 = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9805))
      | U_9804 = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9804))
      | ~ class_Orderings_Olinorder(U_9803) ),
    inference(variable_rename,[status(thm)],[f_2668_1]) ).

fof(f_2668_3,plain,
    ! [U_9805,U_9803,U_9804] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9803,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9803,tc_HOL_Obool)),U_9804),U_9805)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9803),c_Big__Operators_Olinorder__class_OMax(U_9803,U_9804)),c_Big__Operators_Olinorder__class_OMax(U_9803,U_9805))
      | U_9805 = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9805))
      | U_9804 = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9804))
      | ~ class_Orderings_Olinorder(U_9803) ),
    inference(definitional_conversion,[status(esa)],[f_2668_2]) ).

cnf(f_2668_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9803,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9803,tc_HOL_Obool)),U_9804),U_9805)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9803),c_Big__Operators_Olinorder__class_OMax(U_9803,U_9804)),c_Big__Operators_Olinorder__class_OMax(U_9803,U_9805))
    | U_9805 = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9805))
    | U_9804 = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9804))
    | ~ class_Orderings_Olinorder(U_9803) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

fof(f_2669_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__subset__iff]) ).

fof(f_2669_2,plain,
    ! [U_9809,U_9808,U_9807,U_9806] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9806,U_9807)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9808,U_9809)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9807),U_9809))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9808),U_9806)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9806),U_9807)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9807),U_9809))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9808),U_9806)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9806),U_9807))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9806,U_9807)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9808,U_9809))) ) ),
    inference(variable_rename,[status(thm)],[f_2669_1]) ).

fof(f_2669_3,plain,
    ( ! [U_9817,U_9815,U_9813,U_9811] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9811,U_9813)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9815,U_9817)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9813),U_9817))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9815),U_9811)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9811),U_9813)) ) )
    & ! [U_9816,U_9814,U_9812,U_9810] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9812),U_9816))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9814),U_9810)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9810),U_9812))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9810,U_9812)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9814,U_9816))) ) ),
    inference(miniscope,[status(thm)],[f_2669_2]) ).

fof(f_2669_4,plain,
    ( ! [U_9813,U_9811,U_9817,U_9815] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9813),U_9817))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9815),U_9811))
        | ~ sP768(U_9813,U_9811,U_9817,U_9815) )
    & ! [U_9813,U_9811,U_9817,U_9815] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9811),U_9813))
        | ~ sP768(U_9813,U_9811,U_9817,U_9815) )
    & ! [U_9810,U_9812,U_9814,U_9816] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9812),U_9816))
        | ~ sP767(U_9810,U_9812,U_9814,U_9816) )
    & ! [U_9810,U_9812,U_9814,U_9816] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9814),U_9810))
        | ~ sP767(U_9810,U_9812,U_9814,U_9816) )
    & ! [U_9813,U_9811,U_9817,U_9815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9811,U_9813)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9815,U_9817)))
        | sP768(U_9813,U_9811,U_9817,U_9815) )
    & ! [U_9810,U_9812,U_9814,U_9816] :
        ( sP767(U_9810,U_9812,U_9814,U_9816)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9810),U_9812))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9810,U_9812)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9814,U_9816))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP767,sP768])],[f_2669_3]) ).

cnf(f_2669_5,plain,
    ( sP767(U_9810,U_9812,U_9814,U_9816)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9810),U_9812))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9810,U_9812)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9814,U_9816))) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9811,U_9813)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9815,U_9817)))
    | sP768(U_9813,U_9811,U_9817,U_9815) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9814),U_9810))
    | ~ sP767(U_9810,U_9812,U_9814,U_9816) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9812),U_9816))
    | ~ sP767(U_9810,U_9812,U_9814,U_9816) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9811),U_9813))
    | ~ sP768(U_9813,U_9811,U_9817,U_9815) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9813),U_9817))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9815),U_9811))
    | ~ sP768(U_9813,U_9811,U_9817,U_9815) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

fof(f_2670_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__psubset__iff]) ).

fof(f_2670_2,plain,
    ! [U_9821,U_9820,U_9819,U_9818] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9818,U_9819)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820,U_9821)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820),U_9821))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9821),U_9819))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9819),U_9821)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9818),U_9820))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820),U_9818)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9819),U_9821))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820),U_9818)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9818),U_9819)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820),U_9821))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9821),U_9819))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9819),U_9821)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9818),U_9820))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820),U_9818)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9819),U_9821))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820),U_9818)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9818),U_9819)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9818,U_9819)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9820,U_9821))) ) ),
    inference(variable_rename,[status(thm)],[f_2670_1]) ).

fof(f_2670_3,plain,
    ( ! [U_9829,U_9827,U_9825,U_9823] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823,U_9825)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827,U_9829)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9829))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9829),U_9825))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9825),U_9829)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823),U_9827))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9823)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9825),U_9829))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9823)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823),U_9825)) ) )
    & ! [U_9828,U_9826,U_9824,U_9822] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9828))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9828),U_9824))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9824),U_9828)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822),U_9826))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9822)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9824),U_9828))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9822)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822),U_9824)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822,U_9824)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826,U_9828))) ) ),
    inference(miniscope,[status(thm)],[f_2670_2]) ).

fof(f_2670_4,plain,
    ( ! [U_9823,U_9825,U_9827,U_9829] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9829),U_9825))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9825),U_9829))
        | ~ sP773(U_9823,U_9825,U_9827,U_9829) )
    & ! [U_9823,U_9825,U_9827,U_9829] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823),U_9827))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9823))
        | ~ sP773(U_9823,U_9825,U_9827,U_9829) )
    & ! [U_9823,U_9825,U_9827,U_9829] :
        ( sP773(U_9823,U_9825,U_9827,U_9829)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9825),U_9829))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9823))
        | ~ sP774(U_9823,U_9825,U_9827,U_9829) )
    & ! [U_9823,U_9825,U_9827,U_9829] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823),U_9825))
        | ~ sP774(U_9823,U_9825,U_9827,U_9829) )
    & ! [U_9828,U_9824] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9828),U_9824))
        | ~ sP770(U_9828,U_9824) )
    & ! [U_9828,U_9824] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9824),U_9828))
        | ~ sP770(U_9828,U_9824) )
    & ! [U_9822,U_9826] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822),U_9826))
        | ~ sP769(U_9822,U_9826) )
    & ! [U_9822,U_9826] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9822))
        | ~ sP769(U_9822,U_9826) )
    & ! [U_9822,U_9828,U_9826,U_9824] :
        ( sP770(U_9828,U_9824)
        | sP769(U_9822,U_9826)
        | ~ sP771(U_9822,U_9828,U_9826,U_9824) )
    & ! [U_9822,U_9828,U_9826,U_9824] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9824),U_9828))
        | ~ sP771(U_9822,U_9828,U_9826,U_9824) )
    & ! [U_9822,U_9828,U_9826,U_9824] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9822))
        | ~ sP771(U_9822,U_9828,U_9826,U_9824) )
    & ! [U_9822,U_9828,U_9826,U_9824] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9828))
        | ~ sP772(U_9822,U_9828,U_9826,U_9824) )
    & ! [U_9822,U_9828,U_9826,U_9824] :
        ( sP771(U_9822,U_9828,U_9826,U_9824)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822),U_9824))
        | ~ sP772(U_9822,U_9828,U_9826,U_9824) )
    & ! [U_9823,U_9825,U_9827,U_9829] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823,U_9825)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827,U_9829)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9829))
        | sP774(U_9823,U_9825,U_9827,U_9829) )
    & ! [U_9822,U_9828,U_9826,U_9824] :
        ( sP772(U_9822,U_9828,U_9826,U_9824)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822,U_9824)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826,U_9828))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP769,sP770,sP771,sP772,sP773,sP774])],[f_2670_3]) ).

cnf(f_2670_5,plain,
    ( sP772(U_9822,U_9828,U_9826,U_9824)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822,U_9824)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826,U_9828))) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823,U_9825)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827,U_9829)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9829))
    | sP774(U_9823,U_9825,U_9827,U_9829) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_7,plain,
    ( sP771(U_9822,U_9828,U_9826,U_9824)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822),U_9824))
    | ~ sP772(U_9822,U_9828,U_9826,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9828))
    | ~ sP772(U_9822,U_9828,U_9826,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9822))
    | ~ sP771(U_9822,U_9828,U_9826,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_10,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9824),U_9828))
    | ~ sP771(U_9822,U_9828,U_9826,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_11,plain,
    ( sP770(U_9828,U_9824)
    | sP769(U_9822,U_9826)
    | ~ sP771(U_9822,U_9828,U_9826,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_12,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9826),U_9822))
    | ~ sP769(U_9822,U_9826) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9822),U_9826))
    | ~ sP769(U_9822,U_9826) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_14,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9824),U_9828))
    | ~ sP770(U_9828,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9828),U_9824))
    | ~ sP770(U_9828,U_9824) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_16,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823),U_9825))
    | ~ sP774(U_9823,U_9825,U_9827,U_9829) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_17,plain,
    ( sP773(U_9823,U_9825,U_9827,U_9829)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9825),U_9829))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9823))
    | ~ sP774(U_9823,U_9825,U_9827,U_9829) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_18,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9823),U_9827))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9827),U_9823))
    | ~ sP773(U_9823,U_9825,U_9827,U_9829) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_19,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9829),U_9825))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9825),U_9829))
    | ~ sP773(U_9823,U_9825,U_9827,U_9829) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

fof(f_2671_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(f_2671_2,plain,
    ! [U_9832,U_9831,U_9830] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9830,hAPP(hAPP(c_Set_Oinsert(U_9830),U_9832),U_9831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9830),U_9832),c_Big__Operators_Olattice__class_OSup__fin(U_9830,U_9831))
      | U_9831 = c_Orderings_Obot__class_Obot(tc_fun(U_9830,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9830),U_9832),U_9831))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831))
      | ~ class_Lattices_Olattice(U_9830) ),
    inference(variable_rename,[status(thm)],[f_2671_1]) ).

fof(f_2671_3,plain,
    ! [U_9832,U_9830,U_9831] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9830,hAPP(hAPP(c_Set_Oinsert(U_9830),U_9832),U_9831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9830),U_9832),c_Big__Operators_Olattice__class_OSup__fin(U_9830,U_9831))
      | U_9831 = c_Orderings_Obot__class_Obot(tc_fun(U_9830,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9830),U_9832),U_9831))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831))
      | ~ class_Lattices_Olattice(U_9830) ),
    inference(definitional_conversion,[status(esa)],[f_2671_2]) ).

cnf(f_2671_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9830,hAPP(hAPP(c_Set_Oinsert(U_9830),U_9832),U_9831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9830),U_9832),c_Big__Operators_Olattice__class_OSup__fin(U_9830,U_9831))
    | U_9831 = c_Orderings_Obot__class_Obot(tc_fun(U_9830,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9830),U_9832),U_9831))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831))
    | ~ class_Lattices_Olattice(U_9830) ),
    inference(clausify,[status(thm)],[f_2671_3]) ).

fof(f_2672_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(f_2672_2,plain,
    ! [U_9835,U_9834,U_9833] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9833,hAPP(hAPP(c_Set_Oinsert(U_9833),U_9835),U_9834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9833),U_9835),c_Big__Operators_Olattice__class_OInf__fin(U_9833,U_9834))
      | U_9834 = c_Orderings_Obot__class_Obot(tc_fun(U_9833,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9833),U_9835),U_9834))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9833),U_9834))
      | ~ class_Lattices_Olattice(U_9833) ),
    inference(variable_rename,[status(thm)],[f_2672_1]) ).

fof(f_2672_3,plain,
    ! [U_9833,U_9834,U_9835] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9833,hAPP(hAPP(c_Set_Oinsert(U_9833),U_9835),U_9834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9833),U_9835),c_Big__Operators_Olattice__class_OInf__fin(U_9833,U_9834))
      | U_9834 = c_Orderings_Obot__class_Obot(tc_fun(U_9833,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9833),U_9835),U_9834))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9833),U_9834))
      | ~ class_Lattices_Olattice(U_9833) ),
    inference(definitional_conversion,[status(esa)],[f_2672_2]) ).

cnf(f_2672_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9833,hAPP(hAPP(c_Set_Oinsert(U_9833),U_9835),U_9834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9833),U_9835),c_Big__Operators_Olattice__class_OInf__fin(U_9833,U_9834))
    | U_9834 = c_Orderings_Obot__class_Obot(tc_fun(U_9833,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9833),U_9835),U_9834))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9833),U_9834))
    | ~ class_Lattices_Olattice(U_9833) ),
    inference(clausify,[status(thm)],[f_2672_3]) ).

fof(f_2673_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oinsert]) ).

fof(f_2673_2,plain,
    ! [U_9838,U_9837,U_9836] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9836,hAPP(hAPP(c_Set_Oinsert(U_9836),U_9838),U_9837)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9836),U_9838),c_Big__Operators_Olinorder__class_OMax(U_9836,U_9837))
      | U_9837 = c_Orderings_Obot__class_Obot(tc_fun(U_9836,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9836),U_9838),U_9837))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9836),U_9837))
      | ~ class_Orderings_Olinorder(U_9836) ),
    inference(variable_rename,[status(thm)],[f_2673_1]) ).

fof(f_2673_3,plain,
    ! [U_9836,U_9837,U_9838] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9836,hAPP(hAPP(c_Set_Oinsert(U_9836),U_9838),U_9837)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9836),U_9838),c_Big__Operators_Olinorder__class_OMax(U_9836,U_9837))
      | U_9837 = c_Orderings_Obot__class_Obot(tc_fun(U_9836,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9836),U_9838),U_9837))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9836),U_9837))
      | ~ class_Orderings_Olinorder(U_9836) ),
    inference(definitional_conversion,[status(esa)],[f_2673_2]) ).

cnf(f_2673_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9836,hAPP(hAPP(c_Set_Oinsert(U_9836),U_9838),U_9837)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9836),U_9838),c_Big__Operators_Olinorder__class_OMax(U_9836,U_9837))
    | U_9837 = c_Orderings_Obot__class_Obot(tc_fun(U_9836,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9836),U_9838),U_9837))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9836),U_9837))
    | ~ class_Orderings_Olinorder(U_9836) ),
    inference(clausify,[status(thm)],[f_2673_3]) ).

fof(f_2674_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove]) ).

fof(f_2674_2,plain,
    ! [U_9841,U_9840,U_9839] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),U_9840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9839),U_9841),c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),U_9840)) = U_9841
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9839),U_9840))
      | ~ class_Lattices_Olattice(U_9839) ),
    inference(variable_rename,[status(thm)],[f_2674_1]) ).

fof(f_2674_3,plain,
    ( ! [U_9841,U_9839,U_9840] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),U_9840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9839),U_9841),c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))
        | ~ sP775(U_9841,U_9839,U_9840) )
    & ! [U_9841,U_9839,U_9840] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),U_9840)) = U_9841
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))
        | ~ sP775(U_9841,U_9839,U_9840) )
    & ! [U_9841,U_9839,U_9840] :
        ( sP775(U_9841,U_9839,U_9840)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9839),U_9840))
        | ~ class_Lattices_Olattice(U_9839) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP775])],[f_2674_2]) ).

cnf(f_2674_4,plain,
    ( sP775(U_9841,U_9839,U_9840)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9839),U_9840))
    | ~ class_Lattices_Olattice(U_9839) ),
    inference(clausify,[status(thm)],[f_2674_3]) ).

cnf(f_2674_5,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),U_9840)) = U_9841
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))
    | ~ sP775(U_9841,U_9839,U_9840) ),
    inference(clausify,[status(thm)],[f_2674_3]) ).

cnf(f_2674_6,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),U_9840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9839),U_9841),c_Big__Operators_Olattice__class_OSup__fin(U_9839,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9839,tc_HOL_Obool)),U_9840),hAPP(hAPP(c_Set_Oinsert(U_9839),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9839,tc_HOL_Obool))
    | ~ sP775(U_9841,U_9839,U_9840) ),
    inference(clausify,[status(thm)],[f_2674_3]) ).

fof(f_2675_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove]) ).

fof(f_2675_2,plain,
    ! [U_9844,U_9843,U_9842] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),U_9843)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9842),U_9844),c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),U_9843)) = U_9844
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843))
      | ~ class_Lattices_Olattice(U_9842) ),
    inference(variable_rename,[status(thm)],[f_2675_1]) ).

fof(f_2675_3,plain,
    ( ! [U_9844,U_9842,U_9843] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),U_9843)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9842),U_9844),c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))
        | ~ sP776(U_9844,U_9842,U_9843) )
    & ! [U_9844,U_9842,U_9843] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),U_9843)) = U_9844
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))
        | ~ sP776(U_9844,U_9842,U_9843) )
    & ! [U_9844,U_9842,U_9843] :
        ( sP776(U_9844,U_9842,U_9843)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843))
        | ~ class_Lattices_Olattice(U_9842) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP776])],[f_2675_2]) ).

cnf(f_2675_4,plain,
    ( sP776(U_9844,U_9842,U_9843)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843))
    | ~ class_Lattices_Olattice(U_9842) ),
    inference(clausify,[status(thm)],[f_2675_3]) ).

cnf(f_2675_5,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),U_9843)) = U_9844
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))
    | ~ sP776(U_9844,U_9842,U_9843) ),
    inference(clausify,[status(thm)],[f_2675_3]) ).

cnf(f_2675_6,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),U_9843)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9842),U_9844),c_Big__Operators_Olattice__class_OInf__fin(U_9842,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool))
    | ~ sP776(U_9844,U_9842,U_9843) ),
    inference(clausify,[status(thm)],[f_2675_3]) ).

fof(f_2676_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint]) ).

fof(f_2676_2,plain,
    ! [U_9847,U_9846,U_9845] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9845,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9847)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9845),c_Big__Operators_Olattice__class_OSup__fin(U_9845,U_9846)),c_Big__Operators_Olattice__class_OSup__fin(U_9845,U_9847))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9847) != c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
      | U_9847 = c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9847))
      | U_9846 = c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9846))
      | ~ class_Lattices_Olattice(U_9845) ),
    inference(variable_rename,[status(thm)],[f_2676_1]) ).

fof(f_2676_3,plain,
    ! [U_9845,U_9846,U_9847] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_9845,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9847)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9845),c_Big__Operators_Olattice__class_OSup__fin(U_9845,U_9846)),c_Big__Operators_Olattice__class_OSup__fin(U_9845,U_9847))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9847) != c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
      | U_9847 = c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9847))
      | U_9846 = c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9846))
      | ~ class_Lattices_Olattice(U_9845) ),
    inference(definitional_conversion,[status(esa)],[f_2676_2]) ).

cnf(f_2676_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_9845,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9847)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9845),c_Big__Operators_Olattice__class_OSup__fin(U_9845,U_9846)),c_Big__Operators_Olattice__class_OSup__fin(U_9845,U_9847))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9847) != c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
    | U_9847 = c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9847))
    | U_9846 = c_Orderings_Obot__class_Obot(tc_fun(U_9845,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9846))
    | ~ class_Lattices_Olattice(U_9845) ),
    inference(clausify,[status(thm)],[f_2676_3]) ).

fof(f_2677_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter]) ).

fof(f_2677_2,plain,
    ! [U_9850,U_9849,U_9848] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9848),c_Big__Operators_Olattice__class_OSup__fin(U_9848,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850))),c_Big__Operators_Olattice__class_OSup__fin(U_9848,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9848),c_Big__Operators_Olattice__class_OSup__fin(U_9848,U_9849)),c_Big__Operators_Olattice__class_OSup__fin(U_9848,U_9850))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850) = c_Orderings_Obot__class_Obot(tc_fun(U_9848,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9848),U_9850))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9848),U_9849))
      | ~ class_Lattices_Olattice(U_9848) ),
    inference(variable_rename,[status(thm)],[f_2677_1]) ).

fof(f_2677_3,plain,
    ! [U_9849,U_9848,U_9850] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9848),c_Big__Operators_Olattice__class_OSup__fin(U_9848,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850))),c_Big__Operators_Olattice__class_OSup__fin(U_9848,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9848),c_Big__Operators_Olattice__class_OSup__fin(U_9848,U_9849)),c_Big__Operators_Olattice__class_OSup__fin(U_9848,U_9850))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850) = c_Orderings_Obot__class_Obot(tc_fun(U_9848,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9848),U_9850))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9848),U_9849))
      | ~ class_Lattices_Olattice(U_9848) ),
    inference(definitional_conversion,[status(esa)],[f_2677_2]) ).

cnf(f_2677_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9848),c_Big__Operators_Olattice__class_OSup__fin(U_9848,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850))),c_Big__Operators_Olattice__class_OSup__fin(U_9848,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9848),c_Big__Operators_Olattice__class_OSup__fin(U_9848,U_9849)),c_Big__Operators_Olattice__class_OSup__fin(U_9848,U_9850))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9848,tc_HOL_Obool)),U_9849),U_9850) = c_Orderings_Obot__class_Obot(tc_fun(U_9848,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9848),U_9850))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9848),U_9849))
    | ~ class_Lattices_Olattice(U_9848) ),
    inference(clausify,[status(thm)],[f_2677_3]) ).

fof(f_2678_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove]) ).

fof(f_2678_2,plain,
    ! [U_9853,U_9852,U_9851] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),U_9852)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9851),U_9853),c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),U_9852)) = U_9853
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9851),U_9852))
      | ~ class_Orderings_Olinorder(U_9851) ),
    inference(variable_rename,[status(thm)],[f_2678_1]) ).

fof(f_2678_3,plain,
    ( ! [U_9851,U_9852,U_9853] :
        ( c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),U_9852)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9851),U_9853),c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))
        | ~ sP777(U_9851,U_9852,U_9853) )
    & ! [U_9851,U_9852,U_9853] :
        ( c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),U_9852)) = U_9853
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))
        | ~ sP777(U_9851,U_9852,U_9853) )
    & ! [U_9851,U_9852,U_9853] :
        ( sP777(U_9851,U_9852,U_9853)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9851),U_9852))
        | ~ class_Orderings_Olinorder(U_9851) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP777])],[f_2678_2]) ).

cnf(f_2678_4,plain,
    ( sP777(U_9851,U_9852,U_9853)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9851),U_9852))
    | ~ class_Orderings_Olinorder(U_9851) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

cnf(f_2678_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),U_9852)) = U_9853
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))
    | ~ sP777(U_9851,U_9852,U_9853) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

cnf(f_2678_6,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),U_9852)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9851),U_9853),c_Big__Operators_Olinorder__class_OMax(U_9851,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9851,tc_HOL_Obool)),U_9852),hAPP(hAPP(c_Set_Oinsert(U_9851),U_9853),c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9851,tc_HOL_Obool))
    | ~ sP777(U_9851,U_9852,U_9853) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

fof(f_2679_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter]) ).

fof(f_2679_2,plain,
    ! [U_9856,U_9855,U_9854] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9854),c_Big__Operators_Olattice__class_OInf__fin(U_9854,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856))),c_Big__Operators_Olattice__class_OInf__fin(U_9854,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9854),c_Big__Operators_Olattice__class_OInf__fin(U_9854,U_9855)),c_Big__Operators_Olattice__class_OInf__fin(U_9854,U_9856))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856) = c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9856))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9855))
      | ~ class_Lattices_Olattice(U_9854) ),
    inference(variable_rename,[status(thm)],[f_2679_1]) ).

fof(f_2679_3,plain,
    ! [U_9855,U_9856,U_9854] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9854),c_Big__Operators_Olattice__class_OInf__fin(U_9854,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856))),c_Big__Operators_Olattice__class_OInf__fin(U_9854,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9854),c_Big__Operators_Olattice__class_OInf__fin(U_9854,U_9855)),c_Big__Operators_Olattice__class_OInf__fin(U_9854,U_9856))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856) = c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9856))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9855))
      | ~ class_Lattices_Olattice(U_9854) ),
    inference(definitional_conversion,[status(esa)],[f_2679_2]) ).

cnf(f_2679_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9854),c_Big__Operators_Olattice__class_OInf__fin(U_9854,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856))),c_Big__Operators_Olattice__class_OInf__fin(U_9854,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9854),c_Big__Operators_Olattice__class_OInf__fin(U_9854,U_9855)),c_Big__Operators_Olattice__class_OInf__fin(U_9854,U_9856))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9854,tc_HOL_Obool)),U_9855),U_9856) = c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9856))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9855))
    | ~ class_Lattices_Olattice(U_9854) ),
    inference(clausify,[status(thm)],[f_2679_3]) ).

fof(f_2680_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint]) ).

fof(f_2680_2,plain,
    ! [U_9859,U_9858,U_9857] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9857,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9857,tc_HOL_Obool)),U_9858),U_9859)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9857),c_Big__Operators_Olattice__class_OInf__fin(U_9857,U_9858)),c_Big__Operators_Olattice__class_OInf__fin(U_9857,U_9859))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9857,tc_HOL_Obool)),U_9858),U_9859) != c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
      | U_9859 = c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9857),U_9859))
      | U_9858 = c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9857),U_9858))
      | ~ class_Lattices_Olattice(U_9857) ),
    inference(variable_rename,[status(thm)],[f_2680_1]) ).

fof(f_2680_3,plain,
    ! [U_9858,U_9857,U_9859] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_9857,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9857,tc_HOL_Obool)),U_9858),U_9859)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9857),c_Big__Operators_Olattice__class_OInf__fin(U_9857,U_9858)),c_Big__Operators_Olattice__class_OInf__fin(U_9857,U_9859))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9857,tc_HOL_Obool)),U_9858),U_9859) != c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
      | U_9859 = c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9857),U_9859))
      | U_9858 = c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9857),U_9858))
      | ~ class_Lattices_Olattice(U_9857) ),
    inference(definitional_conversion,[status(esa)],[f_2680_2]) ).

cnf(f_2680_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_9857,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9857,tc_HOL_Obool)),U_9858),U_9859)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9857),c_Big__Operators_Olattice__class_OInf__fin(U_9857,U_9858)),c_Big__Operators_Olattice__class_OInf__fin(U_9857,U_9859))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9857,tc_HOL_Obool)),U_9858),U_9859) != c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
    | U_9859 = c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9857),U_9859))
    | U_9858 = c_Orderings_Obot__class_Obot(tc_fun(U_9857,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9857),U_9858))
    | ~ class_Lattices_Olattice(U_9857) ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

fof(f_2681_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter]) ).

fof(f_2681_2,plain,
    ! [U_9862,U_9861,U_9860] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9860),c_Big__Operators_Olinorder__class_OMax(U_9860,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862))),c_Big__Operators_Olinorder__class_OMax(U_9860,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9860),c_Big__Operators_Olinorder__class_OMax(U_9860,U_9861)),c_Big__Operators_Olinorder__class_OMax(U_9860,U_9862))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862) = c_Orderings_Obot__class_Obot(tc_fun(U_9860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9860),U_9862))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9860),U_9861))
      | ~ class_Orderings_Olinorder(U_9860) ),
    inference(variable_rename,[status(thm)],[f_2681_1]) ).

fof(f_2681_3,plain,
    ! [U_9862,U_9860,U_9861] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9860),c_Big__Operators_Olinorder__class_OMax(U_9860,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862))),c_Big__Operators_Olinorder__class_OMax(U_9860,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9860),c_Big__Operators_Olinorder__class_OMax(U_9860,U_9861)),c_Big__Operators_Olinorder__class_OMax(U_9860,U_9862))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862) = c_Orderings_Obot__class_Obot(tc_fun(U_9860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9860),U_9862))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9860),U_9861))
      | ~ class_Orderings_Olinorder(U_9860) ),
    inference(definitional_conversion,[status(esa)],[f_2681_2]) ).

cnf(f_2681_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9860),c_Big__Operators_Olinorder__class_OMax(U_9860,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862))),c_Big__Operators_Olinorder__class_OMax(U_9860,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9860),c_Big__Operators_Olinorder__class_OMax(U_9860,U_9861)),c_Big__Operators_Olinorder__class_OMax(U_9860,U_9862))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9860,tc_HOL_Obool)),U_9861),U_9862) = c_Orderings_Obot__class_Obot(tc_fun(U_9860,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9860),U_9862))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9860),U_9861))
    | ~ class_Orderings_Olinorder(U_9860) ),
    inference(clausify,[status(thm)],[f_2681_3]) ).

fof(f_2682_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint]) ).

fof(f_2682_2,plain,
    ! [U_9865,U_9864,U_9863] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9863,tc_HOL_Obool)),U_9864),U_9865)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9863),c_Big__Operators_Olinorder__class_OMax(U_9863,U_9864)),c_Big__Operators_Olinorder__class_OMax(U_9863,U_9865))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9863,tc_HOL_Obool)),U_9864),U_9865) != c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
      | U_9865 = c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9863),U_9865))
      | U_9864 = c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9863),U_9864))
      | ~ class_Orderings_Olinorder(U_9863) ),
    inference(variable_rename,[status(thm)],[f_2682_1]) ).

fof(f_2682_3,plain,
    ! [U_9864,U_9863,U_9865] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9863,tc_HOL_Obool)),U_9864),U_9865)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9863),c_Big__Operators_Olinorder__class_OMax(U_9863,U_9864)),c_Big__Operators_Olinorder__class_OMax(U_9863,U_9865))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9863,tc_HOL_Obool)),U_9864),U_9865) != c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
      | U_9865 = c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9863),U_9865))
      | U_9864 = c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9863),U_9864))
      | ~ class_Orderings_Olinorder(U_9863) ),
    inference(definitional_conversion,[status(esa)],[f_2682_2]) ).

cnf(f_2682_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9863,tc_HOL_Obool)),U_9864),U_9865)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9863),c_Big__Operators_Olinorder__class_OMax(U_9863,U_9864)),c_Big__Operators_Olinorder__class_OMax(U_9863,U_9865))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9863,tc_HOL_Obool)),U_9864),U_9865) != c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
    | U_9865 = c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9863),U_9865))
    | U_9864 = c_Orderings_Obot__class_Obot(tc_fun(U_9863,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9863),U_9864))
    | ~ class_Orderings_Olinorder(U_9863) ),
    inference(clausify,[status(thm)],[f_2682_3]) ).

fof(f_2683_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oclosed]) ).

fof(f_2683_2,plain,
    ! [U_9869,U_9868] :
      ( hBOOL(hAPP(hAPP(c_member(U_9868),c_Big__Operators_Olinorder__class_OMax(U_9868,U_9869)),U_9869))
      | ? [U_9867,U_9866] : ~ hBOOL(hAPP(hAPP(c_member(U_9868),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9868),U_9867),U_9866)),hAPP(hAPP(c_Set_Oinsert(U_9868),U_9867),hAPP(hAPP(c_Set_Oinsert(U_9868),U_9866),c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))))))
      | U_9869 = c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),U_9869))
      | ~ class_Orderings_Olinorder(U_9868) ),
    inference(variable_rename,[status(thm)],[f_2683_1]) ).

fof(f_2683_3,plain,
    ! [U_9869,U_9868] :
      ( hBOOL(hAPP(hAPP(c_member(U_9868),c_Big__Operators_Olinorder__class_OMax(U_9868,U_9869)),U_9869))
      | ? [U_9866] : ~ hBOOL(hAPP(hAPP(c_member(U_9868),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9868),sK140(U_9869,U_9868)),U_9866)),hAPP(hAPP(c_Set_Oinsert(U_9868),sK140(U_9869,U_9868)),hAPP(hAPP(c_Set_Oinsert(U_9868),U_9866),c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))))))
      | U_9869 = c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),U_9869))
      | ~ class_Orderings_Olinorder(U_9868) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_9867,sK140(U_9869,U_9868))],[f_2683_2]) ).

fof(f_2683_4,plain,
    ! [U_9869,U_9868] :
      ( hBOOL(hAPP(hAPP(c_member(U_9868),c_Big__Operators_Olinorder__class_OMax(U_9868,U_9869)),U_9869))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9868),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9868),sK140(U_9869,U_9868)),sK141(U_9869,U_9868))),hAPP(hAPP(c_Set_Oinsert(U_9868),sK140(U_9869,U_9868)),hAPP(hAPP(c_Set_Oinsert(U_9868),sK141(U_9869,U_9868)),c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))))))
      | U_9869 = c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),U_9869))
      | ~ class_Orderings_Olinorder(U_9868) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_9866,sK141(U_9869,U_9868))],[f_2683_3]) ).

fof(f_2683_5,plain,
    ! [U_9868,U_9869] :
      ( hBOOL(hAPP(hAPP(c_member(U_9868),c_Big__Operators_Olinorder__class_OMax(U_9868,U_9869)),U_9869))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9868),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9868),sK140(U_9869,U_9868)),sK141(U_9869,U_9868))),hAPP(hAPP(c_Set_Oinsert(U_9868),sK140(U_9869,U_9868)),hAPP(hAPP(c_Set_Oinsert(U_9868),sK141(U_9869,U_9868)),c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))))))
      | U_9869 = c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),U_9869))
      | ~ class_Orderings_Olinorder(U_9868) ),
    inference(definitional_conversion,[status(esa)],[f_2683_4]) ).

cnf(f_2683_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9868),c_Big__Operators_Olinorder__class_OMax(U_9868,U_9869)),U_9869))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9868),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9868),sK140(U_9869,U_9868)),sK141(U_9869,U_9868))),hAPP(hAPP(c_Set_Oinsert(U_9868),sK140(U_9869,U_9868)),hAPP(hAPP(c_Set_Oinsert(U_9868),sK141(U_9869,U_9868)),c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))))))
    | U_9869 = c_Orderings_Obot__class_Obot(tc_fun(U_9868,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),U_9869))
    | ~ class_Orderings_Olinorder(U_9868) ),
    inference(clausify,[status(thm)],[f_2683_5]) ).

fof(f_2684_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed]) ).

fof(f_2684_2,plain,
    ! [U_9873,U_9872] :
      ( hBOOL(hAPP(hAPP(c_member(U_9872),c_Big__Operators_Olattice__class_OInf__fin(U_9872,U_9873)),U_9873))
      | ? [U_9871,U_9870] : ~ hBOOL(hAPP(hAPP(c_member(U_9872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9872),U_9871),U_9870)),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9871),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9870),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | U_9873 = c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9873))
      | ~ class_Lattices_Olattice(U_9872) ),
    inference(variable_rename,[status(thm)],[f_2684_1]) ).

fof(f_2684_3,plain,
    ! [U_9873,U_9872] :
      ( hBOOL(hAPP(hAPP(c_member(U_9872),c_Big__Operators_Olattice__class_OInf__fin(U_9872,U_9873)),U_9873))
      | ? [U_9870] : ~ hBOOL(hAPP(hAPP(c_member(U_9872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9872),sK142(U_9873,U_9872)),U_9870)),hAPP(hAPP(c_Set_Oinsert(U_9872),sK142(U_9873,U_9872)),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9870),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | U_9873 = c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9873))
      | ~ class_Lattices_Olattice(U_9872) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_9871,sK142(U_9873,U_9872))],[f_2684_2]) ).

fof(f_2684_4,plain,
    ! [U_9873,U_9872] :
      ( hBOOL(hAPP(hAPP(c_member(U_9872),c_Big__Operators_Olattice__class_OInf__fin(U_9872,U_9873)),U_9873))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9872),sK142(U_9873,U_9872)),sK143(U_9873,U_9872))),hAPP(hAPP(c_Set_Oinsert(U_9872),sK142(U_9873,U_9872)),hAPP(hAPP(c_Set_Oinsert(U_9872),sK143(U_9873,U_9872)),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | U_9873 = c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9873))
      | ~ class_Lattices_Olattice(U_9872) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_9870,sK143(U_9873,U_9872))],[f_2684_3]) ).

fof(f_2684_5,plain,
    ! [U_9872,U_9873] :
      ( hBOOL(hAPP(hAPP(c_member(U_9872),c_Big__Operators_Olattice__class_OInf__fin(U_9872,U_9873)),U_9873))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9872),sK142(U_9873,U_9872)),sK143(U_9873,U_9872))),hAPP(hAPP(c_Set_Oinsert(U_9872),sK142(U_9873,U_9872)),hAPP(hAPP(c_Set_Oinsert(U_9872),sK143(U_9873,U_9872)),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | U_9873 = c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9873))
      | ~ class_Lattices_Olattice(U_9872) ),
    inference(definitional_conversion,[status(esa)],[f_2684_4]) ).

cnf(f_2684_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9872),c_Big__Operators_Olattice__class_OInf__fin(U_9872,U_9873)),U_9873))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9872),sK142(U_9873,U_9872)),sK143(U_9873,U_9872))),hAPP(hAPP(c_Set_Oinsert(U_9872),sK142(U_9873,U_9872)),hAPP(hAPP(c_Set_Oinsert(U_9872),sK143(U_9873,U_9872)),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
    | U_9873 = c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9873))
    | ~ class_Lattices_Olattice(U_9872) ),
    inference(clausify,[status(thm)],[f_2684_5]) ).

fof(f_2685_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed]) ).

fof(f_2685_2,plain,
    ! [U_9877,U_9876] :
      ( hBOOL(hAPP(hAPP(c_member(U_9876),c_Big__Operators_Olattice__class_OSup__fin(U_9876,U_9877)),U_9877))
      | ? [U_9875,U_9874] : ~ hBOOL(hAPP(hAPP(c_member(U_9876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9876),U_9875),U_9874)),hAPP(hAPP(c_Set_Oinsert(U_9876),U_9875),hAPP(hAPP(c_Set_Oinsert(U_9876),U_9874),c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))))))
      | U_9877 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),U_9877))
      | ~ class_Lattices_Olattice(U_9876) ),
    inference(variable_rename,[status(thm)],[f_2685_1]) ).

fof(f_2685_3,plain,
    ! [U_9877,U_9876] :
      ( hBOOL(hAPP(hAPP(c_member(U_9876),c_Big__Operators_Olattice__class_OSup__fin(U_9876,U_9877)),U_9877))
      | ? [U_9874] : ~ hBOOL(hAPP(hAPP(c_member(U_9876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9876),sK144(U_9877,U_9876)),U_9874)),hAPP(hAPP(c_Set_Oinsert(U_9876),sK144(U_9877,U_9876)),hAPP(hAPP(c_Set_Oinsert(U_9876),U_9874),c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))))))
      | U_9877 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),U_9877))
      | ~ class_Lattices_Olattice(U_9876) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_9875,sK144(U_9877,U_9876))],[f_2685_2]) ).

fof(f_2685_4,plain,
    ! [U_9877,U_9876] :
      ( hBOOL(hAPP(hAPP(c_member(U_9876),c_Big__Operators_Olattice__class_OSup__fin(U_9876,U_9877)),U_9877))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9876),sK144(U_9877,U_9876)),sK145(U_9877,U_9876))),hAPP(hAPP(c_Set_Oinsert(U_9876),sK144(U_9877,U_9876)),hAPP(hAPP(c_Set_Oinsert(U_9876),sK145(U_9877,U_9876)),c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))))))
      | U_9877 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),U_9877))
      | ~ class_Lattices_Olattice(U_9876) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_9874,sK145(U_9877,U_9876))],[f_2685_3]) ).

fof(f_2685_5,plain,
    ! [U_9876,U_9877] :
      ( hBOOL(hAPP(hAPP(c_member(U_9876),c_Big__Operators_Olattice__class_OSup__fin(U_9876,U_9877)),U_9877))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9876),sK144(U_9877,U_9876)),sK145(U_9877,U_9876))),hAPP(hAPP(c_Set_Oinsert(U_9876),sK144(U_9877,U_9876)),hAPP(hAPP(c_Set_Oinsert(U_9876),sK145(U_9877,U_9876)),c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))))))
      | U_9877 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),U_9877))
      | ~ class_Lattices_Olattice(U_9876) ),
    inference(definitional_conversion,[status(esa)],[f_2685_4]) ).

cnf(f_2685_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9876),c_Big__Operators_Olattice__class_OSup__fin(U_9876,U_9877)),U_9877))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9876),sK144(U_9877,U_9876)),sK145(U_9877,U_9876))),hAPP(hAPP(c_Set_Oinsert(U_9876),sK144(U_9877,U_9876)),hAPP(hAPP(c_Set_Oinsert(U_9876),sK145(U_9877,U_9876)),c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))))))
    | U_9877 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),U_9877))
    | ~ class_Lattices_Olattice(U_9876) ),
    inference(clausify,[status(thm)],[f_2685_5]) ).

fof(f_2686_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oremove]) ).

fof(f_2686_2,plain,
    ! [U_9880,U_9879,U_9878] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_9878,U_9879) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9878),U_9880),c_Big__Operators_Olinorder__class_OMin(U_9878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_9878,U_9879) = U_9880
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9878),U_9880),U_9879))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9878),U_9879))
      | ~ class_Orderings_Olinorder(U_9878) ),
    inference(variable_rename,[status(thm)],[f_2686_1]) ).

fof(f_2686_3,plain,
    ( ! [U_9879,U_9880,U_9878] :
        ( c_Big__Operators_Olinorder__class_OMin(U_9878,U_9879) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9878),U_9880),c_Big__Operators_Olinorder__class_OMin(U_9878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))
        | ~ sP778(U_9879,U_9880,U_9878) )
    & ! [U_9879,U_9880,U_9878] :
        ( c_Big__Operators_Olinorder__class_OMin(U_9878,U_9879) = U_9880
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))
        | ~ sP778(U_9879,U_9880,U_9878) )
    & ! [U_9879,U_9880,U_9878] :
        ( sP778(U_9879,U_9880,U_9878)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9878),U_9880),U_9879))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9878),U_9879))
        | ~ class_Orderings_Olinorder(U_9878) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP778])],[f_2686_2]) ).

cnf(f_2686_4,plain,
    ( sP778(U_9879,U_9880,U_9878)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9878),U_9880),U_9879))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9878),U_9879))
    | ~ class_Orderings_Olinorder(U_9878) ),
    inference(clausify,[status(thm)],[f_2686_3]) ).

cnf(f_2686_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9878,U_9879) = U_9880
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))
    | ~ sP778(U_9879,U_9880,U_9878) ),
    inference(clausify,[status(thm)],[f_2686_3]) ).

cnf(f_2686_6,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9878,U_9879) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9878),U_9880),c_Big__Operators_Olinorder__class_OMin(U_9878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9878,tc_HOL_Obool)),U_9879),hAPP(hAPP(c_Set_Oinsert(U_9878),U_9880),c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9878,tc_HOL_Obool))
    | ~ sP778(U_9879,U_9880,U_9878) ),
    inference(clausify,[status(thm)],[f_2686_3]) ).

fof(f_2687_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Osingleton]) ).

fof(f_2687_2,plain,
    ! [U_9882,U_9881] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9881,hAPP(hAPP(c_Set_Oinsert(U_9881),U_9882),c_Orderings_Obot__class_Obot(tc_fun(U_9881,tc_HOL_Obool)))) = U_9882
      | ~ class_Orderings_Olinorder(U_9881) ),
    inference(variable_rename,[status(thm)],[f_2687_1]) ).

fof(f_2687_3,plain,
    ! [U_9882,U_9881] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9881,hAPP(hAPP(c_Set_Oinsert(U_9881),U_9882),c_Orderings_Obot__class_Obot(tc_fun(U_9881,tc_HOL_Obool)))) = U_9882
      | ~ class_Orderings_Olinorder(U_9881) ),
    inference(definitional_conversion,[status(esa)],[f_2687_2]) ).

cnf(f_2687_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9881,hAPP(hAPP(c_Set_Oinsert(U_9881),U_9882),c_Orderings_Obot__class_Obot(tc_fun(U_9881,tc_HOL_Obool)))) = U_9882
    | ~ class_Orderings_Olinorder(U_9881) ),
    inference(clausify,[status(thm)],[f_2687_3]) ).

fof(f_2688_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__le]) ).

fof(f_2688_2,plain,
    ! [U_9885,U_9884,U_9883] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9883),c_Big__Operators_Olinorder__class_OMin(U_9883,U_9884)),U_9885))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9883),U_9885),U_9884))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9883),U_9884))
      | ~ class_Orderings_Olinorder(U_9883) ),
    inference(variable_rename,[status(thm)],[f_2688_1]) ).

fof(f_2688_3,plain,
    ! [U_9885,U_9883,U_9884] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9883),c_Big__Operators_Olinorder__class_OMin(U_9883,U_9884)),U_9885))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9883),U_9885),U_9884))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9883),U_9884))
      | ~ class_Orderings_Olinorder(U_9883) ),
    inference(definitional_conversion,[status(esa)],[f_2688_2]) ).

cnf(f_2688_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9883),c_Big__Operators_Olinorder__class_OMin(U_9883,U_9884)),U_9885))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9883),U_9885),U_9884))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9883),U_9884))
    | ~ class_Orderings_Olinorder(U_9883) ),
    inference(clausify,[status(thm)],[f_2688_3]) ).

fof(f_2689_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__in]) ).

fof(f_2689_2,plain,
    ! [U_9887,U_9886] :
      ( hBOOL(hAPP(hAPP(c_member(U_9886),c_Big__Operators_Olinorder__class_OMin(U_9886,U_9887)),U_9887))
      | U_9887 = c_Orderings_Obot__class_Obot(tc_fun(U_9886,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9886),U_9887))
      | ~ class_Orderings_Olinorder(U_9886) ),
    inference(variable_rename,[status(thm)],[f_2689_1]) ).

fof(f_2689_3,plain,
    ! [U_9886,U_9887] :
      ( hBOOL(hAPP(hAPP(c_member(U_9886),c_Big__Operators_Olinorder__class_OMin(U_9886,U_9887)),U_9887))
      | U_9887 = c_Orderings_Obot__class_Obot(tc_fun(U_9886,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9886),U_9887))
      | ~ class_Orderings_Olinorder(U_9886) ),
    inference(definitional_conversion,[status(esa)],[f_2689_2]) ).

cnf(f_2689_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9886),c_Big__Operators_Olinorder__class_OMin(U_9886,U_9887)),U_9887))
    | U_9887 = c_Orderings_Obot__class_Obot(tc_fun(U_9886,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9886),U_9887))
    | ~ class_Orderings_Olinorder(U_9886) ),
    inference(clausify,[status(thm)],[f_2689_3]) ).

fof(f_2690_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem]) ).

fof(f_2690_2,plain,
    ! [U_9890,U_9889,U_9888] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9888),U_9890),c_Big__Operators_Olinorder__class_OMin(U_9888,U_9889)) = c_Big__Operators_Olinorder__class_OMin(U_9888,U_9889)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9888),U_9890),U_9889))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9888),U_9889))
      | ~ class_Orderings_Olinorder(U_9888) ),
    inference(variable_rename,[status(thm)],[f_2690_1]) ).

fof(f_2690_3,plain,
    ! [U_9889,U_9888,U_9890] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9888),U_9890),c_Big__Operators_Olinorder__class_OMin(U_9888,U_9889)) = c_Big__Operators_Olinorder__class_OMin(U_9888,U_9889)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9888),U_9890),U_9889))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9888),U_9889))
      | ~ class_Orderings_Olinorder(U_9888) ),
    inference(definitional_conversion,[status(esa)],[f_2690_2]) ).

cnf(f_2690_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9888),U_9890),c_Big__Operators_Olinorder__class_OMin(U_9888,U_9889)) = c_Big__Operators_Olinorder__class_OMin(U_9888,U_9889)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9888),U_9890),U_9889))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9888),U_9889))
    | ~ class_Orderings_Olinorder(U_9888) ),
    inference(clausify,[status(thm)],[f_2690_3]) ).

fof(f_2691_1,plain,
    ! [V_N_2,V_M_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__antimono]) ).

fof(f_2691_2,plain,
    ! [U_9893,U_9892,U_9891] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9891),c_Big__Operators_Olinorder__class_OMin(U_9891,U_9893)),c_Big__Operators_Olinorder__class_OMin(U_9891,U_9892)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9891),U_9893))
      | U_9892 = c_Orderings_Obot__class_Obot(tc_fun(U_9891,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9891,tc_HOL_Obool)),U_9892),U_9893))
      | ~ class_Orderings_Olinorder(U_9891) ),
    inference(variable_rename,[status(thm)],[f_2691_1]) ).

fof(f_2691_3,plain,
    ! [U_9891,U_9892,U_9893] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9891),c_Big__Operators_Olinorder__class_OMin(U_9891,U_9893)),c_Big__Operators_Olinorder__class_OMin(U_9891,U_9892)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9891),U_9893))
      | U_9892 = c_Orderings_Obot__class_Obot(tc_fun(U_9891,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9891,tc_HOL_Obool)),U_9892),U_9893))
      | ~ class_Orderings_Olinorder(U_9891) ),
    inference(definitional_conversion,[status(esa)],[f_2691_2]) ).

cnf(f_2691_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9891),c_Big__Operators_Olinorder__class_OMin(U_9891,U_9893)),c_Big__Operators_Olinorder__class_OMin(U_9891,U_9892)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9891),U_9893))
    | U_9892 = c_Orderings_Obot__class_Obot(tc_fun(U_9891,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9891,tc_HOL_Obool)),U_9892),U_9893))
    | ~ class_Orderings_Olinorder(U_9891) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

fof(f_2692_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__insert]) ).

fof(f_2692_2,plain,
    ! [U_9896,U_9895,U_9894] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9894,hAPP(hAPP(c_Set_Oinsert(U_9894),U_9896),U_9895)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9894),U_9896),c_Big__Operators_Olinorder__class_OMin(U_9894,U_9895))
      | U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9894,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9894),U_9895))
      | ~ class_Orderings_Olinorder(U_9894) ),
    inference(variable_rename,[status(thm)],[f_2692_1]) ).

fof(f_2692_3,plain,
    ! [U_9894,U_9895,U_9896] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9894,hAPP(hAPP(c_Set_Oinsert(U_9894),U_9896),U_9895)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9894),U_9896),c_Big__Operators_Olinorder__class_OMin(U_9894,U_9895))
      | U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9894,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9894),U_9895))
      | ~ class_Orderings_Olinorder(U_9894) ),
    inference(definitional_conversion,[status(esa)],[f_2692_2]) ).

cnf(f_2692_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9894,hAPP(hAPP(c_Set_Oinsert(U_9894),U_9896),U_9895)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9894),U_9896),c_Big__Operators_Olinorder__class_OMin(U_9894,U_9895))
    | U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9894,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9894),U_9895))
    | ~ class_Orderings_Olinorder(U_9894) ),
    inference(clausify,[status(thm)],[f_2692_3]) ).

fof(f_2693_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem]) ).

fof(f_2693_2,plain,
    ! [U_9899,U_9898,U_9897] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9897),c_Big__Operators_Olinorder__class_OMin(U_9897,U_9899)),c_Big__Operators_Olinorder__class_OMin(U_9897,U_9898)) = c_Big__Operators_Olinorder__class_OMin(U_9897,U_9898)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9897,tc_HOL_Obool)),U_9899),U_9898))
      | U_9899 = c_Orderings_Obot__class_Obot(tc_fun(U_9897,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898))
      | ~ class_Orderings_Olinorder(U_9897) ),
    inference(variable_rename,[status(thm)],[f_2693_1]) ).

fof(f_2693_3,plain,
    ! [U_9897,U_9898,U_9899] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9897),c_Big__Operators_Olinorder__class_OMin(U_9897,U_9899)),c_Big__Operators_Olinorder__class_OMin(U_9897,U_9898)) = c_Big__Operators_Olinorder__class_OMin(U_9897,U_9898)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9897,tc_HOL_Obool)),U_9899),U_9898))
      | U_9899 = c_Orderings_Obot__class_Obot(tc_fun(U_9897,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898))
      | ~ class_Orderings_Olinorder(U_9897) ),
    inference(definitional_conversion,[status(esa)],[f_2693_2]) ).

cnf(f_2693_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9897),c_Big__Operators_Olinorder__class_OMin(U_9897,U_9899)),c_Big__Operators_Olinorder__class_OMin(U_9897,U_9898)) = c_Big__Operators_Olinorder__class_OMin(U_9897,U_9898)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9897,tc_HOL_Obool)),U_9899),U_9898))
    | U_9899 = c_Orderings_Obot__class_Obot(tc_fun(U_9897,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898))
    | ~ class_Orderings_Olinorder(U_9897) ),
    inference(clausify,[status(thm)],[f_2693_3]) ).

fof(f_2694_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__Un]) ).

fof(f_2694_2,plain,
    ! [U_9902,U_9901,U_9900] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9900,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9900,tc_HOL_Obool)),U_9901),U_9902)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9900),c_Big__Operators_Olinorder__class_OMin(U_9900,U_9901)),c_Big__Operators_Olinorder__class_OMin(U_9900,U_9902))
      | U_9902 = c_Orderings_Obot__class_Obot(tc_fun(U_9900,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9900),U_9902))
      | U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9900,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9900),U_9901))
      | ~ class_Orderings_Olinorder(U_9900) ),
    inference(variable_rename,[status(thm)],[f_2694_1]) ).

fof(f_2694_3,plain,
    ! [U_9901,U_9900,U_9902] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9900,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9900,tc_HOL_Obool)),U_9901),U_9902)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9900),c_Big__Operators_Olinorder__class_OMin(U_9900,U_9901)),c_Big__Operators_Olinorder__class_OMin(U_9900,U_9902))
      | U_9902 = c_Orderings_Obot__class_Obot(tc_fun(U_9900,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9900),U_9902))
      | U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9900,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9900),U_9901))
      | ~ class_Orderings_Olinorder(U_9900) ),
    inference(definitional_conversion,[status(esa)],[f_2694_2]) ).

cnf(f_2694_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9900,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9900,tc_HOL_Obool)),U_9901),U_9902)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9900),c_Big__Operators_Olinorder__class_OMin(U_9900,U_9901)),c_Big__Operators_Olinorder__class_OMin(U_9900,U_9902))
    | U_9902 = c_Orderings_Obot__class_Obot(tc_fun(U_9900,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9900),U_9902))
    | U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9900,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9900),U_9901))
    | ~ class_Orderings_Olinorder(U_9900) ),
    inference(clausify,[status(thm)],[f_2694_3]) ).

fof(f_2695_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oinsert]) ).

fof(f_2695_2,plain,
    ! [U_9905,U_9904,U_9903] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9903,hAPP(hAPP(c_Set_Oinsert(U_9903),U_9905),U_9904)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9903),U_9905),c_Big__Operators_Olinorder__class_OMin(U_9903,U_9904))
      | U_9904 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9903),U_9905),U_9904))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904))
      | ~ class_Orderings_Olinorder(U_9903) ),
    inference(variable_rename,[status(thm)],[f_2695_1]) ).

fof(f_2695_3,plain,
    ! [U_9904,U_9903,U_9905] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9903,hAPP(hAPP(c_Set_Oinsert(U_9903),U_9905),U_9904)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9903),U_9905),c_Big__Operators_Olinorder__class_OMin(U_9903,U_9904))
      | U_9904 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9903),U_9905),U_9904))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904))
      | ~ class_Orderings_Olinorder(U_9903) ),
    inference(definitional_conversion,[status(esa)],[f_2695_2]) ).

cnf(f_2695_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9903,hAPP(hAPP(c_Set_Oinsert(U_9903),U_9905),U_9904)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9903),U_9905),c_Big__Operators_Olinorder__class_OMin(U_9903,U_9904))
    | U_9904 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9903),U_9905),U_9904))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904))
    | ~ class_Orderings_Olinorder(U_9903) ),
    inference(clausify,[status(thm)],[f_2695_3]) ).

fof(f_2696_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove]) ).

fof(f_2696_2,plain,
    ! [U_9908,U_9907,U_9906] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),U_9907)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9906),U_9908),c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),U_9907)) = U_9908
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9906),U_9907))
      | ~ class_Orderings_Olinorder(U_9906) ),
    inference(variable_rename,[status(thm)],[f_2696_1]) ).

fof(f_2696_3,plain,
    ( ! [U_9906,U_9907,U_9908] :
        ( c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),U_9907)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9906),U_9908),c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))
        | ~ sP779(U_9906,U_9907,U_9908) )
    & ! [U_9906,U_9907,U_9908] :
        ( c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),U_9907)) = U_9908
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))
        | ~ sP779(U_9906,U_9907,U_9908) )
    & ! [U_9906,U_9907,U_9908] :
        ( sP779(U_9906,U_9907,U_9908)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9906),U_9907))
        | ~ class_Orderings_Olinorder(U_9906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP779])],[f_2696_2]) ).

cnf(f_2696_4,plain,
    ( sP779(U_9906,U_9907,U_9908)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9906),U_9907))
    | ~ class_Orderings_Olinorder(U_9906) ),
    inference(clausify,[status(thm)],[f_2696_3]) ).

cnf(f_2696_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),U_9907)) = U_9908
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))
    | ~ sP779(U_9906,U_9907,U_9908) ),
    inference(clausify,[status(thm)],[f_2696_3]) ).

cnf(f_2696_6,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),U_9907)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9906),U_9908),c_Big__Operators_Olinorder__class_OMin(U_9906,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9906,tc_HOL_Obool)),U_9907),hAPP(hAPP(c_Set_Oinsert(U_9906),U_9908),c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9906,tc_HOL_Obool))
    | ~ sP779(U_9906,U_9907,U_9908) ),
    inference(clausify,[status(thm)],[f_2696_3]) ).

fof(f_2697_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter]) ).

fof(f_2697_2,plain,
    ! [U_9911,U_9910,U_9909] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9909),c_Big__Operators_Olinorder__class_OMin(U_9909,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911))),c_Big__Operators_Olinorder__class_OMin(U_9909,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9909),c_Big__Operators_Olinorder__class_OMin(U_9909,U_9910)),c_Big__Operators_Olinorder__class_OMin(U_9909,U_9911))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911) = c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9911))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9910))
      | ~ class_Orderings_Olinorder(U_9909) ),
    inference(variable_rename,[status(thm)],[f_2697_1]) ).

fof(f_2697_3,plain,
    ! [U_9910,U_9909,U_9911] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9909),c_Big__Operators_Olinorder__class_OMin(U_9909,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911))),c_Big__Operators_Olinorder__class_OMin(U_9909,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9909),c_Big__Operators_Olinorder__class_OMin(U_9909,U_9910)),c_Big__Operators_Olinorder__class_OMin(U_9909,U_9911))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911) = c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9911))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9910))
      | ~ class_Orderings_Olinorder(U_9909) ),
    inference(definitional_conversion,[status(esa)],[f_2697_2]) ).

cnf(f_2697_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9909),c_Big__Operators_Olinorder__class_OMin(U_9909,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911))),c_Big__Operators_Olinorder__class_OMin(U_9909,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9909),c_Big__Operators_Olinorder__class_OMin(U_9909,U_9910)),c_Big__Operators_Olinorder__class_OMin(U_9909,U_9911))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9909,tc_HOL_Obool)),U_9910),U_9911) = c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9911))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9910))
    | ~ class_Orderings_Olinorder(U_9909) ),
    inference(clausify,[status(thm)],[f_2697_3]) ).

fof(f_2698_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint]) ).

fof(f_2698_2,plain,
    ! [U_9914,U_9913,U_9912] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9912,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9912,tc_HOL_Obool)),U_9913),U_9914)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9912),c_Big__Operators_Olinorder__class_OMin(U_9912,U_9913)),c_Big__Operators_Olinorder__class_OMin(U_9912,U_9914))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9912,tc_HOL_Obool)),U_9913),U_9914) != c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
      | U_9914 = c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9912),U_9914))
      | U_9913 = c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9912),U_9913))
      | ~ class_Orderings_Olinorder(U_9912) ),
    inference(variable_rename,[status(thm)],[f_2698_1]) ).

fof(f_2698_3,plain,
    ! [U_9913,U_9912,U_9914] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9912,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9912,tc_HOL_Obool)),U_9913),U_9914)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9912),c_Big__Operators_Olinorder__class_OMin(U_9912,U_9913)),c_Big__Operators_Olinorder__class_OMin(U_9912,U_9914))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9912,tc_HOL_Obool)),U_9913),U_9914) != c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
      | U_9914 = c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9912),U_9914))
      | U_9913 = c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9912),U_9913))
      | ~ class_Orderings_Olinorder(U_9912) ),
    inference(definitional_conversion,[status(esa)],[f_2698_2]) ).

cnf(f_2698_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9912,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9912,tc_HOL_Obool)),U_9913),U_9914)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9912),c_Big__Operators_Olinorder__class_OMin(U_9912,U_9913)),c_Big__Operators_Olinorder__class_OMin(U_9912,U_9914))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9912,tc_HOL_Obool)),U_9913),U_9914) != c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
    | U_9914 = c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9912),U_9914))
    | U_9913 = c_Orderings_Obot__class_Obot(tc_fun(U_9912,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9912),U_9913))
    | ~ class_Orderings_Olinorder(U_9912) ),
    inference(clausify,[status(thm)],[f_2698_3]) ).

fof(f_2699_1,plain,
    ! [V_S_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2))
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min]) ).

fof(f_2699_2,plain,
    ! [U_9916,U_9915] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9915),c_Big__Operators_Olinorder__class_OMax(U_9915,U_9916)) = c_Big__Operators_Olinorder__class_OMin(U_9915,hAPP(c_Set_Oimage(U_9915,U_9915,c_Groups_Ouminus__class_Ouminus(U_9915)),U_9916))
      | U_9916 = c_Orderings_Obot__class_Obot(tc_fun(U_9915,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9916))
      | ~ class_Groups_Olinordered__ab__group__add(U_9915) ),
    inference(variable_rename,[status(thm)],[f_2699_1]) ).

fof(f_2699_3,plain,
    ! [U_9916,U_9915] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9915),c_Big__Operators_Olinorder__class_OMax(U_9915,U_9916)) = c_Big__Operators_Olinorder__class_OMin(U_9915,hAPP(c_Set_Oimage(U_9915,U_9915,c_Groups_Ouminus__class_Ouminus(U_9915)),U_9916))
      | U_9916 = c_Orderings_Obot__class_Obot(tc_fun(U_9915,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9916))
      | ~ class_Groups_Olinordered__ab__group__add(U_9915) ),
    inference(definitional_conversion,[status(esa)],[f_2699_2]) ).

cnf(f_2699_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9915),c_Big__Operators_Olinorder__class_OMax(U_9915,U_9916)) = c_Big__Operators_Olinorder__class_OMin(U_9915,hAPP(c_Set_Oimage(U_9915,U_9915,c_Groups_Ouminus__class_Ouminus(U_9915)),U_9916))
    | U_9916 = c_Orderings_Obot__class_Obot(tc_fun(U_9915,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9916))
    | ~ class_Groups_Olinordered__ab__group__add(U_9915) ),
    inference(clausify,[status(thm)],[f_2699_3]) ).

fof(f_2700_1,plain,
    ! [V_S_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2))
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max]) ).

fof(f_2700_2,plain,
    ! [U_9918,U_9917] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9917),c_Big__Operators_Olinorder__class_OMin(U_9917,U_9918)) = c_Big__Operators_Olinorder__class_OMax(U_9917,hAPP(c_Set_Oimage(U_9917,U_9917,c_Groups_Ouminus__class_Ouminus(U_9917)),U_9918))
      | U_9918 = c_Orderings_Obot__class_Obot(tc_fun(U_9917,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9917),U_9918))
      | ~ class_Groups_Olinordered__ab__group__add(U_9917) ),
    inference(variable_rename,[status(thm)],[f_2700_1]) ).

fof(f_2700_3,plain,
    ! [U_9917,U_9918] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9917),c_Big__Operators_Olinorder__class_OMin(U_9917,U_9918)) = c_Big__Operators_Olinorder__class_OMax(U_9917,hAPP(c_Set_Oimage(U_9917,U_9917,c_Groups_Ouminus__class_Ouminus(U_9917)),U_9918))
      | U_9918 = c_Orderings_Obot__class_Obot(tc_fun(U_9917,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9917),U_9918))
      | ~ class_Groups_Olinordered__ab__group__add(U_9917) ),
    inference(definitional_conversion,[status(esa)],[f_2700_2]) ).

cnf(f_2700_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9917),c_Big__Operators_Olinorder__class_OMin(U_9917,U_9918)) = c_Big__Operators_Olinorder__class_OMax(U_9917,hAPP(c_Set_Oimage(U_9917,U_9917,c_Groups_Ouminus__class_Ouminus(U_9917)),U_9918))
    | U_9918 = c_Orderings_Obot__class_Obot(tc_fun(U_9917,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9917),U_9918))
    | ~ class_Groups_Olinordered__ab__group__add(U_9917) ),
    inference(clausify,[status(thm)],[f_2700_3]) ).

fof(f_2701_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oclosed]) ).

fof(f_2701_2,plain,
    ! [U_9922,U_9921] :
      ( hBOOL(hAPP(hAPP(c_member(U_9921),c_Big__Operators_Olinorder__class_OMin(U_9921,U_9922)),U_9922))
      | ? [U_9920,U_9919] : ~ hBOOL(hAPP(hAPP(c_member(U_9921),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9921),U_9920),U_9919)),hAPP(hAPP(c_Set_Oinsert(U_9921),U_9920),hAPP(hAPP(c_Set_Oinsert(U_9921),U_9919),c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))))))
      | U_9922 = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9921),U_9922))
      | ~ class_Orderings_Olinorder(U_9921) ),
    inference(variable_rename,[status(thm)],[f_2701_1]) ).

fof(f_2701_3,plain,
    ! [U_9922,U_9921] :
      ( hBOOL(hAPP(hAPP(c_member(U_9921),c_Big__Operators_Olinorder__class_OMin(U_9921,U_9922)),U_9922))
      | ? [U_9919] : ~ hBOOL(hAPP(hAPP(c_member(U_9921),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9921),sK146(U_9922,U_9921)),U_9919)),hAPP(hAPP(c_Set_Oinsert(U_9921),sK146(U_9922,U_9921)),hAPP(hAPP(c_Set_Oinsert(U_9921),U_9919),c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))))))
      | U_9922 = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9921),U_9922))
      | ~ class_Orderings_Olinorder(U_9921) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_9920,sK146(U_9922,U_9921))],[f_2701_2]) ).

fof(f_2701_4,plain,
    ! [U_9922,U_9921] :
      ( hBOOL(hAPP(hAPP(c_member(U_9921),c_Big__Operators_Olinorder__class_OMin(U_9921,U_9922)),U_9922))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9921),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9921),sK146(U_9922,U_9921)),sK147(U_9922,U_9921))),hAPP(hAPP(c_Set_Oinsert(U_9921),sK146(U_9922,U_9921)),hAPP(hAPP(c_Set_Oinsert(U_9921),sK147(U_9922,U_9921)),c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))))))
      | U_9922 = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9921),U_9922))
      | ~ class_Orderings_Olinorder(U_9921) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_9919,sK147(U_9922,U_9921))],[f_2701_3]) ).

fof(f_2701_5,plain,
    ! [U_9921,U_9922] :
      ( hBOOL(hAPP(hAPP(c_member(U_9921),c_Big__Operators_Olinorder__class_OMin(U_9921,U_9922)),U_9922))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9921),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9921),sK146(U_9922,U_9921)),sK147(U_9922,U_9921))),hAPP(hAPP(c_Set_Oinsert(U_9921),sK146(U_9922,U_9921)),hAPP(hAPP(c_Set_Oinsert(U_9921),sK147(U_9922,U_9921)),c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))))))
      | U_9922 = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9921),U_9922))
      | ~ class_Orderings_Olinorder(U_9921) ),
    inference(definitional_conversion,[status(esa)],[f_2701_4]) ).

cnf(f_2701_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9921),c_Big__Operators_Olinorder__class_OMin(U_9921,U_9922)),U_9922))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9921),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9921),sK146(U_9922,U_9921)),sK147(U_9922,U_9921))),hAPP(hAPP(c_Set_Oinsert(U_9921),sK146(U_9922,U_9921)),hAPP(hAPP(c_Set_Oinsert(U_9921),sK147(U_9922,U_9921)),c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))))))
    | U_9922 = c_Orderings_Obot__class_Obot(tc_fun(U_9921,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9921),U_9922))
    | ~ class_Orderings_Olinorder(U_9921) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

fof(f_2702_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove]) ).

fof(f_2702_2,plain,
    ! [U_9925,U_9924,U_9923] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),U_9924) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9923),U_9925),c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),U_9924) = U_9925
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9923),U_9925),U_9924))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9923),U_9924))
      | ~ class_Orderings_Olinorder(U_9923) ),
    inference(variable_rename,[status(thm)],[f_2702_1]) ).

fof(f_2702_3,plain,
    ( ! [U_9923,U_9924,U_9925] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),U_9924) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9923),U_9925),c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))
        | ~ sP780(U_9923,U_9924,U_9925) )
    & ! [U_9923,U_9924,U_9925] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),U_9924) = U_9925
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))
        | ~ sP780(U_9923,U_9924,U_9925) )
    & ! [U_9923,U_9924,U_9925] :
        ( sP780(U_9923,U_9924,U_9925)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9923),U_9925),U_9924))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9923),U_9924))
        | ~ class_Orderings_Olinorder(U_9923) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP780])],[f_2702_2]) ).

cnf(f_2702_4,plain,
    ( sP780(U_9923,U_9924,U_9925)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9923),U_9925),U_9924))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9923),U_9924))
    | ~ class_Orderings_Olinorder(U_9923) ),
    inference(clausify,[status(thm)],[f_2702_3]) ).

cnf(f_2702_5,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),U_9924) = U_9925
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))
    | ~ sP780(U_9923,U_9924,U_9925) ),
    inference(clausify,[status(thm)],[f_2702_3]) ).

cnf(f_2702_6,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),U_9924) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9923),U_9925),c_Big__Operators_Olattice_OSup__fin(U_9923,c_Orderings_Oord__class_Omax(U_9923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9923,tc_HOL_Obool)),U_9924),hAPP(hAPP(c_Set_Oinsert(U_9923),U_9925),c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9923,tc_HOL_Obool))
    | ~ sP780(U_9923,U_9924,U_9925) ),
    inference(clausify,[status(thm)],[f_2702_3]) ).

fof(f_2703_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove]) ).

fof(f_2703_2,plain,
    ! [U_9928,U_9927,U_9926] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),U_9927) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9926),U_9928),c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),U_9927) = U_9928
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9928),U_9927))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
      | ~ class_Orderings_Olinorder(U_9926) ),
    inference(variable_rename,[status(thm)],[f_2703_1]) ).

fof(f_2703_3,plain,
    ( ! [U_9928,U_9927,U_9926] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),U_9927) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9926),U_9928),c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))
        | ~ sP781(U_9928,U_9927,U_9926) )
    & ! [U_9928,U_9927,U_9926] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),U_9927) = U_9928
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))
        | ~ sP781(U_9928,U_9927,U_9926) )
    & ! [U_9928,U_9927,U_9926] :
        ( sP781(U_9928,U_9927,U_9926)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9928),U_9927))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
        | ~ class_Orderings_Olinorder(U_9926) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP781])],[f_2703_2]) ).

cnf(f_2703_4,plain,
    ( sP781(U_9928,U_9927,U_9926)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9928),U_9927))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
    | ~ class_Orderings_Olinorder(U_9926) ),
    inference(clausify,[status(thm)],[f_2703_3]) ).

cnf(f_2703_5,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),U_9927) = U_9928
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))
    | ~ sP781(U_9928,U_9927,U_9926) ),
    inference(clausify,[status(thm)],[f_2703_3]) ).

cnf(f_2703_6,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),U_9927) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9926),U_9928),c_Big__Operators_Olattice_OInf__fin(U_9926,c_Orderings_Oord__class_Omin(U_9926),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9926,tc_HOL_Obool)),U_9927),hAPP(hAPP(c_Set_Oinsert(U_9926),U_9928),c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9926,tc_HOL_Obool))
    | ~ sP781(U_9928,U_9927,U_9926) ),
    inference(clausify,[status(thm)],[f_2703_3]) ).

fof(f_2704_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed]) ).

fof(f_2704_2,plain,
    ! [U_9934,U_9933,U_9932,U_9931] :
      ( hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(U_9933,U_9934)),U_9934))
      | ? [U_9930,U_9929] : ~ hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(hAPP(U_9932,U_9930),U_9929)),hAPP(hAPP(c_Set_Oinsert(U_9931),U_9930),hAPP(hAPP(c_Set_Oinsert(U_9931),U_9929),c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))))))
      | U_9934 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9934))
      | ~ c_Finite__Set_Ofolding__one(U_9931,U_9932,U_9933) ),
    inference(variable_rename,[status(thm)],[f_2704_1]) ).

fof(f_2704_3,plain,
    ! [U_9934,U_9933,U_9932,U_9931] :
      ( hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(U_9933,U_9934)),U_9934))
      | ? [U_9929] : ~ hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(hAPP(U_9932,sK148(U_9934,U_9933,U_9932,U_9931)),U_9929)),hAPP(hAPP(c_Set_Oinsert(U_9931),sK148(U_9934,U_9933,U_9932,U_9931)),hAPP(hAPP(c_Set_Oinsert(U_9931),U_9929),c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))))))
      | U_9934 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9934))
      | ~ c_Finite__Set_Ofolding__one(U_9931,U_9932,U_9933) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_9930,sK148(U_9934,U_9933,U_9932,U_9931))],[f_2704_2]) ).

fof(f_2704_4,plain,
    ! [U_9934,U_9933,U_9932,U_9931] :
      ( hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(U_9933,U_9934)),U_9934))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(hAPP(U_9932,sK148(U_9934,U_9933,U_9932,U_9931)),sK149(U_9934,U_9933,U_9932,U_9931))),hAPP(hAPP(c_Set_Oinsert(U_9931),sK148(U_9934,U_9933,U_9932,U_9931)),hAPP(hAPP(c_Set_Oinsert(U_9931),sK149(U_9934,U_9933,U_9932,U_9931)),c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))))))
      | U_9934 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9934))
      | ~ c_Finite__Set_Ofolding__one(U_9931,U_9932,U_9933) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_9929,sK149(U_9934,U_9933,U_9932,U_9931))],[f_2704_3]) ).

fof(f_2704_5,plain,
    ! [U_9931,U_9933,U_9932,U_9934] :
      ( hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(U_9933,U_9934)),U_9934))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(hAPP(U_9932,sK148(U_9934,U_9933,U_9932,U_9931)),sK149(U_9934,U_9933,U_9932,U_9931))),hAPP(hAPP(c_Set_Oinsert(U_9931),sK148(U_9934,U_9933,U_9932,U_9931)),hAPP(hAPP(c_Set_Oinsert(U_9931),sK149(U_9934,U_9933,U_9932,U_9931)),c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))))))
      | U_9934 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9934))
      | ~ c_Finite__Set_Ofolding__one(U_9931,U_9932,U_9933) ),
    inference(definitional_conversion,[status(esa)],[f_2704_4]) ).

cnf(f_2704_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(U_9933,U_9934)),U_9934))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9931),hAPP(hAPP(U_9932,sK148(U_9934,U_9933,U_9932,U_9931)),sK149(U_9934,U_9933,U_9932,U_9931))),hAPP(hAPP(c_Set_Oinsert(U_9931),sK148(U_9934,U_9933,U_9932,U_9931)),hAPP(hAPP(c_Set_Oinsert(U_9931),sK149(U_9934,U_9933,U_9932,U_9931)),c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))))))
    | U_9934 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9934))
    | ~ c_Finite__Set_Ofolding__one(U_9931,U_9932,U_9933) ),
    inference(clausify,[status(thm)],[f_2704_5]) ).

fof(f_2705_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup]) ).

fof(f_2705_2,plain,
    ! [U_9936,U_9935] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9935),c_Big__Operators_Olattice_OInf__fin(U_9935,c_Orderings_Oord__class_Omin(U_9935),U_9936)),c_Big__Operators_Olattice_OSup__fin(U_9935,c_Orderings_Oord__class_Omax(U_9935),U_9936)))
      | U_9936 = c_Orderings_Obot__class_Obot(tc_fun(U_9935,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9935),U_9936))
      | ~ class_Orderings_Olinorder(U_9935) ),
    inference(variable_rename,[status(thm)],[f_2705_1]) ).

fof(f_2705_3,plain,
    ! [U_9935,U_9936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9935),c_Big__Operators_Olattice_OInf__fin(U_9935,c_Orderings_Oord__class_Omin(U_9935),U_9936)),c_Big__Operators_Olattice_OSup__fin(U_9935,c_Orderings_Oord__class_Omax(U_9935),U_9936)))
      | U_9936 = c_Orderings_Obot__class_Obot(tc_fun(U_9935,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9935),U_9936))
      | ~ class_Orderings_Olinorder(U_9935) ),
    inference(definitional_conversion,[status(esa)],[f_2705_2]) ).

cnf(f_2705_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9935),c_Big__Operators_Olattice_OInf__fin(U_9935,c_Orderings_Oord__class_Omin(U_9935),U_9936)),c_Big__Operators_Olattice_OSup__fin(U_9935,c_Orderings_Oord__class_Omax(U_9935),U_9936)))
    | U_9936 = c_Orderings_Obot__class_Obot(tc_fun(U_9935,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9935),U_9936))
    | ~ class_Orderings_Olinorder(U_9935) ),
    inference(clausify,[status(thm)],[f_2705_3]) ).

fof(f_2706_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem]) ).

fof(f_2706_2,plain,
    ! [U_9939,U_9938,U_9937] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9937),U_9939),c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)) = c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9937),U_9939),U_9938))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9937),U_9938))
      | ~ class_Orderings_Olinorder(U_9937) ),
    inference(variable_rename,[status(thm)],[f_2706_1]) ).

fof(f_2706_3,plain,
    ! [U_9938,U_9937,U_9939] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9937),U_9939),c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)) = c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9937),U_9939),U_9938))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9937),U_9938))
      | ~ class_Orderings_Olinorder(U_9937) ),
    inference(definitional_conversion,[status(esa)],[f_2706_2]) ).

cnf(f_2706_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9937),U_9939),c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)) = c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9937),U_9939),U_9938))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9937),U_9938))
    | ~ class_Orderings_Olinorder(U_9937) ),
    inference(clausify,[status(thm)],[f_2706_3]) ).

fof(f_2707_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem]) ).

fof(f_2707_2,plain,
    ! [U_9942,U_9941,U_9940] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9940),U_9942),c_Big__Operators_Olattice_OSup__fin(U_9940,c_Orderings_Oord__class_Omax(U_9940),U_9941)) = c_Big__Operators_Olattice_OSup__fin(U_9940,c_Orderings_Oord__class_Omax(U_9940),U_9941)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9940),U_9942),U_9941))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9940),U_9941))
      | ~ class_Orderings_Olinorder(U_9940) ),
    inference(variable_rename,[status(thm)],[f_2707_1]) ).

fof(f_2707_3,plain,
    ! [U_9940,U_9941,U_9942] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9940),U_9942),c_Big__Operators_Olattice_OSup__fin(U_9940,c_Orderings_Oord__class_Omax(U_9940),U_9941)) = c_Big__Operators_Olattice_OSup__fin(U_9940,c_Orderings_Oord__class_Omax(U_9940),U_9941)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9940),U_9942),U_9941))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9940),U_9941))
      | ~ class_Orderings_Olinorder(U_9940) ),
    inference(definitional_conversion,[status(esa)],[f_2707_2]) ).

cnf(f_2707_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9940),U_9942),c_Big__Operators_Olattice_OSup__fin(U_9940,c_Orderings_Oord__class_Omax(U_9940),U_9941)) = c_Big__Operators_Olattice_OSup__fin(U_9940,c_Orderings_Oord__class_Omax(U_9940),U_9941)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9940),U_9942),U_9941))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9940),U_9941))
    | ~ class_Orderings_Olinorder(U_9940) ),
    inference(clausify,[status(thm)],[f_2707_3]) ).

fof(f_2708_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton]) ).

fof(f_2708_2,plain,
    ! [U_9944,U_9943] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9943,c_Orderings_Oord__class_Omin(U_9943),hAPP(hAPP(c_Set_Oinsert(U_9943),U_9944),c_Orderings_Obot__class_Obot(tc_fun(U_9943,tc_HOL_Obool)))) = U_9944
      | ~ class_Orderings_Olinorder(U_9943) ),
    inference(variable_rename,[status(thm)],[f_2708_1]) ).

fof(f_2708_3,plain,
    ! [U_9944,U_9943] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9943,c_Orderings_Oord__class_Omin(U_9943),hAPP(hAPP(c_Set_Oinsert(U_9943),U_9944),c_Orderings_Obot__class_Obot(tc_fun(U_9943,tc_HOL_Obool)))) = U_9944
      | ~ class_Orderings_Olinorder(U_9943) ),
    inference(definitional_conversion,[status(esa)],[f_2708_2]) ).

cnf(f_2708_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9943,c_Orderings_Oord__class_Omin(U_9943),hAPP(hAPP(c_Set_Oinsert(U_9943),U_9944),c_Orderings_Obot__class_Obot(tc_fun(U_9943,tc_HOL_Obool)))) = U_9944
    | ~ class_Orderings_Olinorder(U_9943) ),
    inference(clausify,[status(thm)],[f_2708_3]) ).

fof(f_2709_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton]) ).

fof(f_2709_2,plain,
    ! [U_9946,U_9945] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9945,c_Orderings_Oord__class_Omax(U_9945),hAPP(hAPP(c_Set_Oinsert(U_9945),U_9946),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool)))) = U_9946
      | ~ class_Orderings_Olinorder(U_9945) ),
    inference(variable_rename,[status(thm)],[f_2709_1]) ).

fof(f_2709_3,plain,
    ! [U_9945,U_9946] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9945,c_Orderings_Oord__class_Omax(U_9945),hAPP(hAPP(c_Set_Oinsert(U_9945),U_9946),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool)))) = U_9946
      | ~ class_Orderings_Olinorder(U_9945) ),
    inference(definitional_conversion,[status(esa)],[f_2709_2]) ).

cnf(f_2709_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9945,c_Orderings_Oord__class_Omax(U_9945),hAPP(hAPP(c_Set_Oinsert(U_9945),U_9946),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool)))) = U_9946
    | ~ class_Orderings_Olinorder(U_9945) ),
    inference(clausify,[status(thm)],[f_2709_3]) ).

fof(f_2710_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem]) ).

fof(f_2710_2,plain,
    ! [U_9949,U_9948,U_9947] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9947,c_Orderings_Oord__class_Omin(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9949),U_9948)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9947),U_9949),c_Big__Operators_Olattice_OInf__fin(U_9947,c_Orderings_Oord__class_Omin(U_9947),U_9948))
      | U_9948 = c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9947),U_9948))
      | ~ class_Orderings_Olinorder(U_9947) ),
    inference(variable_rename,[status(thm)],[f_2710_1]) ).

fof(f_2710_3,plain,
    ! [U_9949,U_9948,U_9947] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9947,c_Orderings_Oord__class_Omin(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9949),U_9948)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9947),U_9949),c_Big__Operators_Olattice_OInf__fin(U_9947,c_Orderings_Oord__class_Omin(U_9947),U_9948))
      | U_9948 = c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9947),U_9948))
      | ~ class_Orderings_Olinorder(U_9947) ),
    inference(definitional_conversion,[status(esa)],[f_2710_2]) ).

cnf(f_2710_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9947,c_Orderings_Oord__class_Omin(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9949),U_9948)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9947),U_9949),c_Big__Operators_Olattice_OInf__fin(U_9947,c_Orderings_Oord__class_Omin(U_9947),U_9948))
    | U_9948 = c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9947),U_9948))
    | ~ class_Orderings_Olinorder(U_9947) ),
    inference(clausify,[status(thm)],[f_2710_3]) ).

fof(f_2711_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem]) ).

fof(f_2711_2,plain,
    ! [U_9952,U_9951,U_9950] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9950,c_Orderings_Oord__class_Omax(U_9950),hAPP(hAPP(c_Set_Oinsert(U_9950),U_9952),U_9951)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9950),U_9952),c_Big__Operators_Olattice_OSup__fin(U_9950,c_Orderings_Oord__class_Omax(U_9950),U_9951))
      | U_9951 = c_Orderings_Obot__class_Obot(tc_fun(U_9950,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9950),U_9951))
      | ~ class_Orderings_Olinorder(U_9950) ),
    inference(variable_rename,[status(thm)],[f_2711_1]) ).

fof(f_2711_3,plain,
    ! [U_9950,U_9951,U_9952] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9950,c_Orderings_Oord__class_Omax(U_9950),hAPP(hAPP(c_Set_Oinsert(U_9950),U_9952),U_9951)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9950),U_9952),c_Big__Operators_Olattice_OSup__fin(U_9950,c_Orderings_Oord__class_Omax(U_9950),U_9951))
      | U_9951 = c_Orderings_Obot__class_Obot(tc_fun(U_9950,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9950),U_9951))
      | ~ class_Orderings_Olinorder(U_9950) ),
    inference(definitional_conversion,[status(esa)],[f_2711_2]) ).

cnf(f_2711_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9950,c_Orderings_Oord__class_Omax(U_9950),hAPP(hAPP(c_Set_Oinsert(U_9950),U_9952),U_9951)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9950),U_9952),c_Big__Operators_Olattice_OSup__fin(U_9950,c_Orderings_Oord__class_Omax(U_9950),U_9951))
    | U_9951 = c_Orderings_Obot__class_Obot(tc_fun(U_9950,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9950),U_9951))
    | ~ class_Orderings_Olinorder(U_9950) ),
    inference(clausify,[status(thm)],[f_2711_3]) ).

fof(f_2712_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem]) ).

fof(f_2712_2,plain,
    ! [U_9955,U_9954,U_9953] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9953),c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9955)),c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9954)) = c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9954)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9953,tc_HOL_Obool)),U_9955),U_9954))
      | U_9955 = c_Orderings_Obot__class_Obot(tc_fun(U_9953,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9953),U_9954))
      | ~ class_Orderings_Olinorder(U_9953) ),
    inference(variable_rename,[status(thm)],[f_2712_1]) ).

fof(f_2712_3,plain,
    ! [U_9953,U_9954,U_9955] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9953),c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9955)),c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9954)) = c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9954)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9953,tc_HOL_Obool)),U_9955),U_9954))
      | U_9955 = c_Orderings_Obot__class_Obot(tc_fun(U_9953,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9953),U_9954))
      | ~ class_Orderings_Olinorder(U_9953) ),
    inference(definitional_conversion,[status(esa)],[f_2712_2]) ).

cnf(f_2712_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9953),c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9955)),c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9954)) = c_Big__Operators_Olattice_OInf__fin(U_9953,c_Orderings_Oord__class_Omin(U_9953),U_9954)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9953,tc_HOL_Obool)),U_9955),U_9954))
    | U_9955 = c_Orderings_Obot__class_Obot(tc_fun(U_9953,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9953),U_9954))
    | ~ class_Orderings_Olinorder(U_9953) ),
    inference(clausify,[status(thm)],[f_2712_3]) ).

fof(f_2713_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem]) ).

fof(f_2713_2,plain,
    ! [U_9958,U_9957,U_9956] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9956),c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9958)),c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9957)) = c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9957)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9956,tc_HOL_Obool)),U_9958),U_9957))
      | U_9958 = c_Orderings_Obot__class_Obot(tc_fun(U_9956,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9956),U_9957))
      | ~ class_Orderings_Olinorder(U_9956) ),
    inference(variable_rename,[status(thm)],[f_2713_1]) ).

fof(f_2713_3,plain,
    ! [U_9956,U_9957,U_9958] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9956),c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9958)),c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9957)) = c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9957)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9956,tc_HOL_Obool)),U_9958),U_9957))
      | U_9958 = c_Orderings_Obot__class_Obot(tc_fun(U_9956,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9956),U_9957))
      | ~ class_Orderings_Olinorder(U_9956) ),
    inference(definitional_conversion,[status(esa)],[f_2713_2]) ).

cnf(f_2713_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9956),c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9958)),c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9957)) = c_Big__Operators_Olattice_OSup__fin(U_9956,c_Orderings_Oord__class_Omax(U_9956),U_9957)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9956,tc_HOL_Obool)),U_9958),U_9957))
    | U_9958 = c_Orderings_Obot__class_Obot(tc_fun(U_9956,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9956),U_9957))
    | ~ class_Orderings_Olinorder(U_9956) ),
    inference(clausify,[status(thm)],[f_2713_3]) ).

fof(f_2714_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb]) ).

fof(f_2714_2,plain,
    ! [U_9961,U_9960,U_9959] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9959),U_9961),c_Big__Operators_Olattice_OInf__fin(U_9959,c_Orderings_Oord__class_Omin(U_9959),U_9960)) = U_9961
      | ~ hBOOL(hAPP(hAPP(c_member(U_9959),U_9961),U_9960))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9959),U_9960))
      | ~ class_Orderings_Olinorder(U_9959) ),
    inference(variable_rename,[status(thm)],[f_2714_1]) ).

fof(f_2714_3,plain,
    ! [U_9961,U_9959,U_9960] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9959),U_9961),c_Big__Operators_Olattice_OInf__fin(U_9959,c_Orderings_Oord__class_Omin(U_9959),U_9960)) = U_9961
      | ~ hBOOL(hAPP(hAPP(c_member(U_9959),U_9961),U_9960))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9959),U_9960))
      | ~ class_Orderings_Olinorder(U_9959) ),
    inference(definitional_conversion,[status(esa)],[f_2714_2]) ).

cnf(f_2714_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9959),U_9961),c_Big__Operators_Olattice_OInf__fin(U_9959,c_Orderings_Oord__class_Omin(U_9959),U_9960)) = U_9961
    | ~ hBOOL(hAPP(hAPP(c_member(U_9959),U_9961),U_9960))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9959),U_9960))
    | ~ class_Orderings_Olinorder(U_9959) ),
    inference(clausify,[status(thm)],[f_2714_3]) ).

fof(f_2715_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb]) ).

fof(f_2715_2,plain,
    ! [U_9964,U_9963,U_9962] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9962),U_9964),c_Big__Operators_Olattice_OSup__fin(U_9962,c_Orderings_Oord__class_Omax(U_9962),U_9963)) = U_9964
      | ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9964),U_9963))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9962),U_9963))
      | ~ class_Orderings_Olinorder(U_9962) ),
    inference(variable_rename,[status(thm)],[f_2715_1]) ).

fof(f_2715_3,plain,
    ! [U_9963,U_9962,U_9964] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9962),U_9964),c_Big__Operators_Olattice_OSup__fin(U_9962,c_Orderings_Oord__class_Omax(U_9962),U_9963)) = U_9964
      | ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9964),U_9963))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9962),U_9963))
      | ~ class_Orderings_Olinorder(U_9962) ),
    inference(definitional_conversion,[status(esa)],[f_2715_2]) ).

cnf(f_2715_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9962),U_9964),c_Big__Operators_Olattice_OSup__fin(U_9962,c_Orderings_Oord__class_Omax(U_9962),U_9963)) = U_9964
    | ~ hBOOL(hAPP(hAPP(c_member(U_9962),U_9964),U_9963))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9962),U_9963))
    | ~ class_Orderings_Olinorder(U_9962) ),
    inference(clausify,[status(thm)],[f_2715_3]) ).

fof(f_2716_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem]) ).

fof(f_2716_2,plain,
    ! [U_9967,U_9966,U_9965] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9965,tc_HOL_Obool)),U_9966),U_9967)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9965),c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),U_9966)),c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),U_9967))
      | U_9967 = c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9965),U_9967))
      | U_9966 = c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9965),U_9966))
      | ~ class_Orderings_Olinorder(U_9965) ),
    inference(variable_rename,[status(thm)],[f_2716_1]) ).

fof(f_2716_3,plain,
    ! [U_9965,U_9966,U_9967] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9965,tc_HOL_Obool)),U_9966),U_9967)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9965),c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),U_9966)),c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),U_9967))
      | U_9967 = c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9965),U_9967))
      | U_9966 = c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9965),U_9966))
      | ~ class_Orderings_Olinorder(U_9965) ),
    inference(definitional_conversion,[status(esa)],[f_2716_2]) ).

cnf(f_2716_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9965,tc_HOL_Obool)),U_9966),U_9967)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9965),c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),U_9966)),c_Big__Operators_Olattice_OInf__fin(U_9965,c_Orderings_Oord__class_Omin(U_9965),U_9967))
    | U_9967 = c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9965),U_9967))
    | U_9966 = c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9965),U_9966))
    | ~ class_Orderings_Olinorder(U_9965) ),
    inference(clausify,[status(thm)],[f_2716_3]) ).

fof(f_2717_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem]) ).

fof(f_2717_2,plain,
    ! [U_9970,U_9969,U_9968] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9968,tc_HOL_Obool)),U_9969),U_9970)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9968),c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),U_9969)),c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),U_9970))
      | U_9970 = c_Orderings_Obot__class_Obot(tc_fun(U_9968,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9968),U_9970))
      | U_9969 = c_Orderings_Obot__class_Obot(tc_fun(U_9968,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9968),U_9969))
      | ~ class_Orderings_Olinorder(U_9968) ),
    inference(variable_rename,[status(thm)],[f_2717_1]) ).

fof(f_2717_3,plain,
    ! [U_9968,U_9969,U_9970] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9968,tc_HOL_Obool)),U_9969),U_9970)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9968),c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),U_9969)),c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),U_9970))
      | U_9970 = c_Orderings_Obot__class_Obot(tc_fun(U_9968,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9968),U_9970))
      | U_9969 = c_Orderings_Obot__class_Obot(tc_fun(U_9968,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9968),U_9969))
      | ~ class_Orderings_Olinorder(U_9968) ),
    inference(definitional_conversion,[status(esa)],[f_2717_2]) ).

cnf(f_2717_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9968,tc_HOL_Obool)),U_9969),U_9970)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9968),c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),U_9969)),c_Big__Operators_Olattice_OSup__fin(U_9968,c_Orderings_Oord__class_Omax(U_9968),U_9970))
    | U_9970 = c_Orderings_Obot__class_Obot(tc_fun(U_9968,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9968),U_9970))
    | U_9969 = c_Orderings_Obot__class_Obot(tc_fun(U_9968,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9968),U_9969))
    | ~ class_Orderings_Olinorder(U_9968) ),
    inference(clausify,[status(thm)],[f_2717_3]) ).

fof(f_2718_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(f_2718_2,plain,
    ! [U_9973,U_9972,U_9971] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9971,c_Orderings_Oord__class_Omin(U_9971),hAPP(hAPP(c_Set_Oinsert(U_9971),U_9973),U_9972)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9971),U_9973),c_Big__Operators_Olattice_OInf__fin(U_9971,c_Orderings_Oord__class_Omin(U_9971),U_9972))
      | U_9972 = c_Orderings_Obot__class_Obot(tc_fun(U_9971,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9971),U_9973),U_9972))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9971),U_9972))
      | ~ class_Orderings_Olinorder(U_9971) ),
    inference(variable_rename,[status(thm)],[f_2718_1]) ).

fof(f_2718_3,plain,
    ! [U_9971,U_9972,U_9973] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9971,c_Orderings_Oord__class_Omin(U_9971),hAPP(hAPP(c_Set_Oinsert(U_9971),U_9973),U_9972)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9971),U_9973),c_Big__Operators_Olattice_OInf__fin(U_9971,c_Orderings_Oord__class_Omin(U_9971),U_9972))
      | U_9972 = c_Orderings_Obot__class_Obot(tc_fun(U_9971,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9971),U_9973),U_9972))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9971),U_9972))
      | ~ class_Orderings_Olinorder(U_9971) ),
    inference(definitional_conversion,[status(esa)],[f_2718_2]) ).

cnf(f_2718_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9971,c_Orderings_Oord__class_Omin(U_9971),hAPP(hAPP(c_Set_Oinsert(U_9971),U_9973),U_9972)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9971),U_9973),c_Big__Operators_Olattice_OInf__fin(U_9971,c_Orderings_Oord__class_Omin(U_9971),U_9972))
    | U_9972 = c_Orderings_Obot__class_Obot(tc_fun(U_9971,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9971),U_9973),U_9972))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9971),U_9972))
    | ~ class_Orderings_Olinorder(U_9971) ),
    inference(clausify,[status(thm)],[f_2718_3]) ).

fof(f_2719_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(f_2719_2,plain,
    ! [U_9976,U_9975,U_9974] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9974,c_Orderings_Oord__class_Omax(U_9974),hAPP(hAPP(c_Set_Oinsert(U_9974),U_9976),U_9975)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9974),U_9976),c_Big__Operators_Olattice_OSup__fin(U_9974,c_Orderings_Oord__class_Omax(U_9974),U_9975))
      | U_9975 = c_Orderings_Obot__class_Obot(tc_fun(U_9974,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9974),U_9976),U_9975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9974),U_9975))
      | ~ class_Orderings_Olinorder(U_9974) ),
    inference(variable_rename,[status(thm)],[f_2719_1]) ).

fof(f_2719_3,plain,
    ! [U_9974,U_9975,U_9976] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9974,c_Orderings_Oord__class_Omax(U_9974),hAPP(hAPP(c_Set_Oinsert(U_9974),U_9976),U_9975)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9974),U_9976),c_Big__Operators_Olattice_OSup__fin(U_9974,c_Orderings_Oord__class_Omax(U_9974),U_9975))
      | U_9975 = c_Orderings_Obot__class_Obot(tc_fun(U_9974,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9974),U_9976),U_9975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9974),U_9975))
      | ~ class_Orderings_Olinorder(U_9974) ),
    inference(definitional_conversion,[status(esa)],[f_2719_2]) ).

cnf(f_2719_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9974,c_Orderings_Oord__class_Omax(U_9974),hAPP(hAPP(c_Set_Oinsert(U_9974),U_9976),U_9975)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9974),U_9976),c_Big__Operators_Olattice_OSup__fin(U_9974,c_Orderings_Oord__class_Omax(U_9974),U_9975))
    | U_9975 = c_Orderings_Obot__class_Obot(tc_fun(U_9974,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9974),U_9976),U_9975))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9974),U_9975))
    | ~ class_Orderings_Olinorder(U_9974) ),
    inference(clausify,[status(thm)],[f_2719_3]) ).

fof(f_2720_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove]) ).

fof(f_2720_2,plain,
    ! [U_9979,U_9978,U_9977] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),U_9978)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9977),U_9979),c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),U_9978)) = U_9979
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9977),U_9978))
      | ~ class_Orderings_Olinorder(U_9977) ),
    inference(variable_rename,[status(thm)],[f_2720_1]) ).

fof(f_2720_3,plain,
    ( ! [U_9978,U_9977,U_9979] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),U_9978)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9977),U_9979),c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))
        | ~ sP782(U_9978,U_9977,U_9979) )
    & ! [U_9978,U_9977,U_9979] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),U_9978)) = U_9979
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))
        | ~ sP782(U_9978,U_9977,U_9979) )
    & ! [U_9978,U_9977,U_9979] :
        ( sP782(U_9978,U_9977,U_9979)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9977),U_9978))
        | ~ class_Orderings_Olinorder(U_9977) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP782])],[f_2720_2]) ).

cnf(f_2720_4,plain,
    ( sP782(U_9978,U_9977,U_9979)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9977),U_9978))
    | ~ class_Orderings_Olinorder(U_9977) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

cnf(f_2720_5,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),U_9978)) = U_9979
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))
    | ~ sP782(U_9978,U_9977,U_9979) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

cnf(f_2720_6,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),U_9978)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9977),U_9979),c_Big__Operators_Olattice_OInf__fin(U_9977,c_Orderings_Oord__class_Omin(U_9977),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9977,tc_HOL_Obool)),U_9978),hAPP(hAPP(c_Set_Oinsert(U_9977),U_9979),c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9977,tc_HOL_Obool))
    | ~ sP782(U_9978,U_9977,U_9979) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

fof(f_2721_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove]) ).

fof(f_2721_2,plain,
    ! [U_9982,U_9981,U_9980] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),U_9981)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9980),U_9982),c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),U_9981)) = U_9982
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9980),U_9981))
      | ~ class_Orderings_Olinorder(U_9980) ),
    inference(variable_rename,[status(thm)],[f_2721_1]) ).

fof(f_2721_3,plain,
    ( ! [U_9982,U_9981,U_9980] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),U_9981)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9980),U_9982),c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))
        | ~ sP783(U_9982,U_9981,U_9980) )
    & ! [U_9982,U_9981,U_9980] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),U_9981)) = U_9982
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))
        | ~ sP783(U_9982,U_9981,U_9980) )
    & ! [U_9982,U_9981,U_9980] :
        ( sP783(U_9982,U_9981,U_9980)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9980),U_9981))
        | ~ class_Orderings_Olinorder(U_9980) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP783])],[f_2721_2]) ).

cnf(f_2721_4,plain,
    ( sP783(U_9982,U_9981,U_9980)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9980),U_9981))
    | ~ class_Orderings_Olinorder(U_9980) ),
    inference(clausify,[status(thm)],[f_2721_3]) ).

cnf(f_2721_5,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),U_9981)) = U_9982
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))
    | ~ sP783(U_9982,U_9981,U_9980) ),
    inference(clausify,[status(thm)],[f_2721_3]) ).

cnf(f_2721_6,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),U_9981)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9980),U_9982),c_Big__Operators_Olattice_OSup__fin(U_9980,c_Orderings_Oord__class_Omax(U_9980),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9980,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_Set_Oinsert(U_9980),U_9982),c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9980,tc_HOL_Obool))
    | ~ sP783(U_9982,U_9981,U_9980) ),
    inference(clausify,[status(thm)],[f_2721_3]) ).

fof(f_2722_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint]) ).

fof(f_2722_2,plain,
    ! [U_9985,U_9984,U_9983] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9983,tc_HOL_Obool)),U_9984),U_9985)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9983),c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),U_9984)),c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),U_9985))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9983,tc_HOL_Obool)),U_9984),U_9985) != c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
      | U_9985 = c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9983),U_9985))
      | U_9984 = c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9983),U_9984))
      | ~ class_Orderings_Olinorder(U_9983) ),
    inference(variable_rename,[status(thm)],[f_2722_1]) ).

fof(f_2722_3,plain,
    ! [U_9985,U_9984,U_9983] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9983,tc_HOL_Obool)),U_9984),U_9985)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9983),c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),U_9984)),c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),U_9985))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9983,tc_HOL_Obool)),U_9984),U_9985) != c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
      | U_9985 = c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9983),U_9985))
      | U_9984 = c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9983),U_9984))
      | ~ class_Orderings_Olinorder(U_9983) ),
    inference(definitional_conversion,[status(esa)],[f_2722_2]) ).

cnf(f_2722_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9983,tc_HOL_Obool)),U_9984),U_9985)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9983),c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),U_9984)),c_Big__Operators_Olattice_OInf__fin(U_9983,c_Orderings_Oord__class_Omin(U_9983),U_9985))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9983,tc_HOL_Obool)),U_9984),U_9985) != c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
    | U_9985 = c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9983),U_9985))
    | U_9984 = c_Orderings_Obot__class_Obot(tc_fun(U_9983,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9983),U_9984))
    | ~ class_Orderings_Olinorder(U_9983) ),
    inference(clausify,[status(thm)],[f_2722_3]) ).

fof(f_2723_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter]) ).

fof(f_2723_2,plain,
    ! [U_9988,U_9987,U_9986] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9986),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988))),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9986),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),U_9987)),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),U_9988))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988) = c_Orderings_Obot__class_Obot(tc_fun(U_9986,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9986),U_9988))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9986),U_9987))
      | ~ class_Orderings_Olinorder(U_9986) ),
    inference(variable_rename,[status(thm)],[f_2723_1]) ).

fof(f_2723_3,plain,
    ! [U_9987,U_9986,U_9988] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9986),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988))),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9986),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),U_9987)),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),U_9988))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988) = c_Orderings_Obot__class_Obot(tc_fun(U_9986,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9986),U_9988))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9986),U_9987))
      | ~ class_Orderings_Olinorder(U_9986) ),
    inference(definitional_conversion,[status(esa)],[f_2723_2]) ).

cnf(f_2723_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9986),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988))),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9986),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),U_9987)),c_Big__Operators_Olattice_OInf__fin(U_9986,c_Orderings_Oord__class_Omin(U_9986),U_9988))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9986,tc_HOL_Obool)),U_9987),U_9988) = c_Orderings_Obot__class_Obot(tc_fun(U_9986,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9986),U_9988))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9986),U_9987))
    | ~ class_Orderings_Olinorder(U_9986) ),
    inference(clausify,[status(thm)],[f_2723_3]) ).

fof(f_2724_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter]) ).

fof(f_2724_2,plain,
    ! [U_9991,U_9990,U_9989] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9989),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991))),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9989),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),U_9990)),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),U_9991))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991) = c_Orderings_Obot__class_Obot(tc_fun(U_9989,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9989),U_9991))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9989),U_9990))
      | ~ class_Orderings_Olinorder(U_9989) ),
    inference(variable_rename,[status(thm)],[f_2724_1]) ).

fof(f_2724_3,plain,
    ! [U_9990,U_9989,U_9991] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9989),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991))),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9989),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),U_9990)),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),U_9991))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991) = c_Orderings_Obot__class_Obot(tc_fun(U_9989,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9989),U_9991))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9989),U_9990))
      | ~ class_Orderings_Olinorder(U_9989) ),
    inference(definitional_conversion,[status(esa)],[f_2724_2]) ).

cnf(f_2724_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9989),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991))),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9989),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),U_9990)),c_Big__Operators_Olattice_OSup__fin(U_9989,c_Orderings_Oord__class_Omax(U_9989),U_9991))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9991) = c_Orderings_Obot__class_Obot(tc_fun(U_9989,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9989),U_9991))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9989),U_9990))
    | ~ class_Orderings_Olinorder(U_9989) ),
    inference(clausify,[status(thm)],[f_2724_3]) ).

fof(f_2725_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint]) ).

fof(f_2725_2,plain,
    ! [U_9994,U_9993,U_9992] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9992),c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),U_9993)),c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),U_9994))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994) != c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
      | U_9994 = c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9992),U_9994))
      | U_9993 = c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9992),U_9993))
      | ~ class_Orderings_Olinorder(U_9992) ),
    inference(variable_rename,[status(thm)],[f_2725_1]) ).

fof(f_2725_3,plain,
    ! [U_9993,U_9992,U_9994] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9992),c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),U_9993)),c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),U_9994))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994) != c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
      | U_9994 = c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9992),U_9994))
      | U_9993 = c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9992),U_9993))
      | ~ class_Orderings_Olinorder(U_9992) ),
    inference(definitional_conversion,[status(esa)],[f_2725_2]) ).

cnf(f_2725_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9992),c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),U_9993)),c_Big__Operators_Olattice_OSup__fin(U_9992,c_Orderings_Oord__class_Omax(U_9992),U_9994))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994) != c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
    | U_9994 = c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9992),U_9994))
    | U_9993 = c_Orderings_Obot__class_Obot(tc_fun(U_9992,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9992),U_9993))
    | ~ class_Orderings_Olinorder(U_9992) ),
    inference(clausify,[status(thm)],[f_2725_3]) ).

fof(f_2726_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed]) ).

fof(f_2726_2,plain,
    ! [U_9998,U_9997] :
      ( hBOOL(hAPP(hAPP(c_member(U_9997),c_Big__Operators_Olattice_OSup__fin(U_9997,c_Orderings_Oord__class_Omax(U_9997),U_9998)),U_9998))
      | ? [U_9996,U_9995] : ~ hBOOL(hAPP(hAPP(c_member(U_9997),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9997),U_9996),U_9995)),hAPP(hAPP(c_Set_Oinsert(U_9997),U_9996),hAPP(hAPP(c_Set_Oinsert(U_9997),U_9995),c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))))))
      | U_9998 = c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9997),U_9998))
      | ~ class_Orderings_Olinorder(U_9997) ),
    inference(variable_rename,[status(thm)],[f_2726_1]) ).

fof(f_2726_3,plain,
    ! [U_9998,U_9997] :
      ( hBOOL(hAPP(hAPP(c_member(U_9997),c_Big__Operators_Olattice_OSup__fin(U_9997,c_Orderings_Oord__class_Omax(U_9997),U_9998)),U_9998))
      | ? [U_9995] : ~ hBOOL(hAPP(hAPP(c_member(U_9997),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9997),sK150(U_9998,U_9997)),U_9995)),hAPP(hAPP(c_Set_Oinsert(U_9997),sK150(U_9998,U_9997)),hAPP(hAPP(c_Set_Oinsert(U_9997),U_9995),c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))))))
      | U_9998 = c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9997),U_9998))
      | ~ class_Orderings_Olinorder(U_9997) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_9996,sK150(U_9998,U_9997))],[f_2726_2]) ).

fof(f_2726_4,plain,
    ! [U_9998,U_9997] :
      ( hBOOL(hAPP(hAPP(c_member(U_9997),c_Big__Operators_Olattice_OSup__fin(U_9997,c_Orderings_Oord__class_Omax(U_9997),U_9998)),U_9998))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9997),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9997),sK150(U_9998,U_9997)),sK151(U_9998,U_9997))),hAPP(hAPP(c_Set_Oinsert(U_9997),sK150(U_9998,U_9997)),hAPP(hAPP(c_Set_Oinsert(U_9997),sK151(U_9998,U_9997)),c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))))))
      | U_9998 = c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9997),U_9998))
      | ~ class_Orderings_Olinorder(U_9997) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_9995,sK151(U_9998,U_9997))],[f_2726_3]) ).

fof(f_2726_5,plain,
    ! [U_9997,U_9998] :
      ( hBOOL(hAPP(hAPP(c_member(U_9997),c_Big__Operators_Olattice_OSup__fin(U_9997,c_Orderings_Oord__class_Omax(U_9997),U_9998)),U_9998))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9997),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9997),sK150(U_9998,U_9997)),sK151(U_9998,U_9997))),hAPP(hAPP(c_Set_Oinsert(U_9997),sK150(U_9998,U_9997)),hAPP(hAPP(c_Set_Oinsert(U_9997),sK151(U_9998,U_9997)),c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))))))
      | U_9998 = c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9997),U_9998))
      | ~ class_Orderings_Olinorder(U_9997) ),
    inference(definitional_conversion,[status(esa)],[f_2726_4]) ).

cnf(f_2726_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9997),c_Big__Operators_Olattice_OSup__fin(U_9997,c_Orderings_Oord__class_Omax(U_9997),U_9998)),U_9998))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9997),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9997),sK150(U_9998,U_9997)),sK151(U_9998,U_9997))),hAPP(hAPP(c_Set_Oinsert(U_9997),sK150(U_9998,U_9997)),hAPP(hAPP(c_Set_Oinsert(U_9997),sK151(U_9998,U_9997)),c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))))))
    | U_9998 = c_Orderings_Obot__class_Obot(tc_fun(U_9997,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9997),U_9998))
    | ~ class_Orderings_Olinorder(U_9997) ),
    inference(clausify,[status(thm)],[f_2726_5]) ).

fof(f_2727_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed]) ).

fof(f_2727_2,plain,
    ! [U_10002,U_10001] :
      ( hBOOL(hAPP(hAPP(c_member(U_10001),c_Big__Operators_Olattice_OInf__fin(U_10001,c_Orderings_Oord__class_Omin(U_10001),U_10002)),U_10002))
      | ? [U_10000,U_9999] : ~ hBOOL(hAPP(hAPP(c_member(U_10001),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10001),U_10000),U_9999)),hAPP(hAPP(c_Set_Oinsert(U_10001),U_10000),hAPP(hAPP(c_Set_Oinsert(U_10001),U_9999),c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))))))
      | U_10002 = c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10001),U_10002))
      | ~ class_Orderings_Olinorder(U_10001) ),
    inference(variable_rename,[status(thm)],[f_2727_1]) ).

fof(f_2727_3,plain,
    ! [U_10002,U_10001] :
      ( hBOOL(hAPP(hAPP(c_member(U_10001),c_Big__Operators_Olattice_OInf__fin(U_10001,c_Orderings_Oord__class_Omin(U_10001),U_10002)),U_10002))
      | ? [U_9999] : ~ hBOOL(hAPP(hAPP(c_member(U_10001),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10001),sK152(U_10002,U_10001)),U_9999)),hAPP(hAPP(c_Set_Oinsert(U_10001),sK152(U_10002,U_10001)),hAPP(hAPP(c_Set_Oinsert(U_10001),U_9999),c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))))))
      | U_10002 = c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10001),U_10002))
      | ~ class_Orderings_Olinorder(U_10001) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_10000,sK152(U_10002,U_10001))],[f_2727_2]) ).

fof(f_2727_4,plain,
    ! [U_10002,U_10001] :
      ( hBOOL(hAPP(hAPP(c_member(U_10001),c_Big__Operators_Olattice_OInf__fin(U_10001,c_Orderings_Oord__class_Omin(U_10001),U_10002)),U_10002))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10001),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10001),sK152(U_10002,U_10001)),sK153(U_10002,U_10001))),hAPP(hAPP(c_Set_Oinsert(U_10001),sK152(U_10002,U_10001)),hAPP(hAPP(c_Set_Oinsert(U_10001),sK153(U_10002,U_10001)),c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))))))
      | U_10002 = c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10001),U_10002))
      | ~ class_Orderings_Olinorder(U_10001) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_9999,sK153(U_10002,U_10001))],[f_2727_3]) ).

fof(f_2727_5,plain,
    ! [U_10001,U_10002] :
      ( hBOOL(hAPP(hAPP(c_member(U_10001),c_Big__Operators_Olattice_OInf__fin(U_10001,c_Orderings_Oord__class_Omin(U_10001),U_10002)),U_10002))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10001),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10001),sK152(U_10002,U_10001)),sK153(U_10002,U_10001))),hAPP(hAPP(c_Set_Oinsert(U_10001),sK152(U_10002,U_10001)),hAPP(hAPP(c_Set_Oinsert(U_10001),sK153(U_10002,U_10001)),c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))))))
      | U_10002 = c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10001),U_10002))
      | ~ class_Orderings_Olinorder(U_10001) ),
    inference(definitional_conversion,[status(esa)],[f_2727_4]) ).

cnf(f_2727_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10001),c_Big__Operators_Olattice_OInf__fin(U_10001,c_Orderings_Oord__class_Omin(U_10001),U_10002)),U_10002))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10001),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10001),sK152(U_10002,U_10001)),sK153(U_10002,U_10001))),hAPP(hAPP(c_Set_Oinsert(U_10001),sK152(U_10002,U_10001)),hAPP(hAPP(c_Set_Oinsert(U_10001),sK153(U_10002,U_10001)),c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))))))
    | U_10002 = c_Orderings_Obot__class_Obot(tc_fun(U_10001,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10001),U_10002))
    | ~ class_Orderings_Olinorder(U_10001) ),
    inference(clausify,[status(thm)],[f_2727_5]) ).

fof(f_2728_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        & ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(f_2728_2,plain,
    ! [U_10005,U_10004,U_10003] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_10003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10003,tc_HOL_Obool)),U_10004),hAPP(hAPP(c_Set_Oinsert(U_10003),U_10005),c_Orderings_Obot__class_Obot(tc_fun(U_10003,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_10003),U_10004)
          | hBOOL(hAPP(hAPP(c_member(U_10003),U_10005),U_10004)) )
        & ( hAPP(c_Finite__Set_Ocard(U_10003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10003,tc_HOL_Obool)),U_10004),hAPP(hAPP(c_Set_Oinsert(U_10003),U_10005),c_Orderings_Obot__class_Obot(tc_fun(U_10003,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10003),U_10004)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10003),U_10005),U_10004)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10003),U_10004)) ),
    inference(variable_rename,[status(thm)],[f_2728_1]) ).

fof(f_2728_3,plain,
    ( ! [U_10004,U_10003,U_10005] :
        ( hAPP(c_Finite__Set_Ocard(U_10003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10003,tc_HOL_Obool)),U_10004),hAPP(hAPP(c_Set_Oinsert(U_10003),U_10005),c_Orderings_Obot__class_Obot(tc_fun(U_10003,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_10003),U_10004)
        | hBOOL(hAPP(hAPP(c_member(U_10003),U_10005),U_10004))
        | ~ sP784(U_10004,U_10003,U_10005) )
    & ! [U_10004,U_10003,U_10005] :
        ( hAPP(c_Finite__Set_Ocard(U_10003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10003,tc_HOL_Obool)),U_10004),hAPP(hAPP(c_Set_Oinsert(U_10003),U_10005),c_Orderings_Obot__class_Obot(tc_fun(U_10003,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10003),U_10004)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10003),U_10005),U_10004))
        | ~ sP784(U_10004,U_10003,U_10005) )
    & ! [U_10004,U_10003,U_10005] :
        ( sP784(U_10004,U_10003,U_10005)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10003),U_10004)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP784])],[f_2728_2]) ).

cnf(f_2728_4,plain,
    ( sP784(U_10004,U_10003,U_10005)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10003),U_10004)) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

cnf(f_2728_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10003,tc_HOL_Obool)),U_10004),hAPP(hAPP(c_Set_Oinsert(U_10003),U_10005),c_Orderings_Obot__class_Obot(tc_fun(U_10003,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10003),U_10004)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10003),U_10005),U_10004))
    | ~ sP784(U_10004,U_10003,U_10005) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

cnf(f_2728_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10003,tc_HOL_Obool)),U_10004),hAPP(hAPP(c_Set_Oinsert(U_10003),U_10005),c_Orderings_Obot__class_Obot(tc_fun(U_10003,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_10003),U_10004)
    | hBOOL(hAPP(hAPP(c_member(U_10003),U_10005),U_10004))
    | ~ sP784(U_10004,U_10003,U_10005) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

fof(f_2729_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton]) ).

fof(f_2729_2,plain,
    ! [U_10008,U_10007,U_10006] :
      ( hAPP(c_Finite__Set_Ocard(U_10006),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10006,tc_HOL_Obool)),U_10007),hAPP(hAPP(c_Set_Oinsert(U_10006),U_10008),c_Orderings_Obot__class_Obot(tc_fun(U_10006,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10006),U_10007)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10006),U_10008),U_10007))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10006),U_10007)) ),
    inference(variable_rename,[status(thm)],[f_2729_1]) ).

fof(f_2729_3,plain,
    ! [U_10006,U_10007,U_10008] :
      ( hAPP(c_Finite__Set_Ocard(U_10006),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10006,tc_HOL_Obool)),U_10007),hAPP(hAPP(c_Set_Oinsert(U_10006),U_10008),c_Orderings_Obot__class_Obot(tc_fun(U_10006,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10006),U_10007)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10006),U_10008),U_10007))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10006),U_10007)) ),
    inference(definitional_conversion,[status(esa)],[f_2729_2]) ).

cnf(f_2729_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10006),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10006,tc_HOL_Obool)),U_10007),hAPP(hAPP(c_Set_Oinsert(U_10006),U_10008),c_Orderings_Obot__class_Obot(tc_fun(U_10006,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10006),U_10007)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10006),U_10008),U_10007))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10006),U_10007)) ),
    inference(clausify,[status(thm)],[f_2729_3]) ).

fof(f_2730_1,plain,
    ! [V_A_2] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J]) ).

fof(f_2730_2,plain,
    ! [U_10009] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_10009) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10009))
      | ~ c_Nat__Transfer_Onat__set(U_10009) ),
    inference(variable_rename,[status(thm)],[f_2730_1]) ).

fof(f_2730_3,plain,
    ! [U_10009] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_10009) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10009))
      | ~ c_Nat__Transfer_Onat__set(U_10009) ),
    inference(definitional_conversion,[status(esa)],[f_2730_2]) ).

cnf(f_2730_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_10009) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10009))
    | ~ c_Nat__Transfer_Onat__set(U_10009) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

fof(f_2731_1,plain,
    ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(f_2731_2,plain,
    ! [U_10010] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10010) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10010)),
    inference(variable_rename,[status(thm)],[f_2731_1]) ).

fof(f_2731_3,plain,
    ! [U_10010] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10010) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10010)),
    inference(definitional_conversion,[status(esa)],[f_2731_2]) ).

cnf(f_2731_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10010) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10010)),
    inference(clausify,[status(thm)],[f_2731_3]) ).

fof(f_2732_1,plain,
    ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_card_Oempty]) ).

fof(f_2732_2,plain,
    ! [U_10011] : hAPP(c_Finite__Set_Ocard(U_10011),c_Orderings_Obot__class_Obot(tc_fun(U_10011,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2732_1]) ).

fof(f_2732_3,plain,
    ! [U_10011] : hAPP(c_Finite__Set_Ocard(U_10011),c_Orderings_Obot__class_Obot(tc_fun(U_10011,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2732_2]) ).

cnf(f_2732_4,plain,
    hAPP(c_Finite__Set_Ocard(U_10011),c_Orderings_Obot__class_Obot(tc_fun(U_10011,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2732_3]) ).

fof(f_2733_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__infinite]) ).

fof(f_2733_2,plain,
    ! [U_10013,U_10012] :
      ( hAPP(c_Finite__Set_Ocard(U_10012),U_10013) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10012),U_10013)) ),
    inference(variable_rename,[status(thm)],[f_2733_1]) ).

fof(f_2733_3,plain,
    ! [U_10012,U_10013] :
      ( hAPP(c_Finite__Set_Ocard(U_10012),U_10013) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10012),U_10013)) ),
    inference(definitional_conversion,[status(esa)],[f_2733_2]) ).

cnf(f_2733_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10012),U_10013) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10012),U_10013)) ),
    inference(clausify,[status(thm)],[f_2733_3]) ).

fof(f_2734_1,plain,
    ! [V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__eq__0__iff]) ).

fof(f_2734_2,plain,
    ! [U_10015,U_10014] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10014),U_10015) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10014),U_10015))
          & U_10015 != c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10014),U_10015))
        | U_10015 = c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_10014),U_10015) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2734_1]) ).

fof(f_2734_3,plain,
    ( ! [U_10019,U_10017] :
        ( hAPP(c_Finite__Set_Ocard(U_10017),U_10019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10017),U_10019))
          & U_10019 != c_Orderings_Obot__class_Obot(tc_fun(U_10017,tc_HOL_Obool)) ) )
    & ! [U_10018,U_10016] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10016),U_10018))
        | U_10018 = c_Orderings_Obot__class_Obot(tc_fun(U_10016,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_10016),U_10018) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2734_2]) ).

fof(f_2734_4,plain,
    ( ! [U_10019,U_10017] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10017),U_10019))
        | ~ sP785(U_10019,U_10017) )
    & ! [U_10019,U_10017] :
        ( U_10019 != c_Orderings_Obot__class_Obot(tc_fun(U_10017,tc_HOL_Obool))
        | ~ sP785(U_10019,U_10017) )
    & ! [U_10019,U_10017] :
        ( hAPP(c_Finite__Set_Ocard(U_10017),U_10019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP785(U_10019,U_10017) )
    & ! [U_10018,U_10016] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10016),U_10018))
        | U_10018 = c_Orderings_Obot__class_Obot(tc_fun(U_10016,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_10016),U_10018) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP785])],[f_2734_3]) ).

cnf(f_2734_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10016),U_10018))
    | U_10018 = c_Orderings_Obot__class_Obot(tc_fun(U_10016,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_10016),U_10018) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2734_4]) ).

cnf(f_2734_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10017),U_10019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP785(U_10019,U_10017) ),
    inference(clausify,[status(thm)],[f_2734_4]) ).

cnf(f_2734_7,plain,
    ( U_10019 != c_Orderings_Obot__class_Obot(tc_fun(U_10017,tc_HOL_Obool))
    | ~ sP785(U_10019,U_10017) ),
    inference(clausify,[status(thm)],[f_2734_4]) ).

cnf(f_2734_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10017),U_10019))
    | ~ sP785(U_10019,U_10017) ),
    inference(clausify,[status(thm)],[f_2734_4]) ).

fof(f_2735_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite]) ).

fof(f_2735_2,plain,
    ! [U_10021,U_10020] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10020),U_10021))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10020),U_10021))) ),
    inference(variable_rename,[status(thm)],[f_2735_1]) ).

fof(f_2735_3,plain,
    ! [U_10020,U_10021] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10020),U_10021))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10020),U_10021))) ),
    inference(definitional_conversion,[status(esa)],[f_2735_2]) ).

cnf(f_2735_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10020),U_10021))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10020),U_10021))) ),
    inference(clausify,[status(thm)],[f_2735_3]) ).

fof(f_2736_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__le]) ).

fof(f_2736_2,plain,
    ! [U_10024,U_10023,U_10022] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10022),U_10023)),hAPP(c_Finite__Set_Ocard(U_10022),hAPP(hAPP(c_Set_Oinsert(U_10022),U_10024),U_10023))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10023)) ),
    inference(variable_rename,[status(thm)],[f_2736_1]) ).

fof(f_2736_3,plain,
    ! [U_10022,U_10023,U_10024] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10022),U_10023)),hAPP(c_Finite__Set_Ocard(U_10022),hAPP(hAPP(c_Set_Oinsert(U_10022),U_10024),U_10023))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10023)) ),
    inference(definitional_conversion,[status(esa)],[f_2736_2]) ).

cnf(f_2736_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10022),U_10023)),hAPP(c_Finite__Set_Ocard(U_10022),hAPP(hAPP(c_Set_Oinsert(U_10022),U_10024),U_10023))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10023)) ),
    inference(clausify,[status(thm)],[f_2736_3]) ).

fof(f_2737_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( V_A_2 = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__seteq]) ).

fof(f_2737_2,plain,
    ! [U_10027,U_10026,U_10025] :
      ( U_10027 = U_10026
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10025),U_10026)),hAPP(c_Finite__Set_Ocard(U_10025),U_10027)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10025,tc_HOL_Obool)),U_10027),U_10026))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10025),U_10026)) ),
    inference(variable_rename,[status(thm)],[f_2737_1]) ).

fof(f_2737_3,plain,
    ! [U_10025,U_10026,U_10027] :
      ( U_10027 = U_10026
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10025),U_10026)),hAPP(c_Finite__Set_Ocard(U_10025),U_10027)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10025,tc_HOL_Obool)),U_10027),U_10026))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10025),U_10026)) ),
    inference(definitional_conversion,[status(esa)],[f_2737_2]) ).

cnf(f_2737_4,plain,
    ( U_10027 = U_10026
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10025),U_10026)),hAPP(c_Finite__Set_Ocard(U_10025),U_10027)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10025,tc_HOL_Obool)),U_10027),U_10026))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10025),U_10026)) ),
    inference(clausify,[status(thm)],[f_2737_3]) ).

fof(f_2738_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__mono]) ).

fof(f_2738_2,plain,
    ! [U_10030,U_10029,U_10028] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10028),U_10030)),hAPP(c_Finite__Set_Ocard(U_10028),U_10029)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10028,tc_HOL_Obool)),U_10030),U_10029))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10028),U_10029)) ),
    inference(variable_rename,[status(thm)],[f_2738_1]) ).

fof(f_2738_3,plain,
    ! [U_10028,U_10029,U_10030] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10028),U_10030)),hAPP(c_Finite__Set_Ocard(U_10028),U_10029)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10028,tc_HOL_Obool)),U_10030),U_10029))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10028),U_10029)) ),
    inference(definitional_conversion,[status(esa)],[f_2738_2]) ).

cnf(f_2738_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10028),U_10030)),hAPP(c_Finite__Set_Ocard(U_10028),U_10029)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10028,tc_HOL_Obool)),U_10030),U_10029))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10028),U_10029)) ),
    inference(clausify,[status(thm)],[f_2738_3]) ).

fof(f_2739_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__image__le]) ).

fof(f_2739_2,plain,
    ! [U_10034,U_10033,U_10032,U_10031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10033),hAPP(c_Set_Oimage(U_10031,U_10033,U_10034),U_10032))),hAPP(c_Finite__Set_Ocard(U_10031),U_10032)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10031),U_10032)) ),
    inference(variable_rename,[status(thm)],[f_2739_1]) ).

fof(f_2739_3,plain,
    ! [U_10031,U_10032,U_10033,U_10034] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10033),hAPP(c_Set_Oimage(U_10031,U_10033,U_10034),U_10032))),hAPP(c_Finite__Set_Ocard(U_10031),U_10032)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10031),U_10032)) ),
    inference(definitional_conversion,[status(esa)],[f_2739_2]) ).

cnf(f_2739_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10033),hAPP(c_Set_Oimage(U_10031,U_10033,U_10034),U_10032))),hAPP(c_Finite__Set_Ocard(U_10031),U_10032)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10031),U_10032)) ),
    inference(clausify,[status(thm)],[f_2739_3]) ).

fof(f_2740_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__card__mono]) ).

fof(f_2740_2,plain,
    ! [U_10037,U_10036,U_10035] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10035),U_10037)),hAPP(c_Finite__Set_Ocard(U_10035),U_10036)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10035,tc_HOL_Obool)),U_10037),U_10036))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10035),U_10036)) ),
    inference(variable_rename,[status(thm)],[f_2740_1]) ).

fof(f_2740_3,plain,
    ! [U_10035,U_10036,U_10037] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10035),U_10037)),hAPP(c_Finite__Set_Ocard(U_10035),U_10036)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10035,tc_HOL_Obool)),U_10037),U_10036))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10035),U_10036)) ),
    inference(definitional_conversion,[status(esa)],[f_2740_2]) ).

cnf(f_2740_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10035),U_10037)),hAPP(c_Finite__Set_Ocard(U_10035),U_10036)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10035,tc_HOL_Obool)),U_10037),U_10036))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10035),U_10036)) ),
    inference(clausify,[status(thm)],[f_2740_3]) ).

fof(f_2741_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__disjoint]) ).

fof(f_2741_2,plain,
    ! [U_10040,U_10039,U_10038] :
      ( hAPP(c_Finite__Set_Ocard(U_10038),hAPP(hAPP(c_Set_Oinsert(U_10038),U_10040),U_10039)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10038),U_10039))
      | hBOOL(hAPP(hAPP(c_member(U_10038),U_10040),U_10039))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10038),U_10039)) ),
    inference(variable_rename,[status(thm)],[f_2741_1]) ).

fof(f_2741_3,plain,
    ! [U_10038,U_10039,U_10040] :
      ( hAPP(c_Finite__Set_Ocard(U_10038),hAPP(hAPP(c_Set_Oinsert(U_10038),U_10040),U_10039)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10038),U_10039))
      | hBOOL(hAPP(hAPP(c_member(U_10038),U_10040),U_10039))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10038),U_10039)) ),
    inference(definitional_conversion,[status(esa)],[f_2741_2]) ).

cnf(f_2741_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10038),hAPP(hAPP(c_Set_Oinsert(U_10038),U_10040),U_10039)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10038),U_10039))
    | hBOOL(hAPP(hAPP(c_member(U_10038),U_10040),U_10039))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10038),U_10039)) ),
    inference(clausify,[status(thm)],[f_2741_3]) ).

fof(f_2742_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        & ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__if]) ).

fof(f_2742_2,plain,
    ! [U_10043,U_10042,U_10041] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_10041),hAPP(hAPP(c_Set_Oinsert(U_10041),U_10043),U_10042)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10041),U_10042))
          | hBOOL(hAPP(hAPP(c_member(U_10041),U_10043),U_10042)) )
        & ( hAPP(c_Finite__Set_Ocard(U_10041),hAPP(hAPP(c_Set_Oinsert(U_10041),U_10043),U_10042)) = hAPP(c_Finite__Set_Ocard(U_10041),U_10042)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10041),U_10043),U_10042)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10041),U_10042)) ),
    inference(variable_rename,[status(thm)],[f_2742_1]) ).

fof(f_2742_3,plain,
    ( ! [U_10041,U_10042,U_10043] :
        ( hAPP(c_Finite__Set_Ocard(U_10041),hAPP(hAPP(c_Set_Oinsert(U_10041),U_10043),U_10042)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10041),U_10042))
        | hBOOL(hAPP(hAPP(c_member(U_10041),U_10043),U_10042))
        | ~ sP786(U_10041,U_10042,U_10043) )
    & ! [U_10041,U_10042,U_10043] :
        ( hAPP(c_Finite__Set_Ocard(U_10041),hAPP(hAPP(c_Set_Oinsert(U_10041),U_10043),U_10042)) = hAPP(c_Finite__Set_Ocard(U_10041),U_10042)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10041),U_10043),U_10042))
        | ~ sP786(U_10041,U_10042,U_10043) )
    & ! [U_10041,U_10042,U_10043] :
        ( sP786(U_10041,U_10042,U_10043)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10041),U_10042)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP786])],[f_2742_2]) ).

cnf(f_2742_4,plain,
    ( sP786(U_10041,U_10042,U_10043)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10041),U_10042)) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

cnf(f_2742_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10041),hAPP(hAPP(c_Set_Oinsert(U_10041),U_10043),U_10042)) = hAPP(c_Finite__Set_Ocard(U_10041),U_10042)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10041),U_10043),U_10042))
    | ~ sP786(U_10041,U_10042,U_10043) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

cnf(f_2742_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10041),hAPP(hAPP(c_Set_Oinsert(U_10041),U_10043),U_10042)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10041),U_10042))
    | hBOOL(hAPP(hAPP(c_member(U_10041),U_10043),U_10042))
    | ~ sP786(U_10041,U_10042,U_10043) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

fof(f_2743_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff]) ).

fof(f_2743_2,plain,
    ! [U_10045,U_10044] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10044),U_10045)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10044),U_10045))
        | U_10045 = c_Orderings_Obot__class_Obot(tc_fun(U_10044,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10044),U_10045))
          & U_10045 != c_Orderings_Obot__class_Obot(tc_fun(U_10044,tc_HOL_Obool)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10044),U_10045))) ) ),
    inference(variable_rename,[status(thm)],[f_2743_1]) ).

fof(f_2743_3,plain,
    ( ! [U_10049,U_10047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10047),U_10049)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),U_10049))
        | U_10049 = c_Orderings_Obot__class_Obot(tc_fun(U_10047,tc_HOL_Obool)) )
    & ! [U_10048,U_10046] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10046),U_10048))
          & U_10048 != c_Orderings_Obot__class_Obot(tc_fun(U_10046,tc_HOL_Obool)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10046),U_10048))) ) ),
    inference(miniscope,[status(thm)],[f_2743_2]) ).

fof(f_2743_4,plain,
    ( ! [U_10048,U_10046] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10046),U_10048))
        | ~ sP787(U_10048,U_10046) )
    & ! [U_10048,U_10046] :
        ( U_10048 != c_Orderings_Obot__class_Obot(tc_fun(U_10046,tc_HOL_Obool))
        | ~ sP787(U_10048,U_10046) )
    & ! [U_10047,U_10049] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10047),U_10049)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),U_10049))
        | U_10049 = c_Orderings_Obot__class_Obot(tc_fun(U_10047,tc_HOL_Obool)) )
    & ! [U_10048,U_10046] :
        ( sP787(U_10048,U_10046)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10046),U_10048))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP787])],[f_2743_3]) ).

cnf(f_2743_5,plain,
    ( sP787(U_10048,U_10046)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10046),U_10048))) ),
    inference(clausify,[status(thm)],[f_2743_4]) ).

cnf(f_2743_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10047),U_10049)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10047),U_10049))
    | U_10049 = c_Orderings_Obot__class_Obot(tc_fun(U_10047,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2743_4]) ).

cnf(f_2743_7,plain,
    ( U_10048 != c_Orderings_Obot__class_Obot(tc_fun(U_10046,tc_HOL_Obool))
    | ~ sP787(U_10048,U_10046) ),
    inference(clausify,[status(thm)],[f_2743_4]) ).

cnf(f_2743_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10046),U_10048))
    | ~ sP787(U_10048,U_10046) ),
    inference(clausify,[status(thm)],[f_2743_4]) ).

fof(f_2744_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter]) ).

fof(f_2744_2,plain,
    ! [U_10052,U_10051,U_10050] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10050,tc_HOL_Obool)),U_10051),U_10052))),hAPP(c_Finite__Set_Ocard(U_10050),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10050,tc_HOL_Obool)),U_10051),U_10052))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10050),U_10051)),hAPP(c_Finite__Set_Ocard(U_10050),U_10052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051)) ),
    inference(variable_rename,[status(thm)],[f_2744_1]) ).

fof(f_2744_3,plain,
    ! [U_10050,U_10051,U_10052] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10050,tc_HOL_Obool)),U_10051),U_10052))),hAPP(c_Finite__Set_Ocard(U_10050),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10050,tc_HOL_Obool)),U_10051),U_10052))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10050),U_10051)),hAPP(c_Finite__Set_Ocard(U_10050),U_10052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051)) ),
    inference(definitional_conversion,[status(esa)],[f_2744_2]) ).

cnf(f_2744_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10050,tc_HOL_Obool)),U_10051),U_10052))),hAPP(c_Finite__Set_Ocard(U_10050),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10050,tc_HOL_Obool)),U_10051),U_10052))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10050),U_10051)),hAPP(c_Finite__Set_Ocard(U_10050),U_10052))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10052))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051)) ),
    inference(clausify,[status(thm)],[f_2744_3]) ).

fof(f_2745_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Un__Int]) ).

fof(f_2745_2,plain,
    ! [U_10055,U_10054,U_10053] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10053),U_10054)),hAPP(c_Finite__Set_Ocard(U_10053),U_10055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10053),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10053,tc_HOL_Obool)),U_10054),U_10055))),hAPP(c_Finite__Set_Ocard(U_10053),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10053,tc_HOL_Obool)),U_10054),U_10055)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10053),U_10055))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10053),U_10054)) ),
    inference(variable_rename,[status(thm)],[f_2745_1]) ).

fof(f_2745_3,plain,
    ! [U_10053,U_10054,U_10055] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10053),U_10054)),hAPP(c_Finite__Set_Ocard(U_10053),U_10055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10053),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10053,tc_HOL_Obool)),U_10054),U_10055))),hAPP(c_Finite__Set_Ocard(U_10053),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10053,tc_HOL_Obool)),U_10054),U_10055)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10053),U_10055))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10053),U_10054)) ),
    inference(definitional_conversion,[status(esa)],[f_2745_2]) ).

cnf(f_2745_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10053),U_10054)),hAPP(c_Finite__Set_Ocard(U_10053),U_10055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10053),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10053,tc_HOL_Obool)),U_10054),U_10055))),hAPP(c_Finite__Set_Ocard(U_10053),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10053,tc_HOL_Obool)),U_10054),U_10055)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10053),U_10055))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10053),U_10054)) ),
    inference(clausify,[status(thm)],[f_2745_3]) ).

fof(f_2746_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__subset]) ).

fof(f_2746_2,plain,
    ! [U_10058,U_10057,U_10056] :
      ( hAPP(c_Finite__Set_Ocard(U_10056),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10056,tc_HOL_Obool)),U_10058),U_10057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10056),U_10058)),hAPP(c_Finite__Set_Ocard(U_10056),U_10057))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10056,tc_HOL_Obool)),U_10057),U_10058))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10057)) ),
    inference(variable_rename,[status(thm)],[f_2746_1]) ).

fof(f_2746_3,plain,
    ! [U_10056,U_10057,U_10058] :
      ( hAPP(c_Finite__Set_Ocard(U_10056),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10056,tc_HOL_Obool)),U_10058),U_10057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10056),U_10058)),hAPP(c_Finite__Set_Ocard(U_10056),U_10057))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10056,tc_HOL_Obool)),U_10057),U_10058))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10057)) ),
    inference(definitional_conversion,[status(esa)],[f_2746_2]) ).

cnf(f_2746_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10056),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10056,tc_HOL_Obool)),U_10058),U_10057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10056),U_10058)),hAPP(c_Finite__Set_Ocard(U_10056),U_10057))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10056,tc_HOL_Obool)),U_10057),U_10058))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10057)) ),
    inference(clausify,[status(thm)],[f_2746_3]) ).

fof(f_2747_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int]) ).

fof(f_2747_2,plain,
    ! [U_10061,U_10060,U_10059] :
      ( hAPP(c_Finite__Set_Ocard(U_10059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10059),U_10060)),hAPP(c_Finite__Set_Ocard(U_10059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061))) ),
    inference(variable_rename,[status(thm)],[f_2747_1]) ).

fof(f_2747_3,plain,
    ! [U_10059,U_10060,U_10061] :
      ( hAPP(c_Finite__Set_Ocard(U_10059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10059),U_10060)),hAPP(c_Finite__Set_Ocard(U_10059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061))) ),
    inference(definitional_conversion,[status(esa)],[f_2747_2]) ).

cnf(f_2747_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10059),U_10060)),hAPP(c_Finite__Set_Ocard(U_10059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10059,tc_HOL_Obool)),U_10060),U_10061))) ),
    inference(clausify,[status(thm)],[f_2747_3]) ).

fof(f_2748_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff]) ).

fof(f_2748_2,plain,
    ! [U_10064,U_10063,U_10062] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10062),U_10064)),hAPP(c_Finite__Set_Ocard(U_10062),U_10063))),hAPP(c_Finite__Set_Ocard(U_10062),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10062,tc_HOL_Obool)),U_10064),U_10063))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10062),U_10063)) ),
    inference(variable_rename,[status(thm)],[f_2748_1]) ).

fof(f_2748_3,plain,
    ! [U_10062,U_10063,U_10064] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10062),U_10064)),hAPP(c_Finite__Set_Ocard(U_10062),U_10063))),hAPP(c_Finite__Set_Ocard(U_10062),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10062,tc_HOL_Obool)),U_10064),U_10063))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10062),U_10063)) ),
    inference(definitional_conversion,[status(esa)],[f_2748_2]) ).

cnf(f_2748_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10062),U_10064)),hAPP(c_Finite__Set_Ocard(U_10062),U_10063))),hAPP(c_Finite__Set_Ocard(U_10062),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10062,tc_HOL_Obool)),U_10064),U_10063))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10062),U_10063)) ),
    inference(clausify,[status(thm)],[f_2748_3]) ).

fof(f_2749_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__psubset]) ).

fof(f_2749_2,plain,
    ! [U_10067,U_10066,U_10065] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10065,tc_HOL_Obool)),U_10067),U_10066))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10065),U_10067)),hAPP(c_Finite__Set_Ocard(U_10065),U_10066)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10065,tc_HOL_Obool)),U_10067),U_10066))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066)) ),
    inference(variable_rename,[status(thm)],[f_2749_1]) ).

fof(f_2749_3,plain,
    ! [U_10065,U_10066,U_10067] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10065,tc_HOL_Obool)),U_10067),U_10066))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10065),U_10067)),hAPP(c_Finite__Set_Ocard(U_10065),U_10066)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10065,tc_HOL_Obool)),U_10067),U_10066))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066)) ),
    inference(definitional_conversion,[status(esa)],[f_2749_2]) ).

cnf(f_2749_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10065,tc_HOL_Obool)),U_10067),U_10066))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10065),U_10067)),hAPP(c_Finite__Set_Ocard(U_10065),U_10066)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10065,tc_HOL_Obool)),U_10067),U_10066))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066)) ),
    inference(clausify,[status(thm)],[f_2749_3]) ).

fof(f_2750_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert]) ).

fof(f_2750_2,plain,
    ! [U_10070,U_10069,U_10068] :
      ( hAPP(c_Finite__Set_Ocard(U_10068),hAPP(hAPP(c_Set_Oinsert(U_10068),U_10070),U_10069)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10068,tc_HOL_Obool)),U_10069),hAPP(hAPP(c_Set_Oinsert(U_10068),U_10070),c_Orderings_Obot__class_Obot(tc_fun(U_10068,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10068),U_10069)) ),
    inference(variable_rename,[status(thm)],[f_2750_1]) ).

fof(f_2750_3,plain,
    ! [U_10068,U_10069,U_10070] :
      ( hAPP(c_Finite__Set_Ocard(U_10068),hAPP(hAPP(c_Set_Oinsert(U_10068),U_10070),U_10069)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10068,tc_HOL_Obool)),U_10069),hAPP(hAPP(c_Set_Oinsert(U_10068),U_10070),c_Orderings_Obot__class_Obot(tc_fun(U_10068,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10068),U_10069)) ),
    inference(definitional_conversion,[status(esa)],[f_2750_2]) ).

cnf(f_2750_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10068),hAPP(hAPP(c_Set_Oinsert(U_10068),U_10070),U_10069)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10068,tc_HOL_Obool)),U_10069),hAPP(hAPP(c_Set_Oinsert(U_10068),U_10070),c_Orderings_Obot__class_Obot(tc_fun(U_10068,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10068),U_10069)) ),
    inference(clausify,[status(thm)],[f_2750_3]) ).

fof(f_2751_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint]) ).

fof(f_2751_2,plain,
    ! [U_10073,U_10072,U_10071] :
      ( hAPP(c_Finite__Set_Ocard(U_10071),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10071,tc_HOL_Obool)),U_10072),U_10073)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10071),U_10072)),hAPP(c_Finite__Set_Ocard(U_10071),U_10073))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10071,tc_HOL_Obool)),U_10072),U_10073) != c_Orderings_Obot__class_Obot(tc_fun(U_10071,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10071),U_10073))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10071),U_10072)) ),
    inference(variable_rename,[status(thm)],[f_2751_1]) ).

fof(f_2751_3,plain,
    ! [U_10071,U_10072,U_10073] :
      ( hAPP(c_Finite__Set_Ocard(U_10071),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10071,tc_HOL_Obool)),U_10072),U_10073)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10071),U_10072)),hAPP(c_Finite__Set_Ocard(U_10071),U_10073))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10071,tc_HOL_Obool)),U_10072),U_10073) != c_Orderings_Obot__class_Obot(tc_fun(U_10071,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10071),U_10073))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10071),U_10072)) ),
    inference(definitional_conversion,[status(esa)],[f_2751_2]) ).

cnf(f_2751_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10071),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10071,tc_HOL_Obool)),U_10072),U_10073)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10071),U_10072)),hAPP(c_Finite__Set_Ocard(U_10071),U_10073))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10071,tc_HOL_Obool)),U_10072),U_10073) != c_Orderings_Obot__class_Obot(tc_fun(U_10071,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10071),U_10073))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10071),U_10072)) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

fof(f_2752_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff1__le]) ).

fof(f_2752_2,plain,
    ! [U_10076,U_10075,U_10074] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(hAPP(c_Set_Oinsert(U_10074),U_10076),c_Orderings_Obot__class_Obot(tc_fun(U_10074,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10074),U_10075)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10074),U_10075)) ),
    inference(variable_rename,[status(thm)],[f_2752_1]) ).

fof(f_2752_3,plain,
    ! [U_10074,U_10075,U_10076] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(hAPP(c_Set_Oinsert(U_10074),U_10076),c_Orderings_Obot__class_Obot(tc_fun(U_10074,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10074),U_10075)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10074),U_10075)) ),
    inference(definitional_conversion,[status(esa)],[f_2752_2]) ).

cnf(f_2752_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(hAPP(c_Set_Oinsert(U_10074),U_10076),c_Orderings_Obot__class_Obot(tc_fun(U_10074,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10074),U_10075)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10074),U_10075)) ),
    inference(clausify,[status(thm)],[f_2752_3]) ).

fof(f_2753_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oinsert]) ).

fof(f_2753_2,plain,
    ! [U_10079,U_10078,U_10077] :
      ( hAPP(c_Finite__Set_Ocard(U_10077),hAPP(hAPP(c_Set_Oinsert(U_10077),U_10079),U_10078)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10077),U_10078))
      | hBOOL(hAPP(hAPP(c_member(U_10077),U_10079),U_10078))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10077),U_10078)) ),
    inference(variable_rename,[status(thm)],[f_2753_1]) ).

fof(f_2753_3,plain,
    ! [U_10077,U_10078,U_10079] :
      ( hAPP(c_Finite__Set_Ocard(U_10077),hAPP(hAPP(c_Set_Oinsert(U_10077),U_10079),U_10078)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10077),U_10078))
      | hBOOL(hAPP(hAPP(c_member(U_10077),U_10079),U_10078))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10077),U_10078)) ),
    inference(definitional_conversion,[status(esa)],[f_2753_2]) ).

cnf(f_2753_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10077),hAPP(hAPP(c_Set_Oinsert(U_10077),U_10079),U_10078)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10077),U_10078))
    | hBOOL(hAPP(hAPP(c_member(U_10077),U_10079),U_10078))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10077),U_10078)) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

fof(f_2754_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1]) ).

fof(f_2754_2,plain,
    ! [U_10082,U_10081,U_10080] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10080),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10080,tc_HOL_Obool)),U_10081),hAPP(hAPP(c_Set_Oinsert(U_10080),U_10082),c_Orderings_Obot__class_Obot(tc_fun(U_10080,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_10080),U_10081)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10080),U_10082),U_10081))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10080),U_10081)) ),
    inference(variable_rename,[status(thm)],[f_2754_1]) ).

fof(f_2754_3,plain,
    ! [U_10080,U_10081,U_10082] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10080),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10080,tc_HOL_Obool)),U_10081),hAPP(hAPP(c_Set_Oinsert(U_10080),U_10082),c_Orderings_Obot__class_Obot(tc_fun(U_10080,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_10080),U_10081)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10080),U_10082),U_10081))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10080),U_10081)) ),
    inference(definitional_conversion,[status(esa)],[f_2754_2]) ).

cnf(f_2754_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10080),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10080,tc_HOL_Obool)),U_10081),hAPP(hAPP(c_Set_Oinsert(U_10080),U_10082),c_Orderings_Obot__class_Obot(tc_fun(U_10080,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_10080),U_10081)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10080),U_10082),U_10081))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10080),U_10081)) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

fof(f_2755_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff1__less]) ).

fof(f_2755_2,plain,
    ! [U_10085,U_10084,U_10083] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10083,tc_HOL_Obool)),U_10084),hAPP(hAPP(c_Set_Oinsert(U_10083),U_10085),c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10083),U_10084)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10085),U_10084))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10083),U_10084)) ),
    inference(variable_rename,[status(thm)],[f_2755_1]) ).

fof(f_2755_3,plain,
    ! [U_10083,U_10084,U_10085] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10083,tc_HOL_Obool)),U_10084),hAPP(hAPP(c_Set_Oinsert(U_10083),U_10085),c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10083),U_10084)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10085),U_10084))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10083),U_10084)) ),
    inference(definitional_conversion,[status(esa)],[f_2755_2]) ).

cnf(f_2755_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10083,tc_HOL_Obool)),U_10084),hAPP(hAPP(c_Set_Oinsert(U_10083),U_10085),c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10083),U_10084)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10085),U_10084))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10083),U_10084)) ),
    inference(clausify,[status(thm)],[f_2755_3]) ).

fof(f_2756_1,plain,
    ! [V_y_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff2__less]) ).

fof(f_2756_2,plain,
    ! [U_10089,U_10088,U_10087,U_10086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10086,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10086,tc_HOL_Obool)),U_10087),hAPP(hAPP(c_Set_Oinsert(U_10086),U_10088),c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_10086),U_10089),c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10086),U_10087)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10089),U_10087))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10088),U_10087))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10086),U_10087)) ),
    inference(variable_rename,[status(thm)],[f_2756_1]) ).

fof(f_2756_3,plain,
    ! [U_10086,U_10087,U_10088,U_10089] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10086,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10086,tc_HOL_Obool)),U_10087),hAPP(hAPP(c_Set_Oinsert(U_10086),U_10088),c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_10086),U_10089),c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10086),U_10087)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10089),U_10087))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10088),U_10087))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10086),U_10087)) ),
    inference(definitional_conversion,[status(esa)],[f_2756_2]) ).

cnf(f_2756_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10086,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10086,tc_HOL_Obool)),U_10087),hAPP(hAPP(c_Set_Oinsert(U_10086),U_10088),c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_10086),U_10089),c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10086),U_10087)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10089),U_10087))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10088),U_10087))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10086),U_10087)) ),
    inference(clausify,[status(thm)],[f_2756_3]) ).

fof(f_2757_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__insert]) ).

fof(f_2757_2,plain,
    ! [U_10093,U_10092,U_10091,U_10090] :
      ( hAPP(c_Finite__Set_Ocard(U_10090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10090,tc_HOL_Obool)),U_10091),hAPP(hAPP(c_Set_Oinsert(U_10090),U_10092),U_10093))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10090,tc_HOL_Obool)),U_10091),U_10093))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_10090),U_10092),U_10093))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10090),U_10092),U_10091))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10090),U_10091)) ),
    inference(variable_rename,[status(thm)],[f_2757_1]) ).

fof(f_2757_3,plain,
    ! [U_10090,U_10091,U_10092,U_10093] :
      ( hAPP(c_Finite__Set_Ocard(U_10090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10090,tc_HOL_Obool)),U_10091),hAPP(hAPP(c_Set_Oinsert(U_10090),U_10092),U_10093))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10090,tc_HOL_Obool)),U_10091),U_10093))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_10090),U_10092),U_10093))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10090),U_10092),U_10091))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10090),U_10091)) ),
    inference(definitional_conversion,[status(esa)],[f_2757_2]) ).

cnf(f_2757_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10090,tc_HOL_Obool)),U_10091),hAPP(hAPP(c_Set_Oinsert(U_10090),U_10092),U_10093))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10090,tc_HOL_Obool)),U_10091),U_10093))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_member(U_10090),U_10092),U_10093))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10090),U_10092),U_10091))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10090),U_10091)) ),
    inference(clausify,[status(thm)],[f_2757_3]) ).

fof(f_2758_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove]) ).

fof(f_2758_2,plain,
    ! [U_10096,U_10095,U_10094] :
      ( hAPP(c_Finite__Set_Ocard(U_10094),hAPP(hAPP(c_Set_Oinsert(U_10094),U_10096),U_10095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10094,tc_HOL_Obool)),U_10095),hAPP(hAPP(c_Set_Oinsert(U_10094),U_10096),c_Orderings_Obot__class_Obot(tc_fun(U_10094,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095)) ),
    inference(variable_rename,[status(thm)],[f_2758_1]) ).

fof(f_2758_3,plain,
    ! [U_10094,U_10095,U_10096] :
      ( hAPP(c_Finite__Set_Ocard(U_10094),hAPP(hAPP(c_Set_Oinsert(U_10094),U_10096),U_10095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10094,tc_HOL_Obool)),U_10095),hAPP(hAPP(c_Set_Oinsert(U_10094),U_10096),c_Orderings_Obot__class_Obot(tc_fun(U_10094,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095)) ),
    inference(definitional_conversion,[status(esa)],[f_2758_2]) ).

cnf(f_2758_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10094),hAPP(hAPP(c_Set_Oinsert(U_10094),U_10096),U_10095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10094,tc_HOL_Obool)),U_10095),hAPP(hAPP(c_Set_Oinsert(U_10094),U_10096),c_Orderings_Obot__class_Obot(tc_fun(U_10094,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095)) ),
    inference(clausify,[status(thm)],[f_2758_3]) ).

fof(f_2759_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oremove]) ).

fof(f_2759_2,plain,
    ! [U_10099,U_10098,U_10097] :
      ( hAPP(c_Finite__Set_Ocard(U_10097),U_10098) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10097),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10097,tc_HOL_Obool)),U_10098),hAPP(hAPP(c_Set_Oinsert(U_10097),U_10099),c_Orderings_Obot__class_Obot(tc_fun(U_10097,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10097),U_10099),U_10098))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10097),U_10098)) ),
    inference(variable_rename,[status(thm)],[f_2759_1]) ).

fof(f_2759_3,plain,
    ! [U_10097,U_10098,U_10099] :
      ( hAPP(c_Finite__Set_Ocard(U_10097),U_10098) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10097),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10097,tc_HOL_Obool)),U_10098),hAPP(hAPP(c_Set_Oinsert(U_10097),U_10099),c_Orderings_Obot__class_Obot(tc_fun(U_10097,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10097),U_10099),U_10098))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10097),U_10098)) ),
    inference(definitional_conversion,[status(esa)],[f_2759_2]) ).

cnf(f_2759_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10097),U_10098) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10097),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10097,tc_HOL_Obool)),U_10098),hAPP(hAPP(c_Set_Oinsert(U_10097),U_10099),c_Orderings_Obot__class_Obot(tc_fun(U_10097,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10097),U_10099),U_10098))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10097),U_10098)) ),
    inference(clausify,[status(thm)],[f_2759_3]) ).

fof(f_2760_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral]) ).

fof(f_2760_2,plain,
    ! [U_10103,U_10102,U_10101] :
      ( hAPP(c_Finite__Set_Ocard(U_10101),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10101),U_10102)),hAPP(c_Finite__Set_Ocard(U_10101),U_10103))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_10100] : hBOOL(hAPP(hAPP(c_member(U_10101),U_10100),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10103))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10102)) ),
    inference(variable_rename,[status(thm)],[f_2760_1]) ).

fof(f_2760_3,plain,
    ! [U_10103,U_10102,U_10101] :
      ( hAPP(c_Finite__Set_Ocard(U_10101),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10101),U_10102)),hAPP(c_Finite__Set_Ocard(U_10101),U_10103))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_10101),sK154(U_10103,U_10102,U_10101)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10103))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10102)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_10100,sK154(U_10103,U_10102,U_10101))],[f_2760_2]) ).

fof(f_2760_4,plain,
    ( ! [U_10101,U_10102,U_10103] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP788(U_10101,U_10102,U_10103) )
    & ! [U_10101,U_10102,U_10103] :
        ( hBOOL(hAPP(hAPP(c_member(U_10101),sK154(U_10103,U_10102,U_10101)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103)))
        | ~ sP788(U_10101,U_10102,U_10103) )
    & ! [U_10101,U_10102,U_10103] :
        ( hAPP(c_Finite__Set_Ocard(U_10101),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10101),U_10102)),hAPP(c_Finite__Set_Ocard(U_10101),U_10103))
        | sP788(U_10101,U_10102,U_10103)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10103))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10102)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP788])],[f_2760_3]) ).

cnf(f_2760_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10101),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10101),U_10102)),hAPP(c_Finite__Set_Ocard(U_10101),U_10103))
    | sP788(U_10101,U_10102,U_10103)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10103))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10101),U_10102)) ),
    inference(clausify,[status(thm)],[f_2760_4]) ).

cnf(f_2760_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10101),sK154(U_10103,U_10102,U_10101)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10101,tc_HOL_Obool)),U_10102),U_10103)))
    | ~ sP788(U_10101,U_10102,U_10103) ),
    inference(clausify,[status(thm)],[f_2760_4]) ).

cnf(f_2760_7,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP788(U_10101,U_10102,U_10103) ),
    inference(clausify,[status(thm)],[f_2760_4]) ).

fof(f_2761_1,plain,
    ! [V_k_2,V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
        | ! [B_b,B_B] :
            ( ( B_B != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(T_b),B_B) != V_k_2
            | hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
            | V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) )
      & ( ? [B_b,B_B] :
            ( ( B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
            & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
            & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) )
        | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Nat_OSuc,V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__Suc__eq]) ).

fof(f_2761_2,plain,
    ! [U_10110,U_10109,U_10108] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10108),U_10109) = hAPP(c_Nat_OSuc,U_10110)
        | ! [U_10107,U_10106] :
            ( ( U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))
              & U_10110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10108),U_10106) != U_10110
            | hBOOL(hAPP(hAPP(c_member(U_10108),U_10107),U_10106))
            | U_10109 != hAPP(hAPP(c_Set_Oinsert(U_10108),U_10107),U_10106) ) )
      & ( ? [U_10105,U_10104] :
            ( ( U_10104 = c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))
              | U_10110 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10108),U_10104) = U_10110
            & ~ hBOOL(hAPP(hAPP(c_member(U_10108),U_10105),U_10104))
            & U_10109 = hAPP(hAPP(c_Set_Oinsert(U_10108),U_10105),U_10104) )
        | hAPP(c_Finite__Set_Ocard(U_10108),U_10109) != hAPP(c_Nat_OSuc,U_10110) ) ),
    inference(variable_rename,[status(thm)],[f_2761_1]) ).

fof(f_2761_3,plain,
    ( ! [U_10116,U_10114,U_10112] :
        ( hAPP(c_Finite__Set_Ocard(U_10112),U_10114) = hAPP(c_Nat_OSuc,U_10116)
        | ! [U_10107,U_10106] :
            ( ( U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10112,tc_HOL_Obool))
              & U_10116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10112),U_10106) != U_10116
            | hBOOL(hAPP(hAPP(c_member(U_10112),U_10107),U_10106))
            | U_10114 != hAPP(hAPP(c_Set_Oinsert(U_10112),U_10107),U_10106) ) )
    & ! [U_10115,U_10113,U_10111] :
        ( ? [U_10105,U_10104] :
            ( ( U_10104 = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
              | U_10115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10111),U_10104) = U_10115
            & ~ hBOOL(hAPP(hAPP(c_member(U_10111),U_10105),U_10104))
            & U_10113 = hAPP(hAPP(c_Set_Oinsert(U_10111),U_10105),U_10104) )
        | hAPP(c_Finite__Set_Ocard(U_10111),U_10113) != hAPP(c_Nat_OSuc,U_10115) ) ),
    inference(miniscope,[status(thm)],[f_2761_2]) ).

fof(f_2761_4,plain,
    ( ! [U_10116,U_10114,U_10112] :
        ( hAPP(c_Finite__Set_Ocard(U_10112),U_10114) = hAPP(c_Nat_OSuc,U_10116)
        | ! [U_10107,U_10106] :
            ( ( U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10112,tc_HOL_Obool))
              & U_10116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10112),U_10106) != U_10116
            | hBOOL(hAPP(hAPP(c_member(U_10112),U_10107),U_10106))
            | U_10114 != hAPP(hAPP(c_Set_Oinsert(U_10112),U_10107),U_10106) ) )
    & ! [U_10115,U_10113,U_10111] :
        ( ? [U_10104] :
            ( ( U_10104 = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
              | U_10115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10111),U_10104) = U_10115
            & ~ hBOOL(hAPP(hAPP(c_member(U_10111),sK155(U_10115,U_10113,U_10111)),U_10104))
            & U_10113 = hAPP(hAPP(c_Set_Oinsert(U_10111),sK155(U_10115,U_10113,U_10111)),U_10104) )
        | hAPP(c_Finite__Set_Ocard(U_10111),U_10113) != hAPP(c_Nat_OSuc,U_10115) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_10105,sK155(U_10115,U_10113,U_10111))],[f_2761_3]) ).

fof(f_2761_5,plain,
    ( ! [U_10116,U_10114,U_10112] :
        ( hAPP(c_Finite__Set_Ocard(U_10112),U_10114) = hAPP(c_Nat_OSuc,U_10116)
        | ! [U_10107,U_10106] :
            ( ( U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10112,tc_HOL_Obool))
              & U_10116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10112),U_10106) != U_10116
            | hBOOL(hAPP(hAPP(c_member(U_10112),U_10107),U_10106))
            | U_10114 != hAPP(hAPP(c_Set_Oinsert(U_10112),U_10107),U_10106) ) )
    & ! [U_10115,U_10113,U_10111] :
        ( ( ( sK156(U_10115,U_10113,U_10111) = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
            | U_10115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hAPP(c_Finite__Set_Ocard(U_10111),sK156(U_10115,U_10113,U_10111)) = U_10115
          & ~ hBOOL(hAPP(hAPP(c_member(U_10111),sK155(U_10115,U_10113,U_10111)),sK156(U_10115,U_10113,U_10111)))
          & U_10113 = hAPP(hAPP(c_Set_Oinsert(U_10111),sK155(U_10115,U_10113,U_10111)),sK156(U_10115,U_10113,U_10111)) )
        | hAPP(c_Finite__Set_Ocard(U_10111),U_10113) != hAPP(c_Nat_OSuc,U_10115) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_10104,sK156(U_10115,U_10113,U_10111))],[f_2761_4]) ).

fof(f_2761_6,plain,
    ( ! [U_10106,U_10116,U_10112] :
        ( U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10112,tc_HOL_Obool))
        | ~ sP790(U_10106,U_10116,U_10112) )
    & ! [U_10106,U_10116,U_10112] :
        ( U_10116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP790(U_10106,U_10116,U_10112) )
    & ! [U_10115,U_10113,U_10111] :
        ( sK156(U_10115,U_10113,U_10111) = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
        | U_10115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP789(U_10115,U_10113,U_10111) )
    & ! [U_10115,U_10113,U_10111] :
        ( hAPP(c_Finite__Set_Ocard(U_10111),sK156(U_10115,U_10113,U_10111)) = U_10115
        | ~ sP789(U_10115,U_10113,U_10111) )
    & ! [U_10115,U_10113,U_10111] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_10111),sK155(U_10115,U_10113,U_10111)),sK156(U_10115,U_10113,U_10111)))
        | ~ sP789(U_10115,U_10113,U_10111) )
    & ! [U_10115,U_10113,U_10111] :
        ( U_10113 = hAPP(hAPP(c_Set_Oinsert(U_10111),sK155(U_10115,U_10113,U_10111)),sK156(U_10115,U_10113,U_10111))
        | ~ sP789(U_10115,U_10113,U_10111) )
    & ! [U_10106,U_10116,U_10107,U_10114,U_10112] :
        ( hAPP(c_Finite__Set_Ocard(U_10112),U_10114) = hAPP(c_Nat_OSuc,U_10116)
        | sP790(U_10106,U_10116,U_10112)
        | hAPP(c_Finite__Set_Ocard(U_10112),U_10106) != U_10116
        | hBOOL(hAPP(hAPP(c_member(U_10112),U_10107),U_10106))
        | U_10114 != hAPP(hAPP(c_Set_Oinsert(U_10112),U_10107),U_10106) )
    & ! [U_10115,U_10113,U_10111] :
        ( sP789(U_10115,U_10113,U_10111)
        | hAPP(c_Finite__Set_Ocard(U_10111),U_10113) != hAPP(c_Nat_OSuc,U_10115) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP789,sP790])],[f_2761_5]) ).

cnf(f_2761_7,plain,
    ( sP789(U_10115,U_10113,U_10111)
    | hAPP(c_Finite__Set_Ocard(U_10111),U_10113) != hAPP(c_Nat_OSuc,U_10115) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_8,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10112),U_10114) = hAPP(c_Nat_OSuc,U_10116)
    | sP790(U_10106,U_10116,U_10112)
    | hAPP(c_Finite__Set_Ocard(U_10112),U_10106) != U_10116
    | hBOOL(hAPP(hAPP(c_member(U_10112),U_10107),U_10106))
    | U_10114 != hAPP(hAPP(c_Set_Oinsert(U_10112),U_10107),U_10106) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_9,plain,
    ( U_10113 = hAPP(hAPP(c_Set_Oinsert(U_10111),sK155(U_10115,U_10113,U_10111)),sK156(U_10115,U_10113,U_10111))
    | ~ sP789(U_10115,U_10113,U_10111) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_10111),sK155(U_10115,U_10113,U_10111)),sK156(U_10115,U_10113,U_10111)))
    | ~ sP789(U_10115,U_10113,U_10111) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_11,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10111),sK156(U_10115,U_10113,U_10111)) = U_10115
    | ~ sP789(U_10115,U_10113,U_10111) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_12,plain,
    ( sK156(U_10115,U_10113,U_10111) = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
    | U_10115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP789(U_10115,U_10113,U_10111) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_13,plain,
    ( U_10116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP790(U_10106,U_10116,U_10112) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

cnf(f_2761_14,plain,
    ( U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10112,tc_HOL_Obool))
    | ~ sP790(U_10106,U_10116,U_10112) ),
    inference(clausify,[status(thm)],[f_2761_6]) ).

fof(f_2762_1,plain,
    ! [V_k_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) )
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__imp__dvd__card]) ).

fof(f_2762_2,plain,
    ! [U_10121,U_10120,U_10119,U_10118] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),U_10119)))
      | ? [U_10117] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),U_10117)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_10118,tc_HOL_Obool)),U_10117),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10118),U_10119),U_10120))) )
      | ~ c_Equiv__Relations_Oequiv(U_10118,U_10119,U_10120)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10118),U_10119)) ),
    inference(variable_rename,[status(thm)],[f_2762_1]) ).

fof(f_2762_3,plain,
    ! [U_10121,U_10120,U_10119,U_10118] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),U_10119)))
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),sK157(U_10121,U_10120,U_10119,U_10118))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_10118,tc_HOL_Obool)),sK157(U_10121,U_10120,U_10119,U_10118)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10118),U_10119),U_10120))) )
      | ~ c_Equiv__Relations_Oequiv(U_10118,U_10119,U_10120)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10118),U_10119)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_10117,sK157(U_10121,U_10120,U_10119,U_10118))],[f_2762_2]) ).

fof(f_2762_4,plain,
    ( ! [U_10118,U_10120,U_10119,U_10121] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),sK157(U_10121,U_10120,U_10119,U_10118))))
        | ~ sP791(U_10118,U_10120,U_10119,U_10121) )
    & ! [U_10118,U_10120,U_10119,U_10121] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10118,tc_HOL_Obool)),sK157(U_10121,U_10120,U_10119,U_10118)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10118),U_10119),U_10120)))
        | ~ sP791(U_10118,U_10120,U_10119,U_10121) )
    & ! [U_10118,U_10120,U_10119,U_10121] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),U_10119)))
        | sP791(U_10118,U_10120,U_10119,U_10121)
        | ~ c_Equiv__Relations_Oequiv(U_10118,U_10119,U_10120)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10118),U_10119)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP791])],[f_2762_3]) ).

cnf(f_2762_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),U_10119)))
    | sP791(U_10118,U_10120,U_10119,U_10121)
    | ~ c_Equiv__Relations_Oequiv(U_10118,U_10119,U_10120)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10118),U_10119)) ),
    inference(clausify,[status(thm)],[f_2762_4]) ).

cnf(f_2762_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10118,tc_HOL_Obool)),sK157(U_10121,U_10120,U_10119,U_10118)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10118),U_10119),U_10120)))
    | ~ sP791(U_10118,U_10120,U_10119,U_10121) ),
    inference(clausify,[status(thm)],[f_2762_4]) ).

cnf(f_2762_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10121),hAPP(c_Finite__Set_Ocard(U_10118),sK157(U_10121,U_10120,U_10119,U_10118))))
    | ~ sP791(U_10118,U_10120,U_10119,U_10121) ),
    inference(clausify,[status(thm)],[f_2762_4]) ).

fof(f_2763_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if]) ).

fof(f_2763_2,plain,
    ! [U_10125,U_10124,U_10123,U_10122] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10122,U_10124)),c_Sum__Type_OPlus(U_10122,U_10124,U_10123,U_10125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10124),U_10125))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10122),U_10123)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10122,U_10124)),c_Sum__Type_OPlus(U_10122,U_10124,U_10123,U_10125)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10122),U_10123)),hAPP(c_Finite__Set_Ocard(U_10124),U_10125))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10124),U_10125))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10122),U_10123)) ) ),
    inference(variable_rename,[status(thm)],[f_2763_1]) ).

fof(f_2763_3,plain,
    ( ! [U_10133,U_10131,U_10129,U_10127] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10127,U_10131)),c_Sum__Type_OPlus(U_10127,U_10131,U_10129,U_10133)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10131),U_10133))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10127),U_10129)) ) )
    & ! [U_10132,U_10130,U_10128,U_10126] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10126,U_10130)),c_Sum__Type_OPlus(U_10126,U_10130,U_10128,U_10132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10126),U_10128)),hAPP(c_Finite__Set_Ocard(U_10130),U_10132))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10130),U_10132))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10126),U_10128)) ) ),
    inference(miniscope,[status(thm)],[f_2763_2]) ).

fof(f_2763_4,plain,
    ( ! [U_10127,U_10129,U_10131,U_10133] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10131),U_10133))
        | ~ sP792(U_10127,U_10129,U_10131,U_10133) )
    & ! [U_10127,U_10129,U_10131,U_10133] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10127),U_10129))
        | ~ sP792(U_10127,U_10129,U_10131,U_10133) )
    & ! [U_10127,U_10129,U_10131,U_10133] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10127,U_10131)),c_Sum__Type_OPlus(U_10127,U_10131,U_10129,U_10133)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP792(U_10127,U_10129,U_10131,U_10133) )
    & ! [U_10126,U_10128,U_10130,U_10132] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10126,U_10130)),c_Sum__Type_OPlus(U_10126,U_10130,U_10128,U_10132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10126),U_10128)),hAPP(c_Finite__Set_Ocard(U_10130),U_10132))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10130),U_10132))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10126),U_10128)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP792])],[f_2763_3]) ).

cnf(f_2763_5,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10126,U_10130)),c_Sum__Type_OPlus(U_10126,U_10130,U_10128,U_10132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10126),U_10128)),hAPP(c_Finite__Set_Ocard(U_10130),U_10132))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10130),U_10132))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10126),U_10128)) ),
    inference(clausify,[status(thm)],[f_2763_4]) ).

cnf(f_2763_6,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10127,U_10131)),c_Sum__Type_OPlus(U_10127,U_10131,U_10129,U_10133)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP792(U_10127,U_10129,U_10131,U_10133) ),
    inference(clausify,[status(thm)],[f_2763_4]) ).

cnf(f_2763_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10127),U_10129))
    | ~ sP792(U_10127,U_10129,U_10131,U_10133) ),
    inference(clausify,[status(thm)],[f_2763_4]) ).

cnf(f_2763_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10131),U_10133))
    | ~ sP792(U_10127,U_10129,U_10131,U_10133) ),
    inference(clausify,[status(thm)],[f_2763_4]) ).

fof(f_2764_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff]) ).

fof(f_2764_2,plain,
    ! [U_10137,U_10136,U_10135,U_10134] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10134,U_10135)),c_Sum__Type_OPlus(U_10134,U_10135,U_10136,U_10137)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10135),U_10137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10134),U_10136)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10135),U_10137))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10134),U_10136)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10134,U_10135)),c_Sum__Type_OPlus(U_10134,U_10135,U_10136,U_10137))) ) ),
    inference(variable_rename,[status(thm)],[f_2764_1]) ).

fof(f_2764_3,plain,
    ( ! [U_10145,U_10143,U_10141,U_10139] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10139,U_10141)),c_Sum__Type_OPlus(U_10139,U_10141,U_10143,U_10145)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10141),U_10145))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10139),U_10143)) )
    & ! [U_10144,U_10142,U_10140,U_10138] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10140),U_10144))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10138),U_10142)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10138,U_10140)),c_Sum__Type_OPlus(U_10138,U_10140,U_10142,U_10144))) ) ),
    inference(miniscope,[status(thm)],[f_2764_2]) ).

fof(f_2764_4,plain,
    ( ! [U_10138,U_10140,U_10144,U_10142] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10140),U_10144))
        | ~ sP793(U_10138,U_10140,U_10144,U_10142) )
    & ! [U_10138,U_10140,U_10144,U_10142] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10138),U_10142))
        | ~ sP793(U_10138,U_10140,U_10144,U_10142) )
    & ! [U_10141,U_10139,U_10145,U_10143] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10139,U_10141)),c_Sum__Type_OPlus(U_10139,U_10141,U_10143,U_10145)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10141),U_10145))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10139),U_10143)) )
    & ! [U_10138,U_10140,U_10144,U_10142] :
        ( sP793(U_10138,U_10140,U_10144,U_10142)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10138,U_10140)),c_Sum__Type_OPlus(U_10138,U_10140,U_10142,U_10144))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP793])],[f_2764_3]) ).

cnf(f_2764_5,plain,
    ( sP793(U_10138,U_10140,U_10144,U_10142)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10138,U_10140)),c_Sum__Type_OPlus(U_10138,U_10140,U_10142,U_10144))) ),
    inference(clausify,[status(thm)],[f_2764_4]) ).

cnf(f_2764_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10139,U_10141)),c_Sum__Type_OPlus(U_10139,U_10141,U_10143,U_10145)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10141),U_10145))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10139),U_10143)) ),
    inference(clausify,[status(thm)],[f_2764_4]) ).

cnf(f_2764_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10138),U_10142))
    | ~ sP793(U_10138,U_10140,U_10144,U_10142) ),
    inference(clausify,[status(thm)],[f_2764_4]) ).

cnf(f_2764_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10140),U_10144))
    | ~ sP793(U_10138,U_10140,U_10144,U_10142) ),
    inference(clausify,[status(thm)],[f_2764_4]) ).

fof(f_2765_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus]) ).

fof(f_2765_2,plain,
    ! [U_10149,U_10148,U_10147,U_10146] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10146,U_10148)),c_Sum__Type_OPlus(U_10146,U_10148,U_10147,U_10149)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10148),U_10149))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10146),U_10147)) ),
    inference(variable_rename,[status(thm)],[f_2765_1]) ).

fof(f_2765_3,plain,
    ! [U_10146,U_10147,U_10148,U_10149] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10146,U_10148)),c_Sum__Type_OPlus(U_10146,U_10148,U_10147,U_10149)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10148),U_10149))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10146),U_10147)) ),
    inference(definitional_conversion,[status(esa)],[f_2765_2]) ).

cnf(f_2765_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10146,U_10148)),c_Sum__Type_OPlus(U_10146,U_10148,U_10147,U_10149)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10148),U_10149))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10146),U_10147)) ),
    inference(clausify,[status(thm)],[f_2765_3]) ).

fof(f_2766_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J]) ).

fof(f_2766_2,plain,
    ! [U_10153,U_10152,U_10151,U_10150] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10150),U_10152))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10150,U_10151)),c_Sum__Type_OPlus(U_10150,U_10151,U_10152,U_10153))) ),
    inference(variable_rename,[status(thm)],[f_2766_1]) ).

fof(f_2766_3,plain,
    ! [U_10150,U_10151,U_10152,U_10153] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10150),U_10152))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10150,U_10151)),c_Sum__Type_OPlus(U_10150,U_10151,U_10152,U_10153))) ),
    inference(definitional_conversion,[status(esa)],[f_2766_2]) ).

cnf(f_2766_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10150),U_10152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10150,U_10151)),c_Sum__Type_OPlus(U_10150,U_10151,U_10152,U_10153))) ),
    inference(clausify,[status(thm)],[f_2766_3]) ).

fof(f_2767_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J]) ).

fof(f_2767_2,plain,
    ! [U_10157,U_10156,U_10155,U_10154] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10157))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10154,U_10155)),c_Sum__Type_OPlus(U_10154,U_10155,U_10156,U_10157))) ),
    inference(variable_rename,[status(thm)],[f_2767_1]) ).

fof(f_2767_3,plain,
    ! [U_10157,U_10156,U_10155] :
      ( ! [U_10154] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10154,U_10155)),c_Sum__Type_OPlus(U_10154,U_10155,U_10156,U_10157)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10157)) ),
    inference(miniscope,[status(thm)],[f_2767_2]) ).

fof(f_2767_4,plain,
    ! [U_10154,U_10155,U_10156,U_10157] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10154,U_10155)),c_Sum__Type_OPlus(U_10154,U_10155,U_10156,U_10157)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10157)) ),
    inference(definitional_conversion,[status(esa)],[f_2767_3]) ).

cnf(f_2767_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10154,U_10155)),c_Sum__Type_OPlus(U_10154,U_10155,U_10156,U_10157)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10157)) ),
    inference(clausify,[status(thm)],[f_2767_4]) ).

fof(f_2768_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Plus]) ).

fof(f_2768_2,plain,
    ! [U_10161,U_10160,U_10159,U_10158] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10158,U_10160)),c_Sum__Type_OPlus(U_10158,U_10160,U_10159,U_10161)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10158),U_10159)),hAPP(c_Finite__Set_Ocard(U_10160),U_10161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10160),U_10161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159)) ),
    inference(variable_rename,[status(thm)],[f_2768_1]) ).

fof(f_2768_3,plain,
    ! [U_10158,U_10159,U_10160,U_10161] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10158,U_10160)),c_Sum__Type_OPlus(U_10158,U_10160,U_10159,U_10161)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10158),U_10159)),hAPP(c_Finite__Set_Ocard(U_10160),U_10161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10160),U_10161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159)) ),
    inference(definitional_conversion,[status(esa)],[f_2768_2]) ).

cnf(f_2768_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10158,U_10160)),c_Sum__Type_OPlus(U_10158,U_10160,U_10159,U_10161)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10158),U_10159)),hAPP(c_Finite__Set_Ocard(U_10160),U_10161))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10160),U_10161))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159)) ),
    inference(clausify,[status(thm)],[f_2768_3]) ).

fof(f_2769_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv]) ).

fof(f_2769_2,plain,
    ! [U_10165,U_10164,U_10163,U_10162] :
      ( ( c_Sum__Type_OPlus(U_10162,U_10163,U_10164,U_10165) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10162,U_10163),tc_HOL_Obool))
        | U_10165 != c_Orderings_Obot__class_Obot(tc_fun(U_10163,tc_HOL_Obool))
        | U_10164 != c_Orderings_Obot__class_Obot(tc_fun(U_10162,tc_HOL_Obool)) )
      & ( ( U_10165 = c_Orderings_Obot__class_Obot(tc_fun(U_10163,tc_HOL_Obool))
          & U_10164 = c_Orderings_Obot__class_Obot(tc_fun(U_10162,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_10162,U_10163,U_10164,U_10165) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10162,U_10163),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2769_1]) ).

fof(f_2769_3,plain,
    ( ! [U_10173,U_10171,U_10169,U_10167] :
        ( c_Sum__Type_OPlus(U_10167,U_10169,U_10171,U_10173) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10167,U_10169),tc_HOL_Obool))
        | U_10173 != c_Orderings_Obot__class_Obot(tc_fun(U_10169,tc_HOL_Obool))
        | U_10171 != c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool)) )
    & ! [U_10172,U_10170,U_10168,U_10166] :
        ( ( U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10168,tc_HOL_Obool))
          & U_10170 = c_Orderings_Obot__class_Obot(tc_fun(U_10166,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_10166,U_10168,U_10170,U_10172) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10166,U_10168),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2769_2]) ).

fof(f_2769_4,plain,
    ( ! [U_10168,U_10170,U_10172,U_10166] :
        ( U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10168,tc_HOL_Obool))
        | ~ sP794(U_10168,U_10170,U_10172,U_10166) )
    & ! [U_10168,U_10170,U_10172,U_10166] :
        ( U_10170 = c_Orderings_Obot__class_Obot(tc_fun(U_10166,tc_HOL_Obool))
        | ~ sP794(U_10168,U_10170,U_10172,U_10166) )
    & ! [U_10171,U_10173,U_10167,U_10169] :
        ( c_Sum__Type_OPlus(U_10167,U_10169,U_10171,U_10173) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10167,U_10169),tc_HOL_Obool))
        | U_10173 != c_Orderings_Obot__class_Obot(tc_fun(U_10169,tc_HOL_Obool))
        | U_10171 != c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool)) )
    & ! [U_10168,U_10170,U_10172,U_10166] :
        ( sP794(U_10168,U_10170,U_10172,U_10166)
        | c_Sum__Type_OPlus(U_10166,U_10168,U_10170,U_10172) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10166,U_10168),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP794])],[f_2769_3]) ).

cnf(f_2769_5,plain,
    ( sP794(U_10168,U_10170,U_10172,U_10166)
    | c_Sum__Type_OPlus(U_10166,U_10168,U_10170,U_10172) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10166,U_10168),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2769_4]) ).

cnf(f_2769_6,plain,
    ( c_Sum__Type_OPlus(U_10167,U_10169,U_10171,U_10173) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10167,U_10169),tc_HOL_Obool))
    | U_10173 != c_Orderings_Obot__class_Obot(tc_fun(U_10169,tc_HOL_Obool))
    | U_10171 != c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2769_4]) ).

cnf(f_2769_7,plain,
    ( U_10170 = c_Orderings_Obot__class_Obot(tc_fun(U_10166,tc_HOL_Obool))
    | ~ sP794(U_10168,U_10170,U_10172,U_10166) ),
    inference(clausify,[status(thm)],[f_2769_4]) ).

cnf(f_2769_8,plain,
    ( U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10168,tc_HOL_Obool))
    | ~ sP794(U_10168,U_10170,U_10172,U_10166) ),
    inference(clausify,[status(thm)],[f_2769_4]) ).

fof(f_2770_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanLessThan__int]) ).

fof(f_2770_2,plain,
    ! [U_10175,U_10174] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10174,U_10175)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10175),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10174),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2770_1]) ).

fof(f_2770_3,plain,
    ! [U_10175,U_10174] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10174,U_10175)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10175),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10174),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_2770_2]) ).

cnf(f_2770_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10174,U_10175)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10175),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10174),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2770_3]) ).

fof(f_2771_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2))
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).

fof(f_2771_2,plain,
    ! [U_10181,U_10180,U_10179,U_10178,U_10177,U_10176] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10177,U_10176),hAPP(hAPP(c_COMBC(U_10177,U_10176,U_10176),hAPP(hAPP(c_COMBS(U_10177,U_10176,tc_fun(U_10176,U_10176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10176,tc_fun(U_10176,U_10176)),U_10177),c_If(U_10176)),hAPP(hAPP(c_COMBC(U_10177,U_10177,tc_HOL_Obool),c_fequal),U_10179))),U_10180)),U_10181)),U_10178) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10176),U_10181),hAPP(c_Finite__Set_Ocard(U_10177),U_10178))
          | hBOOL(hAPP(hAPP(c_member(U_10177),U_10179),U_10178)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10177,U_10176),hAPP(hAPP(c_COMBC(U_10177,U_10176,U_10176),hAPP(hAPP(c_COMBS(U_10177,U_10176,tc_fun(U_10176,U_10176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10176,tc_fun(U_10176,U_10176)),U_10177),c_If(U_10176)),hAPP(hAPP(c_COMBC(U_10177,U_10177,tc_HOL_Obool),c_fequal),U_10179))),U_10180)),U_10181)),U_10178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10176),hAPP(U_10180,U_10179)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10176),U_10181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10177),U_10178)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10177),U_10179),U_10178)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10177),U_10178))
      | ~ class_Groups_Ocomm__monoid__mult(U_10176) ),
    inference(variable_rename,[status(thm)],[f_2771_1]) ).

fof(f_2771_3,plain,
    ( ! [U_10176,U_10177,U_10178,U_10179,U_10180,U_10181] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10177,U_10176),hAPP(hAPP(c_COMBC(U_10177,U_10176,U_10176),hAPP(hAPP(c_COMBS(U_10177,U_10176,tc_fun(U_10176,U_10176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10176,tc_fun(U_10176,U_10176)),U_10177),c_If(U_10176)),hAPP(hAPP(c_COMBC(U_10177,U_10177,tc_HOL_Obool),c_fequal),U_10179))),U_10180)),U_10181)),U_10178) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10176),U_10181),hAPP(c_Finite__Set_Ocard(U_10177),U_10178))
        | hBOOL(hAPP(hAPP(c_member(U_10177),U_10179),U_10178))
        | ~ sP795(U_10176,U_10177,U_10178,U_10179,U_10180,U_10181) )
    & ! [U_10176,U_10177,U_10178,U_10179,U_10180,U_10181] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10177,U_10176),hAPP(hAPP(c_COMBC(U_10177,U_10176,U_10176),hAPP(hAPP(c_COMBS(U_10177,U_10176,tc_fun(U_10176,U_10176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10176,tc_fun(U_10176,U_10176)),U_10177),c_If(U_10176)),hAPP(hAPP(c_COMBC(U_10177,U_10177,tc_HOL_Obool),c_fequal),U_10179))),U_10180)),U_10181)),U_10178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10176),hAPP(U_10180,U_10179)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10176),U_10181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10177),U_10178)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10177),U_10179),U_10178))
        | ~ sP795(U_10176,U_10177,U_10178,U_10179,U_10180,U_10181) )
    & ! [U_10176,U_10177,U_10178,U_10179,U_10180,U_10181] :
        ( sP795(U_10176,U_10177,U_10178,U_10179,U_10180,U_10181)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10177),U_10178))
        | ~ class_Groups_Ocomm__monoid__mult(U_10176) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP795])],[f_2771_2]) ).

cnf(f_2771_4,plain,
    ( sP795(U_10176,U_10177,U_10178,U_10179,U_10180,U_10181)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10177),U_10178))
    | ~ class_Groups_Ocomm__monoid__mult(U_10176) ),
    inference(clausify,[status(thm)],[f_2771_3]) ).

cnf(f_2771_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10177,U_10176),hAPP(hAPP(c_COMBC(U_10177,U_10176,U_10176),hAPP(hAPP(c_COMBS(U_10177,U_10176,tc_fun(U_10176,U_10176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10176,tc_fun(U_10176,U_10176)),U_10177),c_If(U_10176)),hAPP(hAPP(c_COMBC(U_10177,U_10177,tc_HOL_Obool),c_fequal),U_10179))),U_10180)),U_10181)),U_10178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10176),hAPP(U_10180,U_10179)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10176),U_10181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10177),U_10178)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10177),U_10179),U_10178))
    | ~ sP795(U_10176,U_10177,U_10178,U_10179,U_10180,U_10181) ),
    inference(clausify,[status(thm)],[f_2771_3]) ).

cnf(f_2771_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10177,U_10176),hAPP(hAPP(c_COMBC(U_10177,U_10176,U_10176),hAPP(hAPP(c_COMBS(U_10177,U_10176,tc_fun(U_10176,U_10176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10176,tc_fun(U_10176,U_10176)),U_10177),c_If(U_10176)),hAPP(hAPP(c_COMBC(U_10177,U_10177,tc_HOL_Obool),c_fequal),U_10179))),U_10180)),U_10181)),U_10178) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10176),U_10181),hAPP(c_Finite__Set_Ocard(U_10177),U_10178))
    | hBOOL(hAPP(hAPP(c_member(U_10177),U_10179),U_10178))
    | ~ sP795(U_10176,U_10177,U_10178,U_10179,U_10180,U_10181) ),
    inference(clausify,[status(thm)],[f_2771_3]) ).

fof(f_2772_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(f_2772_2,plain,
    ! [U_10183,U_10182] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10182,U_10183))),
    inference(variable_rename,[status(thm)],[f_2772_1]) ).

fof(f_2772_3,plain,
    ! [U_10183,U_10182] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10182,U_10183))),
    inference(definitional_conversion,[status(esa)],[f_2772_2]) ).

cnf(f_2772_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10182,U_10183))),
    inference(clausify,[status(thm)],[f_2772_3]) ).

fof(f_2773_1,plain,
    ! [V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J]) ).

fof(f_2773_2,plain,
    ! [U_10186,U_10185,U_10184] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10184),U_10185),U_10186) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10184),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10184,tc_Int_Oint),U_10185),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10186))
      | ~ class_Groups_Ocomm__monoid__mult(U_10184)
      | ~ class_Groups_Ocomm__monoid__add(U_10184) ),
    inference(variable_rename,[status(thm)],[f_2773_1]) ).

fof(f_2773_3,plain,
    ! [U_10186,U_10185,U_10184] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10184),U_10185),U_10186) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10184),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10184,tc_Int_Oint),U_10185),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10186))
      | ~ class_Groups_Ocomm__monoid__mult(U_10184)
      | ~ class_Groups_Ocomm__monoid__add(U_10184) ),
    inference(definitional_conversion,[status(esa)],[f_2773_2]) ).

cnf(f_2773_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10184),U_10185),U_10186) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10184),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10184,tc_Int_Oint),U_10185),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10186))
    | ~ class_Groups_Ocomm__monoid__mult(U_10184)
    | ~ class_Groups_Ocomm__monoid__add(U_10184) ),
    inference(clausify,[status(thm)],[f_2773_3]) ).

fof(f_2774_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Oring__1(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__setprod]) ).

fof(f_2774_2,plain,
    ! [U_10190,U_10189,U_10188,U_10187] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10187),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10188,tc_Int_Oint),U_10189),U_10190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10188,U_10187),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10187,U_10188),c_Int_Oring__1__class_Oof__int(U_10187)),U_10189)),U_10190)
      | ~ class_Rings_Oring__1(U_10187)
      | ~ class_Groups_Ocomm__monoid__mult(U_10187) ),
    inference(variable_rename,[status(thm)],[f_2774_1]) ).

fof(f_2774_3,plain,
    ! [U_10187,U_10188,U_10189,U_10190] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10187),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10188,tc_Int_Oint),U_10189),U_10190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10188,U_10187),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10187,U_10188),c_Int_Oring__1__class_Oof__int(U_10187)),U_10189)),U_10190)
      | ~ class_Rings_Oring__1(U_10187)
      | ~ class_Groups_Ocomm__monoid__mult(U_10187) ),
    inference(definitional_conversion,[status(esa)],[f_2774_2]) ).

cnf(f_2774_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10187),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10188,tc_Int_Oint),U_10189),U_10190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10188,U_10187),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10187,U_10188),c_Int_Oring__1__class_Oof__int(U_10187)),U_10189)),U_10190)
    | ~ class_Rings_Oring__1(U_10187)
    | ~ class_Groups_Ocomm__monoid__mult(U_10187) ),
    inference(clausify,[status(thm)],[f_2774_3]) ).

fof(f_2775_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).

fof(f_2775_2,plain,
    ! [U_10193,U_10192,U_10191] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10191,tc_Nat_Onat),U_10192),U_10193) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10191,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10191),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10192)),U_10193)),
    inference(variable_rename,[status(thm)],[f_2775_1]) ).

fof(f_2775_3,plain,
    ! [U_10191,U_10192,U_10193] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10191,tc_Nat_Onat),U_10192),U_10193) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10191,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10191),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10192)),U_10193)),
    inference(definitional_conversion,[status(esa)],[f_2775_2]) ).

cnf(f_2775_4,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10191,tc_Nat_Onat),U_10192),U_10193) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10191,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10191),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10192)),U_10193)),
    inference(clausify,[status(thm)],[f_2775_3]) ).

fof(f_2776_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__1(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__setprod]) ).

fof(f_2776_2,plain,
    ! [U_10197,U_10196,U_10195,U_10194] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10195,tc_Nat_Onat),U_10196),U_10197)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10195,U_10194),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10194,U_10195),c_Nat_Osemiring__1__class_Oof__nat(U_10194)),U_10196)),U_10197)
      | ~ class_Rings_Osemiring__1(U_10194)
      | ~ class_Groups_Ocomm__monoid__mult(U_10194) ),
    inference(variable_rename,[status(thm)],[f_2776_1]) ).

fof(f_2776_3,plain,
    ! [U_10194,U_10195,U_10196,U_10197] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10195,tc_Nat_Onat),U_10196),U_10197)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10195,U_10194),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10194,U_10195),c_Nat_Osemiring__1__class_Oof__nat(U_10194)),U_10196)),U_10197)
      | ~ class_Rings_Osemiring__1(U_10194)
      | ~ class_Groups_Ocomm__monoid__mult(U_10194) ),
    inference(definitional_conversion,[status(esa)],[f_2776_2]) ).

cnf(f_2776_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10195,tc_Nat_Onat),U_10196),U_10197)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10195,U_10194),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10194,U_10195),c_Nat_Osemiring__1__class_Oof__nat(U_10194)),U_10196)),U_10197)
    | ~ class_Rings_Osemiring__1(U_10194)
    | ~ class_Groups_Ocomm__monoid__mult(U_10194) ),
    inference(clausify,[status(thm)],[f_2776_3]) ).

fof(f_2777_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_int__setprod]) ).

fof(f_2777_2,plain,
    ! [U_10200,U_10199,U_10198] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10198,tc_Nat_Onat),U_10199),U_10200)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10198,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10198),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10199)),U_10200),
    inference(variable_rename,[status(thm)],[f_2777_1]) ).

fof(f_2777_3,plain,
    ! [U_10198,U_10199,U_10200] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10198,tc_Nat_Onat),U_10199),U_10200)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10198,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10198),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10199)),U_10200),
    inference(definitional_conversion,[status(esa)],[f_2777_2]) ).

cnf(f_2777_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10198,tc_Nat_Onat),U_10199),U_10200)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10198,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10198),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10199)),U_10200),
    inference(clausify,[status(thm)],[f_2777_3]) ).

fof(f_2778_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__timesf]) ).

fof(f_2778_2,plain,
    ! [U_10205,U_10204,U_10203,U_10202,U_10201] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),hAPP(hAPP(c_COMBS(U_10202,U_10201,U_10201),hAPP(hAPP(c_COMBB(U_10201,tc_fun(U_10201,U_10201),U_10202),c_Groups_Otimes__class_Otimes(U_10201)),U_10203)),U_10204)),U_10205) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10201),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),U_10203),U_10205)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),U_10204),U_10205))
      | ~ class_Groups_Ocomm__monoid__mult(U_10201) ),
    inference(variable_rename,[status(thm)],[f_2778_1]) ).

fof(f_2778_3,plain,
    ! [U_10201,U_10202,U_10203,U_10204,U_10205] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),hAPP(hAPP(c_COMBS(U_10202,U_10201,U_10201),hAPP(hAPP(c_COMBB(U_10201,tc_fun(U_10201,U_10201),U_10202),c_Groups_Otimes__class_Otimes(U_10201)),U_10203)),U_10204)),U_10205) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10201),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),U_10203),U_10205)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),U_10204),U_10205))
      | ~ class_Groups_Ocomm__monoid__mult(U_10201) ),
    inference(definitional_conversion,[status(esa)],[f_2778_2]) ).

cnf(f_2778_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),hAPP(hAPP(c_COMBS(U_10202,U_10201,U_10201),hAPP(hAPP(c_COMBB(U_10201,tc_fun(U_10201,U_10201),U_10202),c_Groups_Otimes__class_Otimes(U_10201)),U_10203)),U_10204)),U_10205) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10201),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),U_10203),U_10205)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10202,U_10201),U_10204),U_10205))
    | ~ class_Groups_Ocomm__monoid__mult(U_10201) ),
    inference(clausify,[status(thm)],[f_2778_3]) ).

fof(f_2779_1,plain,
    ! [V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__1]) ).

fof(f_2779_2,plain,
    ! [U_10208,U_10207,U_10206] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10207,U_10206),hAPP(c_COMBK(U_10206,U_10207),c_Groups_Oone__class_Oone(U_10206))),U_10208) = c_Groups_Oone__class_Oone(U_10206)
      | ~ class_Groups_Ocomm__monoid__mult(U_10206) ),
    inference(variable_rename,[status(thm)],[f_2779_1]) ).

fof(f_2779_3,plain,
    ! [U_10206,U_10207,U_10208] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10207,U_10206),hAPP(c_COMBK(U_10206,U_10207),c_Groups_Oone__class_Oone(U_10206))),U_10208) = c_Groups_Oone__class_Oone(U_10206)
      | ~ class_Groups_Ocomm__monoid__mult(U_10206) ),
    inference(definitional_conversion,[status(esa)],[f_2779_2]) ).

cnf(f_2779_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10207,U_10206),hAPP(c_COMBK(U_10206,U_10207),c_Groups_Oone__class_Oone(U_10206))),U_10208) = c_Groups_Oone__class_Oone(U_10206)
    | ~ class_Groups_Ocomm__monoid__mult(U_10206) ),
    inference(clausify,[status(thm)],[f_2779_3]) ).

fof(f_2780_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__setprod]) ).

fof(f_2780_2,plain,
    ! [U_10212,U_10211,U_10210,U_10209] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10210,U_10209),U_10211),U_10212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10210,U_10209),hAPP(hAPP(c_COMBB(U_10209,U_10209,U_10210),c_Groups_Oabs__class_Oabs(U_10209)),U_10211)),U_10212)
      | ~ class_Fields_Olinordered__field(U_10209) ),
    inference(variable_rename,[status(thm)],[f_2780_1]) ).

fof(f_2780_3,plain,
    ! [U_10209,U_10210,U_10211,U_10212] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10210,U_10209),U_10211),U_10212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10210,U_10209),hAPP(hAPP(c_COMBB(U_10209,U_10209,U_10210),c_Groups_Oabs__class_Oabs(U_10209)),U_10211)),U_10212)
      | ~ class_Fields_Olinordered__field(U_10209) ),
    inference(definitional_conversion,[status(esa)],[f_2780_2]) ).

cnf(f_2780_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10210,U_10209),U_10211),U_10212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10210,U_10209),hAPP(hAPP(c_COMBB(U_10209,U_10209,U_10210),c_Groups_Oabs__class_Oabs(U_10209)),U_10211)),U_10212)
    | ~ class_Fields_Olinordered__field(U_10209) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

fof(f_2781_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
      | ! [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Ocomm__semiring__1(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__zero]) ).

fof(f_2781_2,plain,
    ! [U_10217,U_10216,U_10215,U_10214] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10215,U_10214),U_10217),U_10216) = c_Groups_Ozero__class_Ozero(U_10214)
      | ! [U_10213] :
          ( hAPP(U_10217,U_10213) != c_Groups_Ozero__class_Ozero(U_10214)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10215),U_10213),U_10216)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10216))
      | ~ class_Rings_Ocomm__semiring__1(U_10214) ),
    inference(variable_rename,[status(thm)],[f_2781_1]) ).

fof(f_2781_3,plain,
    ! [U_10213,U_10214,U_10215,U_10216,U_10217] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10215,U_10214),U_10217),U_10216) = c_Groups_Ozero__class_Ozero(U_10214)
      | hAPP(U_10217,U_10213) != c_Groups_Ozero__class_Ozero(U_10214)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10215),U_10213),U_10216))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10216))
      | ~ class_Rings_Ocomm__semiring__1(U_10214) ),
    inference(definitional_conversion,[status(esa)],[f_2781_2]) ).

cnf(f_2781_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10215,U_10214),U_10217),U_10216) = c_Groups_Ozero__class_Ozero(U_10214)
    | hAPP(U_10217,U_10213) != c_Groups_Ozero__class_Ozero(U_10214)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10215),U_10213),U_10216))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10216))
    | ~ class_Rings_Ocomm__semiring__1(U_10214) ),
    inference(clausify,[status(thm)],[f_2781_3]) ).

fof(f_2782_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
          | ! [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Ono__zero__divisors(T_c)
      | ~ class_Rings_Ocomm__semiring__1(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff]) ).

fof(f_2782_2,plain,
    ! [U_10223,U_10222,U_10221,U_10220] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) = c_Groups_Ozero__class_Ozero(U_10220)
          | ! [U_10219] :
              ( hAPP(U_10223,U_10219) != c_Groups_Ozero__class_Ozero(U_10220)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10221),U_10219),U_10222)) ) )
        & ( ? [U_10218] :
              ( hAPP(U_10223,U_10218) = c_Groups_Ozero__class_Ozero(U_10220)
              & hBOOL(hAPP(hAPP(c_member(U_10221),U_10218),U_10222)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) != c_Groups_Ozero__class_Ozero(U_10220) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
      | ~ class_Rings_Ono__zero__divisors(U_10220)
      | ~ class_Rings_Ocomm__semiring__1(U_10220) ),
    inference(variable_rename,[status(thm)],[f_2782_1]) ).

fof(f_2782_3,plain,
    ! [U_10223,U_10222,U_10221,U_10220] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) = c_Groups_Ozero__class_Ozero(U_10220)
          | ! [U_10219] :
              ( hAPP(U_10223,U_10219) != c_Groups_Ozero__class_Ozero(U_10220)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10221),U_10219),U_10222)) ) )
        & ( ( hAPP(U_10223,sK158(U_10223,U_10222,U_10221,U_10220)) = c_Groups_Ozero__class_Ozero(U_10220)
            & hBOOL(hAPP(hAPP(c_member(U_10221),sK158(U_10223,U_10222,U_10221,U_10220)),U_10222)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) != c_Groups_Ozero__class_Ozero(U_10220) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
      | ~ class_Rings_Ono__zero__divisors(U_10220)
      | ~ class_Rings_Ocomm__semiring__1(U_10220) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_10218,sK158(U_10223,U_10222,U_10221,U_10220))],[f_2782_2]) ).

fof(f_2782_4,plain,
    ( ! [U_10221,U_10220,U_10222,U_10223] :
        ( hAPP(U_10223,sK158(U_10223,U_10222,U_10221,U_10220)) = c_Groups_Ozero__class_Ozero(U_10220)
        | ~ sP796(U_10221,U_10220,U_10222,U_10223) )
    & ! [U_10221,U_10220,U_10222,U_10223] :
        ( hBOOL(hAPP(hAPP(c_member(U_10221),sK158(U_10223,U_10222,U_10221,U_10220)),U_10222))
        | ~ sP796(U_10221,U_10220,U_10222,U_10223) )
    & ! [U_10221,U_10219,U_10220,U_10222,U_10223] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) = c_Groups_Ozero__class_Ozero(U_10220)
        | hAPP(U_10223,U_10219) != c_Groups_Ozero__class_Ozero(U_10220)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10221),U_10219),U_10222))
        | ~ sP797(U_10221,U_10219,U_10220,U_10222,U_10223) )
    & ! [U_10221,U_10219,U_10220,U_10222,U_10223] :
        ( sP796(U_10221,U_10220,U_10222,U_10223)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) != c_Groups_Ozero__class_Ozero(U_10220)
        | ~ sP797(U_10221,U_10219,U_10220,U_10222,U_10223) )
    & ! [U_10221,U_10219,U_10220,U_10222,U_10223] :
        ( sP797(U_10221,U_10219,U_10220,U_10222,U_10223)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
        | ~ class_Rings_Ono__zero__divisors(U_10220)
        | ~ class_Rings_Ocomm__semiring__1(U_10220) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP796,sP797])],[f_2782_3]) ).

cnf(f_2782_5,plain,
    ( sP797(U_10221,U_10219,U_10220,U_10222,U_10223)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
    | ~ class_Rings_Ono__zero__divisors(U_10220)
    | ~ class_Rings_Ocomm__semiring__1(U_10220) ),
    inference(clausify,[status(thm)],[f_2782_4]) ).

cnf(f_2782_6,plain,
    ( sP796(U_10221,U_10220,U_10222,U_10223)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) != c_Groups_Ozero__class_Ozero(U_10220)
    | ~ sP797(U_10221,U_10219,U_10220,U_10222,U_10223) ),
    inference(clausify,[status(thm)],[f_2782_4]) ).

cnf(f_2782_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10221,U_10220),U_10223),U_10222) = c_Groups_Ozero__class_Ozero(U_10220)
    | hAPP(U_10223,U_10219) != c_Groups_Ozero__class_Ozero(U_10220)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10221),U_10219),U_10222))
    | ~ sP797(U_10221,U_10219,U_10220,U_10222,U_10223) ),
    inference(clausify,[status(thm)],[f_2782_4]) ).

cnf(f_2782_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10221),sK158(U_10223,U_10222,U_10221,U_10220)),U_10222))
    | ~ sP796(U_10221,U_10220,U_10222,U_10223) ),
    inference(clausify,[status(thm)],[f_2782_4]) ).

cnf(f_2782_9,plain,
    ( hAPP(U_10223,sK158(U_10223,U_10222,U_10221,U_10220)) = c_Groups_Ozero__class_Ozero(U_10220)
    | ~ sP796(U_10221,U_10220,U_10222,U_10223) ),
    inference(clausify,[status(thm)],[f_2782_4]) ).

fof(f_2783_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__empty]) ).

fof(f_2783_2,plain,
    ! [U_10226,U_10225,U_10224] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10225,U_10224),U_10226),c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10224)
      | ~ class_Groups_Ocomm__monoid__mult(U_10224) ),
    inference(variable_rename,[status(thm)],[f_2783_1]) ).

fof(f_2783_3,plain,
    ! [U_10225,U_10224,U_10226] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10225,U_10224),U_10226),c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10224)
      | ~ class_Groups_Ocomm__monoid__mult(U_10224) ),
    inference(definitional_conversion,[status(esa)],[f_2783_2]) ).

cnf(f_2783_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10225,U_10224),U_10226),c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10224)
    | ~ class_Groups_Ocomm__monoid__mult(U_10224) ),
    inference(clausify,[status(thm)],[f_2783_3]) ).

fof(f_2784_1,plain,
    ! [V_g_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oempty]) ).

fof(f_2784_2,plain,
    ! [U_10229,U_10228,U_10227] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10228,U_10227),U_10229),c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10227)
      | ~ class_Groups_Ocomm__monoid__mult(U_10227) ),
    inference(variable_rename,[status(thm)],[f_2784_1]) ).

fof(f_2784_3,plain,
    ! [U_10227,U_10228,U_10229] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10228,U_10227),U_10229),c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10227)
      | ~ class_Groups_Ocomm__monoid__mult(U_10227) ),
    inference(definitional_conversion,[status(esa)],[f_2784_2]) ).

cnf(f_2784_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10228,U_10227),U_10229),c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10227)
    | ~ class_Groups_Ocomm__monoid__mult(U_10227) ),
    inference(clausify,[status(thm)],[f_2784_3]) ).

fof(f_2785_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__infinite]) ).

fof(f_2785_2,plain,
    ! [U_10233,U_10232,U_10231,U_10230] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10231,U_10230),U_10233),U_10232) = c_Groups_Oone__class_Oone(U_10230)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10231),U_10232))
      | ~ class_Groups_Ocomm__monoid__mult(U_10230) ),
    inference(variable_rename,[status(thm)],[f_2785_1]) ).

fof(f_2785_3,plain,
    ! [U_10231,U_10230,U_10232,U_10233] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10231,U_10230),U_10233),U_10232) = c_Groups_Oone__class_Oone(U_10230)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10231),U_10232))
      | ~ class_Groups_Ocomm__monoid__mult(U_10230) ),
    inference(definitional_conversion,[status(esa)],[f_2785_2]) ).

cnf(f_2785_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10231,U_10230),U_10233),U_10232) = c_Groups_Oone__class_Oone(U_10230)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10231),U_10232))
    | ~ class_Groups_Ocomm__monoid__mult(U_10230) ),
    inference(clausify,[status(thm)],[f_2785_3]) ).

fof(f_2786_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(f_2786_2,plain,
    ! [U_10237,U_10236,U_10235,U_10234] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10235,U_10234),U_10237),U_10236) = c_Groups_Oone__class_Oone(U_10234)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10235),U_10236))
      | ~ class_Groups_Ocomm__monoid__mult(U_10234) ),
    inference(variable_rename,[status(thm)],[f_2786_1]) ).

fof(f_2786_3,plain,
    ! [U_10234,U_10235,U_10236,U_10237] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10235,U_10234),U_10237),U_10236) = c_Groups_Oone__class_Oone(U_10234)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10235),U_10236))
      | ~ class_Groups_Ocomm__monoid__mult(U_10234) ),
    inference(definitional_conversion,[status(esa)],[f_2786_2]) ).

cnf(f_2786_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10235,U_10234),U_10237),U_10236) = c_Groups_Oone__class_Oone(U_10234)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10235),U_10236))
    | ~ class_Groups_Ocomm__monoid__mult(U_10234) ),
    inference(clausify,[status(thm)],[f_2786_3]) ).

fof(f_2787_1,plain,
    ! [V_f_2,V_F_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
        & ( ! [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff]) ).

fof(f_2787_2,plain,
    ! [U_10242,U_10241,U_10240] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [U_10239] :
              ( hAPP(U_10242,U_10239) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_10240),U_10239),U_10241)) ) )
        & ( ! [U_10238] :
              ( hAPP(U_10242,U_10238) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10238),U_10241)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241)) ),
    inference(variable_rename,[status(thm)],[f_2787_1]) ).

fof(f_2787_3,plain,
    ! [U_10242,U_10241,U_10240] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ( hAPP(U_10242,sK159(U_10242,U_10241,U_10240)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_10240),sK159(U_10242,U_10241,U_10240)),U_10241)) ) )
        & ( ! [U_10238] :
              ( hAPP(U_10242,U_10238) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10238),U_10241)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_10239,sK159(U_10242,U_10241,U_10240))],[f_2787_2]) ).

fof(f_2787_4,plain,
    ( ! [U_10240,U_10241,U_10242] :
        ( hAPP(U_10242,sK159(U_10242,U_10241,U_10240)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP798(U_10240,U_10241,U_10242) )
    & ! [U_10240,U_10241,U_10242] :
        ( hBOOL(hAPP(hAPP(c_member(U_10240),sK159(U_10242,U_10241,U_10240)),U_10241))
        | ~ sP798(U_10240,U_10241,U_10242) )
    & ! [U_10238,U_10240,U_10241,U_10242] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | sP798(U_10240,U_10241,U_10242)
        | ~ sP799(U_10238,U_10240,U_10241,U_10242) )
    & ! [U_10238,U_10240,U_10241,U_10242] :
        ( hAPP(U_10242,U_10238) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10238),U_10241))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP799(U_10238,U_10240,U_10241,U_10242) )
    & ! [U_10238,U_10240,U_10241,U_10242] :
        ( sP799(U_10238,U_10240,U_10241,U_10242)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP798,sP799])],[f_2787_3]) ).

cnf(f_2787_5,plain,
    ( sP799(U_10238,U_10240,U_10241,U_10242)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241)) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_6,plain,
    ( hAPP(U_10242,U_10238) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10238),U_10241))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP799(U_10238,U_10240,U_10241,U_10242) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10240,tc_Nat_Onat),U_10242),U_10241) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | sP798(U_10240,U_10241,U_10242)
    | ~ sP799(U_10238,U_10240,U_10241,U_10242) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10240),sK159(U_10242,U_10241,U_10240)),U_10241))
    | ~ sP798(U_10240,U_10241,U_10242) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_9,plain,
    ( hAPP(U_10242,sK159(U_10242,U_10241,U_10240)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP798(U_10240,U_10241,U_10242) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

fof(f_2788_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J]) ).

fof(f_2788_2,plain,
    ! [U_10245,U_10244,U_10243] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10243),U_10245),U_10244) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10243),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10243,tc_Nat_Onat),U_10245),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10244))
      | ~ c_Nat__Transfer_Onat__set(U_10244)
      | ~ class_Groups_Ocomm__monoid__mult(U_10243)
      | ~ class_Groups_Ocomm__monoid__add(U_10243) ),
    inference(variable_rename,[status(thm)],[f_2788_1]) ).

fof(f_2788_3,plain,
    ! [U_10244,U_10245,U_10243] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10243),U_10245),U_10244) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10243),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10243,tc_Nat_Onat),U_10245),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10244))
      | ~ c_Nat__Transfer_Onat__set(U_10244)
      | ~ class_Groups_Ocomm__monoid__mult(U_10243)
      | ~ class_Groups_Ocomm__monoid__add(U_10243) ),
    inference(definitional_conversion,[status(esa)],[f_2788_2]) ).

cnf(f_2788_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10243),U_10245),U_10244) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10243),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10243,tc_Nat_Onat),U_10245),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10244))
    | ~ c_Nat__Transfer_Onat__set(U_10244)
    | ~ class_Groups_Ocomm__monoid__mult(U_10243)
    | ~ class_Groups_Ocomm__monoid__add(U_10243) ),
    inference(clausify,[status(thm)],[f_2788_3]) ).

fof(f_2789_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib]) ).

fof(f_2789_2,plain,
    ! [U_10250,U_10249,U_10248,U_10247,U_10246] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),hAPP(hAPP(c_COMBS(U_10247,U_10246,U_10246),hAPP(hAPP(c_COMBB(U_10246,tc_fun(U_10246,U_10246),U_10247),c_Groups_Otimes__class_Otimes(U_10246)),U_10249)),U_10250)),U_10248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10246),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),U_10249),U_10248)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),U_10250),U_10248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10247),U_10248))
      | ~ class_Groups_Ocomm__monoid__mult(U_10246) ),
    inference(variable_rename,[status(thm)],[f_2789_1]) ).

fof(f_2789_3,plain,
    ! [U_10246,U_10247,U_10248,U_10249,U_10250] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),hAPP(hAPP(c_COMBS(U_10247,U_10246,U_10246),hAPP(hAPP(c_COMBB(U_10246,tc_fun(U_10246,U_10246),U_10247),c_Groups_Otimes__class_Otimes(U_10246)),U_10249)),U_10250)),U_10248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10246),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),U_10249),U_10248)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),U_10250),U_10248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10247),U_10248))
      | ~ class_Groups_Ocomm__monoid__mult(U_10246) ),
    inference(definitional_conversion,[status(esa)],[f_2789_2]) ).

cnf(f_2789_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),hAPP(hAPP(c_COMBS(U_10247,U_10246,U_10246),hAPP(hAPP(c_COMBB(U_10246,tc_fun(U_10246,U_10246),U_10247),c_Groups_Otimes__class_Otimes(U_10246)),U_10249)),U_10250)),U_10248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10246),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),U_10249),U_10248)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10247,U_10246),U_10250),U_10248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10247),U_10248))
    | ~ class_Groups_Ocomm__monoid__mult(U_10246) ),
    inference(clausify,[status(thm)],[f_2789_3]) ).

fof(f_2790_1,plain,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Fields_Ofield__inverse__zero(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__dividef]) ).

fof(f_2790_2,plain,
    ! [U_10255,U_10254,U_10253,U_10252,U_10251] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),hAPP(hAPP(c_COMBS(U_10252,U_10251,U_10251),hAPP(hAPP(c_COMBB(U_10251,tc_fun(U_10251,U_10251),U_10252),c_Rings_Oinverse__class_Odivide(U_10251)),U_10254)),U_10255)),U_10253) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10251),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),U_10254),U_10253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),U_10255),U_10253))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10252),U_10253))
      | ~ class_Fields_Ofield__inverse__zero(U_10251) ),
    inference(variable_rename,[status(thm)],[f_2790_1]) ).

fof(f_2790_3,plain,
    ! [U_10251,U_10252,U_10253,U_10254,U_10255] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),hAPP(hAPP(c_COMBS(U_10252,U_10251,U_10251),hAPP(hAPP(c_COMBB(U_10251,tc_fun(U_10251,U_10251),U_10252),c_Rings_Oinverse__class_Odivide(U_10251)),U_10254)),U_10255)),U_10253) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10251),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),U_10254),U_10253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),U_10255),U_10253))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10252),U_10253))
      | ~ class_Fields_Ofield__inverse__zero(U_10251) ),
    inference(definitional_conversion,[status(esa)],[f_2790_2]) ).

cnf(f_2790_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),hAPP(hAPP(c_COMBS(U_10252,U_10251,U_10251),hAPP(hAPP(c_COMBB(U_10251,tc_fun(U_10251,U_10251),U_10252),c_Rings_Oinverse__class_Odivide(U_10251)),U_10254)),U_10255)),U_10253) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10251),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),U_10254),U_10253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10252,U_10251),U_10255),U_10253))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10252),U_10253))
    | ~ class_Fields_Ofield__inverse__zero(U_10251) ),
    inference(clausify,[status(thm)],[f_2790_3]) ).

fof(f_2791_1,plain,
    ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Ocomm__semiring__1(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__setprod]) ).

fof(f_2791_2,plain,
    ! [U_10260,U_10259,U_10258,U_10257,U_10256] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10256),hAPP(U_10260,U_10259)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10257,U_10256),U_10260),U_10258)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10257),U_10259),U_10258))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10257),U_10258))
      | ~ class_Rings_Ocomm__semiring__1(U_10256) ),
    inference(variable_rename,[status(thm)],[f_2791_1]) ).

fof(f_2791_3,plain,
    ! [U_10256,U_10257,U_10258,U_10259,U_10260] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10256),hAPP(U_10260,U_10259)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10257,U_10256),U_10260),U_10258)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10257),U_10259),U_10258))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10257),U_10258))
      | ~ class_Rings_Ocomm__semiring__1(U_10256) ),
    inference(definitional_conversion,[status(esa)],[f_2791_2]) ).

cnf(f_2791_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10256),hAPP(U_10260,U_10259)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10257,U_10256),U_10260),U_10258)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10257),U_10259),U_10258))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10257),U_10258))
    | ~ class_Rings_Ocomm__semiring__1(U_10256) ),
    inference(clausify,[status(thm)],[f_2791_3]) ).

fof(f_2792_1,plain,
    ! [V_f_2,V_S_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff]) ).

fof(f_2792_2,plain,
    ! [U_10265,U_10264,U_10263] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264)))
          | ? [U_10262] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,U_10262)))
              & hBOOL(hAPP(hAPP(c_member(U_10263),U_10262),U_10264)) ) )
        & ( ! [U_10261] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,U_10261)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10263),U_10261),U_10264)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10263),U_10264)) ),
    inference(variable_rename,[status(thm)],[f_2792_1]) ).

fof(f_2792_3,plain,
    ! [U_10265,U_10264,U_10263] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,sK160(U_10265,U_10264,U_10263))))
            & hBOOL(hAPP(hAPP(c_member(U_10263),sK160(U_10265,U_10264,U_10263)),U_10264)) ) )
        & ( ! [U_10261] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,U_10261)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10263),U_10261),U_10264)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10263),U_10264)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_10262,sK160(U_10265,U_10264,U_10263))],[f_2792_2]) ).

fof(f_2792_4,plain,
    ( ! [U_10263,U_10264,U_10265] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,sK160(U_10265,U_10264,U_10263))))
        | ~ sP800(U_10263,U_10264,U_10265) )
    & ! [U_10263,U_10264,U_10265] :
        ( hBOOL(hAPP(hAPP(c_member(U_10263),sK160(U_10265,U_10264,U_10263)),U_10264))
        | ~ sP800(U_10263,U_10264,U_10265) )
    & ! [U_10261,U_10263,U_10264,U_10265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264)))
        | sP800(U_10263,U_10264,U_10265)
        | ~ sP801(U_10261,U_10263,U_10264,U_10265) )
    & ! [U_10261,U_10263,U_10264,U_10265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,U_10261)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10263),U_10261),U_10264))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264)))
        | ~ sP801(U_10261,U_10263,U_10264,U_10265) )
    & ! [U_10261,U_10263,U_10264,U_10265] :
        ( sP801(U_10261,U_10263,U_10264,U_10265)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10263),U_10264)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP800,sP801])],[f_2792_3]) ).

cnf(f_2792_5,plain,
    ( sP801(U_10261,U_10263,U_10264,U_10265)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10263),U_10264)) ),
    inference(clausify,[status(thm)],[f_2792_4]) ).

cnf(f_2792_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,U_10261)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10263),U_10261),U_10264))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264)))
    | ~ sP801(U_10261,U_10263,U_10264,U_10265) ),
    inference(clausify,[status(thm)],[f_2792_4]) ).

cnf(f_2792_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10263,tc_Nat_Onat),U_10265),U_10264)))
    | sP800(U_10263,U_10264,U_10265)
    | ~ sP801(U_10261,U_10263,U_10264,U_10265) ),
    inference(clausify,[status(thm)],[f_2792_4]) ).

cnf(f_2792_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10263),sK160(U_10265,U_10264,U_10263)),U_10264))
    | ~ sP800(U_10263,U_10264,U_10265) ),
    inference(clausify,[status(thm)],[f_2792_4]) ).

cnf(f_2792_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10265,sK160(U_10265,U_10264,U_10263))))
    | ~ sP800(U_10263,U_10264,U_10265) ),
    inference(clausify,[status(thm)],[f_2792_4]) ).

fof(f_2793_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ class_Rings_Odvd(T_c)
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset]) ).

fof(f_2793_2,plain,
    ! [U_10270,U_10269,U_10268,U_10267,U_10266] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10266),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10267,U_10266),U_10270),U_10269)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10267,U_10266),U_10270),U_10268)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10267,tc_HOL_Obool)),U_10269),U_10268))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10267),U_10268))
      | ~ class_Rings_Odvd(U_10266)
      | ~ class_Groups_Ocomm__monoid__mult(U_10266) ),
    inference(variable_rename,[status(thm)],[f_2793_1]) ).

fof(f_2793_3,plain,
    ! [U_10270,U_10267,U_10266,U_10268,U_10269] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10266),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10267,U_10266),U_10270),U_10269)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10267,U_10266),U_10270),U_10268)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10267,tc_HOL_Obool)),U_10269),U_10268))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10267),U_10268))
      | ~ class_Rings_Odvd(U_10266)
      | ~ class_Groups_Ocomm__monoid__mult(U_10266) ),
    inference(definitional_conversion,[status(esa)],[f_2793_2]) ).

cnf(f_2793_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10266),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10267,U_10266),U_10270),U_10269)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10267,U_10266),U_10270),U_10268)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10267,tc_HOL_Obool)),U_10269),U_10268))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10267),U_10268))
    | ~ class_Rings_Odvd(U_10266)
    | ~ class_Groups_Ocomm__monoid__mult(U_10266) ),
    inference(clausify,[status(thm)],[f_2793_3]) ).

fof(f_2794_1,plain,
    ! [V_k_2,V_l_2,T_b] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty]) ).

fof(f_2794_2,plain,
    ! [U_10273,U_10272,U_10271] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10271,U_10273,U_10272) = c_Orderings_Obot__class_Obot(tc_fun(U_10271,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10271),U_10272),U_10273))
      | ~ class_Orderings_Oorder(U_10271) ),
    inference(variable_rename,[status(thm)],[f_2794_1]) ).

fof(f_2794_3,plain,
    ! [U_10272,U_10273,U_10271] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10271,U_10273,U_10272) = c_Orderings_Obot__class_Obot(tc_fun(U_10271,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10271),U_10272),U_10273))
      | ~ class_Orderings_Oorder(U_10271) ),
    inference(definitional_conversion,[status(esa)],[f_2794_2]) ).

cnf(f_2794_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10271,U_10273,U_10272) = c_Orderings_Obot__class_Obot(tc_fun(U_10271,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10271),U_10272),U_10273))
    | ~ class_Orderings_Oorder(U_10271) ),
    inference(clausify,[status(thm)],[f_2794_3]) ).

fof(f_2795_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan]) ).

fof(f_2795_2,plain,
    ! [U_10276,U_10275,U_10274] :
      ( hAPP(c_Set_Oimage(U_10274,U_10274,c_Groups_Ouminus__class_Ouminus(U_10274)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10274,U_10275,U_10276)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10274,hAPP(c_Groups_Ouminus__class_Ouminus(U_10274),U_10276),hAPP(c_Groups_Ouminus__class_Ouminus(U_10274),U_10275))
      | ~ class_Groups_Oordered__ab__group__add(U_10274) ),
    inference(variable_rename,[status(thm)],[f_2795_1]) ).

fof(f_2795_3,plain,
    ! [U_10274,U_10275,U_10276] :
      ( hAPP(c_Set_Oimage(U_10274,U_10274,c_Groups_Ouminus__class_Ouminus(U_10274)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10274,U_10275,U_10276)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10274,hAPP(c_Groups_Ouminus__class_Ouminus(U_10274),U_10276),hAPP(c_Groups_Ouminus__class_Ouminus(U_10274),U_10275))
      | ~ class_Groups_Oordered__ab__group__add(U_10274) ),
    inference(definitional_conversion,[status(esa)],[f_2795_2]) ).

cnf(f_2795_4,plain,
    ( hAPP(c_Set_Oimage(U_10274,U_10274,c_Groups_Ouminus__class_Ouminus(U_10274)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10274,U_10275,U_10276)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10274,hAPP(c_Groups_Ouminus__class_Ouminus(U_10274),U_10276),hAPP(c_Groups_Ouminus__class_Ouminus(U_10274),U_10275))
    | ~ class_Groups_Oordered__ab__group__add(U_10274) ),
    inference(clausify,[status(thm)],[f_2795_3]) ).

fof(f_2796_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__delta_H]) ).

fof(f_2796_2,plain,
    ! [U_10281,U_10280,U_10279,U_10278,U_10277] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10278,U_10277),hAPP(hAPP(c_COMBC(U_10278,U_10277,U_10277),hAPP(hAPP(c_COMBS(U_10278,U_10277,tc_fun(U_10277,U_10277)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10277,tc_fun(U_10277,U_10277)),U_10278),c_If(U_10277)),hAPP(c_fequal,U_10280))),U_10281)),c_Groups_Oone__class_Oone(U_10277))),U_10279) = c_Groups_Oone__class_Oone(U_10277)
          | hBOOL(hAPP(hAPP(c_member(U_10278),U_10280),U_10279)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10278,U_10277),hAPP(hAPP(c_COMBC(U_10278,U_10277,U_10277),hAPP(hAPP(c_COMBS(U_10278,U_10277,tc_fun(U_10277,U_10277)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10277,tc_fun(U_10277,U_10277)),U_10278),c_If(U_10277)),hAPP(c_fequal,U_10280))),U_10281)),c_Groups_Oone__class_Oone(U_10277))),U_10279) = hAPP(U_10281,U_10280)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10280),U_10279)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10279))
      | ~ class_Groups_Ocomm__monoid__mult(U_10277) ),
    inference(variable_rename,[status(thm)],[f_2796_1]) ).

fof(f_2796_3,plain,
    ( ! [U_10277,U_10278,U_10279,U_10280,U_10281] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10278,U_10277),hAPP(hAPP(c_COMBC(U_10278,U_10277,U_10277),hAPP(hAPP(c_COMBS(U_10278,U_10277,tc_fun(U_10277,U_10277)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10277,tc_fun(U_10277,U_10277)),U_10278),c_If(U_10277)),hAPP(c_fequal,U_10280))),U_10281)),c_Groups_Oone__class_Oone(U_10277))),U_10279) = c_Groups_Oone__class_Oone(U_10277)
        | hBOOL(hAPP(hAPP(c_member(U_10278),U_10280),U_10279))
        | ~ sP802(U_10277,U_10278,U_10279,U_10280,U_10281) )
    & ! [U_10277,U_10278,U_10279,U_10280,U_10281] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10278,U_10277),hAPP(hAPP(c_COMBC(U_10278,U_10277,U_10277),hAPP(hAPP(c_COMBS(U_10278,U_10277,tc_fun(U_10277,U_10277)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10277,tc_fun(U_10277,U_10277)),U_10278),c_If(U_10277)),hAPP(c_fequal,U_10280))),U_10281)),c_Groups_Oone__class_Oone(U_10277))),U_10279) = hAPP(U_10281,U_10280)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10280),U_10279))
        | ~ sP802(U_10277,U_10278,U_10279,U_10280,U_10281) )
    & ! [U_10277,U_10278,U_10279,U_10280,U_10281] :
        ( sP802(U_10277,U_10278,U_10279,U_10280,U_10281)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10279))
        | ~ class_Groups_Ocomm__monoid__mult(U_10277) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP802])],[f_2796_2]) ).

cnf(f_2796_4,plain,
    ( sP802(U_10277,U_10278,U_10279,U_10280,U_10281)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10279))
    | ~ class_Groups_Ocomm__monoid__mult(U_10277) ),
    inference(clausify,[status(thm)],[f_2796_3]) ).

cnf(f_2796_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10278,U_10277),hAPP(hAPP(c_COMBC(U_10278,U_10277,U_10277),hAPP(hAPP(c_COMBS(U_10278,U_10277,tc_fun(U_10277,U_10277)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10277,tc_fun(U_10277,U_10277)),U_10278),c_If(U_10277)),hAPP(c_fequal,U_10280))),U_10281)),c_Groups_Oone__class_Oone(U_10277))),U_10279) = hAPP(U_10281,U_10280)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10280),U_10279))
    | ~ sP802(U_10277,U_10278,U_10279,U_10280,U_10281) ),
    inference(clausify,[status(thm)],[f_2796_3]) ).

cnf(f_2796_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10278,U_10277),hAPP(hAPP(c_COMBC(U_10278,U_10277,U_10277),hAPP(hAPP(c_COMBS(U_10278,U_10277,tc_fun(U_10277,U_10277)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10277,tc_fun(U_10277,U_10277)),U_10278),c_If(U_10277)),hAPP(c_fequal,U_10280))),U_10281)),c_Groups_Oone__class_Oone(U_10277))),U_10279) = c_Groups_Oone__class_Oone(U_10277)
    | hBOOL(hAPP(hAPP(c_member(U_10278),U_10280),U_10279))
    | ~ sP802(U_10277,U_10278,U_10279,U_10280,U_10281) ),
    inference(clausify,[status(thm)],[f_2796_3]) ).

fof(f_2797_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__delta]) ).

fof(f_2797_2,plain,
    ! [U_10286,U_10285,U_10284,U_10283,U_10282] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10283,U_10282),hAPP(hAPP(c_COMBC(U_10283,U_10282,U_10282),hAPP(hAPP(c_COMBS(U_10283,U_10282,tc_fun(U_10282,U_10282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10282,tc_fun(U_10282,U_10282)),U_10283),c_If(U_10282)),hAPP(hAPP(c_COMBC(U_10283,U_10283,tc_HOL_Obool),c_fequal),U_10285))),U_10286)),c_Groups_Oone__class_Oone(U_10282))),U_10284) = c_Groups_Oone__class_Oone(U_10282)
          | hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),U_10284)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10283,U_10282),hAPP(hAPP(c_COMBC(U_10283,U_10282,U_10282),hAPP(hAPP(c_COMBS(U_10283,U_10282,tc_fun(U_10282,U_10282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10282,tc_fun(U_10282,U_10282)),U_10283),c_If(U_10282)),hAPP(hAPP(c_COMBC(U_10283,U_10283,tc_HOL_Obool),c_fequal),U_10285))),U_10286)),c_Groups_Oone__class_Oone(U_10282))),U_10284) = hAPP(U_10286,U_10285)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),U_10284)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10283),U_10284))
      | ~ class_Groups_Ocomm__monoid__mult(U_10282) ),
    inference(variable_rename,[status(thm)],[f_2797_1]) ).

fof(f_2797_3,plain,
    ( ! [U_10283,U_10282,U_10284,U_10285,U_10286] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10283,U_10282),hAPP(hAPP(c_COMBC(U_10283,U_10282,U_10282),hAPP(hAPP(c_COMBS(U_10283,U_10282,tc_fun(U_10282,U_10282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10282,tc_fun(U_10282,U_10282)),U_10283),c_If(U_10282)),hAPP(hAPP(c_COMBC(U_10283,U_10283,tc_HOL_Obool),c_fequal),U_10285))),U_10286)),c_Groups_Oone__class_Oone(U_10282))),U_10284) = c_Groups_Oone__class_Oone(U_10282)
        | hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),U_10284))
        | ~ sP803(U_10283,U_10282,U_10284,U_10285,U_10286) )
    & ! [U_10283,U_10282,U_10284,U_10285,U_10286] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10283,U_10282),hAPP(hAPP(c_COMBC(U_10283,U_10282,U_10282),hAPP(hAPP(c_COMBS(U_10283,U_10282,tc_fun(U_10282,U_10282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10282,tc_fun(U_10282,U_10282)),U_10283),c_If(U_10282)),hAPP(hAPP(c_COMBC(U_10283,U_10283,tc_HOL_Obool),c_fequal),U_10285))),U_10286)),c_Groups_Oone__class_Oone(U_10282))),U_10284) = hAPP(U_10286,U_10285)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),U_10284))
        | ~ sP803(U_10283,U_10282,U_10284,U_10285,U_10286) )
    & ! [U_10283,U_10282,U_10284,U_10285,U_10286] :
        ( sP803(U_10283,U_10282,U_10284,U_10285,U_10286)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10283),U_10284))
        | ~ class_Groups_Ocomm__monoid__mult(U_10282) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP803])],[f_2797_2]) ).

cnf(f_2797_4,plain,
    ( sP803(U_10283,U_10282,U_10284,U_10285,U_10286)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10283),U_10284))
    | ~ class_Groups_Ocomm__monoid__mult(U_10282) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

cnf(f_2797_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10283,U_10282),hAPP(hAPP(c_COMBC(U_10283,U_10282,U_10282),hAPP(hAPP(c_COMBS(U_10283,U_10282,tc_fun(U_10282,U_10282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10282,tc_fun(U_10282,U_10282)),U_10283),c_If(U_10282)),hAPP(hAPP(c_COMBC(U_10283,U_10283,tc_HOL_Obool),c_fequal),U_10285))),U_10286)),c_Groups_Oone__class_Oone(U_10282))),U_10284) = hAPP(U_10286,U_10285)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),U_10284))
    | ~ sP803(U_10283,U_10282,U_10284,U_10285,U_10286) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

cnf(f_2797_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10283,U_10282),hAPP(hAPP(c_COMBC(U_10283,U_10282,U_10282),hAPP(hAPP(c_COMBS(U_10283,U_10282,tc_fun(U_10282,U_10282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10282,tc_fun(U_10282,U_10282)),U_10283),c_If(U_10282)),hAPP(hAPP(c_COMBC(U_10283,U_10283,tc_HOL_Obool),c_fequal),U_10285))),U_10286)),c_Groups_Oone__class_Oone(U_10282))),U_10284) = c_Groups_Oone__class_Oone(U_10282)
    | hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),U_10284))
    | ~ sP803(U_10283,U_10282,U_10284,U_10285,U_10286) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

fof(f_2798_1,plain,
    ! [V_y_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__constant]) ).

fof(f_2798_2,plain,
    ! [U_10290,U_10289,U_10288,U_10287] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10288,U_10287),hAPP(c_COMBK(U_10287,U_10288),U_10290)),U_10289) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10287),U_10290),hAPP(c_Finite__Set_Ocard(U_10288),U_10289))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
      | ~ class_Groups_Ocomm__monoid__mult(U_10287) ),
    inference(variable_rename,[status(thm)],[f_2798_1]) ).

fof(f_2798_3,plain,
    ! [U_10288,U_10289,U_10287,U_10290] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10288,U_10287),hAPP(c_COMBK(U_10287,U_10288),U_10290)),U_10289) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10287),U_10290),hAPP(c_Finite__Set_Ocard(U_10288),U_10289))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
      | ~ class_Groups_Ocomm__monoid__mult(U_10287) ),
    inference(definitional_conversion,[status(esa)],[f_2798_2]) ).

cnf(f_2798_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10288,U_10287),hAPP(c_COMBK(U_10287,U_10288),U_10290)),U_10289) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10287),U_10290),hAPP(c_Finite__Set_Ocard(U_10288),U_10289))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
    | ~ class_Groups_Ocomm__monoid__mult(U_10287) ),
    inference(clausify,[status(thm)],[f_2798_3]) ).

fof(f_2799_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__insert]) ).

fof(f_2799_2,plain,
    ! [U_10295,U_10294,U_10293,U_10292,U_10291] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10292,U_10291),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10292),U_10294),U_10293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10291),hAPP(U_10295,U_10294)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10292,U_10291),U_10295),U_10293))
      | hBOOL(hAPP(hAPP(c_member(U_10292),U_10294),U_10293))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10292),U_10293))
      | ~ class_Groups_Ocomm__monoid__mult(U_10291) ),
    inference(variable_rename,[status(thm)],[f_2799_1]) ).

fof(f_2799_3,plain,
    ! [U_10292,U_10291,U_10293,U_10294,U_10295] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10292,U_10291),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10292),U_10294),U_10293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10291),hAPP(U_10295,U_10294)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10292,U_10291),U_10295),U_10293))
      | hBOOL(hAPP(hAPP(c_member(U_10292),U_10294),U_10293))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10292),U_10293))
      | ~ class_Groups_Ocomm__monoid__mult(U_10291) ),
    inference(definitional_conversion,[status(esa)],[f_2799_2]) ).

cnf(f_2799_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10292,U_10291),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10292),U_10294),U_10293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10291),hAPP(U_10295,U_10294)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10292,U_10291),U_10295),U_10293))
    | hBOOL(hAPP(hAPP(c_member(U_10292),U_10294),U_10293))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10292),U_10293))
    | ~ class_Groups_Ocomm__monoid__mult(U_10291) ),
    inference(clausify,[status(thm)],[f_2799_3]) ).

fof(f_2800_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert]) ).

fof(f_2800_2,plain,
    ! [U_10300,U_10299,U_10298,U_10297,U_10296] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10297,U_10296),U_10300),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),U_10298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10296),hAPP(U_10300,U_10299)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10297,U_10296),U_10300),U_10298))
      | hBOOL(hAPP(hAPP(c_member(U_10297),U_10299),U_10298))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10297),U_10298))
      | ~ class_Groups_Ocomm__monoid__mult(U_10296) ),
    inference(variable_rename,[status(thm)],[f_2800_1]) ).

fof(f_2800_3,plain,
    ! [U_10296,U_10297,U_10298,U_10299,U_10300] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10297,U_10296),U_10300),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),U_10298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10296),hAPP(U_10300,U_10299)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10297,U_10296),U_10300),U_10298))
      | hBOOL(hAPP(hAPP(c_member(U_10297),U_10299),U_10298))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10297),U_10298))
      | ~ class_Groups_Ocomm__monoid__mult(U_10296) ),
    inference(definitional_conversion,[status(esa)],[f_2800_2]) ).

cnf(f_2800_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10297,U_10296),U_10300),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),U_10298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10296),hAPP(U_10300,U_10299)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10297,U_10296),U_10300),U_10298))
    | hBOOL(hAPP(hAPP(c_member(U_10297),U_10299),U_10298))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10297),U_10298))
    | ~ class_Groups_Ocomm__monoid__mult(U_10296) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

fof(f_2801_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter]) ).

fof(f_2801_2,plain,
    ! [U_10305,U_10304,U_10303,U_10302,U_10301] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10302,tc_HOL_Obool)),U_10303),U_10304))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10302,tc_HOL_Obool)),U_10303),U_10304))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),U_10303)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),U_10304))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10302),U_10304))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10302),U_10303))
      | ~ class_Groups_Ocomm__monoid__mult(U_10301) ),
    inference(variable_rename,[status(thm)],[f_2801_1]) ).

fof(f_2801_3,plain,
    ! [U_10302,U_10301,U_10303,U_10304,U_10305] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10302,tc_HOL_Obool)),U_10303),U_10304))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10302,tc_HOL_Obool)),U_10303),U_10304))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),U_10303)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),U_10304))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10302),U_10304))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10302),U_10303))
      | ~ class_Groups_Ocomm__monoid__mult(U_10301) ),
    inference(definitional_conversion,[status(esa)],[f_2801_2]) ).

cnf(f_2801_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10302,tc_HOL_Obool)),U_10303),U_10304))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10302,tc_HOL_Obool)),U_10303),U_10304))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),U_10303)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10302,U_10301),U_10305),U_10304))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10302),U_10304))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10302),U_10303))
    | ~ class_Groups_Ocomm__monoid__mult(U_10301) ),
    inference(clausify,[status(thm)],[f_2801_3]) ).

fof(f_2802_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int]) ).

fof(f_2802_2,plain,
    ! [U_10310,U_10309,U_10308,U_10307,U_10306] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10306),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10307,tc_HOL_Obool)),U_10308),U_10309))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10307,tc_HOL_Obool)),U_10308),U_10309))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10306),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),U_10308)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),U_10309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10307),U_10309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10307),U_10308))
      | ~ class_Groups_Ocomm__monoid__mult(U_10306) ),
    inference(variable_rename,[status(thm)],[f_2802_1]) ).

fof(f_2802_3,plain,
    ! [U_10306,U_10307,U_10308,U_10309,U_10310] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10306),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10307,tc_HOL_Obool)),U_10308),U_10309))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10307,tc_HOL_Obool)),U_10308),U_10309))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10306),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),U_10308)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),U_10309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10307),U_10309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10307),U_10308))
      | ~ class_Groups_Ocomm__monoid__mult(U_10306) ),
    inference(definitional_conversion,[status(esa)],[f_2802_2]) ).

cnf(f_2802_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10306),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10307,tc_HOL_Obool)),U_10308),U_10309))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10307,tc_HOL_Obool)),U_10308),U_10309))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10306),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),U_10308)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10307,U_10306),U_10310),U_10309))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10307),U_10309))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10307),U_10308))
    | ~ class_Groups_Ocomm__monoid__mult(U_10306) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

fof(f_2803_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).

fof(f_2803_2,plain,
    ! [U_10315,U_10314,U_10313,U_10312,U_10311] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10311,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,U_10312,U_10313)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,U_10314,U_10315)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10311),U_10312),U_10314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10311),U_10313),U_10315))
      | ~ class_Orderings_Olinorder(U_10311) ),
    inference(variable_rename,[status(thm)],[f_2803_1]) ).

fof(f_2803_3,plain,
    ! [U_10313,U_10311,U_10312,U_10314,U_10315] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10311,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,U_10312,U_10313)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,U_10314,U_10315)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10311),U_10312),U_10314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10311),U_10313),U_10315))
      | ~ class_Orderings_Olinorder(U_10311) ),
    inference(definitional_conversion,[status(esa)],[f_2803_2]) ).

cnf(f_2803_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10311,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,U_10312,U_10313)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,U_10314,U_10315)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10311,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10311),U_10312),U_10314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10311),U_10313),U_10315))
    | ~ class_Orderings_Olinorder(U_10311) ),
    inference(clausify,[status(thm)],[f_2803_3]) ).

fof(f_2804_1,plain,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove]) ).

fof(f_2804_2,plain,
    ! [U_10320,U_10319,U_10318,U_10317,U_10316] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10317,U_10316),U_10319),hAPP(hAPP(c_Set_Oinsert(U_10317),U_10320),U_10318)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10316),hAPP(U_10319,U_10320)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10317,U_10316),U_10319),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10317,tc_HOL_Obool)),U_10318),hAPP(hAPP(c_Set_Oinsert(U_10317),U_10320),c_Orderings_Obot__class_Obot(tc_fun(U_10317,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10317),U_10318))
      | ~ class_Groups_Ocomm__monoid__mult(U_10316) ),
    inference(variable_rename,[status(thm)],[f_2804_1]) ).

fof(f_2804_3,plain,
    ! [U_10316,U_10317,U_10318,U_10319,U_10320] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10317,U_10316),U_10319),hAPP(hAPP(c_Set_Oinsert(U_10317),U_10320),U_10318)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10316),hAPP(U_10319,U_10320)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10317,U_10316),U_10319),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10317,tc_HOL_Obool)),U_10318),hAPP(hAPP(c_Set_Oinsert(U_10317),U_10320),c_Orderings_Obot__class_Obot(tc_fun(U_10317,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10317),U_10318))
      | ~ class_Groups_Ocomm__monoid__mult(U_10316) ),
    inference(definitional_conversion,[status(esa)],[f_2804_2]) ).

cnf(f_2804_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10317,U_10316),U_10319),hAPP(hAPP(c_Set_Oinsert(U_10317),U_10320),U_10318)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10316),hAPP(U_10319,U_10320)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10317,U_10316),U_10319),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10317,tc_HOL_Obool)),U_10318),hAPP(hAPP(c_Set_Oinsert(U_10317),U_10320),c_Orderings_Obot__class_Obot(tc_fun(U_10317,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10317),U_10318))
    | ~ class_Groups_Ocomm__monoid__mult(U_10316) ),
    inference(clausify,[status(thm)],[f_2804_3]) ).

fof(f_2805_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint]) ).

fof(f_2805_2,plain,
    ! [U_10325,U_10324,U_10323,U_10322,U_10321] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10322,tc_HOL_Obool)),U_10323),U_10324)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),U_10323)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),U_10324))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10322,tc_HOL_Obool)),U_10323),U_10324) != c_Orderings_Obot__class_Obot(tc_fun(U_10322,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10323))
      | ~ class_Groups_Ocomm__monoid__mult(U_10321) ),
    inference(variable_rename,[status(thm)],[f_2805_1]) ).

fof(f_2805_3,plain,
    ! [U_10322,U_10321,U_10323,U_10324,U_10325] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10322,tc_HOL_Obool)),U_10323),U_10324)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),U_10323)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),U_10324))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10322,tc_HOL_Obool)),U_10323),U_10324) != c_Orderings_Obot__class_Obot(tc_fun(U_10322,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10323))
      | ~ class_Groups_Ocomm__monoid__mult(U_10321) ),
    inference(definitional_conversion,[status(esa)],[f_2805_2]) ).

cnf(f_2805_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10322,tc_HOL_Obool)),U_10323),U_10324)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),U_10323)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10322,U_10321),U_10325),U_10324))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10322,tc_HOL_Obool)),U_10323),U_10324) != c_Orderings_Obot__class_Obot(tc_fun(U_10322,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10324))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10323))
    | ~ class_Groups_Ocomm__monoid__mult(U_10321) ),
    inference(clausify,[status(thm)],[f_2805_3]) ).

fof(f_2806_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint]) ).

fof(f_2806_2,plain,
    ! [U_10330,U_10329,U_10328,U_10327,U_10326] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10327,tc_HOL_Obool)),U_10328),U_10329)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),U_10328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),U_10329))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10327,tc_HOL_Obool)),U_10328),U_10329) != c_Orderings_Obot__class_Obot(tc_fun(U_10327,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10327),U_10329))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10327),U_10328))
      | ~ class_Groups_Ocomm__monoid__mult(U_10326) ),
    inference(variable_rename,[status(thm)],[f_2806_1]) ).

fof(f_2806_3,plain,
    ! [U_10326,U_10327,U_10328,U_10329,U_10330] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10327,tc_HOL_Obool)),U_10328),U_10329)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),U_10328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),U_10329))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10327,tc_HOL_Obool)),U_10328),U_10329) != c_Orderings_Obot__class_Obot(tc_fun(U_10327,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10327),U_10329))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10327),U_10328))
      | ~ class_Groups_Ocomm__monoid__mult(U_10326) ),
    inference(definitional_conversion,[status(esa)],[f_2806_2]) ).

cnf(f_2806_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10327,tc_HOL_Obool)),U_10328),U_10329)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),U_10328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10327,U_10326),U_10330),U_10329))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10327,tc_HOL_Obool)),U_10328),U_10329) != c_Orderings_Obot__class_Obot(tc_fun(U_10327,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10327),U_10329))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10327),U_10328))
    | ~ class_Groups_Ocomm__monoid__mult(U_10326) ),
    inference(clausify,[status(thm)],[f_2806_3]) ).

fof(f_2807_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oremove]) ).

fof(f_2807_2,plain,
    ! [U_10335,U_10334,U_10333,U_10332,U_10331] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10332,U_10331),U_10335),U_10333) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10331),hAPP(U_10335,U_10334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10332,U_10331),U_10335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10332,tc_HOL_Obool)),U_10333),hAPP(hAPP(c_Set_Oinsert(U_10332),U_10334),c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10332),U_10334),U_10333))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10333))
      | ~ class_Groups_Ocomm__monoid__mult(U_10331) ),
    inference(variable_rename,[status(thm)],[f_2807_1]) ).

fof(f_2807_3,plain,
    ! [U_10331,U_10332,U_10333,U_10334,U_10335] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10332,U_10331),U_10335),U_10333) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10331),hAPP(U_10335,U_10334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10332,U_10331),U_10335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10332,tc_HOL_Obool)),U_10333),hAPP(hAPP(c_Set_Oinsert(U_10332),U_10334),c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10332),U_10334),U_10333))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10333))
      | ~ class_Groups_Ocomm__monoid__mult(U_10331) ),
    inference(definitional_conversion,[status(esa)],[f_2807_2]) ).

cnf(f_2807_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10332,U_10331),U_10335),U_10333) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10331),hAPP(U_10335,U_10334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10332,U_10331),U_10335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10332,tc_HOL_Obool)),U_10333),hAPP(hAPP(c_Set_Oinsert(U_10332),U_10334),c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10332),U_10334),U_10333))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10333))
    | ~ class_Groups_Ocomm__monoid__mult(U_10331) ),
    inference(clausify,[status(thm)],[f_2807_3]) ).

fof(f_2808_1,plain,
    ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
      | hAPP(V_f_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Fields_Ofield(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__diff1]) ).

fof(f_2808_2,plain,
    ! [U_10340,U_10339,U_10338,U_10337,U_10336] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10337,tc_HOL_Obool)),U_10338),hAPP(hAPP(c_Set_Oinsert(U_10337),U_10340),c_Orderings_Obot__class_Obot(tc_fun(U_10337,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),U_10338)
          | hBOOL(hAPP(hAPP(c_member(U_10337),U_10340),U_10338)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10337,tc_HOL_Obool)),U_10338),hAPP(hAPP(c_Set_Oinsert(U_10337),U_10340),c_Orderings_Obot__class_Obot(tc_fun(U_10337,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10336),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),U_10338)),hAPP(U_10339,U_10340))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10337),U_10340),U_10338)) ) )
      | hAPP(U_10339,U_10340) = c_Groups_Ozero__class_Ozero(U_10336)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10337),U_10338))
      | ~ class_Fields_Ofield(U_10336) ),
    inference(variable_rename,[status(thm)],[f_2808_1]) ).

fof(f_2808_3,plain,
    ( ! [U_10337,U_10336,U_10338,U_10339,U_10340] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10337,tc_HOL_Obool)),U_10338),hAPP(hAPP(c_Set_Oinsert(U_10337),U_10340),c_Orderings_Obot__class_Obot(tc_fun(U_10337,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),U_10338)
        | hBOOL(hAPP(hAPP(c_member(U_10337),U_10340),U_10338))
        | ~ sP804(U_10337,U_10336,U_10338,U_10339,U_10340) )
    & ! [U_10337,U_10336,U_10338,U_10339,U_10340] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10337,tc_HOL_Obool)),U_10338),hAPP(hAPP(c_Set_Oinsert(U_10337),U_10340),c_Orderings_Obot__class_Obot(tc_fun(U_10337,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10336),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),U_10338)),hAPP(U_10339,U_10340))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10337),U_10340),U_10338))
        | ~ sP804(U_10337,U_10336,U_10338,U_10339,U_10340) )
    & ! [U_10337,U_10336,U_10338,U_10339,U_10340] :
        ( sP804(U_10337,U_10336,U_10338,U_10339,U_10340)
        | hAPP(U_10339,U_10340) = c_Groups_Ozero__class_Ozero(U_10336)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10337),U_10338))
        | ~ class_Fields_Ofield(U_10336) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP804])],[f_2808_2]) ).

cnf(f_2808_4,plain,
    ( sP804(U_10337,U_10336,U_10338,U_10339,U_10340)
    | hAPP(U_10339,U_10340) = c_Groups_Ozero__class_Ozero(U_10336)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10337),U_10338))
    | ~ class_Fields_Ofield(U_10336) ),
    inference(clausify,[status(thm)],[f_2808_3]) ).

cnf(f_2808_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10337,tc_HOL_Obool)),U_10338),hAPP(hAPP(c_Set_Oinsert(U_10337),U_10340),c_Orderings_Obot__class_Obot(tc_fun(U_10337,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10336),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),U_10338)),hAPP(U_10339,U_10340))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10337),U_10340),U_10338))
    | ~ sP804(U_10337,U_10336,U_10338,U_10339,U_10340) ),
    inference(clausify,[status(thm)],[f_2808_3]) ).

cnf(f_2808_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10337,tc_HOL_Obool)),U_10338),hAPP(hAPP(c_Set_Oinsert(U_10337),U_10340),c_Orderings_Obot__class_Obot(tc_fun(U_10337,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10337,U_10336),U_10339),U_10338)
    | hBOOL(hAPP(hAPP(c_member(U_10337),U_10340),U_10338))
    | ~ sP804(U_10337,U_10336,U_10338,U_10339,U_10340) ),
    inference(clausify,[status(thm)],[f_2808_3]) ).

fof(f_2809_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Fields_Ofield(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un]) ).

fof(f_2809_2,plain,
    ! [U_10346,U_10345,U_10344,U_10343,U_10342] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10342),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10344)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10345))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)))
      | ? [U_10341] :
          ( hAPP(U_10346,U_10341) = c_Groups_Ozero__class_Ozero(U_10342)
          & hBOOL(hAPP(hAPP(c_member(U_10343),U_10341),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10345))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10344))
      | ~ class_Fields_Ofield(U_10342) ),
    inference(variable_rename,[status(thm)],[f_2809_1]) ).

fof(f_2809_3,plain,
    ! [U_10346,U_10345,U_10344,U_10343,U_10342] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10342),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10344)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10345))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)))
      | ( hAPP(U_10346,sK161(U_10346,U_10345,U_10344,U_10343,U_10342)) = c_Groups_Ozero__class_Ozero(U_10342)
        & hBOOL(hAPP(hAPP(c_member(U_10343),sK161(U_10346,U_10345,U_10344,U_10343,U_10342)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10345))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10344))
      | ~ class_Fields_Ofield(U_10342) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_10341,sK161(U_10346,U_10345,U_10344,U_10343,U_10342))],[f_2809_2]) ).

fof(f_2809_4,plain,
    ( ! [U_10342,U_10344,U_10343,U_10345,U_10346] :
        ( hAPP(U_10346,sK161(U_10346,U_10345,U_10344,U_10343,U_10342)) = c_Groups_Ozero__class_Ozero(U_10342)
        | ~ sP805(U_10342,U_10344,U_10343,U_10345,U_10346) )
    & ! [U_10342,U_10344,U_10343,U_10345,U_10346] :
        ( hBOOL(hAPP(hAPP(c_member(U_10343),sK161(U_10346,U_10345,U_10344,U_10343,U_10342)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)))
        | ~ sP805(U_10342,U_10344,U_10343,U_10345,U_10346) )
    & ! [U_10342,U_10344,U_10343,U_10345,U_10346] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10342),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10344)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10345))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)))
        | sP805(U_10342,U_10344,U_10343,U_10345,U_10346)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10345))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10344))
        | ~ class_Fields_Ofield(U_10342) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP805])],[f_2809_3]) ).

cnf(f_2809_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10342),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10344)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),U_10345))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10343,U_10342),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)))
    | sP805(U_10342,U_10344,U_10343,U_10345,U_10346)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10345))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10343),U_10344))
    | ~ class_Fields_Ofield(U_10342) ),
    inference(clausify,[status(thm)],[f_2809_4]) ).

cnf(f_2809_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10343),sK161(U_10346,U_10345,U_10344,U_10343,U_10342)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10343,tc_HOL_Obool)),U_10344),U_10345)))
    | ~ sP805(U_10342,U_10344,U_10343,U_10345,U_10346) ),
    inference(clausify,[status(thm)],[f_2809_4]) ).

cnf(f_2809_7,plain,
    ( hAPP(U_10346,sK161(U_10346,U_10345,U_10344,U_10343,U_10342)) = c_Groups_Ozero__class_Ozero(U_10342)
    | ~ sP805(U_10342,U_10344,U_10343,U_10345,U_10346) ),
    inference(clausify,[status(thm)],[f_2809_4]) ).

fof(f_2810_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral]) ).

fof(f_2810_2,plain,
    ! [U_10352,U_10351,U_10350,U_10349,U_10348] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10348),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10350)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10351))
      | ? [U_10347] :
          ( hAPP(U_10352,U_10347) != c_Groups_Oone__class_Oone(U_10348)
          & hBOOL(hAPP(hAPP(c_member(U_10349),U_10347),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10351))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10350))
      | ~ class_Groups_Ocomm__monoid__mult(U_10348) ),
    inference(variable_rename,[status(thm)],[f_2810_1]) ).

fof(f_2810_3,plain,
    ! [U_10352,U_10351,U_10350,U_10349,U_10348] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10348),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10350)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10351))
      | ( hAPP(U_10352,sK162(U_10352,U_10351,U_10350,U_10349,U_10348)) != c_Groups_Oone__class_Oone(U_10348)
        & hBOOL(hAPP(hAPP(c_member(U_10349),sK162(U_10352,U_10351,U_10350,U_10349,U_10348)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10351))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10350))
      | ~ class_Groups_Ocomm__monoid__mult(U_10348) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_10347,sK162(U_10352,U_10351,U_10350,U_10349,U_10348))],[f_2810_2]) ).

fof(f_2810_4,plain,
    ( ! [U_10350,U_10348,U_10351,U_10349,U_10352] :
        ( hAPP(U_10352,sK162(U_10352,U_10351,U_10350,U_10349,U_10348)) != c_Groups_Oone__class_Oone(U_10348)
        | ~ sP806(U_10350,U_10348,U_10351,U_10349,U_10352) )
    & ! [U_10350,U_10348,U_10351,U_10349,U_10352] :
        ( hBOOL(hAPP(hAPP(c_member(U_10349),sK162(U_10352,U_10351,U_10350,U_10349,U_10348)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351)))
        | ~ sP806(U_10350,U_10348,U_10351,U_10349,U_10352) )
    & ! [U_10350,U_10348,U_10351,U_10349,U_10352] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10348),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10350)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10351))
        | sP806(U_10350,U_10348,U_10351,U_10349,U_10352)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10351))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10350))
        | ~ class_Groups_Ocomm__monoid__mult(U_10348) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP806])],[f_2810_3]) ).

cnf(f_2810_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10348),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10350)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10349,U_10348),U_10352),U_10351))
    | sP806(U_10350,U_10348,U_10351,U_10349,U_10352)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10351))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10349),U_10350))
    | ~ class_Groups_Ocomm__monoid__mult(U_10348) ),
    inference(clausify,[status(thm)],[f_2810_4]) ).

cnf(f_2810_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10349),sK162(U_10352,U_10351,U_10350,U_10349,U_10348)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10349,tc_HOL_Obool)),U_10350),U_10351)))
    | ~ sP806(U_10350,U_10348,U_10351,U_10349,U_10352) ),
    inference(clausify,[status(thm)],[f_2810_4]) ).

cnf(f_2810_7,plain,
    ( hAPP(U_10352,sK162(U_10352,U_10351,U_10350,U_10349,U_10348)) != c_Groups_Oone__class_Oone(U_10348)
    | ~ sP806(U_10350,U_10348,U_10351,U_10349,U_10352) ),
    inference(clausify,[status(thm)],[f_2810_4]) ).

fof(f_2811_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__one]) ).

fof(f_2811_2,plain,
    ! [U_10358,U_10357,U_10356,U_10355,U_10354] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10354),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10356)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10357))
      | ? [U_10353] :
          ( hAPP(U_10358,U_10353) != c_Groups_Oone__class_Oone(U_10354)
          & hBOOL(hAPP(hAPP(c_member(U_10355),U_10353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10357))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10356))
      | ~ class_Groups_Ocomm__monoid__mult(U_10354) ),
    inference(variable_rename,[status(thm)],[f_2811_1]) ).

fof(f_2811_3,plain,
    ! [U_10358,U_10357,U_10356,U_10355,U_10354] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10354),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10356)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10357))
      | ( hAPP(U_10358,sK163(U_10358,U_10357,U_10356,U_10355,U_10354)) != c_Groups_Oone__class_Oone(U_10354)
        & hBOOL(hAPP(hAPP(c_member(U_10355),sK163(U_10358,U_10357,U_10356,U_10355,U_10354)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10357))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10356))
      | ~ class_Groups_Ocomm__monoid__mult(U_10354) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_10353,sK163(U_10358,U_10357,U_10356,U_10355,U_10354))],[f_2811_2]) ).

fof(f_2811_4,plain,
    ( ! [U_10354,U_10355,U_10356,U_10357,U_10358] :
        ( hAPP(U_10358,sK163(U_10358,U_10357,U_10356,U_10355,U_10354)) != c_Groups_Oone__class_Oone(U_10354)
        | ~ sP807(U_10354,U_10355,U_10356,U_10357,U_10358) )
    & ! [U_10354,U_10355,U_10356,U_10357,U_10358] :
        ( hBOOL(hAPP(hAPP(c_member(U_10355),sK163(U_10358,U_10357,U_10356,U_10355,U_10354)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357)))
        | ~ sP807(U_10354,U_10355,U_10356,U_10357,U_10358) )
    & ! [U_10354,U_10355,U_10356,U_10357,U_10358] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10354),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10356)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10357))
        | sP807(U_10354,U_10355,U_10356,U_10357,U_10358)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10357))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10356))
        | ~ class_Groups_Ocomm__monoid__mult(U_10354) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP807])],[f_2811_3]) ).

cnf(f_2811_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10354),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10356)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10355,U_10354),U_10358),U_10357))
    | sP807(U_10354,U_10355,U_10356,U_10357,U_10358)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10357))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10355),U_10356))
    | ~ class_Groups_Ocomm__monoid__mult(U_10354) ),
    inference(clausify,[status(thm)],[f_2811_4]) ).

cnf(f_2811_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10355),sK163(U_10358,U_10357,U_10356,U_10355,U_10354)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10355,tc_HOL_Obool)),U_10356),U_10357)))
    | ~ sP807(U_10354,U_10355,U_10356,U_10357,U_10358) ),
    inference(clausify,[status(thm)],[f_2811_4]) ).

cnf(f_2811_7,plain,
    ( hAPP(U_10358,sK163(U_10358,U_10357,U_10356,U_10355,U_10354)) != c_Groups_Oone__class_Oone(U_10354)
    | ~ sP807(U_10354,U_10355,U_10356,U_10357,U_10358) ),
    inference(clausify,[status(thm)],[f_2811_4]) ).

fof(f_2812_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan]) ).

fof(f_2812_2,plain,
    ! [U_10360,U_10359] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10359,U_10360))),
    inference(variable_rename,[status(thm)],[f_2812_1]) ).

fof(f_2812_3,plain,
    ! [U_10360,U_10359] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10359,U_10360))),
    inference(definitional_conversion,[status(esa)],[f_2812_2]) ).

cnf(f_2812_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10359,U_10360))),
    inference(clausify,[status(thm)],[f_2812_3]) ).

fof(f_2813_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanLessThan]) ).

fof(f_2813_2,plain,
    ! [U_10362,U_10361] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10361,U_10362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10362),hAPP(c_Nat_OSuc,U_10361)),
    inference(variable_rename,[status(thm)],[f_2813_1]) ).

fof(f_2813_3,plain,
    ! [U_10362,U_10361] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10361,U_10362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10362),hAPP(c_Nat_OSuc,U_10361)),
    inference(definitional_conversion,[status(esa)],[f_2813_2]) ).

cnf(f_2813_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10361,U_10362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10362),hAPP(c_Nat_OSuc,U_10361)),
    inference(clausify,[status(thm)],[f_2813_3]) ).

fof(f_2814_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2))
      | ? [B_x] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J]) ).

fof(f_2814_2,plain,
    ! [U_10366,U_10365,U_10364] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Int_Oint),U_10366),U_10365) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10364),c_Int_Onat),U_10366)),U_10365))
      | ? [U_10363] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10366,U_10363))
          & hBOOL(hAPP(hAPP(c_member(U_10364),U_10363),U_10365)) ) ),
    inference(variable_rename,[status(thm)],[f_2814_1]) ).

fof(f_2814_3,plain,
    ! [U_10366,U_10365,U_10364] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Int_Oint),U_10366),U_10365) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10364),c_Int_Onat),U_10366)),U_10365))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10366,sK164(U_10366,U_10365,U_10364)))
        & hBOOL(hAPP(hAPP(c_member(U_10364),sK164(U_10366,U_10365,U_10364)),U_10365)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_10363,sK164(U_10366,U_10365,U_10364))],[f_2814_2]) ).

fof(f_2814_4,plain,
    ( ! [U_10364,U_10365,U_10366] :
        ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10366,sK164(U_10366,U_10365,U_10364)))
        | ~ sP808(U_10364,U_10365,U_10366) )
    & ! [U_10364,U_10365,U_10366] :
        ( hBOOL(hAPP(hAPP(c_member(U_10364),sK164(U_10366,U_10365,U_10364)),U_10365))
        | ~ sP808(U_10364,U_10365,U_10366) )
    & ! [U_10364,U_10365,U_10366] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Int_Oint),U_10366),U_10365) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10364),c_Int_Onat),U_10366)),U_10365))
        | sP808(U_10364,U_10365,U_10366) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP808])],[f_2814_3]) ).

cnf(f_2814_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Int_Oint),U_10366),U_10365) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10364,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10364),c_Int_Onat),U_10366)),U_10365))
    | sP808(U_10364,U_10365,U_10366) ),
    inference(clausify,[status(thm)],[f_2814_4]) ).

cnf(f_2814_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10364),sK164(U_10366,U_10365,U_10364)),U_10365))
    | ~ sP808(U_10364,U_10365,U_10366) ),
    inference(clausify,[status(thm)],[f_2814_4]) ).

cnf(f_2814_7,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10366,sK164(U_10366,U_10365,U_10364)))
    | ~ sP808(U_10364,U_10365,U_10366) ),
    inference(clausify,[status(thm)],[f_2814_4]) ).

fof(f_2815_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J]) ).

fof(f_2815_2,plain,
    ! [U_10369,U_10368,U_10367] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10367,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10367,U_10368,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10367),U_10369),c_Orderings_Obot__class_Obot(tc_fun(U_10367,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10367,U_10368,U_10369)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10367),U_10368),U_10369))
      | ~ class_Orderings_Olinorder(U_10367) ),
    inference(variable_rename,[status(thm)],[f_2815_1]) ).

fof(f_2815_3,plain,
    ! [U_10367,U_10368,U_10369] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10367,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10367,U_10368,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10367),U_10369),c_Orderings_Obot__class_Obot(tc_fun(U_10367,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10367,U_10368,U_10369)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10367),U_10368),U_10369))
      | ~ class_Orderings_Olinorder(U_10367) ),
    inference(definitional_conversion,[status(esa)],[f_2815_2]) ).

cnf(f_2815_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10367,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10367,U_10368,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10367),U_10369),c_Orderings_Obot__class_Obot(tc_fun(U_10367,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10367,U_10368,U_10369)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10367),U_10368),U_10369))
    | ~ class_Orderings_Olinorder(U_10367) ),
    inference(clausify,[status(thm)],[f_2815_3]) ).

fof(f_2816_1,plain,
    ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_quotient__def]) ).

fof(f_2816_2,plain,
    ! [U_10372,U_10371,U_10370] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10370),U_10371),U_10372) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10370,tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),U_10371),hAPP(hAPP(c_COMBC(U_10370,tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10370,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),U_10370),c_Set_Oinsert(tc_fun(U_10370,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10370,tc_HOL_Obool),tc_fun(U_10370,tc_HOL_Obool),U_10370),c_Relation_OImage(U_10370,U_10370,U_10372)),hAPP(hAPP(c_COMBC(U_10370,tc_fun(U_10370,tc_HOL_Obool),tc_fun(U_10370,tc_HOL_Obool)),c_Set_Oinsert(U_10370)),c_Orderings_Obot__class_Obot(tc_fun(U_10370,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2816_1]) ).

fof(f_2816_3,plain,
    ! [U_10370,U_10371,U_10372] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10370),U_10371),U_10372) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10370,tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),U_10371),hAPP(hAPP(c_COMBC(U_10370,tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10370,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),U_10370),c_Set_Oinsert(tc_fun(U_10370,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10370,tc_HOL_Obool),tc_fun(U_10370,tc_HOL_Obool),U_10370),c_Relation_OImage(U_10370,U_10370,U_10372)),hAPP(hAPP(c_COMBC(U_10370,tc_fun(U_10370,tc_HOL_Obool),tc_fun(U_10370,tc_HOL_Obool)),c_Set_Oinsert(U_10370)),c_Orderings_Obot__class_Obot(tc_fun(U_10370,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2816_2]) ).

cnf(f_2816_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10370),U_10371),U_10372) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10370,tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),U_10371),hAPP(hAPP(c_COMBC(U_10370,tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10370,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)),U_10370),c_Set_Oinsert(tc_fun(U_10370,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10370,tc_HOL_Obool),tc_fun(U_10370,tc_HOL_Obool),U_10370),c_Relation_OImage(U_10370,U_10370,U_10372)),hAPP(hAPP(c_COMBC(U_10370,tc_fun(U_10370,tc_HOL_Obool),tc_fun(U_10370,tc_HOL_Obool)),c_Set_Oinsert(U_10370)),c_Orderings_Obot__class_Obot(tc_fun(U_10370,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10370,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2816_3]) ).

fof(f_2817_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanAtMost]) ).

fof(f_2817_2,plain,
    ! [U_10374,U_10373] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10373,U_10374))),
    inference(variable_rename,[status(thm)],[f_2817_1]) ).

fof(f_2817_3,plain,
    ! [U_10373,U_10374] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10373,U_10374))),
    inference(definitional_conversion,[status(esa)],[f_2817_2]) ).

cnf(f_2817_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10373,U_10374))),
    inference(clausify,[status(thm)],[f_2817_3]) ).

fof(f_2818_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).

fof(f_2818_2,plain,
    ! [U_10376,U_10375] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10375,U_10376))),
    inference(variable_rename,[status(thm)],[f_2818_1]) ).

fof(f_2818_3,plain,
    ! [U_10375,U_10376] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10375,U_10376))),
    inference(definitional_conversion,[status(esa)],[f_2818_2]) ).

cnf(f_2818_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10375,U_10376))),
    inference(clausify,[status(thm)],[f_2818_3]) ).

fof(f_2819_1,plain,
    ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP1__I]) ).

fof(f_2819_2,plain,
    ! [U_10382,U_10381,U_10380,U_10379,U_10378,U_10377] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10377,tc_fun(U_10382,tc_HOL_Obool)),U_10379),U_10380),U_10381))
      | ~ hBOOL(hAPP(hAPP(U_10380,U_10378),U_10381))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10377),U_10378),U_10379)) ),
    inference(variable_rename,[status(thm)],[f_2819_1]) ).

fof(f_2819_3,plain,
    ! [U_10377,U_10378,U_10379,U_10380,U_10381,U_10382] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10377,tc_fun(U_10382,tc_HOL_Obool)),U_10379),U_10380),U_10381))
      | ~ hBOOL(hAPP(hAPP(U_10380,U_10378),U_10381))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10377),U_10378),U_10379)) ),
    inference(definitional_conversion,[status(esa)],[f_2819_2]) ).

cnf(f_2819_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10377,tc_fun(U_10382,tc_HOL_Obool)),U_10379),U_10380),U_10381))
    | ~ hBOOL(hAPP(hAPP(U_10380,U_10378),U_10381))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10377),U_10378),U_10379)) ),
    inference(clausify,[status(thm)],[f_2819_3]) ).

fof(f_2820_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP1__iff]) ).

fof(f_2820_2,plain,
    ! [U_10389,U_10388,U_10387,U_10386,U_10385] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10385,tc_fun(U_10386,tc_HOL_Obool)),U_10387),U_10388),U_10389))
        | ! [U_10384] :
            ( ~ hBOOL(hAPP(hAPP(U_10388,U_10384),U_10389))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10385),U_10384),U_10387)) ) )
      & ( ? [U_10383] :
            ( hBOOL(hAPP(hAPP(U_10388,U_10383),U_10389))
            & hBOOL(hAPP(hAPP(c_member(U_10385),U_10383),U_10387)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10385,tc_fun(U_10386,tc_HOL_Obool)),U_10387),U_10388),U_10389)) ) ),
    inference(variable_rename,[status(thm)],[f_2820_1]) ).

fof(f_2820_3,plain,
    ( ! [U_10399,U_10397,U_10395,U_10393,U_10391] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10391,tc_fun(U_10393,tc_HOL_Obool)),U_10395),U_10397),U_10399))
        | ! [U_10384] :
            ( ~ hBOOL(hAPP(hAPP(U_10397,U_10384),U_10399))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10391),U_10384),U_10395)) ) )
    & ! [U_10398,U_10396,U_10394,U_10392,U_10390] :
        ( ? [U_10383] :
            ( hBOOL(hAPP(hAPP(U_10396,U_10383),U_10398))
            & hBOOL(hAPP(hAPP(c_member(U_10390),U_10383),U_10394)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10394),U_10396),U_10398)) ) ),
    inference(miniscope,[status(thm)],[f_2820_2]) ).

fof(f_2820_4,plain,
    ( ! [U_10399,U_10397,U_10395,U_10393,U_10391] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10391,tc_fun(U_10393,tc_HOL_Obool)),U_10395),U_10397),U_10399))
        | ! [U_10384] :
            ( ~ hBOOL(hAPP(hAPP(U_10397,U_10384),U_10399))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10391),U_10384),U_10395)) ) )
    & ! [U_10398,U_10396,U_10394,U_10392,U_10390] :
        ( ( hBOOL(hAPP(hAPP(U_10396,sK165(U_10398,U_10396,U_10394,U_10392,U_10390)),U_10398))
          & hBOOL(hAPP(hAPP(c_member(U_10390),sK165(U_10398,U_10396,U_10394,U_10392,U_10390)),U_10394)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10394),U_10396),U_10398)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_10383,sK165(U_10398,U_10396,U_10394,U_10392,U_10390))],[f_2820_3]) ).

fof(f_2820_5,plain,
    ( ! [U_10396,U_10392,U_10394,U_10390,U_10398] :
        ( hBOOL(hAPP(hAPP(U_10396,sK165(U_10398,U_10396,U_10394,U_10392,U_10390)),U_10398))
        | ~ sP809(U_10396,U_10392,U_10394,U_10390,U_10398) )
    & ! [U_10396,U_10392,U_10394,U_10390,U_10398] :
        ( hBOOL(hAPP(hAPP(c_member(U_10390),sK165(U_10398,U_10396,U_10394,U_10392,U_10390)),U_10394))
        | ~ sP809(U_10396,U_10392,U_10394,U_10390,U_10398) )
    & ! [U_10384,U_10391,U_10393,U_10397,U_10395,U_10399] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10391,tc_fun(U_10393,tc_HOL_Obool)),U_10395),U_10397),U_10399))
        | ~ hBOOL(hAPP(hAPP(U_10397,U_10384),U_10399))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10391),U_10384),U_10395)) )
    & ! [U_10396,U_10392,U_10394,U_10390,U_10398] :
        ( sP809(U_10396,U_10392,U_10394,U_10390,U_10398)
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10394),U_10396),U_10398)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP809])],[f_2820_4]) ).

cnf(f_2820_6,plain,
    ( sP809(U_10396,U_10392,U_10394,U_10390,U_10398)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10394),U_10396),U_10398)) ),
    inference(clausify,[status(thm)],[f_2820_5]) ).

cnf(f_2820_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10391,tc_fun(U_10393,tc_HOL_Obool)),U_10395),U_10397),U_10399))
    | ~ hBOOL(hAPP(hAPP(U_10397,U_10384),U_10399))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10391),U_10384),U_10395)) ),
    inference(clausify,[status(thm)],[f_2820_5]) ).

cnf(f_2820_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10390),sK165(U_10398,U_10396,U_10394,U_10392,U_10390)),U_10394))
    | ~ sP809(U_10396,U_10392,U_10394,U_10390,U_10398) ),
    inference(clausify,[status(thm)],[f_2820_5]) ).

cnf(f_2820_9,plain,
    ( hBOOL(hAPP(hAPP(U_10396,sK165(U_10398,U_10396,U_10394,U_10392,U_10390)),U_10398))
    | ~ sP809(U_10396,U_10392,U_10394,U_10390,U_10398) ),
    inference(clausify,[status(thm)],[f_2820_5]) ).

fof(f_2821_1,plain,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__UN]) ).

fof(f_2821_2,plain,
    ! [U_10405,U_10404,U_10403,U_10402,U_10401,U_10400] : hAPP(c_Relation_OImage(U_10400,U_10401,U_10402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10403,tc_fun(U_10400,tc_HOL_Obool)),U_10404),U_10405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10403,tc_fun(U_10401,tc_HOL_Obool)),U_10404),hAPP(hAPP(c_COMBB(tc_fun(U_10400,tc_HOL_Obool),tc_fun(U_10401,tc_HOL_Obool),U_10403),c_Relation_OImage(U_10400,U_10401,U_10402)),U_10405)),
    inference(variable_rename,[status(thm)],[f_2821_1]) ).

fof(f_2821_3,plain,
    ! [U_10401,U_10400,U_10402,U_10403,U_10404,U_10405] : hAPP(c_Relation_OImage(U_10400,U_10401,U_10402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10403,tc_fun(U_10400,tc_HOL_Obool)),U_10404),U_10405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10403,tc_fun(U_10401,tc_HOL_Obool)),U_10404),hAPP(hAPP(c_COMBB(tc_fun(U_10400,tc_HOL_Obool),tc_fun(U_10401,tc_HOL_Obool),U_10403),c_Relation_OImage(U_10400,U_10401,U_10402)),U_10405)),
    inference(definitional_conversion,[status(esa)],[f_2821_2]) ).

cnf(f_2821_4,plain,
    hAPP(c_Relation_OImage(U_10400,U_10401,U_10402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10403,tc_fun(U_10400,tc_HOL_Obool)),U_10404),U_10405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10403,tc_fun(U_10401,tc_HOL_Obool)),U_10404),hAPP(hAPP(c_COMBB(tc_fun(U_10400,tc_HOL_Obool),tc_fun(U_10401,tc_HOL_Obool),U_10403),c_Relation_OImage(U_10400,U_10401,U_10402)),U_10405)),
    inference(clausify,[status(thm)],[f_2821_3]) ).

fof(f_2822_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UN]) ).

fof(f_2822_2,plain,
    ! [U_10411,U_10410,U_10409,U_10408] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411)))
          | ? [U_10407] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,U_10407)))
              & hBOOL(hAPP(hAPP(c_member(U_10408),U_10407),U_10409)) ) )
        & ( ! [U_10406] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,U_10406)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10408),U_10406),U_10409)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ),
    inference(variable_rename,[status(thm)],[f_2822_1]) ).

fof(f_2822_3,plain,
    ! [U_10411,U_10410,U_10409,U_10408] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411)))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,sK166(U_10411,U_10410,U_10409,U_10408))))
            & hBOOL(hAPP(hAPP(c_member(U_10408),sK166(U_10411,U_10410,U_10409,U_10408)),U_10409)) ) )
        & ( ! [U_10406] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,U_10406)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10408),U_10406),U_10409)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_10407,sK166(U_10411,U_10410,U_10409,U_10408))],[f_2822_2]) ).

fof(f_2822_4,plain,
    ( ! [U_10408,U_10409,U_10410,U_10411] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,sK166(U_10411,U_10410,U_10409,U_10408))))
        | ~ sP810(U_10408,U_10409,U_10410,U_10411) )
    & ! [U_10408,U_10409,U_10410,U_10411] :
        ( hBOOL(hAPP(hAPP(c_member(U_10408),sK166(U_10411,U_10410,U_10409,U_10408)),U_10409))
        | ~ sP810(U_10408,U_10409,U_10410,U_10411) )
    & ! [U_10406,U_10408,U_10409,U_10410,U_10411] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411)))
        | sP810(U_10408,U_10409,U_10410,U_10411)
        | ~ sP811(U_10406,U_10408,U_10409,U_10410,U_10411) )
    & ! [U_10406,U_10408,U_10409,U_10410,U_10411] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,U_10406)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10408),U_10406),U_10409))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411)))
        | ~ sP811(U_10406,U_10408,U_10409,U_10410,U_10411) )
    & ! [U_10406,U_10408,U_10409,U_10410,U_10411] :
        ( sP811(U_10406,U_10408,U_10409,U_10410,U_10411)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP810,sP811])],[f_2822_3]) ).

cnf(f_2822_5,plain,
    ( sP811(U_10406,U_10408,U_10409,U_10410,U_10411)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ),
    inference(clausify,[status(thm)],[f_2822_4]) ).

cnf(f_2822_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,U_10406)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10408),U_10406),U_10409))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411)))
    | ~ sP811(U_10406,U_10408,U_10409,U_10410,U_10411) ),
    inference(clausify,[status(thm)],[f_2822_4]) ).

cnf(f_2822_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10408,tc_fun(U_10410,tc_HOL_Obool)),U_10409),U_10411)))
    | sP810(U_10408,U_10409,U_10410,U_10411)
    | ~ sP811(U_10406,U_10408,U_10409,U_10410,U_10411) ),
    inference(clausify,[status(thm)],[f_2822_4]) ).

cnf(f_2822_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10408),sK166(U_10411,U_10410,U_10409,U_10408)),U_10409))
    | ~ sP810(U_10408,U_10409,U_10410,U_10411) ),
    inference(clausify,[status(thm)],[f_2822_4]) ).

cnf(f_2822_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10410),hAPP(U_10411,sK166(U_10411,U_10410,U_10409,U_10408))))
    | ~ sP810(U_10408,U_10409,U_10410,U_10411) ),
    inference(clausify,[status(thm)],[f_2822_4]) ).

fof(f_2823_1,plain,
    ! [V_k_2,V_l_2,T_b] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty]) ).

fof(f_2823_2,plain,
    ! [U_10414,U_10413,U_10412] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10412,U_10414,U_10413) = c_Orderings_Obot__class_Obot(tc_fun(U_10412,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10412),U_10413),U_10414))
      | ~ class_Orderings_Oorder(U_10412) ),
    inference(variable_rename,[status(thm)],[f_2823_1]) ).

fof(f_2823_3,plain,
    ! [U_10413,U_10412,U_10414] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10412,U_10414,U_10413) = c_Orderings_Obot__class_Obot(tc_fun(U_10412,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10412),U_10413),U_10414))
      | ~ class_Orderings_Oorder(U_10412) ),
    inference(definitional_conversion,[status(esa)],[f_2823_2]) ).

cnf(f_2823_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10412,U_10414,U_10413) = c_Orderings_Obot__class_Obot(tc_fun(U_10412,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10412),U_10413),U_10414))
    | ~ class_Orderings_Oorder(U_10412) ),
    inference(clausify,[status(thm)],[f_2823_3]) ).

fof(f_2824_1,plain,
    ! [V_l_2,V_k_2,T_b] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(f_2824_2,plain,
    ! [U_10417,U_10416,U_10415] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10415,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10415,U_10416,U_10417)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10415),U_10416),U_10417)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10415),U_10416),U_10417))
          | c_Orderings_Obot__class_Obot(tc_fun(U_10415,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10415,U_10416,U_10417) ) )
      | ~ class_Orderings_Oorder(U_10415) ),
    inference(variable_rename,[status(thm)],[f_2824_1]) ).

fof(f_2824_3,plain,
    ( ! [U_10415,U_10416,U_10417] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10415,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10415,U_10416,U_10417)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10415),U_10416),U_10417))
        | ~ sP812(U_10415,U_10416,U_10417) )
    & ! [U_10415,U_10416,U_10417] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10415),U_10416),U_10417))
        | c_Orderings_Obot__class_Obot(tc_fun(U_10415,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10415,U_10416,U_10417)
        | ~ sP812(U_10415,U_10416,U_10417) )
    & ! [U_10415,U_10416,U_10417] :
        ( sP812(U_10415,U_10416,U_10417)
        | ~ class_Orderings_Oorder(U_10415) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP812])],[f_2824_2]) ).

cnf(f_2824_4,plain,
    ( sP812(U_10415,U_10416,U_10417)
    | ~ class_Orderings_Oorder(U_10415) ),
    inference(clausify,[status(thm)],[f_2824_3]) ).

cnf(f_2824_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10415),U_10416),U_10417))
    | c_Orderings_Obot__class_Obot(tc_fun(U_10415,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10415,U_10416,U_10417)
    | ~ sP812(U_10415,U_10416,U_10417) ),
    inference(clausify,[status(thm)],[f_2824_3]) ).

cnf(f_2824_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10415,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10415,U_10416,U_10417)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10415),U_10416),U_10417))
    | ~ sP812(U_10415,U_10416,U_10417) ),
    inference(clausify,[status(thm)],[f_2824_3]) ).

fof(f_2825_1,plain,
    ! [V_l_2,V_k_2,T_b] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(f_2825_2,plain,
    ! [U_10420,U_10419,U_10418] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10418,U_10419,U_10420) = c_Orderings_Obot__class_Obot(tc_fun(U_10418,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10418),U_10419),U_10420)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10418),U_10419),U_10420))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10418,U_10419,U_10420) != c_Orderings_Obot__class_Obot(tc_fun(U_10418,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_10418) ),
    inference(variable_rename,[status(thm)],[f_2825_1]) ).

fof(f_2825_3,plain,
    ( ! [U_10419,U_10420,U_10418] :
        ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10418,U_10419,U_10420) = c_Orderings_Obot__class_Obot(tc_fun(U_10418,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10418),U_10419),U_10420))
        | ~ sP813(U_10419,U_10420,U_10418) )
    & ! [U_10419,U_10420,U_10418] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10418),U_10419),U_10420))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10418,U_10419,U_10420) != c_Orderings_Obot__class_Obot(tc_fun(U_10418,tc_HOL_Obool))
        | ~ sP813(U_10419,U_10420,U_10418) )
    & ! [U_10419,U_10420,U_10418] :
        ( sP813(U_10419,U_10420,U_10418)
        | ~ class_Orderings_Oorder(U_10418) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP813])],[f_2825_2]) ).

cnf(f_2825_4,plain,
    ( sP813(U_10419,U_10420,U_10418)
    | ~ class_Orderings_Oorder(U_10418) ),
    inference(clausify,[status(thm)],[f_2825_3]) ).

cnf(f_2825_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10418),U_10419),U_10420))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10418,U_10419,U_10420) != c_Orderings_Obot__class_Obot(tc_fun(U_10418,tc_HOL_Obool))
    | ~ sP813(U_10419,U_10420,U_10418) ),
    inference(clausify,[status(thm)],[f_2825_3]) ).

cnf(f_2825_6,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10418,U_10419,U_10420) = c_Orderings_Obot__class_Obot(tc_fun(U_10418,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10418),U_10419),U_10420))
    | ~ sP813(U_10419,U_10420,U_10418) ),
    inference(clausify,[status(thm)],[f_2825_3]) ).

fof(f_2826_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J]) ).

fof(f_2826_2,plain,
    ! [U_10424,U_10423,U_10422,U_10421] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10421,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10422,U_10423)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10423,U_10424)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10422,U_10424)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10421),U_10423),U_10424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10421),U_10422),U_10423))
      | ~ class_Orderings_Olinorder(U_10421) ),
    inference(variable_rename,[status(thm)],[f_2826_1]) ).

fof(f_2826_3,plain,
    ! [U_10421,U_10422,U_10423,U_10424] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10421,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10422,U_10423)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10423,U_10424)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10422,U_10424)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10421),U_10423),U_10424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10421),U_10422),U_10423))
      | ~ class_Orderings_Olinorder(U_10421) ),
    inference(definitional_conversion,[status(esa)],[f_2826_2]) ).

cnf(f_2826_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10421,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10422,U_10423)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10423,U_10424)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10421,U_10422,U_10424)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10421),U_10423),U_10424))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10421),U_10422),U_10423))
    | ~ class_Orderings_Olinorder(U_10421) ),
    inference(clausify,[status(thm)],[f_2826_3]) ).

fof(f_2827_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J]) ).

fof(f_2827_2,plain,
    ! [U_10428,U_10427,U_10426,U_10425] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10425,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10425,U_10426,U_10427)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10425,U_10427,U_10428)) = c_Orderings_Obot__class_Obot(tc_fun(U_10425,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10425) ),
    inference(variable_rename,[status(thm)],[f_2827_1]) ).

fof(f_2827_3,plain,
    ! [U_10426,U_10427,U_10425,U_10428] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10425,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10425,U_10426,U_10427)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10425,U_10427,U_10428)) = c_Orderings_Obot__class_Obot(tc_fun(U_10425,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10425) ),
    inference(definitional_conversion,[status(esa)],[f_2827_2]) ).

cnf(f_2827_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10425,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10425,U_10426,U_10427)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10425,U_10427,U_10428)) = c_Orderings_Obot__class_Obot(tc_fun(U_10425,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10425) ),
    inference(clausify,[status(thm)],[f_2827_3]) ).

fof(f_2828_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanAtMost]) ).

fof(f_2828_2,plain,
    ! [U_10430,U_10429] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10429,U_10430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10430),U_10429),
    inference(variable_rename,[status(thm)],[f_2828_1]) ).

fof(f_2828_3,plain,
    ! [U_10429,U_10430] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10429,U_10430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10430),U_10429),
    inference(definitional_conversion,[status(esa)],[f_2828_2]) ).

cnf(f_2828_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10429,U_10430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10430),U_10429),
    inference(clausify,[status(thm)],[f_2828_3]) ).

fof(f_2829_1,plain,
    ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Image__eq__UN]) ).

fof(f_2829_2,plain,
    ! [U_10434,U_10433,U_10432,U_10431] : hAPP(c_Relation_OImage(U_10431,U_10432,U_10433),U_10434) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10431,tc_fun(U_10432,tc_HOL_Obool)),U_10434),hAPP(hAPP(c_COMBB(tc_fun(U_10431,tc_HOL_Obool),tc_fun(U_10432,tc_HOL_Obool),U_10431),c_Relation_OImage(U_10431,U_10432,U_10433)),hAPP(hAPP(c_COMBC(U_10431,tc_fun(U_10431,tc_HOL_Obool),tc_fun(U_10431,tc_HOL_Obool)),c_Set_Oinsert(U_10431)),c_Orderings_Obot__class_Obot(tc_fun(U_10431,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2829_1]) ).

fof(f_2829_3,plain,
    ! [U_10431,U_10432,U_10433,U_10434] : hAPP(c_Relation_OImage(U_10431,U_10432,U_10433),U_10434) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10431,tc_fun(U_10432,tc_HOL_Obool)),U_10434),hAPP(hAPP(c_COMBB(tc_fun(U_10431,tc_HOL_Obool),tc_fun(U_10432,tc_HOL_Obool),U_10431),c_Relation_OImage(U_10431,U_10432,U_10433)),hAPP(hAPP(c_COMBC(U_10431,tc_fun(U_10431,tc_HOL_Obool),tc_fun(U_10431,tc_HOL_Obool)),c_Set_Oinsert(U_10431)),c_Orderings_Obot__class_Obot(tc_fun(U_10431,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2829_2]) ).

cnf(f_2829_4,plain,
    hAPP(c_Relation_OImage(U_10431,U_10432,U_10433),U_10434) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10431,tc_fun(U_10432,tc_HOL_Obool)),U_10434),hAPP(hAPP(c_COMBB(tc_fun(U_10431,tc_HOL_Obool),tc_fun(U_10432,tc_HOL_Obool),U_10431),c_Relation_OImage(U_10431,U_10432,U_10433)),hAPP(hAPP(c_COMBC(U_10431,tc_fun(U_10431,tc_HOL_Obool),tc_fun(U_10431,tc_HOL_Obool)),c_Set_Oinsert(U_10431)),c_Orderings_Obot__class_Obot(tc_fun(U_10431,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2829_3]) ).

fof(f_2830_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).

fof(f_2830_2,plain,
    ! [U_10439,U_10438,U_10437,U_10436,U_10435] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10435,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,U_10436,U_10437)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,U_10438,U_10439)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10435),U_10436),U_10438),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10435),U_10437),U_10439))
      | ~ class_Orderings_Olinorder(U_10435) ),
    inference(variable_rename,[status(thm)],[f_2830_1]) ).

fof(f_2830_3,plain,
    ! [U_10435,U_10436,U_10437,U_10438,U_10439] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10435,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,U_10436,U_10437)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,U_10438,U_10439)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10435),U_10436),U_10438),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10435),U_10437),U_10439))
      | ~ class_Orderings_Olinorder(U_10435) ),
    inference(definitional_conversion,[status(esa)],[f_2830_2]) ).

cnf(f_2830_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10435,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,U_10436,U_10437)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,U_10438,U_10439)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10435,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10435),U_10436),U_10438),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10435),U_10437),U_10439))
    | ~ class_Orderings_Olinorder(U_10435) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

fof(f_2831_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J]) ).

fof(f_2831_2,plain,
    ! [U_10443,U_10442,U_10441,U_10440] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10440,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10440,U_10441,U_10442)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10440,U_10442,U_10443)) = c_Orderings_Obot__class_Obot(tc_fun(U_10440,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10440) ),
    inference(variable_rename,[status(thm)],[f_2831_1]) ).

fof(f_2831_3,plain,
    ! [U_10440,U_10441,U_10442,U_10443] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10440,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10440,U_10441,U_10442)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10440,U_10442,U_10443)) = c_Orderings_Obot__class_Obot(tc_fun(U_10440,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10440) ),
    inference(definitional_conversion,[status(esa)],[f_2831_2]) ).

cnf(f_2831_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10440,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10440,U_10441,U_10442)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10440,U_10442,U_10443)) = c_Orderings_Obot__class_Obot(tc_fun(U_10440,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10440) ),
    inference(clausify,[status(thm)],[f_2831_3]) ).

fof(f_2832_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanAtMost__int]) ).

fof(f_2832_2,plain,
    ! [U_10445,U_10444] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10444,U_10445)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10445),U_10444)),
    inference(variable_rename,[status(thm)],[f_2832_1]) ).

fof(f_2832_3,plain,
    ! [U_10444,U_10445] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10444,U_10445)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10445),U_10444)),
    inference(definitional_conversion,[status(esa)],[f_2832_2]) ).

cnf(f_2832_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10444,U_10445)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10445),U_10444)),
    inference(clausify,[status(thm)],[f_2832_3]) ).

fof(f_2833_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J]) ).

fof(f_2833_2,plain,
    ! [U_10449,U_10448,U_10447,U_10446] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10446,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10446,U_10447,U_10448)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10446,U_10448,U_10449)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10446,U_10447,U_10449)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10446),U_10448),U_10449))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10446),U_10447),U_10448))
      | ~ class_Orderings_Olinorder(U_10446) ),
    inference(variable_rename,[status(thm)],[f_2833_1]) ).

fof(f_2833_3,plain,
    ! [U_10446,U_10447,U_10448,U_10449] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10446,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10446,U_10447,U_10448)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10446,U_10448,U_10449)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10446,U_10447,U_10449)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10446),U_10448),U_10449))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10446),U_10447),U_10448))
      | ~ class_Orderings_Olinorder(U_10446) ),
    inference(definitional_conversion,[status(esa)],[f_2833_2]) ).

cnf(f_2833_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10446,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10446,U_10447,U_10448)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10446,U_10448,U_10449)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10446,U_10447,U_10449)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10446),U_10448),U_10449))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10446),U_10447),U_10448))
    | ~ class_Orderings_Olinorder(U_10446) ),
    inference(clausify,[status(thm)],[f_2833_3]) ).

fof(f_2834_1,plain,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__I]) ).

fof(f_2834_2,plain,
    ! [U_10455,U_10454,U_10453,U_10452,U_10451,U_10450] :
      ( hBOOL(hAPP(hAPP(c_member(U_10453),U_10454),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10450,tc_fun(U_10453,tc_HOL_Obool)),U_10452),U_10455)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10454),hAPP(U_10455,U_10451)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10450),U_10451),U_10452)) ),
    inference(variable_rename,[status(thm)],[f_2834_1]) ).

fof(f_2834_3,plain,
    ! [U_10452,U_10451,U_10453,U_10450,U_10454,U_10455] :
      ( hBOOL(hAPP(hAPP(c_member(U_10453),U_10454),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10450,tc_fun(U_10453,tc_HOL_Obool)),U_10452),U_10455)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10454),hAPP(U_10455,U_10451)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10450),U_10451),U_10452)) ),
    inference(definitional_conversion,[status(esa)],[f_2834_2]) ).

cnf(f_2834_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10453),U_10454),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10450,tc_fun(U_10453,tc_HOL_Obool)),U_10452),U_10455)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10454),hAPP(U_10455,U_10451)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10450),U_10451),U_10452)) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

fof(f_2835_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_image__eq__UN]) ).

fof(f_2835_2,plain,
    ! [U_10459,U_10458,U_10457,U_10456] : hAPP(c_Set_Oimage(U_10456,U_10457,U_10458),U_10459) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10456,tc_fun(U_10457,tc_HOL_Obool)),U_10459),hAPP(hAPP(c_COMBC(U_10456,tc_fun(U_10457,tc_HOL_Obool),tc_fun(U_10457,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10457,tc_fun(tc_fun(U_10457,tc_HOL_Obool),tc_fun(U_10457,tc_HOL_Obool)),U_10456),c_Set_Oinsert(U_10457)),U_10458)),c_Orderings_Obot__class_Obot(tc_fun(U_10457,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2835_1]) ).

fof(f_2835_3,plain,
    ! [U_10457,U_10456,U_10458,U_10459] : hAPP(c_Set_Oimage(U_10456,U_10457,U_10458),U_10459) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10456,tc_fun(U_10457,tc_HOL_Obool)),U_10459),hAPP(hAPP(c_COMBC(U_10456,tc_fun(U_10457,tc_HOL_Obool),tc_fun(U_10457,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10457,tc_fun(tc_fun(U_10457,tc_HOL_Obool),tc_fun(U_10457,tc_HOL_Obool)),U_10456),c_Set_Oinsert(U_10457)),U_10458)),c_Orderings_Obot__class_Obot(tc_fun(U_10457,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2835_2]) ).

cnf(f_2835_4,plain,
    hAPP(c_Set_Oimage(U_10456,U_10457,U_10458),U_10459) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10456,tc_fun(U_10457,tc_HOL_Obool)),U_10459),hAPP(hAPP(c_COMBC(U_10456,tc_fun(U_10457,tc_HOL_Obool),tc_fun(U_10457,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10457,tc_fun(tc_fun(U_10457,tc_HOL_Obool),tc_fun(U_10457,tc_HOL_Obool)),U_10456),c_Set_Oinsert(U_10457)),U_10458)),c_Orderings_Obot__class_Obot(tc_fun(U_10457,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2835_3]) ).

fof(f_2836_1,plain,
    ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2]) ).

fof(f_2836_2,plain,
    ! [U_10469,U_10468,U_10467,U_10466,U_10465,U_10464,U_10463,U_10462,U_10461,U_10460] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10460,tc_fun(U_10466,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10460,U_10460,U_10462),hAPP(hAPP(c_Set_Oinsert(U_10460),U_10468),c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10463,tc_fun(U_10466,tc_HOL_Obool)),tc_fun(U_10466,tc_HOL_Obool),U_10460),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10463,tc_fun(U_10466,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10463,U_10463,U_10465),hAPP(hAPP(c_Set_Oinsert(U_10463),U_10469),c_Orderings_Obot__class_Obot(tc_fun(U_10463,tc_HOL_Obool)))))),U_10467)) = hAPP(hAPP(U_10467,U_10468),U_10469)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10463),U_10469),U_10464))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10460),U_10468),U_10461))
      | ~ c_Equiv__Relations_Ocongruent2(U_10460,U_10463,tc_fun(U_10466,tc_HOL_Obool),U_10462,U_10465,U_10467)
      | ~ c_Equiv__Relations_Oequiv(U_10463,U_10464,U_10465)
      | ~ c_Equiv__Relations_Oequiv(U_10460,U_10461,U_10462) ),
    inference(variable_rename,[status(thm)],[f_2836_1]) ).

fof(f_2836_3,plain,
    ! [U_10460,U_10461,U_10462,U_10463,U_10464,U_10465,U_10466,U_10467,U_10468,U_10469] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10460,tc_fun(U_10466,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10460,U_10460,U_10462),hAPP(hAPP(c_Set_Oinsert(U_10460),U_10468),c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10463,tc_fun(U_10466,tc_HOL_Obool)),tc_fun(U_10466,tc_HOL_Obool),U_10460),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10463,tc_fun(U_10466,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10463,U_10463,U_10465),hAPP(hAPP(c_Set_Oinsert(U_10463),U_10469),c_Orderings_Obot__class_Obot(tc_fun(U_10463,tc_HOL_Obool)))))),U_10467)) = hAPP(hAPP(U_10467,U_10468),U_10469)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10463),U_10469),U_10464))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10460),U_10468),U_10461))
      | ~ c_Equiv__Relations_Ocongruent2(U_10460,U_10463,tc_fun(U_10466,tc_HOL_Obool),U_10462,U_10465,U_10467)
      | ~ c_Equiv__Relations_Oequiv(U_10463,U_10464,U_10465)
      | ~ c_Equiv__Relations_Oequiv(U_10460,U_10461,U_10462) ),
    inference(definitional_conversion,[status(esa)],[f_2836_2]) ).

cnf(f_2836_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10460,tc_fun(U_10466,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10460,U_10460,U_10462),hAPP(hAPP(c_Set_Oinsert(U_10460),U_10468),c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10463,tc_fun(U_10466,tc_HOL_Obool)),tc_fun(U_10466,tc_HOL_Obool),U_10460),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10463,tc_fun(U_10466,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10463,U_10463,U_10465),hAPP(hAPP(c_Set_Oinsert(U_10463),U_10469),c_Orderings_Obot__class_Obot(tc_fun(U_10463,tc_HOL_Obool)))))),U_10467)) = hAPP(hAPP(U_10467,U_10468),U_10469)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10463),U_10469),U_10464))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10460),U_10468),U_10461))
    | ~ c_Equiv__Relations_Ocongruent2(U_10460,U_10463,tc_fun(U_10466,tc_HOL_Obool),U_10462,U_10465,U_10467)
    | ~ c_Equiv__Relations_Oequiv(U_10463,U_10464,U_10465)
    | ~ c_Equiv__Relations_Oequiv(U_10460,U_10461,U_10462) ),
    inference(clausify,[status(thm)],[f_2836_3]) ).

fof(f_2837_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ? [B_x] :
            ( ? [B_xa] :
                ( ~ hBOOL(hAPP(V_P_2,B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(V_P_2,B_xa))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).

fof(f_2837_2,plain,
    ! [U_10480,U_10479,U_10478,U_10477,U_10476] :
      ( ( ! [U_10475] :
            ( hBOOL(hAPP(U_10480,U_10475))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10476),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10477,tc_fun(U_10476,tc_HOL_Obool)),U_10478),U_10479))) )
        | ? [U_10474] :
            ( ? [U_10473] :
                ( ~ hBOOL(hAPP(U_10480,U_10473))
                & hBOOL(hAPP(hAPP(c_member(U_10476),U_10473),hAPP(U_10479,U_10474))) )
            & hBOOL(hAPP(hAPP(c_member(U_10477),U_10474),U_10478)) ) )
      & ( ! [U_10472] :
            ( ! [U_10471] :
                ( hBOOL(hAPP(U_10480,U_10471))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10476),U_10471),hAPP(U_10479,U_10472))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10477),U_10472),U_10478)) )
        | ? [U_10470] :
            ( ~ hBOOL(hAPP(U_10480,U_10470))
            & hBOOL(hAPP(hAPP(c_member(U_10476),U_10470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10477,tc_fun(U_10476,tc_HOL_Obool)),U_10478),U_10479))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2837_1]) ).

fof(f_2837_3,plain,
    ( ! [U_10490,U_10488,U_10486,U_10484,U_10482] :
        ( ! [U_10475] :
            ( hBOOL(hAPP(U_10490,U_10475))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10484,tc_fun(U_10482,tc_HOL_Obool)),U_10486),U_10488))) )
        | ? [U_10474] :
            ( ? [U_10473] :
                ( ~ hBOOL(hAPP(U_10490,U_10473))
                & hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),hAPP(U_10488,U_10474))) )
            & hBOOL(hAPP(hAPP(c_member(U_10484),U_10474),U_10486)) ) )
    & ! [U_10489,U_10487,U_10485,U_10483,U_10481] :
        ( ! [U_10472] :
            ( ! [U_10471] :
                ( hBOOL(hAPP(U_10489,U_10471))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10471),hAPP(U_10487,U_10472))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10472),U_10485)) )
        | ? [U_10470] :
            ( ~ hBOOL(hAPP(U_10489,U_10470))
            & hBOOL(hAPP(hAPP(c_member(U_10481),U_10470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10483,tc_fun(U_10481,tc_HOL_Obool)),U_10485),U_10487))) ) ) ),
    inference(miniscope,[status(thm)],[f_2837_2]) ).

fof(f_2837_4,plain,
    ( ! [U_10490,U_10488,U_10486,U_10484,U_10482] :
        ( ! [U_10475] :
            ( hBOOL(hAPP(U_10490,U_10475))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10484,tc_fun(U_10482,tc_HOL_Obool)),U_10486),U_10488))) )
        | ? [U_10474] :
            ( ? [U_10473] :
                ( ~ hBOOL(hAPP(U_10490,U_10473))
                & hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),hAPP(U_10488,U_10474))) )
            & hBOOL(hAPP(hAPP(c_member(U_10484),U_10474),U_10486)) ) )
    & ! [U_10489,U_10487,U_10485,U_10483,U_10481] :
        ( ! [U_10472] :
            ( ! [U_10471] :
                ( hBOOL(hAPP(U_10489,U_10471))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10471),hAPP(U_10487,U_10472))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10472),U_10485)) )
        | ( ~ hBOOL(hAPP(U_10489,sK167(U_10489,U_10487,U_10485,U_10483,U_10481)))
          & hBOOL(hAPP(hAPP(c_member(U_10481),sK167(U_10489,U_10487,U_10485,U_10483,U_10481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10483,tc_fun(U_10481,tc_HOL_Obool)),U_10485),U_10487))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_10470,sK167(U_10489,U_10487,U_10485,U_10483,U_10481))],[f_2837_3]) ).

fof(f_2837_5,plain,
    ( ! [U_10490,U_10488,U_10486,U_10484,U_10482] :
        ( ! [U_10475] :
            ( hBOOL(hAPP(U_10490,U_10475))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10484,tc_fun(U_10482,tc_HOL_Obool)),U_10486),U_10488))) )
        | ( ? [U_10473] :
              ( ~ hBOOL(hAPP(U_10490,U_10473))
              & hBOOL(hAPP(hAPP(c_member(U_10482),U_10473),hAPP(U_10488,sK168(U_10490,U_10488,U_10486,U_10484,U_10482)))) )
          & hBOOL(hAPP(hAPP(c_member(U_10484),sK168(U_10490,U_10488,U_10486,U_10484,U_10482)),U_10486)) ) )
    & ! [U_10489,U_10487,U_10485,U_10483,U_10481] :
        ( ! [U_10472] :
            ( ! [U_10471] :
                ( hBOOL(hAPP(U_10489,U_10471))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10471),hAPP(U_10487,U_10472))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10472),U_10485)) )
        | ( ~ hBOOL(hAPP(U_10489,sK167(U_10489,U_10487,U_10485,U_10483,U_10481)))
          & hBOOL(hAPP(hAPP(c_member(U_10481),sK167(U_10489,U_10487,U_10485,U_10483,U_10481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10483,tc_fun(U_10481,tc_HOL_Obool)),U_10485),U_10487))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_10474,sK168(U_10490,U_10488,U_10486,U_10484,U_10482))],[f_2837_4]) ).

fof(f_2837_6,plain,
    ( ! [U_10490,U_10488,U_10486,U_10484,U_10482] :
        ( ! [U_10475] :
            ( hBOOL(hAPP(U_10490,U_10475))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10484,tc_fun(U_10482,tc_HOL_Obool)),U_10486),U_10488))) )
        | ( ~ hBOOL(hAPP(U_10490,sK169(U_10490,U_10488,U_10486,U_10484,U_10482)))
          & hBOOL(hAPP(hAPP(c_member(U_10482),sK169(U_10490,U_10488,U_10486,U_10484,U_10482)),hAPP(U_10488,sK168(U_10490,U_10488,U_10486,U_10484,U_10482))))
          & hBOOL(hAPP(hAPP(c_member(U_10484),sK168(U_10490,U_10488,U_10486,U_10484,U_10482)),U_10486)) ) )
    & ! [U_10489,U_10487,U_10485,U_10483,U_10481] :
        ( ! [U_10472] :
            ( ! [U_10471] :
                ( hBOOL(hAPP(U_10489,U_10471))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10471),hAPP(U_10487,U_10472))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10472),U_10485)) )
        | ( ~ hBOOL(hAPP(U_10489,sK167(U_10489,U_10487,U_10485,U_10483,U_10481)))
          & hBOOL(hAPP(hAPP(c_member(U_10481),sK167(U_10489,U_10487,U_10485,U_10483,U_10481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10483,tc_fun(U_10481,tc_HOL_Obool)),U_10485),U_10487))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_10473,sK169(U_10490,U_10488,U_10486,U_10484,U_10482))],[f_2837_5]) ).

fof(f_2837_7,plain,
    ( ! [U_10484,U_10482,U_10486,U_10488,U_10490] :
        ( ~ hBOOL(hAPP(U_10490,sK169(U_10490,U_10488,U_10486,U_10484,U_10482)))
        | ~ sP815(U_10484,U_10482,U_10486,U_10488,U_10490) )
    & ! [U_10484,U_10482,U_10486,U_10488,U_10490] :
        ( hBOOL(hAPP(hAPP(c_member(U_10482),sK169(U_10490,U_10488,U_10486,U_10484,U_10482)),hAPP(U_10488,sK168(U_10490,U_10488,U_10486,U_10484,U_10482))))
        | ~ sP815(U_10484,U_10482,U_10486,U_10488,U_10490) )
    & ! [U_10484,U_10482,U_10486,U_10488,U_10490] :
        ( hBOOL(hAPP(hAPP(c_member(U_10484),sK168(U_10490,U_10488,U_10486,U_10484,U_10482)),U_10486))
        | ~ sP815(U_10484,U_10482,U_10486,U_10488,U_10490) )
    & ! [U_10487,U_10485,U_10481,U_10483,U_10489] :
        ( ~ hBOOL(hAPP(U_10489,sK167(U_10489,U_10487,U_10485,U_10483,U_10481)))
        | ~ sP814(U_10487,U_10485,U_10481,U_10483,U_10489) )
    & ! [U_10487,U_10485,U_10481,U_10483,U_10489] :
        ( hBOOL(hAPP(hAPP(c_member(U_10481),sK167(U_10489,U_10487,U_10485,U_10483,U_10481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10483,tc_fun(U_10481,tc_HOL_Obool)),U_10485),U_10487)))
        | ~ sP814(U_10487,U_10485,U_10481,U_10483,U_10489) )
    & ! [U_10484,U_10475,U_10482,U_10486,U_10488,U_10490] :
        ( hBOOL(hAPP(U_10490,U_10475))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10484,tc_fun(U_10482,tc_HOL_Obool)),U_10486),U_10488)))
        | sP815(U_10484,U_10482,U_10486,U_10488,U_10490) )
    & ! [U_10472,U_10471,U_10487,U_10485,U_10481,U_10483,U_10489] :
        ( hBOOL(hAPP(U_10489,U_10471))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10471),hAPP(U_10487,U_10472)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10472),U_10485))
        | sP814(U_10487,U_10485,U_10481,U_10483,U_10489) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP814,sP815])],[f_2837_6]) ).

cnf(f_2837_8,plain,
    ( hBOOL(hAPP(U_10489,U_10471))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10471),hAPP(U_10487,U_10472)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10472),U_10485))
    | sP814(U_10487,U_10485,U_10481,U_10483,U_10489) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

cnf(f_2837_9,plain,
    ( hBOOL(hAPP(U_10490,U_10475))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10482),U_10475),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10484,tc_fun(U_10482,tc_HOL_Obool)),U_10486),U_10488)))
    | sP815(U_10484,U_10482,U_10486,U_10488,U_10490) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

cnf(f_2837_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10481),sK167(U_10489,U_10487,U_10485,U_10483,U_10481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10483,tc_fun(U_10481,tc_HOL_Obool)),U_10485),U_10487)))
    | ~ sP814(U_10487,U_10485,U_10481,U_10483,U_10489) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

cnf(f_2837_11,plain,
    ( ~ hBOOL(hAPP(U_10489,sK167(U_10489,U_10487,U_10485,U_10483,U_10481)))
    | ~ sP814(U_10487,U_10485,U_10481,U_10483,U_10489) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

cnf(f_2837_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10484),sK168(U_10490,U_10488,U_10486,U_10484,U_10482)),U_10486))
    | ~ sP815(U_10484,U_10482,U_10486,U_10488,U_10490) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

cnf(f_2837_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10482),sK169(U_10490,U_10488,U_10486,U_10484,U_10482)),hAPP(U_10488,sK168(U_10490,U_10488,U_10486,U_10484,U_10482))))
    | ~ sP815(U_10484,U_10482,U_10486,U_10488,U_10490) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

cnf(f_2837_14,plain,
    ( ~ hBOOL(hAPP(U_10490,sK169(U_10490,U_10488,U_10486,U_10484,U_10482)))
    | ~ sP815(U_10484,U_10482,U_10486,U_10488,U_10490) ),
    inference(clausify,[status(thm)],[f_2837_7]) ).

fof(f_2838_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__commute]) ).

fof(f_2838_2,plain,
    ! [U_10496,U_10495,U_10494,U_10493,U_10492,U_10491] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10492,U_10491),U_10493),hAPP(hAPP(c_COMBB(tc_fun(U_10494,U_10491),U_10491,U_10492),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10494,U_10491),U_10495)),U_10496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10494,U_10491),U_10495),hAPP(hAPP(c_COMBB(tc_fun(U_10492,U_10491),U_10491,U_10494),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10492,U_10491),U_10493)),hAPP(c_COMBC(U_10492,U_10494,U_10491),U_10496)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10491) ),
    inference(variable_rename,[status(thm)],[f_2838_1]) ).

fof(f_2838_3,plain,
    ! [U_10492,U_10493,U_10491,U_10494,U_10495,U_10496] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10492,U_10491),U_10493),hAPP(hAPP(c_COMBB(tc_fun(U_10494,U_10491),U_10491,U_10492),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10494,U_10491),U_10495)),U_10496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10494,U_10491),U_10495),hAPP(hAPP(c_COMBB(tc_fun(U_10492,U_10491),U_10491,U_10494),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10492,U_10491),U_10493)),hAPP(c_COMBC(U_10492,U_10494,U_10491),U_10496)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10491) ),
    inference(definitional_conversion,[status(esa)],[f_2838_2]) ).

cnf(f_2838_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10492,U_10491),U_10493),hAPP(hAPP(c_COMBB(tc_fun(U_10494,U_10491),U_10491,U_10492),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10494,U_10491),U_10495)),U_10496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10494,U_10491),U_10495),hAPP(hAPP(c_COMBB(tc_fun(U_10492,U_10491),U_10491,U_10494),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10492,U_10491),U_10493)),hAPP(c_COMBC(U_10492,U_10494,U_10491),U_10496)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10491) ),
    inference(clausify,[status(thm)],[f_2838_3]) ).

fof(f_2839_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__UN__flatten]) ).

fof(f_2839_2,plain,
    ! [U_10502,U_10501,U_10500,U_10499,U_10498,U_10497] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10497,tc_fun(U_10498,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10499,tc_fun(U_10497,tc_HOL_Obool)),U_10500),U_10501)),U_10502) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10499,tc_fun(U_10498,tc_HOL_Obool)),U_10500),hAPP(hAPP(c_COMBC(U_10499,tc_fun(U_10497,tc_fun(U_10498,tc_HOL_Obool)),tc_fun(U_10498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10497,tc_HOL_Obool),tc_fun(tc_fun(U_10497,tc_fun(U_10498,tc_HOL_Obool)),tc_fun(U_10498,tc_HOL_Obool)),U_10499),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10497,tc_fun(U_10498,tc_HOL_Obool))),U_10501)),U_10502)),
    inference(variable_rename,[status(thm)],[f_2839_1]) ).

fof(f_2839_3,plain,
    ! [U_10497,U_10498,U_10499,U_10500,U_10501,U_10502] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10497,tc_fun(U_10498,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10499,tc_fun(U_10497,tc_HOL_Obool)),U_10500),U_10501)),U_10502) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10499,tc_fun(U_10498,tc_HOL_Obool)),U_10500),hAPP(hAPP(c_COMBC(U_10499,tc_fun(U_10497,tc_fun(U_10498,tc_HOL_Obool)),tc_fun(U_10498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10497,tc_HOL_Obool),tc_fun(tc_fun(U_10497,tc_fun(U_10498,tc_HOL_Obool)),tc_fun(U_10498,tc_HOL_Obool)),U_10499),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10497,tc_fun(U_10498,tc_HOL_Obool))),U_10501)),U_10502)),
    inference(definitional_conversion,[status(esa)],[f_2839_2]) ).

cnf(f_2839_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10497,tc_fun(U_10498,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10499,tc_fun(U_10497,tc_HOL_Obool)),U_10500),U_10501)),U_10502) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10499,tc_fun(U_10498,tc_HOL_Obool)),U_10500),hAPP(hAPP(c_COMBC(U_10499,tc_fun(U_10497,tc_fun(U_10498,tc_HOL_Obool)),tc_fun(U_10498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10497,tc_HOL_Obool),tc_fun(tc_fun(U_10497,tc_fun(U_10498,tc_HOL_Obool)),tc_fun(U_10498,tc_HOL_Obool)),U_10499),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10497,tc_fun(U_10498,tc_HOL_Obool))),U_10501)),U_10502)),
    inference(clausify,[status(thm)],[f_2839_3]) ).

fof(f_2840_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(f_2840_2,plain,
    ! [U_10508,U_10507,U_10506,U_10505,U_10504,U_10503] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10503,tc_fun(U_10504,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,tc_fun(U_10503,tc_HOL_Obool)),U_10506),U_10507)),U_10508) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,tc_fun(U_10504,tc_HOL_Obool)),U_10506),hAPP(hAPP(c_COMBC(U_10505,tc_fun(U_10503,tc_fun(U_10504,tc_HOL_Obool)),tc_fun(U_10504,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10503,tc_HOL_Obool),tc_fun(tc_fun(U_10503,tc_fun(U_10504,tc_HOL_Obool)),tc_fun(U_10504,tc_HOL_Obool)),U_10505),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10503,tc_fun(U_10504,tc_HOL_Obool))),U_10507)),U_10508)),
    inference(variable_rename,[status(thm)],[f_2840_1]) ).

fof(f_2840_3,plain,
    ! [U_10503,U_10504,U_10505,U_10506,U_10507,U_10508] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10503,tc_fun(U_10504,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,tc_fun(U_10503,tc_HOL_Obool)),U_10506),U_10507)),U_10508) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,tc_fun(U_10504,tc_HOL_Obool)),U_10506),hAPP(hAPP(c_COMBC(U_10505,tc_fun(U_10503,tc_fun(U_10504,tc_HOL_Obool)),tc_fun(U_10504,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10503,tc_HOL_Obool),tc_fun(tc_fun(U_10503,tc_fun(U_10504,tc_HOL_Obool)),tc_fun(U_10504,tc_HOL_Obool)),U_10505),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10503,tc_fun(U_10504,tc_HOL_Obool))),U_10507)),U_10508)),
    inference(definitional_conversion,[status(esa)],[f_2840_2]) ).

cnf(f_2840_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10503,tc_fun(U_10504,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,tc_fun(U_10503,tc_HOL_Obool)),U_10506),U_10507)),U_10508) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,tc_fun(U_10504,tc_HOL_Obool)),U_10506),hAPP(hAPP(c_COMBC(U_10505,tc_fun(U_10503,tc_fun(U_10504,tc_HOL_Obool)),tc_fun(U_10504,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10503,tc_HOL_Obool),tc_fun(tc_fun(U_10503,tc_fun(U_10504,tc_HOL_Obool)),tc_fun(U_10504,tc_HOL_Obool)),U_10505),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10503,tc_fun(U_10504,tc_HOL_Obool))),U_10507)),U_10508)),
    inference(clausify,[status(thm)],[f_2840_3]) ).

fof(f_2841_1,plain,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(f_2841_2,plain,
    ! [U_10514,U_10513,U_10512,U_10511,U_10510,U_10509] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10509,tc_fun(U_10510,tc_HOL_Obool)),U_10511),hAPP(hAPP(c_COMBC(U_10509,tc_fun(U_10512,tc_fun(U_10510,tc_HOL_Obool)),tc_fun(U_10510,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10512,tc_HOL_Obool),tc_fun(tc_fun(U_10512,tc_fun(U_10510,tc_HOL_Obool)),tc_fun(U_10510,tc_HOL_Obool)),U_10509),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10512,tc_fun(U_10510,tc_HOL_Obool))),U_10513)),U_10514)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10512,tc_fun(U_10510,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10509,tc_fun(U_10512,tc_HOL_Obool)),U_10511),U_10513)),U_10514),
    inference(variable_rename,[status(thm)],[f_2841_1]) ).

fof(f_2841_3,plain,
    ! [U_10509,U_10510,U_10511,U_10512,U_10513,U_10514] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10509,tc_fun(U_10510,tc_HOL_Obool)),U_10511),hAPP(hAPP(c_COMBC(U_10509,tc_fun(U_10512,tc_fun(U_10510,tc_HOL_Obool)),tc_fun(U_10510,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10512,tc_HOL_Obool),tc_fun(tc_fun(U_10512,tc_fun(U_10510,tc_HOL_Obool)),tc_fun(U_10510,tc_HOL_Obool)),U_10509),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10512,tc_fun(U_10510,tc_HOL_Obool))),U_10513)),U_10514)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10512,tc_fun(U_10510,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10509,tc_fun(U_10512,tc_HOL_Obool)),U_10511),U_10513)),U_10514),
    inference(definitional_conversion,[status(esa)],[f_2841_2]) ).

cnf(f_2841_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10509,tc_fun(U_10510,tc_HOL_Obool)),U_10511),hAPP(hAPP(c_COMBC(U_10509,tc_fun(U_10512,tc_fun(U_10510,tc_HOL_Obool)),tc_fun(U_10510,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10512,tc_HOL_Obool),tc_fun(tc_fun(U_10512,tc_fun(U_10510,tc_HOL_Obool)),tc_fun(U_10510,tc_HOL_Obool)),U_10509),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10512,tc_fun(U_10510,tc_HOL_Obool))),U_10513)),U_10514)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10512,tc_fun(U_10510,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10509,tc_fun(U_10512,tc_HOL_Obool)),U_10511),U_10513)),U_10514),
    inference(clausify,[status(thm)],[f_2841_3]) ).

fof(f_2842_1,plain,
    ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2D]) ).

fof(f_2842_2,plain,
    ! [U_10524,U_10523,U_10522,U_10521,U_10520,U_10519,U_10518,U_10517,U_10516,U_10515] :
      ( hAPP(hAPP(U_10520,U_10521),U_10523) = hAPP(hAPP(U_10520,U_10522),U_10524)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10516,U_10516)),hAPP(hAPP(c_Product__Type_OPair(U_10516,U_10516),U_10523),U_10524)),U_10519))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10515,U_10515)),hAPP(hAPP(c_Product__Type_OPair(U_10515,U_10515),U_10521),U_10522)),U_10518))
      | ~ c_Equiv__Relations_Ocongruent2(U_10515,U_10516,U_10517,U_10518,U_10519,U_10520) ),
    inference(variable_rename,[status(thm)],[f_2842_1]) ).

fof(f_2842_3,plain,
    ! [U_10515,U_10516,U_10517,U_10518,U_10519,U_10520,U_10521,U_10522,U_10523,U_10524] :
      ( hAPP(hAPP(U_10520,U_10521),U_10523) = hAPP(hAPP(U_10520,U_10522),U_10524)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10516,U_10516)),hAPP(hAPP(c_Product__Type_OPair(U_10516,U_10516),U_10523),U_10524)),U_10519))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10515,U_10515)),hAPP(hAPP(c_Product__Type_OPair(U_10515,U_10515),U_10521),U_10522)),U_10518))
      | ~ c_Equiv__Relations_Ocongruent2(U_10515,U_10516,U_10517,U_10518,U_10519,U_10520) ),
    inference(definitional_conversion,[status(esa)],[f_2842_2]) ).

cnf(f_2842_4,plain,
    ( hAPP(hAPP(U_10520,U_10521),U_10523) = hAPP(hAPP(U_10520,U_10522),U_10524)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10516,U_10516)),hAPP(hAPP(c_Product__Type_OPair(U_10516,U_10516),U_10523),U_10524)),U_10519))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10515,U_10515)),hAPP(hAPP(c_Product__Type_OPair(U_10515,U_10515),U_10521),U_10522)),U_10518))
    | ~ c_Equiv__Relations_Ocongruent2(U_10515,U_10516,U_10517,U_10518,U_10519,U_10520) ),
    inference(clausify,[status(thm)],[f_2842_3]) ).

fof(f_2843_1,plain,
    ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__le__iff]) ).

fof(f_2843_2,plain,
    ! [U_10531,U_10530,U_10529,U_10528,U_10527] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531))
          | ? [U_10526] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,U_10526)),U_10531))
              & hBOOL(hAPP(hAPP(c_member(U_10528),U_10526),U_10529)) ) )
        & ( ! [U_10525] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,U_10525)),U_10531))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10528),U_10525),U_10529)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10527) ),
    inference(variable_rename,[status(thm)],[f_2843_1]) ).

fof(f_2843_3,plain,
    ! [U_10531,U_10530,U_10529,U_10528,U_10527] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,sK170(U_10531,U_10530,U_10529,U_10528,U_10527))),U_10531))
            & hBOOL(hAPP(hAPP(c_member(U_10528),sK170(U_10531,U_10530,U_10529,U_10528,U_10527)),U_10529)) ) )
        & ( ! [U_10525] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,U_10525)),U_10531))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10528),U_10525),U_10529)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10527) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_10526,sK170(U_10531,U_10530,U_10529,U_10528,U_10527))],[f_2843_2]) ).

fof(f_2843_4,plain,
    ( ! [U_10527,U_10528,U_10529,U_10530,U_10531] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,sK170(U_10531,U_10530,U_10529,U_10528,U_10527))),U_10531))
        | ~ sP816(U_10527,U_10528,U_10529,U_10530,U_10531) )
    & ! [U_10527,U_10528,U_10529,U_10530,U_10531] :
        ( hBOOL(hAPP(hAPP(c_member(U_10528),sK170(U_10531,U_10530,U_10529,U_10528,U_10527)),U_10529))
        | ~ sP816(U_10527,U_10528,U_10529,U_10530,U_10531) )
    & ! [U_10525,U_10527,U_10528,U_10529,U_10530,U_10531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531))
        | sP816(U_10527,U_10528,U_10529,U_10530,U_10531)
        | ~ sP817(U_10525,U_10527,U_10528,U_10529,U_10530,U_10531) )
    & ! [U_10525,U_10527,U_10528,U_10529,U_10530,U_10531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,U_10525)),U_10531))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10528),U_10525),U_10529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531))
        | ~ sP817(U_10525,U_10527,U_10528,U_10529,U_10530,U_10531) )
    & ! [U_10525,U_10527,U_10528,U_10529,U_10530,U_10531] :
        ( sP817(U_10525,U_10527,U_10528,U_10529,U_10530,U_10531)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_10527) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP816,sP817])],[f_2843_3]) ).

cnf(f_2843_5,plain,
    ( sP817(U_10525,U_10527,U_10528,U_10529,U_10530,U_10531)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10527) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,U_10525)),U_10531))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10528),U_10525),U_10529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531))
    | ~ sP817(U_10525,U_10527,U_10528,U_10529,U_10530,U_10531) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,U_10527),U_10529),U_10530)),U_10531))
    | sP816(U_10527,U_10528,U_10529,U_10530,U_10531)
    | ~ sP817(U_10525,U_10527,U_10528,U_10529,U_10530,U_10531) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10528),sK170(U_10531,U_10530,U_10529,U_10528,U_10527)),U_10529))
    | ~ sP816(U_10527,U_10528,U_10529,U_10530,U_10531) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10527),hAPP(U_10530,sK170(U_10531,U_10530,U_10529,U_10528,U_10527))),U_10531))
    | ~ sP816(U_10527,U_10528,U_10529,U_10530,U_10531) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

fof(f_2844_1,plain,
    ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__SUP__iff]) ).

fof(f_2844_2,plain,
    ! [U_10538,U_10537,U_10536,U_10535,U_10534] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538)))
          | ! [U_10533] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,U_10533)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10536),U_10533),U_10537)) ) )
        & ( ? [U_10532] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,U_10532)))
              & hBOOL(hAPP(hAPP(c_member(U_10536),U_10532),U_10537)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538))) ) )
      | ~ class_Orderings_Olinorder(U_10534)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10534) ),
    inference(variable_rename,[status(thm)],[f_2844_1]) ).

fof(f_2844_3,plain,
    ! [U_10538,U_10537,U_10536,U_10535,U_10534] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538)))
          | ! [U_10533] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,U_10533)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10536),U_10533),U_10537)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,sK171(U_10538,U_10537,U_10536,U_10535,U_10534))))
            & hBOOL(hAPP(hAPP(c_member(U_10536),sK171(U_10538,U_10537,U_10536,U_10535,U_10534)),U_10537)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538))) ) )
      | ~ class_Orderings_Olinorder(U_10534)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10534) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_10532,sK171(U_10538,U_10537,U_10536,U_10535,U_10534))],[f_2844_2]) ).

fof(f_2844_4,plain,
    ( ! [U_10536,U_10537,U_10538,U_10534,U_10535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,sK171(U_10538,U_10537,U_10536,U_10535,U_10534))))
        | ~ sP818(U_10536,U_10537,U_10538,U_10534,U_10535) )
    & ! [U_10536,U_10537,U_10538,U_10534,U_10535] :
        ( hBOOL(hAPP(hAPP(c_member(U_10536),sK171(U_10538,U_10537,U_10536,U_10535,U_10534)),U_10537))
        | ~ sP818(U_10536,U_10537,U_10538,U_10534,U_10535) )
    & ! [U_10536,U_10537,U_10533,U_10538,U_10534,U_10535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,U_10533)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10536),U_10533),U_10537))
        | ~ sP819(U_10536,U_10537,U_10533,U_10538,U_10534,U_10535) )
    & ! [U_10536,U_10537,U_10533,U_10538,U_10534,U_10535] :
        ( sP818(U_10536,U_10537,U_10538,U_10534,U_10535)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538)))
        | ~ sP819(U_10536,U_10537,U_10533,U_10538,U_10534,U_10535) )
    & ! [U_10536,U_10537,U_10533,U_10538,U_10534,U_10535] :
        ( sP819(U_10536,U_10537,U_10533,U_10538,U_10534,U_10535)
        | ~ class_Orderings_Olinorder(U_10534)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_10534) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP818,sP819])],[f_2844_3]) ).

cnf(f_2844_5,plain,
    ( sP819(U_10536,U_10537,U_10533,U_10538,U_10534,U_10535)
    | ~ class_Orderings_Olinorder(U_10534)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10534) ),
    inference(clausify,[status(thm)],[f_2844_4]) ).

cnf(f_2844_6,plain,
    ( sP818(U_10536,U_10537,U_10538,U_10534,U_10535)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538)))
    | ~ sP819(U_10536,U_10537,U_10533,U_10538,U_10534,U_10535) ),
    inference(clausify,[status(thm)],[f_2844_4]) ).

cnf(f_2844_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10536,U_10534),U_10537),U_10538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,U_10533)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10536),U_10533),U_10537))
    | ~ sP819(U_10536,U_10537,U_10533,U_10538,U_10534,U_10535) ),
    inference(clausify,[status(thm)],[f_2844_4]) ).

cnf(f_2844_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10536),sK171(U_10538,U_10537,U_10536,U_10535,U_10534)),U_10537))
    | ~ sP818(U_10536,U_10537,U_10538,U_10534,U_10535) ),
    inference(clausify,[status(thm)],[f_2844_4]) ).

cnf(f_2844_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10534),U_10535),hAPP(U_10538,sK171(U_10538,U_10537,U_10536,U_10535,U_10534))))
    | ~ sP818(U_10536,U_10537,U_10538,U_10534,U_10535) ),
    inference(clausify,[status(thm)],[f_2844_4]) ).

fof(f_2845_1,plain,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__iff]) ).

fof(f_2845_2,plain,
    ! [U_10545,U_10544,U_10543,U_10542,U_10541] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10541),U_10542),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10543,tc_fun(U_10541,tc_HOL_Obool)),U_10544),U_10545)))
        | ! [U_10540] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_10541),U_10542),hAPP(U_10545,U_10540)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10543),U_10540),U_10544)) ) )
      & ( ? [U_10539] :
            ( hBOOL(hAPP(hAPP(c_member(U_10541),U_10542),hAPP(U_10545,U_10539)))
            & hBOOL(hAPP(hAPP(c_member(U_10543),U_10539),U_10544)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10541),U_10542),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10543,tc_fun(U_10541,tc_HOL_Obool)),U_10544),U_10545))) ) ),
    inference(variable_rename,[status(thm)],[f_2845_1]) ).

fof(f_2845_3,plain,
    ( ! [U_10555,U_10553,U_10551,U_10549,U_10547] :
        ( hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10551,tc_fun(U_10547,tc_HOL_Obool)),U_10553),U_10555)))
        | ! [U_10540] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(U_10555,U_10540)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10551),U_10540),U_10553)) ) )
    & ! [U_10554,U_10552,U_10550,U_10548,U_10546] :
        ( ? [U_10539] :
            ( hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(U_10554,U_10539)))
            & hBOOL(hAPP(hAPP(c_member(U_10550),U_10539),U_10552)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10550,tc_fun(U_10546,tc_HOL_Obool)),U_10552),U_10554))) ) ),
    inference(miniscope,[status(thm)],[f_2845_2]) ).

fof(f_2845_4,plain,
    ( ! [U_10555,U_10553,U_10551,U_10549,U_10547] :
        ( hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10551,tc_fun(U_10547,tc_HOL_Obool)),U_10553),U_10555)))
        | ! [U_10540] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(U_10555,U_10540)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10551),U_10540),U_10553)) ) )
    & ! [U_10554,U_10552,U_10550,U_10548,U_10546] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(U_10554,sK172(U_10554,U_10552,U_10550,U_10548,U_10546))))
          & hBOOL(hAPP(hAPP(c_member(U_10550),sK172(U_10554,U_10552,U_10550,U_10548,U_10546)),U_10552)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10550,tc_fun(U_10546,tc_HOL_Obool)),U_10552),U_10554))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_10539,sK172(U_10554,U_10552,U_10550,U_10548,U_10546))],[f_2845_3]) ).

fof(f_2845_5,plain,
    ( ! [U_10550,U_10548,U_10546,U_10554,U_10552] :
        ( hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(U_10554,sK172(U_10554,U_10552,U_10550,U_10548,U_10546))))
        | ~ sP820(U_10550,U_10548,U_10546,U_10554,U_10552) )
    & ! [U_10550,U_10548,U_10546,U_10554,U_10552] :
        ( hBOOL(hAPP(hAPP(c_member(U_10550),sK172(U_10554,U_10552,U_10550,U_10548,U_10546)),U_10552))
        | ~ sP820(U_10550,U_10548,U_10546,U_10554,U_10552) )
    & ! [U_10540,U_10549,U_10547,U_10553,U_10551,U_10555] :
        ( hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10551,tc_fun(U_10547,tc_HOL_Obool)),U_10553),U_10555)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(U_10555,U_10540)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10551),U_10540),U_10553)) )
    & ! [U_10550,U_10548,U_10546,U_10554,U_10552] :
        ( sP820(U_10550,U_10548,U_10546,U_10554,U_10552)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10550,tc_fun(U_10546,tc_HOL_Obool)),U_10552),U_10554))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP820])],[f_2845_4]) ).

cnf(f_2845_6,plain,
    ( sP820(U_10550,U_10548,U_10546,U_10554,U_10552)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10550,tc_fun(U_10546,tc_HOL_Obool)),U_10552),U_10554))) ),
    inference(clausify,[status(thm)],[f_2845_5]) ).

cnf(f_2845_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10551,tc_fun(U_10547,tc_HOL_Obool)),U_10553),U_10555)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10547),U_10549),hAPP(U_10555,U_10540)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10551),U_10540),U_10553)) ),
    inference(clausify,[status(thm)],[f_2845_5]) ).

cnf(f_2845_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10550),sK172(U_10554,U_10552,U_10550,U_10548,U_10546)),U_10552))
    | ~ sP820(U_10550,U_10548,U_10546,U_10554,U_10552) ),
    inference(clausify,[status(thm)],[f_2845_5]) ).

cnf(f_2845_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10546),U_10548),hAPP(U_10554,sK172(U_10554,U_10552,U_10550,U_10548,U_10546))))
    | ~ sP820(U_10550,U_10548,U_10546,U_10554,U_10552) ),
    inference(clausify,[status(thm)],[f_2845_5]) ).

fof(f_2846_1,plain,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__const]) ).

fof(f_2846_2,plain,
    ! [U_10559,U_10558,U_10557,U_10556] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10558,U_10556),U_10557),hAPP(c_COMBK(U_10556,U_10558),U_10559)) = U_10559
      | U_10557 = c_Orderings_Obot__class_Obot(tc_fun(U_10558,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10556) ),
    inference(variable_rename,[status(thm)],[f_2846_1]) ).

fof(f_2846_3,plain,
    ! [U_10557,U_10556,U_10558,U_10559] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10558,U_10556),U_10557),hAPP(c_COMBK(U_10556,U_10558),U_10559)) = U_10559
      | U_10557 = c_Orderings_Obot__class_Obot(tc_fun(U_10558,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10556) ),
    inference(definitional_conversion,[status(esa)],[f_2846_2]) ).

cnf(f_2846_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10558,U_10556),U_10557),hAPP(c_COMBK(U_10556,U_10558),U_10559)) = U_10559
    | U_10557 = c_Orderings_Obot__class_Obot(tc_fun(U_10558,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10556) ),
    inference(clausify,[status(thm)],[f_2846_3]) ).

fof(f_2847_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J]) ).

fof(f_2847_2,plain,
    ! [U_10565,U_10564,U_10563,U_10562] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10562,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10563,tc_fun(U_10562,tc_HOL_Obool)),U_10564),U_10565)
        | ? [U_10561] :
            ( hAPP(U_10565,U_10561) != c_Orderings_Obot__class_Obot(tc_fun(U_10562,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10563),U_10561),U_10564)) ) )
      & ( ! [U_10560] :
            ( hAPP(U_10565,U_10560) = c_Orderings_Obot__class_Obot(tc_fun(U_10562,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10563),U_10560),U_10564)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_10562,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10563,tc_fun(U_10562,tc_HOL_Obool)),U_10564),U_10565) ) ),
    inference(variable_rename,[status(thm)],[f_2847_1]) ).

fof(f_2847_3,plain,
    ( ! [U_10573,U_10571,U_10569,U_10567] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10569,tc_fun(U_10567,tc_HOL_Obool)),U_10571),U_10573)
        | ? [U_10561] :
            ( hAPP(U_10573,U_10561) != c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10569),U_10561),U_10571)) ) )
    & ! [U_10572,U_10570,U_10568,U_10566] :
        ( ! [U_10560] :
            ( hAPP(U_10572,U_10560) = c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10568),U_10560),U_10570)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10568,tc_fun(U_10566,tc_HOL_Obool)),U_10570),U_10572) ) ),
    inference(miniscope,[status(thm)],[f_2847_2]) ).

fof(f_2847_4,plain,
    ( ! [U_10573,U_10571,U_10569,U_10567] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10569,tc_fun(U_10567,tc_HOL_Obool)),U_10571),U_10573)
        | ( hAPP(U_10573,sK173(U_10573,U_10571,U_10569,U_10567)) != c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_10569),sK173(U_10573,U_10571,U_10569,U_10567)),U_10571)) ) )
    & ! [U_10572,U_10570,U_10568,U_10566] :
        ( ! [U_10560] :
            ( hAPP(U_10572,U_10560) = c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10568),U_10560),U_10570)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10568,tc_fun(U_10566,tc_HOL_Obool)),U_10570),U_10572) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_10561,sK173(U_10573,U_10571,U_10569,U_10567))],[f_2847_3]) ).

fof(f_2847_5,plain,
    ( ! [U_10573,U_10571,U_10567,U_10569] :
        ( hAPP(U_10573,sK173(U_10573,U_10571,U_10569,U_10567)) != c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool))
        | ~ sP821(U_10573,U_10571,U_10567,U_10569) )
    & ! [U_10573,U_10571,U_10567,U_10569] :
        ( hBOOL(hAPP(hAPP(c_member(U_10569),sK173(U_10573,U_10571,U_10569,U_10567)),U_10571))
        | ~ sP821(U_10573,U_10571,U_10567,U_10569) )
    & ! [U_10573,U_10571,U_10567,U_10569] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10569,tc_fun(U_10567,tc_HOL_Obool)),U_10571),U_10573)
        | sP821(U_10573,U_10571,U_10567,U_10569) )
    & ! [U_10568,U_10572,U_10560,U_10566,U_10570] :
        ( hAPP(U_10572,U_10560) = c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10568),U_10560),U_10570))
        | c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10568,tc_fun(U_10566,tc_HOL_Obool)),U_10570),U_10572) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP821])],[f_2847_4]) ).

cnf(f_2847_6,plain,
    ( hAPP(U_10572,U_10560) = c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10568),U_10560),U_10570))
    | c_Orderings_Obot__class_Obot(tc_fun(U_10566,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10568,tc_fun(U_10566,tc_HOL_Obool)),U_10570),U_10572) ),
    inference(clausify,[status(thm)],[f_2847_5]) ).

cnf(f_2847_7,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10569,tc_fun(U_10567,tc_HOL_Obool)),U_10571),U_10573)
    | sP821(U_10573,U_10571,U_10567,U_10569) ),
    inference(clausify,[status(thm)],[f_2847_5]) ).

cnf(f_2847_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10569),sK173(U_10573,U_10571,U_10569,U_10567)),U_10571))
    | ~ sP821(U_10573,U_10571,U_10567,U_10569) ),
    inference(clausify,[status(thm)],[f_2847_5]) ).

cnf(f_2847_9,plain,
    ( hAPP(U_10573,sK173(U_10573,U_10571,U_10569,U_10567)) != c_Orderings_Obot__class_Obot(tc_fun(U_10567,tc_HOL_Obool))
    | ~ sP821(U_10573,U_10571,U_10567,U_10569) ),
    inference(clausify,[status(thm)],[f_2847_5]) ).

fof(f_2848_1,plain,
    ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__empty2]) ).

fof(f_2848_2,plain,
    ! [U_10576,U_10575,U_10574] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10574,tc_fun(U_10575,tc_HOL_Obool)),U_10576),hAPP(c_COMBK(tc_fun(U_10575,tc_HOL_Obool),U_10574),c_Orderings_Obot__class_Obot(tc_fun(U_10575,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10575,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2848_1]) ).

fof(f_2848_3,plain,
    ! [U_10576,U_10574,U_10575] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10574,tc_fun(U_10575,tc_HOL_Obool)),U_10576),hAPP(c_COMBK(tc_fun(U_10575,tc_HOL_Obool),U_10574),c_Orderings_Obot__class_Obot(tc_fun(U_10575,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10575,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2848_2]) ).

cnf(f_2848_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10574,tc_fun(U_10575,tc_HOL_Obool)),U_10576),hAPP(c_COMBK(tc_fun(U_10575,tc_HOL_Obool),U_10574),c_Orderings_Obot__class_Obot(tc_fun(U_10575,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10575,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2848_3]) ).

fof(f_2849_1,plain,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).

fof(f_2849_2,plain,
    ! [U_10580,U_10579,U_10578,U_10577] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10578,tc_fun(U_10579,tc_HOL_Obool)),U_10577),hAPP(c_COMBK(tc_fun(U_10579,tc_HOL_Obool),U_10578),U_10580)) = U_10580
        | U_10577 = c_Orderings_Obot__class_Obot(tc_fun(U_10578,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10578,tc_fun(U_10579,tc_HOL_Obool)),U_10577),hAPP(c_COMBK(tc_fun(U_10579,tc_HOL_Obool),U_10578),U_10580)) = c_Orderings_Obot__class_Obot(tc_fun(U_10579,tc_HOL_Obool))
        | U_10577 != c_Orderings_Obot__class_Obot(tc_fun(U_10578,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2849_1]) ).

fof(f_2849_3,plain,
    ( ! [U_10588,U_10586,U_10584,U_10582] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10584,tc_fun(U_10586,tc_HOL_Obool)),U_10582),hAPP(c_COMBK(tc_fun(U_10586,tc_HOL_Obool),U_10584),U_10588)) = U_10588
        | U_10582 = c_Orderings_Obot__class_Obot(tc_fun(U_10584,tc_HOL_Obool)) )
    & ! [U_10587,U_10585,U_10583,U_10581] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10583,tc_fun(U_10585,tc_HOL_Obool)),U_10581),hAPP(c_COMBK(tc_fun(U_10585,tc_HOL_Obool),U_10583),U_10587)) = c_Orderings_Obot__class_Obot(tc_fun(U_10585,tc_HOL_Obool))
        | U_10581 != c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2849_2]) ).

fof(f_2849_4,plain,
    ( ! [U_10582,U_10584,U_10586,U_10588] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10584,tc_fun(U_10586,tc_HOL_Obool)),U_10582),hAPP(c_COMBK(tc_fun(U_10586,tc_HOL_Obool),U_10584),U_10588)) = U_10588
        | U_10582 = c_Orderings_Obot__class_Obot(tc_fun(U_10584,tc_HOL_Obool)) )
    & ! [U_10585,U_10587,U_10583,U_10581] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10583,tc_fun(U_10585,tc_HOL_Obool)),U_10581),hAPP(c_COMBK(tc_fun(U_10585,tc_HOL_Obool),U_10583),U_10587)) = c_Orderings_Obot__class_Obot(tc_fun(U_10585,tc_HOL_Obool))
        | U_10581 != c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2849_3]) ).

cnf(f_2849_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10583,tc_fun(U_10585,tc_HOL_Obool)),U_10581),hAPP(c_COMBK(tc_fun(U_10585,tc_HOL_Obool),U_10583),U_10587)) = c_Orderings_Obot__class_Obot(tc_fun(U_10585,tc_HOL_Obool))
    | U_10581 != c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2849_4]) ).

cnf(f_2849_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10584,tc_fun(U_10586,tc_HOL_Obool)),U_10582),hAPP(c_COMBK(tc_fun(U_10586,tc_HOL_Obool),U_10584),U_10588)) = U_10588
    | U_10582 = c_Orderings_Obot__class_Obot(tc_fun(U_10584,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2849_4]) ).

fof(f_2850_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J]) ).

fof(f_2850_2,plain,
    ! [U_10594,U_10593,U_10592,U_10591] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10591,tc_fun(U_10592,tc_HOL_Obool)),U_10593),U_10594) = c_Orderings_Obot__class_Obot(tc_fun(U_10592,tc_HOL_Obool))
        | ? [U_10590] :
            ( hAPP(U_10594,U_10590) != c_Orderings_Obot__class_Obot(tc_fun(U_10592,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10591),U_10590),U_10593)) ) )
      & ( ! [U_10589] :
            ( hAPP(U_10594,U_10589) = c_Orderings_Obot__class_Obot(tc_fun(U_10592,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10591),U_10589),U_10593)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10591,tc_fun(U_10592,tc_HOL_Obool)),U_10593),U_10594) != c_Orderings_Obot__class_Obot(tc_fun(U_10592,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2850_1]) ).

fof(f_2850_3,plain,
    ( ! [U_10602,U_10600,U_10598,U_10596] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10596,tc_fun(U_10598,tc_HOL_Obool)),U_10600),U_10602) = c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
        | ? [U_10590] :
            ( hAPP(U_10602,U_10590) != c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10596),U_10590),U_10600)) ) )
    & ! [U_10601,U_10599,U_10597,U_10595] :
        ( ! [U_10589] :
            ( hAPP(U_10601,U_10589) = c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10595),U_10589),U_10599)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10595,tc_fun(U_10597,tc_HOL_Obool)),U_10599),U_10601) != c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2850_2]) ).

fof(f_2850_4,plain,
    ( ! [U_10602,U_10600,U_10598,U_10596] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10596,tc_fun(U_10598,tc_HOL_Obool)),U_10600),U_10602) = c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
        | ( hAPP(U_10602,sK174(U_10602,U_10600,U_10598,U_10596)) != c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_10596),sK174(U_10602,U_10600,U_10598,U_10596)),U_10600)) ) )
    & ! [U_10601,U_10599,U_10597,U_10595] :
        ( ! [U_10589] :
            ( hAPP(U_10601,U_10589) = c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10595),U_10589),U_10599)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10595,tc_fun(U_10597,tc_HOL_Obool)),U_10599),U_10601) != c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_10590,sK174(U_10602,U_10600,U_10598,U_10596))],[f_2850_3]) ).

fof(f_2850_5,plain,
    ( ! [U_10600,U_10596,U_10598,U_10602] :
        ( hAPP(U_10602,sK174(U_10602,U_10600,U_10598,U_10596)) != c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
        | ~ sP822(U_10600,U_10596,U_10598,U_10602) )
    & ! [U_10600,U_10596,U_10598,U_10602] :
        ( hBOOL(hAPP(hAPP(c_member(U_10596),sK174(U_10602,U_10600,U_10598,U_10596)),U_10600))
        | ~ sP822(U_10600,U_10596,U_10598,U_10602) )
    & ! [U_10600,U_10596,U_10598,U_10602] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10596,tc_fun(U_10598,tc_HOL_Obool)),U_10600),U_10602) = c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
        | sP822(U_10600,U_10596,U_10598,U_10602) )
    & ! [U_10589,U_10597,U_10601,U_10595,U_10599] :
        ( hAPP(U_10601,U_10589) = c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10595),U_10589),U_10599))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10595,tc_fun(U_10597,tc_HOL_Obool)),U_10599),U_10601) != c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP822])],[f_2850_4]) ).

cnf(f_2850_6,plain,
    ( hAPP(U_10601,U_10589) = c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10595),U_10589),U_10599))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10595,tc_fun(U_10597,tc_HOL_Obool)),U_10599),U_10601) != c_Orderings_Obot__class_Obot(tc_fun(U_10597,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2850_5]) ).

cnf(f_2850_7,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10596,tc_fun(U_10598,tc_HOL_Obool)),U_10600),U_10602) = c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
    | sP822(U_10600,U_10596,U_10598,U_10602) ),
    inference(clausify,[status(thm)],[f_2850_5]) ).

cnf(f_2850_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10596),sK174(U_10602,U_10600,U_10598,U_10596)),U_10600))
    | ~ sP822(U_10600,U_10596,U_10598,U_10602) ),
    inference(clausify,[status(thm)],[f_2850_5]) ).

cnf(f_2850_9,plain,
    ( hAPP(U_10602,sK174(U_10602,U_10600,U_10598,U_10596)) != c_Orderings_Obot__class_Obot(tc_fun(U_10598,tc_HOL_Obool))
    | ~ sP822(U_10600,U_10596,U_10598,U_10602) ),
    inference(clausify,[status(thm)],[f_2850_5]) ).

fof(f_2851_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__subset__iff]) ).

fof(f_2851_2,plain,
    ! [U_10609,U_10608,U_10607,U_10606,U_10605] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10605,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10606,tc_fun(U_10605,tc_HOL_Obool)),U_10607),U_10608)),U_10609))
        | ? [U_10604] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10605,tc_HOL_Obool)),hAPP(U_10608,U_10604)),U_10609))
            & hBOOL(hAPP(hAPP(c_member(U_10606),U_10604),U_10607)) ) )
      & ( ! [U_10603] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10605,tc_HOL_Obool)),hAPP(U_10608,U_10603)),U_10609))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10606),U_10603),U_10607)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10605,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10606,tc_fun(U_10605,tc_HOL_Obool)),U_10607),U_10608)),U_10609)) ) ),
    inference(variable_rename,[status(thm)],[f_2851_1]) ).

fof(f_2851_3,plain,
    ( ! [U_10619,U_10617,U_10615,U_10613,U_10611] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10613,tc_fun(U_10611,tc_HOL_Obool)),U_10615),U_10617)),U_10619))
        | ? [U_10604] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(U_10617,U_10604)),U_10619))
            & hBOOL(hAPP(hAPP(c_member(U_10613),U_10604),U_10615)) ) )
    & ! [U_10618,U_10616,U_10614,U_10612,U_10610] :
        ( ! [U_10603] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(U_10616,U_10603)),U_10618))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10612),U_10603),U_10614)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10612,tc_fun(U_10610,tc_HOL_Obool)),U_10614),U_10616)),U_10618)) ) ),
    inference(miniscope,[status(thm)],[f_2851_2]) ).

fof(f_2851_4,plain,
    ( ! [U_10619,U_10617,U_10615,U_10613,U_10611] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10613,tc_fun(U_10611,tc_HOL_Obool)),U_10615),U_10617)),U_10619))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(U_10617,sK175(U_10619,U_10617,U_10615,U_10613,U_10611))),U_10619))
          & hBOOL(hAPP(hAPP(c_member(U_10613),sK175(U_10619,U_10617,U_10615,U_10613,U_10611)),U_10615)) ) )
    & ! [U_10618,U_10616,U_10614,U_10612,U_10610] :
        ( ! [U_10603] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(U_10616,U_10603)),U_10618))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10612),U_10603),U_10614)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10612,tc_fun(U_10610,tc_HOL_Obool)),U_10614),U_10616)),U_10618)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_10604,sK175(U_10619,U_10617,U_10615,U_10613,U_10611))],[f_2851_3]) ).

fof(f_2851_5,plain,
    ( ! [U_10615,U_10611,U_10613,U_10617,U_10619] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(U_10617,sK175(U_10619,U_10617,U_10615,U_10613,U_10611))),U_10619))
        | ~ sP823(U_10615,U_10611,U_10613,U_10617,U_10619) )
    & ! [U_10615,U_10611,U_10613,U_10617,U_10619] :
        ( hBOOL(hAPP(hAPP(c_member(U_10613),sK175(U_10619,U_10617,U_10615,U_10613,U_10611)),U_10615))
        | ~ sP823(U_10615,U_10611,U_10613,U_10617,U_10619) )
    & ! [U_10615,U_10611,U_10613,U_10617,U_10619] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10613,tc_fun(U_10611,tc_HOL_Obool)),U_10615),U_10617)),U_10619))
        | sP823(U_10615,U_10611,U_10613,U_10617,U_10619) )
    & ! [U_10603,U_10610,U_10616,U_10612,U_10618,U_10614] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(U_10616,U_10603)),U_10618))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10612),U_10603),U_10614))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10612,tc_fun(U_10610,tc_HOL_Obool)),U_10614),U_10616)),U_10618)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP823])],[f_2851_4]) ).

cnf(f_2851_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(U_10616,U_10603)),U_10618))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10612),U_10603),U_10614))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10610,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10612,tc_fun(U_10610,tc_HOL_Obool)),U_10614),U_10616)),U_10618)) ),
    inference(clausify,[status(thm)],[f_2851_5]) ).

cnf(f_2851_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10613,tc_fun(U_10611,tc_HOL_Obool)),U_10615),U_10617)),U_10619))
    | sP823(U_10615,U_10611,U_10613,U_10617,U_10619) ),
    inference(clausify,[status(thm)],[f_2851_5]) ).

cnf(f_2851_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10613),sK175(U_10619,U_10617,U_10615,U_10613,U_10611)),U_10615))
    | ~ sP823(U_10615,U_10611,U_10613,U_10617,U_10619) ),
    inference(clausify,[status(thm)],[f_2851_5]) ).

cnf(f_2851_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(U_10617,sK175(U_10619,U_10617,U_10615,U_10613,U_10611))),U_10619))
    | ~ sP823(U_10615,U_10611,U_10613,U_10617,U_10619) ),
    inference(clausify,[status(thm)],[f_2851_5]) ).

fof(f_2852_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(f_2852_2,plain,
    ! [U_10625,U_10624,U_10623,U_10622,U_10621,U_10620] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10620,tc_fun(U_10621,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10622,U_10620,U_10623),U_10624)),U_10625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10622,tc_fun(U_10621,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_COMBB(U_10620,tc_fun(U_10621,tc_HOL_Obool),U_10622),U_10625),U_10623)),
    inference(variable_rename,[status(thm)],[f_2852_1]) ).

fof(f_2852_3,plain,
    ! [U_10621,U_10620,U_10622,U_10623,U_10624,U_10625] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10620,tc_fun(U_10621,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10622,U_10620,U_10623),U_10624)),U_10625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10622,tc_fun(U_10621,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_COMBB(U_10620,tc_fun(U_10621,tc_HOL_Obool),U_10622),U_10625),U_10623)),
    inference(definitional_conversion,[status(esa)],[f_2852_2]) ).

cnf(f_2852_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10620,tc_fun(U_10621,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10622,U_10620,U_10623),U_10624)),U_10625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10622,tc_fun(U_10621,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_COMBB(U_10620,tc_fun(U_10621,tc_HOL_Obool),U_10622),U_10625),U_10623)),
    inference(clausify,[status(thm)],[f_2852_3]) ).

fof(f_2853_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__UN]) ).

fof(f_2853_2,plain,
    ! [U_10631,U_10630,U_10629,U_10628,U_10627,U_10626] : hAPP(c_Set_Oimage(U_10626,U_10627,U_10628),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10629,tc_fun(U_10626,tc_HOL_Obool)),U_10630),U_10631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10629,tc_fun(U_10627,tc_HOL_Obool)),U_10630),hAPP(hAPP(c_COMBB(tc_fun(U_10626,tc_HOL_Obool),tc_fun(U_10627,tc_HOL_Obool),U_10629),c_Set_Oimage(U_10626,U_10627,U_10628)),U_10631)),
    inference(variable_rename,[status(thm)],[f_2853_1]) ).

fof(f_2853_3,plain,
    ! [U_10626,U_10627,U_10628,U_10629,U_10630,U_10631] : hAPP(c_Set_Oimage(U_10626,U_10627,U_10628),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10629,tc_fun(U_10626,tc_HOL_Obool)),U_10630),U_10631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10629,tc_fun(U_10627,tc_HOL_Obool)),U_10630),hAPP(hAPP(c_COMBB(tc_fun(U_10626,tc_HOL_Obool),tc_fun(U_10627,tc_HOL_Obool),U_10629),c_Set_Oimage(U_10626,U_10627,U_10628)),U_10631)),
    inference(definitional_conversion,[status(esa)],[f_2853_2]) ).

cnf(f_2853_4,plain,
    hAPP(c_Set_Oimage(U_10626,U_10627,U_10628),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10629,tc_fun(U_10626,tc_HOL_Obool)),U_10630),U_10631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10629,tc_fun(U_10627,tc_HOL_Obool)),U_10630),hAPP(hAPP(c_COMBB(tc_fun(U_10626,tc_HOL_Obool),tc_fun(U_10627,tc_HOL_Obool),U_10629),c_Set_Oimage(U_10626,U_10627,U_10628)),U_10631)),
    inference(clausify,[status(thm)],[f_2853_3]) ).

fof(f_2854_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(f_2854_2,plain,
    ! [U_10637,U_10636,U_10635,U_10634,U_10633,U_10632] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10632,tc_fun(U_10633,tc_HOL_Obool)),U_10634),hAPP(hAPP(c_COMBB(U_10635,tc_fun(U_10633,tc_HOL_Obool),U_10632),U_10636),U_10637)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10635,tc_fun(U_10633,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10632,U_10635,U_10637),U_10634)),U_10636),
    inference(variable_rename,[status(thm)],[f_2854_1]) ).

fof(f_2854_3,plain,
    ! [U_10632,U_10633,U_10634,U_10635,U_10636,U_10637] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10632,tc_fun(U_10633,tc_HOL_Obool)),U_10634),hAPP(hAPP(c_COMBB(U_10635,tc_fun(U_10633,tc_HOL_Obool),U_10632),U_10636),U_10637)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10635,tc_fun(U_10633,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10632,U_10635,U_10637),U_10634)),U_10636),
    inference(definitional_conversion,[status(esa)],[f_2854_2]) ).

cnf(f_2854_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10632,tc_fun(U_10633,tc_HOL_Obool)),U_10634),hAPP(hAPP(c_COMBB(U_10635,tc_fun(U_10633,tc_HOL_Obool),U_10632),U_10636),U_10637)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10635,tc_fun(U_10633,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10632,U_10635,U_10637),U_10634)),U_10636),
    inference(clausify,[status(thm)],[f_2854_3]) ).

fof(f_2855_1,plain,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__Un]) ).

fof(f_2855_2,plain,
    ! [U_10642,U_10641,U_10640,U_10639,U_10638] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10638,tc_HOL_Obool)),U_10640),U_10641)),U_10642) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10639,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),U_10640),U_10642)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),U_10641),U_10642)),
    inference(variable_rename,[status(thm)],[f_2855_1]) ).

fof(f_2855_3,plain,
    ! [U_10638,U_10639,U_10640,U_10641,U_10642] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10638,tc_HOL_Obool)),U_10640),U_10641)),U_10642) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10639,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),U_10640),U_10642)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),U_10641),U_10642)),
    inference(definitional_conversion,[status(esa)],[f_2855_2]) ).

cnf(f_2855_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10638,tc_HOL_Obool)),U_10640),U_10641)),U_10642) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10639,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),U_10640),U_10642)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10638,tc_fun(U_10639,tc_HOL_Obool)),U_10641),U_10642)),
    inference(clausify,[status(thm)],[f_2855_3]) ).

fof(f_2856_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__Un__distrib]) ).

fof(f_2856_2,plain,
    ! [U_10647,U_10646,U_10645,U_10644,U_10643] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),hAPP(hAPP(c_COMBS(U_10643,tc_fun(U_10644,tc_HOL_Obool),tc_fun(U_10644,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10644,tc_HOL_Obool),tc_fun(tc_fun(U_10644,tc_HOL_Obool),tc_fun(U_10644,tc_HOL_Obool)),U_10643),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10644,tc_HOL_Obool))),U_10646)),U_10647)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10644,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),U_10646)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),U_10647)),
    inference(variable_rename,[status(thm)],[f_2856_1]) ).

fof(f_2856_3,plain,
    ! [U_10643,U_10644,U_10645,U_10646,U_10647] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),hAPP(hAPP(c_COMBS(U_10643,tc_fun(U_10644,tc_HOL_Obool),tc_fun(U_10644,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10644,tc_HOL_Obool),tc_fun(tc_fun(U_10644,tc_HOL_Obool),tc_fun(U_10644,tc_HOL_Obool)),U_10643),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10644,tc_HOL_Obool))),U_10646)),U_10647)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10644,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),U_10646)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),U_10647)),
    inference(definitional_conversion,[status(esa)],[f_2856_2]) ).

cnf(f_2856_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),hAPP(hAPP(c_COMBS(U_10643,tc_fun(U_10644,tc_HOL_Obool),tc_fun(U_10644,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10644,tc_HOL_Obool),tc_fun(tc_fun(U_10644,tc_HOL_Obool),tc_fun(U_10644,tc_HOL_Obool)),U_10643),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10644,tc_HOL_Obool))),U_10646)),U_10647)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10644,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),U_10646)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10643,tc_fun(U_10644,tc_HOL_Obool)),U_10645),U_10647)),
    inference(clausify,[status(thm)],[f_2856_3]) ).

fof(f_2857_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(f_2857_2,plain,
    ! [U_10652,U_10651,U_10650,U_10649,U_10648] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10648,tc_fun(U_10649,tc_HOL_Obool)),U_10650),hAPP(hAPP(c_COMBB(tc_fun(U_10649,tc_HOL_Obool),tc_fun(U_10649,tc_HOL_Obool),U_10648),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10649,tc_HOL_Obool)),U_10651)),U_10652)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10649,tc_HOL_Obool)),U_10651),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10648,tc_fun(U_10649,tc_HOL_Obool)),U_10650),U_10652)),
    inference(variable_rename,[status(thm)],[f_2857_1]) ).

fof(f_2857_3,plain,
    ! [U_10648,U_10649,U_10650,U_10651,U_10652] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10648,tc_fun(U_10649,tc_HOL_Obool)),U_10650),hAPP(hAPP(c_COMBB(tc_fun(U_10649,tc_HOL_Obool),tc_fun(U_10649,tc_HOL_Obool),U_10648),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10649,tc_HOL_Obool)),U_10651)),U_10652)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10649,tc_HOL_Obool)),U_10651),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10648,tc_fun(U_10649,tc_HOL_Obool)),U_10650),U_10652)),
    inference(definitional_conversion,[status(esa)],[f_2857_2]) ).

cnf(f_2857_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10648,tc_fun(U_10649,tc_HOL_Obool)),U_10650),hAPP(hAPP(c_COMBB(tc_fun(U_10649,tc_HOL_Obool),tc_fun(U_10649,tc_HOL_Obool),U_10648),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10649,tc_HOL_Obool)),U_10651)),U_10652)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10649,tc_HOL_Obool)),U_10651),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10648,tc_fun(U_10649,tc_HOL_Obool)),U_10650),U_10652)),
    inference(clausify,[status(thm)],[f_2857_3]) ).

fof(f_2858_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(f_2858_2,plain,
    ! [U_10657,U_10656,U_10655,U_10654,U_10653] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10653,tc_fun(U_10654,tc_HOL_Obool)),U_10655),hAPP(hAPP(c_COMBC(U_10653,tc_fun(U_10654,tc_HOL_Obool),tc_fun(U_10654,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10654,tc_HOL_Obool),tc_fun(tc_fun(U_10654,tc_HOL_Obool),tc_fun(U_10654,tc_HOL_Obool)),U_10653),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10654,tc_HOL_Obool))),U_10656)),U_10657)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10654,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10653,tc_fun(U_10654,tc_HOL_Obool)),U_10655),U_10656)),U_10657),
    inference(variable_rename,[status(thm)],[f_2858_1]) ).

fof(f_2858_3,plain,
    ! [U_10653,U_10654,U_10655,U_10656,U_10657] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10653,tc_fun(U_10654,tc_HOL_Obool)),U_10655),hAPP(hAPP(c_COMBC(U_10653,tc_fun(U_10654,tc_HOL_Obool),tc_fun(U_10654,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10654,tc_HOL_Obool),tc_fun(tc_fun(U_10654,tc_HOL_Obool),tc_fun(U_10654,tc_HOL_Obool)),U_10653),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10654,tc_HOL_Obool))),U_10656)),U_10657)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10654,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10653,tc_fun(U_10654,tc_HOL_Obool)),U_10655),U_10656)),U_10657),
    inference(definitional_conversion,[status(esa)],[f_2858_2]) ).

cnf(f_2858_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10653,tc_fun(U_10654,tc_HOL_Obool)),U_10655),hAPP(hAPP(c_COMBC(U_10653,tc_fun(U_10654,tc_HOL_Obool),tc_fun(U_10654,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10654,tc_HOL_Obool),tc_fun(tc_fun(U_10654,tc_HOL_Obool),tc_fun(U_10654,tc_HOL_Obool)),U_10653),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10654,tc_HOL_Obool))),U_10656)),U_10657)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10654,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10653,tc_fun(U_10654,tc_HOL_Obool)),U_10655),U_10656)),U_10657),
    inference(clausify,[status(thm)],[f_2858_3]) ).

fof(f_2859_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(f_2859_2,plain,
    ! [U_10662,U_10661,U_10660,U_10659,U_10658] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10658,tc_HOL_Obool)),U_10659),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10660,tc_fun(U_10658,tc_HOL_Obool)),U_10661),U_10662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10660,tc_fun(U_10658,tc_HOL_Obool)),U_10661),hAPP(hAPP(c_COMBB(tc_fun(U_10658,tc_HOL_Obool),tc_fun(U_10658,tc_HOL_Obool),U_10660),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10658,tc_HOL_Obool)),U_10659)),U_10662)),
    inference(variable_rename,[status(thm)],[f_2859_1]) ).

fof(f_2859_3,plain,
    ! [U_10658,U_10659,U_10660,U_10661,U_10662] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10658,tc_HOL_Obool)),U_10659),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10660,tc_fun(U_10658,tc_HOL_Obool)),U_10661),U_10662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10660,tc_fun(U_10658,tc_HOL_Obool)),U_10661),hAPP(hAPP(c_COMBB(tc_fun(U_10658,tc_HOL_Obool),tc_fun(U_10658,tc_HOL_Obool),U_10660),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10658,tc_HOL_Obool)),U_10659)),U_10662)),
    inference(definitional_conversion,[status(esa)],[f_2859_2]) ).

cnf(f_2859_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10658,tc_HOL_Obool)),U_10659),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10660,tc_fun(U_10658,tc_HOL_Obool)),U_10661),U_10662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10660,tc_fun(U_10658,tc_HOL_Obool)),U_10661),hAPP(hAPP(c_COMBB(tc_fun(U_10658,tc_HOL_Obool),tc_fun(U_10658,tc_HOL_Obool),U_10660),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10658,tc_HOL_Obool)),U_10659)),U_10662)),
    inference(clausify,[status(thm)],[f_2859_3]) ).

fof(f_2860_1,plain,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib]) ).

fof(f_2860_2,plain,
    ! [U_10667,U_10666,U_10665,U_10664,U_10663] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10663,tc_HOL_Obool)),U_10664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10665,tc_fun(U_10663,tc_HOL_Obool)),U_10666),U_10667)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10665,tc_fun(U_10663,tc_HOL_Obool)),U_10666),hAPP(hAPP(c_COMBB(tc_fun(U_10663,tc_HOL_Obool),tc_fun(U_10663,tc_HOL_Obool),U_10665),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10663,tc_HOL_Obool)),U_10664)),U_10667)),
    inference(variable_rename,[status(thm)],[f_2860_1]) ).

fof(f_2860_3,plain,
    ! [U_10663,U_10664,U_10665,U_10666,U_10667] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10663,tc_HOL_Obool)),U_10664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10665,tc_fun(U_10663,tc_HOL_Obool)),U_10666),U_10667)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10665,tc_fun(U_10663,tc_HOL_Obool)),U_10666),hAPP(hAPP(c_COMBB(tc_fun(U_10663,tc_HOL_Obool),tc_fun(U_10663,tc_HOL_Obool),U_10665),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10663,tc_HOL_Obool)),U_10664)),U_10667)),
    inference(definitional_conversion,[status(esa)],[f_2860_2]) ).

cnf(f_2860_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10663,tc_HOL_Obool)),U_10664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10665,tc_fun(U_10663,tc_HOL_Obool)),U_10666),U_10667)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10665,tc_fun(U_10663,tc_HOL_Obool)),U_10666),hAPP(hAPP(c_COMBB(tc_fun(U_10663,tc_HOL_Obool),tc_fun(U_10663,tc_HOL_Obool),U_10665),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10663,tc_HOL_Obool)),U_10664)),U_10667)),
    inference(clausify,[status(thm)],[f_2860_3]) ).

fof(f_2861_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(f_2861_2,plain,
    ! [U_10672,U_10671,U_10670,U_10669,U_10668] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10668,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10669,tc_fun(U_10668,tc_HOL_Obool)),U_10670),U_10671)),U_10672) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10669,tc_fun(U_10668,tc_HOL_Obool)),U_10670),hAPP(hAPP(c_COMBC(U_10669,tc_fun(U_10668,tc_HOL_Obool),tc_fun(U_10668,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10668,tc_HOL_Obool),tc_fun(tc_fun(U_10668,tc_HOL_Obool),tc_fun(U_10668,tc_HOL_Obool)),U_10669),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10668,tc_HOL_Obool))),U_10671)),U_10672)),
    inference(variable_rename,[status(thm)],[f_2861_1]) ).

fof(f_2861_3,plain,
    ! [U_10668,U_10669,U_10670,U_10671,U_10672] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10668,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10669,tc_fun(U_10668,tc_HOL_Obool)),U_10670),U_10671)),U_10672) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10669,tc_fun(U_10668,tc_HOL_Obool)),U_10670),hAPP(hAPP(c_COMBC(U_10669,tc_fun(U_10668,tc_HOL_Obool),tc_fun(U_10668,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10668,tc_HOL_Obool),tc_fun(tc_fun(U_10668,tc_HOL_Obool),tc_fun(U_10668,tc_HOL_Obool)),U_10669),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10668,tc_HOL_Obool))),U_10671)),U_10672)),
    inference(definitional_conversion,[status(esa)],[f_2861_2]) ).

cnf(f_2861_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10668,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10669,tc_fun(U_10668,tc_HOL_Obool)),U_10670),U_10671)),U_10672) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10669,tc_fun(U_10668,tc_HOL_Obool)),U_10670),hAPP(hAPP(c_COMBC(U_10669,tc_fun(U_10668,tc_HOL_Obool),tc_fun(U_10668,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10668,tc_HOL_Obool),tc_fun(tc_fun(U_10668,tc_HOL_Obool),tc_fun(U_10668,tc_HOL_Obool)),U_10669),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10668,tc_HOL_Obool))),U_10671)),U_10672)),
    inference(clausify,[status(thm)],[f_2861_3]) ).

fof(f_2862_1,plain,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(f_2862_2,plain,
    ! [U_10679,U_10678,U_10677,U_10676,U_10675,U_10674,U_10673] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10673,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10673,tc_HOL_Obool)),U_10675),U_10676)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10677,tc_fun(U_10673,tc_HOL_Obool)),U_10678),U_10679)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10673,tc_HOL_Obool)),U_10675),hAPP(hAPP(c_COMBB(tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10673,tc_HOL_Obool),U_10674),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10677,tc_fun(U_10673,tc_HOL_Obool)),U_10678)),hAPP(hAPP(c_COMBC(U_10674,tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool)),tc_fun(tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool))),U_10674),c_COMBB(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool),U_10677)),hAPP(hAPP(c_COMBB(tc_fun(U_10673,tc_HOL_Obool),tc_fun(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool)),U_10674),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10673,tc_HOL_Obool))),U_10676))),U_10679))),
    inference(variable_rename,[status(thm)],[f_2862_1]) ).

fof(f_2862_3,plain,
    ! [U_10673,U_10674,U_10675,U_10676,U_10677,U_10678,U_10679] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10673,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10673,tc_HOL_Obool)),U_10675),U_10676)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10677,tc_fun(U_10673,tc_HOL_Obool)),U_10678),U_10679)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10673,tc_HOL_Obool)),U_10675),hAPP(hAPP(c_COMBB(tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10673,tc_HOL_Obool),U_10674),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10677,tc_fun(U_10673,tc_HOL_Obool)),U_10678)),hAPP(hAPP(c_COMBC(U_10674,tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool)),tc_fun(tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool))),U_10674),c_COMBB(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool),U_10677)),hAPP(hAPP(c_COMBB(tc_fun(U_10673,tc_HOL_Obool),tc_fun(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool)),U_10674),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10673,tc_HOL_Obool))),U_10676))),U_10679))),
    inference(definitional_conversion,[status(esa)],[f_2862_2]) ).

cnf(f_2862_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10673,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10673,tc_HOL_Obool)),U_10675),U_10676)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10677,tc_fun(U_10673,tc_HOL_Obool)),U_10678),U_10679)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10673,tc_HOL_Obool)),U_10675),hAPP(hAPP(c_COMBB(tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10673,tc_HOL_Obool),U_10674),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10677,tc_fun(U_10673,tc_HOL_Obool)),U_10678)),hAPP(hAPP(c_COMBC(U_10674,tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool)),tc_fun(tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool)),tc_fun(U_10677,tc_fun(U_10673,tc_HOL_Obool))),U_10674),c_COMBB(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool),U_10677)),hAPP(hAPP(c_COMBB(tc_fun(U_10673,tc_HOL_Obool),tc_fun(tc_fun(U_10673,tc_HOL_Obool),tc_fun(U_10673,tc_HOL_Obool)),U_10674),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10673,tc_HOL_Obool))),U_10676))),U_10679))),
    inference(clausify,[status(thm)],[f_2862_3]) ).

fof(f_2863_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__apply]) ).

fof(f_2863_2,plain,
    ! [U_10685,U_10684,U_10683,U_10682,U_10681,U_10680] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10681,tc_fun(U_10682,U_10680)),U_10683),U_10684),U_10685) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10681,U_10680),U_10683),hAPP(hAPP(c_COMBC(U_10681,U_10682,U_10680),U_10684),U_10685))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10680) ),
    inference(variable_rename,[status(thm)],[f_2863_1]) ).

fof(f_2863_3,plain,
    ! [U_10680,U_10681,U_10682,U_10683,U_10684,U_10685] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10681,tc_fun(U_10682,U_10680)),U_10683),U_10684),U_10685) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10681,U_10680),U_10683),hAPP(hAPP(c_COMBC(U_10681,U_10682,U_10680),U_10684),U_10685))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10680) ),
    inference(definitional_conversion,[status(esa)],[f_2863_2]) ).

cnf(f_2863_4,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10681,tc_fun(U_10682,U_10680)),U_10683),U_10684),U_10685) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10681,U_10680),U_10683),hAPP(hAPP(c_COMBC(U_10681,U_10682,U_10680),U_10684),U_10685))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10680) ),
    inference(clausify,[status(thm)],[f_2863_3]) ).

fof(f_2864_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(f_2864_2,plain,
    ! [U_10690,U_10689,U_10688,U_10687,U_10686] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10686,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10687,tc_fun(U_10686,tc_HOL_Obool)),U_10688),U_10689)),U_10690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10687,tc_fun(U_10686,tc_HOL_Obool)),U_10688),hAPP(hAPP(c_COMBC(U_10687,tc_fun(U_10686,tc_HOL_Obool),tc_fun(U_10686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10686,tc_HOL_Obool),tc_fun(tc_fun(U_10686,tc_HOL_Obool),tc_fun(U_10686,tc_HOL_Obool)),U_10687),c_Groups_Ominus__class_Ominus(tc_fun(U_10686,tc_HOL_Obool))),U_10689)),U_10690)),
    inference(variable_rename,[status(thm)],[f_2864_1]) ).

fof(f_2864_3,plain,
    ! [U_10686,U_10687,U_10688,U_10689,U_10690] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10686,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10687,tc_fun(U_10686,tc_HOL_Obool)),U_10688),U_10689)),U_10690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10687,tc_fun(U_10686,tc_HOL_Obool)),U_10688),hAPP(hAPP(c_COMBC(U_10687,tc_fun(U_10686,tc_HOL_Obool),tc_fun(U_10686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10686,tc_HOL_Obool),tc_fun(tc_fun(U_10686,tc_HOL_Obool),tc_fun(U_10686,tc_HOL_Obool)),U_10687),c_Groups_Ominus__class_Ominus(tc_fun(U_10686,tc_HOL_Obool))),U_10689)),U_10690)),
    inference(definitional_conversion,[status(esa)],[f_2864_2]) ).

cnf(f_2864_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10686,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10687,tc_fun(U_10686,tc_HOL_Obool)),U_10688),U_10689)),U_10690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10687,tc_fun(U_10686,tc_HOL_Obool)),U_10688),hAPP(hAPP(c_COMBC(U_10687,tc_fun(U_10686,tc_HOL_Obool),tc_fun(U_10686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10686,tc_HOL_Obool),tc_fun(tc_fun(U_10686,tc_HOL_Obool),tc_fun(U_10686,tc_HOL_Obool)),U_10687),c_Groups_Ominus__class_Ominus(tc_fun(U_10686,tc_HOL_Obool))),U_10689)),U_10690)),
    inference(clausify,[status(thm)],[f_2864_3]) ).

fof(f_2865_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(f_2865_2,plain,
    ! [U_10695,U_10694,U_10693,U_10692,U_10691] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10691,tc_fun(U_10692,tc_HOL_Obool)),U_10693),hAPP(hAPP(c_COMBC(U_10691,tc_fun(U_10692,tc_HOL_Obool),tc_fun(U_10692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10692,tc_HOL_Obool),tc_fun(tc_fun(U_10692,tc_HOL_Obool),tc_fun(U_10692,tc_HOL_Obool)),U_10691),c_Groups_Ominus__class_Ominus(tc_fun(U_10692,tc_HOL_Obool))),U_10694)),U_10695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10692,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10691,tc_fun(U_10692,tc_HOL_Obool)),U_10693),U_10694)),U_10695),
    inference(variable_rename,[status(thm)],[f_2865_1]) ).

fof(f_2865_3,plain,
    ! [U_10691,U_10692,U_10693,U_10694,U_10695] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10691,tc_fun(U_10692,tc_HOL_Obool)),U_10693),hAPP(hAPP(c_COMBC(U_10691,tc_fun(U_10692,tc_HOL_Obool),tc_fun(U_10692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10692,tc_HOL_Obool),tc_fun(tc_fun(U_10692,tc_HOL_Obool),tc_fun(U_10692,tc_HOL_Obool)),U_10691),c_Groups_Ominus__class_Ominus(tc_fun(U_10692,tc_HOL_Obool))),U_10694)),U_10695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10692,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10691,tc_fun(U_10692,tc_HOL_Obool)),U_10693),U_10694)),U_10695),
    inference(definitional_conversion,[status(esa)],[f_2865_2]) ).

cnf(f_2865_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10691,tc_fun(U_10692,tc_HOL_Obool)),U_10693),hAPP(hAPP(c_COMBC(U_10691,tc_fun(U_10692,tc_HOL_Obool),tc_fun(U_10692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10692,tc_HOL_Obool),tc_fun(tc_fun(U_10692,tc_HOL_Obool),tc_fun(U_10692,tc_HOL_Obool)),U_10691),c_Groups_Ominus__class_Ominus(tc_fun(U_10692,tc_HOL_Obool))),U_10694)),U_10695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10692,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10691,tc_fun(U_10692,tc_HOL_Obool)),U_10693),U_10694)),U_10695),
    inference(clausify,[status(thm)],[f_2865_3]) ).

fof(f_2866_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__subset]) ).

fof(f_2866_2,plain,
    ! [U_10700,U_10699,U_10698,U_10697,U_10696] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10696),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10697,U_10696),U_10698),U_10700)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10697,U_10696),U_10699),U_10700)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10697,tc_HOL_Obool)),U_10698),U_10699))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10696) ),
    inference(variable_rename,[status(thm)],[f_2866_1]) ).

fof(f_2866_3,plain,
    ! [U_10696,U_10697,U_10698,U_10699,U_10700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10696),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10697,U_10696),U_10698),U_10700)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10697,U_10696),U_10699),U_10700)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10697,tc_HOL_Obool)),U_10698),U_10699))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10696) ),
    inference(definitional_conversion,[status(esa)],[f_2866_2]) ).

cnf(f_2866_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10696),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10697,U_10696),U_10698),U_10700)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10697,U_10696),U_10699),U_10700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10697,tc_HOL_Obool)),U_10698),U_10699))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10696) ),
    inference(clausify,[status(thm)],[f_2866_3]) ).

fof(f_2867_1,plain,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__SUPI]) ).

fof(f_2867_2,plain,
    ! [U_10705,U_10704,U_10703,U_10702,U_10701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10701),hAPP(U_10705,U_10703)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10702,U_10701),U_10704),U_10705)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10702),U_10703),U_10704))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10701) ),
    inference(variable_rename,[status(thm)],[f_2867_1]) ).

fof(f_2867_3,plain,
    ! [U_10702,U_10701,U_10703,U_10704,U_10705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10701),hAPP(U_10705,U_10703)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10702,U_10701),U_10704),U_10705)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10702),U_10703),U_10704))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10701) ),
    inference(definitional_conversion,[status(esa)],[f_2867_2]) ).

cnf(f_2867_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10701),hAPP(U_10705,U_10703)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10702,U_10701),U_10704),U_10705)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10702),U_10703),U_10704))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10701) ),
    inference(clausify,[status(thm)],[f_2867_3]) ).

fof(f_2868_1,plain,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib]) ).

fof(f_2868_2,plain,
    ! [U_10711,U_10710,U_10709,U_10708,U_10707,U_10706] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10706,tc_fun(U_10709,tc_HOL_Obool)),U_10708),hAPP(hAPP(c_COMBB(tc_fun(U_10709,tc_HOL_Obool),tc_fun(U_10709,tc_HOL_Obool),U_10706),hAPP(c_Set_Oinsert(U_10709),U_10710)),U_10711)) = hAPP(hAPP(c_Set_Oinsert(U_10709),U_10710),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10706,tc_fun(U_10709,tc_HOL_Obool)),U_10708),U_10711))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10706),U_10707),U_10708)) ),
    inference(variable_rename,[status(thm)],[f_2868_1]) ).

fof(f_2868_3,plain,
    ! [U_10706,U_10707,U_10708,U_10709,U_10710,U_10711] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10706,tc_fun(U_10709,tc_HOL_Obool)),U_10708),hAPP(hAPP(c_COMBB(tc_fun(U_10709,tc_HOL_Obool),tc_fun(U_10709,tc_HOL_Obool),U_10706),hAPP(c_Set_Oinsert(U_10709),U_10710)),U_10711)) = hAPP(hAPP(c_Set_Oinsert(U_10709),U_10710),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10706,tc_fun(U_10709,tc_HOL_Obool)),U_10708),U_10711))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10706),U_10707),U_10708)) ),
    inference(definitional_conversion,[status(esa)],[f_2868_2]) ).

cnf(f_2868_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10706,tc_fun(U_10709,tc_HOL_Obool)),U_10708),hAPP(hAPP(c_COMBB(tc_fun(U_10709,tc_HOL_Obool),tc_fun(U_10709,tc_HOL_Obool),U_10706),hAPP(c_Set_Oinsert(U_10709),U_10710)),U_10711)) = hAPP(hAPP(c_Set_Oinsert(U_10709),U_10710),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10706,tc_fun(U_10709,tc_HOL_Obool)),U_10708),U_10711))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10706),U_10707),U_10708)) ),
    inference(clausify,[status(thm)],[f_2868_3]) ).

fof(f_2869_1,plain,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__upper]) ).

fof(f_2869_2,plain,
    ! [U_10716,U_10715,U_10714,U_10713,U_10712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10715,tc_HOL_Obool)),hAPP(U_10716,U_10713)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10712,tc_fun(U_10715,tc_HOL_Obool)),U_10714),U_10716)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10712),U_10713),U_10714)) ),
    inference(variable_rename,[status(thm)],[f_2869_1]) ).

fof(f_2869_3,plain,
    ! [U_10713,U_10712,U_10714,U_10715,U_10716] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10715,tc_HOL_Obool)),hAPP(U_10716,U_10713)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10712,tc_fun(U_10715,tc_HOL_Obool)),U_10714),U_10716)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10712),U_10713),U_10714)) ),
    inference(definitional_conversion,[status(esa)],[f_2869_2]) ).

cnf(f_2869_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10715,tc_HOL_Obool)),hAPP(U_10716,U_10713)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10712,tc_fun(U_10715,tc_HOL_Obool)),U_10714),U_10716)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10712),U_10713),U_10714)) ),
    inference(clausify,[status(thm)],[f_2869_3]) ).

fof(f_2870_1,plain,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__absorb]) ).

fof(f_2870_2,plain,
    ! [U_10721,U_10720,U_10719,U_10718,U_10717] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10720,tc_HOL_Obool)),hAPP(U_10721,U_10718)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10717,tc_fun(U_10720,tc_HOL_Obool)),U_10719),U_10721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10717,tc_fun(U_10720,tc_HOL_Obool)),U_10719),U_10721)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10717),U_10718),U_10719)) ),
    inference(variable_rename,[status(thm)],[f_2870_1]) ).

fof(f_2870_3,plain,
    ! [U_10717,U_10718,U_10719,U_10720,U_10721] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10720,tc_HOL_Obool)),hAPP(U_10721,U_10718)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10717,tc_fun(U_10720,tc_HOL_Obool)),U_10719),U_10721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10717,tc_fun(U_10720,tc_HOL_Obool)),U_10719),U_10721)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10717),U_10718),U_10719)) ),
    inference(definitional_conversion,[status(esa)],[f_2870_2]) ).

cnf(f_2870_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10720,tc_HOL_Obool)),hAPP(U_10721,U_10718)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10717,tc_fun(U_10720,tc_HOL_Obool)),U_10719),U_10721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10717,tc_fun(U_10720,tc_HOL_Obool)),U_10719),U_10721)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10717),U_10718),U_10719)) ),
    inference(clausify,[status(thm)],[f_2870_3]) ).

fof(f_2871_1,plain,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J]) ).

fof(f_2871_2,plain,
    ! [U_10726,U_10725,U_10724,U_10723,U_10722] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_10724),U_10725),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10723,tc_fun(U_10724,tc_HOL_Obool)),U_10722),U_10726)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10723,tc_fun(U_10724,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_COMBB(tc_fun(U_10724,tc_HOL_Obool),tc_fun(U_10724,tc_HOL_Obool),U_10723),hAPP(c_Set_Oinsert(U_10724),U_10725)),U_10726))
        | U_10722 = c_Orderings_Obot__class_Obot(tc_fun(U_10723,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(U_10724),U_10725),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10723,tc_fun(U_10724,tc_HOL_Obool)),U_10722),U_10726)) = hAPP(hAPP(c_Set_Oinsert(U_10724),U_10725),c_Orderings_Obot__class_Obot(tc_fun(U_10724,tc_HOL_Obool)))
        | U_10722 != c_Orderings_Obot__class_Obot(tc_fun(U_10723,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2871_1]) ).

fof(f_2871_3,plain,
    ( ! [U_10736,U_10734,U_10732,U_10730,U_10728] :
        ( hAPP(hAPP(c_Set_Oinsert(U_10732),U_10734),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10730,tc_fun(U_10732,tc_HOL_Obool)),U_10728),U_10736)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10730,tc_fun(U_10732,tc_HOL_Obool)),U_10728),hAPP(hAPP(c_COMBB(tc_fun(U_10732,tc_HOL_Obool),tc_fun(U_10732,tc_HOL_Obool),U_10730),hAPP(c_Set_Oinsert(U_10732),U_10734)),U_10736))
        | U_10728 = c_Orderings_Obot__class_Obot(tc_fun(U_10730,tc_HOL_Obool)) )
    & ! [U_10735,U_10733,U_10731,U_10729,U_10727] :
        ( hAPP(hAPP(c_Set_Oinsert(U_10731),U_10733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10729,tc_fun(U_10731,tc_HOL_Obool)),U_10727),U_10735)) = hAPP(hAPP(c_Set_Oinsert(U_10731),U_10733),c_Orderings_Obot__class_Obot(tc_fun(U_10731,tc_HOL_Obool)))
        | U_10727 != c_Orderings_Obot__class_Obot(tc_fun(U_10729,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2871_2]) ).

fof(f_2871_4,plain,
    ( ! [U_10728,U_10730,U_10732,U_10734,U_10736] :
        ( hAPP(hAPP(c_Set_Oinsert(U_10732),U_10734),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10730,tc_fun(U_10732,tc_HOL_Obool)),U_10728),U_10736)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10730,tc_fun(U_10732,tc_HOL_Obool)),U_10728),hAPP(hAPP(c_COMBB(tc_fun(U_10732,tc_HOL_Obool),tc_fun(U_10732,tc_HOL_Obool),U_10730),hAPP(c_Set_Oinsert(U_10732),U_10734)),U_10736))
        | U_10728 = c_Orderings_Obot__class_Obot(tc_fun(U_10730,tc_HOL_Obool)) )
    & ! [U_10729,U_10733,U_10727,U_10731,U_10735] :
        ( hAPP(hAPP(c_Set_Oinsert(U_10731),U_10733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10729,tc_fun(U_10731,tc_HOL_Obool)),U_10727),U_10735)) = hAPP(hAPP(c_Set_Oinsert(U_10731),U_10733),c_Orderings_Obot__class_Obot(tc_fun(U_10731,tc_HOL_Obool)))
        | U_10727 != c_Orderings_Obot__class_Obot(tc_fun(U_10729,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2871_3]) ).

cnf(f_2871_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_10731),U_10733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10729,tc_fun(U_10731,tc_HOL_Obool)),U_10727),U_10735)) = hAPP(hAPP(c_Set_Oinsert(U_10731),U_10733),c_Orderings_Obot__class_Obot(tc_fun(U_10731,tc_HOL_Obool)))
    | U_10727 != c_Orderings_Obot__class_Obot(tc_fun(U_10729,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2871_4]) ).

cnf(f_2871_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_10732),U_10734),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10730,tc_fun(U_10732,tc_HOL_Obool)),U_10728),U_10736)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10730,tc_fun(U_10732,tc_HOL_Obool)),U_10728),hAPP(hAPP(c_COMBB(tc_fun(U_10732,tc_HOL_Obool),tc_fun(U_10732,tc_HOL_Obool),U_10730),hAPP(c_Set_Oinsert(U_10732),U_10734)),U_10736))
    | U_10728 = c_Orderings_Obot__class_Obot(tc_fun(U_10730,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2871_4]) ).

fof(f_2872_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_UN__singleton]) ).

fof(f_2872_2,plain,
    ! [U_10738,U_10737] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10737,tc_fun(U_10737,tc_HOL_Obool)),U_10738),hAPP(hAPP(c_COMBC(U_10737,tc_fun(U_10737,tc_HOL_Obool),tc_fun(U_10737,tc_HOL_Obool)),c_Set_Oinsert(U_10737)),c_Orderings_Obot__class_Obot(tc_fun(U_10737,tc_HOL_Obool)))) = U_10738,
    inference(variable_rename,[status(thm)],[f_2872_1]) ).

fof(f_2872_3,plain,
    ! [U_10738,U_10737] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10737,tc_fun(U_10737,tc_HOL_Obool)),U_10738),hAPP(hAPP(c_COMBC(U_10737,tc_fun(U_10737,tc_HOL_Obool),tc_fun(U_10737,tc_HOL_Obool)),c_Set_Oinsert(U_10737)),c_Orderings_Obot__class_Obot(tc_fun(U_10737,tc_HOL_Obool)))) = U_10738,
    inference(definitional_conversion,[status(esa)],[f_2872_2]) ).

cnf(f_2872_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10737,tc_fun(U_10737,tc_HOL_Obool)),U_10738),hAPP(hAPP(c_COMBC(U_10737,tc_fun(U_10737,tc_HOL_Obool),tc_fun(U_10737,tc_HOL_Obool)),c_Set_Oinsert(U_10737)),c_Orderings_Obot__class_Obot(tc_fun(U_10737,tc_HOL_Obool)))) = U_10738,
    inference(clausify,[status(thm)],[f_2872_3]) ).

fof(f_2873_1,plain,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J]) ).

fof(f_2873_2,plain,
    ! [U_10743,U_10742,U_10741,U_10740,U_10739] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10740,tc_fun(U_10741,tc_HOL_Obool)),U_10739),hAPP(hAPP(c_COMBB(tc_fun(U_10741,tc_HOL_Obool),tc_fun(U_10741,tc_HOL_Obool),U_10740),hAPP(c_Set_Oinsert(U_10741),U_10742)),U_10743)) = hAPP(hAPP(c_Set_Oinsert(U_10741),U_10742),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10740,tc_fun(U_10741,tc_HOL_Obool)),U_10739),U_10743))
        | U_10739 = c_Orderings_Obot__class_Obot(tc_fun(U_10740,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10740,tc_fun(U_10741,tc_HOL_Obool)),U_10739),hAPP(hAPP(c_COMBB(tc_fun(U_10741,tc_HOL_Obool),tc_fun(U_10741,tc_HOL_Obool),U_10740),hAPP(c_Set_Oinsert(U_10741),U_10742)),U_10743)) = c_Orderings_Obot__class_Obot(tc_fun(U_10741,tc_HOL_Obool))
        | U_10739 != c_Orderings_Obot__class_Obot(tc_fun(U_10740,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2873_1]) ).

fof(f_2873_3,plain,
    ( ! [U_10753,U_10751,U_10749,U_10747,U_10745] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10747,tc_fun(U_10749,tc_HOL_Obool)),U_10745),hAPP(hAPP(c_COMBB(tc_fun(U_10749,tc_HOL_Obool),tc_fun(U_10749,tc_HOL_Obool),U_10747),hAPP(c_Set_Oinsert(U_10749),U_10751)),U_10753)) = hAPP(hAPP(c_Set_Oinsert(U_10749),U_10751),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10747,tc_fun(U_10749,tc_HOL_Obool)),U_10745),U_10753))
        | U_10745 = c_Orderings_Obot__class_Obot(tc_fun(U_10747,tc_HOL_Obool)) )
    & ! [U_10752,U_10750,U_10748,U_10746,U_10744] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10746,tc_fun(U_10748,tc_HOL_Obool)),U_10744),hAPP(hAPP(c_COMBB(tc_fun(U_10748,tc_HOL_Obool),tc_fun(U_10748,tc_HOL_Obool),U_10746),hAPP(c_Set_Oinsert(U_10748),U_10750)),U_10752)) = c_Orderings_Obot__class_Obot(tc_fun(U_10748,tc_HOL_Obool))
        | U_10744 != c_Orderings_Obot__class_Obot(tc_fun(U_10746,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2873_2]) ).

fof(f_2873_4,plain,
    ( ! [U_10745,U_10747,U_10749,U_10751,U_10753] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10747,tc_fun(U_10749,tc_HOL_Obool)),U_10745),hAPP(hAPP(c_COMBB(tc_fun(U_10749,tc_HOL_Obool),tc_fun(U_10749,tc_HOL_Obool),U_10747),hAPP(c_Set_Oinsert(U_10749),U_10751)),U_10753)) = hAPP(hAPP(c_Set_Oinsert(U_10749),U_10751),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10747,tc_fun(U_10749,tc_HOL_Obool)),U_10745),U_10753))
        | U_10745 = c_Orderings_Obot__class_Obot(tc_fun(U_10747,tc_HOL_Obool)) )
    & ! [U_10750,U_10746,U_10744,U_10748,U_10752] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10746,tc_fun(U_10748,tc_HOL_Obool)),U_10744),hAPP(hAPP(c_COMBB(tc_fun(U_10748,tc_HOL_Obool),tc_fun(U_10748,tc_HOL_Obool),U_10746),hAPP(c_Set_Oinsert(U_10748),U_10750)),U_10752)) = c_Orderings_Obot__class_Obot(tc_fun(U_10748,tc_HOL_Obool))
        | U_10744 != c_Orderings_Obot__class_Obot(tc_fun(U_10746,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2873_3]) ).

cnf(f_2873_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10746,tc_fun(U_10748,tc_HOL_Obool)),U_10744),hAPP(hAPP(c_COMBB(tc_fun(U_10748,tc_HOL_Obool),tc_fun(U_10748,tc_HOL_Obool),U_10746),hAPP(c_Set_Oinsert(U_10748),U_10750)),U_10752)) = c_Orderings_Obot__class_Obot(tc_fun(U_10748,tc_HOL_Obool))
    | U_10744 != c_Orderings_Obot__class_Obot(tc_fun(U_10746,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2873_4]) ).

cnf(f_2873_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10747,tc_fun(U_10749,tc_HOL_Obool)),U_10745),hAPP(hAPP(c_COMBB(tc_fun(U_10749,tc_HOL_Obool),tc_fun(U_10749,tc_HOL_Obool),U_10747),hAPP(c_Set_Oinsert(U_10749),U_10751)),U_10753)) = hAPP(hAPP(c_Set_Oinsert(U_10749),U_10751),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10747,tc_fun(U_10749,tc_HOL_Obool)),U_10745),U_10753))
    | U_10745 = c_Orderings_Obot__class_Obot(tc_fun(U_10747,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2873_4]) ).

fof(f_2874_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J]) ).

fof(f_2874_2,plain,
    ! [U_10758,U_10757,U_10756,U_10755,U_10754] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10756,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10755,tc_fun(U_10756,tc_HOL_Obool)),U_10754),U_10757)),U_10758) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10755,tc_fun(U_10756,tc_HOL_Obool)),U_10754),hAPP(hAPP(c_COMBC(U_10755,tc_fun(U_10756,tc_HOL_Obool),tc_fun(U_10756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10756,tc_HOL_Obool),tc_fun(tc_fun(U_10756,tc_HOL_Obool),tc_fun(U_10756,tc_HOL_Obool)),U_10755),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10756,tc_HOL_Obool))),U_10757)),U_10758))
        | U_10754 = c_Orderings_Obot__class_Obot(tc_fun(U_10755,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10756,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10755,tc_fun(U_10756,tc_HOL_Obool)),U_10754),U_10757)),U_10758) = U_10758
        | U_10754 != c_Orderings_Obot__class_Obot(tc_fun(U_10755,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2874_1]) ).

fof(f_2874_3,plain,
    ( ! [U_10768,U_10766,U_10764,U_10762,U_10760] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10764,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10762,tc_fun(U_10764,tc_HOL_Obool)),U_10760),U_10766)),U_10768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10762,tc_fun(U_10764,tc_HOL_Obool)),U_10760),hAPP(hAPP(c_COMBC(U_10762,tc_fun(U_10764,tc_HOL_Obool),tc_fun(U_10764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10764,tc_HOL_Obool),tc_fun(tc_fun(U_10764,tc_HOL_Obool),tc_fun(U_10764,tc_HOL_Obool)),U_10762),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10764,tc_HOL_Obool))),U_10766)),U_10768))
        | U_10760 = c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool)) )
    & ! [U_10767,U_10765,U_10763,U_10761,U_10759] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10763,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10761,tc_fun(U_10763,tc_HOL_Obool)),U_10759),U_10765)),U_10767) = U_10767
        | U_10759 != c_Orderings_Obot__class_Obot(tc_fun(U_10761,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2874_2]) ).

fof(f_2874_4,plain,
    ( ! [U_10768,U_10760,U_10762,U_10764,U_10766] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10764,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10762,tc_fun(U_10764,tc_HOL_Obool)),U_10760),U_10766)),U_10768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10762,tc_fun(U_10764,tc_HOL_Obool)),U_10760),hAPP(hAPP(c_COMBC(U_10762,tc_fun(U_10764,tc_HOL_Obool),tc_fun(U_10764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10764,tc_HOL_Obool),tc_fun(tc_fun(U_10764,tc_HOL_Obool),tc_fun(U_10764,tc_HOL_Obool)),U_10762),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10764,tc_HOL_Obool))),U_10766)),U_10768))
        | U_10760 = c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool)) )
    & ! [U_10765,U_10761,U_10759,U_10763,U_10767] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10763,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10761,tc_fun(U_10763,tc_HOL_Obool)),U_10759),U_10765)),U_10767) = U_10767
        | U_10759 != c_Orderings_Obot__class_Obot(tc_fun(U_10761,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2874_3]) ).

cnf(f_2874_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10763,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10761,tc_fun(U_10763,tc_HOL_Obool)),U_10759),U_10765)),U_10767) = U_10767
    | U_10759 != c_Orderings_Obot__class_Obot(tc_fun(U_10761,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2874_4]) ).

cnf(f_2874_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10764,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10762,tc_fun(U_10764,tc_HOL_Obool)),U_10760),U_10766)),U_10768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10762,tc_fun(U_10764,tc_HOL_Obool)),U_10760),hAPP(hAPP(c_COMBC(U_10762,tc_fun(U_10764,tc_HOL_Obool),tc_fun(U_10764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10764,tc_HOL_Obool),tc_fun(tc_fun(U_10764,tc_HOL_Obool),tc_fun(U_10764,tc_HOL_Obool)),U_10762),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10764,tc_HOL_Obool))),U_10766)),U_10768))
    | U_10760 = c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2874_4]) ).

fof(f_2875_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J]) ).

fof(f_2875_2,plain,
    ! [U_10773,U_10772,U_10771,U_10770,U_10769] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10771,tc_HOL_Obool)),U_10772),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10770,tc_fun(U_10771,tc_HOL_Obool)),U_10769),U_10773)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10770,tc_fun(U_10771,tc_HOL_Obool)),U_10769),hAPP(hAPP(c_COMBB(tc_fun(U_10771,tc_HOL_Obool),tc_fun(U_10771,tc_HOL_Obool),U_10770),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10771,tc_HOL_Obool)),U_10772)),U_10773))
        | U_10769 = c_Orderings_Obot__class_Obot(tc_fun(U_10770,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10771,tc_HOL_Obool)),U_10772),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10770,tc_fun(U_10771,tc_HOL_Obool)),U_10769),U_10773)) = U_10772
        | U_10769 != c_Orderings_Obot__class_Obot(tc_fun(U_10770,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2875_1]) ).

fof(f_2875_3,plain,
    ( ! [U_10783,U_10781,U_10779,U_10777,U_10775] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10779,tc_HOL_Obool)),U_10781),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10777,tc_fun(U_10779,tc_HOL_Obool)),U_10775),U_10783)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10777,tc_fun(U_10779,tc_HOL_Obool)),U_10775),hAPP(hAPP(c_COMBB(tc_fun(U_10779,tc_HOL_Obool),tc_fun(U_10779,tc_HOL_Obool),U_10777),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10779,tc_HOL_Obool)),U_10781)),U_10783))
        | U_10775 = c_Orderings_Obot__class_Obot(tc_fun(U_10777,tc_HOL_Obool)) )
    & ! [U_10782,U_10780,U_10778,U_10776,U_10774] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10778,tc_HOL_Obool)),U_10780),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10776,tc_fun(U_10778,tc_HOL_Obool)),U_10774),U_10782)) = U_10780
        | U_10774 != c_Orderings_Obot__class_Obot(tc_fun(U_10776,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2875_2]) ).

fof(f_2875_4,plain,
    ( ! [U_10775,U_10777,U_10779,U_10781,U_10783] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10779,tc_HOL_Obool)),U_10781),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10777,tc_fun(U_10779,tc_HOL_Obool)),U_10775),U_10783)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10777,tc_fun(U_10779,tc_HOL_Obool)),U_10775),hAPP(hAPP(c_COMBB(tc_fun(U_10779,tc_HOL_Obool),tc_fun(U_10779,tc_HOL_Obool),U_10777),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10779,tc_HOL_Obool)),U_10781)),U_10783))
        | U_10775 = c_Orderings_Obot__class_Obot(tc_fun(U_10777,tc_HOL_Obool)) )
    & ! [U_10776,U_10780,U_10774,U_10778,U_10782] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10778,tc_HOL_Obool)),U_10780),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10776,tc_fun(U_10778,tc_HOL_Obool)),U_10774),U_10782)) = U_10780
        | U_10774 != c_Orderings_Obot__class_Obot(tc_fun(U_10776,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2875_3]) ).

cnf(f_2875_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10778,tc_HOL_Obool)),U_10780),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10776,tc_fun(U_10778,tc_HOL_Obool)),U_10774),U_10782)) = U_10780
    | U_10774 != c_Orderings_Obot__class_Obot(tc_fun(U_10776,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

cnf(f_2875_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10779,tc_HOL_Obool)),U_10781),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10777,tc_fun(U_10779,tc_HOL_Obool)),U_10775),U_10783)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10777,tc_fun(U_10779,tc_HOL_Obool)),U_10775),hAPP(hAPP(c_COMBB(tc_fun(U_10779,tc_HOL_Obool),tc_fun(U_10779,tc_HOL_Obool),U_10777),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10779,tc_HOL_Obool)),U_10781)),U_10783))
    | U_10775 = c_Orderings_Obot__class_Obot(tc_fun(U_10777,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

fof(f_2876_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J]) ).

fof(f_2876_2,plain,
    ! [U_10788,U_10787,U_10786,U_10785,U_10784] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10785,tc_fun(U_10786,tc_HOL_Obool)),U_10784),hAPP(hAPP(c_COMBC(U_10785,tc_fun(U_10786,tc_HOL_Obool),tc_fun(U_10786,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10786,tc_HOL_Obool),tc_fun(tc_fun(U_10786,tc_HOL_Obool),tc_fun(U_10786,tc_HOL_Obool)),U_10785),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10786,tc_HOL_Obool))),U_10787)),U_10788)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10786,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10785,tc_fun(U_10786,tc_HOL_Obool)),U_10784),U_10787)),U_10788)
        | U_10784 = c_Orderings_Obot__class_Obot(tc_fun(U_10785,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10785,tc_fun(U_10786,tc_HOL_Obool)),U_10784),hAPP(hAPP(c_COMBC(U_10785,tc_fun(U_10786,tc_HOL_Obool),tc_fun(U_10786,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10786,tc_HOL_Obool),tc_fun(tc_fun(U_10786,tc_HOL_Obool),tc_fun(U_10786,tc_HOL_Obool)),U_10785),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10786,tc_HOL_Obool))),U_10787)),U_10788)) = c_Orderings_Obot__class_Obot(tc_fun(U_10786,tc_HOL_Obool))
        | U_10784 != c_Orderings_Obot__class_Obot(tc_fun(U_10785,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2876_1]) ).

fof(f_2876_3,plain,
    ( ! [U_10798,U_10796,U_10794,U_10792,U_10790] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10792,tc_fun(U_10794,tc_HOL_Obool)),U_10790),hAPP(hAPP(c_COMBC(U_10792,tc_fun(U_10794,tc_HOL_Obool),tc_fun(U_10794,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10794,tc_HOL_Obool),tc_fun(tc_fun(U_10794,tc_HOL_Obool),tc_fun(U_10794,tc_HOL_Obool)),U_10792),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10794,tc_HOL_Obool))),U_10796)),U_10798)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10794,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10792,tc_fun(U_10794,tc_HOL_Obool)),U_10790),U_10796)),U_10798)
        | U_10790 = c_Orderings_Obot__class_Obot(tc_fun(U_10792,tc_HOL_Obool)) )
    & ! [U_10797,U_10795,U_10793,U_10791,U_10789] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10791,tc_fun(U_10793,tc_HOL_Obool)),U_10789),hAPP(hAPP(c_COMBC(U_10791,tc_fun(U_10793,tc_HOL_Obool),tc_fun(U_10793,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10793,tc_HOL_Obool),tc_fun(tc_fun(U_10793,tc_HOL_Obool),tc_fun(U_10793,tc_HOL_Obool)),U_10791),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10793,tc_HOL_Obool))),U_10795)),U_10797)) = c_Orderings_Obot__class_Obot(tc_fun(U_10793,tc_HOL_Obool))
        | U_10789 != c_Orderings_Obot__class_Obot(tc_fun(U_10791,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2876_2]) ).

fof(f_2876_4,plain,
    ( ! [U_10790,U_10792,U_10794,U_10796,U_10798] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10792,tc_fun(U_10794,tc_HOL_Obool)),U_10790),hAPP(hAPP(c_COMBC(U_10792,tc_fun(U_10794,tc_HOL_Obool),tc_fun(U_10794,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10794,tc_HOL_Obool),tc_fun(tc_fun(U_10794,tc_HOL_Obool),tc_fun(U_10794,tc_HOL_Obool)),U_10792),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10794,tc_HOL_Obool))),U_10796)),U_10798)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10794,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10792,tc_fun(U_10794,tc_HOL_Obool)),U_10790),U_10796)),U_10798)
        | U_10790 = c_Orderings_Obot__class_Obot(tc_fun(U_10792,tc_HOL_Obool)) )
    & ! [U_10795,U_10791,U_10789,U_10793,U_10797] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10791,tc_fun(U_10793,tc_HOL_Obool)),U_10789),hAPP(hAPP(c_COMBC(U_10791,tc_fun(U_10793,tc_HOL_Obool),tc_fun(U_10793,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10793,tc_HOL_Obool),tc_fun(tc_fun(U_10793,tc_HOL_Obool),tc_fun(U_10793,tc_HOL_Obool)),U_10791),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10793,tc_HOL_Obool))),U_10795)),U_10797)) = c_Orderings_Obot__class_Obot(tc_fun(U_10793,tc_HOL_Obool))
        | U_10789 != c_Orderings_Obot__class_Obot(tc_fun(U_10791,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2876_3]) ).

cnf(f_2876_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10791,tc_fun(U_10793,tc_HOL_Obool)),U_10789),hAPP(hAPP(c_COMBC(U_10791,tc_fun(U_10793,tc_HOL_Obool),tc_fun(U_10793,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10793,tc_HOL_Obool),tc_fun(tc_fun(U_10793,tc_HOL_Obool),tc_fun(U_10793,tc_HOL_Obool)),U_10791),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10793,tc_HOL_Obool))),U_10795)),U_10797)) = c_Orderings_Obot__class_Obot(tc_fun(U_10793,tc_HOL_Obool))
    | U_10789 != c_Orderings_Obot__class_Obot(tc_fun(U_10791,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2876_4]) ).

cnf(f_2876_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10792,tc_fun(U_10794,tc_HOL_Obool)),U_10790),hAPP(hAPP(c_COMBC(U_10792,tc_fun(U_10794,tc_HOL_Obool),tc_fun(U_10794,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10794,tc_HOL_Obool),tc_fun(tc_fun(U_10794,tc_HOL_Obool),tc_fun(U_10794,tc_HOL_Obool)),U_10792),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10794,tc_HOL_Obool))),U_10796)),U_10798)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10794,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10792,tc_fun(U_10794,tc_HOL_Obool)),U_10790),U_10796)),U_10798)
    | U_10790 = c_Orderings_Obot__class_Obot(tc_fun(U_10792,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2876_4]) ).

fof(f_2877_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J]) ).

fof(f_2877_2,plain,
    ! [U_10803,U_10802,U_10801,U_10800,U_10799] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10800,tc_fun(U_10801,tc_HOL_Obool)),U_10799),hAPP(hAPP(c_COMBB(tc_fun(U_10801,tc_HOL_Obool),tc_fun(U_10801,tc_HOL_Obool),U_10800),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10801,tc_HOL_Obool)),U_10802)),U_10803)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10801,tc_HOL_Obool)),U_10802),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10800,tc_fun(U_10801,tc_HOL_Obool)),U_10799),U_10803))
        | U_10799 = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10800,tc_fun(U_10801,tc_HOL_Obool)),U_10799),hAPP(hAPP(c_COMBB(tc_fun(U_10801,tc_HOL_Obool),tc_fun(U_10801,tc_HOL_Obool),U_10800),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10801,tc_HOL_Obool)),U_10802)),U_10803)) = c_Orderings_Obot__class_Obot(tc_fun(U_10801,tc_HOL_Obool))
        | U_10799 != c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2877_1]) ).

fof(f_2877_3,plain,
    ( ! [U_10813,U_10811,U_10809,U_10807,U_10805] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10807,tc_fun(U_10809,tc_HOL_Obool)),U_10805),hAPP(hAPP(c_COMBB(tc_fun(U_10809,tc_HOL_Obool),tc_fun(U_10809,tc_HOL_Obool),U_10807),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10809,tc_HOL_Obool)),U_10811)),U_10813)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10809,tc_HOL_Obool)),U_10811),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10807,tc_fun(U_10809,tc_HOL_Obool)),U_10805),U_10813))
        | U_10805 = c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool)) )
    & ! [U_10812,U_10810,U_10808,U_10806,U_10804] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10806,tc_fun(U_10808,tc_HOL_Obool)),U_10804),hAPP(hAPP(c_COMBB(tc_fun(U_10808,tc_HOL_Obool),tc_fun(U_10808,tc_HOL_Obool),U_10806),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10808,tc_HOL_Obool)),U_10810)),U_10812)) = c_Orderings_Obot__class_Obot(tc_fun(U_10808,tc_HOL_Obool))
        | U_10804 != c_Orderings_Obot__class_Obot(tc_fun(U_10806,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2877_2]) ).

fof(f_2877_4,plain,
    ( ! [U_10805,U_10807,U_10809,U_10811,U_10813] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10807,tc_fun(U_10809,tc_HOL_Obool)),U_10805),hAPP(hAPP(c_COMBB(tc_fun(U_10809,tc_HOL_Obool),tc_fun(U_10809,tc_HOL_Obool),U_10807),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10809,tc_HOL_Obool)),U_10811)),U_10813)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10809,tc_HOL_Obool)),U_10811),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10807,tc_fun(U_10809,tc_HOL_Obool)),U_10805),U_10813))
        | U_10805 = c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool)) )
    & ! [U_10806,U_10810,U_10804,U_10808,U_10812] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10806,tc_fun(U_10808,tc_HOL_Obool)),U_10804),hAPP(hAPP(c_COMBB(tc_fun(U_10808,tc_HOL_Obool),tc_fun(U_10808,tc_HOL_Obool),U_10806),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10808,tc_HOL_Obool)),U_10810)),U_10812)) = c_Orderings_Obot__class_Obot(tc_fun(U_10808,tc_HOL_Obool))
        | U_10804 != c_Orderings_Obot__class_Obot(tc_fun(U_10806,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2877_3]) ).

cnf(f_2877_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10806,tc_fun(U_10808,tc_HOL_Obool)),U_10804),hAPP(hAPP(c_COMBB(tc_fun(U_10808,tc_HOL_Obool),tc_fun(U_10808,tc_HOL_Obool),U_10806),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10808,tc_HOL_Obool)),U_10810)),U_10812)) = c_Orderings_Obot__class_Obot(tc_fun(U_10808,tc_HOL_Obool))
    | U_10804 != c_Orderings_Obot__class_Obot(tc_fun(U_10806,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

cnf(f_2877_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10807,tc_fun(U_10809,tc_HOL_Obool)),U_10805),hAPP(hAPP(c_COMBB(tc_fun(U_10809,tc_HOL_Obool),tc_fun(U_10809,tc_HOL_Obool),U_10807),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10809,tc_HOL_Obool)),U_10811)),U_10813)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10809,tc_HOL_Obool)),U_10811),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10807,tc_fun(U_10809,tc_HOL_Obool)),U_10805),U_10813))
    | U_10805 = c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

fof(f_2878_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__insert]) ).

fof(f_2878_2,plain,
    ! [U_10818,U_10817,U_10816,U_10815,U_10814] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10814,tc_fun(U_10815,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10814),U_10816),U_10817)),U_10818) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10815,tc_HOL_Obool)),hAPP(U_10818,U_10816)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10814,tc_fun(U_10815,tc_HOL_Obool)),U_10817),U_10818)),
    inference(variable_rename,[status(thm)],[f_2878_1]) ).

fof(f_2878_3,plain,
    ! [U_10815,U_10814,U_10816,U_10817,U_10818] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10814,tc_fun(U_10815,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10814),U_10816),U_10817)),U_10818) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10815,tc_HOL_Obool)),hAPP(U_10818,U_10816)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10814,tc_fun(U_10815,tc_HOL_Obool)),U_10817),U_10818)),
    inference(definitional_conversion,[status(esa)],[f_2878_2]) ).

cnf(f_2878_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10814,tc_fun(U_10815,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10814),U_10816),U_10817)),U_10818) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10815,tc_HOL_Obool)),hAPP(U_10818,U_10816)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10814,tc_fun(U_10815,tc_HOL_Obool)),U_10817),U_10818)),
    inference(clausify,[status(thm)],[f_2878_3]) ).

fof(f_2879_1,plain,
    ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN]) ).

fof(f_2879_2,plain,
    ! [U_10827,U_10826,U_10825,U_10824,U_10823,U_10822,U_10821,U_10820,U_10819] :
      ( c_Equiv__Relations_Ocongruent(U_10819,tc_fun(U_10825,tc_HOL_Obool),U_10821,hAPP(hAPP(c_COMBB(tc_fun(U_10822,tc_fun(U_10825,tc_HOL_Obool)),tc_fun(U_10825,tc_HOL_Obool),U_10819),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10822,tc_fun(U_10825,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10822,U_10822,U_10824),hAPP(hAPP(c_Set_Oinsert(U_10822),U_10827),c_Orderings_Obot__class_Obot(tc_fun(U_10822,tc_HOL_Obool)))))),U_10826))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10822),U_10827),U_10823))
      | ~ c_Equiv__Relations_Ocongruent2(U_10819,U_10822,tc_fun(U_10825,tc_HOL_Obool),U_10821,U_10824,U_10826)
      | ~ c_Equiv__Relations_Oequiv(U_10822,U_10823,U_10824)
      | ~ c_Equiv__Relations_Oequiv(U_10819,U_10820,U_10821) ),
    inference(variable_rename,[status(thm)],[f_2879_1]) ).

fof(f_2879_3,plain,
    ! [U_10819,U_10821,U_10820,U_10822,U_10823,U_10824,U_10825,U_10826,U_10827] :
      ( c_Equiv__Relations_Ocongruent(U_10819,tc_fun(U_10825,tc_HOL_Obool),U_10821,hAPP(hAPP(c_COMBB(tc_fun(U_10822,tc_fun(U_10825,tc_HOL_Obool)),tc_fun(U_10825,tc_HOL_Obool),U_10819),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10822,tc_fun(U_10825,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10822,U_10822,U_10824),hAPP(hAPP(c_Set_Oinsert(U_10822),U_10827),c_Orderings_Obot__class_Obot(tc_fun(U_10822,tc_HOL_Obool)))))),U_10826))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10822),U_10827),U_10823))
      | ~ c_Equiv__Relations_Ocongruent2(U_10819,U_10822,tc_fun(U_10825,tc_HOL_Obool),U_10821,U_10824,U_10826)
      | ~ c_Equiv__Relations_Oequiv(U_10822,U_10823,U_10824)
      | ~ c_Equiv__Relations_Oequiv(U_10819,U_10820,U_10821) ),
    inference(definitional_conversion,[status(esa)],[f_2879_2]) ).

cnf(f_2879_4,plain,
    ( c_Equiv__Relations_Ocongruent(U_10819,tc_fun(U_10825,tc_HOL_Obool),U_10821,hAPP(hAPP(c_COMBB(tc_fun(U_10822,tc_fun(U_10825,tc_HOL_Obool)),tc_fun(U_10825,tc_HOL_Obool),U_10819),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10822,tc_fun(U_10825,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10822,U_10822,U_10824),hAPP(hAPP(c_Set_Oinsert(U_10822),U_10827),c_Orderings_Obot__class_Obot(tc_fun(U_10822,tc_HOL_Obool)))))),U_10826))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10822),U_10827),U_10823))
    | ~ c_Equiv__Relations_Ocongruent2(U_10819,U_10822,tc_fun(U_10825,tc_HOL_Obool),U_10821,U_10824,U_10826)
    | ~ c_Equiv__Relations_Oequiv(U_10822,U_10823,U_10824)
    | ~ c_Equiv__Relations_Oequiv(U_10819,U_10820,U_10821) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

fof(f_2880_1,plain,
    ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(fof_nnf,[status(thm)],[fact_minus__int__def]) ).

fof(f_2880_2,plain,
    ! [U_10828] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10828) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10828)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(variable_rename,[status(thm)],[f_2880_1]) ).

fof(f_2880_3,plain,
    ! [U_10828] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10828) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10828)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(definitional_conversion,[status(esa)],[f_2880_2]) ).

cnf(f_2880_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10828) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10828)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(clausify,[status(thm)],[f_2880_3]) ).

fof(f_2881_1,plain,
    ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class]) ).

fof(f_2881_2,plain,
    ! [U_10834,U_10833,U_10832,U_10831,U_10830,U_10829] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10829,tc_fun(U_10832,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10829,U_10829,U_10831),hAPP(hAPP(c_Set_Oinsert(U_10829),U_10834),c_Orderings_Obot__class_Obot(tc_fun(U_10829,tc_HOL_Obool))))),U_10833) = hAPP(U_10833,U_10834)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10829),U_10834),U_10830))
      | ~ c_Equiv__Relations_Ocongruent(U_10829,tc_fun(U_10832,tc_HOL_Obool),U_10831,U_10833)
      | ~ c_Equiv__Relations_Oequiv(U_10829,U_10830,U_10831) ),
    inference(variable_rename,[status(thm)],[f_2881_1]) ).

fof(f_2881_3,plain,
    ! [U_10830,U_10832,U_10831,U_10829,U_10833,U_10834] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10829,tc_fun(U_10832,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10829,U_10829,U_10831),hAPP(hAPP(c_Set_Oinsert(U_10829),U_10834),c_Orderings_Obot__class_Obot(tc_fun(U_10829,tc_HOL_Obool))))),U_10833) = hAPP(U_10833,U_10834)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10829),U_10834),U_10830))
      | ~ c_Equiv__Relations_Ocongruent(U_10829,tc_fun(U_10832,tc_HOL_Obool),U_10831,U_10833)
      | ~ c_Equiv__Relations_Oequiv(U_10829,U_10830,U_10831) ),
    inference(definitional_conversion,[status(esa)],[f_2881_2]) ).

cnf(f_2881_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10829,tc_fun(U_10832,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10829,U_10829,U_10831),hAPP(hAPP(c_Set_Oinsert(U_10829),U_10834),c_Orderings_Obot__class_Obot(tc_fun(U_10829,tc_HOL_Obool))))),U_10833) = hAPP(U_10833,U_10834)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10829),U_10834),U_10830))
    | ~ c_Equiv__Relations_Ocongruent(U_10829,tc_fun(U_10832,tc_HOL_Obool),U_10831,U_10833)
    | ~ c_Equiv__Relations_Oequiv(U_10829,U_10830,U_10831) ),
    inference(clausify,[status(thm)],[f_2881_3]) ).

fof(f_2882_1,plain,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).

fof(f_2882_2,plain,
    ! [U_10842,U_10841,U_10840,U_10839,U_10838,U_10837,U_10836,U_10835] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10835,tc_fun(U_10841,tc_fun(U_10842,tc_HOL_Obool))),U_10837),U_10838),U_10839),U_10840))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_10838,U_10836),U_10839),U_10840))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10835),U_10836),U_10837)) ),
    inference(variable_rename,[status(thm)],[f_2882_1]) ).

fof(f_2882_3,plain,
    ! [U_10835,U_10837,U_10836,U_10838,U_10839,U_10840,U_10841,U_10842] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10835,tc_fun(U_10841,tc_fun(U_10842,tc_HOL_Obool))),U_10837),U_10838),U_10839),U_10840))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_10838,U_10836),U_10839),U_10840))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10835),U_10836),U_10837)) ),
    inference(definitional_conversion,[status(esa)],[f_2882_2]) ).

cnf(f_2882_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10835,tc_fun(U_10841,tc_fun(U_10842,tc_HOL_Obool))),U_10837),U_10838),U_10839),U_10840))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_10838,U_10836),U_10839),U_10840))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10835),U_10836),U_10837)) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

fof(f_2883_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Int_ORep__Integ,V_x_2) != hAPP(c_Int_ORep__Integ,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject]) ).

fof(f_2883_2,plain,
    ! [U_10844,U_10843] :
      ( ( hAPP(c_Int_ORep__Integ,U_10843) = hAPP(c_Int_ORep__Integ,U_10844)
        | U_10843 != U_10844 )
      & ( U_10843 = U_10844
        | hAPP(c_Int_ORep__Integ,U_10843) != hAPP(c_Int_ORep__Integ,U_10844) ) ),
    inference(variable_rename,[status(thm)],[f_2883_1]) ).

fof(f_2883_3,plain,
    ( ! [U_10848,U_10846] :
        ( hAPP(c_Int_ORep__Integ,U_10846) = hAPP(c_Int_ORep__Integ,U_10848)
        | U_10846 != U_10848 )
    & ! [U_10847,U_10845] :
        ( U_10845 = U_10847
        | hAPP(c_Int_ORep__Integ,U_10845) != hAPP(c_Int_ORep__Integ,U_10847) ) ),
    inference(miniscope,[status(thm)],[f_2883_2]) ).

fof(f_2883_4,plain,
    ( ! [U_10846,U_10848] :
        ( hAPP(c_Int_ORep__Integ,U_10846) = hAPP(c_Int_ORep__Integ,U_10848)
        | U_10846 != U_10848 )
    & ! [U_10847,U_10845] :
        ( U_10845 = U_10847
        | hAPP(c_Int_ORep__Integ,U_10845) != hAPP(c_Int_ORep__Integ,U_10847) ) ),
    inference(definitional_conversion,[status(esa)],[f_2883_3]) ).

cnf(f_2883_5,plain,
    ( U_10845 = U_10847
    | hAPP(c_Int_ORep__Integ,U_10845) != hAPP(c_Int_ORep__Integ,U_10847) ),
    inference(clausify,[status(thm)],[f_2883_4]) ).

cnf(f_2883_6,plain,
    ( hAPP(c_Int_ORep__Integ,U_10846) = hAPP(c_Int_ORep__Integ,U_10848)
    | U_10846 != U_10848 ),
    inference(clausify,[status(thm)],[f_2883_4]) ).

fof(f_2884_1,plain,
    ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inverse]) ).

fof(f_2884_2,plain,
    ! [U_10849] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_10849)) = U_10849,
    inference(variable_rename,[status(thm)],[f_2884_1]) ).

fof(f_2884_3,plain,
    ! [U_10849] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_10849)) = U_10849,
    inference(definitional_conversion,[status(esa)],[f_2884_2]) ).

cnf(f_2884_4,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_10849)) = U_10849,
    inference(clausify,[status(thm)],[f_2884_3]) ).

fof(f_2885_1,plain,
    ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
      ( hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
      | ~ c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruentD]) ).

fof(f_2885_2,plain,
    ! [U_10855,U_10854,U_10853,U_10852,U_10851,U_10850] :
      ( hAPP(U_10853,U_10854) = hAPP(U_10853,U_10855)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10850,U_10850)),hAPP(hAPP(c_Product__Type_OPair(U_10850,U_10850),U_10854),U_10855)),U_10852))
      | ~ c_Equiv__Relations_Ocongruent(U_10850,U_10851,U_10852,U_10853) ),
    inference(variable_rename,[status(thm)],[f_2885_1]) ).

fof(f_2885_3,plain,
    ! [U_10850,U_10851,U_10852,U_10853,U_10854,U_10855] :
      ( hAPP(U_10853,U_10854) = hAPP(U_10853,U_10855)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10850,U_10850)),hAPP(hAPP(c_Product__Type_OPair(U_10850,U_10850),U_10854),U_10855)),U_10852))
      | ~ c_Equiv__Relations_Ocongruent(U_10850,U_10851,U_10852,U_10853) ),
    inference(definitional_conversion,[status(esa)],[f_2885_2]) ).

cnf(f_2885_4,plain,
    ( hAPP(U_10853,U_10854) = hAPP(U_10853,U_10855)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10850,U_10850)),hAPP(hAPP(c_Product__Type_OPair(U_10850,U_10850),U_10854),U_10855)),U_10852))
    | ~ c_Equiv__Relations_Ocongruent(U_10850,U_10851,U_10852,U_10853) ),
    inference(clausify,[status(thm)],[f_2885_3]) ).

fof(f_2886_1,plain,
    ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(fof_nnf,[status(thm)],[fact_nat__def]) ).

fof(f_2886_2,plain,
    ! [U_10856] : hAPP(c_Int_Onat,U_10856) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10856)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(variable_rename,[status(thm)],[f_2886_1]) ).

fof(f_2886_3,plain,
    ! [U_10856] : hAPP(c_Int_Onat,U_10856) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10856)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(definitional_conversion,[status(esa)],[f_2886_2]) ).

cnf(f_2886_4,plain,
    hAPP(c_Int_Onat,U_10856) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10856)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(clausify,[status(thm)],[f_2886_3]) ).

fof(f_2887_1,plain,
    ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent]) ).

fof(f_2887_2,plain,
    ! [U_10864,U_10863,U_10862,U_10861,U_10860,U_10859,U_10858,U_10857] :
      ( c_Equiv__Relations_Ocongruent(U_10860,U_10861,U_10862,hAPP(U_10863,U_10864))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10864),U_10858))
      | ~ c_Equiv__Relations_Ocongruent2(U_10857,U_10860,U_10861,U_10859,U_10862,U_10863)
      | ~ c_Equiv__Relations_Oequiv(U_10857,U_10858,U_10859) ),
    inference(variable_rename,[status(thm)],[f_2887_1]) ).

fof(f_2887_3,plain,
    ! [U_10857,U_10858,U_10859,U_10860,U_10861,U_10862,U_10863,U_10864] :
      ( c_Equiv__Relations_Ocongruent(U_10860,U_10861,U_10862,hAPP(U_10863,U_10864))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10864),U_10858))
      | ~ c_Equiv__Relations_Ocongruent2(U_10857,U_10860,U_10861,U_10859,U_10862,U_10863)
      | ~ c_Equiv__Relations_Oequiv(U_10857,U_10858,U_10859) ),
    inference(definitional_conversion,[status(esa)],[f_2887_2]) ).

cnf(f_2887_4,plain,
    ( c_Equiv__Relations_Ocongruent(U_10860,U_10861,U_10862,hAPP(U_10863,U_10864))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10864),U_10858))
    | ~ c_Equiv__Relations_Ocongruent2(U_10857,U_10860,U_10861,U_10859,U_10862,U_10863)
    | ~ c_Equiv__Relations_Oequiv(U_10857,U_10858,U_10859) ),
    inference(clausify,[status(thm)],[f_2887_3]) ).

fof(f_2888_1,plain,
    ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( V_X_2 = V_Y_2
      | ? [B_x] :
          ( ? [B_y] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
              & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
      | ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject]) ).

fof(f_2888_2,plain,
    ! [U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867] :
      ( U_10872 = U_10873
      | ? [U_10866] :
          ( ? [U_10865] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10867,U_10867)),hAPP(hAPP(c_Product__Type_OPair(U_10867,U_10867),U_10866),U_10865)),U_10869))
              & hAPP(U_10871,U_10866) = hAPP(U_10871,U_10865)
              & hBOOL(hAPP(hAPP(c_member(U_10867),U_10865),U_10868)) )
          & hBOOL(hAPP(hAPP(c_member(U_10867),U_10866),U_10868)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10873),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10872),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10872),U_10871) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10871)
      | ~ c_Equiv__Relations_Ocongruent(U_10867,tc_fun(U_10870,tc_HOL_Obool),U_10869,U_10871)
      | ~ c_Equiv__Relations_Oequiv(U_10867,U_10868,U_10869) ),
    inference(variable_rename,[status(thm)],[f_2888_1]) ).

fof(f_2888_3,plain,
    ! [U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867] :
      ( U_10872 = U_10873
      | ( ? [U_10865] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10867,U_10867)),hAPP(hAPP(c_Product__Type_OPair(U_10867,U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10865)),U_10869))
            & hAPP(U_10871,sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)) = hAPP(U_10871,U_10865)
            & hBOOL(hAPP(hAPP(c_member(U_10867),U_10865),U_10868)) )
        & hBOOL(hAPP(hAPP(c_member(U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10873),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10872),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10872),U_10871) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10871)
      | ~ c_Equiv__Relations_Ocongruent(U_10867,tc_fun(U_10870,tc_HOL_Obool),U_10869,U_10871)
      | ~ c_Equiv__Relations_Oequiv(U_10867,U_10868,U_10869) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_10866,sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))],[f_2888_2]) ).

fof(f_2888_4,plain,
    ! [U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867] :
      ( U_10872 = U_10873
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10867,U_10867)),hAPP(hAPP(c_Product__Type_OPair(U_10867,U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))),U_10869))
        & hAPP(U_10871,sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)) = hAPP(U_10871,sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))
        & hBOOL(hAPP(hAPP(c_member(U_10867),sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868))
        & hBOOL(hAPP(hAPP(c_member(U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10873),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10872),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10872),U_10871) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10871)
      | ~ c_Equiv__Relations_Ocongruent(U_10867,tc_fun(U_10870,tc_HOL_Obool),U_10869,U_10871)
      | ~ c_Equiv__Relations_Oequiv(U_10867,U_10868,U_10869) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_10865,sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))],[f_2888_3]) ).

fof(f_2888_5,plain,
    ( ! [U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10867,U_10867)),hAPP(hAPP(c_Product__Type_OPair(U_10867,U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))),U_10869))
        | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) )
    & ! [U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873] :
        ( hAPP(U_10871,sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)) = hAPP(U_10871,sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))
        | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) )
    & ! [U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873] :
        ( hBOOL(hAPP(hAPP(c_member(U_10867),sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868))
        | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) )
    & ! [U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873] :
        ( hBOOL(hAPP(hAPP(c_member(U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868))
        | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) )
    & ! [U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873] :
        ( U_10872 = U_10873
        | sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10873),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10872),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10872),U_10871) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10871)
        | ~ c_Equiv__Relations_Ocongruent(U_10867,tc_fun(U_10870,tc_HOL_Obool),U_10869,U_10871)
        | ~ c_Equiv__Relations_Oequiv(U_10867,U_10868,U_10869) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP824])],[f_2888_4]) ).

cnf(f_2888_6,plain,
    ( U_10872 = U_10873
    | sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10873),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10867,tc_HOL_Obool)),U_10872),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),U_10868),U_10869)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10872),U_10871) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10867,tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10871)
    | ~ c_Equiv__Relations_Ocongruent(U_10867,tc_fun(U_10870,tc_HOL_Obool),U_10869,U_10871)
    | ~ c_Equiv__Relations_Oequiv(U_10867,U_10868,U_10869) ),
    inference(clausify,[status(thm)],[f_2888_5]) ).

cnf(f_2888_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868))
    | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) ),
    inference(clausify,[status(thm)],[f_2888_5]) ).

cnf(f_2888_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10867),sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),U_10868))
    | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) ),
    inference(clausify,[status(thm)],[f_2888_5]) ).

cnf(f_2888_9,plain,
    ( hAPP(U_10871,sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)) = hAPP(U_10871,sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))
    | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) ),
    inference(clausify,[status(thm)],[f_2888_5]) ).

cnf(f_2888_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10867,U_10867)),hAPP(hAPP(c_Product__Type_OPair(U_10867,U_10867),sK176(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867)),sK177(U_10873,U_10872,U_10871,U_10870,U_10869,U_10868,U_10867))),U_10869))
    | ~ sP824(U_10867,U_10868,U_10869,U_10870,U_10871,U_10872,U_10873) ),
    inference(clausify,[status(thm)],[f_2888_5]) ).

fof(f_2889_1,plain,
    ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2))
      | ? [B_x1] :
          ( ? [B_x2] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2]) ).

fof(f_2889_2,plain,
    ! [U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10876,tc_fun(U_10882,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_fun(U_10882,tc_HOL_Obool)),tc_fun(U_10882,tc_HOL_Obool),U_10876),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10879,tc_fun(U_10882,tc_HOL_Obool)),U_10885)),U_10883))),U_10886))
      | ? [U_10875] :
          ( ? [U_10874] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(U_10883,U_10875),U_10874)),U_10886))
              & hBOOL(hAPP(hAPP(c_member(U_10879),U_10874),U_10880)) )
          & hBOOL(hAPP(hAPP(c_member(U_10876),U_10875),U_10877)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10879,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10879),U_10880),U_10881)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10876,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10876),U_10877),U_10878)))
      | ~ c_Equiv__Relations_Ocongruent2(U_10876,U_10879,tc_fun(U_10882,tc_HOL_Obool),U_10878,U_10881,U_10883)
      | ~ c_Equiv__Relations_Oequiv(U_10879,U_10880,U_10881)
      | ~ c_Equiv__Relations_Oequiv(U_10876,U_10877,U_10878) ),
    inference(variable_rename,[status(thm)],[f_2889_1]) ).

fof(f_2889_3,plain,
    ! [U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10876,tc_fun(U_10882,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_fun(U_10882,tc_HOL_Obool)),tc_fun(U_10882,tc_HOL_Obool),U_10876),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10879,tc_fun(U_10882,tc_HOL_Obool)),U_10885)),U_10883))),U_10886))
      | ( ? [U_10874] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(U_10883,sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10874)),U_10886))
            & hBOOL(hAPP(hAPP(c_member(U_10879),U_10874),U_10880)) )
        & hBOOL(hAPP(hAPP(c_member(U_10876),sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10877)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10879,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10879),U_10880),U_10881)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10876,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10876),U_10877),U_10878)))
      | ~ c_Equiv__Relations_Ocongruent2(U_10876,U_10879,tc_fun(U_10882,tc_HOL_Obool),U_10878,U_10881,U_10883)
      | ~ c_Equiv__Relations_Oequiv(U_10879,U_10880,U_10881)
      | ~ c_Equiv__Relations_Oequiv(U_10876,U_10877,U_10878) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_10875,sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876))],[f_2889_2]) ).

fof(f_2889_4,plain,
    ! [U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10876,tc_fun(U_10882,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_fun(U_10882,tc_HOL_Obool)),tc_fun(U_10882,tc_HOL_Obool),U_10876),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10879,tc_fun(U_10882,tc_HOL_Obool)),U_10885)),U_10883))),U_10886))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(U_10883,sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876))),U_10886))
        & hBOOL(hAPP(hAPP(c_member(U_10879),sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10880))
        & hBOOL(hAPP(hAPP(c_member(U_10876),sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10877)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10879,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10879),U_10880),U_10881)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10876,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10876),U_10877),U_10878)))
      | ~ c_Equiv__Relations_Ocongruent2(U_10876,U_10879,tc_fun(U_10882,tc_HOL_Obool),U_10878,U_10881,U_10883)
      | ~ c_Equiv__Relations_Oequiv(U_10879,U_10880,U_10881)
      | ~ c_Equiv__Relations_Oequiv(U_10876,U_10877,U_10878) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_10874,sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876))],[f_2889_3]) ).

fof(f_2889_5,plain,
    ( ! [U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(U_10883,sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876))),U_10886))
        | ~ sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886) )
    & ! [U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886] :
        ( hBOOL(hAPP(hAPP(c_member(U_10879),sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10880))
        | ~ sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886) )
    & ! [U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886] :
        ( hBOOL(hAPP(hAPP(c_member(U_10876),sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10877))
        | ~ sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886) )
    & ! [U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10876,tc_fun(U_10882,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_fun(U_10882,tc_HOL_Obool)),tc_fun(U_10882,tc_HOL_Obool),U_10876),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10879,tc_fun(U_10882,tc_HOL_Obool)),U_10885)),U_10883))),U_10886))
        | sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10879,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10879),U_10880),U_10881)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10876,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10876),U_10877),U_10878)))
        | ~ c_Equiv__Relations_Ocongruent2(U_10876,U_10879,tc_fun(U_10882,tc_HOL_Obool),U_10878,U_10881,U_10883)
        | ~ c_Equiv__Relations_Oequiv(U_10879,U_10880,U_10881)
        | ~ c_Equiv__Relations_Oequiv(U_10876,U_10877,U_10878) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP825])],[f_2889_4]) ).

cnf(f_2889_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10876,tc_fun(U_10882,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_fun(U_10882,tc_HOL_Obool)),tc_fun(U_10882,tc_HOL_Obool),U_10876),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10879,tc_fun(U_10882,tc_HOL_Obool)),U_10885)),U_10883))),U_10886))
    | sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10879,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10879),U_10880),U_10881)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10876,tc_HOL_Obool)),U_10884),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10876),U_10877),U_10878)))
    | ~ c_Equiv__Relations_Ocongruent2(U_10876,U_10879,tc_fun(U_10882,tc_HOL_Obool),U_10878,U_10881,U_10883)
    | ~ c_Equiv__Relations_Oequiv(U_10879,U_10880,U_10881)
    | ~ c_Equiv__Relations_Oequiv(U_10876,U_10877,U_10878) ),
    inference(clausify,[status(thm)],[f_2889_5]) ).

cnf(f_2889_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10876),sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10877))
    | ~ sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886) ),
    inference(clausify,[status(thm)],[f_2889_5]) ).

cnf(f_2889_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10879),sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),U_10880))
    | ~ sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886) ),
    inference(clausify,[status(thm)],[f_2889_5]) ).

cnf(f_2889_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10882,tc_HOL_Obool)),hAPP(hAPP(U_10883,sK178(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876)),sK179(U_10886,U_10885,U_10884,U_10883,U_10882,U_10881,U_10880,U_10879,U_10878,U_10877,U_10876))),U_10886))
    | ~ sP825(U_10876,U_10878,U_10877,U_10879,U_10883,U_10884,U_10885,U_10880,U_10881,U_10882,U_10886) ),
    inference(clausify,[status(thm)],[f_2889_5]) ).

fof(f_2890_1,plain,
    ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type]) ).

fof(f_2890_2,plain,
    ! [U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,tc_fun(U_10891,tc_HOL_Obool)),U_10893),U_10892)),U_10894))
      | ? [U_10887] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(U_10892,U_10887)),U_10894))
          & hBOOL(hAPP(hAPP(c_member(U_10888),U_10887),U_10889)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10888,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10888),U_10889),U_10890)))
      | ~ c_Equiv__Relations_Ocongruent(U_10888,tc_fun(U_10891,tc_HOL_Obool),U_10890,U_10892)
      | ~ c_Equiv__Relations_Oequiv(U_10888,U_10889,U_10890) ),
    inference(variable_rename,[status(thm)],[f_2890_1]) ).

fof(f_2890_3,plain,
    ! [U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,tc_fun(U_10891,tc_HOL_Obool)),U_10893),U_10892)),U_10894))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(U_10892,sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888))),U_10894))
        & hBOOL(hAPP(hAPP(c_member(U_10888),sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888)),U_10889)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10888,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10888),U_10889),U_10890)))
      | ~ c_Equiv__Relations_Ocongruent(U_10888,tc_fun(U_10891,tc_HOL_Obool),U_10890,U_10892)
      | ~ c_Equiv__Relations_Oequiv(U_10888,U_10889,U_10890) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_10887,sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888))],[f_2890_2]) ).

fof(f_2890_4,plain,
    ( ! [U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(U_10892,sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888))),U_10894))
        | ~ sP826(U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894) )
    & ! [U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894] :
        ( hBOOL(hAPP(hAPP(c_member(U_10888),sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888)),U_10889))
        | ~ sP826(U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894) )
    & ! [U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,tc_fun(U_10891,tc_HOL_Obool)),U_10893),U_10892)),U_10894))
        | sP826(U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10888,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10888),U_10889),U_10890)))
        | ~ c_Equiv__Relations_Ocongruent(U_10888,tc_fun(U_10891,tc_HOL_Obool),U_10890,U_10892)
        | ~ c_Equiv__Relations_Oequiv(U_10888,U_10889,U_10890) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP826])],[f_2890_3]) ).

cnf(f_2890_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,tc_fun(U_10891,tc_HOL_Obool)),U_10893),U_10892)),U_10894))
    | sP826(U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10888,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10888),U_10889),U_10890)))
    | ~ c_Equiv__Relations_Ocongruent(U_10888,tc_fun(U_10891,tc_HOL_Obool),U_10890,U_10892)
    | ~ c_Equiv__Relations_Oequiv(U_10888,U_10889,U_10890) ),
    inference(clausify,[status(thm)],[f_2890_4]) ).

cnf(f_2890_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10888),sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888)),U_10889))
    | ~ sP826(U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894) ),
    inference(clausify,[status(thm)],[f_2890_4]) ).

cnf(f_2890_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10891,tc_HOL_Obool)),hAPP(U_10892,sK180(U_10894,U_10893,U_10892,U_10891,U_10890,U_10889,U_10888))),U_10894))
    | ~ sP826(U_10890,U_10888,U_10889,U_10892,U_10891,U_10893,U_10894) ),
    inference(clausify,[status(thm)],[f_2890_4]) ).

fof(f_2891_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).

fof(f_2891_2,plain,
    ! [U_10903,U_10902,U_10901,U_10900,U_10899,U_10898,U_10897] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_fun(U_10899,tc_HOL_Obool))),U_10900),U_10901),U_10902),U_10903))
        | ! [U_10896] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10901,U_10896),U_10902),U_10903))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10897),U_10896),U_10900)) ) )
      & ( ? [U_10895] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10901,U_10895),U_10902),U_10903))
            & hBOOL(hAPP(hAPP(c_member(U_10897),U_10895),U_10900)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_fun(U_10899,tc_HOL_Obool))),U_10900),U_10901),U_10902),U_10903)) ) ),
    inference(variable_rename,[status(thm)],[f_2891_1]) ).

fof(f_2891_3,plain,
    ( ! [U_10917,U_10915,U_10913,U_10911,U_10909,U_10907,U_10905] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10907,tc_fun(U_10909,tc_HOL_Obool))),U_10911),U_10913),U_10915),U_10917))
        | ! [U_10896] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10913,U_10896),U_10915),U_10917))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10905),U_10896),U_10911)) ) )
    & ! [U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904] :
        ( ? [U_10895] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10912,U_10895),U_10914),U_10916))
            & hBOOL(hAPP(hAPP(c_member(U_10904),U_10895),U_10910)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10904,tc_fun(U_10906,tc_fun(U_10908,tc_HOL_Obool))),U_10910),U_10912),U_10914),U_10916)) ) ),
    inference(miniscope,[status(thm)],[f_2891_2]) ).

fof(f_2891_4,plain,
    ( ! [U_10917,U_10915,U_10913,U_10911,U_10909,U_10907,U_10905] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10907,tc_fun(U_10909,tc_HOL_Obool))),U_10911),U_10913),U_10915),U_10917))
        | ! [U_10896] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10913,U_10896),U_10915),U_10917))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10905),U_10896),U_10911)) ) )
    & ! [U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904] :
        ( ( hBOOL(hAPP(hAPP(hAPP(U_10912,sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904)),U_10914),U_10916))
          & hBOOL(hAPP(hAPP(c_member(U_10904),sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904)),U_10910)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10904,tc_fun(U_10906,tc_fun(U_10908,tc_HOL_Obool))),U_10910),U_10912),U_10914),U_10916)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_10895,sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904))],[f_2891_3]) ).

fof(f_2891_5,plain,
    ( ! [U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914] :
        ( hBOOL(hAPP(hAPP(hAPP(U_10912,sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904)),U_10914),U_10916))
        | ~ sP827(U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914) )
    & ! [U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914] :
        ( hBOOL(hAPP(hAPP(c_member(U_10904),sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904)),U_10910))
        | ~ sP827(U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914) )
    & ! [U_10896,U_10905,U_10907,U_10909,U_10911,U_10915,U_10913,U_10917] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10907,tc_fun(U_10909,tc_HOL_Obool))),U_10911),U_10913),U_10915),U_10917))
        | ~ hBOOL(hAPP(hAPP(hAPP(U_10913,U_10896),U_10915),U_10917))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10905),U_10896),U_10911)) )
    & ! [U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914] :
        ( sP827(U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914)
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10904,tc_fun(U_10906,tc_fun(U_10908,tc_HOL_Obool))),U_10910),U_10912),U_10914),U_10916)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP827])],[f_2891_4]) ).

cnf(f_2891_6,plain,
    ( sP827(U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914)
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10904,tc_fun(U_10906,tc_fun(U_10908,tc_HOL_Obool))),U_10910),U_10912),U_10914),U_10916)) ),
    inference(clausify,[status(thm)],[f_2891_5]) ).

cnf(f_2891_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10907,tc_fun(U_10909,tc_HOL_Obool))),U_10911),U_10913),U_10915),U_10917))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_10913,U_10896),U_10915),U_10917))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10905),U_10896),U_10911)) ),
    inference(clausify,[status(thm)],[f_2891_5]) ).

cnf(f_2891_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10904),sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904)),U_10910))
    | ~ sP827(U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914) ),
    inference(clausify,[status(thm)],[f_2891_5]) ).

cnf(f_2891_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_10912,sK181(U_10916,U_10914,U_10912,U_10910,U_10908,U_10906,U_10904)),U_10914),U_10916))
    | ~ sP827(U_10908,U_10906,U_10904,U_10912,U_10916,U_10910,U_10914) ),
    inference(clausify,[status(thm)],[f_2891_5]) ).

fof(f_2892_1,plain,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Id__on__def]) ).

fof(f_2892_2,plain,
    ! [U_10919,U_10918] : c_Relation_OId__on(U_10918,U_10919) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),U_10919),hAPP(hAPP(c_COMBC(U_10918,tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool),tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10918,U_10918),tc_fun(tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool),tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),U_10918),c_Set_Oinsert(tc_prod(U_10918,U_10918))),hAPP(hAPP(c_COMBS(U_10918,U_10918,tc_prod(U_10918,U_10918)),c_Product__Type_OPair(U_10918,U_10918)),c_COMBI(U_10918)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2892_1]) ).

fof(f_2892_3,plain,
    ! [U_10918,U_10919] : c_Relation_OId__on(U_10918,U_10919) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),U_10919),hAPP(hAPP(c_COMBC(U_10918,tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool),tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10918,U_10918),tc_fun(tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool),tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),U_10918),c_Set_Oinsert(tc_prod(U_10918,U_10918))),hAPP(hAPP(c_COMBS(U_10918,U_10918,tc_prod(U_10918,U_10918)),c_Product__Type_OPair(U_10918,U_10918)),c_COMBI(U_10918)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2892_2]) ).

cnf(f_2892_4,plain,
    c_Relation_OId__on(U_10918,U_10919) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),U_10919),hAPP(hAPP(c_COMBC(U_10918,tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool),tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10918,U_10918),tc_fun(tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool),tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)),U_10918),c_Set_Oinsert(tc_prod(U_10918,U_10918))),hAPP(hAPP(c_COMBS(U_10918,U_10918,tc_prod(U_10918,U_10918)),c_Product__Type_OPair(U_10918,U_10918)),c_COMBI(U_10918)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10918,U_10918),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2892_3]) ).

fof(f_2893_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint]) ).

fof(f_2893_2,plain,
    ! [U_10924,U_10923,U_10922,U_10921,U_10920] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10921,tc_HOL_Obool)),U_10922),U_10923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10920),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),U_10922)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),U_10923))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10921,tc_HOL_Obool)),U_10922),U_10923) != c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10923))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10922))
      | ~ class_Groups_Ocomm__monoid__mult(U_10920) ),
    inference(variable_rename,[status(thm)],[f_2893_1]) ).

fof(f_2893_3,plain,
    ! [U_10921,U_10920,U_10922,U_10923,U_10924] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10921,tc_HOL_Obool)),U_10922),U_10923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10920),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),U_10922)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),U_10923))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10921,tc_HOL_Obool)),U_10922),U_10923) != c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10923))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10922))
      | ~ class_Groups_Ocomm__monoid__mult(U_10920) ),
    inference(definitional_conversion,[status(esa)],[f_2893_2]) ).

cnf(f_2893_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10921,tc_HOL_Obool)),U_10922),U_10923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10920),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),U_10922)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10920,U_10921,c_Groups_Otimes__class_Otimes(U_10920)),U_10924),c_Groups_Oone__class_Oone(U_10920)),U_10923))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10921,tc_HOL_Obool)),U_10922),U_10923) != c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10923))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10922))
    | ~ class_Groups_Ocomm__monoid__mult(U_10920) ),
    inference(clausify,[status(thm)],[f_2893_3]) ).

fof(f_2894_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute]) ).

fof(f_2894_2,plain,
    ! [U_10929,U_10928,U_10927] :
      ( hAPP(U_10928,c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),U_10929)) = c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),hAPP(c_Set_Oimage(U_10927,U_10927,U_10928),U_10929))
      | U_10929 = c_Orderings_Obot__class_Obot(tc_fun(U_10927,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10929))
      | ? [U_10926,U_10925] : hAPP(U_10928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),U_10926),U_10925)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),hAPP(U_10928,U_10926)),hAPP(U_10928,U_10925))
      | ~ class_Orderings_Olinorder(U_10927) ),
    inference(variable_rename,[status(thm)],[f_2894_1]) ).

fof(f_2894_3,plain,
    ! [U_10929,U_10928,U_10927] :
      ( hAPP(U_10928,c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),U_10929)) = c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),hAPP(c_Set_Oimage(U_10927,U_10927,U_10928),U_10929))
      | U_10929 = c_Orderings_Obot__class_Obot(tc_fun(U_10927,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10929))
      | ? [U_10925] : hAPP(U_10928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),sK182(U_10929,U_10928,U_10927)),U_10925)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),hAPP(U_10928,sK182(U_10929,U_10928,U_10927))),hAPP(U_10928,U_10925))
      | ~ class_Orderings_Olinorder(U_10927) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_10926,sK182(U_10929,U_10928,U_10927))],[f_2894_2]) ).

fof(f_2894_4,plain,
    ! [U_10929,U_10928,U_10927] :
      ( hAPP(U_10928,c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),U_10929)) = c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),hAPP(c_Set_Oimage(U_10927,U_10927,U_10928),U_10929))
      | U_10929 = c_Orderings_Obot__class_Obot(tc_fun(U_10927,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10929))
      | hAPP(U_10928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),sK182(U_10929,U_10928,U_10927)),sK183(U_10929,U_10928,U_10927))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),hAPP(U_10928,sK182(U_10929,U_10928,U_10927))),hAPP(U_10928,sK183(U_10929,U_10928,U_10927)))
      | ~ class_Orderings_Olinorder(U_10927) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_10925,sK183(U_10929,U_10928,U_10927))],[f_2894_3]) ).

fof(f_2894_5,plain,
    ! [U_10928,U_10929,U_10927] :
      ( hAPP(U_10928,c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),U_10929)) = c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),hAPP(c_Set_Oimage(U_10927,U_10927,U_10928),U_10929))
      | U_10929 = c_Orderings_Obot__class_Obot(tc_fun(U_10927,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10929))
      | hAPP(U_10928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),sK182(U_10929,U_10928,U_10927)),sK183(U_10929,U_10928,U_10927))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),hAPP(U_10928,sK182(U_10929,U_10928,U_10927))),hAPP(U_10928,sK183(U_10929,U_10928,U_10927)))
      | ~ class_Orderings_Olinorder(U_10927) ),
    inference(definitional_conversion,[status(esa)],[f_2894_4]) ).

cnf(f_2894_6,plain,
    ( hAPP(U_10928,c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),U_10929)) = c_Big__Operators_Olattice_OSup__fin(U_10927,c_Orderings_Oord__class_Omax(U_10927),hAPP(c_Set_Oimage(U_10927,U_10927,U_10928),U_10929))
    | U_10929 = c_Orderings_Obot__class_Obot(tc_fun(U_10927,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10929))
    | hAPP(U_10928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),sK182(U_10929,U_10928,U_10927)),sK183(U_10929,U_10928,U_10927))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),hAPP(U_10928,sK182(U_10929,U_10928,U_10927))),hAPP(U_10928,sK183(U_10929,U_10928,U_10927)))
    | ~ class_Orderings_Olinorder(U_10927) ),
    inference(clausify,[status(thm)],[f_2894_5]) ).

fof(f_2895_1,plain,
    ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_fold__image__empty]) ).

fof(f_2895_2,plain,
    ! [U_10934,U_10933,U_10932,U_10931,U_10930] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10930,U_10931,U_10932),U_10933),U_10934),c_Orderings_Obot__class_Obot(tc_fun(U_10931,tc_HOL_Obool))) = U_10934,
    inference(variable_rename,[status(thm)],[f_2895_1]) ).

fof(f_2895_3,plain,
    ! [U_10931,U_10930,U_10933,U_10934,U_10932] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10930,U_10931,U_10932),U_10933),U_10934),c_Orderings_Obot__class_Obot(tc_fun(U_10931,tc_HOL_Obool))) = U_10934,
    inference(definitional_conversion,[status(esa)],[f_2895_2]) ).

cnf(f_2895_4,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10930,U_10931,U_10932),U_10933),U_10934),c_Orderings_Obot__class_Obot(tc_fun(U_10931,tc_HOL_Obool))) = U_10934,
    inference(clausify,[status(thm)],[f_2895_3]) ).

fof(f_2896_1,plain,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Id__on__def_H]) ).

fof(f_2896_2,plain,
    ! [U_10936,U_10935] : c_Relation_OId__on(U_10935,U_10936) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10935,U_10935,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10935,tc_HOL_Obool,tc_fun(U_10935,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10935,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10935,tc_HOL_Obool)),U_10935),c_COMBC(U_10935,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10935,tc_HOL_Obool),tc_fun(U_10935,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10935),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10935),c_fconj)),c_fequal))),U_10936)),
    inference(variable_rename,[status(thm)],[f_2896_1]) ).

fof(f_2896_3,plain,
    ! [U_10935,U_10936] : c_Relation_OId__on(U_10935,U_10936) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10935,U_10935,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10935,tc_HOL_Obool,tc_fun(U_10935,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10935,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10935,tc_HOL_Obool)),U_10935),c_COMBC(U_10935,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10935,tc_HOL_Obool),tc_fun(U_10935,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10935),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10935),c_fconj)),c_fequal))),U_10936)),
    inference(definitional_conversion,[status(esa)],[f_2896_2]) ).

cnf(f_2896_4,plain,
    c_Relation_OId__on(U_10935,U_10936) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10935,U_10935,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10935,tc_HOL_Obool,tc_fun(U_10935,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10935,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10935,tc_HOL_Obool)),U_10935),c_COMBC(U_10935,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10935,tc_HOL_Obool),tc_fun(U_10935,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10935),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10935),c_fconj)),c_fequal))),U_10936)),
    inference(clausify,[status(thm)],[f_2896_3]) ).

fof(f_2897_1,plain,
    ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g]) ).

fof(f_2897_2,plain,
    ! [U_10943,U_10942,U_10941,U_10940,U_10939,U_10938,U_10937] :
      ( hAPP(U_10942,U_10943) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10937,U_10938,U_10939),U_10941),U_10940),U_10943)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10938),U_10943))
      | ~ c_Finite__Set_Ofolding__image__simple(U_10937,U_10938,U_10939,U_10940,U_10941,U_10942) ),
    inference(variable_rename,[status(thm)],[f_2897_1]) ).

fof(f_2897_3,plain,
    ! [U_10937,U_10938,U_10939,U_10940,U_10941,U_10942,U_10943] :
      ( hAPP(U_10942,U_10943) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10937,U_10938,U_10939),U_10941),U_10940),U_10943)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10938),U_10943))
      | ~ c_Finite__Set_Ofolding__image__simple(U_10937,U_10938,U_10939,U_10940,U_10941,U_10942) ),
    inference(definitional_conversion,[status(esa)],[f_2897_2]) ).

cnf(f_2897_4,plain,
    ( hAPP(U_10942,U_10943) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10937,U_10938,U_10939),U_10941),U_10940),U_10943)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10938),U_10943))
    | ~ c_Finite__Set_Ofolding__image__simple(U_10937,U_10938,U_10939,U_10940,U_10941,U_10942) ),
    inference(clausify,[status(thm)],[f_2897_3]) ).

fof(f_2898_1,plain,
    ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Id__on__empty]) ).

fof(f_2898_2,plain,
    ! [U_10944] : c_Relation_OId__on(U_10944,c_Orderings_Obot__class_Obot(tc_fun(U_10944,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10944,U_10944),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2898_1]) ).

fof(f_2898_3,plain,
    ! [U_10944] : c_Relation_OId__on(U_10944,c_Orderings_Obot__class_Obot(tc_fun(U_10944,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10944,U_10944),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2898_2]) ).

cnf(f_2898_4,plain,
    c_Relation_OId__on(U_10944,c_Orderings_Obot__class_Obot(tc_fun(U_10944,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10944,U_10944),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2898_3]) ).

fof(f_2899_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Image__Id__on]) ).

fof(f_2899_2,plain,
    ! [U_10947,U_10946,U_10945] : hAPP(c_Relation_OImage(U_10945,U_10945,c_Relation_OId__on(U_10945,U_10946)),U_10947) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10945,tc_HOL_Obool)),U_10946),U_10947),
    inference(variable_rename,[status(thm)],[f_2899_1]) ).

fof(f_2899_3,plain,
    ! [U_10945,U_10946,U_10947] : hAPP(c_Relation_OImage(U_10945,U_10945,c_Relation_OId__on(U_10945,U_10946)),U_10947) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10945,tc_HOL_Obool)),U_10946),U_10947),
    inference(definitional_conversion,[status(esa)],[f_2899_2]) ).

cnf(f_2899_4,plain,
    hAPP(c_Relation_OImage(U_10945,U_10945,c_Relation_OId__on(U_10945,U_10946)),U_10947) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10945,tc_HOL_Obool)),U_10946),U_10947),
    inference(clausify,[status(thm)],[f_2899_3]) ).

fof(f_2900_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__distrib]) ).

fof(f_2900_2,plain,
    ! [U_10952,U_10951,U_10950,U_10949,U_10948] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),hAPP(hAPP(c_COMBS(U_10949,U_10948,U_10948),hAPP(hAPP(c_COMBB(U_10948,tc_fun(U_10948,U_10948),U_10949),c_Groups_Otimes__class_Otimes(U_10948)),U_10951)),U_10952)),c_Groups_Oone__class_Oone(U_10948)),U_10950) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10948),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),c_Groups_Oone__class_Oone(U_10948)),U_10950)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),c_Groups_Oone__class_Oone(U_10948)),U_10950))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
      | ~ class_Groups_Ocomm__monoid__mult(U_10948) ),
    inference(variable_rename,[status(thm)],[f_2900_1]) ).

fof(f_2900_3,plain,
    ! [U_10948,U_10949,U_10950,U_10951,U_10952] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),hAPP(hAPP(c_COMBS(U_10949,U_10948,U_10948),hAPP(hAPP(c_COMBB(U_10948,tc_fun(U_10948,U_10948),U_10949),c_Groups_Otimes__class_Otimes(U_10948)),U_10951)),U_10952)),c_Groups_Oone__class_Oone(U_10948)),U_10950) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10948),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),c_Groups_Oone__class_Oone(U_10948)),U_10950)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),c_Groups_Oone__class_Oone(U_10948)),U_10950))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
      | ~ class_Groups_Ocomm__monoid__mult(U_10948) ),
    inference(definitional_conversion,[status(esa)],[f_2900_2]) ).

cnf(f_2900_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),hAPP(hAPP(c_COMBS(U_10949,U_10948,U_10948),hAPP(hAPP(c_COMBB(U_10948,tc_fun(U_10948,U_10948),U_10949),c_Groups_Otimes__class_Otimes(U_10948)),U_10951)),U_10952)),c_Groups_Oone__class_Oone(U_10948)),U_10950) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10948),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),c_Groups_Oone__class_Oone(U_10948)),U_10950)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),c_Groups_Oone__class_Oone(U_10948)),U_10950))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
    | ~ class_Groups_Ocomm__monoid__mult(U_10948) ),
    inference(clausify,[status(thm)],[f_2900_3]) ).

fof(f_2901_1,plain,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__insert]) ).

fof(f_2901_2,plain,
    ! [U_10958,U_10957,U_10956,U_10955,U_10954,U_10953] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10953,U_10954,c_Groups_Otimes__class_Otimes(U_10953)),U_10957),U_10958),hAPP(hAPP(c_Set_Oinsert(U_10954),U_10956),U_10955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10953),hAPP(U_10957,U_10956)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10953,U_10954,c_Groups_Otimes__class_Otimes(U_10953)),U_10957),U_10958),U_10955))
      | hBOOL(hAPP(hAPP(c_member(U_10954),U_10956),U_10955))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10954),U_10955))
      | ~ class_Groups_Oab__semigroup__mult(U_10953) ),
    inference(variable_rename,[status(thm)],[f_2901_1]) ).

fof(f_2901_3,plain,
    ! [U_10953,U_10954,U_10955,U_10956,U_10957,U_10958] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10953,U_10954,c_Groups_Otimes__class_Otimes(U_10953)),U_10957),U_10958),hAPP(hAPP(c_Set_Oinsert(U_10954),U_10956),U_10955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10953),hAPP(U_10957,U_10956)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10953,U_10954,c_Groups_Otimes__class_Otimes(U_10953)),U_10957),U_10958),U_10955))
      | hBOOL(hAPP(hAPP(c_member(U_10954),U_10956),U_10955))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10954),U_10955))
      | ~ class_Groups_Oab__semigroup__mult(U_10953) ),
    inference(definitional_conversion,[status(esa)],[f_2901_2]) ).

cnf(f_2901_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10953,U_10954,c_Groups_Otimes__class_Otimes(U_10953)),U_10957),U_10958),hAPP(hAPP(c_Set_Oinsert(U_10954),U_10956),U_10955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10953),hAPP(U_10957,U_10956)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10953,U_10954,c_Groups_Otimes__class_Otimes(U_10953)),U_10957),U_10958),U_10955))
    | hBOOL(hAPP(hAPP(c_member(U_10954),U_10956),U_10955))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10954),U_10955))
    | ~ class_Groups_Oab__semigroup__mult(U_10953) ),
    inference(clausify,[status(thm)],[f_2901_3]) ).

fof(f_2902_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_OF__eq]) ).

fof(f_2902_2,plain,
    ! [U_10962,U_10961,U_10960,U_10959] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10960,U_10959),U_10962),U_10961) = c_Groups_Oone__class_Oone(U_10959)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10960),U_10961)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10960,U_10959),U_10962),U_10961) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10959,U_10960,c_Groups_Otimes__class_Otimes(U_10959)),U_10962),c_Groups_Oone__class_Oone(U_10959)),U_10961)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10960),U_10961)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(U_10959) ),
    inference(variable_rename,[status(thm)],[f_2902_1]) ).

fof(f_2902_3,plain,
    ( ! [U_10959,U_10960,U_10961,U_10962] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10960,U_10959),U_10962),U_10961) = c_Groups_Oone__class_Oone(U_10959)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10960),U_10961))
        | ~ sP828(U_10959,U_10960,U_10961,U_10962) )
    & ! [U_10959,U_10960,U_10961,U_10962] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10960,U_10959),U_10962),U_10961) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10959,U_10960,c_Groups_Otimes__class_Otimes(U_10959)),U_10962),c_Groups_Oone__class_Oone(U_10959)),U_10961)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10960),U_10961))
        | ~ sP828(U_10959,U_10960,U_10961,U_10962) )
    & ! [U_10959,U_10960,U_10961,U_10962] :
        ( sP828(U_10959,U_10960,U_10961,U_10962)
        | ~ class_Groups_Ocomm__monoid__mult(U_10959) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP828])],[f_2902_2]) ).

cnf(f_2902_4,plain,
    ( sP828(U_10959,U_10960,U_10961,U_10962)
    | ~ class_Groups_Ocomm__monoid__mult(U_10959) ),
    inference(clausify,[status(thm)],[f_2902_3]) ).

cnf(f_2902_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10960,U_10959),U_10962),U_10961) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10959,U_10960,c_Groups_Otimes__class_Otimes(U_10959)),U_10962),c_Groups_Oone__class_Oone(U_10959)),U_10961)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10960),U_10961))
    | ~ sP828(U_10959,U_10960,U_10961,U_10962) ),
    inference(clausify,[status(thm)],[f_2902_3]) ).

cnf(f_2902_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10960,U_10959),U_10962),U_10961) = c_Groups_Oone__class_Oone(U_10959)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10960),U_10961))
    | ~ sP828(U_10959,U_10960,U_10961,U_10962) ),
    inference(clausify,[status(thm)],[f_2902_3]) ).

fof(f_2903_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold]) ).

fof(f_2903_2,plain,
    ! [U_10966,U_10965,U_10964,U_10963] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10964,U_10963),U_10966),U_10965) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10963,U_10964,c_Groups_Otimes__class_Otimes(U_10963)),U_10966),c_Groups_Oone__class_Oone(U_10963)),U_10965)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10964),U_10965))
      | ~ class_Groups_Ocomm__monoid__mult(U_10963) ),
    inference(variable_rename,[status(thm)],[f_2903_1]) ).

fof(f_2903_3,plain,
    ! [U_10964,U_10963,U_10965,U_10966] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10964,U_10963),U_10966),U_10965) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10963,U_10964,c_Groups_Otimes__class_Otimes(U_10963)),U_10966),c_Groups_Oone__class_Oone(U_10963)),U_10965)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10964),U_10965))
      | ~ class_Groups_Ocomm__monoid__mult(U_10963) ),
    inference(definitional_conversion,[status(esa)],[f_2903_2]) ).

cnf(f_2903_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10964,U_10963),U_10966),U_10965) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10963,U_10964,c_Groups_Otimes__class_Otimes(U_10963)),U_10966),c_Groups_Oone__class_Oone(U_10963)),U_10965)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10964),U_10965))
    | ~ class_Groups_Ocomm__monoid__mult(U_10963) ),
    inference(clausify,[status(thm)],[f_2903_3]) ).

fof(f_2904_1,plain,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_Id__on__eqI]) ).

fof(f_2904_2,plain,
    ! [U_10970,U_10969,U_10968,U_10967] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10969,U_10969)),hAPP(hAPP(c_Product__Type_OPair(U_10969,U_10969),U_10967),U_10968)),c_Relation_OId__on(U_10969,U_10970)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10969),U_10967),U_10970))
      | U_10967 != U_10968 ),
    inference(variable_rename,[status(thm)],[f_2904_1]) ).

fof(f_2904_3,plain,
    ! [U_10967,U_10968,U_10969,U_10970] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10969,U_10969)),hAPP(hAPP(c_Product__Type_OPair(U_10969,U_10969),U_10967),U_10968)),c_Relation_OId__on(U_10969,U_10970)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10969),U_10967),U_10970))
      | U_10967 != U_10968 ),
    inference(definitional_conversion,[status(esa)],[f_2904_2]) ).

cnf(f_2904_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10969,U_10969)),hAPP(hAPP(c_Product__Type_OPair(U_10969,U_10969),U_10967),U_10968)),c_Relation_OId__on(U_10969,U_10970)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10969),U_10967),U_10970))
    | U_10967 != U_10968 ),
    inference(clausify,[status(thm)],[f_2904_3]) ).

fof(f_2905_1,plain,
    ! [V_A_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | V_x_2 != V_y_2 )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          & V_x_2 = V_y_2 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Id__on__iff]) ).

fof(f_2905_2,plain,
    ! [U_10974,U_10973,U_10972,U_10971] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10971,U_10971)),hAPP(hAPP(c_Product__Type_OPair(U_10971,U_10971),U_10972),U_10973)),c_Relation_OId__on(U_10971,U_10974)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10971),U_10972),U_10974))
        | U_10972 != U_10973 )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_10971),U_10972),U_10974))
          & U_10972 = U_10973 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10971,U_10971)),hAPP(hAPP(c_Product__Type_OPair(U_10971,U_10971),U_10972),U_10973)),c_Relation_OId__on(U_10971,U_10974))) ) ),
    inference(variable_rename,[status(thm)],[f_2905_1]) ).

fof(f_2905_3,plain,
    ( ! [U_10982,U_10980,U_10978,U_10976] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10976,U_10976)),hAPP(hAPP(c_Product__Type_OPair(U_10976,U_10976),U_10978),U_10980)),c_Relation_OId__on(U_10976,U_10982)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10976),U_10978),U_10982))
        | U_10978 != U_10980 )
    & ! [U_10981,U_10979,U_10977,U_10975] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_10975),U_10977),U_10981))
          & U_10977 = U_10979 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10975,U_10975)),hAPP(hAPP(c_Product__Type_OPair(U_10975,U_10975),U_10977),U_10979)),c_Relation_OId__on(U_10975,U_10981))) ) ),
    inference(miniscope,[status(thm)],[f_2905_2]) ).

fof(f_2905_4,plain,
    ( ! [U_10977,U_10975,U_10979,U_10981] :
        ( hBOOL(hAPP(hAPP(c_member(U_10975),U_10977),U_10981))
        | ~ sP829(U_10977,U_10975,U_10979,U_10981) )
    & ! [U_10977,U_10975,U_10979,U_10981] :
        ( U_10977 = U_10979
        | ~ sP829(U_10977,U_10975,U_10979,U_10981) )
    & ! [U_10980,U_10976,U_10982,U_10978] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10976,U_10976)),hAPP(hAPP(c_Product__Type_OPair(U_10976,U_10976),U_10978),U_10980)),c_Relation_OId__on(U_10976,U_10982)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10976),U_10978),U_10982))
        | U_10978 != U_10980 )
    & ! [U_10977,U_10975,U_10979,U_10981] :
        ( sP829(U_10977,U_10975,U_10979,U_10981)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10975,U_10975)),hAPP(hAPP(c_Product__Type_OPair(U_10975,U_10975),U_10977),U_10979)),c_Relation_OId__on(U_10975,U_10981))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP829])],[f_2905_3]) ).

cnf(f_2905_5,plain,
    ( sP829(U_10977,U_10975,U_10979,U_10981)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10975,U_10975)),hAPP(hAPP(c_Product__Type_OPair(U_10975,U_10975),U_10977),U_10979)),c_Relation_OId__on(U_10975,U_10981))) ),
    inference(clausify,[status(thm)],[f_2905_4]) ).

cnf(f_2905_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10976,U_10976)),hAPP(hAPP(c_Product__Type_OPair(U_10976,U_10976),U_10978),U_10980)),c_Relation_OId__on(U_10976,U_10982)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10976),U_10978),U_10982))
    | U_10978 != U_10980 ),
    inference(clausify,[status(thm)],[f_2905_4]) ).

cnf(f_2905_7,plain,
    ( U_10977 = U_10979
    | ~ sP829(U_10977,U_10975,U_10979,U_10981) ),
    inference(clausify,[status(thm)],[f_2905_4]) ).

cnf(f_2905_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10975),U_10977),U_10981))
    | ~ sP829(U_10977,U_10975,U_10979,U_10981) ),
    inference(clausify,[status(thm)],[f_2905_4]) ).

fof(f_2906_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int]) ).

fof(f_2906_2,plain,
    ! [U_10987,U_10986,U_10985,U_10984,U_10983] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10983),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),U_10985)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),U_10986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10983),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10984,tc_HOL_Obool)),U_10985),U_10986))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10984,tc_HOL_Obool)),U_10985),U_10986)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10984),U_10986))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10984),U_10985))
      | ~ class_Groups_Ocomm__monoid__mult(U_10983) ),
    inference(variable_rename,[status(thm)],[f_2906_1]) ).

fof(f_2906_3,plain,
    ! [U_10983,U_10984,U_10985,U_10986,U_10987] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10983),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),U_10985)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),U_10986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10983),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10984,tc_HOL_Obool)),U_10985),U_10986))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10984,tc_HOL_Obool)),U_10985),U_10986)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10984),U_10986))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10984),U_10985))
      | ~ class_Groups_Ocomm__monoid__mult(U_10983) ),
    inference(definitional_conversion,[status(esa)],[f_2906_2]) ).

cnf(f_2906_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10983),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),U_10985)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),U_10986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10983),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10984,tc_HOL_Obool)),U_10985),U_10986))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10983,U_10984,c_Groups_Otimes__class_Otimes(U_10983)),U_10987),c_Groups_Oone__class_Oone(U_10983)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10984,tc_HOL_Obool)),U_10985),U_10986)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10984),U_10986))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10984),U_10985))
    | ~ class_Groups_Ocomm__monoid__mult(U_10983) ),
    inference(clausify,[status(thm)],[f_2906_3]) ).

fof(f_2907_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image]) ).

fof(f_2907_2,plain,
    ! [U_10991,U_10990,U_10989,U_10988] :
      ( hAPP(c_Set_Oimage(U_10988,U_10990,U_10991),U_10989) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10990,tc_HOL_Obool),U_10988,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10990,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10988,tc_fun(U_10990,tc_HOL_Obool),tc_fun(U_10990,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10990,tc_fun(tc_fun(U_10990,tc_HOL_Obool),tc_fun(U_10990,tc_HOL_Obool)),U_10988),c_Set_Oinsert(U_10990)),U_10991)),c_Orderings_Obot__class_Obot(tc_fun(U_10990,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10990,tc_HOL_Obool))),U_10989)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10988),U_10989)) ),
    inference(variable_rename,[status(thm)],[f_2907_1]) ).

fof(f_2907_3,plain,
    ! [U_10990,U_10988,U_10989,U_10991] :
      ( hAPP(c_Set_Oimage(U_10988,U_10990,U_10991),U_10989) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10990,tc_HOL_Obool),U_10988,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10990,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10988,tc_fun(U_10990,tc_HOL_Obool),tc_fun(U_10990,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10990,tc_fun(tc_fun(U_10990,tc_HOL_Obool),tc_fun(U_10990,tc_HOL_Obool)),U_10988),c_Set_Oinsert(U_10990)),U_10991)),c_Orderings_Obot__class_Obot(tc_fun(U_10990,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10990,tc_HOL_Obool))),U_10989)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10988),U_10989)) ),
    inference(definitional_conversion,[status(esa)],[f_2907_2]) ).

cnf(f_2907_4,plain,
    ( hAPP(c_Set_Oimage(U_10988,U_10990,U_10991),U_10989) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10990,tc_HOL_Obool),U_10988,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10990,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10988,tc_fun(U_10990,tc_HOL_Obool),tc_fun(U_10990,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10990,tc_fun(tc_fun(U_10990,tc_HOL_Obool),tc_fun(U_10990,tc_HOL_Obool)),U_10988),c_Set_Oinsert(U_10990)),U_10991)),c_Orderings_Obot__class_Obot(tc_fun(U_10990,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10990,tc_HOL_Obool))),U_10989)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10988),U_10989)) ),
    inference(clausify,[status(thm)],[f_2907_3]) ).

fof(f_2908_1,plain,
    ! [V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__def]) ).

fof(f_2908_2,plain,
    ! [U_10993,U_10992] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10992),U_10993) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10992),U_10993)) )
      & ( hAPP(c_Finite__Set_Ocard(U_10992),U_10993) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10992,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10992),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10993)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10992),U_10993)) ) ),
    inference(variable_rename,[status(thm)],[f_2908_1]) ).

fof(f_2908_3,plain,
    ( ! [U_10997,U_10995] :
        ( hAPP(c_Finite__Set_Ocard(U_10995),U_10997) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10995),U_10997)) )
    & ! [U_10996,U_10994] :
        ( hAPP(c_Finite__Set_Ocard(U_10994),U_10996) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10994,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10994),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10996)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10994),U_10996)) ) ),
    inference(miniscope,[status(thm)],[f_2908_2]) ).

fof(f_2908_4,plain,
    ( ! [U_10995,U_10997] :
        ( hAPP(c_Finite__Set_Ocard(U_10995),U_10997) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10995),U_10997)) )
    & ! [U_10996,U_10994] :
        ( hAPP(c_Finite__Set_Ocard(U_10994),U_10996) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10994,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10994),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10996)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10994),U_10996)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2908_3]) ).

cnf(f_2908_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10994),U_10996) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10994,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10994),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10996)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10994),U_10996)) ),
    inference(clausify,[status(thm)],[f_2908_4]) ).

cnf(f_2908_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10995),U_10997) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10995),U_10997)) ),
    inference(clausify,[status(thm)],[f_2908_4]) ).

fof(f_2909_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g]) ).

fof(f_2909_2,plain,
    ! [U_10999,U_10998] :
      ( hAPP(c_Finite__Set_Ocard(U_10998),U_10999) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10998,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10998),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10999)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10998),U_10999)) ),
    inference(variable_rename,[status(thm)],[f_2909_1]) ).

fof(f_2909_3,plain,
    ! [U_10998,U_10999] :
      ( hAPP(c_Finite__Set_Ocard(U_10998),U_10999) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10998,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10998),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10999)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10998),U_10999)) ),
    inference(definitional_conversion,[status(esa)],[f_2909_2]) ).

cnf(f_2909_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10998),U_10999) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10998,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10998),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10999)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10998),U_10999)) ),
    inference(clausify,[status(thm)],[f_2909_3]) ).

fof(f_2910_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
        & ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(f_2910_2,plain,
    ! [U_11006,U_11005,U_11004,U_11003,U_11002,U_11001,U_11000] :
      ( ( ( hAPP(hAPP(U_11004,U_11006),U_11005) = U_11003
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11001),U_11005)) )
        & ( hAPP(hAPP(U_11004,U_11006),U_11005) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11000,U_11001,U_11002),U_11006),U_11003),U_11005)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11001),U_11005)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(U_11000,U_11001,U_11002,U_11003,U_11004) ),
    inference(variable_rename,[status(thm)],[f_2910_1]) ).

fof(f_2910_3,plain,
    ( ! [U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006] :
        ( hAPP(hAPP(U_11004,U_11006),U_11005) = U_11003
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11001),U_11005))
        | ~ sP830(U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006) )
    & ! [U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006] :
        ( hAPP(hAPP(U_11004,U_11006),U_11005) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11000,U_11001,U_11002),U_11006),U_11003),U_11005)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11001),U_11005))
        | ~ sP830(U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006) )
    & ! [U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006] :
        ( sP830(U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006)
        | ~ c_Big__Operators_Ocomm__monoid__big(U_11000,U_11001,U_11002,U_11003,U_11004) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP830])],[f_2910_2]) ).

cnf(f_2910_4,plain,
    ( sP830(U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006)
    | ~ c_Big__Operators_Ocomm__monoid__big(U_11000,U_11001,U_11002,U_11003,U_11004) ),
    inference(clausify,[status(thm)],[f_2910_3]) ).

cnf(f_2910_5,plain,
    ( hAPP(hAPP(U_11004,U_11006),U_11005) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11000,U_11001,U_11002),U_11006),U_11003),U_11005)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11001),U_11005))
    | ~ sP830(U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006) ),
    inference(clausify,[status(thm)],[f_2910_3]) ).

cnf(f_2910_6,plain,
    ( hAPP(hAPP(U_11004,U_11006),U_11005) = U_11003
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11001),U_11005))
    | ~ sP830(U_11000,U_11001,U_11002,U_11003,U_11004,U_11005,U_11006) ),
    inference(clausify,[status(thm)],[f_2910_3]) ).

fof(f_2911_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one]) ).

fof(f_2911_2,plain,
    ! [U_11012,U_11011,U_11010,U_11009,U_11008] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11008),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11010)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11011))
      | ? [U_11007] :
          ( hAPP(U_11012,U_11007) != c_Groups_Oone__class_Oone(U_11008)
          & hBOOL(hAPP(hAPP(c_member(U_11009),U_11007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11011))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11010))
      | ~ class_Groups_Ocomm__monoid__mult(U_11008) ),
    inference(variable_rename,[status(thm)],[f_2911_1]) ).

fof(f_2911_3,plain,
    ! [U_11012,U_11011,U_11010,U_11009,U_11008] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11008),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11010)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11011))
      | ( hAPP(U_11012,sK184(U_11012,U_11011,U_11010,U_11009,U_11008)) != c_Groups_Oone__class_Oone(U_11008)
        & hBOOL(hAPP(hAPP(c_member(U_11009),sK184(U_11012,U_11011,U_11010,U_11009,U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11011))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11010))
      | ~ class_Groups_Ocomm__monoid__mult(U_11008) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_11007,sK184(U_11012,U_11011,U_11010,U_11009,U_11008))],[f_2911_2]) ).

fof(f_2911_4,plain,
    ( ! [U_11008,U_11009,U_11010,U_11011,U_11012] :
        ( hAPP(U_11012,sK184(U_11012,U_11011,U_11010,U_11009,U_11008)) != c_Groups_Oone__class_Oone(U_11008)
        | ~ sP831(U_11008,U_11009,U_11010,U_11011,U_11012) )
    & ! [U_11008,U_11009,U_11010,U_11011,U_11012] :
        ( hBOOL(hAPP(hAPP(c_member(U_11009),sK184(U_11012,U_11011,U_11010,U_11009,U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011)))
        | ~ sP831(U_11008,U_11009,U_11010,U_11011,U_11012) )
    & ! [U_11008,U_11009,U_11010,U_11011,U_11012] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11008),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11010)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11011))
        | sP831(U_11008,U_11009,U_11010,U_11011,U_11012)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11011))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11010))
        | ~ class_Groups_Ocomm__monoid__mult(U_11008) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP831])],[f_2911_3]) ).

cnf(f_2911_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11008),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11010)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11008,U_11009,c_Groups_Otimes__class_Otimes(U_11008)),U_11012),c_Groups_Oone__class_Oone(U_11008)),U_11011))
    | sP831(U_11008,U_11009,U_11010,U_11011,U_11012)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11011))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11009),U_11010))
    | ~ class_Groups_Ocomm__monoid__mult(U_11008) ),
    inference(clausify,[status(thm)],[f_2911_4]) ).

cnf(f_2911_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11009),sK184(U_11012,U_11011,U_11010,U_11009,U_11008)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11009,tc_HOL_Obool)),U_11010),U_11011)))
    | ~ sP831(U_11008,U_11009,U_11010,U_11011,U_11012) ),
    inference(clausify,[status(thm)],[f_2911_4]) ).

cnf(f_2911_7,plain,
    ( hAPP(U_11012,sK184(U_11012,U_11011,U_11010,U_11009,U_11008)) != c_Groups_Oone__class_Oone(U_11008)
    | ~ sP831(U_11008,U_11009,U_11010,U_11011,U_11012) ),
    inference(clausify,[status(thm)],[f_2911_4]) ).

fof(f_2912_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ? [B_x] :
          ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).

fof(f_2912_2,plain,
    ! [U_11016,U_11015,U_11014] :
      ( ? [U_11013] :
          ( U_11015 = hAPP(hAPP(c_Product__Type_OPair(U_11014,U_11014),U_11013),U_11013)
          & hBOOL(hAPP(hAPP(c_member(U_11014),U_11013),U_11016)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11014,U_11014)),U_11015),c_Relation_OId__on(U_11014,U_11016))) ),
    inference(variable_rename,[status(thm)],[f_2912_1]) ).

fof(f_2912_3,plain,
    ! [U_11016,U_11015,U_11014] :
      ( ( U_11015 = hAPP(hAPP(c_Product__Type_OPair(U_11014,U_11014),sK185(U_11016,U_11015,U_11014)),sK185(U_11016,U_11015,U_11014))
        & hBOOL(hAPP(hAPP(c_member(U_11014),sK185(U_11016,U_11015,U_11014)),U_11016)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11014,U_11014)),U_11015),c_Relation_OId__on(U_11014,U_11016))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_11013,sK185(U_11016,U_11015,U_11014))],[f_2912_2]) ).

fof(f_2912_4,plain,
    ( ! [U_11015,U_11016,U_11014] :
        ( U_11015 = hAPP(hAPP(c_Product__Type_OPair(U_11014,U_11014),sK185(U_11016,U_11015,U_11014)),sK185(U_11016,U_11015,U_11014))
        | ~ sP832(U_11015,U_11016,U_11014) )
    & ! [U_11015,U_11016,U_11014] :
        ( hBOOL(hAPP(hAPP(c_member(U_11014),sK185(U_11016,U_11015,U_11014)),U_11016))
        | ~ sP832(U_11015,U_11016,U_11014) )
    & ! [U_11015,U_11016,U_11014] :
        ( sP832(U_11015,U_11016,U_11014)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11014,U_11014)),U_11015),c_Relation_OId__on(U_11014,U_11016))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP832])],[f_2912_3]) ).

cnf(f_2912_5,plain,
    ( sP832(U_11015,U_11016,U_11014)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11014,U_11014)),U_11015),c_Relation_OId__on(U_11014,U_11016))) ),
    inference(clausify,[status(thm)],[f_2912_4]) ).

cnf(f_2912_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11014),sK185(U_11016,U_11015,U_11014)),U_11016))
    | ~ sP832(U_11015,U_11016,U_11014) ),
    inference(clausify,[status(thm)],[f_2912_4]) ).

cnf(f_2912_7,plain,
    ( U_11015 = hAPP(hAPP(c_Product__Type_OPair(U_11014,U_11014),sK185(U_11016,U_11015,U_11014)),sK185(U_11016,U_11015,U_11014))
    | ~ sP832(U_11015,U_11016,U_11014) ),
    inference(clausify,[status(thm)],[f_2912_4]) ).

fof(f_2913_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(f_2913_2,plain,
    ! [U_11023,U_11022,U_11021,U_11020,U_11019,U_11018,U_11017] :
      ( hAPP(hAPP(U_11021,U_11023),U_11022) = U_11020
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11018),U_11022))
      | ~ c_Big__Operators_Ocomm__monoid__big(U_11017,U_11018,U_11019,U_11020,U_11021) ),
    inference(variable_rename,[status(thm)],[f_2913_1]) ).

fof(f_2913_3,plain,
    ! [U_11023,U_11022,U_11021,U_11020,U_11019,U_11018] :
      ( ! [U_11017] : ~ c_Big__Operators_Ocomm__monoid__big(U_11017,U_11018,U_11019,U_11020,U_11021)
      | hAPP(hAPP(U_11021,U_11023),U_11022) = U_11020
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11018),U_11022)) ),
    inference(miniscope,[status(thm)],[f_2913_2]) ).

fof(f_2913_4,plain,
    ! [U_11019,U_11017,U_11020,U_11018,U_11021,U_11022,U_11023] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(U_11017,U_11018,U_11019,U_11020,U_11021)
      | hAPP(hAPP(U_11021,U_11023),U_11022) = U_11020
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11018),U_11022)) ),
    inference(definitional_conversion,[status(esa)],[f_2913_3]) ).

cnf(f_2913_5,plain,
    ( ~ c_Big__Operators_Ocomm__monoid__big(U_11017,U_11018,U_11019,U_11020,U_11021)
    | hAPP(hAPP(U_11021,U_11023),U_11022) = U_11020
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11018),U_11022)) ),
    inference(clausify,[status(thm)],[f_2913_4]) ).

fof(f_2914_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute]) ).

fof(f_2914_2,plain,
    ! [U_11028,U_11027,U_11026] :
      ( hAPP(U_11027,c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),U_11028)) = c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),hAPP(c_Set_Oimage(U_11026,U_11026,U_11027),U_11028))
      | U_11028 = c_Orderings_Obot__class_Obot(tc_fun(U_11026,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11026),U_11028))
      | ? [U_11025,U_11024] : hAPP(U_11027,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),U_11025),U_11024)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),hAPP(U_11027,U_11025)),hAPP(U_11027,U_11024))
      | ~ class_Orderings_Olinorder(U_11026) ),
    inference(variable_rename,[status(thm)],[f_2914_1]) ).

fof(f_2914_3,plain,
    ! [U_11028,U_11027,U_11026] :
      ( hAPP(U_11027,c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),U_11028)) = c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),hAPP(c_Set_Oimage(U_11026,U_11026,U_11027),U_11028))
      | U_11028 = c_Orderings_Obot__class_Obot(tc_fun(U_11026,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11026),U_11028))
      | ? [U_11024] : hAPP(U_11027,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),sK186(U_11028,U_11027,U_11026)),U_11024)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),hAPP(U_11027,sK186(U_11028,U_11027,U_11026))),hAPP(U_11027,U_11024))
      | ~ class_Orderings_Olinorder(U_11026) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_11025,sK186(U_11028,U_11027,U_11026))],[f_2914_2]) ).

fof(f_2914_4,plain,
    ! [U_11028,U_11027,U_11026] :
      ( hAPP(U_11027,c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),U_11028)) = c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),hAPP(c_Set_Oimage(U_11026,U_11026,U_11027),U_11028))
      | U_11028 = c_Orderings_Obot__class_Obot(tc_fun(U_11026,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11026),U_11028))
      | hAPP(U_11027,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),sK186(U_11028,U_11027,U_11026)),sK187(U_11028,U_11027,U_11026))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),hAPP(U_11027,sK186(U_11028,U_11027,U_11026))),hAPP(U_11027,sK187(U_11028,U_11027,U_11026)))
      | ~ class_Orderings_Olinorder(U_11026) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_11024,sK187(U_11028,U_11027,U_11026))],[f_2914_3]) ).

fof(f_2914_5,plain,
    ! [U_11026,U_11027,U_11028] :
      ( hAPP(U_11027,c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),U_11028)) = c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),hAPP(c_Set_Oimage(U_11026,U_11026,U_11027),U_11028))
      | U_11028 = c_Orderings_Obot__class_Obot(tc_fun(U_11026,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11026),U_11028))
      | hAPP(U_11027,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),sK186(U_11028,U_11027,U_11026)),sK187(U_11028,U_11027,U_11026))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),hAPP(U_11027,sK186(U_11028,U_11027,U_11026))),hAPP(U_11027,sK187(U_11028,U_11027,U_11026)))
      | ~ class_Orderings_Olinorder(U_11026) ),
    inference(definitional_conversion,[status(esa)],[f_2914_4]) ).

cnf(f_2914_6,plain,
    ( hAPP(U_11027,c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),U_11028)) = c_Big__Operators_Olattice_OInf__fin(U_11026,c_Orderings_Oord__class_Omin(U_11026),hAPP(c_Set_Oimage(U_11026,U_11026,U_11027),U_11028))
    | U_11028 = c_Orderings_Obot__class_Obot(tc_fun(U_11026,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11026),U_11028))
    | hAPP(U_11027,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),sK186(U_11028,U_11027,U_11026)),sK187(U_11028,U_11027,U_11026))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11026),hAPP(U_11027,sK186(U_11028,U_11027,U_11026))),hAPP(U_11027,sK187(U_11028,U_11027,U_11026)))
    | ~ class_Orderings_Olinorder(U_11026) ),
    inference(clausify,[status(thm)],[f_2914_5]) ).

fof(f_2915_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute]) ).

fof(f_2915_2,plain,
    ! [U_11033,U_11032,U_11031] :
      ( hAPP(U_11032,c_Big__Operators_Olinorder__class_OMax(U_11031,U_11033)) = c_Big__Operators_Olinorder__class_OMax(U_11031,hAPP(c_Set_Oimage(U_11031,U_11031,U_11032),U_11033))
      | U_11033 = c_Orderings_Obot__class_Obot(tc_fun(U_11031,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11031),U_11033))
      | ? [U_11030,U_11029] : hAPP(U_11032,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),U_11030),U_11029)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),hAPP(U_11032,U_11030)),hAPP(U_11032,U_11029))
      | ~ class_Orderings_Olinorder(U_11031) ),
    inference(variable_rename,[status(thm)],[f_2915_1]) ).

fof(f_2915_3,plain,
    ! [U_11033,U_11032,U_11031] :
      ( hAPP(U_11032,c_Big__Operators_Olinorder__class_OMax(U_11031,U_11033)) = c_Big__Operators_Olinorder__class_OMax(U_11031,hAPP(c_Set_Oimage(U_11031,U_11031,U_11032),U_11033))
      | U_11033 = c_Orderings_Obot__class_Obot(tc_fun(U_11031,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11031),U_11033))
      | ? [U_11029] : hAPP(U_11032,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),sK188(U_11033,U_11032,U_11031)),U_11029)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),hAPP(U_11032,sK188(U_11033,U_11032,U_11031))),hAPP(U_11032,U_11029))
      | ~ class_Orderings_Olinorder(U_11031) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_11030,sK188(U_11033,U_11032,U_11031))],[f_2915_2]) ).

fof(f_2915_4,plain,
    ! [U_11033,U_11032,U_11031] :
      ( hAPP(U_11032,c_Big__Operators_Olinorder__class_OMax(U_11031,U_11033)) = c_Big__Operators_Olinorder__class_OMax(U_11031,hAPP(c_Set_Oimage(U_11031,U_11031,U_11032),U_11033))
      | U_11033 = c_Orderings_Obot__class_Obot(tc_fun(U_11031,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11031),U_11033))
      | hAPP(U_11032,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),sK188(U_11033,U_11032,U_11031)),sK189(U_11033,U_11032,U_11031))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),hAPP(U_11032,sK188(U_11033,U_11032,U_11031))),hAPP(U_11032,sK189(U_11033,U_11032,U_11031)))
      | ~ class_Orderings_Olinorder(U_11031) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_11029,sK189(U_11033,U_11032,U_11031))],[f_2915_3]) ).

fof(f_2915_5,plain,
    ! [U_11031,U_11032,U_11033] :
      ( hAPP(U_11032,c_Big__Operators_Olinorder__class_OMax(U_11031,U_11033)) = c_Big__Operators_Olinorder__class_OMax(U_11031,hAPP(c_Set_Oimage(U_11031,U_11031,U_11032),U_11033))
      | U_11033 = c_Orderings_Obot__class_Obot(tc_fun(U_11031,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11031),U_11033))
      | hAPP(U_11032,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),sK188(U_11033,U_11032,U_11031)),sK189(U_11033,U_11032,U_11031))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),hAPP(U_11032,sK188(U_11033,U_11032,U_11031))),hAPP(U_11032,sK189(U_11033,U_11032,U_11031)))
      | ~ class_Orderings_Olinorder(U_11031) ),
    inference(definitional_conversion,[status(esa)],[f_2915_4]) ).

cnf(f_2915_6,plain,
    ( hAPP(U_11032,c_Big__Operators_Olinorder__class_OMax(U_11031,U_11033)) = c_Big__Operators_Olinorder__class_OMax(U_11031,hAPP(c_Set_Oimage(U_11031,U_11031,U_11032),U_11033))
    | U_11033 = c_Orderings_Obot__class_Obot(tc_fun(U_11031,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11031),U_11033))
    | hAPP(U_11032,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),sK188(U_11033,U_11032,U_11031)),sK189(U_11033,U_11032,U_11031))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11031),hAPP(U_11032,sK188(U_11033,U_11032,U_11031))),hAPP(U_11032,sK189(U_11033,U_11032,U_11031)))
    | ~ class_Orderings_Olinorder(U_11031) ),
    inference(clausify,[status(thm)],[f_2915_5]) ).

fof(f_2916_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute]) ).

fof(f_2916_2,plain,
    ! [U_11038,U_11037,U_11036] :
      ( hAPP(U_11037,c_Big__Operators_Olinorder__class_OMin(U_11036,U_11038)) = c_Big__Operators_Olinorder__class_OMin(U_11036,hAPP(c_Set_Oimage(U_11036,U_11036,U_11037),U_11038))
      | U_11038 = c_Orderings_Obot__class_Obot(tc_fun(U_11036,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11036),U_11038))
      | ? [U_11035,U_11034] : hAPP(U_11037,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),U_11035),U_11034)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),hAPP(U_11037,U_11035)),hAPP(U_11037,U_11034))
      | ~ class_Orderings_Olinorder(U_11036) ),
    inference(variable_rename,[status(thm)],[f_2916_1]) ).

fof(f_2916_3,plain,
    ! [U_11038,U_11037,U_11036] :
      ( hAPP(U_11037,c_Big__Operators_Olinorder__class_OMin(U_11036,U_11038)) = c_Big__Operators_Olinorder__class_OMin(U_11036,hAPP(c_Set_Oimage(U_11036,U_11036,U_11037),U_11038))
      | U_11038 = c_Orderings_Obot__class_Obot(tc_fun(U_11036,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11036),U_11038))
      | ? [U_11034] : hAPP(U_11037,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),sK190(U_11038,U_11037,U_11036)),U_11034)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),hAPP(U_11037,sK190(U_11038,U_11037,U_11036))),hAPP(U_11037,U_11034))
      | ~ class_Orderings_Olinorder(U_11036) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_11035,sK190(U_11038,U_11037,U_11036))],[f_2916_2]) ).

fof(f_2916_4,plain,
    ! [U_11038,U_11037,U_11036] :
      ( hAPP(U_11037,c_Big__Operators_Olinorder__class_OMin(U_11036,U_11038)) = c_Big__Operators_Olinorder__class_OMin(U_11036,hAPP(c_Set_Oimage(U_11036,U_11036,U_11037),U_11038))
      | U_11038 = c_Orderings_Obot__class_Obot(tc_fun(U_11036,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11036),U_11038))
      | hAPP(U_11037,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),sK190(U_11038,U_11037,U_11036)),sK191(U_11038,U_11037,U_11036))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),hAPP(U_11037,sK190(U_11038,U_11037,U_11036))),hAPP(U_11037,sK191(U_11038,U_11037,U_11036)))
      | ~ class_Orderings_Olinorder(U_11036) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_11034,sK191(U_11038,U_11037,U_11036))],[f_2916_3]) ).

fof(f_2916_5,plain,
    ! [U_11036,U_11037,U_11038] :
      ( hAPP(U_11037,c_Big__Operators_Olinorder__class_OMin(U_11036,U_11038)) = c_Big__Operators_Olinorder__class_OMin(U_11036,hAPP(c_Set_Oimage(U_11036,U_11036,U_11037),U_11038))
      | U_11038 = c_Orderings_Obot__class_Obot(tc_fun(U_11036,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11036),U_11038))
      | hAPP(U_11037,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),sK190(U_11038,U_11037,U_11036)),sK191(U_11038,U_11037,U_11036))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),hAPP(U_11037,sK190(U_11038,U_11037,U_11036))),hAPP(U_11037,sK191(U_11038,U_11037,U_11036)))
      | ~ class_Orderings_Olinorder(U_11036) ),
    inference(definitional_conversion,[status(esa)],[f_2916_4]) ).

cnf(f_2916_6,plain,
    ( hAPP(U_11037,c_Big__Operators_Olinorder__class_OMin(U_11036,U_11038)) = c_Big__Operators_Olinorder__class_OMin(U_11036,hAPP(c_Set_Oimage(U_11036,U_11036,U_11037),U_11038))
    | U_11038 = c_Orderings_Obot__class_Obot(tc_fun(U_11036,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11036),U_11038))
    | hAPP(U_11037,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),sK190(U_11038,U_11037,U_11036)),sK191(U_11038,U_11037,U_11036))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11036),hAPP(U_11037,sK190(U_11038,U_11037,U_11036))),hAPP(U_11037,sK191(U_11038,U_11037,U_11036)))
    | ~ class_Orderings_Olinorder(U_11036) ),
    inference(clausify,[status(thm)],[f_2916_5]) ).

fof(f_2917_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute]) ).

fof(f_2917_2,plain,
    ! [U_11043,U_11042,U_11041] :
      ( hAPP(U_11042,c_Big__Operators_Olattice__class_OInf__fin(U_11041,U_11043)) = c_Big__Operators_Olattice__class_OInf__fin(U_11041,hAPP(c_Set_Oimage(U_11041,U_11041,U_11042),U_11043))
      | U_11043 = c_Orderings_Obot__class_Obot(tc_fun(U_11041,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11041),U_11043))
      | ? [U_11040,U_11039] : hAPP(U_11042,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),U_11040),U_11039)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),hAPP(U_11042,U_11040)),hAPP(U_11042,U_11039))
      | ~ class_Lattices_Olattice(U_11041) ),
    inference(variable_rename,[status(thm)],[f_2917_1]) ).

fof(f_2917_3,plain,
    ! [U_11043,U_11042,U_11041] :
      ( hAPP(U_11042,c_Big__Operators_Olattice__class_OInf__fin(U_11041,U_11043)) = c_Big__Operators_Olattice__class_OInf__fin(U_11041,hAPP(c_Set_Oimage(U_11041,U_11041,U_11042),U_11043))
      | U_11043 = c_Orderings_Obot__class_Obot(tc_fun(U_11041,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11041),U_11043))
      | ? [U_11039] : hAPP(U_11042,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),sK192(U_11043,U_11042,U_11041)),U_11039)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),hAPP(U_11042,sK192(U_11043,U_11042,U_11041))),hAPP(U_11042,U_11039))
      | ~ class_Lattices_Olattice(U_11041) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_11040,sK192(U_11043,U_11042,U_11041))],[f_2917_2]) ).

fof(f_2917_4,plain,
    ! [U_11043,U_11042,U_11041] :
      ( hAPP(U_11042,c_Big__Operators_Olattice__class_OInf__fin(U_11041,U_11043)) = c_Big__Operators_Olattice__class_OInf__fin(U_11041,hAPP(c_Set_Oimage(U_11041,U_11041,U_11042),U_11043))
      | U_11043 = c_Orderings_Obot__class_Obot(tc_fun(U_11041,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11041),U_11043))
      | hAPP(U_11042,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),sK192(U_11043,U_11042,U_11041)),sK193(U_11043,U_11042,U_11041))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),hAPP(U_11042,sK192(U_11043,U_11042,U_11041))),hAPP(U_11042,sK193(U_11043,U_11042,U_11041)))
      | ~ class_Lattices_Olattice(U_11041) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_11039,sK193(U_11043,U_11042,U_11041))],[f_2917_3]) ).

fof(f_2917_5,plain,
    ! [U_11041,U_11042,U_11043] :
      ( hAPP(U_11042,c_Big__Operators_Olattice__class_OInf__fin(U_11041,U_11043)) = c_Big__Operators_Olattice__class_OInf__fin(U_11041,hAPP(c_Set_Oimage(U_11041,U_11041,U_11042),U_11043))
      | U_11043 = c_Orderings_Obot__class_Obot(tc_fun(U_11041,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11041),U_11043))
      | hAPP(U_11042,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),sK192(U_11043,U_11042,U_11041)),sK193(U_11043,U_11042,U_11041))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),hAPP(U_11042,sK192(U_11043,U_11042,U_11041))),hAPP(U_11042,sK193(U_11043,U_11042,U_11041)))
      | ~ class_Lattices_Olattice(U_11041) ),
    inference(definitional_conversion,[status(esa)],[f_2917_4]) ).

cnf(f_2917_6,plain,
    ( hAPP(U_11042,c_Big__Operators_Olattice__class_OInf__fin(U_11041,U_11043)) = c_Big__Operators_Olattice__class_OInf__fin(U_11041,hAPP(c_Set_Oimage(U_11041,U_11041,U_11042),U_11043))
    | U_11043 = c_Orderings_Obot__class_Obot(tc_fun(U_11041,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11041),U_11043))
    | hAPP(U_11042,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),sK192(U_11043,U_11042,U_11041)),sK193(U_11043,U_11042,U_11041))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11041),hAPP(U_11042,sK192(U_11043,U_11042,U_11041))),hAPP(U_11042,sK193(U_11043,U_11042,U_11041)))
    | ~ class_Lattices_Olattice(U_11041) ),
    inference(clausify,[status(thm)],[f_2917_5]) ).

fof(f_2918_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute]) ).

fof(f_2918_2,plain,
    ! [U_11048,U_11047,U_11046] :
      ( hAPP(U_11047,c_Big__Operators_Olattice__class_OSup__fin(U_11046,U_11048)) = c_Big__Operators_Olattice__class_OSup__fin(U_11046,hAPP(c_Set_Oimage(U_11046,U_11046,U_11047),U_11048))
      | U_11048 = c_Orderings_Obot__class_Obot(tc_fun(U_11046,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11046),U_11048))
      | ? [U_11045,U_11044] : hAPP(U_11047,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),U_11045),U_11044)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),hAPP(U_11047,U_11045)),hAPP(U_11047,U_11044))
      | ~ class_Lattices_Olattice(U_11046) ),
    inference(variable_rename,[status(thm)],[f_2918_1]) ).

fof(f_2918_3,plain,
    ! [U_11048,U_11047,U_11046] :
      ( hAPP(U_11047,c_Big__Operators_Olattice__class_OSup__fin(U_11046,U_11048)) = c_Big__Operators_Olattice__class_OSup__fin(U_11046,hAPP(c_Set_Oimage(U_11046,U_11046,U_11047),U_11048))
      | U_11048 = c_Orderings_Obot__class_Obot(tc_fun(U_11046,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11046),U_11048))
      | ? [U_11044] : hAPP(U_11047,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),sK194(U_11048,U_11047,U_11046)),U_11044)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),hAPP(U_11047,sK194(U_11048,U_11047,U_11046))),hAPP(U_11047,U_11044))
      | ~ class_Lattices_Olattice(U_11046) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_11045,sK194(U_11048,U_11047,U_11046))],[f_2918_2]) ).

fof(f_2918_4,plain,
    ! [U_11048,U_11047,U_11046] :
      ( hAPP(U_11047,c_Big__Operators_Olattice__class_OSup__fin(U_11046,U_11048)) = c_Big__Operators_Olattice__class_OSup__fin(U_11046,hAPP(c_Set_Oimage(U_11046,U_11046,U_11047),U_11048))
      | U_11048 = c_Orderings_Obot__class_Obot(tc_fun(U_11046,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11046),U_11048))
      | hAPP(U_11047,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),sK194(U_11048,U_11047,U_11046)),sK195(U_11048,U_11047,U_11046))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),hAPP(U_11047,sK194(U_11048,U_11047,U_11046))),hAPP(U_11047,sK195(U_11048,U_11047,U_11046)))
      | ~ class_Lattices_Olattice(U_11046) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_11044,sK195(U_11048,U_11047,U_11046))],[f_2918_3]) ).

fof(f_2918_5,plain,
    ! [U_11046,U_11047,U_11048] :
      ( hAPP(U_11047,c_Big__Operators_Olattice__class_OSup__fin(U_11046,U_11048)) = c_Big__Operators_Olattice__class_OSup__fin(U_11046,hAPP(c_Set_Oimage(U_11046,U_11046,U_11047),U_11048))
      | U_11048 = c_Orderings_Obot__class_Obot(tc_fun(U_11046,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11046),U_11048))
      | hAPP(U_11047,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),sK194(U_11048,U_11047,U_11046)),sK195(U_11048,U_11047,U_11046))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),hAPP(U_11047,sK194(U_11048,U_11047,U_11046))),hAPP(U_11047,sK195(U_11048,U_11047,U_11046)))
      | ~ class_Lattices_Olattice(U_11046) ),
    inference(definitional_conversion,[status(esa)],[f_2918_4]) ).

cnf(f_2918_6,plain,
    ( hAPP(U_11047,c_Big__Operators_Olattice__class_OSup__fin(U_11046,U_11048)) = c_Big__Operators_Olattice__class_OSup__fin(U_11046,hAPP(c_Set_Oimage(U_11046,U_11046,U_11047),U_11048))
    | U_11048 = c_Orderings_Obot__class_Obot(tc_fun(U_11046,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11046),U_11048))
    | hAPP(U_11047,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),sK194(U_11048,U_11047,U_11046)),sK195(U_11048,U_11047,U_11046))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11046),hAPP(U_11047,sK194(U_11048,U_11047,U_11046))),hAPP(U_11047,sK195(U_11048,U_11047,U_11046)))
    | ~ class_Lattices_Olattice(U_11046) ),
    inference(clausify,[status(thm)],[f_2918_5]) ).

fof(f_2919_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right]) ).

fof(f_2919_2,plain,
    ! [U_11054,U_11053,U_11052,U_11051,U_11050] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11053)
      | ? [U_11049] :
          ( hAPP(U_11054,U_11049) != c_Groups_Oone__class_Oone(U_11050)
          & hBOOL(hAPP(hAPP(c_member(U_11051),U_11049),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11051,tc_HOL_Obool)),U_11052),U_11053))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11051,tc_HOL_Obool)),U_11053),U_11052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11051),U_11052))
      | ~ class_Groups_Ocomm__monoid__mult(U_11050) ),
    inference(variable_rename,[status(thm)],[f_2919_1]) ).

fof(f_2919_3,plain,
    ! [U_11054,U_11053,U_11052,U_11051,U_11050] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11053)
      | ( hAPP(U_11054,sK196(U_11054,U_11053,U_11052,U_11051,U_11050)) != c_Groups_Oone__class_Oone(U_11050)
        & hBOOL(hAPP(hAPP(c_member(U_11051),sK196(U_11054,U_11053,U_11052,U_11051,U_11050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11051,tc_HOL_Obool)),U_11052),U_11053))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11051,tc_HOL_Obool)),U_11053),U_11052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11051),U_11052))
      | ~ class_Groups_Ocomm__monoid__mult(U_11050) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_11049,sK196(U_11054,U_11053,U_11052,U_11051,U_11050))],[f_2919_2]) ).

fof(f_2919_4,plain,
    ( ! [U_11050,U_11051,U_11052,U_11053,U_11054] :
        ( hAPP(U_11054,sK196(U_11054,U_11053,U_11052,U_11051,U_11050)) != c_Groups_Oone__class_Oone(U_11050)
        | ~ sP833(U_11050,U_11051,U_11052,U_11053,U_11054) )
    & ! [U_11050,U_11051,U_11052,U_11053,U_11054] :
        ( hBOOL(hAPP(hAPP(c_member(U_11051),sK196(U_11054,U_11053,U_11052,U_11051,U_11050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11051,tc_HOL_Obool)),U_11052),U_11053)))
        | ~ sP833(U_11050,U_11051,U_11052,U_11053,U_11054) )
    & ! [U_11050,U_11051,U_11052,U_11053,U_11054] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11053)
        | sP833(U_11050,U_11051,U_11052,U_11053,U_11054)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11051,tc_HOL_Obool)),U_11053),U_11052))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11051),U_11052))
        | ~ class_Groups_Ocomm__monoid__mult(U_11050) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP833])],[f_2919_3]) ).

cnf(f_2919_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11051,U_11050),U_11054),U_11053)
    | sP833(U_11050,U_11051,U_11052,U_11053,U_11054)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11051,tc_HOL_Obool)),U_11053),U_11052))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11051),U_11052))
    | ~ class_Groups_Ocomm__monoid__mult(U_11050) ),
    inference(clausify,[status(thm)],[f_2919_4]) ).

cnf(f_2919_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11051),sK196(U_11054,U_11053,U_11052,U_11051,U_11050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11051,tc_HOL_Obool)),U_11052),U_11053)))
    | ~ sP833(U_11050,U_11051,U_11052,U_11053,U_11054) ),
    inference(clausify,[status(thm)],[f_2919_4]) ).

cnf(f_2919_7,plain,
    ( hAPP(U_11054,sK196(U_11054,U_11053,U_11052,U_11051,U_11050)) != c_Groups_Oone__class_Oone(U_11050)
    | ~ sP833(U_11050,U_11051,U_11052,U_11053,U_11054) ),
    inference(clausify,[status(thm)],[f_2919_4]) ).

fof(f_2920_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left]) ).

fof(f_2920_2,plain,
    ! [U_11060,U_11059,U_11058,U_11057,U_11056] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11058)
      | ? [U_11055] :
          ( hAPP(U_11060,U_11055) != c_Groups_Oone__class_Oone(U_11056)
          & hBOOL(hAPP(hAPP(c_member(U_11057),U_11055),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11057,tc_HOL_Obool)),U_11058),U_11059))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11057,tc_HOL_Obool)),U_11059),U_11058))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11057),U_11058))
      | ~ class_Groups_Ocomm__monoid__mult(U_11056) ),
    inference(variable_rename,[status(thm)],[f_2920_1]) ).

fof(f_2920_3,plain,
    ! [U_11060,U_11059,U_11058,U_11057,U_11056] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11058)
      | ( hAPP(U_11060,sK197(U_11060,U_11059,U_11058,U_11057,U_11056)) != c_Groups_Oone__class_Oone(U_11056)
        & hBOOL(hAPP(hAPP(c_member(U_11057),sK197(U_11060,U_11059,U_11058,U_11057,U_11056)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11057,tc_HOL_Obool)),U_11058),U_11059))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11057,tc_HOL_Obool)),U_11059),U_11058))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11057),U_11058))
      | ~ class_Groups_Ocomm__monoid__mult(U_11056) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_11055,sK197(U_11060,U_11059,U_11058,U_11057,U_11056))],[f_2920_2]) ).

fof(f_2920_4,plain,
    ( ! [U_11057,U_11058,U_11056,U_11060,U_11059] :
        ( hAPP(U_11060,sK197(U_11060,U_11059,U_11058,U_11057,U_11056)) != c_Groups_Oone__class_Oone(U_11056)
        | ~ sP834(U_11057,U_11058,U_11056,U_11060,U_11059) )
    & ! [U_11057,U_11058,U_11056,U_11060,U_11059] :
        ( hBOOL(hAPP(hAPP(c_member(U_11057),sK197(U_11060,U_11059,U_11058,U_11057,U_11056)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11057,tc_HOL_Obool)),U_11058),U_11059)))
        | ~ sP834(U_11057,U_11058,U_11056,U_11060,U_11059) )
    & ! [U_11057,U_11058,U_11056,U_11060,U_11059] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11058)
        | sP834(U_11057,U_11058,U_11056,U_11060,U_11059)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11057,tc_HOL_Obool)),U_11059),U_11058))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11057),U_11058))
        | ~ class_Groups_Ocomm__monoid__mult(U_11056) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP834])],[f_2920_3]) ).

cnf(f_2920_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11057,U_11056),U_11060),U_11058)
    | sP834(U_11057,U_11058,U_11056,U_11060,U_11059)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11057,tc_HOL_Obool)),U_11059),U_11058))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11057),U_11058))
    | ~ class_Groups_Ocomm__monoid__mult(U_11056) ),
    inference(clausify,[status(thm)],[f_2920_4]) ).

cnf(f_2920_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11057),sK197(U_11060,U_11059,U_11058,U_11057,U_11056)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11057,tc_HOL_Obool)),U_11058),U_11059)))
    | ~ sP834(U_11057,U_11058,U_11056,U_11060,U_11059) ),
    inference(clausify,[status(thm)],[f_2920_4]) ).

cnf(f_2920_7,plain,
    ( hAPP(U_11060,sK197(U_11060,U_11059,U_11058,U_11057,U_11056)) != c_Groups_Oone__class_Oone(U_11056)
    | ~ sP834(U_11057,U_11058,U_11056,U_11060,U_11059) ),
    inference(clausify,[status(thm)],[f_2920_4]) ).

fof(f_2921_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Pow]) ).

fof(f_2921_2,plain,
    ! [U_11062,U_11061] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11061,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11061),U_11062)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(U_11061),U_11062))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11061),U_11062)) ),
    inference(variable_rename,[status(thm)],[f_2921_1]) ).

fof(f_2921_3,plain,
    ! [U_11062,U_11061] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11061,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11061),U_11062)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(U_11061),U_11062))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11061),U_11062)) ),
    inference(definitional_conversion,[status(esa)],[f_2921_2]) ).

cnf(f_2921_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11061,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11061),U_11062)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(U_11061),U_11062))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11061),U_11062)) ),
    inference(clausify,[status(thm)],[f_2921_3]) ).

fof(f_2922_1,plain,
    ! [V_P_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          & hBOOL(hAPP(V_P_2,B_A))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) )
      | ~ hBOOL(hAPP(V_P_2,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).

fof(f_2922_2,plain,
    ! [U_11067,U_11066,U_11065] :
      ( hBOOL(hAPP(U_11067,c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))
      | ? [U_11064,U_11063] :
          ( ~ hBOOL(hAPP(U_11067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11065,tc_HOL_Obool)),U_11063),hAPP(hAPP(c_Set_Oinsert(U_11065),U_11064),c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_11067,U_11063))
          & hBOOL(hAPP(hAPP(c_member(U_11065),U_11064),U_11063))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11063)) )
      | ~ hBOOL(hAPP(U_11067,U_11066))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11066)) ),
    inference(variable_rename,[status(thm)],[f_2922_1]) ).

fof(f_2922_3,plain,
    ! [U_11067,U_11066,U_11065] :
      ( hBOOL(hAPP(U_11067,c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))
      | ? [U_11063] :
          ( ~ hBOOL(hAPP(U_11067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11065,tc_HOL_Obool)),U_11063),hAPP(hAPP(c_Set_Oinsert(U_11065),sK198(U_11067,U_11066,U_11065)),c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_11067,U_11063))
          & hBOOL(hAPP(hAPP(c_member(U_11065),sK198(U_11067,U_11066,U_11065)),U_11063))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11063)) )
      | ~ hBOOL(hAPP(U_11067,U_11066))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11066)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_11064,sK198(U_11067,U_11066,U_11065))],[f_2922_2]) ).

fof(f_2922_4,plain,
    ! [U_11067,U_11066,U_11065] :
      ( hBOOL(hAPP(U_11067,c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(U_11067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11065,tc_HOL_Obool)),sK199(U_11067,U_11066,U_11065)),hAPP(hAPP(c_Set_Oinsert(U_11065),sK198(U_11067,U_11066,U_11065)),c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))))
        & hBOOL(hAPP(U_11067,sK199(U_11067,U_11066,U_11065)))
        & hBOOL(hAPP(hAPP(c_member(U_11065),sK198(U_11067,U_11066,U_11065)),sK199(U_11067,U_11066,U_11065)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),sK199(U_11067,U_11066,U_11065))) )
      | ~ hBOOL(hAPP(U_11067,U_11066))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11066)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_11063,sK199(U_11067,U_11066,U_11065))],[f_2922_3]) ).

fof(f_2922_5,plain,
    ( ! [U_11065,U_11066,U_11067] :
        ( ~ hBOOL(hAPP(U_11067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11065,tc_HOL_Obool)),sK199(U_11067,U_11066,U_11065)),hAPP(hAPP(c_Set_Oinsert(U_11065),sK198(U_11067,U_11066,U_11065)),c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))))
        | ~ sP835(U_11065,U_11066,U_11067) )
    & ! [U_11065,U_11066,U_11067] :
        ( hBOOL(hAPP(U_11067,sK199(U_11067,U_11066,U_11065)))
        | ~ sP835(U_11065,U_11066,U_11067) )
    & ! [U_11065,U_11066,U_11067] :
        ( hBOOL(hAPP(hAPP(c_member(U_11065),sK198(U_11067,U_11066,U_11065)),sK199(U_11067,U_11066,U_11065)))
        | ~ sP835(U_11065,U_11066,U_11067) )
    & ! [U_11065,U_11066,U_11067] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),sK199(U_11067,U_11066,U_11065)))
        | ~ sP835(U_11065,U_11066,U_11067) )
    & ! [U_11065,U_11066,U_11067] :
        ( hBOOL(hAPP(U_11067,c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))
        | sP835(U_11065,U_11066,U_11067)
        | ~ hBOOL(hAPP(U_11067,U_11066))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11066)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP835])],[f_2922_4]) ).

cnf(f_2922_6,plain,
    ( hBOOL(hAPP(U_11067,c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))
    | sP835(U_11065,U_11066,U_11067)
    | ~ hBOOL(hAPP(U_11067,U_11066))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),U_11066)) ),
    inference(clausify,[status(thm)],[f_2922_5]) ).

cnf(f_2922_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11065),sK199(U_11067,U_11066,U_11065)))
    | ~ sP835(U_11065,U_11066,U_11067) ),
    inference(clausify,[status(thm)],[f_2922_5]) ).

cnf(f_2922_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11065),sK198(U_11067,U_11066,U_11065)),sK199(U_11067,U_11066,U_11065)))
    | ~ sP835(U_11065,U_11066,U_11067) ),
    inference(clausify,[status(thm)],[f_2922_5]) ).

cnf(f_2922_9,plain,
    ( hBOOL(hAPP(U_11067,sK199(U_11067,U_11066,U_11065)))
    | ~ sP835(U_11065,U_11066,U_11067) ),
    inference(clausify,[status(thm)],[f_2922_5]) ).

cnf(f_2922_10,plain,
    ( ~ hBOOL(hAPP(U_11067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11065,tc_HOL_Obool)),sK199(U_11067,U_11066,U_11065)),hAPP(hAPP(c_Set_Oinsert(U_11065),sK198(U_11067,U_11066,U_11065)),c_Orderings_Obot__class_Obot(tc_fun(U_11065,tc_HOL_Obool))))))
    | ~ sP835(U_11065,U_11066,U_11067) ),
    inference(clausify,[status(thm)],[f_2922_5]) ).

fof(f_2923_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_PowI]) ).

fof(f_2923_2,plain,
    ! [U_11070,U_11069,U_11068] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11068,tc_HOL_Obool)),U_11069),hAPP(c_Set_OPow(U_11068),U_11070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11068,tc_HOL_Obool)),U_11069),U_11070)) ),
    inference(variable_rename,[status(thm)],[f_2923_1]) ).

fof(f_2923_3,plain,
    ! [U_11070,U_11069,U_11068] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11068,tc_HOL_Obool)),U_11069),hAPP(c_Set_OPow(U_11068),U_11070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11068,tc_HOL_Obool)),U_11069),U_11070)) ),
    inference(definitional_conversion,[status(esa)],[f_2923_2]) ).

cnf(f_2923_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11068,tc_HOL_Obool)),U_11069),hAPP(c_Set_OPow(U_11068),U_11070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11068,tc_HOL_Obool)),U_11069),U_11070)) ),
    inference(clausify,[status(thm)],[f_2923_3]) ).

fof(f_2924_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__top]) ).

fof(f_2924_2,plain,
    ! [U_11072,U_11071] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11071,tc_HOL_Obool)),U_11072),hAPP(c_Set_OPow(U_11071),U_11072))),
    inference(variable_rename,[status(thm)],[f_2924_1]) ).

fof(f_2924_3,plain,
    ! [U_11071,U_11072] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11071,tc_HOL_Obool)),U_11072),hAPP(c_Set_OPow(U_11071),U_11072))),
    inference(definitional_conversion,[status(esa)],[f_2924_2]) ).

cnf(f_2924_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_11071,tc_HOL_Obool)),U_11072),hAPP(c_Set_OPow(U_11071),U_11072))),
    inference(clausify,[status(thm)],[f_2924_3]) ).

fof(f_2925_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2)
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_image__Pow__surj]) ).

fof(f_2925_2,plain,
    ! [U_11077,U_11076,U_11075,U_11074,U_11073] :
      ( hAPP(c_Set_Oimage(tc_fun(U_11073,tc_HOL_Obool),tc_fun(U_11074,tc_HOL_Obool),c_Set_Oimage(U_11073,U_11074,U_11075)),hAPP(c_Set_OPow(U_11073),U_11076)) = hAPP(c_Set_OPow(U_11074),U_11077)
      | hAPP(c_Set_Oimage(U_11073,U_11074,U_11075),U_11076) != U_11077 ),
    inference(variable_rename,[status(thm)],[f_2925_1]) ).

fof(f_2925_3,plain,
    ! [U_11073,U_11074,U_11075,U_11076,U_11077] :
      ( hAPP(c_Set_Oimage(tc_fun(U_11073,tc_HOL_Obool),tc_fun(U_11074,tc_HOL_Obool),c_Set_Oimage(U_11073,U_11074,U_11075)),hAPP(c_Set_OPow(U_11073),U_11076)) = hAPP(c_Set_OPow(U_11074),U_11077)
      | hAPP(c_Set_Oimage(U_11073,U_11074,U_11075),U_11076) != U_11077 ),
    inference(definitional_conversion,[status(esa)],[f_2925_2]) ).

cnf(f_2925_4,plain,
    ( hAPP(c_Set_Oimage(tc_fun(U_11073,tc_HOL_Obool),tc_fun(U_11074,tc_HOL_Obool),c_Set_Oimage(U_11073,U_11074,U_11075)),hAPP(c_Set_OPow(U_11073),U_11076)) = hAPP(c_Set_OPow(U_11074),U_11077)
    | hAPP(c_Set_Oimage(U_11073,U_11074,U_11075),U_11076) != U_11077 ),
    inference(clausify,[status(thm)],[f_2925_3]) ).

fof(f_2926_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Pow__mono]) ).

fof(f_2926_2,plain,
    ! [U_11080,U_11079,U_11078] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11078,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11078),U_11079)),hAPP(c_Set_OPow(U_11078),U_11080)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11078,tc_HOL_Obool)),U_11079),U_11080)) ),
    inference(variable_rename,[status(thm)],[f_2926_1]) ).

fof(f_2926_3,plain,
    ! [U_11078,U_11079,U_11080] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11078,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11078),U_11079)),hAPP(c_Set_OPow(U_11078),U_11080)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11078,tc_HOL_Obool)),U_11079),U_11080)) ),
    inference(definitional_conversion,[status(esa)],[f_2926_2]) ).

cnf(f_2926_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11078,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11078),U_11079)),hAPP(c_Set_OPow(U_11078),U_11080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11078,tc_HOL_Obool)),U_11079),U_11080)) ),
    inference(clausify,[status(thm)],[f_2926_3]) ).

fof(f_2927_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Un__Pow__subset]) ).

fof(f_2927_2,plain,
    ! [U_11083,U_11082,U_11081] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11081,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11081,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11081),U_11082)),hAPP(c_Set_OPow(U_11081),U_11083))),hAPP(c_Set_OPow(U_11081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11081,tc_HOL_Obool)),U_11082),U_11083)))),
    inference(variable_rename,[status(thm)],[f_2927_1]) ).

fof(f_2927_3,plain,
    ! [U_11081,U_11082,U_11083] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11081,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11081,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11081),U_11082)),hAPP(c_Set_OPow(U_11081),U_11083))),hAPP(c_Set_OPow(U_11081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11081,tc_HOL_Obool)),U_11082),U_11083)))),
    inference(definitional_conversion,[status(esa)],[f_2927_2]) ).

cnf(f_2927_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11081,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11081,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11081),U_11082)),hAPP(c_Set_OPow(U_11081),U_11083))),hAPP(c_Set_OPow(U_11081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11081,tc_HOL_Obool)),U_11082),U_11083)))),
    inference(clausify,[status(thm)],[f_2927_3]) ).

fof(f_2928_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__Int__eq]) ).

fof(f_2928_2,plain,
    ! [U_11086,U_11085,U_11084] : hAPP(c_Set_OPow(U_11084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11084,tc_HOL_Obool)),U_11085),U_11086)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11084,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11084),U_11085)),hAPP(c_Set_OPow(U_11084),U_11086)),
    inference(variable_rename,[status(thm)],[f_2928_1]) ).

fof(f_2928_3,plain,
    ! [U_11084,U_11085,U_11086] : hAPP(c_Set_OPow(U_11084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11084,tc_HOL_Obool)),U_11085),U_11086)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11084,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11084),U_11085)),hAPP(c_Set_OPow(U_11084),U_11086)),
    inference(definitional_conversion,[status(esa)],[f_2928_2]) ).

cnf(f_2928_4,plain,
    hAPP(c_Set_OPow(U_11084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11084,tc_HOL_Obool)),U_11085),U_11086)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11084,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11084),U_11085)),hAPP(c_Set_OPow(U_11084),U_11086)),
    inference(clausify,[status(thm)],[f_2928_3]) ).

fof(f_2929_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__insert]) ).

fof(f_2929_2,plain,
    ! [U_11089,U_11088,U_11087] : hAPP(c_Set_OPow(U_11087),hAPP(hAPP(c_Set_Oinsert(U_11087),U_11088),U_11089)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11087,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11087),U_11089)),hAPP(c_Set_Oimage(tc_fun(U_11087,tc_HOL_Obool),tc_fun(U_11087,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11087),U_11088)),hAPP(c_Set_OPow(U_11087),U_11089))),
    inference(variable_rename,[status(thm)],[f_2929_1]) ).

fof(f_2929_3,plain,
    ! [U_11087,U_11088,U_11089] : hAPP(c_Set_OPow(U_11087),hAPP(hAPP(c_Set_Oinsert(U_11087),U_11088),U_11089)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11087,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11087),U_11089)),hAPP(c_Set_Oimage(tc_fun(U_11087,tc_HOL_Obool),tc_fun(U_11087,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11087),U_11088)),hAPP(c_Set_OPow(U_11087),U_11089))),
    inference(definitional_conversion,[status(esa)],[f_2929_2]) ).

cnf(f_2929_4,plain,
    hAPP(c_Set_OPow(U_11087),hAPP(hAPP(c_Set_Oinsert(U_11087),U_11088),U_11089)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11087,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11087),U_11089)),hAPP(c_Set_Oimage(tc_fun(U_11087,tc_HOL_Obool),tc_fun(U_11087,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11087),U_11088)),hAPP(c_Set_OPow(U_11087),U_11089))),
    inference(clausify,[status(thm)],[f_2929_3]) ).

fof(f_2930_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff]) ).

fof(f_2930_2,plain,
    ! [U_11091,U_11090] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11090,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11090),U_11091)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11090),U_11091)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11090),U_11091))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11090,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11090),U_11091))) ) ),
    inference(variable_rename,[status(thm)],[f_2930_1]) ).

fof(f_2930_3,plain,
    ( ! [U_11095,U_11093] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11093,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11093),U_11095)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11093),U_11095)) )
    & ! [U_11094,U_11092] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11092),U_11094))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11092,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11092),U_11094))) ) ),
    inference(miniscope,[status(thm)],[f_2930_2]) ).

fof(f_2930_4,plain,
    ( ! [U_11093,U_11095] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11093,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11093),U_11095)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11093),U_11095)) )
    & ! [U_11094,U_11092] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11092),U_11094))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11092,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11092),U_11094))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2930_3]) ).

cnf(f_2930_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11092),U_11094))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11092,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11092),U_11094))) ),
    inference(clausify,[status(thm)],[f_2930_4]) ).

cnf(f_2930_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11093,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11093),U_11095)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11093),U_11095)) ),
    inference(clausify,[status(thm)],[f_2930_4]) ).

fof(f_2931_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Pow__not__empty]) ).

fof(f_2931_2,plain,
    ! [U_11097,U_11096] : hAPP(c_Set_OPow(U_11096),U_11097) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11096,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2931_1]) ).

fof(f_2931_3,plain,
    ! [U_11096,U_11097] : hAPP(c_Set_OPow(U_11096),U_11097) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11096,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2931_2]) ).

cnf(f_2931_4,plain,
    hAPP(c_Set_OPow(U_11096),U_11097) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11096,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2931_3]) ).

fof(f_2932_1,plain,
    ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__bottom]) ).

fof(f_2932_2,plain,
    ! [U_11099,U_11098] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11098,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11098,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11098),U_11099))),
    inference(variable_rename,[status(thm)],[f_2932_1]) ).

fof(f_2932_3,plain,
    ! [U_11098,U_11099] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11098,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11098,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11098),U_11099))),
    inference(definitional_conversion,[status(esa)],[f_2932_2]) ).

cnf(f_2932_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_11098,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11098,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11098),U_11099))),
    inference(clausify,[status(thm)],[f_2932_3]) ).

fof(f_2933_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__Pow__mono]) ).

fof(f_2933_2,plain,
    ! [U_11104,U_11103,U_11102,U_11101,U_11100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11100,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11101,tc_HOL_Obool),tc_fun(U_11100,tc_HOL_Obool),c_Set_Oimage(U_11101,U_11100,U_11102)),hAPP(c_Set_OPow(U_11101),U_11103))),hAPP(c_Set_OPow(U_11100),U_11104)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11100,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11101,U_11100,U_11102),U_11103)),U_11104)) ),
    inference(variable_rename,[status(thm)],[f_2933_1]) ).

fof(f_2933_3,plain,
    ! [U_11100,U_11101,U_11102,U_11103,U_11104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11100,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11101,tc_HOL_Obool),tc_fun(U_11100,tc_HOL_Obool),c_Set_Oimage(U_11101,U_11100,U_11102)),hAPP(c_Set_OPow(U_11101),U_11103))),hAPP(c_Set_OPow(U_11100),U_11104)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11100,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11101,U_11100,U_11102),U_11103)),U_11104)) ),
    inference(definitional_conversion,[status(esa)],[f_2933_2]) ).

cnf(f_2933_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11100,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11101,tc_HOL_Obool),tc_fun(U_11100,tc_HOL_Obool),c_Set_Oimage(U_11101,U_11100,U_11102)),hAPP(c_Set_OPow(U_11101),U_11103))),hAPP(c_Set_OPow(U_11100),U_11104)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11100,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11101,U_11100,U_11102),U_11103)),U_11104)) ),
    inference(clausify,[status(thm)],[f_2933_3]) ).

fof(f_2934_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_PowD]) ).

fof(f_2934_2,plain,
    ! [U_11107,U_11106,U_11105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11105,tc_HOL_Obool)),U_11106),U_11107))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11105,tc_HOL_Obool)),U_11106),hAPP(c_Set_OPow(U_11105),U_11107))) ),
    inference(variable_rename,[status(thm)],[f_2934_1]) ).

fof(f_2934_3,plain,
    ! [U_11105,U_11106,U_11107] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11105,tc_HOL_Obool)),U_11106),U_11107))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11105,tc_HOL_Obool)),U_11106),hAPP(c_Set_OPow(U_11105),U_11107))) ),
    inference(definitional_conversion,[status(esa)],[f_2934_2]) ).

cnf(f_2934_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11105,tc_HOL_Obool)),U_11106),U_11107))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11105,tc_HOL_Obool)),U_11106),hAPP(c_Set_OPow(U_11105),U_11107))) ),
    inference(clausify,[status(thm)],[f_2934_3]) ).

fof(f_2935_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Pow__iff]) ).

fof(f_2935_2,plain,
    ! [U_11110,U_11109,U_11108] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11108,tc_HOL_Obool)),U_11109),hAPP(c_Set_OPow(U_11108),U_11110)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11108,tc_HOL_Obool)),U_11109),U_11110)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11108,tc_HOL_Obool)),U_11109),U_11110))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11108,tc_HOL_Obool)),U_11109),hAPP(c_Set_OPow(U_11108),U_11110))) ) ),
    inference(variable_rename,[status(thm)],[f_2935_1]) ).

fof(f_2935_3,plain,
    ( ! [U_11116,U_11114,U_11112] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11112,tc_HOL_Obool)),U_11114),hAPP(c_Set_OPow(U_11112),U_11116)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11112,tc_HOL_Obool)),U_11114),U_11116)) )
    & ! [U_11115,U_11113,U_11111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11111,tc_HOL_Obool)),U_11113),U_11115))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11111,tc_HOL_Obool)),U_11113),hAPP(c_Set_OPow(U_11111),U_11115))) ) ),
    inference(miniscope,[status(thm)],[f_2935_2]) ).

fof(f_2935_4,plain,
    ( ! [U_11112,U_11114,U_11116] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11112,tc_HOL_Obool)),U_11114),hAPP(c_Set_OPow(U_11112),U_11116)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11112,tc_HOL_Obool)),U_11114),U_11116)) )
    & ! [U_11113,U_11115,U_11111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11111,tc_HOL_Obool)),U_11113),U_11115))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11111,tc_HOL_Obool)),U_11113),hAPP(c_Set_OPow(U_11111),U_11115))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2935_3]) ).

cnf(f_2935_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11111,tc_HOL_Obool)),U_11113),U_11115))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11111,tc_HOL_Obool)),U_11113),hAPP(c_Set_OPow(U_11111),U_11115))) ),
    inference(clausify,[status(thm)],[f_2935_4]) ).

cnf(f_2935_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11112,tc_HOL_Obool)),U_11114),hAPP(c_Set_OPow(U_11112),U_11116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11112,tc_HOL_Obool)),U_11114),U_11116)) ),
    inference(clausify,[status(thm)],[f_2935_4]) ).

fof(f_2936_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_UN__Pow__subset]) ).

fof(f_2936_2,plain,
    ! [U_11120,U_11119,U_11118,U_11117] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11118,tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool)),U_11119),hAPP(hAPP(c_COMBB(tc_fun(U_11117,tc_HOL_Obool),tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool),U_11118),c_Set_OPow(U_11117)),U_11120))),hAPP(c_Set_OPow(U_11117),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11118,tc_fun(U_11117,tc_HOL_Obool)),U_11119),U_11120)))),
    inference(variable_rename,[status(thm)],[f_2936_1]) ).

fof(f_2936_3,plain,
    ! [U_11117,U_11118,U_11119,U_11120] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11118,tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool)),U_11119),hAPP(hAPP(c_COMBB(tc_fun(U_11117,tc_HOL_Obool),tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool),U_11118),c_Set_OPow(U_11117)),U_11120))),hAPP(c_Set_OPow(U_11117),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11118,tc_fun(U_11117,tc_HOL_Obool)),U_11119),U_11120)))),
    inference(definitional_conversion,[status(esa)],[f_2936_2]) ).

cnf(f_2936_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11118,tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool)),U_11119),hAPP(hAPP(c_COMBB(tc_fun(U_11117,tc_HOL_Obool),tc_fun(tc_fun(U_11117,tc_HOL_Obool),tc_HOL_Obool),U_11118),c_Set_OPow(U_11117)),U_11120))),hAPP(c_Set_OPow(U_11117),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11118,tc_fun(U_11117,tc_HOL_Obool)),U_11119),U_11120)))),
    inference(clausify,[status(thm)],[f_2936_3]) ).

fof(f_2937_1,plain,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Pow__empty]) ).

fof(f_2937_2,plain,
    ! [U_11121] : hAPP(c_Set_OPow(U_11121),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11121,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11121,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2937_1]) ).

fof(f_2937_3,plain,
    ! [U_11121] : hAPP(c_Set_OPow(U_11121),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11121,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11121,tc_HOL_Obool),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2937_2]) ).

cnf(f_2937_4,plain,
    hAPP(c_Set_OPow(U_11121),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11121,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11121,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2937_3]) ).

fof(f_2938_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq]) ).

fof(f_2938_2,plain,
    ! [U_11124,U_11123,U_11122] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_11122,hAPP(hAPP(c_COMBC(U_11122,tc_fun(U_11122,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11122)),U_11123)),U_11124))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11122,tc_HOL_Obool)),U_11124),hAPP(c_Set_OPow(U_11122),U_11123))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11122,tc_HOL_Obool)),U_11124),hAPP(c_Set_OPow(U_11122),U_11123)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11122,hAPP(hAPP(c_COMBC(U_11122,tc_fun(U_11122,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11122)),U_11123)),U_11124)) ) ),
    inference(variable_rename,[status(thm)],[f_2938_1]) ).

fof(f_2938_3,plain,
    ( ! [U_11130,U_11128,U_11126] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_11126,hAPP(hAPP(c_COMBC(U_11126,tc_fun(U_11126,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11126)),U_11128)),U_11130))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11126,tc_HOL_Obool)),U_11130),hAPP(c_Set_OPow(U_11126),U_11128))) )
    & ! [U_11129,U_11127,U_11125] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11125,tc_HOL_Obool)),U_11129),hAPP(c_Set_OPow(U_11125),U_11127)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11125,hAPP(hAPP(c_COMBC(U_11125,tc_fun(U_11125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11125)),U_11127)),U_11129)) ) ),
    inference(miniscope,[status(thm)],[f_2938_2]) ).

fof(f_2938_4,plain,
    ( ! [U_11128,U_11126,U_11130] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_11126,hAPP(hAPP(c_COMBC(U_11126,tc_fun(U_11126,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11126)),U_11128)),U_11130))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11126,tc_HOL_Obool)),U_11130),hAPP(c_Set_OPow(U_11126),U_11128))) )
    & ! [U_11127,U_11129,U_11125] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11125,tc_HOL_Obool)),U_11129),hAPP(c_Set_OPow(U_11125),U_11127)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11125,hAPP(hAPP(c_COMBC(U_11125,tc_fun(U_11125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11125)),U_11127)),U_11129)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2938_3]) ).

cnf(f_2938_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11125,tc_HOL_Obool)),U_11129),hAPP(c_Set_OPow(U_11125),U_11127)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11125,hAPP(hAPP(c_COMBC(U_11125,tc_fun(U_11125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11125)),U_11127)),U_11129)) ),
    inference(clausify,[status(thm)],[f_2938_4]) ).

cnf(f_2938_6,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_11126,hAPP(hAPP(c_COMBC(U_11126,tc_fun(U_11126,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11126)),U_11128)),U_11130))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11126,tc_HOL_Obool)),U_11130),hAPP(c_Set_OPow(U_11126),U_11128))) ),
    inference(clausify,[status(thm)],[f_2938_4]) ).

fof(f_2939_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint]) ).

fof(f_2939_2,plain,
    ! [U_11133,U_11132,U_11131] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11131,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11131),U_11132),U_11133)) = hAPP(c_Finite__Set_Ocard(U_11131),U_11132)
      | ~ c_Fun_Oinj__on(U_11131,tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11131,tc_fun(tc_prod(U_11131,U_11131),tc_HOL_Obool),tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11131,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11131,U_11131),tc_HOL_Obool),tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool)),U_11131),c_Equiv__Relations_Oquotient(U_11131)),hAPP(hAPP(c_COMBC(U_11131,tc_fun(U_11131,tc_HOL_Obool),tc_fun(U_11131,tc_HOL_Obool)),c_Set_Oinsert(U_11131)),c_Orderings_Obot__class_Obot(tc_fun(U_11131,tc_HOL_Obool))))),U_11133),U_11132)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11131),U_11132)) ),
    inference(variable_rename,[status(thm)],[f_2939_1]) ).

fof(f_2939_3,plain,
    ! [U_11131,U_11132,U_11133] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11131,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11131),U_11132),U_11133)) = hAPP(c_Finite__Set_Ocard(U_11131),U_11132)
      | ~ c_Fun_Oinj__on(U_11131,tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11131,tc_fun(tc_prod(U_11131,U_11131),tc_HOL_Obool),tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11131,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11131,U_11131),tc_HOL_Obool),tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool)),U_11131),c_Equiv__Relations_Oquotient(U_11131)),hAPP(hAPP(c_COMBC(U_11131,tc_fun(U_11131,tc_HOL_Obool),tc_fun(U_11131,tc_HOL_Obool)),c_Set_Oinsert(U_11131)),c_Orderings_Obot__class_Obot(tc_fun(U_11131,tc_HOL_Obool))))),U_11133),U_11132)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11131),U_11132)) ),
    inference(definitional_conversion,[status(esa)],[f_2939_2]) ).

cnf(f_2939_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11131,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11131),U_11132),U_11133)) = hAPP(c_Finite__Set_Ocard(U_11131),U_11132)
    | ~ c_Fun_Oinj__on(U_11131,tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11131,tc_fun(tc_prod(U_11131,U_11131),tc_HOL_Obool),tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11131,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11131,U_11131),tc_HOL_Obool),tc_fun(tc_fun(U_11131,tc_HOL_Obool),tc_HOL_Obool)),U_11131),c_Equiv__Relations_Oquotient(U_11131)),hAPP(hAPP(c_COMBC(U_11131,tc_fun(U_11131,tc_HOL_Obool),tc_fun(U_11131,tc_HOL_Obool)),c_Set_Oinsert(U_11131)),c_Orderings_Obot__class_Obot(tc_fun(U_11131,tc_HOL_Obool))))),U_11133),U_11132)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11131),U_11132)) ),
    inference(clausify,[status(thm)],[f_2939_3]) ).

fof(f_2940_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J]) ).

fof(f_2940_2,plain,
    ! [U_11137,U_11136,U_11135,U_11134] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11134,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11134,U_11135,U_11136)),c_SetInterval_Oord__class_OatLeastAtMost(U_11134,U_11136,U_11137)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11134,U_11135,U_11137)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11134),U_11136),U_11137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11134),U_11135),U_11136))
      | ~ class_Orderings_Olinorder(U_11134) ),
    inference(variable_rename,[status(thm)],[f_2940_1]) ).

fof(f_2940_3,plain,
    ! [U_11135,U_11134,U_11136,U_11137] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11134,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11134,U_11135,U_11136)),c_SetInterval_Oord__class_OatLeastAtMost(U_11134,U_11136,U_11137)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11134,U_11135,U_11137)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11134),U_11136),U_11137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11134),U_11135),U_11136))
      | ~ class_Orderings_Olinorder(U_11134) ),
    inference(definitional_conversion,[status(esa)],[f_2940_2]) ).

cnf(f_2940_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11134,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11134,U_11135,U_11136)),c_SetInterval_Oord__class_OatLeastAtMost(U_11134,U_11136,U_11137)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11134,U_11135,U_11137)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11134),U_11136),U_11137))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11134),U_11135),U_11136))
    | ~ class_Orderings_Olinorder(U_11134) ),
    inference(clausify,[status(thm)],[f_2940_3]) ).

fof(f_2941_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastAtMost]) ).

fof(f_2941_2,plain,
    ! [U_11139,U_11138] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11138,U_11139))),
    inference(variable_rename,[status(thm)],[f_2941_1]) ).

fof(f_2941_3,plain,
    ! [U_11138,U_11139] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11138,U_11139))),
    inference(definitional_conversion,[status(esa)],[f_2941_2]) ).

cnf(f_2941_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11138,U_11139))),
    inference(clausify,[status(thm)],[f_2941_3]) ).

fof(f_2942_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastAtMost__int]) ).

fof(f_2942_2,plain,
    ! [U_11141,U_11140] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11140,U_11141))),
    inference(variable_rename,[status(thm)],[f_2942_1]) ).

fof(f_2942_3,plain,
    ! [U_11140,U_11141] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11140,U_11141))),
    inference(definitional_conversion,[status(esa)],[f_2942_2]) ).

cnf(f_2942_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11140,U_11141))),
    inference(clausify,[status(thm)],[f_2942_3]) ).

fof(f_2943_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).

fof(f_2943_2,plain,
    ! [U_11143,U_11142] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11142,U_11143)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11142),hAPP(c_Nat_OSuc,U_11143)),
    inference(variable_rename,[status(thm)],[f_2943_1]) ).

fof(f_2943_3,plain,
    ! [U_11142,U_11143] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11142,U_11143)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11142),hAPP(c_Nat_OSuc,U_11143)),
    inference(definitional_conversion,[status(esa)],[f_2943_2]) ).

cnf(f_2943_4,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11142,U_11143)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11142),hAPP(c_Nat_OSuc,U_11143)),
    inference(clausify,[status(thm)],[f_2943_3]) ).

fof(f_2944_1,plain,
    ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).

fof(f_2944_2,plain,
    ! [U_11145,U_11144] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11144,U_11145) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11144),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11145))),
    inference(variable_rename,[status(thm)],[f_2944_1]) ).

fof(f_2944_3,plain,
    ! [U_11144,U_11145] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11144,U_11145) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11144),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11145))),
    inference(definitional_conversion,[status(esa)],[f_2944_2]) ).

cnf(f_2944_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11144,U_11145) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11144),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11145))),
    inference(clausify,[status(thm)],[f_2944_3]) ).

fof(f_2945_1,plain,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_image__add__atLeastAtMost]) ).

fof(f_2945_2,plain,
    ! [U_11148,U_11147,U_11146] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11146)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11147,U_11148)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11147),U_11146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11148),U_11146)),
    inference(variable_rename,[status(thm)],[f_2945_1]) ).

fof(f_2945_3,plain,
    ! [U_11146,U_11147,U_11148] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11146)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11147,U_11148)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11147),U_11146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11148),U_11146)),
    inference(definitional_conversion,[status(esa)],[f_2945_2]) ).

cnf(f_2945_4,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11146)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11147,U_11148)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11147),U_11146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11148),U_11146)),
    inference(clausify,[status(thm)],[f_2945_3]) ).

fof(f_2946_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__imageD]) ).

fof(f_2946_2,plain,
    ! [U_11152,U_11151,U_11150,U_11149] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11150),U_11152))
      | ~ c_Fun_Oinj__on(U_11150,U_11149,U_11151,U_11152)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11149),hAPP(c_Set_Oimage(U_11150,U_11149,U_11151),U_11152))) ),
    inference(variable_rename,[status(thm)],[f_2946_1]) ).

fof(f_2946_3,plain,
    ! [U_11149,U_11150,U_11151,U_11152] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11150),U_11152))
      | ~ c_Fun_Oinj__on(U_11150,U_11149,U_11151,U_11152)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11149),hAPP(c_Set_Oimage(U_11150,U_11149,U_11151),U_11152))) ),
    inference(definitional_conversion,[status(esa)],[f_2946_2]) ).

cnf(f_2946_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11150),U_11152))
    | ~ c_Fun_Oinj__on(U_11150,U_11149,U_11151,U_11152)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11149),hAPP(c_Set_Oimage(U_11150,U_11149,U_11151),U_11152))) ),
    inference(clausify,[status(thm)],[f_2946_3]) ).

fof(f_2947_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__image]) ).

fof(f_2947_2,plain,
    ! [U_11156,U_11155,U_11154,U_11153] :
      ( hAPP(c_Finite__Set_Ocard(U_11154),hAPP(c_Set_Oimage(U_11153,U_11154,U_11155),U_11156)) = hAPP(c_Finite__Set_Ocard(U_11153),U_11156)
      | ~ c_Fun_Oinj__on(U_11153,U_11154,U_11155,U_11156) ),
    inference(variable_rename,[status(thm)],[f_2947_1]) ).

fof(f_2947_3,plain,
    ! [U_11153,U_11154,U_11155,U_11156] :
      ( hAPP(c_Finite__Set_Ocard(U_11154),hAPP(c_Set_Oimage(U_11153,U_11154,U_11155),U_11156)) = hAPP(c_Finite__Set_Ocard(U_11153),U_11156)
      | ~ c_Fun_Oinj__on(U_11153,U_11154,U_11155,U_11156) ),
    inference(definitional_conversion,[status(esa)],[f_2947_2]) ).

cnf(f_2947_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11154),hAPP(c_Set_Oimage(U_11153,U_11154,U_11155),U_11156)) = hAPP(c_Finite__Set_Ocard(U_11153),U_11156)
    | ~ c_Fun_Oinj__on(U_11153,U_11154,U_11155,U_11156) ),
    inference(clausify,[status(thm)],[f_2947_3]) ).

fof(f_2948_1,plain,
    ! [V_n_2,V_m_2] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2)))
      | ~ c_Nat__Transfer_Ois__nat(V_n_2)
      | ~ c_Nat__Transfer_Ois__nat(V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions]) ).

fof(f_2948_2,plain,
    ! [U_11158,U_11157] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11157,U_11158) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,U_11157),hAPP(c_Int_Onat,U_11158)))
      | ~ c_Nat__Transfer_Ois__nat(U_11158)
      | ~ c_Nat__Transfer_Ois__nat(U_11157) ),
    inference(variable_rename,[status(thm)],[f_2948_1]) ).

fof(f_2948_3,plain,
    ! [U_11157,U_11158] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11157,U_11158) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,U_11157),hAPP(c_Int_Onat,U_11158)))
      | ~ c_Nat__Transfer_Ois__nat(U_11158)
      | ~ c_Nat__Transfer_Ois__nat(U_11157) ),
    inference(definitional_conversion,[status(esa)],[f_2948_2]) ).

cnf(f_2948_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11157,U_11158) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,U_11157),hAPP(c_Int_Onat,U_11158)))
    | ~ c_Nat__Transfer_Ois__nat(U_11158)
    | ~ c_Nat__Transfer_Ois__nat(U_11157) ),
    inference(clausify,[status(thm)],[f_2948_3]) ).

fof(f_2949_1,plain,
    ! [V_y_2,V_x_2] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2))
      | ~ c_Nat__Transfer_Ois__nat(V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures]) ).

fof(f_2949_2,plain,
    ! [U_11160,U_11159] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11159,U_11160))
      | ~ c_Nat__Transfer_Ois__nat(U_11159) ),
    inference(variable_rename,[status(thm)],[f_2949_1]) ).

fof(f_2949_3,plain,
    ! [U_11160,U_11159] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11159,U_11160))
      | ~ c_Nat__Transfer_Ois__nat(U_11159) ),
    inference(definitional_conversion,[status(esa)],[f_2949_2]) ).

cnf(f_2949_4,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11159,U_11160))
    | ~ c_Nat__Transfer_Ois__nat(U_11159) ),
    inference(clausify,[status(thm)],[f_2949_3]) ).

fof(f_2950_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(f_2950_2,plain,
    ! [U_11163,U_11162,U_11161] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11161,U_11162,U_11163)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
          | c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11161,U_11162,U_11163) ) )
      | ~ class_Orderings_Oorder(U_11161) ),
    inference(variable_rename,[status(thm)],[f_2950_1]) ).

fof(f_2950_3,plain,
    ( ! [U_11161,U_11162,U_11163] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11161,U_11162,U_11163)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
        | ~ sP836(U_11161,U_11162,U_11163) )
    & ! [U_11161,U_11162,U_11163] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
        | c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11161,U_11162,U_11163)
        | ~ sP836(U_11161,U_11162,U_11163) )
    & ! [U_11161,U_11162,U_11163] :
        ( sP836(U_11161,U_11162,U_11163)
        | ~ class_Orderings_Oorder(U_11161) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP836])],[f_2950_2]) ).

cnf(f_2950_4,plain,
    ( sP836(U_11161,U_11162,U_11163)
    | ~ class_Orderings_Oorder(U_11161) ),
    inference(clausify,[status(thm)],[f_2950_3]) ).

cnf(f_2950_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
    | c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11161,U_11162,U_11163)
    | ~ sP836(U_11161,U_11162,U_11163) ),
    inference(clausify,[status(thm)],[f_2950_3]) ).

cnf(f_2950_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11161,U_11162,U_11163)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
    | ~ sP836(U_11161,U_11162,U_11163) ),
    inference(clausify,[status(thm)],[f_2950_3]) ).

fof(f_2951_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(f_2951_2,plain,
    ! [U_11166,U_11165,U_11164] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_11164,U_11165,U_11166) = c_Orderings_Obot__class_Obot(tc_fun(U_11164,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11164),U_11165),U_11166)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11164),U_11165),U_11166))
          | c_SetInterval_Oord__class_OatLeastAtMost(U_11164,U_11165,U_11166) != c_Orderings_Obot__class_Obot(tc_fun(U_11164,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_11164) ),
    inference(variable_rename,[status(thm)],[f_2951_1]) ).

fof(f_2951_3,plain,
    ( ! [U_11164,U_11165,U_11166] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(U_11164,U_11165,U_11166) = c_Orderings_Obot__class_Obot(tc_fun(U_11164,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11164),U_11165),U_11166))
        | ~ sP837(U_11164,U_11165,U_11166) )
    & ! [U_11164,U_11165,U_11166] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11164),U_11165),U_11166))
        | c_SetInterval_Oord__class_OatLeastAtMost(U_11164,U_11165,U_11166) != c_Orderings_Obot__class_Obot(tc_fun(U_11164,tc_HOL_Obool))
        | ~ sP837(U_11164,U_11165,U_11166) )
    & ! [U_11164,U_11165,U_11166] :
        ( sP837(U_11164,U_11165,U_11166)
        | ~ class_Orderings_Oorder(U_11164) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP837])],[f_2951_2]) ).

cnf(f_2951_4,plain,
    ( sP837(U_11164,U_11165,U_11166)
    | ~ class_Orderings_Oorder(U_11164) ),
    inference(clausify,[status(thm)],[f_2951_3]) ).

cnf(f_2951_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11164),U_11165),U_11166))
    | c_SetInterval_Oord__class_OatLeastAtMost(U_11164,U_11165,U_11166) != c_Orderings_Obot__class_Obot(tc_fun(U_11164,tc_HOL_Obool))
    | ~ sP837(U_11164,U_11165,U_11166) ),
    inference(clausify,[status(thm)],[f_2951_3]) ).

cnf(f_2951_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11164,U_11165,U_11166) = c_Orderings_Obot__class_Obot(tc_fun(U_11164,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11164),U_11165),U_11166))
    | ~ sP837(U_11164,U_11165,U_11166) ),
    inference(clausify,[status(thm)],[f_2951_3]) ).

fof(f_2952_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty]) ).

fof(f_2952_2,plain,
    ! [U_11169,U_11168,U_11167] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11167,U_11169,U_11168) = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11167),U_11168),U_11169))
      | ~ class_Orderings_Oorder(U_11167) ),
    inference(variable_rename,[status(thm)],[f_2952_1]) ).

fof(f_2952_3,plain,
    ! [U_11169,U_11168,U_11167] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11167,U_11169,U_11168) = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11167),U_11168),U_11169))
      | ~ class_Orderings_Oorder(U_11167) ),
    inference(definitional_conversion,[status(esa)],[f_2952_2]) ).

cnf(f_2952_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11167,U_11169,U_11168) = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11167),U_11168),U_11169))
    | ~ class_Orderings_Oorder(U_11167) ),
    inference(clausify,[status(thm)],[f_2952_3]) ).

fof(f_2953_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(f_2953_2,plain,
    ! [U_11174,U_11173,U_11172,U_11171,U_11170] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11171,U_11172)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11173,U_11174)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11172),U_11174))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11173),U_11171)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11171),U_11172)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11172),U_11174))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11173),U_11171)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11171),U_11172))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11171,U_11172)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11173,U_11174))) ) )
      | ~ class_Orderings_Oorder(U_11170) ),
    inference(variable_rename,[status(thm)],[f_2953_1]) ).

fof(f_2953_3,plain,
    ( ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11172),U_11174))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11173),U_11171))
        | ~ sP839(U_11170,U_11171,U_11172,U_11173,U_11174) )
    & ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11171),U_11172))
        | ~ sP839(U_11170,U_11171,U_11172,U_11173,U_11174) )
    & ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11172),U_11174))
        | ~ sP838(U_11170,U_11171,U_11172,U_11173,U_11174) )
    & ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11173),U_11171))
        | ~ sP838(U_11170,U_11171,U_11172,U_11173,U_11174) )
    & ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11171,U_11172)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11173,U_11174)))
        | sP839(U_11170,U_11171,U_11172,U_11173,U_11174)
        | ~ sP840(U_11170,U_11171,U_11172,U_11173,U_11174) )
    & ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( sP838(U_11170,U_11171,U_11172,U_11173,U_11174)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11171),U_11172))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11171,U_11172)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11173,U_11174)))
        | ~ sP840(U_11170,U_11171,U_11172,U_11173,U_11174) )
    & ! [U_11170,U_11171,U_11172,U_11173,U_11174] :
        ( sP840(U_11170,U_11171,U_11172,U_11173,U_11174)
        | ~ class_Orderings_Oorder(U_11170) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP838,sP839,sP840])],[f_2953_2]) ).

cnf(f_2953_4,plain,
    ( sP840(U_11170,U_11171,U_11172,U_11173,U_11174)
    | ~ class_Orderings_Oorder(U_11170) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

cnf(f_2953_5,plain,
    ( sP838(U_11170,U_11171,U_11172,U_11173,U_11174)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11171),U_11172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11171,U_11172)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11173,U_11174)))
    | ~ sP840(U_11170,U_11171,U_11172,U_11173,U_11174) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

cnf(f_2953_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11171,U_11172)),c_SetInterval_Oord__class_OatLeastAtMost(U_11170,U_11173,U_11174)))
    | sP839(U_11170,U_11171,U_11172,U_11173,U_11174)
    | ~ sP840(U_11170,U_11171,U_11172,U_11173,U_11174) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

cnf(f_2953_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11173),U_11171))
    | ~ sP838(U_11170,U_11171,U_11172,U_11173,U_11174) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

cnf(f_2953_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11172),U_11174))
    | ~ sP838(U_11170,U_11171,U_11172,U_11173,U_11174) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

cnf(f_2953_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11171),U_11172))
    | ~ sP839(U_11170,U_11171,U_11172,U_11173,U_11174) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

cnf(f_2953_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11172),U_11174))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11170),U_11173),U_11171))
    | ~ sP839(U_11170,U_11171,U_11172,U_11173,U_11174) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

fof(f_2954_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | V_a_2 != V_b_2
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H]) ).

fof(f_2954_2,plain,
    ! [U_11177,U_11176,U_11175] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11175,U_11176,U_11177) = hAPP(hAPP(c_Set_Oinsert(U_11175),U_11176),c_Orderings_Obot__class_Obot(tc_fun(U_11175,tc_HOL_Obool)))
      | U_11176 != U_11177
      | ~ class_Orderings_Oorder(U_11175) ),
    inference(variable_rename,[status(thm)],[f_2954_1]) ).

fof(f_2954_3,plain,
    ! [U_11177,U_11175,U_11176] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11175,U_11176,U_11177) = hAPP(hAPP(c_Set_Oinsert(U_11175),U_11176),c_Orderings_Obot__class_Obot(tc_fun(U_11175,tc_HOL_Obool)))
      | U_11176 != U_11177
      | ~ class_Orderings_Oorder(U_11175) ),
    inference(definitional_conversion,[status(esa)],[f_2954_2]) ).

cnf(f_2954_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11175,U_11176,U_11177) = hAPP(hAPP(c_Set_Oinsert(U_11175),U_11176),c_Orderings_Obot__class_Obot(tc_fun(U_11175,tc_HOL_Obool)))
    | U_11176 != U_11177
    | ~ class_Orderings_Oorder(U_11175) ),
    inference(clausify,[status(thm)],[f_2954_3]) ).

fof(f_2955_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
          | V_b_2 != V_c_2
          | V_a_2 != V_b_2 )
        & ( ( V_b_2 = V_c_2
            & V_a_2 = V_b_2 )
          | c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).

fof(f_2955_2,plain,
    ! [U_11181,U_11180,U_11179,U_11178] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_11178,U_11179,U_11180) = hAPP(hAPP(c_Set_Oinsert(U_11178),U_11181),c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool)))
          | U_11180 != U_11181
          | U_11179 != U_11180 )
        & ( ( U_11180 = U_11181
            & U_11179 = U_11180 )
          | c_SetInterval_Oord__class_OatLeastAtMost(U_11178,U_11179,U_11180) != hAPP(hAPP(c_Set_Oinsert(U_11178),U_11181),c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(U_11178) ),
    inference(variable_rename,[status(thm)],[f_2955_1]) ).

fof(f_2955_3,plain,
    ( ! [U_11181,U_11179,U_11180] :
        ( U_11180 = U_11181
        | ~ sP841(U_11181,U_11179,U_11180) )
    & ! [U_11181,U_11179,U_11180] :
        ( U_11179 = U_11180
        | ~ sP841(U_11181,U_11179,U_11180) )
    & ! [U_11178,U_11181,U_11179,U_11180] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(U_11178,U_11179,U_11180) = hAPP(hAPP(c_Set_Oinsert(U_11178),U_11181),c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool)))
        | U_11180 != U_11181
        | U_11179 != U_11180
        | ~ sP842(U_11178,U_11181,U_11179,U_11180) )
    & ! [U_11178,U_11181,U_11179,U_11180] :
        ( sP841(U_11181,U_11179,U_11180)
        | c_SetInterval_Oord__class_OatLeastAtMost(U_11178,U_11179,U_11180) != hAPP(hAPP(c_Set_Oinsert(U_11178),U_11181),c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool)))
        | ~ sP842(U_11178,U_11181,U_11179,U_11180) )
    & ! [U_11178,U_11181,U_11179,U_11180] :
        ( sP842(U_11178,U_11181,U_11179,U_11180)
        | ~ class_Orderings_Oorder(U_11178) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP841,sP842])],[f_2955_2]) ).

cnf(f_2955_4,plain,
    ( sP842(U_11178,U_11181,U_11179,U_11180)
    | ~ class_Orderings_Oorder(U_11178) ),
    inference(clausify,[status(thm)],[f_2955_3]) ).

cnf(f_2955_5,plain,
    ( sP841(U_11181,U_11179,U_11180)
    | c_SetInterval_Oord__class_OatLeastAtMost(U_11178,U_11179,U_11180) != hAPP(hAPP(c_Set_Oinsert(U_11178),U_11181),c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool)))
    | ~ sP842(U_11178,U_11181,U_11179,U_11180) ),
    inference(clausify,[status(thm)],[f_2955_3]) ).

cnf(f_2955_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11178,U_11179,U_11180) = hAPP(hAPP(c_Set_Oinsert(U_11178),U_11181),c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool)))
    | U_11180 != U_11181
    | U_11179 != U_11180
    | ~ sP842(U_11178,U_11181,U_11179,U_11180) ),
    inference(clausify,[status(thm)],[f_2955_3]) ).

cnf(f_2955_7,plain,
    ( U_11179 = U_11180
    | ~ sP841(U_11181,U_11179,U_11180) ),
    inference(clausify,[status(thm)],[f_2955_3]) ).

cnf(f_2955_8,plain,
    ( U_11180 = U_11181
    | ~ sP841(U_11181,U_11179,U_11180) ),
    inference(clausify,[status(thm)],[f_2955_3]) ).

fof(f_2956_1,plain,
    ! [V_a_2,T_b] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton]) ).

fof(f_2956_2,plain,
    ! [U_11183,U_11182] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11182,U_11183,U_11183) = hAPP(hAPP(c_Set_Oinsert(U_11182),U_11183),c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11182) ),
    inference(variable_rename,[status(thm)],[f_2956_1]) ).

fof(f_2956_3,plain,
    ! [U_11182,U_11183] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11182,U_11183,U_11183) = hAPP(hAPP(c_Set_Oinsert(U_11182),U_11183),c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11182) ),
    inference(definitional_conversion,[status(esa)],[f_2956_2]) ).

cnf(f_2956_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11182,U_11183,U_11183) = hAPP(hAPP(c_Set_Oinsert(U_11182),U_11183),c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_11182) ),
    inference(clausify,[status(thm)],[f_2956_3]) ).

fof(f_2957_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost]) ).

fof(f_2957_2,plain,
    ! [U_11186,U_11185,U_11184] :
      ( hAPP(c_Set_Oimage(U_11184,U_11184,c_Groups_Ouminus__class_Ouminus(U_11184)),c_SetInterval_Oord__class_OatLeastAtMost(U_11184,U_11185,U_11186)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11184,hAPP(c_Groups_Ouminus__class_Ouminus(U_11184),U_11186),hAPP(c_Groups_Ouminus__class_Ouminus(U_11184),U_11185))
      | ~ class_Groups_Oordered__ab__group__add(U_11184) ),
    inference(variable_rename,[status(thm)],[f_2957_1]) ).

fof(f_2957_3,plain,
    ! [U_11184,U_11186,U_11185] :
      ( hAPP(c_Set_Oimage(U_11184,U_11184,c_Groups_Ouminus__class_Ouminus(U_11184)),c_SetInterval_Oord__class_OatLeastAtMost(U_11184,U_11185,U_11186)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11184,hAPP(c_Groups_Ouminus__class_Ouminus(U_11184),U_11186),hAPP(c_Groups_Ouminus__class_Ouminus(U_11184),U_11185))
      | ~ class_Groups_Oordered__ab__group__add(U_11184) ),
    inference(definitional_conversion,[status(esa)],[f_2957_2]) ).

cnf(f_2957_4,plain,
    ( hAPP(c_Set_Oimage(U_11184,U_11184,c_Groups_Ouminus__class_Ouminus(U_11184)),c_SetInterval_Oord__class_OatLeastAtMost(U_11184,U_11185,U_11186)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11184,hAPP(c_Groups_Ouminus__class_Ouminus(U_11184),U_11186),hAPP(c_Groups_Ouminus__class_Ouminus(U_11184),U_11185))
    | ~ class_Groups_Oordered__ab__group__add(U_11184) ),
    inference(clausify,[status(thm)],[f_2957_3]) ).

fof(f_2958_1,plain,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).

fof(f_2958_2,plain,
    ! [U_11188,U_11187] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11187),U_11188) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11187,U_11188),
    inference(variable_rename,[status(thm)],[f_2958_1]) ).

fof(f_2958_3,plain,
    ! [U_11188,U_11187] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11187),U_11188) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11187,U_11188),
    inference(definitional_conversion,[status(esa)],[f_2958_2]) ).

cnf(f_2958_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11187),U_11188) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11187,U_11188),
    inference(clausify,[status(thm)],[f_2958_3]) ).

fof(f_2959_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__surj__inj]) ).

fof(f_2959_2,plain,
    ! [U_11191,U_11190,U_11189] :
      ( c_Fun_Oinj__on(U_11189,U_11189,U_11191,U_11190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11189,tc_HOL_Obool)),U_11190),hAPP(c_Set_Oimage(U_11189,U_11189,U_11191),U_11190)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11189),U_11190)) ),
    inference(variable_rename,[status(thm)],[f_2959_1]) ).

fof(f_2959_3,plain,
    ! [U_11189,U_11190,U_11191] :
      ( c_Fun_Oinj__on(U_11189,U_11189,U_11191,U_11190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11189,tc_HOL_Obool)),U_11190),hAPP(c_Set_Oimage(U_11189,U_11189,U_11191),U_11190)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11189),U_11190)) ),
    inference(definitional_conversion,[status(esa)],[f_2959_2]) ).

cnf(f_2959_4,plain,
    ( c_Fun_Oinj__on(U_11189,U_11189,U_11191,U_11190)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11189,tc_HOL_Obool)),U_11190),hAPP(c_Set_Oimage(U_11189,U_11189,U_11191),U_11190)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11189),U_11190)) ),
    inference(clausify,[status(thm)],[f_2959_3]) ).

fof(f_2960_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_endo__inj__surj]) ).

fof(f_2960_2,plain,
    ! [U_11194,U_11193,U_11192] :
      ( hAPP(c_Set_Oimage(U_11192,U_11192,U_11194),U_11193) = U_11193
      | ~ c_Fun_Oinj__on(U_11192,U_11192,U_11194,U_11193)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11192,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11192,U_11192,U_11194),U_11193)),U_11193))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11193)) ),
    inference(variable_rename,[status(thm)],[f_2960_1]) ).

fof(f_2960_3,plain,
    ! [U_11192,U_11193,U_11194] :
      ( hAPP(c_Set_Oimage(U_11192,U_11192,U_11194),U_11193) = U_11193
      | ~ c_Fun_Oinj__on(U_11192,U_11192,U_11194,U_11193)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11192,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11192,U_11192,U_11194),U_11193)),U_11193))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11193)) ),
    inference(definitional_conversion,[status(esa)],[f_2960_2]) ).

cnf(f_2960_4,plain,
    ( hAPP(c_Set_Oimage(U_11192,U_11192,U_11194),U_11193) = U_11193
    | ~ c_Fun_Oinj__on(U_11192,U_11192,U_11194,U_11193)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11192,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11192,U_11192,U_11194),U_11193)),U_11193))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11193)) ),
    inference(clausify,[status(thm)],[f_2960_3]) ).

fof(f_2961_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on]) ).

fof(f_2961_2,plain,
    ! [U_11198,U_11197,U_11196,U_11195] :
      ( c_Fun_Oinj__on(U_11195,U_11197,U_11198,U_11196)
      | hAPP(c_Finite__Set_Ocard(U_11197),hAPP(c_Set_Oimage(U_11195,U_11197,U_11198),U_11196)) != hAPP(c_Finite__Set_Ocard(U_11195),U_11196)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11195),U_11196)) ),
    inference(variable_rename,[status(thm)],[f_2961_1]) ).

fof(f_2961_3,plain,
    ! [U_11195,U_11196,U_11197,U_11198] :
      ( c_Fun_Oinj__on(U_11195,U_11197,U_11198,U_11196)
      | hAPP(c_Finite__Set_Ocard(U_11197),hAPP(c_Set_Oimage(U_11195,U_11197,U_11198),U_11196)) != hAPP(c_Finite__Set_Ocard(U_11195),U_11196)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11195),U_11196)) ),
    inference(definitional_conversion,[status(esa)],[f_2961_2]) ).

cnf(f_2961_4,plain,
    ( c_Fun_Oinj__on(U_11195,U_11197,U_11198,U_11196)
    | hAPP(c_Finite__Set_Ocard(U_11197),hAPP(c_Set_Oimage(U_11195,U_11197,U_11198),U_11196)) != hAPP(c_Finite__Set_Ocard(U_11195),U_11196)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11195),U_11196)) ),
    inference(clausify,[status(thm)],[f_2961_3]) ).

fof(f_2962_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
          | hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
        & ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
          | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card]) ).

fof(f_2962_2,plain,
    ! [U_11202,U_11201,U_11200,U_11199] :
      ( ( ( c_Fun_Oinj__on(U_11199,U_11201,U_11202,U_11200)
          | hAPP(c_Finite__Set_Ocard(U_11201),hAPP(c_Set_Oimage(U_11199,U_11201,U_11202),U_11200)) != hAPP(c_Finite__Set_Ocard(U_11199),U_11200) )
        & ( hAPP(c_Finite__Set_Ocard(U_11201),hAPP(c_Set_Oimage(U_11199,U_11201,U_11202),U_11200)) = hAPP(c_Finite__Set_Ocard(U_11199),U_11200)
          | ~ c_Fun_Oinj__on(U_11199,U_11201,U_11202,U_11200) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11199),U_11200)) ),
    inference(variable_rename,[status(thm)],[f_2962_1]) ).

fof(f_2962_3,plain,
    ( ! [U_11199,U_11200,U_11201,U_11202] :
        ( c_Fun_Oinj__on(U_11199,U_11201,U_11202,U_11200)
        | hAPP(c_Finite__Set_Ocard(U_11201),hAPP(c_Set_Oimage(U_11199,U_11201,U_11202),U_11200)) != hAPP(c_Finite__Set_Ocard(U_11199),U_11200)
        | ~ sP843(U_11199,U_11200,U_11201,U_11202) )
    & ! [U_11199,U_11200,U_11201,U_11202] :
        ( hAPP(c_Finite__Set_Ocard(U_11201),hAPP(c_Set_Oimage(U_11199,U_11201,U_11202),U_11200)) = hAPP(c_Finite__Set_Ocard(U_11199),U_11200)
        | ~ c_Fun_Oinj__on(U_11199,U_11201,U_11202,U_11200)
        | ~ sP843(U_11199,U_11200,U_11201,U_11202) )
    & ! [U_11199,U_11200,U_11201,U_11202] :
        ( sP843(U_11199,U_11200,U_11201,U_11202)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11199),U_11200)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP843])],[f_2962_2]) ).

cnf(f_2962_4,plain,
    ( sP843(U_11199,U_11200,U_11201,U_11202)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11199),U_11200)) ),
    inference(clausify,[status(thm)],[f_2962_3]) ).

cnf(f_2962_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11201),hAPP(c_Set_Oimage(U_11199,U_11201,U_11202),U_11200)) = hAPP(c_Finite__Set_Ocard(U_11199),U_11200)
    | ~ c_Fun_Oinj__on(U_11199,U_11201,U_11202,U_11200)
    | ~ sP843(U_11199,U_11200,U_11201,U_11202) ),
    inference(clausify,[status(thm)],[f_2962_3]) ).

cnf(f_2962_6,plain,
    ( c_Fun_Oinj__on(U_11199,U_11201,U_11202,U_11200)
    | hAPP(c_Finite__Set_Ocard(U_11201),hAPP(c_Set_Oimage(U_11199,U_11201,U_11202),U_11200)) != hAPP(c_Finite__Set_Ocard(U_11199),U_11200)
    | ~ sP843(U_11199,U_11200,U_11201,U_11202) ),
    inference(clausify,[status(thm)],[f_2962_3]) ).

fof(f_2963_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_pigeonhole]) ).

fof(f_2963_2,plain,
    ! [U_11206,U_11205,U_11204,U_11203] :
      ( ~ c_Fun_Oinj__on(U_11204,U_11203,U_11205,U_11206)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11203),hAPP(c_Set_Oimage(U_11204,U_11203,U_11205),U_11206))),hAPP(c_Finite__Set_Ocard(U_11204),U_11206))) ),
    inference(variable_rename,[status(thm)],[f_2963_1]) ).

fof(f_2963_3,plain,
    ! [U_11203,U_11205,U_11204,U_11206] :
      ( ~ c_Fun_Oinj__on(U_11204,U_11203,U_11205,U_11206)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11203),hAPP(c_Set_Oimage(U_11204,U_11203,U_11205),U_11206))),hAPP(c_Finite__Set_Ocard(U_11204),U_11206))) ),
    inference(definitional_conversion,[status(esa)],[f_2963_2]) ).

cnf(f_2963_4,plain,
    ( ~ c_Fun_Oinj__on(U_11204,U_11203,U_11205,U_11206)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11203),hAPP(c_Set_Oimage(U_11204,U_11203,U_11205),U_11206))),hAPP(c_Finite__Set_Ocard(U_11204),U_11206))) ),
    inference(clausify,[status(thm)],[f_2963_3]) ).

fof(f_2964_1,plain,
    ! [V_y_2,V_x_2] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures]) ).

fof(f_2964_2,plain,
    ! [U_11208,U_11207] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11207,U_11208))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11207)) ),
    inference(variable_rename,[status(thm)],[f_2964_1]) ).

fof(f_2964_3,plain,
    ! [U_11207,U_11208] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11207,U_11208))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11207)) ),
    inference(definitional_conversion,[status(esa)],[f_2964_2]) ).

cnf(f_2964_4,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11207,U_11208))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11207)) ),
    inference(clausify,[status(thm)],[f_2964_3]) ).

fof(f_2965_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastAtMost]) ).

fof(f_2965_2,plain,
    ! [U_11210,U_11209] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11209,U_11210)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11210)),U_11209),
    inference(variable_rename,[status(thm)],[f_2965_1]) ).

fof(f_2965_3,plain,
    ! [U_11209,U_11210] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11209,U_11210)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11210)),U_11209),
    inference(definitional_conversion,[status(esa)],[f_2965_2]) ).

cnf(f_2965_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11209,U_11210)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11210)),U_11209),
    inference(clausify,[status(thm)],[f_2965_3]) ).

fof(f_2966_1,plain,
    ! [V_n_2,V_m_2] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv]) ).

fof(f_2966_2,plain,
    ! [U_11212,U_11211] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11211,hAPP(c_Nat_OSuc,U_11212)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11212)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11211,U_11212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11211),hAPP(c_Nat_OSuc,U_11212))) ),
    inference(variable_rename,[status(thm)],[f_2966_1]) ).

fof(f_2966_3,plain,
    ! [U_11211,U_11212] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11211,hAPP(c_Nat_OSuc,U_11212)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11212)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11211,U_11212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11211),hAPP(c_Nat_OSuc,U_11212))) ),
    inference(definitional_conversion,[status(esa)],[f_2966_2]) ).

cnf(f_2966_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11211,hAPP(c_Nat_OSuc,U_11212)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11212)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11211,U_11212))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11211),hAPP(c_Nat_OSuc,U_11212))) ),
    inference(clausify,[status(thm)],[f_2966_3]) ).

fof(f_2967_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__mono]) ).

fof(f_2967_2,plain,
    ! [U_11215,U_11214,U_11213] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11213,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_11213,U_11214)),c_Predicate_OPowp(U_11213,U_11215)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11213,tc_HOL_Obool)),U_11214),U_11215)) ),
    inference(variable_rename,[status(thm)],[f_2967_1]) ).

fof(f_2967_3,plain,
    ! [U_11213,U_11214,U_11215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11213,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_11213,U_11214)),c_Predicate_OPowp(U_11213,U_11215)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11213,tc_HOL_Obool)),U_11214),U_11215)) ),
    inference(definitional_conversion,[status(esa)],[f_2967_2]) ).

cnf(f_2967_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11213,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_11213,U_11214)),c_Predicate_OPowp(U_11213,U_11215)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11213,tc_HOL_Obool)),U_11214),U_11215)) ),
    inference(clausify,[status(thm)],[f_2967_3]) ).

fof(f_2968_1,plain,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).

fof(f_2968_2,plain,
    ! [U_11217,U_11216] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11216),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11217) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11216,U_11217),
    inference(variable_rename,[status(thm)],[f_2968_1]) ).

fof(f_2968_3,plain,
    ! [U_11216,U_11217] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11216),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11217) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11216,U_11217),
    inference(definitional_conversion,[status(esa)],[f_2968_2]) ).

cnf(f_2968_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11216),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11217) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11216,U_11217),
    inference(clausify,[status(thm)],[f_2968_3]) ).

fof(f_2969_1,plain,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__bij__eq]) ).

fof(f_2969_2,plain,
    ! [U_11223,U_11222,U_11221,U_11220,U_11219,U_11218] :
      ( hAPP(c_Finite__Set_Ocard(U_11218),U_11221) = hAPP(c_Finite__Set_Ocard(U_11219),U_11222)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11219),U_11222))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11218),U_11221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11218,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11219,U_11218,U_11223),U_11222)),U_11221))
      | ~ c_Fun_Oinj__on(U_11219,U_11218,U_11223,U_11222)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11219,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11218,U_11219,U_11220),U_11221)),U_11222))
      | ~ c_Fun_Oinj__on(U_11218,U_11219,U_11220,U_11221) ),
    inference(variable_rename,[status(thm)],[f_2969_1]) ).

fof(f_2969_3,plain,
    ! [U_11218,U_11219,U_11220,U_11221,U_11222,U_11223] :
      ( hAPP(c_Finite__Set_Ocard(U_11218),U_11221) = hAPP(c_Finite__Set_Ocard(U_11219),U_11222)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11219),U_11222))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11218),U_11221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11218,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11219,U_11218,U_11223),U_11222)),U_11221))
      | ~ c_Fun_Oinj__on(U_11219,U_11218,U_11223,U_11222)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11219,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11218,U_11219,U_11220),U_11221)),U_11222))
      | ~ c_Fun_Oinj__on(U_11218,U_11219,U_11220,U_11221) ),
    inference(definitional_conversion,[status(esa)],[f_2969_2]) ).

cnf(f_2969_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11218),U_11221) = hAPP(c_Finite__Set_Ocard(U_11219),U_11222)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11219),U_11222))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11218),U_11221))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11218,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11219,U_11218,U_11223),U_11222)),U_11221))
    | ~ c_Fun_Oinj__on(U_11219,U_11218,U_11223,U_11222)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11219,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11218,U_11219,U_11220),U_11221)),U_11222))
    | ~ c_Fun_Oinj__on(U_11218,U_11219,U_11220,U_11221) ),
    inference(clausify,[status(thm)],[f_2969_3]) ).

fof(f_2970_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).

fof(f_2970_2,plain,
    ! [U_11228,U_11227,U_11226,U_11225,U_11224] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11224,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11224,U_11225,U_11226)),c_SetInterval_Oord__class_OatLeastAtMost(U_11224,U_11227,U_11228)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11224,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11224),U_11225),U_11227),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11224),U_11226),U_11228))
      | ~ class_Orderings_Olinorder(U_11224) ),
    inference(variable_rename,[status(thm)],[f_2970_1]) ).

fof(f_2970_3,plain,
    ! [U_11226,U_11225,U_11227,U_11224,U_11228] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11224,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11224,U_11225,U_11226)),c_SetInterval_Oord__class_OatLeastAtMost(U_11224,U_11227,U_11228)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11224,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11224),U_11225),U_11227),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11224),U_11226),U_11228))
      | ~ class_Orderings_Olinorder(U_11224) ),
    inference(definitional_conversion,[status(esa)],[f_2970_2]) ).

cnf(f_2970_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11224,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11224,U_11225,U_11226)),c_SetInterval_Oord__class_OatLeastAtMost(U_11224,U_11227,U_11228)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11224,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11224),U_11225),U_11227),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11224),U_11226),U_11228))
    | ~ class_Orderings_Olinorder(U_11224) ),
    inference(clausify,[status(thm)],[f_2970_3]) ).

fof(f_2971_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(f_2971_2,plain,
    ! [U_11233,U_11232,U_11231,U_11230,U_11229] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11230,U_11231)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11232,U_11233)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11233))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11231),U_11233))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11232),U_11230)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11231),U_11233))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11230)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11230),U_11231)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11233))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11231),U_11233))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11232),U_11230)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11231),U_11233))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11230)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11230),U_11231)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11230,U_11231)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11232,U_11233))) ) )
      | ~ class_Orderings_Oorder(U_11229) ),
    inference(variable_rename,[status(thm)],[f_2971_1]) ).

fof(f_2971_3,plain,
    ( ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11231),U_11233))
        | ~ sP846(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11232),U_11230))
        | ~ sP846(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( sP846(U_11229,U_11230,U_11231,U_11232,U_11233)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11231),U_11233))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11230))
        | ~ sP847(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11230),U_11231))
        | ~ sP847(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11231),U_11233))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11232),U_11230))
        | ~ sP844(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11231),U_11233))
        | ~ sP844(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11230))
        | ~ sP844(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11233))
        | ~ sP845(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( sP844(U_11229,U_11230,U_11231,U_11232,U_11233)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11230),U_11231))
        | ~ sP845(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11230,U_11231)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11232,U_11233)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11233))
        | sP847(U_11229,U_11230,U_11231,U_11232,U_11233)
        | ~ sP848(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( sP845(U_11229,U_11230,U_11231,U_11232,U_11233)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11230,U_11231)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11232,U_11233)))
        | ~ sP848(U_11229,U_11230,U_11231,U_11232,U_11233) )
    & ! [U_11229,U_11230,U_11231,U_11232,U_11233] :
        ( sP848(U_11229,U_11230,U_11231,U_11232,U_11233)
        | ~ class_Orderings_Oorder(U_11229) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP844,sP845,sP846,sP847,sP848])],[f_2971_2]) ).

cnf(f_2971_4,plain,
    ( sP848(U_11229,U_11230,U_11231,U_11232,U_11233)
    | ~ class_Orderings_Oorder(U_11229) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_5,plain,
    ( sP845(U_11229,U_11230,U_11231,U_11232,U_11233)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11230,U_11231)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11232,U_11233)))
    | ~ sP848(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11230,U_11231)),c_SetInterval_Oord__class_OatLeastAtMost(U_11229,U_11232,U_11233)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11233))
    | sP847(U_11229,U_11230,U_11231,U_11232,U_11233)
    | ~ sP848(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_7,plain,
    ( sP844(U_11229,U_11230,U_11231,U_11232,U_11233)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11230),U_11231))
    | ~ sP845(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11233))
    | ~ sP845(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11230))
    | ~ sP844(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11231),U_11233))
    | ~ sP844(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11231),U_11233))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11232),U_11230))
    | ~ sP844(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11230),U_11231))
    | ~ sP847(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_13,plain,
    ( sP846(U_11229,U_11230,U_11231,U_11232,U_11233)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11231),U_11233))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11229),U_11232),U_11230))
    | ~ sP847(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11232),U_11230))
    | ~ sP846(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

cnf(f_2971_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11229),U_11231),U_11233))
    | ~ sP846(U_11229,U_11230,U_11231,U_11232,U_11233) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

fof(f_2972_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J]) ).

fof(f_2972_2,plain,
    ! [U_11237,U_11236,U_11235,U_11234] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11234,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11234,U_11235,U_11236)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11234,U_11236,U_11237)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11234,U_11235,U_11237)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11234),U_11236),U_11237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11234),U_11235),U_11236))
      | ~ class_Orderings_Olinorder(U_11234) ),
    inference(variable_rename,[status(thm)],[f_2972_1]) ).

fof(f_2972_3,plain,
    ! [U_11237,U_11235,U_11236,U_11234] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11234,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11234,U_11235,U_11236)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11234,U_11236,U_11237)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11234,U_11235,U_11237)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11234),U_11236),U_11237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11234),U_11235),U_11236))
      | ~ class_Orderings_Olinorder(U_11234) ),
    inference(definitional_conversion,[status(esa)],[f_2972_2]) ).

cnf(f_2972_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11234,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11234,U_11235,U_11236)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11234,U_11236,U_11237)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11234,U_11235,U_11237)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11234),U_11236),U_11237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11234),U_11235),U_11236))
    | ~ class_Orderings_Olinorder(U_11234) ),
    inference(clausify,[status(thm)],[f_2972_3]) ).

fof(f_2973_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J]) ).

fof(f_2973_2,plain,
    ! [U_11241,U_11240,U_11239,U_11238] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11238,U_11239,U_11240)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11238,U_11240,U_11241)) = c_Orderings_Obot__class_Obot(tc_fun(U_11238,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11238) ),
    inference(variable_rename,[status(thm)],[f_2973_1]) ).

fof(f_2973_3,plain,
    ! [U_11238,U_11239,U_11240,U_11241] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11238,U_11239,U_11240)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11238,U_11240,U_11241)) = c_Orderings_Obot__class_Obot(tc_fun(U_11238,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11238) ),
    inference(definitional_conversion,[status(esa)],[f_2973_2]) ).

cnf(f_2973_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11238,U_11239,U_11240)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11238,U_11240,U_11241)) = c_Orderings_Obot__class_Obot(tc_fun(U_11238,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11238) ),
    inference(clausify,[status(thm)],[f_2973_3]) ).

fof(f_2974_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J]) ).

fof(f_2974_2,plain,
    ! [U_11245,U_11244,U_11243,U_11242] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11242,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11242,U_11243,U_11244)),c_SetInterval_Oord__class_OatLeastAtMost(U_11242,U_11244,U_11245)) = c_Orderings_Obot__class_Obot(tc_fun(U_11242,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11242) ),
    inference(variable_rename,[status(thm)],[f_2974_1]) ).

fof(f_2974_3,plain,
    ! [U_11242,U_11245,U_11243,U_11244] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11242,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11242,U_11243,U_11244)),c_SetInterval_Oord__class_OatLeastAtMost(U_11242,U_11244,U_11245)) = c_Orderings_Obot__class_Obot(tc_fun(U_11242,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11242) ),
    inference(definitional_conversion,[status(esa)],[f_2974_2]) ).

cnf(f_2974_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11242,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11242,U_11243,U_11244)),c_SetInterval_Oord__class_OatLeastAtMost(U_11242,U_11244,U_11245)) = c_Orderings_Obot__class_Obot(tc_fun(U_11242,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11242) ),
    inference(clausify,[status(thm)],[f_2974_3]) ).

fof(f_2975_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J]) ).

fof(f_2975_2,plain,
    ! [U_11249,U_11248,U_11247,U_11246] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11246,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11246,U_11247,U_11248)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11246,U_11248,U_11249)) = c_Orderings_Obot__class_Obot(tc_fun(U_11246,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11246) ),
    inference(variable_rename,[status(thm)],[f_2975_1]) ).

fof(f_2975_3,plain,
    ! [U_11246,U_11247,U_11248,U_11249] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11246,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11246,U_11247,U_11248)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11246,U_11248,U_11249)) = c_Orderings_Obot__class_Obot(tc_fun(U_11246,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11246) ),
    inference(definitional_conversion,[status(esa)],[f_2975_2]) ).

cnf(f_2975_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11246,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11246,U_11247,U_11248)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11246,U_11248,U_11249)) = c_Orderings_Obot__class_Obot(tc_fun(U_11246,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11246) ),
    inference(clausify,[status(thm)],[f_2975_3]) ).

fof(f_2976_1,plain,
    ! [V_i_2,V_j_2] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_simp__from__to]) ).

fof(f_2976_2,plain,
    ! [U_11251,U_11250] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11251,U_11250) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11251),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11251),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11250),U_11251)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11251,U_11250) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11250),U_11251)) ) ),
    inference(variable_rename,[status(thm)],[f_2976_1]) ).

fof(f_2976_3,plain,
    ( ! [U_11255,U_11253] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11255,U_11253) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11255),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11255),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11253))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11253),U_11255)) )
    & ! [U_11254,U_11252] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11254,U_11252) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11252),U_11254)) ) ),
    inference(miniscope,[status(thm)],[f_2976_2]) ).

fof(f_2976_4,plain,
    ( ! [U_11255,U_11253] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11255,U_11253) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11255),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11255),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11253))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11253),U_11255)) )
    & ! [U_11254,U_11252] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11254,U_11252) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11252),U_11254)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2976_3]) ).

cnf(f_2976_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11254,U_11252) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11252),U_11254)) ),
    inference(clausify,[status(thm)],[f_2976_4]) ).

cnf(f_2976_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11255,U_11253) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11255),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11255),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11253))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11253),U_11255)) ),
    inference(clausify,[status(thm)],[f_2976_4]) ).

fof(f_2977_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__inj__on__le]) ).

fof(f_2977_2,plain,
    ! [U_11260,U_11259,U_11258,U_11257,U_11256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11256),U_11259)),hAPP(c_Finite__Set_Ocard(U_11257),U_11260)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11257),U_11260))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11257,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11256,U_11257,U_11258),U_11259)),U_11260))
      | ~ c_Fun_Oinj__on(U_11256,U_11257,U_11258,U_11259) ),
    inference(variable_rename,[status(thm)],[f_2977_1]) ).

fof(f_2977_3,plain,
    ! [U_11256,U_11257,U_11258,U_11259,U_11260] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11256),U_11259)),hAPP(c_Finite__Set_Ocard(U_11257),U_11260)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11257),U_11260))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11257,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11256,U_11257,U_11258),U_11259)),U_11260))
      | ~ c_Fun_Oinj__on(U_11256,U_11257,U_11258,U_11259) ),
    inference(definitional_conversion,[status(esa)],[f_2977_2]) ).

cnf(f_2977_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11256),U_11259)),hAPP(c_Finite__Set_Ocard(U_11257),U_11260)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11257),U_11260))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11257,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11256,U_11257,U_11258),U_11259)),U_11260))
    | ~ c_Fun_Oinj__on(U_11256,U_11257,U_11258,U_11259) ),
    inference(clausify,[status(thm)],[f_2977_3]) ).

fof(f_2978_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
              & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
          | ! [B_f] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
              | ~ c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le]) ).

fof(f_2978_2,plain,
    ! [U_11266,U_11265,U_11264,U_11263] :
      ( ( ( ? [U_11262] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,U_11262),U_11264)),U_11266))
              & c_Fun_Oinj__on(U_11263,U_11265,U_11262,U_11264) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266)))
          | ! [U_11261] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,U_11261),U_11264)),U_11266))
              | ~ c_Fun_Oinj__on(U_11263,U_11265,U_11261,U_11264) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11265),U_11266))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264)) ),
    inference(variable_rename,[status(thm)],[f_2978_1]) ).

fof(f_2978_3,plain,
    ! [U_11266,U_11265,U_11264,U_11263] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,sK200(U_11266,U_11265,U_11264,U_11263)),U_11264)),U_11266))
            & c_Fun_Oinj__on(U_11263,U_11265,sK200(U_11266,U_11265,U_11264,U_11263),U_11264) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266)))
          | ! [U_11261] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,U_11261),U_11264)),U_11266))
              | ~ c_Fun_Oinj__on(U_11263,U_11265,U_11261,U_11264) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11265),U_11266))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_11262,sK200(U_11266,U_11265,U_11264,U_11263))],[f_2978_2]) ).

fof(f_2978_4,plain,
    ( ! [U_11263,U_11264,U_11265,U_11266] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,sK200(U_11266,U_11265,U_11264,U_11263)),U_11264)),U_11266))
        | ~ sP849(U_11263,U_11264,U_11265,U_11266) )
    & ! [U_11263,U_11264,U_11265,U_11266] :
        ( c_Fun_Oinj__on(U_11263,U_11265,sK200(U_11266,U_11265,U_11264,U_11263),U_11264)
        | ~ sP849(U_11263,U_11264,U_11265,U_11266) )
    & ! [U_11263,U_11261,U_11264,U_11265,U_11266] :
        ( sP849(U_11263,U_11264,U_11265,U_11266)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266)))
        | ~ sP850(U_11263,U_11261,U_11264,U_11265,U_11266) )
    & ! [U_11263,U_11261,U_11264,U_11265,U_11266] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,U_11261),U_11264)),U_11266))
        | ~ c_Fun_Oinj__on(U_11263,U_11265,U_11261,U_11264)
        | ~ sP850(U_11263,U_11261,U_11264,U_11265,U_11266) )
    & ! [U_11263,U_11261,U_11264,U_11265,U_11266] :
        ( sP850(U_11263,U_11261,U_11264,U_11265,U_11266)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11265),U_11266))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP849,sP850])],[f_2978_3]) ).

cnf(f_2978_5,plain,
    ( sP850(U_11263,U_11261,U_11264,U_11265,U_11266)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11265),U_11266))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11263),U_11264)) ),
    inference(clausify,[status(thm)],[f_2978_4]) ).

cnf(f_2978_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,U_11261),U_11264)),U_11266))
    | ~ c_Fun_Oinj__on(U_11263,U_11265,U_11261,U_11264)
    | ~ sP850(U_11263,U_11261,U_11264,U_11265,U_11266) ),
    inference(clausify,[status(thm)],[f_2978_4]) ).

cnf(f_2978_7,plain,
    ( sP849(U_11263,U_11264,U_11265,U_11266)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11263),U_11264)),hAPP(c_Finite__Set_Ocard(U_11265),U_11266)))
    | ~ sP850(U_11263,U_11261,U_11264,U_11265,U_11266) ),
    inference(clausify,[status(thm)],[f_2978_4]) ).

cnf(f_2978_8,plain,
    ( c_Fun_Oinj__on(U_11263,U_11265,sK200(U_11266,U_11265,U_11264,U_11263),U_11264)
    | ~ sP849(U_11263,U_11264,U_11265,U_11266) ),
    inference(clausify,[status(thm)],[f_2978_4]) ).

cnf(f_2978_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11263,U_11265,sK200(U_11266,U_11265,U_11264,U_11263)),U_11264)),U_11266))
    | ~ sP849(U_11263,U_11264,U_11265,U_11266) ),
    inference(clausify,[status(thm)],[f_2978_4]) ).

fof(f_2979_1,plain,
    ! [V_a_2,V_A_2,V_r_2,T_b] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__diff1]) ).

fof(f_2979_2,plain,
    ! [U_11270,U_11269,U_11268,U_11267] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11267,tc_HOL_Obool)),U_11269),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11270),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool))))),U_11268) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),U_11269),U_11268)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11270),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool)))),U_11268))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11267),U_11270),U_11269))
      | ~ c_Fun_Oinj__on(U_11267,tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11267,tc_fun(tc_prod(U_11267,U_11267),tc_HOL_Obool),tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11267,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11267,U_11267),tc_HOL_Obool),tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),U_11267),c_Equiv__Relations_Oquotient(U_11267)),hAPP(hAPP(c_COMBC(U_11267,tc_fun(U_11267,tc_HOL_Obool),tc_fun(U_11267,tc_HOL_Obool)),c_Set_Oinsert(U_11267)),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool))))),U_11268),U_11269) ),
    inference(variable_rename,[status(thm)],[f_2979_1]) ).

fof(f_2979_3,plain,
    ! [U_11267,U_11269,U_11270,U_11268] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11267,tc_HOL_Obool)),U_11269),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11270),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool))))),U_11268) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),U_11269),U_11268)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11270),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool)))),U_11268))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11267),U_11270),U_11269))
      | ~ c_Fun_Oinj__on(U_11267,tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11267,tc_fun(tc_prod(U_11267,U_11267),tc_HOL_Obool),tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11267,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11267,U_11267),tc_HOL_Obool),tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),U_11267),c_Equiv__Relations_Oquotient(U_11267)),hAPP(hAPP(c_COMBC(U_11267,tc_fun(U_11267,tc_HOL_Obool),tc_fun(U_11267,tc_HOL_Obool)),c_Set_Oinsert(U_11267)),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool))))),U_11268),U_11269) ),
    inference(definitional_conversion,[status(esa)],[f_2979_2]) ).

cnf(f_2979_4,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11267,tc_HOL_Obool)),U_11269),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11270),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool))))),U_11268) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),U_11269),U_11268)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11267),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11270),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool)))),U_11268))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11267),U_11270),U_11269))
    | ~ c_Fun_Oinj__on(U_11267,tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11267,tc_fun(tc_prod(U_11267,U_11267),tc_HOL_Obool),tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11267,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11267,U_11267),tc_HOL_Obool),tc_fun(tc_fun(U_11267,tc_HOL_Obool),tc_HOL_Obool)),U_11267),c_Equiv__Relations_Oquotient(U_11267)),hAPP(hAPP(c_COMBC(U_11267,tc_fun(U_11267,tc_HOL_Obool),tc_fun(U_11267,tc_HOL_Obool)),c_Set_Oinsert(U_11267)),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool))))),U_11268),U_11269) ),
    inference(clausify,[status(thm)],[f_2979_3]) ).

fof(f_2980_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastAtMost__int]) ).

fof(f_2980_2,plain,
    ! [U_11272,U_11271] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11271,U_11272)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11272),U_11271)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2980_1]) ).

fof(f_2980_3,plain,
    ! [U_11272,U_11271] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11271,U_11272)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11272),U_11271)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_2980_2]) ).

cnf(f_2980_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11271,U_11272)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11272),U_11271)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2980_3]) ).

fof(f_2981_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J]) ).

fof(f_2981_2,plain,
    ! [U_11275,U_11274,U_11273] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11273,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11273),U_11274),c_Orderings_Obot__class_Obot(tc_fun(U_11273,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11273,U_11274,U_11275)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11273,U_11274,U_11275)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11273),U_11274),U_11275))
      | ~ class_Orderings_Olinorder(U_11273) ),
    inference(variable_rename,[status(thm)],[f_2981_1]) ).

fof(f_2981_3,plain,
    ! [U_11273,U_11274,U_11275] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11273,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11273),U_11274),c_Orderings_Obot__class_Obot(tc_fun(U_11273,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11273,U_11274,U_11275)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11273,U_11274,U_11275)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11273),U_11274),U_11275))
      | ~ class_Orderings_Olinorder(U_11273) ),
    inference(definitional_conversion,[status(esa)],[f_2981_2]) ).

cnf(f_2981_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11273,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11273),U_11274),c_Orderings_Obot__class_Obot(tc_fun(U_11273,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11273,U_11274,U_11275)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11273,U_11274,U_11275)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11273),U_11274),U_11275))
    | ~ class_Orderings_Olinorder(U_11273) ),
    inference(clausify,[status(thm)],[f_2981_3]) ).

fof(f_2982_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Un]) ).

fof(f_2982_2,plain,
    ! [U_11280,U_11279,U_11278,U_11277,U_11276] :
      ( ( c_Fun_Oinj__on(U_11276,U_11277,U_11278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11276,tc_HOL_Obool)),U_11279),U_11280))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11277,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11276,U_11277,U_11278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11276,tc_HOL_Obool)),U_11279),U_11280))),hAPP(c_Set_Oimage(U_11276,U_11277,U_11278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11276,tc_HOL_Obool)),U_11280),U_11279))) != c_Orderings_Obot__class_Obot(tc_fun(U_11277,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11276,U_11277,U_11278,U_11280)
        | ~ c_Fun_Oinj__on(U_11276,U_11277,U_11278,U_11279) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11277,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11276,U_11277,U_11278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11276,tc_HOL_Obool)),U_11279),U_11280))),hAPP(c_Set_Oimage(U_11276,U_11277,U_11278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11276,tc_HOL_Obool)),U_11280),U_11279))) = c_Orderings_Obot__class_Obot(tc_fun(U_11277,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_11276,U_11277,U_11278,U_11280)
          & c_Fun_Oinj__on(U_11276,U_11277,U_11278,U_11279) )
        | ~ c_Fun_Oinj__on(U_11276,U_11277,U_11278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11276,tc_HOL_Obool)),U_11279),U_11280)) ) ),
    inference(variable_rename,[status(thm)],[f_2982_1]) ).

fof(f_2982_3,plain,
    ( ! [U_11290,U_11288,U_11286,U_11284,U_11282] :
        ( c_Fun_Oinj__on(U_11282,U_11284,U_11286,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11282,tc_HOL_Obool)),U_11288),U_11290))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11284,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11282,U_11284,U_11286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11282,tc_HOL_Obool)),U_11288),U_11290))),hAPP(c_Set_Oimage(U_11282,U_11284,U_11286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11282,tc_HOL_Obool)),U_11290),U_11288))) != c_Orderings_Obot__class_Obot(tc_fun(U_11284,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11282,U_11284,U_11286,U_11290)
        | ~ c_Fun_Oinj__on(U_11282,U_11284,U_11286,U_11288) )
    & ! [U_11289,U_11287,U_11285,U_11283,U_11281] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11283,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11281,U_11283,U_11285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11281,tc_HOL_Obool)),U_11287),U_11289))),hAPP(c_Set_Oimage(U_11281,U_11283,U_11285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11281,tc_HOL_Obool)),U_11289),U_11287))) = c_Orderings_Obot__class_Obot(tc_fun(U_11283,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_11281,U_11283,U_11285,U_11289)
          & c_Fun_Oinj__on(U_11281,U_11283,U_11285,U_11287) )
        | ~ c_Fun_Oinj__on(U_11281,U_11283,U_11285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11281,tc_HOL_Obool)),U_11287),U_11289)) ) ),
    inference(miniscope,[status(thm)],[f_2982_2]) ).

fof(f_2982_4,plain,
    ( ! [U_11285,U_11283,U_11281,U_11287,U_11289] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11283,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11281,U_11283,U_11285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11281,tc_HOL_Obool)),U_11287),U_11289))),hAPP(c_Set_Oimage(U_11281,U_11283,U_11285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11281,tc_HOL_Obool)),U_11289),U_11287))) = c_Orderings_Obot__class_Obot(tc_fun(U_11283,tc_HOL_Obool))
        | ~ sP851(U_11285,U_11283,U_11281,U_11287,U_11289) )
    & ! [U_11285,U_11283,U_11281,U_11287,U_11289] :
        ( c_Fun_Oinj__on(U_11281,U_11283,U_11285,U_11289)
        | ~ sP851(U_11285,U_11283,U_11281,U_11287,U_11289) )
    & ! [U_11285,U_11283,U_11281,U_11287,U_11289] :
        ( c_Fun_Oinj__on(U_11281,U_11283,U_11285,U_11287)
        | ~ sP851(U_11285,U_11283,U_11281,U_11287,U_11289) )
    & ! [U_11284,U_11282,U_11286,U_11288,U_11290] :
        ( c_Fun_Oinj__on(U_11282,U_11284,U_11286,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11282,tc_HOL_Obool)),U_11288),U_11290))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11284,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11282,U_11284,U_11286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11282,tc_HOL_Obool)),U_11288),U_11290))),hAPP(c_Set_Oimage(U_11282,U_11284,U_11286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11282,tc_HOL_Obool)),U_11290),U_11288))) != c_Orderings_Obot__class_Obot(tc_fun(U_11284,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11282,U_11284,U_11286,U_11290)
        | ~ c_Fun_Oinj__on(U_11282,U_11284,U_11286,U_11288) )
    & ! [U_11285,U_11283,U_11281,U_11287,U_11289] :
        ( sP851(U_11285,U_11283,U_11281,U_11287,U_11289)
        | ~ c_Fun_Oinj__on(U_11281,U_11283,U_11285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11281,tc_HOL_Obool)),U_11287),U_11289)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP851])],[f_2982_3]) ).

cnf(f_2982_5,plain,
    ( sP851(U_11285,U_11283,U_11281,U_11287,U_11289)
    | ~ c_Fun_Oinj__on(U_11281,U_11283,U_11285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11281,tc_HOL_Obool)),U_11287),U_11289)) ),
    inference(clausify,[status(thm)],[f_2982_4]) ).

cnf(f_2982_6,plain,
    ( c_Fun_Oinj__on(U_11282,U_11284,U_11286,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11282,tc_HOL_Obool)),U_11288),U_11290))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11284,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11282,U_11284,U_11286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11282,tc_HOL_Obool)),U_11288),U_11290))),hAPP(c_Set_Oimage(U_11282,U_11284,U_11286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11282,tc_HOL_Obool)),U_11290),U_11288))) != c_Orderings_Obot__class_Obot(tc_fun(U_11284,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_11282,U_11284,U_11286,U_11290)
    | ~ c_Fun_Oinj__on(U_11282,U_11284,U_11286,U_11288) ),
    inference(clausify,[status(thm)],[f_2982_4]) ).

cnf(f_2982_7,plain,
    ( c_Fun_Oinj__on(U_11281,U_11283,U_11285,U_11287)
    | ~ sP851(U_11285,U_11283,U_11281,U_11287,U_11289) ),
    inference(clausify,[status(thm)],[f_2982_4]) ).

cnf(f_2982_8,plain,
    ( c_Fun_Oinj__on(U_11281,U_11283,U_11285,U_11289)
    | ~ sP851(U_11285,U_11283,U_11281,U_11287,U_11289) ),
    inference(clausify,[status(thm)],[f_2982_4]) ).

cnf(f_2982_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11283,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11281,U_11283,U_11285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11281,tc_HOL_Obool)),U_11287),U_11289))),hAPP(c_Set_Oimage(U_11281,U_11283,U_11285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11281,tc_HOL_Obool)),U_11289),U_11287))) = c_Orderings_Obot__class_Obot(tc_fun(U_11283,tc_HOL_Obool))
    | ~ sP851(U_11285,U_11283,U_11281,U_11287,U_11289) ),
    inference(clausify,[status(thm)],[f_2982_4]) ).

fof(f_2983_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
        | hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__insert]) ).

fof(f_2983_2,plain,
    ! [U_11295,U_11294,U_11293,U_11292,U_11291] :
      ( ( c_Fun_Oinj__on(U_11291,U_11292,U_11293,hAPP(hAPP(c_Set_Oinsert(U_11291),U_11294),U_11295))
        | hBOOL(hAPP(hAPP(c_member(U_11292),hAPP(U_11293,U_11294)),hAPP(c_Set_Oimage(U_11291,U_11292,U_11293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11291,tc_HOL_Obool)),U_11295),hAPP(hAPP(c_Set_Oinsert(U_11291),U_11294),c_Orderings_Obot__class_Obot(tc_fun(U_11291,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11291,U_11292,U_11293,U_11295) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11292),hAPP(U_11293,U_11294)),hAPP(c_Set_Oimage(U_11291,U_11292,U_11293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11291,tc_HOL_Obool)),U_11295),hAPP(hAPP(c_Set_Oinsert(U_11291),U_11294),c_Orderings_Obot__class_Obot(tc_fun(U_11291,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_11291,U_11292,U_11293,U_11295) )
        | ~ c_Fun_Oinj__on(U_11291,U_11292,U_11293,hAPP(hAPP(c_Set_Oinsert(U_11291),U_11294),U_11295)) ) ),
    inference(variable_rename,[status(thm)],[f_2983_1]) ).

fof(f_2983_3,plain,
    ( ! [U_11305,U_11303,U_11301,U_11299,U_11297] :
        ( c_Fun_Oinj__on(U_11297,U_11299,U_11301,hAPP(hAPP(c_Set_Oinsert(U_11297),U_11303),U_11305))
        | hBOOL(hAPP(hAPP(c_member(U_11299),hAPP(U_11301,U_11303)),hAPP(c_Set_Oimage(U_11297,U_11299,U_11301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11297,tc_HOL_Obool)),U_11305),hAPP(hAPP(c_Set_Oinsert(U_11297),U_11303),c_Orderings_Obot__class_Obot(tc_fun(U_11297,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11297,U_11299,U_11301,U_11305) )
    & ! [U_11304,U_11302,U_11300,U_11298,U_11296] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11298),hAPP(U_11300,U_11302)),hAPP(c_Set_Oimage(U_11296,U_11298,U_11300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11296,tc_HOL_Obool)),U_11304),hAPP(hAPP(c_Set_Oinsert(U_11296),U_11302),c_Orderings_Obot__class_Obot(tc_fun(U_11296,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_11296,U_11298,U_11300,U_11304) )
        | ~ c_Fun_Oinj__on(U_11296,U_11298,U_11300,hAPP(hAPP(c_Set_Oinsert(U_11296),U_11302),U_11304)) ) ),
    inference(miniscope,[status(thm)],[f_2983_2]) ).

fof(f_2983_4,plain,
    ( ! [U_11298,U_11296,U_11300,U_11302,U_11304] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_11298),hAPP(U_11300,U_11302)),hAPP(c_Set_Oimage(U_11296,U_11298,U_11300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11296,tc_HOL_Obool)),U_11304),hAPP(hAPP(c_Set_Oinsert(U_11296),U_11302),c_Orderings_Obot__class_Obot(tc_fun(U_11296,tc_HOL_Obool)))))))
        | ~ sP852(U_11298,U_11296,U_11300,U_11302,U_11304) )
    & ! [U_11298,U_11296,U_11300,U_11302,U_11304] :
        ( c_Fun_Oinj__on(U_11296,U_11298,U_11300,U_11304)
        | ~ sP852(U_11298,U_11296,U_11300,U_11302,U_11304) )
    & ! [U_11299,U_11297,U_11303,U_11301,U_11305] :
        ( c_Fun_Oinj__on(U_11297,U_11299,U_11301,hAPP(hAPP(c_Set_Oinsert(U_11297),U_11303),U_11305))
        | hBOOL(hAPP(hAPP(c_member(U_11299),hAPP(U_11301,U_11303)),hAPP(c_Set_Oimage(U_11297,U_11299,U_11301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11297,tc_HOL_Obool)),U_11305),hAPP(hAPP(c_Set_Oinsert(U_11297),U_11303),c_Orderings_Obot__class_Obot(tc_fun(U_11297,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11297,U_11299,U_11301,U_11305) )
    & ! [U_11298,U_11296,U_11300,U_11302,U_11304] :
        ( sP852(U_11298,U_11296,U_11300,U_11302,U_11304)
        | ~ c_Fun_Oinj__on(U_11296,U_11298,U_11300,hAPP(hAPP(c_Set_Oinsert(U_11296),U_11302),U_11304)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP852])],[f_2983_3]) ).

cnf(f_2983_5,plain,
    ( sP852(U_11298,U_11296,U_11300,U_11302,U_11304)
    | ~ c_Fun_Oinj__on(U_11296,U_11298,U_11300,hAPP(hAPP(c_Set_Oinsert(U_11296),U_11302),U_11304)) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

cnf(f_2983_6,plain,
    ( c_Fun_Oinj__on(U_11297,U_11299,U_11301,hAPP(hAPP(c_Set_Oinsert(U_11297),U_11303),U_11305))
    | hBOOL(hAPP(hAPP(c_member(U_11299),hAPP(U_11301,U_11303)),hAPP(c_Set_Oimage(U_11297,U_11299,U_11301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11297,tc_HOL_Obool)),U_11305),hAPP(hAPP(c_Set_Oinsert(U_11297),U_11303),c_Orderings_Obot__class_Obot(tc_fun(U_11297,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_11297,U_11299,U_11301,U_11305) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

cnf(f_2983_7,plain,
    ( c_Fun_Oinj__on(U_11296,U_11298,U_11300,U_11304)
    | ~ sP852(U_11298,U_11296,U_11300,U_11302,U_11304) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

cnf(f_2983_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_11298),hAPP(U_11300,U_11302)),hAPP(c_Set_Oimage(U_11296,U_11298,U_11300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11296,tc_HOL_Obool)),U_11304),hAPP(hAPP(c_Set_Oinsert(U_11296),U_11302),c_Orderings_Obot__class_Obot(tc_fun(U_11296,tc_HOL_Obool)))))))
    | ~ sP852(U_11298,U_11296,U_11300,U_11302,U_11304) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

fof(f_2984_1,plain,
    ! [V_A_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inj__uminus]) ).

fof(f_2984_2,plain,
    ! [U_11307,U_11306] :
      ( c_Fun_Oinj__on(U_11306,U_11306,c_Groups_Ouminus__class_Ouminus(U_11306),U_11307)
      | ~ class_Groups_Oordered__ab__group__add(U_11306) ),
    inference(variable_rename,[status(thm)],[f_2984_1]) ).

fof(f_2984_3,plain,
    ! [U_11307,U_11306] :
      ( c_Fun_Oinj__on(U_11306,U_11306,c_Groups_Ouminus__class_Ouminus(U_11306),U_11307)
      | ~ class_Groups_Oordered__ab__group__add(U_11306) ),
    inference(definitional_conversion,[status(esa)],[f_2984_2]) ).

cnf(f_2984_4,plain,
    ( c_Fun_Oinj__on(U_11306,U_11306,c_Groups_Ouminus__class_Ouminus(U_11306),U_11307)
    | ~ class_Groups_Oordered__ab__group__add(U_11306) ),
    inference(clausify,[status(thm)],[f_2984_3]) ).

fof(f_2985_1,plain,
    ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__on__empty]) ).

fof(f_2985_2,plain,
    ! [U_11310,U_11309,U_11308] : c_Fun_Oinj__on(U_11308,U_11309,U_11310,c_Orderings_Obot__class_Obot(tc_fun(U_11308,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2985_1]) ).

fof(f_2985_3,plain,
    ! [U_11309,U_11308,U_11310] : c_Fun_Oinj__on(U_11308,U_11309,U_11310,c_Orderings_Obot__class_Obot(tc_fun(U_11308,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2985_2]) ).

cnf(f_2985_4,plain,
    c_Fun_Oinj__on(U_11308,U_11309,U_11310,c_Orderings_Obot__class_Obot(tc_fun(U_11308,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2985_3]) ).

fof(f_2986_1,plain,
    ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
    inference(fof_nnf,[status(thm)],[fact_inj__Suc]) ).

fof(f_2986_2,plain,
    ! [U_11311] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11311),
    inference(variable_rename,[status(thm)],[f_2986_1]) ).

fof(f_2986_3,plain,
    ! [U_11311] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11311),
    inference(definitional_conversion,[status(esa)],[f_2986_2]) ).

cnf(f_2986_4,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11311),
    inference(clausify,[status(thm)],[f_2986_3]) ).

fof(f_2987_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__Some]) ).

fof(f_2987_2,plain,
    ! [U_11313,U_11312] : c_Fun_Oinj__on(U_11312,tc_Option_Ooption(U_11312),c_Option_Ooption_OSome(U_11312),U_11313),
    inference(variable_rename,[status(thm)],[f_2987_1]) ).

fof(f_2987_3,plain,
    ! [U_11312,U_11313] : c_Fun_Oinj__on(U_11312,tc_Option_Ooption(U_11312),c_Option_Ooption_OSome(U_11312),U_11313),
    inference(definitional_conversion,[status(esa)],[f_2987_2]) ).

cnf(f_2987_4,plain,
    c_Fun_Oinj__on(U_11312,tc_Option_Ooption(U_11312),c_Option_Ooption_OSome(U_11312),U_11313),
    inference(clausify,[status(thm)],[f_2987_3]) ).

fof(f_2988_1,plain,
    ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__add__nat]) ).

fof(f_2988_2,plain,
    ! [U_11315,U_11314] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11314),U_11315),
    inference(variable_rename,[status(thm)],[f_2988_1]) ).

fof(f_2988_3,plain,
    ! [U_11314,U_11315] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11314),U_11315),
    inference(definitional_conversion,[status(esa)],[f_2988_2]) ).

cnf(f_2988_4,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11314),U_11315),
    inference(clausify,[status(thm)],[f_2988_3]) ).

fof(f_2989_1,plain,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_swap__inj__on]) ).

fof(f_2989_2,plain,
    ! [U_11318,U_11317,U_11316] : c_Fun_Oinj__on(tc_prod(U_11316,U_11317),tc_prod(U_11317,U_11316),hAPP(c_Product__Type_Oprod_Oprod__case(U_11316,U_11317,tc_prod(U_11317,U_11316)),hAPP(c_COMBC(U_11317,U_11316,tc_prod(U_11317,U_11316)),c_Product__Type_OPair(U_11317,U_11316))),U_11318),
    inference(variable_rename,[status(thm)],[f_2989_1]) ).

fof(f_2989_3,plain,
    ! [U_11316,U_11317,U_11318] : c_Fun_Oinj__on(tc_prod(U_11316,U_11317),tc_prod(U_11317,U_11316),hAPP(c_Product__Type_Oprod_Oprod__case(U_11316,U_11317,tc_prod(U_11317,U_11316)),hAPP(c_COMBC(U_11317,U_11316,tc_prod(U_11317,U_11316)),c_Product__Type_OPair(U_11317,U_11316))),U_11318),
    inference(definitional_conversion,[status(esa)],[f_2989_2]) ).

cnf(f_2989_4,plain,
    c_Fun_Oinj__on(tc_prod(U_11316,U_11317),tc_prod(U_11317,U_11316),hAPP(c_Product__Type_Oprod_Oprod__case(U_11316,U_11317,tc_prod(U_11317,U_11316)),hAPP(c_COMBC(U_11317,U_11316,tc_prod(U_11317,U_11316)),c_Product__Type_OPair(U_11317,U_11316))),U_11318),
    inference(clausify,[status(thm)],[f_2989_3]) ).

fof(f_2990_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
        | ? [B_x] :
            ( ? [B_xa] :
                ( B_x != B_xa
                & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( B_x = B_xa
                | hAPP(V_f_2,B_x) != hAPP(V_f_2,B_xa)
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__def]) ).

fof(f_2990_2,plain,
    ! [U_11326,U_11325,U_11324,U_11323] :
      ( ( c_Fun_Oinj__on(U_11323,U_11324,U_11325,U_11326)
        | ? [U_11322] :
            ( ? [U_11321] :
                ( U_11322 != U_11321
                & hAPP(U_11325,U_11322) = hAPP(U_11325,U_11321)
                & hBOOL(hAPP(hAPP(c_member(U_11323),U_11321),U_11326)) )
            & hBOOL(hAPP(hAPP(c_member(U_11323),U_11322),U_11326)) ) )
      & ( ! [U_11320] :
            ( ! [U_11319] :
                ( U_11320 = U_11319
                | hAPP(U_11325,U_11320) != hAPP(U_11325,U_11319)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11323),U_11319),U_11326)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11323),U_11320),U_11326)) )
        | ~ c_Fun_Oinj__on(U_11323,U_11324,U_11325,U_11326) ) ),
    inference(variable_rename,[status(thm)],[f_2990_1]) ).

fof(f_2990_3,plain,
    ( ! [U_11334,U_11332,U_11330,U_11328] :
        ( c_Fun_Oinj__on(U_11328,U_11330,U_11332,U_11334)
        | ? [U_11322] :
            ( ? [U_11321] :
                ( U_11322 != U_11321
                & hAPP(U_11332,U_11322) = hAPP(U_11332,U_11321)
                & hBOOL(hAPP(hAPP(c_member(U_11328),U_11321),U_11334)) )
            & hBOOL(hAPP(hAPP(c_member(U_11328),U_11322),U_11334)) ) )
    & ! [U_11333,U_11331,U_11329,U_11327] :
        ( ! [U_11320] :
            ( ! [U_11319] :
                ( U_11320 = U_11319
                | hAPP(U_11331,U_11320) != hAPP(U_11331,U_11319)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11319),U_11333)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11320),U_11333)) )
        | ~ c_Fun_Oinj__on(U_11327,U_11329,U_11331,U_11333) ) ),
    inference(miniscope,[status(thm)],[f_2990_2]) ).

fof(f_2990_4,plain,
    ( ! [U_11334,U_11332,U_11330,U_11328] :
        ( c_Fun_Oinj__on(U_11328,U_11330,U_11332,U_11334)
        | ( ? [U_11321] :
              ( sK201(U_11334,U_11332,U_11330,U_11328) != U_11321
              & hAPP(U_11332,sK201(U_11334,U_11332,U_11330,U_11328)) = hAPP(U_11332,U_11321)
              & hBOOL(hAPP(hAPP(c_member(U_11328),U_11321),U_11334)) )
          & hBOOL(hAPP(hAPP(c_member(U_11328),sK201(U_11334,U_11332,U_11330,U_11328)),U_11334)) ) )
    & ! [U_11333,U_11331,U_11329,U_11327] :
        ( ! [U_11320] :
            ( ! [U_11319] :
                ( U_11320 = U_11319
                | hAPP(U_11331,U_11320) != hAPP(U_11331,U_11319)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11319),U_11333)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11320),U_11333)) )
        | ~ c_Fun_Oinj__on(U_11327,U_11329,U_11331,U_11333) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_11322,sK201(U_11334,U_11332,U_11330,U_11328))],[f_2990_3]) ).

fof(f_2990_5,plain,
    ( ! [U_11334,U_11332,U_11330,U_11328] :
        ( c_Fun_Oinj__on(U_11328,U_11330,U_11332,U_11334)
        | ( sK201(U_11334,U_11332,U_11330,U_11328) != sK202(U_11334,U_11332,U_11330,U_11328)
          & hAPP(U_11332,sK201(U_11334,U_11332,U_11330,U_11328)) = hAPP(U_11332,sK202(U_11334,U_11332,U_11330,U_11328))
          & hBOOL(hAPP(hAPP(c_member(U_11328),sK202(U_11334,U_11332,U_11330,U_11328)),U_11334))
          & hBOOL(hAPP(hAPP(c_member(U_11328),sK201(U_11334,U_11332,U_11330,U_11328)),U_11334)) ) )
    & ! [U_11333,U_11331,U_11329,U_11327] :
        ( ! [U_11320] :
            ( ! [U_11319] :
                ( U_11320 = U_11319
                | hAPP(U_11331,U_11320) != hAPP(U_11331,U_11319)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11319),U_11333)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11320),U_11333)) )
        | ~ c_Fun_Oinj__on(U_11327,U_11329,U_11331,U_11333) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_11321,sK202(U_11334,U_11332,U_11330,U_11328))],[f_2990_4]) ).

fof(f_2990_6,plain,
    ( ! [U_11330,U_11334,U_11332,U_11328] :
        ( sK201(U_11334,U_11332,U_11330,U_11328) != sK202(U_11334,U_11332,U_11330,U_11328)
        | ~ sP853(U_11330,U_11334,U_11332,U_11328) )
    & ! [U_11330,U_11334,U_11332,U_11328] :
        ( hAPP(U_11332,sK201(U_11334,U_11332,U_11330,U_11328)) = hAPP(U_11332,sK202(U_11334,U_11332,U_11330,U_11328))
        | ~ sP853(U_11330,U_11334,U_11332,U_11328) )
    & ! [U_11330,U_11334,U_11332,U_11328] :
        ( hBOOL(hAPP(hAPP(c_member(U_11328),sK202(U_11334,U_11332,U_11330,U_11328)),U_11334))
        | ~ sP853(U_11330,U_11334,U_11332,U_11328) )
    & ! [U_11330,U_11334,U_11332,U_11328] :
        ( hBOOL(hAPP(hAPP(c_member(U_11328),sK201(U_11334,U_11332,U_11330,U_11328)),U_11334))
        | ~ sP853(U_11330,U_11334,U_11332,U_11328) )
    & ! [U_11330,U_11334,U_11332,U_11328] :
        ( c_Fun_Oinj__on(U_11328,U_11330,U_11332,U_11334)
        | sP853(U_11330,U_11334,U_11332,U_11328) )
    & ! [U_11331,U_11319,U_11320,U_11329,U_11327,U_11333] :
        ( U_11320 = U_11319
        | hAPP(U_11331,U_11320) != hAPP(U_11331,U_11319)
        | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11319),U_11333))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11320),U_11333))
        | ~ c_Fun_Oinj__on(U_11327,U_11329,U_11331,U_11333) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP853])],[f_2990_5]) ).

cnf(f_2990_7,plain,
    ( U_11320 = U_11319
    | hAPP(U_11331,U_11320) != hAPP(U_11331,U_11319)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11319),U_11333))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11327),U_11320),U_11333))
    | ~ c_Fun_Oinj__on(U_11327,U_11329,U_11331,U_11333) ),
    inference(clausify,[status(thm)],[f_2990_6]) ).

cnf(f_2990_8,plain,
    ( c_Fun_Oinj__on(U_11328,U_11330,U_11332,U_11334)
    | sP853(U_11330,U_11334,U_11332,U_11328) ),
    inference(clausify,[status(thm)],[f_2990_6]) ).

cnf(f_2990_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11328),sK201(U_11334,U_11332,U_11330,U_11328)),U_11334))
    | ~ sP853(U_11330,U_11334,U_11332,U_11328) ),
    inference(clausify,[status(thm)],[f_2990_6]) ).

cnf(f_2990_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11328),sK202(U_11334,U_11332,U_11330,U_11328)),U_11334))
    | ~ sP853(U_11330,U_11334,U_11332,U_11328) ),
    inference(clausify,[status(thm)],[f_2990_6]) ).

cnf(f_2990_11,plain,
    ( hAPP(U_11332,sK201(U_11334,U_11332,U_11330,U_11328)) = hAPP(U_11332,sK202(U_11334,U_11332,U_11330,U_11328))
    | ~ sP853(U_11330,U_11334,U_11332,U_11328) ),
    inference(clausify,[status(thm)],[f_2990_6]) ).

cnf(f_2990_12,plain,
    ( sK201(U_11334,U_11332,U_11330,U_11328) != sK202(U_11334,U_11332,U_11330,U_11328)
    | ~ sP853(U_11330,U_11334,U_11332,U_11328) ),
    inference(clausify,[status(thm)],[f_2990_6]) ).

fof(f_2991_1,plain,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_image__ident]) ).

fof(f_2991_2,plain,
    ! [U_11336,U_11335] : hAPP(c_Set_Oimage(U_11335,U_11335,c_COMBI(U_11335)),U_11336) = U_11336,
    inference(variable_rename,[status(thm)],[f_2991_1]) ).

fof(f_2991_3,plain,
    ! [U_11336,U_11335] : hAPP(c_Set_Oimage(U_11335,U_11335,c_COMBI(U_11335)),U_11336) = U_11336,
    inference(definitional_conversion,[status(esa)],[f_2991_2]) ).

cnf(f_2991_4,plain,
    hAPP(c_Set_Oimage(U_11335,U_11335,c_COMBI(U_11335)),U_11336) = U_11336,
    inference(clausify,[status(thm)],[f_2991_3]) ).

fof(f_2992_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__id2]) ).

fof(f_2992_2,plain,
    ! [U_11338,U_11337] : c_Fun_Oinj__on(U_11337,U_11337,c_COMBI(U_11337),U_11338),
    inference(variable_rename,[status(thm)],[f_2992_1]) ).

fof(f_2992_3,plain,
    ! [U_11337,U_11338] : c_Fun_Oinj__on(U_11337,U_11337,c_COMBI(U_11337),U_11338),
    inference(definitional_conversion,[status(esa)],[f_2992_2]) ).

cnf(f_2992_4,plain,
    c_Fun_Oinj__on(U_11337,U_11337,c_COMBI(U_11337),U_11338),
    inference(clausify,[status(thm)],[f_2992_3]) ).

fof(f_2993_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__onD]) ).

fof(f_2993_2,plain,
    ! [U_11344,U_11343,U_11342,U_11341,U_11340,U_11339] :
      ( U_11343 = U_11344
      | ~ hBOOL(hAPP(hAPP(c_member(U_11339),U_11344),U_11342))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11339),U_11343),U_11342))
      | hAPP(U_11341,U_11343) != hAPP(U_11341,U_11344)
      | ~ c_Fun_Oinj__on(U_11339,U_11340,U_11341,U_11342) ),
    inference(variable_rename,[status(thm)],[f_2993_1]) ).

fof(f_2993_3,plain,
    ! [U_11339,U_11344,U_11340,U_11342,U_11343,U_11341] :
      ( U_11343 = U_11344
      | ~ hBOOL(hAPP(hAPP(c_member(U_11339),U_11344),U_11342))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11339),U_11343),U_11342))
      | hAPP(U_11341,U_11343) != hAPP(U_11341,U_11344)
      | ~ c_Fun_Oinj__on(U_11339,U_11340,U_11341,U_11342) ),
    inference(definitional_conversion,[status(esa)],[f_2993_2]) ).

cnf(f_2993_4,plain,
    ( U_11343 = U_11344
    | ~ hBOOL(hAPP(hAPP(c_member(U_11339),U_11344),U_11342))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11339),U_11343),U_11342))
    | hAPP(U_11341,U_11343) != hAPP(U_11341,U_11344)
    | ~ c_Fun_Oinj__on(U_11339,U_11340,U_11341,U_11342) ),
    inference(clausify,[status(thm)],[f_2993_3]) ).

fof(f_2994_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff]) ).

fof(f_2994_2,plain,
    ! [U_11350,U_11349,U_11348,U_11347,U_11346,U_11345] :
      ( ( ( hAPP(U_11347,U_11349) = hAPP(U_11347,U_11350)
          | U_11349 != U_11350 )
        & ( U_11349 = U_11350
          | hAPP(U_11347,U_11349) != hAPP(U_11347,U_11350) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11345),U_11350),U_11348))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11345),U_11349),U_11348))
      | ~ c_Fun_Oinj__on(U_11345,U_11346,U_11347,U_11348) ),
    inference(variable_rename,[status(thm)],[f_2994_1]) ).

fof(f_2994_3,plain,
    ( ! [U_11347,U_11349,U_11350] :
        ( hAPP(U_11347,U_11349) = hAPP(U_11347,U_11350)
        | U_11349 != U_11350
        | ~ sP854(U_11347,U_11349,U_11350) )
    & ! [U_11347,U_11349,U_11350] :
        ( U_11349 = U_11350
        | hAPP(U_11347,U_11349) != hAPP(U_11347,U_11350)
        | ~ sP854(U_11347,U_11349,U_11350) )
    & ! [U_11345,U_11346,U_11347,U_11348,U_11349,U_11350] :
        ( sP854(U_11347,U_11349,U_11350)
        | ~ hBOOL(hAPP(hAPP(c_member(U_11345),U_11350),U_11348))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11345),U_11349),U_11348))
        | ~ c_Fun_Oinj__on(U_11345,U_11346,U_11347,U_11348) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP854])],[f_2994_2]) ).

cnf(f_2994_4,plain,
    ( sP854(U_11347,U_11349,U_11350)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11345),U_11350),U_11348))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11345),U_11349),U_11348))
    | ~ c_Fun_Oinj__on(U_11345,U_11346,U_11347,U_11348) ),
    inference(clausify,[status(thm)],[f_2994_3]) ).

cnf(f_2994_5,plain,
    ( U_11349 = U_11350
    | hAPP(U_11347,U_11349) != hAPP(U_11347,U_11350)
    | ~ sP854(U_11347,U_11349,U_11350) ),
    inference(clausify,[status(thm)],[f_2994_3]) ).

cnf(f_2994_6,plain,
    ( hAPP(U_11347,U_11349) = hAPP(U_11347,U_11350)
    | U_11349 != U_11350
    | ~ sP854(U_11347,U_11349,U_11350) ),
    inference(clausify,[status(thm)],[f_2994_3]) ).

fof(f_2995_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | V_x_2 = V_y_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__contraD]) ).

fof(f_2995_2,plain,
    ! [U_11356,U_11355,U_11354,U_11353,U_11352,U_11351] :
      ( hAPP(U_11353,U_11355) != hAPP(U_11353,U_11356)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11351),U_11356),U_11354))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11351),U_11355),U_11354))
      | U_11355 = U_11356
      | ~ c_Fun_Oinj__on(U_11351,U_11352,U_11353,U_11354) ),
    inference(variable_rename,[status(thm)],[f_2995_1]) ).

fof(f_2995_3,plain,
    ! [U_11356,U_11354,U_11355,U_11352,U_11353,U_11351] :
      ( hAPP(U_11353,U_11355) != hAPP(U_11353,U_11356)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11351),U_11356),U_11354))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11351),U_11355),U_11354))
      | U_11355 = U_11356
      | ~ c_Fun_Oinj__on(U_11351,U_11352,U_11353,U_11354) ),
    inference(definitional_conversion,[status(esa)],[f_2995_2]) ).

cnf(f_2995_4,plain,
    ( hAPP(U_11353,U_11355) != hAPP(U_11353,U_11356)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11351),U_11356),U_11354))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11351),U_11355),U_11354))
    | U_11355 = U_11356
    | ~ c_Fun_Oinj__on(U_11351,U_11352,U_11353,U_11354) ),
    inference(clausify,[status(thm)],[f_2995_3]) ).

fof(f_2996_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_subset__inj__on]) ).

fof(f_2996_2,plain,
    ! [U_11361,U_11360,U_11359,U_11358,U_11357] :
      ( c_Fun_Oinj__on(U_11357,U_11358,U_11359,U_11361)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11357,tc_HOL_Obool)),U_11361),U_11360))
      | ~ c_Fun_Oinj__on(U_11357,U_11358,U_11359,U_11360) ),
    inference(variable_rename,[status(thm)],[f_2996_1]) ).

fof(f_2996_3,plain,
    ! [U_11357,U_11361,U_11359,U_11360,U_11358] :
      ( c_Fun_Oinj__on(U_11357,U_11358,U_11359,U_11361)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11357,tc_HOL_Obool)),U_11361),U_11360))
      | ~ c_Fun_Oinj__on(U_11357,U_11358,U_11359,U_11360) ),
    inference(definitional_conversion,[status(esa)],[f_2996_2]) ).

cnf(f_2996_4,plain,
    ( c_Fun_Oinj__on(U_11357,U_11358,U_11359,U_11361)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11357,tc_HOL_Obool)),U_11361),U_11360))
    | ~ c_Fun_Oinj__on(U_11357,U_11358,U_11359,U_11360) ),
    inference(clausify,[status(thm)],[f_2996_3]) ).

fof(f_2997_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Int]) ).

fof(f_2997_2,plain,
    ! [U_11366,U_11365,U_11364,U_11363,U_11362] :
      ( c_Fun_Oinj__on(U_11362,U_11363,U_11364,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11362,tc_HOL_Obool)),U_11365),U_11366))
      | ~ c_Fun_Oinj__on(U_11362,U_11363,U_11364,U_11366)
      | ~ c_Fun_Oinj__on(U_11362,U_11363,U_11364,U_11365) ),
    inference(variable_rename,[status(thm)],[f_2997_1]) ).

fof(f_2997_3,plain,
    ! [U_11362,U_11364,U_11363,U_11365,U_11366] :
      ( c_Fun_Oinj__on(U_11362,U_11363,U_11364,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11362,tc_HOL_Obool)),U_11365),U_11366))
      | ~ c_Fun_Oinj__on(U_11362,U_11363,U_11364,U_11366)
      | ~ c_Fun_Oinj__on(U_11362,U_11363,U_11364,U_11365) ),
    inference(definitional_conversion,[status(esa)],[f_2997_2]) ).

cnf(f_2997_4,plain,
    ( c_Fun_Oinj__on(U_11362,U_11363,U_11364,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11362,tc_HOL_Obool)),U_11365),U_11366))
    | ~ c_Fun_Oinj__on(U_11362,U_11363,U_11364,U_11366)
    | ~ c_Fun_Oinj__on(U_11362,U_11363,U_11364,U_11365) ),
    inference(clausify,[status(thm)],[f_2997_3]) ).

fof(f_2998_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__diff]) ).

fof(f_2998_2,plain,
    ! [U_11371,U_11370,U_11369,U_11368,U_11367] :
      ( c_Fun_Oinj__on(U_11367,U_11368,U_11369,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11367,tc_HOL_Obool)),U_11370),U_11371))
      | ~ c_Fun_Oinj__on(U_11367,U_11368,U_11369,U_11370) ),
    inference(variable_rename,[status(thm)],[f_2998_1]) ).

fof(f_2998_3,plain,
    ! [U_11367,U_11371,U_11370,U_11369,U_11368] :
      ( c_Fun_Oinj__on(U_11367,U_11368,U_11369,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11367,tc_HOL_Obool)),U_11370),U_11371))
      | ~ c_Fun_Oinj__on(U_11367,U_11368,U_11369,U_11370) ),
    inference(definitional_conversion,[status(esa)],[f_2998_2]) ).

cnf(f_2998_4,plain,
    ( c_Fun_Oinj__on(U_11367,U_11368,U_11369,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11367,tc_HOL_Obool)),U_11370),U_11371))
    | ~ c_Fun_Oinj__on(U_11367,U_11368,U_11369,U_11370) ),
    inference(clausify,[status(thm)],[f_2998_3]) ).

fof(f_2999_1,plain,
    ! [V_A_2,T_b,B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) != hAPP(c_Set_OPow(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Cantors__paradox]) ).

fof(f_2999_2,plain,
    ! [U_11374,U_11373,U_11372] : hAPP(c_Set_Oimage(U_11373,tc_fun(U_11373,tc_HOL_Obool),U_11372),U_11374) != hAPP(c_Set_OPow(U_11373),U_11374),
    inference(variable_rename,[status(thm)],[f_2999_1]) ).

fof(f_2999_3,plain,
    ! [U_11373,U_11372,U_11374] : hAPP(c_Set_Oimage(U_11373,tc_fun(U_11373,tc_HOL_Obool),U_11372),U_11374) != hAPP(c_Set_OPow(U_11373),U_11374),
    inference(definitional_conversion,[status(esa)],[f_2999_2]) ).

cnf(f_2999_4,plain,
    hAPP(c_Set_Oimage(U_11373,tc_fun(U_11373,tc_HOL_Obool),U_11372),U_11374) != hAPP(c_Set_OPow(U_11373),U_11374),
    inference(clausify,[status(thm)],[f_2999_3]) ).

fof(f_3000_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff]) ).

fof(f_3000_2,plain,
    ! [U_11379,U_11378,U_11377,U_11376,U_11375] :
      ( ( ( hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11378) = hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11379)
          | U_11378 != U_11379 )
        & ( U_11378 = U_11379
          | hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11378) != hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11379) ) )
      | ~ c_Fun_Oinj__on(U_11375,U_11376,U_11377,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11378),U_11379)) ),
    inference(variable_rename,[status(thm)],[f_3000_1]) ).

fof(f_3000_3,plain,
    ( ! [U_11375,U_11376,U_11377,U_11378,U_11379] :
        ( hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11378) = hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11379)
        | U_11378 != U_11379
        | ~ sP855(U_11375,U_11376,U_11377,U_11378,U_11379) )
    & ! [U_11375,U_11376,U_11377,U_11378,U_11379] :
        ( U_11378 = U_11379
        | hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11378) != hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11379)
        | ~ sP855(U_11375,U_11376,U_11377,U_11378,U_11379) )
    & ! [U_11375,U_11376,U_11377,U_11378,U_11379] :
        ( sP855(U_11375,U_11376,U_11377,U_11378,U_11379)
        | ~ c_Fun_Oinj__on(U_11375,U_11376,U_11377,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11378),U_11379)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP855])],[f_3000_2]) ).

cnf(f_3000_4,plain,
    ( sP855(U_11375,U_11376,U_11377,U_11378,U_11379)
    | ~ c_Fun_Oinj__on(U_11375,U_11376,U_11377,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11378),U_11379)) ),
    inference(clausify,[status(thm)],[f_3000_3]) ).

cnf(f_3000_5,plain,
    ( U_11378 = U_11379
    | hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11378) != hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11379)
    | ~ sP855(U_11375,U_11376,U_11377,U_11378,U_11379) ),
    inference(clausify,[status(thm)],[f_3000_3]) ).

cnf(f_3000_6,plain,
    ( hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11378) = hAPP(c_Set_Oimage(U_11375,U_11376,U_11377),U_11379)
    | U_11378 != U_11379
    | ~ sP855(U_11375,U_11376,U_11377,U_11378,U_11379) ),
    inference(clausify,[status(thm)],[f_3000_3]) ).

fof(f_3001_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset]) ).

fof(f_3001_2,plain,
    ! [U_11384,U_11383,U_11382,U_11381,U_11380] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11381,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11380,U_11381,U_11382),U_11384)),hAPP(c_Set_Oimage(U_11380,U_11381,U_11382),U_11383)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11380,tc_HOL_Obool)),U_11384),U_11383))
      | ~ c_Fun_Oinj__on(U_11380,U_11381,U_11382,U_11383) ),
    inference(variable_rename,[status(thm)],[f_3001_1]) ).

fof(f_3001_3,plain,
    ! [U_11381,U_11380,U_11382,U_11383,U_11384] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11381,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11380,U_11381,U_11382),U_11384)),hAPP(c_Set_Oimage(U_11380,U_11381,U_11382),U_11383)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11380,tc_HOL_Obool)),U_11384),U_11383))
      | ~ c_Fun_Oinj__on(U_11380,U_11381,U_11382,U_11383) ),
    inference(definitional_conversion,[status(esa)],[f_3001_2]) ).

cnf(f_3001_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11381,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11380,U_11381,U_11382),U_11384)),hAPP(c_Set_Oimage(U_11380,U_11381,U_11382),U_11383)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11380,tc_HOL_Obool)),U_11384),U_11383))
    | ~ c_Fun_Oinj__on(U_11380,U_11381,U_11382,U_11383) ),
    inference(clausify,[status(thm)],[f_3001_3]) ).

fof(f_3002_1,plain,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int]) ).

fof(f_3002_2,plain,
    ! [U_11390,U_11389,U_11388,U_11387,U_11386,U_11385] :
      ( hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11389),U_11390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11386,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),U_11389)),hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),U_11390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11385,tc_HOL_Obool)),U_11390),U_11388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11385,tc_HOL_Obool)),U_11389),U_11388))
      | ~ c_Fun_Oinj__on(U_11385,U_11386,U_11387,U_11388) ),
    inference(variable_rename,[status(thm)],[f_3002_1]) ).

fof(f_3002_3,plain,
    ! [U_11385,U_11386,U_11387,U_11388,U_11389,U_11390] :
      ( hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11389),U_11390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11386,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),U_11389)),hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),U_11390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11385,tc_HOL_Obool)),U_11390),U_11388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11385,tc_HOL_Obool)),U_11389),U_11388))
      | ~ c_Fun_Oinj__on(U_11385,U_11386,U_11387,U_11388) ),
    inference(definitional_conversion,[status(esa)],[f_3002_2]) ).

cnf(f_3002_4,plain,
    ( hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11389),U_11390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11386,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),U_11389)),hAPP(c_Set_Oimage(U_11385,U_11386,U_11387),U_11390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11385,tc_HOL_Obool)),U_11390),U_11388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11385,tc_HOL_Obool)),U_11389),U_11388))
    | ~ c_Fun_Oinj__on(U_11385,U_11386,U_11387,U_11388) ),
    inference(clausify,[status(thm)],[f_3002_3]) ).

fof(f_3003_1,plain,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff]) ).

fof(f_3003_2,plain,
    ! [U_11396,U_11395,U_11394,U_11393,U_11392,U_11391] :
      ( hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11391,tc_HOL_Obool)),U_11395),U_11396)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),U_11395)),hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),U_11396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11391,tc_HOL_Obool)),U_11396),U_11394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11391,tc_HOL_Obool)),U_11395),U_11394))
      | ~ c_Fun_Oinj__on(U_11391,U_11392,U_11393,U_11394) ),
    inference(variable_rename,[status(thm)],[f_3003_1]) ).

fof(f_3003_3,plain,
    ! [U_11391,U_11392,U_11393,U_11394,U_11395,U_11396] :
      ( hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11391,tc_HOL_Obool)),U_11395),U_11396)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),U_11395)),hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),U_11396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11391,tc_HOL_Obool)),U_11396),U_11394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11391,tc_HOL_Obool)),U_11395),U_11394))
      | ~ c_Fun_Oinj__on(U_11391,U_11392,U_11393,U_11394) ),
    inference(definitional_conversion,[status(esa)],[f_3003_2]) ).

cnf(f_3003_4,plain,
    ( hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11391,tc_HOL_Obool)),U_11395),U_11396)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),U_11395)),hAPP(c_Set_Oimage(U_11391,U_11392,U_11393),U_11396))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11391,tc_HOL_Obool)),U_11396),U_11394))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11391,tc_HOL_Obool)),U_11395),U_11394))
    | ~ c_Fun_Oinj__on(U_11391,U_11392,U_11393,U_11394) ),
    inference(clausify,[status(thm)],[f_3003_3]) ).

fof(f_3004_1,plain,
    ! [V_A_H_2,T_c,T_b,V_A_2] :
      ( ( ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
              & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
          | ! [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) != V_A_2 )
        & ( ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2
          | ! [B_f] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
              | ~ c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) ) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj]) ).

fof(f_3004_2,plain,
    ! [U_11404,U_11403,U_11402,U_11401] :
      ( ( ( ? [U_11400] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11400),U_11401)),U_11404))
              & c_Fun_Oinj__on(U_11402,U_11403,U_11400,U_11401) )
          | ! [U_11399] : hAPP(c_Set_Oimage(U_11403,U_11402,U_11399),U_11404) != U_11401 )
        & ( ? [U_11398] : hAPP(c_Set_Oimage(U_11403,U_11402,U_11398),U_11404) = U_11401
          | ! [U_11397] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11397),U_11401)),U_11404))
              | ~ c_Fun_Oinj__on(U_11402,U_11403,U_11397,U_11401) ) ) )
      | U_11401 = c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3004_1]) ).

fof(f_3004_3,plain,
    ! [U_11404,U_11403,U_11402,U_11401] :
      ( ( ( ? [U_11400] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11400),U_11401)),U_11404))
              & c_Fun_Oinj__on(U_11402,U_11403,U_11400,U_11401) )
          | ! [U_11399] : hAPP(c_Set_Oimage(U_11403,U_11402,U_11399),U_11404) != U_11401 )
        & ( hAPP(c_Set_Oimage(U_11403,U_11402,sK203(U_11404,U_11403,U_11402,U_11401)),U_11404) = U_11401
          | ! [U_11397] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11397),U_11401)),U_11404))
              | ~ c_Fun_Oinj__on(U_11402,U_11403,U_11397,U_11401) ) ) )
      | U_11401 = c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_11398,sK203(U_11404,U_11403,U_11402,U_11401))],[f_3004_2]) ).

fof(f_3004_4,plain,
    ! [U_11404,U_11403,U_11402,U_11401] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,sK204(U_11404,U_11403,U_11402,U_11401)),U_11401)),U_11404))
            & c_Fun_Oinj__on(U_11402,U_11403,sK204(U_11404,U_11403,U_11402,U_11401),U_11401) )
          | ! [U_11399] : hAPP(c_Set_Oimage(U_11403,U_11402,U_11399),U_11404) != U_11401 )
        & ( hAPP(c_Set_Oimage(U_11403,U_11402,sK203(U_11404,U_11403,U_11402,U_11401)),U_11404) = U_11401
          | ! [U_11397] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11397),U_11401)),U_11404))
              | ~ c_Fun_Oinj__on(U_11402,U_11403,U_11397,U_11401) ) ) )
      | U_11401 = c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_11400,sK204(U_11404,U_11403,U_11402,U_11401))],[f_3004_3]) ).

fof(f_3004_5,plain,
    ( ! [U_11401,U_11402,U_11403,U_11404] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,sK204(U_11404,U_11403,U_11402,U_11401)),U_11401)),U_11404))
        | ~ sP856(U_11401,U_11402,U_11403,U_11404) )
    & ! [U_11401,U_11402,U_11403,U_11404] :
        ( c_Fun_Oinj__on(U_11402,U_11403,sK204(U_11404,U_11403,U_11402,U_11401),U_11401)
        | ~ sP856(U_11401,U_11402,U_11403,U_11404) )
    & ! [U_11397,U_11399,U_11401,U_11402,U_11403,U_11404] :
        ( sP856(U_11401,U_11402,U_11403,U_11404)
        | hAPP(c_Set_Oimage(U_11403,U_11402,U_11399),U_11404) != U_11401
        | ~ sP857(U_11397,U_11399,U_11401,U_11402,U_11403,U_11404) )
    & ! [U_11397,U_11399,U_11401,U_11402,U_11403,U_11404] :
        ( hAPP(c_Set_Oimage(U_11403,U_11402,sK203(U_11404,U_11403,U_11402,U_11401)),U_11404) = U_11401
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11397),U_11401)),U_11404))
        | ~ c_Fun_Oinj__on(U_11402,U_11403,U_11397,U_11401)
        | ~ sP857(U_11397,U_11399,U_11401,U_11402,U_11403,U_11404) )
    & ! [U_11397,U_11399,U_11401,U_11402,U_11403,U_11404] :
        ( sP857(U_11397,U_11399,U_11401,U_11402,U_11403,U_11404)
        | U_11401 = c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP856,sP857])],[f_3004_4]) ).

cnf(f_3004_6,plain,
    ( sP857(U_11397,U_11399,U_11401,U_11402,U_11403,U_11404)
    | U_11401 = c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3004_5]) ).

cnf(f_3004_7,plain,
    ( hAPP(c_Set_Oimage(U_11403,U_11402,sK203(U_11404,U_11403,U_11402,U_11401)),U_11404) = U_11401
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,U_11397),U_11401)),U_11404))
    | ~ c_Fun_Oinj__on(U_11402,U_11403,U_11397,U_11401)
    | ~ sP857(U_11397,U_11399,U_11401,U_11402,U_11403,U_11404) ),
    inference(clausify,[status(thm)],[f_3004_5]) ).

cnf(f_3004_8,plain,
    ( sP856(U_11401,U_11402,U_11403,U_11404)
    | hAPP(c_Set_Oimage(U_11403,U_11402,U_11399),U_11404) != U_11401
    | ~ sP857(U_11397,U_11399,U_11401,U_11402,U_11403,U_11404) ),
    inference(clausify,[status(thm)],[f_3004_5]) ).

cnf(f_3004_9,plain,
    ( c_Fun_Oinj__on(U_11402,U_11403,sK204(U_11404,U_11403,U_11402,U_11401),U_11401)
    | ~ sP856(U_11401,U_11402,U_11403,U_11404) ),
    inference(clausify,[status(thm)],[f_3004_5]) ).

cnf(f_3004_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11403,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11402,U_11403,sK204(U_11404,U_11403,U_11402,U_11401)),U_11401)),U_11404))
    | ~ sP856(U_11401,U_11402,U_11403,U_11404) ),
    inference(clausify,[status(thm)],[f_3004_5]) ).

fof(f_3005_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
        | ? [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat__less]) ).

fof(f_3005_2,plain,
    ! [U_11410,U_11409] :
      ( ( ! [U_11408] :
            ( hBOOL(hAPP(U_11410,U_11408))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11408),U_11409)) )
        | ? [U_11407] :
            ( ~ hBOOL(hAPP(U_11410,U_11407))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11407),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11409))) ) )
      & ( ! [U_11406] :
            ( hBOOL(hAPP(U_11410,U_11406))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11409))) )
        | ? [U_11405] :
            ( ~ hBOOL(hAPP(U_11410,U_11405))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11405),U_11409)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3005_1]) ).

fof(f_3005_3,plain,
    ( ! [U_11414,U_11412] :
        ( ! [U_11408] :
            ( hBOOL(hAPP(U_11414,U_11408))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11408),U_11412)) )
        | ? [U_11407] :
            ( ~ hBOOL(hAPP(U_11414,U_11407))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11407),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11412))) ) )
    & ! [U_11413,U_11411] :
        ( ! [U_11406] :
            ( hBOOL(hAPP(U_11413,U_11406))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11411))) )
        | ? [U_11405] :
            ( ~ hBOOL(hAPP(U_11413,U_11405))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11405),U_11411)) ) ) ),
    inference(miniscope,[status(thm)],[f_3005_2]) ).

fof(f_3005_4,plain,
    ( ! [U_11414,U_11412] :
        ( ! [U_11408] :
            ( hBOOL(hAPP(U_11414,U_11408))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11408),U_11412)) )
        | ? [U_11407] :
            ( ~ hBOOL(hAPP(U_11414,U_11407))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11407),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11412))) ) )
    & ! [U_11413,U_11411] :
        ( ! [U_11406] :
            ( hBOOL(hAPP(U_11413,U_11406))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11411))) )
        | ( ~ hBOOL(hAPP(U_11413,sK205(U_11413,U_11411)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK205(U_11413,U_11411)),U_11411)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_11405,sK205(U_11413,U_11411))],[f_3005_3]) ).

fof(f_3005_5,plain,
    ( ! [U_11414,U_11412] :
        ( ! [U_11408] :
            ( hBOOL(hAPP(U_11414,U_11408))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11408),U_11412)) )
        | ( ~ hBOOL(hAPP(U_11414,sK206(U_11414,U_11412)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK206(U_11414,U_11412)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11412))) ) )
    & ! [U_11413,U_11411] :
        ( ! [U_11406] :
            ( hBOOL(hAPP(U_11413,U_11406))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11411))) )
        | ( ~ hBOOL(hAPP(U_11413,sK205(U_11413,U_11411)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK205(U_11413,U_11411)),U_11411)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_11407,sK206(U_11414,U_11412))],[f_3005_4]) ).

fof(f_3005_6,plain,
    ( ! [U_11414,U_11412] :
        ( ~ hBOOL(hAPP(U_11414,sK206(U_11414,U_11412)))
        | ~ sP859(U_11414,U_11412) )
    & ! [U_11414,U_11412] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK206(U_11414,U_11412)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11412)))
        | ~ sP859(U_11414,U_11412) )
    & ! [U_11411,U_11413] :
        ( ~ hBOOL(hAPP(U_11413,sK205(U_11413,U_11411)))
        | ~ sP858(U_11411,U_11413) )
    & ! [U_11411,U_11413] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK205(U_11413,U_11411)),U_11411))
        | ~ sP858(U_11411,U_11413) )
    & ! [U_11414,U_11412,U_11408] :
        ( hBOOL(hAPP(U_11414,U_11408))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11408),U_11412))
        | sP859(U_11414,U_11412) )
    & ! [U_11406,U_11411,U_11413] :
        ( hBOOL(hAPP(U_11413,U_11406))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11411)))
        | sP858(U_11411,U_11413) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP858,sP859])],[f_3005_5]) ).

cnf(f_3005_7,plain,
    ( hBOOL(hAPP(U_11413,U_11406))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11411)))
    | sP858(U_11411,U_11413) ),
    inference(clausify,[status(thm)],[f_3005_6]) ).

cnf(f_3005_8,plain,
    ( hBOOL(hAPP(U_11414,U_11408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11408),U_11412))
    | sP859(U_11414,U_11412) ),
    inference(clausify,[status(thm)],[f_3005_6]) ).

cnf(f_3005_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK205(U_11413,U_11411)),U_11411))
    | ~ sP858(U_11411,U_11413) ),
    inference(clausify,[status(thm)],[f_3005_6]) ).

cnf(f_3005_10,plain,
    ( ~ hBOOL(hAPP(U_11413,sK205(U_11413,U_11411)))
    | ~ sP858(U_11411,U_11413) ),
    inference(clausify,[status(thm)],[f_3005_6]) ).

cnf(f_3005_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK206(U_11414,U_11412)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11412)))
    | ~ sP859(U_11414,U_11412) ),
    inference(clausify,[status(thm)],[f_3005_6]) ).

cnf(f_3005_12,plain,
    ( ~ hBOOL(hAPP(U_11414,sK206(U_11414,U_11412)))
    | ~ sP859(U_11414,U_11412) ),
    inference(clausify,[status(thm)],[f_3005_6]) ).

fof(f_3006_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
        | ! [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat__less]) ).

fof(f_3006_2,plain,
    ! [U_11420,U_11419] :
      ( ( ? [U_11418] :
            ( hBOOL(hAPP(U_11420,U_11418))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11418),U_11419)) )
        | ! [U_11417] :
            ( ~ hBOOL(hAPP(U_11420,U_11417))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11419))) ) )
      & ( ? [U_11416] :
            ( hBOOL(hAPP(U_11420,U_11416))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11416),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11419))) )
        | ! [U_11415] :
            ( ~ hBOOL(hAPP(U_11420,U_11415))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11415),U_11419)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3006_1]) ).

fof(f_3006_3,plain,
    ( ! [U_11424,U_11422] :
        ( ? [U_11418] :
            ( hBOOL(hAPP(U_11424,U_11418))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11418),U_11422)) )
        | ! [U_11417] :
            ( ~ hBOOL(hAPP(U_11424,U_11417))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11422))) ) )
    & ! [U_11423,U_11421] :
        ( ? [U_11416] :
            ( hBOOL(hAPP(U_11423,U_11416))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11416),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11421))) )
        | ! [U_11415] :
            ( ~ hBOOL(hAPP(U_11423,U_11415))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11415),U_11421)) ) ) ),
    inference(miniscope,[status(thm)],[f_3006_2]) ).

fof(f_3006_4,plain,
    ( ! [U_11424,U_11422] :
        ( ? [U_11418] :
            ( hBOOL(hAPP(U_11424,U_11418))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11418),U_11422)) )
        | ! [U_11417] :
            ( ~ hBOOL(hAPP(U_11424,U_11417))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11422))) ) )
    & ! [U_11423,U_11421] :
        ( ( hBOOL(hAPP(U_11423,sK207(U_11423,U_11421)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK207(U_11423,U_11421)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11421))) )
        | ! [U_11415] :
            ( ~ hBOOL(hAPP(U_11423,U_11415))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11415),U_11421)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_11416,sK207(U_11423,U_11421))],[f_3006_3]) ).

fof(f_3006_5,plain,
    ( ! [U_11424,U_11422] :
        ( ( hBOOL(hAPP(U_11424,sK208(U_11424,U_11422)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK208(U_11424,U_11422)),U_11422)) )
        | ! [U_11417] :
            ( ~ hBOOL(hAPP(U_11424,U_11417))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11422))) ) )
    & ! [U_11423,U_11421] :
        ( ( hBOOL(hAPP(U_11423,sK207(U_11423,U_11421)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK207(U_11423,U_11421)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11421))) )
        | ! [U_11415] :
            ( ~ hBOOL(hAPP(U_11423,U_11415))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11415),U_11421)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_11418,sK208(U_11424,U_11422))],[f_3006_4]) ).

fof(f_3006_6,plain,
    ( ! [U_11424,U_11422] :
        ( hBOOL(hAPP(U_11424,sK208(U_11424,U_11422)))
        | ~ sP861(U_11424,U_11422) )
    & ! [U_11424,U_11422] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK208(U_11424,U_11422)),U_11422))
        | ~ sP861(U_11424,U_11422) )
    & ! [U_11421,U_11423] :
        ( hBOOL(hAPP(U_11423,sK207(U_11423,U_11421)))
        | ~ sP860(U_11421,U_11423) )
    & ! [U_11421,U_11423] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK207(U_11423,U_11421)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11421)))
        | ~ sP860(U_11421,U_11423) )
    & ! [U_11417,U_11424,U_11422] :
        ( sP861(U_11424,U_11422)
        | ~ hBOOL(hAPP(U_11424,U_11417))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11422))) )
    & ! [U_11415,U_11421,U_11423] :
        ( sP860(U_11421,U_11423)
        | ~ hBOOL(hAPP(U_11423,U_11415))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11415),U_11421)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP860,sP861])],[f_3006_5]) ).

cnf(f_3006_7,plain,
    ( sP860(U_11421,U_11423)
    | ~ hBOOL(hAPP(U_11423,U_11415))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11415),U_11421)) ),
    inference(clausify,[status(thm)],[f_3006_6]) ).

cnf(f_3006_8,plain,
    ( sP861(U_11424,U_11422)
    | ~ hBOOL(hAPP(U_11424,U_11417))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11422))) ),
    inference(clausify,[status(thm)],[f_3006_6]) ).

cnf(f_3006_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK207(U_11423,U_11421)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11421)))
    | ~ sP860(U_11421,U_11423) ),
    inference(clausify,[status(thm)],[f_3006_6]) ).

cnf(f_3006_10,plain,
    ( hBOOL(hAPP(U_11423,sK207(U_11423,U_11421)))
    | ~ sP860(U_11421,U_11423) ),
    inference(clausify,[status(thm)],[f_3006_6]) ).

cnf(f_3006_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK208(U_11424,U_11422)),U_11422))
    | ~ sP861(U_11424,U_11422) ),
    inference(clausify,[status(thm)],[f_3006_6]) ).

cnf(f_3006_12,plain,
    ( hBOOL(hAPP(U_11424,sK208(U_11424,U_11422)))
    | ~ sP861(U_11424,U_11422) ),
    inference(clausify,[status(thm)],[f_3006_6]) ).

fof(f_3007_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I6_J]) ).

fof(f_3007_2,plain,
    ! [U_11430,U_11429,U_11428] :
      ( ! [U_11427] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11427),U_11428)),U_11429))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11427),U_11429))
          | ? [U_11426] :
              ( ? [U_11425] :
                  ( U_11427 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11425),U_11426)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11425),U_11430)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11426),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11428))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11429),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11428)) ),
    inference(variable_rename,[status(thm)],[f_3007_1]) ).

fof(f_3007_3,plain,
    ! [U_11430,U_11429,U_11428] :
      ( ! [U_11427] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11427),U_11428)),U_11429))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11427),U_11429))
          | ( ? [U_11425] :
                ( U_11427 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11425),sK209(U_11430,U_11429,U_11428,U_11427))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11425),U_11430)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11430,U_11429,U_11428,U_11427)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11428))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11429),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11428)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_11426,sK209(U_11430,U_11429,U_11428,U_11427))],[f_3007_2]) ).

fof(f_3007_4,plain,
    ! [U_11430,U_11429,U_11428] :
      ( ! [U_11427] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11427),U_11428)),U_11429))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11427),U_11429))
          | ( U_11427 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK210(U_11430,U_11429,U_11428,U_11427)),sK209(U_11430,U_11429,U_11428,U_11427))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11430,U_11429,U_11428,U_11427)),U_11430))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11430,U_11429,U_11428,U_11427)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11428))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11429),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11428)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_11425,sK210(U_11430,U_11429,U_11428,U_11427))],[f_3007_3]) ).

fof(f_3007_5,plain,
    ( ! [U_11428,U_11427,U_11430,U_11429] :
        ( U_11427 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK210(U_11430,U_11429,U_11428,U_11427)),sK209(U_11430,U_11429,U_11428,U_11427))
        | ~ sP862(U_11428,U_11427,U_11430,U_11429) )
    & ! [U_11428,U_11427,U_11430,U_11429] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11430,U_11429,U_11428,U_11427)),U_11430))
        | ~ sP862(U_11428,U_11427,U_11430,U_11429) )
    & ! [U_11428,U_11427,U_11430,U_11429] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11430,U_11429,U_11428,U_11427)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11428)))
        | ~ sP862(U_11428,U_11427,U_11430,U_11429) )
    & ! [U_11428,U_11427,U_11430,U_11429] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11427),U_11428)),U_11429))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11427),U_11429))
        | sP862(U_11428,U_11427,U_11430,U_11429)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11429),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11430))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11428)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP862])],[f_3007_4]) ).

cnf(f_3007_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11427),U_11428)),U_11429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11427),U_11429))
    | sP862(U_11428,U_11427,U_11430,U_11429)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11429),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11430))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11428)) ),
    inference(clausify,[status(thm)],[f_3007_5]) ).

cnf(f_3007_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11430,U_11429,U_11428,U_11427)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11428)))
    | ~ sP862(U_11428,U_11427,U_11430,U_11429) ),
    inference(clausify,[status(thm)],[f_3007_5]) ).

cnf(f_3007_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11430,U_11429,U_11428,U_11427)),U_11430))
    | ~ sP862(U_11428,U_11427,U_11430,U_11429) ),
    inference(clausify,[status(thm)],[f_3007_5]) ).

cnf(f_3007_9,plain,
    ( U_11427 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK210(U_11430,U_11429,U_11428,U_11427)),sK209(U_11430,U_11429,U_11428,U_11427))
    | ~ sP862(U_11428,U_11427,U_11430,U_11429) ),
    inference(clausify,[status(thm)],[f_3007_5]) ).

fof(f_3008_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I8_J]) ).

fof(f_3008_2,plain,
    ! [U_11436,U_11435,U_11434] :
      ( ! [U_11433] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11433),U_11434)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),U_11433))
          | ? [U_11432] :
              ( ? [U_11431] :
                  ( U_11433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11431),U_11432)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11431),U_11436)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11432),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11434))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11435),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11434)) ),
    inference(variable_rename,[status(thm)],[f_3008_1]) ).

fof(f_3008_3,plain,
    ! [U_11436,U_11435,U_11434] :
      ( ! [U_11433] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11433),U_11434)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),U_11433))
          | ( ? [U_11431] :
                ( U_11433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11431),sK211(U_11436,U_11435,U_11434,U_11433))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11431),U_11436)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11436,U_11435,U_11434,U_11433)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11434))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11435),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11434)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_11432,sK211(U_11436,U_11435,U_11434,U_11433))],[f_3008_2]) ).

fof(f_3008_4,plain,
    ! [U_11436,U_11435,U_11434] :
      ( ! [U_11433] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11433),U_11434)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),U_11433))
          | ( U_11433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK212(U_11436,U_11435,U_11434,U_11433)),sK211(U_11436,U_11435,U_11434,U_11433))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK212(U_11436,U_11435,U_11434,U_11433)),U_11436))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11436,U_11435,U_11434,U_11433)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11434))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11435),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11434)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_11431,sK212(U_11436,U_11435,U_11434,U_11433))],[f_3008_3]) ).

fof(f_3008_5,plain,
    ( ! [U_11433,U_11434,U_11435,U_11436] :
        ( U_11433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK212(U_11436,U_11435,U_11434,U_11433)),sK211(U_11436,U_11435,U_11434,U_11433))
        | ~ sP863(U_11433,U_11434,U_11435,U_11436) )
    & ! [U_11433,U_11434,U_11435,U_11436] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK212(U_11436,U_11435,U_11434,U_11433)),U_11436))
        | ~ sP863(U_11433,U_11434,U_11435,U_11436) )
    & ! [U_11433,U_11434,U_11435,U_11436] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11436,U_11435,U_11434,U_11433)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11434)))
        | ~ sP863(U_11433,U_11434,U_11435,U_11436) )
    & ! [U_11433,U_11434,U_11435,U_11436] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11433),U_11434)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),U_11433))
        | sP863(U_11433,U_11434,U_11435,U_11436)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11435),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11436))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11434)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP863])],[f_3008_4]) ).

cnf(f_3008_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11433),U_11434)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11435),U_11433))
    | sP863(U_11433,U_11434,U_11435,U_11436)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11435),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11436))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11434)) ),
    inference(clausify,[status(thm)],[f_3008_5]) ).

cnf(f_3008_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11436,U_11435,U_11434,U_11433)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11434)))
    | ~ sP863(U_11433,U_11434,U_11435,U_11436) ),
    inference(clausify,[status(thm)],[f_3008_5]) ).

cnf(f_3008_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK212(U_11436,U_11435,U_11434,U_11433)),U_11436))
    | ~ sP863(U_11433,U_11434,U_11435,U_11436) ),
    inference(clausify,[status(thm)],[f_3008_5]) ).

cnf(f_3008_9,plain,
    ( U_11433 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK212(U_11436,U_11435,U_11434,U_11433)),sK211(U_11436,U_11435,U_11434,U_11433))
    | ~ sP863(U_11433,U_11434,U_11435,U_11436) ),
    inference(clausify,[status(thm)],[f_3008_5]) ).

fof(f_3009_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2
      | ? [B_x] :
          ( ? [B_xa] :
              ( V_t_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I3_J]) ).

fof(f_3009_2,plain,
    ! [U_11441,U_11440,U_11439] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),U_11439) = U_11440
      | ? [U_11438] :
          ( ? [U_11437] :
              ( U_11440 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11437),U_11438)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11437),U_11441)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11438),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11439))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11439)) ),
    inference(variable_rename,[status(thm)],[f_3009_1]) ).

fof(f_3009_3,plain,
    ! [U_11441,U_11440,U_11439] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),U_11439) = U_11440
      | ( ? [U_11437] :
            ( U_11440 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11437),sK213(U_11441,U_11440,U_11439))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11437),U_11441)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_11441,U_11440,U_11439)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11439))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11439)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_11438,sK213(U_11441,U_11440,U_11439))],[f_3009_2]) ).

fof(f_3009_4,plain,
    ! [U_11441,U_11440,U_11439] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),U_11439) = U_11440
      | ( U_11440 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK214(U_11441,U_11440,U_11439)),sK213(U_11441,U_11440,U_11439))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK214(U_11441,U_11440,U_11439)),U_11441))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_11441,U_11440,U_11439)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11439))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11439)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_11437,sK214(U_11441,U_11440,U_11439))],[f_3009_3]) ).

fof(f_3009_5,plain,
    ( ! [U_11440,U_11441,U_11439] :
        ( U_11440 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK214(U_11441,U_11440,U_11439)),sK213(U_11441,U_11440,U_11439))
        | ~ sP864(U_11440,U_11441,U_11439) )
    & ! [U_11440,U_11441,U_11439] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK214(U_11441,U_11440,U_11439)),U_11441))
        | ~ sP864(U_11440,U_11441,U_11439) )
    & ! [U_11440,U_11441,U_11439] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_11441,U_11440,U_11439)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11439)))
        | ~ sP864(U_11440,U_11441,U_11439) )
    & ! [U_11440,U_11441,U_11439] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),U_11439) = U_11440
        | sP864(U_11440,U_11441,U_11439)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11441))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11439)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP864])],[f_3009_4]) ).

cnf(f_3009_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),U_11439) = U_11440
    | sP864(U_11440,U_11441,U_11439)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11440),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11439)) ),
    inference(clausify,[status(thm)],[f_3009_5]) ).

cnf(f_3009_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_11441,U_11440,U_11439)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11439)))
    | ~ sP864(U_11440,U_11441,U_11439) ),
    inference(clausify,[status(thm)],[f_3009_5]) ).

cnf(f_3009_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK214(U_11441,U_11440,U_11439)),U_11441))
    | ~ sP864(U_11440,U_11441,U_11439) ),
    inference(clausify,[status(thm)],[f_3009_5]) ).

cnf(f_3009_9,plain,
    ( U_11440 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK214(U_11441,U_11440,U_11439)),sK213(U_11441,U_11440,U_11439))
    | ~ sP864(U_11440,U_11441,U_11439) ),
    inference(clausify,[status(thm)],[f_3009_5]) ).

fof(f_3010_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2
          | B_x = V_t_2
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I4_J]) ).

fof(f_3010_2,plain,
    ! [U_11447,U_11446,U_11445] :
      ( ! [U_11444] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11444),U_11445) != U_11446
          | U_11444 = U_11446
          | ? [U_11443] :
              ( ? [U_11442] :
                  ( U_11444 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11442),U_11443)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11442),U_11447)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11443),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11445))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11446),U_11447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11445)) ),
    inference(variable_rename,[status(thm)],[f_3010_1]) ).

fof(f_3010_3,plain,
    ! [U_11447,U_11446,U_11445] :
      ( ! [U_11444] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11444),U_11445) != U_11446
          | U_11444 = U_11446
          | ( ? [U_11442] :
                ( U_11444 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11442),sK215(U_11447,U_11446,U_11445,U_11444))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11442),U_11447)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_11447,U_11446,U_11445,U_11444)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11445))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11446),U_11447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11445)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_11443,sK215(U_11447,U_11446,U_11445,U_11444))],[f_3010_2]) ).

fof(f_3010_4,plain,
    ! [U_11447,U_11446,U_11445] :
      ( ! [U_11444] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11444),U_11445) != U_11446
          | U_11444 = U_11446
          | ( U_11444 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK216(U_11447,U_11446,U_11445,U_11444)),sK215(U_11447,U_11446,U_11445,U_11444))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11447,U_11446,U_11445,U_11444)),U_11447))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_11447,U_11446,U_11445,U_11444)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11445))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11446),U_11447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11445)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_11442,sK216(U_11447,U_11446,U_11445,U_11444))],[f_3010_3]) ).

fof(f_3010_5,plain,
    ( ! [U_11445,U_11446,U_11444,U_11447] :
        ( U_11444 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK216(U_11447,U_11446,U_11445,U_11444)),sK215(U_11447,U_11446,U_11445,U_11444))
        | ~ sP865(U_11445,U_11446,U_11444,U_11447) )
    & ! [U_11445,U_11446,U_11444,U_11447] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11447,U_11446,U_11445,U_11444)),U_11447))
        | ~ sP865(U_11445,U_11446,U_11444,U_11447) )
    & ! [U_11445,U_11446,U_11444,U_11447] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_11447,U_11446,U_11445,U_11444)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11445)))
        | ~ sP865(U_11445,U_11446,U_11444,U_11447) )
    & ! [U_11445,U_11446,U_11444,U_11447] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11444),U_11445) != U_11446
        | U_11444 = U_11446
        | sP865(U_11445,U_11446,U_11444,U_11447)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11446),U_11447))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11445)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP865])],[f_3010_4]) ).

cnf(f_3010_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11444),U_11445) != U_11446
    | U_11444 = U_11446
    | sP865(U_11445,U_11446,U_11444,U_11447)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11446),U_11447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11445)) ),
    inference(clausify,[status(thm)],[f_3010_5]) ).

cnf(f_3010_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_11447,U_11446,U_11445,U_11444)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11445)))
    | ~ sP865(U_11445,U_11446,U_11444,U_11447) ),
    inference(clausify,[status(thm)],[f_3010_5]) ).

cnf(f_3010_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11447,U_11446,U_11445,U_11444)),U_11447))
    | ~ sP865(U_11445,U_11446,U_11444,U_11447) ),
    inference(clausify,[status(thm)],[f_3010_5]) ).

cnf(f_3010_9,plain,
    ( U_11444 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK216(U_11447,U_11446,U_11445,U_11444)),sK215(U_11447,U_11446,U_11445,U_11444))
    | ~ sP865(U_11445,U_11446,U_11444,U_11447) ),
    inference(clausify,[status(thm)],[f_3010_5]) ).

fof(f_3011_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2
          | B_x = V_t_2
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I4_J]) ).

fof(f_3011_2,plain,
    ! [U_11453,U_11452,U_11451] :
      ( ! [U_11450] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11450),U_11451) != U_11452
          | U_11450 = U_11452
          | ? [U_11449] :
              ( ? [U_11448] :
                  ( U_11450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11448),U_11449)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11448),U_11453)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11449),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11451))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11452),U_11453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11451)) ),
    inference(variable_rename,[status(thm)],[f_3011_1]) ).

fof(f_3011_3,plain,
    ! [U_11453,U_11452,U_11451] :
      ( ! [U_11450] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11450),U_11451) != U_11452
          | U_11450 = U_11452
          | ( ? [U_11448] :
                ( U_11450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11448),sK217(U_11453,U_11452,U_11451,U_11450))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11448),U_11453)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11453,U_11452,U_11451,U_11450)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11451))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11452),U_11453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11451)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_11449,sK217(U_11453,U_11452,U_11451,U_11450))],[f_3011_2]) ).

fof(f_3011_4,plain,
    ! [U_11453,U_11452,U_11451] :
      ( ! [U_11450] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11450),U_11451) != U_11452
          | U_11450 = U_11452
          | ( U_11450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK218(U_11453,U_11452,U_11451,U_11450)),sK217(U_11453,U_11452,U_11451,U_11450))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11453,U_11452,U_11451,U_11450)),U_11453))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11453,U_11452,U_11451,U_11450)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11451))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11452),U_11453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11451)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_11448,sK218(U_11453,U_11452,U_11451,U_11450))],[f_3011_3]) ).

fof(f_3011_5,plain,
    ( ! [U_11451,U_11452,U_11453,U_11450] :
        ( U_11450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK218(U_11453,U_11452,U_11451,U_11450)),sK217(U_11453,U_11452,U_11451,U_11450))
        | ~ sP866(U_11451,U_11452,U_11453,U_11450) )
    & ! [U_11451,U_11452,U_11453,U_11450] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11453,U_11452,U_11451,U_11450)),U_11453))
        | ~ sP866(U_11451,U_11452,U_11453,U_11450) )
    & ! [U_11451,U_11452,U_11453,U_11450] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11453,U_11452,U_11451,U_11450)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11451)))
        | ~ sP866(U_11451,U_11452,U_11453,U_11450) )
    & ! [U_11451,U_11452,U_11453,U_11450] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11450),U_11451) != U_11452
        | U_11450 = U_11452
        | sP866(U_11451,U_11452,U_11453,U_11450)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11452),U_11453))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11451)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP866])],[f_3011_4]) ).

cnf(f_3011_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11450),U_11451) != U_11452
    | U_11450 = U_11452
    | sP866(U_11451,U_11452,U_11453,U_11450)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11452),U_11453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11451)) ),
    inference(clausify,[status(thm)],[f_3011_5]) ).

cnf(f_3011_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11453,U_11452,U_11451,U_11450)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11451)))
    | ~ sP866(U_11451,U_11452,U_11453,U_11450) ),
    inference(clausify,[status(thm)],[f_3011_5]) ).

cnf(f_3011_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11453,U_11452,U_11451,U_11450)),U_11453))
    | ~ sP866(U_11451,U_11452,U_11453,U_11450) ),
    inference(clausify,[status(thm)],[f_3011_5]) ).

cnf(f_3011_9,plain,
    ( U_11450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK218(U_11453,U_11452,U_11451,U_11450)),sK217(U_11453,U_11452,U_11451,U_11450))
    | ~ sP866(U_11451,U_11452,U_11453,U_11450) ),
    inference(clausify,[status(thm)],[f_3011_5]) ).

fof(f_3012_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I7_J]) ).

fof(f_3012_2,plain,
    ! [U_11459,U_11458,U_11457] :
      ( ! [U_11456] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11456),U_11457)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),U_11456))
          | ? [U_11455] :
              ( ? [U_11454] :
                  ( U_11456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11454),U_11455)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11454),U_11459)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11455),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11457))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11458),U_11459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11457)) ),
    inference(variable_rename,[status(thm)],[f_3012_1]) ).

fof(f_3012_3,plain,
    ! [U_11459,U_11458,U_11457] :
      ( ! [U_11456] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11456),U_11457)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),U_11456))
          | ( ? [U_11454] :
                ( U_11456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11454),sK219(U_11459,U_11458,U_11457,U_11456))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11454),U_11459)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11459,U_11458,U_11457,U_11456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11457))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11458),U_11459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11457)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_11455,sK219(U_11459,U_11458,U_11457,U_11456))],[f_3012_2]) ).

fof(f_3012_4,plain,
    ! [U_11459,U_11458,U_11457] :
      ( ! [U_11456] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11456),U_11457)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),U_11456))
          | ( U_11456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK220(U_11459,U_11458,U_11457,U_11456)),sK219(U_11459,U_11458,U_11457,U_11456))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11459,U_11458,U_11457,U_11456)),U_11459))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11459,U_11458,U_11457,U_11456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11457))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11458),U_11459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11457)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_11454,sK220(U_11459,U_11458,U_11457,U_11456))],[f_3012_3]) ).

fof(f_3012_5,plain,
    ( ! [U_11456,U_11457,U_11458,U_11459] :
        ( U_11456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK220(U_11459,U_11458,U_11457,U_11456)),sK219(U_11459,U_11458,U_11457,U_11456))
        | ~ sP867(U_11456,U_11457,U_11458,U_11459) )
    & ! [U_11456,U_11457,U_11458,U_11459] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11459,U_11458,U_11457,U_11456)),U_11459))
        | ~ sP867(U_11456,U_11457,U_11458,U_11459) )
    & ! [U_11456,U_11457,U_11458,U_11459] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11459,U_11458,U_11457,U_11456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11457)))
        | ~ sP867(U_11456,U_11457,U_11458,U_11459) )
    & ! [U_11456,U_11457,U_11458,U_11459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11456),U_11457)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),U_11456))
        | sP867(U_11456,U_11457,U_11458,U_11459)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11458),U_11459))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11457)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP867])],[f_3012_4]) ).

cnf(f_3012_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11456),U_11457)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11458),U_11456))
    | sP867(U_11456,U_11457,U_11458,U_11459)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11458),U_11459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11457)) ),
    inference(clausify,[status(thm)],[f_3012_5]) ).

cnf(f_3012_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11459,U_11458,U_11457,U_11456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11457)))
    | ~ sP867(U_11456,U_11457,U_11458,U_11459) ),
    inference(clausify,[status(thm)],[f_3012_5]) ).

cnf(f_3012_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11459,U_11458,U_11457,U_11456)),U_11459))
    | ~ sP867(U_11456,U_11457,U_11458,U_11459) ),
    inference(clausify,[status(thm)],[f_3012_5]) ).

cnf(f_3012_9,plain,
    ( U_11456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK220(U_11459,U_11458,U_11457,U_11456)),sK219(U_11459,U_11458,U_11457,U_11456))
    | ~ sP867(U_11456,U_11457,U_11458,U_11459) ),
    inference(clausify,[status(thm)],[f_3012_5]) ).

fof(f_3013_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2
      | ? [B_x] :
          ( ? [B_xa] :
              ( V_t_2 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I3_J]) ).

fof(f_3013_2,plain,
    ! [U_11464,U_11463,U_11462] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),U_11462) = U_11463
      | ? [U_11461] :
          ( ? [U_11460] :
              ( U_11463 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11460),U_11461)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11460),U_11464)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11461),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11462))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11462)) ),
    inference(variable_rename,[status(thm)],[f_3013_1]) ).

fof(f_3013_3,plain,
    ! [U_11464,U_11463,U_11462] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),U_11462) = U_11463
      | ( ? [U_11460] :
            ( U_11463 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11460),sK221(U_11464,U_11463,U_11462))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11460),U_11464)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11464,U_11463,U_11462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11462))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11462)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_11461,sK221(U_11464,U_11463,U_11462))],[f_3013_2]) ).

fof(f_3013_4,plain,
    ! [U_11464,U_11463,U_11462] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),U_11462) = U_11463
      | ( U_11463 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK222(U_11464,U_11463,U_11462)),sK221(U_11464,U_11463,U_11462))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11464,U_11463,U_11462)),U_11464))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11464,U_11463,U_11462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11462))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11462)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_11460,sK222(U_11464,U_11463,U_11462))],[f_3013_3]) ).

fof(f_3013_5,plain,
    ( ! [U_11463,U_11464,U_11462] :
        ( U_11463 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK222(U_11464,U_11463,U_11462)),sK221(U_11464,U_11463,U_11462))
        | ~ sP868(U_11463,U_11464,U_11462) )
    & ! [U_11463,U_11464,U_11462] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11464,U_11463,U_11462)),U_11464))
        | ~ sP868(U_11463,U_11464,U_11462) )
    & ! [U_11463,U_11464,U_11462] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11464,U_11463,U_11462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11462)))
        | ~ sP868(U_11463,U_11464,U_11462) )
    & ! [U_11463,U_11464,U_11462] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),U_11462) = U_11463
        | sP868(U_11463,U_11464,U_11462)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11462)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP868])],[f_3013_4]) ).

cnf(f_3013_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),U_11462) = U_11463
    | sP868(U_11463,U_11464,U_11462)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11463),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11462)) ),
    inference(clausify,[status(thm)],[f_3013_5]) ).

cnf(f_3013_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11464,U_11463,U_11462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11462)))
    | ~ sP868(U_11463,U_11464,U_11462) ),
    inference(clausify,[status(thm)],[f_3013_5]) ).

cnf(f_3013_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11464,U_11463,U_11462)),U_11464))
    | ~ sP868(U_11463,U_11464,U_11462) ),
    inference(clausify,[status(thm)],[f_3013_5]) ).

cnf(f_3013_9,plain,
    ( U_11463 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK222(U_11464,U_11463,U_11462)),sK221(U_11464,U_11463,U_11462))
    | ~ sP868(U_11463,U_11464,U_11462) ),
    inference(clausify,[status(thm)],[f_3013_5]) ).

fof(f_3014_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I5_J]) ).

fof(f_3014_2,plain,
    ! [U_11470,U_11469,U_11468] :
      ( ! [U_11467] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11467),U_11468)),U_11469))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11467),U_11469))
          | ? [U_11466] :
              ( ? [U_11465] :
                  ( U_11467 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11465),U_11466)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11465),U_11470)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11466),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11468))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11469),U_11470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11468)) ),
    inference(variable_rename,[status(thm)],[f_3014_1]) ).

fof(f_3014_3,plain,
    ! [U_11470,U_11469,U_11468] :
      ( ! [U_11467] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11467),U_11468)),U_11469))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11467),U_11469))
          | ( ? [U_11465] :
                ( U_11467 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11465),sK223(U_11470,U_11469,U_11468,U_11467))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11465),U_11470)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11470,U_11469,U_11468,U_11467)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11468))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11469),U_11470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11468)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_11466,sK223(U_11470,U_11469,U_11468,U_11467))],[f_3014_2]) ).

fof(f_3014_4,plain,
    ! [U_11470,U_11469,U_11468] :
      ( ! [U_11467] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11467),U_11468)),U_11469))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11467),U_11469))
          | ( U_11467 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK224(U_11470,U_11469,U_11468,U_11467)),sK223(U_11470,U_11469,U_11468,U_11467))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11470,U_11469,U_11468,U_11467)),U_11470))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11470,U_11469,U_11468,U_11467)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11468))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11469),U_11470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11468)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_11465,sK224(U_11470,U_11469,U_11468,U_11467))],[f_3014_3]) ).

fof(f_3014_5,plain,
    ( ! [U_11467,U_11468,U_11469,U_11470] :
        ( U_11467 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK224(U_11470,U_11469,U_11468,U_11467)),sK223(U_11470,U_11469,U_11468,U_11467))
        | ~ sP869(U_11467,U_11468,U_11469,U_11470) )
    & ! [U_11467,U_11468,U_11469,U_11470] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11470,U_11469,U_11468,U_11467)),U_11470))
        | ~ sP869(U_11467,U_11468,U_11469,U_11470) )
    & ! [U_11467,U_11468,U_11469,U_11470] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11470,U_11469,U_11468,U_11467)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11468)))
        | ~ sP869(U_11467,U_11468,U_11469,U_11470) )
    & ! [U_11467,U_11468,U_11469,U_11470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11467),U_11468)),U_11469))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11467),U_11469))
        | sP869(U_11467,U_11468,U_11469,U_11470)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11469),U_11470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11468)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP869])],[f_3014_4]) ).

cnf(f_3014_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11467),U_11468)),U_11469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11467),U_11469))
    | sP869(U_11467,U_11468,U_11469,U_11470)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11469),U_11470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11468)) ),
    inference(clausify,[status(thm)],[f_3014_5]) ).

cnf(f_3014_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11470,U_11469,U_11468,U_11467)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11468)))
    | ~ sP869(U_11467,U_11468,U_11469,U_11470) ),
    inference(clausify,[status(thm)],[f_3014_5]) ).

cnf(f_3014_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11470,U_11469,U_11468,U_11467)),U_11470))
    | ~ sP869(U_11467,U_11468,U_11469,U_11470) ),
    inference(clausify,[status(thm)],[f_3014_5]) ).

cnf(f_3014_9,plain,
    ( U_11467 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK224(U_11470,U_11469,U_11468,U_11467)),sK223(U_11470,U_11469,U_11468,U_11467))
    | ~ sP869(U_11467,U_11468,U_11469,U_11470) ),
    inference(clausify,[status(thm)],[f_3014_5]) ).

fof(f_3015_1,plain,
    ! [V_t_2,V_B_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I6_J]) ).

fof(f_3015_2,plain,
    ! [U_11476,U_11475,U_11474] :
      ( ! [U_11473] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11473),U_11474)),U_11476))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11473),U_11476))
          | ? [U_11472] :
              ( ? [U_11471] :
                  ( U_11473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11471),U_11472)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11471),U_11475)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11472),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11474))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11474)) ),
    inference(variable_rename,[status(thm)],[f_3015_1]) ).

fof(f_3015_3,plain,
    ! [U_11476,U_11475,U_11474] :
      ( ! [U_11473] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11473),U_11474)),U_11476))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11473),U_11476))
          | ( ? [U_11471] :
                ( U_11473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11471),sK225(U_11476,U_11475,U_11474,U_11473))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11471),U_11475)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11476,U_11475,U_11474,U_11473)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11474))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11474)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_11472,sK225(U_11476,U_11475,U_11474,U_11473))],[f_3015_2]) ).

fof(f_3015_4,plain,
    ! [U_11476,U_11475,U_11474] :
      ( ! [U_11473] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11473),U_11474)),U_11476))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11473),U_11476))
          | ( U_11473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK226(U_11476,U_11475,U_11474,U_11473)),sK225(U_11476,U_11475,U_11474,U_11473))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11476,U_11475,U_11474,U_11473)),U_11475))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11476,U_11475,U_11474,U_11473)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11474))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11474)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_11471,sK226(U_11476,U_11475,U_11474,U_11473))],[f_3015_3]) ).

fof(f_3015_5,plain,
    ( ! [U_11474,U_11476,U_11473,U_11475] :
        ( U_11473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK226(U_11476,U_11475,U_11474,U_11473)),sK225(U_11476,U_11475,U_11474,U_11473))
        | ~ sP870(U_11474,U_11476,U_11473,U_11475) )
    & ! [U_11474,U_11476,U_11473,U_11475] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11476,U_11475,U_11474,U_11473)),U_11475))
        | ~ sP870(U_11474,U_11476,U_11473,U_11475) )
    & ! [U_11474,U_11476,U_11473,U_11475] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11476,U_11475,U_11474,U_11473)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11474)))
        | ~ sP870(U_11474,U_11476,U_11473,U_11475) )
    & ! [U_11474,U_11476,U_11473,U_11475] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11473),U_11474)),U_11476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11473),U_11476))
        | sP870(U_11474,U_11476,U_11473,U_11475)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11474)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP870])],[f_3015_4]) ).

cnf(f_3015_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11473),U_11474)),U_11476))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11473),U_11476))
    | sP870(U_11474,U_11476,U_11473,U_11475)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11474)) ),
    inference(clausify,[status(thm)],[f_3015_5]) ).

cnf(f_3015_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11476,U_11475,U_11474,U_11473)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11474)))
    | ~ sP870(U_11474,U_11476,U_11473,U_11475) ),
    inference(clausify,[status(thm)],[f_3015_5]) ).

cnf(f_3015_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11476,U_11475,U_11474,U_11473)),U_11475))
    | ~ sP870(U_11474,U_11476,U_11473,U_11475) ),
    inference(clausify,[status(thm)],[f_3015_5]) ).

cnf(f_3015_9,plain,
    ( U_11473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK226(U_11476,U_11475,U_11474,U_11473)),sK225(U_11476,U_11475,U_11474,U_11473))
    | ~ sP870(U_11474,U_11476,U_11473,U_11475) ),
    inference(clausify,[status(thm)],[f_3015_5]) ).

fof(f_3016_1,plain,
    ! [V_t_2,V_A_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I8_J]) ).

fof(f_3016_2,plain,
    ! [U_11482,U_11481,U_11480] :
      ( ! [U_11479] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11479),U_11480)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),U_11479))
          | ? [U_11478] :
              ( ? [U_11477] :
                  ( U_11479 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11477),U_11478)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11477),U_11481)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11478),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11480))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11480)) ),
    inference(variable_rename,[status(thm)],[f_3016_1]) ).

fof(f_3016_3,plain,
    ! [U_11482,U_11481,U_11480] :
      ( ! [U_11479] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11479),U_11480)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),U_11479))
          | ( ? [U_11477] :
                ( U_11479 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11477),sK227(U_11482,U_11481,U_11480,U_11479))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11477),U_11481)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11482,U_11481,U_11480,U_11479)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11480))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11480)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_11478,sK227(U_11482,U_11481,U_11480,U_11479))],[f_3016_2]) ).

fof(f_3016_4,plain,
    ! [U_11482,U_11481,U_11480] :
      ( ! [U_11479] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11479),U_11480)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),U_11479))
          | ( U_11479 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK228(U_11482,U_11481,U_11480,U_11479)),sK227(U_11482,U_11481,U_11480,U_11479))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11482,U_11481,U_11480,U_11479)),U_11481))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11482,U_11481,U_11480,U_11479)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11480))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11480)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_11477,sK228(U_11482,U_11481,U_11480,U_11479))],[f_3016_3]) ).

fof(f_3016_5,plain,
    ( ! [U_11481,U_11482,U_11479,U_11480] :
        ( U_11479 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK228(U_11482,U_11481,U_11480,U_11479)),sK227(U_11482,U_11481,U_11480,U_11479))
        | ~ sP871(U_11481,U_11482,U_11479,U_11480) )
    & ! [U_11481,U_11482,U_11479,U_11480] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11482,U_11481,U_11480,U_11479)),U_11481))
        | ~ sP871(U_11481,U_11482,U_11479,U_11480) )
    & ! [U_11481,U_11482,U_11479,U_11480] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11482,U_11481,U_11480,U_11479)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11480)))
        | ~ sP871(U_11481,U_11482,U_11479,U_11480) )
    & ! [U_11481,U_11482,U_11479,U_11480] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11479),U_11480)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),U_11479))
        | sP871(U_11481,U_11482,U_11479,U_11480)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11480)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP871])],[f_3016_4]) ).

cnf(f_3016_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11479),U_11480)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11482),U_11479))
    | sP871(U_11481,U_11482,U_11479,U_11480)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11480)) ),
    inference(clausify,[status(thm)],[f_3016_5]) ).

cnf(f_3016_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11482,U_11481,U_11480,U_11479)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11480)))
    | ~ sP871(U_11481,U_11482,U_11479,U_11480) ),
    inference(clausify,[status(thm)],[f_3016_5]) ).

cnf(f_3016_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11482,U_11481,U_11480,U_11479)),U_11481))
    | ~ sP871(U_11481,U_11482,U_11479,U_11480) ),
    inference(clausify,[status(thm)],[f_3016_5]) ).

cnf(f_3016_9,plain,
    ( U_11479 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK228(U_11482,U_11481,U_11480,U_11479)),sK227(U_11482,U_11481,U_11480,U_11479))
    | ~ sP871(U_11481,U_11482,U_11479,U_11480) ),
    inference(clausify,[status(thm)],[f_3016_5]) ).

fof(f_3017_1,plain,
    ! [V_P_2,V_d_2] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) )
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ? [B_x,B_k] :
          ( ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
          | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2))))
            & hBOOL(hAPP(V_P_2,B_x)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex]) ).

fof(f_3017_2,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ? [U_11486] :
              ( hBOOL(hAPP(U_11490,U_11486))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ? [U_11484,U_11483] :
          ( ( ~ hBOOL(hAPP(U_11490,U_11484))
            & hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11483),U_11489)))) )
          | ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11483),U_11489))))
            & hBOOL(hAPP(U_11490,U_11484)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(variable_rename,[status(thm)],[f_3017_1]) ).

fof(f_3017_3,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ? [U_11486] :
              ( hBOOL(hAPP(U_11490,U_11486))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ? [U_11494] :
          ( ? [U_11492] : hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11492),U_11489))))
          & ~ hBOOL(hAPP(U_11490,U_11494)) )
      | ? [U_11493] :
          ( ? [U_11491] : ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11491),U_11489))))
          & hBOOL(hAPP(U_11490,U_11493)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(miniscope,[status(thm)],[f_3017_2]) ).

fof(f_3017_4,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ? [U_11486] :
              ( hBOOL(hAPP(U_11490,U_11486))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ? [U_11494] :
          ( ? [U_11492] : hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11492),U_11489))))
          & ~ hBOOL(hAPP(U_11490,U_11494)) )
      | ( ? [U_11491] : ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11491),U_11489))))
        & hBOOL(hAPP(U_11490,sK229(U_11490,U_11489))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_11493,sK229(U_11490,U_11489))],[f_3017_3]) ).

fof(f_3017_5,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ? [U_11486] :
              ( hBOOL(hAPP(U_11490,U_11486))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ? [U_11494] :
          ( ? [U_11492] : hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11492),U_11489))))
          & ~ hBOOL(hAPP(U_11490,U_11494)) )
      | ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
        & hBOOL(hAPP(U_11490,sK229(U_11490,U_11489))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_11491,sK230(U_11490,U_11489))],[f_3017_4]) ).

fof(f_3017_6,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ? [U_11486] :
              ( hBOOL(hAPP(U_11490,U_11486))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ( ? [U_11492] : hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11492),U_11489))))
        & ~ hBOOL(hAPP(U_11490,sK231(U_11490,U_11489))) )
      | ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
        & hBOOL(hAPP(U_11490,sK229(U_11490,U_11489))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_11494,sK231(U_11490,U_11489))],[f_3017_5]) ).

fof(f_3017_7,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ? [U_11486] :
              ( hBOOL(hAPP(U_11490,U_11486))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ( hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK232(U_11490,U_11489)),U_11489))))
        & ~ hBOOL(hAPP(U_11490,sK231(U_11490,U_11489))) )
      | ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
        & hBOOL(hAPP(U_11490,sK229(U_11490,U_11489))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_11492,sK232(U_11490,U_11489))],[f_3017_6]) ).

fof(f_3017_8,plain,
    ! [U_11490,U_11489] :
      ( ( ( ? [U_11488] : hBOOL(hAPP(U_11490,U_11488))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ( hBOOL(hAPP(U_11490,sK233(U_11490,U_11489)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11490,U_11489)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ( hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK232(U_11490,U_11489)),U_11489))))
        & ~ hBOOL(hAPP(U_11490,sK231(U_11490,U_11489))) )
      | ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
        & hBOOL(hAPP(U_11490,sK229(U_11490,U_11489))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_11486,sK233(U_11490,U_11489))],[f_3017_7]) ).

fof(f_3017_9,plain,
    ! [U_11490,U_11489] :
      ( ( ( hBOOL(hAPP(U_11490,sK234(U_11490,U_11489)))
          | ! [U_11487] :
              ( ~ hBOOL(hAPP(U_11490,U_11487))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) ) )
        & ( ( hBOOL(hAPP(U_11490,sK233(U_11490,U_11489)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11490,U_11489)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489))) )
          | ! [U_11485] : ~ hBOOL(hAPP(U_11490,U_11485)) ) )
      | ( hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK232(U_11490,U_11489)),U_11489))))
        & ~ hBOOL(hAPP(U_11490,sK231(U_11490,U_11489))) )
      | ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
        & hBOOL(hAPP(U_11490,sK229(U_11490,U_11489))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_11488,sK234(U_11490,U_11489))],[f_3017_8]) ).

fof(f_3017_10,plain,
    ( ! [U_11489,U_11490] :
        ( hBOOL(hAPP(U_11490,sK233(U_11490,U_11489)))
        | ~ sP874(U_11489,U_11490) )
    & ! [U_11489,U_11490] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11490,U_11489)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489)))
        | ~ sP874(U_11489,U_11490) )
    & ! [U_11485,U_11487,U_11489,U_11490] :
        ( hBOOL(hAPP(U_11490,sK234(U_11490,U_11489)))
        | ~ hBOOL(hAPP(U_11490,U_11487))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489)))
        | ~ sP875(U_11485,U_11487,U_11489,U_11490) )
    & ! [U_11485,U_11487,U_11489,U_11490] :
        ( sP874(U_11489,U_11490)
        | ~ hBOOL(hAPP(U_11490,U_11485))
        | ~ sP875(U_11485,U_11487,U_11489,U_11490) )
    & ! [U_11489,U_11490] :
        ( hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK232(U_11490,U_11489)),U_11489))))
        | ~ sP873(U_11489,U_11490) )
    & ! [U_11489,U_11490] :
        ( ~ hBOOL(hAPP(U_11490,sK231(U_11490,U_11489)))
        | ~ sP873(U_11489,U_11490) )
    & ! [U_11489,U_11490] :
        ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
        | ~ sP872(U_11489,U_11490) )
    & ! [U_11489,U_11490] :
        ( hBOOL(hAPP(U_11490,sK229(U_11490,U_11489)))
        | ~ sP872(U_11489,U_11490) )
    & ! [U_11485,U_11487,U_11489,U_11490] :
        ( sP875(U_11485,U_11487,U_11489,U_11490)
        | sP873(U_11489,U_11490)
        | sP872(U_11489,U_11490)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP872,sP873,sP874,sP875])],[f_3017_9]) ).

cnf(f_3017_11,plain,
    ( sP875(U_11485,U_11487,U_11489,U_11490)
    | sP873(U_11489,U_11490)
    | sP872(U_11489,U_11490)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11489)) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_12,plain,
    ( hBOOL(hAPP(U_11490,sK229(U_11490,U_11489)))
    | ~ sP872(U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_13,plain,
    ( ~ hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK230(U_11490,U_11489)),U_11489))))
    | ~ sP872(U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_14,plain,
    ( ~ hBOOL(hAPP(U_11490,sK231(U_11490,U_11489)))
    | ~ sP873(U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_15,plain,
    ( hBOOL(hAPP(U_11490,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11490,U_11489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK232(U_11490,U_11489)),U_11489))))
    | ~ sP873(U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_16,plain,
    ( sP874(U_11489,U_11490)
    | ~ hBOOL(hAPP(U_11490,U_11485))
    | ~ sP875(U_11485,U_11487,U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_17,plain,
    ( hBOOL(hAPP(U_11490,sK234(U_11490,U_11489)))
    | ~ hBOOL(hAPP(U_11490,U_11487))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11487),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489)))
    | ~ sP875(U_11485,U_11487,U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_18,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11490,U_11489)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11489)))
    | ~ sP874(U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

cnf(f_3017_19,plain,
    ( hBOOL(hAPP(U_11490,sK233(U_11490,U_11489)))
    | ~ sP874(U_11489,U_11490) ),
    inference(clausify,[status(thm)],[f_3017_10]) ).

fof(f_3018_1,plain,
    ! [V_t_2,V_B_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I5_J]) ).

fof(f_3018_2,plain,
    ! [U_11500,U_11499,U_11498] :
      ( ! [U_11497] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11497),U_11498)),U_11500))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11497),U_11500))
          | ? [U_11496] :
              ( ? [U_11495] :
                  ( U_11497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11495),U_11496)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11495),U_11499)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11496),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11498))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11498)) ),
    inference(variable_rename,[status(thm)],[f_3018_1]) ).

fof(f_3018_3,plain,
    ! [U_11500,U_11499,U_11498] :
      ( ! [U_11497] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11497),U_11498)),U_11500))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11497),U_11500))
          | ( ? [U_11495] :
                ( U_11497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11495),sK235(U_11500,U_11499,U_11498,U_11497))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11495),U_11499)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11500,U_11499,U_11498,U_11497)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11498))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11498)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_11496,sK235(U_11500,U_11499,U_11498,U_11497))],[f_3018_2]) ).

fof(f_3018_4,plain,
    ! [U_11500,U_11499,U_11498] :
      ( ! [U_11497] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11497),U_11498)),U_11500))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11497),U_11500))
          | ( U_11497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK236(U_11500,U_11499,U_11498,U_11497)),sK235(U_11500,U_11499,U_11498,U_11497))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11500,U_11499,U_11498,U_11497)),U_11499))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11500,U_11499,U_11498,U_11497)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11498))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11498)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_11495,sK236(U_11500,U_11499,U_11498,U_11497))],[f_3018_3]) ).

fof(f_3018_5,plain,
    ( ! [U_11499,U_11500,U_11498,U_11497] :
        ( U_11497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK236(U_11500,U_11499,U_11498,U_11497)),sK235(U_11500,U_11499,U_11498,U_11497))
        | ~ sP876(U_11499,U_11500,U_11498,U_11497) )
    & ! [U_11499,U_11500,U_11498,U_11497] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11500,U_11499,U_11498,U_11497)),U_11499))
        | ~ sP876(U_11499,U_11500,U_11498,U_11497) )
    & ! [U_11499,U_11500,U_11498,U_11497] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11500,U_11499,U_11498,U_11497)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11498)))
        | ~ sP876(U_11499,U_11500,U_11498,U_11497) )
    & ! [U_11499,U_11500,U_11498,U_11497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11497),U_11498)),U_11500))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11497),U_11500))
        | sP876(U_11499,U_11500,U_11498,U_11497)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11498)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP876])],[f_3018_4]) ).

cnf(f_3018_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11497),U_11498)),U_11500))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11497),U_11500))
    | sP876(U_11499,U_11500,U_11498,U_11497)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11498)) ),
    inference(clausify,[status(thm)],[f_3018_5]) ).

cnf(f_3018_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11500,U_11499,U_11498,U_11497)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11498)))
    | ~ sP876(U_11499,U_11500,U_11498,U_11497) ),
    inference(clausify,[status(thm)],[f_3018_5]) ).

cnf(f_3018_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11500,U_11499,U_11498,U_11497)),U_11499))
    | ~ sP876(U_11499,U_11500,U_11498,U_11497) ),
    inference(clausify,[status(thm)],[f_3018_5]) ).

cnf(f_3018_9,plain,
    ( U_11497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK236(U_11500,U_11499,U_11498,U_11497)),sK235(U_11500,U_11499,U_11498,U_11497))
    | ~ sP876(U_11499,U_11500,U_11498,U_11497) ),
    inference(clausify,[status(thm)],[f_3018_5]) ).

fof(f_3019_1,plain,
    ! [V_t_2,V_A_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I7_J]) ).

fof(f_3019_2,plain,
    ! [U_11506,U_11505,U_11504] :
      ( ! [U_11503] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11503),U_11504)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),U_11503))
          | ? [U_11502] :
              ( ? [U_11501] :
                  ( U_11503 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11501),U_11502)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11501),U_11505)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11502),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11504))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11504)) ),
    inference(variable_rename,[status(thm)],[f_3019_1]) ).

fof(f_3019_3,plain,
    ! [U_11506,U_11505,U_11504] :
      ( ! [U_11503] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11503),U_11504)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),U_11503))
          | ( ? [U_11501] :
                ( U_11503 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11501),sK237(U_11506,U_11505,U_11504,U_11503))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11501),U_11505)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11506,U_11505,U_11504,U_11503)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11504))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11504)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_11502,sK237(U_11506,U_11505,U_11504,U_11503))],[f_3019_2]) ).

fof(f_3019_4,plain,
    ! [U_11506,U_11505,U_11504] :
      ( ! [U_11503] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11503),U_11504)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),U_11503))
          | ( U_11503 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK238(U_11506,U_11505,U_11504,U_11503)),sK237(U_11506,U_11505,U_11504,U_11503))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11506,U_11505,U_11504,U_11503)),U_11505))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11506,U_11505,U_11504,U_11503)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11504))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11504)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_11501,sK238(U_11506,U_11505,U_11504,U_11503))],[f_3019_3]) ).

fof(f_3019_5,plain,
    ( ! [U_11506,U_11503,U_11505,U_11504] :
        ( U_11503 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK238(U_11506,U_11505,U_11504,U_11503)),sK237(U_11506,U_11505,U_11504,U_11503))
        | ~ sP877(U_11506,U_11503,U_11505,U_11504) )
    & ! [U_11506,U_11503,U_11505,U_11504] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11506,U_11505,U_11504,U_11503)),U_11505))
        | ~ sP877(U_11506,U_11503,U_11505,U_11504) )
    & ! [U_11506,U_11503,U_11505,U_11504] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11506,U_11505,U_11504,U_11503)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11504)))
        | ~ sP877(U_11506,U_11503,U_11505,U_11504) )
    & ! [U_11506,U_11503,U_11505,U_11504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11503),U_11504)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),U_11503))
        | sP877(U_11506,U_11503,U_11505,U_11504)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11504)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP877])],[f_3019_4]) ).

cnf(f_3019_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11503),U_11504)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11506),U_11503))
    | sP877(U_11506,U_11503,U_11505,U_11504)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11504)) ),
    inference(clausify,[status(thm)],[f_3019_5]) ).

cnf(f_3019_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11506,U_11505,U_11504,U_11503)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11504)))
    | ~ sP877(U_11506,U_11503,U_11505,U_11504) ),
    inference(clausify,[status(thm)],[f_3019_5]) ).

cnf(f_3019_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11506,U_11505,U_11504,U_11503)),U_11505))
    | ~ sP877(U_11506,U_11503,U_11505,U_11504) ),
    inference(clausify,[status(thm)],[f_3019_5]) ).

cnf(f_3019_9,plain,
    ( U_11503 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK238(U_11506,U_11505,U_11504,U_11503)),sK237(U_11506,U_11505,U_11504,U_11503))
    | ~ sP877(U_11506,U_11503,U_11505,U_11504) ),
    inference(clausify,[status(thm)],[f_3019_5]) ).

fof(f_3020_1,plain,
    ! [V_x_2,V_y_2,V_c_2] :
      ( ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
          & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).

fof(f_3020_2,plain,
    ! [U_11509,U_11508,U_11507] :
      ( ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11507)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11509),U_11508)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11509),U_11508)) )
          & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11507)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11509),U_11508)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11509),U_11508)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11507),U_11508)) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11507)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11509),U_11508)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11509),U_11507)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11508),U_11507))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11507),U_11508)) ) ),
    inference(variable_rename,[status(thm)],[f_3020_1]) ).

fof(f_3020_3,plain,
    ( ! [U_11515,U_11513,U_11511] :
        ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11515),U_11513)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11515),U_11513)) )
          & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11515),U_11513)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11515),U_11513)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11511),U_11513)) )
    & ! [U_11514,U_11512,U_11510] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11510)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11514),U_11512)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11514),U_11510)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11512),U_11510))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11510),U_11512)) ) ),
    inference(miniscope,[status(thm)],[f_3020_2]) ).

fof(f_3020_4,plain,
    ( ! [U_11513,U_11515,U_11511] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11515),U_11513)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11515),U_11513))
        | ~ sP878(U_11513,U_11515,U_11511) )
    & ! [U_11513,U_11515,U_11511] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11515),U_11513)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11515),U_11513))
        | ~ sP878(U_11513,U_11515,U_11511) )
    & ! [U_11513,U_11515,U_11511] :
        ( sP878(U_11513,U_11515,U_11511)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11511),U_11513)) )
    & ! [U_11514,U_11510,U_11512] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11510)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11514),U_11512)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11514),U_11510)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11512),U_11510))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11510),U_11512)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP878])],[f_3020_3]) ).

cnf(f_3020_5,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11510)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11514),U_11512)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11514),U_11510)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11512),U_11510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11510),U_11512)) ),
    inference(clausify,[status(thm)],[f_3020_4]) ).

cnf(f_3020_6,plain,
    ( sP878(U_11513,U_11515,U_11511)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11511),U_11513)) ),
    inference(clausify,[status(thm)],[f_3020_4]) ).

cnf(f_3020_7,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11515),U_11513)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11515),U_11513))
    | ~ sP878(U_11513,U_11515,U_11511) ),
    inference(clausify,[status(thm)],[f_3020_4]) ).

cnf(f_3020_8,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11515),U_11513)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11515),U_11513))
    | ~ sP878(U_11513,U_11515,U_11511) ),
    inference(clausify,[status(thm)],[f_3020_4]) ).

fof(f_3021_1,plain,
    ! [V_t_2,V_B_2,V_D_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I9_J]) ).

fof(f_3021_2,plain,
    ! [U_11522,U_11521,U_11520,U_11519] :
      ( ! [U_11518] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11518),U_11520)),U_11522)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11518),U_11522)))
          | ? [U_11517] :
              ( ? [U_11516] :
                  ( U_11518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11516),U_11517)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11516),U_11521)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11517),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11520))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),U_11520)) ),
    inference(variable_rename,[status(thm)],[f_3021_1]) ).

fof(f_3021_3,plain,
    ! [U_11522,U_11521,U_11520,U_11519] :
      ( ! [U_11518] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11518),U_11520)),U_11522)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11518),U_11522)))
          | ( ? [U_11516] :
                ( U_11518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11516),sK239(U_11522,U_11521,U_11520,U_11519,U_11518))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11516),U_11521)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11522,U_11521,U_11520,U_11519,U_11518)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11520))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),U_11520)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_11517,sK239(U_11522,U_11521,U_11520,U_11519,U_11518))],[f_3021_2]) ).

fof(f_3021_4,plain,
    ! [U_11522,U_11521,U_11520,U_11519] :
      ( ! [U_11518] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11518),U_11520)),U_11522)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11518),U_11522)))
          | ( U_11518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK240(U_11522,U_11521,U_11520,U_11519,U_11518)),sK239(U_11522,U_11521,U_11520,U_11519,U_11518))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK240(U_11522,U_11521,U_11520,U_11519,U_11518)),U_11521))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11522,U_11521,U_11520,U_11519,U_11518)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11520))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),U_11520)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_11516,sK240(U_11522,U_11521,U_11520,U_11519,U_11518))],[f_3021_3]) ).

fof(f_3021_5,plain,
    ( ! [U_11520,U_11519,U_11518,U_11521,U_11522] :
        ( U_11518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK240(U_11522,U_11521,U_11520,U_11519,U_11518)),sK239(U_11522,U_11521,U_11520,U_11519,U_11518))
        | ~ sP879(U_11520,U_11519,U_11518,U_11521,U_11522) )
    & ! [U_11520,U_11519,U_11518,U_11521,U_11522] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK240(U_11522,U_11521,U_11520,U_11519,U_11518)),U_11521))
        | ~ sP879(U_11520,U_11519,U_11518,U_11521,U_11522) )
    & ! [U_11520,U_11519,U_11518,U_11521,U_11522] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11522,U_11521,U_11520,U_11519,U_11518)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11520)))
        | ~ sP879(U_11520,U_11519,U_11518,U_11521,U_11522) )
    & ! [U_11520,U_11519,U_11518,U_11521,U_11522] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11518),U_11520)),U_11522)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11518),U_11522)))
        | sP879(U_11520,U_11519,U_11518,U_11521,U_11522)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),U_11520)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP879])],[f_3021_4]) ).

cnf(f_3021_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11518),U_11520)),U_11522)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11518),U_11522)))
    | sP879(U_11520,U_11519,U_11518,U_11521,U_11522)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11519),U_11520)) ),
    inference(clausify,[status(thm)],[f_3021_5]) ).

cnf(f_3021_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11522,U_11521,U_11520,U_11519,U_11518)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11520)))
    | ~ sP879(U_11520,U_11519,U_11518,U_11521,U_11522) ),
    inference(clausify,[status(thm)],[f_3021_5]) ).

cnf(f_3021_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK240(U_11522,U_11521,U_11520,U_11519,U_11518)),U_11521))
    | ~ sP879(U_11520,U_11519,U_11518,U_11521,U_11522) ),
    inference(clausify,[status(thm)],[f_3021_5]) ).

cnf(f_3021_9,plain,
    ( U_11518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK240(U_11522,U_11521,U_11520,U_11519,U_11518)),sK239(U_11522,U_11521,U_11520,U_11519,U_11518))
    | ~ sP879(U_11520,U_11519,U_11518,U_11521,U_11522) ),
    inference(clausify,[status(thm)],[f_3021_5]) ).

fof(f_3022_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(f_3022_2,plain,
    ! [U_11524,U_11523] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11523),U_11524))),
    inference(variable_rename,[status(thm)],[f_3022_1]) ).

fof(f_3022_3,plain,
    ! [U_11524,U_11523] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11523),U_11524))),
    inference(definitional_conversion,[status(esa)],[f_3022_2]) ).

cnf(f_3022_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11523),U_11524))),
    inference(clausify,[status(thm)],[f_3022_3]) ).

fof(f_3023_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
          | V_b_2 != V_d_2
          | V_a_2 != V_c_2 )
        & ( ( V_b_2 = V_d_2
            & V_a_2 = V_c_2 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).

fof(f_3023_2,plain,
    ! [U_11529,U_11528,U_11527,U_11526,U_11525] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11526),U_11527) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11528),U_11529)
          | U_11527 != U_11529
          | U_11526 != U_11528 )
        & ( ( U_11527 = U_11529
            & U_11526 = U_11528 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11526),U_11527) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11528),U_11529) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11525),U_11528),U_11529))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11525),U_11526),U_11527))
      | ~ class_Orderings_Olinorder(U_11525) ),
    inference(variable_rename,[status(thm)],[f_3023_1]) ).

fof(f_3023_3,plain,
    ( ! [U_11526,U_11527,U_11528,U_11529] :
        ( U_11527 = U_11529
        | ~ sP880(U_11526,U_11527,U_11528,U_11529) )
    & ! [U_11526,U_11527,U_11528,U_11529] :
        ( U_11526 = U_11528
        | ~ sP880(U_11526,U_11527,U_11528,U_11529) )
    & ! [U_11525,U_11526,U_11527,U_11528,U_11529] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11526),U_11527) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11528),U_11529)
        | U_11527 != U_11529
        | U_11526 != U_11528
        | ~ sP881(U_11525,U_11526,U_11527,U_11528,U_11529) )
    & ! [U_11525,U_11526,U_11527,U_11528,U_11529] :
        ( sP880(U_11526,U_11527,U_11528,U_11529)
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11526),U_11527) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11528),U_11529)
        | ~ sP881(U_11525,U_11526,U_11527,U_11528,U_11529) )
    & ! [U_11525,U_11526,U_11527,U_11528,U_11529] :
        ( sP881(U_11525,U_11526,U_11527,U_11528,U_11529)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11525),U_11528),U_11529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11525),U_11526),U_11527))
        | ~ class_Orderings_Olinorder(U_11525) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP880,sP881])],[f_3023_2]) ).

cnf(f_3023_4,plain,
    ( sP881(U_11525,U_11526,U_11527,U_11528,U_11529)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11525),U_11528),U_11529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11525),U_11526),U_11527))
    | ~ class_Orderings_Olinorder(U_11525) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

cnf(f_3023_5,plain,
    ( sP880(U_11526,U_11527,U_11528,U_11529)
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11526),U_11527) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11528),U_11529)
    | ~ sP881(U_11525,U_11526,U_11527,U_11528,U_11529) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

cnf(f_3023_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11526),U_11527) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11525,U_11528),U_11529)
    | U_11527 != U_11529
    | U_11526 != U_11528
    | ~ sP881(U_11525,U_11526,U_11527,U_11528,U_11529) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

cnf(f_3023_7,plain,
    ( U_11526 = U_11528
    | ~ sP880(U_11526,U_11527,U_11528,U_11529) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

cnf(f_3023_8,plain,
    ( U_11527 = U_11529
    | ~ sP880(U_11526,U_11527,U_11528,U_11529) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

fof(f_3024_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( V_a_2 = V_c_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).

fof(f_3024_2,plain,
    ! [U_11534,U_11533,U_11532,U_11531,U_11530] :
      ( U_11531 = U_11533
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11530),U_11533),U_11534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11530),U_11531),U_11532))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11530,U_11531),U_11532) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11530,U_11533),U_11534)
      | ~ class_Orderings_Olinorder(U_11530) ),
    inference(variable_rename,[status(thm)],[f_3024_1]) ).

fof(f_3024_3,plain,
    ! [U_11533,U_11531,U_11532,U_11534,U_11530] :
      ( U_11531 = U_11533
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11530),U_11533),U_11534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11530),U_11531),U_11532))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11530,U_11531),U_11532) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11530,U_11533),U_11534)
      | ~ class_Orderings_Olinorder(U_11530) ),
    inference(definitional_conversion,[status(esa)],[f_3024_2]) ).

cnf(f_3024_4,plain,
    ( U_11531 = U_11533
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11530),U_11533),U_11534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11530),U_11531),U_11532))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11530,U_11531),U_11532) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11530,U_11533),U_11534)
    | ~ class_Orderings_Olinorder(U_11530) ),
    inference(clausify,[status(thm)],[f_3024_3]) ).

fof(f_3025_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( V_b_2 = V_d_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).

fof(f_3025_2,plain,
    ! [U_11539,U_11538,U_11537,U_11536,U_11535] :
      ( U_11537 = U_11539
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11535),U_11538),U_11539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11535),U_11536),U_11537))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11535,U_11536),U_11537) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11535,U_11538),U_11539)
      | ~ class_Orderings_Olinorder(U_11535) ),
    inference(variable_rename,[status(thm)],[f_3025_1]) ).

fof(f_3025_3,plain,
    ! [U_11535,U_11536,U_11537,U_11538,U_11539] :
      ( U_11537 = U_11539
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11535),U_11538),U_11539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11535),U_11536),U_11537))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11535,U_11536),U_11537) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11535,U_11538),U_11539)
      | ~ class_Orderings_Olinorder(U_11535) ),
    inference(definitional_conversion,[status(esa)],[f_3025_2]) ).

cnf(f_3025_4,plain,
    ( U_11537 = U_11539
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11535),U_11538),U_11539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11535),U_11536),U_11537))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11535,U_11536),U_11537) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11535,U_11538),U_11539)
    | ~ class_Orderings_Olinorder(U_11535) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

fof(f_3026_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
        | ? [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq]) ).

fof(f_3026_2,plain,
    ! [U_11545,U_11544] :
      ( ( ! [U_11543] :
            ( hBOOL(hAPP(U_11545,U_11543))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11543),U_11544)) )
        | ? [U_11542] :
            ( ~ hBOOL(hAPP(U_11545,U_11542))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11542),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11544))) ) )
      & ( ! [U_11541] :
            ( hBOOL(hAPP(U_11545,U_11541))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11544))) )
        | ? [U_11540] :
            ( ~ hBOOL(hAPP(U_11545,U_11540))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11540),U_11544)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3026_1]) ).

fof(f_3026_3,plain,
    ( ! [U_11549,U_11547] :
        ( ! [U_11543] :
            ( hBOOL(hAPP(U_11549,U_11543))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11543),U_11547)) )
        | ? [U_11542] :
            ( ~ hBOOL(hAPP(U_11549,U_11542))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11542),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11547))) ) )
    & ! [U_11548,U_11546] :
        ( ! [U_11541] :
            ( hBOOL(hAPP(U_11548,U_11541))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11546))) )
        | ? [U_11540] :
            ( ~ hBOOL(hAPP(U_11548,U_11540))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11540),U_11546)) ) ) ),
    inference(miniscope,[status(thm)],[f_3026_2]) ).

fof(f_3026_4,plain,
    ( ! [U_11549,U_11547] :
        ( ! [U_11543] :
            ( hBOOL(hAPP(U_11549,U_11543))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11543),U_11547)) )
        | ? [U_11542] :
            ( ~ hBOOL(hAPP(U_11549,U_11542))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11542),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11547))) ) )
    & ! [U_11548,U_11546] :
        ( ! [U_11541] :
            ( hBOOL(hAPP(U_11548,U_11541))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11546))) )
        | ( ~ hBOOL(hAPP(U_11548,sK241(U_11548,U_11546)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK241(U_11548,U_11546)),U_11546)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_11540,sK241(U_11548,U_11546))],[f_3026_3]) ).

fof(f_3026_5,plain,
    ( ! [U_11549,U_11547] :
        ( ! [U_11543] :
            ( hBOOL(hAPP(U_11549,U_11543))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11543),U_11547)) )
        | ( ~ hBOOL(hAPP(U_11549,sK242(U_11549,U_11547)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11549,U_11547)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11547))) ) )
    & ! [U_11548,U_11546] :
        ( ! [U_11541] :
            ( hBOOL(hAPP(U_11548,U_11541))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11546))) )
        | ( ~ hBOOL(hAPP(U_11548,sK241(U_11548,U_11546)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK241(U_11548,U_11546)),U_11546)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_11542,sK242(U_11549,U_11547))],[f_3026_4]) ).

fof(f_3026_6,plain,
    ( ! [U_11549,U_11547] :
        ( ~ hBOOL(hAPP(U_11549,sK242(U_11549,U_11547)))
        | ~ sP883(U_11549,U_11547) )
    & ! [U_11549,U_11547] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11549,U_11547)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11547)))
        | ~ sP883(U_11549,U_11547) )
    & ! [U_11546,U_11548] :
        ( ~ hBOOL(hAPP(U_11548,sK241(U_11548,U_11546)))
        | ~ sP882(U_11546,U_11548) )
    & ! [U_11546,U_11548] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK241(U_11548,U_11546)),U_11546))
        | ~ sP882(U_11546,U_11548) )
    & ! [U_11543,U_11549,U_11547] :
        ( hBOOL(hAPP(U_11549,U_11543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11543),U_11547))
        | sP883(U_11549,U_11547) )
    & ! [U_11541,U_11546,U_11548] :
        ( hBOOL(hAPP(U_11548,U_11541))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11546)))
        | sP882(U_11546,U_11548) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP882,sP883])],[f_3026_5]) ).

cnf(f_3026_7,plain,
    ( hBOOL(hAPP(U_11548,U_11541))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11546)))
    | sP882(U_11546,U_11548) ),
    inference(clausify,[status(thm)],[f_3026_6]) ).

cnf(f_3026_8,plain,
    ( hBOOL(hAPP(U_11549,U_11543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11543),U_11547))
    | sP883(U_11549,U_11547) ),
    inference(clausify,[status(thm)],[f_3026_6]) ).

cnf(f_3026_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK241(U_11548,U_11546)),U_11546))
    | ~ sP882(U_11546,U_11548) ),
    inference(clausify,[status(thm)],[f_3026_6]) ).

cnf(f_3026_10,plain,
    ( ~ hBOOL(hAPP(U_11548,sK241(U_11548,U_11546)))
    | ~ sP882(U_11546,U_11548) ),
    inference(clausify,[status(thm)],[f_3026_6]) ).

cnf(f_3026_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11549,U_11547)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11547)))
    | ~ sP883(U_11549,U_11547) ),
    inference(clausify,[status(thm)],[f_3026_6]) ).

cnf(f_3026_12,plain,
    ( ~ hBOOL(hAPP(U_11549,sK242(U_11549,U_11547)))
    | ~ sP883(U_11549,U_11547) ),
    inference(clausify,[status(thm)],[f_3026_6]) ).

fof(f_3027_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
        | ! [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq]) ).

fof(f_3027_2,plain,
    ! [U_11555,U_11554] :
      ( ( ? [U_11553] :
            ( hBOOL(hAPP(U_11555,U_11553))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11553),U_11554)) )
        | ! [U_11552] :
            ( ~ hBOOL(hAPP(U_11555,U_11552))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11552),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11554))) ) )
      & ( ? [U_11551] :
            ( hBOOL(hAPP(U_11555,U_11551))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11551),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11554))) )
        | ! [U_11550] :
            ( ~ hBOOL(hAPP(U_11555,U_11550))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11550),U_11554)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3027_1]) ).

fof(f_3027_3,plain,
    ( ! [U_11559,U_11557] :
        ( ? [U_11553] :
            ( hBOOL(hAPP(U_11559,U_11553))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11553),U_11557)) )
        | ! [U_11552] :
            ( ~ hBOOL(hAPP(U_11559,U_11552))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11552),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11557))) ) )
    & ! [U_11558,U_11556] :
        ( ? [U_11551] :
            ( hBOOL(hAPP(U_11558,U_11551))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11551),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11556))) )
        | ! [U_11550] :
            ( ~ hBOOL(hAPP(U_11558,U_11550))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11550),U_11556)) ) ) ),
    inference(miniscope,[status(thm)],[f_3027_2]) ).

fof(f_3027_4,plain,
    ( ! [U_11559,U_11557] :
        ( ? [U_11553] :
            ( hBOOL(hAPP(U_11559,U_11553))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11553),U_11557)) )
        | ! [U_11552] :
            ( ~ hBOOL(hAPP(U_11559,U_11552))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11552),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11557))) ) )
    & ! [U_11558,U_11556] :
        ( ( hBOOL(hAPP(U_11558,sK243(U_11558,U_11556)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK243(U_11558,U_11556)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11556))) )
        | ! [U_11550] :
            ( ~ hBOOL(hAPP(U_11558,U_11550))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11550),U_11556)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_11551,sK243(U_11558,U_11556))],[f_3027_3]) ).

fof(f_3027_5,plain,
    ( ! [U_11559,U_11557] :
        ( ( hBOOL(hAPP(U_11559,sK244(U_11559,U_11557)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK244(U_11559,U_11557)),U_11557)) )
        | ! [U_11552] :
            ( ~ hBOOL(hAPP(U_11559,U_11552))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11552),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11557))) ) )
    & ! [U_11558,U_11556] :
        ( ( hBOOL(hAPP(U_11558,sK243(U_11558,U_11556)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK243(U_11558,U_11556)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11556))) )
        | ! [U_11550] :
            ( ~ hBOOL(hAPP(U_11558,U_11550))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11550),U_11556)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_11553,sK244(U_11559,U_11557))],[f_3027_4]) ).

fof(f_3027_6,plain,
    ( ! [U_11557,U_11559] :
        ( hBOOL(hAPP(U_11559,sK244(U_11559,U_11557)))
        | ~ sP885(U_11557,U_11559) )
    & ! [U_11557,U_11559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK244(U_11559,U_11557)),U_11557))
        | ~ sP885(U_11557,U_11559) )
    & ! [U_11556,U_11558] :
        ( hBOOL(hAPP(U_11558,sK243(U_11558,U_11556)))
        | ~ sP884(U_11556,U_11558) )
    & ! [U_11556,U_11558] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK243(U_11558,U_11556)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11556)))
        | ~ sP884(U_11556,U_11558) )
    & ! [U_11552,U_11557,U_11559] :
        ( sP885(U_11557,U_11559)
        | ~ hBOOL(hAPP(U_11559,U_11552))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11552),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11557))) )
    & ! [U_11556,U_11558,U_11550] :
        ( sP884(U_11556,U_11558)
        | ~ hBOOL(hAPP(U_11558,U_11550))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11550),U_11556)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP884,sP885])],[f_3027_5]) ).

cnf(f_3027_7,plain,
    ( sP884(U_11556,U_11558)
    | ~ hBOOL(hAPP(U_11558,U_11550))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11550),U_11556)) ),
    inference(clausify,[status(thm)],[f_3027_6]) ).

cnf(f_3027_8,plain,
    ( sP885(U_11557,U_11559)
    | ~ hBOOL(hAPP(U_11559,U_11552))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11552),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11557))) ),
    inference(clausify,[status(thm)],[f_3027_6]) ).

cnf(f_3027_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK243(U_11558,U_11556)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11556)))
    | ~ sP884(U_11556,U_11558) ),
    inference(clausify,[status(thm)],[f_3027_6]) ).

cnf(f_3027_10,plain,
    ( hBOOL(hAPP(U_11558,sK243(U_11558,U_11556)))
    | ~ sP884(U_11556,U_11558) ),
    inference(clausify,[status(thm)],[f_3027_6]) ).

cnf(f_3027_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK244(U_11559,U_11557)),U_11557))
    | ~ sP885(U_11557,U_11559) ),
    inference(clausify,[status(thm)],[f_3027_6]) ).

cnf(f_3027_12,plain,
    ( hBOOL(hAPP(U_11559,sK244(U_11559,U_11557)))
    | ~ sP885(U_11557,U_11559) ),
    inference(clausify,[status(thm)],[f_3027_6]) ).

fof(f_3028_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).

fof(f_3028_2,plain,
    ! [U_11561,U_11560] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11560),hAPP(c_Nat_OSuc,U_11561)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11560,U_11561),
    inference(variable_rename,[status(thm)],[f_3028_1]) ).

fof(f_3028_3,plain,
    ! [U_11561,U_11560] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11560),hAPP(c_Nat_OSuc,U_11561)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11560,U_11561),
    inference(definitional_conversion,[status(esa)],[f_3028_2]) ).

cnf(f_3028_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11560),hAPP(c_Nat_OSuc,U_11561)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11560,U_11561),
    inference(clausify,[status(thm)],[f_3028_3]) ).

fof(f_3029_1,plain,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan0]) ).

fof(f_3029_2,plain,
    ! [U_11562] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3029_1]) ).

fof(f_3029_3,plain,
    ! [U_11562] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3029_2]) ).

cnf(f_3029_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3029_3]) ).

fof(f_3030_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastLessThan]) ).

fof(f_3030_2,plain,
    ! [U_11564,U_11563] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11563),U_11564)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11564),U_11563),
    inference(variable_rename,[status(thm)],[f_3030_1]) ).

fof(f_3030_3,plain,
    ! [U_11564,U_11563] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11563),U_11564)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11564),U_11563),
    inference(definitional_conversion,[status(esa)],[f_3030_2]) ).

cnf(f_3030_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11563),U_11564)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11564),U_11563),
    inference(clausify,[status(thm)],[f_3030_3]) ).

fof(f_3031_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(f_3031_2,plain,
    ! [U_11566,U_11565] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11565),U_11566)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11565)),hAPP(c_Nat_OSuc,U_11566)),
    inference(variable_rename,[status(thm)],[f_3031_1]) ).

fof(f_3031_3,plain,
    ! [U_11565,U_11566] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11565),U_11566)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11565)),hAPP(c_Nat_OSuc,U_11566)),
    inference(definitional_conversion,[status(esa)],[f_3031_2]) ).

cnf(f_3031_4,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11565),U_11566)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11565)),hAPP(c_Nat_OSuc,U_11566)),
    inference(clausify,[status(thm)],[f_3031_3]) ).

fof(f_3032_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty]) ).

fof(f_3032_2,plain,
    ! [U_11569,U_11568,U_11567] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11567,U_11569),U_11568) = c_Orderings_Obot__class_Obot(tc_fun(U_11567,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11567),U_11568),U_11569))
      | ~ class_Orderings_Oorder(U_11567) ),
    inference(variable_rename,[status(thm)],[f_3032_1]) ).

fof(f_3032_3,plain,
    ! [U_11567,U_11568,U_11569] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11567,U_11569),U_11568) = c_Orderings_Obot__class_Obot(tc_fun(U_11567,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11567),U_11568),U_11569))
      | ~ class_Orderings_Oorder(U_11567) ),
    inference(definitional_conversion,[status(esa)],[f_3032_2]) ).

cnf(f_3032_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11567,U_11569),U_11568) = c_Orderings_Obot__class_Obot(tc_fun(U_11567,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11567),U_11568),U_11569))
    | ~ class_Orderings_Oorder(U_11567) ),
    inference(clausify,[status(thm)],[f_3032_3]) ).

fof(f_3033_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(f_3033_2,plain,
    ! [U_11572,U_11571,U_11570] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11570,U_11571),U_11572) = c_Orderings_Obot__class_Obot(tc_fun(U_11570,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11570),U_11571),U_11572)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11570),U_11571),U_11572))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11570,U_11571),U_11572) != c_Orderings_Obot__class_Obot(tc_fun(U_11570,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_11570) ),
    inference(variable_rename,[status(thm)],[f_3033_1]) ).

fof(f_3033_3,plain,
    ( ! [U_11570,U_11571,U_11572] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11570,U_11571),U_11572) = c_Orderings_Obot__class_Obot(tc_fun(U_11570,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11570),U_11571),U_11572))
        | ~ sP886(U_11570,U_11571,U_11572) )
    & ! [U_11570,U_11571,U_11572] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11570),U_11571),U_11572))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11570,U_11571),U_11572) != c_Orderings_Obot__class_Obot(tc_fun(U_11570,tc_HOL_Obool))
        | ~ sP886(U_11570,U_11571,U_11572) )
    & ! [U_11570,U_11571,U_11572] :
        ( sP886(U_11570,U_11571,U_11572)
        | ~ class_Orderings_Oorder(U_11570) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP886])],[f_3033_2]) ).

cnf(f_3033_4,plain,
    ( sP886(U_11570,U_11571,U_11572)
    | ~ class_Orderings_Oorder(U_11570) ),
    inference(clausify,[status(thm)],[f_3033_3]) ).

cnf(f_3033_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11570),U_11571),U_11572))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11570,U_11571),U_11572) != c_Orderings_Obot__class_Obot(tc_fun(U_11570,tc_HOL_Obool))
    | ~ sP886(U_11570,U_11571,U_11572) ),
    inference(clausify,[status(thm)],[f_3033_3]) ).

cnf(f_3033_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11570,U_11571),U_11572) = c_Orderings_Obot__class_Obot(tc_fun(U_11570,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11570),U_11571),U_11572))
    | ~ sP886(U_11570,U_11571,U_11572) ),
    inference(clausify,[status(thm)],[f_3033_3]) ).

fof(f_3034_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(f_3034_2,plain,
    ! [U_11575,U_11574,U_11573] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_11573,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11573,U_11574),U_11575)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11573),U_11574),U_11575)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11573),U_11574),U_11575))
          | c_Orderings_Obot__class_Obot(tc_fun(U_11573,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11573,U_11574),U_11575) ) )
      | ~ class_Orderings_Oorder(U_11573) ),
    inference(variable_rename,[status(thm)],[f_3034_1]) ).

fof(f_3034_3,plain,
    ( ! [U_11574,U_11575,U_11573] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_11573,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11573,U_11574),U_11575)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11573),U_11574),U_11575))
        | ~ sP887(U_11574,U_11575,U_11573) )
    & ! [U_11574,U_11575,U_11573] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11573),U_11574),U_11575))
        | c_Orderings_Obot__class_Obot(tc_fun(U_11573,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11573,U_11574),U_11575)
        | ~ sP887(U_11574,U_11575,U_11573) )
    & ! [U_11574,U_11575,U_11573] :
        ( sP887(U_11574,U_11575,U_11573)
        | ~ class_Orderings_Oorder(U_11573) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP887])],[f_3034_2]) ).

cnf(f_3034_4,plain,
    ( sP887(U_11574,U_11575,U_11573)
    | ~ class_Orderings_Oorder(U_11573) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11573),U_11574),U_11575))
    | c_Orderings_Obot__class_Obot(tc_fun(U_11573,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11573,U_11574),U_11575)
    | ~ sP887(U_11574,U_11575,U_11573) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_11573,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11573,U_11574),U_11575)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11573),U_11574),U_11575))
    | ~ sP887(U_11574,U_11575,U_11573) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

fof(f_3035_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).

fof(f_3035_2,plain,
    ! [U_11580,U_11579,U_11578,U_11577,U_11576] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11578),U_11580))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11579),U_11577)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11578),U_11577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11576,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11576,U_11577),U_11578)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11576,U_11579),U_11580)))
      | ~ class_Orderings_Olinorder(U_11576) ),
    inference(variable_rename,[status(thm)],[f_3035_1]) ).

fof(f_3035_3,plain,
    ( ! [U_11577,U_11576,U_11578,U_11579,U_11580] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11578),U_11580))
        | ~ sP888(U_11577,U_11576,U_11578,U_11579,U_11580) )
    & ! [U_11577,U_11576,U_11578,U_11579,U_11580] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11579),U_11577))
        | ~ sP888(U_11577,U_11576,U_11578,U_11579,U_11580) )
    & ! [U_11577,U_11576,U_11578,U_11579,U_11580] :
        ( sP888(U_11577,U_11576,U_11578,U_11579,U_11580)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11578),U_11577))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11576,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11576,U_11577),U_11578)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11576,U_11579),U_11580)))
        | ~ class_Orderings_Olinorder(U_11576) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP888])],[f_3035_2]) ).

cnf(f_3035_4,plain,
    ( sP888(U_11577,U_11576,U_11578,U_11579,U_11580)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11578),U_11577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11576,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11576,U_11577),U_11578)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11576,U_11579),U_11580)))
    | ~ class_Orderings_Olinorder(U_11576) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

cnf(f_3035_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11579),U_11577))
    | ~ sP888(U_11577,U_11576,U_11578,U_11579,U_11580) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

cnf(f_3035_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11576),U_11578),U_11580))
    | ~ sP888(U_11577,U_11576,U_11578,U_11579,U_11580) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

fof(f_3036_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J]) ).

fof(f_3036_2,plain,
    ! [U_11584,U_11583,U_11582,U_11581] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11581,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11582),U_11583)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11583),U_11584)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11582),U_11584)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),U_11583),U_11584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),U_11582),U_11583))
      | ~ class_Orderings_Olinorder(U_11581) ),
    inference(variable_rename,[status(thm)],[f_3036_1]) ).

fof(f_3036_3,plain,
    ! [U_11581,U_11582,U_11583,U_11584] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11581,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11582),U_11583)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11583),U_11584)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11582),U_11584)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),U_11583),U_11584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),U_11582),U_11583))
      | ~ class_Orderings_Olinorder(U_11581) ),
    inference(definitional_conversion,[status(esa)],[f_3036_2]) ).

cnf(f_3036_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11581,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11582),U_11583)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11583),U_11584)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11581,U_11582),U_11584)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),U_11583),U_11584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),U_11582),U_11583))
    | ~ class_Orderings_Olinorder(U_11581) ),
    inference(clausify,[status(thm)],[f_3036_3]) ).

fof(f_3037_1,plain,
    ! [V_m_2,V_n_2,V_i_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__diff]) ).

fof(f_3037_2,plain,
    ! [U_11588,U_11587,U_11586,U_11585] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11585,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11586),U_11588)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11586),U_11587)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11587),U_11588)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11585),U_11586),U_11587))
      | ~ class_Orderings_Olinorder(U_11585) ),
    inference(variable_rename,[status(thm)],[f_3037_1]) ).

fof(f_3037_3,plain,
    ! [U_11585,U_11586,U_11587,U_11588] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11585,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11586),U_11588)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11586),U_11587)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11587),U_11588)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11585),U_11586),U_11587))
      | ~ class_Orderings_Olinorder(U_11585) ),
    inference(definitional_conversion,[status(esa)],[f_3037_2]) ).

cnf(f_3037_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11585,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11586),U_11588)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11586),U_11587)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11585,U_11587),U_11588)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11585),U_11586),U_11587))
    | ~ class_Orderings_Olinorder(U_11585) ),
    inference(clausify,[status(thm)],[f_3037_3]) ).

fof(f_3038_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J]) ).

fof(f_3038_2,plain,
    ! [U_11592,U_11591,U_11590,U_11589] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11589,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11589,U_11590),U_11591)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11589,U_11591),U_11592)) = c_Orderings_Obot__class_Obot(tc_fun(U_11589,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11589) ),
    inference(variable_rename,[status(thm)],[f_3038_1]) ).

fof(f_3038_3,plain,
    ! [U_11589,U_11590,U_11591,U_11592] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11589,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11589,U_11590),U_11591)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11589,U_11591),U_11592)) = c_Orderings_Obot__class_Obot(tc_fun(U_11589,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11589) ),
    inference(definitional_conversion,[status(esa)],[f_3038_2]) ).

cnf(f_3038_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11589,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11589,U_11590),U_11591)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11589,U_11591),U_11592)) = c_Orderings_Obot__class_Obot(tc_fun(U_11589,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11589) ),
    inference(clausify,[status(thm)],[f_3038_3]) ).

fof(f_3039_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).

fof(f_3039_2,plain,
    ! [U_11594,U_11593] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11593)),U_11594) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_11593,U_11594),
    inference(variable_rename,[status(thm)],[f_3039_1]) ).

fof(f_3039_3,plain,
    ! [U_11593,U_11594] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11593)),U_11594) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_11593,U_11594),
    inference(definitional_conversion,[status(esa)],[f_3039_2]) ).

cnf(f_3039_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11593)),U_11594) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_11593,U_11594),
    inference(clausify,[status(thm)],[f_3039_3]) ).

fof(f_3040_1,plain,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(f_3040_2,plain,
    ! [U_11597,U_11596,U_11595] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11595)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11596),U_11597)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11596),U_11595)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11597),U_11595)),
    inference(variable_rename,[status(thm)],[f_3040_1]) ).

fof(f_3040_3,plain,
    ! [U_11595,U_11596,U_11597] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11595)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11596),U_11597)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11596),U_11595)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11597),U_11595)),
    inference(definitional_conversion,[status(esa)],[f_3040_2]) ).

cnf(f_3040_4,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11595)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11596),U_11597)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11596),U_11595)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11597),U_11595)),
    inference(clausify,[status(thm)],[f_3040_3]) ).

fof(f_3041_1,plain,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__singleton]) ).

fof(f_3041_2,plain,
    ! [U_11598] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11598),hAPP(c_Nat_OSuc,U_11598)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11598),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3041_1]) ).

fof(f_3041_3,plain,
    ! [U_11598] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11598),hAPP(c_Nat_OSuc,U_11598)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11598),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3041_2]) ).

cnf(f_3041_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11598),hAPP(c_Nat_OSuc,U_11598)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11598),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3041_3]) ).

fof(f_3042_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J]) ).

fof(f_3042_2,plain,
    ! [U_11602,U_11601,U_11600,U_11599] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11599,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11599,U_11600),U_11601)),c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11601,U_11602)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11602)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11601),U_11602))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
      | ~ class_Orderings_Olinorder(U_11599) ),
    inference(variable_rename,[status(thm)],[f_3042_1]) ).

fof(f_3042_3,plain,
    ! [U_11599,U_11600,U_11601,U_11602] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11599,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11599,U_11600),U_11601)),c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11601,U_11602)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11602)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11601),U_11602))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
      | ~ class_Orderings_Olinorder(U_11599) ),
    inference(definitional_conversion,[status(esa)],[f_3042_2]) ).

cnf(f_3042_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11599,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11599,U_11600),U_11601)),c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11601,U_11602)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11602)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11601),U_11602))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
    | ~ class_Orderings_Olinorder(U_11599) ),
    inference(clausify,[status(thm)],[f_3042_3]) ).

fof(f_3043_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un]) ).

fof(f_3043_2,plain,
    ! [U_11605,U_11604,U_11603] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11604),U_11605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11603),U_11604)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11604),U_11605)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11603),U_11604)) ),
    inference(variable_rename,[status(thm)],[f_3043_1]) ).

fof(f_3043_3,plain,
    ! [U_11605,U_11604,U_11603] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11604),U_11605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11603),U_11604)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11604),U_11605)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11603),U_11604)) ),
    inference(definitional_conversion,[status(esa)],[f_3043_2]) ).

cnf(f_3043_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11604),U_11605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11603),U_11604)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11604),U_11605)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11603),U_11604)) ),
    inference(clausify,[status(thm)],[f_3043_3]) ).

fof(f_3044_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J]) ).

fof(f_3044_2,plain,
    ! [U_11609,U_11608,U_11607,U_11606] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11606,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11606,U_11607),U_11608)),c_SetInterval_Oord__class_OatLeastAtMost(U_11606,U_11608,U_11609)) = c_Orderings_Obot__class_Obot(tc_fun(U_11606,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11606) ),
    inference(variable_rename,[status(thm)],[f_3044_1]) ).

fof(f_3044_3,plain,
    ! [U_11606,U_11607,U_11608,U_11609] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11606,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11606,U_11607),U_11608)),c_SetInterval_Oord__class_OatLeastAtMost(U_11606,U_11608,U_11609)) = c_Orderings_Obot__class_Obot(tc_fun(U_11606,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11606) ),
    inference(definitional_conversion,[status(esa)],[f_3044_2]) ).

cnf(f_3044_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11606,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11606,U_11607),U_11608)),c_SetInterval_Oord__class_OatLeastAtMost(U_11606,U_11608,U_11609)) = c_Orderings_Obot__class_Obot(tc_fun(U_11606,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11606) ),
    inference(clausify,[status(thm)],[f_3044_3]) ).

fof(f_3045_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).

fof(f_3045_2,plain,
    ! [U_11614,U_11613,U_11612,U_11611,U_11610] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,U_11611),U_11612)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,U_11613),U_11614)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11610),U_11611),U_11613)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11610),U_11612),U_11614))
      | ~ class_Orderings_Olinorder(U_11610) ),
    inference(variable_rename,[status(thm)],[f_3045_1]) ).

fof(f_3045_3,plain,
    ! [U_11610,U_11611,U_11612,U_11613,U_11614] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,U_11611),U_11612)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,U_11613),U_11614)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11610),U_11611),U_11613)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11610),U_11612),U_11614))
      | ~ class_Orderings_Olinorder(U_11610) ),
    inference(definitional_conversion,[status(esa)],[f_3045_2]) ).

cnf(f_3045_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,U_11611),U_11612)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,U_11613),U_11614)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11610,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11610),U_11611),U_11613)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11610),U_11612),U_11614))
    | ~ class_Orderings_Olinorder(U_11610) ),
    inference(clausify,[status(thm)],[f_3045_3]) ).

fof(f_3046_1,plain,
    ! [V_k_2,V_A_2] :
      ( V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) ),
    inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl]) ).

fof(f_3046_2,plain,
    ! [U_11616,U_11615] :
      ( U_11615 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11616),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_11615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_11615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11616),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_11615))))) ),
    inference(variable_rename,[status(thm)],[f_3046_1]) ).

fof(f_3046_3,plain,
    ! [U_11615,U_11616] :
      ( U_11615 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11616),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_11615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_11615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11616),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_11615))))) ),
    inference(definitional_conversion,[status(esa)],[f_3046_2]) ).

cnf(f_3046_4,plain,
    ( U_11615 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11616),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_11615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_11615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11616),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_11615))))) ),
    inference(clausify,[status(thm)],[f_3046_3]) ).

fof(f_3047_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J]) ).

fof(f_3047_2,plain,
    ! [U_11620,U_11619,U_11618,U_11617] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11617,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11617,U_11618,U_11619)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11617,U_11619),U_11620)) = c_Orderings_Obot__class_Obot(tc_fun(U_11617,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11617) ),
    inference(variable_rename,[status(thm)],[f_3047_1]) ).

fof(f_3047_3,plain,
    ! [U_11617,U_11618,U_11619,U_11620] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11617,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11617,U_11618,U_11619)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11617,U_11619),U_11620)) = c_Orderings_Obot__class_Obot(tc_fun(U_11617,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11617) ),
    inference(definitional_conversion,[status(esa)],[f_3047_2]) ).

cnf(f_3047_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11617,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11617,U_11618,U_11619)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11617,U_11619),U_11620)) = c_Orderings_Obot__class_Obot(tc_fun(U_11617,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11617) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

fof(f_3048_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost]) ).

fof(f_3048_2,plain,
    ! [U_11623,U_11622,U_11621] :
      ( hAPP(c_Set_Oimage(U_11621,U_11621,c_Groups_Ouminus__class_Ouminus(U_11621)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11621,U_11622,U_11623)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11621,hAPP(c_Groups_Ouminus__class_Ouminus(U_11621),U_11623)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11621),U_11622))
      | ~ class_Groups_Oordered__ab__group__add(U_11621) ),
    inference(variable_rename,[status(thm)],[f_3048_1]) ).

fof(f_3048_3,plain,
    ! [U_11621,U_11622,U_11623] :
      ( hAPP(c_Set_Oimage(U_11621,U_11621,c_Groups_Ouminus__class_Ouminus(U_11621)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11621,U_11622,U_11623)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11621,hAPP(c_Groups_Ouminus__class_Ouminus(U_11621),U_11623)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11621),U_11622))
      | ~ class_Groups_Oordered__ab__group__add(U_11621) ),
    inference(definitional_conversion,[status(esa)],[f_3048_2]) ).

cnf(f_3048_4,plain,
    ( hAPP(c_Set_Oimage(U_11621,U_11621,c_Groups_Ouminus__class_Ouminus(U_11621)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11621,U_11622,U_11623)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11621,hAPP(c_Groups_Ouminus__class_Ouminus(U_11621),U_11623)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11621),U_11622))
    | ~ class_Groups_Oordered__ab__group__add(U_11621) ),
    inference(clausify,[status(thm)],[f_3048_3]) ).

fof(f_3049_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan]) ).

fof(f_3049_2,plain,
    ! [U_11626,U_11625,U_11624] :
      ( hAPP(c_Set_Oimage(U_11624,U_11624,c_Groups_Ouminus__class_Ouminus(U_11624)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11624,U_11625),U_11626)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11624,hAPP(c_Groups_Ouminus__class_Ouminus(U_11624),U_11626),hAPP(c_Groups_Ouminus__class_Ouminus(U_11624),U_11625))
      | ~ class_Groups_Oordered__ab__group__add(U_11624) ),
    inference(variable_rename,[status(thm)],[f_3049_1]) ).

fof(f_3049_3,plain,
    ! [U_11624,U_11625,U_11626] :
      ( hAPP(c_Set_Oimage(U_11624,U_11624,c_Groups_Ouminus__class_Ouminus(U_11624)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11624,U_11625),U_11626)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11624,hAPP(c_Groups_Ouminus__class_Ouminus(U_11624),U_11626),hAPP(c_Groups_Ouminus__class_Ouminus(U_11624),U_11625))
      | ~ class_Groups_Oordered__ab__group__add(U_11624) ),
    inference(definitional_conversion,[status(esa)],[f_3049_2]) ).

cnf(f_3049_4,plain,
    ( hAPP(c_Set_Oimage(U_11624,U_11624,c_Groups_Ouminus__class_Ouminus(U_11624)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11624,U_11625),U_11626)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11624,hAPP(c_Groups_Ouminus__class_Ouminus(U_11624),U_11626),hAPP(c_Groups_Ouminus__class_Ouminus(U_11624),U_11625))
    | ~ class_Groups_Oordered__ab__group__add(U_11624) ),
    inference(clausify,[status(thm)],[f_3049_3]) ).

fof(f_3050_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc]) ).

fof(f_3050_2,plain,
    ! [U_11628,U_11627] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11627),hAPP(c_Nat_OSuc,U_11628)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11627),U_11628)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11627),hAPP(c_Nat_OSuc,U_11628)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11628),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11627),U_11628))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11627),U_11628)) ) ),
    inference(variable_rename,[status(thm)],[f_3050_1]) ).

fof(f_3050_3,plain,
    ( ! [U_11632,U_11630] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11630),hAPP(c_Nat_OSuc,U_11632)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11630),U_11632)) )
    & ! [U_11631,U_11629] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11629),hAPP(c_Nat_OSuc,U_11631)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11629),U_11631))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11629),U_11631)) ) ),
    inference(miniscope,[status(thm)],[f_3050_2]) ).

fof(f_3050_4,plain,
    ( ! [U_11630,U_11632] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11630),hAPP(c_Nat_OSuc,U_11632)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11630),U_11632)) )
    & ! [U_11631,U_11629] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11629),hAPP(c_Nat_OSuc,U_11631)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11629),U_11631))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11629),U_11631)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3050_3]) ).

cnf(f_3050_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11629),hAPP(c_Nat_OSuc,U_11631)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11629),U_11631))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11629),U_11631)) ),
    inference(clausify,[status(thm)],[f_3050_4]) ).

cnf(f_3050_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11630),hAPP(c_Nat_OSuc,U_11632)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11630),U_11632)) ),
    inference(clausify,[status(thm)],[f_3050_4]) ).

fof(f_3051_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J]) ).

fof(f_3051_2,plain,
    ! [U_11636,U_11635,U_11634,U_11633] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11633,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11633,U_11634,U_11635)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11633,U_11635),U_11636)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11633,U_11634,U_11636)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11633),U_11635),U_11636))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11633),U_11634),U_11635))
      | ~ class_Orderings_Olinorder(U_11633) ),
    inference(variable_rename,[status(thm)],[f_3051_1]) ).

fof(f_3051_3,plain,
    ! [U_11633,U_11634,U_11635,U_11636] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11633,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11633,U_11634,U_11635)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11633,U_11635),U_11636)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11633,U_11634,U_11636)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11633),U_11635),U_11636))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11633),U_11634),U_11635))
      | ~ class_Orderings_Olinorder(U_11633) ),
    inference(definitional_conversion,[status(esa)],[f_3051_2]) ).

cnf(f_3051_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11633,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11633,U_11634,U_11635)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11633,U_11635),U_11636)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11633,U_11634,U_11636)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11633),U_11635),U_11636))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11633),U_11634),U_11635))
    | ~ class_Orderings_Olinorder(U_11633) ),
    inference(clausify,[status(thm)],[f_3051_3]) ).

fof(f_3052_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J]) ).

fof(f_3052_2,plain,
    ! [U_11639,U_11638,U_11637] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11637,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11637,U_11638),U_11639)),hAPP(hAPP(c_Set_Oinsert(U_11637),U_11639),c_Orderings_Obot__class_Obot(tc_fun(U_11637,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_11637,U_11638,U_11639)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11637),U_11638),U_11639))
      | ~ class_Orderings_Olinorder(U_11637) ),
    inference(variable_rename,[status(thm)],[f_3052_1]) ).

fof(f_3052_3,plain,
    ! [U_11637,U_11638,U_11639] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11637,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11637,U_11638),U_11639)),hAPP(hAPP(c_Set_Oinsert(U_11637),U_11639),c_Orderings_Obot__class_Obot(tc_fun(U_11637,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_11637,U_11638,U_11639)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11637),U_11638),U_11639))
      | ~ class_Orderings_Olinorder(U_11637) ),
    inference(definitional_conversion,[status(esa)],[f_3052_2]) ).

cnf(f_3052_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11637,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11637,U_11638),U_11639)),hAPP(hAPP(c_Set_Oinsert(U_11637),U_11639),c_Orderings_Obot__class_Obot(tc_fun(U_11637,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_11637,U_11638,U_11639)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11637),U_11638),U_11639))
    | ~ class_Orderings_Olinorder(U_11637) ),
    inference(clausify,[status(thm)],[f_3052_3]) ).

fof(f_3053_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J]) ).

fof(f_3053_2,plain,
    ! [U_11642,U_11641,U_11640] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11640,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11640),U_11641),c_Orderings_Obot__class_Obot(tc_fun(U_11640,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11640,U_11641,U_11642)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11640,U_11641),U_11642)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11640),U_11641),U_11642))
      | ~ class_Orderings_Olinorder(U_11640) ),
    inference(variable_rename,[status(thm)],[f_3053_1]) ).

fof(f_3053_3,plain,
    ! [U_11640,U_11641,U_11642] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11640,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11640),U_11641),c_Orderings_Obot__class_Obot(tc_fun(U_11640,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11640,U_11641,U_11642)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11640,U_11641),U_11642)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11640),U_11641),U_11642))
      | ~ class_Orderings_Olinorder(U_11640) ),
    inference(definitional_conversion,[status(esa)],[f_3053_2]) ).

cnf(f_3053_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11640,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11640),U_11641),c_Orderings_Obot__class_Obot(tc_fun(U_11640,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11640,U_11641,U_11642)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11640,U_11641),U_11642)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11640),U_11641),U_11642))
    | ~ class_Orderings_Olinorder(U_11640) ),
    inference(clausify,[status(thm)],[f_3053_3]) ).

fof(f_3054_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J]) ).

fof(f_3054_2,plain,
    ! [U_11646,U_11645,U_11644,U_11643] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11643,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11643,U_11644,U_11645)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11643,U_11645,U_11646)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11643,U_11644),U_11646)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11643),U_11645),U_11646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11643),U_11644),U_11645))
      | ~ class_Orderings_Olinorder(U_11643) ),
    inference(variable_rename,[status(thm)],[f_3054_1]) ).

fof(f_3054_3,plain,
    ! [U_11643,U_11644,U_11645,U_11646] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11643,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11643,U_11644,U_11645)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11643,U_11645,U_11646)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11643,U_11644),U_11646)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11643),U_11645),U_11646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11643),U_11644),U_11645))
      | ~ class_Orderings_Olinorder(U_11643) ),
    inference(definitional_conversion,[status(esa)],[f_3054_2]) ).

cnf(f_3054_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11643,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11643,U_11644,U_11645)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11643,U_11645,U_11646)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11643,U_11644),U_11646)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11643),U_11645),U_11646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11643),U_11644),U_11645))
    | ~ class_Orderings_Olinorder(U_11643) ),
    inference(clausify,[status(thm)],[f_3054_3]) ).

fof(f_3055_1,plain,
    ! [V_t_2,V_A_2,V_D_2,V_d_2] :
      ( ! [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I10_J]) ).

fof(f_3055_2,plain,
    ! [U_11653,U_11652,U_11651,U_11650] :
      ( ! [U_11649] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11651)),U_11653)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11653)))
          | ? [U_11648] :
              ( ? [U_11647] :
                  ( U_11649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11647),U_11648)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11647),U_11652)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11648),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11651))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),U_11651)) ),
    inference(variable_rename,[status(thm)],[f_3055_1]) ).

fof(f_3055_3,plain,
    ! [U_11653,U_11652,U_11651,U_11650] :
      ( ! [U_11649] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11651)),U_11653)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11653)))
          | ( ? [U_11647] :
                ( U_11649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11647),sK245(U_11653,U_11652,U_11651,U_11650,U_11649))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11647),U_11652)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_11653,U_11652,U_11651,U_11650,U_11649)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11651))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),U_11651)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_11648,sK245(U_11653,U_11652,U_11651,U_11650,U_11649))],[f_3055_2]) ).

fof(f_3055_4,plain,
    ! [U_11653,U_11652,U_11651,U_11650] :
      ( ! [U_11649] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11651)),U_11653)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11653)))
          | ( U_11649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK246(U_11653,U_11652,U_11651,U_11650,U_11649)),sK245(U_11653,U_11652,U_11651,U_11650,U_11649))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11653,U_11652,U_11651,U_11650,U_11649)),U_11652))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_11653,U_11652,U_11651,U_11650,U_11649)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11651))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),U_11651)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_11647,sK246(U_11653,U_11652,U_11651,U_11650,U_11649))],[f_3055_3]) ).

fof(f_3055_5,plain,
    ( ! [U_11649,U_11650,U_11651,U_11652,U_11653] :
        ( U_11649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK246(U_11653,U_11652,U_11651,U_11650,U_11649)),sK245(U_11653,U_11652,U_11651,U_11650,U_11649))
        | ~ sP889(U_11649,U_11650,U_11651,U_11652,U_11653) )
    & ! [U_11649,U_11650,U_11651,U_11652,U_11653] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11653,U_11652,U_11651,U_11650,U_11649)),U_11652))
        | ~ sP889(U_11649,U_11650,U_11651,U_11652,U_11653) )
    & ! [U_11649,U_11650,U_11651,U_11652,U_11653] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_11653,U_11652,U_11651,U_11650,U_11649)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11651)))
        | ~ sP889(U_11649,U_11650,U_11651,U_11652,U_11653) )
    & ! [U_11649,U_11650,U_11651,U_11652,U_11653] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11651)),U_11653)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11653)))
        | sP889(U_11649,U_11650,U_11651,U_11652,U_11653)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),U_11651)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP889])],[f_3055_4]) ).

cnf(f_3055_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11651)),U_11653)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11649),U_11653)))
    | sP889(U_11649,U_11650,U_11651,U_11652,U_11653)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11650),U_11651)) ),
    inference(clausify,[status(thm)],[f_3055_5]) ).

cnf(f_3055_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_11653,U_11652,U_11651,U_11650,U_11649)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11651)))
    | ~ sP889(U_11649,U_11650,U_11651,U_11652,U_11653) ),
    inference(clausify,[status(thm)],[f_3055_5]) ).

cnf(f_3055_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11653,U_11652,U_11651,U_11650,U_11649)),U_11652))
    | ~ sP889(U_11649,U_11650,U_11651,U_11652,U_11653) ),
    inference(clausify,[status(thm)],[f_3055_5]) ).

cnf(f_3055_9,plain,
    ( U_11649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK246(U_11653,U_11652,U_11651,U_11650,U_11649)),sK245(U_11653,U_11652,U_11651,U_11650,U_11649))
    | ~ sP889(U_11649,U_11650,U_11651,U_11652,U_11653) ),
    inference(clausify,[status(thm)],[f_3055_5]) ).

fof(f_3056_1,plain,
    ! [V_t_2,V_B_2,V_D_2,V_d_2] :
      ( ! [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I10_J]) ).

fof(f_3056_2,plain,
    ! [U_11660,U_11659,U_11658,U_11657] :
      ( ! [U_11656] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11656),U_11658)),U_11660)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11656),U_11660)))
          | ? [U_11655] :
              ( ? [U_11654] :
                  ( U_11656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11654),U_11655)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11654),U_11659)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11655),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11658))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),U_11658)) ),
    inference(variable_rename,[status(thm)],[f_3056_1]) ).

fof(f_3056_3,plain,
    ! [U_11660,U_11659,U_11658,U_11657] :
      ( ! [U_11656] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11656),U_11658)),U_11660)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11656),U_11660)))
          | ( ? [U_11654] :
                ( U_11656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11654),sK247(U_11660,U_11659,U_11658,U_11657,U_11656))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11654),U_11659)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11660,U_11659,U_11658,U_11657,U_11656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11658))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),U_11658)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_11655,sK247(U_11660,U_11659,U_11658,U_11657,U_11656))],[f_3056_2]) ).

fof(f_3056_4,plain,
    ! [U_11660,U_11659,U_11658,U_11657] :
      ( ! [U_11656] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11656),U_11658)),U_11660)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11656),U_11660)))
          | ( U_11656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK248(U_11660,U_11659,U_11658,U_11657,U_11656)),sK247(U_11660,U_11659,U_11658,U_11657,U_11656))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11660,U_11659,U_11658,U_11657,U_11656)),U_11659))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11660,U_11659,U_11658,U_11657,U_11656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11658))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),U_11658)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_11654,sK248(U_11660,U_11659,U_11658,U_11657,U_11656))],[f_3056_3]) ).

fof(f_3056_5,plain,
    ( ! [U_11660,U_11659,U_11656,U_11657,U_11658] :
        ( U_11656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK248(U_11660,U_11659,U_11658,U_11657,U_11656)),sK247(U_11660,U_11659,U_11658,U_11657,U_11656))
        | ~ sP890(U_11660,U_11659,U_11656,U_11657,U_11658) )
    & ! [U_11660,U_11659,U_11656,U_11657,U_11658] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11660,U_11659,U_11658,U_11657,U_11656)),U_11659))
        | ~ sP890(U_11660,U_11659,U_11656,U_11657,U_11658) )
    & ! [U_11660,U_11659,U_11656,U_11657,U_11658] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11660,U_11659,U_11658,U_11657,U_11656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11658)))
        | ~ sP890(U_11660,U_11659,U_11656,U_11657,U_11658) )
    & ! [U_11660,U_11659,U_11656,U_11657,U_11658] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11656),U_11658)),U_11660)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11656),U_11660)))
        | sP890(U_11660,U_11659,U_11656,U_11657,U_11658)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),U_11658)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP890])],[f_3056_4]) ).

cnf(f_3056_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11656),U_11658)),U_11660)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11656),U_11660)))
    | sP890(U_11660,U_11659,U_11656,U_11657,U_11658)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11657),U_11658)) ),
    inference(clausify,[status(thm)],[f_3056_5]) ).

cnf(f_3056_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11660,U_11659,U_11658,U_11657,U_11656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11658)))
    | ~ sP890(U_11660,U_11659,U_11656,U_11657,U_11658) ),
    inference(clausify,[status(thm)],[f_3056_5]) ).

cnf(f_3056_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11660,U_11659,U_11658,U_11657,U_11656)),U_11659))
    | ~ sP890(U_11660,U_11659,U_11656,U_11657,U_11658) ),
    inference(clausify,[status(thm)],[f_3056_5]) ).

cnf(f_3056_9,plain,
    ( U_11656 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK248(U_11660,U_11659,U_11658,U_11657,U_11656)),sK247(U_11660,U_11659,U_11658,U_11657,U_11656))
    | ~ sP890(U_11660,U_11659,U_11656,U_11657,U_11658) ),
    inference(clausify,[status(thm)],[f_3056_5]) ).

fof(f_3057_1,plain,
    ! [V_t_2,V_A_2,V_D_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I9_J]) ).

fof(f_3057_2,plain,
    ! [U_11667,U_11666,U_11665,U_11664] :
      ( ! [U_11663] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11665)),U_11667)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11667)))
          | ? [U_11662] :
              ( ? [U_11661] :
                  ( U_11663 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11661),U_11662)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11661),U_11666)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11662),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11665))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),U_11665)) ),
    inference(variable_rename,[status(thm)],[f_3057_1]) ).

fof(f_3057_3,plain,
    ! [U_11667,U_11666,U_11665,U_11664] :
      ( ! [U_11663] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11665)),U_11667)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11667)))
          | ( ? [U_11661] :
                ( U_11663 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11661),sK249(U_11667,U_11666,U_11665,U_11664,U_11663))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11661),U_11666)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11667,U_11666,U_11665,U_11664,U_11663)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11665))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),U_11665)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_11662,sK249(U_11667,U_11666,U_11665,U_11664,U_11663))],[f_3057_2]) ).

fof(f_3057_4,plain,
    ! [U_11667,U_11666,U_11665,U_11664] :
      ( ! [U_11663] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11665)),U_11667)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11667)))
          | ( U_11663 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK250(U_11667,U_11666,U_11665,U_11664,U_11663)),sK249(U_11667,U_11666,U_11665,U_11664,U_11663))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11667,U_11666,U_11665,U_11664,U_11663)),U_11666))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11667,U_11666,U_11665,U_11664,U_11663)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11665))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),U_11665)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_11661,sK250(U_11667,U_11666,U_11665,U_11664,U_11663))],[f_3057_3]) ).

fof(f_3057_5,plain,
    ( ! [U_11665,U_11667,U_11666,U_11663,U_11664] :
        ( U_11663 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK250(U_11667,U_11666,U_11665,U_11664,U_11663)),sK249(U_11667,U_11666,U_11665,U_11664,U_11663))
        | ~ sP891(U_11665,U_11667,U_11666,U_11663,U_11664) )
    & ! [U_11665,U_11667,U_11666,U_11663,U_11664] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11667,U_11666,U_11665,U_11664,U_11663)),U_11666))
        | ~ sP891(U_11665,U_11667,U_11666,U_11663,U_11664) )
    & ! [U_11665,U_11667,U_11666,U_11663,U_11664] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11667,U_11666,U_11665,U_11664,U_11663)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11665)))
        | ~ sP891(U_11665,U_11667,U_11666,U_11663,U_11664) )
    & ! [U_11665,U_11667,U_11666,U_11663,U_11664] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11665)),U_11667)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11667)))
        | sP891(U_11665,U_11667,U_11666,U_11663,U_11664)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),U_11665)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP891])],[f_3057_4]) ).

cnf(f_3057_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11665)),U_11667)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11663),U_11667)))
    | sP891(U_11665,U_11667,U_11666,U_11663,U_11664)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11664),U_11665)) ),
    inference(clausify,[status(thm)],[f_3057_5]) ).

cnf(f_3057_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11667,U_11666,U_11665,U_11664,U_11663)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11665)))
    | ~ sP891(U_11665,U_11667,U_11666,U_11663,U_11664) ),
    inference(clausify,[status(thm)],[f_3057_5]) ).

cnf(f_3057_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11667,U_11666,U_11665,U_11664,U_11663)),U_11666))
    | ~ sP891(U_11665,U_11667,U_11666,U_11663,U_11664) ),
    inference(clausify,[status(thm)],[f_3057_5]) ).

cnf(f_3057_9,plain,
    ( U_11663 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK250(U_11667,U_11666,U_11665,U_11664,U_11663)),sK249(U_11667,U_11666,U_11665,U_11664,U_11663))
    | ~ sP891(U_11665,U_11667,U_11666,U_11663,U_11664) ),
    inference(clausify,[status(thm)],[f_3057_5]) ).

fof(f_3058_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastLessThan__int]) ).

fof(f_3058_2,plain,
    ! [U_11669,U_11668] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11668),U_11669))),
    inference(variable_rename,[status(thm)],[f_3058_1]) ).

fof(f_3058_3,plain,
    ! [U_11669,U_11668] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11668),U_11669))),
    inference(definitional_conversion,[status(esa)],[f_3058_2]) ).

cnf(f_3058_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11668),U_11669))),
    inference(clausify,[status(thm)],[f_3058_3]) ).

fof(f_3059_1,plain,
    ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).

fof(f_3059_2,plain,
    ! [U_11670] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11670))),
    inference(variable_rename,[status(thm)],[f_3059_1]) ).

fof(f_3059_3,plain,
    ! [U_11670] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11670))),
    inference(definitional_conversion,[status(esa)],[f_3059_2]) ).

cnf(f_3059_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11670))),
    inference(clausify,[status(thm)],[f_3059_3]) ).

fof(f_3060_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).

fof(f_3060_2,plain,
    ! [U_11672,U_11671] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11672),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11671,U_11672),
    inference(variable_rename,[status(thm)],[f_3060_1]) ).

fof(f_3060_3,plain,
    ! [U_11671,U_11672] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11672),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11671,U_11672),
    inference(definitional_conversion,[status(esa)],[f_3060_2]) ).

cnf(f_3060_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11672),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11671,U_11672),
    inference(clausify,[status(thm)],[f_3060_3]) ).

fof(f_3061_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2),
    inference(fof_nnf,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).

fof(f_3061_2,plain,
    ! [U_11674,U_11673] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),U_11673)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11674),U_11673))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11673),U_11674),
    inference(variable_rename,[status(thm)],[f_3061_1]) ).

fof(f_3061_3,plain,
    ! [U_11673,U_11674] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),U_11673)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11674),U_11673))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11673),U_11674),
    inference(definitional_conversion,[status(esa)],[f_3061_2]) ).

cnf(f_3061_4,plain,
    hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),U_11673)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11674),U_11673))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11673),U_11674),
    inference(clausify,[status(thm)],[f_3061_3]) ).

fof(f_3062_1,plain,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).

fof(f_3062_2,plain,
    ! [U_11675] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11675)) = hAPP(c_Int_Onat,U_11675),
    inference(variable_rename,[status(thm)],[f_3062_1]) ).

fof(f_3062_3,plain,
    ! [U_11675] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11675)) = hAPP(c_Int_Onat,U_11675),
    inference(definitional_conversion,[status(esa)],[f_3062_2]) ).

cnf(f_3062_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11675)) = hAPP(c_Int_Onat,U_11675),
    inference(clausify,[status(thm)],[f_3062_3]) ).

fof(f_3063_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastLessThan__int]) ).

fof(f_3063_2,plain,
    ! [U_11677,U_11676] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11676),U_11677)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11677),U_11676)),
    inference(variable_rename,[status(thm)],[f_3063_1]) ).

fof(f_3063_3,plain,
    ! [U_11676,U_11677] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11676),U_11677)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11677),U_11676)),
    inference(definitional_conversion,[status(esa)],[f_3063_2]) ).

cnf(f_3063_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_11676),U_11677)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11677),U_11676)),
    inference(clausify,[status(thm)],[f_3063_3]) ).

fof(f_3064_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).

fof(f_3064_2,plain,
    ! [U_11679,U_11678] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11678),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11679) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_11678,U_11679),
    inference(variable_rename,[status(thm)],[f_3064_1]) ).

fof(f_3064_3,plain,
    ! [U_11678,U_11679] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11678),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11679) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_11678,U_11679),
    inference(definitional_conversion,[status(esa)],[f_3064_2]) ).

cnf(f_3064_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11678),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11679) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_11678,U_11679),
    inference(clausify,[status(thm)],[f_3064_3]) ).

fof(f_3065_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).

fof(f_3065_2,plain,
    ! [U_11680] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11680) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11680))),
    inference(variable_rename,[status(thm)],[f_3065_1]) ).

fof(f_3065_3,plain,
    ! [U_11680] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11680) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11680))),
    inference(definitional_conversion,[status(esa)],[f_3065_2]) ).

cnf(f_3065_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11680) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11680))),
    inference(clausify,[status(thm)],[f_3065_3]) ).

fof(f_3066_1,plain,
    ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__image]) ).

fof(f_3066_2,plain,
    ! [U_11686,U_11685,U_11684,U_11683,U_11682,U_11681] :
      ( ( hAPP(c_Set_Oimage(U_11681,U_11684,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11681,U_11684),U_11685),U_11682),U_11686)),U_11683) = hAPP(c_Set_Oimage(U_11681,U_11684,U_11685),U_11683)
        | hBOOL(hAPP(hAPP(c_member(U_11681),U_11682),U_11683)) )
      & ( hAPP(c_Set_Oimage(U_11681,U_11684,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11681,U_11684),U_11685),U_11682),U_11686)),U_11683) = hAPP(hAPP(c_Set_Oinsert(U_11684),U_11686),hAPP(c_Set_Oimage(U_11681,U_11684,U_11685),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11681,tc_HOL_Obool)),U_11683),hAPP(hAPP(c_Set_Oinsert(U_11681),U_11682),c_Orderings_Obot__class_Obot(tc_fun(U_11681,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11681),U_11682),U_11683)) ) ),
    inference(variable_rename,[status(thm)],[f_3066_1]) ).

fof(f_3066_3,plain,
    ( ! [U_11698,U_11696,U_11694,U_11692,U_11690,U_11688] :
        ( hAPP(c_Set_Oimage(U_11688,U_11694,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11688,U_11694),U_11696),U_11690),U_11698)),U_11692) = hAPP(c_Set_Oimage(U_11688,U_11694,U_11696),U_11692)
        | hBOOL(hAPP(hAPP(c_member(U_11688),U_11690),U_11692)) )
    & ! [U_11697,U_11695,U_11693,U_11691,U_11689,U_11687] :
        ( hAPP(c_Set_Oimage(U_11687,U_11693,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11687,U_11693),U_11695),U_11689),U_11697)),U_11691) = hAPP(hAPP(c_Set_Oinsert(U_11693),U_11697),hAPP(c_Set_Oimage(U_11687,U_11693,U_11695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11687,tc_HOL_Obool)),U_11691),hAPP(hAPP(c_Set_Oinsert(U_11687),U_11689),c_Orderings_Obot__class_Obot(tc_fun(U_11687,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11687),U_11689),U_11691)) ) ),
    inference(miniscope,[status(thm)],[f_3066_2]) ).

fof(f_3066_4,plain,
    ( ! [U_11688,U_11690,U_11692,U_11694,U_11696,U_11698] :
        ( hAPP(c_Set_Oimage(U_11688,U_11694,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11688,U_11694),U_11696),U_11690),U_11698)),U_11692) = hAPP(c_Set_Oimage(U_11688,U_11694,U_11696),U_11692)
        | hBOOL(hAPP(hAPP(c_member(U_11688),U_11690),U_11692)) )
    & ! [U_11693,U_11687,U_11689,U_11695,U_11691,U_11697] :
        ( hAPP(c_Set_Oimage(U_11687,U_11693,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11687,U_11693),U_11695),U_11689),U_11697)),U_11691) = hAPP(hAPP(c_Set_Oinsert(U_11693),U_11697),hAPP(c_Set_Oimage(U_11687,U_11693,U_11695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11687,tc_HOL_Obool)),U_11691),hAPP(hAPP(c_Set_Oinsert(U_11687),U_11689),c_Orderings_Obot__class_Obot(tc_fun(U_11687,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11687),U_11689),U_11691)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3066_3]) ).

cnf(f_3066_5,plain,
    ( hAPP(c_Set_Oimage(U_11687,U_11693,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11687,U_11693),U_11695),U_11689),U_11697)),U_11691) = hAPP(hAPP(c_Set_Oinsert(U_11693),U_11697),hAPP(c_Set_Oimage(U_11687,U_11693,U_11695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11687,tc_HOL_Obool)),U_11691),hAPP(hAPP(c_Set_Oinsert(U_11687),U_11689),c_Orderings_Obot__class_Obot(tc_fun(U_11687,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11687),U_11689),U_11691)) ),
    inference(clausify,[status(thm)],[f_3066_4]) ).

cnf(f_3066_6,plain,
    ( hAPP(c_Set_Oimage(U_11688,U_11694,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11688,U_11694),U_11696),U_11690),U_11698)),U_11692) = hAPP(c_Set_Oimage(U_11688,U_11694,U_11696),U_11692)
    | hBOOL(hAPP(hAPP(c_member(U_11688),U_11690),U_11692)) ),
    inference(clausify,[status(thm)],[f_3066_4]) ).

fof(f_3067_1,plain,
    ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__into]) ).

fof(f_3067_2,plain,
    ! [U_11704,U_11703,U_11702,U_11701,U_11700,U_11699] :
      ( hBOOL(hAPP(hAPP(c_member(U_11699),hAPP(c_Fun_Othe__inv__into(U_11699,U_11700,U_11702,U_11701),U_11703)),U_11704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11699,tc_HOL_Obool)),U_11702),U_11704))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11700),U_11703),hAPP(c_Set_Oimage(U_11699,U_11700,U_11701),U_11702)))
      | ~ c_Fun_Oinj__on(U_11699,U_11700,U_11701,U_11702) ),
    inference(variable_rename,[status(thm)],[f_3067_1]) ).

fof(f_3067_3,plain,
    ! [U_11699,U_11700,U_11701,U_11702,U_11703,U_11704] :
      ( hBOOL(hAPP(hAPP(c_member(U_11699),hAPP(c_Fun_Othe__inv__into(U_11699,U_11700,U_11702,U_11701),U_11703)),U_11704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11699,tc_HOL_Obool)),U_11702),U_11704))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11700),U_11703),hAPP(c_Set_Oimage(U_11699,U_11700,U_11701),U_11702)))
      | ~ c_Fun_Oinj__on(U_11699,U_11700,U_11701,U_11702) ),
    inference(definitional_conversion,[status(esa)],[f_3067_2]) ).

cnf(f_3067_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11699),hAPP(c_Fun_Othe__inv__into(U_11699,U_11700,U_11702,U_11701),U_11703)),U_11704))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11699,tc_HOL_Obool)),U_11702),U_11704))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11700),U_11703),hAPP(c_Set_Oimage(U_11699,U_11700,U_11701),U_11702)))
    | ~ c_Fun_Oinj__on(U_11699,U_11700,U_11701,U_11702) ),
    inference(clausify,[status(thm)],[f_3067_3]) ).

fof(f_3068_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_fun__upd__triv]) ).

fof(f_3068_2,plain,
    ! [U_11708,U_11707,U_11706,U_11705] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11705,U_11706),U_11707),U_11708),hAPP(U_11707,U_11708)) = U_11707,
    inference(variable_rename,[status(thm)],[f_3068_1]) ).

fof(f_3068_3,plain,
    ! [U_11705,U_11707,U_11706,U_11708] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11705,U_11706),U_11707),U_11708),hAPP(U_11707,U_11708)) = U_11707,
    inference(definitional_conversion,[status(esa)],[f_3068_2]) ).

cnf(f_3068_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11705,U_11706),U_11707),U_11708),hAPP(U_11707,U_11708)) = U_11707,
    inference(clausify,[status(thm)],[f_3068_3]) ).

fof(f_3069_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atMost]) ).

fof(f_3069_2,plain,
    ! [U_11709] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11709))),
    inference(variable_rename,[status(thm)],[f_3069_1]) ).

fof(f_3069_3,plain,
    ! [U_11709] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11709))),
    inference(definitional_conversion,[status(esa)],[f_3069_2]) ).

cnf(f_3069_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11709))),
    inference(clausify,[status(thm)],[f_3069_3]) ).

fof(f_3070_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff]) ).

fof(f_3070_2,plain,
    ! [U_11712,U_11711,U_11710] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11711) = hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11712)
          | U_11711 != U_11712 )
        & ( U_11711 = U_11712
          | hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11711) != hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11712) ) )
      | ~ class_Orderings_Olinorder(U_11710) ),
    inference(variable_rename,[status(thm)],[f_3070_1]) ).

fof(f_3070_3,plain,
    ( ! [U_11710,U_11711,U_11712] :
        ( hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11711) = hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11712)
        | U_11711 != U_11712
        | ~ sP892(U_11710,U_11711,U_11712) )
    & ! [U_11710,U_11711,U_11712] :
        ( U_11711 = U_11712
        | hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11711) != hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11712)
        | ~ sP892(U_11710,U_11711,U_11712) )
    & ! [U_11710,U_11711,U_11712] :
        ( sP892(U_11710,U_11711,U_11712)
        | ~ class_Orderings_Olinorder(U_11710) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP892])],[f_3070_2]) ).

cnf(f_3070_4,plain,
    ( sP892(U_11710,U_11711,U_11712)
    | ~ class_Orderings_Olinorder(U_11710) ),
    inference(clausify,[status(thm)],[f_3070_3]) ).

cnf(f_3070_5,plain,
    ( U_11711 = U_11712
    | hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11711) != hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11712)
    | ~ sP892(U_11710,U_11711,U_11712) ),
    inference(clausify,[status(thm)],[f_3070_3]) ).

cnf(f_3070_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11711) = hAPP(c_SetInterval_Oord__class_OatMost(U_11710),U_11712)
    | U_11711 != U_11712
    | ~ sP892(U_11710,U_11711,U_11712) ),
    inference(clausify,[status(thm)],[f_3070_3]) ).

fof(f_3071_1,plain,
    ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
      | hAPP(V_f_2,V_x_2) != V_y_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__idem]) ).

fof(f_3071_2,plain,
    ! [U_11717,U_11716,U_11715,U_11714,U_11713] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11716,U_11717),U_11713),U_11714),U_11715) = U_11713
      | hAPP(U_11713,U_11714) != U_11715 ),
    inference(variable_rename,[status(thm)],[f_3071_1]) ).

fof(f_3071_3,plain,
    ! [U_11715,U_11714,U_11716,U_11713,U_11717] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11716,U_11717),U_11713),U_11714),U_11715) = U_11713
      | hAPP(U_11713,U_11714) != U_11715 ),
    inference(definitional_conversion,[status(esa)],[f_3071_2]) ).

cnf(f_3071_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11716,U_11717),U_11713),U_11714),U_11715) = U_11713
    | hAPP(U_11713,U_11714) != U_11715 ),
    inference(clausify,[status(thm)],[f_3071_3]) ).

fof(f_3072_1,plain,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)
      | V_z_2 = V_x_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__other]) ).

fof(f_3072_2,plain,
    ! [U_11723,U_11722,U_11721,U_11720,U_11719,U_11718] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11720,U_11721),U_11722),U_11719),U_11723),U_11718) = hAPP(U_11722,U_11718)
      | U_11718 = U_11719 ),
    inference(variable_rename,[status(thm)],[f_3072_1]) ).

fof(f_3072_3,plain,
    ! [U_11722,U_11719,U_11718,U_11720,U_11721,U_11723] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11720,U_11721),U_11722),U_11719),U_11723),U_11718) = hAPP(U_11722,U_11718)
      | U_11718 = U_11719 ),
    inference(definitional_conversion,[status(esa)],[f_3072_2]) ).

cnf(f_3072_4,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11720,U_11721),U_11722),U_11719),U_11723),U_11718) = hAPP(U_11722,U_11718)
    | U_11718 = U_11719 ),
    inference(clausify,[status(thm)],[f_3072_3]) ).

fof(f_3073_1,plain,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2)
      | V_a_2 = V_c_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).

fof(f_3073_2,plain,
    ! [U_11730,U_11729,U_11728,U_11727,U_11726,U_11725,U_11724] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),U_11728),U_11724),U_11729)),U_11725),U_11730) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),U_11728),U_11725),U_11730)),U_11724),U_11729)
      | U_11724 = U_11725 ),
    inference(variable_rename,[status(thm)],[f_3073_1]) ).

fof(f_3073_3,plain,
    ! [U_11724,U_11725,U_11726,U_11727,U_11728,U_11729,U_11730] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),U_11728),U_11724),U_11729)),U_11725),U_11730) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),U_11728),U_11725),U_11730)),U_11724),U_11729)
      | U_11724 = U_11725 ),
    inference(definitional_conversion,[status(esa)],[f_3073_2]) ).

cnf(f_3073_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),U_11728),U_11724),U_11729)),U_11725),U_11730) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11726,U_11727),U_11728),U_11725),U_11730)),U_11724),U_11729)
    | U_11724 = U_11725 ),
    inference(clausify,[status(thm)],[f_3073_3]) ).

fof(f_3074_1,plain,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)
        | V_z_2 = V_x_2 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2
        | V_z_2 != V_x_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__apply]) ).

fof(f_3074_2,plain,
    ! [U_11736,U_11735,U_11734,U_11733,U_11732,U_11731] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11733,U_11734),U_11735),U_11732),U_11736),U_11731) = hAPP(U_11735,U_11731)
        | U_11731 = U_11732 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11733,U_11734),U_11735),U_11732),U_11736),U_11731) = U_11736
        | U_11731 != U_11732 ) ),
    inference(variable_rename,[status(thm)],[f_3074_1]) ).

fof(f_3074_3,plain,
    ( ! [U_11748,U_11746,U_11744,U_11742,U_11740,U_11738] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11742,U_11744),U_11746),U_11740),U_11748),U_11738) = hAPP(U_11746,U_11738)
        | U_11738 = U_11740 )
    & ! [U_11747,U_11745,U_11743,U_11741,U_11739,U_11737] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11741,U_11743),U_11745),U_11739),U_11747),U_11737) = U_11747
        | U_11737 != U_11739 ) ),
    inference(miniscope,[status(thm)],[f_3074_2]) ).

fof(f_3074_4,plain,
    ( ! [U_11738,U_11740,U_11742,U_11744,U_11746,U_11748] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11742,U_11744),U_11746),U_11740),U_11748),U_11738) = hAPP(U_11746,U_11738)
        | U_11738 = U_11740 )
    & ! [U_11739,U_11743,U_11737,U_11741,U_11745,U_11747] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11741,U_11743),U_11745),U_11739),U_11747),U_11737) = U_11747
        | U_11737 != U_11739 ) ),
    inference(definitional_conversion,[status(esa)],[f_3074_3]) ).

cnf(f_3074_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11741,U_11743),U_11745),U_11739),U_11747),U_11737) = U_11747
    | U_11737 != U_11739 ),
    inference(clausify,[status(thm)],[f_3074_4]) ).

cnf(f_3074_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11742,U_11744),U_11746),U_11740),U_11748),U_11738) = hAPP(U_11746,U_11738)
    | U_11738 = U_11740 ),
    inference(clausify,[status(thm)],[f_3074_4]) ).

fof(f_3075_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2,
    inference(fof_nnf,[status(thm)],[fact_fun__upd__same]) ).

fof(f_3075_2,plain,
    ! [U_11753,U_11752,U_11751,U_11750,U_11749] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11749,U_11750),U_11751),U_11752),U_11753),U_11752) = U_11753,
    inference(variable_rename,[status(thm)],[f_3075_1]) ).

fof(f_3075_3,plain,
    ! [U_11750,U_11749,U_11751,U_11752,U_11753] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11749,U_11750),U_11751),U_11752),U_11753),U_11752) = U_11753,
    inference(definitional_conversion,[status(esa)],[f_3075_2]) ).

cnf(f_3075_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11749,U_11750),U_11751),U_11752),U_11753),U_11752) = U_11753,
    inference(clausify,[status(thm)],[f_3075_3]) ).

fof(f_3076_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).

fof(f_3076_2,plain,
    ! [U_11759,U_11758,U_11757,U_11756,U_11755,U_11754] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),U_11756),U_11757),U_11758)),U_11757),U_11759) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),U_11756),U_11757),U_11759),
    inference(variable_rename,[status(thm)],[f_3076_1]) ).

fof(f_3076_3,plain,
    ! [U_11754,U_11755,U_11756,U_11757,U_11758,U_11759] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),U_11756),U_11757),U_11758)),U_11757),U_11759) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),U_11756),U_11757),U_11759),
    inference(definitional_conversion,[status(esa)],[f_3076_2]) ).

cnf(f_3076_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),U_11756),U_11757),U_11758)),U_11757),U_11759) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11754,U_11755),U_11756),U_11757),U_11759),
    inference(clausify,[status(thm)],[f_3076_3]) ).

fof(f_3077_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
        | hAPP(V_f_2,V_x_2) != V_y_2 )
      & ( hAPP(V_f_2,V_x_2) = V_y_2
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) != V_f_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).

fof(f_3077_2,plain,
    ! [U_11764,U_11763,U_11762,U_11761,U_11760] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11760,U_11761),U_11762),U_11763),U_11764) = U_11762
        | hAPP(U_11762,U_11763) != U_11764 )
      & ( hAPP(U_11762,U_11763) = U_11764
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11760,U_11761),U_11762),U_11763),U_11764) != U_11762 ) ),
    inference(variable_rename,[status(thm)],[f_3077_1]) ).

fof(f_3077_3,plain,
    ( ! [U_11774,U_11772,U_11770] :
        ( ! [U_11768,U_11766] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11766,U_11768),U_11770),U_11772),U_11774) = U_11770
        | hAPP(U_11770,U_11772) != U_11774 )
    & ! [U_11773,U_11771,U_11769] :
        ( ! [U_11767,U_11765] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11765,U_11767),U_11769),U_11771),U_11773) != U_11769
        | hAPP(U_11769,U_11771) = U_11773 ) ),
    inference(miniscope,[status(thm)],[f_3077_2]) ).

fof(f_3077_4,plain,
    ( ! [U_11774,U_11766,U_11768,U_11770,U_11772] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11766,U_11768),U_11770),U_11772),U_11774) = U_11770
        | hAPP(U_11770,U_11772) != U_11774 )
    & ! [U_11769,U_11773,U_11767,U_11765,U_11771] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11765,U_11767),U_11769),U_11771),U_11773) != U_11769
        | hAPP(U_11769,U_11771) = U_11773 ) ),
    inference(definitional_conversion,[status(esa)],[f_3077_3]) ).

cnf(f_3077_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11765,U_11767),U_11769),U_11771),U_11773) != U_11769
    | hAPP(U_11769,U_11771) = U_11773 ),
    inference(clausify,[status(thm)],[f_3077_4]) ).

cnf(f_3077_6,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11766,U_11768),U_11770),U_11772),U_11774) = U_11770
    | hAPP(U_11770,U_11772) != U_11774 ),
    inference(clausify,[status(thm)],[f_3077_4]) ).

fof(f_3078_1,plain,
    ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2)
        | V_x_2 = V_a_2 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2
        | V_x_2 != V_a_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__def]) ).

fof(f_3078_2,plain,
    ! [U_11780,U_11779,U_11778,U_11777,U_11776,U_11775] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11777,U_11778),U_11779),U_11776),U_11780),U_11775) = hAPP(U_11779,U_11775)
        | U_11775 = U_11776 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11777,U_11778),U_11779),U_11776),U_11780),U_11775) = U_11780
        | U_11775 != U_11776 ) ),
    inference(variable_rename,[status(thm)],[f_3078_1]) ).

fof(f_3078_3,plain,
    ( ! [U_11792,U_11790,U_11788,U_11786,U_11784,U_11782] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11786,U_11788),U_11790),U_11784),U_11792),U_11782) = hAPP(U_11790,U_11782)
        | U_11782 = U_11784 )
    & ! [U_11791,U_11789,U_11787,U_11785,U_11783,U_11781] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11785,U_11787),U_11789),U_11783),U_11791),U_11781) = U_11791
        | U_11781 != U_11783 ) ),
    inference(miniscope,[status(thm)],[f_3078_2]) ).

fof(f_3078_4,plain,
    ( ! [U_11782,U_11784,U_11786,U_11788,U_11790,U_11792] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11786,U_11788),U_11790),U_11784),U_11792),U_11782) = hAPP(U_11790,U_11782)
        | U_11782 = U_11784 )
    & ! [U_11785,U_11787,U_11783,U_11781,U_11789,U_11791] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11785,U_11787),U_11789),U_11783),U_11791),U_11781) = U_11791
        | U_11781 != U_11783 ) ),
    inference(definitional_conversion,[status(esa)],[f_3078_3]) ).

cnf(f_3078_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11785,U_11787),U_11789),U_11783),U_11791),U_11781) = U_11791
    | U_11781 != U_11783 ),
    inference(clausify,[status(thm)],[f_3078_4]) ).

cnf(f_3078_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11786,U_11788),U_11790),U_11784),U_11792),U_11782) = hAPP(U_11790,U_11782)
    | U_11782 = U_11784 ),
    inference(clausify,[status(thm)],[f_3078_4]) ).

fof(f_3079_1,plain,
    ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_atLeast0AtMost]) ).

fof(f_3079_2,plain,
    ! [U_11793] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11793) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11793),
    inference(variable_rename,[status(thm)],[f_3079_1]) ).

fof(f_3079_3,plain,
    ! [U_11793] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11793) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11793),
    inference(definitional_conversion,[status(esa)],[f_3079_2]) ).

cnf(f_3079_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11793) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11793),
    inference(clausify,[status(thm)],[f_3079_3]) ).

fof(f_3080_1,plain,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_card__atMost]) ).

fof(f_3080_2,plain,
    ! [U_11794] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11794)) = hAPP(c_Nat_OSuc,U_11794),
    inference(variable_rename,[status(thm)],[f_3080_1]) ).

fof(f_3080_3,plain,
    ! [U_11794] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11794)) = hAPP(c_Nat_OSuc,U_11794),
    inference(definitional_conversion,[status(esa)],[f_3080_2]) ).

cnf(f_3080_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11794)) = hAPP(c_Nat_OSuc,U_11794),
    inference(clausify,[status(thm)],[f_3080_3]) ).

fof(f_3081_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_atMost__Suc]) ).

fof(f_3081_2,plain,
    ! [U_11795] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11795)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11795)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11795)),
    inference(variable_rename,[status(thm)],[f_3081_1]) ).

fof(f_3081_3,plain,
    ! [U_11795] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11795)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11795)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11795)),
    inference(definitional_conversion,[status(esa)],[f_3081_2]) ).

cnf(f_3081_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11795)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11795)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11795)),
    inference(clausify,[status(thm)],[f_3081_3]) ).

fof(f_3082_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__iff]) ).

fof(f_3082_2,plain,
    ! [U_11798,U_11797,U_11796] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11796),U_11797),hAPP(c_SetInterval_Oord__class_OatMost(U_11796),U_11798)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11796),U_11797),U_11798)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11796),U_11797),U_11798))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11796),U_11797),hAPP(c_SetInterval_Oord__class_OatMost(U_11796),U_11798))) ) )
      | ~ class_Orderings_Oord(U_11796) ),
    inference(variable_rename,[status(thm)],[f_3082_1]) ).

fof(f_3082_3,plain,
    ( ! [U_11796,U_11797,U_11798] :
        ( hBOOL(hAPP(hAPP(c_member(U_11796),U_11797),hAPP(c_SetInterval_Oord__class_OatMost(U_11796),U_11798)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11796),U_11797),U_11798))
        | ~ sP893(U_11796,U_11797,U_11798) )
    & ! [U_11796,U_11797,U_11798] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11796),U_11797),U_11798))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11796),U_11797),hAPP(c_SetInterval_Oord__class_OatMost(U_11796),U_11798)))
        | ~ sP893(U_11796,U_11797,U_11798) )
    & ! [U_11796,U_11797,U_11798] :
        ( sP893(U_11796,U_11797,U_11798)
        | ~ class_Orderings_Oord(U_11796) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP893])],[f_3082_2]) ).

cnf(f_3082_4,plain,
    ( sP893(U_11796,U_11797,U_11798)
    | ~ class_Orderings_Oord(U_11796) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11796),U_11797),U_11798))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11796),U_11797),hAPP(c_SetInterval_Oord__class_OatMost(U_11796),U_11798)))
    | ~ sP893(U_11796,U_11797,U_11798) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11796),U_11797),hAPP(c_SetInterval_Oord__class_OatMost(U_11796),U_11798)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11796),U_11797),U_11798))
    | ~ sP893(U_11796,U_11797,U_11798) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

fof(f_3083_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff]) ).

fof(f_3083_2,plain,
    ! [U_11801,U_11800,U_11799] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11799,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11800)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11801)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11799),U_11800),U_11801)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11799),U_11800),U_11801))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11799,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11800)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11801))) ) )
      | ~ class_Orderings_Oorder(U_11799) ),
    inference(variable_rename,[status(thm)],[f_3083_1]) ).

fof(f_3083_3,plain,
    ( ! [U_11801,U_11800,U_11799] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11799,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11800)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11801)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11799),U_11800),U_11801))
        | ~ sP894(U_11801,U_11800,U_11799) )
    & ! [U_11801,U_11800,U_11799] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11799),U_11800),U_11801))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11799,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11800)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11801)))
        | ~ sP894(U_11801,U_11800,U_11799) )
    & ! [U_11801,U_11800,U_11799] :
        ( sP894(U_11801,U_11800,U_11799)
        | ~ class_Orderings_Oorder(U_11799) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP894])],[f_3083_2]) ).

cnf(f_3083_4,plain,
    ( sP894(U_11801,U_11800,U_11799)
    | ~ class_Orderings_Oorder(U_11799) ),
    inference(clausify,[status(thm)],[f_3083_3]) ).

cnf(f_3083_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11799),U_11800),U_11801))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11799,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11800)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11801)))
    | ~ sP894(U_11801,U_11800,U_11799) ),
    inference(clausify,[status(thm)],[f_3083_3]) ).

cnf(f_3083_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11799,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11800)),hAPP(c_SetInterval_Oord__class_OatMost(U_11799),U_11801)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11799),U_11800),U_11801))
    | ~ sP894(U_11801,U_11800,U_11799) ),
    inference(clausify,[status(thm)],[f_3083_3]) ).

fof(f_3084_1,plain,
    ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2),
    inference(fof_nnf,[status(thm)],[fact_UN__le__add__shift]) ).

fof(f_3084_2,plain,
    ! [U_11805,U_11804,U_11803,U_11802] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11803)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool),tc_Nat_Onat),U_11804),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11805))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11803),U_11805))),U_11804),
    inference(variable_rename,[status(thm)],[f_3084_1]) ).

fof(f_3084_3,plain,
    ! [U_11803,U_11802,U_11804,U_11805] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11803)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool),tc_Nat_Onat),U_11804),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11805))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11803),U_11805))),U_11804),
    inference(definitional_conversion,[status(esa)],[f_3084_2]) ).

cnf(f_3084_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11803)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool),tc_Nat_Onat),U_11804),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_11805))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11802,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11803),U_11805))),U_11804),
    inference(clausify,[status(thm)],[f_3084_3]) ).

fof(f_3085_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | hAPP(V_f_2,V_x_2) != V_y_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq]) ).

fof(f_3085_2,plain,
    ! [U_11811,U_11810,U_11809,U_11808,U_11807,U_11806] :
      ( hAPP(c_Fun_Othe__inv__into(U_11806,U_11807,U_11809,U_11808),U_11811) = U_11810
      | ~ hBOOL(hAPP(hAPP(c_member(U_11806),U_11810),U_11809))
      | hAPP(U_11808,U_11810) != U_11811
      | ~ c_Fun_Oinj__on(U_11806,U_11807,U_11808,U_11809) ),
    inference(variable_rename,[status(thm)],[f_3085_1]) ).

fof(f_3085_3,plain,
    ! [U_11807,U_11806,U_11808,U_11809,U_11810,U_11811] :
      ( hAPP(c_Fun_Othe__inv__into(U_11806,U_11807,U_11809,U_11808),U_11811) = U_11810
      | ~ hBOOL(hAPP(hAPP(c_member(U_11806),U_11810),U_11809))
      | hAPP(U_11808,U_11810) != U_11811
      | ~ c_Fun_Oinj__on(U_11806,U_11807,U_11808,U_11809) ),
    inference(definitional_conversion,[status(esa)],[f_3085_2]) ).

cnf(f_3085_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_11806,U_11807,U_11809,U_11808),U_11811) = U_11810
    | ~ hBOOL(hAPP(hAPP(c_member(U_11806),U_11810),U_11809))
    | hAPP(U_11808,U_11810) != U_11811
    | ~ c_Fun_Oinj__on(U_11806,U_11807,U_11808,U_11809) ),
    inference(clausify,[status(thm)],[f_3085_3]) ).

fof(f_3086_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f]) ).

fof(f_3086_2,plain,
    ! [U_11816,U_11815,U_11814,U_11813,U_11812] :
      ( hAPP(c_Fun_Othe__inv__into(U_11812,U_11813,U_11815,U_11814),hAPP(U_11814,U_11816)) = U_11816
      | ~ hBOOL(hAPP(hAPP(c_member(U_11812),U_11816),U_11815))
      | ~ c_Fun_Oinj__on(U_11812,U_11813,U_11814,U_11815) ),
    inference(variable_rename,[status(thm)],[f_3086_1]) ).

fof(f_3086_3,plain,
    ! [U_11812,U_11813,U_11814,U_11815,U_11816] :
      ( hAPP(c_Fun_Othe__inv__into(U_11812,U_11813,U_11815,U_11814),hAPP(U_11814,U_11816)) = U_11816
      | ~ hBOOL(hAPP(hAPP(c_member(U_11812),U_11816),U_11815))
      | ~ c_Fun_Oinj__on(U_11812,U_11813,U_11814,U_11815) ),
    inference(definitional_conversion,[status(esa)],[f_3086_2]) ).

cnf(f_3086_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_11812,U_11813,U_11815,U_11814),hAPP(U_11814,U_11816)) = U_11816
    | ~ hBOOL(hAPP(hAPP(c_member(U_11812),U_11816),U_11815))
    | ~ c_Fun_Oinj__on(U_11812,U_11813,U_11814,U_11815) ),
    inference(clausify,[status(thm)],[f_3086_3]) ).

fof(f_3087_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into]) ).

fof(f_3087_2,plain,
    ! [U_11820,U_11819,U_11818,U_11817] :
      ( c_Fun_Oinj__on(U_11818,U_11817,c_Fun_Othe__inv__into(U_11817,U_11818,U_11820,U_11819),hAPP(c_Set_Oimage(U_11817,U_11818,U_11819),U_11820))
      | ~ c_Fun_Oinj__on(U_11817,U_11818,U_11819,U_11820) ),
    inference(variable_rename,[status(thm)],[f_3087_1]) ).

fof(f_3087_3,plain,
    ! [U_11817,U_11819,U_11818,U_11820] :
      ( c_Fun_Oinj__on(U_11818,U_11817,c_Fun_Othe__inv__into(U_11817,U_11818,U_11820,U_11819),hAPP(c_Set_Oimage(U_11817,U_11818,U_11819),U_11820))
      | ~ c_Fun_Oinj__on(U_11817,U_11818,U_11819,U_11820) ),
    inference(definitional_conversion,[status(esa)],[f_3087_2]) ).

cnf(f_3087_4,plain,
    ( c_Fun_Oinj__on(U_11818,U_11817,c_Fun_Othe__inv__into(U_11817,U_11818,U_11820,U_11819),hAPP(c_Set_Oimage(U_11817,U_11818,U_11819),U_11820))
    | ~ c_Fun_Oinj__on(U_11817,U_11818,U_11819,U_11820) ),
    inference(clausify,[status(thm)],[f_3087_3]) ).

fof(f_3088_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto]) ).

fof(f_3088_2,plain,
    ! [U_11824,U_11823,U_11822,U_11821] :
      ( hAPP(c_Set_Oimage(U_11822,U_11821,c_Fun_Othe__inv__into(U_11821,U_11822,U_11824,U_11823)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11824)) = U_11824
      | ~ c_Fun_Oinj__on(U_11821,U_11822,U_11823,U_11824) ),
    inference(variable_rename,[status(thm)],[f_3088_1]) ).

fof(f_3088_3,plain,
    ! [U_11821,U_11822,U_11823,U_11824] :
      ( hAPP(c_Set_Oimage(U_11822,U_11821,c_Fun_Othe__inv__into(U_11821,U_11822,U_11824,U_11823)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11824)) = U_11824
      | ~ c_Fun_Oinj__on(U_11821,U_11822,U_11823,U_11824) ),
    inference(definitional_conversion,[status(esa)],[f_3088_2]) ).

cnf(f_3088_4,plain,
    ( hAPP(c_Set_Oimage(U_11822,U_11821,c_Fun_Othe__inv__into(U_11821,U_11822,U_11824,U_11823)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11824)) = U_11824
    | ~ c_Fun_Oinj__on(U_11821,U_11822,U_11823,U_11824) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

fof(f_3089_1,plain,
    ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(f_3089_2,plain,
    ! [U_11830,U_11829,U_11828,U_11827,U_11826,U_11825] :
      ( c_Fun_Oinj__on(U_11825,U_11826,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11825,U_11826),U_11827),U_11830),U_11829),U_11828)
      | hBOOL(hAPP(hAPP(c_member(U_11826),U_11829),hAPP(c_Set_Oimage(U_11825,U_11826,U_11827),U_11828)))
      | ~ c_Fun_Oinj__on(U_11825,U_11826,U_11827,U_11828) ),
    inference(variable_rename,[status(thm)],[f_3089_1]) ).

fof(f_3089_3,plain,
    ! [U_11826,U_11825,U_11827,U_11828,U_11829,U_11830] :
      ( c_Fun_Oinj__on(U_11825,U_11826,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11825,U_11826),U_11827),U_11830),U_11829),U_11828)
      | hBOOL(hAPP(hAPP(c_member(U_11826),U_11829),hAPP(c_Set_Oimage(U_11825,U_11826,U_11827),U_11828)))
      | ~ c_Fun_Oinj__on(U_11825,U_11826,U_11827,U_11828) ),
    inference(definitional_conversion,[status(esa)],[f_3089_2]) ).

cnf(f_3089_4,plain,
    ( c_Fun_Oinj__on(U_11825,U_11826,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11825,U_11826),U_11827),U_11830),U_11829),U_11828)
    | hBOOL(hAPP(hAPP(c_member(U_11826),U_11829),hAPP(c_Set_Oimage(U_11825,U_11826,U_11827),U_11828)))
    | ~ c_Fun_Oinj__on(U_11825,U_11826,U_11827,U_11828) ),
    inference(clausify,[status(thm)],[f_3089_3]) ).

fof(f_3090_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__def]) ).

fof(f_3090_2,plain,
    ! [U_11835,U_11834,U_11833,U_11832,U_11831] : hAPP(c_Fun_Othe__inv__into(U_11831,U_11832,U_11833,U_11834),U_11835) = c_HOL_OThe(U_11831,hAPP(hAPP(c_COMBS(U_11831,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11831),c_fconj),hAPP(hAPP(c_COMBC(U_11831,tc_fun(U_11831,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11831)),U_11833))),hAPP(hAPP(c_COMBC(U_11831,U_11832,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11832,tc_fun(U_11832,tc_HOL_Obool),U_11831),c_fequal),U_11834)),U_11835))),
    inference(variable_rename,[status(thm)],[f_3090_1]) ).

fof(f_3090_3,plain,
    ! [U_11831,U_11832,U_11833,U_11834,U_11835] : hAPP(c_Fun_Othe__inv__into(U_11831,U_11832,U_11833,U_11834),U_11835) = c_HOL_OThe(U_11831,hAPP(hAPP(c_COMBS(U_11831,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11831),c_fconj),hAPP(hAPP(c_COMBC(U_11831,tc_fun(U_11831,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11831)),U_11833))),hAPP(hAPP(c_COMBC(U_11831,U_11832,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11832,tc_fun(U_11832,tc_HOL_Obool),U_11831),c_fequal),U_11834)),U_11835))),
    inference(definitional_conversion,[status(esa)],[f_3090_2]) ).

cnf(f_3090_4,plain,
    hAPP(c_Fun_Othe__inv__into(U_11831,U_11832,U_11833,U_11834),U_11835) = c_HOL_OThe(U_11831,hAPP(hAPP(c_COMBS(U_11831,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11831),c_fconj),hAPP(hAPP(c_COMBC(U_11831,tc_fun(U_11831,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11831)),U_11833))),hAPP(hAPP(c_COMBC(U_11831,U_11832,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11832,tc_fun(U_11832,tc_HOL_Obool),U_11831),c_fequal),U_11834)),U_11835))),
    inference(clausify,[status(thm)],[f_3090_3]) ).

fof(f_3091_1,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_atMost__0]) ).

fof(f_3091_2,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3091_1]) ).

cnf(f_3091_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3091_2]) ).

fof(f_3092_1,plain,
    ! [V_d_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1]) ).

fof(f_3092_2,plain,
    ! [U_11839,U_11838,U_11837,U_11836] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11836,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11836,U_11837,U_11838)),hAPP(c_SetInterval_Oord__class_OatMost(U_11836),U_11839)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11836,U_11837,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11836),U_11838),U_11839))
      | ~ class_Orderings_Olinorder(U_11836) ),
    inference(variable_rename,[status(thm)],[f_3092_1]) ).

fof(f_3092_3,plain,
    ! [U_11836,U_11837,U_11838,U_11839] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11836,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11836,U_11837,U_11838)),hAPP(c_SetInterval_Oord__class_OatMost(U_11836),U_11839)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11836,U_11837,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11836),U_11838),U_11839))
      | ~ class_Orderings_Olinorder(U_11836) ),
    inference(definitional_conversion,[status(esa)],[f_3092_2]) ).

cnf(f_3092_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11836,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11836,U_11837,U_11838)),hAPP(c_SetInterval_Oord__class_OatMost(U_11836),U_11839)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11836,U_11837,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11836),U_11838),U_11839))
    | ~ class_Orderings_Olinorder(U_11836) ),
    inference(clausify,[status(thm)],[f_3092_3]) ).

fof(f_3093_1,plain,
    ! [V_d_2,V_c_2,V_b_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).

fof(f_3093_2,plain,
    ! [U_11843,U_11842,U_11841,U_11840] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11840),U_11841)),c_SetInterval_Oord__class_OatLeastAtMost(U_11840,U_11842,U_11843)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11840,U_11842,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11840),U_11841),U_11843))
      | ~ class_Orderings_Olinorder(U_11840) ),
    inference(variable_rename,[status(thm)],[f_3093_1]) ).

fof(f_3093_3,plain,
    ! [U_11840,U_11841,U_11842,U_11843] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11840),U_11841)),c_SetInterval_Oord__class_OatLeastAtMost(U_11840,U_11842,U_11843)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11840,U_11842,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11840),U_11841),U_11843))
      | ~ class_Orderings_Olinorder(U_11840) ),
    inference(definitional_conversion,[status(esa)],[f_3093_2]) ).

cnf(f_3093_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11840),U_11841)),c_SetInterval_Oord__class_OatLeastAtMost(U_11840,U_11842,U_11843)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11840,U_11842,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11840),U_11841),U_11843))
    | ~ class_Orderings_Olinorder(U_11840) ),
    inference(clausify,[status(thm)],[f_3093_3]) ).

fof(f_3094_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J]) ).

fof(f_3094_2,plain,
    ! [U_11846,U_11845,U_11844] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11844),U_11845)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11844,U_11845,U_11846)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11844),U_11846)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11844),U_11845),U_11846))
      | ~ class_Orderings_Olinorder(U_11844) ),
    inference(variable_rename,[status(thm)],[f_3094_1]) ).

fof(f_3094_3,plain,
    ! [U_11844,U_11845,U_11846] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11844),U_11845)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11844,U_11845,U_11846)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11844),U_11846)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11844),U_11845),U_11846))
      | ~ class_Orderings_Olinorder(U_11844) ),
    inference(definitional_conversion,[status(esa)],[f_3094_2]) ).

cnf(f_3094_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11844),U_11845)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11844,U_11845,U_11846)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11844),U_11846)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11844),U_11845),U_11846))
    | ~ class_Orderings_Olinorder(U_11844) ),
    inference(clausify,[status(thm)],[f_3094_3]) ).

fof(f_3095_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J]) ).

fof(f_3095_2,plain,
    ! [U_11849,U_11848,U_11847] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11847,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11847),U_11848)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11847,U_11848,U_11849)) = c_Orderings_Obot__class_Obot(tc_fun(U_11847,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11847) ),
    inference(variable_rename,[status(thm)],[f_3095_1]) ).

fof(f_3095_3,plain,
    ! [U_11847,U_11848,U_11849] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11847,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11847),U_11848)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11847,U_11848,U_11849)) = c_Orderings_Obot__class_Obot(tc_fun(U_11847,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11847) ),
    inference(definitional_conversion,[status(esa)],[f_3095_2]) ).

cnf(f_3095_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11847,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11847),U_11848)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11847,U_11848,U_11849)) = c_Orderings_Obot__class_Obot(tc_fun(U_11847,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11847) ),
    inference(clausify,[status(thm)],[f_3095_3]) ).

fof(f_3096_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J]) ).

fof(f_3096_2,plain,
    ! [U_11852,U_11851,U_11850] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11850,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11850),U_11851)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11850,U_11851,U_11852)) = c_Orderings_Obot__class_Obot(tc_fun(U_11850,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11850) ),
    inference(variable_rename,[status(thm)],[f_3096_1]) ).

fof(f_3096_3,plain,
    ! [U_11850,U_11851,U_11852] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11850,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11850),U_11851)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11850,U_11851,U_11852)) = c_Orderings_Obot__class_Obot(tc_fun(U_11850,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11850) ),
    inference(definitional_conversion,[status(esa)],[f_3096_2]) ).

cnf(f_3096_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11850,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11850),U_11851)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11850,U_11851,U_11852)) = c_Orderings_Obot__class_Obot(tc_fun(U_11850,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11850) ),
    inference(clausify,[status(thm)],[f_3096_3]) ).

fof(f_3097_1,plain,
    ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f]) ).

fof(f_3097_2,plain,
    ! [U_11857,U_11856,U_11855,U_11854,U_11853] :
      ( hAPP(U_11855,hAPP(c_Fun_Othe__inv__into(U_11853,U_11854,U_11856,U_11855),U_11857)) = U_11857
      | ~ hBOOL(hAPP(hAPP(c_member(U_11854),U_11857),hAPP(c_Set_Oimage(U_11853,U_11854,U_11855),U_11856)))
      | ~ c_Fun_Oinj__on(U_11853,U_11854,U_11855,U_11856) ),
    inference(variable_rename,[status(thm)],[f_3097_1]) ).

fof(f_3097_3,plain,
    ! [U_11853,U_11854,U_11855,U_11856,U_11857] :
      ( hAPP(U_11855,hAPP(c_Fun_Othe__inv__into(U_11853,U_11854,U_11856,U_11855),U_11857)) = U_11857
      | ~ hBOOL(hAPP(hAPP(c_member(U_11854),U_11857),hAPP(c_Set_Oimage(U_11853,U_11854,U_11855),U_11856)))
      | ~ c_Fun_Oinj__on(U_11853,U_11854,U_11855,U_11856) ),
    inference(definitional_conversion,[status(esa)],[f_3097_2]) ).

cnf(f_3097_4,plain,
    ( hAPP(U_11855,hAPP(c_Fun_Othe__inv__into(U_11853,U_11854,U_11856,U_11855),U_11857)) = U_11857
    | ~ hBOOL(hAPP(hAPP(c_member(U_11854),U_11857),hAPP(c_Set_Oimage(U_11853,U_11854,U_11855),U_11856)))
    | ~ c_Fun_Oinj__on(U_11853,U_11854,U_11855,U_11856) ),
    inference(clausify,[status(thm)],[f_3097_3]) ).

fof(f_3098_1,plain,
    ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_UN__le__eq__Un0]) ).

fof(f_3098_2,plain,
    ! [U_11860,U_11859,U_11858] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11858,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11859)),U_11860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11858,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11858,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_11859)),U_11860)),hAPP(U_11860,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3098_1]) ).

fof(f_3098_3,plain,
    ! [U_11858,U_11859,U_11860] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11858,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11859)),U_11860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11858,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11858,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_11859)),U_11860)),hAPP(U_11860,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_3098_2]) ).

cnf(f_3098_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11858,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11859)),U_11860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11858,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11858,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_11859)),U_11860)),hAPP(U_11860,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3098_3]) ).

fof(f_3099_1,plain,
    ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),
    inference(fof_nnf,[status(thm)],[fact_map__upd__nonempty]) ).

fof(f_3099_2,plain,
    ! [U_11865,U_11864,U_11863,U_11862,U_11861] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11861,tc_Option_Ooption(U_11862)),U_11863),U_11864),hAPP(c_Option_Ooption_OSome(U_11862),U_11865)) != hAPP(c_COMBK(tc_Option_Ooption(U_11862),U_11861),c_Option_Ooption_ONone(U_11862)),
    inference(variable_rename,[status(thm)],[f_3099_1]) ).

fof(f_3099_3,plain,
    ! [U_11861,U_11862,U_11863,U_11864,U_11865] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11861,tc_Option_Ooption(U_11862)),U_11863),U_11864),hAPP(c_Option_Ooption_OSome(U_11862),U_11865)) != hAPP(c_COMBK(tc_Option_Ooption(U_11862),U_11861),c_Option_Ooption_ONone(U_11862)),
    inference(definitional_conversion,[status(esa)],[f_3099_2]) ).

cnf(f_3099_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11861,tc_Option_Ooption(U_11862)),U_11863),U_11864),hAPP(c_Option_Ooption_OSome(U_11862),U_11865)) != hAPP(c_COMBK(tc_Option_Ooption(U_11862),U_11861),c_Option_Ooption_ONone(U_11862)),
    inference(clausify,[status(thm)],[f_3099_3]) ).

fof(f_3100_1,plain,
    ! [V_u_2] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int]) ).

fof(f_3100_2,plain,
    ! [U_11866] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11866) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,U_11866)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11866)) ),
    inference(variable_rename,[status(thm)],[f_3100_1]) ).

fof(f_3100_3,plain,
    ! [U_11866] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11866) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,U_11866)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11866)) ),
    inference(definitional_conversion,[status(esa)],[f_3100_2]) ).

cnf(f_3100_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11866) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,U_11866)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11866)) ),
    inference(clausify,[status(thm)],[f_3100_3]) ).

fof(f_3101_1,plain,
    ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__map__upd]) ).

fof(f_3101_2,plain,
    ! [U_11872,U_11871,U_11870,U_11869,U_11868,U_11867] :
      ( hAPP(c_Set_Oimage(U_11867,tc_Option_Ooption(U_11870),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11867,tc_Option_Ooption(U_11870)),U_11871),U_11868),hAPP(c_Option_Ooption_OSome(U_11870),U_11872))),U_11869) = hAPP(c_Set_Oimage(U_11867,tc_Option_Ooption(U_11870),U_11871),U_11869)
      | hBOOL(hAPP(hAPP(c_member(U_11867),U_11868),U_11869)) ),
    inference(variable_rename,[status(thm)],[f_3101_1]) ).

fof(f_3101_3,plain,
    ! [U_11867,U_11868,U_11869,U_11870,U_11871,U_11872] :
      ( hAPP(c_Set_Oimage(U_11867,tc_Option_Ooption(U_11870),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11867,tc_Option_Ooption(U_11870)),U_11871),U_11868),hAPP(c_Option_Ooption_OSome(U_11870),U_11872))),U_11869) = hAPP(c_Set_Oimage(U_11867,tc_Option_Ooption(U_11870),U_11871),U_11869)
      | hBOOL(hAPP(hAPP(c_member(U_11867),U_11868),U_11869)) ),
    inference(definitional_conversion,[status(esa)],[f_3101_2]) ).

cnf(f_3101_4,plain,
    ( hAPP(c_Set_Oimage(U_11867,tc_Option_Ooption(U_11870),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11867,tc_Option_Ooption(U_11870)),U_11871),U_11868),hAPP(c_Option_Ooption_OSome(U_11870),U_11872))),U_11869) = hAPP(c_Set_Oimage(U_11867,tc_Option_Ooption(U_11870),U_11871),U_11869)
    | hBOOL(hAPP(hAPP(c_member(U_11867),U_11868),U_11869)) ),
    inference(clausify,[status(thm)],[f_3101_3]) ).

fof(f_3102_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__lessThan]) ).

fof(f_3102_2,plain,
    ! [U_11873] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11873))),
    inference(variable_rename,[status(thm)],[f_3102_1]) ).

fof(f_3102_3,plain,
    ! [U_11873] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11873))),
    inference(definitional_conversion,[status(esa)],[f_3102_2]) ).

cnf(f_3102_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11873))),
    inference(clausify,[status(thm)],[f_3102_3]) ).

fof(f_3103_1,plain,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2,
    inference(fof_nnf,[status(thm)],[fact_card__lessThan]) ).

fof(f_3103_2,plain,
    ! [U_11874] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11874)) = U_11874,
    inference(variable_rename,[status(thm)],[f_3103_1]) ).

fof(f_3103_3,plain,
    ! [U_11874] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11874)) = U_11874,
    inference(definitional_conversion,[status(esa)],[f_3103_2]) ).

cnf(f_3103_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11874)) = U_11874,
    inference(clausify,[status(thm)],[f_3103_3]) ).

fof(f_3104_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff]) ).

fof(f_3104_2,plain,
    ! [U_11877,U_11876,U_11875] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11876) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11877)
          | U_11876 != U_11877 )
        & ( U_11876 = U_11877
          | hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11876) != hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11877) ) )
      | ~ class_Orderings_Olinorder(U_11875) ),
    inference(variable_rename,[status(thm)],[f_3104_1]) ).

fof(f_3104_3,plain,
    ( ! [U_11875,U_11876,U_11877] :
        ( hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11876) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11877)
        | U_11876 != U_11877
        | ~ sP895(U_11875,U_11876,U_11877) )
    & ! [U_11875,U_11876,U_11877] :
        ( U_11876 = U_11877
        | hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11876) != hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11877)
        | ~ sP895(U_11875,U_11876,U_11877) )
    & ! [U_11875,U_11876,U_11877] :
        ( sP895(U_11875,U_11876,U_11877)
        | ~ class_Orderings_Olinorder(U_11875) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP895])],[f_3104_2]) ).

cnf(f_3104_4,plain,
    ( sP895(U_11875,U_11876,U_11877)
    | ~ class_Orderings_Olinorder(U_11875) ),
    inference(clausify,[status(thm)],[f_3104_3]) ).

cnf(f_3104_5,plain,
    ( U_11876 = U_11877
    | hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11876) != hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11877)
    | ~ sP895(U_11875,U_11876,U_11877) ),
    inference(clausify,[status(thm)],[f_3104_3]) ).

cnf(f_3104_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11876) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11875),U_11877)
    | U_11876 != U_11877
    | ~ sP895(U_11875,U_11876,U_11877) ),
    inference(clausify,[status(thm)],[f_3104_3]) ).

fof(f_3105_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_atLeast0LessThan]) ).

fof(f_3105_2,plain,
    ! [U_11878] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11878) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11878),
    inference(variable_rename,[status(thm)],[f_3105_1]) ).

fof(f_3105_3,plain,
    ! [U_11878] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11878) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11878),
    inference(definitional_conversion,[status(esa)],[f_3105_2]) ).

cnf(f_3105_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11878) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11878),
    inference(clausify,[status(thm)],[f_3105_3]) ).

fof(f_3106_1,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lessThan__0]) ).

fof(f_3106_2,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3106_1]) ).

cnf(f_3106_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3106_2]) ).

fof(f_3107_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_lessThan__Suc]) ).

fof(f_3107_2,plain,
    ! [U_11879] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11879)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11879),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11879)),
    inference(variable_rename,[status(thm)],[f_3107_1]) ).

fof(f_3107_3,plain,
    ! [U_11879] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11879)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11879),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11879)),
    inference(definitional_conversion,[status(esa)],[f_3107_2]) ).

cnf(f_3107_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11879)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11879),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11879)),
    inference(clausify,[status(thm)],[f_3107_3]) ).

fof(f_3108_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2),
    inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__atMost]) ).

fof(f_3108_2,plain,
    ! [U_11880] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11880)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11880),
    inference(variable_rename,[status(thm)],[f_3108_1]) ).

fof(f_3108_3,plain,
    ! [U_11880] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11880)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11880),
    inference(definitional_conversion,[status(esa)],[f_3108_2]) ).

cnf(f_3108_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11880)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11880),
    inference(clausify,[status(thm)],[f_3108_3]) ).

fof(f_3109_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__iff]) ).

fof(f_3109_2,plain,
    ! [U_11883,U_11882,U_11881] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11881),U_11882),hAPP(c_SetInterval_Oord__class_OlessThan(U_11881),U_11883)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11881),U_11882),U_11883)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11881),U_11882),U_11883))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11881),U_11882),hAPP(c_SetInterval_Oord__class_OlessThan(U_11881),U_11883))) ) )
      | ~ class_Orderings_Oord(U_11881) ),
    inference(variable_rename,[status(thm)],[f_3109_1]) ).

fof(f_3109_3,plain,
    ( ! [U_11881,U_11882,U_11883] :
        ( hBOOL(hAPP(hAPP(c_member(U_11881),U_11882),hAPP(c_SetInterval_Oord__class_OlessThan(U_11881),U_11883)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11881),U_11882),U_11883))
        | ~ sP896(U_11881,U_11882,U_11883) )
    & ! [U_11881,U_11882,U_11883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11881),U_11882),U_11883))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11881),U_11882),hAPP(c_SetInterval_Oord__class_OlessThan(U_11881),U_11883)))
        | ~ sP896(U_11881,U_11882,U_11883) )
    & ! [U_11881,U_11882,U_11883] :
        ( sP896(U_11881,U_11882,U_11883)
        | ~ class_Orderings_Oord(U_11881) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP896])],[f_3109_2]) ).

cnf(f_3109_4,plain,
    ( sP896(U_11881,U_11882,U_11883)
    | ~ class_Orderings_Oord(U_11881) ),
    inference(clausify,[status(thm)],[f_3109_3]) ).

cnf(f_3109_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11881),U_11882),U_11883))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11881),U_11882),hAPP(c_SetInterval_Oord__class_OlessThan(U_11881),U_11883)))
    | ~ sP896(U_11881,U_11882,U_11883) ),
    inference(clausify,[status(thm)],[f_3109_3]) ).

cnf(f_3109_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11881),U_11882),hAPP(c_SetInterval_Oord__class_OlessThan(U_11881),U_11883)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11881),U_11882),U_11883))
    | ~ sP896(U_11881,U_11882,U_11883) ),
    inference(clausify,[status(thm)],[f_3109_3]) ).

fof(f_3110_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff]) ).

fof(f_3110_2,plain,
    ! [U_11886,U_11885,U_11884] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11884,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11885)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11886)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11884),U_11885),U_11886)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11884),U_11885),U_11886))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11884,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11885)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11886))) ) )
      | ~ class_Orderings_Olinorder(U_11884) ),
    inference(variable_rename,[status(thm)],[f_3110_1]) ).

fof(f_3110_3,plain,
    ( ! [U_11885,U_11884,U_11886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11884,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11885)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11886)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11884),U_11885),U_11886))
        | ~ sP897(U_11885,U_11884,U_11886) )
    & ! [U_11885,U_11884,U_11886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11884),U_11885),U_11886))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11884,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11885)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11886)))
        | ~ sP897(U_11885,U_11884,U_11886) )
    & ! [U_11885,U_11884,U_11886] :
        ( sP897(U_11885,U_11884,U_11886)
        | ~ class_Orderings_Olinorder(U_11884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP897])],[f_3110_2]) ).

cnf(f_3110_4,plain,
    ( sP897(U_11885,U_11884,U_11886)
    | ~ class_Orderings_Olinorder(U_11884) ),
    inference(clausify,[status(thm)],[f_3110_3]) ).

cnf(f_3110_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11884),U_11885),U_11886))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11884,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11885)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11886)))
    | ~ sP897(U_11885,U_11884,U_11886) ),
    inference(clausify,[status(thm)],[f_3110_3]) ).

cnf(f_3110_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11884,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11885)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11884),U_11886)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11884),U_11885),U_11886))
    | ~ sP897(U_11885,U_11884,U_11886) ),
    inference(clausify,[status(thm)],[f_3110_3]) ).

fof(f_3111_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff]) ).

fof(f_3111_2,plain,
    ! [U_11889,U_11888,U_11887] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11888)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11889)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11887),U_11888),U_11889)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11887),U_11888),U_11889))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11888)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11889))) ) )
      | ~ class_Orderings_Olinorder(U_11887) ),
    inference(variable_rename,[status(thm)],[f_3111_1]) ).

fof(f_3111_3,plain,
    ( ! [U_11888,U_11889,U_11887] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11888)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11889)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11887),U_11888),U_11889))
        | ~ sP898(U_11888,U_11889,U_11887) )
    & ! [U_11888,U_11889,U_11887] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11887),U_11888),U_11889))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11888)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11889)))
        | ~ sP898(U_11888,U_11889,U_11887) )
    & ! [U_11888,U_11889,U_11887] :
        ( sP898(U_11888,U_11889,U_11887)
        | ~ class_Orderings_Olinorder(U_11887) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP898])],[f_3111_2]) ).

cnf(f_3111_4,plain,
    ( sP898(U_11888,U_11889,U_11887)
    | ~ class_Orderings_Olinorder(U_11887) ),
    inference(clausify,[status(thm)],[f_3111_3]) ).

cnf(f_3111_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11887),U_11888),U_11889))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11888)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11889)))
    | ~ sP898(U_11888,U_11889,U_11887) ),
    inference(clausify,[status(thm)],[f_3111_3]) ).

cnf(f_3111_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11888)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11887),U_11889)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11887),U_11888),U_11889))
    | ~ sP898(U_11888,U_11889,U_11887) ),
    inference(clausify,[status(thm)],[f_3111_3]) ).

fof(f_3112_1,plain,
    ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
        | ( ( hAPP(V_m_2,V_x_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
            | V_x_2 = V_a_2 )
          & ( V_b_2 != V_y_2
            | V_x_2 != V_a_2 ) ) )
      & ( ( hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
          & V_x_2 != V_a_2 )
        | ( V_b_2 = V_y_2
          & V_x_2 = V_a_2 )
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold]) ).

fof(f_3112_2,plain,
    ! [U_11896,U_11895,U_11894,U_11893,U_11892,U_11891,U_11890] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11890,tc_Option_Ooption(U_11891)),U_11892),U_11893),hAPP(c_Option_Ooption_OSome(U_11891),U_11894)),U_11895) = hAPP(c_Option_Ooption_OSome(U_11891),U_11896)
        | ( ( hAPP(U_11892,U_11895) != hAPP(c_Option_Ooption_OSome(U_11891),U_11896)
            | U_11895 = U_11893 )
          & ( U_11894 != U_11896
            | U_11895 != U_11893 ) ) )
      & ( ( hAPP(U_11892,U_11895) = hAPP(c_Option_Ooption_OSome(U_11891),U_11896)
          & U_11895 != U_11893 )
        | ( U_11894 = U_11896
          & U_11895 = U_11893 )
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11890,tc_Option_Ooption(U_11891)),U_11892),U_11893),hAPP(c_Option_Ooption_OSome(U_11891),U_11894)),U_11895) != hAPP(c_Option_Ooption_OSome(U_11891),U_11896) ) ),
    inference(variable_rename,[status(thm)],[f_3112_1]) ).

fof(f_3112_3,plain,
    ( ! [U_11910,U_11908,U_11906,U_11904,U_11902,U_11900] :
        ( ! [U_11898] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11898,tc_Option_Ooption(U_11900)),U_11902),U_11904),hAPP(c_Option_Ooption_OSome(U_11900),U_11906)),U_11908) = hAPP(c_Option_Ooption_OSome(U_11900),U_11910)
        | ( ( hAPP(U_11902,U_11908) != hAPP(c_Option_Ooption_OSome(U_11900),U_11910)
            | U_11908 = U_11904 )
          & ( U_11906 != U_11910
            | U_11908 != U_11904 ) ) )
    & ! [U_11909,U_11907,U_11905,U_11903,U_11901,U_11899] :
        ( ! [U_11897] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11897,tc_Option_Ooption(U_11899)),U_11901),U_11903),hAPP(c_Option_Ooption_OSome(U_11899),U_11905)),U_11907) != hAPP(c_Option_Ooption_OSome(U_11899),U_11909)
        | ( hAPP(U_11901,U_11907) = hAPP(c_Option_Ooption_OSome(U_11899),U_11909)
          & U_11907 != U_11903 )
        | ( U_11905 = U_11909
          & U_11907 = U_11903 ) ) ),
    inference(miniscope,[status(thm)],[f_3112_2]) ).

fof(f_3112_4,plain,
    ( ! [U_11906,U_11908,U_11900,U_11910,U_11904,U_11902] :
        ( hAPP(U_11902,U_11908) != hAPP(c_Option_Ooption_OSome(U_11900),U_11910)
        | U_11908 = U_11904
        | ~ sP901(U_11906,U_11908,U_11900,U_11910,U_11904,U_11902) )
    & ! [U_11906,U_11908,U_11900,U_11910,U_11904,U_11902] :
        ( U_11906 != U_11910
        | U_11908 != U_11904
        | ~ sP901(U_11906,U_11908,U_11900,U_11910,U_11904,U_11902) )
    & ! [U_11901,U_11903,U_11907,U_11899,U_11909] :
        ( hAPP(U_11901,U_11907) = hAPP(c_Option_Ooption_OSome(U_11899),U_11909)
        | ~ sP900(U_11901,U_11903,U_11907,U_11899,U_11909) )
    & ! [U_11901,U_11903,U_11907,U_11899,U_11909] :
        ( U_11907 != U_11903
        | ~ sP900(U_11901,U_11903,U_11907,U_11899,U_11909) )
    & ! [U_11903,U_11907,U_11905,U_11909] :
        ( U_11905 = U_11909
        | ~ sP899(U_11903,U_11907,U_11905,U_11909) )
    & ! [U_11903,U_11907,U_11905,U_11909] :
        ( U_11907 = U_11903
        | ~ sP899(U_11903,U_11907,U_11905,U_11909) )
    & ! [U_11898,U_11906,U_11908,U_11900,U_11910,U_11904,U_11902] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11898,tc_Option_Ooption(U_11900)),U_11902),U_11904),hAPP(c_Option_Ooption_OSome(U_11900),U_11906)),U_11908) = hAPP(c_Option_Ooption_OSome(U_11900),U_11910)
        | sP901(U_11906,U_11908,U_11900,U_11910,U_11904,U_11902) )
    & ! [U_11901,U_11903,U_11907,U_11897,U_11899,U_11905,U_11909] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11897,tc_Option_Ooption(U_11899)),U_11901),U_11903),hAPP(c_Option_Ooption_OSome(U_11899),U_11905)),U_11907) != hAPP(c_Option_Ooption_OSome(U_11899),U_11909)
        | sP900(U_11901,U_11903,U_11907,U_11899,U_11909)
        | sP899(U_11903,U_11907,U_11905,U_11909) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP899,sP900,sP901])],[f_3112_3]) ).

cnf(f_3112_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11897,tc_Option_Ooption(U_11899)),U_11901),U_11903),hAPP(c_Option_Ooption_OSome(U_11899),U_11905)),U_11907) != hAPP(c_Option_Ooption_OSome(U_11899),U_11909)
    | sP900(U_11901,U_11903,U_11907,U_11899,U_11909)
    | sP899(U_11903,U_11907,U_11905,U_11909) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11898,tc_Option_Ooption(U_11900)),U_11902),U_11904),hAPP(c_Option_Ooption_OSome(U_11900),U_11906)),U_11908) = hAPP(c_Option_Ooption_OSome(U_11900),U_11910)
    | sP901(U_11906,U_11908,U_11900,U_11910,U_11904,U_11902) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_7,plain,
    ( U_11907 = U_11903
    | ~ sP899(U_11903,U_11907,U_11905,U_11909) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_8,plain,
    ( U_11905 = U_11909
    | ~ sP899(U_11903,U_11907,U_11905,U_11909) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_9,plain,
    ( U_11907 != U_11903
    | ~ sP900(U_11901,U_11903,U_11907,U_11899,U_11909) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_10,plain,
    ( hAPP(U_11901,U_11907) = hAPP(c_Option_Ooption_OSome(U_11899),U_11909)
    | ~ sP900(U_11901,U_11903,U_11907,U_11899,U_11909) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_11,plain,
    ( U_11906 != U_11910
    | U_11908 != U_11904
    | ~ sP901(U_11906,U_11908,U_11900,U_11910,U_11904,U_11902) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_12,plain,
    ( hAPP(U_11902,U_11908) != hAPP(c_Option_Ooption_OSome(U_11900),U_11910)
    | U_11908 = U_11904
    | ~ sP901(U_11906,U_11908,U_11900,U_11910,U_11904,U_11902) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

fof(f_3113_1,plain,
    ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2
      | hAPP(V_t_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__triv]) ).

fof(f_3113_2,plain,
    ! [U_11915,U_11914,U_11913,U_11912,U_11911] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11915,tc_Option_Ooption(U_11913)),U_11911),U_11912),hAPP(c_Option_Ooption_OSome(U_11913),U_11914)) = U_11911
      | hAPP(U_11911,U_11912) != hAPP(c_Option_Ooption_OSome(U_11913),U_11914) ),
    inference(variable_rename,[status(thm)],[f_3113_1]) ).

fof(f_3113_3,plain,
    ! [U_11913,U_11911,U_11914,U_11912,U_11915] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11915,tc_Option_Ooption(U_11913)),U_11911),U_11912),hAPP(c_Option_Ooption_OSome(U_11913),U_11914)) = U_11911
      | hAPP(U_11911,U_11912) != hAPP(c_Option_Ooption_OSome(U_11913),U_11914) ),
    inference(definitional_conversion,[status(esa)],[f_3113_2]) ).

cnf(f_3113_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11915,tc_Option_Ooption(U_11913)),U_11911),U_11912),hAPP(c_Option_Ooption_OSome(U_11913),U_11914)) = U_11911
    | hAPP(U_11911,U_11912) != hAPP(c_Option_Ooption_OSome(U_11913),U_11914) ),
    inference(clausify,[status(thm)],[f_3113_3]) ).

fof(f_3114_1,plain,
    ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
      ( V_x_2 = V_y_2
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__eqD1]) ).

fof(f_3114_2,plain,
    ! [U_11922,U_11921,U_11920,U_11919,U_11918,U_11917,U_11916] :
      ( U_11920 = U_11922
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11918),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11920)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11921),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11922)) ),
    inference(variable_rename,[status(thm)],[f_3114_1]) ).

fof(f_3114_3,plain,
    ! [U_11922,U_11921,U_11920] :
      ( ! [U_11919,U_11918,U_11917,U_11916] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11918),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11920)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11921),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11922))
      | U_11920 = U_11922 ),
    inference(miniscope,[status(thm)],[f_3114_2]) ).

fof(f_3114_4,plain,
    ! [U_11916,U_11917,U_11918,U_11919,U_11920,U_11921,U_11922] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11918),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11920)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11921),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11922))
      | U_11920 = U_11922 ),
    inference(definitional_conversion,[status(esa)],[f_3114_3]) ).

cnf(f_3114_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11918),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11920)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11916,tc_Option_Ooption(U_11917)),U_11921),U_11919),hAPP(c_Option_Ooption_OSome(U_11917),U_11922))
    | U_11920 = U_11922 ),
    inference(clausify,[status(thm)],[f_3114_4]) ).

fof(f_3115_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan]) ).

fof(f_3115_2,plain,
    ! [U_11924,U_11923] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11923,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11923),U_11924),c_Orderings_Obot__class_Obot(tc_fun(U_11923,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_11923),U_11924)) = hAPP(hAPP(c_Set_Oinsert(U_11923),U_11924),c_Orderings_Obot__class_Obot(tc_fun(U_11923,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11923) ),
    inference(variable_rename,[status(thm)],[f_3115_1]) ).

fof(f_3115_3,plain,
    ! [U_11923,U_11924] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11923,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11923),U_11924),c_Orderings_Obot__class_Obot(tc_fun(U_11923,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_11923),U_11924)) = hAPP(hAPP(c_Set_Oinsert(U_11923),U_11924),c_Orderings_Obot__class_Obot(tc_fun(U_11923,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11923) ),
    inference(definitional_conversion,[status(esa)],[f_3115_2]) ).

cnf(f_3115_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11923,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11923),U_11924),c_Orderings_Obot__class_Obot(tc_fun(U_11923,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_11923),U_11924)) = hAPP(hAPP(c_Set_Oinsert(U_11923),U_11924),c_Orderings_Obot__class_Obot(tc_fun(U_11923,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_11923) ),
    inference(clausify,[status(thm)],[f_3115_3]) ).

fof(f_3116_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J]) ).

fof(f_3116_2,plain,
    ! [U_11927,U_11926,U_11925] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11925,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11925),U_11926)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11925,U_11926),U_11927)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11925),U_11927)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11925),U_11926),U_11927))
      | ~ class_Orderings_Olinorder(U_11925) ),
    inference(variable_rename,[status(thm)],[f_3116_1]) ).

fof(f_3116_3,plain,
    ! [U_11925,U_11926,U_11927] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11925,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11925),U_11926)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11925,U_11926),U_11927)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11925),U_11927)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11925),U_11926),U_11927))
      | ~ class_Orderings_Olinorder(U_11925) ),
    inference(definitional_conversion,[status(esa)],[f_3116_2]) ).

cnf(f_3116_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11925,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11925),U_11926)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11925,U_11926),U_11927)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11925),U_11927)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11925),U_11926),U_11927))
    | ~ class_Orderings_Olinorder(U_11925) ),
    inference(clausify,[status(thm)],[f_3116_3]) ).

fof(f_3117_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J]) ).

fof(f_3117_2,plain,
    ! [U_11930,U_11929,U_11928] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11928),U_11929)),c_SetInterval_Oord__class_OatLeastAtMost(U_11928,U_11929,U_11930)) = c_Orderings_Obot__class_Obot(tc_fun(U_11928,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11928) ),
    inference(variable_rename,[status(thm)],[f_3117_1]) ).

fof(f_3117_3,plain,
    ! [U_11928,U_11929,U_11930] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11928),U_11929)),c_SetInterval_Oord__class_OatLeastAtMost(U_11928,U_11929,U_11930)) = c_Orderings_Obot__class_Obot(tc_fun(U_11928,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11928) ),
    inference(definitional_conversion,[status(esa)],[f_3117_2]) ).

cnf(f_3117_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11928),U_11929)),c_SetInterval_Oord__class_OatLeastAtMost(U_11928,U_11929,U_11930)) = c_Orderings_Obot__class_Obot(tc_fun(U_11928,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11928) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

fof(f_3118_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J]) ).

fof(f_3118_2,plain,
    ! [U_11933,U_11932,U_11931] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11931),U_11932)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11931,U_11932),U_11933)) = c_Orderings_Obot__class_Obot(tc_fun(U_11931,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11931) ),
    inference(variable_rename,[status(thm)],[f_3118_1]) ).

fof(f_3118_3,plain,
    ! [U_11931,U_11932,U_11933] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11931),U_11932)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11931,U_11932),U_11933)) = c_Orderings_Obot__class_Obot(tc_fun(U_11931,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11931) ),
    inference(definitional_conversion,[status(esa)],[f_3118_2]) ).

cnf(f_3118_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11931),U_11932)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11931,U_11932),U_11933)) = c_Orderings_Obot__class_Obot(tc_fun(U_11931,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11931) ),
    inference(clausify,[status(thm)],[f_3118_3]) ).

fof(f_3119_1,plain,
    ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_empty__upd__none]) ).

fof(f_3119_2,plain,
    ! [U_11937,U_11936,U_11935,U_11934] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11934,tc_Option_Ooption(U_11935)),hAPP(c_COMBK(tc_Option_Ooption(U_11935),U_11934),c_Option_Ooption_ONone(U_11935))),U_11936),c_Option_Ooption_ONone(U_11935)),U_11937) = c_Option_Ooption_ONone(U_11935),
    inference(variable_rename,[status(thm)],[f_3119_1]) ).

fof(f_3119_3,plain,
    ! [U_11934,U_11935,U_11936,U_11937] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11934,tc_Option_Ooption(U_11935)),hAPP(c_COMBK(tc_Option_Ooption(U_11935),U_11934),c_Option_Ooption_ONone(U_11935))),U_11936),c_Option_Ooption_ONone(U_11935)),U_11937) = c_Option_Ooption_ONone(U_11935),
    inference(definitional_conversion,[status(esa)],[f_3119_2]) ).

cnf(f_3119_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11934,tc_Option_Ooption(U_11935)),hAPP(c_COMBK(tc_Option_Ooption(U_11935),U_11934),c_Option_Ooption_ONone(U_11935))),U_11936),c_Option_Ooption_ONone(U_11935)),U_11937) = c_Option_Ooption_ONone(U_11935),
    inference(clausify,[status(thm)],[f_3119_3]) ).

fof(f_3120_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).

fof(f_3120_2,plain,
    ! [U_11938] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11938)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11938))),
    inference(variable_rename,[status(thm)],[f_3120_1]) ).

fof(f_3120_3,plain,
    ! [U_11938] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11938)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11938))),
    inference(definitional_conversion,[status(esa)],[f_3120_2]) ).

cnf(f_3120_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11938)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11938))),
    inference(clausify,[status(thm)],[f_3120_3]) ).

fof(f_3121_1,plain,
    ! [V_u_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).

fof(f_3121_2,plain,
    ! [U_11940,U_11939] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11939,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11939),U_11940)),hAPP(hAPP(c_Set_Oinsert(U_11939),U_11940),c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_11939),U_11940)
      | ~ class_Orderings_Olinorder(U_11939) ),
    inference(variable_rename,[status(thm)],[f_3121_1]) ).

fof(f_3121_3,plain,
    ! [U_11939,U_11940] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11939,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11939),U_11940)),hAPP(hAPP(c_Set_Oinsert(U_11939),U_11940),c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_11939),U_11940)
      | ~ class_Orderings_Olinorder(U_11939) ),
    inference(definitional_conversion,[status(esa)],[f_3121_2]) ).

cnf(f_3121_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11939,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11939),U_11940)),hAPP(hAPP(c_Set_Oinsert(U_11939),U_11940),c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_11939),U_11940)
    | ~ class_Orderings_Olinorder(U_11939) ),
    inference(clausify,[status(thm)],[f_3121_3]) ).

fof(f_3122_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J]) ).

fof(f_3122_2,plain,
    ! [U_11943,U_11942,U_11941] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11941,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11941),U_11942)),c_SetInterval_Oord__class_OatLeastAtMost(U_11941,U_11942,U_11943)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11941),U_11943)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11941),U_11942),U_11943))
      | ~ class_Orderings_Olinorder(U_11941) ),
    inference(variable_rename,[status(thm)],[f_3122_1]) ).

fof(f_3122_3,plain,
    ! [U_11941,U_11942,U_11943] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11941,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11941),U_11942)),c_SetInterval_Oord__class_OatLeastAtMost(U_11941,U_11942,U_11943)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11941),U_11943)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11941),U_11942),U_11943))
      | ~ class_Orderings_Olinorder(U_11941) ),
    inference(definitional_conversion,[status(esa)],[f_3122_2]) ).

cnf(f_3122_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11941,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11941),U_11942)),c_SetInterval_Oord__class_OatLeastAtMost(U_11941,U_11942,U_11943)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11941),U_11943)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11941),U_11942),U_11943))
    | ~ class_Orderings_Olinorder(U_11941) ),
    inference(clausify,[status(thm)],[f_3122_3]) ).

fof(f_3123_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J]) ).

fof(f_3123_2,plain,
    ! [U_11946,U_11945,U_11944] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11944,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11944),U_11945)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11944,U_11945,U_11946)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11944),U_11946)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11944),U_11945),U_11946))
      | ~ class_Orderings_Olinorder(U_11944) ),
    inference(variable_rename,[status(thm)],[f_3123_1]) ).

fof(f_3123_3,plain,
    ! [U_11944,U_11945,U_11946] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11944,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11944),U_11945)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11944,U_11945,U_11946)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11944),U_11946)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11944),U_11945),U_11946))
      | ~ class_Orderings_Olinorder(U_11944) ),
    inference(definitional_conversion,[status(esa)],[f_3123_2]) ).

cnf(f_3123_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11944,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11944),U_11945)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11944,U_11945,U_11946)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11944),U_11946)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11944),U_11945),U_11946))
    | ~ class_Orderings_Olinorder(U_11944) ),
    inference(clausify,[status(thm)],[f_3123_3]) ).

fof(f_3124_1,plain,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
    inference(fof_nnf,[status(thm)],[fact_arith__series__int]) ).

fof(f_3124_2,plain,
    ! [U_11949,U_11948,U_11947] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),U_11948))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11949))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11949),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_11948)))),
    inference(variable_rename,[status(thm)],[f_3124_1]) ).

fof(f_3124_3,plain,
    ! [U_11947,U_11948,U_11949] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),U_11948))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11949))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11949),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_11948)))),
    inference(definitional_conversion,[status(esa)],[f_3124_2]) ).

cnf(f_3124_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),U_11948))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11949))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11949),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_11948)))),
    inference(clausify,[status(thm)],[f_3124_3]) ).

fof(f_3125_1,plain,
    ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
      ( c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))
      | hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ran__map__upd]) ).

fof(f_3125_2,plain,
    ! [U_11954,U_11953,U_11952,U_11951,U_11950] :
      ( c_Map_Oran(U_11953,U_11952,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11953,tc_Option_Ooption(U_11952)),U_11950),U_11951),hAPP(c_Option_Ooption_OSome(U_11952),U_11954))) = hAPP(hAPP(c_Set_Oinsert(U_11952),U_11954),c_Map_Oran(U_11953,U_11952,U_11950))
      | hAPP(U_11950,U_11951) != c_Option_Ooption_ONone(U_11952) ),
    inference(variable_rename,[status(thm)],[f_3125_1]) ).

fof(f_3125_3,plain,
    ! [U_11950,U_11951,U_11952,U_11953,U_11954] :
      ( c_Map_Oran(U_11953,U_11952,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11953,tc_Option_Ooption(U_11952)),U_11950),U_11951),hAPP(c_Option_Ooption_OSome(U_11952),U_11954))) = hAPP(hAPP(c_Set_Oinsert(U_11952),U_11954),c_Map_Oran(U_11953,U_11952,U_11950))
      | hAPP(U_11950,U_11951) != c_Option_Ooption_ONone(U_11952) ),
    inference(definitional_conversion,[status(esa)],[f_3125_2]) ).

cnf(f_3125_4,plain,
    ( c_Map_Oran(U_11953,U_11952,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11953,tc_Option_Ooption(U_11952)),U_11950),U_11951),hAPP(c_Option_Ooption_OSome(U_11952),U_11954))) = hAPP(hAPP(c_Set_Oinsert(U_11952),U_11954),c_Map_Oran(U_11953,U_11952,U_11950))
    | hAPP(U_11950,U_11951) != c_Option_Ooption_ONone(U_11952) ),
    inference(clausify,[status(thm)],[f_3125_3]) ).

fof(f_3126_1,plain,
    ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) )
      & ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__None__restrict]) ).

fof(f_3126_2,plain,
    ! [U_11959,U_11958,U_11957,U_11956,U_11955] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11955,tc_Option_Ooption(U_11958)),c_Map_Orestrict__map(U_11955,U_11958,U_11959,U_11957)),U_11956),c_Option_Ooption_ONone(U_11958)) = c_Map_Orestrict__map(U_11955,U_11958,U_11959,U_11957)
        | hBOOL(hAPP(hAPP(c_member(U_11955),U_11956),U_11957)) )
      & ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11955,tc_Option_Ooption(U_11958)),c_Map_Orestrict__map(U_11955,U_11958,U_11959,U_11957)),U_11956),c_Option_Ooption_ONone(U_11958)) = c_Map_Orestrict__map(U_11955,U_11958,U_11959,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11955,tc_HOL_Obool)),U_11957),hAPP(hAPP(c_Set_Oinsert(U_11955),U_11956),c_Orderings_Obot__class_Obot(tc_fun(U_11955,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11955),U_11956),U_11957)) ) ),
    inference(variable_rename,[status(thm)],[f_3126_1]) ).

fof(f_3126_3,plain,
    ( ! [U_11969,U_11967,U_11965,U_11963,U_11961] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11961,tc_Option_Ooption(U_11967)),c_Map_Orestrict__map(U_11961,U_11967,U_11969,U_11965)),U_11963),c_Option_Ooption_ONone(U_11967)) = c_Map_Orestrict__map(U_11961,U_11967,U_11969,U_11965)
        | hBOOL(hAPP(hAPP(c_member(U_11961),U_11963),U_11965)) )
    & ! [U_11968,U_11966,U_11964,U_11962,U_11960] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11960,tc_Option_Ooption(U_11966)),c_Map_Orestrict__map(U_11960,U_11966,U_11968,U_11964)),U_11962),c_Option_Ooption_ONone(U_11966)) = c_Map_Orestrict__map(U_11960,U_11966,U_11968,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11960,tc_HOL_Obool)),U_11964),hAPP(hAPP(c_Set_Oinsert(U_11960),U_11962),c_Orderings_Obot__class_Obot(tc_fun(U_11960,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),U_11964)) ) ),
    inference(miniscope,[status(thm)],[f_3126_2]) ).

fof(f_3126_4,plain,
    ( ! [U_11961,U_11963,U_11965,U_11967,U_11969] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11961,tc_Option_Ooption(U_11967)),c_Map_Orestrict__map(U_11961,U_11967,U_11969,U_11965)),U_11963),c_Option_Ooption_ONone(U_11967)) = c_Map_Orestrict__map(U_11961,U_11967,U_11969,U_11965)
        | hBOOL(hAPP(hAPP(c_member(U_11961),U_11963),U_11965)) )
    & ! [U_11960,U_11962,U_11964,U_11966,U_11968] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11960,tc_Option_Ooption(U_11966)),c_Map_Orestrict__map(U_11960,U_11966,U_11968,U_11964)),U_11962),c_Option_Ooption_ONone(U_11966)) = c_Map_Orestrict__map(U_11960,U_11966,U_11968,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11960,tc_HOL_Obool)),U_11964),hAPP(hAPP(c_Set_Oinsert(U_11960),U_11962),c_Orderings_Obot__class_Obot(tc_fun(U_11960,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),U_11964)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3126_3]) ).

cnf(f_3126_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11960,tc_Option_Ooption(U_11966)),c_Map_Orestrict__map(U_11960,U_11966,U_11968,U_11964)),U_11962),c_Option_Ooption_ONone(U_11966)) = c_Map_Orestrict__map(U_11960,U_11966,U_11968,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11960,tc_HOL_Obool)),U_11964),hAPP(hAPP(c_Set_Oinsert(U_11960),U_11962),c_Orderings_Obot__class_Obot(tc_fun(U_11960,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),U_11964)) ),
    inference(clausify,[status(thm)],[f_3126_4]) ).

cnf(f_3126_6,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_11961,tc_Option_Ooption(U_11967)),c_Map_Orestrict__map(U_11961,U_11967,U_11969,U_11965)),U_11963),c_Option_Ooption_ONone(U_11967)) = c_Map_Orestrict__map(U_11961,U_11967,U_11969,U_11965)
    | hBOOL(hAPP(hAPP(c_member(U_11961),U_11963),U_11965)) ),
    inference(clausify,[status(thm)],[f_3126_4]) ).

fof(f_3127_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__abs]) ).

fof(f_3127_2,plain,
    ! [U_11973,U_11972,U_11971,U_11970] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11970),hAPP(c_Groups_Oabs__class_Oabs(U_11970),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11971,U_11970),U_11972),U_11973))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11971,U_11970),hAPP(hAPP(c_COMBB(U_11970,U_11970,U_11971),c_Groups_Oabs__class_Oabs(U_11970)),U_11972)),U_11973)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_11970) ),
    inference(variable_rename,[status(thm)],[f_3127_1]) ).

fof(f_3127_3,plain,
    ! [U_11970,U_11971,U_11972,U_11973] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11970),hAPP(c_Groups_Oabs__class_Oabs(U_11970),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11971,U_11970),U_11972),U_11973))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11971,U_11970),hAPP(hAPP(c_COMBB(U_11970,U_11970,U_11971),c_Groups_Oabs__class_Oabs(U_11970)),U_11972)),U_11973)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_11970) ),
    inference(definitional_conversion,[status(esa)],[f_3127_2]) ).

cnf(f_3127_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11970),hAPP(c_Groups_Oabs__class_Oabs(U_11970),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11971,U_11970),U_11972),U_11973))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11971,U_11970),hAPP(hAPP(c_COMBB(U_11970,U_11970,U_11971),c_Groups_Oabs__class_Oabs(U_11970)),U_11972)),U_11973)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_11970) ),
    inference(clausify,[status(thm)],[f_3127_3]) ).

fof(f_3128_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero]) ).

fof(f_3128_2,plain,
    ! [U_11977,U_11976,U_11975,U_11974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11974),c_Groups_Ozero__class_Ozero(U_11974)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11975,U_11974),hAPP(hAPP(c_COMBB(U_11974,U_11974,U_11975),c_Groups_Oabs__class_Oabs(U_11974)),U_11976)),U_11977)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_11974) ),
    inference(variable_rename,[status(thm)],[f_3128_1]) ).

fof(f_3128_3,plain,
    ! [U_11974,U_11975,U_11976,U_11977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11974),c_Groups_Ozero__class_Ozero(U_11974)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11975,U_11974),hAPP(hAPP(c_COMBB(U_11974,U_11974,U_11975),c_Groups_Oabs__class_Oabs(U_11974)),U_11976)),U_11977)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_11974) ),
    inference(definitional_conversion,[status(esa)],[f_3128_2]) ).

cnf(f_3128_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11974),c_Groups_Ozero__class_Ozero(U_11974)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11975,U_11974),hAPP(hAPP(c_COMBB(U_11974,U_11974,U_11975),c_Groups_Oabs__class_Oabs(U_11974)),U_11976)),U_11977)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_11974) ),
    inference(clausify,[status(thm)],[f_3128_3]) ).

fof(f_3129_1,plain,
    ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__in]) ).

fof(f_3129_2,plain,
    ! [U_11982,U_11981,U_11980,U_11979,U_11978] :
      ( hAPP(c_Map_Orestrict__map(U_11978,U_11981,U_11982,U_11980),U_11979) = hAPP(U_11982,U_11979)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11978),U_11979),U_11980)) ),
    inference(variable_rename,[status(thm)],[f_3129_1]) ).

fof(f_3129_3,plain,
    ! [U_11978,U_11979,U_11980,U_11981,U_11982] :
      ( hAPP(c_Map_Orestrict__map(U_11978,U_11981,U_11982,U_11980),U_11979) = hAPP(U_11982,U_11979)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11978),U_11979),U_11980)) ),
    inference(definitional_conversion,[status(esa)],[f_3129_2]) ).

cnf(f_3129_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_11978,U_11981,U_11982,U_11980),U_11979) = hAPP(U_11982,U_11979)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11978),U_11979),U_11980)) ),
    inference(clausify,[status(thm)],[f_3129_3]) ).

fof(f_3130_1,plain,
    ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_restrict__restrict]) ).

fof(f_3130_2,plain,
    ! [U_11987,U_11986,U_11985,U_11984,U_11983] : c_Map_Orestrict__map(U_11983,U_11984,c_Map_Orestrict__map(U_11983,U_11984,U_11985,U_11986),U_11987) = c_Map_Orestrict__map(U_11983,U_11984,U_11985,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11983,tc_HOL_Obool)),U_11986),U_11987)),
    inference(variable_rename,[status(thm)],[f_3130_1]) ).

fof(f_3130_3,plain,
    ! [U_11984,U_11983,U_11985,U_11986,U_11987] : c_Map_Orestrict__map(U_11983,U_11984,c_Map_Orestrict__map(U_11983,U_11984,U_11985,U_11986),U_11987) = c_Map_Orestrict__map(U_11983,U_11984,U_11985,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11983,tc_HOL_Obool)),U_11986),U_11987)),
    inference(definitional_conversion,[status(esa)],[f_3130_2]) ).

cnf(f_3130_4,plain,
    c_Map_Orestrict__map(U_11983,U_11984,c_Map_Orestrict__map(U_11983,U_11984,U_11985,U_11986),U_11987) = c_Map_Orestrict__map(U_11983,U_11984,U_11985,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11983,tc_HOL_Obool)),U_11986),U_11987)),
    inference(clausify,[status(thm)],[f_3130_3]) ).

fof(f_3131_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__empty]) ).

fof(f_3131_2,plain,
    ! [U_11990,U_11989,U_11988] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11989,U_11988),U_11990),c_Orderings_Obot__class_Obot(tc_fun(U_11989,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_11988)
      | ~ class_Groups_Ocomm__monoid__add(U_11988) ),
    inference(variable_rename,[status(thm)],[f_3131_1]) ).

fof(f_3131_3,plain,
    ! [U_11988,U_11989,U_11990] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11989,U_11988),U_11990),c_Orderings_Obot__class_Obot(tc_fun(U_11989,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_11988)
      | ~ class_Groups_Ocomm__monoid__add(U_11988) ),
    inference(definitional_conversion,[status(esa)],[f_3131_2]) ).

cnf(f_3131_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11989,U_11988),U_11990),c_Orderings_Obot__class_Obot(tc_fun(U_11989,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_11988)
    | ~ class_Groups_Ocomm__monoid__add(U_11988) ),
    inference(clausify,[status(thm)],[f_3131_3]) ).

fof(f_3132_1,plain,
    ! [V_g_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oempty]) ).

fof(f_3132_2,plain,
    ! [U_11993,U_11992,U_11991] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11992,U_11991),U_11993),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_11991)
      | ~ class_Groups_Ocomm__monoid__add(U_11991) ),
    inference(variable_rename,[status(thm)],[f_3132_1]) ).

fof(f_3132_3,plain,
    ! [U_11991,U_11992,U_11993] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11992,U_11991),U_11993),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_11991)
      | ~ class_Groups_Ocomm__monoid__add(U_11991) ),
    inference(definitional_conversion,[status(esa)],[f_3132_2]) ).

cnf(f_3132_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11992,U_11991),U_11993),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_11991)
    | ~ class_Groups_Ocomm__monoid__add(U_11991) ),
    inference(clausify,[status(thm)],[f_3132_3]) ).

fof(f_3133_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__infinite]) ).

fof(f_3133_2,plain,
    ! [U_11997,U_11996,U_11995,U_11994] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11995,U_11994),U_11997),U_11996) = c_Groups_Ozero__class_Ozero(U_11994)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11995),U_11996))
      | ~ class_Groups_Ocomm__monoid__add(U_11994) ),
    inference(variable_rename,[status(thm)],[f_3133_1]) ).

fof(f_3133_3,plain,
    ! [U_11994,U_11995,U_11996,U_11997] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11995,U_11994),U_11997),U_11996) = c_Groups_Ozero__class_Ozero(U_11994)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11995),U_11996))
      | ~ class_Groups_Ocomm__monoid__add(U_11994) ),
    inference(definitional_conversion,[status(esa)],[f_3133_2]) ).

cnf(f_3133_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11995,U_11994),U_11997),U_11996) = c_Groups_Ozero__class_Ozero(U_11994)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11995),U_11996))
    | ~ class_Groups_Ocomm__monoid__add(U_11994) ),
    inference(clausify,[status(thm)],[f_3133_3]) ).

fof(f_3134_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(f_3134_2,plain,
    ! [U_12001,U_12000,U_11999,U_11998] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11999,U_11998),U_12001),U_12000) = c_Groups_Ozero__class_Ozero(U_11998)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11999),U_12000))
      | ~ class_Groups_Ocomm__monoid__add(U_11998) ),
    inference(variable_rename,[status(thm)],[f_3134_1]) ).

fof(f_3134_3,plain,
    ! [U_11999,U_11998,U_12000,U_12001] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11999,U_11998),U_12001),U_12000) = c_Groups_Ozero__class_Ozero(U_11998)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11999),U_12000))
      | ~ class_Groups_Ocomm__monoid__add(U_11998) ),
    inference(definitional_conversion,[status(esa)],[f_3134_2]) ).

cnf(f_3134_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11999,U_11998),U_12001),U_12000) = c_Groups_Ozero__class_Ozero(U_11998)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11999),U_12000))
    | ~ class_Groups_Ocomm__monoid__add(U_11998) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

fof(f_3135_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__negf]) ).

fof(f_3135_2,plain,
    ! [U_12005,U_12004,U_12003,U_12002] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12003,U_12002),hAPP(hAPP(c_COMBB(U_12002,U_12002,U_12003),c_Groups_Ouminus__class_Ouminus(U_12002)),U_12004)),U_12005) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12002),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12003,U_12002),U_12004),U_12005))
      | ~ class_Groups_Oab__group__add(U_12002) ),
    inference(variable_rename,[status(thm)],[f_3135_1]) ).

fof(f_3135_3,plain,
    ! [U_12002,U_12003,U_12004,U_12005] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12003,U_12002),hAPP(hAPP(c_COMBB(U_12002,U_12002,U_12003),c_Groups_Ouminus__class_Ouminus(U_12002)),U_12004)),U_12005) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12002),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12003,U_12002),U_12004),U_12005))
      | ~ class_Groups_Oab__group__add(U_12002) ),
    inference(definitional_conversion,[status(esa)],[f_3135_2]) ).

cnf(f_3135_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12003,U_12002),hAPP(hAPP(c_COMBB(U_12002,U_12002,U_12003),c_Groups_Ouminus__class_Ouminus(U_12002)),U_12004)),U_12005) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12002),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12003,U_12002),U_12004),U_12005))
    | ~ class_Groups_Oab__group__add(U_12002) ),
    inference(clausify,[status(thm)],[f_3135_3]) ).

fof(f_3136_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__setsum]) ).

fof(f_3136_2,plain,
    ! [U_12009,U_12008,U_12007,U_12006] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12006),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12007,tc_Int_Oint),U_12008),U_12009)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12007,U_12006),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12006,U_12007),c_Int_Oring__1__class_Oof__int(U_12006)),U_12008)),U_12009)
      | ~ class_Rings_Oring__1(U_12006) ),
    inference(variable_rename,[status(thm)],[f_3136_1]) ).

fof(f_3136_3,plain,
    ! [U_12006,U_12007,U_12008,U_12009] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12006),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12007,tc_Int_Oint),U_12008),U_12009)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12007,U_12006),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12006,U_12007),c_Int_Oring__1__class_Oof__int(U_12006)),U_12008)),U_12009)
      | ~ class_Rings_Oring__1(U_12006) ),
    inference(definitional_conversion,[status(esa)],[f_3136_2]) ).

cnf(f_3136_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_12006),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12007,tc_Int_Oint),U_12008),U_12009)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12007,U_12006),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12006,U_12007),c_Int_Oring__1__class_Oof__int(U_12006)),U_12008)),U_12009)
    | ~ class_Rings_Oring__1(U_12006) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

fof(f_3137_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__commute]) ).

fof(f_3137_2,plain,
    ! [U_12015,U_12014,U_12013,U_12012,U_12011,U_12010] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12011,U_12010),hAPP(hAPP(c_COMBC(U_12011,tc_fun(U_12012,tc_HOL_Obool),U_12010),hAPP(hAPP(c_COMBB(tc_fun(U_12012,U_12010),tc_fun(tc_fun(U_12012,tc_HOL_Obool),U_12010),U_12011),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12012,U_12010)),U_12013)),U_12014)),U_12015) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12012,U_12010),hAPP(hAPP(c_COMBC(U_12012,tc_fun(U_12011,tc_HOL_Obool),U_12010),hAPP(hAPP(c_COMBB(tc_fun(U_12011,U_12010),tc_fun(tc_fun(U_12011,tc_HOL_Obool),U_12010),U_12012),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12011,U_12010)),hAPP(c_COMBC(U_12011,U_12012,U_12010),U_12013))),U_12015)),U_12014)
      | ~ class_Groups_Ocomm__monoid__add(U_12010) ),
    inference(variable_rename,[status(thm)],[f_3137_1]) ).

fof(f_3137_3,plain,
    ! [U_12010,U_12011,U_12012,U_12013,U_12014,U_12015] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12011,U_12010),hAPP(hAPP(c_COMBC(U_12011,tc_fun(U_12012,tc_HOL_Obool),U_12010),hAPP(hAPP(c_COMBB(tc_fun(U_12012,U_12010),tc_fun(tc_fun(U_12012,tc_HOL_Obool),U_12010),U_12011),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12012,U_12010)),U_12013)),U_12014)),U_12015) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12012,U_12010),hAPP(hAPP(c_COMBC(U_12012,tc_fun(U_12011,tc_HOL_Obool),U_12010),hAPP(hAPP(c_COMBB(tc_fun(U_12011,U_12010),tc_fun(tc_fun(U_12011,tc_HOL_Obool),U_12010),U_12012),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12011,U_12010)),hAPP(c_COMBC(U_12011,U_12012,U_12010),U_12013))),U_12015)),U_12014)
      | ~ class_Groups_Ocomm__monoid__add(U_12010) ),
    inference(definitional_conversion,[status(esa)],[f_3137_2]) ).

cnf(f_3137_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12011,U_12010),hAPP(hAPP(c_COMBC(U_12011,tc_fun(U_12012,tc_HOL_Obool),U_12010),hAPP(hAPP(c_COMBB(tc_fun(U_12012,U_12010),tc_fun(tc_fun(U_12012,tc_HOL_Obool),U_12010),U_12011),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12012,U_12010)),U_12013)),U_12014)),U_12015) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12012,U_12010),hAPP(hAPP(c_COMBC(U_12012,tc_fun(U_12011,tc_HOL_Obool),U_12010),hAPP(hAPP(c_COMBB(tc_fun(U_12011,U_12010),tc_fun(tc_fun(U_12011,tc_HOL_Obool),U_12010),U_12012),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12011,U_12010)),hAPP(c_COMBC(U_12011,U_12012,U_12010),U_12013))),U_12015)),U_12014)
    | ~ class_Groups_Ocomm__monoid__add(U_12010) ),
    inference(clausify,[status(thm)],[f_3137_3]) ).

fof(f_3138_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__setsum]) ).

fof(f_3138_2,plain,
    ! [U_12019,U_12018,U_12017,U_12016] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12017,tc_Nat_Onat),U_12018),U_12019)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12017,U_12016),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12016,U_12017),c_Nat_Osemiring__1__class_Oof__nat(U_12016)),U_12018)),U_12019)
      | ~ class_Rings_Osemiring__1(U_12016) ),
    inference(variable_rename,[status(thm)],[f_3138_1]) ).

fof(f_3138_3,plain,
    ! [U_12017,U_12016,U_12018,U_12019] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12017,tc_Nat_Onat),U_12018),U_12019)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12017,U_12016),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12016,U_12017),c_Nat_Osemiring__1__class_Oof__nat(U_12016)),U_12018)),U_12019)
      | ~ class_Rings_Osemiring__1(U_12016) ),
    inference(definitional_conversion,[status(esa)],[f_3138_2]) ).

cnf(f_3138_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12017,tc_Nat_Onat),U_12018),U_12019)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12017,U_12016),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12016,U_12017),c_Nat_Osemiring__1__class_Oof__nat(U_12016)),U_12018)),U_12019)
    | ~ class_Rings_Osemiring__1(U_12016) ),
    inference(clausify,[status(thm)],[f_3138_3]) ).

fof(f_3139_1,plain,
    ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__product]) ).

fof(f_3139_2,plain,
    ! [U_12026,U_12025,U_12024,U_12023,U_12022,U_12021,U_12020] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12020),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12021,U_12020),U_12022),U_12023)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12024,U_12020),U_12025),U_12026)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12021,U_12020),hAPP(hAPP(c_COMBC(U_12021,tc_fun(U_12024,tc_HOL_Obool),U_12020),hAPP(hAPP(c_COMBB(tc_fun(U_12024,U_12020),tc_fun(tc_fun(U_12024,tc_HOL_Obool),U_12020),U_12021),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12024,U_12020)),hAPP(hAPP(c_COMBC(U_12021,tc_fun(U_12024,U_12020),tc_fun(U_12024,U_12020)),hAPP(hAPP(c_COMBB(tc_fun(U_12020,U_12020),tc_fun(tc_fun(U_12024,U_12020),tc_fun(U_12024,U_12020)),U_12021),c_COMBB(U_12020,U_12020,U_12024)),hAPP(hAPP(c_COMBB(U_12020,tc_fun(U_12020,U_12020),U_12021),c_Groups_Otimes__class_Otimes(U_12020)),U_12022))),U_12025))),U_12026)),U_12023)
      | ~ class_Rings_Osemiring__0(U_12020) ),
    inference(variable_rename,[status(thm)],[f_3139_1]) ).

fof(f_3139_3,plain,
    ! [U_12020,U_12021,U_12022,U_12023,U_12024,U_12025,U_12026] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12020),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12021,U_12020),U_12022),U_12023)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12024,U_12020),U_12025),U_12026)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12021,U_12020),hAPP(hAPP(c_COMBC(U_12021,tc_fun(U_12024,tc_HOL_Obool),U_12020),hAPP(hAPP(c_COMBB(tc_fun(U_12024,U_12020),tc_fun(tc_fun(U_12024,tc_HOL_Obool),U_12020),U_12021),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12024,U_12020)),hAPP(hAPP(c_COMBC(U_12021,tc_fun(U_12024,U_12020),tc_fun(U_12024,U_12020)),hAPP(hAPP(c_COMBB(tc_fun(U_12020,U_12020),tc_fun(tc_fun(U_12024,U_12020),tc_fun(U_12024,U_12020)),U_12021),c_COMBB(U_12020,U_12020,U_12024)),hAPP(hAPP(c_COMBB(U_12020,tc_fun(U_12020,U_12020),U_12021),c_Groups_Otimes__class_Otimes(U_12020)),U_12022))),U_12025))),U_12026)),U_12023)
      | ~ class_Rings_Osemiring__0(U_12020) ),
    inference(definitional_conversion,[status(esa)],[f_3139_2]) ).

cnf(f_3139_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12020),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12021,U_12020),U_12022),U_12023)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12024,U_12020),U_12025),U_12026)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12021,U_12020),hAPP(hAPP(c_COMBC(U_12021,tc_fun(U_12024,tc_HOL_Obool),U_12020),hAPP(hAPP(c_COMBB(tc_fun(U_12024,U_12020),tc_fun(tc_fun(U_12024,tc_HOL_Obool),U_12020),U_12021),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12024,U_12020)),hAPP(hAPP(c_COMBC(U_12021,tc_fun(U_12024,U_12020),tc_fun(U_12024,U_12020)),hAPP(hAPP(c_COMBB(tc_fun(U_12020,U_12020),tc_fun(tc_fun(U_12024,U_12020),tc_fun(U_12024,U_12020)),U_12021),c_COMBB(U_12020,U_12020,U_12024)),hAPP(hAPP(c_COMBB(U_12020,tc_fun(U_12020,U_12020),U_12021),c_Groups_Otimes__class_Otimes(U_12020)),U_12022))),U_12025))),U_12026)),U_12023)
    | ~ class_Rings_Osemiring__0(U_12020) ),
    inference(clausify,[status(thm)],[f_3139_3]) ).

fof(f_3140_1,plain,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib]) ).

fof(f_3140_2,plain,
    ! [U_12031,U_12030,U_12029,U_12028,U_12027] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12027),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12028,U_12027),U_12029),U_12030)),U_12031) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12028,U_12027),hAPP(hAPP(c_COMBC(U_12028,U_12027,U_12027),hAPP(hAPP(c_COMBB(U_12027,tc_fun(U_12027,U_12027),U_12028),c_Groups_Otimes__class_Otimes(U_12027)),U_12029)),U_12031)),U_12030)
      | ~ class_Rings_Osemiring__0(U_12027) ),
    inference(variable_rename,[status(thm)],[f_3140_1]) ).

fof(f_3140_3,plain,
    ! [U_12027,U_12028,U_12029,U_12030,U_12031] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12027),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12028,U_12027),U_12029),U_12030)),U_12031) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12028,U_12027),hAPP(hAPP(c_COMBC(U_12028,U_12027,U_12027),hAPP(hAPP(c_COMBB(U_12027,tc_fun(U_12027,U_12027),U_12028),c_Groups_Otimes__class_Otimes(U_12027)),U_12029)),U_12031)),U_12030)
      | ~ class_Rings_Osemiring__0(U_12027) ),
    inference(definitional_conversion,[status(esa)],[f_3140_2]) ).

cnf(f_3140_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12027),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12028,U_12027),U_12029),U_12030)),U_12031) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12028,U_12027),hAPP(hAPP(c_COMBC(U_12028,U_12027,U_12027),hAPP(hAPP(c_COMBB(U_12027,tc_fun(U_12027,U_12027),U_12028),c_Groups_Otimes__class_Otimes(U_12027)),U_12029)),U_12031)),U_12030)
    | ~ class_Rings_Osemiring__0(U_12027) ),
    inference(clausify,[status(thm)],[f_3140_3]) ).

fof(f_3141_1,plain,
    ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib]) ).

fof(f_3141_2,plain,
    ! [U_12036,U_12035,U_12034,U_12033,U_12032] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12032),U_12033),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12034,U_12032),U_12035),U_12036)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12034,U_12032),hAPP(hAPP(c_COMBB(U_12032,U_12032,U_12034),hAPP(c_Groups_Otimes__class_Otimes(U_12032),U_12033)),U_12035)),U_12036)
      | ~ class_Rings_Osemiring__0(U_12032) ),
    inference(variable_rename,[status(thm)],[f_3141_1]) ).

fof(f_3141_3,plain,
    ! [U_12032,U_12033,U_12034,U_12035,U_12036] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12032),U_12033),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12034,U_12032),U_12035),U_12036)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12034,U_12032),hAPP(hAPP(c_COMBB(U_12032,U_12032,U_12034),hAPP(c_Groups_Otimes__class_Otimes(U_12032),U_12033)),U_12035)),U_12036)
      | ~ class_Rings_Osemiring__0(U_12032) ),
    inference(definitional_conversion,[status(esa)],[f_3141_2]) ).

cnf(f_3141_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12032),U_12033),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12034,U_12032),U_12035),U_12036)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12034,U_12032),hAPP(hAPP(c_COMBB(U_12032,U_12032,U_12034),hAPP(c_Groups_Otimes__class_Otimes(U_12032),U_12033)),U_12035)),U_12036)
    | ~ class_Rings_Osemiring__0(U_12032) ),
    inference(clausify,[status(thm)],[f_3141_3]) ).

fof(f_3142_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__addf]) ).

fof(f_3142_2,plain,
    ! [U_12041,U_12040,U_12039,U_12038,U_12037] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),hAPP(hAPP(c_COMBS(U_12038,U_12037,U_12037),hAPP(hAPP(c_COMBB(U_12037,tc_fun(U_12037,U_12037),U_12038),c_Groups_Oplus__class_Oplus(U_12037)),U_12039)),U_12040)),U_12041) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12037),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),U_12039),U_12041)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),U_12040),U_12041))
      | ~ class_Groups_Ocomm__monoid__add(U_12037) ),
    inference(variable_rename,[status(thm)],[f_3142_1]) ).

fof(f_3142_3,plain,
    ! [U_12037,U_12038,U_12039,U_12040,U_12041] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),hAPP(hAPP(c_COMBS(U_12038,U_12037,U_12037),hAPP(hAPP(c_COMBB(U_12037,tc_fun(U_12037,U_12037),U_12038),c_Groups_Oplus__class_Oplus(U_12037)),U_12039)),U_12040)),U_12041) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12037),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),U_12039),U_12041)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),U_12040),U_12041))
      | ~ class_Groups_Ocomm__monoid__add(U_12037) ),
    inference(definitional_conversion,[status(esa)],[f_3142_2]) ).

cnf(f_3142_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),hAPP(hAPP(c_COMBS(U_12038,U_12037,U_12037),hAPP(hAPP(c_COMBB(U_12037,tc_fun(U_12037,U_12037),U_12038),c_Groups_Oplus__class_Oplus(U_12037)),U_12039)),U_12040)),U_12041) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12037),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),U_12039),U_12041)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12038,U_12037),U_12040),U_12041))
    | ~ class_Groups_Ocomm__monoid__add(U_12037) ),
    inference(clausify,[status(thm)],[f_3142_3]) ).

fof(f_3143_1,plain,
    ! [V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__0]) ).

fof(f_3143_2,plain,
    ! [U_12044,U_12043,U_12042] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12043,U_12042),hAPP(c_COMBK(U_12042,U_12043),c_Groups_Ozero__class_Ozero(U_12042))),U_12044) = c_Groups_Ozero__class_Ozero(U_12042)
      | ~ class_Groups_Ocomm__monoid__add(U_12042) ),
    inference(variable_rename,[status(thm)],[f_3143_1]) ).

fof(f_3143_3,plain,
    ! [U_12043,U_12042,U_12044] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12043,U_12042),hAPP(c_COMBK(U_12042,U_12043),c_Groups_Ozero__class_Ozero(U_12042))),U_12044) = c_Groups_Ozero__class_Ozero(U_12042)
      | ~ class_Groups_Ocomm__monoid__add(U_12042) ),
    inference(definitional_conversion,[status(esa)],[f_3143_2]) ).

cnf(f_3143_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12043,U_12042),hAPP(c_COMBK(U_12042,U_12043),c_Groups_Ozero__class_Ozero(U_12042))),U_12044) = c_Groups_Ozero__class_Ozero(U_12042)
    | ~ class_Groups_Ocomm__monoid__add(U_12042) ),
    inference(clausify,[status(thm)],[f_3143_3]) ).

fof(f_3144_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs]) ).

fof(f_3144_2,plain,
    ! [U_12048,U_12047,U_12046,U_12045] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_12045),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12046,U_12045),hAPP(hAPP(c_COMBB(U_12045,U_12045,U_12046),c_Groups_Oabs__class_Oabs(U_12045)),U_12047)),U_12048)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12046,U_12045),hAPP(hAPP(c_COMBB(U_12045,U_12045,U_12046),c_Groups_Oabs__class_Oabs(U_12045)),U_12047)),U_12048)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12045) ),
    inference(variable_rename,[status(thm)],[f_3144_1]) ).

fof(f_3144_3,plain,
    ! [U_12045,U_12046,U_12047,U_12048] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_12045),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12046,U_12045),hAPP(hAPP(c_COMBB(U_12045,U_12045,U_12046),c_Groups_Oabs__class_Oabs(U_12045)),U_12047)),U_12048)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12046,U_12045),hAPP(hAPP(c_COMBB(U_12045,U_12045,U_12046),c_Groups_Oabs__class_Oabs(U_12045)),U_12047)),U_12048)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12045) ),
    inference(definitional_conversion,[status(esa)],[f_3144_2]) ).

cnf(f_3144_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_12045),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12046,U_12045),hAPP(hAPP(c_COMBB(U_12045,U_12045,U_12046),c_Groups_Oabs__class_Oabs(U_12045)),U_12047)),U_12048)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12046,U_12045),hAPP(hAPP(c_COMBB(U_12045,U_12045,U_12046),c_Groups_Oabs__class_Oabs(U_12045)),U_12047)),U_12048)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12045) ),
    inference(clausify,[status(thm)],[f_3144_3]) ).

fof(f_3145_1,plain,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2)
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib]) ).

fof(f_3145_2,plain,
    ! [U_12053,U_12052,U_12051,U_12050,U_12049] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12049),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12050,U_12049),U_12051),U_12052)),U_12053) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12050,U_12049),hAPP(hAPP(c_COMBC(U_12050,U_12049,U_12049),hAPP(hAPP(c_COMBB(U_12049,tc_fun(U_12049,U_12049),U_12050),c_Rings_Oinverse__class_Odivide(U_12049)),U_12051)),U_12053)),U_12052)
      | ~ class_Fields_Ofield(U_12049) ),
    inference(variable_rename,[status(thm)],[f_3145_1]) ).

fof(f_3145_3,plain,
    ! [U_12049,U_12050,U_12051,U_12052,U_12053] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12049),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12050,U_12049),U_12051),U_12052)),U_12053) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12050,U_12049),hAPP(hAPP(c_COMBC(U_12050,U_12049,U_12049),hAPP(hAPP(c_COMBB(U_12049,tc_fun(U_12049,U_12049),U_12050),c_Rings_Oinverse__class_Odivide(U_12049)),U_12051)),U_12053)),U_12052)
      | ~ class_Fields_Ofield(U_12049) ),
    inference(definitional_conversion,[status(esa)],[f_3145_2]) ).

cnf(f_3145_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12049),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12050,U_12049),U_12051),U_12052)),U_12053) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12050,U_12049),hAPP(hAPP(c_COMBC(U_12050,U_12049,U_12049),hAPP(hAPP(c_COMBB(U_12049,tc_fun(U_12049,U_12049),U_12050),c_Rings_Oinverse__class_Odivide(U_12049)),U_12051)),U_12053)),U_12052)
    | ~ class_Fields_Ofield(U_12049) ),
    inference(clausify,[status(thm)],[f_3145_3]) ).

fof(f_3146_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__subtractf]) ).

fof(f_3146_2,plain,
    ! [U_12058,U_12057,U_12056,U_12055,U_12054] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),hAPP(hAPP(c_COMBS(U_12055,U_12054,U_12054),hAPP(hAPP(c_COMBB(U_12054,tc_fun(U_12054,U_12054),U_12055),c_Groups_Ominus__class_Ominus(U_12054)),U_12056)),U_12057)),U_12058) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12054),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),U_12056),U_12058)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),U_12057),U_12058))
      | ~ class_Groups_Oab__group__add(U_12054) ),
    inference(variable_rename,[status(thm)],[f_3146_1]) ).

fof(f_3146_3,plain,
    ! [U_12054,U_12055,U_12056,U_12057,U_12058] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),hAPP(hAPP(c_COMBS(U_12055,U_12054,U_12054),hAPP(hAPP(c_COMBB(U_12054,tc_fun(U_12054,U_12054),U_12055),c_Groups_Ominus__class_Ominus(U_12054)),U_12056)),U_12057)),U_12058) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12054),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),U_12056),U_12058)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),U_12057),U_12058))
      | ~ class_Groups_Oab__group__add(U_12054) ),
    inference(definitional_conversion,[status(esa)],[f_3146_2]) ).

cnf(f_3146_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),hAPP(hAPP(c_COMBS(U_12055,U_12054,U_12054),hAPP(hAPP(c_COMBB(U_12054,tc_fun(U_12054,U_12054),U_12055),c_Groups_Ominus__class_Ominus(U_12054)),U_12056)),U_12057)),U_12058) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12054),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),U_12056),U_12058)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12055,U_12054),U_12057),U_12058))
    | ~ class_Groups_Oab__group__add(U_12054) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

fof(f_3147_1,plain,
    ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__empty]) ).

fof(f_3147_2,plain,
    ! [U_12062,U_12061,U_12060,U_12059] : hAPP(c_Map_Orestrict__map(U_12059,U_12060,hAPP(c_COMBK(tc_Option_Ooption(U_12060),U_12059),c_Option_Ooption_ONone(U_12060)),U_12061),U_12062) = c_Option_Ooption_ONone(U_12060),
    inference(variable_rename,[status(thm)],[f_3147_1]) ).

fof(f_3147_3,plain,
    ! [U_12060,U_12059,U_12061,U_12062] : hAPP(c_Map_Orestrict__map(U_12059,U_12060,hAPP(c_COMBK(tc_Option_Ooption(U_12060),U_12059),c_Option_Ooption_ONone(U_12060)),U_12061),U_12062) = c_Option_Ooption_ONone(U_12060),
    inference(definitional_conversion,[status(esa)],[f_3147_2]) ).

cnf(f_3147_4,plain,
    hAPP(c_Map_Orestrict__map(U_12059,U_12060,hAPP(c_COMBK(tc_Option_Ooption(U_12060),U_12059),c_Option_Ooption_ONone(U_12060)),U_12061),U_12062) = c_Option_Ooption_ONone(U_12060),
    inference(clausify,[status(thm)],[f_3147_3]) ).

fof(f_3148_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib]) ).

fof(f_3148_2,plain,
    ! [U_12067,U_12066,U_12065,U_12064,U_12063] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),hAPP(hAPP(c_COMBS(U_12064,U_12063,U_12063),hAPP(hAPP(c_COMBB(U_12063,tc_fun(U_12063,U_12063),U_12064),c_Groups_Oplus__class_Oplus(U_12063)),U_12066)),U_12067)),U_12065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),U_12066),U_12065)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),U_12067),U_12065))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12064),U_12065))
      | ~ class_Groups_Ocomm__monoid__add(U_12063) ),
    inference(variable_rename,[status(thm)],[f_3148_1]) ).

fof(f_3148_3,plain,
    ! [U_12063,U_12064,U_12065,U_12066,U_12067] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),hAPP(hAPP(c_COMBS(U_12064,U_12063,U_12063),hAPP(hAPP(c_COMBB(U_12063,tc_fun(U_12063,U_12063),U_12064),c_Groups_Oplus__class_Oplus(U_12063)),U_12066)),U_12067)),U_12065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),U_12066),U_12065)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),U_12067),U_12065))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12064),U_12065))
      | ~ class_Groups_Ocomm__monoid__add(U_12063) ),
    inference(definitional_conversion,[status(esa)],[f_3148_2]) ).

cnf(f_3148_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),hAPP(hAPP(c_COMBS(U_12064,U_12063,U_12063),hAPP(hAPP(c_COMBB(U_12063,tc_fun(U_12063,U_12063),U_12064),c_Groups_Oplus__class_Oplus(U_12063)),U_12066)),U_12067)),U_12065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),U_12066),U_12065)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12064,U_12063),U_12067),U_12065))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12064),U_12065))
    | ~ class_Groups_Ocomm__monoid__add(U_12063) ),
    inference(clausify,[status(thm)],[f_3148_3]) ).

fof(f_3149_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl]) ).

fof(f_3149_2,plain,
    ! [U_12071,U_12070,U_12069,U_12068] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12068),U_12069),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12070)),hAPP(c_Nat_OSuc,U_12071))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12068),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12068,tc_Nat_Onat),U_12069),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),U_12071))
      | ~ class_Groups_Ocomm__monoid__add(U_12068) ),
    inference(variable_rename,[status(thm)],[f_3149_1]) ).

fof(f_3149_3,plain,
    ! [U_12069,U_12068,U_12070,U_12071] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12068),U_12069),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12070)),hAPP(c_Nat_OSuc,U_12071))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12068),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12068,tc_Nat_Onat),U_12069),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),U_12071))
      | ~ class_Groups_Ocomm__monoid__add(U_12068) ),
    inference(definitional_conversion,[status(esa)],[f_3149_2]) ).

cnf(f_3149_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12068),U_12069),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12070)),hAPP(c_Nat_OSuc,U_12071))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12068),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12068,tc_Nat_Onat),U_12069),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),U_12071))
    | ~ class_Groups_Ocomm__monoid__add(U_12068) ),
    inference(clausify,[status(thm)],[f_3149_3]) ).

fof(f_3150_1,plain,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl]) ).

fof(f_3150_2,plain,
    ! [U_12076,U_12075,U_12074,U_12073,U_12072] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12072),U_12073),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12074),U_12075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12076),U_12075))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12072),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12072,tc_Nat_Onat),U_12073),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12075))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12074),U_12076))
      | ~ class_Groups_Ocomm__monoid__add(U_12072) ),
    inference(variable_rename,[status(thm)],[f_3150_1]) ).

fof(f_3150_3,plain,
    ! [U_12072,U_12073,U_12074,U_12075,U_12076] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12072),U_12073),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12074),U_12075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12076),U_12075))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12072),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12072,tc_Nat_Onat),U_12073),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12075))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12074),U_12076))
      | ~ class_Groups_Ocomm__monoid__add(U_12072) ),
    inference(definitional_conversion,[status(esa)],[f_3150_2]) ).

cnf(f_3150_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12072),U_12073),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12074),U_12075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12076),U_12075))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12072),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12072,tc_Nat_Onat),U_12073),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12075))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12074),U_12076))
    | ~ class_Groups_Ocomm__monoid__add(U_12072) ),
    inference(clausify,[status(thm)],[f_3150_3]) ).

fof(f_3151_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl]) ).

fof(f_3151_2,plain,
    ! [U_12080,U_12079,U_12078,U_12077] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12077),U_12078),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12079),hAPP(c_Nat_OSuc,U_12080))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12077),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12077,tc_Nat_Onat),U_12078),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12079,U_12080))
      | ~ class_Groups_Ocomm__monoid__add(U_12077) ),
    inference(variable_rename,[status(thm)],[f_3151_1]) ).

fof(f_3151_3,plain,
    ! [U_12077,U_12078,U_12079,U_12080] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12077),U_12078),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12079),hAPP(c_Nat_OSuc,U_12080))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12077),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12077,tc_Nat_Onat),U_12078),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12079,U_12080))
      | ~ class_Groups_Ocomm__monoid__add(U_12077) ),
    inference(definitional_conversion,[status(esa)],[f_3151_2]) ).

cnf(f_3151_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12077),U_12078),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12079),hAPP(c_Nat_OSuc,U_12080))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12077),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12077,tc_Nat_Onat),U_12078),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12079,U_12080))
    | ~ class_Groups_Ocomm__monoid__add(U_12077) ),
    inference(clausify,[status(thm)],[f_3151_3]) ).

fof(f_3152_1,plain,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl]) ).

fof(f_3152_2,plain,
    ! [U_12085,U_12084,U_12083,U_12082,U_12081] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12081),U_12082),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12083),U_12084),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12085),U_12084))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12081),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12081,tc_Nat_Onat),U_12082),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12084))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12083,U_12085))
      | ~ class_Groups_Ocomm__monoid__add(U_12081) ),
    inference(variable_rename,[status(thm)],[f_3152_1]) ).

fof(f_3152_3,plain,
    ! [U_12081,U_12082,U_12083,U_12084,U_12085] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12081),U_12082),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12083),U_12084),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12085),U_12084))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12081),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12081,tc_Nat_Onat),U_12082),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12084))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12083,U_12085))
      | ~ class_Groups_Ocomm__monoid__add(U_12081) ),
    inference(definitional_conversion,[status(esa)],[f_3152_2]) ).

cnf(f_3152_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12081),U_12082),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12083),U_12084),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12085),U_12084))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12081),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12081,tc_Nat_Onat),U_12082),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12084))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12083,U_12085))
    | ~ class_Groups_Ocomm__monoid__add(U_12081) ),
    inference(clausify,[status(thm)],[f_3152_3]) ).

fof(f_3153_1,plain,
    ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__out]) ).

fof(f_3153_2,plain,
    ! [U_12090,U_12089,U_12088,U_12087,U_12086] :
      ( hAPP(c_Map_Orestrict__map(U_12086,U_12089,U_12090,U_12088),U_12087) = c_Option_Ooption_ONone(U_12089)
      | hBOOL(hAPP(hAPP(c_member(U_12086),U_12087),U_12088)) ),
    inference(variable_rename,[status(thm)],[f_3153_1]) ).

fof(f_3153_3,plain,
    ! [U_12086,U_12087,U_12088,U_12089,U_12090] :
      ( hAPP(c_Map_Orestrict__map(U_12086,U_12089,U_12090,U_12088),U_12087) = c_Option_Ooption_ONone(U_12089)
      | hBOOL(hAPP(hAPP(c_member(U_12086),U_12087),U_12088)) ),
    inference(definitional_conversion,[status(esa)],[f_3153_2]) ).

cnf(f_3153_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_12086,U_12089,U_12090,U_12088),U_12087) = c_Option_Ooption_ONone(U_12089)
    | hBOOL(hAPP(hAPP(c_member(U_12086),U_12087),U_12088)) ),
    inference(clausify,[status(thm)],[f_3153_3]) ).

fof(f_3154_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__insert]) ).

fof(f_3154_2,plain,
    ! [U_12095,U_12094,U_12093,U_12092,U_12091] : c_Map_Orestrict__map(U_12091,U_12092,U_12093,hAPP(hAPP(c_Set_Oinsert(U_12091),U_12094),U_12095)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12091,tc_Option_Ooption(U_12092)),c_Map_Orestrict__map(U_12091,U_12092,U_12093,U_12095)),U_12094),hAPP(U_12093,U_12094)),
    inference(variable_rename,[status(thm)],[f_3154_1]) ).

fof(f_3154_3,plain,
    ! [U_12091,U_12092,U_12093,U_12094,U_12095] : c_Map_Orestrict__map(U_12091,U_12092,U_12093,hAPP(hAPP(c_Set_Oinsert(U_12091),U_12094),U_12095)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12091,tc_Option_Ooption(U_12092)),c_Map_Orestrict__map(U_12091,U_12092,U_12093,U_12095)),U_12094),hAPP(U_12093,U_12094)),
    inference(definitional_conversion,[status(esa)],[f_3154_2]) ).

cnf(f_3154_4,plain,
    c_Map_Orestrict__map(U_12091,U_12092,U_12093,hAPP(hAPP(c_Set_Oinsert(U_12091),U_12094),U_12095)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12091,tc_Option_Ooption(U_12092)),c_Map_Orestrict__map(U_12091,U_12092,U_12093,U_12095)),U_12094),hAPP(U_12093,U_12094)),
    inference(clausify,[status(thm)],[f_3154_3]) ).

fof(f_3155_1,plain,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl]) ).

fof(f_3155_2,plain,
    ! [U_12100,U_12099,U_12098,U_12097,U_12096] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12096),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12097),U_12098))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12098),U_12099))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12097),U_12099))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12098),U_12099))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12097),U_12098))
      | ~ class_Groups_Ocomm__monoid__add(U_12096) ),
    inference(variable_rename,[status(thm)],[f_3155_1]) ).

fof(f_3155_3,plain,
    ! [U_12096,U_12097,U_12098,U_12099,U_12100] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12096),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12097),U_12098))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12098),U_12099))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12097),U_12099))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12098),U_12099))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12097),U_12098))
      | ~ class_Groups_Ocomm__monoid__add(U_12096) ),
    inference(definitional_conversion,[status(esa)],[f_3155_2]) ).

cnf(f_3155_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12096),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12097),U_12098))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12098),U_12099))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12096),U_12100),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12097),U_12099))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12098),U_12099))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12097),U_12098))
    | ~ class_Groups_Ocomm__monoid__add(U_12096) ),
    inference(clausify,[status(thm)],[f_3155_3]) ).

fof(f_3156_1,plain,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl]) ).

fof(f_3156_2,plain,
    ! [U_12105,U_12104,U_12103,U_12102,U_12101] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12101),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12102),U_12104))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12102),U_12103))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12103),U_12104))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12103),U_12104))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12102),U_12103))
      | ~ class_Groups_Oab__group__add(U_12101) ),
    inference(variable_rename,[status(thm)],[f_3156_1]) ).

fof(f_3156_3,plain,
    ! [U_12102,U_12101,U_12103,U_12104,U_12105] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12101),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12102),U_12104))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12102),U_12103))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12103),U_12104))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12103),U_12104))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12102),U_12103))
      | ~ class_Groups_Oab__group__add(U_12101) ),
    inference(definitional_conversion,[status(esa)],[f_3156_2]) ).

cnf(f_3156_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12101),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12102),U_12104))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12102),U_12103))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12101),U_12105),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12103),U_12104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12103),U_12104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12102),U_12103))
    | ~ class_Groups_Oab__group__add(U_12101) ),
    inference(clausify,[status(thm)],[f_3156_3]) ).

fof(f_3157_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__delta]) ).

fof(f_3157_2,plain,
    ! [U_12110,U_12109,U_12108,U_12107,U_12106] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12107,U_12106),hAPP(hAPP(c_COMBC(U_12107,U_12106,U_12106),hAPP(hAPP(c_COMBS(U_12107,U_12106,tc_fun(U_12106,U_12106)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12106,tc_fun(U_12106,U_12106)),U_12107),c_If(U_12106)),hAPP(hAPP(c_COMBC(U_12107,U_12107,tc_HOL_Obool),c_fequal),U_12109))),U_12110)),c_Groups_Ozero__class_Ozero(U_12106))),U_12108) = c_Groups_Ozero__class_Ozero(U_12106)
          | hBOOL(hAPP(hAPP(c_member(U_12107),U_12109),U_12108)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12107,U_12106),hAPP(hAPP(c_COMBC(U_12107,U_12106,U_12106),hAPP(hAPP(c_COMBS(U_12107,U_12106,tc_fun(U_12106,U_12106)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12106,tc_fun(U_12106,U_12106)),U_12107),c_If(U_12106)),hAPP(hAPP(c_COMBC(U_12107,U_12107,tc_HOL_Obool),c_fequal),U_12109))),U_12110)),c_Groups_Ozero__class_Ozero(U_12106))),U_12108) = hAPP(U_12110,U_12109)
          | ~ hBOOL(hAPP(hAPP(c_member(U_12107),U_12109),U_12108)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12107),U_12108))
      | ~ class_Groups_Ocomm__monoid__add(U_12106) ),
    inference(variable_rename,[status(thm)],[f_3157_1]) ).

fof(f_3157_3,plain,
    ( ! [U_12106,U_12107,U_12108,U_12109,U_12110] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12107,U_12106),hAPP(hAPP(c_COMBC(U_12107,U_12106,U_12106),hAPP(hAPP(c_COMBS(U_12107,U_12106,tc_fun(U_12106,U_12106)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12106,tc_fun(U_12106,U_12106)),U_12107),c_If(U_12106)),hAPP(hAPP(c_COMBC(U_12107,U_12107,tc_HOL_Obool),c_fequal),U_12109))),U_12110)),c_Groups_Ozero__class_Ozero(U_12106))),U_12108) = c_Groups_Ozero__class_Ozero(U_12106)
        | hBOOL(hAPP(hAPP(c_member(U_12107),U_12109),U_12108))
        | ~ sP902(U_12106,U_12107,U_12108,U_12109,U_12110) )
    & ! [U_12106,U_12107,U_12108,U_12109,U_12110] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12107,U_12106),hAPP(hAPP(c_COMBC(U_12107,U_12106,U_12106),hAPP(hAPP(c_COMBS(U_12107,U_12106,tc_fun(U_12106,U_12106)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12106,tc_fun(U_12106,U_12106)),U_12107),c_If(U_12106)),hAPP(hAPP(c_COMBC(U_12107,U_12107,tc_HOL_Obool),c_fequal),U_12109))),U_12110)),c_Groups_Ozero__class_Ozero(U_12106))),U_12108) = hAPP(U_12110,U_12109)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12107),U_12109),U_12108))
        | ~ sP902(U_12106,U_12107,U_12108,U_12109,U_12110) )
    & ! [U_12106,U_12107,U_12108,U_12109,U_12110] :
        ( sP902(U_12106,U_12107,U_12108,U_12109,U_12110)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12107),U_12108))
        | ~ class_Groups_Ocomm__monoid__add(U_12106) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP902])],[f_3157_2]) ).

cnf(f_3157_4,plain,
    ( sP902(U_12106,U_12107,U_12108,U_12109,U_12110)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12107),U_12108))
    | ~ class_Groups_Ocomm__monoid__add(U_12106) ),
    inference(clausify,[status(thm)],[f_3157_3]) ).

cnf(f_3157_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12107,U_12106),hAPP(hAPP(c_COMBC(U_12107,U_12106,U_12106),hAPP(hAPP(c_COMBS(U_12107,U_12106,tc_fun(U_12106,U_12106)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12106,tc_fun(U_12106,U_12106)),U_12107),c_If(U_12106)),hAPP(hAPP(c_COMBC(U_12107,U_12107,tc_HOL_Obool),c_fequal),U_12109))),U_12110)),c_Groups_Ozero__class_Ozero(U_12106))),U_12108) = hAPP(U_12110,U_12109)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12107),U_12109),U_12108))
    | ~ sP902(U_12106,U_12107,U_12108,U_12109,U_12110) ),
    inference(clausify,[status(thm)],[f_3157_3]) ).

cnf(f_3157_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12107,U_12106),hAPP(hAPP(c_COMBC(U_12107,U_12106,U_12106),hAPP(hAPP(c_COMBS(U_12107,U_12106,tc_fun(U_12106,U_12106)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12106,tc_fun(U_12106,U_12106)),U_12107),c_If(U_12106)),hAPP(hAPP(c_COMBC(U_12107,U_12107,tc_HOL_Obool),c_fequal),U_12109))),U_12110)),c_Groups_Ozero__class_Ozero(U_12106))),U_12108) = c_Groups_Ozero__class_Ozero(U_12106)
    | hBOOL(hAPP(hAPP(c_member(U_12107),U_12109),U_12108))
    | ~ sP902(U_12106,U_12107,U_12108,U_12109,U_12110) ),
    inference(clausify,[status(thm)],[f_3157_3]) ).

fof(f_3158_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__delta_H]) ).

fof(f_3158_2,plain,
    ! [U_12115,U_12114,U_12113,U_12112,U_12111] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12112,U_12111),hAPP(hAPP(c_COMBC(U_12112,U_12111,U_12111),hAPP(hAPP(c_COMBS(U_12112,U_12111,tc_fun(U_12111,U_12111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12111,tc_fun(U_12111,U_12111)),U_12112),c_If(U_12111)),hAPP(c_fequal,U_12114))),U_12115)),c_Groups_Ozero__class_Ozero(U_12111))),U_12113) = c_Groups_Ozero__class_Ozero(U_12111)
          | hBOOL(hAPP(hAPP(c_member(U_12112),U_12114),U_12113)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12112,U_12111),hAPP(hAPP(c_COMBC(U_12112,U_12111,U_12111),hAPP(hAPP(c_COMBS(U_12112,U_12111,tc_fun(U_12111,U_12111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12111,tc_fun(U_12111,U_12111)),U_12112),c_If(U_12111)),hAPP(c_fequal,U_12114))),U_12115)),c_Groups_Ozero__class_Ozero(U_12111))),U_12113) = hAPP(U_12115,U_12114)
          | ~ hBOOL(hAPP(hAPP(c_member(U_12112),U_12114),U_12113)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12112),U_12113))
      | ~ class_Groups_Ocomm__monoid__add(U_12111) ),
    inference(variable_rename,[status(thm)],[f_3158_1]) ).

fof(f_3158_3,plain,
    ( ! [U_12115,U_12114,U_12113,U_12111,U_12112] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12112,U_12111),hAPP(hAPP(c_COMBC(U_12112,U_12111,U_12111),hAPP(hAPP(c_COMBS(U_12112,U_12111,tc_fun(U_12111,U_12111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12111,tc_fun(U_12111,U_12111)),U_12112),c_If(U_12111)),hAPP(c_fequal,U_12114))),U_12115)),c_Groups_Ozero__class_Ozero(U_12111))),U_12113) = c_Groups_Ozero__class_Ozero(U_12111)
        | hBOOL(hAPP(hAPP(c_member(U_12112),U_12114),U_12113))
        | ~ sP903(U_12115,U_12114,U_12113,U_12111,U_12112) )
    & ! [U_12115,U_12114,U_12113,U_12111,U_12112] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12112,U_12111),hAPP(hAPP(c_COMBC(U_12112,U_12111,U_12111),hAPP(hAPP(c_COMBS(U_12112,U_12111,tc_fun(U_12111,U_12111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12111,tc_fun(U_12111,U_12111)),U_12112),c_If(U_12111)),hAPP(c_fequal,U_12114))),U_12115)),c_Groups_Ozero__class_Ozero(U_12111))),U_12113) = hAPP(U_12115,U_12114)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12112),U_12114),U_12113))
        | ~ sP903(U_12115,U_12114,U_12113,U_12111,U_12112) )
    & ! [U_12115,U_12114,U_12113,U_12111,U_12112] :
        ( sP903(U_12115,U_12114,U_12113,U_12111,U_12112)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12112),U_12113))
        | ~ class_Groups_Ocomm__monoid__add(U_12111) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP903])],[f_3158_2]) ).

cnf(f_3158_4,plain,
    ( sP903(U_12115,U_12114,U_12113,U_12111,U_12112)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12112),U_12113))
    | ~ class_Groups_Ocomm__monoid__add(U_12111) ),
    inference(clausify,[status(thm)],[f_3158_3]) ).

cnf(f_3158_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12112,U_12111),hAPP(hAPP(c_COMBC(U_12112,U_12111,U_12111),hAPP(hAPP(c_COMBS(U_12112,U_12111,tc_fun(U_12111,U_12111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12111,tc_fun(U_12111,U_12111)),U_12112),c_If(U_12111)),hAPP(c_fequal,U_12114))),U_12115)),c_Groups_Ozero__class_Ozero(U_12111))),U_12113) = hAPP(U_12115,U_12114)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12112),U_12114),U_12113))
    | ~ sP903(U_12115,U_12114,U_12113,U_12111,U_12112) ),
    inference(clausify,[status(thm)],[f_3158_3]) ).

cnf(f_3158_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12112,U_12111),hAPP(hAPP(c_COMBC(U_12112,U_12111,U_12111),hAPP(hAPP(c_COMBS(U_12112,U_12111,tc_fun(U_12111,U_12111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12111,tc_fun(U_12111,U_12111)),U_12112),c_If(U_12111)),hAPP(c_fequal,U_12114))),U_12115)),c_Groups_Ozero__class_Ozero(U_12111))),U_12113) = c_Groups_Ozero__class_Ozero(U_12111)
    | hBOOL(hAPP(hAPP(c_member(U_12112),U_12114),U_12113))
    | ~ sP903(U_12115,U_12114,U_12113,U_12111,U_12112) ),
    inference(clausify,[status(thm)],[f_3158_3]) ).

fof(f_3159_1,plain,
    ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
      ( ( hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__def]) ).

fof(f_3159_2,plain,
    ! [U_12120,U_12119,U_12118,U_12117,U_12116] :
      ( ( hAPP(c_Map_Orestrict__map(U_12116,U_12119,U_12120,U_12118),U_12117) = c_Option_Ooption_ONone(U_12119)
        | hBOOL(hAPP(hAPP(c_member(U_12116),U_12117),U_12118)) )
      & ( hAPP(c_Map_Orestrict__map(U_12116,U_12119,U_12120,U_12118),U_12117) = hAPP(U_12120,U_12117)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12116),U_12117),U_12118)) ) ),
    inference(variable_rename,[status(thm)],[f_3159_1]) ).

fof(f_3159_3,plain,
    ( ! [U_12130,U_12128,U_12126,U_12124,U_12122] :
        ( hAPP(c_Map_Orestrict__map(U_12122,U_12128,U_12130,U_12126),U_12124) = c_Option_Ooption_ONone(U_12128)
        | hBOOL(hAPP(hAPP(c_member(U_12122),U_12124),U_12126)) )
    & ! [U_12129,U_12127,U_12125,U_12123,U_12121] :
        ( hAPP(c_Map_Orestrict__map(U_12121,U_12127,U_12129,U_12125),U_12123) = hAPP(U_12129,U_12123)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12121),U_12123),U_12125)) ) ),
    inference(miniscope,[status(thm)],[f_3159_2]) ).

fof(f_3159_4,plain,
    ( ! [U_12128,U_12126,U_12122,U_12124,U_12130] :
        ( hAPP(c_Map_Orestrict__map(U_12122,U_12128,U_12130,U_12126),U_12124) = c_Option_Ooption_ONone(U_12128)
        | hBOOL(hAPP(hAPP(c_member(U_12122),U_12124),U_12126)) )
    & ! [U_12121,U_12123,U_12129,U_12125,U_12127] :
        ( hAPP(c_Map_Orestrict__map(U_12121,U_12127,U_12129,U_12125),U_12123) = hAPP(U_12129,U_12123)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12121),U_12123),U_12125)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3159_3]) ).

cnf(f_3159_5,plain,
    ( hAPP(c_Map_Orestrict__map(U_12121,U_12127,U_12129,U_12125),U_12123) = hAPP(U_12129,U_12123)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12121),U_12123),U_12125)) ),
    inference(clausify,[status(thm)],[f_3159_4]) ).

cnf(f_3159_6,plain,
    ( hAPP(c_Map_Orestrict__map(U_12122,U_12128,U_12130,U_12126),U_12124) = c_Option_Ooption_ONone(U_12128)
    | hBOOL(hAPP(hAPP(c_member(U_12122),U_12124),U_12126)) ),
    inference(clausify,[status(thm)],[f_3159_4]) ).

fof(f_3160_1,plain,
    ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__to__empty]) ).

fof(f_3160_2,plain,
    ! [U_12134,U_12133,U_12132,U_12131] : hAPP(c_Map_Orestrict__map(U_12131,U_12132,U_12133,c_Orderings_Obot__class_Obot(tc_fun(U_12131,tc_HOL_Obool))),U_12134) = c_Option_Ooption_ONone(U_12132),
    inference(variable_rename,[status(thm)],[f_3160_1]) ).

fof(f_3160_3,plain,
    ! [U_12132,U_12131,U_12133,U_12134] : hAPP(c_Map_Orestrict__map(U_12131,U_12132,U_12133,c_Orderings_Obot__class_Obot(tc_fun(U_12131,tc_HOL_Obool))),U_12134) = c_Option_Ooption_ONone(U_12132),
    inference(definitional_conversion,[status(esa)],[f_3160_2]) ).

cnf(f_3160_4,plain,
    hAPP(c_Map_Orestrict__map(U_12131,U_12132,U_12133,c_Orderings_Obot__class_Obot(tc_fun(U_12131,tc_HOL_Obool))),U_12134) = c_Option_Ooption_ONone(U_12132),
    inference(clausify,[status(thm)],[f_3160_3]) ).

fof(f_3161_1,plain,
    ! [V_A_2,V_y_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2)
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__constant]) ).

fof(f_3161_2,plain,
    ! [U_12138,U_12137,U_12136,U_12135] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12136,U_12135),hAPP(c_COMBK(U_12135,U_12136),U_12137)),U_12138) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12135),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12135),hAPP(c_Finite__Set_Ocard(U_12136),U_12138))),U_12137)
      | ~ class_Rings_Osemiring__1(U_12135) ),
    inference(variable_rename,[status(thm)],[f_3161_1]) ).

fof(f_3161_3,plain,
    ! [U_12135,U_12136,U_12137,U_12138] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12136,U_12135),hAPP(c_COMBK(U_12135,U_12136),U_12137)),U_12138) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12135),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12135),hAPP(c_Finite__Set_Ocard(U_12136),U_12138))),U_12137)
      | ~ class_Rings_Osemiring__1(U_12135) ),
    inference(definitional_conversion,[status(esa)],[f_3161_2]) ).

cnf(f_3161_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12136,U_12135),hAPP(c_COMBK(U_12135,U_12136),U_12137)),U_12138) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12135),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12135),hAPP(c_Finite__Set_Ocard(U_12136),U_12138))),U_12137)
    | ~ class_Rings_Osemiring__1(U_12135) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

fof(f_3162_1,plain,
    ! [V_n_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc]) ).

fof(f_3162_2,plain,
    ! [U_12141,U_12140,U_12139] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12139),U_12140),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12141))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12139),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12139),U_12140),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12141))),hAPP(U_12140,U_12141))
      | ~ class_Groups_Ocomm__monoid__add(U_12139) ),
    inference(variable_rename,[status(thm)],[f_3162_1]) ).

fof(f_3162_3,plain,
    ! [U_12139,U_12140,U_12141] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12139),U_12140),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12141))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12139),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12139),U_12140),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12141))),hAPP(U_12140,U_12141))
      | ~ class_Groups_Ocomm__monoid__add(U_12139) ),
    inference(definitional_conversion,[status(esa)],[f_3162_2]) ).

cnf(f_3162_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12139),U_12140),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12141))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12139),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12139),U_12140),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12141))),hAPP(U_12140,U_12141))
    | ~ class_Groups_Ocomm__monoid__add(U_12139) ),
    inference(clausify,[status(thm)],[f_3162_3]) ).

fof(f_3163_1,plain,
    ! [V_n_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc]) ).

fof(f_3163_2,plain,
    ! [U_12144,U_12143,U_12142] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12142),U_12143),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12144))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12142),U_12143),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12144))),hAPP(U_12143,hAPP(c_Nat_OSuc,U_12144)))
      | ~ class_Groups_Ocomm__monoid__add(U_12142) ),
    inference(variable_rename,[status(thm)],[f_3163_1]) ).

fof(f_3163_3,plain,
    ! [U_12142,U_12143,U_12144] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12142),U_12143),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12144))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12142),U_12143),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12144))),hAPP(U_12143,hAPP(c_Nat_OSuc,U_12144)))
      | ~ class_Groups_Ocomm__monoid__add(U_12142) ),
    inference(definitional_conversion,[status(esa)],[f_3163_2]) ).

cnf(f_3163_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12142),U_12143),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12144))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12142),U_12143),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12144))),hAPP(U_12143,hAPP(c_Nat_OSuc,U_12144)))
    | ~ class_Groups_Ocomm__monoid__add(U_12142) ),
    inference(clausify,[status(thm)],[f_3163_3]) ).

fof(f_3164_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert]) ).

fof(f_3164_2,plain,
    ! [U_12149,U_12148,U_12147,U_12146,U_12145] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12146,U_12145),U_12149),hAPP(hAPP(c_Set_Oinsert(U_12146),U_12148),U_12147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12145),hAPP(U_12149,U_12148)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12146,U_12145),U_12149),U_12147))
      | hBOOL(hAPP(hAPP(c_member(U_12146),U_12148),U_12147))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12146),U_12147))
      | ~ class_Groups_Ocomm__monoid__add(U_12145) ),
    inference(variable_rename,[status(thm)],[f_3164_1]) ).

fof(f_3164_3,plain,
    ! [U_12145,U_12146,U_12147,U_12148,U_12149] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12146,U_12145),U_12149),hAPP(hAPP(c_Set_Oinsert(U_12146),U_12148),U_12147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12145),hAPP(U_12149,U_12148)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12146,U_12145),U_12149),U_12147))
      | hBOOL(hAPP(hAPP(c_member(U_12146),U_12148),U_12147))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12146),U_12147))
      | ~ class_Groups_Ocomm__monoid__add(U_12145) ),
    inference(definitional_conversion,[status(esa)],[f_3164_2]) ).

cnf(f_3164_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12146,U_12145),U_12149),hAPP(hAPP(c_Set_Oinsert(U_12146),U_12148),U_12147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12145),hAPP(U_12149,U_12148)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12146,U_12145),U_12149),U_12147))
    | hBOOL(hAPP(hAPP(c_member(U_12146),U_12148),U_12147))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12146),U_12147))
    | ~ class_Groups_Ocomm__monoid__add(U_12145) ),
    inference(clausify,[status(thm)],[f_3164_3]) ).

fof(f_3165_1,plain,
    ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__insert]) ).

fof(f_3165_2,plain,
    ! [U_12154,U_12153,U_12152,U_12151,U_12150] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12151,U_12150),U_12154),hAPP(hAPP(c_Set_Oinsert(U_12151),U_12153),U_12152)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12150),hAPP(U_12154,U_12153)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12151,U_12150),U_12154),U_12152))
      | hBOOL(hAPP(hAPP(c_member(U_12151),U_12153),U_12152))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12151),U_12152))
      | ~ class_Groups_Ocomm__monoid__add(U_12150) ),
    inference(variable_rename,[status(thm)],[f_3165_1]) ).

fof(f_3165_3,plain,
    ! [U_12150,U_12151,U_12152,U_12153,U_12154] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12151,U_12150),U_12154),hAPP(hAPP(c_Set_Oinsert(U_12151),U_12153),U_12152)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12150),hAPP(U_12154,U_12153)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12151,U_12150),U_12154),U_12152))
      | hBOOL(hAPP(hAPP(c_member(U_12151),U_12153),U_12152))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12151),U_12152))
      | ~ class_Groups_Ocomm__monoid__add(U_12150) ),
    inference(definitional_conversion,[status(esa)],[f_3165_2]) ).

cnf(f_3165_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12151,U_12150),U_12154),hAPP(hAPP(c_Set_Oinsert(U_12151),U_12153),U_12152)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12150),hAPP(U_12154,U_12153)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12151,U_12150),U_12154),U_12152))
    | hBOOL(hAPP(hAPP(c_member(U_12151),U_12153),U_12152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12151),U_12152))
    | ~ class_Groups_Ocomm__monoid__add(U_12150) ),
    inference(clausify,[status(thm)],[f_3165_3]) ).

fof(f_3166_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int]) ).

fof(f_3166_2,plain,
    ! [U_12159,U_12158,U_12157,U_12156,U_12155] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12155),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12156,tc_HOL_Obool)),U_12157),U_12158))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12156,tc_HOL_Obool)),U_12157),U_12158))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12155),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),U_12157)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),U_12158))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12156),U_12158))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12156),U_12157))
      | ~ class_Groups_Ocomm__monoid__add(U_12155) ),
    inference(variable_rename,[status(thm)],[f_3166_1]) ).

fof(f_3166_3,plain,
    ! [U_12155,U_12156,U_12157,U_12158,U_12159] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12155),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12156,tc_HOL_Obool)),U_12157),U_12158))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12156,tc_HOL_Obool)),U_12157),U_12158))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12155),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),U_12157)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),U_12158))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12156),U_12158))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12156),U_12157))
      | ~ class_Groups_Ocomm__monoid__add(U_12155) ),
    inference(definitional_conversion,[status(esa)],[f_3166_2]) ).

cnf(f_3166_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12155),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12156,tc_HOL_Obool)),U_12157),U_12158))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12156,tc_HOL_Obool)),U_12157),U_12158))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12155),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),U_12157)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12156,U_12155),U_12159),U_12158))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12156),U_12158))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12156),U_12157))
    | ~ class_Groups_Ocomm__monoid__add(U_12155) ),
    inference(clausify,[status(thm)],[f_3166_3]) ).

fof(f_3167_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff]) ).

fof(f_3167_2,plain,
    ! [U_12164,U_12163,U_12162,U_12161,U_12160] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12161,tc_HOL_Obool)),U_12162),U_12163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12160),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),U_12162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),U_12163))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12161,tc_HOL_Obool)),U_12163),U_12162))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12161),U_12162))
      | ~ class_Groups_Oab__group__add(U_12160) ),
    inference(variable_rename,[status(thm)],[f_3167_1]) ).

fof(f_3167_3,plain,
    ! [U_12160,U_12161,U_12162,U_12163,U_12164] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12161,tc_HOL_Obool)),U_12162),U_12163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12160),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),U_12162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),U_12163))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12161,tc_HOL_Obool)),U_12163),U_12162))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12161),U_12162))
      | ~ class_Groups_Oab__group__add(U_12160) ),
    inference(definitional_conversion,[status(esa)],[f_3167_2]) ).

cnf(f_3167_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12161,tc_HOL_Obool)),U_12162),U_12163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12160),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),U_12162)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12161,U_12160),U_12164),U_12163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12161,tc_HOL_Obool)),U_12163),U_12162))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12161),U_12162))
    | ~ class_Groups_Oab__group__add(U_12160) ),
    inference(clausify,[status(thm)],[f_3167_3]) ).

fof(f_3168_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold]) ).

fof(f_3168_2,plain,
    ! [U_12168,U_12167,U_12166,U_12165] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12166,U_12165),U_12168),U_12167) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12165,U_12166,c_Groups_Oplus__class_Oplus(U_12165)),U_12168),c_Groups_Ozero__class_Ozero(U_12165)),U_12167)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12166),U_12167))
      | ~ class_Groups_Ocomm__monoid__add(U_12165) ),
    inference(variable_rename,[status(thm)],[f_3168_1]) ).

fof(f_3168_3,plain,
    ! [U_12165,U_12166,U_12167,U_12168] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12166,U_12165),U_12168),U_12167) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12165,U_12166,c_Groups_Oplus__class_Oplus(U_12165)),U_12168),c_Groups_Ozero__class_Ozero(U_12165)),U_12167)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12166),U_12167))
      | ~ class_Groups_Ocomm__monoid__add(U_12165) ),
    inference(definitional_conversion,[status(esa)],[f_3168_2]) ).

cnf(f_3168_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12166,U_12165),U_12168),U_12167) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12165,U_12166,c_Groups_Oplus__class_Oplus(U_12165)),U_12168),c_Groups_Ozero__class_Ozero(U_12165)),U_12167)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12166),U_12167))
    | ~ class_Groups_Ocomm__monoid__add(U_12165) ),
    inference(clausify,[status(thm)],[f_3168_3]) ).

fof(f_3169_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_OF__eq]) ).

fof(f_3169_2,plain,
    ! [U_12172,U_12171,U_12170,U_12169] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12170,U_12169),U_12172),U_12171) = c_Groups_Ozero__class_Ozero(U_12169)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12170),U_12171)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12170,U_12169),U_12172),U_12171) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12169,U_12170,c_Groups_Oplus__class_Oplus(U_12169)),U_12172),c_Groups_Ozero__class_Ozero(U_12169)),U_12171)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12170),U_12171)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12169) ),
    inference(variable_rename,[status(thm)],[f_3169_1]) ).

fof(f_3169_3,plain,
    ( ! [U_12169,U_12170,U_12171,U_12172] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12170,U_12169),U_12172),U_12171) = c_Groups_Ozero__class_Ozero(U_12169)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12170),U_12171))
        | ~ sP904(U_12169,U_12170,U_12171,U_12172) )
    & ! [U_12169,U_12170,U_12171,U_12172] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12170,U_12169),U_12172),U_12171) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12169,U_12170,c_Groups_Oplus__class_Oplus(U_12169)),U_12172),c_Groups_Ozero__class_Ozero(U_12169)),U_12171)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12170),U_12171))
        | ~ sP904(U_12169,U_12170,U_12171,U_12172) )
    & ! [U_12169,U_12170,U_12171,U_12172] :
        ( sP904(U_12169,U_12170,U_12171,U_12172)
        | ~ class_Groups_Ocomm__monoid__add(U_12169) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP904])],[f_3169_2]) ).

cnf(f_3169_4,plain,
    ( sP904(U_12169,U_12170,U_12171,U_12172)
    | ~ class_Groups_Ocomm__monoid__add(U_12169) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

cnf(f_3169_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12170,U_12169),U_12172),U_12171) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12169,U_12170,c_Groups_Oplus__class_Oplus(U_12169)),U_12172),c_Groups_Ozero__class_Ozero(U_12169)),U_12171)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12170),U_12171))
    | ~ sP904(U_12169,U_12170,U_12171,U_12172) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

cnf(f_3169_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12170,U_12169),U_12172),U_12171) = c_Groups_Ozero__class_Ozero(U_12169)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12170),U_12171))
    | ~ sP904(U_12169,U_12170,U_12171,U_12172) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

fof(f_3170_1,plain,
    ! [V_k_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
      | hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt]) ).

fof(f_3170_2,plain,
    ! [U_12175,U_12174,U_12173] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12173),U_12174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12175)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12173),U_12174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12175))
      | hAPP(U_12174,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12173)
      | ~ class_Groups_Ocomm__monoid__add(U_12173) ),
    inference(variable_rename,[status(thm)],[f_3170_1]) ).

fof(f_3170_3,plain,
    ! [U_12174,U_12175,U_12173] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12173),U_12174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12175)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12173),U_12174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12175))
      | hAPP(U_12174,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12173)
      | ~ class_Groups_Ocomm__monoid__add(U_12173) ),
    inference(definitional_conversion,[status(esa)],[f_3170_2]) ).

cnf(f_3170_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12173),U_12174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12175)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12173),U_12174),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12175))
    | hAPP(U_12174,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12173)
    | ~ class_Groups_Ocomm__monoid__add(U_12173) ),
    inference(clausify,[status(thm)],[f_3170_3]) ).

fof(f_3171_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc]) ).

fof(f_3171_2,plain,
    ! [U_12179,U_12178,U_12177,U_12176] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12176),U_12179),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12177),U_12178)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12176),hAPP(U_12179,U_12177)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12176),U_12179),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12177)),U_12178)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12177),U_12178))
      | ~ class_Groups_Ocomm__monoid__add(U_12176) ),
    inference(variable_rename,[status(thm)],[f_3171_1]) ).

fof(f_3171_3,plain,
    ! [U_12177,U_12176,U_12178,U_12179] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12176),U_12179),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12177),U_12178)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12176),hAPP(U_12179,U_12177)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12176),U_12179),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12177)),U_12178)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12177),U_12178))
      | ~ class_Groups_Ocomm__monoid__add(U_12176) ),
    inference(definitional_conversion,[status(esa)],[f_3171_2]) ).

cnf(f_3171_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12176),U_12179),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12177),U_12178)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12176),hAPP(U_12179,U_12177)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12176),U_12179),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12177)),U_12178)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12177),U_12178))
    | ~ class_Groups_Ocomm__monoid__add(U_12176) ),
    inference(clausify,[status(thm)],[f_3171_3]) ).

fof(f_3172_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc]) ).

fof(f_3172_2,plain,
    ! [U_12183,U_12182,U_12181,U_12180] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12180),U_12183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12181,U_12182)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12180),hAPP(U_12183,U_12181)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12180),U_12183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12181),U_12182)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12181),U_12182))
      | ~ class_Groups_Ocomm__monoid__add(U_12180) ),
    inference(variable_rename,[status(thm)],[f_3172_1]) ).

fof(f_3172_3,plain,
    ! [U_12181,U_12180,U_12182,U_12183] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12180),U_12183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12181,U_12182)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12180),hAPP(U_12183,U_12181)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12180),U_12183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12181),U_12182)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12181),U_12182))
      | ~ class_Groups_Ocomm__monoid__add(U_12180) ),
    inference(definitional_conversion,[status(esa)],[f_3172_2]) ).

cnf(f_3172_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12180),U_12183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12181,U_12182)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12180),hAPP(U_12183,U_12181)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12180),U_12183),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12181),U_12182)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12181),U_12182))
    | ~ class_Groups_Ocomm__monoid__add(U_12180) ),
    inference(clausify,[status(thm)],[f_3172_3]) ).

fof(f_3173_1,plain,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set]) ).

fof(f_3173_2,plain,
    ! [U_12188,U_12187,U_12186,U_12185,U_12184] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12185,U_12184),U_12187),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12185,tc_HOL_Obool)),U_12186),U_12188)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12185,U_12184),hAPP(hAPP(c_COMBC(U_12185,U_12184,U_12184),hAPP(hAPP(c_COMBS(U_12185,U_12184,tc_fun(U_12184,U_12184)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12184,tc_fun(U_12184,U_12184)),U_12185),c_If(U_12184)),hAPP(hAPP(c_COMBC(U_12185,tc_fun(U_12185,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12185)),U_12188))),U_12187)),c_Groups_Ozero__class_Ozero(U_12184))),U_12186)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12185),U_12186))
      | ~ class_Groups_Ocomm__monoid__add(U_12184) ),
    inference(variable_rename,[status(thm)],[f_3173_1]) ).

fof(f_3173_3,plain,
    ! [U_12184,U_12185,U_12186,U_12187,U_12188] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12185,U_12184),U_12187),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12185,tc_HOL_Obool)),U_12186),U_12188)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12185,U_12184),hAPP(hAPP(c_COMBC(U_12185,U_12184,U_12184),hAPP(hAPP(c_COMBS(U_12185,U_12184,tc_fun(U_12184,U_12184)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12184,tc_fun(U_12184,U_12184)),U_12185),c_If(U_12184)),hAPP(hAPP(c_COMBC(U_12185,tc_fun(U_12185,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12185)),U_12188))),U_12187)),c_Groups_Ozero__class_Ozero(U_12184))),U_12186)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12185),U_12186))
      | ~ class_Groups_Ocomm__monoid__add(U_12184) ),
    inference(definitional_conversion,[status(esa)],[f_3173_2]) ).

cnf(f_3173_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12185,U_12184),U_12187),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12185,tc_HOL_Obool)),U_12186),U_12188)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12185,U_12184),hAPP(hAPP(c_COMBC(U_12185,U_12184,U_12184),hAPP(hAPP(c_COMBS(U_12185,U_12184,tc_fun(U_12184,U_12184)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12184,tc_fun(U_12184,U_12184)),U_12185),c_If(U_12184)),hAPP(hAPP(c_COMBC(U_12185,tc_fun(U_12185,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12185)),U_12188))),U_12187)),c_Groups_Ozero__class_Ozero(U_12184))),U_12186)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12185),U_12186))
    | ~ class_Groups_Ocomm__monoid__add(U_12184) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

fof(f_3174_1,plain,
    ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)))
      | hAPP(V_m_2,V_a_2) != hAPP(c_Option_Ooption_OSome(T_b),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_ranI]) ).

fof(f_3174_2,plain,
    ! [U_12193,U_12192,U_12191,U_12190,U_12189] :
      ( hBOOL(hAPP(hAPP(c_member(U_12191),U_12192),c_Map_Oran(U_12193,U_12191,U_12189)))
      | hAPP(U_12189,U_12190) != hAPP(c_Option_Ooption_OSome(U_12191),U_12192) ),
    inference(variable_rename,[status(thm)],[f_3174_1]) ).

fof(f_3174_3,plain,
    ! [U_12191,U_12190,U_12189,U_12192,U_12193] :
      ( hBOOL(hAPP(hAPP(c_member(U_12191),U_12192),c_Map_Oran(U_12193,U_12191,U_12189)))
      | hAPP(U_12189,U_12190) != hAPP(c_Option_Ooption_OSome(U_12191),U_12192) ),
    inference(definitional_conversion,[status(esa)],[f_3174_2]) ).

cnf(f_3174_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12191),U_12192),c_Map_Oran(U_12193,U_12191,U_12189)))
    | hAPP(U_12189,U_12190) != hAPP(c_Option_Ooption_OSome(U_12191),U_12192) ),
    inference(clausify,[status(thm)],[f_3174_3]) ).

fof(f_3175_1,plain,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove]) ).

fof(f_3175_2,plain,
    ! [U_12198,U_12197,U_12196,U_12195,U_12194] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12197),hAPP(hAPP(c_Set_Oinsert(U_12195),U_12198),U_12196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12194),hAPP(U_12197,U_12198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12196),hAPP(hAPP(c_Set_Oinsert(U_12195),U_12198),c_Orderings_Obot__class_Obot(tc_fun(U_12195,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12195),U_12196))
      | ~ class_Groups_Ocomm__monoid__add(U_12194) ),
    inference(variable_rename,[status(thm)],[f_3175_1]) ).

fof(f_3175_3,plain,
    ! [U_12194,U_12195,U_12196,U_12197,U_12198] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12197),hAPP(hAPP(c_Set_Oinsert(U_12195),U_12198),U_12196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12194),hAPP(U_12197,U_12198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12196),hAPP(hAPP(c_Set_Oinsert(U_12195),U_12198),c_Orderings_Obot__class_Obot(tc_fun(U_12195,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12195),U_12196))
      | ~ class_Groups_Ocomm__monoid__add(U_12194) ),
    inference(definitional_conversion,[status(esa)],[f_3175_2]) ).

cnf(f_3175_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12197),hAPP(hAPP(c_Set_Oinsert(U_12195),U_12198),U_12196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12194),hAPP(U_12197,U_12198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12196),hAPP(hAPP(c_Set_Oinsert(U_12195),U_12198),c_Orderings_Obot__class_Obot(tc_fun(U_12195,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12195),U_12196))
    | ~ class_Groups_Ocomm__monoid__add(U_12194) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

fof(f_3176_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint]) ).

fof(f_3176_2,plain,
    ! [U_12203,U_12202,U_12201,U_12200,U_12199] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12200,tc_HOL_Obool)),U_12201),U_12202)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12199),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),U_12201)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),U_12202))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12200,tc_HOL_Obool)),U_12201),U_12202) != c_Orderings_Obot__class_Obot(tc_fun(U_12200,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12200),U_12202))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12200),U_12201))
      | ~ class_Groups_Ocomm__monoid__add(U_12199) ),
    inference(variable_rename,[status(thm)],[f_3176_1]) ).

fof(f_3176_3,plain,
    ! [U_12199,U_12200,U_12201,U_12202,U_12203] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12200,tc_HOL_Obool)),U_12201),U_12202)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12199),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),U_12201)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),U_12202))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12200,tc_HOL_Obool)),U_12201),U_12202) != c_Orderings_Obot__class_Obot(tc_fun(U_12200,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12200),U_12202))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12200),U_12201))
      | ~ class_Groups_Ocomm__monoid__add(U_12199) ),
    inference(definitional_conversion,[status(esa)],[f_3176_2]) ).

cnf(f_3176_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12200,tc_HOL_Obool)),U_12201),U_12202)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12199),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),U_12201)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12200,U_12199),U_12203),U_12202))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12200,tc_HOL_Obool)),U_12201),U_12202) != c_Orderings_Obot__class_Obot(tc_fun(U_12200,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12200),U_12202))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12200),U_12201))
    | ~ class_Groups_Ocomm__monoid__add(U_12199) ),
    inference(clausify,[status(thm)],[f_3176_3]) ).

fof(f_3177_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un]) ).

fof(f_3177_2,plain,
    ! [U_12208,U_12207,U_12206,U_12205,U_12204] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12205,tc_HOL_Obool)),U_12206),U_12207)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12204),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),U_12206)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),U_12207))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12205,tc_HOL_Obool)),U_12206),U_12207)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12205),U_12207))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12205),U_12206))
      | ~ class_Groups_Oab__group__add(U_12204) ),
    inference(variable_rename,[status(thm)],[f_3177_1]) ).

fof(f_3177_3,plain,
    ! [U_12205,U_12204,U_12206,U_12207,U_12208] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12205,tc_HOL_Obool)),U_12206),U_12207)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12204),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),U_12206)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),U_12207))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12205,tc_HOL_Obool)),U_12206),U_12207)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12205),U_12207))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12205),U_12206))
      | ~ class_Groups_Oab__group__add(U_12204) ),
    inference(definitional_conversion,[status(esa)],[f_3177_2]) ).

cnf(f_3177_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12205,tc_HOL_Obool)),U_12206),U_12207)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12204),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),U_12206)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),U_12207))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12205,U_12204),U_12208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12205,tc_HOL_Obool)),U_12206),U_12207)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12205),U_12207))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12205),U_12206))
    | ~ class_Groups_Oab__group__add(U_12204) ),
    inference(clausify,[status(thm)],[f_3177_3]) ).

fof(f_3178_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(f_3178_2,plain,
    ! [U_12212,U_12211,U_12210,U_12209] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),hAPP(c_Nat_OSuc,U_12210))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),U_12210))),hAPP(U_12212,U_12210))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12210),U_12211)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),hAPP(c_Nat_OSuc,U_12210))) = c_Groups_Ozero__class_Ozero(U_12209)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12210),U_12211)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12209) ),
    inference(variable_rename,[status(thm)],[f_3178_1]) ).

fof(f_3178_3,plain,
    ( ! [U_12209,U_12210,U_12211,U_12212] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),hAPP(c_Nat_OSuc,U_12210))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),U_12210))),hAPP(U_12212,U_12210))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12210),U_12211))
        | ~ sP905(U_12209,U_12210,U_12211,U_12212) )
    & ! [U_12209,U_12210,U_12211,U_12212] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),hAPP(c_Nat_OSuc,U_12210))) = c_Groups_Ozero__class_Ozero(U_12209)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12210),U_12211))
        | ~ sP905(U_12209,U_12210,U_12211,U_12212) )
    & ! [U_12209,U_12210,U_12211,U_12212] :
        ( sP905(U_12209,U_12210,U_12211,U_12212)
        | ~ class_Groups_Ocomm__monoid__add(U_12209) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP905])],[f_3178_2]) ).

cnf(f_3178_4,plain,
    ( sP905(U_12209,U_12210,U_12211,U_12212)
    | ~ class_Groups_Ocomm__monoid__add(U_12209) ),
    inference(clausify,[status(thm)],[f_3178_3]) ).

cnf(f_3178_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),hAPP(c_Nat_OSuc,U_12210))) = c_Groups_Ozero__class_Ozero(U_12209)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12210),U_12211))
    | ~ sP905(U_12209,U_12210,U_12211,U_12212) ),
    inference(clausify,[status(thm)],[f_3178_3]) ).

cnf(f_3178_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),hAPP(c_Nat_OSuc,U_12210))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12209),U_12212),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12211),U_12210))),hAPP(U_12212,U_12210))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12210),U_12211))
    | ~ sP905(U_12209,U_12210,U_12211,U_12212) ),
    inference(clausify,[status(thm)],[f_3178_3]) ).

fof(f_3179_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(f_3179_2,plain,
    ! [U_12216,U_12215,U_12214,U_12213] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,hAPP(c_Nat_OSuc,U_12214))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,U_12214))),hAPP(U_12216,hAPP(c_Nat_OSuc,U_12214)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12214)),U_12215)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,hAPP(c_Nat_OSuc,U_12214))) = c_Groups_Ozero__class_Ozero(U_12213)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12214)),U_12215)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12213) ),
    inference(variable_rename,[status(thm)],[f_3179_1]) ).

fof(f_3179_3,plain,
    ( ! [U_12216,U_12215,U_12213,U_12214] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,hAPP(c_Nat_OSuc,U_12214))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,U_12214))),hAPP(U_12216,hAPP(c_Nat_OSuc,U_12214)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12214)),U_12215))
        | ~ sP906(U_12216,U_12215,U_12213,U_12214) )
    & ! [U_12216,U_12215,U_12213,U_12214] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,hAPP(c_Nat_OSuc,U_12214))) = c_Groups_Ozero__class_Ozero(U_12213)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12214)),U_12215))
        | ~ sP906(U_12216,U_12215,U_12213,U_12214) )
    & ! [U_12216,U_12215,U_12213,U_12214] :
        ( sP906(U_12216,U_12215,U_12213,U_12214)
        | ~ class_Groups_Ocomm__monoid__add(U_12213) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP906])],[f_3179_2]) ).

cnf(f_3179_4,plain,
    ( sP906(U_12216,U_12215,U_12213,U_12214)
    | ~ class_Groups_Ocomm__monoid__add(U_12213) ),
    inference(clausify,[status(thm)],[f_3179_3]) ).

cnf(f_3179_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,hAPP(c_Nat_OSuc,U_12214))) = c_Groups_Ozero__class_Ozero(U_12213)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12214)),U_12215))
    | ~ sP906(U_12216,U_12215,U_12213,U_12214) ),
    inference(clausify,[status(thm)],[f_3179_3]) ).

cnf(f_3179_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,hAPP(c_Nat_OSuc,U_12214))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12213),U_12216),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12215,U_12214))),hAPP(U_12216,hAPP(c_Nat_OSuc,U_12214)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12214)),U_12215))
    | ~ sP906(U_12216,U_12215,U_12213,U_12214) ),
    inference(clausify,[status(thm)],[f_3179_3]) ).

fof(f_3180_1,plain,
    ! [V_P_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).

fof(f_3180_2,plain,
    ! [U_12220,U_12219,U_12218,U_12217] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12217),U_12220),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12218,U_12219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12217),hAPP(U_12220,U_12218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12217),U_12220),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12218,U_12219)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12218),U_12219))
      | ~ class_Groups_Ocomm__monoid__add(U_12217) ),
    inference(variable_rename,[status(thm)],[f_3180_1]) ).

fof(f_3180_3,plain,
    ! [U_12218,U_12219,U_12217,U_12220] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12217),U_12220),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12218,U_12219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12217),hAPP(U_12220,U_12218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12217),U_12220),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12218,U_12219)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12218),U_12219))
      | ~ class_Groups_Ocomm__monoid__add(U_12217) ),
    inference(definitional_conversion,[status(esa)],[f_3180_2]) ).

cnf(f_3180_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12217),U_12220),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12218,U_12219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12217),hAPP(U_12220,U_12218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12217),U_12220),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12218,U_12219)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12218),U_12219))
    | ~ class_Groups_Ocomm__monoid__add(U_12217) ),
    inference(clausify,[status(thm)],[f_3180_3]) ).

fof(f_3181_1,plain,
    ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat]) ).

fof(f_3181_2,plain,
    ! [U_12225,U_12224,U_12223,U_12222,U_12221] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12222,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),U_12225))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12222,U_12223))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),U_12225))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_12221) ),
    inference(variable_rename,[status(thm)],[f_3181_1]) ).

fof(f_3181_3,plain,
    ! [U_12222,U_12221,U_12223,U_12224,U_12225] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12222,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),U_12225))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12222,U_12223))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),U_12225))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_12221) ),
    inference(definitional_conversion,[status(esa)],[f_3181_2]) ).

cnf(f_3181_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12222,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),U_12225))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12222,U_12223))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12221),U_12224),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),U_12225))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12223),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_Groups_Ocomm__monoid__add(U_12221) ),
    inference(clausify,[status(thm)],[f_3181_3]) ).

fof(f_3182_1,plain,
    ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict]) ).

fof(f_3182_2,plain,
    ! [U_12231,U_12230,U_12229,U_12228,U_12227,U_12226] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12226,tc_Option_Ooption(U_12227)),c_Map_Orestrict__map(U_12226,U_12227,U_12228,U_12229)),U_12230),U_12231) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12226,tc_Option_Ooption(U_12227)),c_Map_Orestrict__map(U_12226,U_12227,U_12228,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12226,tc_HOL_Obool)),U_12229),hAPP(hAPP(c_Set_Oinsert(U_12226),U_12230),c_Orderings_Obot__class_Obot(tc_fun(U_12226,tc_HOL_Obool)))))),U_12230),U_12231),
    inference(variable_rename,[status(thm)],[f_3182_1]) ).

fof(f_3182_3,plain,
    ! [U_12227,U_12226,U_12228,U_12229,U_12230,U_12231] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12226,tc_Option_Ooption(U_12227)),c_Map_Orestrict__map(U_12226,U_12227,U_12228,U_12229)),U_12230),U_12231) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12226,tc_Option_Ooption(U_12227)),c_Map_Orestrict__map(U_12226,U_12227,U_12228,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12226,tc_HOL_Obool)),U_12229),hAPP(hAPP(c_Set_Oinsert(U_12226),U_12230),c_Orderings_Obot__class_Obot(tc_fun(U_12226,tc_HOL_Obool)))))),U_12230),U_12231),
    inference(definitional_conversion,[status(esa)],[f_3182_2]) ).

cnf(f_3182_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12226,tc_Option_Ooption(U_12227)),c_Map_Orestrict__map(U_12226,U_12227,U_12228,U_12229)),U_12230),U_12231) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12226,tc_Option_Ooption(U_12227)),c_Map_Orestrict__map(U_12226,U_12227,U_12228,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12226,tc_HOL_Obool)),U_12229),hAPP(hAPP(c_Set_Oinsert(U_12226),U_12230),c_Orderings_Obot__class_Obot(tc_fun(U_12226,tc_HOL_Obool)))))),U_12230),U_12231),
    inference(clausify,[status(thm)],[f_3182_3]) ).

fof(f_3183_1,plain,
    ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_ran__empty]) ).

fof(f_3183_2,plain,
    ! [U_12233,U_12232] : c_Map_Oran(U_12232,U_12233,hAPP(c_COMBK(tc_Option_Ooption(U_12233),U_12232),c_Option_Ooption_ONone(U_12233))) = c_Orderings_Obot__class_Obot(tc_fun(U_12233,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3183_1]) ).

fof(f_3183_3,plain,
    ! [U_12233,U_12232] : c_Map_Oran(U_12232,U_12233,hAPP(c_COMBK(tc_Option_Ooption(U_12233),U_12232),c_Option_Ooption_ONone(U_12233))) = c_Orderings_Obot__class_Obot(tc_fun(U_12233,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3183_2]) ).

cnf(f_3183_4,plain,
    c_Map_Oran(U_12232,U_12233,hAPP(c_COMBK(tc_Option_Ooption(U_12233),U_12232),c_Option_Ooption_ONone(U_12233))) = c_Orderings_Obot__class_Obot(tc_fun(U_12233,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3183_3]) ).

fof(f_3184_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H]) ).

fof(f_3184_2,plain,
    ! [U_12238,U_12237,U_12236,U_12235,U_12234] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12238),U_12236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12234),hAPP(U_12238,U_12237)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12235,tc_HOL_Obool)),U_12236),hAPP(hAPP(c_Set_Oinsert(U_12235),U_12237),c_Orderings_Obot__class_Obot(tc_fun(U_12235,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12235),U_12237),U_12236))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12235),U_12236))
      | ~ class_Groups_Ocomm__monoid__add(U_12234) ),
    inference(variable_rename,[status(thm)],[f_3184_1]) ).

fof(f_3184_3,plain,
    ! [U_12234,U_12235,U_12236,U_12237,U_12238] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12238),U_12236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12234),hAPP(U_12238,U_12237)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12235,tc_HOL_Obool)),U_12236),hAPP(hAPP(c_Set_Oinsert(U_12235),U_12237),c_Orderings_Obot__class_Obot(tc_fun(U_12235,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12235),U_12237),U_12236))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12235),U_12236))
      | ~ class_Groups_Ocomm__monoid__add(U_12234) ),
    inference(definitional_conversion,[status(esa)],[f_3184_2]) ).

cnf(f_3184_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12238),U_12236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12234),hAPP(U_12238,U_12237)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12235,tc_HOL_Obool)),U_12236),hAPP(hAPP(c_Set_Oinsert(U_12235),U_12237),c_Orderings_Obot__class_Obot(tc_fun(U_12235,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12235),U_12237),U_12236))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12235),U_12236))
    | ~ class_Groups_Ocomm__monoid__add(U_12234) ),
    inference(clausify,[status(thm)],[f_3184_3]) ).

fof(f_3185_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oremove]) ).

fof(f_3185_2,plain,
    ! [U_12243,U_12242,U_12241,U_12240,U_12239] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12240,U_12239),U_12243),U_12241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12239),hAPP(U_12243,U_12242)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12240,U_12239),U_12243),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12240,tc_HOL_Obool)),U_12241),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12242),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12240),U_12242),U_12241))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12240),U_12241))
      | ~ class_Groups_Ocomm__monoid__add(U_12239) ),
    inference(variable_rename,[status(thm)],[f_3185_1]) ).

fof(f_3185_3,plain,
    ! [U_12239,U_12240,U_12241,U_12242,U_12243] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12240,U_12239),U_12243),U_12241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12239),hAPP(U_12243,U_12242)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12240,U_12239),U_12243),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12240,tc_HOL_Obool)),U_12241),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12242),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12240),U_12242),U_12241))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12240),U_12241))
      | ~ class_Groups_Ocomm__monoid__add(U_12239) ),
    inference(definitional_conversion,[status(esa)],[f_3185_2]) ).

cnf(f_3185_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12240,U_12239),U_12243),U_12241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12239),hAPP(U_12243,U_12242)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12240,U_12239),U_12243),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12240,tc_HOL_Obool)),U_12241),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12242),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12240),U_12242),U_12241))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12240),U_12241))
    | ~ class_Groups_Ocomm__monoid__add(U_12239) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

fof(f_3186_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Oring(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring]) ).

fof(f_3186_2,plain,
    ! [U_12248,U_12247,U_12246,U_12245,U_12244] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12245,U_12244),U_12248),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12245,tc_HOL_Obool)),U_12246),hAPP(hAPP(c_Set_Oinsert(U_12245),U_12247),c_Orderings_Obot__class_Obot(tc_fun(U_12245,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12244),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12245,U_12244),U_12248),U_12246)),hAPP(U_12248,U_12247))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12245),U_12247),U_12246))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12245),U_12246))
      | ~ class_Rings_Oring(U_12244) ),
    inference(variable_rename,[status(thm)],[f_3186_1]) ).

fof(f_3186_3,plain,
    ! [U_12245,U_12244,U_12246,U_12247,U_12248] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12245,U_12244),U_12248),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12245,tc_HOL_Obool)),U_12246),hAPP(hAPP(c_Set_Oinsert(U_12245),U_12247),c_Orderings_Obot__class_Obot(tc_fun(U_12245,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12244),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12245,U_12244),U_12248),U_12246)),hAPP(U_12248,U_12247))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12245),U_12247),U_12246))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12245),U_12246))
      | ~ class_Rings_Oring(U_12244) ),
    inference(definitional_conversion,[status(esa)],[f_3186_2]) ).

cnf(f_3186_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12245,U_12244),U_12248),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12245,tc_HOL_Obool)),U_12246),hAPP(hAPP(c_Set_Oinsert(U_12245),U_12247),c_Orderings_Obot__class_Obot(tc_fun(U_12245,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12244),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12245,U_12244),U_12248),U_12246)),hAPP(U_12248,U_12247))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12245),U_12247),U_12246))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12245),U_12246))
    | ~ class_Rings_Oring(U_12244) ),
    inference(clausify,[status(thm)],[f_3186_3]) ).

fof(f_3187_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1]) ).

fof(f_3187_2,plain,
    ! [U_12253,U_12252,U_12251,U_12250,U_12249] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12250,tc_HOL_Obool)),U_12251),hAPP(hAPP(c_Set_Oinsert(U_12250),U_12252),c_Orderings_Obot__class_Obot(tc_fun(U_12250,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),U_12251)
          | hBOOL(hAPP(hAPP(c_member(U_12250),U_12252),U_12251)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12250,tc_HOL_Obool)),U_12251),hAPP(hAPP(c_Set_Oinsert(U_12250),U_12252),c_Orderings_Obot__class_Obot(tc_fun(U_12250,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12249),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),U_12251)),hAPP(U_12253,U_12252))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12250),U_12252),U_12251)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12250),U_12251))
      | ~ class_Groups_Oab__group__add(U_12249) ),
    inference(variable_rename,[status(thm)],[f_3187_1]) ).

fof(f_3187_3,plain,
    ( ! [U_12250,U_12249,U_12251,U_12252,U_12253] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12250,tc_HOL_Obool)),U_12251),hAPP(hAPP(c_Set_Oinsert(U_12250),U_12252),c_Orderings_Obot__class_Obot(tc_fun(U_12250,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),U_12251)
        | hBOOL(hAPP(hAPP(c_member(U_12250),U_12252),U_12251))
        | ~ sP907(U_12250,U_12249,U_12251,U_12252,U_12253) )
    & ! [U_12250,U_12249,U_12251,U_12252,U_12253] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12250,tc_HOL_Obool)),U_12251),hAPP(hAPP(c_Set_Oinsert(U_12250),U_12252),c_Orderings_Obot__class_Obot(tc_fun(U_12250,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12249),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),U_12251)),hAPP(U_12253,U_12252))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12250),U_12252),U_12251))
        | ~ sP907(U_12250,U_12249,U_12251,U_12252,U_12253) )
    & ! [U_12250,U_12249,U_12251,U_12252,U_12253] :
        ( sP907(U_12250,U_12249,U_12251,U_12252,U_12253)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12250),U_12251))
        | ~ class_Groups_Oab__group__add(U_12249) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP907])],[f_3187_2]) ).

cnf(f_3187_4,plain,
    ( sP907(U_12250,U_12249,U_12251,U_12252,U_12253)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12250),U_12251))
    | ~ class_Groups_Oab__group__add(U_12249) ),
    inference(clausify,[status(thm)],[f_3187_3]) ).

cnf(f_3187_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12250,tc_HOL_Obool)),U_12251),hAPP(hAPP(c_Set_Oinsert(U_12250),U_12252),c_Orderings_Obot__class_Obot(tc_fun(U_12250,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12249),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),U_12251)),hAPP(U_12253,U_12252))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12250),U_12252),U_12251))
    | ~ sP907(U_12250,U_12249,U_12251,U_12252,U_12253) ),
    inference(clausify,[status(thm)],[f_3187_3]) ).

cnf(f_3187_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12250,tc_HOL_Obool)),U_12251),hAPP(hAPP(c_Set_Oinsert(U_12250),U_12252),c_Orderings_Obot__class_Obot(tc_fun(U_12250,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12250,U_12249),U_12253),U_12251)
    | hBOOL(hAPP(hAPP(c_member(U_12250),U_12252),U_12251))
    | ~ sP907(U_12250,U_12249,U_12251,U_12252,U_12253) ),
    inference(clausify,[status(thm)],[f_3187_3]) ).

fof(f_3188_1,plain,
    ! [V_n_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b)))
      | V_x_2 = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_geometric__sum]) ).

fof(f_3188_2,plain,
    ! [U_12256,U_12255,U_12254] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12254),hAPP(c_Power_Opower__class_Opower(U_12254),U_12255)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12256)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12254),hAPP(hAPP(c_Power_Opower__class_Opower(U_12254),U_12255),U_12256)),c_Groups_Oone__class_Oone(U_12254))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12254),U_12255),c_Groups_Oone__class_Oone(U_12254)))
      | U_12255 = c_Groups_Oone__class_Oone(U_12254)
      | ~ class_Fields_Ofield(U_12254) ),
    inference(variable_rename,[status(thm)],[f_3188_1]) ).

fof(f_3188_3,plain,
    ! [U_12255,U_12256,U_12254] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12254),hAPP(c_Power_Opower__class_Opower(U_12254),U_12255)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12256)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12254),hAPP(hAPP(c_Power_Opower__class_Opower(U_12254),U_12255),U_12256)),c_Groups_Oone__class_Oone(U_12254))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12254),U_12255),c_Groups_Oone__class_Oone(U_12254)))
      | U_12255 = c_Groups_Oone__class_Oone(U_12254)
      | ~ class_Fields_Ofield(U_12254) ),
    inference(definitional_conversion,[status(esa)],[f_3188_2]) ).

cnf(f_3188_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12254),hAPP(c_Power_Opower__class_Opower(U_12254),U_12255)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12256)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12254),hAPP(hAPP(c_Power_Opower__class_Opower(U_12254),U_12255),U_12256)),c_Groups_Oone__class_Oone(U_12254))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12254),U_12255),c_Groups_Oone__class_Oone(U_12254)))
    | U_12255 = c_Groups_Oone__class_Oone(U_12254)
    | ~ class_Fields_Ofield(U_12254) ),
    inference(clausify,[status(thm)],[f_3188_3]) ).

fof(f_3189_1,plain,
    ! [V_n_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b)))
      | ~ class_Rings_Ocomm__semiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_gauss__sum]) ).

fof(f_3189_2,plain,
    ! [U_12258,U_12257] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12257),c_Groups_Oone__class_Oone(U_12257)),c_Groups_Oone__class_Oone(U_12257))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12257),c_Nat_Osemiring__1__class_Oof__nat(U_12257)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12258))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12257),U_12258)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12257),U_12258)),c_Groups_Oone__class_Oone(U_12257)))
      | ~ class_Rings_Ocomm__semiring__1(U_12257) ),
    inference(variable_rename,[status(thm)],[f_3189_1]) ).

fof(f_3189_3,plain,
    ! [U_12257,U_12258] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12257),c_Groups_Oone__class_Oone(U_12257)),c_Groups_Oone__class_Oone(U_12257))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12257),c_Nat_Osemiring__1__class_Oof__nat(U_12257)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12258))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12257),U_12258)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12257),U_12258)),c_Groups_Oone__class_Oone(U_12257)))
      | ~ class_Rings_Ocomm__semiring__1(U_12257) ),
    inference(definitional_conversion,[status(esa)],[f_3189_2]) ).

cnf(f_3189_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12257),c_Groups_Oone__class_Oone(U_12257)),c_Groups_Oone__class_Oone(U_12257))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12257),c_Nat_Osemiring__1__class_Oof__nat(U_12257)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12258))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12257),U_12258)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12257),U_12258)),c_Groups_Oone__class_Oone(U_12257)))
    | ~ class_Rings_Ocomm__semiring__1(U_12257) ),
    inference(clausify,[status(thm)],[f_3189_3]) ).

fof(f_3190_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(f_3190_2,plain,
    ! [U_12262,U_12261,U_12260,U_12259] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12259),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12259,U_12259),hAPP(hAPP(c_COMBB(U_12259,tc_fun(U_12259,U_12259),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12259)),U_12262)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12259,tc_Nat_Onat),U_12262),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12260,U_12261)) = c_Groups_Ozero__class_Ozero(U_12259)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12260),U_12261)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12259),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12259,U_12259),hAPP(hAPP(c_COMBB(U_12259,tc_fun(U_12259,U_12259),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12259)),U_12262)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12259,tc_Nat_Onat),U_12262),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12260,U_12261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12259),hAPP(U_12262,U_12260)),hAPP(U_12262,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12261),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12260),U_12261)) ) )
      | ~ class_Groups_Oab__group__add(U_12259) ),
    inference(variable_rename,[status(thm)],[f_3190_1]) ).

fof(f_3190_3,plain,
    ( ! [U_12259,U_12260,U_12261,U_12262] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12259),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12259,U_12259),hAPP(hAPP(c_COMBB(U_12259,tc_fun(U_12259,U_12259),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12259)),U_12262)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12259,tc_Nat_Onat),U_12262),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12260,U_12261)) = c_Groups_Ozero__class_Ozero(U_12259)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12260),U_12261))
        | ~ sP908(U_12259,U_12260,U_12261,U_12262) )
    & ! [U_12259,U_12260,U_12261,U_12262] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12259),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12259,U_12259),hAPP(hAPP(c_COMBB(U_12259,tc_fun(U_12259,U_12259),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12259)),U_12262)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12259,tc_Nat_Onat),U_12262),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12260,U_12261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12259),hAPP(U_12262,U_12260)),hAPP(U_12262,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12261),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12260),U_12261))
        | ~ sP908(U_12259,U_12260,U_12261,U_12262) )
    & ! [U_12259,U_12260,U_12261,U_12262] :
        ( sP908(U_12259,U_12260,U_12261,U_12262)
        | ~ class_Groups_Oab__group__add(U_12259) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP908])],[f_3190_2]) ).

cnf(f_3190_4,plain,
    ( sP908(U_12259,U_12260,U_12261,U_12262)
    | ~ class_Groups_Oab__group__add(U_12259) ),
    inference(clausify,[status(thm)],[f_3190_3]) ).

cnf(f_3190_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12259),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12259,U_12259),hAPP(hAPP(c_COMBB(U_12259,tc_fun(U_12259,U_12259),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12259)),U_12262)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12259,tc_Nat_Onat),U_12262),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12260,U_12261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12259),hAPP(U_12262,U_12260)),hAPP(U_12262,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12261),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12260),U_12261))
    | ~ sP908(U_12259,U_12260,U_12261,U_12262) ),
    inference(clausify,[status(thm)],[f_3190_3]) ).

cnf(f_3190_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12259),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12259,U_12259),hAPP(hAPP(c_COMBB(U_12259,tc_fun(U_12259,U_12259),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12259)),U_12262)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12259,tc_Nat_Onat),U_12262),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12260,U_12261)) = c_Groups_Ozero__class_Ozero(U_12259)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12260),U_12261))
    | ~ sP908(U_12259,U_12260,U_12261,U_12262) ),
    inference(clausify,[status(thm)],[f_3190_3]) ).

fof(f_3191_1,plain,
    ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict__conv]) ).

fof(f_3191_2,plain,
    ! [U_12268,U_12267,U_12266,U_12265,U_12264,U_12263] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12263,tc_Option_Ooption(U_12266)),c_Map_Orestrict__map(U_12263,U_12266,U_12267,U_12265)),U_12264),U_12268) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12263,tc_Option_Ooption(U_12266)),c_Map_Orestrict__map(U_12263,U_12266,U_12267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12263,tc_HOL_Obool)),U_12265),hAPP(hAPP(c_Set_Oinsert(U_12263),U_12264),c_Orderings_Obot__class_Obot(tc_fun(U_12263,tc_HOL_Obool)))))),U_12264),U_12268)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12263),U_12264),U_12265)) ),
    inference(variable_rename,[status(thm)],[f_3191_1]) ).

fof(f_3191_3,plain,
    ! [U_12264,U_12265,U_12263,U_12266,U_12267,U_12268] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12263,tc_Option_Ooption(U_12266)),c_Map_Orestrict__map(U_12263,U_12266,U_12267,U_12265)),U_12264),U_12268) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12263,tc_Option_Ooption(U_12266)),c_Map_Orestrict__map(U_12263,U_12266,U_12267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12263,tc_HOL_Obool)),U_12265),hAPP(hAPP(c_Set_Oinsert(U_12263),U_12264),c_Orderings_Obot__class_Obot(tc_fun(U_12263,tc_HOL_Obool)))))),U_12264),U_12268)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12263),U_12264),U_12265)) ),
    inference(definitional_conversion,[status(esa)],[f_3191_2]) ).

cnf(f_3191_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12263,tc_Option_Ooption(U_12266)),c_Map_Orestrict__map(U_12263,U_12266,U_12267,U_12265)),U_12264),U_12268) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12263,tc_Option_Ooption(U_12266)),c_Map_Orestrict__map(U_12263,U_12266,U_12267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12263,tc_HOL_Obool)),U_12265),hAPP(hAPP(c_Set_Oinsert(U_12263),U_12264),c_Orderings_Obot__class_Obot(tc_fun(U_12263,tc_HOL_Obool)))))),U_12264),U_12268)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12263),U_12264),U_12265)) ),
    inference(clausify,[status(thm)],[f_3191_3]) ).

fof(f_3192_1,plain,
    ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
      ( ( c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) )
      & ( c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__fun__upd]) ).

fof(f_3192_2,plain,
    ! [U_12274,U_12273,U_12272,U_12271,U_12270,U_12269] :
      ( ( c_Map_Orestrict__map(U_12269,U_12272,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12269,tc_Option_Ooption(U_12272)),U_12273),U_12270),U_12274),U_12271) = c_Map_Orestrict__map(U_12269,U_12272,U_12273,U_12271)
        | hBOOL(hAPP(hAPP(c_member(U_12269),U_12270),U_12271)) )
      & ( c_Map_Orestrict__map(U_12269,U_12272,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12269,tc_Option_Ooption(U_12272)),U_12273),U_12270),U_12274),U_12271) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12269,tc_Option_Ooption(U_12272)),c_Map_Orestrict__map(U_12269,U_12272,U_12273,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12269,tc_HOL_Obool)),U_12271),hAPP(hAPP(c_Set_Oinsert(U_12269),U_12270),c_Orderings_Obot__class_Obot(tc_fun(U_12269,tc_HOL_Obool)))))),U_12270),U_12274)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12269),U_12270),U_12271)) ) ),
    inference(variable_rename,[status(thm)],[f_3192_1]) ).

fof(f_3192_3,plain,
    ( ! [U_12286,U_12284,U_12282,U_12280,U_12278,U_12276] :
        ( c_Map_Orestrict__map(U_12276,U_12282,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12276,tc_Option_Ooption(U_12282)),U_12284),U_12278),U_12286),U_12280) = c_Map_Orestrict__map(U_12276,U_12282,U_12284,U_12280)
        | hBOOL(hAPP(hAPP(c_member(U_12276),U_12278),U_12280)) )
    & ! [U_12285,U_12283,U_12281,U_12279,U_12277,U_12275] :
        ( c_Map_Orestrict__map(U_12275,U_12281,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12275,tc_Option_Ooption(U_12281)),U_12283),U_12277),U_12285),U_12279) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12275,tc_Option_Ooption(U_12281)),c_Map_Orestrict__map(U_12275,U_12281,U_12283,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12275,tc_HOL_Obool)),U_12279),hAPP(hAPP(c_Set_Oinsert(U_12275),U_12277),c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool)))))),U_12277),U_12285)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12275),U_12277),U_12279)) ) ),
    inference(miniscope,[status(thm)],[f_3192_2]) ).

fof(f_3192_4,plain,
    ( ! [U_12276,U_12278,U_12286,U_12280,U_12282,U_12284] :
        ( c_Map_Orestrict__map(U_12276,U_12282,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12276,tc_Option_Ooption(U_12282)),U_12284),U_12278),U_12286),U_12280) = c_Map_Orestrict__map(U_12276,U_12282,U_12284,U_12280)
        | hBOOL(hAPP(hAPP(c_member(U_12276),U_12278),U_12280)) )
    & ! [U_12275,U_12277,U_12279,U_12281,U_12283,U_12285] :
        ( c_Map_Orestrict__map(U_12275,U_12281,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12275,tc_Option_Ooption(U_12281)),U_12283),U_12277),U_12285),U_12279) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12275,tc_Option_Ooption(U_12281)),c_Map_Orestrict__map(U_12275,U_12281,U_12283,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12275,tc_HOL_Obool)),U_12279),hAPP(hAPP(c_Set_Oinsert(U_12275),U_12277),c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool)))))),U_12277),U_12285)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12275),U_12277),U_12279)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3192_3]) ).

cnf(f_3192_5,plain,
    ( c_Map_Orestrict__map(U_12275,U_12281,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12275,tc_Option_Ooption(U_12281)),U_12283),U_12277),U_12285),U_12279) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12275,tc_Option_Ooption(U_12281)),c_Map_Orestrict__map(U_12275,U_12281,U_12283,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12275,tc_HOL_Obool)),U_12279),hAPP(hAPP(c_Set_Oinsert(U_12275),U_12277),c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool)))))),U_12277),U_12285)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12275),U_12277),U_12279)) ),
    inference(clausify,[status(thm)],[f_3192_4]) ).

cnf(f_3192_6,plain,
    ( c_Map_Orestrict__map(U_12276,U_12282,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12276,tc_Option_Ooption(U_12282)),U_12284),U_12278),U_12286),U_12280) = c_Map_Orestrict__map(U_12276,U_12282,U_12284,U_12280)
    | hBOOL(hAPP(hAPP(c_member(U_12276),U_12278),U_12280)) ),
    inference(clausify,[status(thm)],[f_3192_4]) ).

fof(f_3193_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)),
    inference(fof_nnf,[status(thm)],[fact_restrict__complement__singleton__eq]) ).

fof(f_3193_2,plain,
    ! [U_12290,U_12289,U_12288,U_12287] : c_Map_Orestrict__map(U_12287,U_12288,U_12289,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12287,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12287,tc_Option_Ooption(U_12288)),U_12289),U_12290),c_Option_Ooption_ONone(U_12288)),
    inference(variable_rename,[status(thm)],[f_3193_1]) ).

fof(f_3193_3,plain,
    ! [U_12288,U_12287,U_12289,U_12290] : c_Map_Orestrict__map(U_12287,U_12288,U_12289,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12287,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12287,tc_Option_Ooption(U_12288)),U_12289),U_12290),c_Option_Ooption_ONone(U_12288)),
    inference(definitional_conversion,[status(esa)],[f_3193_2]) ).

cnf(f_3193_4,plain,
    c_Map_Orestrict__map(U_12287,U_12288,U_12289,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12287,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12287,tc_Option_Ooption(U_12288)),U_12289),U_12290),c_Option_Ooption_ONone(U_12288)),
    inference(clausify,[status(thm)],[f_3193_3]) ).

fof(f_3194_1,plain,
    ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_restrict__upd__same]) ).

fof(f_3194_2,plain,
    ! [U_12295,U_12294,U_12293,U_12292,U_12291] : c_Map_Orestrict__map(U_12291,U_12292,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12291,tc_Option_Ooption(U_12292)),U_12293),U_12294),hAPP(c_Option_Ooption_OSome(U_12292),U_12295)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12291,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12291),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_12291,U_12292,U_12293,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12291,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12291),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3194_1]) ).

fof(f_3194_3,plain,
    ! [U_12292,U_12291,U_12293,U_12294,U_12295] : c_Map_Orestrict__map(U_12291,U_12292,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12291,tc_Option_Ooption(U_12292)),U_12293),U_12294),hAPP(c_Option_Ooption_OSome(U_12292),U_12295)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12291,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12291),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_12291,U_12292,U_12293,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12291,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12291),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3194_2]) ).

cnf(f_3194_4,plain,
    c_Map_Orestrict__map(U_12291,U_12292,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12291,tc_Option_Ooption(U_12292)),U_12293),U_12294),hAPP(c_Option_Ooption_OSome(U_12292),U_12295)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12291,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12291),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_12291,U_12292,U_12293,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12291,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12291),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3194_3]) ).

fof(f_3195_1,plain,
    ! [V_n_2,V_d_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2))))
      | ~ class_Rings_Ocomm__semiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_arith__series__general]) ).

fof(f_3195_2,plain,
    ! [U_12299,U_12298,U_12297,U_12296] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),c_Groups_Oone__class_Oone(U_12296)),c_Groups_Oone__class_Oone(U_12296))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12296),hAPP(hAPP(c_COMBB(U_12296,U_12296,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12296,U_12296),hAPP(hAPP(c_COMBB(U_12296,tc_fun(U_12296,U_12296),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12296)),c_Nat_Osemiring__1__class_Oof__nat(U_12296))),U_12298))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12296),U_12299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12299),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12298))))
      | ~ class_Rings_Ocomm__semiring__1(U_12296) ),
    inference(variable_rename,[status(thm)],[f_3195_1]) ).

fof(f_3195_3,plain,
    ! [U_12296,U_12297,U_12298,U_12299] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),c_Groups_Oone__class_Oone(U_12296)),c_Groups_Oone__class_Oone(U_12296))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12296),hAPP(hAPP(c_COMBB(U_12296,U_12296,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12296,U_12296),hAPP(hAPP(c_COMBB(U_12296,tc_fun(U_12296,U_12296),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12296)),c_Nat_Osemiring__1__class_Oof__nat(U_12296))),U_12298))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12296),U_12299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12299),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12298))))
      | ~ class_Rings_Ocomm__semiring__1(U_12296) ),
    inference(definitional_conversion,[status(esa)],[f_3195_2]) ).

cnf(f_3195_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),c_Groups_Oone__class_Oone(U_12296)),c_Groups_Oone__class_Oone(U_12296))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12296),hAPP(hAPP(c_COMBB(U_12296,U_12296,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12296,U_12296),hAPP(hAPP(c_COMBB(U_12296,tc_fun(U_12296,U_12296),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12296)),c_Nat_Osemiring__1__class_Oof__nat(U_12296))),U_12298))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12296),U_12299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12296),U_12297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12299),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12298))))
    | ~ class_Rings_Ocomm__semiring__1(U_12296) ),
    inference(clausify,[status(thm)],[f_3195_3]) ).

fof(f_3196_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))
      | ? [B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ class_Groups_Oordered__comm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono2]) ).

fof(f_3196_2,plain,
    ! [U_12305,U_12304,U_12303,U_12302,U_12301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12304)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12303)))
      | ? [U_12300] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),c_Groups_Ozero__class_Ozero(U_12301)),hAPP(U_12305,U_12300)))
          & hBOOL(hAPP(hAPP(c_member(U_12302),U_12300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12302,tc_HOL_Obool)),U_12303),U_12304))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12302,tc_HOL_Obool)),U_12304),U_12303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12302),U_12303))
      | ~ class_Groups_Oordered__comm__monoid__add(U_12301) ),
    inference(variable_rename,[status(thm)],[f_3196_1]) ).

fof(f_3196_3,plain,
    ! [U_12305,U_12304,U_12303,U_12302,U_12301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12304)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12303)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),c_Groups_Ozero__class_Ozero(U_12301)),hAPP(U_12305,sK251(U_12305,U_12304,U_12303,U_12302,U_12301))))
        & hBOOL(hAPP(hAPP(c_member(U_12302),sK251(U_12305,U_12304,U_12303,U_12302,U_12301)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12302,tc_HOL_Obool)),U_12303),U_12304))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12302,tc_HOL_Obool)),U_12304),U_12303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12302),U_12303))
      | ~ class_Groups_Oordered__comm__monoid__add(U_12301) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_12300,sK251(U_12305,U_12304,U_12303,U_12302,U_12301))],[f_3196_2]) ).

fof(f_3196_4,plain,
    ( ! [U_12301,U_12302,U_12303,U_12304,U_12305] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),c_Groups_Ozero__class_Ozero(U_12301)),hAPP(U_12305,sK251(U_12305,U_12304,U_12303,U_12302,U_12301))))
        | ~ sP909(U_12301,U_12302,U_12303,U_12304,U_12305) )
    & ! [U_12301,U_12302,U_12303,U_12304,U_12305] :
        ( hBOOL(hAPP(hAPP(c_member(U_12302),sK251(U_12305,U_12304,U_12303,U_12302,U_12301)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12302,tc_HOL_Obool)),U_12303),U_12304)))
        | ~ sP909(U_12301,U_12302,U_12303,U_12304,U_12305) )
    & ! [U_12301,U_12302,U_12303,U_12304,U_12305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12304)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12303)))
        | sP909(U_12301,U_12302,U_12303,U_12304,U_12305)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12302,tc_HOL_Obool)),U_12304),U_12303))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12302),U_12303))
        | ~ class_Groups_Oordered__comm__monoid__add(U_12301) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP909])],[f_3196_3]) ).

cnf(f_3196_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12304)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12302,U_12301),U_12305),U_12303)))
    | sP909(U_12301,U_12302,U_12303,U_12304,U_12305)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12302,tc_HOL_Obool)),U_12304),U_12303))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12302),U_12303))
    | ~ class_Groups_Oordered__comm__monoid__add(U_12301) ),
    inference(clausify,[status(thm)],[f_3196_4]) ).

cnf(f_3196_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12302),sK251(U_12305,U_12304,U_12303,U_12302,U_12301)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12302,tc_HOL_Obool)),U_12303),U_12304)))
    | ~ sP909(U_12301,U_12302,U_12303,U_12304,U_12305) ),
    inference(clausify,[status(thm)],[f_3196_4]) ).

cnf(f_3196_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12301),c_Groups_Ozero__class_Ozero(U_12301)),hAPP(U_12305,sK251(U_12305,U_12304,U_12303,U_12302,U_12301))))
    | ~ sP909(U_12301,U_12302,U_12303,U_12304,U_12305) ),
    inference(clausify,[status(thm)],[f_3196_4]) ).

fof(f_3197_1,plain,
    ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) )
      | ~ class_Rings_Osemiring__1(T_c)
      | ~ class_Groups_Oordered__ab__semigroup__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__bounded]) ).

fof(f_3197_2,plain,
    ! [U_12311,U_12310,U_12309,U_12308,U_12307] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12308,U_12307),U_12310),U_12309)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12307),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12307),hAPP(c_Finite__Set_Ocard(U_12308),U_12309))),U_12311)))
      | ? [U_12306] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(U_12310,U_12306)),U_12311))
          & hBOOL(hAPP(hAPP(c_member(U_12308),U_12306),U_12309)) )
      | ~ class_Rings_Osemiring__1(U_12307)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12307) ),
    inference(variable_rename,[status(thm)],[f_3197_1]) ).

fof(f_3197_3,plain,
    ! [U_12311,U_12310,U_12309,U_12308,U_12307] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12308,U_12307),U_12310),U_12309)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12307),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12307),hAPP(c_Finite__Set_Ocard(U_12308),U_12309))),U_12311)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(U_12310,sK252(U_12311,U_12310,U_12309,U_12308,U_12307))),U_12311))
        & hBOOL(hAPP(hAPP(c_member(U_12308),sK252(U_12311,U_12310,U_12309,U_12308,U_12307)),U_12309)) )
      | ~ class_Rings_Osemiring__1(U_12307)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12307) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_12306,sK252(U_12311,U_12310,U_12309,U_12308,U_12307))],[f_3197_2]) ).

fof(f_3197_4,plain,
    ( ! [U_12308,U_12309,U_12307,U_12310,U_12311] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(U_12310,sK252(U_12311,U_12310,U_12309,U_12308,U_12307))),U_12311))
        | ~ sP910(U_12308,U_12309,U_12307,U_12310,U_12311) )
    & ! [U_12308,U_12309,U_12307,U_12310,U_12311] :
        ( hBOOL(hAPP(hAPP(c_member(U_12308),sK252(U_12311,U_12310,U_12309,U_12308,U_12307)),U_12309))
        | ~ sP910(U_12308,U_12309,U_12307,U_12310,U_12311) )
    & ! [U_12308,U_12309,U_12307,U_12310,U_12311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12308,U_12307),U_12310),U_12309)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12307),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12307),hAPP(c_Finite__Set_Ocard(U_12308),U_12309))),U_12311)))
        | sP910(U_12308,U_12309,U_12307,U_12310,U_12311)
        | ~ class_Rings_Osemiring__1(U_12307)
        | ~ class_Groups_Oordered__ab__semigroup__add(U_12307) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP910])],[f_3197_3]) ).

cnf(f_3197_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12308,U_12307),U_12310),U_12309)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12307),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12307),hAPP(c_Finite__Set_Ocard(U_12308),U_12309))),U_12311)))
    | sP910(U_12308,U_12309,U_12307,U_12310,U_12311)
    | ~ class_Rings_Osemiring__1(U_12307)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_12307) ),
    inference(clausify,[status(thm)],[f_3197_4]) ).

cnf(f_3197_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12308),sK252(U_12311,U_12310,U_12309,U_12308,U_12307)),U_12309))
    | ~ sP910(U_12308,U_12309,U_12307,U_12310,U_12311) ),
    inference(clausify,[status(thm)],[f_3197_4]) ).

cnf(f_3197_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12307),hAPP(U_12310,sK252(U_12311,U_12310,U_12309,U_12308,U_12307))),U_12311))
    | ~ sP910(U_12308,U_12309,U_12307,U_12310,U_12311) ),
    inference(clausify,[status(thm)],[f_3197_4]) ).

fof(f_3198_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral]) ).

fof(f_3198_2,plain,
    ! [U_12317,U_12316,U_12315,U_12314,U_12313] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12313),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12315)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12316))
      | ? [U_12312] :
          ( hAPP(U_12317,U_12312) != c_Groups_Ozero__class_Ozero(U_12313)
          & hBOOL(hAPP(hAPP(c_member(U_12314),U_12312),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12316))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12315))
      | ~ class_Groups_Ocomm__monoid__add(U_12313) ),
    inference(variable_rename,[status(thm)],[f_3198_1]) ).

fof(f_3198_3,plain,
    ! [U_12317,U_12316,U_12315,U_12314,U_12313] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12313),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12315)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12316))
      | ( hAPP(U_12317,sK253(U_12317,U_12316,U_12315,U_12314,U_12313)) != c_Groups_Ozero__class_Ozero(U_12313)
        & hBOOL(hAPP(hAPP(c_member(U_12314),sK253(U_12317,U_12316,U_12315,U_12314,U_12313)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12316))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12315))
      | ~ class_Groups_Ocomm__monoid__add(U_12313) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_12312,sK253(U_12317,U_12316,U_12315,U_12314,U_12313))],[f_3198_2]) ).

fof(f_3198_4,plain,
    ( ! [U_12313,U_12314,U_12315,U_12316,U_12317] :
        ( hAPP(U_12317,sK253(U_12317,U_12316,U_12315,U_12314,U_12313)) != c_Groups_Ozero__class_Ozero(U_12313)
        | ~ sP911(U_12313,U_12314,U_12315,U_12316,U_12317) )
    & ! [U_12313,U_12314,U_12315,U_12316,U_12317] :
        ( hBOOL(hAPP(hAPP(c_member(U_12314),sK253(U_12317,U_12316,U_12315,U_12314,U_12313)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316)))
        | ~ sP911(U_12313,U_12314,U_12315,U_12316,U_12317) )
    & ! [U_12313,U_12314,U_12315,U_12316,U_12317] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12313),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12315)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12316))
        | sP911(U_12313,U_12314,U_12315,U_12316,U_12317)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12316))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12315))
        | ~ class_Groups_Ocomm__monoid__add(U_12313) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP911])],[f_3198_3]) ).

cnf(f_3198_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12313),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12315)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12314,U_12313),U_12317),U_12316))
    | sP911(U_12313,U_12314,U_12315,U_12316,U_12317)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12316))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12314),U_12315))
    | ~ class_Groups_Ocomm__monoid__add(U_12313) ),
    inference(clausify,[status(thm)],[f_3198_4]) ).

cnf(f_3198_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12314),sK253(U_12317,U_12316,U_12315,U_12314,U_12313)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12314,tc_HOL_Obool)),U_12315),U_12316)))
    | ~ sP911(U_12313,U_12314,U_12315,U_12316,U_12317) ),
    inference(clausify,[status(thm)],[f_3198_4]) ).

cnf(f_3198_7,plain,
    ( hAPP(U_12317,sK253(U_12317,U_12316,U_12315,U_12314,U_12313)) != c_Groups_Ozero__class_Ozero(U_12313)
    | ~ sP911(U_12313,U_12314,U_12315,U_12316,U_12317) ),
    inference(clausify,[status(thm)],[f_3198_4]) ).

fof(f_3199_1,plain,
    ! [V_f_2,V_F_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
        & ( ! [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff]) ).

fof(f_3199_2,plain,
    ! [U_12322,U_12321,U_12320] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [U_12319] :
              ( hAPP(U_12322,U_12319) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_12320),U_12319),U_12321)) ) )
        & ( ! [U_12318] :
              ( hAPP(U_12322,U_12318) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12318),U_12321)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(variable_rename,[status(thm)],[f_3199_1]) ).

fof(f_3199_3,plain,
    ! [U_12322,U_12321,U_12320] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( hAPP(U_12322,sK254(U_12322,U_12321,U_12320)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12320),sK254(U_12322,U_12321,U_12320)),U_12321)) ) )
        & ( ! [U_12318] :
              ( hAPP(U_12322,U_12318) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12318),U_12321)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_12319,sK254(U_12322,U_12321,U_12320))],[f_3199_2]) ).

fof(f_3199_4,plain,
    ( ! [U_12322,U_12321,U_12320] :
        ( hAPP(U_12322,sK254(U_12322,U_12321,U_12320)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP912(U_12322,U_12321,U_12320) )
    & ! [U_12322,U_12321,U_12320] :
        ( hBOOL(hAPP(hAPP(c_member(U_12320),sK254(U_12322,U_12321,U_12320)),U_12321))
        | ~ sP912(U_12322,U_12321,U_12320) )
    & ! [U_12322,U_12321,U_12320,U_12318] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP912(U_12322,U_12321,U_12320)
        | ~ sP913(U_12322,U_12321,U_12320,U_12318) )
    & ! [U_12322,U_12321,U_12320,U_12318] :
        ( hAPP(U_12322,U_12318) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12318),U_12321))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP913(U_12322,U_12321,U_12320,U_12318) )
    & ! [U_12322,U_12321,U_12320,U_12318] :
        ( sP913(U_12322,U_12321,U_12320,U_12318)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP912,sP913])],[f_3199_3]) ).

cnf(f_3199_5,plain,
    ( sP913(U_12322,U_12321,U_12320,U_12318)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(clausify,[status(thm)],[f_3199_4]) ).

cnf(f_3199_6,plain,
    ( hAPP(U_12322,U_12318) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12318),U_12321))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP913(U_12322,U_12321,U_12320,U_12318) ),
    inference(clausify,[status(thm)],[f_3199_4]) ).

cnf(f_3199_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP912(U_12322,U_12321,U_12320)
    | ~ sP913(U_12322,U_12321,U_12320,U_12318) ),
    inference(clausify,[status(thm)],[f_3199_4]) ).

cnf(f_3199_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12320),sK254(U_12322,U_12321,U_12320)),U_12321))
    | ~ sP912(U_12322,U_12321,U_12320) ),
    inference(clausify,[status(thm)],[f_3199_4]) ).

cnf(f_3199_9,plain,
    ( hAPP(U_12322,sK254(U_12322,U_12321,U_12320)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP912(U_12322,U_12321,U_12320) ),
    inference(clausify,[status(thm)],[f_3199_4]) ).

fof(f_3200_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_card__eq__setsum]) ).

fof(f_3200_2,plain,
    ! [U_12324,U_12323] : hAPP(c_Finite__Set_Ocard(U_12323),U_12324) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12323,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12323),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12324),
    inference(variable_rename,[status(thm)],[f_3200_1]) ).

fof(f_3200_3,plain,
    ! [U_12324,U_12323] : hAPP(c_Finite__Set_Ocard(U_12323),U_12324) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12323,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12323),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12324),
    inference(definitional_conversion,[status(esa)],[f_3200_2]) ).

cnf(f_3200_4,plain,
    hAPP(c_Finite__Set_Ocard(U_12323),U_12324) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12323,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12323),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12324),
    inference(clausify,[status(thm)],[f_3200_3]) ).

fof(f_3201_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_int__setsum]) ).

fof(f_3201_2,plain,
    ! [U_12327,U_12326,U_12325] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12325,tc_Nat_Onat),U_12326),U_12327)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12325,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12325),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12326)),U_12327),
    inference(variable_rename,[status(thm)],[f_3201_1]) ).

fof(f_3201_3,plain,
    ! [U_12325,U_12326,U_12327] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12325,tc_Nat_Onat),U_12326),U_12327)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12325,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12325),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12326)),U_12327),
    inference(definitional_conversion,[status(esa)],[f_3201_2]) ).

cnf(f_3201_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12325,tc_Nat_Onat),U_12326),U_12327)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12325,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12325),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12326)),U_12327),
    inference(clausify,[status(thm)],[f_3201_3]) ).

fof(f_3202_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [B_x] :
              ( ? [B_xa] :
                  ( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & B_x != B_xa
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              | hAPP(V_f_2,B_x) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( ! [B_xa] :
                  ( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | B_x = B_xa
                  | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff]) ).

fof(f_3202_2,plain,
    ! [U_12334,U_12333,U_12332] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12331] :
              ( ? [U_12330] :
                  ( hAPP(U_12334,U_12330) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12331 != U_12330
                  & hBOOL(hAPP(hAPP(c_member(U_12332),U_12330),U_12333)) )
              | hAPP(U_12334,U_12331) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12331),U_12333)) ) )
        & ( ? [U_12329] :
              ( ! [U_12328] :
                  ( hAPP(U_12334,U_12328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_12329 = U_12328
                  | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12328),U_12333)) )
              & hAPP(U_12334,U_12329) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(U_12332),U_12329),U_12333)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12332),U_12333)) ),
    inference(variable_rename,[status(thm)],[f_3202_1]) ).

fof(f_3202_3,plain,
    ! [U_12334,U_12333,U_12332] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12331] :
              ( ? [U_12330] :
                  ( hAPP(U_12334,U_12330) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12331 != U_12330
                  & hBOOL(hAPP(hAPP(c_member(U_12332),U_12330),U_12333)) )
              | hAPP(U_12334,U_12331) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12331),U_12333)) ) )
        & ( ( ! [U_12328] :
                ( hAPP(U_12334,U_12328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK255(U_12334,U_12333,U_12332) = U_12328
                | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12328),U_12333)) )
            & hAPP(U_12334,sK255(U_12334,U_12333,U_12332)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_12332),sK255(U_12334,U_12333,U_12332)),U_12333)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12332),U_12333)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_12329,sK255(U_12334,U_12333,U_12332))],[f_3202_2]) ).

fof(f_3202_4,plain,
    ! [U_12334,U_12333,U_12332] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12331] :
              ( ( hAPP(U_12334,sK256(U_12334,U_12333,U_12332,U_12331)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_12331 != sK256(U_12334,U_12333,U_12332,U_12331)
                & hBOOL(hAPP(hAPP(c_member(U_12332),sK256(U_12334,U_12333,U_12332,U_12331)),U_12333)) )
              | hAPP(U_12334,U_12331) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12331),U_12333)) ) )
        & ( ( ! [U_12328] :
                ( hAPP(U_12334,U_12328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK255(U_12334,U_12333,U_12332) = U_12328
                | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12328),U_12333)) )
            & hAPP(U_12334,sK255(U_12334,U_12333,U_12332)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_12332),sK255(U_12334,U_12333,U_12332)),U_12333)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12332),U_12333)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_12330,sK256(U_12334,U_12333,U_12332,U_12331))],[f_3202_3]) ).

fof(f_3202_5,plain,
    ( ! [U_12331,U_12332,U_12333,U_12334] :
        ( hAPP(U_12334,sK256(U_12334,U_12333,U_12332,U_12331)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP915(U_12331,U_12332,U_12333,U_12334) )
    & ! [U_12331,U_12332,U_12333,U_12334] :
        ( U_12331 != sK256(U_12334,U_12333,U_12332,U_12331)
        | ~ sP915(U_12331,U_12332,U_12333,U_12334) )
    & ! [U_12331,U_12332,U_12333,U_12334] :
        ( hBOOL(hAPP(hAPP(c_member(U_12332),sK256(U_12334,U_12333,U_12332,U_12331)),U_12333))
        | ~ sP915(U_12331,U_12332,U_12333,U_12334) )
    & ! [U_12328,U_12332,U_12333,U_12334] :
        ( hAPP(U_12334,U_12328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sK255(U_12334,U_12333,U_12332) = U_12328
        | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12328),U_12333))
        | ~ sP914(U_12328,U_12332,U_12333,U_12334) )
    & ! [U_12328,U_12332,U_12333,U_12334] :
        ( hAPP(U_12334,sK255(U_12334,U_12333,U_12332)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP914(U_12328,U_12332,U_12333,U_12334) )
    & ! [U_12328,U_12332,U_12333,U_12334] :
        ( hBOOL(hAPP(hAPP(c_member(U_12332),sK255(U_12334,U_12333,U_12332)),U_12333))
        | ~ sP914(U_12328,U_12332,U_12333,U_12334) )
    & ! [U_12328,U_12331,U_12332,U_12333,U_12334] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP915(U_12331,U_12332,U_12333,U_12334)
        | hAPP(U_12334,U_12331) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12331),U_12333))
        | ~ sP916(U_12328,U_12331,U_12332,U_12333,U_12334) )
    & ! [U_12328,U_12331,U_12332,U_12333,U_12334] :
        ( sP914(U_12328,U_12332,U_12333,U_12334)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP916(U_12328,U_12331,U_12332,U_12333,U_12334) )
    & ! [U_12328,U_12331,U_12332,U_12333,U_12334] :
        ( sP916(U_12328,U_12331,U_12332,U_12333,U_12334)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12332),U_12333)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP914,sP915,sP916])],[f_3202_4]) ).

cnf(f_3202_6,plain,
    ( sP916(U_12328,U_12331,U_12332,U_12333,U_12334)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12332),U_12333)) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_7,plain,
    ( sP914(U_12328,U_12332,U_12333,U_12334)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP916(U_12328,U_12331,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_8,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12332,tc_Nat_Onat),U_12334),U_12333) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP915(U_12331,U_12332,U_12333,U_12334)
    | hAPP(U_12334,U_12331) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12331),U_12333))
    | ~ sP916(U_12328,U_12331,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12332),sK255(U_12334,U_12333,U_12332)),U_12333))
    | ~ sP914(U_12328,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_10,plain,
    ( hAPP(U_12334,sK255(U_12334,U_12333,U_12332)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP914(U_12328,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_11,plain,
    ( hAPP(U_12334,U_12328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK255(U_12334,U_12333,U_12332) = U_12328
    | ~ hBOOL(hAPP(hAPP(c_member(U_12332),U_12328),U_12333))
    | ~ sP914(U_12328,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12332),sK256(U_12334,U_12333,U_12332,U_12331)),U_12333))
    | ~ sP915(U_12331,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_13,plain,
    ( U_12331 != sK256(U_12334,U_12333,U_12332,U_12331)
    | ~ sP915(U_12331,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

cnf(f_3202_14,plain,
    ( hAPP(U_12334,sK256(U_12334,U_12333,U_12332,U_12331)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP915(U_12331,U_12332,U_12333,U_12334) ),
    inference(clausify,[status(thm)],[f_3202_5]) ).

fof(f_3203_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [B_x] :
              ( ? [B_xa] :
                  ( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & B_x != B_xa
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              | hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( ! [B_xa] :
                  ( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | B_x = B_xa
                  | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff]) ).

fof(f_3203_2,plain,
    ! [U_12341,U_12340,U_12339] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12338] :
              ( ? [U_12337] :
                  ( hAPP(U_12341,U_12337) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12338 != U_12337
                  & hBOOL(hAPP(hAPP(c_member(U_12339),U_12337),U_12340)) )
              | hAPP(U_12341,U_12338) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12338),U_12340)) ) )
        & ( ? [U_12336] :
              ( ! [U_12335] :
                  ( hAPP(U_12341,U_12335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_12336 = U_12335
                  | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12335),U_12340)) )
              & hAPP(U_12341,U_12336) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_12339),U_12336),U_12340)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12339),U_12340)) ),
    inference(variable_rename,[status(thm)],[f_3203_1]) ).

fof(f_3203_3,plain,
    ! [U_12341,U_12340,U_12339] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12338] :
              ( ? [U_12337] :
                  ( hAPP(U_12341,U_12337) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12338 != U_12337
                  & hBOOL(hAPP(hAPP(c_member(U_12339),U_12337),U_12340)) )
              | hAPP(U_12341,U_12338) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12338),U_12340)) ) )
        & ( ( ! [U_12335] :
                ( hAPP(U_12341,U_12335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK257(U_12341,U_12340,U_12339) = U_12335
                | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12335),U_12340)) )
            & hAPP(U_12341,sK257(U_12341,U_12340,U_12339)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12339),sK257(U_12341,U_12340,U_12339)),U_12340)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12339),U_12340)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_12336,sK257(U_12341,U_12340,U_12339))],[f_3203_2]) ).

fof(f_3203_4,plain,
    ! [U_12341,U_12340,U_12339] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12338] :
              ( ( hAPP(U_12341,sK258(U_12341,U_12340,U_12339,U_12338)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_12338 != sK258(U_12341,U_12340,U_12339,U_12338)
                & hBOOL(hAPP(hAPP(c_member(U_12339),sK258(U_12341,U_12340,U_12339,U_12338)),U_12340)) )
              | hAPP(U_12341,U_12338) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12338),U_12340)) ) )
        & ( ( ! [U_12335] :
                ( hAPP(U_12341,U_12335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK257(U_12341,U_12340,U_12339) = U_12335
                | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12335),U_12340)) )
            & hAPP(U_12341,sK257(U_12341,U_12340,U_12339)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12339),sK257(U_12341,U_12340,U_12339)),U_12340)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12339),U_12340)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_12337,sK258(U_12341,U_12340,U_12339,U_12338))],[f_3203_3]) ).

fof(f_3203_5,plain,
    ( ! [U_12338,U_12341,U_12339,U_12340] :
        ( hAPP(U_12341,sK258(U_12341,U_12340,U_12339,U_12338)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP918(U_12338,U_12341,U_12339,U_12340) )
    & ! [U_12338,U_12341,U_12339,U_12340] :
        ( U_12338 != sK258(U_12341,U_12340,U_12339,U_12338)
        | ~ sP918(U_12338,U_12341,U_12339,U_12340) )
    & ! [U_12338,U_12341,U_12339,U_12340] :
        ( hBOOL(hAPP(hAPP(c_member(U_12339),sK258(U_12341,U_12340,U_12339,U_12338)),U_12340))
        | ~ sP918(U_12338,U_12341,U_12339,U_12340) )
    & ! [U_12341,U_12335,U_12339,U_12340] :
        ( hAPP(U_12341,U_12335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sK257(U_12341,U_12340,U_12339) = U_12335
        | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12335),U_12340))
        | ~ sP917(U_12341,U_12335,U_12339,U_12340) )
    & ! [U_12341,U_12335,U_12339,U_12340] :
        ( hAPP(U_12341,sK257(U_12341,U_12340,U_12339)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP917(U_12341,U_12335,U_12339,U_12340) )
    & ! [U_12341,U_12335,U_12339,U_12340] :
        ( hBOOL(hAPP(hAPP(c_member(U_12339),sK257(U_12341,U_12340,U_12339)),U_12340))
        | ~ sP917(U_12341,U_12335,U_12339,U_12340) )
    & ! [U_12338,U_12341,U_12335,U_12339,U_12340] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | sP918(U_12338,U_12341,U_12339,U_12340)
        | hAPP(U_12341,U_12338) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12338),U_12340))
        | ~ sP919(U_12338,U_12341,U_12335,U_12339,U_12340) )
    & ! [U_12338,U_12341,U_12335,U_12339,U_12340] :
        ( sP917(U_12341,U_12335,U_12339,U_12340)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP919(U_12338,U_12341,U_12335,U_12339,U_12340) )
    & ! [U_12338,U_12341,U_12335,U_12339,U_12340] :
        ( sP919(U_12338,U_12341,U_12335,U_12339,U_12340)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12339),U_12340)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP917,sP918,sP919])],[f_3203_4]) ).

cnf(f_3203_6,plain,
    ( sP919(U_12338,U_12341,U_12335,U_12339,U_12340)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12339),U_12340)) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_7,plain,
    ( sP917(U_12341,U_12335,U_12339,U_12340)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP919(U_12338,U_12341,U_12335,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_8,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12339,tc_Nat_Onat),U_12341),U_12340) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | sP918(U_12338,U_12341,U_12339,U_12340)
    | hAPP(U_12341,U_12338) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12338),U_12340))
    | ~ sP919(U_12338,U_12341,U_12335,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12339),sK257(U_12341,U_12340,U_12339)),U_12340))
    | ~ sP917(U_12341,U_12335,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_10,plain,
    ( hAPP(U_12341,sK257(U_12341,U_12340,U_12339)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP917(U_12341,U_12335,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_11,plain,
    ( hAPP(U_12341,U_12335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK257(U_12341,U_12340,U_12339) = U_12335
    | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12335),U_12340))
    | ~ sP917(U_12341,U_12335,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12339),sK258(U_12341,U_12340,U_12339,U_12338)),U_12340))
    | ~ sP918(U_12338,U_12341,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_13,plain,
    ( U_12338 != sK258(U_12341,U_12340,U_12339,U_12338)
    | ~ sP918(U_12338,U_12341,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

cnf(f_3203_14,plain,
    ( hAPP(U_12341,sK258(U_12341,U_12340,U_12339,U_12338)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP918(U_12338,U_12341,U_12339,U_12340) ),
    inference(clausify,[status(thm)],[f_3203_5]) ).

fof(f_3204_1,plain,
    ! [V_k_2,V_f_2] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2))
      | hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0]) ).

fof(f_3204_2,plain,
    ! [U_12343,U_12342] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12342),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12343)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12342),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12343))
      | hAPP(U_12342,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_3204_1]) ).

fof(f_3204_3,plain,
    ! [U_12342,U_12343] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12342),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12343)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12342),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12343))
      | hAPP(U_12342,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_3204_2]) ).

cnf(f_3204_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12342),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12343)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12342),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12343))
    | hAPP(U_12342,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3204_3]) ).

fof(f_3205_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).

fof(f_3205_2,plain,
    ! [U_12346,U_12345,U_12344] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12344,tc_Nat_Onat),U_12345),U_12346) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12344,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12344),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12345)),U_12346)),
    inference(variable_rename,[status(thm)],[f_3205_1]) ).

fof(f_3205_3,plain,
    ! [U_12345,U_12346,U_12344] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12344,tc_Nat_Onat),U_12345),U_12346) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12344,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12344),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12345)),U_12346)),
    inference(definitional_conversion,[status(esa)],[f_3205_2]) ).

cnf(f_3205_4,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12344,tc_Nat_Onat),U_12345),U_12346) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12344,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12344),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12345)),U_12346)),
    inference(clausify,[status(thm)],[f_3205_3]) ).

fof(f_3206_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat]) ).

fof(f_3206_2,plain,
    ! [U_12350,U_12349,U_12348,U_12347] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12347,tc_HOL_Obool)),U_12349),U_12348)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),U_12349)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),U_12348))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12347,tc_HOL_Obool)),U_12348),U_12349))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12347),U_12348)) ),
    inference(variable_rename,[status(thm)],[f_3206_1]) ).

fof(f_3206_3,plain,
    ! [U_12347,U_12349,U_12348,U_12350] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12347,tc_HOL_Obool)),U_12349),U_12348)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),U_12349)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),U_12348))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12347,tc_HOL_Obool)),U_12348),U_12349))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12347),U_12348)) ),
    inference(definitional_conversion,[status(esa)],[f_3206_2]) ).

cnf(f_3206_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12347,tc_HOL_Obool)),U_12349),U_12348)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),U_12349)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12347,tc_Nat_Onat),U_12350),U_12348))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12347,tc_HOL_Obool)),U_12348),U_12349))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12347),U_12348)) ),
    inference(clausify,[status(thm)],[f_3206_3]) ).

fof(f_3207_1,plain,
    ! [V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J]) ).

fof(f_3207_2,plain,
    ! [U_12353,U_12352,U_12351] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12351),U_12352),U_12353) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12351),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12351,tc_Int_Oint),U_12352),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12353))
      | ~ class_Groups_Ocomm__monoid__mult(U_12351)
      | ~ class_Groups_Ocomm__monoid__add(U_12351) ),
    inference(variable_rename,[status(thm)],[f_3207_1]) ).

fof(f_3207_3,plain,
    ! [U_12351,U_12352,U_12353] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12351),U_12352),U_12353) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12351),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12351,tc_Int_Oint),U_12352),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12353))
      | ~ class_Groups_Ocomm__monoid__mult(U_12351)
      | ~ class_Groups_Ocomm__monoid__add(U_12351) ),
    inference(definitional_conversion,[status(esa)],[f_3207_2]) ).

cnf(f_3207_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12351),U_12352),U_12353) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12351),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12351,tc_Int_Oint),U_12352),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12353))
    | ~ class_Groups_Ocomm__monoid__mult(U_12351)
    | ~ class_Groups_Ocomm__monoid__add(U_12351) ),
    inference(clausify,[status(thm)],[f_3207_3]) ).

fof(f_3208_1,plain,
    ! [V_f_2,V_A_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(f_3208_2,plain,
    ! [U_12357,U_12356,U_12355,U_12354] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12354,tc_Nat_Onat),U_12357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12354,tc_HOL_Obool)),U_12356),hAPP(hAPP(c_Set_Oinsert(U_12354),U_12355),c_Orderings_Obot__class_Obot(tc_fun(U_12354,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12354,tc_Nat_Onat),U_12357),U_12356)
        | hBOOL(hAPP(hAPP(c_member(U_12354),U_12355),U_12356)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12354,tc_Nat_Onat),U_12357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12354,tc_HOL_Obool)),U_12356),hAPP(hAPP(c_Set_Oinsert(U_12354),U_12355),c_Orderings_Obot__class_Obot(tc_fun(U_12354,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12354,tc_Nat_Onat),U_12357),U_12356)),hAPP(U_12357,U_12355))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12354),U_12355),U_12356)) ) ),
    inference(variable_rename,[status(thm)],[f_3208_1]) ).

fof(f_3208_3,plain,
    ( ! [U_12365,U_12363,U_12361,U_12359] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12359,tc_Nat_Onat),U_12365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12359,tc_HOL_Obool)),U_12363),hAPP(hAPP(c_Set_Oinsert(U_12359),U_12361),c_Orderings_Obot__class_Obot(tc_fun(U_12359,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12359,tc_Nat_Onat),U_12365),U_12363)
        | hBOOL(hAPP(hAPP(c_member(U_12359),U_12361),U_12363)) )
    & ! [U_12364,U_12362,U_12360,U_12358] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12358,tc_Nat_Onat),U_12364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12358,tc_HOL_Obool)),U_12362),hAPP(hAPP(c_Set_Oinsert(U_12358),U_12360),c_Orderings_Obot__class_Obot(tc_fun(U_12358,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12358,tc_Nat_Onat),U_12364),U_12362)),hAPP(U_12364,U_12360))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12358),U_12360),U_12362)) ) ),
    inference(miniscope,[status(thm)],[f_3208_2]) ).

fof(f_3208_4,plain,
    ( ! [U_12359,U_12361,U_12363,U_12365] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12359,tc_Nat_Onat),U_12365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12359,tc_HOL_Obool)),U_12363),hAPP(hAPP(c_Set_Oinsert(U_12359),U_12361),c_Orderings_Obot__class_Obot(tc_fun(U_12359,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12359,tc_Nat_Onat),U_12365),U_12363)
        | hBOOL(hAPP(hAPP(c_member(U_12359),U_12361),U_12363)) )
    & ! [U_12362,U_12360,U_12364,U_12358] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12358,tc_Nat_Onat),U_12364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12358,tc_HOL_Obool)),U_12362),hAPP(hAPP(c_Set_Oinsert(U_12358),U_12360),c_Orderings_Obot__class_Obot(tc_fun(U_12358,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12358,tc_Nat_Onat),U_12364),U_12362)),hAPP(U_12364,U_12360))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12358),U_12360),U_12362)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3208_3]) ).

cnf(f_3208_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12358,tc_Nat_Onat),U_12364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12358,tc_HOL_Obool)),U_12362),hAPP(hAPP(c_Set_Oinsert(U_12358),U_12360),c_Orderings_Obot__class_Obot(tc_fun(U_12358,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12358,tc_Nat_Onat),U_12364),U_12362)),hAPP(U_12364,U_12360))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12358),U_12360),U_12362)) ),
    inference(clausify,[status(thm)],[f_3208_4]) ).

cnf(f_3208_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12359,tc_Nat_Onat),U_12365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12359,tc_HOL_Obool)),U_12363),hAPP(hAPP(c_Set_Oinsert(U_12359),U_12361),c_Orderings_Obot__class_Obot(tc_fun(U_12359,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12359,tc_Nat_Onat),U_12365),U_12363)
    | hBOOL(hAPP(hAPP(c_member(U_12359),U_12361),U_12363)) ),
    inference(clausify,[status(thm)],[f_3208_4]) ).

fof(f_3209_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat]) ).

fof(f_3209_2,plain,
    ! [U_12369,U_12368,U_12367,U_12366] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12366,tc_HOL_Obool)),U_12367),U_12368)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),U_12367)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),U_12368))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12366,tc_HOL_Obool)),U_12367),U_12368)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12366),U_12368))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12366),U_12367)) ),
    inference(variable_rename,[status(thm)],[f_3209_1]) ).

fof(f_3209_3,plain,
    ! [U_12366,U_12367,U_12368,U_12369] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12366,tc_HOL_Obool)),U_12367),U_12368)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),U_12367)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),U_12368))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12366,tc_HOL_Obool)),U_12367),U_12368)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12366),U_12368))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12366),U_12367)) ),
    inference(definitional_conversion,[status(esa)],[f_3209_2]) ).

cnf(f_3209_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12366,tc_HOL_Obool)),U_12367),U_12368)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),U_12367)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),U_12368))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12366,tc_Nat_Onat),U_12369),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12366,tc_HOL_Obool)),U_12367),U_12368)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12366),U_12368))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12366),U_12367)) ),
    inference(clausify,[status(thm)],[f_3209_3]) ).

fof(f_3210_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J]) ).

fof(f_3210_2,plain,
    ! [U_12372,U_12371,U_12370] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12370),U_12372),U_12371) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12370),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12370,tc_Nat_Onat),U_12372),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12371))
      | ~ c_Nat__Transfer_Onat__set(U_12371)
      | ~ class_Groups_Ocomm__monoid__mult(U_12370)
      | ~ class_Groups_Ocomm__monoid__add(U_12370) ),
    inference(variable_rename,[status(thm)],[f_3210_1]) ).

fof(f_3210_3,plain,
    ! [U_12371,U_12370,U_12372] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12370),U_12372),U_12371) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12370),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12370,tc_Nat_Onat),U_12372),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12371))
      | ~ c_Nat__Transfer_Onat__set(U_12371)
      | ~ class_Groups_Ocomm__monoid__mult(U_12370)
      | ~ class_Groups_Ocomm__monoid__add(U_12370) ),
    inference(definitional_conversion,[status(esa)],[f_3210_2]) ).

cnf(f_3210_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12370),U_12372),U_12371) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12370),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12370,tc_Nat_Onat),U_12372),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12371))
    | ~ c_Nat__Transfer_Onat__set(U_12371)
    | ~ class_Groups_Ocomm__monoid__mult(U_12370)
    | ~ class_Groups_Ocomm__monoid__add(U_12370) ),
    inference(clausify,[status(thm)],[f_3210_3]) ).

fof(f_3211_1,plain,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
    inference(fof_nnf,[status(thm)],[fact_arith__series__nat]) ).

fof(f_3211_2,plain,
    ! [U_12375,U_12374,U_12373] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12374))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12375))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12375),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12374)))),
    inference(variable_rename,[status(thm)],[f_3211_1]) ).

fof(f_3211_3,plain,
    ! [U_12373,U_12374,U_12375] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12374))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12375))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12375),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12374)))),
    inference(definitional_conversion,[status(esa)],[f_3211_2]) ).

cnf(f_3211_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12374))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12375))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12375),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12374)))),
    inference(clausify,[status(thm)],[f_3211_3]) ).

fof(f_3212_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2))
      | ? [B_x] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J]) ).

fof(f_3212_2,plain,
    ! [U_12379,U_12378,U_12377] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Int_Oint),U_12379),U_12378) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12377),c_Int_Onat),U_12379)),U_12378))
      | ? [U_12376] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12379,U_12376))
          & hBOOL(hAPP(hAPP(c_member(U_12377),U_12376),U_12378)) ) ),
    inference(variable_rename,[status(thm)],[f_3212_1]) ).

fof(f_3212_3,plain,
    ! [U_12379,U_12378,U_12377] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Int_Oint),U_12379),U_12378) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12377),c_Int_Onat),U_12379)),U_12378))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12379,sK259(U_12379,U_12378,U_12377)))
        & hBOOL(hAPP(hAPP(c_member(U_12377),sK259(U_12379,U_12378,U_12377)),U_12378)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_12376,sK259(U_12379,U_12378,U_12377))],[f_3212_2]) ).

fof(f_3212_4,plain,
    ( ! [U_12377,U_12378,U_12379] :
        ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12379,sK259(U_12379,U_12378,U_12377)))
        | ~ sP920(U_12377,U_12378,U_12379) )
    & ! [U_12377,U_12378,U_12379] :
        ( hBOOL(hAPP(hAPP(c_member(U_12377),sK259(U_12379,U_12378,U_12377)),U_12378))
        | ~ sP920(U_12377,U_12378,U_12379) )
    & ! [U_12377,U_12378,U_12379] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Int_Oint),U_12379),U_12378) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12377),c_Int_Onat),U_12379)),U_12378))
        | sP920(U_12377,U_12378,U_12379) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP920])],[f_3212_3]) ).

cnf(f_3212_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Int_Oint),U_12379),U_12378) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12377,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12377),c_Int_Onat),U_12379)),U_12378))
    | sP920(U_12377,U_12378,U_12379) ),
    inference(clausify,[status(thm)],[f_3212_4]) ).

cnf(f_3212_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12377),sK259(U_12379,U_12378,U_12377)),U_12378))
    | ~ sP920(U_12377,U_12378,U_12379) ),
    inference(clausify,[status(thm)],[f_3212_4]) ).

cnf(f_3212_7,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12379,sK259(U_12379,U_12378,U_12377)))
    | ~ sP920(U_12377,U_12378,U_12379) ),
    inference(clausify,[status(thm)],[f_3212_4]) ).

fof(f_3213_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero]) ).

fof(f_3213_2,plain,
    ! [U_12385,U_12384,U_12383,U_12382,U_12381] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12383)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12384))
      | ? [U_12380] :
          ( hAPP(U_12385,U_12380) != c_Groups_Ozero__class_Ozero(U_12381)
          & hBOOL(hAPP(hAPP(c_member(U_12382),U_12380),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12384))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12383))
      | ~ class_Groups_Ocomm__monoid__add(U_12381) ),
    inference(variable_rename,[status(thm)],[f_3213_1]) ).

fof(f_3213_3,plain,
    ! [U_12385,U_12384,U_12383,U_12382,U_12381] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12383)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12384))
      | ( hAPP(U_12385,sK260(U_12385,U_12384,U_12383,U_12382,U_12381)) != c_Groups_Ozero__class_Ozero(U_12381)
        & hBOOL(hAPP(hAPP(c_member(U_12382),sK260(U_12385,U_12384,U_12383,U_12382,U_12381)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12384))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12383))
      | ~ class_Groups_Ocomm__monoid__add(U_12381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_12380,sK260(U_12385,U_12384,U_12383,U_12382,U_12381))],[f_3213_2]) ).

fof(f_3213_4,plain,
    ( ! [U_12381,U_12382,U_12383,U_12384,U_12385] :
        ( hAPP(U_12385,sK260(U_12385,U_12384,U_12383,U_12382,U_12381)) != c_Groups_Ozero__class_Ozero(U_12381)
        | ~ sP921(U_12381,U_12382,U_12383,U_12384,U_12385) )
    & ! [U_12381,U_12382,U_12383,U_12384,U_12385] :
        ( hBOOL(hAPP(hAPP(c_member(U_12382),sK260(U_12385,U_12384,U_12383,U_12382,U_12381)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)))
        | ~ sP921(U_12381,U_12382,U_12383,U_12384,U_12385) )
    & ! [U_12381,U_12382,U_12383,U_12384,U_12385] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12383)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12384))
        | sP921(U_12381,U_12382,U_12383,U_12384,U_12385)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12384))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12383))
        | ~ class_Groups_Ocomm__monoid__add(U_12381) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP921])],[f_3213_3]) ).

cnf(f_3213_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12383)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12382,U_12381),U_12385),U_12384))
    | sP921(U_12381,U_12382,U_12383,U_12384,U_12385)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12384))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12382),U_12383))
    | ~ class_Groups_Ocomm__monoid__add(U_12381) ),
    inference(clausify,[status(thm)],[f_3213_4]) ).

cnf(f_3213_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12382),sK260(U_12385,U_12384,U_12383,U_12382,U_12381)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)))
    | ~ sP921(U_12381,U_12382,U_12383,U_12384,U_12385) ),
    inference(clausify,[status(thm)],[f_3213_4]) ).

cnf(f_3213_7,plain,
    ( hAPP(U_12385,sK260(U_12385,U_12384,U_12383,U_12382,U_12381)) != c_Groups_Ozero__class_Ozero(U_12381)
    | ~ sP921(U_12381,U_12382,U_12383,U_12384,U_12385) ),
    inference(clausify,[status(thm)],[f_3213_4]) ).

fof(f_3214_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_c)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono3]) ).

fof(f_3214_2,plain,
    ! [U_12391,U_12390,U_12389,U_12388,U_12387] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12390)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12389)))
      | ? [U_12386] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),c_Groups_Ozero__class_Ozero(U_12387)),hAPP(U_12391,U_12386)))
          & hBOOL(hAPP(hAPP(c_member(U_12388),U_12386),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12388,tc_HOL_Obool)),U_12389),U_12390))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12388,tc_HOL_Obool)),U_12390),U_12389))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12388),U_12389))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12387)
      | ~ class_Groups_Ocomm__monoid__add(U_12387) ),
    inference(variable_rename,[status(thm)],[f_3214_1]) ).

fof(f_3214_3,plain,
    ! [U_12391,U_12390,U_12389,U_12388,U_12387] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12390)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12389)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),c_Groups_Ozero__class_Ozero(U_12387)),hAPP(U_12391,sK261(U_12391,U_12390,U_12389,U_12388,U_12387))))
        & hBOOL(hAPP(hAPP(c_member(U_12388),sK261(U_12391,U_12390,U_12389,U_12388,U_12387)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12388,tc_HOL_Obool)),U_12389),U_12390))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12388,tc_HOL_Obool)),U_12390),U_12389))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12388),U_12389))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12387)
      | ~ class_Groups_Ocomm__monoid__add(U_12387) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_12386,sK261(U_12391,U_12390,U_12389,U_12388,U_12387))],[f_3214_2]) ).

fof(f_3214_4,plain,
    ( ! [U_12389,U_12388,U_12387,U_12390,U_12391] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),c_Groups_Ozero__class_Ozero(U_12387)),hAPP(U_12391,sK261(U_12391,U_12390,U_12389,U_12388,U_12387))))
        | ~ sP922(U_12389,U_12388,U_12387,U_12390,U_12391) )
    & ! [U_12389,U_12388,U_12387,U_12390,U_12391] :
        ( hBOOL(hAPP(hAPP(c_member(U_12388),sK261(U_12391,U_12390,U_12389,U_12388,U_12387)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12388,tc_HOL_Obool)),U_12389),U_12390)))
        | ~ sP922(U_12389,U_12388,U_12387,U_12390,U_12391) )
    & ! [U_12389,U_12388,U_12387,U_12390,U_12391] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12390)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12389)))
        | sP922(U_12389,U_12388,U_12387,U_12390,U_12391)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12388,tc_HOL_Obool)),U_12390),U_12389))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12388),U_12389))
        | ~ class_Groups_Oordered__ab__semigroup__add(U_12387)
        | ~ class_Groups_Ocomm__monoid__add(U_12387) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP922])],[f_3214_3]) ).

cnf(f_3214_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12390)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12388,U_12387),U_12391),U_12389)))
    | sP922(U_12389,U_12388,U_12387,U_12390,U_12391)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12388,tc_HOL_Obool)),U_12390),U_12389))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12388),U_12389))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_12387)
    | ~ class_Groups_Ocomm__monoid__add(U_12387) ),
    inference(clausify,[status(thm)],[f_3214_4]) ).

cnf(f_3214_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12388),sK261(U_12391,U_12390,U_12389,U_12388,U_12387)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12388,tc_HOL_Obool)),U_12389),U_12390)))
    | ~ sP922(U_12389,U_12388,U_12387,U_12390,U_12391) ),
    inference(clausify,[status(thm)],[f_3214_4]) ).

cnf(f_3214_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12387),c_Groups_Ozero__class_Ozero(U_12387)),hAPP(U_12391,sK261(U_12391,U_12390,U_12389,U_12388,U_12387))))
    | ~ sP922(U_12389,U_12388,U_12387,U_12390,U_12391) ),
    inference(clausify,[status(thm)],[f_3214_4]) ).

fof(f_3215_1,plain,
    ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
      ( hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != c_Groups_Ozero__class_Ozero(T_c)
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
      | ~ class_Groups_Oordered__ab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0]) ).

fof(f_3215_2,plain,
    ! [U_12397,U_12396,U_12395,U_12394,U_12393] :
      ( hAPP(U_12396,U_12397) = c_Groups_Ozero__class_Ozero(U_12393)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12394),U_12397),U_12395))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12394,U_12393),U_12396),U_12395) != c_Groups_Ozero__class_Ozero(U_12393)
      | ? [U_12392] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12393),c_Groups_Ozero__class_Ozero(U_12393)),hAPP(U_12396,U_12392)))
          & hBOOL(hAPP(hAPP(c_member(U_12394),U_12392),U_12395)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12394),U_12395))
      | ~ class_Groups_Oordered__ab__group__add(U_12393) ),
    inference(variable_rename,[status(thm)],[f_3215_1]) ).

fof(f_3215_3,plain,
    ! [U_12397,U_12396,U_12395,U_12394,U_12393] :
      ( hAPP(U_12396,U_12397) = c_Groups_Ozero__class_Ozero(U_12393)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12394),U_12397),U_12395))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12394,U_12393),U_12396),U_12395) != c_Groups_Ozero__class_Ozero(U_12393)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12393),c_Groups_Ozero__class_Ozero(U_12393)),hAPP(U_12396,sK262(U_12397,U_12396,U_12395,U_12394,U_12393))))
        & hBOOL(hAPP(hAPP(c_member(U_12394),sK262(U_12397,U_12396,U_12395,U_12394,U_12393)),U_12395)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12394),U_12395))
      | ~ class_Groups_Oordered__ab__group__add(U_12393) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_12392,sK262(U_12397,U_12396,U_12395,U_12394,U_12393))],[f_3215_2]) ).

fof(f_3215_4,plain,
    ( ! [U_12395,U_12393,U_12397,U_12396,U_12394] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12393),c_Groups_Ozero__class_Ozero(U_12393)),hAPP(U_12396,sK262(U_12397,U_12396,U_12395,U_12394,U_12393))))
        | ~ sP923(U_12395,U_12393,U_12397,U_12396,U_12394) )
    & ! [U_12395,U_12393,U_12397,U_12396,U_12394] :
        ( hBOOL(hAPP(hAPP(c_member(U_12394),sK262(U_12397,U_12396,U_12395,U_12394,U_12393)),U_12395))
        | ~ sP923(U_12395,U_12393,U_12397,U_12396,U_12394) )
    & ! [U_12395,U_12393,U_12397,U_12396,U_12394] :
        ( hAPP(U_12396,U_12397) = c_Groups_Ozero__class_Ozero(U_12393)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12394),U_12397),U_12395))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12394,U_12393),U_12396),U_12395) != c_Groups_Ozero__class_Ozero(U_12393)
        | sP923(U_12395,U_12393,U_12397,U_12396,U_12394)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12394),U_12395))
        | ~ class_Groups_Oordered__ab__group__add(U_12393) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP923])],[f_3215_3]) ).

cnf(f_3215_5,plain,
    ( hAPP(U_12396,U_12397) = c_Groups_Ozero__class_Ozero(U_12393)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12394),U_12397),U_12395))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12394,U_12393),U_12396),U_12395) != c_Groups_Ozero__class_Ozero(U_12393)
    | sP923(U_12395,U_12393,U_12397,U_12396,U_12394)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12394),U_12395))
    | ~ class_Groups_Oordered__ab__group__add(U_12393) ),
    inference(clausify,[status(thm)],[f_3215_4]) ).

cnf(f_3215_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12394),sK262(U_12397,U_12396,U_12395,U_12394,U_12393)),U_12395))
    | ~ sP923(U_12395,U_12393,U_12397,U_12396,U_12394) ),
    inference(clausify,[status(thm)],[f_3215_4]) ).

cnf(f_3215_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12393),c_Groups_Ozero__class_Ozero(U_12393)),hAPP(U_12396,sK262(U_12397,U_12396,U_12395,U_12394,U_12393))))
    | ~ sP923(U_12395,U_12393,U_12397,U_12396,U_12394) ),
    inference(clausify,[status(thm)],[f_3215_4]) ).

fof(f_3216_1,plain,
    ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != V_B_2
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
      | ~ class_Groups_Oordered__ab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound]) ).

fof(f_3216_2,plain,
    ! [U_12404,U_12403,U_12402,U_12401,U_12400,U_12399] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),hAPP(U_12402,U_12404)),U_12403))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12400),U_12404),U_12401))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12400,U_12399),U_12402),U_12401) != U_12403
      | ? [U_12398] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),c_Groups_Ozero__class_Ozero(U_12399)),hAPP(U_12402,U_12398)))
          & hBOOL(hAPP(hAPP(c_member(U_12400),U_12398),U_12401)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12400),U_12401))
      | ~ class_Groups_Oordered__ab__group__add(U_12399) ),
    inference(variable_rename,[status(thm)],[f_3216_1]) ).

fof(f_3216_3,plain,
    ! [U_12404,U_12403,U_12402,U_12401,U_12400,U_12399] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),hAPP(U_12402,U_12404)),U_12403))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12400),U_12404),U_12401))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12400,U_12399),U_12402),U_12401) != U_12403
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),c_Groups_Ozero__class_Ozero(U_12399)),hAPP(U_12402,sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399))))
        & hBOOL(hAPP(hAPP(c_member(U_12400),sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399)),U_12401)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12400),U_12401))
      | ~ class_Groups_Oordered__ab__group__add(U_12399) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_12398,sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399))],[f_3216_2]) ).

fof(f_3216_4,plain,
    ( ! [U_12400,U_12401,U_12399,U_12402,U_12403,U_12404] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),c_Groups_Ozero__class_Ozero(U_12399)),hAPP(U_12402,sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399))))
        | ~ sP924(U_12400,U_12401,U_12399,U_12402,U_12403,U_12404) )
    & ! [U_12400,U_12401,U_12399,U_12402,U_12403,U_12404] :
        ( hBOOL(hAPP(hAPP(c_member(U_12400),sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399)),U_12401))
        | ~ sP924(U_12400,U_12401,U_12399,U_12402,U_12403,U_12404) )
    & ! [U_12400,U_12401,U_12399,U_12402,U_12403,U_12404] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),hAPP(U_12402,U_12404)),U_12403))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12400),U_12404),U_12401))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12400,U_12399),U_12402),U_12401) != U_12403
        | sP924(U_12400,U_12401,U_12399,U_12402,U_12403,U_12404)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12400),U_12401))
        | ~ class_Groups_Oordered__ab__group__add(U_12399) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP924])],[f_3216_3]) ).

cnf(f_3216_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),hAPP(U_12402,U_12404)),U_12403))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12400),U_12404),U_12401))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12400,U_12399),U_12402),U_12401) != U_12403
    | sP924(U_12400,U_12401,U_12399,U_12402,U_12403,U_12404)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12400),U_12401))
    | ~ class_Groups_Oordered__ab__group__add(U_12399) ),
    inference(clausify,[status(thm)],[f_3216_4]) ).

cnf(f_3216_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12400),sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399)),U_12401))
    | ~ sP924(U_12400,U_12401,U_12399,U_12402,U_12403,U_12404) ),
    inference(clausify,[status(thm)],[f_3216_4]) ).

cnf(f_3216_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12399),c_Groups_Ozero__class_Ozero(U_12399)),hAPP(U_12402,sK263(U_12404,U_12403,U_12402,U_12401,U_12400,U_12399))))
    | ~ sP924(U_12400,U_12401,U_12399,U_12402,U_12403,U_12404) ),
    inference(clausify,[status(thm)],[f_3216_4]) ).

fof(f_3217_1,plain,
    ! [V_n_2,V_P_2,V_Q_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))
      | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) ),
    inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).

fof(f_3217_2,plain,
    ! [U_12408,U_12407,U_12406] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12406),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_12407)),U_12406)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))
      | ? [U_12405] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12406,U_12405)),hAPP(U_12407,U_12405))) ),
    inference(variable_rename,[status(thm)],[f_3217_1]) ).

fof(f_3217_3,plain,
    ! [U_12408,U_12407,U_12406] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12406),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_12407)),U_12406)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12406,sK264(U_12408,U_12407,U_12406))),hAPP(U_12407,sK264(U_12408,U_12407,U_12406)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_12405,sK264(U_12408,U_12407,U_12406))],[f_3217_2]) ).

fof(f_3217_4,plain,
    ! [U_12408,U_12407,U_12406] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12406),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_12407)),U_12406)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12406,sK264(U_12408,U_12407,U_12406))),hAPP(U_12407,sK264(U_12408,U_12407,U_12406)))) ),
    inference(definitional_conversion,[status(esa)],[f_3217_3]) ).

cnf(f_3217_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12406),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_12407)),U_12406)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12406,sK264(U_12408,U_12407,U_12406))),hAPP(U_12407,sK264(U_12408,U_12407,U_12406)))) ),
    inference(clausify,[status(thm)],[f_3217_4]) ).

fof(f_3218_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left]) ).

fof(f_3218_2,plain,
    ! [U_12414,U_12413,U_12412,U_12411,U_12410] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12413) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12412)
      | ? [U_12409] :
          ( hAPP(U_12414,U_12409) != c_Groups_Ozero__class_Ozero(U_12410)
          & hBOOL(hAPP(hAPP(c_member(U_12411),U_12409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12413))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12411,tc_HOL_Obool)),U_12413),U_12412))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
      | ~ class_Groups_Ocomm__monoid__add(U_12410) ),
    inference(variable_rename,[status(thm)],[f_3218_1]) ).

fof(f_3218_3,plain,
    ! [U_12414,U_12413,U_12412,U_12411,U_12410] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12413) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12412)
      | ( hAPP(U_12414,sK265(U_12414,U_12413,U_12412,U_12411,U_12410)) != c_Groups_Ozero__class_Ozero(U_12410)
        & hBOOL(hAPP(hAPP(c_member(U_12411),sK265(U_12414,U_12413,U_12412,U_12411,U_12410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12413))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12411,tc_HOL_Obool)),U_12413),U_12412))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
      | ~ class_Groups_Ocomm__monoid__add(U_12410) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_12409,sK265(U_12414,U_12413,U_12412,U_12411,U_12410))],[f_3218_2]) ).

fof(f_3218_4,plain,
    ( ! [U_12411,U_12410,U_12412,U_12413,U_12414] :
        ( hAPP(U_12414,sK265(U_12414,U_12413,U_12412,U_12411,U_12410)) != c_Groups_Ozero__class_Ozero(U_12410)
        | ~ sP925(U_12411,U_12410,U_12412,U_12413,U_12414) )
    & ! [U_12411,U_12410,U_12412,U_12413,U_12414] :
        ( hBOOL(hAPP(hAPP(c_member(U_12411),sK265(U_12414,U_12413,U_12412,U_12411,U_12410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12413)))
        | ~ sP925(U_12411,U_12410,U_12412,U_12413,U_12414) )
    & ! [U_12411,U_12410,U_12412,U_12413,U_12414] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12413) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12412)
        | sP925(U_12411,U_12410,U_12412,U_12413,U_12414)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12411,tc_HOL_Obool)),U_12413),U_12412))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
        | ~ class_Groups_Ocomm__monoid__add(U_12410) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP925])],[f_3218_3]) ).

cnf(f_3218_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12413) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12414),U_12412)
    | sP925(U_12411,U_12410,U_12412,U_12413,U_12414)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12411,tc_HOL_Obool)),U_12413),U_12412))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
    | ~ class_Groups_Ocomm__monoid__add(U_12410) ),
    inference(clausify,[status(thm)],[f_3218_4]) ).

cnf(f_3218_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12411),sK265(U_12414,U_12413,U_12412,U_12411,U_12410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12413)))
    | ~ sP925(U_12411,U_12410,U_12412,U_12413,U_12414) ),
    inference(clausify,[status(thm)],[f_3218_4]) ).

cnf(f_3218_7,plain,
    ( hAPP(U_12414,sK265(U_12414,U_12413,U_12412,U_12411,U_12410)) != c_Groups_Ozero__class_Ozero(U_12410)
    | ~ sP925(U_12411,U_12410,U_12412,U_12413,U_12414) ),
    inference(clausify,[status(thm)],[f_3218_4]) ).

fof(f_3219_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right]) ).

fof(f_3219_2,plain,
    ! [U_12420,U_12419,U_12418,U_12417,U_12416] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12418) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12419)
      | ? [U_12415] :
          ( hAPP(U_12420,U_12415) != c_Groups_Ozero__class_Ozero(U_12416)
          & hBOOL(hAPP(hAPP(c_member(U_12417),U_12415),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12417,tc_HOL_Obool)),U_12418),U_12419))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12417),U_12418))
      | ~ class_Groups_Ocomm__monoid__add(U_12416) ),
    inference(variable_rename,[status(thm)],[f_3219_1]) ).

fof(f_3219_3,plain,
    ! [U_12420,U_12419,U_12418,U_12417,U_12416] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12418) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12419)
      | ( hAPP(U_12420,sK266(U_12420,U_12419,U_12418,U_12417,U_12416)) != c_Groups_Ozero__class_Ozero(U_12416)
        & hBOOL(hAPP(hAPP(c_member(U_12417),sK266(U_12420,U_12419,U_12418,U_12417,U_12416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12417,tc_HOL_Obool)),U_12418),U_12419))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12417),U_12418))
      | ~ class_Groups_Ocomm__monoid__add(U_12416) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_12415,sK266(U_12420,U_12419,U_12418,U_12417,U_12416))],[f_3219_2]) ).

fof(f_3219_4,plain,
    ( ! [U_12417,U_12416,U_12419,U_12418,U_12420] :
        ( hAPP(U_12420,sK266(U_12420,U_12419,U_12418,U_12417,U_12416)) != c_Groups_Ozero__class_Ozero(U_12416)
        | ~ sP926(U_12417,U_12416,U_12419,U_12418,U_12420) )
    & ! [U_12417,U_12416,U_12419,U_12418,U_12420] :
        ( hBOOL(hAPP(hAPP(c_member(U_12417),sK266(U_12420,U_12419,U_12418,U_12417,U_12416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12417,tc_HOL_Obool)),U_12418),U_12419)))
        | ~ sP926(U_12417,U_12416,U_12419,U_12418,U_12420) )
    & ! [U_12417,U_12416,U_12419,U_12418,U_12420] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12418) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12419)
        | sP926(U_12417,U_12416,U_12419,U_12418,U_12420)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12417),U_12418))
        | ~ class_Groups_Ocomm__monoid__add(U_12416) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP926])],[f_3219_3]) ).

cnf(f_3219_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12418) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12417,U_12416),U_12420),U_12419)
    | sP926(U_12417,U_12416,U_12419,U_12418,U_12420)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12417),U_12418))
    | ~ class_Groups_Ocomm__monoid__add(U_12416) ),
    inference(clausify,[status(thm)],[f_3219_4]) ).

cnf(f_3219_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12417),sK266(U_12420,U_12419,U_12418,U_12417,U_12416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12417,tc_HOL_Obool)),U_12418),U_12419)))
    | ~ sP926(U_12417,U_12416,U_12419,U_12418,U_12420) ),
    inference(clausify,[status(thm)],[f_3219_4]) ).

cnf(f_3219_7,plain,
    ( hAPP(U_12420,sK266(U_12420,U_12419,U_12418,U_12417,U_12416)) != c_Groups_Ozero__class_Ozero(U_12416)
    | ~ sP926(U_12417,U_12416,U_12419,U_12418,U_12420) ),
    inference(clausify,[status(thm)],[f_3219_4]) ).

fof(f_3220_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem]) ).

fof(f_3220_2,plain,
    ! [U_12425,U_12424,U_12423,U_12422,U_12421] :
      ( hAPP(U_12423,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12421,tc_HOL_Obool)),U_12424),U_12425)) = hAPP(hAPP(U_12422,hAPP(U_12423,U_12424)),hAPP(U_12423,U_12425))
      | U_12425 = c_Orderings_Obot__class_Obot(tc_fun(U_12421,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12421),U_12425))
      | U_12424 = c_Orderings_Obot__class_Obot(tc_fun(U_12421,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12421),U_12424))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12421,U_12422,U_12423) ),
    inference(variable_rename,[status(thm)],[f_3220_1]) ).

fof(f_3220_3,plain,
    ! [U_12423,U_12425,U_12422,U_12424,U_12421] :
      ( hAPP(U_12423,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12421,tc_HOL_Obool)),U_12424),U_12425)) = hAPP(hAPP(U_12422,hAPP(U_12423,U_12424)),hAPP(U_12423,U_12425))
      | U_12425 = c_Orderings_Obot__class_Obot(tc_fun(U_12421,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12421),U_12425))
      | U_12424 = c_Orderings_Obot__class_Obot(tc_fun(U_12421,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12421),U_12424))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12421,U_12422,U_12423) ),
    inference(definitional_conversion,[status(esa)],[f_3220_2]) ).

cnf(f_3220_4,plain,
    ( hAPP(U_12423,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12421,tc_HOL_Obool)),U_12424),U_12425)) = hAPP(hAPP(U_12422,hAPP(U_12423,U_12424)),hAPP(U_12423,U_12425))
    | U_12425 = c_Orderings_Obot__class_Obot(tc_fun(U_12421,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12421),U_12425))
    | U_12424 = c_Orderings_Obot__class_Obot(tc_fun(U_12421,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12421),U_12424))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12421,U_12422,U_12423) ),
    inference(clausify,[status(thm)],[f_3220_3]) ).

fof(f_3221_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem]) ).

fof(f_3221_2,plain,
    ! [U_12429,U_12428,U_12427,U_12426] :
      ( hAPP(hAPP(U_12427,U_12429),U_12429) = U_12429
      | ~ c_Finite__Set_Ofolding__one__idem(U_12426,U_12427,U_12428) ),
    inference(variable_rename,[status(thm)],[f_3221_1]) ).

fof(f_3221_3,plain,
    ! [U_12429,U_12428,U_12427] :
      ( ! [U_12426] : ~ c_Finite__Set_Ofolding__one__idem(U_12426,U_12427,U_12428)
      | hAPP(hAPP(U_12427,U_12429),U_12429) = U_12429 ),
    inference(miniscope,[status(thm)],[f_3221_2]) ).

fof(f_3221_4,plain,
    ! [U_12428,U_12429,U_12426,U_12427] :
      ( ~ c_Finite__Set_Ofolding__one__idem(U_12426,U_12427,U_12428)
      | hAPP(hAPP(U_12427,U_12429),U_12429) = U_12429 ),
    inference(definitional_conversion,[status(esa)],[f_3221_3]) ).

cnf(f_3221_5,plain,
    ( ~ c_Finite__Set_Ofolding__one__idem(U_12426,U_12427,U_12428)
    | hAPP(hAPP(U_12427,U_12429),U_12429) = U_12429 ),
    inference(clausify,[status(thm)],[f_3221_4]) ).

fof(f_3222_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem]) ).

fof(f_3222_2,plain,
    ! [U_12434,U_12433,U_12432,U_12431,U_12430] :
      ( hAPP(hAPP(U_12431,U_12434),hAPP(U_12432,U_12433)) = hAPP(U_12432,U_12433)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12430),U_12434),U_12433))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12430),U_12433))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12430,U_12431,U_12432) ),
    inference(variable_rename,[status(thm)],[f_3222_1]) ).

fof(f_3222_3,plain,
    ! [U_12430,U_12432,U_12433,U_12434,U_12431] :
      ( hAPP(hAPP(U_12431,U_12434),hAPP(U_12432,U_12433)) = hAPP(U_12432,U_12433)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12430),U_12434),U_12433))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12430),U_12433))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12430,U_12431,U_12432) ),
    inference(definitional_conversion,[status(esa)],[f_3222_2]) ).

cnf(f_3222_4,plain,
    ( hAPP(hAPP(U_12431,U_12434),hAPP(U_12432,U_12433)) = hAPP(U_12432,U_12433)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12430),U_12434),U_12433))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12430),U_12433))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12430,U_12431,U_12432) ),
    inference(clausify,[status(thm)],[f_3222_3]) ).

fof(f_3223_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem]) ).

fof(f_3223_2,plain,
    ! [U_12439,U_12438,U_12437,U_12436,U_12435] :
      ( hAPP(U_12437,hAPP(hAPP(c_Set_Oinsert(U_12435),U_12439),U_12438)) = hAPP(hAPP(U_12436,U_12439),hAPP(U_12437,U_12438))
      | U_12438 = c_Orderings_Obot__class_Obot(tc_fun(U_12435,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12435),U_12438))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12435,U_12436,U_12437) ),
    inference(variable_rename,[status(thm)],[f_3223_1]) ).

fof(f_3223_3,plain,
    ! [U_12436,U_12435,U_12437,U_12438,U_12439] :
      ( hAPP(U_12437,hAPP(hAPP(c_Set_Oinsert(U_12435),U_12439),U_12438)) = hAPP(hAPP(U_12436,U_12439),hAPP(U_12437,U_12438))
      | U_12438 = c_Orderings_Obot__class_Obot(tc_fun(U_12435,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12435),U_12438))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12435,U_12436,U_12437) ),
    inference(definitional_conversion,[status(esa)],[f_3223_2]) ).

cnf(f_3223_4,plain,
    ( hAPP(U_12437,hAPP(hAPP(c_Set_Oinsert(U_12435),U_12439),U_12438)) = hAPP(hAPP(U_12436,U_12439),hAPP(U_12437,U_12438))
    | U_12438 = c_Orderings_Obot__class_Obot(tc_fun(U_12435,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12435),U_12438))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12435,U_12436,U_12437) ),
    inference(clausify,[status(thm)],[f_3223_3]) ).

fof(f_3224_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem]) ).

fof(f_3224_2,plain,
    ! [U_12444,U_12443,U_12442,U_12441,U_12440] :
      ( hAPP(hAPP(U_12441,hAPP(U_12442,U_12444)),hAPP(U_12442,U_12443)) = hAPP(U_12442,U_12443)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12440,tc_HOL_Obool)),U_12444),U_12443))
      | U_12444 = c_Orderings_Obot__class_Obot(tc_fun(U_12440,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12440),U_12443))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12440,U_12441,U_12442) ),
    inference(variable_rename,[status(thm)],[f_3224_1]) ).

fof(f_3224_3,plain,
    ! [U_12440,U_12441,U_12442,U_12443,U_12444] :
      ( hAPP(hAPP(U_12441,hAPP(U_12442,U_12444)),hAPP(U_12442,U_12443)) = hAPP(U_12442,U_12443)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12440,tc_HOL_Obool)),U_12444),U_12443))
      | U_12444 = c_Orderings_Obot__class_Obot(tc_fun(U_12440,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12440),U_12443))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12440,U_12441,U_12442) ),
    inference(definitional_conversion,[status(esa)],[f_3224_2]) ).

cnf(f_3224_4,plain,
    ( hAPP(hAPP(U_12441,hAPP(U_12442,U_12444)),hAPP(U_12442,U_12443)) = hAPP(U_12442,U_12443)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12440,tc_HOL_Obool)),U_12444),U_12443))
    | U_12444 = c_Orderings_Obot__class_Obot(tc_fun(U_12440,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12440),U_12443))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12440,U_12441,U_12442) ),
    inference(clausify,[status(thm)],[f_3224_3]) ).

fof(f_3225_1,plain,
    ! [V_P_2,V_A_2,V_F_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_F_2))
      | ? [B_a,B_F] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
          & hBOOL(hAPP(V_P_2,B_F))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
      | ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).

fof(f_3225_2,plain,
    ! [U_12450,U_12449,U_12448,U_12447] :
      ( hBOOL(hAPP(U_12450,U_12448))
      | ? [U_12446,U_12445] :
          ( ~ hBOOL(hAPP(U_12450,hAPP(hAPP(c_Set_Oinsert(U_12447),U_12446),U_12445)))
          & hBOOL(hAPP(U_12450,U_12445))
          & ~ hBOOL(hAPP(hAPP(c_member(U_12447),U_12446),U_12445))
          & hBOOL(hAPP(hAPP(c_member(U_12447),U_12446),U_12449))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12445)) )
      | ~ hBOOL(hAPP(U_12450,c_Orderings_Obot__class_Obot(tc_fun(U_12447,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12447,tc_HOL_Obool)),U_12448),U_12449))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12448)) ),
    inference(variable_rename,[status(thm)],[f_3225_1]) ).

fof(f_3225_3,plain,
    ! [U_12450,U_12449,U_12448,U_12447] :
      ( hBOOL(hAPP(U_12450,U_12448))
      | ? [U_12445] :
          ( ~ hBOOL(hAPP(U_12450,hAPP(hAPP(c_Set_Oinsert(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),U_12445)))
          & hBOOL(hAPP(U_12450,U_12445))
          & ~ hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),U_12445))
          & hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),U_12449))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12445)) )
      | ~ hBOOL(hAPP(U_12450,c_Orderings_Obot__class_Obot(tc_fun(U_12447,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12447,tc_HOL_Obool)),U_12448),U_12449))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12448)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_12446,sK267(U_12450,U_12449,U_12448,U_12447))],[f_3225_2]) ).

fof(f_3225_4,plain,
    ! [U_12450,U_12449,U_12448,U_12447] :
      ( hBOOL(hAPP(U_12450,U_12448))
      | ( ~ hBOOL(hAPP(U_12450,hAPP(hAPP(c_Set_Oinsert(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),sK268(U_12450,U_12449,U_12448,U_12447))))
        & hBOOL(hAPP(U_12450,sK268(U_12450,U_12449,U_12448,U_12447)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),sK268(U_12450,U_12449,U_12448,U_12447)))
        & hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),U_12449))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),sK268(U_12450,U_12449,U_12448,U_12447))) )
      | ~ hBOOL(hAPP(U_12450,c_Orderings_Obot__class_Obot(tc_fun(U_12447,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12447,tc_HOL_Obool)),U_12448),U_12449))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12448)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_12445,sK268(U_12450,U_12449,U_12448,U_12447))],[f_3225_3]) ).

fof(f_3225_5,plain,
    ( ! [U_12447,U_12448,U_12449,U_12450] :
        ( ~ hBOOL(hAPP(U_12450,hAPP(hAPP(c_Set_Oinsert(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),sK268(U_12450,U_12449,U_12448,U_12447))))
        | ~ sP927(U_12447,U_12448,U_12449,U_12450) )
    & ! [U_12447,U_12448,U_12449,U_12450] :
        ( hBOOL(hAPP(U_12450,sK268(U_12450,U_12449,U_12448,U_12447)))
        | ~ sP927(U_12447,U_12448,U_12449,U_12450) )
    & ! [U_12447,U_12448,U_12449,U_12450] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),sK268(U_12450,U_12449,U_12448,U_12447)))
        | ~ sP927(U_12447,U_12448,U_12449,U_12450) )
    & ! [U_12447,U_12448,U_12449,U_12450] :
        ( hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),U_12449))
        | ~ sP927(U_12447,U_12448,U_12449,U_12450) )
    & ! [U_12447,U_12448,U_12449,U_12450] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),sK268(U_12450,U_12449,U_12448,U_12447)))
        | ~ sP927(U_12447,U_12448,U_12449,U_12450) )
    & ! [U_12447,U_12448,U_12449,U_12450] :
        ( hBOOL(hAPP(U_12450,U_12448))
        | sP927(U_12447,U_12448,U_12449,U_12450)
        | ~ hBOOL(hAPP(U_12450,c_Orderings_Obot__class_Obot(tc_fun(U_12447,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12447,tc_HOL_Obool)),U_12448),U_12449))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12448)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP927])],[f_3225_4]) ).

cnf(f_3225_6,plain,
    ( hBOOL(hAPP(U_12450,U_12448))
    | sP927(U_12447,U_12448,U_12449,U_12450)
    | ~ hBOOL(hAPP(U_12450,c_Orderings_Obot__class_Obot(tc_fun(U_12447,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12447,tc_HOL_Obool)),U_12448),U_12449))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),U_12448)) ),
    inference(clausify,[status(thm)],[f_3225_5]) ).

cnf(f_3225_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12447),sK268(U_12450,U_12449,U_12448,U_12447)))
    | ~ sP927(U_12447,U_12448,U_12449,U_12450) ),
    inference(clausify,[status(thm)],[f_3225_5]) ).

cnf(f_3225_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),U_12449))
    | ~ sP927(U_12447,U_12448,U_12449,U_12450) ),
    inference(clausify,[status(thm)],[f_3225_5]) ).

cnf(f_3225_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),sK268(U_12450,U_12449,U_12448,U_12447)))
    | ~ sP927(U_12447,U_12448,U_12449,U_12450) ),
    inference(clausify,[status(thm)],[f_3225_5]) ).

cnf(f_3225_10,plain,
    ( hBOOL(hAPP(U_12450,sK268(U_12450,U_12449,U_12448,U_12447)))
    | ~ sP927(U_12447,U_12448,U_12449,U_12450) ),
    inference(clausify,[status(thm)],[f_3225_5]) ).

cnf(f_3225_11,plain,
    ( ~ hBOOL(hAPP(U_12450,hAPP(hAPP(c_Set_Oinsert(U_12447),sK267(U_12450,U_12449,U_12448,U_12447)),sK268(U_12450,U_12449,U_12448,U_12447))))
    | ~ sP927(U_12447,U_12448,U_12449,U_12450) ),
    inference(clausify,[status(thm)],[f_3225_5]) ).

fof(f_3226_1,plain,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono]) ).

fof(f_3226_2,plain,
    ! [U_12456,U_12455,U_12454,U_12453,U_12452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12455),U_12454)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12456),U_12454)))
      | ? [U_12451] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(U_12455,U_12451)),hAPP(U_12456,U_12451)))
          & hBOOL(hAPP(hAPP(c_member(U_12453),U_12451),U_12454)) )
      | U_12454 = c_Orderings_Obot__class_Obot(tc_fun(U_12453,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12453),U_12454))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12452)
      | ~ class_Groups_Ocomm__monoid__add(U_12452) ),
    inference(variable_rename,[status(thm)],[f_3226_1]) ).

fof(f_3226_3,plain,
    ! [U_12456,U_12455,U_12454,U_12453,U_12452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12455),U_12454)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12456),U_12454)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(U_12455,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))),hAPP(U_12456,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))))
        & hBOOL(hAPP(hAPP(c_member(U_12453),sK269(U_12456,U_12455,U_12454,U_12453,U_12452)),U_12454)) )
      | U_12454 = c_Orderings_Obot__class_Obot(tc_fun(U_12453,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12453),U_12454))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12452)
      | ~ class_Groups_Ocomm__monoid__add(U_12452) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_12451,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))],[f_3226_2]) ).

fof(f_3226_4,plain,
    ( ! [U_12452,U_12453,U_12456,U_12455,U_12454] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(U_12455,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))),hAPP(U_12456,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))))
        | ~ sP928(U_12452,U_12453,U_12456,U_12455,U_12454) )
    & ! [U_12452,U_12453,U_12456,U_12455,U_12454] :
        ( hBOOL(hAPP(hAPP(c_member(U_12453),sK269(U_12456,U_12455,U_12454,U_12453,U_12452)),U_12454))
        | ~ sP928(U_12452,U_12453,U_12456,U_12455,U_12454) )
    & ! [U_12452,U_12453,U_12456,U_12455,U_12454] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12455),U_12454)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12456),U_12454)))
        | sP928(U_12452,U_12453,U_12456,U_12455,U_12454)
        | U_12454 = c_Orderings_Obot__class_Obot(tc_fun(U_12453,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12453),U_12454))
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12452)
        | ~ class_Groups_Ocomm__monoid__add(U_12452) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP928])],[f_3226_3]) ).

cnf(f_3226_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12455),U_12454)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12453,U_12452),U_12456),U_12454)))
    | sP928(U_12452,U_12453,U_12456,U_12455,U_12454)
    | U_12454 = c_Orderings_Obot__class_Obot(tc_fun(U_12453,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12453),U_12454))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12452)
    | ~ class_Groups_Ocomm__monoid__add(U_12452) ),
    inference(clausify,[status(thm)],[f_3226_4]) ).

cnf(f_3226_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12453),sK269(U_12456,U_12455,U_12454,U_12453,U_12452)),U_12454))
    | ~ sP928(U_12452,U_12453,U_12456,U_12455,U_12454) ),
    inference(clausify,[status(thm)],[f_3226_4]) ).

cnf(f_3226_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12452),hAPP(U_12455,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))),hAPP(U_12456,sK269(U_12456,U_12455,U_12454,U_12453,U_12452))))
    | ~ sP928(U_12452,U_12453,U_12456,U_12455,U_12454) ),
    inference(clausify,[status(thm)],[f_3226_4]) ).

fof(f_3227_1,plain,
    ! [V_n_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).

fof(f_3227_2,plain,
    ! [U_12458,U_12457] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12457,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12457),U_12458)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12457),U_12458)) = hAPP(hAPP(c_Set_Oinsert(U_12457),U_12458),c_Orderings_Obot__class_Obot(tc_fun(U_12457,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12457) ),
    inference(variable_rename,[status(thm)],[f_3227_1]) ).

fof(f_3227_3,plain,
    ! [U_12458,U_12457] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12457,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12457),U_12458)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12457),U_12458)) = hAPP(hAPP(c_Set_Oinsert(U_12457),U_12458),c_Orderings_Obot__class_Obot(tc_fun(U_12457,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12457) ),
    inference(definitional_conversion,[status(esa)],[f_3227_2]) ).

cnf(f_3227_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12457,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12457),U_12458)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12457),U_12458)) = hAPP(hAPP(c_Set_Oinsert(U_12457),U_12458),c_Orderings_Obot__class_Obot(tc_fun(U_12457,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_12457) ),
    inference(clausify,[status(thm)],[f_3227_3]) ).

fof(f_3228_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff]) ).

fof(f_3228_2,plain,
    ! [U_12461,U_12460,U_12459] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12460) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12461)
          | U_12460 != U_12461 )
        & ( U_12460 = U_12461
          | hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12460) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12461) ) )
      | ~ class_Orderings_Olinorder(U_12459) ),
    inference(variable_rename,[status(thm)],[f_3228_1]) ).

fof(f_3228_3,plain,
    ( ! [U_12459,U_12460,U_12461] :
        ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12460) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12461)
        | U_12460 != U_12461
        | ~ sP929(U_12459,U_12460,U_12461) )
    & ! [U_12459,U_12460,U_12461] :
        ( U_12460 = U_12461
        | hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12460) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12461)
        | ~ sP929(U_12459,U_12460,U_12461) )
    & ! [U_12459,U_12460,U_12461] :
        ( sP929(U_12459,U_12460,U_12461)
        | ~ class_Orderings_Olinorder(U_12459) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP929])],[f_3228_2]) ).

cnf(f_3228_4,plain,
    ( sP929(U_12459,U_12460,U_12461)
    | ~ class_Orderings_Olinorder(U_12459) ),
    inference(clausify,[status(thm)],[f_3228_3]) ).

cnf(f_3228_5,plain,
    ( U_12460 = U_12461
    | hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12460) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12461)
    | ~ sP929(U_12459,U_12460,U_12461) ),
    inference(clausify,[status(thm)],[f_3228_3]) ).

cnf(f_3228_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12460) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12459),U_12461)
    | U_12460 != U_12461
    | ~ sP929(U_12459,U_12460,U_12461) ),
    inference(clausify,[status(thm)],[f_3228_3]) ).

fof(f_3229_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__iff]) ).

fof(f_3229_2,plain,
    ! [U_12464,U_12463,U_12462] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12462),U_12463),hAPP(c_SetInterval_Oord__class_OatLeast(U_12462),U_12464)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12462),U_12464),U_12463)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12462),U_12464),U_12463))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12462),U_12463),hAPP(c_SetInterval_Oord__class_OatLeast(U_12462),U_12464))) ) )
      | ~ class_Orderings_Oord(U_12462) ),
    inference(variable_rename,[status(thm)],[f_3229_1]) ).

fof(f_3229_3,plain,
    ( ! [U_12463,U_12464,U_12462] :
        ( hBOOL(hAPP(hAPP(c_member(U_12462),U_12463),hAPP(c_SetInterval_Oord__class_OatLeast(U_12462),U_12464)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12462),U_12464),U_12463))
        | ~ sP930(U_12463,U_12464,U_12462) )
    & ! [U_12463,U_12464,U_12462] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12462),U_12464),U_12463))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12462),U_12463),hAPP(c_SetInterval_Oord__class_OatLeast(U_12462),U_12464)))
        | ~ sP930(U_12463,U_12464,U_12462) )
    & ! [U_12463,U_12464,U_12462] :
        ( sP930(U_12463,U_12464,U_12462)
        | ~ class_Orderings_Oord(U_12462) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP930])],[f_3229_2]) ).

cnf(f_3229_4,plain,
    ( sP930(U_12463,U_12464,U_12462)
    | ~ class_Orderings_Oord(U_12462) ),
    inference(clausify,[status(thm)],[f_3229_3]) ).

cnf(f_3229_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12462),U_12464),U_12463))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12462),U_12463),hAPP(c_SetInterval_Oord__class_OatLeast(U_12462),U_12464)))
    | ~ sP930(U_12463,U_12464,U_12462) ),
    inference(clausify,[status(thm)],[f_3229_3]) ).

cnf(f_3229_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12462),U_12463),hAPP(c_SetInterval_Oord__class_OatLeast(U_12462),U_12464)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12462),U_12464),U_12463))
    | ~ sP930(U_12463,U_12464,U_12462) ),
    inference(clausify,[status(thm)],[f_3229_3]) ).

fof(f_3230_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff]) ).

fof(f_3230_2,plain,
    ! [U_12467,U_12466,U_12465] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12466)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12467)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12465),U_12467),U_12466)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12465),U_12467),U_12466))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12466)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12467))) ) )
      | ~ class_Orderings_Oorder(U_12465) ),
    inference(variable_rename,[status(thm)],[f_3230_1]) ).

fof(f_3230_3,plain,
    ( ! [U_12467,U_12465,U_12466] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12466)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12465),U_12467),U_12466))
        | ~ sP931(U_12467,U_12465,U_12466) )
    & ! [U_12467,U_12465,U_12466] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12465),U_12467),U_12466))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12466)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12467)))
        | ~ sP931(U_12467,U_12465,U_12466) )
    & ! [U_12467,U_12465,U_12466] :
        ( sP931(U_12467,U_12465,U_12466)
        | ~ class_Orderings_Oorder(U_12465) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP931])],[f_3230_2]) ).

cnf(f_3230_4,plain,
    ( sP931(U_12467,U_12465,U_12466)
    | ~ class_Orderings_Oorder(U_12465) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

cnf(f_3230_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12465),U_12467),U_12466))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12466)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12467)))
    | ~ sP931(U_12467,U_12465,U_12466) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

cnf(f_3230_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12466)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12465),U_12467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12465),U_12467),U_12466))
    | ~ sP931(U_12467,U_12465,U_12466) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

fof(f_3231_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__atLeast]) ).

fof(f_3231_2,plain,
    ! [U_12469,U_12468] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12468,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12468),U_12469)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12468),U_12469)
      | ~ class_Orderings_Olinorder(U_12468) ),
    inference(variable_rename,[status(thm)],[f_3231_1]) ).

fof(f_3231_3,plain,
    ! [U_12468,U_12469] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12468,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12468),U_12469)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12468),U_12469)
      | ~ class_Orderings_Olinorder(U_12468) ),
    inference(definitional_conversion,[status(esa)],[f_3231_2]) ).

cnf(f_3231_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12468,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12468),U_12469)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12468),U_12469)
    | ~ class_Orderings_Olinorder(U_12468) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

fof(f_3232_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__lessThan]) ).

fof(f_3232_2,plain,
    ! [U_12471,U_12470] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12470,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12470),U_12471)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12470),U_12471)
      | ~ class_Orderings_Olinorder(U_12470) ),
    inference(variable_rename,[status(thm)],[f_3232_1]) ).

fof(f_3232_3,plain,
    ! [U_12470,U_12471] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12470,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12470),U_12471)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12470),U_12471)
      | ~ class_Orderings_Olinorder(U_12470) ),
    inference(definitional_conversion,[status(esa)],[f_3232_2]) ).

cnf(f_3232_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12470,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12470),U_12471)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12470),U_12471)
    | ~ class_Orderings_Olinorder(U_12470) ),
    inference(clausify,[status(thm)],[f_3232_3]) ).

fof(f_3233_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J]) ).

fof(f_3233_2,plain,
    ! [U_12474,U_12473,U_12472] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12472,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12472,U_12473),U_12474)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12472),U_12474)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12472),U_12473)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12472),U_12473),U_12474))
      | ~ class_Orderings_Olinorder(U_12472) ),
    inference(variable_rename,[status(thm)],[f_3233_1]) ).

fof(f_3233_3,plain,
    ! [U_12472,U_12473,U_12474] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12472,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12472,U_12473),U_12474)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12472),U_12474)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12472),U_12473)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12472),U_12473),U_12474))
      | ~ class_Orderings_Olinorder(U_12472) ),
    inference(definitional_conversion,[status(esa)],[f_3233_2]) ).

cnf(f_3233_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12472,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12472,U_12473),U_12474)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12472),U_12474)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12472),U_12473)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12472),U_12473),U_12474))
    | ~ class_Orderings_Olinorder(U_12472) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

fof(f_3234_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J]) ).

fof(f_3234_2,plain,
    ! [U_12477,U_12476,U_12475] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12475,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12475,U_12476),U_12477)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12475),U_12477)) = c_Orderings_Obot__class_Obot(tc_fun(U_12475,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12475) ),
    inference(variable_rename,[status(thm)],[f_3234_1]) ).

fof(f_3234_3,plain,
    ! [U_12475,U_12476,U_12477] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12475,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12475,U_12476),U_12477)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12475),U_12477)) = c_Orderings_Obot__class_Obot(tc_fun(U_12475,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12475) ),
    inference(definitional_conversion,[status(esa)],[f_3234_2]) ).

cnf(f_3234_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12475,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12475,U_12476),U_12477)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12475),U_12477)) = c_Orderings_Obot__class_Obot(tc_fun(U_12475,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12475) ),
    inference(clausify,[status(thm)],[f_3234_3]) ).

fof(f_3235_1,plain,
    ! [V_d_2,V_c_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).

fof(f_3235_2,plain,
    ! [U_12481,U_12480,U_12479,U_12478] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12478,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12478),U_12479)),c_SetInterval_Oord__class_OatLeastAtMost(U_12478,U_12480,U_12481)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12478,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12478),U_12479),U_12480),U_12481)
      | ~ class_Orderings_Olinorder(U_12478) ),
    inference(variable_rename,[status(thm)],[f_3235_1]) ).

fof(f_3235_3,plain,
    ! [U_12478,U_12479,U_12480,U_12481] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12478,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12478),U_12479)),c_SetInterval_Oord__class_OatLeastAtMost(U_12478,U_12480,U_12481)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12478,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12478),U_12479),U_12480),U_12481)
      | ~ class_Orderings_Olinorder(U_12478) ),
    inference(definitional_conversion,[status(esa)],[f_3235_2]) ).

cnf(f_3235_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12478,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12478),U_12479)),c_SetInterval_Oord__class_OatLeastAtMost(U_12478,U_12480,U_12481)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12478,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12478),U_12479),U_12480),U_12481)
    | ~ class_Orderings_Olinorder(U_12478) ),
    inference(clausify,[status(thm)],[f_3235_3]) ).

fof(f_3236_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).

fof(f_3236_2,plain,
    ! [U_12485,U_12484,U_12483,U_12482] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12482,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12482,U_12483,U_12484)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12482),U_12485)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12482,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12482),U_12483),U_12485),U_12484)
      | ~ class_Orderings_Olinorder(U_12482) ),
    inference(variable_rename,[status(thm)],[f_3236_1]) ).

fof(f_3236_3,plain,
    ! [U_12482,U_12483,U_12484,U_12485] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12482,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12482,U_12483,U_12484)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12482),U_12485)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12482,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12482),U_12483),U_12485),U_12484)
      | ~ class_Orderings_Olinorder(U_12482) ),
    inference(definitional_conversion,[status(esa)],[f_3236_2]) ).

cnf(f_3236_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12482,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12482,U_12483,U_12484)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12482),U_12485)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12482,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12482),U_12483),U_12485),U_12484)
    | ~ class_Orderings_Olinorder(U_12482) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

fof(f_3237_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J]) ).

fof(f_3237_2,plain,
    ! [U_12488,U_12487,U_12486] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12486,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12486,U_12487,U_12488)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12486),U_12488)) = c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12486) ),
    inference(variable_rename,[status(thm)],[f_3237_1]) ).

fof(f_3237_3,plain,
    ! [U_12486,U_12487,U_12488] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12486,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12486,U_12487,U_12488)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12486),U_12488)) = c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12486) ),
    inference(definitional_conversion,[status(esa)],[f_3237_2]) ).

cnf(f_3237_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12486,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12486,U_12487,U_12488)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12486),U_12488)) = c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12486) ),
    inference(clausify,[status(thm)],[f_3237_3]) ).

fof(f_3238_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast]) ).

fof(f_3238_2,plain,
    ! [U_12490,U_12489] :
      ( hAPP(c_Set_Oimage(U_12489,U_12489,c_Groups_Ouminus__class_Ouminus(U_12489)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12489),U_12490)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12489),hAPP(c_Groups_Ouminus__class_Ouminus(U_12489),U_12490))
      | ~ class_Groups_Oordered__ab__group__add(U_12489) ),
    inference(variable_rename,[status(thm)],[f_3238_1]) ).

fof(f_3238_3,plain,
    ! [U_12489,U_12490] :
      ( hAPP(c_Set_Oimage(U_12489,U_12489,c_Groups_Ouminus__class_Ouminus(U_12489)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12489),U_12490)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12489),hAPP(c_Groups_Ouminus__class_Ouminus(U_12489),U_12490))
      | ~ class_Groups_Oordered__ab__group__add(U_12489) ),
    inference(definitional_conversion,[status(esa)],[f_3238_2]) ).

cnf(f_3238_4,plain,
    ( hAPP(c_Set_Oimage(U_12489,U_12489,c_Groups_Ouminus__class_Ouminus(U_12489)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12489),U_12490)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12489),hAPP(c_Groups_Ouminus__class_Ouminus(U_12489),U_12490))
    | ~ class_Groups_Oordered__ab__group__add(U_12489) ),
    inference(clausify,[status(thm)],[f_3238_3]) ).

fof(f_3239_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost]) ).

fof(f_3239_2,plain,
    ! [U_12492,U_12491] :
      ( hAPP(c_Set_Oimage(U_12491,U_12491,c_Groups_Ouminus__class_Ouminus(U_12491)),hAPP(c_SetInterval_Oord__class_OatMost(U_12491),U_12492)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12491),hAPP(c_Groups_Ouminus__class_Ouminus(U_12491),U_12492))
      | ~ class_Groups_Oordered__ab__group__add(U_12491) ),
    inference(variable_rename,[status(thm)],[f_3239_1]) ).

fof(f_3239_3,plain,
    ! [U_12491,U_12492] :
      ( hAPP(c_Set_Oimage(U_12491,U_12491,c_Groups_Ouminus__class_Ouminus(U_12491)),hAPP(c_SetInterval_Oord__class_OatMost(U_12491),U_12492)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12491),hAPP(c_Groups_Ouminus__class_Ouminus(U_12491),U_12492))
      | ~ class_Groups_Oordered__ab__group__add(U_12491) ),
    inference(definitional_conversion,[status(esa)],[f_3239_2]) ).

cnf(f_3239_4,plain,
    ( hAPP(c_Set_Oimage(U_12491,U_12491,c_Groups_Ouminus__class_Ouminus(U_12491)),hAPP(c_SetInterval_Oord__class_OatMost(U_12491),U_12492)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12491),hAPP(c_Groups_Ouminus__class_Ouminus(U_12491),U_12492))
    | ~ class_Groups_Oordered__ab__group__add(U_12491) ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

fof(f_3240_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_atLeast__Suc]) ).

fof(f_3240_2,plain,
    ! [U_12493] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_12493)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12493),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3240_1]) ).

fof(f_3240_3,plain,
    ! [U_12493] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_12493)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12493),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3240_2]) ).

cnf(f_3240_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_12493)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12493),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3240_3]) ).

fof(f_3241_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J]) ).

fof(f_3241_2,plain,
    ! [U_12496,U_12495,U_12494] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12494,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12494,U_12495,U_12496)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12494),U_12496)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12494),U_12495)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12494),U_12495),U_12496))
      | ~ class_Orderings_Olinorder(U_12494) ),
    inference(variable_rename,[status(thm)],[f_3241_1]) ).

fof(f_3241_3,plain,
    ! [U_12494,U_12495,U_12496] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12494,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12494,U_12495,U_12496)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12494),U_12496)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12494),U_12495)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12494),U_12495),U_12496))
      | ~ class_Orderings_Olinorder(U_12494) ),
    inference(definitional_conversion,[status(esa)],[f_3241_2]) ).

cnf(f_3241_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12494,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12494,U_12495,U_12496)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12494),U_12496)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12494),U_12495)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12494),U_12495),U_12496))
    | ~ class_Orderings_Olinorder(U_12494) ),
    inference(clausify,[status(thm)],[f_3241_3]) ).

fof(f_3242_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J]) ).

fof(f_3242_2,plain,
    ! [U_12499,U_12498,U_12497] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12497,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12497,U_12498,U_12499)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12497),U_12499)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12497),U_12498)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12497),U_12498),U_12499))
      | ~ class_Orderings_Olinorder(U_12497) ),
    inference(variable_rename,[status(thm)],[f_3242_1]) ).

fof(f_3242_3,plain,
    ! [U_12497,U_12498,U_12499] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12497,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12497,U_12498,U_12499)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12497),U_12499)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12497),U_12498)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12497),U_12498),U_12499))
      | ~ class_Orderings_Olinorder(U_12497) ),
    inference(definitional_conversion,[status(esa)],[f_3242_2]) ).

cnf(f_3242_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12497,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12497,U_12498,U_12499)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12497),U_12499)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12497),U_12498)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12497),U_12498),U_12499))
    | ~ class_Orderings_Olinorder(U_12497) ),
    inference(clausify,[status(thm)],[f_3242_3]) ).

fof(f_3243_1,plain,
    ! [V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).

fof(f_3243_2,plain,
    ! [U_12501,U_12500] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12500),U_12501),c_Orderings_Obot__class_Obot(tc_fun(U_12500,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12500),U_12501)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12500),U_12501)
      | ~ class_Orderings_Olinorder(U_12500) ),
    inference(variable_rename,[status(thm)],[f_3243_1]) ).

fof(f_3243_3,plain,
    ! [U_12500,U_12501] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12500),U_12501),c_Orderings_Obot__class_Obot(tc_fun(U_12500,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12500),U_12501)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12500),U_12501)
      | ~ class_Orderings_Olinorder(U_12500) ),
    inference(definitional_conversion,[status(esa)],[f_3243_2]) ).

cnf(f_3243_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12500),U_12501),c_Orderings_Obot__class_Obot(tc_fun(U_12500,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12500),U_12501)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12500),U_12501)
    | ~ class_Orderings_Olinorder(U_12500) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

fof(f_3244_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2),
    inference(fof_nnf,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).

fof(f_3244_2,plain,
    ! [U_12502] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12502)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12502),
    inference(variable_rename,[status(thm)],[f_3244_1]) ).

fof(f_3244_3,plain,
    ! [U_12502] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12502)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12502),
    inference(definitional_conversion,[status(esa)],[f_3244_2]) ).

cnf(f_3244_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12502)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12502),
    inference(clausify,[status(thm)],[f_3244_3]) ).

fof(f_3245_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff]) ).

fof(f_3245_2,plain,
    ! [U_12505,U_12504,U_12503] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12504) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12505)
          | U_12504 != U_12505 )
        & ( U_12504 = U_12505
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12504) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12505) ) )
      | ~ class_Orderings_Olinorder(U_12503) ),
    inference(variable_rename,[status(thm)],[f_3245_1]) ).

fof(f_3245_3,plain,
    ( ! [U_12503,U_12504,U_12505] :
        ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12504) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12505)
        | U_12504 != U_12505
        | ~ sP932(U_12503,U_12504,U_12505) )
    & ! [U_12503,U_12504,U_12505] :
        ( U_12504 = U_12505
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12504) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12505)
        | ~ sP932(U_12503,U_12504,U_12505) )
    & ! [U_12503,U_12504,U_12505] :
        ( sP932(U_12503,U_12504,U_12505)
        | ~ class_Orderings_Olinorder(U_12503) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP932])],[f_3245_2]) ).

cnf(f_3245_4,plain,
    ( sP932(U_12503,U_12504,U_12505)
    | ~ class_Orderings_Olinorder(U_12503) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

cnf(f_3245_5,plain,
    ( U_12504 = U_12505
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12504) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12505)
    | ~ sP932(U_12503,U_12504,U_12505) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

cnf(f_3245_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12504) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12503),U_12505)
    | U_12504 != U_12505
    | ~ sP932(U_12503,U_12504,U_12505) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

fof(f_3246_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__iff]) ).

fof(f_3246_2,plain,
    ! [U_12508,U_12507,U_12506] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12506),U_12507),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12506),U_12508)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12506),U_12508),U_12507)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12506),U_12508),U_12507))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12507),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12506),U_12508))) ) )
      | ~ class_Orderings_Oord(U_12506) ),
    inference(variable_rename,[status(thm)],[f_3246_1]) ).

fof(f_3246_3,plain,
    ( ! [U_12507,U_12506,U_12508] :
        ( hBOOL(hAPP(hAPP(c_member(U_12506),U_12507),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12506),U_12508)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12506),U_12508),U_12507))
        | ~ sP933(U_12507,U_12506,U_12508) )
    & ! [U_12507,U_12506,U_12508] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12506),U_12508),U_12507))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12507),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12506),U_12508)))
        | ~ sP933(U_12507,U_12506,U_12508) )
    & ! [U_12507,U_12506,U_12508] :
        ( sP933(U_12507,U_12506,U_12508)
        | ~ class_Orderings_Oord(U_12506) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP933])],[f_3246_2]) ).

cnf(f_3246_4,plain,
    ( sP933(U_12507,U_12506,U_12508)
    | ~ class_Orderings_Oord(U_12506) ),
    inference(clausify,[status(thm)],[f_3246_3]) ).

cnf(f_3246_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12506),U_12508),U_12507))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12507),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12506),U_12508)))
    | ~ sP933(U_12507,U_12506,U_12508) ),
    inference(clausify,[status(thm)],[f_3246_3]) ).

cnf(f_3246_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12506),U_12507),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12506),U_12508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12506),U_12508),U_12507))
    | ~ sP933(U_12507,U_12506,U_12508) ),
    inference(clausify,[status(thm)],[f_3246_3]) ).

fof(f_3247_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff]) ).

fof(f_3247_2,plain,
    ! [U_12511,U_12510,U_12509] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12509,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12510)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12511)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),U_12511),U_12510)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),U_12511),U_12510))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12509,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12510)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12511))) ) )
      | ~ class_Orderings_Olinorder(U_12509) ),
    inference(variable_rename,[status(thm)],[f_3247_1]) ).

fof(f_3247_3,plain,
    ( ! [U_12510,U_12511,U_12509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12509,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12510)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12511)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),U_12511),U_12510))
        | ~ sP934(U_12510,U_12511,U_12509) )
    & ! [U_12510,U_12511,U_12509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),U_12511),U_12510))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12509,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12510)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12511)))
        | ~ sP934(U_12510,U_12511,U_12509) )
    & ! [U_12510,U_12511,U_12509] :
        ( sP934(U_12510,U_12511,U_12509)
        | ~ class_Orderings_Olinorder(U_12509) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP934])],[f_3247_2]) ).

cnf(f_3247_4,plain,
    ( sP934(U_12510,U_12511,U_12509)
    | ~ class_Orderings_Olinorder(U_12509) ),
    inference(clausify,[status(thm)],[f_3247_3]) ).

cnf(f_3247_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),U_12511),U_12510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12509,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12510)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12511)))
    | ~ sP934(U_12510,U_12511,U_12509) ),
    inference(clausify,[status(thm)],[f_3247_3]) ).

cnf(f_3247_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12509,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12510)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12509),U_12511)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),U_12511),U_12510))
    | ~ sP934(U_12510,U_12511,U_12509) ),
    inference(clausify,[status(thm)],[f_3247_3]) ).

fof(f_3248_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan]) ).

fof(f_3248_2,plain,
    ! [U_12513,U_12512] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12512,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12512),U_12513)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12512),U_12513)
      | ~ class_Orderings_Olinorder(U_12512) ),
    inference(variable_rename,[status(thm)],[f_3248_1]) ).

fof(f_3248_3,plain,
    ! [U_12513,U_12512] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12512,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12512),U_12513)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12512),U_12513)
      | ~ class_Orderings_Olinorder(U_12512) ),
    inference(definitional_conversion,[status(esa)],[f_3248_2]) ).

cnf(f_3248_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12512,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12512),U_12513)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12512),U_12513)
    | ~ class_Orderings_Olinorder(U_12512) ),
    inference(clausify,[status(thm)],[f_3248_3]) ).

fof(f_3249_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__atMost]) ).

fof(f_3249_2,plain,
    ! [U_12515,U_12514] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12514,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12514),U_12515)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12514),U_12515)
      | ~ class_Orderings_Olinorder(U_12514) ),
    inference(variable_rename,[status(thm)],[f_3249_1]) ).

fof(f_3249_3,plain,
    ! [U_12514,U_12515] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12514,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12514),U_12515)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12514),U_12515)
      | ~ class_Orderings_Olinorder(U_12514) ),
    inference(definitional_conversion,[status(esa)],[f_3249_2]) ).

cnf(f_3249_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12514,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12514),U_12515)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12514),U_12515)
    | ~ class_Orderings_Olinorder(U_12514) ),
    inference(clausify,[status(thm)],[f_3249_3]) ).

fof(f_3250_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J]) ).

fof(f_3250_2,plain,
    ! [U_12518,U_12517,U_12516] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12516,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12516,U_12517,U_12518)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12516),U_12518)) = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12516) ),
    inference(variable_rename,[status(thm)],[f_3250_1]) ).

fof(f_3250_3,plain,
    ! [U_12516,U_12517,U_12518] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12516,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12516,U_12517,U_12518)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12516),U_12518)) = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12516) ),
    inference(definitional_conversion,[status(esa)],[f_3250_2]) ).

cnf(f_3250_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12516,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12516,U_12517,U_12518)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12516),U_12518)) = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12516) ),
    inference(clausify,[status(thm)],[f_3250_3]) ).

fof(f_3251_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J]) ).

fof(f_3251_2,plain,
    ! [U_12521,U_12520,U_12519] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12519,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12519,U_12520,U_12521)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12519),U_12521)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12519),U_12520)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12519),U_12520),U_12521))
      | ~ class_Orderings_Olinorder(U_12519) ),
    inference(variable_rename,[status(thm)],[f_3251_1]) ).

fof(f_3251_3,plain,
    ! [U_12519,U_12520,U_12521] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12519,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12519,U_12520,U_12521)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12519),U_12521)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12519),U_12520)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12519),U_12520),U_12521))
      | ~ class_Orderings_Olinorder(U_12519) ),
    inference(definitional_conversion,[status(esa)],[f_3251_2]) ).

cnf(f_3251_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12519,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12519,U_12520,U_12521)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12519),U_12521)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12519),U_12520)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12519),U_12520),U_12521))
    | ~ class_Orderings_Olinorder(U_12519) ),
    inference(clausify,[status(thm)],[f_3251_3]) ).

fof(f_3252_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan]) ).

fof(f_3252_2,plain,
    ! [U_12523,U_12522] :
      ( hAPP(c_Set_Oimage(U_12522,U_12522,c_Groups_Ouminus__class_Ouminus(U_12522)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12522),U_12523)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12522),hAPP(c_Groups_Ouminus__class_Ouminus(U_12522),U_12523))
      | ~ class_Groups_Oordered__ab__group__add(U_12522) ),
    inference(variable_rename,[status(thm)],[f_3252_1]) ).

fof(f_3252_3,plain,
    ! [U_12522,U_12523] :
      ( hAPP(c_Set_Oimage(U_12522,U_12522,c_Groups_Ouminus__class_Ouminus(U_12522)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12522),U_12523)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12522),hAPP(c_Groups_Ouminus__class_Ouminus(U_12522),U_12523))
      | ~ class_Groups_Oordered__ab__group__add(U_12522) ),
    inference(definitional_conversion,[status(esa)],[f_3252_2]) ).

cnf(f_3252_4,plain,
    ( hAPP(c_Set_Oimage(U_12522,U_12522,c_Groups_Ouminus__class_Ouminus(U_12522)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12522),U_12523)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12522),hAPP(c_Groups_Ouminus__class_Ouminus(U_12522),U_12523))
    | ~ class_Groups_Oordered__ab__group__add(U_12522) ),
    inference(clausify,[status(thm)],[f_3252_3]) ).

fof(f_3253_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan]) ).

fof(f_3253_2,plain,
    ! [U_12525,U_12524] :
      ( hAPP(c_Set_Oimage(U_12524,U_12524,c_Groups_Ouminus__class_Ouminus(U_12524)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12524),U_12525)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12524),hAPP(c_Groups_Ouminus__class_Ouminus(U_12524),U_12525))
      | ~ class_Groups_Oordered__ab__group__add(U_12524) ),
    inference(variable_rename,[status(thm)],[f_3253_1]) ).

fof(f_3253_3,plain,
    ! [U_12524,U_12525] :
      ( hAPP(c_Set_Oimage(U_12524,U_12524,c_Groups_Ouminus__class_Ouminus(U_12524)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12524),U_12525)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12524),hAPP(c_Groups_Ouminus__class_Ouminus(U_12524),U_12525))
      | ~ class_Groups_Oordered__ab__group__add(U_12524) ),
    inference(definitional_conversion,[status(esa)],[f_3253_2]) ).

cnf(f_3253_4,plain,
    ( hAPP(c_Set_Oimage(U_12524,U_12524,c_Groups_Ouminus__class_Ouminus(U_12524)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12524),U_12525)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12524),hAPP(c_Groups_Ouminus__class_Ouminus(U_12524),U_12525))
    | ~ class_Groups_Oordered__ab__group__add(U_12524) ),
    inference(clausify,[status(thm)],[f_3253_3]) ).

fof(f_3254_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J]) ).

fof(f_3254_2,plain,
    ! [U_12528,U_12527,U_12526] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12526,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12526,U_12527,U_12528)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12526),U_12528)) = c_Orderings_Obot__class_Obot(tc_fun(U_12526,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12526) ),
    inference(variable_rename,[status(thm)],[f_3254_1]) ).

fof(f_3254_3,plain,
    ! [U_12526,U_12527,U_12528] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12526,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12526,U_12527,U_12528)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12526),U_12528)) = c_Orderings_Obot__class_Obot(tc_fun(U_12526,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12526) ),
    inference(definitional_conversion,[status(esa)],[f_3254_2]) ).

cnf(f_3254_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12526,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12526,U_12527,U_12528)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12526),U_12528)) = c_Orderings_Obot__class_Obot(tc_fun(U_12526,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12526) ),
    inference(clausify,[status(thm)],[f_3254_3]) ).

fof(f_3255_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__Suc]) ).

fof(f_3255_2,plain,
    ! [U_12529] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12529)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12529)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12529)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3255_1]) ).

fof(f_3255_3,plain,
    ! [U_12529] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12529)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12529)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12529)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3255_2]) ).

cnf(f_3255_4,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12529)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12529)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12529)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3255_3]) ).

fof(f_3256_1,plain,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | V_A_2 != V_B_2
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J]) ).

fof(f_3256_2,plain,
    ! [U_12535,U_12534,U_12533,U_12532,U_12531] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12534),U_12532) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12535),U_12533)
      | ? [U_12530] :
          ( hAPP(U_12534,U_12530) != hAPP(U_12535,U_12530)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12530)) )
      | ~ c_Nat__Transfer_Onat__set(U_12533)
      | U_12532 != U_12533
      | ~ class_Groups_Ocomm__monoid__mult(U_12531)
      | ~ class_Groups_Ocomm__monoid__add(U_12531) ),
    inference(variable_rename,[status(thm)],[f_3256_1]) ).

fof(f_3256_3,plain,
    ! [U_12535,U_12534,U_12533,U_12532,U_12531] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12534),U_12532) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12535),U_12533)
      | ( hAPP(U_12534,sK270(U_12535,U_12534,U_12533,U_12532,U_12531)) != hAPP(U_12535,sK270(U_12535,U_12534,U_12533,U_12532,U_12531))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK270(U_12535,U_12534,U_12533,U_12532,U_12531))) )
      | ~ c_Nat__Transfer_Onat__set(U_12533)
      | U_12532 != U_12533
      | ~ class_Groups_Ocomm__monoid__mult(U_12531)
      | ~ class_Groups_Ocomm__monoid__add(U_12531) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_12530,sK270(U_12535,U_12534,U_12533,U_12532,U_12531))],[f_3256_2]) ).

fof(f_3256_4,plain,
    ( ! [U_12531,U_12532,U_12533,U_12534,U_12535] :
        ( hAPP(U_12534,sK270(U_12535,U_12534,U_12533,U_12532,U_12531)) != hAPP(U_12535,sK270(U_12535,U_12534,U_12533,U_12532,U_12531))
        | ~ sP935(U_12531,U_12532,U_12533,U_12534,U_12535) )
    & ! [U_12531,U_12532,U_12533,U_12534,U_12535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK270(U_12535,U_12534,U_12533,U_12532,U_12531)))
        | ~ sP935(U_12531,U_12532,U_12533,U_12534,U_12535) )
    & ! [U_12531,U_12532,U_12533,U_12534,U_12535] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12534),U_12532) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12535),U_12533)
        | sP935(U_12531,U_12532,U_12533,U_12534,U_12535)
        | ~ c_Nat__Transfer_Onat__set(U_12533)
        | U_12532 != U_12533
        | ~ class_Groups_Ocomm__monoid__mult(U_12531)
        | ~ class_Groups_Ocomm__monoid__add(U_12531) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP935])],[f_3256_3]) ).

cnf(f_3256_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12534),U_12532) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12531),U_12535),U_12533)
    | sP935(U_12531,U_12532,U_12533,U_12534,U_12535)
    | ~ c_Nat__Transfer_Onat__set(U_12533)
    | U_12532 != U_12533
    | ~ class_Groups_Ocomm__monoid__mult(U_12531)
    | ~ class_Groups_Ocomm__monoid__add(U_12531) ),
    inference(clausify,[status(thm)],[f_3256_4]) ).

cnf(f_3256_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK270(U_12535,U_12534,U_12533,U_12532,U_12531)))
    | ~ sP935(U_12531,U_12532,U_12533,U_12534,U_12535) ),
    inference(clausify,[status(thm)],[f_3256_4]) ).

cnf(f_3256_7,plain,
    ( hAPP(U_12534,sK270(U_12535,U_12534,U_12533,U_12532,U_12531)) != hAPP(U_12535,sK270(U_12535,U_12534,U_12533,U_12532,U_12531))
    | ~ sP935(U_12531,U_12532,U_12533,U_12534,U_12535) ),
    inference(clausify,[status(thm)],[f_3256_4]) ).

fof(f_3257_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( ( c_Map_Odom(T_b,T_c,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | ! [B_v] : V_f_2 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) )
      & ( ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v))
        | c_Map_Odom(T_b,T_c,V_f_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dom__eq__singleton__conv]) ).

fof(f_3257_2,plain,
    ! [U_12541,U_12540,U_12539,U_12538] :
      ( ( c_Map_Odom(U_12538,U_12539,U_12540) = hAPP(hAPP(c_Set_Oinsert(U_12538),U_12541),c_Orderings_Obot__class_Obot(tc_fun(U_12538,tc_HOL_Obool)))
        | ! [U_12537] : U_12540 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12538,tc_Option_Ooption(U_12539)),hAPP(c_COMBK(tc_Option_Ooption(U_12539),U_12538),c_Option_Ooption_ONone(U_12539))),U_12541),hAPP(c_Option_Ooption_OSome(U_12539),U_12537)) )
      & ( ? [U_12536] : U_12540 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12538,tc_Option_Ooption(U_12539)),hAPP(c_COMBK(tc_Option_Ooption(U_12539),U_12538),c_Option_Ooption_ONone(U_12539))),U_12541),hAPP(c_Option_Ooption_OSome(U_12539),U_12536))
        | c_Map_Odom(U_12538,U_12539,U_12540) != hAPP(hAPP(c_Set_Oinsert(U_12538),U_12541),c_Orderings_Obot__class_Obot(tc_fun(U_12538,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_3257_1]) ).

fof(f_3257_3,plain,
    ( ! [U_12549,U_12547,U_12545,U_12543] :
        ( c_Map_Odom(U_12543,U_12545,U_12547) = hAPP(hAPP(c_Set_Oinsert(U_12543),U_12549),c_Orderings_Obot__class_Obot(tc_fun(U_12543,tc_HOL_Obool)))
        | ! [U_12537] : U_12547 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12543,tc_Option_Ooption(U_12545)),hAPP(c_COMBK(tc_Option_Ooption(U_12545),U_12543),c_Option_Ooption_ONone(U_12545))),U_12549),hAPP(c_Option_Ooption_OSome(U_12545),U_12537)) )
    & ! [U_12548,U_12546,U_12544,U_12542] :
        ( ? [U_12536] : U_12546 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12542,tc_Option_Ooption(U_12544)),hAPP(c_COMBK(tc_Option_Ooption(U_12544),U_12542),c_Option_Ooption_ONone(U_12544))),U_12548),hAPP(c_Option_Ooption_OSome(U_12544),U_12536))
        | c_Map_Odom(U_12542,U_12544,U_12546) != hAPP(hAPP(c_Set_Oinsert(U_12542),U_12548),c_Orderings_Obot__class_Obot(tc_fun(U_12542,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_3257_2]) ).

fof(f_3257_4,plain,
    ( ! [U_12549,U_12547,U_12545,U_12543] :
        ( c_Map_Odom(U_12543,U_12545,U_12547) = hAPP(hAPP(c_Set_Oinsert(U_12543),U_12549),c_Orderings_Obot__class_Obot(tc_fun(U_12543,tc_HOL_Obool)))
        | ! [U_12537] : U_12547 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12543,tc_Option_Ooption(U_12545)),hAPP(c_COMBK(tc_Option_Ooption(U_12545),U_12543),c_Option_Ooption_ONone(U_12545))),U_12549),hAPP(c_Option_Ooption_OSome(U_12545),U_12537)) )
    & ! [U_12548,U_12546,U_12544,U_12542] :
        ( U_12546 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12542,tc_Option_Ooption(U_12544)),hAPP(c_COMBK(tc_Option_Ooption(U_12544),U_12542),c_Option_Ooption_ONone(U_12544))),U_12548),hAPP(c_Option_Ooption_OSome(U_12544),sK271(U_12548,U_12546,U_12544,U_12542)))
        | c_Map_Odom(U_12542,U_12544,U_12546) != hAPP(hAPP(c_Set_Oinsert(U_12542),U_12548),c_Orderings_Obot__class_Obot(tc_fun(U_12542,tc_HOL_Obool))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_12536,sK271(U_12548,U_12546,U_12544,U_12542))],[f_3257_3]) ).

fof(f_3257_5,plain,
    ( ! [U_12537,U_12547,U_12543,U_12545,U_12549] :
        ( c_Map_Odom(U_12543,U_12545,U_12547) = hAPP(hAPP(c_Set_Oinsert(U_12543),U_12549),c_Orderings_Obot__class_Obot(tc_fun(U_12543,tc_HOL_Obool)))
        | U_12547 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12543,tc_Option_Ooption(U_12545)),hAPP(c_COMBK(tc_Option_Ooption(U_12545),U_12543),c_Option_Ooption_ONone(U_12545))),U_12549),hAPP(c_Option_Ooption_OSome(U_12545),U_12537)) )
    & ! [U_12544,U_12548,U_12542,U_12546] :
        ( U_12546 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12542,tc_Option_Ooption(U_12544)),hAPP(c_COMBK(tc_Option_Ooption(U_12544),U_12542),c_Option_Ooption_ONone(U_12544))),U_12548),hAPP(c_Option_Ooption_OSome(U_12544),sK271(U_12548,U_12546,U_12544,U_12542)))
        | c_Map_Odom(U_12542,U_12544,U_12546) != hAPP(hAPP(c_Set_Oinsert(U_12542),U_12548),c_Orderings_Obot__class_Obot(tc_fun(U_12542,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3257_4]) ).

cnf(f_3257_6,plain,
    ( U_12546 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12542,tc_Option_Ooption(U_12544)),hAPP(c_COMBK(tc_Option_Ooption(U_12544),U_12542),c_Option_Ooption_ONone(U_12544))),U_12548),hAPP(c_Option_Ooption_OSome(U_12544),sK271(U_12548,U_12546,U_12544,U_12542)))
    | c_Map_Odom(U_12542,U_12544,U_12546) != hAPP(hAPP(c_Set_Oinsert(U_12542),U_12548),c_Orderings_Obot__class_Obot(tc_fun(U_12542,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3257_5]) ).

cnf(f_3257_7,plain,
    ( c_Map_Odom(U_12543,U_12545,U_12547) = hAPP(hAPP(c_Set_Oinsert(U_12543),U_12549),c_Orderings_Obot__class_Obot(tc_fun(U_12543,tc_HOL_Obool)))
    | U_12547 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12543,tc_Option_Ooption(U_12545)),hAPP(c_COMBK(tc_Option_Ooption(U_12545),U_12543),c_Option_Ooption_ONone(U_12545))),U_12549),hAPP(c_Option_Ooption_OSome(U_12545),U_12537)) ),
    inference(clausify,[status(thm)],[f_3257_5]) ).

fof(f_3258_1,plain,
    ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(f_3258_2,plain,
    ! [U_12554,U_12553,U_12552,U_12551,U_12550] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12550,U_12550,c_Groups_Otimes__class_Otimes(U_12550),U_12554,hAPP(hAPP(c_Set_Oinsert(U_12550),U_12551),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12550,tc_HOL_Obool)),U_12552),hAPP(hAPP(c_Set_Oinsert(U_12550),U_12554),c_Orderings_Obot__class_Obot(tc_fun(U_12550,tc_HOL_Obool)))))),U_12553))
      | hBOOL(hAPP(hAPP(c_member(U_12550),U_12551),U_12552))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12550),U_12554),U_12552))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12550,U_12550,c_Groups_Otimes__class_Otimes(U_12550),U_12551,U_12552),U_12553))
      | ~ class_Groups_Oab__semigroup__mult(U_12550) ),
    inference(variable_rename,[status(thm)],[f_3258_1]) ).

fof(f_3258_3,plain,
    ! [U_12550,U_12551,U_12552,U_12553,U_12554] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12550,U_12550,c_Groups_Otimes__class_Otimes(U_12550),U_12554,hAPP(hAPP(c_Set_Oinsert(U_12550),U_12551),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12550,tc_HOL_Obool)),U_12552),hAPP(hAPP(c_Set_Oinsert(U_12550),U_12554),c_Orderings_Obot__class_Obot(tc_fun(U_12550,tc_HOL_Obool)))))),U_12553))
      | hBOOL(hAPP(hAPP(c_member(U_12550),U_12551),U_12552))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12550),U_12554),U_12552))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12550,U_12550,c_Groups_Otimes__class_Otimes(U_12550),U_12551,U_12552),U_12553))
      | ~ class_Groups_Oab__semigroup__mult(U_12550) ),
    inference(definitional_conversion,[status(esa)],[f_3258_2]) ).

cnf(f_3258_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12550,U_12550,c_Groups_Otimes__class_Otimes(U_12550),U_12554,hAPP(hAPP(c_Set_Oinsert(U_12550),U_12551),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12550,tc_HOL_Obool)),U_12552),hAPP(hAPP(c_Set_Oinsert(U_12550),U_12554),c_Orderings_Obot__class_Obot(tc_fun(U_12550,tc_HOL_Obool)))))),U_12553))
    | hBOOL(hAPP(hAPP(c_member(U_12550),U_12551),U_12552))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12550),U_12554),U_12552))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12550,U_12550,c_Groups_Otimes__class_Otimes(U_12550),U_12551,U_12552),U_12553))
    | ~ class_Groups_Oab__semigroup__mult(U_12550) ),
    inference(clausify,[status(thm)],[f_3258_3]) ).

fof(f_3259_1,plain,
    ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( V_x_2 = V_z_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE]) ).

fof(f_3259_2,plain,
    ! [U_12559,U_12558,U_12557,U_12556,U_12555] :
      ( U_12559 = U_12558
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12555,U_12556,U_12557,U_12558,c_Orderings_Obot__class_Obot(tc_fun(U_12555,tc_HOL_Obool))),U_12559)) ),
    inference(variable_rename,[status(thm)],[f_3259_1]) ).

fof(f_3259_3,plain,
    ! [U_12559,U_12558] :
      ( ! [U_12557,U_12556,U_12555] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12555,U_12556,U_12557,U_12558,c_Orderings_Obot__class_Obot(tc_fun(U_12555,tc_HOL_Obool))),U_12559))
      | U_12559 = U_12558 ),
    inference(miniscope,[status(thm)],[f_3259_2]) ).

fof(f_3259_4,plain,
    ! [U_12556,U_12559,U_12557,U_12558,U_12555] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12555,U_12556,U_12557,U_12558,c_Orderings_Obot__class_Obot(tc_fun(U_12555,tc_HOL_Obool))),U_12559))
      | U_12559 = U_12558 ),
    inference(definitional_conversion,[status(esa)],[f_3259_3]) ).

cnf(f_3259_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12555,U_12556,U_12557,U_12558,c_Orderings_Obot__class_Obot(tc_fun(U_12555,tc_HOL_Obool))),U_12559))
    | U_12559 = U_12558 ),
    inference(clausify,[status(thm)],[f_3259_4]) ).

fof(f_3260_1,plain,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(f_3260_2,plain,
    ! [U_12563,U_12562,U_12561,U_12560] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12560,U_12561,U_12562,U_12563,c_Orderings_Obot__class_Obot(tc_fun(U_12560,tc_HOL_Obool))),U_12563)),
    inference(variable_rename,[status(thm)],[f_3260_1]) ).

fof(f_3260_3,plain,
    ! [U_12560,U_12561,U_12562,U_12563] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12560,U_12561,U_12562,U_12563,c_Orderings_Obot__class_Obot(tc_fun(U_12560,tc_HOL_Obool))),U_12563)),
    inference(definitional_conversion,[status(esa)],[f_3260_2]) ).

cnf(f_3260_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12560,U_12561,U_12562,U_12563,c_Orderings_Obot__class_Obot(tc_fun(U_12560,tc_HOL_Obool))),U_12563)),
    inference(clausify,[status(thm)],[f_3260_3]) ).

fof(f_3261_1,plain,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(f_3261_2,plain,
    ! [U_12567,U_12566,U_12565,U_12564] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12564,U_12565,U_12566,U_12567,c_Orderings_Obot__class_Obot(tc_fun(U_12564,tc_HOL_Obool))),U_12567)),
    inference(variable_rename,[status(thm)],[f_3261_1]) ).

fof(f_3261_3,plain,
    ! [U_12564,U_12565,U_12566,U_12567] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12564,U_12565,U_12566,U_12567,c_Orderings_Obot__class_Obot(tc_fun(U_12564,tc_HOL_Obool))),U_12567)),
    inference(definitional_conversion,[status(esa)],[f_3261_2]) ).

cnf(f_3261_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12564,U_12565,U_12566,U_12567,c_Orderings_Obot__class_Obot(tc_fun(U_12564,tc_HOL_Obool))),U_12567)),
    inference(clausify,[status(thm)],[f_3261_3]) ).

fof(f_3262_1,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
    inference(fof_nnf,[status(thm)],[fact_finite__dom__body]) ).

fof(f_3262_2,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
    inference(definitional_conversion,[status(esa)],[f_3262_1]) ).

cnf(f_3262_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
    inference(clausify,[status(thm)],[f_3262_2]) ).

fof(f_3263_1,plain,
    ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite]) ).

fof(f_3263_2,plain,
    ! [U_12573,U_12572,U_12571,U_12570,U_12569,U_12568] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12568),U_12572))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12568,U_12569,U_12570,U_12571,U_12572),U_12573)) ),
    inference(variable_rename,[status(thm)],[f_3263_1]) ).

fof(f_3263_3,plain,
    ! [U_12568,U_12569,U_12570,U_12571,U_12572,U_12573] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12568),U_12572))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12568,U_12569,U_12570,U_12571,U_12572),U_12573)) ),
    inference(definitional_conversion,[status(esa)],[f_3263_2]) ).

cnf(f_3263_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12568),U_12572))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12568,U_12569,U_12570,U_12571,U_12572),U_12573)) ),
    inference(clausify,[status(thm)],[f_3263_3]) ).

fof(f_3264_1,plain,
    ! [V_m_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
        | hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_c) )
      & ( hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_domIff]) ).

fof(f_3264_2,plain,
    ! [U_12577,U_12576,U_12575,U_12574] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12574),U_12575),c_Map_Odom(U_12574,U_12576,U_12577)))
        | hAPP(U_12577,U_12575) = c_Option_Ooption_ONone(U_12576) )
      & ( hAPP(U_12577,U_12575) != c_Option_Ooption_ONone(U_12576)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12574),U_12575),c_Map_Odom(U_12574,U_12576,U_12577))) ) ),
    inference(variable_rename,[status(thm)],[f_3264_1]) ).

fof(f_3264_3,plain,
    ( ! [U_12585,U_12583,U_12581] :
        ( ! [U_12579] : hBOOL(hAPP(hAPP(c_member(U_12579),U_12581),c_Map_Odom(U_12579,U_12583,U_12585)))
        | hAPP(U_12585,U_12581) = c_Option_Ooption_ONone(U_12583) )
    & ! [U_12584,U_12582,U_12580] :
        ( ! [U_12578] : ~ hBOOL(hAPP(hAPP(c_member(U_12578),U_12580),c_Map_Odom(U_12578,U_12582,U_12584)))
        | hAPP(U_12584,U_12580) != c_Option_Ooption_ONone(U_12582) ) ),
    inference(miniscope,[status(thm)],[f_3264_2]) ).

fof(f_3264_4,plain,
    ( ! [U_12579,U_12583,U_12585,U_12581] :
        ( hBOOL(hAPP(hAPP(c_member(U_12579),U_12581),c_Map_Odom(U_12579,U_12583,U_12585)))
        | hAPP(U_12585,U_12581) = c_Option_Ooption_ONone(U_12583) )
    & ! [U_12582,U_12578,U_12580,U_12584] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_12578),U_12580),c_Map_Odom(U_12578,U_12582,U_12584)))
        | hAPP(U_12584,U_12580) != c_Option_Ooption_ONone(U_12582) ) ),
    inference(definitional_conversion,[status(esa)],[f_3264_3]) ).

cnf(f_3264_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12578),U_12580),c_Map_Odom(U_12578,U_12582,U_12584)))
    | hAPP(U_12584,U_12580) != c_Option_Ooption_ONone(U_12582) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

cnf(f_3264_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12579),U_12581),c_Map_Odom(U_12579,U_12583,U_12585)))
    | hAPP(U_12585,U_12581) = c_Option_Ooption_ONone(U_12583) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

fof(f_3265_1,plain,
    ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2)))
      | hAPP(V_m_2,V_a_2) != hAPP(c_Option_Ooption_OSome(T_b),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_domI]) ).

fof(f_3265_2,plain,
    ! [U_12590,U_12589,U_12588,U_12587,U_12586] :
      ( hBOOL(hAPP(hAPP(c_member(U_12590),U_12587),c_Map_Odom(U_12590,U_12588,U_12586)))
      | hAPP(U_12586,U_12587) != hAPP(c_Option_Ooption_OSome(U_12588),U_12589) ),
    inference(variable_rename,[status(thm)],[f_3265_1]) ).

fof(f_3265_3,plain,
    ! [U_12587,U_12586,U_12588,U_12589,U_12590] :
      ( hBOOL(hAPP(hAPP(c_member(U_12590),U_12587),c_Map_Odom(U_12590,U_12588,U_12586)))
      | hAPP(U_12586,U_12587) != hAPP(c_Option_Ooption_OSome(U_12588),U_12589) ),
    inference(definitional_conversion,[status(esa)],[f_3265_2]) ).

cnf(f_3265_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12590),U_12587),c_Map_Odom(U_12590,U_12588,U_12586)))
    | hAPP(U_12586,U_12587) != hAPP(c_Option_Ooption_OSome(U_12588),U_12589) ),
    inference(clausify,[status(thm)],[f_3265_3]) ).

fof(f_3266_1,plain,
    ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
      ( hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2)
      | hAPP(V_f_2,V_x_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_insert__dom]) ).

fof(f_3266_2,plain,
    ! [U_12595,U_12594,U_12593,U_12592,U_12591] :
      ( hAPP(hAPP(c_Set_Oinsert(U_12595),U_12592),c_Map_Odom(U_12595,U_12593,U_12591)) = c_Map_Odom(U_12595,U_12593,U_12591)
      | hAPP(U_12591,U_12592) != hAPP(c_Option_Ooption_OSome(U_12593),U_12594) ),
    inference(variable_rename,[status(thm)],[f_3266_1]) ).

fof(f_3266_3,plain,
    ! [U_12592,U_12591,U_12593,U_12594,U_12595] :
      ( hAPP(hAPP(c_Set_Oinsert(U_12595),U_12592),c_Map_Odom(U_12595,U_12593,U_12591)) = c_Map_Odom(U_12595,U_12593,U_12591)
      | hAPP(U_12591,U_12592) != hAPP(c_Option_Ooption_OSome(U_12593),U_12594) ),
    inference(definitional_conversion,[status(esa)],[f_3266_2]) ).

cnf(f_3266_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_12595),U_12592),c_Map_Odom(U_12595,U_12593,U_12591)) = c_Map_Odom(U_12595,U_12593,U_12591)
    | hAPP(U_12591,U_12592) != hAPP(c_Option_Ooption_OSome(U_12593),U_12594) ),
    inference(clausify,[status(thm)],[f_3266_3]) ).

fof(f_3267_1,plain,
    ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_dom__restrict]) ).

fof(f_3267_2,plain,
    ! [U_12599,U_12598,U_12597,U_12596] : c_Map_Odom(U_12596,U_12597,c_Map_Orestrict__map(U_12596,U_12597,U_12598,U_12599)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12596,tc_HOL_Obool)),c_Map_Odom(U_12596,U_12597,U_12598)),U_12599),
    inference(variable_rename,[status(thm)],[f_3267_1]) ).

fof(f_3267_3,plain,
    ! [U_12596,U_12597,U_12598,U_12599] : c_Map_Odom(U_12596,U_12597,c_Map_Orestrict__map(U_12596,U_12597,U_12598,U_12599)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12596,tc_HOL_Obool)),c_Map_Odom(U_12596,U_12597,U_12598)),U_12599),
    inference(definitional_conversion,[status(esa)],[f_3267_2]) ).

cnf(f_3267_4,plain,
    c_Map_Odom(U_12596,U_12597,c_Map_Orestrict__map(U_12596,U_12597,U_12598,U_12599)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12596,tc_HOL_Obool)),c_Map_Odom(U_12596,U_12597,U_12598)),U_12599),
    inference(clausify,[status(thm)],[f_3267_3]) ).

fof(f_3268_1,plain,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(f_3268_2,plain,
    ! [U_12606,U_12605,U_12604,U_12603,U_12602,U_12601,U_12600] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12600,U_12603,U_12604,U_12605,hAPP(hAPP(c_Set_Oinsert(U_12600),U_12601),U_12602)),hAPP(hAPP(U_12604,U_12601),U_12606)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12600,U_12603,U_12604,U_12605,U_12602),U_12606))
      | hBOOL(hAPP(hAPP(c_member(U_12600),U_12601),U_12602)) ),
    inference(variable_rename,[status(thm)],[f_3268_1]) ).

fof(f_3268_3,plain,
    ! [U_12600,U_12601,U_12602,U_12603,U_12604,U_12605,U_12606] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12600,U_12603,U_12604,U_12605,hAPP(hAPP(c_Set_Oinsert(U_12600),U_12601),U_12602)),hAPP(hAPP(U_12604,U_12601),U_12606)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12600,U_12603,U_12604,U_12605,U_12602),U_12606))
      | hBOOL(hAPP(hAPP(c_member(U_12600),U_12601),U_12602)) ),
    inference(definitional_conversion,[status(esa)],[f_3268_2]) ).

cnf(f_3268_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12600,U_12603,U_12604,U_12605,hAPP(hAPP(c_Set_Oinsert(U_12600),U_12601),U_12602)),hAPP(hAPP(U_12604,U_12601),U_12606)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12600,U_12603,U_12604,U_12605,U_12602),U_12606))
    | hBOOL(hAPP(hAPP(c_member(U_12600),U_12601),U_12602)) ),
    inference(clausify,[status(thm)],[f_3268_3]) ).

fof(f_3269_1,plain,
    ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_dom__empty]) ).

fof(f_3269_2,plain,
    ! [U_12608,U_12607] : c_Map_Odom(U_12607,U_12608,hAPP(c_COMBK(tc_Option_Ooption(U_12608),U_12607),c_Option_Ooption_ONone(U_12608))) = c_Orderings_Obot__class_Obot(tc_fun(U_12607,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3269_1]) ).

fof(f_3269_3,plain,
    ! [U_12608,U_12607] : c_Map_Odom(U_12607,U_12608,hAPP(c_COMBK(tc_Option_Ooption(U_12608),U_12607),c_Option_Ooption_ONone(U_12608))) = c_Orderings_Obot__class_Obot(tc_fun(U_12607,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3269_2]) ).

cnf(f_3269_4,plain,
    c_Map_Odom(U_12607,U_12608,hAPP(c_COMBK(tc_Option_Ooption(U_12608),U_12607),c_Option_Ooption_ONone(U_12608))) = c_Orderings_Obot__class_Obot(tc_fun(U_12607,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3269_3]) ).

fof(f_3270_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_f_2 != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) )
      & ( V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))
        | c_Map_Odom(T_b,T_c,V_f_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv]) ).

fof(f_3270_2,plain,
    ! [U_12611,U_12610,U_12609] :
      ( ( c_Map_Odom(U_12609,U_12610,U_12611) = c_Orderings_Obot__class_Obot(tc_fun(U_12609,tc_HOL_Obool))
        | U_12611 != hAPP(c_COMBK(tc_Option_Ooption(U_12610),U_12609),c_Option_Ooption_ONone(U_12610)) )
      & ( U_12611 = hAPP(c_COMBK(tc_Option_Ooption(U_12610),U_12609),c_Option_Ooption_ONone(U_12610))
        | c_Map_Odom(U_12609,U_12610,U_12611) != c_Orderings_Obot__class_Obot(tc_fun(U_12609,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3270_1]) ).

fof(f_3270_3,plain,
    ( ! [U_12617,U_12615,U_12613] :
        ( c_Map_Odom(U_12613,U_12615,U_12617) = c_Orderings_Obot__class_Obot(tc_fun(U_12613,tc_HOL_Obool))
        | U_12617 != hAPP(c_COMBK(tc_Option_Ooption(U_12615),U_12613),c_Option_Ooption_ONone(U_12615)) )
    & ! [U_12616,U_12614,U_12612] :
        ( U_12616 = hAPP(c_COMBK(tc_Option_Ooption(U_12614),U_12612),c_Option_Ooption_ONone(U_12614))
        | c_Map_Odom(U_12612,U_12614,U_12616) != c_Orderings_Obot__class_Obot(tc_fun(U_12612,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3270_2]) ).

fof(f_3270_4,plain,
    ( ! [U_12617,U_12613,U_12615] :
        ( c_Map_Odom(U_12613,U_12615,U_12617) = c_Orderings_Obot__class_Obot(tc_fun(U_12613,tc_HOL_Obool))
        | U_12617 != hAPP(c_COMBK(tc_Option_Ooption(U_12615),U_12613),c_Option_Ooption_ONone(U_12615)) )
    & ! [U_12614,U_12612,U_12616] :
        ( U_12616 = hAPP(c_COMBK(tc_Option_Ooption(U_12614),U_12612),c_Option_Ooption_ONone(U_12614))
        | c_Map_Odom(U_12612,U_12614,U_12616) != c_Orderings_Obot__class_Obot(tc_fun(U_12612,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3270_3]) ).

cnf(f_3270_5,plain,
    ( U_12616 = hAPP(c_COMBK(tc_Option_Ooption(U_12614),U_12612),c_Option_Ooption_ONone(U_12614))
    | c_Map_Odom(U_12612,U_12614,U_12616) != c_Orderings_Obot__class_Obot(tc_fun(U_12612,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3270_4]) ).

cnf(f_3270_6,plain,
    ( c_Map_Odom(U_12613,U_12615,U_12617) = c_Orderings_Obot__class_Obot(tc_fun(U_12613,tc_HOL_Obool))
    | U_12617 != hAPP(c_COMBK(tc_Option_Ooption(U_12615),U_12613),c_Option_Ooption_ONone(U_12615)) ),
    inference(clausify,[status(thm)],[f_3270_4]) ).

fof(f_3271_1,plain,
    ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2)
      | hAPP(V_f_2,V_x_2) != c_Option_Ooption_ONone(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dom__minus]) ).

fof(f_3271_2,plain,
    ! [U_12622,U_12621,U_12620,U_12619,U_12618] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12621,tc_HOL_Obool)),c_Map_Odom(U_12621,U_12620,U_12618)),hAPP(hAPP(c_Set_Oinsert(U_12621),U_12619),U_12622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12621,tc_HOL_Obool)),c_Map_Odom(U_12621,U_12620,U_12618)),U_12622)
      | hAPP(U_12618,U_12619) != c_Option_Ooption_ONone(U_12620) ),
    inference(variable_rename,[status(thm)],[f_3271_1]) ).

fof(f_3271_3,plain,
    ! [U_12619,U_12618,U_12620,U_12621,U_12622] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12621,tc_HOL_Obool)),c_Map_Odom(U_12621,U_12620,U_12618)),hAPP(hAPP(c_Set_Oinsert(U_12621),U_12619),U_12622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12621,tc_HOL_Obool)),c_Map_Odom(U_12621,U_12620,U_12618)),U_12622)
      | hAPP(U_12618,U_12619) != c_Option_Ooption_ONone(U_12620) ),
    inference(definitional_conversion,[status(esa)],[f_3271_2]) ).

cnf(f_3271_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12621,tc_HOL_Obool)),c_Map_Odom(U_12621,U_12620,U_12618)),hAPP(hAPP(c_Set_Oinsert(U_12621),U_12619),U_12622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12621,tc_HOL_Obool)),c_Map_Odom(U_12621,U_12620,U_12618)),U_12622)
    | hAPP(U_12618,U_12619) != c_Option_Ooption_ONone(U_12620) ),
    inference(clausify,[status(thm)],[f_3271_3]) ).

fof(f_3272_1,plain,
    ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(f_3272_2,plain,
    ! [U_12627,U_12626,U_12625,U_12624,U_12623] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12623,U_12623,c_Groups_Otimes__class_Otimes(U_12623),U_12627,hAPP(hAPP(c_Set_Oinsert(U_12623),U_12624),U_12625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12623),U_12627),U_12626)))
      | hBOOL(hAPP(hAPP(c_member(U_12623),U_12624),U_12625))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12623,U_12623,c_Groups_Otimes__class_Otimes(U_12623),U_12624,U_12625),U_12626))
      | ~ class_Groups_Oab__semigroup__mult(U_12623) ),
    inference(variable_rename,[status(thm)],[f_3272_1]) ).

fof(f_3272_3,plain,
    ! [U_12623,U_12624,U_12625,U_12626,U_12627] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12623,U_12623,c_Groups_Otimes__class_Otimes(U_12623),U_12627,hAPP(hAPP(c_Set_Oinsert(U_12623),U_12624),U_12625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12623),U_12627),U_12626)))
      | hBOOL(hAPP(hAPP(c_member(U_12623),U_12624),U_12625))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12623,U_12623,c_Groups_Otimes__class_Otimes(U_12623),U_12624,U_12625),U_12626))
      | ~ class_Groups_Oab__semigroup__mult(U_12623) ),
    inference(definitional_conversion,[status(esa)],[f_3272_2]) ).

cnf(f_3272_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12623,U_12623,c_Groups_Otimes__class_Otimes(U_12623),U_12627,hAPP(hAPP(c_Set_Oinsert(U_12623),U_12624),U_12625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12623),U_12627),U_12626)))
    | hBOOL(hAPP(hAPP(c_member(U_12623),U_12624),U_12625))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12623,U_12623,c_Groups_Otimes__class_Otimes(U_12623),U_12624,U_12625),U_12626))
    | ~ class_Groups_Oab__semigroup__mult(U_12623) ),
    inference(clausify,[status(thm)],[f_3272_3]) ).

fof(f_3273_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph]) ).

fof(f_3273_2,plain,
    ! [U_12634,U_12633,U_12632,U_12631,U_12630,U_12629,U_12628] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12628,U_12629,U_12630,U_12631,U_12632),hAPP(hAPP(U_12630,U_12633),U_12634)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12628),U_12633),U_12632))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12628,U_12629,U_12630,U_12631,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12628,tc_HOL_Obool)),U_12632),hAPP(hAPP(c_Set_Oinsert(U_12628),U_12633),c_Orderings_Obot__class_Obot(tc_fun(U_12628,tc_HOL_Obool))))),U_12634)) ),
    inference(variable_rename,[status(thm)],[f_3273_1]) ).

fof(f_3273_3,plain,
    ! [U_12629,U_12628,U_12630,U_12631,U_12632,U_12633,U_12634] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12628,U_12629,U_12630,U_12631,U_12632),hAPP(hAPP(U_12630,U_12633),U_12634)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12628),U_12633),U_12632))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12628,U_12629,U_12630,U_12631,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12628,tc_HOL_Obool)),U_12632),hAPP(hAPP(c_Set_Oinsert(U_12628),U_12633),c_Orderings_Obot__class_Obot(tc_fun(U_12628,tc_HOL_Obool))))),U_12634)) ),
    inference(definitional_conversion,[status(esa)],[f_3273_2]) ).

cnf(f_3273_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12628,U_12629,U_12630,U_12631,U_12632),hAPP(hAPP(U_12630,U_12633),U_12634)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12628),U_12633),U_12632))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12628,U_12629,U_12630,U_12631,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12628,tc_HOL_Obool)),U_12632),hAPP(hAPP(c_Set_Oinsert(U_12628),U_12633),c_Orderings_Obot__class_Obot(tc_fun(U_12628,tc_HOL_Obool))))),U_12634)) ),
    inference(clausify,[status(thm)],[f_3273_3]) ).

fof(f_3274_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
      ( ( c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2))
        | V_y_2 = c_Option_Ooption_ONone(T_b) )
      & ( c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
        | V_y_2 != c_Option_Ooption_ONone(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_dom__fun__upd]) ).

fof(f_3274_2,plain,
    ! [U_12639,U_12638,U_12637,U_12636,U_12635] :
      ( ( c_Map_Odom(U_12637,U_12636,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12637,tc_Option_Ooption(U_12636)),U_12638),U_12639),U_12635)) = hAPP(hAPP(c_Set_Oinsert(U_12637),U_12639),c_Map_Odom(U_12637,U_12636,U_12638))
        | U_12635 = c_Option_Ooption_ONone(U_12636) )
      & ( c_Map_Odom(U_12637,U_12636,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12637,tc_Option_Ooption(U_12636)),U_12638),U_12639),U_12635)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12637,tc_HOL_Obool)),c_Map_Odom(U_12637,U_12636,U_12638)),hAPP(hAPP(c_Set_Oinsert(U_12637),U_12639),c_Orderings_Obot__class_Obot(tc_fun(U_12637,tc_HOL_Obool))))
        | U_12635 != c_Option_Ooption_ONone(U_12636) ) ),
    inference(variable_rename,[status(thm)],[f_3274_1]) ).

fof(f_3274_3,plain,
    ( ! [U_12649,U_12647,U_12645,U_12643,U_12641] :
        ( c_Map_Odom(U_12645,U_12643,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12645,tc_Option_Ooption(U_12643)),U_12647),U_12649),U_12641)) = hAPP(hAPP(c_Set_Oinsert(U_12645),U_12649),c_Map_Odom(U_12645,U_12643,U_12647))
        | U_12641 = c_Option_Ooption_ONone(U_12643) )
    & ! [U_12648,U_12646,U_12644,U_12642,U_12640] :
        ( c_Map_Odom(U_12644,U_12642,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12644,tc_Option_Ooption(U_12642)),U_12646),U_12648),U_12640)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12644,tc_HOL_Obool)),c_Map_Odom(U_12644,U_12642,U_12646)),hAPP(hAPP(c_Set_Oinsert(U_12644),U_12648),c_Orderings_Obot__class_Obot(tc_fun(U_12644,tc_HOL_Obool))))
        | U_12640 != c_Option_Ooption_ONone(U_12642) ) ),
    inference(miniscope,[status(thm)],[f_3274_2]) ).

fof(f_3274_4,plain,
    ( ! [U_12641,U_12643,U_12645,U_12647,U_12649] :
        ( c_Map_Odom(U_12645,U_12643,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12645,tc_Option_Ooption(U_12643)),U_12647),U_12649),U_12641)) = hAPP(hAPP(c_Set_Oinsert(U_12645),U_12649),c_Map_Odom(U_12645,U_12643,U_12647))
        | U_12641 = c_Option_Ooption_ONone(U_12643) )
    & ! [U_12646,U_12640,U_12644,U_12642,U_12648] :
        ( c_Map_Odom(U_12644,U_12642,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12644,tc_Option_Ooption(U_12642)),U_12646),U_12648),U_12640)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12644,tc_HOL_Obool)),c_Map_Odom(U_12644,U_12642,U_12646)),hAPP(hAPP(c_Set_Oinsert(U_12644),U_12648),c_Orderings_Obot__class_Obot(tc_fun(U_12644,tc_HOL_Obool))))
        | U_12640 != c_Option_Ooption_ONone(U_12642) ) ),
    inference(definitional_conversion,[status(esa)],[f_3274_3]) ).

cnf(f_3274_5,plain,
    ( c_Map_Odom(U_12644,U_12642,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12644,tc_Option_Ooption(U_12642)),U_12646),U_12648),U_12640)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12644,tc_HOL_Obool)),c_Map_Odom(U_12644,U_12642,U_12646)),hAPP(hAPP(c_Set_Oinsert(U_12644),U_12648),c_Orderings_Obot__class_Obot(tc_fun(U_12644,tc_HOL_Obool))))
    | U_12640 != c_Option_Ooption_ONone(U_12642) ),
    inference(clausify,[status(thm)],[f_3274_4]) ).

cnf(f_3274_6,plain,
    ( c_Map_Odom(U_12645,U_12643,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12645,tc_Option_Ooption(U_12643)),U_12647),U_12649),U_12641)) = hAPP(hAPP(c_Set_Oinsert(U_12645),U_12649),c_Map_Odom(U_12645,U_12643,U_12647))
    | U_12641 = c_Option_Ooption_ONone(U_12643) ),
    inference(clausify,[status(thm)],[f_3274_4]) ).

fof(f_3275_1,plain,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(f_3275_2,plain,
    ! [U_12654,U_12653,U_12652,U_12651,U_12650] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12650,U_12651,hAPP(hAPP(c_Set_Oinsert(U_12650),U_12652),U_12653)),U_12654))
      | hBOOL(hAPP(hAPP(c_member(U_12650),U_12652),U_12653))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12650,U_12650,U_12651,U_12652,U_12653),U_12654)) ),
    inference(variable_rename,[status(thm)],[f_3275_1]) ).

fof(f_3275_3,plain,
    ! [U_12650,U_12651,U_12652,U_12653,U_12654] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12650,U_12651,hAPP(hAPP(c_Set_Oinsert(U_12650),U_12652),U_12653)),U_12654))
      | hBOOL(hAPP(hAPP(c_member(U_12650),U_12652),U_12653))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12650,U_12650,U_12651,U_12652,U_12653),U_12654)) ),
    inference(definitional_conversion,[status(esa)],[f_3275_2]) ).

cnf(f_3275_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12650,U_12651,hAPP(hAPP(c_Set_Oinsert(U_12650),U_12652),U_12653)),U_12654))
    | hBOOL(hAPP(hAPP(c_member(U_12650),U_12652),U_12653))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12650,U_12650,U_12651,U_12652,U_12653),U_12654)) ),
    inference(clausify,[status(thm)],[f_3275_3]) ).

fof(f_3276_1,plain,
    ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
      ( ? [B_x] :
          ( hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_ran__restrictD]) ).

fof(f_3276_2,plain,
    ! [U_12660,U_12659,U_12658,U_12657,U_12656] :
      ( ? [U_12655] :
          ( hAPP(U_12659,U_12655) = hAPP(c_Option_Ooption_OSome(U_12656),U_12657)
          & hBOOL(hAPP(hAPP(c_member(U_12658),U_12655),U_12660)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12656),U_12657),c_Map_Oran(U_12658,U_12656,c_Map_Orestrict__map(U_12658,U_12656,U_12659,U_12660)))) ),
    inference(variable_rename,[status(thm)],[f_3276_1]) ).

fof(f_3276_3,plain,
    ! [U_12660,U_12659,U_12658,U_12657,U_12656] :
      ( ( hAPP(U_12659,sK272(U_12660,U_12659,U_12658,U_12657,U_12656)) = hAPP(c_Option_Ooption_OSome(U_12656),U_12657)
        & hBOOL(hAPP(hAPP(c_member(U_12658),sK272(U_12660,U_12659,U_12658,U_12657,U_12656)),U_12660)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12656),U_12657),c_Map_Oran(U_12658,U_12656,c_Map_Orestrict__map(U_12658,U_12656,U_12659,U_12660)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_12655,sK272(U_12660,U_12659,U_12658,U_12657,U_12656))],[f_3276_2]) ).

fof(f_3276_4,plain,
    ( ! [U_12656,U_12657,U_12658,U_12659,U_12660] :
        ( hAPP(U_12659,sK272(U_12660,U_12659,U_12658,U_12657,U_12656)) = hAPP(c_Option_Ooption_OSome(U_12656),U_12657)
        | ~ sP936(U_12656,U_12657,U_12658,U_12659,U_12660) )
    & ! [U_12656,U_12657,U_12658,U_12659,U_12660] :
        ( hBOOL(hAPP(hAPP(c_member(U_12658),sK272(U_12660,U_12659,U_12658,U_12657,U_12656)),U_12660))
        | ~ sP936(U_12656,U_12657,U_12658,U_12659,U_12660) )
    & ! [U_12656,U_12657,U_12658,U_12659,U_12660] :
        ( sP936(U_12656,U_12657,U_12658,U_12659,U_12660)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12656),U_12657),c_Map_Oran(U_12658,U_12656,c_Map_Orestrict__map(U_12658,U_12656,U_12659,U_12660)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP936])],[f_3276_3]) ).

cnf(f_3276_5,plain,
    ( sP936(U_12656,U_12657,U_12658,U_12659,U_12660)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12656),U_12657),c_Map_Oran(U_12658,U_12656,c_Map_Orestrict__map(U_12658,U_12656,U_12659,U_12660)))) ),
    inference(clausify,[status(thm)],[f_3276_4]) ).

cnf(f_3276_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12658),sK272(U_12660,U_12659,U_12658,U_12657,U_12656)),U_12660))
    | ~ sP936(U_12656,U_12657,U_12658,U_12659,U_12660) ),
    inference(clausify,[status(thm)],[f_3276_4]) ).

cnf(f_3276_7,plain,
    ( hAPP(U_12659,sK272(U_12660,U_12659,U_12658,U_12657,U_12656)) = hAPP(c_Option_Ooption_OSome(U_12656),U_12657)
    | ~ sP936(U_12656,U_12657,U_12658,U_12659,U_12660) ),
    inference(clausify,[status(thm)],[f_3276_4]) ).

fof(f_3277_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) != c_Orderings_Otop__class_Otop(T_a)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) != c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__unique]) ).

fof(f_3277_2,plain,
    ! [U_12663,U_12662,U_12661] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12661),U_12662) = U_12663
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12661),U_12662),U_12663) != c_Orderings_Otop__class_Otop(U_12661)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12661),U_12662),U_12663) != c_Orderings_Obot__class_Obot(U_12661)
      | ~ class_Lattices_Oboolean__algebra(U_12661) ),
    inference(variable_rename,[status(thm)],[f_3277_1]) ).

fof(f_3277_3,plain,
    ! [U_12661,U_12662,U_12663] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12661),U_12662) = U_12663
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12661),U_12662),U_12663) != c_Orderings_Otop__class_Otop(U_12661)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12661),U_12662),U_12663) != c_Orderings_Obot__class_Obot(U_12661)
      | ~ class_Lattices_Oboolean__algebra(U_12661) ),
    inference(definitional_conversion,[status(esa)],[f_3277_2]) ).

cnf(f_3277_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12661),U_12662) = U_12663
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12661),U_12662),U_12663) != c_Orderings_Otop__class_Otop(U_12661)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12661),U_12662),U_12663) != c_Orderings_Obot__class_Obot(U_12661)
    | ~ class_Lattices_Oboolean__algebra(U_12661) ),
    inference(clausify,[status(thm)],[f_3277_3]) ).

fof(f_3278_1,plain,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_UNIV__I]) ).

fof(f_3278_2,plain,
    ! [U_12665,U_12664] : hBOOL(hAPP(hAPP(c_member(U_12664),U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3278_1]) ).

fof(f_3278_3,plain,
    ! [U_12664,U_12665] : hBOOL(hAPP(hAPP(c_member(U_12664),U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3278_2]) ).

cnf(f_3278_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_12664),U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3278_3]) ).

fof(f_3279_1,plain,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_UNIV__option__conv]) ).

fof(f_3279_2,plain,
    ! [U_12666] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12666),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_12666)),c_Option_Ooption_ONone(U_12666)),hAPP(c_Set_Oimage(U_12666,tc_Option_Ooption(U_12666),c_Option_Ooption_OSome(U_12666)),c_Orderings_Otop__class_Otop(tc_fun(U_12666,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3279_1]) ).

fof(f_3279_3,plain,
    ! [U_12666] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12666),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_12666)),c_Option_Ooption_ONone(U_12666)),hAPP(c_Set_Oimage(U_12666,tc_Option_Ooption(U_12666),c_Option_Ooption_OSome(U_12666)),c_Orderings_Otop__class_Otop(tc_fun(U_12666,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3279_2]) ).

cnf(f_3279_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12666),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_12666)),c_Option_Ooption_ONone(U_12666)),hAPP(c_Set_Oimage(U_12666,tc_Option_Ooption(U_12666),c_Option_Ooption_OSome(U_12666)),c_Orderings_Otop__class_Otop(tc_fun(U_12666,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3279_3]) ).

fof(f_3280_1,plain,
    ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_range__composition]) ).

fof(f_3280_2,plain,
    ! [U_12671,U_12670,U_12669,U_12668,U_12667] : hAPP(c_Set_Oimage(U_12667,U_12668,hAPP(hAPP(c_COMBB(U_12669,U_12668,U_12667),U_12670),U_12671)),c_Orderings_Otop__class_Otop(tc_fun(U_12667,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_12669,U_12668,U_12670),hAPP(c_Set_Oimage(U_12667,U_12669,U_12671),c_Orderings_Otop__class_Otop(tc_fun(U_12667,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3280_1]) ).

fof(f_3280_3,plain,
    ! [U_12667,U_12668,U_12669,U_12670,U_12671] : hAPP(c_Set_Oimage(U_12667,U_12668,hAPP(hAPP(c_COMBB(U_12669,U_12668,U_12667),U_12670),U_12671)),c_Orderings_Otop__class_Otop(tc_fun(U_12667,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_12669,U_12668,U_12670),hAPP(c_Set_Oimage(U_12667,U_12669,U_12671),c_Orderings_Otop__class_Otop(tc_fun(U_12667,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3280_2]) ).

cnf(f_3280_4,plain,
    hAPP(c_Set_Oimage(U_12667,U_12668,hAPP(hAPP(c_COMBB(U_12669,U_12668,U_12667),U_12670),U_12671)),c_Orderings_Otop__class_Otop(tc_fun(U_12667,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_12669,U_12668,U_12670),hAPP(c_Set_Oimage(U_12667,U_12669,U_12671),c_Orderings_Otop__class_Otop(tc_fun(U_12667,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3280_3]) ).

fof(f_3281_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__atMost__UNIV]) ).

fof(f_3281_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3281_1]) ).

cnf(f_3281_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3281_2]) ).

fof(f_3282_1,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__int]) ).

fof(f_3282_2,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3282_1]) ).

cnf(f_3282_3,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3282_2]) ).

fof(f_3283_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( V_x_2 = V_y_2
      | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_injD]) ).

fof(f_3283_2,plain,
    ! [U_12676,U_12675,U_12674,U_12673,U_12672] :
      ( U_12675 = U_12676
      | hAPP(U_12674,U_12675) != hAPP(U_12674,U_12676)
      | ~ c_Fun_Oinj__on(U_12672,U_12673,U_12674,c_Orderings_Otop__class_Otop(tc_fun(U_12672,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3283_1]) ).

fof(f_3283_3,plain,
    ! [U_12676,U_12675,U_12674] :
      ( ! [U_12673,U_12672] : ~ c_Fun_Oinj__on(U_12672,U_12673,U_12674,c_Orderings_Otop__class_Otop(tc_fun(U_12672,tc_HOL_Obool)))
      | U_12675 = U_12676
      | hAPP(U_12674,U_12675) != hAPP(U_12674,U_12676) ),
    inference(miniscope,[status(thm)],[f_3283_2]) ).

fof(f_3283_4,plain,
    ! [U_12672,U_12673,U_12674,U_12675,U_12676] :
      ( ~ c_Fun_Oinj__on(U_12672,U_12673,U_12674,c_Orderings_Otop__class_Otop(tc_fun(U_12672,tc_HOL_Obool)))
      | U_12675 = U_12676
      | hAPP(U_12674,U_12675) != hAPP(U_12674,U_12676) ),
    inference(definitional_conversion,[status(esa)],[f_3283_3]) ).

cnf(f_3283_5,plain,
    ( ~ c_Fun_Oinj__on(U_12672,U_12673,U_12674,c_Orderings_Otop__class_Otop(tc_fun(U_12672,tc_HOL_Obool)))
    | U_12675 = U_12676
    | hAPP(U_12674,U_12675) != hAPP(U_12674,U_12676) ),
    inference(clausify,[status(thm)],[f_3283_4]) ).

fof(f_3284_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__eq]) ).

fof(f_3284_2,plain,
    ! [U_12681,U_12680,U_12679,U_12678,U_12677] :
      ( ( ( hAPP(U_12679,U_12680) = hAPP(U_12679,U_12681)
          | U_12680 != U_12681 )
        & ( U_12680 = U_12681
          | hAPP(U_12679,U_12680) != hAPP(U_12679,U_12681) ) )
      | ~ c_Fun_Oinj__on(U_12677,U_12678,U_12679,c_Orderings_Otop__class_Otop(tc_fun(U_12677,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3284_1]) ).

fof(f_3284_3,plain,
    ! [U_12681,U_12680,U_12679] :
      ( ! [U_12678,U_12677] : ~ c_Fun_Oinj__on(U_12677,U_12678,U_12679,c_Orderings_Otop__class_Otop(tc_fun(U_12677,tc_HOL_Obool)))
      | ( ( hAPP(U_12679,U_12680) = hAPP(U_12679,U_12681)
          | U_12680 != U_12681 )
        & ( U_12680 = U_12681
          | hAPP(U_12679,U_12680) != hAPP(U_12679,U_12681) ) ) ),
    inference(miniscope,[status(thm)],[f_3284_2]) ).

fof(f_3284_4,plain,
    ( ! [U_12679,U_12680,U_12681] :
        ( hAPP(U_12679,U_12680) = hAPP(U_12679,U_12681)
        | U_12680 != U_12681
        | ~ sP937(U_12679,U_12680,U_12681) )
    & ! [U_12679,U_12680,U_12681] :
        ( U_12680 = U_12681
        | hAPP(U_12679,U_12680) != hAPP(U_12679,U_12681)
        | ~ sP937(U_12679,U_12680,U_12681) )
    & ! [U_12678,U_12679,U_12677,U_12680,U_12681] :
        ( ~ c_Fun_Oinj__on(U_12677,U_12678,U_12679,c_Orderings_Otop__class_Otop(tc_fun(U_12677,tc_HOL_Obool)))
        | sP937(U_12679,U_12680,U_12681) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP937])],[f_3284_3]) ).

cnf(f_3284_5,plain,
    ( ~ c_Fun_Oinj__on(U_12677,U_12678,U_12679,c_Orderings_Otop__class_Otop(tc_fun(U_12677,tc_HOL_Obool)))
    | sP937(U_12679,U_12680,U_12681) ),
    inference(clausify,[status(thm)],[f_3284_4]) ).

cnf(f_3284_6,plain,
    ( U_12680 = U_12681
    | hAPP(U_12679,U_12680) != hAPP(U_12679,U_12681)
    | ~ sP937(U_12679,U_12680,U_12681) ),
    inference(clausify,[status(thm)],[f_3284_4]) ).

cnf(f_3284_7,plain,
    ( hAPP(U_12679,U_12680) = hAPP(U_12679,U_12681)
    | U_12680 != U_12681
    | ~ sP937(U_12679,U_12680,U_12681) ),
    inference(clausify,[status(thm)],[f_3284_4]) ).

fof(f_3285_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
          | V_y_2 != c_Orderings_Otop__class_Otop(T_b)
          | V_x_2 != c_Orderings_Otop__class_Otop(T_b) )
        & ( ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
            & V_x_2 = c_Orderings_Otop__class_Otop(T_b) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != c_Orderings_Otop__class_Otop(T_b) ) )
      | ~ class_Lattices_Obounded__lattice__top(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff]) ).

fof(f_3285_2,plain,
    ! [U_12684,U_12683,U_12682] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12682),U_12683),U_12684) = c_Orderings_Otop__class_Otop(U_12682)
          | U_12684 != c_Orderings_Otop__class_Otop(U_12682)
          | U_12683 != c_Orderings_Otop__class_Otop(U_12682) )
        & ( ( U_12684 = c_Orderings_Otop__class_Otop(U_12682)
            & U_12683 = c_Orderings_Otop__class_Otop(U_12682) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12682),U_12683),U_12684) != c_Orderings_Otop__class_Otop(U_12682) ) )
      | ~ class_Lattices_Obounded__lattice__top(U_12682) ),
    inference(variable_rename,[status(thm)],[f_3285_1]) ).

fof(f_3285_3,plain,
    ( ! [U_12683,U_12682,U_12684] :
        ( U_12684 = c_Orderings_Otop__class_Otop(U_12682)
        | ~ sP938(U_12683,U_12682,U_12684) )
    & ! [U_12683,U_12682,U_12684] :
        ( U_12683 = c_Orderings_Otop__class_Otop(U_12682)
        | ~ sP938(U_12683,U_12682,U_12684) )
    & ! [U_12683,U_12682,U_12684] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12682),U_12683),U_12684) = c_Orderings_Otop__class_Otop(U_12682)
        | U_12684 != c_Orderings_Otop__class_Otop(U_12682)
        | U_12683 != c_Orderings_Otop__class_Otop(U_12682)
        | ~ sP939(U_12683,U_12682,U_12684) )
    & ! [U_12683,U_12682,U_12684] :
        ( sP938(U_12683,U_12682,U_12684)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12682),U_12683),U_12684) != c_Orderings_Otop__class_Otop(U_12682)
        | ~ sP939(U_12683,U_12682,U_12684) )
    & ! [U_12683,U_12682,U_12684] :
        ( sP939(U_12683,U_12682,U_12684)
        | ~ class_Lattices_Obounded__lattice__top(U_12682) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP938,sP939])],[f_3285_2]) ).

cnf(f_3285_4,plain,
    ( sP939(U_12683,U_12682,U_12684)
    | ~ class_Lattices_Obounded__lattice__top(U_12682) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

cnf(f_3285_5,plain,
    ( sP938(U_12683,U_12682,U_12684)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12682),U_12683),U_12684) != c_Orderings_Otop__class_Otop(U_12682)
    | ~ sP939(U_12683,U_12682,U_12684) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

cnf(f_3285_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12682),U_12683),U_12684) = c_Orderings_Otop__class_Otop(U_12682)
    | U_12684 != c_Orderings_Otop__class_Otop(U_12682)
    | U_12683 != c_Orderings_Otop__class_Otop(U_12682)
    | ~ sP939(U_12683,U_12682,U_12684) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

cnf(f_3285_7,plain,
    ( U_12683 = c_Orderings_Otop__class_Otop(U_12682)
    | ~ sP938(U_12683,U_12682,U_12684) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

cnf(f_3285_8,plain,
    ( U_12684 = c_Orderings_Otop__class_Otop(U_12682)
    | ~ sP938(U_12683,U_12682,U_12684) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

fof(f_3286_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__top__right]) ).

fof(f_3286_2,plain,
    ! [U_12686,U_12685] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12685),U_12686),c_Orderings_Otop__class_Otop(U_12685)) = U_12686
      | ~ class_Lattices_Obounded__lattice__top(U_12685) ),
    inference(variable_rename,[status(thm)],[f_3286_1]) ).

fof(f_3286_3,plain,
    ! [U_12686,U_12685] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12685),U_12686),c_Orderings_Otop__class_Otop(U_12685)) = U_12686
      | ~ class_Lattices_Obounded__lattice__top(U_12685) ),
    inference(definitional_conversion,[status(esa)],[f_3286_2]) ).

cnf(f_3286_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12685),U_12686),c_Orderings_Otop__class_Otop(U_12685)) = U_12686
    | ~ class_Lattices_Obounded__lattice__top(U_12685) ),
    inference(clausify,[status(thm)],[f_3286_3]) ).

fof(f_3287_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__top__left]) ).

fof(f_3287_2,plain,
    ! [U_12688,U_12687] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12687),c_Orderings_Otop__class_Otop(U_12687)),U_12688) = U_12688
      | ~ class_Lattices_Obounded__lattice__top(U_12687) ),
    inference(variable_rename,[status(thm)],[f_3287_1]) ).

fof(f_3287_3,plain,
    ! [U_12688,U_12687] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12687),c_Orderings_Otop__class_Otop(U_12687)),U_12688) = U_12688
      | ~ class_Lattices_Obounded__lattice__top(U_12687) ),
    inference(definitional_conversion,[status(esa)],[f_3287_2]) ).

cnf(f_3287_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12687),c_Orderings_Otop__class_Otop(U_12687)),U_12688) = U_12688
    | ~ class_Lattices_Obounded__lattice__top(U_12687) ),
    inference(clausify,[status(thm)],[f_3287_3]) ).

fof(f_3288_1,plain,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV]) ).

fof(f_3288_2,plain,
    ! [U_12690,U_12689] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12689,U_12690)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12689,U_12690),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12690),c_Orderings_Otop__class_Otop(tc_fun(U_12690,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12689),c_Orderings_Otop__class_Otop(tc_fun(U_12689,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3288_1]) ).

fof(f_3288_3,plain,
    ! [U_12689,U_12690] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12689,U_12690)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12689,U_12690),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12690),c_Orderings_Otop__class_Otop(tc_fun(U_12690,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12689),c_Orderings_Otop__class_Otop(tc_fun(U_12689,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3288_2]) ).

cnf(f_3288_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12689,U_12690)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12689,U_12690),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12690),c_Orderings_Otop__class_Otop(tc_fun(U_12690,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12689),c_Orderings_Otop__class_Otop(tc_fun(U_12689,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3288_3]) ).

fof(f_3289_1,plain,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2]) ).

fof(f_3289_2,plain,
    ! [U_12692,U_12691] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12692),c_Orderings_Otop__class_Otop(tc_fun(U_12692,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12691,U_12692)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12691,U_12692),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3289_1]) ).

fof(f_3289_3,plain,
    ! [U_12692] :
      ( ! [U_12691] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12691,U_12692)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12691,U_12692),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12692),c_Orderings_Otop__class_Otop(tc_fun(U_12692,tc_HOL_Obool)))) ),
    inference(miniscope,[status(thm)],[f_3289_2]) ).

fof(f_3289_4,plain,
    ! [U_12691,U_12692] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12691,U_12692)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12691,U_12692),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12692),c_Orderings_Otop__class_Otop(tc_fun(U_12692,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3289_3]) ).

cnf(f_3289_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12691,U_12692)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12691,U_12692),tc_HOL_Obool))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12692),c_Orderings_Otop__class_Otop(tc_fun(U_12692,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3289_4]) ).

fof(f_3290_1,plain,
    ! [T_c,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff]) ).

fof(f_3290_2,plain,
    ! [U_12694,U_12693] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12693,U_12694)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12693,U_12694),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12694),c_Orderings_Otop__class_Otop(tc_fun(U_12694,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12693),c_Orderings_Otop__class_Otop(tc_fun(U_12693,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12694),c_Orderings_Otop__class_Otop(tc_fun(U_12694,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12693),c_Orderings_Otop__class_Otop(tc_fun(U_12693,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12693,U_12694)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12693,U_12694),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3290_1]) ).

fof(f_3290_3,plain,
    ( ! [U_12698,U_12696] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12696,U_12698)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12696,U_12698),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12698),c_Orderings_Otop__class_Otop(tc_fun(U_12698,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12696),c_Orderings_Otop__class_Otop(tc_fun(U_12696,tc_HOL_Obool)))) )
    & ! [U_12697,U_12695] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12697),c_Orderings_Otop__class_Otop(tc_fun(U_12697,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12695),c_Orderings_Otop__class_Otop(tc_fun(U_12695,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12695,U_12697)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12695,U_12697),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3290_2]) ).

fof(f_3290_4,plain,
    ( ! [U_12697,U_12695] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12697),c_Orderings_Otop__class_Otop(tc_fun(U_12697,tc_HOL_Obool))))
        | ~ sP940(U_12697,U_12695) )
    & ! [U_12697,U_12695] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12695),c_Orderings_Otop__class_Otop(tc_fun(U_12695,tc_HOL_Obool))))
        | ~ sP940(U_12697,U_12695) )
    & ! [U_12696,U_12698] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12696,U_12698)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12696,U_12698),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12698),c_Orderings_Otop__class_Otop(tc_fun(U_12698,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12696),c_Orderings_Otop__class_Otop(tc_fun(U_12696,tc_HOL_Obool)))) )
    & ! [U_12697,U_12695] :
        ( sP940(U_12697,U_12695)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12695,U_12697)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12695,U_12697),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP940])],[f_3290_3]) ).

cnf(f_3290_5,plain,
    ( sP940(U_12697,U_12695)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12695,U_12697)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12695,U_12697),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

cnf(f_3290_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_12696,U_12698)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12696,U_12698),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12698),c_Orderings_Otop__class_Otop(tc_fun(U_12698,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12696),c_Orderings_Otop__class_Otop(tc_fun(U_12696,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

cnf(f_3290_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12695),c_Orderings_Otop__class_Otop(tc_fun(U_12695,tc_HOL_Obool))))
    | ~ sP940(U_12697,U_12695) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

cnf(f_3290_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12697),c_Orderings_Otop__class_Otop(tc_fun(U_12697,tc_HOL_Obool))))
    | ~ sP940(U_12697,U_12695) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

fof(f_3291_1,plain,
    ! [T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV]) ).

fof(f_3291_2,plain,
    ! [U_12699] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12699)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12699),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12699),c_Orderings_Otop__class_Otop(tc_fun(U_12699,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12699),c_Orderings_Otop__class_Otop(tc_fun(U_12699,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12699)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12699),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3291_1]) ).

fof(f_3291_3,plain,
    ( ! [U_12701] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12701)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12701),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12701),c_Orderings_Otop__class_Otop(tc_fun(U_12701,tc_HOL_Obool)))) )
    & ! [U_12700] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12700),c_Orderings_Otop__class_Otop(tc_fun(U_12700,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12700)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12700),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3291_2]) ).

fof(f_3291_4,plain,
    ( ! [U_12701] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12701)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12701),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12701),c_Orderings_Otop__class_Otop(tc_fun(U_12701,tc_HOL_Obool)))) )
    & ! [U_12700] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12700),c_Orderings_Otop__class_Otop(tc_fun(U_12700,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12700)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12700),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3291_3]) ).

cnf(f_3291_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12700),c_Orderings_Otop__class_Otop(tc_fun(U_12700,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12700)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12700),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3291_4]) ).

cnf(f_3291_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12701)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_12701),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12701),c_Orderings_Otop__class_Otop(tc_fun(U_12701,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3291_4]) ).

fof(f_3292_1,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__nat]) ).

fof(f_3292_2,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3292_1]) ).

cnf(f_3292_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3292_2]) ).

fof(f_3293_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV]) ).

fof(f_3293_2,plain,
    ! [U_12702] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12702),c_Orderings_Otop__class_Otop(tc_fun(U_12702,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_12702) ),
    inference(variable_rename,[status(thm)],[f_3293_1]) ).

fof(f_3293_3,plain,
    ! [U_12702] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12702),c_Orderings_Otop__class_Otop(tc_fun(U_12702,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_12702) ),
    inference(definitional_conversion,[status(esa)],[f_3293_2]) ).

cnf(f_3293_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12702),c_Orderings_Otop__class_Otop(tc_fun(U_12702,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(U_12702) ),
    inference(clausify,[status(thm)],[f_3293_3]) ).

fof(f_3294_1,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__int]) ).

fof(f_3294_2,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3294_1]) ).

cnf(f_3294_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3294_2]) ).

fof(f_3295_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Int__UNIV__right]) ).

fof(f_3295_2,plain,
    ! [U_12704,U_12703] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12703,tc_HOL_Obool)),U_12704),c_Orderings_Otop__class_Otop(tc_fun(U_12703,tc_HOL_Obool))) = U_12704,
    inference(variable_rename,[status(thm)],[f_3295_1]) ).

fof(f_3295_3,plain,
    ! [U_12703,U_12704] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12703,tc_HOL_Obool)),U_12704),c_Orderings_Otop__class_Otop(tc_fun(U_12703,tc_HOL_Obool))) = U_12704,
    inference(definitional_conversion,[status(esa)],[f_3295_2]) ).

cnf(f_3295_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12703,tc_HOL_Obool)),U_12704),c_Orderings_Otop__class_Otop(tc_fun(U_12703,tc_HOL_Obool))) = U_12704,
    inference(clausify,[status(thm)],[f_3295_3]) ).

fof(f_3296_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    inference(fof_nnf,[status(thm)],[fact_Int__UNIV__left]) ).

fof(f_3296_2,plain,
    ! [U_12706,U_12705] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12705,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12705,tc_HOL_Obool))),U_12706) = U_12706,
    inference(variable_rename,[status(thm)],[f_3296_1]) ).

fof(f_3296_3,plain,
    ! [U_12705,U_12706] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12705,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12705,tc_HOL_Obool))),U_12706) = U_12706,
    inference(definitional_conversion,[status(esa)],[f_3296_2]) ).

cnf(f_3296_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12705,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12705,tc_HOL_Obool))),U_12706) = U_12706,
    inference(clausify,[status(thm)],[f_3296_3]) ).

fof(f_3297_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Un__UNIV__left]) ).

fof(f_3297_2,plain,
    ! [U_12708,U_12707] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12707,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12707,tc_HOL_Obool))),U_12708) = c_Orderings_Otop__class_Otop(tc_fun(U_12707,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3297_1]) ).

fof(f_3297_3,plain,
    ! [U_12707,U_12708] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12707,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12707,tc_HOL_Obool))),U_12708) = c_Orderings_Otop__class_Otop(tc_fun(U_12707,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3297_2]) ).

cnf(f_3297_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12707,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12707,tc_HOL_Obool))),U_12708) = c_Orderings_Otop__class_Otop(tc_fun(U_12707,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3297_3]) ).

fof(f_3298_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Un__UNIV__right]) ).

fof(f_3298_2,plain,
    ! [U_12710,U_12709] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12709,tc_HOL_Obool)),U_12710),c_Orderings_Otop__class_Otop(tc_fun(U_12709,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12709,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3298_1]) ).

fof(f_3298_3,plain,
    ! [U_12709,U_12710] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12709,tc_HOL_Obool)),U_12710),c_Orderings_Otop__class_Otop(tc_fun(U_12709,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12709,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3298_2]) ).

cnf(f_3298_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12709,tc_HOL_Obool)),U_12710),c_Orderings_Otop__class_Otop(tc_fun(U_12709,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12709,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3298_3]) ).

fof(f_3299_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_subset__UNIV]) ).

fof(f_3299_2,plain,
    ! [U_12712,U_12711] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12711,tc_HOL_Obool)),U_12712),c_Orderings_Otop__class_Otop(tc_fun(U_12711,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3299_1]) ).

fof(f_3299_3,plain,
    ! [U_12711,U_12712] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12711,tc_HOL_Obool)),U_12712),c_Orderings_Otop__class_Otop(tc_fun(U_12711,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3299_2]) ).

cnf(f_3299_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12711,tc_HOL_Obool)),U_12712),c_Orderings_Otop__class_Otop(tc_fun(U_12711,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3299_3]) ).

fof(f_3300_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)))
      | ~ class_Orderings_Otop(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_top__greatest]) ).

fof(f_3300_2,plain,
    ! [U_12714,U_12713] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12713),U_12714),c_Orderings_Otop__class_Otop(U_12713)))
      | ~ class_Orderings_Otop(U_12713) ),
    inference(variable_rename,[status(thm)],[f_3300_1]) ).

fof(f_3300_3,plain,
    ! [U_12713,U_12714] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12713),U_12714),c_Orderings_Otop__class_Otop(U_12713)))
      | ~ class_Orderings_Otop(U_12713) ),
    inference(definitional_conversion,[status(esa)],[f_3300_2]) ).

cnf(f_3300_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12713),U_12714),c_Orderings_Otop__class_Otop(U_12713)))
    | ~ class_Orderings_Otop(U_12713) ),
    inference(clausify,[status(thm)],[f_3300_3]) ).

fof(f_3301_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__top__right]) ).

fof(f_3301_2,plain,
    ! [U_12716,U_12715] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12715),U_12716),c_Orderings_Otop__class_Otop(U_12715)) = c_Orderings_Otop__class_Otop(U_12715)
      | ~ class_Lattices_Obounded__lattice__top(U_12715) ),
    inference(variable_rename,[status(thm)],[f_3301_1]) ).

fof(f_3301_3,plain,
    ! [U_12715,U_12716] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12715),U_12716),c_Orderings_Otop__class_Otop(U_12715)) = c_Orderings_Otop__class_Otop(U_12715)
      | ~ class_Lattices_Obounded__lattice__top(U_12715) ),
    inference(definitional_conversion,[status(esa)],[f_3301_2]) ).

cnf(f_3301_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12715),U_12716),c_Orderings_Otop__class_Otop(U_12715)) = c_Orderings_Otop__class_Otop(U_12715)
    | ~ class_Lattices_Obounded__lattice__top(U_12715) ),
    inference(clausify,[status(thm)],[f_3301_3]) ).

fof(f_3302_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__top__left]) ).

fof(f_3302_2,plain,
    ! [U_12718,U_12717] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12717),c_Orderings_Otop__class_Otop(U_12717)),U_12718) = c_Orderings_Otop__class_Otop(U_12717)
      | ~ class_Lattices_Obounded__lattice__top(U_12717) ),
    inference(variable_rename,[status(thm)],[f_3302_1]) ).

fof(f_3302_3,plain,
    ! [U_12717,U_12718] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12717),c_Orderings_Otop__class_Otop(U_12717)),U_12718) = c_Orderings_Otop__class_Otop(U_12717)
      | ~ class_Lattices_Obounded__lattice__top(U_12717) ),
    inference(definitional_conversion,[status(esa)],[f_3302_2]) ).

cnf(f_3302_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12717),c_Orderings_Otop__class_Otop(U_12717)),U_12718) = c_Orderings_Otop__class_Otop(U_12717)
    | ~ class_Lattices_Obounded__lattice__top(U_12717) ),
    inference(clausify,[status(thm)],[f_3302_3]) ).

fof(f_3303_1,plain,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    inference(fof_nnf,[status(thm)],[fact_equiv__intrel]) ).

fof(f_3303_2,plain,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    inference(definitional_conversion,[status(esa)],[f_3303_1]) ).

cnf(f_3303_3,plain,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    inference(clausify,[status(thm)],[f_3303_2]) ).

fof(f_3304_1,plain,
    ! [V_x_2,T_c,T_b] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b)
      | ~ class_Orderings_Otop(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_top__apply]) ).

fof(f_3304_2,plain,
    ! [U_12721,U_12720,U_12719] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12720,U_12719)),U_12721) = c_Orderings_Otop__class_Otop(U_12719)
      | ~ class_Orderings_Otop(U_12719) ),
    inference(variable_rename,[status(thm)],[f_3304_1]) ).

fof(f_3304_3,plain,
    ! [U_12719,U_12720,U_12721] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12720,U_12719)),U_12721) = c_Orderings_Otop__class_Otop(U_12719)
      | ~ class_Orderings_Otop(U_12719) ),
    inference(definitional_conversion,[status(esa)],[f_3304_2]) ).

cnf(f_3304_4,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12720,U_12719)),U_12721) = c_Orderings_Otop__class_Otop(U_12719)
    | ~ class_Orderings_Otop(U_12719) ),
    inference(clausify,[status(thm)],[f_3304_3]) ).

fof(f_3305_1,plain,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__not__empty]) ).

fof(f_3305_2,plain,
    ! [U_12722] : c_Orderings_Otop__class_Otop(tc_fun(U_12722,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_12722,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3305_1]) ).

fof(f_3305_3,plain,
    ! [U_12722] : c_Orderings_Otop__class_Otop(tc_fun(U_12722,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_12722,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3305_2]) ).

cnf(f_3305_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_12722,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_12722,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3305_3]) ).

fof(f_3306_1,plain,
    ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(f_3306_2,plain,
    ! [U_12724,U_12723] : c_Sum__Type_OPlus(U_12723,U_12724,c_Orderings_Otop__class_Otop(tc_fun(U_12723,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12724,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12723,U_12724),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3306_1]) ).

fof(f_3306_3,plain,
    ! [U_12723,U_12724] : c_Sum__Type_OPlus(U_12723,U_12724,c_Orderings_Otop__class_Otop(tc_fun(U_12723,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12724,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12723,U_12724),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3306_2]) ).

cnf(f_3306_4,plain,
    c_Sum__Type_OPlus(U_12723,U_12724,c_Orderings_Otop__class_Otop(tc_fun(U_12723,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12724,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_12723,U_12724),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3306_3]) ).

fof(f_3307_1,plain,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Pow__UNIV]) ).

fof(f_3307_2,plain,
    ! [U_12725] : hAPP(c_Set_OPow(U_12725),c_Orderings_Otop__class_Otop(tc_fun(U_12725,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12725,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3307_1]) ).

fof(f_3307_3,plain,
    ! [U_12725] : hAPP(c_Set_OPow(U_12725),c_Orderings_Otop__class_Otop(tc_fun(U_12725,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12725,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3307_2]) ).

cnf(f_3307_4,plain,
    hAPP(c_Set_OPow(U_12725),c_Orderings_Otop__class_Otop(tc_fun(U_12725,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12725,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3307_3]) ).

fof(f_3308_1,plain,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_card__UNIV__unit]) ).

fof(f_3308_2,plain,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_3308_1]) ).

cnf(f_3308_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3308_2]) ).

fof(f_3309_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__lessThan__UNIV]) ).

fof(f_3309_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3309_1]) ).

cnf(f_3309_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3309_2]) ).

fof(f_3310_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_b] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty]) ).

fof(f_3310_2,plain,
    ! [U_12729,U_12728,U_12727,U_12726] :
      ( U_12728 != c_Orderings_Obot__class_Obot(tc_fun(U_12726,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12726,U_12727,U_12728),U_12729)) ),
    inference(variable_rename,[status(thm)],[f_3310_1]) ).

fof(f_3310_3,plain,
    ! [U_12726,U_12727,U_12728,U_12729] :
      ( U_12728 != c_Orderings_Obot__class_Obot(tc_fun(U_12726,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12726,U_12727,U_12728),U_12729)) ),
    inference(definitional_conversion,[status(esa)],[f_3310_2]) ).

cnf(f_3310_4,plain,
    ( U_12728 != c_Orderings_Obot__class_Obot(tc_fun(U_12726,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12726,U_12727,U_12728),U_12729)) ),
    inference(clausify,[status(thm)],[f_3310_3]) ).

fof(f_3311_1,plain,
    ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_empty__fold1SetE]) ).

fof(f_3311_2,plain,
    ! [U_12732,U_12731,U_12730] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12730,U_12731,c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool))),U_12732)),
    inference(variable_rename,[status(thm)],[f_3311_1]) ).

fof(f_3311_3,plain,
    ! [U_12730,U_12731,U_12732] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12730,U_12731,c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool))),U_12732)),
    inference(definitional_conversion,[status(esa)],[f_3311_2]) ).

cnf(f_3311_4,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12730,U_12731,c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool))),U_12732)),
    inference(clausify,[status(thm)],[f_3311_3]) ).

fof(f_3312_1,plain,
    ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
      | V_b_2 != hAPP(V_f_2,V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_range__eqI]) ).

fof(f_3312_2,plain,
    ! [U_12737,U_12736,U_12735,U_12734,U_12733] :
      ( hBOOL(hAPP(hAPP(c_member(U_12736),U_12733),hAPP(c_Set_Oimage(U_12737,U_12736,U_12734),c_Orderings_Otop__class_Otop(tc_fun(U_12737,tc_HOL_Obool)))))
      | U_12733 != hAPP(U_12734,U_12735) ),
    inference(variable_rename,[status(thm)],[f_3312_1]) ).

fof(f_3312_3,plain,
    ! [U_12733,U_12734,U_12735,U_12736,U_12737] :
      ( hBOOL(hAPP(hAPP(c_member(U_12736),U_12733),hAPP(c_Set_Oimage(U_12737,U_12736,U_12734),c_Orderings_Otop__class_Otop(tc_fun(U_12737,tc_HOL_Obool)))))
      | U_12733 != hAPP(U_12734,U_12735) ),
    inference(definitional_conversion,[status(esa)],[f_3312_2]) ).

cnf(f_3312_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12736),U_12733),hAPP(c_Set_Oimage(U_12737,U_12736,U_12734),c_Orderings_Otop__class_Otop(tc_fun(U_12737,tc_HOL_Obool)))))
    | U_12733 != hAPP(U_12734,U_12735) ),
    inference(clausify,[status(thm)],[f_3312_3]) ).

fof(f_3313_1,plain,
    ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_rangeI]) ).

fof(f_3313_2,plain,
    ! [U_12741,U_12740,U_12739,U_12738] : hBOOL(hAPP(hAPP(c_member(U_12738),hAPP(U_12739,U_12740)),hAPP(c_Set_Oimage(U_12741,U_12738,U_12739),c_Orderings_Otop__class_Otop(tc_fun(U_12741,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3313_1]) ).

fof(f_3313_3,plain,
    ! [U_12738,U_12739,U_12740,U_12741] : hBOOL(hAPP(hAPP(c_member(U_12738),hAPP(U_12739,U_12740)),hAPP(c_Set_Oimage(U_12741,U_12738,U_12739),c_Orderings_Otop__class_Otop(tc_fun(U_12741,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3313_2]) ).

cnf(f_3313_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_12738),hAPP(U_12739,U_12740)),hAPP(c_Set_Oimage(U_12741,U_12738,U_12739),c_Orderings_Otop__class_Otop(tc_fun(U_12741,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3313_3]) ).

fof(f_3314_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__atLeast__UNIV]) ).

fof(f_3314_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3314_1]) ).

cnf(f_3314_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3314_2]) ).

fof(f_3315_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__UNIV]) ).

fof(f_3315_2,plain,
    ! [U_12743,U_12742] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12742,tc_HOL_Obool)),U_12743),c_Orderings_Otop__class_Otop(tc_fun(U_12742,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12742,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3315_1]) ).

fof(f_3315_3,plain,
    ! [U_12742,U_12743] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12742,tc_HOL_Obool)),U_12743),c_Orderings_Otop__class_Otop(tc_fun(U_12742,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12742,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3315_2]) ).

cnf(f_3315_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12742,tc_HOL_Obool)),U_12743),c_Orderings_Otop__class_Otop(tc_fun(U_12742,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12742,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3315_3]) ).

fof(f_3316_1,plain,
    ! [V_A_2,T_b] :
      ( V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV]) ).

fof(f_3316_2,plain,
    ! [U_12745,U_12744] :
      ( U_12745 = c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_12744),U_12745) != hAPP(c_Finite__Set_Ocard(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3316_1]) ).

fof(f_3316_3,plain,
    ! [U_12744,U_12745] :
      ( U_12745 = c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_12744),U_12745) != hAPP(c_Finite__Set_Ocard(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3316_2]) ).

cnf(f_3316_4,plain,
    ( U_12745 = c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_12744),U_12745) != hAPP(c_Finite__Set_Ocard(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

fof(f_3317_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff]) ).

fof(f_3317_2,plain,
    ! [U_12750,U_12749,U_12748,U_12747,U_12746] :
      ( ( ( hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12749) = hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12750)
          | U_12749 != U_12750 )
        & ( U_12749 = U_12750
          | hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12749) != hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12750) ) )
      | ~ c_Fun_Oinj__on(U_12746,U_12747,U_12748,c_Orderings_Otop__class_Otop(tc_fun(U_12746,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3317_1]) ).

fof(f_3317_3,plain,
    ( ! [U_12746,U_12747,U_12748,U_12749,U_12750] :
        ( hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12749) = hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12750)
        | U_12749 != U_12750
        | ~ sP941(U_12746,U_12747,U_12748,U_12749,U_12750) )
    & ! [U_12746,U_12747,U_12748,U_12749,U_12750] :
        ( U_12749 = U_12750
        | hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12749) != hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12750)
        | ~ sP941(U_12746,U_12747,U_12748,U_12749,U_12750) )
    & ! [U_12746,U_12747,U_12748,U_12749,U_12750] :
        ( sP941(U_12746,U_12747,U_12748,U_12749,U_12750)
        | ~ c_Fun_Oinj__on(U_12746,U_12747,U_12748,c_Orderings_Otop__class_Otop(tc_fun(U_12746,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP941])],[f_3317_2]) ).

cnf(f_3317_4,plain,
    ( sP941(U_12746,U_12747,U_12748,U_12749,U_12750)
    | ~ c_Fun_Oinj__on(U_12746,U_12747,U_12748,c_Orderings_Otop__class_Otop(tc_fun(U_12746,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

cnf(f_3317_5,plain,
    ( U_12749 = U_12750
    | hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12749) != hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12750)
    | ~ sP941(U_12746,U_12747,U_12748,U_12749,U_12750) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

cnf(f_3317_6,plain,
    ( hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12749) = hAPP(c_Set_Oimage(U_12746,U_12747,U_12748),U_12750)
    | U_12749 != U_12750
    | ~ sP941(U_12746,U_12747,U_12748,U_12749,U_12750) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

fof(f_3318_1,plain,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(f_3318_2,plain,
    ! [U_12751] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12751,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12751,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3318_1]) ).

fof(f_3318_3,plain,
    ! [U_12751] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12751,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12751,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3318_2]) ).

cnf(f_3318_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12751,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12751,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3318_3]) ).

fof(f_3319_1,plain,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__empty__eq]) ).

fof(f_3319_2,plain,
    ! [U_12752] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12752,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_12752,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12752,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3319_1]) ).

fof(f_3319_3,plain,
    ! [U_12752] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12752,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_12752,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12752,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3319_2]) ).

cnf(f_3319_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12752,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_12752,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12752,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3319_3]) ).

fof(f_3320_1,plain,
    ! [V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__compl]) ).

fof(f_3320_2,plain,
    ! [U_12754,U_12753] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12753,tc_HOL_Obool)),U_12754)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),c_Orderings_Otop__class_Otop(tc_fun(U_12753,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),c_Orderings_Otop__class_Otop(tc_fun(U_12753,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12753,tc_HOL_Obool)),U_12754))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),U_12754)) ),
    inference(variable_rename,[status(thm)],[f_3320_1]) ).

fof(f_3320_3,plain,
    ( ! [U_12753,U_12754] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12753,tc_HOL_Obool)),U_12754)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),c_Orderings_Otop__class_Otop(tc_fun(U_12753,tc_HOL_Obool))))
        | ~ sP942(U_12753,U_12754) )
    & ! [U_12753,U_12754] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),c_Orderings_Otop__class_Otop(tc_fun(U_12753,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12753,tc_HOL_Obool)),U_12754)))
        | ~ sP942(U_12753,U_12754) )
    & ! [U_12753,U_12754] :
        ( sP942(U_12753,U_12754)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),U_12754)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP942])],[f_3320_2]) ).

cnf(f_3320_4,plain,
    ( sP942(U_12753,U_12754)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),U_12754)) ),
    inference(clausify,[status(thm)],[f_3320_3]) ).

cnf(f_3320_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),c_Orderings_Otop__class_Otop(tc_fun(U_12753,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12753,tc_HOL_Obool)),U_12754)))
    | ~ sP942(U_12753,U_12754) ),
    inference(clausify,[status(thm)],[f_3320_3]) ).

cnf(f_3320_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12753,tc_HOL_Obool)),U_12754)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12753),c_Orderings_Otop__class_Otop(tc_fun(U_12753,tc_HOL_Obool))))
    | ~ sP942(U_12753,U_12754) ),
    inference(clausify,[status(thm)],[f_3320_3]) ).

fof(f_3321_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__partition2]) ).

fof(f_3321_2,plain,
    ! [U_12756,U_12755] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12755,tc_HOL_Obool)),U_12756)),U_12756) = c_Orderings_Otop__class_Otop(tc_fun(U_12755,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3321_1]) ).

fof(f_3321_3,plain,
    ! [U_12756,U_12755] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12755,tc_HOL_Obool)),U_12756)),U_12756) = c_Orderings_Otop__class_Otop(tc_fun(U_12755,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3321_2]) ).

cnf(f_3321_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12755,tc_HOL_Obool)),U_12756)),U_12756) = c_Orderings_Otop__class_Otop(tc_fun(U_12755,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3321_3]) ).

fof(f_3322_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__partition]) ).

fof(f_3322_2,plain,
    ! [U_12758,U_12757] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12757,tc_HOL_Obool)),U_12758),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12757,tc_HOL_Obool)),U_12758)) = c_Orderings_Otop__class_Otop(tc_fun(U_12757,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3322_1]) ).

fof(f_3322_3,plain,
    ! [U_12757,U_12758] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12757,tc_HOL_Obool)),U_12758),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12757,tc_HOL_Obool)),U_12758)) = c_Orderings_Otop__class_Otop(tc_fun(U_12757,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3322_2]) ).

cnf(f_3322_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12757,tc_HOL_Obool)),U_12758),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12757,tc_HOL_Obool)),U_12758)) = c_Orderings_Otop__class_Otop(tc_fun(U_12757,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3322_3]) ).

fof(f_3323_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(f_3323_2,plain,
    ! [U_12760,U_12759] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12759,tc_HOL_Obool)),U_12760) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12759,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12759,tc_HOL_Obool))),U_12760),
    inference(variable_rename,[status(thm)],[f_3323_1]) ).

fof(f_3323_3,plain,
    ! [U_12759,U_12760] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12759,tc_HOL_Obool)),U_12760) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12759,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12759,tc_HOL_Obool))),U_12760),
    inference(definitional_conversion,[status(esa)],[f_3323_2]) ).

cnf(f_3323_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12759,tc_HOL_Obool)),U_12760) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12759,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12759,tc_HOL_Obool))),U_12760),
    inference(clausify,[status(thm)],[f_3323_3]) ).

fof(f_3324_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Code__Numeral_Oof__nat,V_x_2) != hAPP(c_Code__Numeral_Oof__nat,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Oof__nat__inject]) ).

fof(f_3324_2,plain,
    ! [U_12762,U_12761] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,U_12761) = hAPP(c_Code__Numeral_Oof__nat,U_12762)
          | U_12761 != U_12762 )
        & ( U_12761 = U_12762
          | hAPP(c_Code__Numeral_Oof__nat,U_12761) != hAPP(c_Code__Numeral_Oof__nat,U_12762) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12762),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12761),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3324_1]) ).

fof(f_3324_3,plain,
    ( ! [U_12761,U_12762] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_12761) = hAPP(c_Code__Numeral_Oof__nat,U_12762)
        | U_12761 != U_12762
        | ~ sP943(U_12761,U_12762) )
    & ! [U_12761,U_12762] :
        ( U_12761 = U_12762
        | hAPP(c_Code__Numeral_Oof__nat,U_12761) != hAPP(c_Code__Numeral_Oof__nat,U_12762)
        | ~ sP943(U_12761,U_12762) )
    & ! [U_12761,U_12762] :
        ( sP943(U_12761,U_12762)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12762),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12761),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP943])],[f_3324_2]) ).

cnf(f_3324_4,plain,
    ( sP943(U_12761,U_12762)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12762),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12761),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3324_3]) ).

cnf(f_3324_5,plain,
    ( U_12761 = U_12762
    | hAPP(c_Code__Numeral_Oof__nat,U_12761) != hAPP(c_Code__Numeral_Oof__nat,U_12762)
    | ~ sP943(U_12761,U_12762) ),
    inference(clausify,[status(thm)],[f_3324_3]) ).

cnf(f_3324_6,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_12761) = hAPP(c_Code__Numeral_Oof__nat,U_12762)
    | U_12761 != U_12762
    | ~ sP943(U_12761,U_12762) ),
    inference(clausify,[status(thm)],[f_3324_3]) ).

fof(f_3325_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq]) ).

fof(f_3325_2,plain,
    ! [U_12766,U_12765,U_12764,U_12763] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12763,tc_fun(U_12764,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12763,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12764,tc_HOL_Obool),tc_fun(U_12764,tc_HOL_Obool),U_12763),hAPP(c_COMBC(U_12764,tc_fun(U_12764,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12764))),U_12765)),U_12766))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12764),U_12766),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12763,tc_fun(U_12764,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12763,tc_HOL_Obool))),U_12765))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_12764),U_12766),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12763,tc_fun(U_12764,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12763,tc_HOL_Obool))),U_12765)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12763,tc_fun(U_12764,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12763,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12764,tc_HOL_Obool),tc_fun(U_12764,tc_HOL_Obool),U_12763),hAPP(c_COMBC(U_12764,tc_fun(U_12764,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12764))),U_12765)),U_12766)) ) ),
    inference(variable_rename,[status(thm)],[f_3325_1]) ).

fof(f_3325_3,plain,
    ( ! [U_12774,U_12772,U_12770,U_12768] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12768,tc_fun(U_12770,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12768,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12770,tc_HOL_Obool),tc_fun(U_12770,tc_HOL_Obool),U_12768),hAPP(c_COMBC(U_12770,tc_fun(U_12770,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12770))),U_12772)),U_12774))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12770),U_12774),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12768,tc_fun(U_12770,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12768,tc_HOL_Obool))),U_12772))) )
    & ! [U_12773,U_12771,U_12769,U_12767] :
        ( hBOOL(hAPP(hAPP(c_member(U_12769),U_12773),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12769,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12767,tc_HOL_Obool))),U_12771)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12769,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12767,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12769,tc_HOL_Obool),tc_fun(U_12769,tc_HOL_Obool),U_12767),hAPP(c_COMBC(U_12769,tc_fun(U_12769,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12769))),U_12771)),U_12773)) ) ),
    inference(miniscope,[status(thm)],[f_3325_2]) ).

fof(f_3325_4,plain,
    ( ! [U_12768,U_12770,U_12772,U_12774] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12768,tc_fun(U_12770,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12768,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12770,tc_HOL_Obool),tc_fun(U_12770,tc_HOL_Obool),U_12768),hAPP(c_COMBC(U_12770,tc_fun(U_12770,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12770))),U_12772)),U_12774))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12770),U_12774),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12768,tc_fun(U_12770,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12768,tc_HOL_Obool))),U_12772))) )
    & ! [U_12773,U_12769,U_12767,U_12771] :
        ( hBOOL(hAPP(hAPP(c_member(U_12769),U_12773),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12769,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12767,tc_HOL_Obool))),U_12771)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12769,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12767,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12769,tc_HOL_Obool),tc_fun(U_12769,tc_HOL_Obool),U_12767),hAPP(c_COMBC(U_12769,tc_fun(U_12769,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12769))),U_12771)),U_12773)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3325_3]) ).

cnf(f_3325_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12769),U_12773),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12769,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12767,tc_HOL_Obool))),U_12771)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12769,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12767,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12769,tc_HOL_Obool),tc_fun(U_12769,tc_HOL_Obool),U_12767),hAPP(c_COMBC(U_12769,tc_fun(U_12769,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12769))),U_12771)),U_12773)) ),
    inference(clausify,[status(thm)],[f_3325_4]) ).

cnf(f_3325_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12768,tc_fun(U_12770,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12768,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12770,tc_HOL_Obool),tc_fun(U_12770,tc_HOL_Obool),U_12768),hAPP(c_COMBC(U_12770,tc_fun(U_12770,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12770))),U_12772)),U_12774))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12770),U_12774),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12768,tc_fun(U_12770,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12768,tc_HOL_Obool))),U_12772))) ),
    inference(clausify,[status(thm)],[f_3325_4]) ).

fof(f_3326_1,plain,
    ! [V_f_2,T_d,V_g_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__imageI]) ).

fof(f_3326_2,plain,
    ! [U_12779,U_12778,U_12777,U_12776,U_12775] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12778),hAPP(c_Set_Oimage(U_12776,U_12778,hAPP(hAPP(c_COMBB(U_12775,U_12778,U_12776),U_12779),U_12777)),c_Orderings_Otop__class_Otop(tc_fun(U_12776,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),hAPP(c_Set_Oimage(U_12776,U_12775,U_12777),c_Orderings_Otop__class_Otop(tc_fun(U_12776,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_3326_1]) ).

fof(f_3326_3,plain,
    ! [U_12775,U_12776,U_12777,U_12778,U_12779] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12778),hAPP(c_Set_Oimage(U_12776,U_12778,hAPP(hAPP(c_COMBB(U_12775,U_12778,U_12776),U_12779),U_12777)),c_Orderings_Otop__class_Otop(tc_fun(U_12776,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),hAPP(c_Set_Oimage(U_12776,U_12775,U_12777),c_Orderings_Otop__class_Otop(tc_fun(U_12776,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_3326_2]) ).

cnf(f_3326_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12778),hAPP(c_Set_Oimage(U_12776,U_12778,hAPP(hAPP(c_COMBB(U_12775,U_12778,U_12776),U_12779),U_12777)),c_Orderings_Otop__class_Otop(tc_fun(U_12776,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),hAPP(c_Set_Oimage(U_12776,U_12775,U_12777),c_Orderings_Otop__class_Otop(tc_fun(U_12776,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

fof(f_3327_1,plain,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_nat__of]) ).

fof(f_3327_2,plain,
    ! [U_12780] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_12780)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3327_1]) ).

fof(f_3327_3,plain,
    ! [U_12780] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_12780)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3327_2]) ).

cnf(f_3327_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_12780)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3327_3]) ).

fof(f_3328_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__f__f]) ).

fof(f_3328_2,plain,
    ! [U_12784,U_12783,U_12782,U_12781] :
      ( hAPP(c_Fun_Othe__inv__into(U_12781,U_12782,c_Orderings_Otop__class_Otop(tc_fun(U_12781,tc_HOL_Obool)),U_12783),hAPP(U_12783,U_12784)) = U_12784
      | ~ c_Fun_Oinj__on(U_12781,U_12782,U_12783,c_Orderings_Otop__class_Otop(tc_fun(U_12781,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3328_1]) ).

fof(f_3328_3,plain,
    ! [U_12781,U_12782,U_12783,U_12784] :
      ( hAPP(c_Fun_Othe__inv__into(U_12781,U_12782,c_Orderings_Otop__class_Otop(tc_fun(U_12781,tc_HOL_Obool)),U_12783),hAPP(U_12783,U_12784)) = U_12784
      | ~ c_Fun_Oinj__on(U_12781,U_12782,U_12783,c_Orderings_Otop__class_Otop(tc_fun(U_12781,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3328_2]) ).

cnf(f_3328_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_12781,U_12782,c_Orderings_Otop__class_Otop(tc_fun(U_12781,tc_HOL_Obool)),U_12783),hAPP(U_12783,U_12784)) = U_12784
    | ~ c_Fun_Oinj__on(U_12781,U_12782,U_12783,c_Orderings_Otop__class_Otop(tc_fun(U_12781,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3328_3]) ).

fof(f_3329_1,plain,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1]) ).

fof(f_3329_2,plain,
    ! [U_12786,U_12785] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12785),c_Orderings_Otop__class_Otop(tc_fun(U_12785,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_12786),c_Orderings_Otop__class_Otop(tc_fun(U_12786,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12785,U_12786)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12785,U_12786),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3329_1]) ).

fof(f_3329_3,plain,
    ! [U_12785,U_12786] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12785),c_Orderings_Otop__class_Otop(tc_fun(U_12785,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_12786),c_Orderings_Otop__class_Otop(tc_fun(U_12786,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12785,U_12786)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12785,U_12786),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3329_2]) ).

cnf(f_3329_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12785),c_Orderings_Otop__class_Otop(tc_fun(U_12785,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(U_12786),c_Orderings_Otop__class_Otop(tc_fun(U_12786,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12785,U_12786)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12785,U_12786),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3329_3]) ).

fof(f_3330_1,plain,
    ! [T_b] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inj__of__nat]) ).

fof(f_3330_2,plain,
    ! [U_12787] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_12787,c_Nat_Osemiring__1__class_Oof__nat(U_12787),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_12787) ),
    inference(variable_rename,[status(thm)],[f_3330_1]) ).

fof(f_3330_3,plain,
    ! [U_12787] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_12787,c_Nat_Osemiring__1__class_Oof__nat(U_12787),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_12787) ),
    inference(definitional_conversion,[status(esa)],[f_3330_2]) ).

cnf(f_3330_4,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,U_12787,c_Nat_Osemiring__1__class_Oof__nat(U_12787),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(U_12787) ),
    inference(clausify,[status(thm)],[f_3330_3]) ).

fof(f_3331_1,plain,
    ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_dom__const]) ).

fof(f_3331_2,plain,
    ! [U_12790,U_12789,U_12788] : c_Map_Odom(U_12788,U_12789,hAPP(hAPP(c_COMBB(U_12789,tc_Option_Ooption(U_12789),U_12788),c_Option_Ooption_OSome(U_12789)),U_12790)) = c_Orderings_Otop__class_Otop(tc_fun(U_12788,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3331_1]) ).

fof(f_3331_3,plain,
    ! [U_12788,U_12789,U_12790] : c_Map_Odom(U_12788,U_12789,hAPP(hAPP(c_COMBB(U_12789,tc_Option_Ooption(U_12789),U_12788),c_Option_Ooption_OSome(U_12789)),U_12790)) = c_Orderings_Otop__class_Otop(tc_fun(U_12788,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3331_2]) ).

cnf(f_3331_4,plain,
    c_Map_Odom(U_12788,U_12789,hAPP(hAPP(c_COMBB(U_12789,tc_Option_Ooption(U_12789),U_12788),c_Option_Ooption_OSome(U_12789)),U_12790)) = c_Orderings_Otop__class_Otop(tc_fun(U_12788,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3331_3]) ).

fof(f_3332_1,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_atLeast__0]) ).

fof(f_3332_2,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3332_1]) ).

cnf(f_3332_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3332_2]) ).

fof(f_3333_1,plain,
    ! [T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__fun]) ).

fof(f_3333_2,plain,
    ! [U_12794,U_12793,U_12792,U_12791] :
      ( c_Fun_Oinj__on(U_12791,tc_fun(U_12794,U_12792),hAPP(hAPP(c_COMBB(U_12792,tc_fun(U_12794,U_12792),U_12791),c_COMBK(U_12792,U_12794)),U_12793),c_Orderings_Otop__class_Otop(tc_fun(U_12791,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_12791,U_12792,U_12793,c_Orderings_Otop__class_Otop(tc_fun(U_12791,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3333_1]) ).

fof(f_3333_3,plain,
    ! [U_12791,U_12792,U_12793,U_12794] :
      ( c_Fun_Oinj__on(U_12791,tc_fun(U_12794,U_12792),hAPP(hAPP(c_COMBB(U_12792,tc_fun(U_12794,U_12792),U_12791),c_COMBK(U_12792,U_12794)),U_12793),c_Orderings_Otop__class_Otop(tc_fun(U_12791,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_12791,U_12792,U_12793,c_Orderings_Otop__class_Otop(tc_fun(U_12791,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3333_2]) ).

cnf(f_3333_4,plain,
    ( c_Fun_Oinj__on(U_12791,tc_fun(U_12794,U_12792),hAPP(hAPP(c_COMBB(U_12792,tc_fun(U_12794,U_12792),U_12791),c_COMBK(U_12792,U_12794)),U_12793),c_Orderings_Otop__class_Otop(tc_fun(U_12791,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_12791,U_12792,U_12793,c_Orderings_Otop__class_Otop(tc_fun(U_12791,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3333_3]) ).

fof(f_3334_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__bot__eq]) ).

fof(f_3334_2,plain,
    ! [U_12795] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12795),c_Orderings_Obot__class_Obot(U_12795)) = c_Orderings_Otop__class_Otop(U_12795)
      | ~ class_Lattices_Oboolean__algebra(U_12795) ),
    inference(variable_rename,[status(thm)],[f_3334_1]) ).

fof(f_3334_3,plain,
    ! [U_12795] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12795),c_Orderings_Obot__class_Obot(U_12795)) = c_Orderings_Otop__class_Otop(U_12795)
      | ~ class_Lattices_Oboolean__algebra(U_12795) ),
    inference(definitional_conversion,[status(esa)],[f_3334_2]) ).

cnf(f_3334_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12795),c_Orderings_Obot__class_Obot(U_12795)) = c_Orderings_Otop__class_Otop(U_12795)
    | ~ class_Lattices_Oboolean__algebra(U_12795) ),
    inference(clausify,[status(thm)],[f_3334_3]) ).

fof(f_3335_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__top__eq]) ).

fof(f_3335_2,plain,
    ! [U_12796] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12796),c_Orderings_Otop__class_Otop(U_12796)) = c_Orderings_Obot__class_Obot(U_12796)
      | ~ class_Lattices_Oboolean__algebra(U_12796) ),
    inference(variable_rename,[status(thm)],[f_3335_1]) ).

fof(f_3335_3,plain,
    ! [U_12796] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12796),c_Orderings_Otop__class_Otop(U_12796)) = c_Orderings_Obot__class_Obot(U_12796)
      | ~ class_Lattices_Oboolean__algebra(U_12796) ),
    inference(definitional_conversion,[status(esa)],[f_3335_2]) ).

cnf(f_3335_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_12796),c_Orderings_Otop__class_Otop(U_12796)) = c_Orderings_Obot__class_Obot(U_12796)
    | ~ class_Lattices_Oboolean__algebra(U_12796) ),
    inference(clausify,[status(thm)],[f_3335_3]) ).

fof(f_3336_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__sup__top]) ).

fof(f_3336_2,plain,
    ! [U_12798,U_12797] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12797),hAPP(c_Groups_Ouminus__class_Ouminus(U_12797),U_12798)),U_12798) = c_Orderings_Otop__class_Otop(U_12797)
      | ~ class_Lattices_Oboolean__algebra(U_12797) ),
    inference(variable_rename,[status(thm)],[f_3336_1]) ).

fof(f_3336_3,plain,
    ! [U_12797,U_12798] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12797),hAPP(c_Groups_Ouminus__class_Ouminus(U_12797),U_12798)),U_12798) = c_Orderings_Otop__class_Otop(U_12797)
      | ~ class_Lattices_Oboolean__algebra(U_12797) ),
    inference(definitional_conversion,[status(esa)],[f_3336_2]) ).

cnf(f_3336_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12797),hAPP(c_Groups_Ouminus__class_Ouminus(U_12797),U_12798)),U_12798) = c_Orderings_Otop__class_Otop(U_12797)
    | ~ class_Lattices_Oboolean__algebra(U_12797) ),
    inference(clausify,[status(thm)],[f_3336_3]) ).

fof(f_3337_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__compl__top]) ).

fof(f_3337_2,plain,
    ! [U_12800,U_12799] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12799),U_12800),hAPP(c_Groups_Ouminus__class_Ouminus(U_12799),U_12800)) = c_Orderings_Otop__class_Otop(U_12799)
      | ~ class_Lattices_Oboolean__algebra(U_12799) ),
    inference(variable_rename,[status(thm)],[f_3337_1]) ).

fof(f_3337_3,plain,
    ! [U_12799,U_12800] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12799),U_12800),hAPP(c_Groups_Ouminus__class_Ouminus(U_12799),U_12800)) = c_Orderings_Otop__class_Otop(U_12799)
      | ~ class_Lattices_Oboolean__algebra(U_12799) ),
    inference(definitional_conversion,[status(esa)],[f_3337_2]) ).

cnf(f_3337_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12799),U_12800),hAPP(c_Groups_Ouminus__class_Ouminus(U_12799),U_12800)) = c_Orderings_Otop__class_Otop(U_12799)
    | ~ class_Lattices_Oboolean__algebra(U_12799) ),
    inference(clausify,[status(thm)],[f_3337_3]) ).

fof(f_3338_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff]) ).

fof(f_3338_2,plain,
    ! [U_12805,U_12804,U_12803,U_12802,U_12801] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12802),hAPP(U_12803,U_12804)),hAPP(c_Set_Oimage(U_12801,U_12802,U_12803),U_12805)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12801),U_12804),U_12805)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_12801),U_12804),U_12805))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12802),hAPP(U_12803,U_12804)),hAPP(c_Set_Oimage(U_12801,U_12802,U_12803),U_12805))) ) )
      | ~ c_Fun_Oinj__on(U_12801,U_12802,U_12803,c_Orderings_Otop__class_Otop(tc_fun(U_12801,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3338_1]) ).

fof(f_3338_3,plain,
    ( ! [U_12801,U_12802,U_12803,U_12804,U_12805] :
        ( hBOOL(hAPP(hAPP(c_member(U_12802),hAPP(U_12803,U_12804)),hAPP(c_Set_Oimage(U_12801,U_12802,U_12803),U_12805)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12801),U_12804),U_12805))
        | ~ sP944(U_12801,U_12802,U_12803,U_12804,U_12805) )
    & ! [U_12801,U_12802,U_12803,U_12804,U_12805] :
        ( hBOOL(hAPP(hAPP(c_member(U_12801),U_12804),U_12805))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12802),hAPP(U_12803,U_12804)),hAPP(c_Set_Oimage(U_12801,U_12802,U_12803),U_12805)))
        | ~ sP944(U_12801,U_12802,U_12803,U_12804,U_12805) )
    & ! [U_12801,U_12802,U_12803,U_12804,U_12805] :
        ( sP944(U_12801,U_12802,U_12803,U_12804,U_12805)
        | ~ c_Fun_Oinj__on(U_12801,U_12802,U_12803,c_Orderings_Otop__class_Otop(tc_fun(U_12801,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP944])],[f_3338_2]) ).

cnf(f_3338_4,plain,
    ( sP944(U_12801,U_12802,U_12803,U_12804,U_12805)
    | ~ c_Fun_Oinj__on(U_12801,U_12802,U_12803,c_Orderings_Otop__class_Otop(tc_fun(U_12801,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3338_3]) ).

cnf(f_3338_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12801),U_12804),U_12805))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12802),hAPP(U_12803,U_12804)),hAPP(c_Set_Oimage(U_12801,U_12802,U_12803),U_12805)))
    | ~ sP944(U_12801,U_12802,U_12803,U_12804,U_12805) ),
    inference(clausify,[status(thm)],[f_3338_3]) ).

cnf(f_3338_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12802),hAPP(U_12803,U_12804)),hAPP(c_Set_Oimage(U_12801,U_12802,U_12803),U_12805)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12801),U_12804),U_12805))
    | ~ sP944(U_12801,U_12802,U_12803,U_12804,U_12805) ),
    inference(clausify,[status(thm)],[f_3338_3]) ).

fof(f_3339_1,plain,
    ! [V_b_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
          | ! [B_x] :
              ( ? [B_y] :
                  ( B_y != B_x
                  & V_b_2 = hAPP(V_f_2,B_y) )
              | V_b_2 != hAPP(V_f_2,B_x) ) )
        & ( ? [B_x] :
              ( ! [B_y] :
                  ( B_y = B_x
                  | V_b_2 != hAPP(V_f_2,B_y) )
              & V_b_2 = hAPP(V_f_2,B_x) )
          | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_range__ex1__eq]) ).

fof(f_3339_2,plain,
    ! [U_12813,U_12812,U_12811,U_12810] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
          | ! [U_12809] :
              ( ? [U_12808] :
                  ( U_12808 != U_12809
                  & U_12813 = hAPP(U_12812,U_12808) )
              | U_12813 != hAPP(U_12812,U_12809) ) )
        & ( ? [U_12807] :
              ( ! [U_12806] :
                  ( U_12806 = U_12807
                  | U_12813 != hAPP(U_12812,U_12806) )
              & U_12813 = hAPP(U_12812,U_12807) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_12810,U_12811,U_12812,c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3339_1]) ).

fof(f_3339_3,plain,
    ! [U_12813,U_12812,U_12811,U_12810] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
          | ! [U_12809] :
              ( ? [U_12808] :
                  ( U_12808 != U_12809
                  & U_12813 = hAPP(U_12812,U_12808) )
              | U_12813 != hAPP(U_12812,U_12809) ) )
        & ( ( ! [U_12806] :
                ( U_12806 = sK273(U_12813,U_12812,U_12811,U_12810)
                | U_12813 != hAPP(U_12812,U_12806) )
            & U_12813 = hAPP(U_12812,sK273(U_12813,U_12812,U_12811,U_12810)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_12810,U_12811,U_12812,c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_12807,sK273(U_12813,U_12812,U_12811,U_12810))],[f_3339_2]) ).

fof(f_3339_4,plain,
    ! [U_12813,U_12812,U_12811,U_12810] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
          | ! [U_12809] :
              ( ( sK274(U_12813,U_12812,U_12811,U_12810,U_12809) != U_12809
                & U_12813 = hAPP(U_12812,sK274(U_12813,U_12812,U_12811,U_12810,U_12809)) )
              | U_12813 != hAPP(U_12812,U_12809) ) )
        & ( ( ! [U_12806] :
                ( U_12806 = sK273(U_12813,U_12812,U_12811,U_12810)
                | U_12813 != hAPP(U_12812,U_12806) )
            & U_12813 = hAPP(U_12812,sK273(U_12813,U_12812,U_12811,U_12810)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_12810,U_12811,U_12812,c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_12808,sK274(U_12813,U_12812,U_12811,U_12810,U_12809))],[f_3339_3]) ).

fof(f_3339_5,plain,
    ( ! [U_12810,U_12809,U_12811,U_12812,U_12813] :
        ( sK274(U_12813,U_12812,U_12811,U_12810,U_12809) != U_12809
        | ~ sP946(U_12810,U_12809,U_12811,U_12812,U_12813) )
    & ! [U_12810,U_12809,U_12811,U_12812,U_12813] :
        ( U_12813 = hAPP(U_12812,sK274(U_12813,U_12812,U_12811,U_12810,U_12809))
        | ~ sP946(U_12810,U_12809,U_12811,U_12812,U_12813) )
    & ! [U_12810,U_12806,U_12811,U_12812,U_12813] :
        ( U_12806 = sK273(U_12813,U_12812,U_12811,U_12810)
        | U_12813 != hAPP(U_12812,U_12806)
        | ~ sP945(U_12810,U_12806,U_12811,U_12812,U_12813) )
    & ! [U_12810,U_12806,U_12811,U_12812,U_12813] :
        ( U_12813 = hAPP(U_12812,sK273(U_12813,U_12812,U_12811,U_12810))
        | ~ sP945(U_12810,U_12806,U_12811,U_12812,U_12813) )
    & ! [U_12810,U_12806,U_12809,U_12811,U_12812,U_12813] :
        ( hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
        | sP946(U_12810,U_12809,U_12811,U_12812,U_12813)
        | U_12813 != hAPP(U_12812,U_12809)
        | ~ sP947(U_12810,U_12806,U_12809,U_12811,U_12812,U_12813) )
    & ! [U_12810,U_12806,U_12809,U_12811,U_12812,U_12813] :
        ( sP945(U_12810,U_12806,U_12811,U_12812,U_12813)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
        | ~ sP947(U_12810,U_12806,U_12809,U_12811,U_12812,U_12813) )
    & ! [U_12810,U_12806,U_12809,U_12811,U_12812,U_12813] :
        ( sP947(U_12810,U_12806,U_12809,U_12811,U_12812,U_12813)
        | ~ c_Fun_Oinj__on(U_12810,U_12811,U_12812,c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP945,sP946,sP947])],[f_3339_4]) ).

cnf(f_3339_6,plain,
    ( sP947(U_12810,U_12806,U_12809,U_12811,U_12812,U_12813)
    | ~ c_Fun_Oinj__on(U_12810,U_12811,U_12812,c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

cnf(f_3339_7,plain,
    ( sP945(U_12810,U_12806,U_12811,U_12812,U_12813)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
    | ~ sP947(U_12810,U_12806,U_12809,U_12811,U_12812,U_12813) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

cnf(f_3339_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12811),U_12813),hAPP(c_Set_Oimage(U_12810,U_12811,U_12812),c_Orderings_Otop__class_Otop(tc_fun(U_12810,tc_HOL_Obool)))))
    | sP946(U_12810,U_12809,U_12811,U_12812,U_12813)
    | U_12813 != hAPP(U_12812,U_12809)
    | ~ sP947(U_12810,U_12806,U_12809,U_12811,U_12812,U_12813) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

cnf(f_3339_9,plain,
    ( U_12813 = hAPP(U_12812,sK273(U_12813,U_12812,U_12811,U_12810))
    | ~ sP945(U_12810,U_12806,U_12811,U_12812,U_12813) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

cnf(f_3339_10,plain,
    ( U_12806 = sK273(U_12813,U_12812,U_12811,U_12810)
    | U_12813 != hAPP(U_12812,U_12806)
    | ~ sP945(U_12810,U_12806,U_12811,U_12812,U_12813) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

cnf(f_3339_11,plain,
    ( U_12813 = hAPP(U_12812,sK274(U_12813,U_12812,U_12811,U_12810,U_12809))
    | ~ sP946(U_12810,U_12809,U_12811,U_12812,U_12813) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

cnf(f_3339_12,plain,
    ( sK274(U_12813,U_12812,U_12811,U_12810,U_12809) != U_12809
    | ~ sP946(U_12810,U_12809,U_12811,U_12812,U_12813) ),
    inference(clausify,[status(thm)],[f_3339_5]) ).

fof(f_3340_1,plain,
    ! [V_f_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj]) ).

fof(f_3340_2,plain,
    ! [U_12815,U_12814] :
      ( c_Fun_Oinj__on(U_12814,U_12814,U_12815,c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_12814,U_12814,U_12815),c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12814),c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3340_1]) ).

fof(f_3340_3,plain,
    ! [U_12814,U_12815] :
      ( c_Fun_Oinj__on(U_12814,U_12814,U_12815,c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_12814,U_12814,U_12815),c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12814),c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3340_2]) ).

cnf(f_3340_4,plain,
    ( c_Fun_Oinj__on(U_12814,U_12814,U_12815,c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_12814,U_12814,U_12815),c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12814),c_Orderings_Otop__class_Otop(tc_fun(U_12814,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3340_3]) ).

fof(f_3341_1,plain,
    ! [V_f_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj]) ).

fof(f_3341_2,plain,
    ! [U_12817,U_12816] :
      ( hAPP(c_Set_Oimage(U_12816,U_12816,U_12817),c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_12816,U_12816,U_12817,c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12816),c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3341_1]) ).

fof(f_3341_3,plain,
    ! [U_12816,U_12817] :
      ( hAPP(c_Set_Oimage(U_12816,U_12816,U_12817),c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_12816,U_12816,U_12817,c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12816),c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3341_2]) ).

cnf(f_3341_4,plain,
    ( hAPP(c_Set_Oimage(U_12816,U_12816,U_12817),c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_12816,U_12816,U_12817,c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12816),c_Orderings_Otop__class_Otop(tc_fun(U_12816,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3341_3]) ).

fof(f_3342_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff]) ).

fof(f_3342_2,plain,
    ! [U_12822,U_12821,U_12820,U_12819,U_12818] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12821)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12822)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12818,tc_HOL_Obool)),U_12821),U_12822)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12818,tc_HOL_Obool)),U_12821),U_12822))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12821)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12822))) ) )
      | ~ c_Fun_Oinj__on(U_12818,U_12819,U_12820,c_Orderings_Otop__class_Otop(tc_fun(U_12818,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3342_1]) ).

fof(f_3342_3,plain,
    ( ! [U_12820,U_12821,U_12822,U_12818,U_12819] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12821)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12822)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12818,tc_HOL_Obool)),U_12821),U_12822))
        | ~ sP948(U_12820,U_12821,U_12822,U_12818,U_12819) )
    & ! [U_12820,U_12821,U_12822,U_12818,U_12819] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12818,tc_HOL_Obool)),U_12821),U_12822))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12821)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12822)))
        | ~ sP948(U_12820,U_12821,U_12822,U_12818,U_12819) )
    & ! [U_12820,U_12821,U_12822,U_12818,U_12819] :
        ( sP948(U_12820,U_12821,U_12822,U_12818,U_12819)
        | ~ c_Fun_Oinj__on(U_12818,U_12819,U_12820,c_Orderings_Otop__class_Otop(tc_fun(U_12818,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP948])],[f_3342_2]) ).

cnf(f_3342_4,plain,
    ( sP948(U_12820,U_12821,U_12822,U_12818,U_12819)
    | ~ c_Fun_Oinj__on(U_12818,U_12819,U_12820,c_Orderings_Otop__class_Otop(tc_fun(U_12818,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3342_3]) ).

cnf(f_3342_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12818,tc_HOL_Obool)),U_12821),U_12822))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12821)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12822)))
    | ~ sP948(U_12820,U_12821,U_12822,U_12818,U_12819) ),
    inference(clausify,[status(thm)],[f_3342_3]) ).

cnf(f_3342_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12821)),hAPP(c_Set_Oimage(U_12818,U_12819,U_12820),U_12822)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12818,tc_HOL_Obool)),U_12821),U_12822))
    | ~ sP948(U_12820,U_12821,U_12822,U_12818,U_12819) ),
    inference(clausify,[status(thm)],[f_3342_3]) ).

fof(f_3343_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__Int]) ).

fof(f_3343_2,plain,
    ! [U_12827,U_12826,U_12825,U_12824,U_12823] :
      ( hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12826),U_12827)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),U_12826)),hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),U_12827))
      | ~ c_Fun_Oinj__on(U_12823,U_12824,U_12825,c_Orderings_Otop__class_Otop(tc_fun(U_12823,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3343_1]) ).

fof(f_3343_3,plain,
    ! [U_12825,U_12826,U_12824,U_12823,U_12827] :
      ( hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12826),U_12827)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),U_12826)),hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),U_12827))
      | ~ c_Fun_Oinj__on(U_12823,U_12824,U_12825,c_Orderings_Otop__class_Otop(tc_fun(U_12823,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3343_2]) ).

cnf(f_3343_4,plain,
    ( hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12826),U_12827)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),U_12826)),hAPP(c_Set_Oimage(U_12823,U_12824,U_12825),U_12827))
    | ~ c_Fun_Oinj__on(U_12823,U_12824,U_12825,c_Orderings_Otop__class_Otop(tc_fun(U_12823,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3343_3]) ).

fof(f_3344_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__set__diff]) ).

fof(f_3344_2,plain,
    ! [U_12832,U_12831,U_12830,U_12829,U_12828] :
      ( hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12828,tc_HOL_Obool)),U_12831),U_12832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),U_12831)),hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),U_12832))
      | ~ c_Fun_Oinj__on(U_12828,U_12829,U_12830,c_Orderings_Otop__class_Otop(tc_fun(U_12828,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3344_1]) ).

fof(f_3344_3,plain,
    ! [U_12828,U_12829,U_12830,U_12831,U_12832] :
      ( hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12828,tc_HOL_Obool)),U_12831),U_12832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),U_12831)),hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),U_12832))
      | ~ c_Fun_Oinj__on(U_12828,U_12829,U_12830,c_Orderings_Otop__class_Otop(tc_fun(U_12828,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3344_2]) ).

cnf(f_3344_4,plain,
    ( hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12828,tc_HOL_Obool)),U_12831),U_12832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),U_12831)),hAPP(c_Set_Oimage(U_12828,U_12829,U_12830),U_12832))
    | ~ c_Fun_Oinj__on(U_12828,U_12829,U_12830,c_Orderings_Otop__class_Otop(tc_fun(U_12828,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3344_3]) ).

fof(f_3345_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset]) ).

fof(f_3345_2,plain,
    ! [U_12836,U_12835,U_12834,U_12833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12834,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12834,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),U_12836))),hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12833,tc_HOL_Obool)),U_12836))))
      | hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),c_Orderings_Otop__class_Otop(tc_fun(U_12833,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12834,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3345_1]) ).

fof(f_3345_3,plain,
    ! [U_12833,U_12834,U_12835,U_12836] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12834,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12834,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),U_12836))),hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12833,tc_HOL_Obool)),U_12836))))
      | hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),c_Orderings_Otop__class_Otop(tc_fun(U_12833,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12834,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3345_2]) ).

cnf(f_3345_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12834,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12834,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),U_12836))),hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12833,tc_HOL_Obool)),U_12836))))
    | hAPP(c_Set_Oimage(U_12833,U_12834,U_12835),c_Orderings_Otop__class_Otop(tc_fun(U_12833,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12834,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3345_3]) ).

fof(f_3346_1,plain,
    ! [V_y_2] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__inverse]) ).

fof(f_3346_2,plain,
    ! [U_12837] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_12837)) = U_12837
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12837),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3346_1]) ).

fof(f_3346_3,plain,
    ! [U_12837] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_12837)) = U_12837
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12837),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3346_2]) ).

cnf(f_3346_4,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_12837)) = U_12837
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12837),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3346_3]) ).

fof(f_3347_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
        | V_a_2 != V_b_2 )
      & ( V_a_2 = V_b_2
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set__sing]) ).

fof(f_3347_2,plain,
    ! [U_12841,U_12840,U_12839,U_12838] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12838,U_12839,hAPP(hAPP(c_Set_Oinsert(U_12838),U_12840),c_Orderings_Obot__class_Obot(tc_fun(U_12838,tc_HOL_Obool)))),U_12841))
        | U_12840 != U_12841 )
      & ( U_12840 = U_12841
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12838,U_12839,hAPP(hAPP(c_Set_Oinsert(U_12838),U_12840),c_Orderings_Obot__class_Obot(tc_fun(U_12838,tc_HOL_Obool)))),U_12841)) ) ),
    inference(variable_rename,[status(thm)],[f_3347_1]) ).

fof(f_3347_3,plain,
    ( ! [U_12849,U_12847] :
        ( ! [U_12845,U_12843] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12843,U_12845,hAPP(hAPP(c_Set_Oinsert(U_12843),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12843,tc_HOL_Obool)))),U_12849))
        | U_12847 != U_12849 )
    & ! [U_12848,U_12846] :
        ( ! [U_12844,U_12842] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12842,U_12844,hAPP(hAPP(c_Set_Oinsert(U_12842),U_12846),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))),U_12848))
        | U_12846 = U_12848 ) ),
    inference(miniscope,[status(thm)],[f_3347_2]) ).

fof(f_3347_4,plain,
    ( ! [U_12843,U_12849,U_12845,U_12847] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12843,U_12845,hAPP(hAPP(c_Set_Oinsert(U_12843),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12843,tc_HOL_Obool)))),U_12849))
        | U_12847 != U_12849 )
    & ! [U_12844,U_12846,U_12842,U_12848] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12842,U_12844,hAPP(hAPP(c_Set_Oinsert(U_12842),U_12846),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))),U_12848))
        | U_12846 = U_12848 ) ),
    inference(definitional_conversion,[status(esa)],[f_3347_3]) ).

cnf(f_3347_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12842,U_12844,hAPP(hAPP(c_Set_Oinsert(U_12842),U_12846),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))),U_12848))
    | U_12846 = U_12848 ),
    inference(clausify,[status(thm)],[f_3347_4]) ).

cnf(f_3347_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12843,U_12845,hAPP(hAPP(c_Set_Oinsert(U_12843),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12843,tc_HOL_Obool)))),U_12849))
    | U_12847 != U_12849 ),
    inference(clausify,[status(thm)],[f_3347_4]) ).

fof(f_3348_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__updI]) ).

fof(f_3348_2,plain,
    ! [U_12854,U_12853,U_12852,U_12851,U_12850] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12850)),hAPP(c_Set_Oimage(U_12851,tc_Option_Ooption(U_12850),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12851,tc_Option_Ooption(U_12850)),U_12852),U_12853),hAPP(c_Option_Ooption_OSome(U_12850),U_12854))),c_Orderings_Otop__class_Otop(tc_fun(U_12851,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12850)),hAPP(c_Set_Oimage(U_12851,tc_Option_Ooption(U_12850),U_12852),c_Orderings_Otop__class_Otop(tc_fun(U_12851,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_3348_1]) ).

fof(f_3348_3,plain,
    ! [U_12850,U_12851,U_12852,U_12853,U_12854] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12850)),hAPP(c_Set_Oimage(U_12851,tc_Option_Ooption(U_12850),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12851,tc_Option_Ooption(U_12850)),U_12852),U_12853),hAPP(c_Option_Ooption_OSome(U_12850),U_12854))),c_Orderings_Otop__class_Otop(tc_fun(U_12851,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12850)),hAPP(c_Set_Oimage(U_12851,tc_Option_Ooption(U_12850),U_12852),c_Orderings_Otop__class_Otop(tc_fun(U_12851,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_3348_2]) ).

cnf(f_3348_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12850)),hAPP(c_Set_Oimage(U_12851,tc_Option_Ooption(U_12850),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12851,tc_Option_Ooption(U_12850)),U_12852),U_12853),hAPP(c_Option_Ooption_OSome(U_12850),U_12854))),c_Orderings_Otop__class_Otop(tc_fun(U_12851,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_12850)),hAPP(c_Set_Oimage(U_12851,tc_Option_Ooption(U_12850),U_12852),c_Orderings_Otop__class_Otop(tc_fun(U_12851,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3348_3]) ).

fof(f_3349_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_UN__UN__finite__eq]) ).

fof(f_3349_2,plain,
    ! [U_12856,U_12855] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),tc_fun(U_12855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),tc_fun(U_12855,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_12856)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12856),
    inference(variable_rename,[status(thm)],[f_3349_1]) ).

fof(f_3349_3,plain,
    ! [U_12856,U_12855] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),tc_fun(U_12855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),tc_fun(U_12855,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_12856)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12856),
    inference(definitional_conversion,[status(esa)],[f_3349_2]) ).

cnf(f_3349_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),tc_fun(U_12855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),tc_fun(U_12855,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_12856)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12855,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12856),
    inference(clausify,[status(thm)],[f_3349_3]) ).

fof(f_3350_1,plain,
    ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__singleton]) ).

fof(f_3350_2,plain,
    ! [U_12857] : c_Fun_Oinj__on(U_12857,tc_fun(U_12857,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),c_Set_Oinsert(U_12857)),c_Orderings_Obot__class_Obot(tc_fun(U_12857,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12857,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3350_1]) ).

fof(f_3350_3,plain,
    ! [U_12857] : c_Fun_Oinj__on(U_12857,tc_fun(U_12857,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),c_Set_Oinsert(U_12857)),c_Orderings_Obot__class_Obot(tc_fun(U_12857,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12857,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3350_2]) ).

cnf(f_3350_4,plain,
    c_Fun_Oinj__on(U_12857,tc_fun(U_12857,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),c_Set_Oinsert(U_12857)),c_Orderings_Obot__class_Obot(tc_fun(U_12857,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12857,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3350_3]) ).

fof(f_3351_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0]) ).

fof(f_3351_2,plain,
    ! [U_12858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_12858),c_Orderings_Otop__class_Otop(tc_fun(U_12858,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),c_Orderings_Otop__class_Otop(tc_fun(U_12858,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3351_1]) ).

fof(f_3351_3,plain,
    ! [U_12858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_12858),c_Orderings_Otop__class_Otop(tc_fun(U_12858,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),c_Orderings_Otop__class_Otop(tc_fun(U_12858,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3351_2]) ).

cnf(f_3351_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_12858),c_Orderings_Otop__class_Otop(tc_fun(U_12858,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),c_Orderings_Otop__class_Otop(tc_fun(U_12858,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3351_3]) ).

fof(f_3352_1,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_card__UNIV__bool]) ).

fof(f_3352_2,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(definitional_conversion,[status(esa)],[f_3352_1]) ).

cnf(f_3352_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(clausify,[status(thm)],[f_3352_2]) ).

fof(f_3353_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset]) ).

fof(f_3353_2,plain,
    ! [U_12862,U_12861,U_12860,U_12859] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12860,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12859,U_12860,U_12861),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12859,tc_HOL_Obool)),U_12862))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12860,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12859,U_12860,U_12861),U_12862))))
      | ~ c_Fun_Oinj__on(U_12859,U_12860,U_12861,c_Orderings_Otop__class_Otop(tc_fun(U_12859,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3353_1]) ).

fof(f_3353_3,plain,
    ! [U_12859,U_12860,U_12861,U_12862] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12860,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12859,U_12860,U_12861),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12859,tc_HOL_Obool)),U_12862))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12860,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12859,U_12860,U_12861),U_12862))))
      | ~ c_Fun_Oinj__on(U_12859,U_12860,U_12861,c_Orderings_Otop__class_Otop(tc_fun(U_12859,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3353_2]) ).

cnf(f_3353_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12860,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12859,U_12860,U_12861),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12859,tc_HOL_Obool)),U_12862))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12860,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12859,U_12860,U_12861),U_12862))))
    | ~ c_Fun_Oinj__on(U_12859,U_12860,U_12861,c_Orderings_Otop__class_Otop(tc_fun(U_12859,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3353_3]) ).

fof(f_3354_1,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__0]) ).

fof(f_3354_2,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3354_1]) ).

cnf(f_3354_3,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3354_2]) ).

fof(f_3355_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2]) ).

fof(f_3355_2,plain,
    ! [U_12868,U_12867,U_12866,U_12865,U_12864,U_12863] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12863,tc_fun(U_12864,tc_fun(U_12865,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12863,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_fun(U_12864,tc_fun(U_12865,tc_HOL_Obool)),U_12863),hAPP(c_COMBC(U_12864,tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_fun(U_12865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12865,tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_fun(U_12865,tc_HOL_Obool)),U_12864),c_COMBC(U_12865,tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12865,tc_prod(U_12864,U_12865)),tc_fun(U_12865,tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool)),U_12864),hAPP(c_COMBB(tc_prod(U_12864,U_12865),tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool),U_12865),c_member(tc_prod(U_12864,U_12865)))),c_Product__Type_OPair(U_12864,U_12865))))),U_12866)),U_12867),U_12868))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12864,U_12865)),hAPP(hAPP(c_Product__Type_OPair(U_12864,U_12865),U_12867),U_12868)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12863,tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12863,tc_HOL_Obool))),U_12866))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12864,U_12865)),hAPP(hAPP(c_Product__Type_OPair(U_12864,U_12865),U_12867),U_12868)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12863,tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12863,tc_HOL_Obool))),U_12866)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12863,tc_fun(U_12864,tc_fun(U_12865,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12863,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_fun(U_12864,tc_fun(U_12865,tc_HOL_Obool)),U_12863),hAPP(c_COMBC(U_12864,tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_fun(U_12865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12865,tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_fun(U_12865,tc_HOL_Obool)),U_12864),c_COMBC(U_12865,tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12865,tc_prod(U_12864,U_12865)),tc_fun(U_12865,tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool)),U_12864),hAPP(c_COMBB(tc_prod(U_12864,U_12865),tc_fun(tc_fun(tc_prod(U_12864,U_12865),tc_HOL_Obool),tc_HOL_Obool),U_12865),c_member(tc_prod(U_12864,U_12865)))),c_Product__Type_OPair(U_12864,U_12865))))),U_12866)),U_12867),U_12868)) ) ),
    inference(variable_rename,[status(thm)],[f_3355_1]) ).

fof(f_3355_3,plain,
    ( ! [U_12880,U_12878,U_12876,U_12874,U_12872,U_12870] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12870,tc_fun(U_12872,tc_fun(U_12874,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12870,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12872,tc_fun(U_12874,tc_HOL_Obool)),U_12870),hAPP(c_COMBC(U_12872,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12874,tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12874,tc_HOL_Obool)),U_12872),c_COMBC(U_12874,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12874,tc_prod(U_12872,U_12874)),tc_fun(U_12874,tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),U_12872),hAPP(c_COMBB(tc_prod(U_12872,U_12874),tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool),U_12874),c_member(tc_prod(U_12872,U_12874)))),c_Product__Type_OPair(U_12872,U_12874))))),U_12876)),U_12878),U_12880))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12872,U_12874)),hAPP(hAPP(c_Product__Type_OPair(U_12872,U_12874),U_12878),U_12880)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12870,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12870,tc_HOL_Obool))),U_12876))) )
    & ! [U_12879,U_12877,U_12875,U_12873,U_12871,U_12869] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12871,U_12873)),hAPP(hAPP(c_Product__Type_OPair(U_12871,U_12873),U_12877),U_12879)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12869,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool))),U_12875)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12869,tc_fun(U_12871,tc_fun(U_12873,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12871,tc_fun(U_12873,tc_HOL_Obool)),U_12869),hAPP(c_COMBC(U_12871,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12873,tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12873,tc_HOL_Obool)),U_12871),c_COMBC(U_12873,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12873,tc_prod(U_12871,U_12873)),tc_fun(U_12873,tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),U_12871),hAPP(c_COMBB(tc_prod(U_12871,U_12873),tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool),U_12873),c_member(tc_prod(U_12871,U_12873)))),c_Product__Type_OPair(U_12871,U_12873))))),U_12875)),U_12877),U_12879)) ) ),
    inference(miniscope,[status(thm)],[f_3355_2]) ).

fof(f_3355_4,plain,
    ( ! [U_12870,U_12872,U_12874,U_12876,U_12878,U_12880] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12870,tc_fun(U_12872,tc_fun(U_12874,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12870,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12872,tc_fun(U_12874,tc_HOL_Obool)),U_12870),hAPP(c_COMBC(U_12872,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12874,tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12874,tc_HOL_Obool)),U_12872),c_COMBC(U_12874,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12874,tc_prod(U_12872,U_12874)),tc_fun(U_12874,tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),U_12872),hAPP(c_COMBB(tc_prod(U_12872,U_12874),tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool),U_12874),c_member(tc_prod(U_12872,U_12874)))),c_Product__Type_OPair(U_12872,U_12874))))),U_12876)),U_12878),U_12880))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12872,U_12874)),hAPP(hAPP(c_Product__Type_OPair(U_12872,U_12874),U_12878),U_12880)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12870,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12870,tc_HOL_Obool))),U_12876))) )
    & ! [U_12871,U_12869,U_12875,U_12877,U_12873,U_12879] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12871,U_12873)),hAPP(hAPP(c_Product__Type_OPair(U_12871,U_12873),U_12877),U_12879)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12869,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool))),U_12875)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12869,tc_fun(U_12871,tc_fun(U_12873,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12871,tc_fun(U_12873,tc_HOL_Obool)),U_12869),hAPP(c_COMBC(U_12871,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12873,tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12873,tc_HOL_Obool)),U_12871),c_COMBC(U_12873,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12873,tc_prod(U_12871,U_12873)),tc_fun(U_12873,tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),U_12871),hAPP(c_COMBB(tc_prod(U_12871,U_12873),tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool),U_12873),c_member(tc_prod(U_12871,U_12873)))),c_Product__Type_OPair(U_12871,U_12873))))),U_12875)),U_12877),U_12879)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3355_3]) ).

cnf(f_3355_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12871,U_12873)),hAPP(hAPP(c_Product__Type_OPair(U_12871,U_12873),U_12877),U_12879)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12869,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool))),U_12875)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12869,tc_fun(U_12871,tc_fun(U_12873,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12871,tc_fun(U_12873,tc_HOL_Obool)),U_12869),hAPP(c_COMBC(U_12871,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12873,tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_fun(U_12873,tc_HOL_Obool)),U_12871),c_COMBC(U_12873,tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12873,tc_prod(U_12871,U_12873)),tc_fun(U_12873,tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool)),U_12871),hAPP(c_COMBB(tc_prod(U_12871,U_12873),tc_fun(tc_fun(tc_prod(U_12871,U_12873),tc_HOL_Obool),tc_HOL_Obool),U_12873),c_member(tc_prod(U_12871,U_12873)))),c_Product__Type_OPair(U_12871,U_12873))))),U_12875)),U_12877),U_12879)) ),
    inference(clausify,[status(thm)],[f_3355_4]) ).

cnf(f_3355_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12870,tc_fun(U_12872,tc_fun(U_12874,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12870,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12872,tc_fun(U_12874,tc_HOL_Obool)),U_12870),hAPP(c_COMBC(U_12872,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12874,tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_fun(U_12874,tc_HOL_Obool)),U_12872),c_COMBC(U_12874,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12874,tc_prod(U_12872,U_12874)),tc_fun(U_12874,tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool)),U_12872),hAPP(c_COMBB(tc_prod(U_12872,U_12874),tc_fun(tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool),tc_HOL_Obool),U_12874),c_member(tc_prod(U_12872,U_12874)))),c_Product__Type_OPair(U_12872,U_12874))))),U_12876)),U_12878),U_12880))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12872,U_12874)),hAPP(hAPP(c_Product__Type_OPair(U_12872,U_12874),U_12878),U_12880)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12870,tc_fun(tc_prod(U_12872,U_12874),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12870,tc_HOL_Obool))),U_12876))) ),
    inference(clausify,[status(thm)],[f_3355_4]) ).

fof(f_3356_1,plain,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2)))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset]) ).

fof(f_3356_2,plain,
    ! [U_12885,U_12884,U_12883,U_12882] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12885)))
      | ? [U_12881] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12881)),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12881),U_12884))),U_12885))) ),
    inference(variable_rename,[status(thm)],[f_3356_1]) ).

fof(f_3356_3,plain,
    ! [U_12885,U_12884,U_12883,U_12882] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12885)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK275(U_12885,U_12884,U_12883,U_12882))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK275(U_12885,U_12884,U_12883,U_12882)),U_12884))),U_12885))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_12881,sK275(U_12885,U_12884,U_12883,U_12882))],[f_3356_2]) ).

fof(f_3356_4,plain,
    ! [U_12882,U_12883,U_12884,U_12885] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12885)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK275(U_12885,U_12884,U_12883,U_12882))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK275(U_12885,U_12884,U_12883,U_12882)),U_12884))),U_12885))) ),
    inference(definitional_conversion,[status(esa)],[f_3356_3]) ).

cnf(f_3356_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12885)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12882,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK275(U_12885,U_12884,U_12883,U_12882))),U_12883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK275(U_12885,U_12884,U_12883,U_12882)),U_12884))),U_12885))) ),
    inference(clausify,[status(thm)],[f_3356_4]) ).

fof(f_3357_1,plain,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2)
      | ? [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq]) ).

fof(f_3357_2,plain,
    ! [U_12890,U_12889,U_12888,U_12887] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12888) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12890)
      | ? [U_12886] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12886)),U_12888) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12886),U_12889))),U_12890) ),
    inference(variable_rename,[status(thm)],[f_3357_1]) ).

fof(f_3357_3,plain,
    ! [U_12890,U_12889,U_12888,U_12887] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12888) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12890)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK276(U_12890,U_12889,U_12888,U_12887))),U_12888) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK276(U_12890,U_12889,U_12888,U_12887)),U_12889))),U_12890) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_12886,sK276(U_12890,U_12889,U_12888,U_12887))],[f_3357_2]) ).

fof(f_3357_4,plain,
    ! [U_12887,U_12888,U_12889,U_12890] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12888) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12890)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK276(U_12890,U_12889,U_12888,U_12887))),U_12888) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK276(U_12890,U_12889,U_12888,U_12887)),U_12889))),U_12890) ),
    inference(definitional_conversion,[status(esa)],[f_3357_3]) ).

cnf(f_3357_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12888) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12890)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK276(U_12890,U_12889,U_12888,U_12887))),U_12888) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12887,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK276(U_12890,U_12889,U_12888,U_12887)),U_12889))),U_12890) ),
    inference(clausify,[status(thm)],[f_3357_4]) ).

fof(f_3358_1,plain,
    ! [V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__finite__subset]) ).

fof(f_3358_2,plain,
    ! [U_12894,U_12893,U_12892] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12893)),U_12894))
      | ? [U_12891] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12891)),U_12893)),U_12894)) ),
    inference(variable_rename,[status(thm)],[f_3358_1]) ).

fof(f_3358_3,plain,
    ! [U_12894,U_12893,U_12892] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12893)),U_12894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK277(U_12894,U_12893,U_12892))),U_12893)),U_12894)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_12891,sK277(U_12894,U_12893,U_12892))],[f_3358_2]) ).

fof(f_3358_4,plain,
    ! [U_12892,U_12893,U_12894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12893)),U_12894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK277(U_12894,U_12893,U_12892))),U_12893)),U_12894)) ),
    inference(definitional_conversion,[status(esa)],[f_3358_3]) ).

cnf(f_3358_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12893)),U_12894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12892,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK277(U_12894,U_12893,U_12892))),U_12893)),U_12894)) ),
    inference(clausify,[status(thm)],[f_3358_4]) ).

fof(f_3359_1,plain,
    ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_top1I]) ).

fof(f_3359_2,plain,
    ! [U_12896,U_12895] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12895,tc_HOL_Obool)),U_12896)),
    inference(variable_rename,[status(thm)],[f_3359_1]) ).

fof(f_3359_3,plain,
    ! [U_12896,U_12895] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12895,tc_HOL_Obool)),U_12896)),
    inference(definitional_conversion,[status(esa)],[f_3359_2]) ).

cnf(f_3359_4,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12895,tc_HOL_Obool)),U_12896)),
    inference(clausify,[status(thm)],[f_3359_3]) ).

fof(f_3360_1,plain,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    inference(fof_nnf,[status(thm)],[fact_Integ__def]) ).

fof(f_3360_2,plain,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    inference(definitional_conversion,[status(esa)],[f_3360_1]) ).

cnf(f_3360_3,plain,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    inference(clausify,[status(thm)],[f_3360_2]) ).

fof(f_3361_1,plain,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(f_3361_2,plain,
    ! [U_12898,U_12897] : hBOOL(hAPP(hAPP(c_member(U_12897),U_12898),c_Orderings_Otop__class_Otop(tc_fun(U_12897,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3361_1]) ).

fof(f_3361_3,plain,
    ! [U_12897,U_12898] : hBOOL(hAPP(hAPP(c_member(U_12897),U_12898),c_Orderings_Otop__class_Otop(tc_fun(U_12897,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3361_2]) ).

cnf(f_3361_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_12897),U_12898),c_Orderings_Otop__class_Otop(tc_fun(U_12897,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3361_3]) ).

fof(f_3362_1,plain,
    ! [V_A_2,T_b] :
      ( ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
        | ~ c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) )
      & ( c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2))
        | ~ c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__equiv]) ).

fof(f_3362_2,plain,
    ! [U_12900,U_12899] :
      ( ( c_Equiv__Relations_Oequiv(U_12899,c_Orderings_Otop__class_Otop(tc_fun(U_12899,tc_HOL_Obool)),U_12900)
        | ~ c_Equiv__Relations_Oequivp(U_12899,hAPP(hAPP(c_COMBC(U_12899,tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_fun(U_12899,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12899,tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_fun(U_12899,tc_HOL_Obool)),U_12899),c_COMBC(U_12899,tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12899,tc_prod(U_12899,U_12899)),tc_fun(U_12899,tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool)),U_12899),hAPP(c_COMBB(tc_prod(U_12899,U_12899),tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool),U_12899),c_member(tc_prod(U_12899,U_12899)))),c_Product__Type_OPair(U_12899,U_12899)))),U_12900)) )
      & ( c_Equiv__Relations_Oequivp(U_12899,hAPP(hAPP(c_COMBC(U_12899,tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_fun(U_12899,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12899,tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_fun(U_12899,tc_HOL_Obool)),U_12899),c_COMBC(U_12899,tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12899,tc_prod(U_12899,U_12899)),tc_fun(U_12899,tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool)),U_12899),hAPP(c_COMBB(tc_prod(U_12899,U_12899),tc_fun(tc_fun(tc_prod(U_12899,U_12899),tc_HOL_Obool),tc_HOL_Obool),U_12899),c_member(tc_prod(U_12899,U_12899)))),c_Product__Type_OPair(U_12899,U_12899)))),U_12900))
        | ~ c_Equiv__Relations_Oequiv(U_12899,c_Orderings_Otop__class_Otop(tc_fun(U_12899,tc_HOL_Obool)),U_12900) ) ),
    inference(variable_rename,[status(thm)],[f_3362_1]) ).

fof(f_3362_3,plain,
    ( ! [U_12904,U_12902] :
        ( c_Equiv__Relations_Oequiv(U_12902,c_Orderings_Otop__class_Otop(tc_fun(U_12902,tc_HOL_Obool)),U_12904)
        | ~ c_Equiv__Relations_Oequivp(U_12902,hAPP(hAPP(c_COMBC(U_12902,tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_fun(U_12902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12902,tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_fun(U_12902,tc_HOL_Obool)),U_12902),c_COMBC(U_12902,tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12902,tc_prod(U_12902,U_12902)),tc_fun(U_12902,tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),U_12902),hAPP(c_COMBB(tc_prod(U_12902,U_12902),tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool),U_12902),c_member(tc_prod(U_12902,U_12902)))),c_Product__Type_OPair(U_12902,U_12902)))),U_12904)) )
    & ! [U_12903,U_12901] :
        ( c_Equiv__Relations_Oequivp(U_12901,hAPP(hAPP(c_COMBC(U_12901,tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_fun(U_12901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12901,tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_fun(U_12901,tc_HOL_Obool)),U_12901),c_COMBC(U_12901,tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12901,tc_prod(U_12901,U_12901)),tc_fun(U_12901,tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),U_12901),hAPP(c_COMBB(tc_prod(U_12901,U_12901),tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool),U_12901),c_member(tc_prod(U_12901,U_12901)))),c_Product__Type_OPair(U_12901,U_12901)))),U_12903))
        | ~ c_Equiv__Relations_Oequiv(U_12901,c_Orderings_Otop__class_Otop(tc_fun(U_12901,tc_HOL_Obool)),U_12903) ) ),
    inference(miniscope,[status(thm)],[f_3362_2]) ).

fof(f_3362_4,plain,
    ( ! [U_12904,U_12902] :
        ( c_Equiv__Relations_Oequiv(U_12902,c_Orderings_Otop__class_Otop(tc_fun(U_12902,tc_HOL_Obool)),U_12904)
        | ~ c_Equiv__Relations_Oequivp(U_12902,hAPP(hAPP(c_COMBC(U_12902,tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_fun(U_12902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12902,tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_fun(U_12902,tc_HOL_Obool)),U_12902),c_COMBC(U_12902,tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12902,tc_prod(U_12902,U_12902)),tc_fun(U_12902,tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),U_12902),hAPP(c_COMBB(tc_prod(U_12902,U_12902),tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool),U_12902),c_member(tc_prod(U_12902,U_12902)))),c_Product__Type_OPair(U_12902,U_12902)))),U_12904)) )
    & ! [U_12903,U_12901] :
        ( c_Equiv__Relations_Oequivp(U_12901,hAPP(hAPP(c_COMBC(U_12901,tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_fun(U_12901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12901,tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_fun(U_12901,tc_HOL_Obool)),U_12901),c_COMBC(U_12901,tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12901,tc_prod(U_12901,U_12901)),tc_fun(U_12901,tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),U_12901),hAPP(c_COMBB(tc_prod(U_12901,U_12901),tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool),U_12901),c_member(tc_prod(U_12901,U_12901)))),c_Product__Type_OPair(U_12901,U_12901)))),U_12903))
        | ~ c_Equiv__Relations_Oequiv(U_12901,c_Orderings_Otop__class_Otop(tc_fun(U_12901,tc_HOL_Obool)),U_12903) ) ),
    inference(definitional_conversion,[status(esa)],[f_3362_3]) ).

cnf(f_3362_5,plain,
    ( c_Equiv__Relations_Oequivp(U_12901,hAPP(hAPP(c_COMBC(U_12901,tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_fun(U_12901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12901,tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_fun(U_12901,tc_HOL_Obool)),U_12901),c_COMBC(U_12901,tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12901,tc_prod(U_12901,U_12901)),tc_fun(U_12901,tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool)),U_12901),hAPP(c_COMBB(tc_prod(U_12901,U_12901),tc_fun(tc_fun(tc_prod(U_12901,U_12901),tc_HOL_Obool),tc_HOL_Obool),U_12901),c_member(tc_prod(U_12901,U_12901)))),c_Product__Type_OPair(U_12901,U_12901)))),U_12903))
    | ~ c_Equiv__Relations_Oequiv(U_12901,c_Orderings_Otop__class_Otop(tc_fun(U_12901,tc_HOL_Obool)),U_12903) ),
    inference(clausify,[status(thm)],[f_3362_4]) ).

cnf(f_3362_6,plain,
    ( c_Equiv__Relations_Oequiv(U_12902,c_Orderings_Otop__class_Otop(tc_fun(U_12902,tc_HOL_Obool)),U_12904)
    | ~ c_Equiv__Relations_Oequivp(U_12902,hAPP(hAPP(c_COMBC(U_12902,tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_fun(U_12902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12902,tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_fun(U_12902,tc_HOL_Obool)),U_12902),c_COMBC(U_12902,tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12902,tc_prod(U_12902,U_12902)),tc_fun(U_12902,tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool)),U_12902),hAPP(c_COMBB(tc_prod(U_12902,U_12902),tc_fun(tc_fun(tc_prod(U_12902,U_12902),tc_HOL_Obool),tc_HOL_Obool),U_12902),c_member(tc_prod(U_12902,U_12902)))),c_Product__Type_OPair(U_12902,U_12902)))),U_12904)) ),
    inference(clausify,[status(thm)],[f_3362_4]) ).

fof(f_3363_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__transp]) ).

fof(f_3363_2,plain,
    ! [U_12909,U_12908,U_12907,U_12906,U_12905] :
      ( hBOOL(hAPP(hAPP(U_12906,U_12907),U_12909))
      | ~ hBOOL(hAPP(hAPP(U_12906,U_12908),U_12909))
      | ~ hBOOL(hAPP(hAPP(U_12906,U_12907),U_12908))
      | ~ c_Equiv__Relations_Oequivp(U_12905,U_12906) ),
    inference(variable_rename,[status(thm)],[f_3363_1]) ).

fof(f_3363_3,plain,
    ! [U_12909,U_12908,U_12907,U_12906] :
      ( ! [U_12905] : ~ c_Equiv__Relations_Oequivp(U_12905,U_12906)
      | hBOOL(hAPP(hAPP(U_12906,U_12907),U_12909))
      | ~ hBOOL(hAPP(hAPP(U_12906,U_12908),U_12909))
      | ~ hBOOL(hAPP(hAPP(U_12906,U_12907),U_12908)) ),
    inference(miniscope,[status(thm)],[f_3363_2]) ).

fof(f_3363_4,plain,
    ! [U_12907,U_12905,U_12906,U_12908,U_12909] :
      ( ~ c_Equiv__Relations_Oequivp(U_12905,U_12906)
      | hBOOL(hAPP(hAPP(U_12906,U_12907),U_12909))
      | ~ hBOOL(hAPP(hAPP(U_12906,U_12908),U_12909))
      | ~ hBOOL(hAPP(hAPP(U_12906,U_12907),U_12908)) ),
    inference(definitional_conversion,[status(esa)],[f_3363_3]) ).

cnf(f_3363_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12905,U_12906)
    | hBOOL(hAPP(hAPP(U_12906,U_12907),U_12909))
    | ~ hBOOL(hAPP(hAPP(U_12906,U_12908),U_12909))
    | ~ hBOOL(hAPP(hAPP(U_12906,U_12907),U_12908)) ),
    inference(clausify,[status(thm)],[f_3363_4]) ).

fof(f_3364_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__symp]) ).

fof(f_3364_2,plain,
    ! [U_12913,U_12912,U_12911,U_12910] :
      ( hBOOL(hAPP(hAPP(U_12911,U_12913),U_12912))
      | ~ hBOOL(hAPP(hAPP(U_12911,U_12912),U_12913))
      | ~ c_Equiv__Relations_Oequivp(U_12910,U_12911) ),
    inference(variable_rename,[status(thm)],[f_3364_1]) ).

fof(f_3364_3,plain,
    ! [U_12913,U_12912,U_12911] :
      ( ! [U_12910] : ~ c_Equiv__Relations_Oequivp(U_12910,U_12911)
      | hBOOL(hAPP(hAPP(U_12911,U_12913),U_12912))
      | ~ hBOOL(hAPP(hAPP(U_12911,U_12912),U_12913)) ),
    inference(miniscope,[status(thm)],[f_3364_2]) ).

fof(f_3364_4,plain,
    ! [U_12912,U_12911,U_12910,U_12913] :
      ( ~ c_Equiv__Relations_Oequivp(U_12910,U_12911)
      | hBOOL(hAPP(hAPP(U_12911,U_12913),U_12912))
      | ~ hBOOL(hAPP(hAPP(U_12911,U_12912),U_12913)) ),
    inference(definitional_conversion,[status(esa)],[f_3364_3]) ).

cnf(f_3364_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12910,U_12911)
    | hBOOL(hAPP(hAPP(U_12911,U_12913),U_12912))
    | ~ hBOOL(hAPP(hAPP(U_12911,U_12912),U_12913)) ),
    inference(clausify,[status(thm)],[f_3364_4]) ).

fof(f_3365_1,plain,
    ! [V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2))
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__reflp]) ).

fof(f_3365_2,plain,
    ! [U_12916,U_12915,U_12914] :
      ( hBOOL(hAPP(hAPP(U_12915,U_12916),U_12916))
      | ~ c_Equiv__Relations_Oequivp(U_12914,U_12915) ),
    inference(variable_rename,[status(thm)],[f_3365_1]) ).

fof(f_3365_3,plain,
    ! [U_12916,U_12915] :
      ( ! [U_12914] : ~ c_Equiv__Relations_Oequivp(U_12914,U_12915)
      | hBOOL(hAPP(hAPP(U_12915,U_12916),U_12916)) ),
    inference(miniscope,[status(thm)],[f_3365_2]) ).

fof(f_3365_4,plain,
    ! [U_12916,U_12914,U_12915] :
      ( ~ c_Equiv__Relations_Oequivp(U_12914,U_12915)
      | hBOOL(hAPP(hAPP(U_12915,U_12916),U_12916)) ),
    inference(definitional_conversion,[status(esa)],[f_3365_3]) ).

cnf(f_3365_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12914,U_12915)
    | hBOOL(hAPP(hAPP(U_12915,U_12916),U_12916)) ),
    inference(clausify,[status(thm)],[f_3365_4]) ).

fof(f_3366_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
        | ? [B_x,B_y] :
            ( ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
              & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) )
            | ( hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y)
              & hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) ) )
      & ( ! [B_x,B_y] :
            ( ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
              | hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y) )
            & ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
              | ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) )
        | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__def]) ).

fof(f_3366_2,plain,
    ! [U_12922,U_12921] :
      ( ( c_Equiv__Relations_Oequivp(U_12921,U_12922)
        | ? [U_12920,U_12919] :
            ( ( ~ hBOOL(hAPP(hAPP(U_12922,U_12920),U_12919))
              & hAPP(U_12922,U_12920) = hAPP(U_12922,U_12919) )
            | ( hAPP(U_12922,U_12920) != hAPP(U_12922,U_12919)
              & hBOOL(hAPP(hAPP(U_12922,U_12920),U_12919)) ) ) )
      & ( ! [U_12918,U_12917] :
            ( ( hBOOL(hAPP(hAPP(U_12922,U_12918),U_12917))
              | hAPP(U_12922,U_12918) != hAPP(U_12922,U_12917) )
            & ( hAPP(U_12922,U_12918) = hAPP(U_12922,U_12917)
              | ~ hBOOL(hAPP(hAPP(U_12922,U_12918),U_12917)) ) )
        | ~ c_Equiv__Relations_Oequivp(U_12921,U_12922) ) ),
    inference(variable_rename,[status(thm)],[f_3366_1]) ).

fof(f_3366_3,plain,
    ( ! [U_12934] :
        ( ! [U_12932] : c_Equiv__Relations_Oequivp(U_12932,U_12934)
        | ? [U_12930,U_12928] :
            ( ~ hBOOL(hAPP(hAPP(U_12934,U_12930),U_12928))
            & hAPP(U_12934,U_12930) = hAPP(U_12934,U_12928) )
        | ? [U_12929,U_12927] :
            ( hAPP(U_12934,U_12929) != hAPP(U_12934,U_12927)
            & hBOOL(hAPP(hAPP(U_12934,U_12929),U_12927)) ) )
    & ! [U_12933] :
        ( ! [U_12931] : ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
        | ( ! [U_12926,U_12924] :
              ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
              | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924) )
          & ! [U_12925,U_12923] :
              ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
              | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923)) ) ) ) ),
    inference(miniscope,[status(thm)],[f_3366_2]) ).

fof(f_3366_4,plain,
    ( ! [U_12934] :
        ( ! [U_12932] : c_Equiv__Relations_Oequivp(U_12932,U_12934)
        | ? [U_12930,U_12928] :
            ( ~ hBOOL(hAPP(hAPP(U_12934,U_12930),U_12928))
            & hAPP(U_12934,U_12930) = hAPP(U_12934,U_12928) )
        | ? [U_12927] :
            ( hAPP(U_12934,sK278(U_12934)) != hAPP(U_12934,U_12927)
            & hBOOL(hAPP(hAPP(U_12934,sK278(U_12934)),U_12927)) ) )
    & ! [U_12933] :
        ( ! [U_12931] : ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
        | ( ! [U_12926,U_12924] :
              ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
              | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924) )
          & ! [U_12925,U_12923] :
              ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
              | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_12929,sK278(U_12934))],[f_3366_3]) ).

fof(f_3366_5,plain,
    ( ! [U_12934] :
        ( ! [U_12932] : c_Equiv__Relations_Oequivp(U_12932,U_12934)
        | ? [U_12930,U_12928] :
            ( ~ hBOOL(hAPP(hAPP(U_12934,U_12930),U_12928))
            & hAPP(U_12934,U_12930) = hAPP(U_12934,U_12928) )
        | ( hAPP(U_12934,sK278(U_12934)) != hAPP(U_12934,sK279(U_12934))
          & hBOOL(hAPP(hAPP(U_12934,sK278(U_12934)),sK279(U_12934))) ) )
    & ! [U_12933] :
        ( ! [U_12931] : ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
        | ( ! [U_12926,U_12924] :
              ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
              | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924) )
          & ! [U_12925,U_12923] :
              ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
              | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_12927,sK279(U_12934))],[f_3366_4]) ).

fof(f_3366_6,plain,
    ( ! [U_12934] :
        ( ! [U_12932] : c_Equiv__Relations_Oequivp(U_12932,U_12934)
        | ? [U_12928] :
            ( ~ hBOOL(hAPP(hAPP(U_12934,sK280(U_12934)),U_12928))
            & hAPP(U_12934,sK280(U_12934)) = hAPP(U_12934,U_12928) )
        | ( hAPP(U_12934,sK278(U_12934)) != hAPP(U_12934,sK279(U_12934))
          & hBOOL(hAPP(hAPP(U_12934,sK278(U_12934)),sK279(U_12934))) ) )
    & ! [U_12933] :
        ( ! [U_12931] : ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
        | ( ! [U_12926,U_12924] :
              ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
              | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924) )
          & ! [U_12925,U_12923] :
              ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
              | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_12930,sK280(U_12934))],[f_3366_5]) ).

fof(f_3366_7,plain,
    ( ! [U_12934] :
        ( ! [U_12932] : c_Equiv__Relations_Oequivp(U_12932,U_12934)
        | ( ~ hBOOL(hAPP(hAPP(U_12934,sK280(U_12934)),sK281(U_12934)))
          & hAPP(U_12934,sK280(U_12934)) = hAPP(U_12934,sK281(U_12934)) )
        | ( hAPP(U_12934,sK278(U_12934)) != hAPP(U_12934,sK279(U_12934))
          & hBOOL(hAPP(hAPP(U_12934,sK278(U_12934)),sK279(U_12934))) ) )
    & ! [U_12933] :
        ( ! [U_12931] : ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
        | ( ! [U_12926,U_12924] :
              ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
              | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924) )
          & ! [U_12925,U_12923] :
              ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
              | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_12928,sK281(U_12934))],[f_3366_6]) ).

fof(f_3366_8,plain,
    ( ! [U_12934] :
        ( ~ hBOOL(hAPP(hAPP(U_12934,sK280(U_12934)),sK281(U_12934)))
        | ~ sP951(U_12934) )
    & ! [U_12934] :
        ( hAPP(U_12934,sK280(U_12934)) = hAPP(U_12934,sK281(U_12934))
        | ~ sP951(U_12934) )
    & ! [U_12934] :
        ( hAPP(U_12934,sK278(U_12934)) != hAPP(U_12934,sK279(U_12934))
        | ~ sP950(U_12934) )
    & ! [U_12934] :
        ( hBOOL(hAPP(hAPP(U_12934,sK278(U_12934)),sK279(U_12934)))
        | ~ sP950(U_12934) )
    & ! [U_12925,U_12923,U_12924,U_12926,U_12933] :
        ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
        | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924)
        | ~ sP949(U_12925,U_12923,U_12924,U_12926,U_12933) )
    & ! [U_12925,U_12923,U_12924,U_12926,U_12933] :
        ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
        | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923))
        | ~ sP949(U_12925,U_12923,U_12924,U_12926,U_12933) )
    & ! [U_12932,U_12934] :
        ( c_Equiv__Relations_Oequivp(U_12932,U_12934)
        | sP951(U_12934)
        | sP950(U_12934) )
    & ! [U_12925,U_12923,U_12924,U_12926,U_12931,U_12933] :
        ( ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
        | sP949(U_12925,U_12923,U_12924,U_12926,U_12933) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP949,sP950,sP951])],[f_3366_7]) ).

cnf(f_3366_9,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12931,U_12933)
    | sP949(U_12925,U_12923,U_12924,U_12926,U_12933) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_10,plain,
    ( c_Equiv__Relations_Oequivp(U_12932,U_12934)
    | sP951(U_12934)
    | sP950(U_12934) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_11,plain,
    ( hAPP(U_12933,U_12925) = hAPP(U_12933,U_12923)
    | ~ hBOOL(hAPP(hAPP(U_12933,U_12925),U_12923))
    | ~ sP949(U_12925,U_12923,U_12924,U_12926,U_12933) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_12,plain,
    ( hBOOL(hAPP(hAPP(U_12933,U_12926),U_12924))
    | hAPP(U_12933,U_12926) != hAPP(U_12933,U_12924)
    | ~ sP949(U_12925,U_12923,U_12924,U_12926,U_12933) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_13,plain,
    ( hBOOL(hAPP(hAPP(U_12934,sK278(U_12934)),sK279(U_12934)))
    | ~ sP950(U_12934) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_14,plain,
    ( hAPP(U_12934,sK278(U_12934)) != hAPP(U_12934,sK279(U_12934))
    | ~ sP950(U_12934) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_15,plain,
    ( hAPP(U_12934,sK280(U_12934)) = hAPP(U_12934,sK281(U_12934))
    | ~ sP951(U_12934) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

cnf(f_3366_16,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12934,sK280(U_12934)),sK281(U_12934)))
    | ~ sP951(U_12934) ),
    inference(clausify,[status(thm)],[f_3366_8]) ).

fof(f_3367_1,plain,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).

fof(f_3367_2,plain,
    ! [U_12935] : c_Equiv__Relations_Oequivp(U_12935,c_fequal),
    inference(variable_rename,[status(thm)],[f_3367_1]) ).

fof(f_3367_3,plain,
    ! [U_12935] : c_Equiv__Relations_Oequivp(U_12935,c_fequal),
    inference(definitional_conversion,[status(esa)],[f_3367_2]) ).

cnf(f_3367_4,plain,
    c_Equiv__Relations_Oequivp(U_12935,c_fequal),
    inference(clausify,[status(thm)],[f_3367_3]) ).

fof(f_3368_1,plain,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ]) ).

fof(f_3368_2,plain,
    ! [U_12936] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12936)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[f_3368_1]) ).

fof(f_3368_3,plain,
    ! [U_12936] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12936)),c_Int_OInteg)),
    inference(definitional_conversion,[status(esa)],[f_3368_2]) ).

cnf(f_3368_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12936)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3368_3]) ).

fof(f_3369_1,plain,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    inference(fof_nnf,[status(thm)],[fact_type__definition__Integ]) ).

fof(f_3369_2,plain,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    inference(definitional_conversion,[status(esa)],[f_3369_1]) ).

cnf(f_3369_3,plain,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    inference(clausify,[status(thm)],[f_3369_2]) ).

fof(f_3370_1,plain,
    ! [V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton]) ).

fof(f_3370_2,plain,
    ! [U_12940,U_12939,U_12938,U_12937] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12937,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12937,U_12938,U_12939),hAPP(hAPP(c_Set_Oinsert(U_12938),U_12940),c_Orderings_Obot__class_Obot(tc_fun(U_12938,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12937),c_HOL_OThe(U_12937,hAPP(hAPP(c_COMBC(U_12937,U_12938,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12938,tc_fun(U_12938,tc_HOL_Obool),U_12937),c_fequal),U_12939)),U_12940))),c_Orderings_Obot__class_Obot(tc_fun(U_12937,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_12937,U_12938,U_12939,c_Orderings_Otop__class_Otop(tc_fun(U_12937,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3370_1]) ).

fof(f_3370_3,plain,
    ! [U_12938,U_12937,U_12939,U_12940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12937,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12937,U_12938,U_12939),hAPP(hAPP(c_Set_Oinsert(U_12938),U_12940),c_Orderings_Obot__class_Obot(tc_fun(U_12938,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12937),c_HOL_OThe(U_12937,hAPP(hAPP(c_COMBC(U_12937,U_12938,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12938,tc_fun(U_12938,tc_HOL_Obool),U_12937),c_fequal),U_12939)),U_12940))),c_Orderings_Obot__class_Obot(tc_fun(U_12937,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_12937,U_12938,U_12939,c_Orderings_Otop__class_Otop(tc_fun(U_12937,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3370_2]) ).

cnf(f_3370_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12937,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12937,U_12938,U_12939),hAPP(hAPP(c_Set_Oinsert(U_12938),U_12940),c_Orderings_Obot__class_Obot(tc_fun(U_12938,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12937),c_HOL_OThe(U_12937,hAPP(hAPP(c_COMBC(U_12937,U_12938,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12938,tc_fun(U_12938,tc_HOL_Obool),U_12937),c_fequal),U_12939)),U_12940))),c_Orderings_Obot__class_Obot(tc_fun(U_12937,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_12937,U_12938,U_12939,c_Orderings_Otop__class_Otop(tc_fun(U_12937,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3370_3]) ).

fof(f_3371_1,plain,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | V_A_2 != V_B_2
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J]) ).

fof(f_3371_2,plain,
    ! [U_12946,U_12945,U_12944,U_12943,U_12942] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12945),U_12943) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12946),U_12944)
      | ? [U_12941] :
          ( hAPP(U_12945,U_12941) != hAPP(U_12946,U_12941)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12941)) )
      | ~ c_Nat__Transfer_Onat__set(U_12944)
      | U_12943 != U_12944
      | ~ class_Groups_Ocomm__monoid__mult(U_12942)
      | ~ class_Groups_Ocomm__monoid__add(U_12942) ),
    inference(variable_rename,[status(thm)],[f_3371_1]) ).

fof(f_3371_3,plain,
    ! [U_12946,U_12945,U_12944,U_12943,U_12942] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12945),U_12943) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12946),U_12944)
      | ( hAPP(U_12945,sK282(U_12946,U_12945,U_12944,U_12943,U_12942)) != hAPP(U_12946,sK282(U_12946,U_12945,U_12944,U_12943,U_12942))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK282(U_12946,U_12945,U_12944,U_12943,U_12942))) )
      | ~ c_Nat__Transfer_Onat__set(U_12944)
      | U_12943 != U_12944
      | ~ class_Groups_Ocomm__monoid__mult(U_12942)
      | ~ class_Groups_Ocomm__monoid__add(U_12942) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_12941,sK282(U_12946,U_12945,U_12944,U_12943,U_12942))],[f_3371_2]) ).

fof(f_3371_4,plain,
    ( ! [U_12943,U_12942,U_12944,U_12945,U_12946] :
        ( hAPP(U_12945,sK282(U_12946,U_12945,U_12944,U_12943,U_12942)) != hAPP(U_12946,sK282(U_12946,U_12945,U_12944,U_12943,U_12942))
        | ~ sP952(U_12943,U_12942,U_12944,U_12945,U_12946) )
    & ! [U_12943,U_12942,U_12944,U_12945,U_12946] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK282(U_12946,U_12945,U_12944,U_12943,U_12942)))
        | ~ sP952(U_12943,U_12942,U_12944,U_12945,U_12946) )
    & ! [U_12943,U_12942,U_12944,U_12945,U_12946] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12945),U_12943) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12946),U_12944)
        | sP952(U_12943,U_12942,U_12944,U_12945,U_12946)
        | ~ c_Nat__Transfer_Onat__set(U_12944)
        | U_12943 != U_12944
        | ~ class_Groups_Ocomm__monoid__mult(U_12942)
        | ~ class_Groups_Ocomm__monoid__add(U_12942) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP952])],[f_3371_3]) ).

cnf(f_3371_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12945),U_12943) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12942),U_12946),U_12944)
    | sP952(U_12943,U_12942,U_12944,U_12945,U_12946)
    | ~ c_Nat__Transfer_Onat__set(U_12944)
    | U_12943 != U_12944
    | ~ class_Groups_Ocomm__monoid__mult(U_12942)
    | ~ class_Groups_Ocomm__monoid__add(U_12942) ),
    inference(clausify,[status(thm)],[f_3371_4]) ).

cnf(f_3371_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK282(U_12946,U_12945,U_12944,U_12943,U_12942)))
    | ~ sP952(U_12943,U_12942,U_12944,U_12945,U_12946) ),
    inference(clausify,[status(thm)],[f_3371_4]) ).

cnf(f_3371_7,plain,
    ( hAPP(U_12945,sK282(U_12946,U_12945,U_12944,U_12943,U_12942)) != hAPP(U_12946,sK282(U_12946,U_12945,U_12944,U_12943,U_12942))
    | ~ sP952(U_12943,U_12942,U_12944,U_12945,U_12946) ),
    inference(clausify,[status(thm)],[f_3371_4]) ).

fof(f_3372_1,plain,
    ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
      | hAPP(V_f_2,V_a_2) != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_vimageI]) ).

fof(f_3372_2,plain,
    ! [U_12952,U_12951,U_12950,U_12949,U_12948,U_12947] :
      ( hBOOL(hAPP(hAPP(c_member(U_12952),U_12948),hAPP(c_Set_Ovimage(U_12952,U_12950,U_12947),U_12951)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12950),U_12949),U_12951))
      | hAPP(U_12947,U_12948) != U_12949 ),
    inference(variable_rename,[status(thm)],[f_3372_1]) ).

fof(f_3372_3,plain,
    ! [U_12949,U_12947,U_12950,U_12951,U_12948,U_12952] :
      ( hBOOL(hAPP(hAPP(c_member(U_12952),U_12948),hAPP(c_Set_Ovimage(U_12952,U_12950,U_12947),U_12951)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12950),U_12949),U_12951))
      | hAPP(U_12947,U_12948) != U_12949 ),
    inference(definitional_conversion,[status(esa)],[f_3372_2]) ).

cnf(f_3372_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12952),U_12948),hAPP(c_Set_Ovimage(U_12952,U_12950,U_12947),U_12951)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12950),U_12949),U_12951))
    | hAPP(U_12947,U_12948) != U_12949 ),
    inference(clausify,[status(thm)],[f_3372_3]) ).

fof(f_3373_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Diff]) ).

fof(f_3373_2,plain,
    ! [U_12957,U_12956,U_12955,U_12954,U_12953] : hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12954,tc_HOL_Obool)),U_12956),U_12957)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12953,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),U_12956)),hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),U_12957)),
    inference(variable_rename,[status(thm)],[f_3373_1]) ).

fof(f_3373_3,plain,
    ! [U_12953,U_12954,U_12955,U_12956,U_12957] : hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12954,tc_HOL_Obool)),U_12956),U_12957)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12953,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),U_12956)),hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),U_12957)),
    inference(definitional_conversion,[status(esa)],[f_3373_2]) ).

cnf(f_3373_4,plain,
    hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12954,tc_HOL_Obool)),U_12956),U_12957)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12953,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),U_12956)),hAPP(c_Set_Ovimage(U_12953,U_12954,U_12955),U_12957)),
    inference(clausify,[status(thm)],[f_3373_3]) ).

fof(f_3374_1,plain,
    ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_vimage__ident]) ).

fof(f_3374_2,plain,
    ! [U_12959,U_12958] : hAPP(c_Set_Ovimage(U_12958,U_12958,c_COMBI(U_12958)),U_12959) = U_12959,
    inference(variable_rename,[status(thm)],[f_3374_1]) ).

fof(f_3374_3,plain,
    ! [U_12958,U_12959] : hAPP(c_Set_Ovimage(U_12958,U_12958,c_COMBI(U_12958)),U_12959) = U_12959,
    inference(definitional_conversion,[status(esa)],[f_3374_2]) ).

cnf(f_3374_4,plain,
    hAPP(c_Set_Ovimage(U_12958,U_12958,c_COMBI(U_12958)),U_12959) = U_12959,
    inference(clausify,[status(thm)],[f_3374_3]) ).

fof(f_3375_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_vimage__empty]) ).

fof(f_3375_2,plain,
    ! [U_12962,U_12961,U_12960] : hAPP(c_Set_Ovimage(U_12960,U_12961,U_12962),c_Orderings_Obot__class_Obot(tc_fun(U_12961,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12960,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3375_1]) ).

fof(f_3375_3,plain,
    ! [U_12960,U_12961,U_12962] : hAPP(c_Set_Ovimage(U_12960,U_12961,U_12962),c_Orderings_Obot__class_Obot(tc_fun(U_12961,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12960,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3375_2]) ).

cnf(f_3375_4,plain,
    hAPP(c_Set_Ovimage(U_12960,U_12961,U_12962),c_Orderings_Obot__class_Obot(tc_fun(U_12961,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12960,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3375_3]) ).

fof(f_3376_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
        | ~ hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) )
      & ( hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__code]) ).

fof(f_3376_2,plain,
    ! [U_12967,U_12966,U_12965,U_12964,U_12963] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12963,U_12964,U_12965),U_12966),U_12967))
        | ~ hBOOL(hAPP(U_12966,hAPP(U_12965,U_12967))) )
      & ( hBOOL(hAPP(U_12966,hAPP(U_12965,U_12967)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12963,U_12964,U_12965),U_12966),U_12967)) ) ),
    inference(variable_rename,[status(thm)],[f_3376_1]) ).

fof(f_3376_3,plain,
    ( ! [U_12977,U_12975,U_12973] :
        ( ! [U_12971,U_12969] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12969,U_12971,U_12973),U_12975),U_12977))
        | ~ hBOOL(hAPP(U_12975,hAPP(U_12973,U_12977))) )
    & ! [U_12976,U_12974,U_12972] :
        ( ! [U_12970,U_12968] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12968,U_12970,U_12972),U_12974),U_12976))
        | hBOOL(hAPP(U_12974,hAPP(U_12972,U_12976))) ) ),
    inference(miniscope,[status(thm)],[f_3376_2]) ).

fof(f_3376_4,plain,
    ( ! [U_12969,U_12971,U_12973,U_12975,U_12977] :
        ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12969,U_12971,U_12973),U_12975),U_12977))
        | ~ hBOOL(hAPP(U_12975,hAPP(U_12973,U_12977))) )
    & ! [U_12976,U_12970,U_12972,U_12968,U_12974] :
        ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12968,U_12970,U_12972),U_12974),U_12976))
        | hBOOL(hAPP(U_12974,hAPP(U_12972,U_12976))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3376_3]) ).

cnf(f_3376_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12968,U_12970,U_12972),U_12974),U_12976))
    | hBOOL(hAPP(U_12974,hAPP(U_12972,U_12976))) ),
    inference(clausify,[status(thm)],[f_3376_4]) ).

cnf(f_3376_6,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12969,U_12971,U_12973),U_12975),U_12977))
    | ~ hBOOL(hAPP(U_12975,hAPP(U_12973,U_12977))) ),
    inference(clausify,[status(thm)],[f_3376_4]) ).

fof(f_3377_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Compl]) ).

fof(f_3377_2,plain,
    ! [U_12981,U_12980,U_12979,U_12978] : hAPP(c_Set_Ovimage(U_12978,U_12979,U_12980),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12979,tc_HOL_Obool)),U_12981)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12978,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12978,U_12979,U_12980),U_12981)),
    inference(variable_rename,[status(thm)],[f_3377_1]) ).

fof(f_3377_3,plain,
    ! [U_12978,U_12979,U_12980,U_12981] : hAPP(c_Set_Ovimage(U_12978,U_12979,U_12980),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12979,tc_HOL_Obool)),U_12981)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12978,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12978,U_12979,U_12980),U_12981)),
    inference(definitional_conversion,[status(esa)],[f_3377_2]) ).

cnf(f_3377_4,plain,
    hAPP(c_Set_Ovimage(U_12978,U_12979,U_12980),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12979,tc_HOL_Obool)),U_12981)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12978,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12978,U_12979,U_12980),U_12981)),
    inference(clausify,[status(thm)],[f_3377_3]) ).

fof(f_3378_1,plain,
    ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_vimageI2]) ).

fof(f_3378_2,plain,
    ! [U_12986,U_12985,U_12984,U_12983,U_12982] :
      ( hBOOL(hAPP(hAPP(c_member(U_12986),U_12984),hAPP(c_Set_Ovimage(U_12986,U_12982,U_12983),U_12985)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12982),hAPP(U_12983,U_12984)),U_12985)) ),
    inference(variable_rename,[status(thm)],[f_3378_1]) ).

fof(f_3378_3,plain,
    ! [U_12982,U_12983,U_12984,U_12985,U_12986] :
      ( hBOOL(hAPP(hAPP(c_member(U_12986),U_12984),hAPP(c_Set_Ovimage(U_12986,U_12982,U_12983),U_12985)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12982),hAPP(U_12983,U_12984)),U_12985)) ),
    inference(definitional_conversion,[status(esa)],[f_3378_2]) ).

cnf(f_3378_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12986),U_12984),hAPP(c_Set_Ovimage(U_12986,U_12982,U_12983),U_12985)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12982),hAPP(U_12983,U_12984)),U_12985)) ),
    inference(clausify,[status(thm)],[f_3378_3]) ).

fof(f_3379_1,plain,
    ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_vimageD]) ).

fof(f_3379_2,plain,
    ! [U_12991,U_12990,U_12989,U_12988,U_12987] :
      ( hBOOL(hAPP(hAPP(c_member(U_12989),hAPP(U_12990,U_12988)),U_12991))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12987),U_12988),hAPP(c_Set_Ovimage(U_12987,U_12989,U_12990),U_12991))) ),
    inference(variable_rename,[status(thm)],[f_3379_1]) ).

fof(f_3379_3,plain,
    ! [U_12991,U_12990,U_12989,U_12988] :
      ( ! [U_12987] : ~ hBOOL(hAPP(hAPP(c_member(U_12987),U_12988),hAPP(c_Set_Ovimage(U_12987,U_12989,U_12990),U_12991)))
      | hBOOL(hAPP(hAPP(c_member(U_12989),hAPP(U_12990,U_12988)),U_12991)) ),
    inference(miniscope,[status(thm)],[f_3379_2]) ).

fof(f_3379_4,plain,
    ! [U_12987,U_12988,U_12989,U_12990,U_12991] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_12987),U_12988),hAPP(c_Set_Ovimage(U_12987,U_12989,U_12990),U_12991)))
      | hBOOL(hAPP(hAPP(c_member(U_12989),hAPP(U_12990,U_12988)),U_12991)) ),
    inference(definitional_conversion,[status(esa)],[f_3379_3]) ).

cnf(f_3379_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12987),U_12988),hAPP(c_Set_Ovimage(U_12987,U_12989,U_12990),U_12991)))
    | hBOOL(hAPP(hAPP(c_member(U_12989),hAPP(U_12990,U_12988)),U_12991)) ),
    inference(clausify,[status(thm)],[f_3379_4]) ).

fof(f_3380_1,plain,
    ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__eq]) ).

fof(f_3380_2,plain,
    ! [U_12996,U_12995,U_12994,U_12993,U_12992] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12992),U_12993),hAPP(c_Set_Ovimage(U_12992,U_12994,U_12995),U_12996)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12994),hAPP(U_12995,U_12993)),U_12996)) )
      & ( hBOOL(hAPP(hAPP(c_member(U_12994),hAPP(U_12995,U_12993)),U_12996))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12992),U_12993),hAPP(c_Set_Ovimage(U_12992,U_12994,U_12995),U_12996))) ) ),
    inference(variable_rename,[status(thm)],[f_3380_1]) ).

fof(f_3380_3,plain,
    ( ! [U_13006,U_13004,U_13002,U_13000] :
        ( ! [U_12998] : hBOOL(hAPP(hAPP(c_member(U_12998),U_13000),hAPP(c_Set_Ovimage(U_12998,U_13002,U_13004),U_13006)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13002),hAPP(U_13004,U_13000)),U_13006)) )
    & ! [U_13005,U_13003,U_13001,U_12999] :
        ( ! [U_12997] : ~ hBOOL(hAPP(hAPP(c_member(U_12997),U_12999),hAPP(c_Set_Ovimage(U_12997,U_13001,U_13003),U_13005)))
        | hBOOL(hAPP(hAPP(c_member(U_13001),hAPP(U_13003,U_12999)),U_13005)) ) ),
    inference(miniscope,[status(thm)],[f_3380_2]) ).

fof(f_3380_4,plain,
    ( ! [U_12998,U_13000,U_13002,U_13004,U_13006] :
        ( hBOOL(hAPP(hAPP(c_member(U_12998),U_13000),hAPP(c_Set_Ovimage(U_12998,U_13002,U_13004),U_13006)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13002),hAPP(U_13004,U_13000)),U_13006)) )
    & ! [U_13001,U_12999,U_12997,U_13003,U_13005] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_12997),U_12999),hAPP(c_Set_Ovimage(U_12997,U_13001,U_13003),U_13005)))
        | hBOOL(hAPP(hAPP(c_member(U_13001),hAPP(U_13003,U_12999)),U_13005)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3380_3]) ).

cnf(f_3380_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12997),U_12999),hAPP(c_Set_Ovimage(U_12997,U_13001,U_13003),U_13005)))
    | hBOOL(hAPP(hAPP(c_member(U_13001),hAPP(U_13003,U_12999)),U_13005)) ),
    inference(clausify,[status(thm)],[f_3380_4]) ).

cnf(f_3380_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12998),U_13000),hAPP(c_Set_Ovimage(U_12998,U_13002,U_13004),U_13006)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13002),hAPP(U_13004,U_13000)),U_13006)) ),
    inference(clausify,[status(thm)],[f_3380_4]) ).

fof(f_3381_1,plain,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__mono]) ).

fof(f_3381_2,plain,
    ! [U_13011,U_13010,U_13009,U_13008,U_13007] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13010,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13010,U_13007,U_13011),U_13008)),hAPP(c_Set_Ovimage(U_13010,U_13007,U_13011),U_13009)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13007,tc_HOL_Obool)),U_13008),U_13009)) ),
    inference(variable_rename,[status(thm)],[f_3381_1]) ).

fof(f_3381_3,plain,
    ! [U_13007,U_13008,U_13009,U_13010,U_13011] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13010,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13010,U_13007,U_13011),U_13008)),hAPP(c_Set_Ovimage(U_13010,U_13007,U_13011),U_13009)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13007,tc_HOL_Obool)),U_13008),U_13009)) ),
    inference(definitional_conversion,[status(esa)],[f_3381_2]) ).

cnf(f_3381_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13010,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13010,U_13007,U_13011),U_13008)),hAPP(c_Set_Ovimage(U_13010,U_13007,U_13011),U_13009)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13007,tc_HOL_Obool)),U_13008),U_13009)) ),
    inference(clausify,[status(thm)],[f_3381_3]) ).

fof(f_3382_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Un]) ).

fof(f_3382_2,plain,
    ! [U_13016,U_13015,U_13014,U_13013,U_13012] : hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13013,tc_HOL_Obool)),U_13015),U_13016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13012,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),U_13015)),hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),U_13016)),
    inference(variable_rename,[status(thm)],[f_3382_1]) ).

fof(f_3382_3,plain,
    ! [U_13012,U_13013,U_13014,U_13015,U_13016] : hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13013,tc_HOL_Obool)),U_13015),U_13016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13012,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),U_13015)),hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),U_13016)),
    inference(definitional_conversion,[status(esa)],[f_3382_2]) ).

cnf(f_3382_4,plain,
    hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13013,tc_HOL_Obool)),U_13015),U_13016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13012,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),U_13015)),hAPP(c_Set_Ovimage(U_13012,U_13013,U_13014),U_13016)),
    inference(clausify,[status(thm)],[f_3382_3]) ).

fof(f_3383_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Int]) ).

fof(f_3383_2,plain,
    ! [U_13021,U_13020,U_13019,U_13018,U_13017] : hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13018,tc_HOL_Obool)),U_13020),U_13021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13017,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),U_13020)),hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),U_13021)),
    inference(variable_rename,[status(thm)],[f_3383_1]) ).

fof(f_3383_3,plain,
    ! [U_13017,U_13018,U_13019,U_13020,U_13021] : hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13018,tc_HOL_Obool)),U_13020),U_13021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13017,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),U_13020)),hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),U_13021)),
    inference(definitional_conversion,[status(esa)],[f_3383_2]) ).

cnf(f_3383_4,plain,
    hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13018,tc_HOL_Obool)),U_13020),U_13021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13017,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),U_13020)),hAPP(c_Set_Ovimage(U_13017,U_13018,U_13019),U_13021)),
    inference(clausify,[status(thm)],[f_3383_3]) ).

fof(f_3384_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__UN]) ).

fof(f_3384_2,plain,
    ! [U_13027,U_13026,U_13025,U_13024,U_13023,U_13022] : hAPP(c_Set_Ovimage(U_13022,U_13023,U_13024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13025,tc_fun(U_13023,tc_HOL_Obool)),U_13026),U_13027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13025,tc_fun(U_13022,tc_HOL_Obool)),U_13026),hAPP(hAPP(c_COMBB(tc_fun(U_13023,tc_HOL_Obool),tc_fun(U_13022,tc_HOL_Obool),U_13025),c_Set_Ovimage(U_13022,U_13023,U_13024)),U_13027)),
    inference(variable_rename,[status(thm)],[f_3384_1]) ).

fof(f_3384_3,plain,
    ! [U_13023,U_13022,U_13024,U_13025,U_13026,U_13027] : hAPP(c_Set_Ovimage(U_13022,U_13023,U_13024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13025,tc_fun(U_13023,tc_HOL_Obool)),U_13026),U_13027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13025,tc_fun(U_13022,tc_HOL_Obool)),U_13026),hAPP(hAPP(c_COMBB(tc_fun(U_13023,tc_HOL_Obool),tc_fun(U_13022,tc_HOL_Obool),U_13025),c_Set_Ovimage(U_13022,U_13023,U_13024)),U_13027)),
    inference(definitional_conversion,[status(esa)],[f_3384_2]) ).

cnf(f_3384_4,plain,
    hAPP(c_Set_Ovimage(U_13022,U_13023,U_13024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13025,tc_fun(U_13023,tc_HOL_Obool)),U_13026),U_13027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13025,tc_fun(U_13022,tc_HOL_Obool)),U_13026),hAPP(hAPP(c_COMBB(tc_fun(U_13023,tc_HOL_Obool),tc_fun(U_13022,tc_HOL_Obool),U_13025),c_Set_Ovimage(U_13022,U_13023,U_13024)),U_13027)),
    inference(clausify,[status(thm)],[f_3384_3]) ).

fof(f_3385_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_vimage__UNIV]) ).

fof(f_3385_2,plain,
    ! [U_13030,U_13029,U_13028] : hAPP(c_Set_Ovimage(U_13028,U_13029,U_13030),c_Orderings_Otop__class_Otop(tc_fun(U_13029,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13028,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3385_1]) ).

fof(f_3385_3,plain,
    ! [U_13030,U_13028,U_13029] : hAPP(c_Set_Ovimage(U_13028,U_13029,U_13030),c_Orderings_Otop__class_Otop(tc_fun(U_13029,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13028,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3385_2]) ).

cnf(f_3385_4,plain,
    hAPP(c_Set_Ovimage(U_13028,U_13029,U_13030),c_Orderings_Otop__class_Otop(tc_fun(U_13029,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13028,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3385_3]) ).

fof(f_3386_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_image__vimage__subset]) ).

fof(f_3386_2,plain,
    ! [U_13034,U_13033,U_13032,U_13031] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13031,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13032,U_13031,U_13033),hAPP(c_Set_Ovimage(U_13032,U_13031,U_13033),U_13034))),U_13034)),
    inference(variable_rename,[status(thm)],[f_3386_1]) ).

fof(f_3386_3,plain,
    ! [U_13031,U_13032,U_13033,U_13034] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13031,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13032,U_13031,U_13033),hAPP(c_Set_Ovimage(U_13032,U_13031,U_13033),U_13034))),U_13034)),
    inference(definitional_conversion,[status(esa)],[f_3386_2]) ).

cnf(f_3386_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13031,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13032,U_13031,U_13033),hAPP(c_Set_Ovimage(U_13032,U_13031,U_13033),U_13034))),U_13034)),
    inference(clausify,[status(thm)],[f_3386_3]) ).

fof(f_3387_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq]) ).

fof(f_3387_2,plain,
    ! [U_13038,U_13037,U_13036,U_13035] :
      ( hAPP(c_Set_Oimage(U_13035,U_13036,U_13037),hAPP(c_Set_Ovimage(U_13035,U_13036,U_13037),U_13038)) = U_13038
      | hAPP(c_Set_Oimage(U_13035,U_13036,U_13037),c_Orderings_Otop__class_Otop(tc_fun(U_13035,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13036,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3387_1]) ).

fof(f_3387_3,plain,
    ! [U_13035,U_13036,U_13037,U_13038] :
      ( hAPP(c_Set_Oimage(U_13035,U_13036,U_13037),hAPP(c_Set_Ovimage(U_13035,U_13036,U_13037),U_13038)) = U_13038
      | hAPP(c_Set_Oimage(U_13035,U_13036,U_13037),c_Orderings_Otop__class_Otop(tc_fun(U_13035,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13036,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3387_2]) ).

cnf(f_3387_4,plain,
    ( hAPP(c_Set_Oimage(U_13035,U_13036,U_13037),hAPP(c_Set_Ovimage(U_13035,U_13036,U_13037),U_13038)) = U_13038
    | hAPP(c_Set_Oimage(U_13035,U_13036,U_13037),c_Orderings_Otop__class_Otop(tc_fun(U_13035,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13036,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

fof(f_3388_1,plain,
    ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
        | hAPP(V_f_2,V_a_2) != V_b_2 )
      & ( hAPP(V_f_2,V_a_2) = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq]) ).

fof(f_3388_2,plain,
    ! [U_13043,U_13042,U_13041,U_13040,U_13039] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13039),U_13040),hAPP(c_Set_Ovimage(U_13039,U_13041,U_13042),hAPP(hAPP(c_Set_Oinsert(U_13041),U_13043),c_Orderings_Obot__class_Obot(tc_fun(U_13041,tc_HOL_Obool))))))
        | hAPP(U_13042,U_13040) != U_13043 )
      & ( hAPP(U_13042,U_13040) = U_13043
        | ~ hBOOL(hAPP(hAPP(c_member(U_13039),U_13040),hAPP(c_Set_Ovimage(U_13039,U_13041,U_13042),hAPP(hAPP(c_Set_Oinsert(U_13041),U_13043),c_Orderings_Obot__class_Obot(tc_fun(U_13041,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3388_1]) ).

fof(f_3388_3,plain,
    ( ! [U_13053,U_13051,U_13049,U_13047] :
        ( ! [U_13045] : hBOOL(hAPP(hAPP(c_member(U_13045),U_13047),hAPP(c_Set_Ovimage(U_13045,U_13049,U_13051),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13053),c_Orderings_Obot__class_Obot(tc_fun(U_13049,tc_HOL_Obool))))))
        | hAPP(U_13051,U_13047) != U_13053 )
    & ! [U_13052,U_13050,U_13048,U_13046] :
        ( ! [U_13044] : ~ hBOOL(hAPP(hAPP(c_member(U_13044),U_13046),hAPP(c_Set_Ovimage(U_13044,U_13048,U_13050),hAPP(hAPP(c_Set_Oinsert(U_13048),U_13052),c_Orderings_Obot__class_Obot(tc_fun(U_13048,tc_HOL_Obool))))))
        | hAPP(U_13050,U_13046) = U_13052 ) ),
    inference(miniscope,[status(thm)],[f_3388_2]) ).

fof(f_3388_4,plain,
    ( ! [U_13045,U_13047,U_13049,U_13051,U_13053] :
        ( hBOOL(hAPP(hAPP(c_member(U_13045),U_13047),hAPP(c_Set_Ovimage(U_13045,U_13049,U_13051),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13053),c_Orderings_Obot__class_Obot(tc_fun(U_13049,tc_HOL_Obool))))))
        | hAPP(U_13051,U_13047) != U_13053 )
    & ! [U_13046,U_13044,U_13048,U_13050,U_13052] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13044),U_13046),hAPP(c_Set_Ovimage(U_13044,U_13048,U_13050),hAPP(hAPP(c_Set_Oinsert(U_13048),U_13052),c_Orderings_Obot__class_Obot(tc_fun(U_13048,tc_HOL_Obool))))))
        | hAPP(U_13050,U_13046) = U_13052 ) ),
    inference(definitional_conversion,[status(esa)],[f_3388_3]) ).

cnf(f_3388_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13044),U_13046),hAPP(c_Set_Ovimage(U_13044,U_13048,U_13050),hAPP(hAPP(c_Set_Oinsert(U_13048),U_13052),c_Orderings_Obot__class_Obot(tc_fun(U_13048,tc_HOL_Obool))))))
    | hAPP(U_13050,U_13046) = U_13052 ),
    inference(clausify,[status(thm)],[f_3388_4]) ).

cnf(f_3388_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13045),U_13047),hAPP(c_Set_Ovimage(U_13045,U_13049,U_13051),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13053),c_Orderings_Obot__class_Obot(tc_fun(U_13049,tc_HOL_Obool))))))
    | hAPP(U_13051,U_13047) != U_13053 ),
    inference(clausify,[status(thm)],[f_3388_4]) ).

fof(f_3389_1,plain,
    ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__insert]) ).

fof(f_3389_2,plain,
    ! [U_13058,U_13057,U_13056,U_13055,U_13054] : hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),hAPP(hAPP(c_Set_Oinsert(U_13055),U_13057),U_13058)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13054,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),hAPP(hAPP(c_Set_Oinsert(U_13055),U_13057),c_Orderings_Obot__class_Obot(tc_fun(U_13055,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),U_13058)),
    inference(variable_rename,[status(thm)],[f_3389_1]) ).

fof(f_3389_3,plain,
    ! [U_13054,U_13055,U_13056,U_13057,U_13058] : hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),hAPP(hAPP(c_Set_Oinsert(U_13055),U_13057),U_13058)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13054,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),hAPP(hAPP(c_Set_Oinsert(U_13055),U_13057),c_Orderings_Obot__class_Obot(tc_fun(U_13055,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),U_13058)),
    inference(definitional_conversion,[status(esa)],[f_3389_2]) ).

cnf(f_3389_4,plain,
    hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),hAPP(hAPP(c_Set_Oinsert(U_13055),U_13057),U_13058)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13054,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),hAPP(hAPP(c_Set_Oinsert(U_13055),U_13057),c_Orderings_Obot__class_Obot(tc_fun(U_13055,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_13054,U_13055,U_13056),U_13058)),
    inference(clausify,[status(thm)],[f_3389_3]) ).

fof(f_3390_1,plain,
    ! [V_F_2,V_h_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
      | hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimageD]) ).

fof(f_3390_2,plain,
    ! [U_13062,U_13061,U_13060,U_13059] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13060),U_13062))
      | hAPP(c_Set_Oimage(U_13059,U_13060,U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13059,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13060,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13059),hAPP(c_Set_Ovimage(U_13059,U_13060,U_13061),U_13062))) ),
    inference(variable_rename,[status(thm)],[f_3390_1]) ).

fof(f_3390_3,plain,
    ! [U_13059,U_13060,U_13061,U_13062] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13060),U_13062))
      | hAPP(c_Set_Oimage(U_13059,U_13060,U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13059,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13060,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13059),hAPP(c_Set_Ovimage(U_13059,U_13060,U_13061),U_13062))) ),
    inference(definitional_conversion,[status(esa)],[f_3390_2]) ).

cnf(f_3390_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13060),U_13062))
    | hAPP(c_Set_Oimage(U_13059,U_13060,U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13059,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13060,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13059),hAPP(c_Set_Ovimage(U_13059,U_13060,U_13061),U_13062))) ),
    inference(clausify,[status(thm)],[f_3390_3]) ).

fof(f_3391_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subsetD]) ).

fof(f_3391_2,plain,
    ! [U_13067,U_13066,U_13065,U_13064,U_13063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13064,tc_HOL_Obool)),U_13066),hAPP(c_Set_Oimage(U_13063,U_13064,U_13065),U_13067)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13063,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13063,U_13064,U_13065),U_13066)),U_13067))
      | hAPP(c_Set_Oimage(U_13063,U_13064,U_13065),c_Orderings_Otop__class_Otop(tc_fun(U_13063,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13064,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3391_1]) ).

fof(f_3391_3,plain,
    ! [U_13063,U_13064,U_13065,U_13066,U_13067] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13064,tc_HOL_Obool)),U_13066),hAPP(c_Set_Oimage(U_13063,U_13064,U_13065),U_13067)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13063,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13063,U_13064,U_13065),U_13066)),U_13067))
      | hAPP(c_Set_Oimage(U_13063,U_13064,U_13065),c_Orderings_Otop__class_Otop(tc_fun(U_13063,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13064,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3391_2]) ).

cnf(f_3391_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13064,tc_HOL_Obool)),U_13066),hAPP(c_Set_Oimage(U_13063,U_13064,U_13065),U_13067)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13063,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13063,U_13064,U_13065),U_13066)),U_13067))
    | hAPP(c_Set_Oimage(U_13063,U_13064,U_13065),c_Orderings_Otop__class_Otop(tc_fun(U_13063,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13064,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3391_3]) ).

fof(f_3392_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_image__vimage__eq]) ).

fof(f_3392_2,plain,
    ! [U_13071,U_13070,U_13069,U_13068] : hAPP(c_Set_Oimage(U_13068,U_13069,U_13070),hAPP(c_Set_Ovimage(U_13068,U_13069,U_13070),U_13071)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13069,tc_HOL_Obool)),U_13071),hAPP(c_Set_Oimage(U_13068,U_13069,U_13070),c_Orderings_Otop__class_Otop(tc_fun(U_13068,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3392_1]) ).

fof(f_3392_3,plain,
    ! [U_13069,U_13068,U_13070,U_13071] : hAPP(c_Set_Oimage(U_13068,U_13069,U_13070),hAPP(c_Set_Ovimage(U_13068,U_13069,U_13070),U_13071)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13069,tc_HOL_Obool)),U_13071),hAPP(c_Set_Oimage(U_13068,U_13069,U_13070),c_Orderings_Otop__class_Otop(tc_fun(U_13068,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3392_2]) ).

cnf(f_3392_4,plain,
    hAPP(c_Set_Oimage(U_13068,U_13069,U_13070),hAPP(c_Set_Ovimage(U_13068,U_13069,U_13070),U_13071)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13069,tc_HOL_Obool)),U_13071),hAPP(c_Set_Oimage(U_13068,U_13069,U_13070),c_Orderings_Otop__class_Otop(tc_fun(U_13068,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3392_3]) ).

fof(f_3393_1,plain,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2)))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimageI]) ).

fof(f_3393_2,plain,
    ! [U_13075,U_13074,U_13073,U_13072] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13074),hAPP(c_Set_Ovimage(U_13074,U_13072,U_13075),U_13073)))
      | ~ c_Fun_Oinj__on(U_13074,U_13072,U_13075,c_Orderings_Otop__class_Otop(tc_fun(U_13074,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13072),U_13073)) ),
    inference(variable_rename,[status(thm)],[f_3393_1]) ).

fof(f_3393_3,plain,
    ! [U_13072,U_13073,U_13074,U_13075] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13074),hAPP(c_Set_Ovimage(U_13074,U_13072,U_13075),U_13073)))
      | ~ c_Fun_Oinj__on(U_13074,U_13072,U_13075,c_Orderings_Otop__class_Otop(tc_fun(U_13074,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13072),U_13073)) ),
    inference(definitional_conversion,[status(esa)],[f_3393_2]) ).

cnf(f_3393_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13074),hAPP(c_Set_Ovimage(U_13074,U_13072,U_13075),U_13073)))
    | ~ c_Fun_Oinj__on(U_13074,U_13072,U_13075,c_Orderings_Otop__class_Otop(tc_fun(U_13074,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13072),U_13073)) ),
    inference(clausify,[status(thm)],[f_3393_3]) ).

fof(f_3394_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq]) ).

fof(f_3394_2,plain,
    ! [U_13079,U_13078,U_13077,U_13076] :
      ( hAPP(c_Set_Ovimage(U_13076,U_13077,U_13078),hAPP(c_Set_Oimage(U_13076,U_13077,U_13078),U_13079)) = U_13079
      | ~ c_Fun_Oinj__on(U_13076,U_13077,U_13078,c_Orderings_Otop__class_Otop(tc_fun(U_13076,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3394_1]) ).

fof(f_3394_3,plain,
    ! [U_13076,U_13077,U_13078,U_13079] :
      ( hAPP(c_Set_Ovimage(U_13076,U_13077,U_13078),hAPP(c_Set_Oimage(U_13076,U_13077,U_13078),U_13079)) = U_13079
      | ~ c_Fun_Oinj__on(U_13076,U_13077,U_13078,c_Orderings_Otop__class_Otop(tc_fun(U_13076,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3394_2]) ).

cnf(f_3394_4,plain,
    ( hAPP(c_Set_Ovimage(U_13076,U_13077,U_13078),hAPP(c_Set_Oimage(U_13076,U_13077,U_13078),U_13079)) = U_13079
    | ~ c_Fun_Oinj__on(U_13076,U_13077,U_13078,c_Orderings_Otop__class_Otop(tc_fun(U_13076,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3394_3]) ).

fof(f_3395_1,plain,
    ! [T_c,V_A_2,V_c_2,T_b] :
      ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).

fof(f_3395_2,plain,
    ! [U_13083,U_13082,U_13081,U_13080] :
      ( ( hAPP(c_Set_Ovimage(U_13083,U_13080,hAPP(c_COMBK(U_13080,U_13083),U_13081)),U_13082) = c_Orderings_Obot__class_Obot(tc_fun(U_13083,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13080),U_13081),U_13082)) )
      & ( hAPP(c_Set_Ovimage(U_13083,U_13080,hAPP(c_COMBK(U_13080,U_13083),U_13081)),U_13082) = c_Orderings_Otop__class_Otop(tc_fun(U_13083,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13080),U_13081),U_13082)) ) ),
    inference(variable_rename,[status(thm)],[f_3395_1]) ).

fof(f_3395_3,plain,
    ( ! [U_13091,U_13089,U_13087,U_13085] :
        ( hAPP(c_Set_Ovimage(U_13091,U_13085,hAPP(c_COMBK(U_13085,U_13091),U_13087)),U_13089) = c_Orderings_Obot__class_Obot(tc_fun(U_13091,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13085),U_13087),U_13089)) )
    & ! [U_13090,U_13088,U_13086,U_13084] :
        ( hAPP(c_Set_Ovimage(U_13090,U_13084,hAPP(c_COMBK(U_13084,U_13090),U_13086)),U_13088) = c_Orderings_Otop__class_Otop(tc_fun(U_13090,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13084),U_13086),U_13088)) ) ),
    inference(miniscope,[status(thm)],[f_3395_2]) ).

fof(f_3395_4,plain,
    ( ! [U_13085,U_13087,U_13089,U_13091] :
        ( hAPP(c_Set_Ovimage(U_13091,U_13085,hAPP(c_COMBK(U_13085,U_13091),U_13087)),U_13089) = c_Orderings_Obot__class_Obot(tc_fun(U_13091,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13085),U_13087),U_13089)) )
    & ! [U_13088,U_13086,U_13090,U_13084] :
        ( hAPP(c_Set_Ovimage(U_13090,U_13084,hAPP(c_COMBK(U_13084,U_13090),U_13086)),U_13088) = c_Orderings_Otop__class_Otop(tc_fun(U_13090,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13084),U_13086),U_13088)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3395_3]) ).

cnf(f_3395_5,plain,
    ( hAPP(c_Set_Ovimage(U_13090,U_13084,hAPP(c_COMBK(U_13084,U_13090),U_13086)),U_13088) = c_Orderings_Otop__class_Otop(tc_fun(U_13090,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13084),U_13086),U_13088)) ),
    inference(clausify,[status(thm)],[f_3395_4]) ).

cnf(f_3395_6,plain,
    ( hAPP(c_Set_Ovimage(U_13091,U_13085,hAPP(c_COMBK(U_13085,U_13091),U_13087)),U_13089) = c_Orderings_Obot__class_Obot(tc_fun(U_13091,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_13085),U_13087),U_13089)) ),
    inference(clausify,[status(thm)],[f_3395_4]) ).

fof(f_3396_1,plain,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_vimage__eq__UN]) ).

fof(f_3396_2,plain,
    ! [U_13095,U_13094,U_13093,U_13092] : hAPP(c_Set_Ovimage(U_13092,U_13093,U_13094),U_13095) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13093,tc_fun(U_13092,tc_HOL_Obool)),U_13095),hAPP(hAPP(c_COMBB(tc_fun(U_13093,tc_HOL_Obool),tc_fun(U_13092,tc_HOL_Obool),U_13093),c_Set_Ovimage(U_13092,U_13093,U_13094)),hAPP(hAPP(c_COMBC(U_13093,tc_fun(U_13093,tc_HOL_Obool),tc_fun(U_13093,tc_HOL_Obool)),c_Set_Oinsert(U_13093)),c_Orderings_Obot__class_Obot(tc_fun(U_13093,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3396_1]) ).

fof(f_3396_3,plain,
    ! [U_13092,U_13093,U_13094,U_13095] : hAPP(c_Set_Ovimage(U_13092,U_13093,U_13094),U_13095) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13093,tc_fun(U_13092,tc_HOL_Obool)),U_13095),hAPP(hAPP(c_COMBB(tc_fun(U_13093,tc_HOL_Obool),tc_fun(U_13092,tc_HOL_Obool),U_13093),c_Set_Ovimage(U_13092,U_13093,U_13094)),hAPP(hAPP(c_COMBC(U_13093,tc_fun(U_13093,tc_HOL_Obool),tc_fun(U_13093,tc_HOL_Obool)),c_Set_Oinsert(U_13093)),c_Orderings_Obot__class_Obot(tc_fun(U_13093,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3396_2]) ).

cnf(f_3396_4,plain,
    hAPP(c_Set_Ovimage(U_13092,U_13093,U_13094),U_13095) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13093,tc_fun(U_13092,tc_HOL_Obool)),U_13095),hAPP(hAPP(c_COMBB(tc_fun(U_13093,tc_HOL_Obool),tc_fun(U_13092,tc_HOL_Obool),U_13093),c_Set_Ovimage(U_13092,U_13093,U_13094)),hAPP(hAPP(c_COMBC(U_13093,tc_fun(U_13093,tc_HOL_Obool),tc_fun(U_13093,tc_HOL_Obool)),c_Set_Oinsert(U_13093)),c_Orderings_Obot__class_Obot(tc_fun(U_13093,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3396_3]) ).

fof(f_3397_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subsetI]) ).

fof(f_3397_2,plain,
    ! [U_13100,U_13099,U_13098,U_13097,U_13096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13096,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13096,U_13097,U_13098),U_13099)),U_13100))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13097,tc_HOL_Obool)),U_13099),hAPP(c_Set_Oimage(U_13096,U_13097,U_13098),U_13100)))
      | ~ c_Fun_Oinj__on(U_13096,U_13097,U_13098,c_Orderings_Otop__class_Otop(tc_fun(U_13096,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3397_1]) ).

fof(f_3397_3,plain,
    ! [U_13096,U_13097,U_13098,U_13099,U_13100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13096,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13096,U_13097,U_13098),U_13099)),U_13100))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13097,tc_HOL_Obool)),U_13099),hAPP(c_Set_Oimage(U_13096,U_13097,U_13098),U_13100)))
      | ~ c_Fun_Oinj__on(U_13096,U_13097,U_13098,c_Orderings_Otop__class_Otop(tc_fun(U_13096,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3397_2]) ).

cnf(f_3397_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13096,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13096,U_13097,U_13098),U_13099)),U_13100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13097,tc_HOL_Obool)),U_13099),hAPP(c_Set_Oimage(U_13096,U_13097,U_13098),U_13100)))
    | ~ c_Fun_Oinj__on(U_13096,U_13097,U_13098,c_Orderings_Otop__class_Otop(tc_fun(U_13096,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3397_3]) ).

fof(f_3398_1,plain,
    ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
      ( ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
          & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2
            | hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
          & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).

fof(f_3398_2,plain,
    ! [U_13106,U_13105,U_13104,U_13103,U_13102,U_13101] :
      ( ( ( ( hAPP(c_Set_Ovimage(U_13105,U_13101,hAPP(hAPP(c_COMBC(U_13105,U_13101,U_13101),hAPP(hAPP(c_COMBC(U_13105,U_13101,tc_fun(U_13101,U_13101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13101,tc_fun(U_13101,U_13101)),U_13105),c_If(U_13101)),hAPP(hAPP(c_COMBC(U_13105,tc_fun(U_13105,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13105)),U_13106))),U_13102)),U_13104)),U_13103) = c_Orderings_Obot__class_Obot(tc_fun(U_13105,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_13101),U_13104),U_13103)) )
          & ( hAPP(c_Set_Ovimage(U_13105,U_13101,hAPP(hAPP(c_COMBC(U_13105,U_13101,U_13101),hAPP(hAPP(c_COMBC(U_13105,U_13101,tc_fun(U_13101,U_13101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13101,tc_fun(U_13101,U_13101)),U_13105),c_If(U_13101)),hAPP(hAPP(c_COMBC(U_13105,tc_fun(U_13105,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13105)),U_13106))),U_13102)),U_13104)),U_13103) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13105,tc_HOL_Obool)),U_13106)
            | ~ hBOOL(hAPP(hAPP(c_member(U_13101),U_13104),U_13103)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_13101),U_13102),U_13103)) )
      & ( ( ( hAPP(c_Set_Ovimage(U_13105,U_13101,hAPP(hAPP(c_COMBC(U_13105,U_13101,U_13101),hAPP(hAPP(c_COMBC(U_13105,U_13101,tc_fun(U_13101,U_13101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13101,tc_fun(U_13101,U_13101)),U_13105),c_If(U_13101)),hAPP(hAPP(c_COMBC(U_13105,tc_fun(U_13105,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13105)),U_13106))),U_13102)),U_13104)),U_13103) = U_13106
            | hBOOL(hAPP(hAPP(c_member(U_13101),U_13104),U_13103)) )
          & ( hAPP(c_Set_Ovimage(U_13105,U_13101,hAPP(hAPP(c_COMBC(U_13105,U_13101,U_13101),hAPP(hAPP(c_COMBC(U_13105,U_13101,tc_fun(U_13101,U_13101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13101,tc_fun(U_13101,U_13101)),U_13105),c_If(U_13101)),hAPP(hAPP(c_COMBC(U_13105,tc_fun(U_13105,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13105)),U_13106))),U_13102)),U_13104)),U_13103) = c_Orderings_Otop__class_Otop(tc_fun(U_13105,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13101),U_13104),U_13103)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13101),U_13102),U_13103)) ) ),
    inference(variable_rename,[status(thm)],[f_3398_1]) ).

fof(f_3398_3,plain,
    ( ! [U_13118,U_13116,U_13114,U_13112,U_13110,U_13108] :
        ( ( ( hAPP(c_Set_Ovimage(U_13116,U_13108,hAPP(hAPP(c_COMBC(U_13116,U_13108,U_13108),hAPP(hAPP(c_COMBC(U_13116,U_13108,tc_fun(U_13108,U_13108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13108,tc_fun(U_13108,U_13108)),U_13116),c_If(U_13108)),hAPP(hAPP(c_COMBC(U_13116,tc_fun(U_13116,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13116)),U_13118))),U_13110)),U_13114)),U_13112) = c_Orderings_Obot__class_Obot(tc_fun(U_13116,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_13108),U_13114),U_13112)) )
          & ( hAPP(c_Set_Ovimage(U_13116,U_13108,hAPP(hAPP(c_COMBC(U_13116,U_13108,U_13108),hAPP(hAPP(c_COMBC(U_13116,U_13108,tc_fun(U_13108,U_13108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13108,tc_fun(U_13108,U_13108)),U_13116),c_If(U_13108)),hAPP(hAPP(c_COMBC(U_13116,tc_fun(U_13116,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13116)),U_13118))),U_13110)),U_13114)),U_13112) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13116,tc_HOL_Obool)),U_13118)
            | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13114),U_13112)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),U_13112)) )
    & ! [U_13117,U_13115,U_13113,U_13111,U_13109,U_13107] :
        ( ( ( hAPP(c_Set_Ovimage(U_13115,U_13107,hAPP(hAPP(c_COMBC(U_13115,U_13107,U_13107),hAPP(hAPP(c_COMBC(U_13115,U_13107,tc_fun(U_13107,U_13107)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13107,tc_fun(U_13107,U_13107)),U_13115),c_If(U_13107)),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),U_13109)),U_13113)),U_13111) = U_13117
            | hBOOL(hAPP(hAPP(c_member(U_13107),U_13113),U_13111)) )
          & ( hAPP(c_Set_Ovimage(U_13115,U_13107,hAPP(hAPP(c_COMBC(U_13115,U_13107,U_13107),hAPP(hAPP(c_COMBC(U_13115,U_13107,tc_fun(U_13107,U_13107)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13107,tc_fun(U_13107,U_13107)),U_13115),c_If(U_13107)),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),U_13109)),U_13113)),U_13111) = c_Orderings_Otop__class_Otop(tc_fun(U_13115,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13113),U_13111)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),U_13111)) ) ),
    inference(miniscope,[status(thm)],[f_3398_2]) ).

fof(f_3398_4,plain,
    ( ! [U_13114,U_13110,U_13112,U_13108,U_13118,U_13116] :
        ( hAPP(c_Set_Ovimage(U_13116,U_13108,hAPP(hAPP(c_COMBC(U_13116,U_13108,U_13108),hAPP(hAPP(c_COMBC(U_13116,U_13108,tc_fun(U_13108,U_13108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13108,tc_fun(U_13108,U_13108)),U_13116),c_If(U_13108)),hAPP(hAPP(c_COMBC(U_13116,tc_fun(U_13116,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13116)),U_13118))),U_13110)),U_13114)),U_13112) = c_Orderings_Obot__class_Obot(tc_fun(U_13116,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13108),U_13114),U_13112))
        | ~ sP954(U_13114,U_13110,U_13112,U_13108,U_13118,U_13116) )
    & ! [U_13114,U_13110,U_13112,U_13108,U_13118,U_13116] :
        ( hAPP(c_Set_Ovimage(U_13116,U_13108,hAPP(hAPP(c_COMBC(U_13116,U_13108,U_13108),hAPP(hAPP(c_COMBC(U_13116,U_13108,tc_fun(U_13108,U_13108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13108,tc_fun(U_13108,U_13108)),U_13116),c_If(U_13108)),hAPP(hAPP(c_COMBC(U_13116,tc_fun(U_13116,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13116)),U_13118))),U_13110)),U_13114)),U_13112) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13116,tc_HOL_Obool)),U_13118)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13114),U_13112))
        | ~ sP954(U_13114,U_13110,U_13112,U_13108,U_13118,U_13116) )
    & ! [U_13107,U_13109,U_13111,U_13113,U_13117,U_13115] :
        ( hAPP(c_Set_Ovimage(U_13115,U_13107,hAPP(hAPP(c_COMBC(U_13115,U_13107,U_13107),hAPP(hAPP(c_COMBC(U_13115,U_13107,tc_fun(U_13107,U_13107)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13107,tc_fun(U_13107,U_13107)),U_13115),c_If(U_13107)),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),U_13109)),U_13113)),U_13111) = U_13117
        | hBOOL(hAPP(hAPP(c_member(U_13107),U_13113),U_13111))
        | ~ sP953(U_13107,U_13109,U_13111,U_13113,U_13117,U_13115) )
    & ! [U_13107,U_13109,U_13111,U_13113,U_13117,U_13115] :
        ( hAPP(c_Set_Ovimage(U_13115,U_13107,hAPP(hAPP(c_COMBC(U_13115,U_13107,U_13107),hAPP(hAPP(c_COMBC(U_13115,U_13107,tc_fun(U_13107,U_13107)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13107,tc_fun(U_13107,U_13107)),U_13115),c_If(U_13107)),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),U_13109)),U_13113)),U_13111) = c_Orderings_Otop__class_Otop(tc_fun(U_13115,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13113),U_13111))
        | ~ sP953(U_13107,U_13109,U_13111,U_13113,U_13117,U_13115) )
    & ! [U_13114,U_13110,U_13112,U_13108,U_13118,U_13116] :
        ( sP954(U_13114,U_13110,U_13112,U_13108,U_13118,U_13116)
        | hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),U_13112)) )
    & ! [U_13107,U_13109,U_13111,U_13113,U_13117,U_13115] :
        ( sP953(U_13107,U_13109,U_13111,U_13113,U_13117,U_13115)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),U_13111)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP953,sP954])],[f_3398_3]) ).

cnf(f_3398_5,plain,
    ( sP953(U_13107,U_13109,U_13111,U_13113,U_13117,U_13115)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),U_13111)) ),
    inference(clausify,[status(thm)],[f_3398_4]) ).

cnf(f_3398_6,plain,
    ( sP954(U_13114,U_13110,U_13112,U_13108,U_13118,U_13116)
    | hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),U_13112)) ),
    inference(clausify,[status(thm)],[f_3398_4]) ).

cnf(f_3398_7,plain,
    ( hAPP(c_Set_Ovimage(U_13115,U_13107,hAPP(hAPP(c_COMBC(U_13115,U_13107,U_13107),hAPP(hAPP(c_COMBC(U_13115,U_13107,tc_fun(U_13107,U_13107)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13107,tc_fun(U_13107,U_13107)),U_13115),c_If(U_13107)),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),U_13109)),U_13113)),U_13111) = c_Orderings_Otop__class_Otop(tc_fun(U_13115,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13113),U_13111))
    | ~ sP953(U_13107,U_13109,U_13111,U_13113,U_13117,U_13115) ),
    inference(clausify,[status(thm)],[f_3398_4]) ).

cnf(f_3398_8,plain,
    ( hAPP(c_Set_Ovimage(U_13115,U_13107,hAPP(hAPP(c_COMBC(U_13115,U_13107,U_13107),hAPP(hAPP(c_COMBC(U_13115,U_13107,tc_fun(U_13107,U_13107)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13107,tc_fun(U_13107,U_13107)),U_13115),c_If(U_13107)),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),U_13109)),U_13113)),U_13111) = U_13117
    | hBOOL(hAPP(hAPP(c_member(U_13107),U_13113),U_13111))
    | ~ sP953(U_13107,U_13109,U_13111,U_13113,U_13117,U_13115) ),
    inference(clausify,[status(thm)],[f_3398_4]) ).

cnf(f_3398_9,plain,
    ( hAPP(c_Set_Ovimage(U_13116,U_13108,hAPP(hAPP(c_COMBC(U_13116,U_13108,U_13108),hAPP(hAPP(c_COMBC(U_13116,U_13108,tc_fun(U_13108,U_13108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13108,tc_fun(U_13108,U_13108)),U_13116),c_If(U_13108)),hAPP(hAPP(c_COMBC(U_13116,tc_fun(U_13116,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13116)),U_13118))),U_13110)),U_13114)),U_13112) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13116,tc_HOL_Obool)),U_13118)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13114),U_13112))
    | ~ sP954(U_13114,U_13110,U_13112,U_13108,U_13118,U_13116) ),
    inference(clausify,[status(thm)],[f_3398_4]) ).

cnf(f_3398_10,plain,
    ( hAPP(c_Set_Ovimage(U_13116,U_13108,hAPP(hAPP(c_COMBC(U_13116,U_13108,U_13108),hAPP(hAPP(c_COMBC(U_13116,U_13108,tc_fun(U_13108,U_13108)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13108,tc_fun(U_13108,U_13108)),U_13116),c_If(U_13108)),hAPP(hAPP(c_COMBC(U_13116,tc_fun(U_13116,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13116)),U_13118))),U_13110)),U_13114)),U_13112) = c_Orderings_Obot__class_Obot(tc_fun(U_13116,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_13108),U_13114),U_13112))
    | ~ sP954(U_13114,U_13110,U_13112,U_13108,U_13118,U_13116) ),
    inference(clausify,[status(thm)],[f_3398_4]) ).

fof(f_3399_1,plain,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range]) ).

fof(f_3399_2,plain,
    ! [U_13123,U_13122,U_13121,U_13120,U_13119] :
      ( hAPP(c_Set_Oimage(U_13119,U_13120,U_13121),c_Orderings_Otop__class_Otop(tc_fun(U_13119,tc_HOL_Obool))) = U_13123
      | ~ c_Typedef_Otype__definition(U_13119,U_13120,U_13121,U_13122,U_13123) ),
    inference(variable_rename,[status(thm)],[f_3399_1]) ).

fof(f_3399_3,plain,
    ! [U_13120,U_13119,U_13122,U_13123,U_13121] :
      ( hAPP(c_Set_Oimage(U_13119,U_13120,U_13121),c_Orderings_Otop__class_Otop(tc_fun(U_13119,tc_HOL_Obool))) = U_13123
      | ~ c_Typedef_Otype__definition(U_13119,U_13120,U_13121,U_13122,U_13123) ),
    inference(definitional_conversion,[status(esa)],[f_3399_2]) ).

cnf(f_3399_4,plain,
    ( hAPP(c_Set_Oimage(U_13119,U_13120,U_13121),c_Orderings_Otop__class_Otop(tc_fun(U_13119,tc_HOL_Obool))) = U_13123
    | ~ c_Typedef_Otype__definition(U_13119,U_13120,U_13121,U_13122,U_13123) ),
    inference(clausify,[status(thm)],[f_3399_3]) ).

fof(f_3400_1,plain,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image]) ).

fof(f_3400_2,plain,
    ! [U_13128,U_13127,U_13126,U_13125,U_13124] :
      ( hAPP(c_Set_Oimage(U_13125,U_13124,U_13127),U_13128) = c_Orderings_Otop__class_Otop(tc_fun(U_13124,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_13124,U_13125,U_13126,U_13127,U_13128) ),
    inference(variable_rename,[status(thm)],[f_3400_1]) ).

fof(f_3400_3,plain,
    ! [U_13125,U_13127,U_13128,U_13124,U_13126] :
      ( hAPP(c_Set_Oimage(U_13125,U_13124,U_13127),U_13128) = c_Orderings_Otop__class_Otop(tc_fun(U_13124,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_13124,U_13125,U_13126,U_13127,U_13128) ),
    inference(definitional_conversion,[status(esa)],[f_3400_2]) ).

cnf(f_3400_4,plain,
    ( hAPP(c_Set_Oimage(U_13125,U_13124,U_13127),U_13128) = c_Orderings_Otop__class_Otop(tc_fun(U_13124,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(U_13124,U_13125,U_13126,U_13127,U_13128) ),
    inference(clausify,[status(thm)],[f_3400_3]) ).

fof(f_3401_1,plain,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep]) ).

fof(f_3401_2,plain,
    ! [U_13134,U_13133,U_13132,U_13131,U_13130,U_13129] :
      ( hBOOL(hAPP(hAPP(c_member(U_13130),hAPP(U_13131,U_13134)),U_13133))
      | ~ c_Typedef_Otype__definition(U_13129,U_13130,U_13131,U_13132,U_13133) ),
    inference(variable_rename,[status(thm)],[f_3401_1]) ).

fof(f_3401_3,plain,
    ! [U_13134,U_13133,U_13132,U_13131,U_13130] :
      ( ! [U_13129] : ~ c_Typedef_Otype__definition(U_13129,U_13130,U_13131,U_13132,U_13133)
      | hBOOL(hAPP(hAPP(c_member(U_13130),hAPP(U_13131,U_13134)),U_13133)) ),
    inference(miniscope,[status(thm)],[f_3401_2]) ).

fof(f_3401_4,plain,
    ! [U_13130,U_13129,U_13131,U_13132,U_13133,U_13134] :
      ( ~ c_Typedef_Otype__definition(U_13129,U_13130,U_13131,U_13132,U_13133)
      | hBOOL(hAPP(hAPP(c_member(U_13130),hAPP(U_13131,U_13134)),U_13133)) ),
    inference(definitional_conversion,[status(esa)],[f_3401_3]) ).

cnf(f_3401_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13129,U_13130,U_13131,U_13132,U_13133)
    | hBOOL(hAPP(hAPP(c_member(U_13130),hAPP(U_13131,U_13134)),U_13133)) ),
    inference(clausify,[status(thm)],[f_3401_4]) ).

fof(f_3402_1,plain,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse]) ).

fof(f_3402_2,plain,
    ! [U_13140,U_13139,U_13138,U_13137,U_13136,U_13135] :
      ( hAPP(U_13138,hAPP(U_13137,U_13140)) = U_13140
      | ~ c_Typedef_Otype__definition(U_13135,U_13136,U_13137,U_13138,U_13139) ),
    inference(variable_rename,[status(thm)],[f_3402_1]) ).

fof(f_3402_3,plain,
    ! [U_13140,U_13139,U_13138,U_13137] :
      ( ! [U_13136,U_13135] : ~ c_Typedef_Otype__definition(U_13135,U_13136,U_13137,U_13138,U_13139)
      | hAPP(U_13138,hAPP(U_13137,U_13140)) = U_13140 ),
    inference(miniscope,[status(thm)],[f_3402_2]) ).

fof(f_3402_4,plain,
    ! [U_13136,U_13135,U_13137,U_13138,U_13139,U_13140] :
      ( ~ c_Typedef_Otype__definition(U_13135,U_13136,U_13137,U_13138,U_13139)
      | hAPP(U_13138,hAPP(U_13137,U_13140)) = U_13140 ),
    inference(definitional_conversion,[status(esa)],[f_3402_3]) ).

cnf(f_3402_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13135,U_13136,U_13137,U_13138,U_13139)
    | hAPP(U_13138,hAPP(U_13137,U_13140)) = U_13140 ),
    inference(clausify,[status(thm)],[f_3402_4]) ).

fof(f_3403_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( ( ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_Rep_2,V_x_2) != hAPP(V_Rep_2,V_y_2) ) )
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject]) ).

fof(f_3403_2,plain,
    ! [U_13147,U_13146,U_13145,U_13144,U_13143,U_13142,U_13141] :
      ( ( ( hAPP(U_13143,U_13146) = hAPP(U_13143,U_13147)
          | U_13146 != U_13147 )
        & ( U_13146 = U_13147
          | hAPP(U_13143,U_13146) != hAPP(U_13143,U_13147) ) )
      | ~ c_Typedef_Otype__definition(U_13141,U_13142,U_13143,U_13144,U_13145) ),
    inference(variable_rename,[status(thm)],[f_3403_1]) ).

fof(f_3403_3,plain,
    ! [U_13147,U_13146,U_13145,U_13144,U_13143] :
      ( ! [U_13142,U_13141] : ~ c_Typedef_Otype__definition(U_13141,U_13142,U_13143,U_13144,U_13145)
      | ( ( hAPP(U_13143,U_13146) = hAPP(U_13143,U_13147)
          | U_13146 != U_13147 )
        & ( U_13146 = U_13147
          | hAPP(U_13143,U_13146) != hAPP(U_13143,U_13147) ) ) ),
    inference(miniscope,[status(thm)],[f_3403_2]) ).

fof(f_3403_4,plain,
    ( ! [U_13143,U_13146,U_13147] :
        ( hAPP(U_13143,U_13146) = hAPP(U_13143,U_13147)
        | U_13146 != U_13147
        | ~ sP955(U_13143,U_13146,U_13147) )
    & ! [U_13143,U_13146,U_13147] :
        ( U_13146 = U_13147
        | hAPP(U_13143,U_13146) != hAPP(U_13143,U_13147)
        | ~ sP955(U_13143,U_13146,U_13147) )
    & ! [U_13141,U_13143,U_13142,U_13144,U_13145,U_13146,U_13147] :
        ( ~ c_Typedef_Otype__definition(U_13141,U_13142,U_13143,U_13144,U_13145)
        | sP955(U_13143,U_13146,U_13147) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP955])],[f_3403_3]) ).

cnf(f_3403_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13141,U_13142,U_13143,U_13144,U_13145)
    | sP955(U_13143,U_13146,U_13147) ),
    inference(clausify,[status(thm)],[f_3403_4]) ).

cnf(f_3403_6,plain,
    ( U_13146 = U_13147
    | hAPP(U_13143,U_13146) != hAPP(U_13143,U_13147)
    | ~ sP955(U_13143,U_13146,U_13147) ),
    inference(clausify,[status(thm)],[f_3403_4]) ).

cnf(f_3403_7,plain,
    ( hAPP(U_13143,U_13146) = hAPP(U_13143,U_13147)
    | U_13146 != U_13147
    | ~ sP955(U_13143,U_13146,U_13147) ),
    inference(clausify,[status(thm)],[f_3403_4]) ).

fof(f_3404_1,plain,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_type__definition__code__numeral]) ).

fof(f_3404_2,plain,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3404_1]) ).

cnf(f_3404_3,plain,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3404_2]) ).

fof(f_3405_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( ( ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_Abs_2,V_x_2) != hAPP(V_Abs_2,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject]) ).

fof(f_3405_2,plain,
    ! [U_13154,U_13153,U_13152,U_13151,U_13150,U_13149,U_13148] :
      ( ( ( hAPP(U_13151,U_13153) = hAPP(U_13151,U_13154)
          | U_13153 != U_13154 )
        & ( U_13153 = U_13154
          | hAPP(U_13151,U_13153) != hAPP(U_13151,U_13154) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13154),U_13152))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13153),U_13152))
      | ~ c_Typedef_Otype__definition(U_13148,U_13149,U_13150,U_13151,U_13152) ),
    inference(variable_rename,[status(thm)],[f_3405_1]) ).

fof(f_3405_3,plain,
    ! [U_13154,U_13153,U_13152,U_13151,U_13150,U_13149] :
      ( ! [U_13148] : ~ c_Typedef_Otype__definition(U_13148,U_13149,U_13150,U_13151,U_13152)
      | ( ( hAPP(U_13151,U_13153) = hAPP(U_13151,U_13154)
          | U_13153 != U_13154 )
        & ( U_13153 = U_13154
          | hAPP(U_13151,U_13153) != hAPP(U_13151,U_13154) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13154),U_13152))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13153),U_13152)) ),
    inference(miniscope,[status(thm)],[f_3405_2]) ).

fof(f_3405_4,plain,
    ( ! [U_13151,U_13153,U_13154] :
        ( hAPP(U_13151,U_13153) = hAPP(U_13151,U_13154)
        | U_13153 != U_13154
        | ~ sP956(U_13151,U_13153,U_13154) )
    & ! [U_13151,U_13153,U_13154] :
        ( U_13153 = U_13154
        | hAPP(U_13151,U_13153) != hAPP(U_13151,U_13154)
        | ~ sP956(U_13151,U_13153,U_13154) )
    & ! [U_13148,U_13149,U_13150,U_13151,U_13152,U_13153,U_13154] :
        ( ~ c_Typedef_Otype__definition(U_13148,U_13149,U_13150,U_13151,U_13152)
        | sP956(U_13151,U_13153,U_13154)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13154),U_13152))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13153),U_13152)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP956])],[f_3405_3]) ).

cnf(f_3405_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13148,U_13149,U_13150,U_13151,U_13152)
    | sP956(U_13151,U_13153,U_13154)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13154),U_13152))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13149),U_13153),U_13152)) ),
    inference(clausify,[status(thm)],[f_3405_4]) ).

cnf(f_3405_6,plain,
    ( U_13153 = U_13154
    | hAPP(U_13151,U_13153) != hAPP(U_13151,U_13154)
    | ~ sP956(U_13151,U_13153,U_13154) ),
    inference(clausify,[status(thm)],[f_3405_4]) ).

cnf(f_3405_7,plain,
    ( hAPP(U_13151,U_13153) = hAPP(U_13151,U_13154)
    | U_13153 != U_13154
    | ~ sP956(U_13151,U_13153,U_13154) ),
    inference(clausify,[status(thm)],[f_3405_4]) ).

fof(f_3406_1,plain,
    ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse]) ).

fof(f_3406_2,plain,
    ! [U_13160,U_13159,U_13158,U_13157,U_13156,U_13155] :
      ( hAPP(U_13157,hAPP(U_13158,U_13160)) = U_13160
      | ~ hBOOL(hAPP(hAPP(c_member(U_13156),U_13160),U_13159))
      | ~ c_Typedef_Otype__definition(U_13155,U_13156,U_13157,U_13158,U_13159) ),
    inference(variable_rename,[status(thm)],[f_3406_1]) ).

fof(f_3406_3,plain,
    ! [U_13160,U_13159,U_13158,U_13157,U_13156] :
      ( ! [U_13155] : ~ c_Typedef_Otype__definition(U_13155,U_13156,U_13157,U_13158,U_13159)
      | hAPP(U_13157,hAPP(U_13158,U_13160)) = U_13160
      | ~ hBOOL(hAPP(hAPP(c_member(U_13156),U_13160),U_13159)) ),
    inference(miniscope,[status(thm)],[f_3406_2]) ).

fof(f_3406_4,plain,
    ! [U_13157,U_13156,U_13159,U_13155,U_13160,U_13158] :
      ( ~ c_Typedef_Otype__definition(U_13155,U_13156,U_13157,U_13158,U_13159)
      | hAPP(U_13157,hAPP(U_13158,U_13160)) = U_13160
      | ~ hBOOL(hAPP(hAPP(c_member(U_13156),U_13160),U_13159)) ),
    inference(definitional_conversion,[status(esa)],[f_3406_3]) ).

cnf(f_3406_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13155,U_13156,U_13157,U_13158,U_13159)
    | hAPP(U_13157,hAPP(U_13158,U_13160)) = U_13160
    | ~ hBOOL(hAPP(hAPP(c_member(U_13156),U_13160),U_13159)) ),
    inference(clausify,[status(thm)],[f_3406_4]) ).

fof(f_3407_1,plain,
    ! [V_a2_2,V_a1_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
        | ? [B_x] :
            ( ! [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
        | ~ c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp_Oequations]) ).

fof(f_3407_2,plain,
    ! [U_13168,U_13167,U_13166,U_13165] :
      ( ( c_Wellfounded_Omax__extp(U_13165,U_13166,U_13167,U_13168)
        | ? [U_13164] :
            ( ! [U_13163] :
                ( ~ hBOOL(hAPP(hAPP(U_13166,U_13164),U_13163))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13165),U_13163),U_13168)) )
            & hBOOL(hAPP(hAPP(c_member(U_13165),U_13164),U_13167)) )
        | U_13168 = c_Orderings_Obot__class_Obot(tc_fun(U_13165,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13165),U_13168))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13165),U_13167)) )
      & ( ( ! [U_13162] :
              ( ? [U_13161] :
                  ( hBOOL(hAPP(hAPP(U_13166,U_13162),U_13161))
                  & hBOOL(hAPP(hAPP(c_member(U_13165),U_13161),U_13168)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13165),U_13162),U_13167)) )
          & U_13168 != c_Orderings_Obot__class_Obot(tc_fun(U_13165,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13165),U_13168))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13165),U_13167)) )
        | ~ c_Wellfounded_Omax__extp(U_13165,U_13166,U_13167,U_13168) ) ),
    inference(variable_rename,[status(thm)],[f_3407_1]) ).

fof(f_3407_3,plain,
    ( ! [U_13176,U_13174,U_13172,U_13170] :
        ( c_Wellfounded_Omax__extp(U_13170,U_13172,U_13174,U_13176)
        | ? [U_13164] :
            ( ! [U_13163] :
                ( ~ hBOOL(hAPP(hAPP(U_13172,U_13164),U_13163))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13170),U_13163),U_13176)) )
            & hBOOL(hAPP(hAPP(c_member(U_13170),U_13164),U_13174)) )
        | U_13176 = c_Orderings_Obot__class_Obot(tc_fun(U_13170,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13174)) )
    & ! [U_13175,U_13173,U_13171,U_13169] :
        ( ( ! [U_13162] :
              ( ? [U_13161] :
                  ( hBOOL(hAPP(hAPP(U_13171,U_13162),U_13161))
                  & hBOOL(hAPP(hAPP(c_member(U_13169),U_13161),U_13175)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13162),U_13173)) )
          & U_13175 != c_Orderings_Obot__class_Obot(tc_fun(U_13169,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13175))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13173)) )
        | ~ c_Wellfounded_Omax__extp(U_13169,U_13171,U_13173,U_13175) ) ),
    inference(miniscope,[status(thm)],[f_3407_2]) ).

fof(f_3407_4,plain,
    ( ! [U_13176,U_13174,U_13172,U_13170] :
        ( c_Wellfounded_Omax__extp(U_13170,U_13172,U_13174,U_13176)
        | ? [U_13164] :
            ( ! [U_13163] :
                ( ~ hBOOL(hAPP(hAPP(U_13172,U_13164),U_13163))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13170),U_13163),U_13176)) )
            & hBOOL(hAPP(hAPP(c_member(U_13170),U_13164),U_13174)) )
        | U_13176 = c_Orderings_Obot__class_Obot(tc_fun(U_13170,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13174)) )
    & ! [U_13175,U_13173,U_13171,U_13169] :
        ( ( ! [U_13162] :
              ( ( hBOOL(hAPP(hAPP(U_13171,U_13162),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)))
                & hBOOL(hAPP(hAPP(c_member(U_13169),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)),U_13175)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13162),U_13173)) )
          & U_13175 != c_Orderings_Obot__class_Obot(tc_fun(U_13169,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13175))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13173)) )
        | ~ c_Wellfounded_Omax__extp(U_13169,U_13171,U_13173,U_13175) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_13161,sK283(U_13175,U_13173,U_13171,U_13169,U_13162))],[f_3407_3]) ).

fof(f_3407_5,plain,
    ( ! [U_13176,U_13174,U_13172,U_13170] :
        ( c_Wellfounded_Omax__extp(U_13170,U_13172,U_13174,U_13176)
        | ( ! [U_13163] :
              ( ~ hBOOL(hAPP(hAPP(U_13172,sK284(U_13176,U_13174,U_13172,U_13170)),U_13163))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13170),U_13163),U_13176)) )
          & hBOOL(hAPP(hAPP(c_member(U_13170),sK284(U_13176,U_13174,U_13172,U_13170)),U_13174)) )
        | U_13176 = c_Orderings_Obot__class_Obot(tc_fun(U_13170,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13174)) )
    & ! [U_13175,U_13173,U_13171,U_13169] :
        ( ( ! [U_13162] :
              ( ( hBOOL(hAPP(hAPP(U_13171,U_13162),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)))
                & hBOOL(hAPP(hAPP(c_member(U_13169),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)),U_13175)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13162),U_13173)) )
          & U_13175 != c_Orderings_Obot__class_Obot(tc_fun(U_13169,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13175))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13173)) )
        | ~ c_Wellfounded_Omax__extp(U_13169,U_13171,U_13173,U_13175) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_13164,sK284(U_13176,U_13174,U_13172,U_13170))],[f_3407_4]) ).

fof(f_3407_6,plain,
    ( ! [U_13163,U_13174,U_13176,U_13172,U_13170] :
        ( ~ hBOOL(hAPP(hAPP(U_13172,sK284(U_13176,U_13174,U_13172,U_13170)),U_13163))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13170),U_13163),U_13176))
        | ~ sP959(U_13163,U_13174,U_13176,U_13172,U_13170) )
    & ! [U_13163,U_13174,U_13176,U_13172,U_13170] :
        ( hBOOL(hAPP(hAPP(c_member(U_13170),sK284(U_13176,U_13174,U_13172,U_13170)),U_13174))
        | ~ sP959(U_13163,U_13174,U_13176,U_13172,U_13170) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( hBOOL(hAPP(hAPP(U_13171,U_13162),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)))
        | ~ sP957(U_13162,U_13173,U_13171,U_13169,U_13175) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( hBOOL(hAPP(hAPP(c_member(U_13169),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)),U_13175))
        | ~ sP957(U_13162,U_13173,U_13171,U_13169,U_13175) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( sP957(U_13162,U_13173,U_13171,U_13169,U_13175)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13162),U_13173))
        | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( U_13175 != c_Orderings_Obot__class_Obot(tc_fun(U_13169,tc_HOL_Obool))
        | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13175))
        | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13173))
        | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) )
    & ! [U_13163,U_13174,U_13176,U_13172,U_13170] :
        ( c_Wellfounded_Omax__extp(U_13170,U_13172,U_13174,U_13176)
        | sP959(U_13163,U_13174,U_13176,U_13172,U_13170)
        | U_13176 = c_Orderings_Obot__class_Obot(tc_fun(U_13170,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13174)) )
    & ! [U_13162,U_13173,U_13171,U_13169,U_13175] :
        ( sP958(U_13162,U_13173,U_13171,U_13169,U_13175)
        | ~ c_Wellfounded_Omax__extp(U_13169,U_13171,U_13173,U_13175) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP957,sP958,sP959])],[f_3407_5]) ).

cnf(f_3407_7,plain,
    ( sP958(U_13162,U_13173,U_13171,U_13169,U_13175)
    | ~ c_Wellfounded_Omax__extp(U_13169,U_13171,U_13173,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_8,plain,
    ( c_Wellfounded_Omax__extp(U_13170,U_13172,U_13174,U_13176)
    | sP959(U_13163,U_13174,U_13176,U_13172,U_13170)
    | U_13176 = c_Orderings_Obot__class_Obot(tc_fun(U_13170,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13176))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),U_13174)) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13173))
    | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13169),U_13175))
    | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_11,plain,
    ( U_13175 != c_Orderings_Obot__class_Obot(tc_fun(U_13169,tc_HOL_Obool))
    | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_12,plain,
    ( sP957(U_13162,U_13173,U_13171,U_13169,U_13175)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13162),U_13173))
    | ~ sP958(U_13162,U_13173,U_13171,U_13169,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13169),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)),U_13175))
    | ~ sP957(U_13162,U_13173,U_13171,U_13169,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_14,plain,
    ( hBOOL(hAPP(hAPP(U_13171,U_13162),sK283(U_13175,U_13173,U_13171,U_13169,U_13162)))
    | ~ sP957(U_13162,U_13173,U_13171,U_13169,U_13175) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13170),sK284(U_13176,U_13174,U_13172,U_13170)),U_13174))
    | ~ sP959(U_13163,U_13174,U_13176,U_13172,U_13170) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

cnf(f_3407_16,plain,
    ( ~ hBOOL(hAPP(hAPP(U_13172,sK284(U_13176,U_13174,U_13172,U_13170)),U_13163))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13170),U_13163),U_13176))
    | ~ sP959(U_13163,U_13174,U_13176,U_13172,U_13170) ),
    inference(clausify,[status(thm)],[f_3407_6]) ).

fof(f_3408_1,plain,
    ! [V_R_2,V_Y_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ? [B_x] :
          ( ! [B_xa] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) )
      | V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros]) ).

fof(f_3408_2,plain,
    ! [U_13182,U_13181,U_13180,U_13179] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),U_13180),U_13181)),c_Wellfounded_Omax__ext(U_13179,U_13182)))
      | ? [U_13178] :
          ( ! [U_13177] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13179,U_13179)),hAPP(hAPP(c_Product__Type_OPair(U_13179,U_13179),U_13178),U_13177)),U_13182))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13179),U_13177),U_13181)) )
          & hBOOL(hAPP(hAPP(c_member(U_13179),U_13178),U_13180)) )
      | U_13181 = c_Orderings_Obot__class_Obot(tc_fun(U_13179,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13181))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13180)) ),
    inference(variable_rename,[status(thm)],[f_3408_1]) ).

fof(f_3408_3,plain,
    ! [U_13182,U_13181,U_13180,U_13179] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),U_13180),U_13181)),c_Wellfounded_Omax__ext(U_13179,U_13182)))
      | ( ! [U_13177] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13179,U_13179)),hAPP(hAPP(c_Product__Type_OPair(U_13179,U_13179),sK285(U_13182,U_13181,U_13180,U_13179)),U_13177)),U_13182))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13179),U_13177),U_13181)) )
        & hBOOL(hAPP(hAPP(c_member(U_13179),sK285(U_13182,U_13181,U_13180,U_13179)),U_13180)) )
      | U_13181 = c_Orderings_Obot__class_Obot(tc_fun(U_13179,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13181))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13180)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_13178,sK285(U_13182,U_13181,U_13180,U_13179))],[f_3408_2]) ).

fof(f_3408_4,plain,
    ( ! [U_13179,U_13177,U_13182,U_13180,U_13181] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13179,U_13179)),hAPP(hAPP(c_Product__Type_OPair(U_13179,U_13179),sK285(U_13182,U_13181,U_13180,U_13179)),U_13177)),U_13182))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13179),U_13177),U_13181))
        | ~ sP960(U_13179,U_13177,U_13182,U_13180,U_13181) )
    & ! [U_13179,U_13177,U_13182,U_13180,U_13181] :
        ( hBOOL(hAPP(hAPP(c_member(U_13179),sK285(U_13182,U_13181,U_13180,U_13179)),U_13180))
        | ~ sP960(U_13179,U_13177,U_13182,U_13180,U_13181) )
    & ! [U_13179,U_13177,U_13182,U_13180,U_13181] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),U_13180),U_13181)),c_Wellfounded_Omax__ext(U_13179,U_13182)))
        | sP960(U_13179,U_13177,U_13182,U_13180,U_13181)
        | U_13181 = c_Orderings_Obot__class_Obot(tc_fun(U_13179,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13181))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13180)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP960])],[f_3408_3]) ).

cnf(f_3408_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),U_13180),U_13181)),c_Wellfounded_Omax__ext(U_13179,U_13182)))
    | sP960(U_13179,U_13177,U_13182,U_13180,U_13181)
    | U_13181 = c_Orderings_Obot__class_Obot(tc_fun(U_13179,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13181))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13179),U_13180)) ),
    inference(clausify,[status(thm)],[f_3408_4]) ).

cnf(f_3408_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13179),sK285(U_13182,U_13181,U_13180,U_13179)),U_13180))
    | ~ sP960(U_13179,U_13177,U_13182,U_13180,U_13181) ),
    inference(clausify,[status(thm)],[f_3408_4]) ).

cnf(f_3408_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13179,U_13179)),hAPP(hAPP(c_Product__Type_OPair(U_13179,U_13179),sK285(U_13182,U_13181,U_13180,U_13179)),U_13177)),U_13182))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13179),U_13177),U_13181))
    | ~ sP960(U_13179,U_13177,U_13182,U_13180,U_13181) ),
    inference(clausify,[status(thm)],[f_3408_4]) ).

fof(f_3409_1,plain,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
      ( ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
          & hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE]) ).

fof(f_3409_2,plain,
    ! [U_13189,U_13188,U_13187,U_13186,U_13185] :
      ( ? [U_13184,U_13183] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13185),U_13184),U_13183))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13185,U_13185,U_13186,U_13184,U_13183),U_13189))
          & hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188) = hAPP(hAPP(c_Set_Oinsert(U_13185),U_13184),U_13183) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13185,U_13186,hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188)),U_13189)) ),
    inference(variable_rename,[status(thm)],[f_3409_1]) ).

fof(f_3409_3,plain,
    ! [U_13189,U_13188,U_13187,U_13186,U_13185] :
      ( ? [U_13183] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),U_13183))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13185,U_13185,U_13186,sK286(U_13189,U_13188,U_13187,U_13186,U_13185),U_13183),U_13189))
          & hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188) = hAPP(hAPP(c_Set_Oinsert(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),U_13183) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13185,U_13186,hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188)),U_13189)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_13184,sK286(U_13189,U_13188,U_13187,U_13186,U_13185))],[f_3409_2]) ).

fof(f_3409_4,plain,
    ! [U_13189,U_13188,U_13187,U_13186,U_13185] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)))
        & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13185,U_13185,U_13186,sK286(U_13189,U_13188,U_13187,U_13186,U_13185),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)),U_13189))
        & hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188) = hAPP(hAPP(c_Set_Oinsert(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13185,U_13186,hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188)),U_13189)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_13183,sK287(U_13189,U_13188,U_13187,U_13186,U_13185))],[f_3409_3]) ).

fof(f_3409_5,plain,
    ( ! [U_13185,U_13187,U_13189,U_13188,U_13186] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)))
        | ~ sP961(U_13185,U_13187,U_13189,U_13188,U_13186) )
    & ! [U_13185,U_13187,U_13189,U_13188,U_13186] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13185,U_13185,U_13186,sK286(U_13189,U_13188,U_13187,U_13186,U_13185),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)),U_13189))
        | ~ sP961(U_13185,U_13187,U_13189,U_13188,U_13186) )
    & ! [U_13185,U_13187,U_13189,U_13188,U_13186] :
        ( hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188) = hAPP(hAPP(c_Set_Oinsert(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),sK287(U_13189,U_13188,U_13187,U_13186,U_13185))
        | ~ sP961(U_13185,U_13187,U_13189,U_13188,U_13186) )
    & ! [U_13185,U_13187,U_13189,U_13188,U_13186] :
        ( sP961(U_13185,U_13187,U_13189,U_13188,U_13186)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13185,U_13186,hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188)),U_13189)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP961])],[f_3409_4]) ).

cnf(f_3409_6,plain,
    ( sP961(U_13185,U_13187,U_13189,U_13188,U_13186)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13185,U_13186,hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188)),U_13189)) ),
    inference(clausify,[status(thm)],[f_3409_5]) ).

cnf(f_3409_7,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_13185),U_13187),U_13188) = hAPP(hAPP(c_Set_Oinsert(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),sK287(U_13189,U_13188,U_13187,U_13186,U_13185))
    | ~ sP961(U_13185,U_13187,U_13189,U_13188,U_13186) ),
    inference(clausify,[status(thm)],[f_3409_5]) ).

cnf(f_3409_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13185,U_13185,U_13186,sK286(U_13189,U_13188,U_13187,U_13186,U_13185),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)),U_13189))
    | ~ sP961(U_13185,U_13187,U_13189,U_13188,U_13186) ),
    inference(clausify,[status(thm)],[f_3409_5]) ).

cnf(f_3409_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13185),sK286(U_13189,U_13188,U_13187,U_13186,U_13185)),sK287(U_13189,U_13188,U_13187,U_13186,U_13185)))
    | ~ sP961(U_13185,U_13187,U_13189,U_13188,U_13186) ),
    inference(clausify,[status(thm)],[f_3409_5]) ).

fof(f_3410_1,plain,
    ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
        | ! [B_a,B_A] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
            | hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) != hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) )
      & ( ? [B_a,B_A] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
            & hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(f_3410_2,plain,
    ! [U_13198,U_13197,U_13196,U_13195,U_13194] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13194,U_13195,hAPP(hAPP(c_Set_Oinsert(U_13194),U_13196),U_13197)),U_13198))
        | ! [U_13193,U_13192] :
            ( hBOOL(hAPP(hAPP(c_member(U_13194),U_13193),U_13192))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13194,U_13194,U_13195,U_13193,U_13192),U_13198))
            | hAPP(hAPP(c_Set_Oinsert(U_13194),U_13196),U_13197) != hAPP(hAPP(c_Set_Oinsert(U_13194),U_13193),U_13192) ) )
      & ( ? [U_13191,U_13190] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13194),U_13191),U_13190))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13194,U_13194,U_13195,U_13191,U_13190),U_13198))
            & hAPP(hAPP(c_Set_Oinsert(U_13194),U_13196),U_13197) = hAPP(hAPP(c_Set_Oinsert(U_13194),U_13191),U_13190) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13194,U_13195,hAPP(hAPP(c_Set_Oinsert(U_13194),U_13196),U_13197)),U_13198)) ) ),
    inference(variable_rename,[status(thm)],[f_3410_1]) ).

fof(f_3410_3,plain,
    ( ! [U_13208,U_13206,U_13204,U_13202,U_13200] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13200,U_13202,hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206)),U_13208))
        | ! [U_13193,U_13192] :
            ( hBOOL(hAPP(hAPP(c_member(U_13200),U_13193),U_13192))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13200,U_13200,U_13202,U_13193,U_13192),U_13208))
            | hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206) != hAPP(hAPP(c_Set_Oinsert(U_13200),U_13193),U_13192) ) )
    & ! [U_13207,U_13205,U_13203,U_13201,U_13199] :
        ( ? [U_13191,U_13190] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13199),U_13191),U_13190))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13199,U_13199,U_13201,U_13191,U_13190),U_13207))
            & hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205) = hAPP(hAPP(c_Set_Oinsert(U_13199),U_13191),U_13190) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13199,U_13201,hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205)),U_13207)) ) ),
    inference(miniscope,[status(thm)],[f_3410_2]) ).

fof(f_3410_4,plain,
    ( ! [U_13208,U_13206,U_13204,U_13202,U_13200] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13200,U_13202,hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206)),U_13208))
        | ! [U_13193,U_13192] :
            ( hBOOL(hAPP(hAPP(c_member(U_13200),U_13193),U_13192))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13200,U_13200,U_13202,U_13193,U_13192),U_13208))
            | hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206) != hAPP(hAPP(c_Set_Oinsert(U_13200),U_13193),U_13192) ) )
    & ! [U_13207,U_13205,U_13203,U_13201,U_13199] :
        ( ? [U_13190] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),U_13190))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13199,U_13199,U_13201,sK288(U_13207,U_13205,U_13203,U_13201,U_13199),U_13190),U_13207))
            & hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205) = hAPP(hAPP(c_Set_Oinsert(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),U_13190) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13199,U_13201,hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205)),U_13207)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_13191,sK288(U_13207,U_13205,U_13203,U_13201,U_13199))],[f_3410_3]) ).

fof(f_3410_5,plain,
    ( ! [U_13208,U_13206,U_13204,U_13202,U_13200] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13200,U_13202,hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206)),U_13208))
        | ! [U_13193,U_13192] :
            ( hBOOL(hAPP(hAPP(c_member(U_13200),U_13193),U_13192))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13200,U_13200,U_13202,U_13193,U_13192),U_13208))
            | hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206) != hAPP(hAPP(c_Set_Oinsert(U_13200),U_13193),U_13192) ) )
    & ! [U_13207,U_13205,U_13203,U_13201,U_13199] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13199,U_13199,U_13201,sK288(U_13207,U_13205,U_13203,U_13201,U_13199),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)),U_13207))
          & hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205) = hAPP(hAPP(c_Set_Oinsert(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13199,U_13201,hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205)),U_13207)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_13190,sK289(U_13207,U_13205,U_13203,U_13201,U_13199))],[f_3410_4]) ).

fof(f_3410_6,plain,
    ( ! [U_13205,U_13201,U_13199,U_13203,U_13207] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)))
        | ~ sP962(U_13205,U_13201,U_13199,U_13203,U_13207) )
    & ! [U_13205,U_13201,U_13199,U_13203,U_13207] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13199,U_13199,U_13201,sK288(U_13207,U_13205,U_13203,U_13201,U_13199),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)),U_13207))
        | ~ sP962(U_13205,U_13201,U_13199,U_13203,U_13207) )
    & ! [U_13205,U_13201,U_13199,U_13203,U_13207] :
        ( hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205) = hAPP(hAPP(c_Set_Oinsert(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),sK289(U_13207,U_13205,U_13203,U_13201,U_13199))
        | ~ sP962(U_13205,U_13201,U_13199,U_13203,U_13207) )
    & ! [U_13193,U_13192,U_13206,U_13200,U_13202,U_13204,U_13208] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13200,U_13202,hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206)),U_13208))
        | hBOOL(hAPP(hAPP(c_member(U_13200),U_13193),U_13192))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13200,U_13200,U_13202,U_13193,U_13192),U_13208))
        | hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206) != hAPP(hAPP(c_Set_Oinsert(U_13200),U_13193),U_13192) )
    & ! [U_13205,U_13201,U_13199,U_13203,U_13207] :
        ( sP962(U_13205,U_13201,U_13199,U_13203,U_13207)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13199,U_13201,hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205)),U_13207)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP962])],[f_3410_5]) ).

cnf(f_3410_7,plain,
    ( sP962(U_13205,U_13201,U_13199,U_13203,U_13207)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13199,U_13201,hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205)),U_13207)) ),
    inference(clausify,[status(thm)],[f_3410_6]) ).

cnf(f_3410_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13200,U_13202,hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206)),U_13208))
    | hBOOL(hAPP(hAPP(c_member(U_13200),U_13193),U_13192))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13200,U_13200,U_13202,U_13193,U_13192),U_13208))
    | hAPP(hAPP(c_Set_Oinsert(U_13200),U_13204),U_13206) != hAPP(hAPP(c_Set_Oinsert(U_13200),U_13193),U_13192) ),
    inference(clausify,[status(thm)],[f_3410_6]) ).

cnf(f_3410_9,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_13199),U_13203),U_13205) = hAPP(hAPP(c_Set_Oinsert(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),sK289(U_13207,U_13205,U_13203,U_13201,U_13199))
    | ~ sP962(U_13205,U_13201,U_13199,U_13203,U_13207) ),
    inference(clausify,[status(thm)],[f_3410_6]) ).

cnf(f_3410_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13199,U_13199,U_13201,sK288(U_13207,U_13205,U_13203,U_13201,U_13199),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)),U_13207))
    | ~ sP962(U_13205,U_13201,U_13199,U_13203,U_13207) ),
    inference(clausify,[status(thm)],[f_3410_6]) ).

cnf(f_3410_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13199),sK288(U_13207,U_13205,U_13203,U_13201,U_13199)),sK289(U_13207,U_13205,U_13203,U_13201,U_13199)))
    | ~ sP962(U_13205,U_13201,U_13199,U_13203,U_13207) ),
    inference(clausify,[status(thm)],[f_3410_6]) ).

fof(f_3411_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_image__split__eq__Sigma]) ).

fof(f_3411_2,plain,
    ! [U_13214,U_13213,U_13212,U_13211,U_13210,U_13209] : hAPP(c_Set_Oimage(U_13209,tc_prod(U_13210,U_13211),hAPP(hAPP(c_COMBS(U_13209,U_13211,tc_prod(U_13210,U_13211)),hAPP(hAPP(c_COMBB(U_13210,tc_fun(U_13211,tc_prod(U_13210,U_13211)),U_13209),c_Product__Type_OPair(U_13210,U_13211)),U_13212)),U_13213)),U_13214) = hAPP(hAPP(c_Product__Type_OSigma(U_13210,U_13211),hAPP(c_Set_Oimage(U_13209,U_13210,U_13212),U_13214)),hAPP(hAPP(c_COMBB(tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13211,tc_HOL_Obool),U_13210),c_Set_Oimage(U_13209,U_13211,U_13213)),hAPP(hAPP(c_COMBC(U_13210,tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13209,tc_HOL_Obool),tc_fun(tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool)),U_13210),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13209,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13210,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool),U_13210),c_Set_Ovimage(U_13209,U_13210,U_13212)),hAPP(hAPP(c_COMBC(U_13210,tc_fun(U_13210,tc_HOL_Obool),tc_fun(U_13210,tc_HOL_Obool)),c_Set_Oinsert(U_13210)),c_Orderings_Obot__class_Obot(tc_fun(U_13210,tc_HOL_Obool)))))),U_13214))),
    inference(variable_rename,[status(thm)],[f_3411_1]) ).

fof(f_3411_3,plain,
    ! [U_13210,U_13209,U_13211,U_13212,U_13213,U_13214] : hAPP(c_Set_Oimage(U_13209,tc_prod(U_13210,U_13211),hAPP(hAPP(c_COMBS(U_13209,U_13211,tc_prod(U_13210,U_13211)),hAPP(hAPP(c_COMBB(U_13210,tc_fun(U_13211,tc_prod(U_13210,U_13211)),U_13209),c_Product__Type_OPair(U_13210,U_13211)),U_13212)),U_13213)),U_13214) = hAPP(hAPP(c_Product__Type_OSigma(U_13210,U_13211),hAPP(c_Set_Oimage(U_13209,U_13210,U_13212),U_13214)),hAPP(hAPP(c_COMBB(tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13211,tc_HOL_Obool),U_13210),c_Set_Oimage(U_13209,U_13211,U_13213)),hAPP(hAPP(c_COMBC(U_13210,tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13209,tc_HOL_Obool),tc_fun(tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool)),U_13210),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13209,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13210,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool),U_13210),c_Set_Ovimage(U_13209,U_13210,U_13212)),hAPP(hAPP(c_COMBC(U_13210,tc_fun(U_13210,tc_HOL_Obool),tc_fun(U_13210,tc_HOL_Obool)),c_Set_Oinsert(U_13210)),c_Orderings_Obot__class_Obot(tc_fun(U_13210,tc_HOL_Obool)))))),U_13214))),
    inference(definitional_conversion,[status(esa)],[f_3411_2]) ).

cnf(f_3411_4,plain,
    hAPP(c_Set_Oimage(U_13209,tc_prod(U_13210,U_13211),hAPP(hAPP(c_COMBS(U_13209,U_13211,tc_prod(U_13210,U_13211)),hAPP(hAPP(c_COMBB(U_13210,tc_fun(U_13211,tc_prod(U_13210,U_13211)),U_13209),c_Product__Type_OPair(U_13210,U_13211)),U_13212)),U_13213)),U_13214) = hAPP(hAPP(c_Product__Type_OSigma(U_13210,U_13211),hAPP(c_Set_Oimage(U_13209,U_13210,U_13212),U_13214)),hAPP(hAPP(c_COMBB(tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13211,tc_HOL_Obool),U_13210),c_Set_Oimage(U_13209,U_13211,U_13213)),hAPP(hAPP(c_COMBC(U_13210,tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13209,tc_HOL_Obool),tc_fun(tc_fun(U_13209,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool)),U_13210),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13209,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13210,tc_HOL_Obool),tc_fun(U_13209,tc_HOL_Obool),U_13210),c_Set_Ovimage(U_13209,U_13210,U_13212)),hAPP(hAPP(c_COMBC(U_13210,tc_fun(U_13210,tc_HOL_Obool),tc_fun(U_13210,tc_HOL_Obool)),c_Set_Oinsert(U_13210)),c_Orderings_Obot__class_Obot(tc_fun(U_13210,tc_HOL_Obool)))))),U_13214))),
    inference(clausify,[status(thm)],[f_3411_3]) ).

fof(f_3412_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__Un]) ).

fof(f_3412_2,plain,
    ! [U_13217,U_13216,U_13215] :
      ( hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13215,tc_HOL_Obool)),U_13216),U_13217)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13215),hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),U_13216)),hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),U_13217))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13215,tc_HOL_Obool)),U_13216),U_13217) != c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
      | U_13217 = c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13215),U_13217))
      | U_13216 = c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13215),U_13216))
      | ~ class_Groups_Oab__semigroup__mult(U_13215) ),
    inference(variable_rename,[status(thm)],[f_3412_1]) ).

fof(f_3412_3,plain,
    ! [U_13215,U_13216,U_13217] :
      ( hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13215,tc_HOL_Obool)),U_13216),U_13217)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13215),hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),U_13216)),hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),U_13217))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13215,tc_HOL_Obool)),U_13216),U_13217) != c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
      | U_13217 = c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13215),U_13217))
      | U_13216 = c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13215),U_13216))
      | ~ class_Groups_Oab__semigroup__mult(U_13215) ),
    inference(definitional_conversion,[status(esa)],[f_3412_2]) ).

cnf(f_3412_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13215,tc_HOL_Obool)),U_13216),U_13217)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13215),hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),U_13216)),hAPP(c_Finite__Set_Ofold1(U_13215,c_Groups_Otimes__class_Otimes(U_13215)),U_13217))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13215,tc_HOL_Obool)),U_13216),U_13217) != c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
    | U_13217 = c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13215),U_13217))
    | U_13216 = c_Orderings_Obot__class_Obot(tc_fun(U_13215,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13215),U_13216))
    | ~ class_Groups_Oab__semigroup__mult(U_13215) ),
    inference(clausify,[status(thm)],[f_3412_3]) ).

fof(f_3413_1,plain,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaI]) ).

fof(f_3413_2,plain,
    ! [U_13223,U_13222,U_13221,U_13220,U_13219,U_13218] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13218,U_13221)),hAPP(hAPP(c_Product__Type_OPair(U_13218,U_13221),U_13219),U_13222)),hAPP(hAPP(c_Product__Type_OSigma(U_13218,U_13221),U_13220),U_13223)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13221),U_13222),hAPP(U_13223,U_13219)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13218),U_13219),U_13220)) ),
    inference(variable_rename,[status(thm)],[f_3413_1]) ).

fof(f_3413_3,plain,
    ! [U_13220,U_13218,U_13221,U_13219,U_13222,U_13223] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13218,U_13221)),hAPP(hAPP(c_Product__Type_OPair(U_13218,U_13221),U_13219),U_13222)),hAPP(hAPP(c_Product__Type_OSigma(U_13218,U_13221),U_13220),U_13223)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13221),U_13222),hAPP(U_13223,U_13219)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13218),U_13219),U_13220)) ),
    inference(definitional_conversion,[status(esa)],[f_3413_2]) ).

cnf(f_3413_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13218,U_13221)),hAPP(hAPP(c_Product__Type_OPair(U_13218,U_13221),U_13219),U_13222)),hAPP(hAPP(c_Product__Type_OSigma(U_13218,U_13221),U_13220),U_13223)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13221),U_13222),hAPP(U_13223,U_13219)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13218),U_13219),U_13220)) ),
    inference(clausify,[status(thm)],[f_3413_3]) ).

fof(f_3414_1,plain,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) != hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2]) ).

fof(f_3414_2,plain,
    ! [U_13229,U_13228,U_13227,U_13226,U_13225,U_13224] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13228),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) = hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13229),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226))
          | U_13228 != U_13229 )
        & ( U_13228 = U_13229
          | hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13228),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) != hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13229),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13224),U_13225),U_13226)) ),
    inference(variable_rename,[status(thm)],[f_3414_1]) ).

fof(f_3414_3,plain,
    ( ! [U_13224,U_13226,U_13227,U_13228,U_13229] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13228),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) = hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13229),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226))
        | U_13228 != U_13229
        | ~ sP963(U_13224,U_13226,U_13227,U_13228,U_13229) )
    & ! [U_13224,U_13226,U_13227,U_13228,U_13229] :
        ( U_13228 = U_13229
        | hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13228),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) != hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13229),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226))
        | ~ sP963(U_13224,U_13226,U_13227,U_13228,U_13229) )
    & ! [U_13224,U_13225,U_13226,U_13227,U_13228,U_13229] :
        ( sP963(U_13224,U_13226,U_13227,U_13228,U_13229)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13224),U_13225),U_13226)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP963])],[f_3414_2]) ).

cnf(f_3414_4,plain,
    ( sP963(U_13224,U_13226,U_13227,U_13228,U_13229)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13224),U_13225),U_13226)) ),
    inference(clausify,[status(thm)],[f_3414_3]) ).

cnf(f_3414_5,plain,
    ( U_13228 = U_13229
    | hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13228),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) != hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13229),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226))
    | ~ sP963(U_13224,U_13226,U_13227,U_13228,U_13229) ),
    inference(clausify,[status(thm)],[f_3414_3]) ).

cnf(f_3414_6,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13228),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226)) = hAPP(hAPP(c_Product__Type_OSigma(U_13227,U_13224),U_13229),hAPP(c_COMBK(tc_fun(U_13224,tc_HOL_Obool),U_13227),U_13226))
    | U_13228 != U_13229
    | ~ sP963(U_13224,U_13226,U_13227,U_13228,U_13229) ),
    inference(clausify,[status(thm)],[f_3414_3]) ).

fof(f_3415_1,plain,
    ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__empty1]) ).

fof(f_3415_2,plain,
    ! [U_13232,U_13231,U_13230] : hAPP(hAPP(c_Product__Type_OSigma(U_13230,U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13230,tc_HOL_Obool))),U_13232) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13230,U_13231),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3415_1]) ).

fof(f_3415_3,plain,
    ! [U_13232,U_13231,U_13230] : hAPP(hAPP(c_Product__Type_OSigma(U_13230,U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13230,tc_HOL_Obool))),U_13232) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13230,U_13231),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3415_2]) ).

cnf(f_3415_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13230,U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13230,tc_HOL_Obool))),U_13232) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13230,U_13231),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3415_3]) ).

fof(f_3416_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(f_3416_2,plain,
    ! [U_13237,U_13236,U_13235,U_13234,U_13233] : hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),hAPP(hAPP(c_COMBS(U_13233,tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_fun(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),U_13233),c_Groups_Ominus__class_Ominus(tc_fun(U_13234,tc_HOL_Obool))),U_13236)),U_13237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13233,U_13234),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),U_13236)),hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),U_13237)),
    inference(variable_rename,[status(thm)],[f_3416_1]) ).

fof(f_3416_3,plain,
    ! [U_13233,U_13234,U_13235,U_13236,U_13237] : hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),hAPP(hAPP(c_COMBS(U_13233,tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_fun(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),U_13233),c_Groups_Ominus__class_Ominus(tc_fun(U_13234,tc_HOL_Obool))),U_13236)),U_13237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13233,U_13234),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),U_13236)),hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),U_13237)),
    inference(definitional_conversion,[status(esa)],[f_3416_2]) ).

cnf(f_3416_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),hAPP(hAPP(c_COMBS(U_13233,tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_fun(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),U_13233),c_Groups_Ominus__class_Ominus(tc_fun(U_13234,tc_HOL_Obool))),U_13236)),U_13237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13233,U_13234),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),U_13236)),hAPP(hAPP(c_Product__Type_OSigma(U_13233,U_13234),U_13235),U_13237)),
    inference(clausify,[status(thm)],[f_3416_3]) ).

fof(f_3417_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(f_3417_2,plain,
    ! [U_13242,U_13241,U_13240,U_13239,U_13238] : hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13238,tc_HOL_Obool)),U_13240),U_13241)),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13238,U_13239),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),U_13240),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242))),hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),U_13241),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242))),
    inference(variable_rename,[status(thm)],[f_3417_1]) ).

fof(f_3417_3,plain,
    ! [U_13238,U_13239,U_13240,U_13241,U_13242] : hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13238,tc_HOL_Obool)),U_13240),U_13241)),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13238,U_13239),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),U_13240),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242))),hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),U_13241),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242))),
    inference(definitional_conversion,[status(esa)],[f_3417_2]) ).

cnf(f_3417_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13238,tc_HOL_Obool)),U_13240),U_13241)),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13238,U_13239),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),U_13240),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242))),hAPP(hAPP(c_Product__Type_OSigma(U_13238,U_13239),U_13241),hAPP(c_COMBK(tc_fun(U_13239,tc_HOL_Obool),U_13238),U_13242))),
    inference(clausify,[status(thm)],[f_3417_3]) ).

fof(f_3418_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

fof(f_3418_2,plain,
    ! [U_13247,U_13246,U_13245,U_13244,U_13243] : hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13243,tc_HOL_Obool)),U_13245),U_13246)),U_13247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13243,U_13244),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),U_13245),U_13247)),hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),U_13246),U_13247)),
    inference(variable_rename,[status(thm)],[f_3418_1]) ).

fof(f_3418_3,plain,
    ! [U_13243,U_13244,U_13245,U_13246,U_13247] : hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13243,tc_HOL_Obool)),U_13245),U_13246)),U_13247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13243,U_13244),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),U_13245),U_13247)),hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),U_13246),U_13247)),
    inference(definitional_conversion,[status(esa)],[f_3418_2]) ).

cnf(f_3418_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13243,tc_HOL_Obool)),U_13245),U_13246)),U_13247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13243,U_13244),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),U_13245),U_13247)),hAPP(hAPP(c_Product__Type_OSigma(U_13243,U_13244),U_13246),U_13247)),
    inference(clausify,[status(thm)],[f_3418_3]) ).

fof(f_3419_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_card__cartesian__product]) ).

fof(f_3419_2,plain,
    ! [U_13251,U_13250,U_13249,U_13248] : hAPP(c_Finite__Set_Ocard(tc_prod(U_13248,U_13249)),hAPP(hAPP(c_Product__Type_OSigma(U_13248,U_13249),U_13250),hAPP(c_COMBK(tc_fun(U_13249,tc_HOL_Obool),U_13248),U_13251))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13248),U_13250)),hAPP(c_Finite__Set_Ocard(U_13249),U_13251)),
    inference(variable_rename,[status(thm)],[f_3419_1]) ).

fof(f_3419_3,plain,
    ! [U_13248,U_13249,U_13250,U_13251] : hAPP(c_Finite__Set_Ocard(tc_prod(U_13248,U_13249)),hAPP(hAPP(c_Product__Type_OSigma(U_13248,U_13249),U_13250),hAPP(c_COMBK(tc_fun(U_13249,tc_HOL_Obool),U_13248),U_13251))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13248),U_13250)),hAPP(c_Finite__Set_Ocard(U_13249),U_13251)),
    inference(definitional_conversion,[status(esa)],[f_3419_2]) ).

cnf(f_3419_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_13248,U_13249)),hAPP(hAPP(c_Product__Type_OSigma(U_13248,U_13249),U_13250),hAPP(c_COMBK(tc_fun(U_13249,tc_HOL_Obool),U_13248),U_13251))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13248),U_13250)),hAPP(c_Finite__Set_Ocard(U_13249),U_13251)),
    inference(clausify,[status(thm)],[f_3419_3]) ).

fof(f_3420_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product]) ).

fof(f_3420_2,plain,
    ! [U_13257,U_13256,U_13255,U_13254,U_13253,U_13252] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13253,U_13252),hAPP(hAPP(c_COMBC(U_13253,tc_fun(U_13254,tc_HOL_Obool),U_13252),hAPP(hAPP(c_COMBB(tc_fun(U_13254,U_13252),tc_fun(tc_fun(U_13254,tc_HOL_Obool),U_13252),U_13253),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13254,U_13252)),U_13255)),U_13256)),U_13257) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13253,U_13254),U_13252),hAPP(c_Product__Type_Oprod_Oprod__case(U_13253,U_13254,U_13252),U_13255)),hAPP(hAPP(c_Product__Type_OSigma(U_13253,U_13254),U_13257),hAPP(c_COMBK(tc_fun(U_13254,tc_HOL_Obool),U_13253),U_13256)))
      | ~ class_Groups_Ocomm__monoid__add(U_13252) ),
    inference(variable_rename,[status(thm)],[f_3420_1]) ).

fof(f_3420_3,plain,
    ! [U_13252,U_13253,U_13254,U_13255,U_13256,U_13257] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13253,U_13252),hAPP(hAPP(c_COMBC(U_13253,tc_fun(U_13254,tc_HOL_Obool),U_13252),hAPP(hAPP(c_COMBB(tc_fun(U_13254,U_13252),tc_fun(tc_fun(U_13254,tc_HOL_Obool),U_13252),U_13253),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13254,U_13252)),U_13255)),U_13256)),U_13257) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13253,U_13254),U_13252),hAPP(c_Product__Type_Oprod_Oprod__case(U_13253,U_13254,U_13252),U_13255)),hAPP(hAPP(c_Product__Type_OSigma(U_13253,U_13254),U_13257),hAPP(c_COMBK(tc_fun(U_13254,tc_HOL_Obool),U_13253),U_13256)))
      | ~ class_Groups_Ocomm__monoid__add(U_13252) ),
    inference(definitional_conversion,[status(esa)],[f_3420_2]) ).

cnf(f_3420_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13253,U_13252),hAPP(hAPP(c_COMBC(U_13253,tc_fun(U_13254,tc_HOL_Obool),U_13252),hAPP(hAPP(c_COMBB(tc_fun(U_13254,U_13252),tc_fun(tc_fun(U_13254,tc_HOL_Obool),U_13252),U_13253),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13254,U_13252)),U_13255)),U_13256)),U_13257) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13253,U_13254),U_13252),hAPP(c_Product__Type_Oprod_Oprod__case(U_13253,U_13254,U_13252),U_13255)),hAPP(hAPP(c_Product__Type_OSigma(U_13253,U_13254),U_13257),hAPP(c_COMBK(tc_fun(U_13254,tc_HOL_Obool),U_13253),U_13256)))
    | ~ class_Groups_Ocomm__monoid__add(U_13252) ),
    inference(clausify,[status(thm)],[f_3420_3]) ).

fof(f_3421_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
        | ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      & ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Times__empty]) ).

fof(f_3421_2,plain,
    ! [U_13261,U_13260,U_13259,U_13258] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(U_13258,U_13259),U_13260),hAPP(c_COMBK(tc_fun(U_13259,tc_HOL_Obool),U_13258),U_13261)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13258,U_13259),tc_HOL_Obool))
        | ( U_13261 != c_Orderings_Obot__class_Obot(tc_fun(U_13259,tc_HOL_Obool))
          & U_13260 != c_Orderings_Obot__class_Obot(tc_fun(U_13258,tc_HOL_Obool)) ) )
      & ( U_13261 = c_Orderings_Obot__class_Obot(tc_fun(U_13259,tc_HOL_Obool))
        | U_13260 = c_Orderings_Obot__class_Obot(tc_fun(U_13258,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_13258,U_13259),U_13260),hAPP(c_COMBK(tc_fun(U_13259,tc_HOL_Obool),U_13258),U_13261)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13258,U_13259),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3421_1]) ).

fof(f_3421_3,plain,
    ( ! [U_13269,U_13267,U_13265,U_13263] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_13263,U_13265),U_13267),hAPP(c_COMBK(tc_fun(U_13265,tc_HOL_Obool),U_13263),U_13269)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13263,U_13265),tc_HOL_Obool))
        | ( U_13269 != c_Orderings_Obot__class_Obot(tc_fun(U_13265,tc_HOL_Obool))
          & U_13267 != c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool)) ) )
    & ! [U_13268,U_13266,U_13264,U_13262] :
        ( U_13268 = c_Orderings_Obot__class_Obot(tc_fun(U_13264,tc_HOL_Obool))
        | U_13266 = c_Orderings_Obot__class_Obot(tc_fun(U_13262,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_13262,U_13264),U_13266),hAPP(c_COMBK(tc_fun(U_13264,tc_HOL_Obool),U_13262),U_13268)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13262,U_13264),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3421_2]) ).

fof(f_3421_4,plain,
    ( ! [U_13265,U_13263,U_13269,U_13267] :
        ( U_13269 != c_Orderings_Obot__class_Obot(tc_fun(U_13265,tc_HOL_Obool))
        | ~ sP964(U_13265,U_13263,U_13269,U_13267) )
    & ! [U_13265,U_13263,U_13269,U_13267] :
        ( U_13267 != c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool))
        | ~ sP964(U_13265,U_13263,U_13269,U_13267) )
    & ! [U_13265,U_13263,U_13269,U_13267] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_13263,U_13265),U_13267),hAPP(c_COMBK(tc_fun(U_13265,tc_HOL_Obool),U_13263),U_13269)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13263,U_13265),tc_HOL_Obool))
        | sP964(U_13265,U_13263,U_13269,U_13267) )
    & ! [U_13264,U_13266,U_13262,U_13268] :
        ( U_13268 = c_Orderings_Obot__class_Obot(tc_fun(U_13264,tc_HOL_Obool))
        | U_13266 = c_Orderings_Obot__class_Obot(tc_fun(U_13262,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_13262,U_13264),U_13266),hAPP(c_COMBK(tc_fun(U_13264,tc_HOL_Obool),U_13262),U_13268)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13262,U_13264),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP964])],[f_3421_3]) ).

cnf(f_3421_5,plain,
    ( U_13268 = c_Orderings_Obot__class_Obot(tc_fun(U_13264,tc_HOL_Obool))
    | U_13266 = c_Orderings_Obot__class_Obot(tc_fun(U_13262,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_13262,U_13264),U_13266),hAPP(c_COMBK(tc_fun(U_13264,tc_HOL_Obool),U_13262),U_13268)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13262,U_13264),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3421_4]) ).

cnf(f_3421_6,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_13263,U_13265),U_13267),hAPP(c_COMBK(tc_fun(U_13265,tc_HOL_Obool),U_13263),U_13269)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13263,U_13265),tc_HOL_Obool))
    | sP964(U_13265,U_13263,U_13269,U_13267) ),
    inference(clausify,[status(thm)],[f_3421_4]) ).

cnf(f_3421_7,plain,
    ( U_13267 != c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool))
    | ~ sP964(U_13265,U_13263,U_13269,U_13267) ),
    inference(clausify,[status(thm)],[f_3421_4]) ).

cnf(f_3421_8,plain,
    ( U_13269 != c_Orderings_Obot__class_Obot(tc_fun(U_13265,tc_HOL_Obool))
    | ~ sP964(U_13265,U_13263,U_13269,U_13267) ),
    inference(clausify,[status(thm)],[f_3421_4]) ).

fof(f_3422_1,plain,
    ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__empty2]) ).

fof(f_3422_2,plain,
    ! [U_13272,U_13271,U_13270] : hAPP(hAPP(c_Product__Type_OSigma(U_13270,U_13271),U_13272),hAPP(c_COMBK(tc_fun(U_13271,tc_HOL_Obool),U_13270),c_Orderings_Obot__class_Obot(tc_fun(U_13271,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13270,U_13271),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3422_1]) ).

fof(f_3422_3,plain,
    ! [U_13270,U_13272,U_13271] : hAPP(hAPP(c_Product__Type_OSigma(U_13270,U_13271),U_13272),hAPP(c_COMBK(tc_fun(U_13271,tc_HOL_Obool),U_13270),c_Orderings_Obot__class_Obot(tc_fun(U_13271,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13270,U_13271),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3422_2]) ).

cnf(f_3422_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13270,U_13271),U_13272),hAPP(c_COMBK(tc_fun(U_13271,tc_HOL_Obool),U_13270),c_Orderings_Obot__class_Obot(tc_fun(U_13271,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13270,U_13271),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3422_3]) ).

fof(f_3423_1,plain,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(f_3423_2,plain,
    ! [U_13275,U_13274,U_13273] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13273,U_13274),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13273,U_13274),c_Orderings_Otop__class_Otop(tc_fun(U_13273,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13274,tc_HOL_Obool),U_13273),U_13275))) = hAPP(hAPP(c_Product__Type_OSigma(U_13273,U_13274),c_Orderings_Otop__class_Otop(tc_fun(U_13273,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13274,tc_HOL_Obool),U_13273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13274,tc_HOL_Obool)),U_13275))),
    inference(variable_rename,[status(thm)],[f_3423_1]) ).

fof(f_3423_3,plain,
    ! [U_13273,U_13274,U_13275] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13273,U_13274),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13273,U_13274),c_Orderings_Otop__class_Otop(tc_fun(U_13273,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13274,tc_HOL_Obool),U_13273),U_13275))) = hAPP(hAPP(c_Product__Type_OSigma(U_13273,U_13274),c_Orderings_Otop__class_Otop(tc_fun(U_13273,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13274,tc_HOL_Obool),U_13273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13274,tc_HOL_Obool)),U_13275))),
    inference(definitional_conversion,[status(esa)],[f_3423_2]) ).

cnf(f_3423_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13273,U_13274),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13273,U_13274),c_Orderings_Otop__class_Otop(tc_fun(U_13273,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13274,tc_HOL_Obool),U_13273),U_13275))) = hAPP(hAPP(c_Product__Type_OSigma(U_13273,U_13274),c_Orderings_Otop__class_Otop(tc_fun(U_13273,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13274,tc_HOL_Obool),U_13273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13274,tc_HOL_Obool)),U_13275))),
    inference(clausify,[status(thm)],[f_3423_3]) ).

fof(f_3424_1,plain,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(f_3424_2,plain,
    ! [U_13278,U_13277,U_13276] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13276,U_13277),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13276,U_13277),U_13278),hAPP(c_COMBK(tc_fun(U_13277,tc_HOL_Obool),U_13276),c_Orderings_Otop__class_Otop(tc_fun(U_13277,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_13276,U_13277),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13276,tc_HOL_Obool)),U_13278)),hAPP(c_COMBK(tc_fun(U_13277,tc_HOL_Obool),U_13276),c_Orderings_Otop__class_Otop(tc_fun(U_13277,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3424_1]) ).

fof(f_3424_3,plain,
    ! [U_13276,U_13277,U_13278] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13276,U_13277),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13276,U_13277),U_13278),hAPP(c_COMBK(tc_fun(U_13277,tc_HOL_Obool),U_13276),c_Orderings_Otop__class_Otop(tc_fun(U_13277,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_13276,U_13277),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13276,tc_HOL_Obool)),U_13278)),hAPP(c_COMBK(tc_fun(U_13277,tc_HOL_Obool),U_13276),c_Orderings_Otop__class_Otop(tc_fun(U_13277,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3424_2]) ).

cnf(f_3424_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13276,U_13277),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13276,U_13277),U_13278),hAPP(c_COMBK(tc_fun(U_13277,tc_HOL_Obool),U_13276),c_Orderings_Otop__class_Otop(tc_fun(U_13277,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_13276,U_13277),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13276,tc_HOL_Obool)),U_13278)),hAPP(c_COMBK(tc_fun(U_13277,tc_HOL_Obool),U_13276),c_Orderings_Otop__class_Otop(tc_fun(U_13277,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3424_3]) ).

fof(f_3425_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product]) ).

fof(f_3425_2,plain,
    ! [U_13284,U_13283,U_13282,U_13281,U_13280,U_13279] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13280,U_13279),hAPP(hAPP(c_COMBC(U_13280,tc_fun(U_13281,tc_HOL_Obool),U_13279),hAPP(hAPP(c_COMBB(tc_fun(U_13281,U_13279),tc_fun(tc_fun(U_13281,tc_HOL_Obool),U_13279),U_13280),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13281,U_13279)),U_13282)),U_13283)),U_13284) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13280,U_13281),U_13279),hAPP(c_Product__Type_Oprod_Oprod__case(U_13280,U_13281,U_13279),U_13282)),hAPP(hAPP(c_Product__Type_OSigma(U_13280,U_13281),U_13284),hAPP(c_COMBK(tc_fun(U_13281,tc_HOL_Obool),U_13280),U_13283)))
      | ~ class_Groups_Ocomm__monoid__mult(U_13279) ),
    inference(variable_rename,[status(thm)],[f_3425_1]) ).

fof(f_3425_3,plain,
    ! [U_13279,U_13280,U_13281,U_13282,U_13283,U_13284] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13280,U_13279),hAPP(hAPP(c_COMBC(U_13280,tc_fun(U_13281,tc_HOL_Obool),U_13279),hAPP(hAPP(c_COMBB(tc_fun(U_13281,U_13279),tc_fun(tc_fun(U_13281,tc_HOL_Obool),U_13279),U_13280),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13281,U_13279)),U_13282)),U_13283)),U_13284) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13280,U_13281),U_13279),hAPP(c_Product__Type_Oprod_Oprod__case(U_13280,U_13281,U_13279),U_13282)),hAPP(hAPP(c_Product__Type_OSigma(U_13280,U_13281),U_13284),hAPP(c_COMBK(tc_fun(U_13281,tc_HOL_Obool),U_13280),U_13283)))
      | ~ class_Groups_Ocomm__monoid__mult(U_13279) ),
    inference(definitional_conversion,[status(esa)],[f_3425_2]) ).

cnf(f_3425_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13280,U_13279),hAPP(hAPP(c_COMBC(U_13280,tc_fun(U_13281,tc_HOL_Obool),U_13279),hAPP(hAPP(c_COMBB(tc_fun(U_13281,U_13279),tc_fun(tc_fun(U_13281,tc_HOL_Obool),U_13279),U_13280),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13281,U_13279)),U_13282)),U_13283)),U_13284) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13280,U_13281),U_13279),hAPP(c_Product__Type_Oprod_Oprod__case(U_13280,U_13281,U_13279),U_13282)),hAPP(hAPP(c_Product__Type_OSigma(U_13280,U_13281),U_13284),hAPP(c_COMBK(tc_fun(U_13281,tc_HOL_Obool),U_13280),U_13283)))
    | ~ class_Groups_Ocomm__monoid__mult(U_13279) ),
    inference(clausify,[status(thm)],[f_3425_3]) ).

fof(f_3426_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(f_3426_2,plain,
    ! [U_13289,U_13288,U_13287,U_13286,U_13285] : hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13285,tc_HOL_Obool)),U_13287),U_13288)),U_13289) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13285,U_13286),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),U_13287),U_13289)),hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),U_13288),U_13289)),
    inference(variable_rename,[status(thm)],[f_3426_1]) ).

fof(f_3426_3,plain,
    ! [U_13285,U_13286,U_13287,U_13288,U_13289] : hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13285,tc_HOL_Obool)),U_13287),U_13288)),U_13289) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13285,U_13286),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),U_13287),U_13289)),hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),U_13288),U_13289)),
    inference(definitional_conversion,[status(esa)],[f_3426_2]) ).

cnf(f_3426_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13285,tc_HOL_Obool)),U_13287),U_13288)),U_13289) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13285,U_13286),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),U_13287),U_13289)),hAPP(hAPP(c_Product__Type_OSigma(U_13285,U_13286),U_13288),U_13289)),
    inference(clausify,[status(thm)],[f_3426_3]) ).

fof(f_3427_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(f_3427_2,plain,
    ! [U_13294,U_13293,U_13292,U_13291,U_13290] : hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13290,tc_HOL_Obool)),U_13292),U_13293)),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13290,U_13291),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),U_13292),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294))),hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),U_13293),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294))),
    inference(variable_rename,[status(thm)],[f_3427_1]) ).

fof(f_3427_3,plain,
    ! [U_13290,U_13291,U_13292,U_13293,U_13294] : hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13290,tc_HOL_Obool)),U_13292),U_13293)),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13290,U_13291),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),U_13292),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294))),hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),U_13293),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294))),
    inference(definitional_conversion,[status(esa)],[f_3427_2]) ).

cnf(f_3427_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13290,tc_HOL_Obool)),U_13292),U_13293)),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13290,U_13291),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),U_13292),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294))),hAPP(hAPP(c_Product__Type_OSigma(U_13290,U_13291),U_13293),hAPP(c_COMBK(tc_fun(U_13291,tc_HOL_Obool),U_13290),U_13294))),
    inference(clausify,[status(thm)],[f_3427_3]) ).

fof(f_3428_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(f_3428_2,plain,
    ! [U_13299,U_13298,U_13297,U_13296,U_13295] : hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),hAPP(hAPP(c_COMBS(U_13295,tc_fun(U_13296,tc_HOL_Obool),tc_fun(U_13296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13296,tc_HOL_Obool),tc_fun(tc_fun(U_13296,tc_HOL_Obool),tc_fun(U_13296,tc_HOL_Obool)),U_13295),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13296,tc_HOL_Obool))),U_13298)),U_13299)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13295,U_13296),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),U_13298)),hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),U_13299)),
    inference(variable_rename,[status(thm)],[f_3428_1]) ).

fof(f_3428_3,plain,
    ! [U_13295,U_13296,U_13297,U_13298,U_13299] : hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),hAPP(hAPP(c_COMBS(U_13295,tc_fun(U_13296,tc_HOL_Obool),tc_fun(U_13296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13296,tc_HOL_Obool),tc_fun(tc_fun(U_13296,tc_HOL_Obool),tc_fun(U_13296,tc_HOL_Obool)),U_13295),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13296,tc_HOL_Obool))),U_13298)),U_13299)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13295,U_13296),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),U_13298)),hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),U_13299)),
    inference(definitional_conversion,[status(esa)],[f_3428_2]) ).

cnf(f_3428_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),hAPP(hAPP(c_COMBS(U_13295,tc_fun(U_13296,tc_HOL_Obool),tc_fun(U_13296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13296,tc_HOL_Obool),tc_fun(tc_fun(U_13296,tc_HOL_Obool),tc_fun(U_13296,tc_HOL_Obool)),U_13295),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13296,tc_HOL_Obool))),U_13298)),U_13299)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13295,U_13296),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),U_13298)),hAPP(hAPP(c_Product__Type_OSigma(U_13295,U_13296),U_13297),U_13299)),
    inference(clausify,[status(thm)],[f_3428_3]) ).

fof(f_3429_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_swap__product]) ).

fof(f_3429_2,plain,
    ! [U_13303,U_13302,U_13301,U_13300] : hAPP(c_Set_Oimage(tc_prod(U_13300,U_13301),tc_prod(U_13301,U_13300),hAPP(c_Product__Type_Oprod_Oprod__case(U_13300,U_13301,tc_prod(U_13301,U_13300)),hAPP(c_COMBC(U_13301,U_13300,tc_prod(U_13301,U_13300)),c_Product__Type_OPair(U_13301,U_13300)))),hAPP(hAPP(c_Product__Type_OSigma(U_13300,U_13301),U_13302),hAPP(c_COMBK(tc_fun(U_13301,tc_HOL_Obool),U_13300),U_13303))) = hAPP(hAPP(c_Product__Type_OSigma(U_13301,U_13300),U_13303),hAPP(c_COMBK(tc_fun(U_13300,tc_HOL_Obool),U_13301),U_13302)),
    inference(variable_rename,[status(thm)],[f_3429_1]) ).

fof(f_3429_3,plain,
    ! [U_13300,U_13301,U_13302,U_13303] : hAPP(c_Set_Oimage(tc_prod(U_13300,U_13301),tc_prod(U_13301,U_13300),hAPP(c_Product__Type_Oprod_Oprod__case(U_13300,U_13301,tc_prod(U_13301,U_13300)),hAPP(c_COMBC(U_13301,U_13300,tc_prod(U_13301,U_13300)),c_Product__Type_OPair(U_13301,U_13300)))),hAPP(hAPP(c_Product__Type_OSigma(U_13300,U_13301),U_13302),hAPP(c_COMBK(tc_fun(U_13301,tc_HOL_Obool),U_13300),U_13303))) = hAPP(hAPP(c_Product__Type_OSigma(U_13301,U_13300),U_13303),hAPP(c_COMBK(tc_fun(U_13300,tc_HOL_Obool),U_13301),U_13302)),
    inference(definitional_conversion,[status(esa)],[f_3429_2]) ).

cnf(f_3429_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13300,U_13301),tc_prod(U_13301,U_13300),hAPP(c_Product__Type_Oprod_Oprod__case(U_13300,U_13301,tc_prod(U_13301,U_13300)),hAPP(c_COMBC(U_13301,U_13300,tc_prod(U_13301,U_13300)),c_Product__Type_OPair(U_13301,U_13300)))),hAPP(hAPP(c_Product__Type_OSigma(U_13300,U_13301),U_13302),hAPP(c_COMBK(tc_fun(U_13301,tc_HOL_Obool),U_13300),U_13303))) = hAPP(hAPP(c_Product__Type_OSigma(U_13301,U_13300),U_13303),hAPP(c_COMBK(tc_fun(U_13300,tc_HOL_Obool),U_13301),U_13302)),
    inference(clausify,[status(thm)],[f_3429_3]) ).

fof(f_3430_1,plain,
    ! [V_a_2,V_f_2,T_b,V_g_2] :
      ( hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
      | V_g_2 != c_Finite__Set_Ofold1(T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def]) ).

fof(f_3430_2,plain,
    ! [U_13307,U_13306,U_13305,U_13304] :
      ( hAPP(U_13304,hAPP(hAPP(c_Set_Oinsert(U_13305),U_13307),c_Orderings_Obot__class_Obot(tc_fun(U_13305,tc_HOL_Obool)))) = U_13307
      | U_13304 != c_Finite__Set_Ofold1(U_13305,U_13306) ),
    inference(variable_rename,[status(thm)],[f_3430_1]) ).

fof(f_3430_3,plain,
    ! [U_13305,U_13304,U_13306,U_13307] :
      ( hAPP(U_13304,hAPP(hAPP(c_Set_Oinsert(U_13305),U_13307),c_Orderings_Obot__class_Obot(tc_fun(U_13305,tc_HOL_Obool)))) = U_13307
      | U_13304 != c_Finite__Set_Ofold1(U_13305,U_13306) ),
    inference(definitional_conversion,[status(esa)],[f_3430_2]) ).

cnf(f_3430_4,plain,
    ( hAPP(U_13304,hAPP(hAPP(c_Set_Oinsert(U_13305),U_13307),c_Orderings_Obot__class_Obot(tc_fun(U_13305,tc_HOL_Obool)))) = U_13307
    | U_13304 != c_Finite__Set_Ofold1(U_13305,U_13306) ),
    inference(clausify,[status(thm)],[f_3430_3]) ).

fof(f_3431_1,plain,
    ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_fold1__singleton]) ).

fof(f_3431_2,plain,
    ! [U_13310,U_13309,U_13308] : hAPP(c_Finite__Set_Ofold1(U_13308,U_13309),hAPP(hAPP(c_Set_Oinsert(U_13308),U_13310),c_Orderings_Obot__class_Obot(tc_fun(U_13308,tc_HOL_Obool)))) = U_13310,
    inference(variable_rename,[status(thm)],[f_3431_1]) ).

fof(f_3431_3,plain,
    ! [U_13308,U_13309,U_13310] : hAPP(c_Finite__Set_Ofold1(U_13308,U_13309),hAPP(hAPP(c_Set_Oinsert(U_13308),U_13310),c_Orderings_Obot__class_Obot(tc_fun(U_13308,tc_HOL_Obool)))) = U_13310,
    inference(definitional_conversion,[status(esa)],[f_3431_2]) ).

cnf(f_3431_4,plain,
    hAPP(c_Finite__Set_Ofold1(U_13308,U_13309),hAPP(hAPP(c_Set_Oinsert(U_13308),U_13310),c_Orderings_Obot__class_Obot(tc_fun(U_13308,tc_HOL_Obool)))) = U_13310,
    inference(clausify,[status(thm)],[f_3431_3]) ).

fof(f_3432_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product]) ).

fof(f_3432_2,plain,
    ! [U_13314,U_13313,U_13312,U_13311] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13311,U_13313)),hAPP(hAPP(c_Product__Type_OSigma(U_13311,U_13313),U_13312),hAPP(c_COMBK(tc_fun(U_13313,tc_HOL_Obool),U_13311),U_13314))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13313),U_13314))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13311),U_13312)) ),
    inference(variable_rename,[status(thm)],[f_3432_1]) ).

fof(f_3432_3,plain,
    ! [U_13311,U_13312,U_13313,U_13314] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13311,U_13313)),hAPP(hAPP(c_Product__Type_OSigma(U_13311,U_13313),U_13312),hAPP(c_COMBK(tc_fun(U_13313,tc_HOL_Obool),U_13311),U_13314))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13313),U_13314))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13311),U_13312)) ),
    inference(definitional_conversion,[status(esa)],[f_3432_2]) ).

cnf(f_3432_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13311,U_13313)),hAPP(hAPP(c_Product__Type_OSigma(U_13311,U_13313),U_13312),hAPP(c_COMBK(tc_fun(U_13313,tc_HOL_Obool),U_13311),U_13314))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13313),U_13314))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13311),U_13312)) ),
    inference(clausify,[status(thm)],[f_3432_3]) ).

fof(f_3433_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__type]) ).

fof(f_3433_2,plain,
    ! [U_13317,U_13316,U_13315] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13315,U_13315),tc_HOL_Obool)),U_13317),hAPP(hAPP(c_Product__Type_OSigma(U_13315,U_13315),U_13316),hAPP(c_COMBK(tc_fun(U_13315,tc_HOL_Obool),U_13315),U_13316))))
      | ~ c_Equiv__Relations_Oequiv(U_13315,U_13316,U_13317) ),
    inference(variable_rename,[status(thm)],[f_3433_1]) ).

fof(f_3433_3,plain,
    ! [U_13315,U_13316,U_13317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13315,U_13315),tc_HOL_Obool)),U_13317),hAPP(hAPP(c_Product__Type_OSigma(U_13315,U_13315),U_13316),hAPP(c_COMBK(tc_fun(U_13315,tc_HOL_Obool),U_13315),U_13316))))
      | ~ c_Equiv__Relations_Oequiv(U_13315,U_13316,U_13317) ),
    inference(definitional_conversion,[status(esa)],[f_3433_2]) ).

cnf(f_3433_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13315,U_13315),tc_HOL_Obool)),U_13317),hAPP(hAPP(c_Product__Type_OSigma(U_13315,U_13315),U_13316),hAPP(c_COMBK(tc_fun(U_13315,tc_HOL_Obool),U_13315),U_13316))))
    | ~ c_Equiv__Relations_Oequiv(U_13315,U_13316,U_13317) ),
    inference(clausify,[status(thm)],[f_3433_3]) ).

fof(f_3434_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(f_3434_2,plain,
    ! [U_13322,U_13321,U_13320,U_13319,U_13318] : hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13318,tc_HOL_Obool)),U_13320),U_13321)),U_13322) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13318,U_13319),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),U_13320),U_13322)),hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),U_13321),U_13322)),
    inference(variable_rename,[status(thm)],[f_3434_1]) ).

fof(f_3434_3,plain,
    ! [U_13318,U_13319,U_13320,U_13321,U_13322] : hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13318,tc_HOL_Obool)),U_13320),U_13321)),U_13322) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13318,U_13319),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),U_13320),U_13322)),hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),U_13321),U_13322)),
    inference(definitional_conversion,[status(esa)],[f_3434_2]) ).

cnf(f_3434_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13318,tc_HOL_Obool)),U_13320),U_13321)),U_13322) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13318,U_13319),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),U_13320),U_13322)),hAPP(hAPP(c_Product__Type_OSigma(U_13318,U_13319),U_13321),U_13322)),
    inference(clausify,[status(thm)],[f_3434_3]) ).

fof(f_3435_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(f_3435_2,plain,
    ! [U_13327,U_13326,U_13325,U_13324,U_13323] : hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13323,tc_HOL_Obool)),U_13325),U_13326)),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13323,U_13324),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),U_13325),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327))),hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),U_13326),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327))),
    inference(variable_rename,[status(thm)],[f_3435_1]) ).

fof(f_3435_3,plain,
    ! [U_13323,U_13324,U_13325,U_13326,U_13327] : hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13323,tc_HOL_Obool)),U_13325),U_13326)),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13323,U_13324),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),U_13325),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327))),hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),U_13326),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327))),
    inference(definitional_conversion,[status(esa)],[f_3435_2]) ).

cnf(f_3435_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13323,tc_HOL_Obool)),U_13325),U_13326)),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13323,U_13324),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),U_13325),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327))),hAPP(hAPP(c_Product__Type_OSigma(U_13323,U_13324),U_13326),hAPP(c_COMBK(tc_fun(U_13324,tc_HOL_Obool),U_13323),U_13327))),
    inference(clausify,[status(thm)],[f_3435_3]) ).

fof(f_3436_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(f_3436_2,plain,
    ! [U_13332,U_13331,U_13330,U_13329,U_13328] : hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),hAPP(hAPP(c_COMBS(U_13328,tc_fun(U_13329,tc_HOL_Obool),tc_fun(U_13329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13329,tc_HOL_Obool),tc_fun(tc_fun(U_13329,tc_HOL_Obool),tc_fun(U_13329,tc_HOL_Obool)),U_13328),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13329,tc_HOL_Obool))),U_13331)),U_13332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13328,U_13329),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),U_13331)),hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),U_13332)),
    inference(variable_rename,[status(thm)],[f_3436_1]) ).

fof(f_3436_3,plain,
    ! [U_13328,U_13329,U_13330,U_13331,U_13332] : hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),hAPP(hAPP(c_COMBS(U_13328,tc_fun(U_13329,tc_HOL_Obool),tc_fun(U_13329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13329,tc_HOL_Obool),tc_fun(tc_fun(U_13329,tc_HOL_Obool),tc_fun(U_13329,tc_HOL_Obool)),U_13328),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13329,tc_HOL_Obool))),U_13331)),U_13332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13328,U_13329),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),U_13331)),hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),U_13332)),
    inference(definitional_conversion,[status(esa)],[f_3436_2]) ).

cnf(f_3436_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),hAPP(hAPP(c_COMBS(U_13328,tc_fun(U_13329,tc_HOL_Obool),tc_fun(U_13329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13329,tc_HOL_Obool),tc_fun(tc_fun(U_13329,tc_HOL_Obool),tc_fun(U_13329,tc_HOL_Obool)),U_13328),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13329,tc_HOL_Obool))),U_13331)),U_13332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13328,U_13329),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),U_13331)),hAPP(hAPP(c_Product__Type_OSigma(U_13328,U_13329),U_13330),U_13332)),
    inference(clausify,[status(thm)],[f_3436_3]) ).

fof(f_3437_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(f_3437_2,plain,
    ! [U_13334,U_13333] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13333,U_13333),tc_HOL_Obool)),c_Relation_OId__on(U_13333,U_13334)),hAPP(hAPP(c_Product__Type_OSigma(U_13333,U_13333),U_13334),hAPP(c_COMBK(tc_fun(U_13333,tc_HOL_Obool),U_13333),U_13334)))),
    inference(variable_rename,[status(thm)],[f_3437_1]) ).

fof(f_3437_3,plain,
    ! [U_13333,U_13334] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13333,U_13333),tc_HOL_Obool)),c_Relation_OId__on(U_13333,U_13334)),hAPP(hAPP(c_Product__Type_OSigma(U_13333,U_13333),U_13334),hAPP(c_COMBK(tc_fun(U_13333,tc_HOL_Obool),U_13333),U_13334)))),
    inference(definitional_conversion,[status(esa)],[f_3437_2]) ).

cnf(f_3437_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13333,U_13333),tc_HOL_Obool)),c_Relation_OId__on(U_13333,U_13334)),hAPP(hAPP(c_Product__Type_OSigma(U_13333,U_13333),U_13334),hAPP(c_COMBK(tc_fun(U_13333,tc_HOL_Obool),U_13333),U_13334)))),
    inference(clausify,[status(thm)],[f_3437_3]) ).

fof(f_3438_1,plain,
    ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(f_3438_2,plain,
    ! [U_13336,U_13335] : hAPP(hAPP(c_Product__Type_OSigma(U_13335,U_13336),c_Orderings_Otop__class_Otop(tc_fun(U_13335,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13336,tc_HOL_Obool),U_13335),c_Orderings_Otop__class_Otop(tc_fun(U_13336,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13335,U_13336),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3438_1]) ).

fof(f_3438_3,plain,
    ! [U_13335,U_13336] : hAPP(hAPP(c_Product__Type_OSigma(U_13335,U_13336),c_Orderings_Otop__class_Otop(tc_fun(U_13335,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13336,tc_HOL_Obool),U_13335),c_Orderings_Otop__class_Otop(tc_fun(U_13336,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13335,U_13336),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3438_2]) ).

cnf(f_3438_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13335,U_13336),c_Orderings_Otop__class_Otop(tc_fun(U_13335,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13336,tc_HOL_Obool),U_13335),c_Orderings_Otop__class_Otop(tc_fun(U_13336,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13335,U_13336),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3438_3]) ).

fof(f_3439_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff]) ).

fof(f_3439_2,plain,
    ! [U_13342,U_13341,U_13340,U_13339,U_13338,U_13337] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13337,U_13338)),hAPP(hAPP(c_Product__Type_OPair(U_13337,U_13338),U_13339),U_13340)),hAPP(hAPP(c_Product__Type_OSigma(U_13337,U_13338),U_13341),U_13342)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13338),U_13340),hAPP(U_13342,U_13339)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13337),U_13339),U_13341)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_13338),U_13340),hAPP(U_13342,U_13339)))
          & hBOOL(hAPP(hAPP(c_member(U_13337),U_13339),U_13341)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13337,U_13338)),hAPP(hAPP(c_Product__Type_OPair(U_13337,U_13338),U_13339),U_13340)),hAPP(hAPP(c_Product__Type_OSigma(U_13337,U_13338),U_13341),U_13342))) ) ),
    inference(variable_rename,[status(thm)],[f_3439_1]) ).

fof(f_3439_3,plain,
    ( ! [U_13354,U_13352,U_13350,U_13348,U_13346,U_13344] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13344,U_13346)),hAPP(hAPP(c_Product__Type_OPair(U_13344,U_13346),U_13348),U_13350)),hAPP(hAPP(c_Product__Type_OSigma(U_13344,U_13346),U_13352),U_13354)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13346),U_13350),hAPP(U_13354,U_13348)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13344),U_13348),U_13352)) )
    & ! [U_13353,U_13351,U_13349,U_13347,U_13345,U_13343] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_13345),U_13349),hAPP(U_13353,U_13347)))
          & hBOOL(hAPP(hAPP(c_member(U_13343),U_13347),U_13351)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13343,U_13345)),hAPP(hAPP(c_Product__Type_OPair(U_13343,U_13345),U_13347),U_13349)),hAPP(hAPP(c_Product__Type_OSigma(U_13343,U_13345),U_13351),U_13353))) ) ),
    inference(miniscope,[status(thm)],[f_3439_2]) ).

fof(f_3439_4,plain,
    ( ! [U_13345,U_13343,U_13351,U_13347,U_13349,U_13353] :
        ( hBOOL(hAPP(hAPP(c_member(U_13345),U_13349),hAPP(U_13353,U_13347)))
        | ~ sP965(U_13345,U_13343,U_13351,U_13347,U_13349,U_13353) )
    & ! [U_13345,U_13343,U_13351,U_13347,U_13349,U_13353] :
        ( hBOOL(hAPP(hAPP(c_member(U_13343),U_13347),U_13351))
        | ~ sP965(U_13345,U_13343,U_13351,U_13347,U_13349,U_13353) )
    & ! [U_13344,U_13350,U_13346,U_13352,U_13348,U_13354] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13344,U_13346)),hAPP(hAPP(c_Product__Type_OPair(U_13344,U_13346),U_13348),U_13350)),hAPP(hAPP(c_Product__Type_OSigma(U_13344,U_13346),U_13352),U_13354)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13346),U_13350),hAPP(U_13354,U_13348)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13344),U_13348),U_13352)) )
    & ! [U_13345,U_13343,U_13351,U_13347,U_13349,U_13353] :
        ( sP965(U_13345,U_13343,U_13351,U_13347,U_13349,U_13353)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13343,U_13345)),hAPP(hAPP(c_Product__Type_OPair(U_13343,U_13345),U_13347),U_13349)),hAPP(hAPP(c_Product__Type_OSigma(U_13343,U_13345),U_13351),U_13353))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP965])],[f_3439_3]) ).

cnf(f_3439_5,plain,
    ( sP965(U_13345,U_13343,U_13351,U_13347,U_13349,U_13353)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13343,U_13345)),hAPP(hAPP(c_Product__Type_OPair(U_13343,U_13345),U_13347),U_13349)),hAPP(hAPP(c_Product__Type_OSigma(U_13343,U_13345),U_13351),U_13353))) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

cnf(f_3439_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13344,U_13346)),hAPP(hAPP(c_Product__Type_OPair(U_13344,U_13346),U_13348),U_13350)),hAPP(hAPP(c_Product__Type_OSigma(U_13344,U_13346),U_13352),U_13354)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13346),U_13350),hAPP(U_13354,U_13348)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13344),U_13348),U_13352)) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

cnf(f_3439_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13343),U_13347),U_13351))
    | ~ sP965(U_13345,U_13343,U_13351,U_13347,U_13349,U_13353) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

cnf(f_3439_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13345),U_13349),hAPP(U_13353,U_13347)))
    | ~ sP965(U_13345,U_13343,U_13351,U_13347,U_13349,U_13353) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

fof(f_3440_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaD1]) ).

fof(f_3440_2,plain,
    ! [U_13360,U_13359,U_13358,U_13357,U_13356,U_13355] :
      ( hBOOL(hAPP(hAPP(c_member(U_13355),U_13357),U_13359))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13355,U_13356)),hAPP(hAPP(c_Product__Type_OPair(U_13355,U_13356),U_13357),U_13358)),hAPP(hAPP(c_Product__Type_OSigma(U_13355,U_13356),U_13359),U_13360))) ),
    inference(variable_rename,[status(thm)],[f_3440_1]) ).

fof(f_3440_3,plain,
    ! [U_13356,U_13355,U_13357,U_13358,U_13359,U_13360] :
      ( hBOOL(hAPP(hAPP(c_member(U_13355),U_13357),U_13359))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13355,U_13356)),hAPP(hAPP(c_Product__Type_OPair(U_13355,U_13356),U_13357),U_13358)),hAPP(hAPP(c_Product__Type_OSigma(U_13355,U_13356),U_13359),U_13360))) ),
    inference(definitional_conversion,[status(esa)],[f_3440_2]) ).

cnf(f_3440_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13355),U_13357),U_13359))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13355,U_13356)),hAPP(hAPP(c_Product__Type_OPair(U_13355,U_13356),U_13357),U_13358)),hAPP(hAPP(c_Product__Type_OSigma(U_13355,U_13356),U_13359),U_13360))) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

fof(f_3441_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaD2]) ).

fof(f_3441_2,plain,
    ! [U_13366,U_13365,U_13364,U_13363,U_13362,U_13361] :
      ( hBOOL(hAPP(hAPP(c_member(U_13362),U_13364),hAPP(U_13366,U_13363)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13361,U_13362)),hAPP(hAPP(c_Product__Type_OPair(U_13361,U_13362),U_13363),U_13364)),hAPP(hAPP(c_Product__Type_OSigma(U_13361,U_13362),U_13365),U_13366))) ),
    inference(variable_rename,[status(thm)],[f_3441_1]) ).

fof(f_3441_3,plain,
    ! [U_13366,U_13365,U_13364,U_13363,U_13362] :
      ( ! [U_13361] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13361,U_13362)),hAPP(hAPP(c_Product__Type_OPair(U_13361,U_13362),U_13363),U_13364)),hAPP(hAPP(c_Product__Type_OSigma(U_13361,U_13362),U_13365),U_13366)))
      | hBOOL(hAPP(hAPP(c_member(U_13362),U_13364),hAPP(U_13366,U_13363))) ),
    inference(miniscope,[status(thm)],[f_3441_2]) ).

fof(f_3441_4,plain,
    ! [U_13361,U_13362,U_13363,U_13364,U_13365,U_13366] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13361,U_13362)),hAPP(hAPP(c_Product__Type_OPair(U_13361,U_13362),U_13363),U_13364)),hAPP(hAPP(c_Product__Type_OSigma(U_13361,U_13362),U_13365),U_13366)))
      | hBOOL(hAPP(hAPP(c_member(U_13362),U_13364),hAPP(U_13366,U_13363))) ),
    inference(definitional_conversion,[status(esa)],[f_3441_3]) ).

cnf(f_3441_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13361,U_13362)),hAPP(hAPP(c_Product__Type_OPair(U_13361,U_13362),U_13363),U_13364)),hAPP(hAPP(c_Product__Type_OSigma(U_13361,U_13362),U_13365),U_13366)))
    | hBOOL(hAPP(hAPP(c_member(U_13362),U_13364),hAPP(U_13366,U_13363))) ),
    inference(clausify,[status(thm)],[f_3441_4]) ).

fof(f_3442_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaE2]) ).

fof(f_3442_2,plain,
    ! [U_13372,U_13371,U_13370,U_13369,U_13368,U_13367] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),hAPP(U_13372,U_13369)))
        & hBOOL(hAPP(hAPP(c_member(U_13367),U_13369),U_13371)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13367,U_13368)),hAPP(hAPP(c_Product__Type_OPair(U_13367,U_13368),U_13369),U_13370)),hAPP(hAPP(c_Product__Type_OSigma(U_13367,U_13368),U_13371),U_13372))) ),
    inference(variable_rename,[status(thm)],[f_3442_1]) ).

fof(f_3442_3,plain,
    ( ! [U_13367,U_13368,U_13369,U_13370,U_13371,U_13372] :
        ( hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),hAPP(U_13372,U_13369)))
        | ~ sP966(U_13367,U_13368,U_13369,U_13370,U_13371,U_13372) )
    & ! [U_13367,U_13368,U_13369,U_13370,U_13371,U_13372] :
        ( hBOOL(hAPP(hAPP(c_member(U_13367),U_13369),U_13371))
        | ~ sP966(U_13367,U_13368,U_13369,U_13370,U_13371,U_13372) )
    & ! [U_13367,U_13368,U_13369,U_13370,U_13371,U_13372] :
        ( sP966(U_13367,U_13368,U_13369,U_13370,U_13371,U_13372)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13367,U_13368)),hAPP(hAPP(c_Product__Type_OPair(U_13367,U_13368),U_13369),U_13370)),hAPP(hAPP(c_Product__Type_OSigma(U_13367,U_13368),U_13371),U_13372))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP966])],[f_3442_2]) ).

cnf(f_3442_4,plain,
    ( sP966(U_13367,U_13368,U_13369,U_13370,U_13371,U_13372)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13367,U_13368)),hAPP(hAPP(c_Product__Type_OPair(U_13367,U_13368),U_13369),U_13370)),hAPP(hAPP(c_Product__Type_OSigma(U_13367,U_13368),U_13371),U_13372))) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

cnf(f_3442_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13367),U_13369),U_13371))
    | ~ sP966(U_13367,U_13368,U_13369,U_13370,U_13371,U_13372) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

cnf(f_3442_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),hAPP(U_13372,U_13369)))
    | ~ sP966(U_13367,U_13368,U_13369,U_13370,U_13371,U_13372) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

fof(f_3443_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold]) ).

fof(f_3443_2,plain,
    ! [U_13376,U_13375,U_13374,U_13373] :
      ( hAPP(U_13375,U_13376) = hAPP(c_Finite__Set_Ofold1(U_13373,U_13374),U_13376)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13373),U_13376))
      | ~ c_Finite__Set_Ofolding__one(U_13373,U_13374,U_13375) ),
    inference(variable_rename,[status(thm)],[f_3443_1]) ).

fof(f_3443_3,plain,
    ! [U_13374,U_13375,U_13373,U_13376] :
      ( hAPP(U_13375,U_13376) = hAPP(c_Finite__Set_Ofold1(U_13373,U_13374),U_13376)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13373),U_13376))
      | ~ c_Finite__Set_Ofolding__one(U_13373,U_13374,U_13375) ),
    inference(definitional_conversion,[status(esa)],[f_3443_2]) ).

cnf(f_3443_4,plain,
    ( hAPP(U_13375,U_13376) = hAPP(c_Finite__Set_Ofold1(U_13373,U_13374),U_13376)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13373),U_13376))
    | ~ c_Finite__Set_Ofolding__one(U_13373,U_13374,U_13375) ),
    inference(clausify,[status(thm)],[f_3443_3]) ).

fof(f_3444_1,plain,
    ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_card__cartesian__product__singleton]) ).

fof(f_3444_2,plain,
    ! [U_13380,U_13379,U_13378,U_13377] : hAPP(c_Finite__Set_Ocard(tc_prod(U_13377,U_13378)),hAPP(hAPP(c_Product__Type_OSigma(U_13377,U_13378),hAPP(hAPP(c_Set_Oinsert(U_13377),U_13379),c_Orderings_Obot__class_Obot(tc_fun(U_13377,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_13378,tc_HOL_Obool),U_13377),U_13380))) = hAPP(c_Finite__Set_Ocard(U_13378),U_13380),
    inference(variable_rename,[status(thm)],[f_3444_1]) ).

fof(f_3444_3,plain,
    ! [U_13377,U_13378,U_13379,U_13380] : hAPP(c_Finite__Set_Ocard(tc_prod(U_13377,U_13378)),hAPP(hAPP(c_Product__Type_OSigma(U_13377,U_13378),hAPP(hAPP(c_Set_Oinsert(U_13377),U_13379),c_Orderings_Obot__class_Obot(tc_fun(U_13377,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_13378,tc_HOL_Obool),U_13377),U_13380))) = hAPP(c_Finite__Set_Ocard(U_13378),U_13380),
    inference(definitional_conversion,[status(esa)],[f_3444_2]) ).

cnf(f_3444_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_13377,U_13378)),hAPP(hAPP(c_Product__Type_OSigma(U_13377,U_13378),hAPP(hAPP(c_Set_Oinsert(U_13377),U_13379),c_Orderings_Obot__class_Obot(tc_fun(U_13377,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_13378,tc_HOL_Obool),U_13377),U_13380))) = hAPP(c_Finite__Set_Ocard(U_13378),U_13380),
    inference(clausify,[status(thm)],[f_3444_3]) ).

fof(f_3445_1,plain,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2]) ).

fof(f_3445_2,plain,
    ! [U_13386,U_13385,U_13384,U_13383,U_13382,U_13381] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13381),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13385),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13386),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13384,tc_HOL_Obool)),U_13385),U_13386)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13384,tc_HOL_Obool)),U_13385),U_13386))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13381),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13385),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13386),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13381),U_13382),U_13383)) ),
    inference(variable_rename,[status(thm)],[f_3445_1]) ).

fof(f_3445_3,plain,
    ( ! [U_13381,U_13383,U_13384,U_13385,U_13386] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13381),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13385),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13386),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13384,tc_HOL_Obool)),U_13385),U_13386))
        | ~ sP967(U_13381,U_13383,U_13384,U_13385,U_13386) )
    & ! [U_13381,U_13383,U_13384,U_13385,U_13386] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13384,tc_HOL_Obool)),U_13385),U_13386))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13381),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13385),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13386),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))))
        | ~ sP967(U_13381,U_13383,U_13384,U_13385,U_13386) )
    & ! [U_13381,U_13382,U_13383,U_13384,U_13385,U_13386] :
        ( sP967(U_13381,U_13383,U_13384,U_13385,U_13386)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13381),U_13382),U_13383)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP967])],[f_3445_2]) ).

cnf(f_3445_4,plain,
    ( sP967(U_13381,U_13383,U_13384,U_13385,U_13386)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13381),U_13382),U_13383)) ),
    inference(clausify,[status(thm)],[f_3445_3]) ).

cnf(f_3445_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13384,tc_HOL_Obool)),U_13385),U_13386))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13381),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13385),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13386),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))))
    | ~ sP967(U_13381,U_13383,U_13384,U_13385,U_13386) ),
    inference(clausify,[status(thm)],[f_3445_3]) ).

cnf(f_3445_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13381),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13385),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))),hAPP(hAPP(c_Product__Type_OSigma(U_13384,U_13381),U_13386),hAPP(c_COMBK(tc_fun(U_13381,tc_HOL_Obool),U_13384),U_13383))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13384,tc_HOL_Obool)),U_13385),U_13386))
    | ~ sP967(U_13381,U_13383,U_13384,U_13385,U_13386) ),
    inference(clausify,[status(thm)],[f_3445_3]) ).

fof(f_3446_1,plain,
    ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_Image__subset]) ).

fof(f_3446_2,plain,
    ! [U_13392,U_13391,U_13390,U_13389,U_13388,U_13387] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13388,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13387,U_13388,U_13389),U_13392)),U_13391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool)),U_13389),hAPP(hAPP(c_Product__Type_OSigma(U_13387,U_13388),U_13390),hAPP(c_COMBK(tc_fun(U_13388,tc_HOL_Obool),U_13387),U_13391)))) ),
    inference(variable_rename,[status(thm)],[f_3446_1]) ).

fof(f_3446_3,plain,
    ! [U_13389,U_13390,U_13391,U_13388,U_13387,U_13392] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13388,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13387,U_13388,U_13389),U_13392)),U_13391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool)),U_13389),hAPP(hAPP(c_Product__Type_OSigma(U_13387,U_13388),U_13390),hAPP(c_COMBK(tc_fun(U_13388,tc_HOL_Obool),U_13387),U_13391)))) ),
    inference(definitional_conversion,[status(esa)],[f_3446_2]) ).

cnf(f_3446_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13388,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13387,U_13388,U_13389),U_13392)),U_13391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool)),U_13389),hAPP(hAPP(c_Product__Type_OSigma(U_13387,U_13388),U_13390),hAPP(c_COMBK(tc_fun(U_13388,tc_HOL_Obool),U_13387),U_13391)))) ),
    inference(clausify,[status(thm)],[f_3446_3]) ).

fof(f_3447_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1]) ).

fof(f_3447_2,plain,
    ! [U_13396,U_13395,U_13394,U_13393] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395))
      | U_13396 = c_Orderings_Obot__class_Obot(tc_fun(U_13394,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13393,U_13394)),hAPP(hAPP(c_Product__Type_OSigma(U_13393,U_13394),U_13395),hAPP(c_COMBK(tc_fun(U_13394,tc_HOL_Obool),U_13393),U_13396)))) ),
    inference(variable_rename,[status(thm)],[f_3447_1]) ).

fof(f_3447_3,plain,
    ! [U_13393,U_13394,U_13395,U_13396] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395))
      | U_13396 = c_Orderings_Obot__class_Obot(tc_fun(U_13394,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13393,U_13394)),hAPP(hAPP(c_Product__Type_OSigma(U_13393,U_13394),U_13395),hAPP(c_COMBK(tc_fun(U_13394,tc_HOL_Obool),U_13393),U_13396)))) ),
    inference(definitional_conversion,[status(esa)],[f_3447_2]) ).

cnf(f_3447_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395))
    | U_13396 = c_Orderings_Obot__class_Obot(tc_fun(U_13394,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13393,U_13394)),hAPP(hAPP(c_Product__Type_OSigma(U_13393,U_13394),U_13395),hAPP(c_COMBK(tc_fun(U_13394,tc_HOL_Obool),U_13393),U_13396)))) ),
    inference(clausify,[status(thm)],[f_3447_3]) ).

fof(f_3448_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2]) ).

fof(f_3448_2,plain,
    ! [U_13400,U_13399,U_13398,U_13397] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13398),U_13400))
      | U_13399 = c_Orderings_Obot__class_Obot(tc_fun(U_13397,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13397,U_13398)),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13398),U_13399),hAPP(c_COMBK(tc_fun(U_13398,tc_HOL_Obool),U_13397),U_13400)))) ),
    inference(variable_rename,[status(thm)],[f_3448_1]) ).

fof(f_3448_3,plain,
    ! [U_13397,U_13398,U_13399,U_13400] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13398),U_13400))
      | U_13399 = c_Orderings_Obot__class_Obot(tc_fun(U_13397,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13397,U_13398)),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13398),U_13399),hAPP(c_COMBK(tc_fun(U_13398,tc_HOL_Obool),U_13397),U_13400)))) ),
    inference(definitional_conversion,[status(esa)],[f_3448_2]) ).

cnf(f_3448_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13398),U_13400))
    | U_13399 = c_Orderings_Obot__class_Obot(tc_fun(U_13397,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13397,U_13398)),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13398),U_13399),hAPP(c_COMBK(tc_fun(U_13398,tc_HOL_Obool),U_13397),U_13400)))) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

fof(f_3449_1,plain,
    ! [V_A_2,T_c,T_b,V_B_2] :
      ( ( hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2
        | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fst__image__times]) ).

fof(f_3449_2,plain,
    ! [U_13404,U_13403,U_13402,U_13401] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_13403,U_13402),U_13403,c_Product__Type_Ofst(U_13403,U_13402)),hAPP(hAPP(c_Product__Type_OSigma(U_13403,U_13402),U_13404),hAPP(c_COMBK(tc_fun(U_13402,tc_HOL_Obool),U_13403),U_13401))) = U_13404
        | U_13401 = c_Orderings_Obot__class_Obot(tc_fun(U_13402,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_13403,U_13402),U_13403,c_Product__Type_Ofst(U_13403,U_13402)),hAPP(hAPP(c_Product__Type_OSigma(U_13403,U_13402),U_13404),hAPP(c_COMBK(tc_fun(U_13402,tc_HOL_Obool),U_13403),U_13401))) = c_Orderings_Obot__class_Obot(tc_fun(U_13403,tc_HOL_Obool))
        | U_13401 != c_Orderings_Obot__class_Obot(tc_fun(U_13402,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3449_1]) ).

fof(f_3449_3,plain,
    ( ! [U_13412,U_13410,U_13408,U_13406] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13410,U_13408),U_13410,c_Product__Type_Ofst(U_13410,U_13408)),hAPP(hAPP(c_Product__Type_OSigma(U_13410,U_13408),U_13412),hAPP(c_COMBK(tc_fun(U_13408,tc_HOL_Obool),U_13410),U_13406))) = U_13412
        | U_13406 = c_Orderings_Obot__class_Obot(tc_fun(U_13408,tc_HOL_Obool)) )
    & ! [U_13411,U_13409,U_13407,U_13405] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13409,U_13407),U_13409,c_Product__Type_Ofst(U_13409,U_13407)),hAPP(hAPP(c_Product__Type_OSigma(U_13409,U_13407),U_13411),hAPP(c_COMBK(tc_fun(U_13407,tc_HOL_Obool),U_13409),U_13405))) = c_Orderings_Obot__class_Obot(tc_fun(U_13409,tc_HOL_Obool))
        | U_13405 != c_Orderings_Obot__class_Obot(tc_fun(U_13407,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3449_2]) ).

fof(f_3449_4,plain,
    ( ! [U_13406,U_13408,U_13410,U_13412] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13410,U_13408),U_13410,c_Product__Type_Ofst(U_13410,U_13408)),hAPP(hAPP(c_Product__Type_OSigma(U_13410,U_13408),U_13412),hAPP(c_COMBK(tc_fun(U_13408,tc_HOL_Obool),U_13410),U_13406))) = U_13412
        | U_13406 = c_Orderings_Obot__class_Obot(tc_fun(U_13408,tc_HOL_Obool)) )
    & ! [U_13409,U_13407,U_13411,U_13405] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13409,U_13407),U_13409,c_Product__Type_Ofst(U_13409,U_13407)),hAPP(hAPP(c_Product__Type_OSigma(U_13409,U_13407),U_13411),hAPP(c_COMBK(tc_fun(U_13407,tc_HOL_Obool),U_13409),U_13405))) = c_Orderings_Obot__class_Obot(tc_fun(U_13409,tc_HOL_Obool))
        | U_13405 != c_Orderings_Obot__class_Obot(tc_fun(U_13407,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3449_3]) ).

cnf(f_3449_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13409,U_13407),U_13409,c_Product__Type_Ofst(U_13409,U_13407)),hAPP(hAPP(c_Product__Type_OSigma(U_13409,U_13407),U_13411),hAPP(c_COMBK(tc_fun(U_13407,tc_HOL_Obool),U_13409),U_13405))) = c_Orderings_Obot__class_Obot(tc_fun(U_13409,tc_HOL_Obool))
    | U_13405 != c_Orderings_Obot__class_Obot(tc_fun(U_13407,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3449_4]) ).

cnf(f_3449_6,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13410,U_13408),U_13410,c_Product__Type_Ofst(U_13410,U_13408)),hAPP(hAPP(c_Product__Type_OSigma(U_13410,U_13408),U_13412),hAPP(c_COMBK(tc_fun(U_13408,tc_HOL_Obool),U_13410),U_13406))) = U_13412
    | U_13406 = c_Orderings_Obot__class_Obot(tc_fun(U_13408,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3449_4]) ).

fof(f_3450_1,plain,
    ! [V_B_2,T_c,T_b,V_A_2] :
      ( ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_snd__image__times]) ).

fof(f_3450_2,plain,
    ! [U_13416,U_13415,U_13414,U_13413] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_13414,U_13415),U_13415,c_Product__Type_Osnd(U_13414,U_13415)),hAPP(hAPP(c_Product__Type_OSigma(U_13414,U_13415),U_13413),hAPP(c_COMBK(tc_fun(U_13415,tc_HOL_Obool),U_13414),U_13416))) = U_13416
        | U_13413 = c_Orderings_Obot__class_Obot(tc_fun(U_13414,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_13414,U_13415),U_13415,c_Product__Type_Osnd(U_13414,U_13415)),hAPP(hAPP(c_Product__Type_OSigma(U_13414,U_13415),U_13413),hAPP(c_COMBK(tc_fun(U_13415,tc_HOL_Obool),U_13414),U_13416))) = c_Orderings_Obot__class_Obot(tc_fun(U_13415,tc_HOL_Obool))
        | U_13413 != c_Orderings_Obot__class_Obot(tc_fun(U_13414,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3450_1]) ).

fof(f_3450_3,plain,
    ( ! [U_13424,U_13422,U_13420,U_13418] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13420,U_13422),U_13422,c_Product__Type_Osnd(U_13420,U_13422)),hAPP(hAPP(c_Product__Type_OSigma(U_13420,U_13422),U_13418),hAPP(c_COMBK(tc_fun(U_13422,tc_HOL_Obool),U_13420),U_13424))) = U_13424
        | U_13418 = c_Orderings_Obot__class_Obot(tc_fun(U_13420,tc_HOL_Obool)) )
    & ! [U_13423,U_13421,U_13419,U_13417] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13419,U_13421),U_13421,c_Product__Type_Osnd(U_13419,U_13421)),hAPP(hAPP(c_Product__Type_OSigma(U_13419,U_13421),U_13417),hAPP(c_COMBK(tc_fun(U_13421,tc_HOL_Obool),U_13419),U_13423))) = c_Orderings_Obot__class_Obot(tc_fun(U_13421,tc_HOL_Obool))
        | U_13417 != c_Orderings_Obot__class_Obot(tc_fun(U_13419,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3450_2]) ).

fof(f_3450_4,plain,
    ( ! [U_13418,U_13420,U_13422,U_13424] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13420,U_13422),U_13422,c_Product__Type_Osnd(U_13420,U_13422)),hAPP(hAPP(c_Product__Type_OSigma(U_13420,U_13422),U_13418),hAPP(c_COMBK(tc_fun(U_13422,tc_HOL_Obool),U_13420),U_13424))) = U_13424
        | U_13418 = c_Orderings_Obot__class_Obot(tc_fun(U_13420,tc_HOL_Obool)) )
    & ! [U_13421,U_13423,U_13419,U_13417] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13419,U_13421),U_13421,c_Product__Type_Osnd(U_13419,U_13421)),hAPP(hAPP(c_Product__Type_OSigma(U_13419,U_13421),U_13417),hAPP(c_COMBK(tc_fun(U_13421,tc_HOL_Obool),U_13419),U_13423))) = c_Orderings_Obot__class_Obot(tc_fun(U_13421,tc_HOL_Obool))
        | U_13417 != c_Orderings_Obot__class_Obot(tc_fun(U_13419,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3450_3]) ).

cnf(f_3450_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13419,U_13421),U_13421,c_Product__Type_Osnd(U_13419,U_13421)),hAPP(hAPP(c_Product__Type_OSigma(U_13419,U_13421),U_13417),hAPP(c_COMBK(tc_fun(U_13421,tc_HOL_Obool),U_13419),U_13423))) = c_Orderings_Obot__class_Obot(tc_fun(U_13421,tc_HOL_Obool))
    | U_13417 != c_Orderings_Obot__class_Obot(tc_fun(U_13419,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3450_4]) ).

cnf(f_3450_6,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13420,U_13422),U_13422,c_Product__Type_Osnd(U_13420,U_13422)),hAPP(hAPP(c_Product__Type_OSigma(U_13420,U_13422),U_13418),hAPP(c_COMBK(tc_fun(U_13422,tc_HOL_Obool),U_13420),U_13424))) = U_13424
    | U_13418 = c_Orderings_Obot__class_Obot(tc_fun(U_13420,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3450_4]) ).

fof(f_3451_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_fold1__def]) ).

fof(f_3451_2,plain,
    ! [U_13427,U_13426,U_13425] : hAPP(c_Finite__Set_Ofold1(U_13425,U_13426),U_13427) = c_HOL_OThe(U_13425,c_Finite__Set_Ofold1Set(U_13425,U_13426,U_13427)),
    inference(variable_rename,[status(thm)],[f_3451_1]) ).

fof(f_3451_3,plain,
    ! [U_13426,U_13425,U_13427] : hAPP(c_Finite__Set_Ofold1(U_13425,U_13426),U_13427) = c_HOL_OThe(U_13425,c_Finite__Set_Ofold1Set(U_13425,U_13426,U_13427)),
    inference(definitional_conversion,[status(esa)],[f_3451_2]) ).

cnf(f_3451_4,plain,
    hAPP(c_Finite__Set_Ofold1(U_13425,U_13426),U_13427) = c_HOL_OThe(U_13425,c_Finite__Set_Ofold1Set(U_13425,U_13426,U_13427)),
    inference(clausify,[status(thm)],[f_3451_3]) ).

fof(f_3452_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq]) ).

fof(f_3452_2,plain,
    ! [U_13429,U_13428] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_13428,U_13429) = hAPP(c_Finite__Set_Ofold1(U_13428,c_Lattices_Osemilattice__sup__class_Osup(U_13428)),U_13429)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13428),U_13429))
      | ~ class_Lattices_Olattice(U_13428) ),
    inference(variable_rename,[status(thm)],[f_3452_1]) ).

fof(f_3452_3,plain,
    ! [U_13428,U_13429] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_13428,U_13429) = hAPP(c_Finite__Set_Ofold1(U_13428,c_Lattices_Osemilattice__sup__class_Osup(U_13428)),U_13429)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13428),U_13429))
      | ~ class_Lattices_Olattice(U_13428) ),
    inference(definitional_conversion,[status(esa)],[f_3452_2]) ).

cnf(f_3452_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_13428,U_13429) = hAPP(c_Finite__Set_Ofold1(U_13428,c_Lattices_Osemilattice__sup__class_Osup(U_13428)),U_13429)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13428),U_13429))
    | ~ class_Lattices_Olattice(U_13428) ),
    inference(clausify,[status(thm)],[f_3452_3]) ).

fof(f_3453_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq]) ).

fof(f_3453_2,plain,
    ! [U_13431,U_13430] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_13430,U_13431) = hAPP(c_Finite__Set_Ofold1(U_13430,c_Lattices_Osemilattice__inf__class_Oinf(U_13430)),U_13431)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13430),U_13431))
      | ~ class_Lattices_Olattice(U_13430) ),
    inference(variable_rename,[status(thm)],[f_3453_1]) ).

fof(f_3453_3,plain,
    ! [U_13430,U_13431] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_13430,U_13431) = hAPP(c_Finite__Set_Ofold1(U_13430,c_Lattices_Osemilattice__inf__class_Oinf(U_13430)),U_13431)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13430),U_13431))
      | ~ class_Lattices_Olattice(U_13430) ),
    inference(definitional_conversion,[status(esa)],[f_3453_2]) ).

cnf(f_3453_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_13430,U_13431) = hAPP(c_Finite__Set_Ofold1(U_13430,c_Lattices_Osemilattice__inf__class_Oinf(U_13430)),U_13431)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13430),U_13431))
    | ~ class_Lattices_Olattice(U_13430) ),
    inference(clausify,[status(thm)],[f_3453_3]) ).

fof(f_3454_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_OF__eq]) ).

fof(f_3454_2,plain,
    ! [U_13433,U_13432] :
      ( c_Big__Operators_Olinorder__class_OMin(U_13432,U_13433) = hAPP(c_Finite__Set_Ofold1(U_13432,c_Orderings_Oord__class_Omin(U_13432)),U_13433)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13432),U_13433))
      | ~ class_Orderings_Olinorder(U_13432) ),
    inference(variable_rename,[status(thm)],[f_3454_1]) ).

fof(f_3454_3,plain,
    ! [U_13432,U_13433] :
      ( c_Big__Operators_Olinorder__class_OMin(U_13432,U_13433) = hAPP(c_Finite__Set_Ofold1(U_13432,c_Orderings_Oord__class_Omin(U_13432)),U_13433)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13432),U_13433))
      | ~ class_Orderings_Olinorder(U_13432) ),
    inference(definitional_conversion,[status(esa)],[f_3454_2]) ).

cnf(f_3454_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_13432,U_13433) = hAPP(c_Finite__Set_Ofold1(U_13432,c_Orderings_Oord__class_Omin(U_13432)),U_13433)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13432),U_13433))
    | ~ class_Orderings_Olinorder(U_13432) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

fof(f_3455_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_OF__eq]) ).

fof(f_3455_2,plain,
    ! [U_13435,U_13434] :
      ( c_Big__Operators_Olinorder__class_OMax(U_13434,U_13435) = hAPP(c_Finite__Set_Ofold1(U_13434,c_Orderings_Oord__class_Omax(U_13434)),U_13435)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13434),U_13435))
      | ~ class_Orderings_Olinorder(U_13434) ),
    inference(variable_rename,[status(thm)],[f_3455_1]) ).

fof(f_3455_3,plain,
    ! [U_13434,U_13435] :
      ( c_Big__Operators_Olinorder__class_OMax(U_13434,U_13435) = hAPP(c_Finite__Set_Ofold1(U_13434,c_Orderings_Oord__class_Omax(U_13434)),U_13435)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13434),U_13435))
      | ~ class_Orderings_Olinorder(U_13434) ),
    inference(definitional_conversion,[status(esa)],[f_3455_2]) ).

cnf(f_3455_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_13434,U_13435) = hAPP(c_Finite__Set_Ofold1(U_13434,c_Orderings_Oord__class_Omax(U_13434)),U_13435)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13434),U_13435))
    | ~ class_Orderings_Olinorder(U_13434) ),
    inference(clausify,[status(thm)],[f_3455_3]) ).

fof(f_3456_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq]) ).

fof(f_3456_2,plain,
    ! [U_13437,U_13436] :
      ( c_Big__Operators_Olattice_OInf__fin(U_13436,c_Orderings_Oord__class_Omin(U_13436),U_13437) = hAPP(c_Finite__Set_Ofold1(U_13436,c_Orderings_Oord__class_Omin(U_13436)),U_13437)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13436),U_13437))
      | ~ class_Orderings_Olinorder(U_13436) ),
    inference(variable_rename,[status(thm)],[f_3456_1]) ).

fof(f_3456_3,plain,
    ! [U_13436,U_13437] :
      ( c_Big__Operators_Olattice_OInf__fin(U_13436,c_Orderings_Oord__class_Omin(U_13436),U_13437) = hAPP(c_Finite__Set_Ofold1(U_13436,c_Orderings_Oord__class_Omin(U_13436)),U_13437)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13436),U_13437))
      | ~ class_Orderings_Olinorder(U_13436) ),
    inference(definitional_conversion,[status(esa)],[f_3456_2]) ).

cnf(f_3456_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_13436,c_Orderings_Oord__class_Omin(U_13436),U_13437) = hAPP(c_Finite__Set_Ofold1(U_13436,c_Orderings_Oord__class_Omin(U_13436)),U_13437)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13436),U_13437))
    | ~ class_Orderings_Olinorder(U_13436) ),
    inference(clausify,[status(thm)],[f_3456_3]) ).

fof(f_3457_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq]) ).

fof(f_3457_2,plain,
    ! [U_13439,U_13438] :
      ( c_Big__Operators_Olattice_OSup__fin(U_13438,c_Orderings_Oord__class_Omax(U_13438),U_13439) = hAPP(c_Finite__Set_Ofold1(U_13438,c_Orderings_Oord__class_Omax(U_13438)),U_13439)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13438),U_13439))
      | ~ class_Orderings_Olinorder(U_13438) ),
    inference(variable_rename,[status(thm)],[f_3457_1]) ).

fof(f_3457_3,plain,
    ! [U_13438,U_13439] :
      ( c_Big__Operators_Olattice_OSup__fin(U_13438,c_Orderings_Oord__class_Omax(U_13438),U_13439) = hAPP(c_Finite__Set_Ofold1(U_13438,c_Orderings_Oord__class_Omax(U_13438)),U_13439)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13438),U_13439))
      | ~ class_Orderings_Olinorder(U_13438) ),
    inference(definitional_conversion,[status(esa)],[f_3457_2]) ).

cnf(f_3457_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_13438,c_Orderings_Oord__class_Omax(U_13438),U_13439) = hAPP(c_Finite__Set_Ofold1(U_13438,c_Orderings_Oord__class_Omax(U_13438)),U_13439)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13438),U_13439))
    | ~ class_Orderings_Olinorder(U_13438) ),
    inference(clausify,[status(thm)],[f_3457_3]) ).

fof(f_3458_1,plain,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_insert__times__insert]) ).

fof(f_3458_2,plain,
    ! [U_13445,U_13444,U_13443,U_13442,U_13441,U_13440] : hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),hAPP(hAPP(c_Set_Oinsert(U_13440),U_13442),U_13443)),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),hAPP(hAPP(c_Set_Oinsert(U_13441),U_13444),U_13445))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13440,U_13441)),hAPP(hAPP(c_Product__Type_OPair(U_13440,U_13441),U_13442),U_13444)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13440,U_13441),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),U_13443),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),hAPP(hAPP(c_Set_Oinsert(U_13441),U_13444),U_13445)))),hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),hAPP(hAPP(c_Set_Oinsert(U_13440),U_13442),U_13443)),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),U_13445)))),
    inference(variable_rename,[status(thm)],[f_3458_1]) ).

fof(f_3458_3,plain,
    ! [U_13440,U_13441,U_13442,U_13443,U_13444,U_13445] : hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),hAPP(hAPP(c_Set_Oinsert(U_13440),U_13442),U_13443)),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),hAPP(hAPP(c_Set_Oinsert(U_13441),U_13444),U_13445))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13440,U_13441)),hAPP(hAPP(c_Product__Type_OPair(U_13440,U_13441),U_13442),U_13444)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13440,U_13441),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),U_13443),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),hAPP(hAPP(c_Set_Oinsert(U_13441),U_13444),U_13445)))),hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),hAPP(hAPP(c_Set_Oinsert(U_13440),U_13442),U_13443)),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),U_13445)))),
    inference(definitional_conversion,[status(esa)],[f_3458_2]) ).

cnf(f_3458_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),hAPP(hAPP(c_Set_Oinsert(U_13440),U_13442),U_13443)),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),hAPP(hAPP(c_Set_Oinsert(U_13441),U_13444),U_13445))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13440,U_13441)),hAPP(hAPP(c_Product__Type_OPair(U_13440,U_13441),U_13442),U_13444)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13440,U_13441),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),U_13443),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),hAPP(hAPP(c_Set_Oinsert(U_13441),U_13444),U_13445)))),hAPP(hAPP(c_Product__Type_OSigma(U_13440,U_13441),hAPP(hAPP(c_Set_Oinsert(U_13440),U_13442),U_13443)),hAPP(c_COMBK(tc_fun(U_13441,tc_HOL_Obool),U_13440),U_13445)))),
    inference(clausify,[status(thm)],[f_3458_3]) ).

fof(f_3459_1,plain,
    ! [V_X_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__equiv__class]) ).

fof(f_3459_2,plain,
    ! [U_13449,U_13448,U_13447,U_13446] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13446),U_13449))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13446,tc_HOL_Obool)),U_13449),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13446),U_13447),U_13448)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)),U_13448),hAPP(hAPP(c_Product__Type_OSigma(U_13446,U_13446),U_13447),hAPP(c_COMBK(tc_fun(U_13446,tc_HOL_Obool),U_13446),U_13447))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13446),U_13447)) ),
    inference(variable_rename,[status(thm)],[f_3459_1]) ).

fof(f_3459_3,plain,
    ! [U_13446,U_13447,U_13448,U_13449] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13446),U_13449))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13446,tc_HOL_Obool)),U_13449),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13446),U_13447),U_13448)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)),U_13448),hAPP(hAPP(c_Product__Type_OSigma(U_13446,U_13446),U_13447),hAPP(c_COMBK(tc_fun(U_13446,tc_HOL_Obool),U_13446),U_13447))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13446),U_13447)) ),
    inference(definitional_conversion,[status(esa)],[f_3459_2]) ).

cnf(f_3459_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13446),U_13449))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13446,tc_HOL_Obool)),U_13449),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13446),U_13447),U_13448)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)),U_13448),hAPP(hAPP(c_Product__Type_OSigma(U_13446,U_13446),U_13447),hAPP(c_COMBK(tc_fun(U_13446,tc_HOL_Obool),U_13446),U_13447))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13446),U_13447)) ),
    inference(clausify,[status(thm)],[f_3459_3]) ).

fof(f_3460_1,plain,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
    inference(fof_nnf,[status(thm)],[fact_UN__Times__distrib]) ).

fof(f_3460_2,plain,
    ! [U_13457,U_13456,U_13455,U_13454,U_13453,U_13452,U_13451,U_13450] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_13450,U_13451),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13450,U_13451),U_13454),hAPP(c_COMBK(tc_fun(U_13451,tc_HOL_Obool),U_13450),U_13455))),hAPP(c_Product__Type_Oprod_Oprod__case(U_13450,U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_13450,tc_fun(U_13451,tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool))),tc_fun(U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),tc_fun(tc_fun(U_13451,tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool))),tc_fun(U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool))),U_13450),c_COMBB(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool),U_13451)),hAPP(hAPP(c_COMBB(tc_fun(U_13452,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),U_13450),c_Product__Type_OSigma(U_13452,U_13453)),U_13456))),hAPP(hAPP(c_COMBB(tc_fun(U_13453,tc_HOL_Obool),tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),U_13451),c_COMBK(tc_fun(U_13453,tc_HOL_Obool),U_13452)),U_13457)))) = hAPP(hAPP(c_Product__Type_OSigma(U_13452,U_13453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,tc_fun(U_13452,tc_HOL_Obool)),U_13454),U_13456)),hAPP(c_COMBK(tc_fun(U_13453,tc_HOL_Obool),U_13452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13451,tc_fun(U_13453,tc_HOL_Obool)),U_13455),U_13457))),
    inference(variable_rename,[status(thm)],[f_3460_1]) ).

fof(f_3460_3,plain,
    ! [U_13450,U_13451,U_13452,U_13453,U_13454,U_13455,U_13456,U_13457] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_13450,U_13451),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13450,U_13451),U_13454),hAPP(c_COMBK(tc_fun(U_13451,tc_HOL_Obool),U_13450),U_13455))),hAPP(c_Product__Type_Oprod_Oprod__case(U_13450,U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_13450,tc_fun(U_13451,tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool))),tc_fun(U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),tc_fun(tc_fun(U_13451,tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool))),tc_fun(U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool))),U_13450),c_COMBB(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool),U_13451)),hAPP(hAPP(c_COMBB(tc_fun(U_13452,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),U_13450),c_Product__Type_OSigma(U_13452,U_13453)),U_13456))),hAPP(hAPP(c_COMBB(tc_fun(U_13453,tc_HOL_Obool),tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),U_13451),c_COMBK(tc_fun(U_13453,tc_HOL_Obool),U_13452)),U_13457)))) = hAPP(hAPP(c_Product__Type_OSigma(U_13452,U_13453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,tc_fun(U_13452,tc_HOL_Obool)),U_13454),U_13456)),hAPP(c_COMBK(tc_fun(U_13453,tc_HOL_Obool),U_13452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13451,tc_fun(U_13453,tc_HOL_Obool)),U_13455),U_13457))),
    inference(definitional_conversion,[status(esa)],[f_3460_2]) ).

cnf(f_3460_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_13450,U_13451),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13450,U_13451),U_13454),hAPP(c_COMBK(tc_fun(U_13451,tc_HOL_Obool),U_13450),U_13455))),hAPP(c_Product__Type_Oprod_Oprod__case(U_13450,U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_13450,tc_fun(U_13451,tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool))),tc_fun(U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),tc_fun(tc_fun(U_13451,tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool))),tc_fun(U_13451,tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool))),U_13450),c_COMBB(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool),U_13451)),hAPP(hAPP(c_COMBB(tc_fun(U_13452,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),tc_fun(tc_prod(U_13452,U_13453),tc_HOL_Obool)),U_13450),c_Product__Type_OSigma(U_13452,U_13453)),U_13456))),hAPP(hAPP(c_COMBB(tc_fun(U_13453,tc_HOL_Obool),tc_fun(U_13452,tc_fun(U_13453,tc_HOL_Obool)),U_13451),c_COMBK(tc_fun(U_13453,tc_HOL_Obool),U_13452)),U_13457)))) = hAPP(hAPP(c_Product__Type_OSigma(U_13452,U_13453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,tc_fun(U_13452,tc_HOL_Obool)),U_13454),U_13456)),hAPP(c_COMBK(tc_fun(U_13453,tc_HOL_Obool),U_13452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13451,tc_fun(U_13453,tc_HOL_Obool)),U_13455),U_13457))),
    inference(clausify,[status(thm)],[f_3460_3]) ).

fof(f_3461_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Sigma__def]) ).

fof(f_3461_2,plain,
    ! [U_13461,U_13460,U_13459,U_13458] : hAPP(hAPP(c_Product__Type_OSigma(U_13458,U_13459),U_13460),U_13461) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13460),hAPP(hAPP(c_COMBS(U_13458,tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_HOL_Obool),tc_fun(tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13458),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13461)),hAPP(hAPP(c_COMBC(U_13458,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13458),c_COMBC(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_prod(U_13458,U_13459)),tc_fun(U_13459,tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13458),hAPP(c_COMBB(tc_prod(U_13458,U_13459),tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13459),c_Set_Oinsert(tc_prod(U_13458,U_13459)))),c_Product__Type_OPair(U_13458,U_13459)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3461_1]) ).

fof(f_3461_3,plain,
    ! [U_13458,U_13459,U_13460,U_13461] : hAPP(hAPP(c_Product__Type_OSigma(U_13458,U_13459),U_13460),U_13461) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13460),hAPP(hAPP(c_COMBS(U_13458,tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_HOL_Obool),tc_fun(tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13458),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13461)),hAPP(hAPP(c_COMBC(U_13458,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13458),c_COMBC(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_prod(U_13458,U_13459)),tc_fun(U_13459,tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13458),hAPP(c_COMBB(tc_prod(U_13458,U_13459),tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13459),c_Set_Oinsert(tc_prod(U_13458,U_13459)))),c_Product__Type_OPair(U_13458,U_13459)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3461_2]) ).

cnf(f_3461_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13458,U_13459),U_13460),U_13461) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13460),hAPP(hAPP(c_COMBS(U_13458,tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_HOL_Obool),tc_fun(tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13458),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13461)),hAPP(hAPP(c_COMBC(U_13458,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13458),c_COMBC(U_13459,tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13459,tc_prod(U_13458,U_13459)),tc_fun(U_13459,tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))),U_13458),hAPP(c_COMBB(tc_prod(U_13458,U_13459),tc_fun(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool),tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool)),U_13459),c_Set_Oinsert(tc_prod(U_13458,U_13459)))),c_Product__Type_OPair(U_13458,U_13459)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13459),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3461_3]) ).

fof(f_3462_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__belowI]) ).

fof(f_3462_2,plain,
    ! [U_13464,U_13463,U_13462] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13462),hAPP(c_Finite__Set_Ofold1(U_13462,c_Lattices_Osemilattice__inf__class_Oinf(U_13462)),U_13463)),U_13464))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13462),U_13464),U_13463))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13462),U_13463))
      | ~ class_Lattices_Osemilattice__inf(U_13462) ),
    inference(variable_rename,[status(thm)],[f_3462_1]) ).

fof(f_3462_3,plain,
    ! [U_13462,U_13463,U_13464] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13462),hAPP(c_Finite__Set_Ofold1(U_13462,c_Lattices_Osemilattice__inf__class_Oinf(U_13462)),U_13463)),U_13464))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13462),U_13464),U_13463))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13462),U_13463))
      | ~ class_Lattices_Osemilattice__inf(U_13462) ),
    inference(definitional_conversion,[status(esa)],[f_3462_2]) ).

cnf(f_3462_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13462),hAPP(c_Finite__Set_Ofold1(U_13462,c_Lattices_Osemilattice__inf__class_Oinf(U_13462)),U_13463)),U_13464))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13462),U_13464),U_13463))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13462),U_13463))
    | ~ class_Lattices_Osemilattice__inf(U_13462) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

fof(f_3463_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__quotient]) ).

fof(f_3463_2,plain,
    ! [U_13467,U_13466,U_13465] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13465,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13465),U_13466),U_13467)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13465,U_13465),tc_HOL_Obool)),U_13467),hAPP(hAPP(c_Product__Type_OSigma(U_13465,U_13465),U_13466),hAPP(c_COMBK(tc_fun(U_13465,tc_HOL_Obool),U_13465),U_13466))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13465),U_13466)) ),
    inference(variable_rename,[status(thm)],[f_3463_1]) ).

fof(f_3463_3,plain,
    ! [U_13465,U_13466,U_13467] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13465,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13465),U_13466),U_13467)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13465,U_13465),tc_HOL_Obool)),U_13467),hAPP(hAPP(c_Product__Type_OSigma(U_13465,U_13465),U_13466),hAPP(c_COMBK(tc_fun(U_13465,tc_HOL_Obool),U_13465),U_13466))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13465),U_13466)) ),
    inference(definitional_conversion,[status(esa)],[f_3463_2]) ).

cnf(f_3463_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13465,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13465),U_13466),U_13467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13465,U_13465),tc_HOL_Obool)),U_13467),hAPP(hAPP(c_Product__Type_OSigma(U_13465,U_13465),U_13466),hAPP(c_COMBK(tc_fun(U_13465,tc_HOL_Obool),U_13465),U_13466))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13465),U_13466)) ),
    inference(clausify,[status(thm)],[f_3463_3]) ).

fof(f_3464_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_below__fold1__iff]) ).

fof(f_3464_2,plain,
    ! [U_13472,U_13471,U_13470] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471)))
          | ? [U_13469] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),U_13469))
              & hBOOL(hAPP(hAPP(c_member(U_13470),U_13469),U_13471)) ) )
        & ( ! [U_13468] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),U_13468))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13468),U_13471)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471))) ) )
      | U_13471 = c_Orderings_Obot__class_Obot(tc_fun(U_13470,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13470),U_13471))
      | ~ class_Lattices_Osemilattice__inf(U_13470) ),
    inference(variable_rename,[status(thm)],[f_3464_1]) ).

fof(f_3464_3,plain,
    ! [U_13472,U_13471,U_13470] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),sK290(U_13472,U_13471,U_13470)))
            & hBOOL(hAPP(hAPP(c_member(U_13470),sK290(U_13472,U_13471,U_13470)),U_13471)) ) )
        & ( ! [U_13468] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),U_13468))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13468),U_13471)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471))) ) )
      | U_13471 = c_Orderings_Obot__class_Obot(tc_fun(U_13470,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13470),U_13471))
      | ~ class_Lattices_Osemilattice__inf(U_13470) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_13469,sK290(U_13472,U_13471,U_13470))],[f_3464_2]) ).

fof(f_3464_4,plain,
    ( ! [U_13470,U_13471,U_13472] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),sK290(U_13472,U_13471,U_13470)))
        | ~ sP968(U_13470,U_13471,U_13472) )
    & ! [U_13470,U_13471,U_13472] :
        ( hBOOL(hAPP(hAPP(c_member(U_13470),sK290(U_13472,U_13471,U_13470)),U_13471))
        | ~ sP968(U_13470,U_13471,U_13472) )
    & ! [U_13468,U_13470,U_13471,U_13472] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471)))
        | sP968(U_13470,U_13471,U_13472)
        | ~ sP969(U_13468,U_13470,U_13471,U_13472) )
    & ! [U_13468,U_13470,U_13471,U_13472] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),U_13468))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13468),U_13471))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471)))
        | ~ sP969(U_13468,U_13470,U_13471,U_13472) )
    & ! [U_13468,U_13470,U_13471,U_13472] :
        ( sP969(U_13468,U_13470,U_13471,U_13472)
        | U_13471 = c_Orderings_Obot__class_Obot(tc_fun(U_13470,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13470),U_13471))
        | ~ class_Lattices_Osemilattice__inf(U_13470) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP968,sP969])],[f_3464_3]) ).

cnf(f_3464_5,plain,
    ( sP969(U_13468,U_13470,U_13471,U_13472)
    | U_13471 = c_Orderings_Obot__class_Obot(tc_fun(U_13470,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13470),U_13471))
    | ~ class_Lattices_Osemilattice__inf(U_13470) ),
    inference(clausify,[status(thm)],[f_3464_4]) ).

cnf(f_3464_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),U_13468))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13468),U_13471))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471)))
    | ~ sP969(U_13468,U_13470,U_13471,U_13472) ),
    inference(clausify,[status(thm)],[f_3464_4]) ).

cnf(f_3464_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),hAPP(c_Finite__Set_Ofold1(U_13470,c_Lattices_Osemilattice__inf__class_Oinf(U_13470)),U_13471)))
    | sP968(U_13470,U_13471,U_13472)
    | ~ sP969(U_13468,U_13470,U_13471,U_13472) ),
    inference(clausify,[status(thm)],[f_3464_4]) ).

cnf(f_3464_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13470),sK290(U_13472,U_13471,U_13470)),U_13471))
    | ~ sP968(U_13470,U_13471,U_13472) ),
    inference(clausify,[status(thm)],[f_3464_4]) ).

cnf(f_3464_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13470),U_13472),sK290(U_13472,U_13471,U_13470)))
    | ~ sP968(U_13470,U_13471,U_13472) ),
    inference(clausify,[status(thm)],[f_3464_4]) ).

fof(f_3465_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI]) ).

fof(f_3465_2,plain,
    ! [U_13475,U_13474,U_13473] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13473),hAPP(c_Finite__Set_Ofold1(U_13473,c_Orderings_Oord__class_Omin(U_13473)),U_13474)),U_13475))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13475),U_13474))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13473),U_13474))
      | ~ class_Orderings_Olinorder(U_13473) ),
    inference(variable_rename,[status(thm)],[f_3465_1]) ).

fof(f_3465_3,plain,
    ! [U_13474,U_13475,U_13473] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13473),hAPP(c_Finite__Set_Ofold1(U_13473,c_Orderings_Oord__class_Omin(U_13473)),U_13474)),U_13475))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13475),U_13474))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13473),U_13474))
      | ~ class_Orderings_Olinorder(U_13473) ),
    inference(definitional_conversion,[status(esa)],[f_3465_2]) ).

cnf(f_3465_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13473),hAPP(c_Finite__Set_Ofold1(U_13473,c_Orderings_Oord__class_Omin(U_13473)),U_13474)),U_13475))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13475),U_13474))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13473),U_13474))
    | ~ class_Orderings_Olinorder(U_13473) ),
    inference(clausify,[status(thm)],[f_3465_3]) ).

fof(f_3466_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem]) ).

fof(f_3466_2,plain,
    ! [U_13478,U_13477,U_13476] :
      ( hAPP(c_Finite__Set_Ofold1(U_13476,c_Groups_Otimes__class_Otimes(U_13476)),hAPP(hAPP(c_Set_Oinsert(U_13476),U_13478),U_13477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13476),U_13478),hAPP(c_Finite__Set_Ofold1(U_13476,c_Groups_Otimes__class_Otimes(U_13476)),U_13477))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13476),U_13477))
      | U_13477 = c_Orderings_Obot__class_Obot(tc_fun(U_13476,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13476) ),
    inference(variable_rename,[status(thm)],[f_3466_1]) ).

fof(f_3466_3,plain,
    ! [U_13476,U_13477,U_13478] :
      ( hAPP(c_Finite__Set_Ofold1(U_13476,c_Groups_Otimes__class_Otimes(U_13476)),hAPP(hAPP(c_Set_Oinsert(U_13476),U_13478),U_13477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13476),U_13478),hAPP(c_Finite__Set_Ofold1(U_13476,c_Groups_Otimes__class_Otimes(U_13476)),U_13477))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13476),U_13477))
      | U_13477 = c_Orderings_Obot__class_Obot(tc_fun(U_13476,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13476) ),
    inference(definitional_conversion,[status(esa)],[f_3466_2]) ).

cnf(f_3466_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_13476,c_Groups_Otimes__class_Otimes(U_13476)),hAPP(hAPP(c_Set_Oinsert(U_13476),U_13478),U_13477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13476),U_13478),hAPP(c_Finite__Set_Ofold1(U_13476,c_Groups_Otimes__class_Otimes(U_13476)),U_13477))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13476),U_13477))
    | U_13477 = c_Orderings_Obot__class_Obot(tc_fun(U_13476,tc_HOL_Obool))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_13476) ),
    inference(clausify,[status(thm)],[f_3466_3]) ).

fof(f_3467_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__below__iff]) ).

fof(f_3467_2,plain,
    ! [U_13483,U_13482,U_13481] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483))
          | ! [U_13480] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),U_13480),U_13483))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13481),U_13480),U_13482)) ) )
        & ( ? [U_13479] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),U_13479),U_13483))
              & hBOOL(hAPP(hAPP(c_member(U_13481),U_13479),U_13482)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483)) ) )
      | U_13482 = c_Orderings_Obot__class_Obot(tc_fun(U_13481,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13481),U_13482))
      | ~ class_Orderings_Olinorder(U_13481) ),
    inference(variable_rename,[status(thm)],[f_3467_1]) ).

fof(f_3467_3,plain,
    ! [U_13483,U_13482,U_13481] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483))
          | ! [U_13480] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),U_13480),U_13483))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13481),U_13480),U_13482)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),sK291(U_13483,U_13482,U_13481)),U_13483))
            & hBOOL(hAPP(hAPP(c_member(U_13481),sK291(U_13483,U_13482,U_13481)),U_13482)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483)) ) )
      | U_13482 = c_Orderings_Obot__class_Obot(tc_fun(U_13481,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13481),U_13482))
      | ~ class_Orderings_Olinorder(U_13481) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_13479,sK291(U_13483,U_13482,U_13481))],[f_3467_2]) ).

fof(f_3467_4,plain,
    ( ! [U_13481,U_13482,U_13483] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),sK291(U_13483,U_13482,U_13481)),U_13483))
        | ~ sP970(U_13481,U_13482,U_13483) )
    & ! [U_13481,U_13482,U_13483] :
        ( hBOOL(hAPP(hAPP(c_member(U_13481),sK291(U_13483,U_13482,U_13481)),U_13482))
        | ~ sP970(U_13481,U_13482,U_13483) )
    & ! [U_13480,U_13481,U_13482,U_13483] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),U_13480),U_13483))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13481),U_13480),U_13482))
        | ~ sP971(U_13480,U_13481,U_13482,U_13483) )
    & ! [U_13480,U_13481,U_13482,U_13483] :
        ( sP970(U_13481,U_13482,U_13483)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483))
        | ~ sP971(U_13480,U_13481,U_13482,U_13483) )
    & ! [U_13480,U_13481,U_13482,U_13483] :
        ( sP971(U_13480,U_13481,U_13482,U_13483)
        | U_13482 = c_Orderings_Obot__class_Obot(tc_fun(U_13481,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13481),U_13482))
        | ~ class_Orderings_Olinorder(U_13481) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP970,sP971])],[f_3467_3]) ).

cnf(f_3467_5,plain,
    ( sP971(U_13480,U_13481,U_13482,U_13483)
    | U_13482 = c_Orderings_Obot__class_Obot(tc_fun(U_13481,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13481),U_13482))
    | ~ class_Orderings_Olinorder(U_13481) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_6,plain,
    ( sP970(U_13481,U_13482,U_13483)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483))
    | ~ sP971(U_13480,U_13481,U_13482,U_13483) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),hAPP(c_Finite__Set_Ofold1(U_13481,c_Orderings_Oord__class_Omin(U_13481)),U_13482)),U_13483))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),U_13480),U_13483))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13481),U_13480),U_13482))
    | ~ sP971(U_13480,U_13481,U_13482,U_13483) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13481),sK291(U_13483,U_13482,U_13481)),U_13482))
    | ~ sP970(U_13481,U_13482,U_13483) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13481),sK291(U_13483,U_13482,U_13481)),U_13483))
    | ~ sP970(U_13481,U_13482,U_13483) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

fof(f_3468_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff]) ).

fof(f_3468_2,plain,
    ! [U_13488,U_13487,U_13486] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487)))
          | ? [U_13485] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),U_13485))
              & hBOOL(hAPP(hAPP(c_member(U_13486),U_13485),U_13487)) ) )
        & ( ! [U_13484] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),U_13484))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13486),U_13484),U_13487)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487))) ) )
      | U_13487 = c_Orderings_Obot__class_Obot(tc_fun(U_13486,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13486),U_13487))
      | ~ class_Orderings_Olinorder(U_13486) ),
    inference(variable_rename,[status(thm)],[f_3468_1]) ).

fof(f_3468_3,plain,
    ! [U_13488,U_13487,U_13486] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),sK292(U_13488,U_13487,U_13486)))
            & hBOOL(hAPP(hAPP(c_member(U_13486),sK292(U_13488,U_13487,U_13486)),U_13487)) ) )
        & ( ! [U_13484] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),U_13484))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13486),U_13484),U_13487)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487))) ) )
      | U_13487 = c_Orderings_Obot__class_Obot(tc_fun(U_13486,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13486),U_13487))
      | ~ class_Orderings_Olinorder(U_13486) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_13485,sK292(U_13488,U_13487,U_13486))],[f_3468_2]) ).

fof(f_3468_4,plain,
    ( ! [U_13486,U_13487,U_13488] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),sK292(U_13488,U_13487,U_13486)))
        | ~ sP972(U_13486,U_13487,U_13488) )
    & ! [U_13486,U_13487,U_13488] :
        ( hBOOL(hAPP(hAPP(c_member(U_13486),sK292(U_13488,U_13487,U_13486)),U_13487))
        | ~ sP972(U_13486,U_13487,U_13488) )
    & ! [U_13486,U_13484,U_13487,U_13488] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487)))
        | sP972(U_13486,U_13487,U_13488)
        | ~ sP973(U_13486,U_13484,U_13487,U_13488) )
    & ! [U_13486,U_13484,U_13487,U_13488] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),U_13484))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13486),U_13484),U_13487))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487)))
        | ~ sP973(U_13486,U_13484,U_13487,U_13488) )
    & ! [U_13486,U_13484,U_13487,U_13488] :
        ( sP973(U_13486,U_13484,U_13487,U_13488)
        | U_13487 = c_Orderings_Obot__class_Obot(tc_fun(U_13486,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13486),U_13487))
        | ~ class_Orderings_Olinorder(U_13486) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP972,sP973])],[f_3468_3]) ).

cnf(f_3468_5,plain,
    ( sP973(U_13486,U_13484,U_13487,U_13488)
    | U_13487 = c_Orderings_Obot__class_Obot(tc_fun(U_13486,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13486),U_13487))
    | ~ class_Orderings_Olinorder(U_13486) ),
    inference(clausify,[status(thm)],[f_3468_4]) ).

cnf(f_3468_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),U_13484))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13486),U_13484),U_13487))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487)))
    | ~ sP973(U_13486,U_13484,U_13487,U_13488) ),
    inference(clausify,[status(thm)],[f_3468_4]) ).

cnf(f_3468_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),hAPP(c_Finite__Set_Ofold1(U_13486,c_Orderings_Oord__class_Omin(U_13486)),U_13487)))
    | sP972(U_13486,U_13487,U_13488)
    | ~ sP973(U_13486,U_13484,U_13487,U_13488) ),
    inference(clausify,[status(thm)],[f_3468_4]) ).

cnf(f_3468_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13486),sK292(U_13488,U_13487,U_13486)),U_13487))
    | ~ sP972(U_13486,U_13487,U_13488) ),
    inference(clausify,[status(thm)],[f_3468_4]) ).

cnf(f_3468_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13486),U_13488),sK292(U_13488,U_13487,U_13486)))
    | ~ sP972(U_13486,U_13487,U_13488) ),
    inference(clausify,[status(thm)],[f_3468_4]) ).

fof(f_3469_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__Un2]) ).

fof(f_3469_2,plain,
    ! [U_13491,U_13490,U_13489] :
      ( hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13489,tc_HOL_Obool)),U_13490),U_13491)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13489),hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),U_13490)),hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),U_13491))
      | U_13491 = c_Orderings_Obot__class_Obot(tc_fun(U_13489,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13489),U_13491))
      | U_13490 = c_Orderings_Obot__class_Obot(tc_fun(U_13489,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13489),U_13490))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13489) ),
    inference(variable_rename,[status(thm)],[f_3469_1]) ).

fof(f_3469_3,plain,
    ! [U_13490,U_13491,U_13489] :
      ( hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13489,tc_HOL_Obool)),U_13490),U_13491)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13489),hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),U_13490)),hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),U_13491))
      | U_13491 = c_Orderings_Obot__class_Obot(tc_fun(U_13489,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13489),U_13491))
      | U_13490 = c_Orderings_Obot__class_Obot(tc_fun(U_13489,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13489),U_13490))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13489) ),
    inference(definitional_conversion,[status(esa)],[f_3469_2]) ).

cnf(f_3469_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13489,tc_HOL_Obool)),U_13490),U_13491)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13489),hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),U_13490)),hAPP(c_Finite__Set_Ofold1(U_13489,c_Groups_Otimes__class_Otimes(U_13489)),U_13491))
    | U_13491 = c_Orderings_Obot__class_Obot(tc_fun(U_13489,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13489),U_13491))
    | U_13490 = c_Orderings_Obot__class_Obot(tc_fun(U_13489,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13489),U_13490))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_13489) ),
    inference(clausify,[status(thm)],[f_3469_3]) ).

fof(f_3470_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff]) ).

fof(f_3470_2,plain,
    ! [U_13496,U_13495,U_13494] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496))
          | ! [U_13493] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),U_13493),U_13496))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13494),U_13493),U_13495)) ) )
        & ( ? [U_13492] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),U_13492),U_13496))
              & hBOOL(hAPP(hAPP(c_member(U_13494),U_13492),U_13495)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496)) ) )
      | U_13495 = c_Orderings_Obot__class_Obot(tc_fun(U_13494,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13494),U_13495))
      | ~ class_Orderings_Olinorder(U_13494) ),
    inference(variable_rename,[status(thm)],[f_3470_1]) ).

fof(f_3470_3,plain,
    ! [U_13496,U_13495,U_13494] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496))
          | ! [U_13493] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),U_13493),U_13496))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13494),U_13493),U_13495)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),sK293(U_13496,U_13495,U_13494)),U_13496))
            & hBOOL(hAPP(hAPP(c_member(U_13494),sK293(U_13496,U_13495,U_13494)),U_13495)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496)) ) )
      | U_13495 = c_Orderings_Obot__class_Obot(tc_fun(U_13494,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13494),U_13495))
      | ~ class_Orderings_Olinorder(U_13494) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_13492,sK293(U_13496,U_13495,U_13494))],[f_3470_2]) ).

fof(f_3470_4,plain,
    ( ! [U_13495,U_13494,U_13496] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),sK293(U_13496,U_13495,U_13494)),U_13496))
        | ~ sP974(U_13495,U_13494,U_13496) )
    & ! [U_13495,U_13494,U_13496] :
        ( hBOOL(hAPP(hAPP(c_member(U_13494),sK293(U_13496,U_13495,U_13494)),U_13495))
        | ~ sP974(U_13495,U_13494,U_13496) )
    & ! [U_13495,U_13493,U_13494,U_13496] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),U_13493),U_13496))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13494),U_13493),U_13495))
        | ~ sP975(U_13495,U_13493,U_13494,U_13496) )
    & ! [U_13495,U_13493,U_13494,U_13496] :
        ( sP974(U_13495,U_13494,U_13496)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496))
        | ~ sP975(U_13495,U_13493,U_13494,U_13496) )
    & ! [U_13495,U_13493,U_13494,U_13496] :
        ( sP975(U_13495,U_13493,U_13494,U_13496)
        | U_13495 = c_Orderings_Obot__class_Obot(tc_fun(U_13494,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13494),U_13495))
        | ~ class_Orderings_Olinorder(U_13494) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP974,sP975])],[f_3470_3]) ).

cnf(f_3470_5,plain,
    ( sP975(U_13495,U_13493,U_13494,U_13496)
    | U_13495 = c_Orderings_Obot__class_Obot(tc_fun(U_13494,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13494),U_13495))
    | ~ class_Orderings_Olinorder(U_13494) ),
    inference(clausify,[status(thm)],[f_3470_4]) ).

cnf(f_3470_6,plain,
    ( sP974(U_13495,U_13494,U_13496)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496))
    | ~ sP975(U_13495,U_13493,U_13494,U_13496) ),
    inference(clausify,[status(thm)],[f_3470_4]) ).

cnf(f_3470_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),hAPP(c_Finite__Set_Ofold1(U_13494,c_Orderings_Oord__class_Omin(U_13494)),U_13495)),U_13496))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),U_13493),U_13496))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13494),U_13493),U_13495))
    | ~ sP975(U_13495,U_13493,U_13494,U_13496) ),
    inference(clausify,[status(thm)],[f_3470_4]) ).

cnf(f_3470_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13494),sK293(U_13496,U_13495,U_13494)),U_13495))
    | ~ sP974(U_13495,U_13494,U_13496) ),
    inference(clausify,[status(thm)],[f_3470_4]) ).

cnf(f_3470_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13494),sK293(U_13496,U_13495,U_13494)),U_13496))
    | ~ sP974(U_13495,U_13494,U_13496) ),
    inference(clausify,[status(thm)],[f_3470_4]) ).

fof(f_3471_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff]) ).

fof(f_3471_2,plain,
    ! [U_13501,U_13500,U_13499] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500)))
          | ? [U_13498] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),U_13498))
              & hBOOL(hAPP(hAPP(c_member(U_13499),U_13498),U_13500)) ) )
        & ( ! [U_13497] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),U_13497))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13499),U_13497),U_13500)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500))) ) )
      | U_13500 = c_Orderings_Obot__class_Obot(tc_fun(U_13499,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13499),U_13500))
      | ~ class_Orderings_Olinorder(U_13499) ),
    inference(variable_rename,[status(thm)],[f_3471_1]) ).

fof(f_3471_3,plain,
    ! [U_13501,U_13500,U_13499] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),sK294(U_13501,U_13500,U_13499)))
            & hBOOL(hAPP(hAPP(c_member(U_13499),sK294(U_13501,U_13500,U_13499)),U_13500)) ) )
        & ( ! [U_13497] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),U_13497))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13499),U_13497),U_13500)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500))) ) )
      | U_13500 = c_Orderings_Obot__class_Obot(tc_fun(U_13499,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13499),U_13500))
      | ~ class_Orderings_Olinorder(U_13499) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_13498,sK294(U_13501,U_13500,U_13499))],[f_3471_2]) ).

fof(f_3471_4,plain,
    ( ! [U_13500,U_13499,U_13501] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),sK294(U_13501,U_13500,U_13499)))
        | ~ sP976(U_13500,U_13499,U_13501) )
    & ! [U_13500,U_13499,U_13501] :
        ( hBOOL(hAPP(hAPP(c_member(U_13499),sK294(U_13501,U_13500,U_13499)),U_13500))
        | ~ sP976(U_13500,U_13499,U_13501) )
    & ! [U_13500,U_13499,U_13501,U_13497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500)))
        | sP976(U_13500,U_13499,U_13501)
        | ~ sP977(U_13500,U_13499,U_13501,U_13497) )
    & ! [U_13500,U_13499,U_13501,U_13497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),U_13497))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13499),U_13497),U_13500))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500)))
        | ~ sP977(U_13500,U_13499,U_13501,U_13497) )
    & ! [U_13500,U_13499,U_13501,U_13497] :
        ( sP977(U_13500,U_13499,U_13501,U_13497)
        | U_13500 = c_Orderings_Obot__class_Obot(tc_fun(U_13499,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13499),U_13500))
        | ~ class_Orderings_Olinorder(U_13499) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP976,sP977])],[f_3471_3]) ).

cnf(f_3471_5,plain,
    ( sP977(U_13500,U_13499,U_13501,U_13497)
    | U_13500 = c_Orderings_Obot__class_Obot(tc_fun(U_13499,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13499),U_13500))
    | ~ class_Orderings_Olinorder(U_13499) ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

cnf(f_3471_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),U_13497))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13499),U_13497),U_13500))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500)))
    | ~ sP977(U_13500,U_13499,U_13501,U_13497) ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

cnf(f_3471_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),hAPP(c_Finite__Set_Ofold1(U_13499,c_Orderings_Oord__class_Omin(U_13499)),U_13500)))
    | sP976(U_13500,U_13499,U_13501)
    | ~ sP977(U_13500,U_13499,U_13501,U_13497) ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

cnf(f_3471_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13499),sK294(U_13501,U_13500,U_13499)),U_13500))
    | ~ sP976(U_13500,U_13499,U_13501) ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

cnf(f_3471_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13499),U_13501),sK294(U_13501,U_13500,U_13499)))
    | ~ sP976(U_13500,U_13499,U_13501) ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

fof(f_3472_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__insert]) ).

fof(f_3472_2,plain,
    ! [U_13504,U_13503,U_13502] :
      ( hAPP(c_Finite__Set_Ofold1(U_13502,c_Groups_Otimes__class_Otimes(U_13502)),hAPP(hAPP(c_Set_Oinsert(U_13502),U_13504),U_13503)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13502),U_13504),hAPP(c_Finite__Set_Ofold1(U_13502,c_Groups_Otimes__class_Otimes(U_13502)),U_13503))
      | hBOOL(hAPP(hAPP(c_member(U_13502),U_13504),U_13503))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13502),U_13503))
      | U_13503 = c_Orderings_Obot__class_Obot(tc_fun(U_13502,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_13502) ),
    inference(variable_rename,[status(thm)],[f_3472_1]) ).

fof(f_3472_3,plain,
    ! [U_13504,U_13503,U_13502] :
      ( hAPP(c_Finite__Set_Ofold1(U_13502,c_Groups_Otimes__class_Otimes(U_13502)),hAPP(hAPP(c_Set_Oinsert(U_13502),U_13504),U_13503)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13502),U_13504),hAPP(c_Finite__Set_Ofold1(U_13502,c_Groups_Otimes__class_Otimes(U_13502)),U_13503))
      | hBOOL(hAPP(hAPP(c_member(U_13502),U_13504),U_13503))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13502),U_13503))
      | U_13503 = c_Orderings_Obot__class_Obot(tc_fun(U_13502,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_13502) ),
    inference(definitional_conversion,[status(esa)],[f_3472_2]) ).

cnf(f_3472_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_13502,c_Groups_Otimes__class_Otimes(U_13502)),hAPP(hAPP(c_Set_Oinsert(U_13502),U_13504),U_13503)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13502),U_13504),hAPP(c_Finite__Set_Ofold1(U_13502,c_Groups_Otimes__class_Otimes(U_13502)),U_13503))
    | hBOOL(hAPP(hAPP(c_member(U_13502),U_13504),U_13503))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13502),U_13503))
    | U_13503 = c_Orderings_Obot__class_Obot(tc_fun(U_13502,tc_HOL_Obool))
    | ~ class_Groups_Oab__semigroup__mult(U_13502) ),
    inference(clausify,[status(thm)],[f_3472_3]) ).

fof(f_3473_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__antimono]) ).

fof(f_3473_2,plain,
    ! [U_13507,U_13506,U_13505] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13505),hAPP(c_Finite__Set_Ofold1(U_13505,c_Orderings_Oord__class_Omin(U_13505)),U_13507)),hAPP(c_Finite__Set_Ofold1(U_13505,c_Orderings_Oord__class_Omin(U_13505)),U_13506)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13505),U_13507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13505,tc_HOL_Obool)),U_13506),U_13507))
      | U_13506 = c_Orderings_Obot__class_Obot(tc_fun(U_13505,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_13505) ),
    inference(variable_rename,[status(thm)],[f_3473_1]) ).

fof(f_3473_3,plain,
    ! [U_13507,U_13505,U_13506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13505),hAPP(c_Finite__Set_Ofold1(U_13505,c_Orderings_Oord__class_Omin(U_13505)),U_13507)),hAPP(c_Finite__Set_Ofold1(U_13505,c_Orderings_Oord__class_Omin(U_13505)),U_13506)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13505),U_13507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13505,tc_HOL_Obool)),U_13506),U_13507))
      | U_13506 = c_Orderings_Obot__class_Obot(tc_fun(U_13505,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_13505) ),
    inference(definitional_conversion,[status(esa)],[f_3473_2]) ).

cnf(f_3473_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13505),hAPP(c_Finite__Set_Ofold1(U_13505,c_Orderings_Oord__class_Omin(U_13505)),U_13507)),hAPP(c_Finite__Set_Ofold1(U_13505,c_Orderings_Oord__class_Omin(U_13505)),U_13506)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13505),U_13507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13505,tc_HOL_Obool)),U_13506),U_13507))
    | U_13506 = c_Orderings_Obot__class_Obot(tc_fun(U_13505,tc_HOL_Obool))
    | ~ class_Orderings_Olinorder(U_13505) ),
    inference(clausify,[status(thm)],[f_3473_3]) ).

fof(f_3474_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq]) ).

fof(f_3474_2,plain,
    ! [U_13511,U_13510,U_13509,U_13508] :
      ( hAPP(U_13510,U_13511) = hAPP(c_Finite__Set_Ofold1(U_13508,U_13509),U_13511)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13508),U_13511))
      | ~ c_Big__Operators_Osemilattice__big(U_13508,U_13509,U_13510) ),
    inference(variable_rename,[status(thm)],[f_3474_1]) ).

fof(f_3474_3,plain,
    ! [U_13508,U_13510,U_13509,U_13511] :
      ( hAPP(U_13510,U_13511) = hAPP(c_Finite__Set_Ofold1(U_13508,U_13509),U_13511)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13508),U_13511))
      | ~ c_Big__Operators_Osemilattice__big(U_13508,U_13509,U_13510) ),
    inference(definitional_conversion,[status(esa)],[f_3474_2]) ).

cnf(f_3474_4,plain,
    ( hAPP(U_13510,U_13511) = hAPP(c_Finite__Set_Ofold1(U_13508,U_13509),U_13511)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13508),U_13511))
    | ~ c_Big__Operators_Osemilattice__big(U_13508,U_13509,U_13510) ),
    inference(clausify,[status(thm)],[f_3474_3]) ).

fof(f_3475_1,plain,
    ! [V_A_2,V_I_2,T_c,T_b] :
    ? [B_f] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
      & c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Ex__inj__on__UNION__Sigma]) ).

fof(f_3475_2,plain,
    ! [U_13516,U_13515,U_13514,U_13513] :
    ? [U_13512] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13513),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13513,tc_prod(U_13514,U_13513),U_13512),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516))),hAPP(hAPP(c_Product__Type_OSigma(U_13514,U_13513),U_13515),U_13516)))
      & c_Fun_Oinj__on(U_13513,tc_prod(U_13514,U_13513),U_13512,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516)) ),
    inference(variable_rename,[status(thm)],[f_3475_1]) ).

fof(f_3475_3,plain,
    ! [U_13516,U_13515,U_13514,U_13513] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13513),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13513,tc_prod(U_13514,U_13513),sK295(U_13516,U_13515,U_13514,U_13513)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516))),hAPP(hAPP(c_Product__Type_OSigma(U_13514,U_13513),U_13515),U_13516)))
      & c_Fun_Oinj__on(U_13513,tc_prod(U_13514,U_13513),sK295(U_13516,U_13515,U_13514,U_13513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_13512,sK295(U_13516,U_13515,U_13514,U_13513))],[f_3475_2]) ).

fof(f_3475_4,plain,
    ( ! [U_13513,U_13514,U_13515,U_13516] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13513),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13513,tc_prod(U_13514,U_13513),sK295(U_13516,U_13515,U_13514,U_13513)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516))),hAPP(hAPP(c_Product__Type_OSigma(U_13514,U_13513),U_13515),U_13516)))
    & ! [U_13513,U_13514,U_13515,U_13516] : c_Fun_Oinj__on(U_13513,tc_prod(U_13514,U_13513),sK295(U_13516,U_13515,U_13514,U_13513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516)) ),
    inference(definitional_conversion,[status(esa)],[f_3475_3]) ).

cnf(f_3475_5,plain,
    c_Fun_Oinj__on(U_13513,tc_prod(U_13514,U_13513),sK295(U_13516,U_13515,U_13514,U_13513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516)),
    inference(clausify,[status(thm)],[f_3475_4]) ).

cnf(f_3475_6,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13513),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13513,tc_prod(U_13514,U_13513),sK295(U_13516,U_13515,U_13514,U_13513)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516))),hAPP(hAPP(c_Product__Type_OSigma(U_13514,U_13513),U_13515),U_13516))),
    inference(clausify,[status(thm)],[f_3475_4]) ).

fof(f_3476_1,plain,
    ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Sigma]) ).

fof(f_3476_2,plain,
    ! [U_13523,U_13522,U_13521,U_13520,U_13519,U_13518] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,U_13519,c_Groups_Otimes__class_Otimes(U_13518)),hAPP(hAPP(c_COMBS(U_13519,tc_fun(U_13521,tc_HOL_Obool),U_13518),hAPP(hAPP(c_COMBC(U_13519,U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,U_13518),tc_fun(U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),U_13519),c_Finite__Set_Ofold__image(U_13518,U_13521,c_Groups_Otimes__class_Otimes(U_13518))),U_13523)),c_Groups_Oone__class_Oone(U_13518))),U_13522)),c_Groups_Oone__class_Oone(U_13518)),U_13520) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,tc_prod(U_13519,U_13521),c_Groups_Otimes__class_Otimes(U_13518)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13519,U_13521,U_13518),U_13523)),c_Groups_Oone__class_Oone(U_13518)),hAPP(hAPP(c_Product__Type_OSigma(U_13519,U_13521),U_13520),U_13522))
      | ? [U_13517] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),hAPP(U_13522,U_13517)))
          & hBOOL(hAPP(hAPP(c_member(U_13519),U_13517),U_13520)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),U_13520))
      | ~ class_Groups_Ocomm__monoid__mult(U_13518) ),
    inference(variable_rename,[status(thm)],[f_3476_1]) ).

fof(f_3476_3,plain,
    ! [U_13523,U_13522,U_13521,U_13520,U_13519,U_13518] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,U_13519,c_Groups_Otimes__class_Otimes(U_13518)),hAPP(hAPP(c_COMBS(U_13519,tc_fun(U_13521,tc_HOL_Obool),U_13518),hAPP(hAPP(c_COMBC(U_13519,U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,U_13518),tc_fun(U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),U_13519),c_Finite__Set_Ofold__image(U_13518,U_13521,c_Groups_Otimes__class_Otimes(U_13518))),U_13523)),c_Groups_Oone__class_Oone(U_13518))),U_13522)),c_Groups_Oone__class_Oone(U_13518)),U_13520) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,tc_prod(U_13519,U_13521),c_Groups_Otimes__class_Otimes(U_13518)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13519,U_13521,U_13518),U_13523)),c_Groups_Oone__class_Oone(U_13518)),hAPP(hAPP(c_Product__Type_OSigma(U_13519,U_13521),U_13520),U_13522))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),hAPP(U_13522,sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518))))
        & hBOOL(hAPP(hAPP(c_member(U_13519),sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518)),U_13520)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),U_13520))
      | ~ class_Groups_Ocomm__monoid__mult(U_13518) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_13517,sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518))],[f_3476_2]) ).

fof(f_3476_4,plain,
    ( ! [U_13518,U_13519,U_13520,U_13521,U_13522,U_13523] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),hAPP(U_13522,sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518))))
        | ~ sP978(U_13518,U_13519,U_13520,U_13521,U_13522,U_13523) )
    & ! [U_13518,U_13519,U_13520,U_13521,U_13522,U_13523] :
        ( hBOOL(hAPP(hAPP(c_member(U_13519),sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518)),U_13520))
        | ~ sP978(U_13518,U_13519,U_13520,U_13521,U_13522,U_13523) )
    & ! [U_13518,U_13519,U_13520,U_13521,U_13522,U_13523] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,U_13519,c_Groups_Otimes__class_Otimes(U_13518)),hAPP(hAPP(c_COMBS(U_13519,tc_fun(U_13521,tc_HOL_Obool),U_13518),hAPP(hAPP(c_COMBC(U_13519,U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,U_13518),tc_fun(U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),U_13519),c_Finite__Set_Ofold__image(U_13518,U_13521,c_Groups_Otimes__class_Otimes(U_13518))),U_13523)),c_Groups_Oone__class_Oone(U_13518))),U_13522)),c_Groups_Oone__class_Oone(U_13518)),U_13520) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,tc_prod(U_13519,U_13521),c_Groups_Otimes__class_Otimes(U_13518)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13519,U_13521,U_13518),U_13523)),c_Groups_Oone__class_Oone(U_13518)),hAPP(hAPP(c_Product__Type_OSigma(U_13519,U_13521),U_13520),U_13522))
        | sP978(U_13518,U_13519,U_13520,U_13521,U_13522,U_13523)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),U_13520))
        | ~ class_Groups_Ocomm__monoid__mult(U_13518) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP978])],[f_3476_3]) ).

cnf(f_3476_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,U_13519,c_Groups_Otimes__class_Otimes(U_13518)),hAPP(hAPP(c_COMBS(U_13519,tc_fun(U_13521,tc_HOL_Obool),U_13518),hAPP(hAPP(c_COMBC(U_13519,U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,U_13518),tc_fun(U_13518,tc_fun(tc_fun(U_13521,tc_HOL_Obool),U_13518)),U_13519),c_Finite__Set_Ofold__image(U_13518,U_13521,c_Groups_Otimes__class_Otimes(U_13518))),U_13523)),c_Groups_Oone__class_Oone(U_13518))),U_13522)),c_Groups_Oone__class_Oone(U_13518)),U_13520) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13518,tc_prod(U_13519,U_13521),c_Groups_Otimes__class_Otimes(U_13518)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13519,U_13521,U_13518),U_13523)),c_Groups_Oone__class_Oone(U_13518)),hAPP(hAPP(c_Product__Type_OSigma(U_13519,U_13521),U_13520),U_13522))
    | sP978(U_13518,U_13519,U_13520,U_13521,U_13522,U_13523)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),U_13520))
    | ~ class_Groups_Ocomm__monoid__mult(U_13518) ),
    inference(clausify,[status(thm)],[f_3476_4]) ).

cnf(f_3476_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13519),sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518)),U_13520))
    | ~ sP978(U_13518,U_13519,U_13520,U_13521,U_13522,U_13523) ),
    inference(clausify,[status(thm)],[f_3476_4]) ).

cnf(f_3476_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),hAPP(U_13522,sK296(U_13523,U_13522,U_13521,U_13520,U_13519,U_13518))))
    | ~ sP978(U_13518,U_13519,U_13520,U_13521,U_13522,U_13523) ),
    inference(clausify,[status(thm)],[f_3476_4]) ).

fof(f_3477_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Sigma]) ).

fof(f_3477_2,plain,
    ! [U_13530,U_13529,U_13528,U_13527,U_13526,U_13525] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13526,U_13525),hAPP(hAPP(c_COMBS(U_13526,tc_fun(U_13528,tc_HOL_Obool),U_13525),hAPP(hAPP(c_COMBB(tc_fun(U_13528,U_13525),tc_fun(tc_fun(U_13528,tc_HOL_Obool),U_13525),U_13526),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13528,U_13525)),U_13530)),U_13529)),U_13527) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13526,U_13528),U_13525),hAPP(c_Product__Type_Oprod_Oprod__case(U_13526,U_13528,U_13525),U_13530)),hAPP(hAPP(c_Product__Type_OSigma(U_13526,U_13528),U_13527),U_13529))
      | ? [U_13524] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13528),hAPP(U_13529,U_13524)))
          & hBOOL(hAPP(hAPP(c_member(U_13526),U_13524),U_13527)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),U_13527))
      | ~ class_Groups_Ocomm__monoid__mult(U_13525) ),
    inference(variable_rename,[status(thm)],[f_3477_1]) ).

fof(f_3477_3,plain,
    ! [U_13530,U_13529,U_13528,U_13527,U_13526,U_13525] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13526,U_13525),hAPP(hAPP(c_COMBS(U_13526,tc_fun(U_13528,tc_HOL_Obool),U_13525),hAPP(hAPP(c_COMBB(tc_fun(U_13528,U_13525),tc_fun(tc_fun(U_13528,tc_HOL_Obool),U_13525),U_13526),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13528,U_13525)),U_13530)),U_13529)),U_13527) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13526,U_13528),U_13525),hAPP(c_Product__Type_Oprod_Oprod__case(U_13526,U_13528,U_13525),U_13530)),hAPP(hAPP(c_Product__Type_OSigma(U_13526,U_13528),U_13527),U_13529))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13528),hAPP(U_13529,sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525))))
        & hBOOL(hAPP(hAPP(c_member(U_13526),sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525)),U_13527)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),U_13527))
      | ~ class_Groups_Ocomm__monoid__mult(U_13525) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_13524,sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525))],[f_3477_2]) ).

fof(f_3477_4,plain,
    ( ! [U_13525,U_13527,U_13526,U_13528,U_13529,U_13530] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13528),hAPP(U_13529,sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525))))
        | ~ sP979(U_13525,U_13527,U_13526,U_13528,U_13529,U_13530) )
    & ! [U_13525,U_13527,U_13526,U_13528,U_13529,U_13530] :
        ( hBOOL(hAPP(hAPP(c_member(U_13526),sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525)),U_13527))
        | ~ sP979(U_13525,U_13527,U_13526,U_13528,U_13529,U_13530) )
    & ! [U_13525,U_13527,U_13526,U_13528,U_13529,U_13530] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13526,U_13525),hAPP(hAPP(c_COMBS(U_13526,tc_fun(U_13528,tc_HOL_Obool),U_13525),hAPP(hAPP(c_COMBB(tc_fun(U_13528,U_13525),tc_fun(tc_fun(U_13528,tc_HOL_Obool),U_13525),U_13526),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13528,U_13525)),U_13530)),U_13529)),U_13527) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13526,U_13528),U_13525),hAPP(c_Product__Type_Oprod_Oprod__case(U_13526,U_13528,U_13525),U_13530)),hAPP(hAPP(c_Product__Type_OSigma(U_13526,U_13528),U_13527),U_13529))
        | sP979(U_13525,U_13527,U_13526,U_13528,U_13529,U_13530)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),U_13527))
        | ~ class_Groups_Ocomm__monoid__mult(U_13525) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP979])],[f_3477_3]) ).

cnf(f_3477_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13526,U_13525),hAPP(hAPP(c_COMBS(U_13526,tc_fun(U_13528,tc_HOL_Obool),U_13525),hAPP(hAPP(c_COMBB(tc_fun(U_13528,U_13525),tc_fun(tc_fun(U_13528,tc_HOL_Obool),U_13525),U_13526),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13528,U_13525)),U_13530)),U_13529)),U_13527) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13526,U_13528),U_13525),hAPP(c_Product__Type_Oprod_Oprod__case(U_13526,U_13528,U_13525),U_13530)),hAPP(hAPP(c_Product__Type_OSigma(U_13526,U_13528),U_13527),U_13529))
    | sP979(U_13525,U_13527,U_13526,U_13528,U_13529,U_13530)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),U_13527))
    | ~ class_Groups_Ocomm__monoid__mult(U_13525) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

cnf(f_3477_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13526),sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525)),U_13527))
    | ~ sP979(U_13525,U_13527,U_13526,U_13528,U_13529,U_13530) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

cnf(f_3477_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13528),hAPP(U_13529,sK297(U_13530,U_13529,U_13528,U_13527,U_13526,U_13525))))
    | ~ sP979(U_13525,U_13527,U_13526,U_13528,U_13529,U_13530) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

fof(f_3478_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Sigma]) ).

fof(f_3478_2,plain,
    ! [U_13537,U_13536,U_13535,U_13534,U_13533,U_13532] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13533,U_13532),hAPP(hAPP(c_COMBS(U_13533,tc_fun(U_13535,tc_HOL_Obool),U_13532),hAPP(hAPP(c_COMBB(tc_fun(U_13535,U_13532),tc_fun(tc_fun(U_13535,tc_HOL_Obool),U_13532),U_13533),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13535,U_13532)),U_13537)),U_13536)),U_13534) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13533,U_13535),U_13532),hAPP(c_Product__Type_Oprod_Oprod__case(U_13533,U_13535,U_13532),U_13537)),hAPP(hAPP(c_Product__Type_OSigma(U_13533,U_13535),U_13534),U_13536))
      | ? [U_13531] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13535),hAPP(U_13536,U_13531)))
          & hBOOL(hAPP(hAPP(c_member(U_13533),U_13531),U_13534)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13533),U_13534))
      | ~ class_Groups_Ocomm__monoid__add(U_13532) ),
    inference(variable_rename,[status(thm)],[f_3478_1]) ).

fof(f_3478_3,plain,
    ! [U_13537,U_13536,U_13535,U_13534,U_13533,U_13532] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13533,U_13532),hAPP(hAPP(c_COMBS(U_13533,tc_fun(U_13535,tc_HOL_Obool),U_13532),hAPP(hAPP(c_COMBB(tc_fun(U_13535,U_13532),tc_fun(tc_fun(U_13535,tc_HOL_Obool),U_13532),U_13533),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13535,U_13532)),U_13537)),U_13536)),U_13534) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13533,U_13535),U_13532),hAPP(c_Product__Type_Oprod_Oprod__case(U_13533,U_13535,U_13532),U_13537)),hAPP(hAPP(c_Product__Type_OSigma(U_13533,U_13535),U_13534),U_13536))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13535),hAPP(U_13536,sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532))))
        & hBOOL(hAPP(hAPP(c_member(U_13533),sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532)),U_13534)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13533),U_13534))
      | ~ class_Groups_Ocomm__monoid__add(U_13532) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_13531,sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532))],[f_3478_2]) ).

fof(f_3478_4,plain,
    ( ! [U_13532,U_13533,U_13534,U_13535,U_13536,U_13537] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13535),hAPP(U_13536,sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532))))
        | ~ sP980(U_13532,U_13533,U_13534,U_13535,U_13536,U_13537) )
    & ! [U_13532,U_13533,U_13534,U_13535,U_13536,U_13537] :
        ( hBOOL(hAPP(hAPP(c_member(U_13533),sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532)),U_13534))
        | ~ sP980(U_13532,U_13533,U_13534,U_13535,U_13536,U_13537) )
    & ! [U_13532,U_13533,U_13534,U_13535,U_13536,U_13537] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13533,U_13532),hAPP(hAPP(c_COMBS(U_13533,tc_fun(U_13535,tc_HOL_Obool),U_13532),hAPP(hAPP(c_COMBB(tc_fun(U_13535,U_13532),tc_fun(tc_fun(U_13535,tc_HOL_Obool),U_13532),U_13533),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13535,U_13532)),U_13537)),U_13536)),U_13534) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13533,U_13535),U_13532),hAPP(c_Product__Type_Oprod_Oprod__case(U_13533,U_13535,U_13532),U_13537)),hAPP(hAPP(c_Product__Type_OSigma(U_13533,U_13535),U_13534),U_13536))
        | sP980(U_13532,U_13533,U_13534,U_13535,U_13536,U_13537)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13533),U_13534))
        | ~ class_Groups_Ocomm__monoid__add(U_13532) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP980])],[f_3478_3]) ).

cnf(f_3478_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13533,U_13532),hAPP(hAPP(c_COMBS(U_13533,tc_fun(U_13535,tc_HOL_Obool),U_13532),hAPP(hAPP(c_COMBB(tc_fun(U_13535,U_13532),tc_fun(tc_fun(U_13535,tc_HOL_Obool),U_13532),U_13533),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13535,U_13532)),U_13537)),U_13536)),U_13534) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13533,U_13535),U_13532),hAPP(c_Product__Type_Oprod_Oprod__case(U_13533,U_13535,U_13532),U_13537)),hAPP(hAPP(c_Product__Type_OSigma(U_13533,U_13535),U_13534),U_13536))
    | sP980(U_13532,U_13533,U_13534,U_13535,U_13536,U_13537)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13533),U_13534))
    | ~ class_Groups_Ocomm__monoid__add(U_13532) ),
    inference(clausify,[status(thm)],[f_3478_4]) ).

cnf(f_3478_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13533),sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532)),U_13534))
    | ~ sP980(U_13532,U_13533,U_13534,U_13535,U_13536,U_13537) ),
    inference(clausify,[status(thm)],[f_3478_4]) ).

cnf(f_3478_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13535),hAPP(U_13536,sK298(U_13537,U_13536,U_13535,U_13534,U_13533,U_13532))))
    | ~ sP980(U_13532,U_13533,U_13534,U_13535,U_13536,U_13537) ),
    inference(clausify,[status(thm)],[f_3478_4]) ).

fof(f_3479_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__SigmaI]) ).

fof(f_3479_2,plain,
    ! [U_13542,U_13541,U_13540,U_13539] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_13539,U_13541)),hAPP(hAPP(c_Product__Type_OSigma(U_13539,U_13541),U_13540),U_13542)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13539,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_HOL_Obool),tc_Nat_Onat,U_13539),c_Finite__Set_Ocard(U_13541)),U_13542)),U_13540)
      | ? [U_13538] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13541),hAPP(U_13542,U_13538)))
          & hBOOL(hAPP(hAPP(c_member(U_13539),U_13538),U_13540)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13539),U_13540)) ),
    inference(variable_rename,[status(thm)],[f_3479_1]) ).

fof(f_3479_3,plain,
    ! [U_13542,U_13541,U_13540,U_13539] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_13539,U_13541)),hAPP(hAPP(c_Product__Type_OSigma(U_13539,U_13541),U_13540),U_13542)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13539,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_HOL_Obool),tc_Nat_Onat,U_13539),c_Finite__Set_Ocard(U_13541)),U_13542)),U_13540)
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13541),hAPP(U_13542,sK299(U_13542,U_13541,U_13540,U_13539))))
        & hBOOL(hAPP(hAPP(c_member(U_13539),sK299(U_13542,U_13541,U_13540,U_13539)),U_13540)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13539),U_13540)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_13538,sK299(U_13542,U_13541,U_13540,U_13539))],[f_3479_2]) ).

fof(f_3479_4,plain,
    ( ! [U_13540,U_13541,U_13539,U_13542] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13541),hAPP(U_13542,sK299(U_13542,U_13541,U_13540,U_13539))))
        | ~ sP981(U_13540,U_13541,U_13539,U_13542) )
    & ! [U_13540,U_13541,U_13539,U_13542] :
        ( hBOOL(hAPP(hAPP(c_member(U_13539),sK299(U_13542,U_13541,U_13540,U_13539)),U_13540))
        | ~ sP981(U_13540,U_13541,U_13539,U_13542) )
    & ! [U_13540,U_13541,U_13539,U_13542] :
        ( hAPP(c_Finite__Set_Ocard(tc_prod(U_13539,U_13541)),hAPP(hAPP(c_Product__Type_OSigma(U_13539,U_13541),U_13540),U_13542)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13539,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_HOL_Obool),tc_Nat_Onat,U_13539),c_Finite__Set_Ocard(U_13541)),U_13542)),U_13540)
        | sP981(U_13540,U_13541,U_13539,U_13542)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13539),U_13540)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP981])],[f_3479_3]) ).

cnf(f_3479_5,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_prod(U_13539,U_13541)),hAPP(hAPP(c_Product__Type_OSigma(U_13539,U_13541),U_13540),U_13542)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13539,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_HOL_Obool),tc_Nat_Onat,U_13539),c_Finite__Set_Ocard(U_13541)),U_13542)),U_13540)
    | sP981(U_13540,U_13541,U_13539,U_13542)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13539),U_13540)) ),
    inference(clausify,[status(thm)],[f_3479_4]) ).

cnf(f_3479_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13539),sK299(U_13542,U_13541,U_13540,U_13539)),U_13540))
    | ~ sP981(U_13540,U_13541,U_13539,U_13542) ),
    inference(clausify,[status(thm)],[f_3479_4]) ).

cnf(f_3479_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13541),hAPP(U_13542,sK299(U_13542,U_13541,U_13540,U_13539))))
    | ~ sP981(U_13540,U_13541,U_13539,U_13542) ),
    inference(clausify,[status(thm)],[f_3479_4]) ).

fof(f_3480_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__in]) ).

fof(f_3480_2,plain,
    ! [U_13546,U_13545] :
      ( hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(c_Finite__Set_Ofold1(U_13545,c_Groups_Otimes__class_Otimes(U_13545)),U_13546)),U_13546))
      | ? [U_13544,U_13543] : ~ hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13545),U_13544),U_13543)),hAPP(hAPP(c_Set_Oinsert(U_13545),U_13544),hAPP(hAPP(c_Set_Oinsert(U_13545),U_13543),c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))))))
      | U_13546 = c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13545),U_13546))
      | ~ class_Groups_Oab__semigroup__mult(U_13545) ),
    inference(variable_rename,[status(thm)],[f_3480_1]) ).

fof(f_3480_3,plain,
    ! [U_13546,U_13545] :
      ( hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(c_Finite__Set_Ofold1(U_13545,c_Groups_Otimes__class_Otimes(U_13545)),U_13546)),U_13546))
      | ? [U_13543] : ~ hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13545),sK300(U_13546,U_13545)),U_13543)),hAPP(hAPP(c_Set_Oinsert(U_13545),sK300(U_13546,U_13545)),hAPP(hAPP(c_Set_Oinsert(U_13545),U_13543),c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))))))
      | U_13546 = c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13545),U_13546))
      | ~ class_Groups_Oab__semigroup__mult(U_13545) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_13544,sK300(U_13546,U_13545))],[f_3480_2]) ).

fof(f_3480_4,plain,
    ! [U_13546,U_13545] :
      ( hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(c_Finite__Set_Ofold1(U_13545,c_Groups_Otimes__class_Otimes(U_13545)),U_13546)),U_13546))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13545),sK300(U_13546,U_13545)),sK301(U_13546,U_13545))),hAPP(hAPP(c_Set_Oinsert(U_13545),sK300(U_13546,U_13545)),hAPP(hAPP(c_Set_Oinsert(U_13545),sK301(U_13546,U_13545)),c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))))))
      | U_13546 = c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13545),U_13546))
      | ~ class_Groups_Oab__semigroup__mult(U_13545) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_13543,sK301(U_13546,U_13545))],[f_3480_3]) ).

fof(f_3480_5,plain,
    ! [U_13545,U_13546] :
      ( hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(c_Finite__Set_Ofold1(U_13545,c_Groups_Otimes__class_Otimes(U_13545)),U_13546)),U_13546))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13545),sK300(U_13546,U_13545)),sK301(U_13546,U_13545))),hAPP(hAPP(c_Set_Oinsert(U_13545),sK300(U_13546,U_13545)),hAPP(hAPP(c_Set_Oinsert(U_13545),sK301(U_13546,U_13545)),c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))))))
      | U_13546 = c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13545),U_13546))
      | ~ class_Groups_Oab__semigroup__mult(U_13545) ),
    inference(definitional_conversion,[status(esa)],[f_3480_4]) ).

cnf(f_3480_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(c_Finite__Set_Ofold1(U_13545,c_Groups_Otimes__class_Otimes(U_13545)),U_13546)),U_13546))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13545),sK300(U_13546,U_13545)),sK301(U_13546,U_13545))),hAPP(hAPP(c_Set_Oinsert(U_13545),sK300(U_13546,U_13545)),hAPP(hAPP(c_Set_Oinsert(U_13545),sK301(U_13546,U_13545)),c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))))))
    | U_13546 = c_Orderings_Obot__class_Obot(tc_fun(U_13545,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13545),U_13546))
    | ~ class_Groups_Oab__semigroup__mult(U_13545) ),
    inference(clausify,[status(thm)],[f_3480_5]) ).

fof(f_3481_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
      | ? [B_a] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__SigmaI]) ).

fof(f_3481_2,plain,
    ! [U_13551,U_13550,U_13549,U_13548] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13548,U_13550)),hAPP(hAPP(c_Product__Type_OSigma(U_13548,U_13550),U_13549),U_13551)))
      | ? [U_13547] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13550),hAPP(U_13551,U_13547)))
          & hBOOL(hAPP(hAPP(c_member(U_13548),U_13547),U_13549)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13548),U_13549)) ),
    inference(variable_rename,[status(thm)],[f_3481_1]) ).

fof(f_3481_3,plain,
    ! [U_13551,U_13550,U_13549,U_13548] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13548,U_13550)),hAPP(hAPP(c_Product__Type_OSigma(U_13548,U_13550),U_13549),U_13551)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13550),hAPP(U_13551,sK302(U_13551,U_13550,U_13549,U_13548))))
        & hBOOL(hAPP(hAPP(c_member(U_13548),sK302(U_13551,U_13550,U_13549,U_13548)),U_13549)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13548),U_13549)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_13547,sK302(U_13551,U_13550,U_13549,U_13548))],[f_3481_2]) ).

fof(f_3481_4,plain,
    ( ! [U_13548,U_13550,U_13549,U_13551] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13550),hAPP(U_13551,sK302(U_13551,U_13550,U_13549,U_13548))))
        | ~ sP982(U_13548,U_13550,U_13549,U_13551) )
    & ! [U_13548,U_13550,U_13549,U_13551] :
        ( hBOOL(hAPP(hAPP(c_member(U_13548),sK302(U_13551,U_13550,U_13549,U_13548)),U_13549))
        | ~ sP982(U_13548,U_13550,U_13549,U_13551) )
    & ! [U_13548,U_13550,U_13549,U_13551] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13548,U_13550)),hAPP(hAPP(c_Product__Type_OSigma(U_13548,U_13550),U_13549),U_13551)))
        | sP982(U_13548,U_13550,U_13549,U_13551)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13548),U_13549)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP982])],[f_3481_3]) ).

cnf(f_3481_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13548,U_13550)),hAPP(hAPP(c_Product__Type_OSigma(U_13548,U_13550),U_13549),U_13551)))
    | sP982(U_13548,U_13550,U_13549,U_13551)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13548),U_13549)) ),
    inference(clausify,[status(thm)],[f_3481_4]) ).

cnf(f_3481_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13548),sK302(U_13551,U_13550,U_13549,U_13548)),U_13549))
    | ~ sP982(U_13548,U_13550,U_13549,U_13551) ),
    inference(clausify,[status(thm)],[f_3481_4]) ).

cnf(f_3481_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13550),hAPP(U_13551,sK302(U_13551,U_13550,U_13549,U_13548))))
    | ~ sP982(U_13548,U_13550,U_13549,U_13551) ),
    inference(clausify,[status(thm)],[f_3481_4]) ).

fof(f_3482_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute]) ).

fof(f_3482_2,plain,
    ! [U_13556,U_13555,U_13554] :
      ( hAPP(U_13555,hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),U_13556)) = hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),hAPP(c_Set_Oimage(U_13554,U_13554,U_13555),U_13556))
      | U_13556 = c_Orderings_Obot__class_Obot(tc_fun(U_13554,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13554),U_13556))
      | ? [U_13553,U_13552] : hAPP(U_13555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),U_13553),U_13552)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),hAPP(U_13555,U_13553)),hAPP(U_13555,U_13552))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13554) ),
    inference(variable_rename,[status(thm)],[f_3482_1]) ).

fof(f_3482_3,plain,
    ! [U_13556,U_13555,U_13554] :
      ( hAPP(U_13555,hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),U_13556)) = hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),hAPP(c_Set_Oimage(U_13554,U_13554,U_13555),U_13556))
      | U_13556 = c_Orderings_Obot__class_Obot(tc_fun(U_13554,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13554),U_13556))
      | ? [U_13552] : hAPP(U_13555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),sK303(U_13556,U_13555,U_13554)),U_13552)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),hAPP(U_13555,sK303(U_13556,U_13555,U_13554))),hAPP(U_13555,U_13552))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13554) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_13553,sK303(U_13556,U_13555,U_13554))],[f_3482_2]) ).

fof(f_3482_4,plain,
    ! [U_13556,U_13555,U_13554] :
      ( hAPP(U_13555,hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),U_13556)) = hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),hAPP(c_Set_Oimage(U_13554,U_13554,U_13555),U_13556))
      | U_13556 = c_Orderings_Obot__class_Obot(tc_fun(U_13554,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13554),U_13556))
      | hAPP(U_13555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),sK303(U_13556,U_13555,U_13554)),sK304(U_13556,U_13555,U_13554))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),hAPP(U_13555,sK303(U_13556,U_13555,U_13554))),hAPP(U_13555,sK304(U_13556,U_13555,U_13554)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13554) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_13552,sK304(U_13556,U_13555,U_13554))],[f_3482_3]) ).

fof(f_3482_5,plain,
    ! [U_13554,U_13555,U_13556] :
      ( hAPP(U_13555,hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),U_13556)) = hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),hAPP(c_Set_Oimage(U_13554,U_13554,U_13555),U_13556))
      | U_13556 = c_Orderings_Obot__class_Obot(tc_fun(U_13554,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13554),U_13556))
      | hAPP(U_13555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),sK303(U_13556,U_13555,U_13554)),sK304(U_13556,U_13555,U_13554))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),hAPP(U_13555,sK303(U_13556,U_13555,U_13554))),hAPP(U_13555,sK304(U_13556,U_13555,U_13554)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13554) ),
    inference(definitional_conversion,[status(esa)],[f_3482_4]) ).

cnf(f_3482_6,plain,
    ( hAPP(U_13555,hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),U_13556)) = hAPP(c_Finite__Set_Ofold1(U_13554,c_Groups_Otimes__class_Otimes(U_13554)),hAPP(c_Set_Oimage(U_13554,U_13554,U_13555),U_13556))
    | U_13556 = c_Orderings_Obot__class_Obot(tc_fun(U_13554,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13554),U_13556))
    | hAPP(U_13555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),sK303(U_13556,U_13555,U_13554)),sK304(U_13556,U_13555,U_13554))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13554),hAPP(U_13555,sK303(U_13556,U_13555,U_13554))),hAPP(U_13555,sK304(U_13556,U_13555,U_13554)))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_13554) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

fof(f_3483_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
      ( ? [B_x] :
          ( ? [B_y] :
              ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
              & hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaE]) ).

fof(f_3483_2,plain,
    ! [U_13563,U_13562,U_13561,U_13560,U_13559] :
      ( ? [U_13558] :
          ( ? [U_13557] :
              ( U_13561 = hAPP(hAPP(c_Product__Type_OPair(U_13559,U_13560),U_13558),U_13557)
              & hBOOL(hAPP(hAPP(c_member(U_13560),U_13557),hAPP(U_13563,U_13558))) )
          & hBOOL(hAPP(hAPP(c_member(U_13559),U_13558),U_13562)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13559,U_13560)),U_13561),hAPP(hAPP(c_Product__Type_OSigma(U_13559,U_13560),U_13562),U_13563))) ),
    inference(variable_rename,[status(thm)],[f_3483_1]) ).

fof(f_3483_3,plain,
    ! [U_13563,U_13562,U_13561,U_13560,U_13559] :
      ( ( ? [U_13557] :
            ( U_13561 = hAPP(hAPP(c_Product__Type_OPair(U_13559,U_13560),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),U_13557)
            & hBOOL(hAPP(hAPP(c_member(U_13560),U_13557),hAPP(U_13563,sK305(U_13563,U_13562,U_13561,U_13560,U_13559)))) )
        & hBOOL(hAPP(hAPP(c_member(U_13559),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),U_13562)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13559,U_13560)),U_13561),hAPP(hAPP(c_Product__Type_OSigma(U_13559,U_13560),U_13562),U_13563))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_13558,sK305(U_13563,U_13562,U_13561,U_13560,U_13559))],[f_3483_2]) ).

fof(f_3483_4,plain,
    ! [U_13563,U_13562,U_13561,U_13560,U_13559] :
      ( ( U_13561 = hAPP(hAPP(c_Product__Type_OPair(U_13559,U_13560),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),sK306(U_13563,U_13562,U_13561,U_13560,U_13559))
        & hBOOL(hAPP(hAPP(c_member(U_13560),sK306(U_13563,U_13562,U_13561,U_13560,U_13559)),hAPP(U_13563,sK305(U_13563,U_13562,U_13561,U_13560,U_13559))))
        & hBOOL(hAPP(hAPP(c_member(U_13559),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),U_13562)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13559,U_13560)),U_13561),hAPP(hAPP(c_Product__Type_OSigma(U_13559,U_13560),U_13562),U_13563))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_13557,sK306(U_13563,U_13562,U_13561,U_13560,U_13559))],[f_3483_3]) ).

fof(f_3483_5,plain,
    ( ! [U_13559,U_13560,U_13561,U_13562,U_13563] :
        ( U_13561 = hAPP(hAPP(c_Product__Type_OPair(U_13559,U_13560),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),sK306(U_13563,U_13562,U_13561,U_13560,U_13559))
        | ~ sP983(U_13559,U_13560,U_13561,U_13562,U_13563) )
    & ! [U_13559,U_13560,U_13561,U_13562,U_13563] :
        ( hBOOL(hAPP(hAPP(c_member(U_13560),sK306(U_13563,U_13562,U_13561,U_13560,U_13559)),hAPP(U_13563,sK305(U_13563,U_13562,U_13561,U_13560,U_13559))))
        | ~ sP983(U_13559,U_13560,U_13561,U_13562,U_13563) )
    & ! [U_13559,U_13560,U_13561,U_13562,U_13563] :
        ( hBOOL(hAPP(hAPP(c_member(U_13559),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),U_13562))
        | ~ sP983(U_13559,U_13560,U_13561,U_13562,U_13563) )
    & ! [U_13559,U_13560,U_13561,U_13562,U_13563] :
        ( sP983(U_13559,U_13560,U_13561,U_13562,U_13563)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13559,U_13560)),U_13561),hAPP(hAPP(c_Product__Type_OSigma(U_13559,U_13560),U_13562),U_13563))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP983])],[f_3483_4]) ).

cnf(f_3483_6,plain,
    ( sP983(U_13559,U_13560,U_13561,U_13562,U_13563)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13559,U_13560)),U_13561),hAPP(hAPP(c_Product__Type_OSigma(U_13559,U_13560),U_13562),U_13563))) ),
    inference(clausify,[status(thm)],[f_3483_5]) ).

cnf(f_3483_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13559),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),U_13562))
    | ~ sP983(U_13559,U_13560,U_13561,U_13562,U_13563) ),
    inference(clausify,[status(thm)],[f_3483_5]) ).

cnf(f_3483_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13560),sK306(U_13563,U_13562,U_13561,U_13560,U_13559)),hAPP(U_13563,sK305(U_13563,U_13562,U_13561,U_13560,U_13559))))
    | ~ sP983(U_13559,U_13560,U_13561,U_13562,U_13563) ),
    inference(clausify,[status(thm)],[f_3483_5]) ).

cnf(f_3483_9,plain,
    ( U_13561 = hAPP(hAPP(c_Product__Type_OPair(U_13559,U_13560),sK305(U_13563,U_13562,U_13561,U_13560,U_13559)),sK306(U_13563,U_13562,U_13561,U_13560,U_13559))
    | ~ sP983(U_13559,U_13560,U_13561,U_13562,U_13563) ),
    inference(clausify,[status(thm)],[f_3483_5]) ).

fof(f_3484_1,plain,
    ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__surj]) ).

fof(f_3484_2,plain,
    ! [U_13569,U_13568,U_13567,U_13566,U_13565,U_13564] :
      ( hAPP(c_Set_Oimage(tc_prod(U_13564,U_13567),tc_prod(U_13565,U_13568),c_Product__Type_Omap__pair(U_13564,U_13565,U_13567,U_13568,U_13566,U_13569)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13564,U_13567),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13565,U_13568),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13567,U_13568,U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13567,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13568,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13564,U_13565,U_13566),c_Orderings_Otop__class_Otop(tc_fun(U_13564,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3484_1]) ).

fof(f_3484_3,plain,
    ! [U_13566,U_13564,U_13565,U_13567,U_13568,U_13569] :
      ( hAPP(c_Set_Oimage(tc_prod(U_13564,U_13567),tc_prod(U_13565,U_13568),c_Product__Type_Omap__pair(U_13564,U_13565,U_13567,U_13568,U_13566,U_13569)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13564,U_13567),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13565,U_13568),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13567,U_13568,U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13567,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13568,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13564,U_13565,U_13566),c_Orderings_Otop__class_Otop(tc_fun(U_13564,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3484_2]) ).

cnf(f_3484_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13564,U_13567),tc_prod(U_13565,U_13568),c_Product__Type_Omap__pair(U_13564,U_13565,U_13567,U_13568,U_13566,U_13569)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13564,U_13567),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13565,U_13568),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_13567,U_13568,U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13567,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13568,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_13564,U_13565,U_13566),c_Orderings_Otop__class_Otop(tc_fun(U_13564,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3484_3]) ).

fof(f_3485_1,plain,
    ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2)))
      | ~ c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on]) ).

fof(f_3485_2,plain,
    ! [U_13577,U_13576,U_13575,U_13574,U_13573,U_13572,U_13571,U_13570] :
      ( c_Fun_Oinj__on(tc_prod(U_13570,U_13574),tc_prod(U_13571,U_13575),c_Product__Type_Omap__pair(U_13570,U_13571,U_13574,U_13575,U_13572,U_13576),hAPP(hAPP(c_Product__Type_OSigma(U_13570,U_13574),U_13573),hAPP(c_COMBK(tc_fun(U_13574,tc_HOL_Obool),U_13570),U_13577)))
      | ~ c_Fun_Oinj__on(U_13574,U_13575,U_13576,U_13577)
      | ~ c_Fun_Oinj__on(U_13570,U_13571,U_13572,U_13573) ),
    inference(variable_rename,[status(thm)],[f_3485_1]) ).

fof(f_3485_3,plain,
    ! [U_13570,U_13571,U_13572,U_13573,U_13574,U_13575,U_13576,U_13577] :
      ( c_Fun_Oinj__on(tc_prod(U_13570,U_13574),tc_prod(U_13571,U_13575),c_Product__Type_Omap__pair(U_13570,U_13571,U_13574,U_13575,U_13572,U_13576),hAPP(hAPP(c_Product__Type_OSigma(U_13570,U_13574),U_13573),hAPP(c_COMBK(tc_fun(U_13574,tc_HOL_Obool),U_13570),U_13577)))
      | ~ c_Fun_Oinj__on(U_13574,U_13575,U_13576,U_13577)
      | ~ c_Fun_Oinj__on(U_13570,U_13571,U_13572,U_13573) ),
    inference(definitional_conversion,[status(esa)],[f_3485_2]) ).

cnf(f_3485_4,plain,
    ( c_Fun_Oinj__on(tc_prod(U_13570,U_13574),tc_prod(U_13571,U_13575),c_Product__Type_Omap__pair(U_13570,U_13571,U_13574,U_13575,U_13572,U_13576),hAPP(hAPP(c_Product__Type_OSigma(U_13570,U_13574),U_13573),hAPP(c_COMBK(tc_fun(U_13574,tc_HOL_Obool),U_13570),U_13577)))
    | ~ c_Fun_Oinj__on(U_13574,U_13575,U_13576,U_13577)
    | ~ c_Fun_Oinj__on(U_13570,U_13571,U_13572,U_13573) ),
    inference(clausify,[status(thm)],[f_3485_3]) ).

fof(f_3486_1,plain,
    ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__imageI]) ).

fof(f_3486_2,plain,
    ! [U_13586,U_13585,U_13584,U_13583,U_13582,U_13581,U_13580,U_13579,U_13578] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13583,U_13584)),hAPP(hAPP(c_Product__Type_OPair(U_13583,U_13584),hAPP(U_13585,U_13580)),hAPP(U_13586,U_13581))),hAPP(c_Set_Oimage(tc_prod(U_13578,U_13579),tc_prod(U_13583,U_13584),c_Product__Type_Omap__pair(U_13578,U_13583,U_13579,U_13584,U_13585,U_13586)),U_13582)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13579)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13579),U_13580),U_13581)),U_13582)) ),
    inference(variable_rename,[status(thm)],[f_3486_1]) ).

fof(f_3486_3,plain,
    ! [U_13578,U_13579,U_13580,U_13581,U_13582,U_13583,U_13584,U_13585,U_13586] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13583,U_13584)),hAPP(hAPP(c_Product__Type_OPair(U_13583,U_13584),hAPP(U_13585,U_13580)),hAPP(U_13586,U_13581))),hAPP(c_Set_Oimage(tc_prod(U_13578,U_13579),tc_prod(U_13583,U_13584),c_Product__Type_Omap__pair(U_13578,U_13583,U_13579,U_13584,U_13585,U_13586)),U_13582)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13579)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13579),U_13580),U_13581)),U_13582)) ),
    inference(definitional_conversion,[status(esa)],[f_3486_2]) ).

cnf(f_3486_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13583,U_13584)),hAPP(hAPP(c_Product__Type_OPair(U_13583,U_13584),hAPP(U_13585,U_13580)),hAPP(U_13586,U_13581))),hAPP(c_Set_Oimage(tc_prod(U_13578,U_13579),tc_prod(U_13583,U_13584),c_Product__Type_Omap__pair(U_13578,U_13583,U_13579,U_13584,U_13585,U_13586)),U_13582)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13579)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13579),U_13580),U_13581)),U_13582)) ),
    inference(clausify,[status(thm)],[f_3486_3]) ).

fof(f_3487_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_snd__prod__fun]) ).

fof(f_3487_2,plain,
    ! [U_13593,U_13592,U_13591,U_13590,U_13589,U_13588,U_13587] : hAPP(c_Product__Type_Osnd(U_13587,U_13588),hAPP(c_Product__Type_Omap__pair(U_13589,U_13587,U_13590,U_13588,U_13591,U_13592),U_13593)) = hAPP(U_13592,hAPP(c_Product__Type_Osnd(U_13589,U_13590),U_13593)),
    inference(variable_rename,[status(thm)],[f_3487_1]) ).

fof(f_3487_3,plain,
    ! [U_13589,U_13587,U_13588,U_13590,U_13591,U_13592,U_13593] : hAPP(c_Product__Type_Osnd(U_13587,U_13588),hAPP(c_Product__Type_Omap__pair(U_13589,U_13587,U_13590,U_13588,U_13591,U_13592),U_13593)) = hAPP(U_13592,hAPP(c_Product__Type_Osnd(U_13589,U_13590),U_13593)),
    inference(definitional_conversion,[status(esa)],[f_3487_2]) ).

cnf(f_3487_4,plain,
    hAPP(c_Product__Type_Osnd(U_13587,U_13588),hAPP(c_Product__Type_Omap__pair(U_13589,U_13587,U_13590,U_13588,U_13591,U_13592),U_13593)) = hAPP(U_13592,hAPP(c_Product__Type_Osnd(U_13589,U_13590),U_13593)),
    inference(clausify,[status(thm)],[f_3487_3]) ).

fof(f_3488_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_fst__map__pair]) ).

fof(f_3488_2,plain,
    ! [U_13600,U_13599,U_13598,U_13597,U_13596,U_13595,U_13594] : hAPP(c_Product__Type_Ofst(U_13594,U_13595),hAPP(c_Product__Type_Omap__pair(U_13596,U_13594,U_13597,U_13595,U_13598,U_13599),U_13600)) = hAPP(U_13598,hAPP(c_Product__Type_Ofst(U_13596,U_13597),U_13600)),
    inference(variable_rename,[status(thm)],[f_3488_1]) ).

fof(f_3488_3,plain,
    ! [U_13594,U_13595,U_13596,U_13597,U_13598,U_13599,U_13600] : hAPP(c_Product__Type_Ofst(U_13594,U_13595),hAPP(c_Product__Type_Omap__pair(U_13596,U_13594,U_13597,U_13595,U_13598,U_13599),U_13600)) = hAPP(U_13598,hAPP(c_Product__Type_Ofst(U_13596,U_13597),U_13600)),
    inference(definitional_conversion,[status(esa)],[f_3488_2]) ).

cnf(f_3488_4,plain,
    hAPP(c_Product__Type_Ofst(U_13594,U_13595),hAPP(c_Product__Type_Omap__pair(U_13596,U_13594,U_13597,U_13595,U_13598,U_13599),U_13600)) = hAPP(U_13598,hAPP(c_Product__Type_Ofst(U_13596,U_13597),U_13600)),
    inference(clausify,[status(thm)],[f_3488_3]) ).

fof(f_3489_1,plain,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__simp]) ).

fof(f_3489_2,plain,
    ! [U_13608,U_13607,U_13606,U_13605,U_13604,U_13603,U_13602,U_13601] : hAPP(c_Product__Type_Omap__pair(U_13601,U_13602,U_13603,U_13604,U_13605,U_13606),hAPP(hAPP(c_Product__Type_OPair(U_13601,U_13603),U_13607),U_13608)) = hAPP(hAPP(c_Product__Type_OPair(U_13602,U_13604),hAPP(U_13605,U_13607)),hAPP(U_13606,U_13608)),
    inference(variable_rename,[status(thm)],[f_3489_1]) ).

fof(f_3489_3,plain,
    ! [U_13601,U_13602,U_13603,U_13604,U_13605,U_13606,U_13607,U_13608] : hAPP(c_Product__Type_Omap__pair(U_13601,U_13602,U_13603,U_13604,U_13605,U_13606),hAPP(hAPP(c_Product__Type_OPair(U_13601,U_13603),U_13607),U_13608)) = hAPP(hAPP(c_Product__Type_OPair(U_13602,U_13604),hAPP(U_13605,U_13607)),hAPP(U_13606,U_13608)),
    inference(definitional_conversion,[status(esa)],[f_3489_2]) ).

cnf(f_3489_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_13601,U_13602,U_13603,U_13604,U_13605,U_13606),hAPP(hAPP(c_Product__Type_OPair(U_13601,U_13603),U_13607),U_13608)) = hAPP(hAPP(c_Product__Type_OPair(U_13602,U_13604),hAPP(U_13605,U_13607)),hAPP(U_13606,U_13608)),
    inference(clausify,[status(thm)],[f_3489_3]) ).

fof(f_3490_1,plain,
    ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_map__pair__ident]) ).

fof(f_3490_2,plain,
    ! [U_13611,U_13610,U_13609] : hAPP(c_Product__Type_Omap__pair(U_13609,U_13609,U_13610,U_13610,c_COMBI(U_13609),c_COMBI(U_13610)),U_13611) = U_13611,
    inference(variable_rename,[status(thm)],[f_3490_1]) ).

fof(f_3490_3,plain,
    ! [U_13609,U_13611,U_13610] : hAPP(c_Product__Type_Omap__pair(U_13609,U_13609,U_13610,U_13610,c_COMBI(U_13609),c_COMBI(U_13610)),U_13611) = U_13611,
    inference(definitional_conversion,[status(esa)],[f_3490_2]) ).

cnf(f_3490_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_13609,U_13609,U_13610,U_13610,c_COMBI(U_13609),c_COMBI(U_13610)),U_13611) = U_13611,
    inference(clausify,[status(thm)],[f_3490_3]) ).

fof(f_3491_1,plain,
    ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__def]) ).

fof(f_3491_2,plain,
    ! [U_13617,U_13616,U_13615,U_13614,U_13613,U_13612] : c_Product__Type_Omap__pair(U_13612,U_13613,U_13614,U_13615,U_13616,U_13617) = hAPP(c_Product__Type_Oprod_Oprod__case(U_13612,U_13614,tc_prod(U_13613,U_13615)),hAPP(hAPP(c_COMBC(U_13612,tc_fun(U_13614,U_13615),tc_fun(U_13614,tc_prod(U_13613,U_13615))),hAPP(hAPP(c_COMBB(tc_fun(U_13615,tc_prod(U_13613,U_13615)),tc_fun(tc_fun(U_13614,U_13615),tc_fun(U_13614,tc_prod(U_13613,U_13615))),U_13612),c_COMBB(U_13615,tc_prod(U_13613,U_13615),U_13614)),hAPP(hAPP(c_COMBB(U_13613,tc_fun(U_13615,tc_prod(U_13613,U_13615)),U_13612),c_Product__Type_OPair(U_13613,U_13615)),U_13616))),U_13617)),
    inference(variable_rename,[status(thm)],[f_3491_1]) ).

fof(f_3491_3,plain,
    ! [U_13612,U_13613,U_13614,U_13615,U_13616,U_13617] : c_Product__Type_Omap__pair(U_13612,U_13613,U_13614,U_13615,U_13616,U_13617) = hAPP(c_Product__Type_Oprod_Oprod__case(U_13612,U_13614,tc_prod(U_13613,U_13615)),hAPP(hAPP(c_COMBC(U_13612,tc_fun(U_13614,U_13615),tc_fun(U_13614,tc_prod(U_13613,U_13615))),hAPP(hAPP(c_COMBB(tc_fun(U_13615,tc_prod(U_13613,U_13615)),tc_fun(tc_fun(U_13614,U_13615),tc_fun(U_13614,tc_prod(U_13613,U_13615))),U_13612),c_COMBB(U_13615,tc_prod(U_13613,U_13615),U_13614)),hAPP(hAPP(c_COMBB(U_13613,tc_fun(U_13615,tc_prod(U_13613,U_13615)),U_13612),c_Product__Type_OPair(U_13613,U_13615)),U_13616))),U_13617)),
    inference(definitional_conversion,[status(esa)],[f_3491_2]) ).

cnf(f_3491_4,plain,
    c_Product__Type_Omap__pair(U_13612,U_13613,U_13614,U_13615,U_13616,U_13617) = hAPP(c_Product__Type_Oprod_Oprod__case(U_13612,U_13614,tc_prod(U_13613,U_13615)),hAPP(hAPP(c_COMBC(U_13612,tc_fun(U_13614,U_13615),tc_fun(U_13614,tc_prod(U_13613,U_13615))),hAPP(hAPP(c_COMBB(tc_fun(U_13615,tc_prod(U_13613,U_13615)),tc_fun(tc_fun(U_13614,U_13615),tc_fun(U_13614,tc_prod(U_13613,U_13615))),U_13612),c_COMBB(U_13615,tc_prod(U_13613,U_13615),U_13614)),hAPP(hAPP(c_COMBB(U_13613,tc_fun(U_13615,tc_prod(U_13613,U_13615)),U_13612),c_Product__Type_OPair(U_13613,U_13615)),U_13616))),U_13617)),
    inference(clausify,[status(thm)],[f_3491_3]) ).

fof(f_3492_1,plain,
    ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2))
      | hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) != V_B_H_2
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_A_H_2 ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on]) ).

fof(f_3492_2,plain,
    ! [U_13627,U_13626,U_13625,U_13624,U_13623,U_13622,U_13621,U_13620,U_13619,U_13618] :
      ( hAPP(c_Set_Oimage(tc_prod(U_13618,U_13623),tc_prod(U_13619,U_13624),c_Product__Type_Omap__pair(U_13618,U_13619,U_13623,U_13624,U_13620,U_13625)),hAPP(hAPP(c_Product__Type_OSigma(U_13618,U_13623),U_13621),hAPP(c_COMBK(tc_fun(U_13623,tc_HOL_Obool),U_13618),U_13626))) = hAPP(hAPP(c_Product__Type_OSigma(U_13619,U_13624),U_13622),hAPP(c_COMBK(tc_fun(U_13624,tc_HOL_Obool),U_13619),U_13627))
      | hAPP(c_Set_Oimage(U_13623,U_13624,U_13625),U_13626) != U_13627
      | hAPP(c_Set_Oimage(U_13618,U_13619,U_13620),U_13621) != U_13622 ),
    inference(variable_rename,[status(thm)],[f_3492_1]) ).

fof(f_3492_3,plain,
    ! [U_13618,U_13619,U_13620,U_13621,U_13622,U_13623,U_13624,U_13625,U_13626,U_13627] :
      ( hAPP(c_Set_Oimage(tc_prod(U_13618,U_13623),tc_prod(U_13619,U_13624),c_Product__Type_Omap__pair(U_13618,U_13619,U_13623,U_13624,U_13620,U_13625)),hAPP(hAPP(c_Product__Type_OSigma(U_13618,U_13623),U_13621),hAPP(c_COMBK(tc_fun(U_13623,tc_HOL_Obool),U_13618),U_13626))) = hAPP(hAPP(c_Product__Type_OSigma(U_13619,U_13624),U_13622),hAPP(c_COMBK(tc_fun(U_13624,tc_HOL_Obool),U_13619),U_13627))
      | hAPP(c_Set_Oimage(U_13623,U_13624,U_13625),U_13626) != U_13627
      | hAPP(c_Set_Oimage(U_13618,U_13619,U_13620),U_13621) != U_13622 ),
    inference(definitional_conversion,[status(esa)],[f_3492_2]) ).

cnf(f_3492_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13618,U_13623),tc_prod(U_13619,U_13624),c_Product__Type_Omap__pair(U_13618,U_13619,U_13623,U_13624,U_13620,U_13625)),hAPP(hAPP(c_Product__Type_OSigma(U_13618,U_13623),U_13621),hAPP(c_COMBK(tc_fun(U_13623,tc_HOL_Obool),U_13618),U_13626))) = hAPP(hAPP(c_Product__Type_OSigma(U_13619,U_13624),U_13622),hAPP(c_COMBK(tc_fun(U_13624,tc_HOL_Obool),U_13619),U_13627))
    | hAPP(c_Set_Oimage(U_13623,U_13624,U_13625),U_13626) != U_13627
    | hAPP(c_Set_Oimage(U_13618,U_13619,U_13620),U_13621) != U_13622 ),
    inference(clausify,[status(thm)],[f_3492_3]) ).

fof(f_3493_1,plain,
    ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2))
          & V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_prod__fun__imageE]) ).

fof(f_3493_2,plain,
    ! [U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630] :
      ( ? [U_13629,U_13628] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13633,U_13634)),hAPP(hAPP(c_Product__Type_OPair(U_13633,U_13634),U_13629),U_13628)),U_13637))
          & U_13632 = hAPP(hAPP(c_Product__Type_OPair(U_13630,U_13631),hAPP(U_13635,U_13629)),hAPP(U_13636,U_13628)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13630,U_13631)),U_13632),hAPP(c_Set_Oimage(tc_prod(U_13633,U_13634),tc_prod(U_13630,U_13631),c_Product__Type_Omap__pair(U_13633,U_13630,U_13634,U_13631,U_13635,U_13636)),U_13637))) ),
    inference(variable_rename,[status(thm)],[f_3493_1]) ).

fof(f_3493_3,plain,
    ! [U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630] :
      ( ? [U_13628] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13633,U_13634)),hAPP(hAPP(c_Product__Type_OPair(U_13633,U_13634),sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630)),U_13628)),U_13637))
          & U_13632 = hAPP(hAPP(c_Product__Type_OPair(U_13630,U_13631),hAPP(U_13635,sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),hAPP(U_13636,U_13628)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13630,U_13631)),U_13632),hAPP(c_Set_Oimage(tc_prod(U_13633,U_13634),tc_prod(U_13630,U_13631),c_Product__Type_Omap__pair(U_13633,U_13630,U_13634,U_13631,U_13635,U_13636)),U_13637))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_13629,sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))],[f_3493_2]) ).

fof(f_3493_4,plain,
    ! [U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13633,U_13634)),hAPP(hAPP(c_Product__Type_OPair(U_13633,U_13634),sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630)),sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),U_13637))
        & U_13632 = hAPP(hAPP(c_Product__Type_OPair(U_13630,U_13631),hAPP(U_13635,sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),hAPP(U_13636,sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13630,U_13631)),U_13632),hAPP(c_Set_Oimage(tc_prod(U_13633,U_13634),tc_prod(U_13630,U_13631),c_Product__Type_Omap__pair(U_13633,U_13630,U_13634,U_13631,U_13635,U_13636)),U_13637))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_13628,sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))],[f_3493_3]) ).

fof(f_3493_5,plain,
    ( ! [U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13633,U_13634)),hAPP(hAPP(c_Product__Type_OPair(U_13633,U_13634),sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630)),sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),U_13637))
        | ~ sP984(U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637) )
    & ! [U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637] :
        ( U_13632 = hAPP(hAPP(c_Product__Type_OPair(U_13630,U_13631),hAPP(U_13635,sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),hAPP(U_13636,sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630)))
        | ~ sP984(U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637) )
    & ! [U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637] :
        ( sP984(U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13630,U_13631)),U_13632),hAPP(c_Set_Oimage(tc_prod(U_13633,U_13634),tc_prod(U_13630,U_13631),c_Product__Type_Omap__pair(U_13633,U_13630,U_13634,U_13631,U_13635,U_13636)),U_13637))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP984])],[f_3493_4]) ).

cnf(f_3493_6,plain,
    ( sP984(U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13630,U_13631)),U_13632),hAPP(c_Set_Oimage(tc_prod(U_13633,U_13634),tc_prod(U_13630,U_13631),c_Product__Type_Omap__pair(U_13633,U_13630,U_13634,U_13631,U_13635,U_13636)),U_13637))) ),
    inference(clausify,[status(thm)],[f_3493_5]) ).

cnf(f_3493_7,plain,
    ( U_13632 = hAPP(hAPP(c_Product__Type_OPair(U_13630,U_13631),hAPP(U_13635,sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),hAPP(U_13636,sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630)))
    | ~ sP984(U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637) ),
    inference(clausify,[status(thm)],[f_3493_5]) ).

cnf(f_3493_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13633,U_13634)),hAPP(hAPP(c_Product__Type_OPair(U_13633,U_13634),sK307(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630)),sK308(U_13637,U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630))),U_13637))
    | ~ sP984(U_13630,U_13631,U_13632,U_13633,U_13634,U_13635,U_13636,U_13637) ),
    inference(clausify,[status(thm)],[f_3493_5]) ).

fof(f_3494_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) )
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__def]) ).

fof(f_3494_2,plain,
    ! [U_13642,U_13641,U_13640] :
      ( ( c_Relation_Orefl__on(U_13640,U_13641,U_13642)
        | ? [U_13639] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13640,U_13640)),hAPP(hAPP(c_Product__Type_OPair(U_13640,U_13640),U_13639),U_13639)),U_13642))
            & hBOOL(hAPP(hAPP(c_member(U_13640),U_13639),U_13641)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13640,U_13640),tc_HOL_Obool)),U_13642),hAPP(hAPP(c_Product__Type_OSigma(U_13640,U_13640),U_13641),hAPP(c_COMBK(tc_fun(U_13640,tc_HOL_Obool),U_13640),U_13641)))) )
      & ( ( ! [U_13638] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13640,U_13640)),hAPP(hAPP(c_Product__Type_OPair(U_13640,U_13640),U_13638),U_13638)),U_13642))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13640),U_13638),U_13641)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13640,U_13640),tc_HOL_Obool)),U_13642),hAPP(hAPP(c_Product__Type_OSigma(U_13640,U_13640),U_13641),hAPP(c_COMBK(tc_fun(U_13640,tc_HOL_Obool),U_13640),U_13641)))) )
        | ~ c_Relation_Orefl__on(U_13640,U_13641,U_13642) ) ),
    inference(variable_rename,[status(thm)],[f_3494_1]) ).

fof(f_3494_3,plain,
    ( ! [U_13648,U_13646,U_13644] :
        ( c_Relation_Orefl__on(U_13644,U_13646,U_13648)
        | ? [U_13639] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),U_13639),U_13639)),U_13648))
            & hBOOL(hAPP(hAPP(c_member(U_13644),U_13639),U_13646)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13644,U_13644),tc_HOL_Obool)),U_13648),hAPP(hAPP(c_Product__Type_OSigma(U_13644,U_13644),U_13646),hAPP(c_COMBK(tc_fun(U_13644,tc_HOL_Obool),U_13644),U_13646)))) )
    & ! [U_13647,U_13645,U_13643] :
        ( ( ! [U_13638] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13643,U_13643)),hAPP(hAPP(c_Product__Type_OPair(U_13643,U_13643),U_13638),U_13638)),U_13647))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13643),U_13638),U_13645)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13643,U_13643),tc_HOL_Obool)),U_13647),hAPP(hAPP(c_Product__Type_OSigma(U_13643,U_13643),U_13645),hAPP(c_COMBK(tc_fun(U_13643,tc_HOL_Obool),U_13643),U_13645)))) )
        | ~ c_Relation_Orefl__on(U_13643,U_13645,U_13647) ) ),
    inference(miniscope,[status(thm)],[f_3494_2]) ).

fof(f_3494_4,plain,
    ( ! [U_13648,U_13646,U_13644] :
        ( c_Relation_Orefl__on(U_13644,U_13646,U_13648)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),sK309(U_13648,U_13646,U_13644)),sK309(U_13648,U_13646,U_13644))),U_13648))
          & hBOOL(hAPP(hAPP(c_member(U_13644),sK309(U_13648,U_13646,U_13644)),U_13646)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13644,U_13644),tc_HOL_Obool)),U_13648),hAPP(hAPP(c_Product__Type_OSigma(U_13644,U_13644),U_13646),hAPP(c_COMBK(tc_fun(U_13644,tc_HOL_Obool),U_13644),U_13646)))) )
    & ! [U_13647,U_13645,U_13643] :
        ( ( ! [U_13638] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13643,U_13643)),hAPP(hAPP(c_Product__Type_OPair(U_13643,U_13643),U_13638),U_13638)),U_13647))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13643),U_13638),U_13645)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13643,U_13643),tc_HOL_Obool)),U_13647),hAPP(hAPP(c_Product__Type_OSigma(U_13643,U_13643),U_13645),hAPP(c_COMBK(tc_fun(U_13643,tc_HOL_Obool),U_13643),U_13645)))) )
        | ~ c_Relation_Orefl__on(U_13643,U_13645,U_13647) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_13639,sK309(U_13648,U_13646,U_13644))],[f_3494_3]) ).

fof(f_3494_5,plain,
    ( ! [U_13648,U_13644,U_13646] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),sK309(U_13648,U_13646,U_13644)),sK309(U_13648,U_13646,U_13644))),U_13648))
        | ~ sP986(U_13648,U_13644,U_13646) )
    & ! [U_13648,U_13644,U_13646] :
        ( hBOOL(hAPP(hAPP(c_member(U_13644),sK309(U_13648,U_13646,U_13644)),U_13646))
        | ~ sP986(U_13648,U_13644,U_13646) )
    & ! [U_13645,U_13638,U_13647,U_13643] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13643,U_13643)),hAPP(hAPP(c_Product__Type_OPair(U_13643,U_13643),U_13638),U_13638)),U_13647))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13643),U_13638),U_13645))
        | ~ sP985(U_13645,U_13638,U_13647,U_13643) )
    & ! [U_13645,U_13638,U_13647,U_13643] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13643,U_13643),tc_HOL_Obool)),U_13647),hAPP(hAPP(c_Product__Type_OSigma(U_13643,U_13643),U_13645),hAPP(c_COMBK(tc_fun(U_13643,tc_HOL_Obool),U_13643),U_13645))))
        | ~ sP985(U_13645,U_13638,U_13647,U_13643) )
    & ! [U_13648,U_13644,U_13646] :
        ( c_Relation_Orefl__on(U_13644,U_13646,U_13648)
        | sP986(U_13648,U_13644,U_13646)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13644,U_13644),tc_HOL_Obool)),U_13648),hAPP(hAPP(c_Product__Type_OSigma(U_13644,U_13644),U_13646),hAPP(c_COMBK(tc_fun(U_13644,tc_HOL_Obool),U_13644),U_13646)))) )
    & ! [U_13645,U_13638,U_13647,U_13643] :
        ( sP985(U_13645,U_13638,U_13647,U_13643)
        | ~ c_Relation_Orefl__on(U_13643,U_13645,U_13647) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP985,sP986])],[f_3494_4]) ).

cnf(f_3494_6,plain,
    ( sP985(U_13645,U_13638,U_13647,U_13643)
    | ~ c_Relation_Orefl__on(U_13643,U_13645,U_13647) ),
    inference(clausify,[status(thm)],[f_3494_5]) ).

cnf(f_3494_7,plain,
    ( c_Relation_Orefl__on(U_13644,U_13646,U_13648)
    | sP986(U_13648,U_13644,U_13646)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13644,U_13644),tc_HOL_Obool)),U_13648),hAPP(hAPP(c_Product__Type_OSigma(U_13644,U_13644),U_13646),hAPP(c_COMBK(tc_fun(U_13644,tc_HOL_Obool),U_13644),U_13646)))) ),
    inference(clausify,[status(thm)],[f_3494_5]) ).

cnf(f_3494_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13643,U_13643),tc_HOL_Obool)),U_13647),hAPP(hAPP(c_Product__Type_OSigma(U_13643,U_13643),U_13645),hAPP(c_COMBK(tc_fun(U_13643,tc_HOL_Obool),U_13643),U_13645))))
    | ~ sP985(U_13645,U_13638,U_13647,U_13643) ),
    inference(clausify,[status(thm)],[f_3494_5]) ).

cnf(f_3494_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13643,U_13643)),hAPP(hAPP(c_Product__Type_OPair(U_13643,U_13643),U_13638),U_13638)),U_13647))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13643),U_13638),U_13645))
    | ~ sP985(U_13645,U_13638,U_13647,U_13643) ),
    inference(clausify,[status(thm)],[f_3494_5]) ).

cnf(f_3494_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13644),sK309(U_13648,U_13646,U_13644)),U_13646))
    | ~ sP986(U_13648,U_13644,U_13646) ),
    inference(clausify,[status(thm)],[f_3494_5]) ).

cnf(f_3494_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),sK309(U_13648,U_13646,U_13644)),sK309(U_13648,U_13646,U_13644))),U_13648))
    | ~ sP986(U_13648,U_13644,U_13646) ),
    inference(clausify,[status(thm)],[f_3494_5]) ).

fof(f_3495_1,plain,
    ! [V_f_2,V_S_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat]) ).

fof(f_3495_2,plain,
    ! [U_13652,U_13651,U_13650] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13650,tc_Nat_Onat),U_13652),U_13651)))
      | ? [U_13649] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13652,U_13649)))
          & hBOOL(hAPP(hAPP(c_member(U_13650),U_13649),U_13651)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13650),U_13651)) ),
    inference(variable_rename,[status(thm)],[f_3495_1]) ).

fof(f_3495_3,plain,
    ! [U_13652,U_13651,U_13650] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13650,tc_Nat_Onat),U_13652),U_13651)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13652,sK310(U_13652,U_13651,U_13650))))
        & hBOOL(hAPP(hAPP(c_member(U_13650),sK310(U_13652,U_13651,U_13650)),U_13651)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13650),U_13651)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_13649,sK310(U_13652,U_13651,U_13650))],[f_3495_2]) ).

fof(f_3495_4,plain,
    ( ! [U_13651,U_13652,U_13650] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13652,sK310(U_13652,U_13651,U_13650))))
        | ~ sP987(U_13651,U_13652,U_13650) )
    & ! [U_13651,U_13652,U_13650] :
        ( hBOOL(hAPP(hAPP(c_member(U_13650),sK310(U_13652,U_13651,U_13650)),U_13651))
        | ~ sP987(U_13651,U_13652,U_13650) )
    & ! [U_13651,U_13652,U_13650] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13650,tc_Nat_Onat),U_13652),U_13651)))
        | sP987(U_13651,U_13652,U_13650)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13650),U_13651)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP987])],[f_3495_3]) ).

cnf(f_3495_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13650,tc_Nat_Onat),U_13652),U_13651)))
    | sP987(U_13651,U_13652,U_13650)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13650),U_13651)) ),
    inference(clausify,[status(thm)],[f_3495_4]) ).

cnf(f_3495_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13650),sK310(U_13652,U_13651,U_13650)),U_13651))
    | ~ sP987(U_13651,U_13652,U_13650) ),
    inference(clausify,[status(thm)],[f_3495_4]) ).

cnf(f_3495_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13652,sK310(U_13652,U_13651,U_13650))))
    | ~ sP987(U_13651,U_13652,U_13650) ),
    inference(clausify,[status(thm)],[f_3495_4]) ).

fof(f_3496_1,plain,
    ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Id__on]) ).

fof(f_3496_2,plain,
    ! [U_13654,U_13653] : c_Relation_Orefl__on(U_13653,U_13654,c_Relation_OId__on(U_13653,U_13654)),
    inference(variable_rename,[status(thm)],[f_3496_1]) ).

fof(f_3496_3,plain,
    ! [U_13654,U_13653] : c_Relation_Orefl__on(U_13653,U_13654,c_Relation_OId__on(U_13653,U_13654)),
    inference(definitional_conversion,[status(esa)],[f_3496_2]) ).

cnf(f_3496_4,plain,
    c_Relation_Orefl__on(U_13653,U_13654,c_Relation_OId__on(U_13653,U_13654)),
    inference(clausify,[status(thm)],[f_3496_3]) ).

fof(f_3497_1,plain,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_refl__on__empty]) ).

fof(f_3497_2,plain,
    ! [U_13655] : c_Relation_Orefl__on(U_13655,c_Orderings_Obot__class_Obot(tc_fun(U_13655,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13655,U_13655),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3497_1]) ).

fof(f_3497_3,plain,
    ! [U_13655] : c_Relation_Orefl__on(U_13655,c_Orderings_Obot__class_Obot(tc_fun(U_13655,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13655,U_13655),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3497_2]) ).

cnf(f_3497_4,plain,
    c_Relation_Orefl__on(U_13655,c_Orderings_Obot__class_Obot(tc_fun(U_13655,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13655,U_13655),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3497_3]) ).

fof(f_3498_1,plain,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Un]) ).

fof(f_3498_2,plain,
    ! [U_13660,U_13659,U_13658,U_13657,U_13656] :
      ( c_Relation_Orefl__on(U_13656,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13656,tc_HOL_Obool)),U_13657),U_13659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13656,U_13656),tc_HOL_Obool)),U_13658),U_13660))
      | ~ c_Relation_Orefl__on(U_13656,U_13659,U_13660)
      | ~ c_Relation_Orefl__on(U_13656,U_13657,U_13658) ),
    inference(variable_rename,[status(thm)],[f_3498_1]) ).

fof(f_3498_3,plain,
    ! [U_13656,U_13657,U_13658,U_13659,U_13660] :
      ( c_Relation_Orefl__on(U_13656,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13656,tc_HOL_Obool)),U_13657),U_13659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13656,U_13656),tc_HOL_Obool)),U_13658),U_13660))
      | ~ c_Relation_Orefl__on(U_13656,U_13659,U_13660)
      | ~ c_Relation_Orefl__on(U_13656,U_13657,U_13658) ),
    inference(definitional_conversion,[status(esa)],[f_3498_2]) ).

cnf(f_3498_4,plain,
    ( c_Relation_Orefl__on(U_13656,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13656,tc_HOL_Obool)),U_13657),U_13659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13656,U_13656),tc_HOL_Obool)),U_13658),U_13660))
    | ~ c_Relation_Orefl__on(U_13656,U_13659,U_13660)
    | ~ c_Relation_Orefl__on(U_13656,U_13657,U_13658) ),
    inference(clausify,[status(thm)],[f_3498_3]) ).

fof(f_3499_1,plain,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Int]) ).

fof(f_3499_2,plain,
    ! [U_13665,U_13664,U_13663,U_13662,U_13661] :
      ( c_Relation_Orefl__on(U_13661,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13661,tc_HOL_Obool)),U_13662),U_13664),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13661,U_13661),tc_HOL_Obool)),U_13663),U_13665))
      | ~ c_Relation_Orefl__on(U_13661,U_13664,U_13665)
      | ~ c_Relation_Orefl__on(U_13661,U_13662,U_13663) ),
    inference(variable_rename,[status(thm)],[f_3499_1]) ).

fof(f_3499_3,plain,
    ! [U_13661,U_13662,U_13663,U_13664,U_13665] :
      ( c_Relation_Orefl__on(U_13661,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13661,tc_HOL_Obool)),U_13662),U_13664),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13661,U_13661),tc_HOL_Obool)),U_13663),U_13665))
      | ~ c_Relation_Orefl__on(U_13661,U_13664,U_13665)
      | ~ c_Relation_Orefl__on(U_13661,U_13662,U_13663) ),
    inference(definitional_conversion,[status(esa)],[f_3499_2]) ).

cnf(f_3499_4,plain,
    ( c_Relation_Orefl__on(U_13661,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13661,tc_HOL_Obool)),U_13662),U_13664),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13661,U_13661),tc_HOL_Obool)),U_13663),U_13665))
    | ~ c_Relation_Orefl__on(U_13661,U_13664,U_13665)
    | ~ c_Relation_Orefl__on(U_13661,U_13662,U_13663) ),
    inference(clausify,[status(thm)],[f_3499_3]) ).

fof(f_3500_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD2]) ).

fof(f_3500_2,plain,
    ! [U_13670,U_13669,U_13668,U_13667,U_13666] :
      ( hBOOL(hAPP(hAPP(c_member(U_13666),U_13670),U_13667))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13666,U_13666)),hAPP(hAPP(c_Product__Type_OPair(U_13666,U_13666),U_13669),U_13670)),U_13668))
      | ~ c_Relation_Orefl__on(U_13666,U_13667,U_13668) ),
    inference(variable_rename,[status(thm)],[f_3500_1]) ).

fof(f_3500_3,plain,
    ! [U_13666,U_13667,U_13668,U_13669,U_13670] :
      ( hBOOL(hAPP(hAPP(c_member(U_13666),U_13670),U_13667))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13666,U_13666)),hAPP(hAPP(c_Product__Type_OPair(U_13666,U_13666),U_13669),U_13670)),U_13668))
      | ~ c_Relation_Orefl__on(U_13666,U_13667,U_13668) ),
    inference(definitional_conversion,[status(esa)],[f_3500_2]) ).

cnf(f_3500_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13666),U_13670),U_13667))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13666,U_13666)),hAPP(hAPP(c_Product__Type_OPair(U_13666,U_13666),U_13669),U_13670)),U_13668))
    | ~ c_Relation_Orefl__on(U_13666,U_13667,U_13668) ),
    inference(clausify,[status(thm)],[f_3500_3]) ).

fof(f_3501_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD1]) ).

fof(f_3501_2,plain,
    ! [U_13675,U_13674,U_13673,U_13672,U_13671] :
      ( hBOOL(hAPP(hAPP(c_member(U_13671),U_13674),U_13672))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13671,U_13671)),hAPP(hAPP(c_Product__Type_OPair(U_13671,U_13671),U_13674),U_13675)),U_13673))
      | ~ c_Relation_Orefl__on(U_13671,U_13672,U_13673) ),
    inference(variable_rename,[status(thm)],[f_3501_1]) ).

fof(f_3501_3,plain,
    ! [U_13671,U_13672,U_13673,U_13674,U_13675] :
      ( hBOOL(hAPP(hAPP(c_member(U_13671),U_13674),U_13672))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13671,U_13671)),hAPP(hAPP(c_Product__Type_OPair(U_13671,U_13671),U_13674),U_13675)),U_13673))
      | ~ c_Relation_Orefl__on(U_13671,U_13672,U_13673) ),
    inference(definitional_conversion,[status(esa)],[f_3501_2]) ).

cnf(f_3501_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13671),U_13674),U_13672))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13671,U_13671)),hAPP(hAPP(c_Product__Type_OPair(U_13671,U_13671),U_13674),U_13675)),U_13673))
    | ~ c_Relation_Orefl__on(U_13671,U_13672,U_13673) ),
    inference(clausify,[status(thm)],[f_3501_3]) ).

fof(f_3502_1,plain,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD]) ).

fof(f_3502_2,plain,
    ! [U_13679,U_13678,U_13677,U_13676] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13676,U_13676)),hAPP(hAPP(c_Product__Type_OPair(U_13676,U_13676),U_13679),U_13679)),U_13678))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13676),U_13679),U_13677))
      | ~ c_Relation_Orefl__on(U_13676,U_13677,U_13678) ),
    inference(variable_rename,[status(thm)],[f_3502_1]) ).

fof(f_3502_3,plain,
    ! [U_13676,U_13677,U_13678,U_13679] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13676,U_13676)),hAPP(hAPP(c_Product__Type_OPair(U_13676,U_13676),U_13679),U_13679)),U_13678))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13676),U_13679),U_13677))
      | ~ c_Relation_Orefl__on(U_13676,U_13677,U_13678) ),
    inference(definitional_conversion,[status(esa)],[f_3502_2]) ).

cnf(f_3502_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13676,U_13676)),hAPP(hAPP(c_Product__Type_OPair(U_13676,U_13676),U_13679),U_13679)),U_13678))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13676),U_13679),U_13677))
    | ~ c_Relation_Orefl__on(U_13676,U_13677,U_13678) ),
    inference(clausify,[status(thm)],[f_3502_3]) ).

fof(f_3503_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onI]) ).

fof(f_3503_2,plain,
    ! [U_13683,U_13682,U_13681] :
      ( c_Relation_Orefl__on(U_13681,U_13683,U_13682)
      | ? [U_13680] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13681,U_13681)),hAPP(hAPP(c_Product__Type_OPair(U_13681,U_13681),U_13680),U_13680)),U_13682))
          & hBOOL(hAPP(hAPP(c_member(U_13681),U_13680),U_13683)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13681,U_13681),tc_HOL_Obool)),U_13682),hAPP(hAPP(c_Product__Type_OSigma(U_13681,U_13681),U_13683),hAPP(c_COMBK(tc_fun(U_13681,tc_HOL_Obool),U_13681),U_13683)))) ),
    inference(variable_rename,[status(thm)],[f_3503_1]) ).

fof(f_3503_3,plain,
    ! [U_13683,U_13682,U_13681] :
      ( c_Relation_Orefl__on(U_13681,U_13683,U_13682)
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13681,U_13681)),hAPP(hAPP(c_Product__Type_OPair(U_13681,U_13681),sK311(U_13683,U_13682,U_13681)),sK311(U_13683,U_13682,U_13681))),U_13682))
        & hBOOL(hAPP(hAPP(c_member(U_13681),sK311(U_13683,U_13682,U_13681)),U_13683)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13681,U_13681),tc_HOL_Obool)),U_13682),hAPP(hAPP(c_Product__Type_OSigma(U_13681,U_13681),U_13683),hAPP(c_COMBK(tc_fun(U_13681,tc_HOL_Obool),U_13681),U_13683)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_13680,sK311(U_13683,U_13682,U_13681))],[f_3503_2]) ).

fof(f_3503_4,plain,
    ( ! [U_13681,U_13682,U_13683] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13681,U_13681)),hAPP(hAPP(c_Product__Type_OPair(U_13681,U_13681),sK311(U_13683,U_13682,U_13681)),sK311(U_13683,U_13682,U_13681))),U_13682))
        | ~ sP988(U_13681,U_13682,U_13683) )
    & ! [U_13681,U_13682,U_13683] :
        ( hBOOL(hAPP(hAPP(c_member(U_13681),sK311(U_13683,U_13682,U_13681)),U_13683))
        | ~ sP988(U_13681,U_13682,U_13683) )
    & ! [U_13681,U_13682,U_13683] :
        ( c_Relation_Orefl__on(U_13681,U_13683,U_13682)
        | sP988(U_13681,U_13682,U_13683)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13681,U_13681),tc_HOL_Obool)),U_13682),hAPP(hAPP(c_Product__Type_OSigma(U_13681,U_13681),U_13683),hAPP(c_COMBK(tc_fun(U_13681,tc_HOL_Obool),U_13681),U_13683)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP988])],[f_3503_3]) ).

cnf(f_3503_5,plain,
    ( c_Relation_Orefl__on(U_13681,U_13683,U_13682)
    | sP988(U_13681,U_13682,U_13683)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13681,U_13681),tc_HOL_Obool)),U_13682),hAPP(hAPP(c_Product__Type_OSigma(U_13681,U_13681),U_13683),hAPP(c_COMBK(tc_fun(U_13681,tc_HOL_Obool),U_13681),U_13683)))) ),
    inference(clausify,[status(thm)],[f_3503_4]) ).

cnf(f_3503_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13681),sK311(U_13683,U_13682,U_13681)),U_13683))
    | ~ sP988(U_13681,U_13682,U_13683) ),
    inference(clausify,[status(thm)],[f_3503_4]) ).

cnf(f_3503_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13681,U_13681)),hAPP(hAPP(c_Product__Type_OPair(U_13681,U_13681),sK311(U_13683,U_13682,U_13681)),sK311(U_13683,U_13682,U_13681))),U_13682))
    | ~ sP988(U_13681,U_13682,U_13683) ),
    inference(clausify,[status(thm)],[f_3503_4]) ).

fof(f_3504_1,plain,
    ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) != hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute]) ).

fof(f_3504_2,plain,
    ! [U_13690,U_13689,U_13688,U_13687,U_13686] :
      ( hAPP(U_13689,hAPP(U_13688,U_13690)) = hAPP(U_13688,hAPP(c_Set_Oimage(U_13686,U_13686,U_13689),U_13690))
      | U_13690 = c_Orderings_Obot__class_Obot(tc_fun(U_13686,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13686),U_13690))
      | ? [U_13685,U_13684] : hAPP(U_13689,hAPP(hAPP(U_13687,U_13685),U_13684)) != hAPP(hAPP(U_13687,hAPP(U_13689,U_13685)),hAPP(U_13689,U_13684))
      | ~ c_Finite__Set_Ofolding__one__idem(U_13686,U_13687,U_13688) ),
    inference(variable_rename,[status(thm)],[f_3504_1]) ).

fof(f_3504_3,plain,
    ! [U_13690,U_13689,U_13688,U_13687,U_13686] :
      ( hAPP(U_13689,hAPP(U_13688,U_13690)) = hAPP(U_13688,hAPP(c_Set_Oimage(U_13686,U_13686,U_13689),U_13690))
      | U_13690 = c_Orderings_Obot__class_Obot(tc_fun(U_13686,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13686),U_13690))
      | ? [U_13684] : hAPP(U_13689,hAPP(hAPP(U_13687,sK312(U_13690,U_13689,U_13688,U_13687,U_13686)),U_13684)) != hAPP(hAPP(U_13687,hAPP(U_13689,sK312(U_13690,U_13689,U_13688,U_13687,U_13686))),hAPP(U_13689,U_13684))
      | ~ c_Finite__Set_Ofolding__one__idem(U_13686,U_13687,U_13688) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_13685,sK312(U_13690,U_13689,U_13688,U_13687,U_13686))],[f_3504_2]) ).

fof(f_3504_4,plain,
    ! [U_13690,U_13689,U_13688,U_13687,U_13686] :
      ( hAPP(U_13689,hAPP(U_13688,U_13690)) = hAPP(U_13688,hAPP(c_Set_Oimage(U_13686,U_13686,U_13689),U_13690))
      | U_13690 = c_Orderings_Obot__class_Obot(tc_fun(U_13686,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13686),U_13690))
      | hAPP(U_13689,hAPP(hAPP(U_13687,sK312(U_13690,U_13689,U_13688,U_13687,U_13686)),sK313(U_13690,U_13689,U_13688,U_13687,U_13686))) != hAPP(hAPP(U_13687,hAPP(U_13689,sK312(U_13690,U_13689,U_13688,U_13687,U_13686))),hAPP(U_13689,sK313(U_13690,U_13689,U_13688,U_13687,U_13686)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_13686,U_13687,U_13688) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_13684,sK313(U_13690,U_13689,U_13688,U_13687,U_13686))],[f_3504_3]) ).

fof(f_3504_5,plain,
    ! [U_13686,U_13687,U_13688,U_13689,U_13690] :
      ( hAPP(U_13689,hAPP(U_13688,U_13690)) = hAPP(U_13688,hAPP(c_Set_Oimage(U_13686,U_13686,U_13689),U_13690))
      | U_13690 = c_Orderings_Obot__class_Obot(tc_fun(U_13686,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13686),U_13690))
      | hAPP(U_13689,hAPP(hAPP(U_13687,sK312(U_13690,U_13689,U_13688,U_13687,U_13686)),sK313(U_13690,U_13689,U_13688,U_13687,U_13686))) != hAPP(hAPP(U_13687,hAPP(U_13689,sK312(U_13690,U_13689,U_13688,U_13687,U_13686))),hAPP(U_13689,sK313(U_13690,U_13689,U_13688,U_13687,U_13686)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_13686,U_13687,U_13688) ),
    inference(definitional_conversion,[status(esa)],[f_3504_4]) ).

cnf(f_3504_6,plain,
    ( hAPP(U_13689,hAPP(U_13688,U_13690)) = hAPP(U_13688,hAPP(c_Set_Oimage(U_13686,U_13686,U_13689),U_13690))
    | U_13690 = c_Orderings_Obot__class_Obot(tc_fun(U_13686,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13686),U_13690))
    | hAPP(U_13689,hAPP(hAPP(U_13687,sK312(U_13690,U_13689,U_13688,U_13687,U_13686)),sK313(U_13690,U_13689,U_13688,U_13687,U_13686))) != hAPP(hAPP(U_13687,hAPP(U_13689,sK312(U_13690,U_13689,U_13688,U_13687,U_13686))),hAPP(U_13689,sK313(U_13690,U_13689,U_13688,U_13687,U_13686)))
    | ~ c_Finite__Set_Ofolding__one__idem(U_13686,U_13687,U_13688) ),
    inference(clausify,[status(thm)],[f_3504_5]) ).

fof(f_3505_1,plain,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(V_P_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct]) ).

fof(f_3505_2,plain,
    ! [U_13693,U_13692] :
      ( hBOOL(hAPP(U_13693,U_13692))
      | ? [U_13691] : ~ hBOOL(hAPP(U_13693,hAPP(c_Int_ORep__Integ,U_13691)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13692),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3505_1]) ).

fof(f_3505_3,plain,
    ! [U_13693,U_13692] :
      ( hBOOL(hAPP(U_13693,U_13692))
      | ~ hBOOL(hAPP(U_13693,hAPP(c_Int_ORep__Integ,sK314(U_13693,U_13692))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13692),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_13691,sK314(U_13693,U_13692))],[f_3505_2]) ).

fof(f_3505_4,plain,
    ! [U_13693,U_13692] :
      ( hBOOL(hAPP(U_13693,U_13692))
      | ~ hBOOL(hAPP(U_13693,hAPP(c_Int_ORep__Integ,sK314(U_13693,U_13692))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13692),c_Int_OInteg)) ),
    inference(definitional_conversion,[status(esa)],[f_3505_3]) ).

cnf(f_3505_5,plain,
    ( hBOOL(hAPP(U_13693,U_13692))
    | ~ hBOOL(hAPP(U_13693,hAPP(c_Int_ORep__Integ,sK314(U_13693,U_13692))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13692),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3505_4]) ).

fof(f_3506_1,plain,
    ! [V_y_2] :
      ( ? [B_x] : V_y_2 = hAPP(c_Int_ORep__Integ,B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases]) ).

fof(f_3506_2,plain,
    ! [U_13695] :
      ( ? [U_13694] : U_13695 = hAPP(c_Int_ORep__Integ,U_13694)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13695),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3506_1]) ).

fof(f_3506_3,plain,
    ! [U_13695] :
      ( U_13695 = hAPP(c_Int_ORep__Integ,sK315(U_13695))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13695),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_13694,sK315(U_13695))],[f_3506_2]) ).

fof(f_3506_4,plain,
    ! [U_13695] :
      ( U_13695 = hAPP(c_Int_ORep__Integ,sK315(U_13695))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13695),c_Int_OInteg)) ),
    inference(definitional_conversion,[status(esa)],[f_3506_3]) ).

cnf(f_3506_5,plain,
    ( U_13695 = hAPP(c_Int_ORep__Integ,sK315(U_13695))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13695),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3506_4]) ).

fof(f_3507_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != V_z_2
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral]) ).

fof(f_3507_2,plain,
    ! [U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698,U_13697] :
      ( hAPP(U_13702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)) = hAPP(hAPP(U_13699,hAPP(U_13702,U_13703)),hAPP(U_13702,U_13704))
      | ? [U_13696] :
          ( hAPP(U_13701,U_13696) != U_13700
          & hBOOL(hAPP(hAPP(c_member(U_13698),U_13696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13704))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13703))
      | ~ c_Finite__Set_Ofolding__image__simple(U_13697,U_13698,U_13699,U_13700,U_13701,U_13702) ),
    inference(variable_rename,[status(thm)],[f_3507_1]) ).

fof(f_3507_3,plain,
    ! [U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698] :
      ( ! [U_13697] : ~ c_Finite__Set_Ofolding__image__simple(U_13697,U_13698,U_13699,U_13700,U_13701,U_13702)
      | hAPP(U_13702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)) = hAPP(hAPP(U_13699,hAPP(U_13702,U_13703)),hAPP(U_13702,U_13704))
      | ? [U_13696] :
          ( hAPP(U_13701,U_13696) != U_13700
          & hBOOL(hAPP(hAPP(c_member(U_13698),U_13696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13704))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13703)) ),
    inference(miniscope,[status(thm)],[f_3507_2]) ).

fof(f_3507_4,plain,
    ! [U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698] :
      ( ! [U_13697] : ~ c_Finite__Set_Ofolding__image__simple(U_13697,U_13698,U_13699,U_13700,U_13701,U_13702)
      | hAPP(U_13702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)) = hAPP(hAPP(U_13699,hAPP(U_13702,U_13703)),hAPP(U_13702,U_13704))
      | ( hAPP(U_13701,sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698)) != U_13700
        & hBOOL(hAPP(hAPP(c_member(U_13698),sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13704))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13703)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_13696,sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698))],[f_3507_3]) ).

fof(f_3507_5,plain,
    ( ! [U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704] :
        ( hAPP(U_13701,sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698)) != U_13700
        | ~ sP989(U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704) )
    & ! [U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704] :
        ( hBOOL(hAPP(hAPP(c_member(U_13698),sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)))
        | ~ sP989(U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704) )
    & ! [U_13697,U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704] :
        ( ~ c_Finite__Set_Ofolding__image__simple(U_13697,U_13698,U_13699,U_13700,U_13701,U_13702)
        | hAPP(U_13702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)) = hAPP(hAPP(U_13699,hAPP(U_13702,U_13703)),hAPP(U_13702,U_13704))
        | sP989(U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13704))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13703)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP989])],[f_3507_4]) ).

cnf(f_3507_6,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_13697,U_13698,U_13699,U_13700,U_13701,U_13702)
    | hAPP(U_13702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)) = hAPP(hAPP(U_13699,hAPP(U_13702,U_13703)),hAPP(U_13702,U_13704))
    | sP989(U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13704))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13698),U_13703)) ),
    inference(clausify,[status(thm)],[f_3507_5]) ).

cnf(f_3507_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13698),sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13698,tc_HOL_Obool)),U_13703),U_13704)))
    | ~ sP989(U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704) ),
    inference(clausify,[status(thm)],[f_3507_5]) ).

cnf(f_3507_8,plain,
    ( hAPP(U_13701,sK316(U_13704,U_13703,U_13702,U_13701,U_13700,U_13699,U_13698)) != U_13700
    | ~ sP989(U_13698,U_13699,U_13700,U_13701,U_13702,U_13703,U_13704) ),
    inference(clausify,[status(thm)],[f_3507_5]) ).

fof(f_3508_1,plain,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

fof(f_3508_2,plain,
    ! [U_13705] : c_Finite__Set_Ofun__left__comm__idem(U_13705,tc_fun(U_13705,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13705,tc_HOL_Obool),tc_fun(tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),U_13705),hAPP(c_COMBC(tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_13705,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_13705,tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),c_Set_Oinsert(U_13705)),c_Orderings_Obot__class_Obot(tc_fun(U_13705,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3508_1]) ).

fof(f_3508_3,plain,
    ! [U_13705] : c_Finite__Set_Ofun__left__comm__idem(U_13705,tc_fun(U_13705,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13705,tc_HOL_Obool),tc_fun(tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),U_13705),hAPP(c_COMBC(tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_13705,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_13705,tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),c_Set_Oinsert(U_13705)),c_Orderings_Obot__class_Obot(tc_fun(U_13705,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3508_2]) ).

cnf(f_3508_4,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_13705,tc_fun(U_13705,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13705,tc_HOL_Obool),tc_fun(tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),U_13705),hAPP(c_COMBC(tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_13705,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_13705,tc_fun(U_13705,tc_HOL_Obool),tc_fun(U_13705,tc_HOL_Obool)),c_Set_Oinsert(U_13705)),c_Orderings_Obot__class_Obot(tc_fun(U_13705,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3508_3]) ).

fof(f_3509_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup]) ).

fof(f_3509_2,plain,
    ! [U_13706] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13706,U_13706,c_Orderings_Oord__class_Omax(U_13706))
      | ~ class_Orderings_Olinorder(U_13706) ),
    inference(variable_rename,[status(thm)],[f_3509_1]) ).

fof(f_3509_3,plain,
    ! [U_13706] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13706,U_13706,c_Orderings_Oord__class_Omax(U_13706))
      | ~ class_Orderings_Olinorder(U_13706) ),
    inference(definitional_conversion,[status(esa)],[f_3509_2]) ).

cnf(f_3509_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_13706,U_13706,c_Orderings_Oord__class_Omax(U_13706))
    | ~ class_Orderings_Olinorder(U_13706) ),
    inference(clausify,[status(thm)],[f_3509_3]) ).

fof(f_3510_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup]) ).

fof(f_3510_2,plain,
    ! [U_13707] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13707,U_13707,c_Lattices_Osemilattice__sup__class_Osup(U_13707))
      | ~ class_Lattices_Osemilattice__sup(U_13707) ),
    inference(variable_rename,[status(thm)],[f_3510_1]) ).

fof(f_3510_3,plain,
    ! [U_13707] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13707,U_13707,c_Lattices_Osemilattice__sup__class_Osup(U_13707))
      | ~ class_Lattices_Osemilattice__sup(U_13707) ),
    inference(definitional_conversion,[status(esa)],[f_3510_2]) ).

cnf(f_3510_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_13707,U_13707,c_Lattices_Osemilattice__sup__class_Osup(U_13707))
    | ~ class_Lattices_Osemilattice__sup(U_13707) ),
    inference(clausify,[status(thm)],[f_3510_3]) ).

fof(f_3511_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf]) ).

fof(f_3511_2,plain,
    ! [U_13708] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13708,U_13708,c_Lattices_Osemilattice__inf__class_Oinf(U_13708))
      | ~ class_Lattices_Osemilattice__inf(U_13708) ),
    inference(variable_rename,[status(thm)],[f_3511_1]) ).

fof(f_3511_3,plain,
    ! [U_13708] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13708,U_13708,c_Lattices_Osemilattice__inf__class_Oinf(U_13708))
      | ~ class_Lattices_Osemilattice__inf(U_13708) ),
    inference(definitional_conversion,[status(esa)],[f_3511_2]) ).

cnf(f_3511_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_13708,U_13708,c_Lattices_Osemilattice__inf__class_Oinf(U_13708))
    | ~ class_Lattices_Osemilattice__inf(U_13708) ),
    inference(clausify,[status(thm)],[f_3511_3]) ).

fof(f_3512_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply]) ).

fof(f_3512_2,plain,
    ! [U_13713,U_13712,U_13711,U_13710,U_13709] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13712,U_13710,hAPP(hAPP(c_COMBB(U_13709,tc_fun(U_13710,U_13710),U_13712),U_13711),U_13713))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_13709,U_13710,U_13711) ),
    inference(variable_rename,[status(thm)],[f_3512_1]) ).

fof(f_3512_3,plain,
    ! [U_13710,U_13709,U_13711,U_13712,U_13713] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13712,U_13710,hAPP(hAPP(c_COMBB(U_13709,tc_fun(U_13710,U_13710),U_13712),U_13711),U_13713))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_13709,U_13710,U_13711) ),
    inference(definitional_conversion,[status(esa)],[f_3512_2]) ).

cnf(f_3512_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_13712,U_13710,hAPP(hAPP(c_COMBB(U_13709,tc_fun(U_13710,U_13710),U_13712),U_13711),U_13713))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_13709,U_13710,U_13711) ),
    inference(clausify,[status(thm)],[f_3512_3]) ).

fof(f_3513_1,plain,
    ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem]) ).

fof(f_3513_2,plain,
    ! [U_13718,U_13717,U_13716,U_13715,U_13714] :
      ( hAPP(hAPP(U_13716,U_13717),hAPP(hAPP(U_13716,U_13717),U_13718)) = hAPP(hAPP(U_13716,U_13717),U_13718)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_13714,U_13715,U_13716) ),
    inference(variable_rename,[status(thm)],[f_3513_1]) ).

fof(f_3513_3,plain,
    ! [U_13718,U_13717,U_13716] :
      ( ! [U_13715,U_13714] : ~ c_Finite__Set_Ofun__left__comm__idem(U_13714,U_13715,U_13716)
      | hAPP(hAPP(U_13716,U_13717),hAPP(hAPP(U_13716,U_13717),U_13718)) = hAPP(hAPP(U_13716,U_13717),U_13718) ),
    inference(miniscope,[status(thm)],[f_3513_2]) ).

fof(f_3513_4,plain,
    ! [U_13716,U_13717,U_13714,U_13715,U_13718] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(U_13714,U_13715,U_13716)
      | hAPP(hAPP(U_13716,U_13717),hAPP(hAPP(U_13716,U_13717),U_13718)) = hAPP(hAPP(U_13716,U_13717),U_13718) ),
    inference(definitional_conversion,[status(esa)],[f_3513_3]) ).

cnf(f_3513_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_13714,U_13715,U_13716)
    | hAPP(hAPP(U_13716,U_13717),hAPP(hAPP(U_13716,U_13717),U_13718)) = hAPP(hAPP(U_13716,U_13717),U_13718) ),
    inference(clausify,[status(thm)],[f_3513_4]) ).

fof(f_3514_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem]) ).

fof(f_3514_2,plain,
    ! [U_13719] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13719,U_13719,c_Groups_Otimes__class_Otimes(U_13719))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13719) ),
    inference(variable_rename,[status(thm)],[f_3514_1]) ).

fof(f_3514_3,plain,
    ! [U_13719] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13719,U_13719,c_Groups_Otimes__class_Otimes(U_13719))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_13719) ),
    inference(definitional_conversion,[status(esa)],[f_3514_2]) ).

cnf(f_3514_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_13719,U_13719,c_Groups_Otimes__class_Otimes(U_13719))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_13719) ),
    inference(clausify,[status(thm)],[f_3514_3]) ).

fof(f_3515_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf]) ).

fof(f_3515_2,plain,
    ! [U_13720] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13720,U_13720,c_Orderings_Oord__class_Omin(U_13720))
      | ~ class_Orderings_Olinorder(U_13720) ),
    inference(variable_rename,[status(thm)],[f_3515_1]) ).

fof(f_3515_3,plain,
    ! [U_13720] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_13720,U_13720,c_Orderings_Oord__class_Omin(U_13720))
      | ~ class_Orderings_Olinorder(U_13720) ),
    inference(definitional_conversion,[status(esa)],[f_3515_2]) ).

cnf(f_3515_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_13720,U_13720,c_Orderings_Oord__class_Omin(U_13720))
    | ~ class_Orderings_Olinorder(U_13720) ),
    inference(clausify,[status(thm)],[f_3515_3]) ).

fof(f_3516_1,plain,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(f_3516_2,plain,
    ! [U_13721] : c_Finite__Set_Ofun__left__comm__idem(U_13721,tc_fun(U_13721,tc_HOL_Obool),c_Set_Oinsert(U_13721)),
    inference(variable_rename,[status(thm)],[f_3516_1]) ).

fof(f_3516_3,plain,
    ! [U_13721] : c_Finite__Set_Ofun__left__comm__idem(U_13721,tc_fun(U_13721,tc_HOL_Obool),c_Set_Oinsert(U_13721)),
    inference(definitional_conversion,[status(esa)],[f_3516_2]) ).

cnf(f_3516_4,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_13721,tc_fun(U_13721,tc_HOL_Obool),c_Set_Oinsert(U_13721)),
    inference(clausify,[status(thm)],[f_3516_3]) ).

fof(f_3517_1,plain,
    ! [V_i_2,V_M_2] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__less__Suc2]) ).

fof(f_3517_2,plain,
    ! [U_13723,U_13722] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13722))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13723)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13722))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13723)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13722)) ),
    inference(variable_rename,[status(thm)],[f_3517_1]) ).

fof(f_3517_3,plain,
    ! [U_13722,U_13723] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13722))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13723)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13722))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13723)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13722)) ),
    inference(definitional_conversion,[status(esa)],[f_3517_2]) ).

cnf(f_3517_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13722))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13723)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13722))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13723)))))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13722)) ),
    inference(clausify,[status(thm)],[f_3517_3]) ).

fof(f_3518_1,plain,
    ! [V_i_2,V_M_2] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__less]) ).

fof(f_3518_2,plain,
    ! [U_13725,U_13724] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13724))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13725))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13724)) ),
    inference(variable_rename,[status(thm)],[f_3518_1]) ).

fof(f_3518_3,plain,
    ! [U_13724,U_13725] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13724))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13725))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13724)) ),
    inference(definitional_conversion,[status(esa)],[f_3518_2]) ).

cnf(f_3518_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13724))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13725))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13724)) ),
    inference(clausify,[status(thm)],[f_3518_3]) ).

fof(f_3519_1,plain,
    ! [V_i_2,V_M_2] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__less__Suc]) ).

fof(f_3519_2,plain,
    ! [U_13727,U_13726] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13726))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13727))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13726))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13727)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13726)) ),
    inference(variable_rename,[status(thm)],[f_3519_1]) ).

fof(f_3519_3,plain,
    ! [U_13726,U_13727] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13726))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13727))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13726))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13727)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13726)) ),
    inference(definitional_conversion,[status(esa)],[f_3519_2]) ).

cnf(f_3519_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13726))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13727))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13726))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13727)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13726)) ),
    inference(clausify,[status(thm)],[f_3519_3]) ).

fof(f_3520_1,plain,
    ! [T_b,V_a_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_CollectI]) ).

fof(f_3520_2,plain,
    ! [U_13730,U_13729,U_13728] :
      ( hBOOL(hAPP(hAPP(c_member(U_13730),U_13729),hAPP(c_Set_OCollect(U_13730),U_13728)))
      | ~ hBOOL(hAPP(U_13728,U_13729)) ),
    inference(variable_rename,[status(thm)],[f_3520_1]) ).

fof(f_3520_3,plain,
    ! [U_13728,U_13729,U_13730] :
      ( hBOOL(hAPP(hAPP(c_member(U_13730),U_13729),hAPP(c_Set_OCollect(U_13730),U_13728)))
      | ~ hBOOL(hAPP(U_13728,U_13729)) ),
    inference(definitional_conversion,[status(esa)],[f_3520_2]) ).

cnf(f_3520_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13730),U_13729),hAPP(c_Set_OCollect(U_13730),U_13728)))
    | ~ hBOOL(hAPP(U_13728,U_13729)) ),
    inference(clausify,[status(thm)],[f_3520_3]) ).

fof(f_3521_1,plain,
    ! [V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).

fof(f_3521_2,plain,
    ! [U_13733,U_13732,U_13731] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),hAPP(hAPP(c_COMBS(U_13731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13731),c_fconj),U_13732)),U_13733))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),U_13733)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),U_13732))) ) ),
    inference(variable_rename,[status(thm)],[f_3521_1]) ).

fof(f_3521_3,plain,
    ( ! [U_13731,U_13732,U_13733] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),U_13733)))
        | ~ sP990(U_13731,U_13732,U_13733) )
    & ! [U_13731,U_13732,U_13733] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),U_13732)))
        | ~ sP990(U_13731,U_13732,U_13733) )
    & ! [U_13731,U_13732,U_13733] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),hAPP(hAPP(c_COMBS(U_13731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13731),c_fconj),U_13732)),U_13733))))
        | sP990(U_13731,U_13732,U_13733) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP990])],[f_3521_2]) ).

cnf(f_3521_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),hAPP(hAPP(c_COMBS(U_13731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13731),c_fconj),U_13732)),U_13733))))
    | sP990(U_13731,U_13732,U_13733) ),
    inference(clausify,[status(thm)],[f_3521_3]) ).

cnf(f_3521_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),U_13732)))
    | ~ sP990(U_13731,U_13732,U_13733) ),
    inference(clausify,[status(thm)],[f_3521_3]) ).

cnf(f_3521_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13731),hAPP(c_Set_OCollect(U_13731),U_13733)))
    | ~ sP990(U_13731,U_13732,U_13733) ),
    inference(clausify,[status(thm)],[f_3521_3]) ).

fof(f_3522_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__less__nat]) ).

fof(f_3522_2,plain,
    ! [U_13734] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13734)))),
    inference(variable_rename,[status(thm)],[f_3522_1]) ).

fof(f_3522_3,plain,
    ! [U_13734] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13734)))),
    inference(definitional_conversion,[status(esa)],[f_3522_2]) ).

cnf(f_3522_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13734)))),
    inference(clausify,[status(thm)],[f_3522_3]) ).

fof(f_3523_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__le__nat]) ).

fof(f_3523_2,plain,
    ! [U_13735] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_13735)))),
    inference(variable_rename,[status(thm)],[f_3523_1]) ).

fof(f_3523_3,plain,
    ! [U_13735] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_13735)))),
    inference(definitional_conversion,[status(esa)],[f_3523_2]) ).

cnf(f_3523_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_13735)))),
    inference(clausify,[status(thm)],[f_3523_3]) ).

fof(f_3524_1,plain,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).

fof(f_3524_2,plain,
    ! [U_13739,U_13738,U_13737,U_13736] : hAPP(c_Set_OCollect(tc_prod(U_13736,U_13737)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13736,U_13737,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13736,tc_fun(U_13737,tc_HOL_Obool),tc_fun(U_13737,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13737,tc_HOL_Obool),tc_fun(U_13737,tc_HOL_Obool)),U_13736),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13737)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13736),c_fconj),U_13738))),U_13739))) = hAPP(hAPP(c_Product__Type_OSigma(U_13736,U_13737),hAPP(c_Set_OCollect(U_13736),U_13738)),hAPP(c_COMBK(tc_fun(U_13737,tc_HOL_Obool),U_13736),hAPP(c_Set_OCollect(U_13737),U_13739))),
    inference(variable_rename,[status(thm)],[f_3524_1]) ).

fof(f_3524_3,plain,
    ! [U_13736,U_13737,U_13738,U_13739] : hAPP(c_Set_OCollect(tc_prod(U_13736,U_13737)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13736,U_13737,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13736,tc_fun(U_13737,tc_HOL_Obool),tc_fun(U_13737,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13737,tc_HOL_Obool),tc_fun(U_13737,tc_HOL_Obool)),U_13736),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13737)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13736),c_fconj),U_13738))),U_13739))) = hAPP(hAPP(c_Product__Type_OSigma(U_13736,U_13737),hAPP(c_Set_OCollect(U_13736),U_13738)),hAPP(c_COMBK(tc_fun(U_13737,tc_HOL_Obool),U_13736),hAPP(c_Set_OCollect(U_13737),U_13739))),
    inference(definitional_conversion,[status(esa)],[f_3524_2]) ).

cnf(f_3524_4,plain,
    hAPP(c_Set_OCollect(tc_prod(U_13736,U_13737)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13736,U_13737,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13736,tc_fun(U_13737,tc_HOL_Obool),tc_fun(U_13737,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13737,tc_HOL_Obool),tc_fun(U_13737,tc_HOL_Obool)),U_13736),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13737)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13736),c_fconj),U_13738))),U_13739))) = hAPP(hAPP(c_Product__Type_OSigma(U_13736,U_13737),hAPP(c_Set_OCollect(U_13736),U_13738)),hAPP(c_COMBK(tc_fun(U_13737,tc_HOL_Obool),U_13736),hAPP(c_Set_OCollect(U_13737),U_13739))),
    inference(clausify,[status(thm)],[f_3524_3]) ).

fof(f_3525_1,plain,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(f_3525_2,plain,
    ! [U_13743,U_13742,U_13741,U_13740] : hAPP(c_Set_OCollect(tc_prod(U_13740,U_13741)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13740,U_13741,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13740,tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool)),U_13740),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13741)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13740),c_fconj),U_13742))),U_13743))) = hAPP(hAPP(c_Product__Type_OSigma(U_13740,U_13741),hAPP(c_Set_OCollect(U_13740),U_13742)),hAPP(hAPP(c_COMBB(tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool),U_13740),c_Set_OCollect(U_13741)),U_13743)),
    inference(variable_rename,[status(thm)],[f_3525_1]) ).

fof(f_3525_3,plain,
    ! [U_13740,U_13741,U_13742,U_13743] : hAPP(c_Set_OCollect(tc_prod(U_13740,U_13741)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13740,U_13741,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13740,tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool)),U_13740),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13741)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13740),c_fconj),U_13742))),U_13743))) = hAPP(hAPP(c_Product__Type_OSigma(U_13740,U_13741),hAPP(c_Set_OCollect(U_13740),U_13742)),hAPP(hAPP(c_COMBB(tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool),U_13740),c_Set_OCollect(U_13741)),U_13743)),
    inference(definitional_conversion,[status(esa)],[f_3525_2]) ).

cnf(f_3525_4,plain,
    hAPP(c_Set_OCollect(tc_prod(U_13740,U_13741)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13740,U_13741,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13740,tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool)),U_13740),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13741)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13740),c_fconj),U_13742))),U_13743))) = hAPP(hAPP(c_Product__Type_OSigma(U_13740,U_13741),hAPP(c_Set_OCollect(U_13740),U_13742)),hAPP(hAPP(c_COMBB(tc_fun(U_13741,tc_HOL_Obool),tc_fun(U_13741,tc_HOL_Obool),U_13740),c_Set_OCollect(U_13741)),U_13743)),
    inference(clausify,[status(thm)],[f_3525_3]) ).

fof(f_3526_1,plain,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).

fof(f_3526_2,plain,
    ! [U_13745,U_13744] : hAPP(c_Set_OCollect(U_13744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13744),c_fNot),U_13745)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13744,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13744),U_13745)),
    inference(variable_rename,[status(thm)],[f_3526_1]) ).

fof(f_3526_3,plain,
    ! [U_13744,U_13745] : hAPP(c_Set_OCollect(U_13744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13744),c_fNot),U_13745)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13744,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13744),U_13745)),
    inference(definitional_conversion,[status(esa)],[f_3526_2]) ).

cnf(f_3526_4,plain,
    hAPP(c_Set_OCollect(U_13744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13744),c_fNot),U_13745)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13744,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13744),U_13745)),
    inference(clausify,[status(thm)],[f_3526_3]) ).

fof(f_3527_1,plain,
    ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(f_3527_2,plain,
    ! [U_13749,U_13748,U_13747,U_13746] : hAPP(c_Set_Ovimage(U_13746,U_13747,U_13748),hAPP(c_Set_OCollect(U_13747),U_13749)) = hAPP(c_Set_OCollect(U_13746),hAPP(hAPP(c_COMBB(U_13747,tc_HOL_Obool,U_13746),U_13749),U_13748)),
    inference(variable_rename,[status(thm)],[f_3527_1]) ).

fof(f_3527_3,plain,
    ! [U_13746,U_13747,U_13748,U_13749] : hAPP(c_Set_Ovimage(U_13746,U_13747,U_13748),hAPP(c_Set_OCollect(U_13747),U_13749)) = hAPP(c_Set_OCollect(U_13746),hAPP(hAPP(c_COMBB(U_13747,tc_HOL_Obool,U_13746),U_13749),U_13748)),
    inference(definitional_conversion,[status(esa)],[f_3527_2]) ).

cnf(f_3527_4,plain,
    hAPP(c_Set_Ovimage(U_13746,U_13747,U_13748),hAPP(c_Set_OCollect(U_13747),U_13749)) = hAPP(c_Set_OCollect(U_13746),hAPP(hAPP(c_COMBB(U_13747,tc_HOL_Obool,U_13746),U_13749),U_13748)),
    inference(clausify,[status(thm)],[f_3527_3]) ).

fof(f_3528_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__mem__eq]) ).

fof(f_3528_2,plain,
    ! [U_13751,U_13750] : hAPP(c_Set_OCollect(U_13750),hAPP(hAPP(c_COMBC(U_13750,tc_fun(U_13750,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13750)),U_13751)) = U_13751,
    inference(variable_rename,[status(thm)],[f_3528_1]) ).

fof(f_3528_3,plain,
    ! [U_13750,U_13751] : hAPP(c_Set_OCollect(U_13750),hAPP(hAPP(c_COMBC(U_13750,tc_fun(U_13750,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13750)),U_13751)) = U_13751,
    inference(definitional_conversion,[status(esa)],[f_3528_2]) ).

cnf(f_3528_4,plain,
    hAPP(c_Set_OCollect(U_13750),hAPP(hAPP(c_COMBC(U_13750,tc_fun(U_13750,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13750)),U_13751)) = U_13751,
    inference(clausify,[status(thm)],[f_3528_3]) ).

fof(f_3529_1,plain,
    ! [V_P_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).

fof(f_3529_2,plain,
    ! [U_13754,U_13753,U_13752] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13752),U_13753),hAPP(c_Set_OCollect(U_13752),U_13754)))
        | ~ hBOOL(hAPP(U_13754,U_13753)) )
      & ( hBOOL(hAPP(U_13754,U_13753))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13752),U_13753),hAPP(c_Set_OCollect(U_13752),U_13754))) ) ),
    inference(variable_rename,[status(thm)],[f_3529_1]) ).

fof(f_3529_3,plain,
    ( ! [U_13760,U_13758] :
        ( ! [U_13756] : hBOOL(hAPP(hAPP(c_member(U_13756),U_13758),hAPP(c_Set_OCollect(U_13756),U_13760)))
        | ~ hBOOL(hAPP(U_13760,U_13758)) )
    & ! [U_13759,U_13757] :
        ( ! [U_13755] : ~ hBOOL(hAPP(hAPP(c_member(U_13755),U_13757),hAPP(c_Set_OCollect(U_13755),U_13759)))
        | hBOOL(hAPP(U_13759,U_13757)) ) ),
    inference(miniscope,[status(thm)],[f_3529_2]) ).

fof(f_3529_4,plain,
    ( ! [U_13760,U_13756,U_13758] :
        ( hBOOL(hAPP(hAPP(c_member(U_13756),U_13758),hAPP(c_Set_OCollect(U_13756),U_13760)))
        | ~ hBOOL(hAPP(U_13760,U_13758)) )
    & ! [U_13757,U_13755,U_13759] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13755),U_13757),hAPP(c_Set_OCollect(U_13755),U_13759)))
        | hBOOL(hAPP(U_13759,U_13757)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3529_3]) ).

cnf(f_3529_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13755),U_13757),hAPP(c_Set_OCollect(U_13755),U_13759)))
    | hBOOL(hAPP(U_13759,U_13757)) ),
    inference(clausify,[status(thm)],[f_3529_4]) ).

cnf(f_3529_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13756),U_13758),hAPP(c_Set_OCollect(U_13756),U_13760)))
    | ~ hBOOL(hAPP(U_13760,U_13758)) ),
    inference(clausify,[status(thm)],[f_3529_4]) ).

fof(f_3530_1,plain,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectD]) ).

fof(f_3530_2,plain,
    ! [U_13763,U_13762,U_13761] :
      ( hBOOL(hAPP(U_13763,U_13762))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13761),U_13762),hAPP(c_Set_OCollect(U_13761),U_13763))) ),
    inference(variable_rename,[status(thm)],[f_3530_1]) ).

fof(f_3530_3,plain,
    ! [U_13763,U_13762] :
      ( ! [U_13761] : ~ hBOOL(hAPP(hAPP(c_member(U_13761),U_13762),hAPP(c_Set_OCollect(U_13761),U_13763)))
      | hBOOL(hAPP(U_13763,U_13762)) ),
    inference(miniscope,[status(thm)],[f_3530_2]) ).

fof(f_3530_4,plain,
    ! [U_13761,U_13762,U_13763] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_13761),U_13762),hAPP(c_Set_OCollect(U_13761),U_13763)))
      | hBOOL(hAPP(U_13763,U_13762)) ),
    inference(definitional_conversion,[status(esa)],[f_3530_3]) ).

cnf(f_3530_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13761),U_13762),hAPP(c_Set_OCollect(U_13761),U_13763)))
    | hBOOL(hAPP(U_13763,U_13762)) ),
    inference(clausify,[status(thm)],[f_3530_4]) ).

fof(f_3531_1,plain,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectE]) ).

fof(f_3531_2,plain,
    ! [U_13766,U_13765,U_13764] :
      ( hBOOL(hAPP(U_13766,U_13765))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13764),U_13765),hAPP(c_Set_OCollect(U_13764),U_13766))) ),
    inference(variable_rename,[status(thm)],[f_3531_1]) ).

fof(f_3531_3,plain,
    ! [U_13766,U_13765] :
      ( ! [U_13764] : ~ hBOOL(hAPP(hAPP(c_member(U_13764),U_13765),hAPP(c_Set_OCollect(U_13764),U_13766)))
      | hBOOL(hAPP(U_13766,U_13765)) ),
    inference(miniscope,[status(thm)],[f_3531_2]) ).

fof(f_3531_4,plain,
    ! [U_13766,U_13764,U_13765] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_13764),U_13765),hAPP(c_Set_OCollect(U_13764),U_13766)))
      | hBOOL(hAPP(U_13766,U_13765)) ),
    inference(definitional_conversion,[status(esa)],[f_3531_3]) ).

cnf(f_3531_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13764),U_13765),hAPP(c_Set_OCollect(U_13764),U_13766)))
    | hBOOL(hAPP(U_13766,U_13765)) ),
    inference(clausify,[status(thm)],[f_3531_4]) ).

fof(f_3532_1,plain,
    ! [V_Q_2,V_P_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).

fof(f_3532_2,plain,
    ! [U_13769,U_13768,U_13767] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13767),hAPP(c_Set_OCollect(U_13767),hAPP(hAPP(c_COMBS(U_13767,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13767),c_fdisj),U_13768)),U_13769))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13767),hAPP(c_Set_OCollect(U_13767),U_13769)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13767),hAPP(c_Set_OCollect(U_13767),U_13768))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13767),hAPP(c_Set_OCollect(U_13767),U_13769)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13767),hAPP(c_Set_OCollect(U_13767),U_13768))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13767),hAPP(c_Set_OCollect(U_13767),hAPP(hAPP(c_COMBS(U_13767,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13767),c_fdisj),U_13768)),U_13769)))) ) ),
    inference(variable_rename,[status(thm)],[f_3532_1]) ).

fof(f_3532_3,plain,
    ( ! [U_13775,U_13773,U_13771] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),hAPP(hAPP(c_COMBS(U_13771,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13771),c_fdisj),U_13773)),U_13775))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),U_13775)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),U_13773))) )
    & ! [U_13774,U_13772,U_13770] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),U_13774)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),U_13772))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),hAPP(hAPP(c_COMBS(U_13770,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13770),c_fdisj),U_13772)),U_13774)))) ) ),
    inference(miniscope,[status(thm)],[f_3532_2]) ).

fof(f_3532_4,plain,
    ( ! [U_13770,U_13774,U_13772] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),U_13774)))
        | ~ sP991(U_13770,U_13774,U_13772) )
    & ! [U_13770,U_13774,U_13772] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),U_13772)))
        | ~ sP991(U_13770,U_13774,U_13772) )
    & ! [U_13775,U_13771,U_13773] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),hAPP(hAPP(c_COMBS(U_13771,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13771),c_fdisj),U_13773)),U_13775))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),U_13775)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),U_13773))) )
    & ! [U_13770,U_13774,U_13772] :
        ( sP991(U_13770,U_13774,U_13772)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),hAPP(hAPP(c_COMBS(U_13770,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13770),c_fdisj),U_13772)),U_13774)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP991])],[f_3532_3]) ).

cnf(f_3532_5,plain,
    ( sP991(U_13770,U_13774,U_13772)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),hAPP(hAPP(c_COMBS(U_13770,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13770),c_fdisj),U_13772)),U_13774)))) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

cnf(f_3532_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),hAPP(hAPP(c_COMBS(U_13771,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13771),c_fdisj),U_13773)),U_13775))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),U_13775)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13771),hAPP(c_Set_OCollect(U_13771),U_13773))) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

cnf(f_3532_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),U_13772)))
    | ~ sP991(U_13770,U_13774,U_13772) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

cnf(f_3532_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13770),hAPP(c_Set_OCollect(U_13770),U_13774)))
    | ~ sP991(U_13770,U_13774,U_13772) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

fof(f_3533_1,plain,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__def]) ).

fof(f_3533_2,plain,
    ! [U_13776] : c_Orderings_Otop__class_Otop(tc_fun(U_13776,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13776),hAPP(c_COMBK(tc_HOL_Obool,U_13776),c_fTrue)),
    inference(variable_rename,[status(thm)],[f_3533_1]) ).

fof(f_3533_3,plain,
    ! [U_13776] : c_Orderings_Otop__class_Otop(tc_fun(U_13776,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13776),hAPP(c_COMBK(tc_HOL_Obool,U_13776),c_fTrue)),
    inference(definitional_conversion,[status(esa)],[f_3533_2]) ).

cnf(f_3533_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_13776,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13776),hAPP(c_COMBK(tc_HOL_Obool,U_13776),c_fTrue)),
    inference(clausify,[status(thm)],[f_3533_3]) ).

fof(f_3534_1,plain,
    ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).

fof(f_3534_2,plain,
    ! [U_13779,U_13778,U_13777] : hAPP(hAPP(c_Set_Oinsert(U_13777),U_13778),hAPP(c_Set_OCollect(U_13777),U_13779)) = hAPP(c_Set_OCollect(U_13777),hAPP(hAPP(c_COMBS(U_13777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13777),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13777),c_fNot),hAPP(hAPP(c_COMBC(U_13777,U_13777,tc_HOL_Obool),c_fequal),U_13778)))),U_13779)),
    inference(variable_rename,[status(thm)],[f_3534_1]) ).

fof(f_3534_3,plain,
    ! [U_13777,U_13778,U_13779] : hAPP(hAPP(c_Set_Oinsert(U_13777),U_13778),hAPP(c_Set_OCollect(U_13777),U_13779)) = hAPP(c_Set_OCollect(U_13777),hAPP(hAPP(c_COMBS(U_13777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13777),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13777),c_fNot),hAPP(hAPP(c_COMBC(U_13777,U_13777,tc_HOL_Obool),c_fequal),U_13778)))),U_13779)),
    inference(definitional_conversion,[status(esa)],[f_3534_2]) ).

cnf(f_3534_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13777),U_13778),hAPP(c_Set_OCollect(U_13777),U_13779)) = hAPP(c_Set_OCollect(U_13777),hAPP(hAPP(c_COMBS(U_13777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13777),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13777),c_fNot),hAPP(hAPP(c_COMBC(U_13777,U_13777,tc_HOL_Obool),c_fequal),U_13778)))),U_13779)),
    inference(clausify,[status(thm)],[f_3534_3]) ).

fof(f_3535_1,plain,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).

fof(f_3535_2,plain,
    ! [U_13782,U_13781,U_13780] : hAPP(c_Set_OCollect(U_13780),hAPP(hAPP(c_COMBS(U_13780,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13780),c_fconj),U_13781)),U_13782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13780,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13780),U_13781)),hAPP(c_Set_OCollect(U_13780),U_13782)),
    inference(variable_rename,[status(thm)],[f_3535_1]) ).

fof(f_3535_3,plain,
    ! [U_13780,U_13781,U_13782] : hAPP(c_Set_OCollect(U_13780),hAPP(hAPP(c_COMBS(U_13780,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13780),c_fconj),U_13781)),U_13782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13780,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13780),U_13781)),hAPP(c_Set_OCollect(U_13780),U_13782)),
    inference(definitional_conversion,[status(esa)],[f_3535_2]) ).

cnf(f_3535_4,plain,
    hAPP(c_Set_OCollect(U_13780),hAPP(hAPP(c_COMBS(U_13780,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13780),c_fconj),U_13781)),U_13782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13780,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13780),U_13781)),hAPP(c_Set_OCollect(U_13780),U_13782)),
    inference(clausify,[status(thm)],[f_3535_3]) ).

fof(f_3536_1,plain,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).

fof(f_3536_2,plain,
    ! [U_13785,U_13784,U_13783] : hAPP(c_Set_OCollect(U_13783),hAPP(hAPP(c_COMBS(U_13783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13783),c_fdisj),U_13784)),U_13785)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13783,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13783),U_13784)),hAPP(c_Set_OCollect(U_13783),U_13785)),
    inference(variable_rename,[status(thm)],[f_3536_1]) ).

fof(f_3536_3,plain,
    ! [U_13783,U_13784,U_13785] : hAPP(c_Set_OCollect(U_13783),hAPP(hAPP(c_COMBS(U_13783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13783),c_fdisj),U_13784)),U_13785)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13783,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13783),U_13784)),hAPP(c_Set_OCollect(U_13783),U_13785)),
    inference(definitional_conversion,[status(esa)],[f_3536_2]) ).

cnf(f_3536_4,plain,
    hAPP(c_Set_OCollect(U_13783),hAPP(hAPP(c_COMBS(U_13783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13783),c_fdisj),U_13784)),U_13785)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13783,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13783),U_13784)),hAPP(c_Set_OCollect(U_13783),U_13785)),
    inference(clausify,[status(thm)],[f_3536_3]) ).

fof(f_3537_1,plain,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).

fof(f_3537_2,plain,
    ! [U_13787,U_13786] : hAPP(c_Set_OCollect(U_13786),U_13787) = U_13787,
    inference(variable_rename,[status(thm)],[f_3537_1]) ).

fof(f_3537_3,plain,
    ! [U_13786,U_13787] : hAPP(c_Set_OCollect(U_13786),U_13787) = U_13787,
    inference(definitional_conversion,[status(esa)],[f_3537_2]) ).

cnf(f_3537_4,plain,
    hAPP(c_Set_OCollect(U_13786),U_13787) = U_13787,
    inference(clausify,[status(thm)],[f_3537_3]) ).

fof(f_3538_1,plain,
    ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)),
    inference(fof_nnf,[status(thm)],[fact_empty__def]) ).

fof(f_3538_2,plain,
    ! [U_13788] : c_Orderings_Obot__class_Obot(tc_fun(U_13788,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13788),hAPP(c_COMBK(tc_HOL_Obool,U_13788),c_fFalse)),
    inference(variable_rename,[status(thm)],[f_3538_1]) ).

fof(f_3538_3,plain,
    ! [U_13788] : c_Orderings_Obot__class_Obot(tc_fun(U_13788,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13788),hAPP(c_COMBK(tc_HOL_Obool,U_13788),c_fFalse)),
    inference(definitional_conversion,[status(esa)],[f_3538_2]) ).

cnf(f_3538_4,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_13788,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13788),hAPP(c_COMBK(tc_HOL_Obool,U_13788),c_fFalse)),
    inference(clausify,[status(thm)],[f_3538_3]) ).

fof(f_3539_1,plain,
    ! [V_P_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
        | ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_P_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).

fof(f_3539_2,plain,
    ! [U_13792,U_13791] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_13791,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13791),U_13792)
        | ? [U_13790] : hBOOL(hAPP(U_13792,U_13790)) )
      & ( ! [U_13789] : ~ hBOOL(hAPP(U_13792,U_13789))
        | c_Orderings_Obot__class_Obot(tc_fun(U_13791,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13791),U_13792) ) ),
    inference(variable_rename,[status(thm)],[f_3539_1]) ).

fof(f_3539_3,plain,
    ( ! [U_13796] :
        ( ! [U_13794] : c_Orderings_Obot__class_Obot(tc_fun(U_13794,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13794),U_13796)
        | ? [U_13790] : hBOOL(hAPP(U_13796,U_13790)) )
    & ! [U_13795] :
        ( ! [U_13793] : c_Orderings_Obot__class_Obot(tc_fun(U_13793,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13793),U_13795)
        | ! [U_13789] : ~ hBOOL(hAPP(U_13795,U_13789)) ) ),
    inference(miniscope,[status(thm)],[f_3539_2]) ).

fof(f_3539_4,plain,
    ( ! [U_13796] :
        ( ! [U_13794] : c_Orderings_Obot__class_Obot(tc_fun(U_13794,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13794),U_13796)
        | hBOOL(hAPP(U_13796,sK317(U_13796))) )
    & ! [U_13795] :
        ( ! [U_13793] : c_Orderings_Obot__class_Obot(tc_fun(U_13793,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13793),U_13795)
        | ! [U_13789] : ~ hBOOL(hAPP(U_13795,U_13789)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_13790,sK317(U_13796))],[f_3539_3]) ).

fof(f_3539_5,plain,
    ( ! [U_13794,U_13796] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_13794,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13794),U_13796)
        | hBOOL(hAPP(U_13796,sK317(U_13796))) )
    & ! [U_13789,U_13793,U_13795] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_13793,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13793),U_13795)
        | ~ hBOOL(hAPP(U_13795,U_13789)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3539_4]) ).

cnf(f_3539_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_13793,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13793),U_13795)
    | ~ hBOOL(hAPP(U_13795,U_13789)) ),
    inference(clausify,[status(thm)],[f_3539_5]) ).

cnf(f_3539_7,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_13794,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13794),U_13796)
    | hBOOL(hAPP(U_13796,sK317(U_13796))) ),
    inference(clausify,[status(thm)],[f_3539_5]) ).

fof(f_3540_1,plain,
    ! [V_P_2,T_b] :
      ( ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
        | hAPP(c_Set_OCollect(T_b),V_P_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).

fof(f_3540_2,plain,
    ! [U_13800,U_13799] :
      ( ( hAPP(c_Set_OCollect(U_13799),U_13800) = c_Orderings_Obot__class_Obot(tc_fun(U_13799,tc_HOL_Obool))
        | ? [U_13798] : hBOOL(hAPP(U_13800,U_13798)) )
      & ( ! [U_13797] : ~ hBOOL(hAPP(U_13800,U_13797))
        | hAPP(c_Set_OCollect(U_13799),U_13800) != c_Orderings_Obot__class_Obot(tc_fun(U_13799,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3540_1]) ).

fof(f_3540_3,plain,
    ( ! [U_13804] :
        ( ! [U_13802] : hAPP(c_Set_OCollect(U_13802),U_13804) = c_Orderings_Obot__class_Obot(tc_fun(U_13802,tc_HOL_Obool))
        | ? [U_13798] : hBOOL(hAPP(U_13804,U_13798)) )
    & ! [U_13803] :
        ( ! [U_13801] : hAPP(c_Set_OCollect(U_13801),U_13803) != c_Orderings_Obot__class_Obot(tc_fun(U_13801,tc_HOL_Obool))
        | ! [U_13797] : ~ hBOOL(hAPP(U_13803,U_13797)) ) ),
    inference(miniscope,[status(thm)],[f_3540_2]) ).

fof(f_3540_4,plain,
    ( ! [U_13804] :
        ( ! [U_13802] : hAPP(c_Set_OCollect(U_13802),U_13804) = c_Orderings_Obot__class_Obot(tc_fun(U_13802,tc_HOL_Obool))
        | hBOOL(hAPP(U_13804,sK318(U_13804))) )
    & ! [U_13803] :
        ( ! [U_13801] : hAPP(c_Set_OCollect(U_13801),U_13803) != c_Orderings_Obot__class_Obot(tc_fun(U_13801,tc_HOL_Obool))
        | ! [U_13797] : ~ hBOOL(hAPP(U_13803,U_13797)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_13798,sK318(U_13804))],[f_3540_3]) ).

fof(f_3540_5,plain,
    ( ! [U_13802,U_13804] :
        ( hAPP(c_Set_OCollect(U_13802),U_13804) = c_Orderings_Obot__class_Obot(tc_fun(U_13802,tc_HOL_Obool))
        | hBOOL(hAPP(U_13804,sK318(U_13804))) )
    & ! [U_13797,U_13803,U_13801] :
        ( hAPP(c_Set_OCollect(U_13801),U_13803) != c_Orderings_Obot__class_Obot(tc_fun(U_13801,tc_HOL_Obool))
        | ~ hBOOL(hAPP(U_13803,U_13797)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3540_4]) ).

cnf(f_3540_6,plain,
    ( hAPP(c_Set_OCollect(U_13801),U_13803) != c_Orderings_Obot__class_Obot(tc_fun(U_13801,tc_HOL_Obool))
    | ~ hBOOL(hAPP(U_13803,U_13797)) ),
    inference(clausify,[status(thm)],[f_3540_5]) ).

cnf(f_3540_7,plain,
    ( hAPP(c_Set_OCollect(U_13802),U_13804) = c_Orderings_Obot__class_Obot(tc_fun(U_13802,tc_HOL_Obool))
    | hBOOL(hAPP(U_13804,sK318(U_13804))) ),
    inference(clausify,[status(thm)],[f_3540_5]) ).

fof(f_3541_1,plain,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insert__compr__raw]) ).

fof(f_3541_2,plain,
    ! [U_13807,U_13806,U_13805] : hAPP(hAPP(c_Set_Oinsert(U_13805),U_13806),U_13807) = hAPP(c_Set_OCollect(U_13805),hAPP(hAPP(c_COMBS(U_13805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13805),c_fdisj),hAPP(hAPP(c_COMBC(U_13805,U_13805,tc_HOL_Obool),c_fequal),U_13806))),hAPP(hAPP(c_COMBC(U_13805,tc_fun(U_13805,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13805)),U_13807))),
    inference(variable_rename,[status(thm)],[f_3541_1]) ).

fof(f_3541_3,plain,
    ! [U_13805,U_13806,U_13807] : hAPP(hAPP(c_Set_Oinsert(U_13805),U_13806),U_13807) = hAPP(c_Set_OCollect(U_13805),hAPP(hAPP(c_COMBS(U_13805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13805),c_fdisj),hAPP(hAPP(c_COMBC(U_13805,U_13805,tc_HOL_Obool),c_fequal),U_13806))),hAPP(hAPP(c_COMBC(U_13805,tc_fun(U_13805,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13805)),U_13807))),
    inference(definitional_conversion,[status(esa)],[f_3541_2]) ).

cnf(f_3541_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13805),U_13806),U_13807) = hAPP(c_Set_OCollect(U_13805),hAPP(hAPP(c_COMBS(U_13805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13805),c_fdisj),hAPP(hAPP(c_COMBC(U_13805,U_13805,tc_HOL_Obool),c_fequal),U_13806))),hAPP(hAPP(c_COMBC(U_13805,tc_fun(U_13805,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13805)),U_13807))),
    inference(clausify,[status(thm)],[f_3541_3]) ).

fof(f_3542_1,plain,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insert__compr]) ).

fof(f_3542_2,plain,
    ! [U_13810,U_13809,U_13808] : hAPP(hAPP(c_Set_Oinsert(U_13808),U_13809),U_13810) = hAPP(c_Set_OCollect(U_13808),hAPP(hAPP(c_COMBS(U_13808,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13808),c_fdisj),hAPP(hAPP(c_COMBC(U_13808,U_13808,tc_HOL_Obool),c_fequal),U_13809))),hAPP(hAPP(c_COMBC(U_13808,tc_fun(U_13808,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13808)),U_13810))),
    inference(variable_rename,[status(thm)],[f_3542_1]) ).

fof(f_3542_3,plain,
    ! [U_13808,U_13809,U_13810] : hAPP(hAPP(c_Set_Oinsert(U_13808),U_13809),U_13810) = hAPP(c_Set_OCollect(U_13808),hAPP(hAPP(c_COMBS(U_13808,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13808),c_fdisj),hAPP(hAPP(c_COMBC(U_13808,U_13808,tc_HOL_Obool),c_fequal),U_13809))),hAPP(hAPP(c_COMBC(U_13808,tc_fun(U_13808,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13808)),U_13810))),
    inference(definitional_conversion,[status(esa)],[f_3542_2]) ).

cnf(f_3542_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13808),U_13809),U_13810) = hAPP(c_Set_OCollect(U_13808),hAPP(hAPP(c_COMBS(U_13808,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13808),c_fdisj),hAPP(hAPP(c_COMBC(U_13808,U_13808,tc_HOL_Obool),c_fequal),U_13809))),hAPP(hAPP(c_COMBC(U_13808,tc_fun(U_13808,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13808)),U_13810))),
    inference(clausify,[status(thm)],[f_3542_3]) ).

fof(f_3543_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__def]) ).

fof(f_3543_2,plain,
    ! [U_13813,U_13812,U_13811] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13811,tc_HOL_Obool)),U_13812),U_13813) = hAPP(c_Set_OCollect(U_13811),hAPP(hAPP(c_COMBS(U_13811,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13811),c_fdisj),hAPP(hAPP(c_COMBC(U_13811,tc_fun(U_13811,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13811)),U_13812))),hAPP(hAPP(c_COMBC(U_13811,tc_fun(U_13811,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13811)),U_13813))),
    inference(variable_rename,[status(thm)],[f_3543_1]) ).

fof(f_3543_3,plain,
    ! [U_13811,U_13812,U_13813] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13811,tc_HOL_Obool)),U_13812),U_13813) = hAPP(c_Set_OCollect(U_13811),hAPP(hAPP(c_COMBS(U_13811,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13811),c_fdisj),hAPP(hAPP(c_COMBC(U_13811,tc_fun(U_13811,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13811)),U_13812))),hAPP(hAPP(c_COMBC(U_13811,tc_fun(U_13811,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13811)),U_13813))),
    inference(definitional_conversion,[status(esa)],[f_3543_2]) ).

cnf(f_3543_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13811,tc_HOL_Obool)),U_13812),U_13813) = hAPP(c_Set_OCollect(U_13811),hAPP(hAPP(c_COMBS(U_13811,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13811),c_fdisj),hAPP(hAPP(c_COMBC(U_13811,tc_fun(U_13811,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13811)),U_13812))),hAPP(hAPP(c_COMBC(U_13811,tc_fun(U_13811,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13811)),U_13813))),
    inference(clausify,[status(thm)],[f_3543_3]) ).

fof(f_3544_1,plain,
    ! [V_P_2,V_A_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
        | ~ hBOOL(hAPP(V_P_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(V_P_2,V_x_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).

fof(f_3544_2,plain,
    ! [U_13817,U_13816,U_13815,U_13814] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13814),U_13815),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13814,tc_HOL_Obool)),U_13816),hAPP(c_Set_OCollect(U_13814),U_13817))))
        | ~ hBOOL(hAPP(U_13817,U_13815))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13814),U_13815),U_13816)) )
      & ( ( hBOOL(hAPP(U_13817,U_13815))
          & hBOOL(hAPP(hAPP(c_member(U_13814),U_13815),U_13816)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13814),U_13815),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13814,tc_HOL_Obool)),U_13816),hAPP(c_Set_OCollect(U_13814),U_13817)))) ) ),
    inference(variable_rename,[status(thm)],[f_3544_1]) ).

fof(f_3544_3,plain,
    ( ! [U_13825,U_13823,U_13821,U_13819] :
        ( hBOOL(hAPP(hAPP(c_member(U_13819),U_13821),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13819,tc_HOL_Obool)),U_13823),hAPP(c_Set_OCollect(U_13819),U_13825))))
        | ~ hBOOL(hAPP(U_13825,U_13821))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13819),U_13821),U_13823)) )
    & ! [U_13824,U_13822,U_13820,U_13818] :
        ( ( hBOOL(hAPP(U_13824,U_13820))
          & hBOOL(hAPP(hAPP(c_member(U_13818),U_13820),U_13822)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13818),U_13820),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13818,tc_HOL_Obool)),U_13822),hAPP(c_Set_OCollect(U_13818),U_13824)))) ) ),
    inference(miniscope,[status(thm)],[f_3544_2]) ).

fof(f_3544_4,plain,
    ( ! [U_13820,U_13822,U_13818,U_13824] :
        ( hBOOL(hAPP(U_13824,U_13820))
        | ~ sP992(U_13820,U_13822,U_13818,U_13824) )
    & ! [U_13820,U_13822,U_13818,U_13824] :
        ( hBOOL(hAPP(hAPP(c_member(U_13818),U_13820),U_13822))
        | ~ sP992(U_13820,U_13822,U_13818,U_13824) )
    & ! [U_13823,U_13819,U_13821,U_13825] :
        ( hBOOL(hAPP(hAPP(c_member(U_13819),U_13821),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13819,tc_HOL_Obool)),U_13823),hAPP(c_Set_OCollect(U_13819),U_13825))))
        | ~ hBOOL(hAPP(U_13825,U_13821))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13819),U_13821),U_13823)) )
    & ! [U_13820,U_13822,U_13818,U_13824] :
        ( sP992(U_13820,U_13822,U_13818,U_13824)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13818),U_13820),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13818,tc_HOL_Obool)),U_13822),hAPP(c_Set_OCollect(U_13818),U_13824)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP992])],[f_3544_3]) ).

cnf(f_3544_5,plain,
    ( sP992(U_13820,U_13822,U_13818,U_13824)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13818),U_13820),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13818,tc_HOL_Obool)),U_13822),hAPP(c_Set_OCollect(U_13818),U_13824)))) ),
    inference(clausify,[status(thm)],[f_3544_4]) ).

cnf(f_3544_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13819),U_13821),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13819,tc_HOL_Obool)),U_13823),hAPP(c_Set_OCollect(U_13819),U_13825))))
    | ~ hBOOL(hAPP(U_13825,U_13821))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13819),U_13821),U_13823)) ),
    inference(clausify,[status(thm)],[f_3544_4]) ).

cnf(f_3544_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13818),U_13820),U_13822))
    | ~ sP992(U_13820,U_13822,U_13818,U_13824) ),
    inference(clausify,[status(thm)],[f_3544_4]) ).

cnf(f_3544_8,plain,
    ( hBOOL(hAPP(U_13824,U_13820))
    | ~ sP992(U_13820,U_13822,U_13818,U_13824) ),
    inference(clausify,[status(thm)],[f_3544_4]) ).

fof(f_3545_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__def]) ).

fof(f_3545_2,plain,
    ! [U_13828,U_13827,U_13826] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13826,tc_HOL_Obool)),U_13827),U_13828) = hAPP(c_Set_OCollect(U_13826),hAPP(hAPP(c_COMBS(U_13826,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13826),c_fconj),hAPP(hAPP(c_COMBC(U_13826,tc_fun(U_13826,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13826)),U_13827))),hAPP(hAPP(c_COMBC(U_13826,tc_fun(U_13826,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13826)),U_13828))),
    inference(variable_rename,[status(thm)],[f_3545_1]) ).

fof(f_3545_3,plain,
    ! [U_13826,U_13827,U_13828] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13826,tc_HOL_Obool)),U_13827),U_13828) = hAPP(c_Set_OCollect(U_13826),hAPP(hAPP(c_COMBS(U_13826,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13826),c_fconj),hAPP(hAPP(c_COMBC(U_13826,tc_fun(U_13826,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13826)),U_13827))),hAPP(hAPP(c_COMBC(U_13826,tc_fun(U_13826,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13826)),U_13828))),
    inference(definitional_conversion,[status(esa)],[f_3545_2]) ).

cnf(f_3545_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13826,tc_HOL_Obool)),U_13827),U_13828) = hAPP(c_Set_OCollect(U_13826),hAPP(hAPP(c_COMBS(U_13826,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13826),c_fconj),hAPP(hAPP(c_COMBC(U_13826,tc_fun(U_13826,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13826)),U_13827))),hAPP(hAPP(c_COMBC(U_13826,tc_fun(U_13826,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13826)),U_13828))),
    inference(clausify,[status(thm)],[f_3545_3]) ).

fof(f_3546_1,plain,
    ! [T_b,V_a_2,V_P_2] :
      ( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).

fof(f_3546_2,plain,
    ! [U_13831,U_13830,U_13829] :
      ( ( hAPP(c_Set_OCollect(U_13831),hAPP(hAPP(c_COMBS(U_13831,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13831),c_fconj),hAPP(hAPP(c_COMBC(U_13831,U_13831,tc_HOL_Obool),c_fequal),U_13830))),U_13829)) = c_Orderings_Obot__class_Obot(tc_fun(U_13831,tc_HOL_Obool))
        | hBOOL(hAPP(U_13829,U_13830)) )
      & ( hAPP(c_Set_OCollect(U_13831),hAPP(hAPP(c_COMBS(U_13831,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13831),c_fconj),hAPP(hAPP(c_COMBC(U_13831,U_13831,tc_HOL_Obool),c_fequal),U_13830))),U_13829)) = hAPP(hAPP(c_Set_Oinsert(U_13831),U_13830),c_Orderings_Obot__class_Obot(tc_fun(U_13831,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13829,U_13830)) ) ),
    inference(variable_rename,[status(thm)],[f_3546_1]) ).

fof(f_3546_3,plain,
    ( ! [U_13837,U_13835,U_13833] :
        ( hAPP(c_Set_OCollect(U_13837),hAPP(hAPP(c_COMBS(U_13837,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13837),c_fconj),hAPP(hAPP(c_COMBC(U_13837,U_13837,tc_HOL_Obool),c_fequal),U_13835))),U_13833)) = c_Orderings_Obot__class_Obot(tc_fun(U_13837,tc_HOL_Obool))
        | hBOOL(hAPP(U_13833,U_13835)) )
    & ! [U_13836,U_13834,U_13832] :
        ( hAPP(c_Set_OCollect(U_13836),hAPP(hAPP(c_COMBS(U_13836,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13836),c_fconj),hAPP(hAPP(c_COMBC(U_13836,U_13836,tc_HOL_Obool),c_fequal),U_13834))),U_13832)) = hAPP(hAPP(c_Set_Oinsert(U_13836),U_13834),c_Orderings_Obot__class_Obot(tc_fun(U_13836,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13832,U_13834)) ) ),
    inference(miniscope,[status(thm)],[f_3546_2]) ).

fof(f_3546_4,plain,
    ( ! [U_13833,U_13835,U_13837] :
        ( hAPP(c_Set_OCollect(U_13837),hAPP(hAPP(c_COMBS(U_13837,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13837),c_fconj),hAPP(hAPP(c_COMBC(U_13837,U_13837,tc_HOL_Obool),c_fequal),U_13835))),U_13833)) = c_Orderings_Obot__class_Obot(tc_fun(U_13837,tc_HOL_Obool))
        | hBOOL(hAPP(U_13833,U_13835)) )
    & ! [U_13834,U_13832,U_13836] :
        ( hAPP(c_Set_OCollect(U_13836),hAPP(hAPP(c_COMBS(U_13836,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13836),c_fconj),hAPP(hAPP(c_COMBC(U_13836,U_13836,tc_HOL_Obool),c_fequal),U_13834))),U_13832)) = hAPP(hAPP(c_Set_Oinsert(U_13836),U_13834),c_Orderings_Obot__class_Obot(tc_fun(U_13836,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13832,U_13834)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3546_3]) ).

cnf(f_3546_5,plain,
    ( hAPP(c_Set_OCollect(U_13836),hAPP(hAPP(c_COMBS(U_13836,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13836),c_fconj),hAPP(hAPP(c_COMBC(U_13836,U_13836,tc_HOL_Obool),c_fequal),U_13834))),U_13832)) = hAPP(hAPP(c_Set_Oinsert(U_13836),U_13834),c_Orderings_Obot__class_Obot(tc_fun(U_13836,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_13832,U_13834)) ),
    inference(clausify,[status(thm)],[f_3546_4]) ).

cnf(f_3546_6,plain,
    ( hAPP(c_Set_OCollect(U_13837),hAPP(hAPP(c_COMBS(U_13837,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13837),c_fconj),hAPP(hAPP(c_COMBC(U_13837,U_13837,tc_HOL_Obool),c_fequal),U_13835))),U_13833)) = c_Orderings_Obot__class_Obot(tc_fun(U_13837,tc_HOL_Obool))
    | hBOOL(hAPP(U_13833,U_13835)) ),
    inference(clausify,[status(thm)],[f_3546_4]) ).

fof(f_3547_1,plain,
    ! [T_b,V_a_2,V_P_2] :
      ( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).

fof(f_3547_2,plain,
    ! [U_13840,U_13839,U_13838] :
      ( ( hAPP(c_Set_OCollect(U_13840),hAPP(hAPP(c_COMBS(U_13840,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13840),c_fconj),hAPP(c_fequal,U_13839))),U_13838)) = c_Orderings_Obot__class_Obot(tc_fun(U_13840,tc_HOL_Obool))
        | hBOOL(hAPP(U_13838,U_13839)) )
      & ( hAPP(c_Set_OCollect(U_13840),hAPP(hAPP(c_COMBS(U_13840,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13840),c_fconj),hAPP(c_fequal,U_13839))),U_13838)) = hAPP(hAPP(c_Set_Oinsert(U_13840),U_13839),c_Orderings_Obot__class_Obot(tc_fun(U_13840,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13838,U_13839)) ) ),
    inference(variable_rename,[status(thm)],[f_3547_1]) ).

fof(f_3547_3,plain,
    ( ! [U_13846,U_13844,U_13842] :
        ( hAPP(c_Set_OCollect(U_13846),hAPP(hAPP(c_COMBS(U_13846,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13846),c_fconj),hAPP(c_fequal,U_13844))),U_13842)) = c_Orderings_Obot__class_Obot(tc_fun(U_13846,tc_HOL_Obool))
        | hBOOL(hAPP(U_13842,U_13844)) )
    & ! [U_13845,U_13843,U_13841] :
        ( hAPP(c_Set_OCollect(U_13845),hAPP(hAPP(c_COMBS(U_13845,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13845),c_fconj),hAPP(c_fequal,U_13843))),U_13841)) = hAPP(hAPP(c_Set_Oinsert(U_13845),U_13843),c_Orderings_Obot__class_Obot(tc_fun(U_13845,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13841,U_13843)) ) ),
    inference(miniscope,[status(thm)],[f_3547_2]) ).

fof(f_3547_4,plain,
    ( ! [U_13842,U_13844,U_13846] :
        ( hAPP(c_Set_OCollect(U_13846),hAPP(hAPP(c_COMBS(U_13846,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13846),c_fconj),hAPP(c_fequal,U_13844))),U_13842)) = c_Orderings_Obot__class_Obot(tc_fun(U_13846,tc_HOL_Obool))
        | hBOOL(hAPP(U_13842,U_13844)) )
    & ! [U_13845,U_13843,U_13841] :
        ( hAPP(c_Set_OCollect(U_13845),hAPP(hAPP(c_COMBS(U_13845,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13845),c_fconj),hAPP(c_fequal,U_13843))),U_13841)) = hAPP(hAPP(c_Set_Oinsert(U_13845),U_13843),c_Orderings_Obot__class_Obot(tc_fun(U_13845,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13841,U_13843)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3547_3]) ).

cnf(f_3547_5,plain,
    ( hAPP(c_Set_OCollect(U_13845),hAPP(hAPP(c_COMBS(U_13845,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13845),c_fconj),hAPP(c_fequal,U_13843))),U_13841)) = hAPP(hAPP(c_Set_Oinsert(U_13845),U_13843),c_Orderings_Obot__class_Obot(tc_fun(U_13845,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_13841,U_13843)) ),
    inference(clausify,[status(thm)],[f_3547_4]) ).

cnf(f_3547_6,plain,
    ( hAPP(c_Set_OCollect(U_13846),hAPP(hAPP(c_COMBS(U_13846,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13846),c_fconj),hAPP(c_fequal,U_13844))),U_13842)) = c_Orderings_Obot__class_Obot(tc_fun(U_13846,tc_HOL_Obool))
    | hBOOL(hAPP(U_13842,U_13844)) ),
    inference(clausify,[status(thm)],[f_3547_4]) ).

fof(f_3548_1,plain,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__conv]) ).

fof(f_3548_2,plain,
    ! [U_13848,U_13847] : hAPP(c_Set_OCollect(U_13847),hAPP(hAPP(c_COMBC(U_13847,U_13847,tc_HOL_Obool),c_fequal),U_13848)) = hAPP(hAPP(c_Set_Oinsert(U_13847),U_13848),c_Orderings_Obot__class_Obot(tc_fun(U_13847,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3548_1]) ).

fof(f_3548_3,plain,
    ! [U_13847,U_13848] : hAPP(c_Set_OCollect(U_13847),hAPP(hAPP(c_COMBC(U_13847,U_13847,tc_HOL_Obool),c_fequal),U_13848)) = hAPP(hAPP(c_Set_Oinsert(U_13847),U_13848),c_Orderings_Obot__class_Obot(tc_fun(U_13847,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3548_2]) ).

cnf(f_3548_4,plain,
    hAPP(c_Set_OCollect(U_13847),hAPP(hAPP(c_COMBC(U_13847,U_13847,tc_HOL_Obool),c_fequal),U_13848)) = hAPP(hAPP(c_Set_Oinsert(U_13847),U_13848),c_Orderings_Obot__class_Obot(tc_fun(U_13847,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3548_3]) ).

fof(f_3549_1,plain,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__conv2]) ).

fof(f_3549_2,plain,
    ! [U_13850,U_13849] : hAPP(c_Set_OCollect(U_13849),hAPP(c_fequal,U_13850)) = hAPP(hAPP(c_Set_Oinsert(U_13849),U_13850),c_Orderings_Obot__class_Obot(tc_fun(U_13849,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3549_1]) ).

fof(f_3549_3,plain,
    ! [U_13849,U_13850] : hAPP(c_Set_OCollect(U_13849),hAPP(c_fequal,U_13850)) = hAPP(hAPP(c_Set_Oinsert(U_13849),U_13850),c_Orderings_Obot__class_Obot(tc_fun(U_13849,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3549_2]) ).

cnf(f_3549_4,plain,
    hAPP(c_Set_OCollect(U_13849),hAPP(c_fequal,U_13850)) = hAPP(hAPP(c_Set_Oinsert(U_13849),U_13850),c_Orderings_Obot__class_Obot(tc_fun(U_13849,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3549_3]) ).

fof(f_3550_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__diff__eq]) ).

fof(f_3550_2,plain,
    ! [U_13853,U_13852,U_13851] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13851,tc_HOL_Obool)),U_13852),U_13853) = hAPP(c_Set_OCollect(U_13851),hAPP(hAPP(c_COMBS(U_13851,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13851),c_fconj),hAPP(hAPP(c_COMBC(U_13851,tc_fun(U_13851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13851)),U_13852))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13851),c_fNot),hAPP(hAPP(c_COMBC(U_13851,tc_fun(U_13851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13851)),U_13853)))),
    inference(variable_rename,[status(thm)],[f_3550_1]) ).

fof(f_3550_3,plain,
    ! [U_13851,U_13852,U_13853] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13851,tc_HOL_Obool)),U_13852),U_13853) = hAPP(c_Set_OCollect(U_13851),hAPP(hAPP(c_COMBS(U_13851,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13851),c_fconj),hAPP(hAPP(c_COMBC(U_13851,tc_fun(U_13851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13851)),U_13852))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13851),c_fNot),hAPP(hAPP(c_COMBC(U_13851,tc_fun(U_13851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13851)),U_13853)))),
    inference(definitional_conversion,[status(esa)],[f_3550_2]) ).

cnf(f_3550_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13851,tc_HOL_Obool)),U_13852),U_13853) = hAPP(c_Set_OCollect(U_13851),hAPP(hAPP(c_COMBS(U_13851,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13851),c_fconj),hAPP(hAPP(c_COMBC(U_13851,tc_fun(U_13851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13851)),U_13852))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13851),c_fNot),hAPP(hAPP(c_COMBC(U_13851,tc_fun(U_13851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13851)),U_13853)))),
    inference(clausify,[status(thm)],[f_3550_3]) ).

fof(f_3551_1,plain,
    ! [V_P_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).

fof(f_3551_2,plain,
    ! [U_13855,U_13854] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13854),c_fNot),U_13855))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),c_Orderings_Otop__class_Otop(tc_fun(U_13854,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),c_Orderings_Otop__class_Otop(tc_fun(U_13854,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13854),c_fNot),U_13855)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),U_13855))) ),
    inference(variable_rename,[status(thm)],[f_3551_1]) ).

fof(f_3551_3,plain,
    ( ! [U_13854,U_13855] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13854),c_fNot),U_13855))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),c_Orderings_Otop__class_Otop(tc_fun(U_13854,tc_HOL_Obool))))
        | ~ sP993(U_13854,U_13855) )
    & ! [U_13854,U_13855] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),c_Orderings_Otop__class_Otop(tc_fun(U_13854,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13854),c_fNot),U_13855))))
        | ~ sP993(U_13854,U_13855) )
    & ! [U_13854,U_13855] :
        ( sP993(U_13854,U_13855)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),U_13855))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP993])],[f_3551_2]) ).

cnf(f_3551_4,plain,
    ( sP993(U_13854,U_13855)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),U_13855))) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

cnf(f_3551_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),c_Orderings_Otop__class_Otop(tc_fun(U_13854,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13854),c_fNot),U_13855))))
    | ~ sP993(U_13854,U_13855) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

cnf(f_3551_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),hAPP(c_Set_OCollect(U_13854),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13854),c_fNot),U_13855))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13854),c_Orderings_Otop__class_Otop(tc_fun(U_13854,tc_HOL_Obool))))
    | ~ sP993(U_13854,U_13855) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

fof(f_3552_1,plain,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_insert__def]) ).

fof(f_3552_2,plain,
    ! [U_13858,U_13857,U_13856] : hAPP(hAPP(c_Set_Oinsert(U_13856),U_13857),U_13858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13856,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13856),hAPP(hAPP(c_COMBC(U_13856,U_13856,tc_HOL_Obool),c_fequal),U_13857))),U_13858),
    inference(variable_rename,[status(thm)],[f_3552_1]) ).

fof(f_3552_3,plain,
    ! [U_13856,U_13857,U_13858] : hAPP(hAPP(c_Set_Oinsert(U_13856),U_13857),U_13858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13856,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13856),hAPP(hAPP(c_COMBC(U_13856,U_13856,tc_HOL_Obool),c_fequal),U_13857))),U_13858),
    inference(definitional_conversion,[status(esa)],[f_3552_2]) ).

cnf(f_3552_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13856),U_13857),U_13858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13856,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13856),hAPP(hAPP(c_COMBC(U_13856,U_13856,tc_HOL_Obool),c_fequal),U_13857))),U_13858),
    inference(clausify,[status(thm)],[f_3552_3]) ).

fof(f_3553_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq]) ).

fof(f_3553_2,plain,
    ! [U_13860,U_13859] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13859,tc_HOL_Obool)),U_13860) = hAPP(c_Set_OCollect(U_13859),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13859),c_fNot),hAPP(hAPP(c_COMBC(U_13859,tc_fun(U_13859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13859)),U_13860))),
    inference(variable_rename,[status(thm)],[f_3553_1]) ).

fof(f_3553_3,plain,
    ! [U_13859,U_13860] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13859,tc_HOL_Obool)),U_13860) = hAPP(c_Set_OCollect(U_13859),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13859),c_fNot),hAPP(hAPP(c_COMBC(U_13859,tc_fun(U_13859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13859)),U_13860))),
    inference(definitional_conversion,[status(esa)],[f_3553_2]) ).

cnf(f_3553_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13859,tc_HOL_Obool)),U_13860) = hAPP(c_Set_OCollect(U_13859),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13859),c_fNot),hAPP(hAPP(c_COMBC(U_13859,tc_fun(U_13859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13859)),U_13860))),
    inference(clausify,[status(thm)],[f_3553_3]) ).

fof(f_3554_1,plain,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__def]) ).

fof(f_3554_2,plain,
    ! [U_13864,U_13863,U_13862,U_13861] : hAPP(c_Set_Ovimage(U_13861,U_13862,U_13863),U_13864) = hAPP(c_Set_OCollect(U_13861),hAPP(hAPP(c_COMBC(U_13861,tc_fun(U_13862,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13862,tc_fun(tc_fun(U_13862,tc_HOL_Obool),tc_HOL_Obool),U_13861),c_member(U_13862)),U_13863)),U_13864)),
    inference(variable_rename,[status(thm)],[f_3554_1]) ).

fof(f_3554_3,plain,
    ! [U_13861,U_13862,U_13863,U_13864] : hAPP(c_Set_Ovimage(U_13861,U_13862,U_13863),U_13864) = hAPP(c_Set_OCollect(U_13861),hAPP(hAPP(c_COMBC(U_13861,tc_fun(U_13862,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13862,tc_fun(tc_fun(U_13862,tc_HOL_Obool),tc_HOL_Obool),U_13861),c_member(U_13862)),U_13863)),U_13864)),
    inference(definitional_conversion,[status(esa)],[f_3554_2]) ).

cnf(f_3554_4,plain,
    hAPP(c_Set_Ovimage(U_13861,U_13862,U_13863),U_13864) = hAPP(c_Set_OCollect(U_13861),hAPP(hAPP(c_COMBC(U_13861,tc_fun(U_13862,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13862,tc_fun(tc_fun(U_13862,tc_HOL_Obool),tc_HOL_Obool),U_13861),c_member(U_13862)),U_13863)),U_13864)),
    inference(clausify,[status(thm)],[f_3554_3]) ).

fof(f_3555_1,plain,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).

fof(f_3555_2,plain,
    ! [U_13867,U_13866,U_13865] : hAPP(c_Set_OCollect(U_13865),hAPP(hAPP(c_COMBS(U_13865,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13865),c_fimplies),U_13866)),U_13867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13865,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13865,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13865),U_13866))),hAPP(c_Set_OCollect(U_13865),U_13867)),
    inference(variable_rename,[status(thm)],[f_3555_1]) ).

fof(f_3555_3,plain,
    ! [U_13865,U_13866,U_13867] : hAPP(c_Set_OCollect(U_13865),hAPP(hAPP(c_COMBS(U_13865,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13865),c_fimplies),U_13866)),U_13867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13865,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13865,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13865),U_13866))),hAPP(c_Set_OCollect(U_13865),U_13867)),
    inference(definitional_conversion,[status(esa)],[f_3555_2]) ).

cnf(f_3555_4,plain,
    hAPP(c_Set_OCollect(U_13865),hAPP(hAPP(c_COMBS(U_13865,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13865),c_fimplies),U_13866)),U_13867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13865,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13865,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13865),U_13866))),hAPP(c_Set_OCollect(U_13865),U_13867)),
    inference(clausify,[status(thm)],[f_3555_3]) ).

fof(f_3556_1,plain,
    ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))),
    inference(fof_nnf,[status(thm)],[fact_dom__def]) ).

fof(f_3556_2,plain,
    ! [U_13870,U_13869,U_13868] : c_Map_Odom(U_13868,U_13869,U_13870) = hAPP(c_Set_OCollect(U_13868),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13868),c_fNot),hAPP(hAPP(c_COMBC(U_13868,tc_Option_Ooption(U_13869),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13869),tc_fun(tc_Option_Ooption(U_13869),tc_HOL_Obool),U_13868),c_fequal),U_13870)),c_Option_Ooption_ONone(U_13869)))),
    inference(variable_rename,[status(thm)],[f_3556_1]) ).

fof(f_3556_3,plain,
    ! [U_13868,U_13869,U_13870] : c_Map_Odom(U_13868,U_13869,U_13870) = hAPP(c_Set_OCollect(U_13868),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13868),c_fNot),hAPP(hAPP(c_COMBC(U_13868,tc_Option_Ooption(U_13869),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13869),tc_fun(tc_Option_Ooption(U_13869),tc_HOL_Obool),U_13868),c_fequal),U_13870)),c_Option_Ooption_ONone(U_13869)))),
    inference(definitional_conversion,[status(esa)],[f_3556_2]) ).

cnf(f_3556_4,plain,
    c_Map_Odom(U_13868,U_13869,U_13870) = hAPP(c_Set_OCollect(U_13868),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13868),c_fNot),hAPP(hAPP(c_COMBC(U_13868,tc_Option_Ooption(U_13869),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13869),tc_fun(tc_Option_Ooption(U_13869),tc_HOL_Obool),U_13868),c_fequal),U_13870)),c_Option_Ooption_ONone(U_13869)))),
    inference(clausify,[status(thm)],[f_3556_3]) ).

fof(f_3557_1,plain,
    ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
    inference(fof_nnf,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(f_3557_2,plain,
    ! [U_13872,U_13871] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),U_13871)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13872))))),
    inference(variable_rename,[status(thm)],[f_3557_1]) ).

fof(f_3557_3,plain,
    ! [U_13871,U_13872] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),U_13871)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13872))))),
    inference(definitional_conversion,[status(esa)],[f_3557_2]) ).

cnf(f_3557_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),U_13871)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13872))))),
    inference(clausify,[status(thm)],[f_3557_3]) ).

fof(f_3558_1,plain,
    ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict]) ).

fof(f_3558_2,plain,
    ! [U_13879,U_13878,U_13877,U_13876,U_13875,U_13874,U_13873] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13874,U_13873),hAPP(hAPP(c_COMBS(U_13874,tc_fun(U_13876,tc_HOL_Obool),U_13873),hAPP(hAPP(c_COMBB(tc_fun(U_13876,U_13873),tc_fun(tc_fun(U_13876,tc_HOL_Obool),U_13873),U_13874),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13876,U_13873)),U_13878)),hAPP(hAPP(c_COMBB(tc_fun(U_13876,tc_HOL_Obool),tc_fun(U_13876,tc_HOL_Obool),U_13874),c_Set_OCollect(U_13876)),hAPP(hAPP(c_COMBB(tc_fun(U_13876,tc_HOL_Obool),tc_fun(U_13876,tc_HOL_Obool),U_13874),hAPP(c_COMBS(U_13876,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13876),c_fconj),hAPP(hAPP(c_COMBC(U_13876,tc_fun(U_13876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13876)),U_13877)))),U_13879)))),U_13875) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13876,U_13873),hAPP(hAPP(c_COMBS(U_13876,tc_fun(U_13874,tc_HOL_Obool),U_13873),hAPP(hAPP(c_COMBB(tc_fun(U_13874,U_13873),tc_fun(tc_fun(U_13874,tc_HOL_Obool),U_13873),U_13876),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13874,U_13873)),hAPP(c_COMBC(U_13874,U_13876,U_13873),U_13878))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(U_13874,tc_HOL_Obool),U_13876),c_Set_OCollect(U_13874)),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(U_13874,tc_HOL_Obool),U_13876),hAPP(c_COMBS(U_13874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13874),c_fconj),hAPP(hAPP(c_COMBC(U_13874,tc_fun(U_13874,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13874)),U_13875)))),hAPP(c_COMBC(U_13874,U_13876,tc_HOL_Obool),U_13879))))),U_13877)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13876),U_13877))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),U_13875))
      | ~ class_Groups_Ocomm__monoid__add(U_13873) ),
    inference(variable_rename,[status(thm)],[f_3558_1]) ).

fof(f_3558_3,plain,
    ! [U_13873,U_13874,U_13875,U_13876,U_13877,U_13878,U_13879] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13874,U_13873),hAPP(hAPP(c_COMBS(U_13874,tc_fun(U_13876,tc_HOL_Obool),U_13873),hAPP(hAPP(c_COMBB(tc_fun(U_13876,U_13873),tc_fun(tc_fun(U_13876,tc_HOL_Obool),U_13873),U_13874),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13876,U_13873)),U_13878)),hAPP(hAPP(c_COMBB(tc_fun(U_13876,tc_HOL_Obool),tc_fun(U_13876,tc_HOL_Obool),U_13874),c_Set_OCollect(U_13876)),hAPP(hAPP(c_COMBB(tc_fun(U_13876,tc_HOL_Obool),tc_fun(U_13876,tc_HOL_Obool),U_13874),hAPP(c_COMBS(U_13876,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13876),c_fconj),hAPP(hAPP(c_COMBC(U_13876,tc_fun(U_13876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13876)),U_13877)))),U_13879)))),U_13875) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13876,U_13873),hAPP(hAPP(c_COMBS(U_13876,tc_fun(U_13874,tc_HOL_Obool),U_13873),hAPP(hAPP(c_COMBB(tc_fun(U_13874,U_13873),tc_fun(tc_fun(U_13874,tc_HOL_Obool),U_13873),U_13876),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13874,U_13873)),hAPP(c_COMBC(U_13874,U_13876,U_13873),U_13878))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(U_13874,tc_HOL_Obool),U_13876),c_Set_OCollect(U_13874)),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(U_13874,tc_HOL_Obool),U_13876),hAPP(c_COMBS(U_13874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13874),c_fconj),hAPP(hAPP(c_COMBC(U_13874,tc_fun(U_13874,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13874)),U_13875)))),hAPP(c_COMBC(U_13874,U_13876,tc_HOL_Obool),U_13879))))),U_13877)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13876),U_13877))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),U_13875))
      | ~ class_Groups_Ocomm__monoid__add(U_13873) ),
    inference(definitional_conversion,[status(esa)],[f_3558_2]) ).

cnf(f_3558_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13874,U_13873),hAPP(hAPP(c_COMBS(U_13874,tc_fun(U_13876,tc_HOL_Obool),U_13873),hAPP(hAPP(c_COMBB(tc_fun(U_13876,U_13873),tc_fun(tc_fun(U_13876,tc_HOL_Obool),U_13873),U_13874),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13876,U_13873)),U_13878)),hAPP(hAPP(c_COMBB(tc_fun(U_13876,tc_HOL_Obool),tc_fun(U_13876,tc_HOL_Obool),U_13874),c_Set_OCollect(U_13876)),hAPP(hAPP(c_COMBB(tc_fun(U_13876,tc_HOL_Obool),tc_fun(U_13876,tc_HOL_Obool),U_13874),hAPP(c_COMBS(U_13876,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13876),c_fconj),hAPP(hAPP(c_COMBC(U_13876,tc_fun(U_13876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13876)),U_13877)))),U_13879)))),U_13875) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13876,U_13873),hAPP(hAPP(c_COMBS(U_13876,tc_fun(U_13874,tc_HOL_Obool),U_13873),hAPP(hAPP(c_COMBB(tc_fun(U_13874,U_13873),tc_fun(tc_fun(U_13874,tc_HOL_Obool),U_13873),U_13876),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13874,U_13873)),hAPP(c_COMBC(U_13874,U_13876,U_13873),U_13878))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(U_13874,tc_HOL_Obool),U_13876),c_Set_OCollect(U_13874)),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(U_13874,tc_HOL_Obool),U_13876),hAPP(c_COMBS(U_13874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13874),c_fconj),hAPP(hAPP(c_COMBC(U_13874,tc_fun(U_13874,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13874)),U_13875)))),hAPP(c_COMBC(U_13874,U_13876,tc_HOL_Obool),U_13879))))),U_13877)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13876),U_13877))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),U_13875))
    | ~ class_Groups_Ocomm__monoid__add(U_13873) ),
    inference(clausify,[status(thm)],[f_3558_3]) ).

fof(f_3559_1,plain,
    ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
    inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).

fof(f_3559_2,plain,
    ! [U_13885,U_13884,U_13883,U_13882,U_13881,U_13880] : hAPP(c_Set_Oimage(U_13880,U_13881,hAPP(hAPP(c_COMBS(U_13880,U_13881,U_13881),hAPP(hAPP(c_COMBS(U_13880,U_13881,tc_fun(U_13881,U_13881)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13881,tc_fun(U_13881,U_13881)),U_13880),c_If(U_13881)),U_13882)),U_13883)),U_13884)),U_13885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13881,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13880,U_13881,U_13883),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13880,tc_HOL_Obool)),U_13885),hAPP(c_Set_OCollect(U_13880),U_13882)))),hAPP(c_Set_Oimage(U_13880,U_13881,U_13884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13880,tc_HOL_Obool)),U_13885),hAPP(c_Set_OCollect(U_13880),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13880),c_fNot),U_13882))))),
    inference(variable_rename,[status(thm)],[f_3559_1]) ).

fof(f_3559_3,plain,
    ! [U_13880,U_13881,U_13882,U_13883,U_13884,U_13885] : hAPP(c_Set_Oimage(U_13880,U_13881,hAPP(hAPP(c_COMBS(U_13880,U_13881,U_13881),hAPP(hAPP(c_COMBS(U_13880,U_13881,tc_fun(U_13881,U_13881)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13881,tc_fun(U_13881,U_13881)),U_13880),c_If(U_13881)),U_13882)),U_13883)),U_13884)),U_13885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13881,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13880,U_13881,U_13883),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13880,tc_HOL_Obool)),U_13885),hAPP(c_Set_OCollect(U_13880),U_13882)))),hAPP(c_Set_Oimage(U_13880,U_13881,U_13884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13880,tc_HOL_Obool)),U_13885),hAPP(c_Set_OCollect(U_13880),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13880),c_fNot),U_13882))))),
    inference(definitional_conversion,[status(esa)],[f_3559_2]) ).

cnf(f_3559_4,plain,
    hAPP(c_Set_Oimage(U_13880,U_13881,hAPP(hAPP(c_COMBS(U_13880,U_13881,U_13881),hAPP(hAPP(c_COMBS(U_13880,U_13881,tc_fun(U_13881,U_13881)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13881,tc_fun(U_13881,U_13881)),U_13880),c_If(U_13881)),U_13882)),U_13883)),U_13884)),U_13885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13881,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13880,U_13881,U_13883),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13880,tc_HOL_Obool)),U_13885),hAPP(c_Set_OCollect(U_13880),U_13882)))),hAPP(c_Set_Oimage(U_13880,U_13881,U_13884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13880,tc_HOL_Obool)),U_13885),hAPP(c_Set_OCollect(U_13880),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13880),c_fNot),U_13882))))),
    inference(clausify,[status(thm)],[f_3559_3]) ).

fof(f_3560_1,plain,
    ! [V_g_2,V_f_2,V_P_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))),
    inference(fof_nnf,[status(thm)],[fact_dom__if]) ).

fof(f_3560_2,plain,
    ! [U_13890,U_13889,U_13888,U_13887,U_13886] : c_Map_Odom(U_13886,U_13887,hAPP(hAPP(c_COMBS(U_13886,tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887)),hAPP(hAPP(c_COMBS(U_13886,tc_Option_Ooption(U_13887),tc_fun(tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_13887),tc_fun(tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887))),U_13886),c_If(tc_Option_Ooption(U_13887))),U_13888)),U_13889)),U_13890)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13886,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13886,tc_HOL_Obool)),c_Map_Odom(U_13886,U_13887,U_13889)),hAPP(c_Set_OCollect(U_13886),U_13888))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13886,tc_HOL_Obool)),c_Map_Odom(U_13886,U_13887,U_13890)),hAPP(c_Set_OCollect(U_13886),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13886),c_fNot),U_13888)))),
    inference(variable_rename,[status(thm)],[f_3560_1]) ).

fof(f_3560_3,plain,
    ! [U_13886,U_13887,U_13888,U_13889,U_13890] : c_Map_Odom(U_13886,U_13887,hAPP(hAPP(c_COMBS(U_13886,tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887)),hAPP(hAPP(c_COMBS(U_13886,tc_Option_Ooption(U_13887),tc_fun(tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_13887),tc_fun(tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887))),U_13886),c_If(tc_Option_Ooption(U_13887))),U_13888)),U_13889)),U_13890)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13886,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13886,tc_HOL_Obool)),c_Map_Odom(U_13886,U_13887,U_13889)),hAPP(c_Set_OCollect(U_13886),U_13888))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13886,tc_HOL_Obool)),c_Map_Odom(U_13886,U_13887,U_13890)),hAPP(c_Set_OCollect(U_13886),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13886),c_fNot),U_13888)))),
    inference(definitional_conversion,[status(esa)],[f_3560_2]) ).

cnf(f_3560_4,plain,
    c_Map_Odom(U_13886,U_13887,hAPP(hAPP(c_COMBS(U_13886,tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887)),hAPP(hAPP(c_COMBS(U_13886,tc_Option_Ooption(U_13887),tc_fun(tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_13887),tc_fun(tc_Option_Ooption(U_13887),tc_Option_Ooption(U_13887))),U_13886),c_If(tc_Option_Ooption(U_13887))),U_13888)),U_13889)),U_13890)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13886,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13886,tc_HOL_Obool)),c_Map_Odom(U_13886,U_13887,U_13889)),hAPP(c_Set_OCollect(U_13886),U_13888))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13886,tc_HOL_Obool)),c_Map_Odom(U_13886,U_13887,U_13890)),hAPP(c_Set_OCollect(U_13886),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13886),c_fNot),U_13888)))),
    inference(clausify,[status(thm)],[f_3560_3]) ).

fof(f_3561_1,plain,
    ! [V_n_2,V_f_2,T_b,V_A_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite]) ).

fof(f_3561_2,plain,
    ! [U_13894,U_13893,U_13892,U_13891] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13892),U_13891))
      | U_13891 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13892,U_13893),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13894))) ),
    inference(variable_rename,[status(thm)],[f_3561_1]) ).

fof(f_3561_3,plain,
    ! [U_13891,U_13892,U_13893,U_13894] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13892),U_13891))
      | U_13891 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13892,U_13893),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13894))) ),
    inference(definitional_conversion,[status(esa)],[f_3561_2]) ).

cnf(f_3561_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13892),U_13891))
    | U_13891 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13892,U_13893),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13894))) ),
    inference(clausify,[status(thm)],[f_3561_3]) ).

fof(f_3562_1,plain,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H]) ).

fof(f_3562_2,plain,
    ! [U_13899,U_13898,U_13897,U_13896,U_13895] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13896,U_13895),U_13898),hAPP(c_Set_OCollect(U_13896),hAPP(hAPP(c_COMBS(U_13896,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13896),c_fconj),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13897))),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13899)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13896,U_13895),hAPP(hAPP(c_COMBC(U_13896,U_13895,U_13895),hAPP(hAPP(c_COMBS(U_13896,U_13895,tc_fun(U_13895,U_13895)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13895,tc_fun(U_13895,U_13895)),U_13896),c_If(U_13895)),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13899))),U_13898)),c_Groups_Ozero__class_Ozero(U_13895))),U_13897)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13896),U_13897))
      | ~ class_Groups_Ocomm__monoid__add(U_13895) ),
    inference(variable_rename,[status(thm)],[f_3562_1]) ).

fof(f_3562_3,plain,
    ! [U_13895,U_13896,U_13897,U_13898,U_13899] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13896,U_13895),U_13898),hAPP(c_Set_OCollect(U_13896),hAPP(hAPP(c_COMBS(U_13896,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13896),c_fconj),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13897))),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13899)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13896,U_13895),hAPP(hAPP(c_COMBC(U_13896,U_13895,U_13895),hAPP(hAPP(c_COMBS(U_13896,U_13895,tc_fun(U_13895,U_13895)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13895,tc_fun(U_13895,U_13895)),U_13896),c_If(U_13895)),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13899))),U_13898)),c_Groups_Ozero__class_Ozero(U_13895))),U_13897)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13896),U_13897))
      | ~ class_Groups_Ocomm__monoid__add(U_13895) ),
    inference(definitional_conversion,[status(esa)],[f_3562_2]) ).

cnf(f_3562_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13896,U_13895),U_13898),hAPP(c_Set_OCollect(U_13896),hAPP(hAPP(c_COMBS(U_13896,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13896),c_fconj),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13897))),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13899)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13896,U_13895),hAPP(hAPP(c_COMBC(U_13896,U_13895,U_13895),hAPP(hAPP(c_COMBS(U_13896,U_13895,tc_fun(U_13895,U_13895)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13895,tc_fun(U_13895,U_13895)),U_13896),c_If(U_13895)),hAPP(hAPP(c_COMBC(U_13896,tc_fun(U_13896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13896)),U_13899))),U_13898)),c_Groups_Ozero__class_Ozero(U_13895))),U_13897)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13896),U_13897))
    | ~ class_Groups_Ocomm__monoid__add(U_13895) ),
    inference(clausify,[status(thm)],[f_3562_3]) ).

fof(f_3563_1,plain,
    ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__image__gen]) ).

fof(f_3563_2,plain,
    ! [U_13905,U_13904,U_13903,U_13902,U_13901,U_13900] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13901,U_13900),U_13903),U_13902) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13904,U_13900),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),U_13900,U_13904),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13901,U_13900),U_13903)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool),U_13904),c_Set_OCollect(U_13901)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool),U_13904),hAPP(c_COMBS(U_13901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13901),c_fconj),hAPP(hAPP(c_COMBC(U_13901,tc_fun(U_13901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13901)),U_13902)))),hAPP(c_COMBC(U_13901,U_13904,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13904,tc_fun(U_13904,tc_HOL_Obool),U_13901),c_fequal),U_13905)))))),hAPP(c_Set_Oimage(U_13901,U_13904,U_13905),U_13902))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13901),U_13902))
      | ~ class_Groups_Ocomm__monoid__add(U_13900) ),
    inference(variable_rename,[status(thm)],[f_3563_1]) ).

fof(f_3563_3,plain,
    ! [U_13900,U_13901,U_13902,U_13903,U_13904,U_13905] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13901,U_13900),U_13903),U_13902) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13904,U_13900),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),U_13900,U_13904),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13901,U_13900),U_13903)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool),U_13904),c_Set_OCollect(U_13901)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool),U_13904),hAPP(c_COMBS(U_13901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13901),c_fconj),hAPP(hAPP(c_COMBC(U_13901,tc_fun(U_13901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13901)),U_13902)))),hAPP(c_COMBC(U_13901,U_13904,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13904,tc_fun(U_13904,tc_HOL_Obool),U_13901),c_fequal),U_13905)))))),hAPP(c_Set_Oimage(U_13901,U_13904,U_13905),U_13902))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13901),U_13902))
      | ~ class_Groups_Ocomm__monoid__add(U_13900) ),
    inference(definitional_conversion,[status(esa)],[f_3563_2]) ).

cnf(f_3563_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13901,U_13900),U_13903),U_13902) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13904,U_13900),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),U_13900,U_13904),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13901,U_13900),U_13903)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool),U_13904),c_Set_OCollect(U_13901)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool),U_13904),hAPP(c_COMBS(U_13901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13901),c_fconj),hAPP(hAPP(c_COMBC(U_13901,tc_fun(U_13901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13901)),U_13902)))),hAPP(c_COMBC(U_13901,U_13904,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13904,tc_fun(U_13904,tc_HOL_Obool),U_13901),c_fequal),U_13905)))))),hAPP(c_Set_Oimage(U_13901,U_13904,U_13905),U_13902))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13901),U_13902))
    | ~ class_Groups_Ocomm__monoid__add(U_13900) ),
    inference(clausify,[status(thm)],[f_3563_3]) ).

fof(f_3564_1,plain,
    ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__singleton]) ).

fof(f_3564_2,plain,
    ! [U_13909,U_13908,U_13907,U_13906] : hAPP(c_Relation_OImage(U_13906,U_13907,U_13908),hAPP(hAPP(c_Set_Oinsert(U_13906),U_13909),c_Orderings_Obot__class_Obot(tc_fun(U_13906,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13907),hAPP(hAPP(c_COMBC(U_13907,tc_fun(tc_prod(U_13906,U_13907),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13906,U_13907),tc_fun(tc_fun(tc_prod(U_13906,U_13907),tc_HOL_Obool),tc_HOL_Obool),U_13907),c_member(tc_prod(U_13906,U_13907))),hAPP(c_Product__Type_OPair(U_13906,U_13907),U_13909))),U_13908)),
    inference(variable_rename,[status(thm)],[f_3564_1]) ).

fof(f_3564_3,plain,
    ! [U_13906,U_13907,U_13908,U_13909] : hAPP(c_Relation_OImage(U_13906,U_13907,U_13908),hAPP(hAPP(c_Set_Oinsert(U_13906),U_13909),c_Orderings_Obot__class_Obot(tc_fun(U_13906,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13907),hAPP(hAPP(c_COMBC(U_13907,tc_fun(tc_prod(U_13906,U_13907),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13906,U_13907),tc_fun(tc_fun(tc_prod(U_13906,U_13907),tc_HOL_Obool),tc_HOL_Obool),U_13907),c_member(tc_prod(U_13906,U_13907))),hAPP(c_Product__Type_OPair(U_13906,U_13907),U_13909))),U_13908)),
    inference(definitional_conversion,[status(esa)],[f_3564_2]) ).

cnf(f_3564_4,plain,
    hAPP(c_Relation_OImage(U_13906,U_13907,U_13908),hAPP(hAPP(c_Set_Oinsert(U_13906),U_13909),c_Orderings_Obot__class_Obot(tc_fun(U_13906,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13907),hAPP(hAPP(c_COMBC(U_13907,tc_fun(tc_prod(U_13906,U_13907),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13906,U_13907),tc_fun(tc_fun(tc_prod(U_13906,U_13907),tc_HOL_Obool),tc_HOL_Obool),U_13907),c_member(tc_prod(U_13906,U_13907))),hAPP(c_Product__Type_OPair(U_13906,U_13907),U_13909))),U_13908)),
    inference(clausify,[status(thm)],[f_3564_3]) ).

fof(f_3565_1,plain,
    ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).

fof(f_3565_2,plain,
    ! [U_13915,U_13914,U_13913,U_13912,U_13911,U_13910] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),hAPP(hAPP(c_COMBS(U_13911,U_13910,U_13910),hAPP(hAPP(c_COMBS(U_13911,U_13910,tc_fun(U_13910,U_13910)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13910,tc_fun(U_13910,U_13910)),U_13911),c_If(U_13910)),U_13913)),U_13914)),U_13915)),U_13912) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13910),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),U_13914),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13911,tc_HOL_Obool)),U_13912),hAPP(c_Set_OCollect(U_13911),U_13913)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),U_13915),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13911,tc_HOL_Obool)),U_13912),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13911,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13911),U_13913)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13911),U_13912))
      | ~ class_Groups_Ocomm__monoid__add(U_13910) ),
    inference(variable_rename,[status(thm)],[f_3565_1]) ).

fof(f_3565_3,plain,
    ! [U_13910,U_13911,U_13912,U_13913,U_13914,U_13915] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),hAPP(hAPP(c_COMBS(U_13911,U_13910,U_13910),hAPP(hAPP(c_COMBS(U_13911,U_13910,tc_fun(U_13910,U_13910)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13910,tc_fun(U_13910,U_13910)),U_13911),c_If(U_13910)),U_13913)),U_13914)),U_13915)),U_13912) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13910),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),U_13914),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13911,tc_HOL_Obool)),U_13912),hAPP(c_Set_OCollect(U_13911),U_13913)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),U_13915),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13911,tc_HOL_Obool)),U_13912),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13911,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13911),U_13913)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13911),U_13912))
      | ~ class_Groups_Ocomm__monoid__add(U_13910) ),
    inference(definitional_conversion,[status(esa)],[f_3565_2]) ).

cnf(f_3565_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),hAPP(hAPP(c_COMBS(U_13911,U_13910,U_13910),hAPP(hAPP(c_COMBS(U_13911,U_13910,tc_fun(U_13910,U_13910)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13910,tc_fun(U_13910,U_13910)),U_13911),c_If(U_13910)),U_13913)),U_13914)),U_13915)),U_13912) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13910),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),U_13914),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13911,tc_HOL_Obool)),U_13912),hAPP(c_Set_OCollect(U_13911),U_13913)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13911,U_13910),U_13915),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13911,tc_HOL_Obool)),U_13912),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13911,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13911),U_13913)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13911),U_13912))
    | ~ class_Groups_Ocomm__monoid__add(U_13910) ),
    inference(clausify,[status(thm)],[f_3565_3]) ).

fof(f_3566_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))),
    inference(fof_nnf,[status(thm)],[fact_dom__override__on]) ).

fof(f_3566_2,plain,
    ! [U_13920,U_13919,U_13918,U_13917,U_13916] : c_Map_Odom(U_13916,U_13917,c_Fun_Ooverride__on(U_13916,tc_Option_Ooption(U_13917),U_13918,U_13919,U_13920)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13916,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),c_Map_Odom(U_13916,U_13917,U_13918)),hAPP(c_Set_OCollect(U_13916),hAPP(hAPP(c_COMBC(U_13916,tc_fun(U_13916,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13916)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),U_13920),c_Map_Odom(U_13916,U_13917,U_13919)))))),hAPP(c_Set_OCollect(U_13916),hAPP(hAPP(c_COMBC(U_13916,tc_fun(U_13916,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13916)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13916,tc_HOL_Obool)),U_13920),c_Map_Odom(U_13916,U_13917,U_13919))))),
    inference(variable_rename,[status(thm)],[f_3566_1]) ).

fof(f_3566_3,plain,
    ! [U_13916,U_13917,U_13918,U_13919,U_13920] : c_Map_Odom(U_13916,U_13917,c_Fun_Ooverride__on(U_13916,tc_Option_Ooption(U_13917),U_13918,U_13919,U_13920)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13916,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),c_Map_Odom(U_13916,U_13917,U_13918)),hAPP(c_Set_OCollect(U_13916),hAPP(hAPP(c_COMBC(U_13916,tc_fun(U_13916,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13916)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),U_13920),c_Map_Odom(U_13916,U_13917,U_13919)))))),hAPP(c_Set_OCollect(U_13916),hAPP(hAPP(c_COMBC(U_13916,tc_fun(U_13916,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13916)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13916,tc_HOL_Obool)),U_13920),c_Map_Odom(U_13916,U_13917,U_13919))))),
    inference(definitional_conversion,[status(esa)],[f_3566_2]) ).

cnf(f_3566_4,plain,
    c_Map_Odom(U_13916,U_13917,c_Fun_Ooverride__on(U_13916,tc_Option_Ooption(U_13917),U_13918,U_13919,U_13920)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13916,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),c_Map_Odom(U_13916,U_13917,U_13918)),hAPP(c_Set_OCollect(U_13916),hAPP(hAPP(c_COMBC(U_13916,tc_fun(U_13916,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13916)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),U_13920),c_Map_Odom(U_13916,U_13917,U_13919)))))),hAPP(c_Set_OCollect(U_13916),hAPP(hAPP(c_COMBC(U_13916,tc_fun(U_13916,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13916)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13916,tc_HOL_Obool)),U_13920),c_Map_Odom(U_13916,U_13917,U_13919))))),
    inference(clausify,[status(thm)],[f_3566_3]) ).

fof(f_3567_1,plain,
    ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2))
      | ? [B_x] :
          ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) != V_k_2
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__multicount]) ).

fof(f_3567_2,plain,
    ! [U_13927,U_13926,U_13925,U_13924,U_13923,U_13922] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13922,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_Nat_Onat,U_13922),c_Finite__Set_Ocard(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),c_Set_OCollect(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),hAPP(c_COMBS(U_13924,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13924),c_fconj),hAPP(hAPP(c_COMBC(U_13924,tc_fun(U_13924,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13924)),U_13925)))),U_13926)))),U_13923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13927),hAPP(c_Finite__Set_Ocard(U_13924),U_13925))
      | ? [U_13921] :
          ( hAPP(c_Finite__Set_Ocard(U_13922),hAPP(c_Set_OCollect(U_13922),hAPP(hAPP(c_COMBS(U_13922,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13922),c_fconj),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13922)),U_13923))),hAPP(hAPP(c_COMBC(U_13922,U_13924,tc_HOL_Obool),U_13926),U_13921)))) != U_13927
          & hBOOL(hAPP(hAPP(c_member(U_13924),U_13921),U_13925)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13924),U_13925))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13922),U_13923)) ),
    inference(variable_rename,[status(thm)],[f_3567_1]) ).

fof(f_3567_3,plain,
    ! [U_13927,U_13926,U_13925,U_13924,U_13923,U_13922] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13922,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_Nat_Onat,U_13922),c_Finite__Set_Ocard(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),c_Set_OCollect(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),hAPP(c_COMBS(U_13924,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13924),c_fconj),hAPP(hAPP(c_COMBC(U_13924,tc_fun(U_13924,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13924)),U_13925)))),U_13926)))),U_13923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13927),hAPP(c_Finite__Set_Ocard(U_13924),U_13925))
      | ( hAPP(c_Finite__Set_Ocard(U_13922),hAPP(c_Set_OCollect(U_13922),hAPP(hAPP(c_COMBS(U_13922,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13922),c_fconj),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13922)),U_13923))),hAPP(hAPP(c_COMBC(U_13922,U_13924,tc_HOL_Obool),U_13926),sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922))))) != U_13927
        & hBOOL(hAPP(hAPP(c_member(U_13924),sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922)),U_13925)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13924),U_13925))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13922),U_13923)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_13921,sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922))],[f_3567_2]) ).

fof(f_3567_4,plain,
    ( ! [U_13922,U_13923,U_13924,U_13925,U_13926,U_13927] :
        ( hAPP(c_Finite__Set_Ocard(U_13922),hAPP(c_Set_OCollect(U_13922),hAPP(hAPP(c_COMBS(U_13922,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13922),c_fconj),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13922)),U_13923))),hAPP(hAPP(c_COMBC(U_13922,U_13924,tc_HOL_Obool),U_13926),sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922))))) != U_13927
        | ~ sP994(U_13922,U_13923,U_13924,U_13925,U_13926,U_13927) )
    & ! [U_13922,U_13923,U_13924,U_13925,U_13926,U_13927] :
        ( hBOOL(hAPP(hAPP(c_member(U_13924),sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922)),U_13925))
        | ~ sP994(U_13922,U_13923,U_13924,U_13925,U_13926,U_13927) )
    & ! [U_13922,U_13923,U_13924,U_13925,U_13926,U_13927] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13922,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_Nat_Onat,U_13922),c_Finite__Set_Ocard(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),c_Set_OCollect(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),hAPP(c_COMBS(U_13924,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13924),c_fconj),hAPP(hAPP(c_COMBC(U_13924,tc_fun(U_13924,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13924)),U_13925)))),U_13926)))),U_13923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13927),hAPP(c_Finite__Set_Ocard(U_13924),U_13925))
        | sP994(U_13922,U_13923,U_13924,U_13925,U_13926,U_13927)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13924),U_13925))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13922),U_13923)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP994])],[f_3567_3]) ).

cnf(f_3567_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13922,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_Nat_Onat,U_13922),c_Finite__Set_Ocard(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),c_Set_OCollect(U_13924)),hAPP(hAPP(c_COMBB(tc_fun(U_13924,tc_HOL_Obool),tc_fun(U_13924,tc_HOL_Obool),U_13922),hAPP(c_COMBS(U_13924,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13924),c_fconj),hAPP(hAPP(c_COMBC(U_13924,tc_fun(U_13924,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13924)),U_13925)))),U_13926)))),U_13923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13927),hAPP(c_Finite__Set_Ocard(U_13924),U_13925))
    | sP994(U_13922,U_13923,U_13924,U_13925,U_13926,U_13927)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13924),U_13925))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13922),U_13923)) ),
    inference(clausify,[status(thm)],[f_3567_4]) ).

cnf(f_3567_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13924),sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922)),U_13925))
    | ~ sP994(U_13922,U_13923,U_13924,U_13925,U_13926,U_13927) ),
    inference(clausify,[status(thm)],[f_3567_4]) ).

cnf(f_3567_7,plain,
    ( hAPP(c_Finite__Set_Ocard(U_13922),hAPP(c_Set_OCollect(U_13922),hAPP(hAPP(c_COMBS(U_13922,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13922),c_fconj),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13922)),U_13923))),hAPP(hAPP(c_COMBC(U_13922,U_13924,tc_HOL_Obool),U_13926),sK319(U_13927,U_13926,U_13925,U_13924,U_13923,U_13922))))) != U_13927
    | ~ sP994(U_13922,U_13923,U_13924,U_13925,U_13926,U_13927) ),
    inference(clausify,[status(thm)],[f_3567_4]) ).

fof(f_3568_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib]) ).

fof(f_3568_2,plain,
    ! [U_13930,U_13929,U_13928] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13928),c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),U_13929)),c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),U_13930)) = c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),hAPP(c_Set_OCollect(U_13928),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool,U_13928),c_HOL_OEx(U_13928)),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_HOL_Obool),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool,U_13928),c_HOL_OEx(U_13928))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),tc_fun(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),U_13928),c_COMBS(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13928,tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBS(U_13928,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13928),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13928),c_fconj))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_fun(U_13928,U_13928)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool)),tc_fun(tc_fun(U_13928,tc_fun(U_13928,U_13928)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),U_13928),c_COMBB(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool),U_13928)),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_fun(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBB(U_13928,tc_HOL_Obool,U_13928)),c_fequal))),c_Orderings_Oord__class_Omin(U_13928)))))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13928),c_fconj),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13928)),U_13929)))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13928)),U_13930)))))))
      | U_13930 = c_Orderings_Obot__class_Obot(tc_fun(U_13928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13928),U_13930))
      | U_13929 = c_Orderings_Obot__class_Obot(tc_fun(U_13928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13928),U_13929))
      | ~ class_Orderings_Olinorder(U_13928) ),
    inference(variable_rename,[status(thm)],[f_3568_1]) ).

fof(f_3568_3,plain,
    ! [U_13928,U_13929,U_13930] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13928),c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),U_13929)),c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),U_13930)) = c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),hAPP(c_Set_OCollect(U_13928),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool,U_13928),c_HOL_OEx(U_13928)),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_HOL_Obool),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool,U_13928),c_HOL_OEx(U_13928))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),tc_fun(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),U_13928),c_COMBS(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13928,tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBS(U_13928,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13928),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13928),c_fconj))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_fun(U_13928,U_13928)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool)),tc_fun(tc_fun(U_13928,tc_fun(U_13928,U_13928)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),U_13928),c_COMBB(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool),U_13928)),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_fun(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBB(U_13928,tc_HOL_Obool,U_13928)),c_fequal))),c_Orderings_Oord__class_Omin(U_13928)))))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13928),c_fconj),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13928)),U_13929)))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13928)),U_13930)))))))
      | U_13930 = c_Orderings_Obot__class_Obot(tc_fun(U_13928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13928),U_13930))
      | U_13929 = c_Orderings_Obot__class_Obot(tc_fun(U_13928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13928),U_13929))
      | ~ class_Orderings_Olinorder(U_13928) ),
    inference(definitional_conversion,[status(esa)],[f_3568_2]) ).

cnf(f_3568_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13928),c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),U_13929)),c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),U_13930)) = c_Big__Operators_Olattice_OSup__fin(U_13928,c_Orderings_Oord__class_Omax(U_13928),hAPP(c_Set_OCollect(U_13928),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool,U_13928),c_HOL_OEx(U_13928)),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_HOL_Obool),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool,U_13928),c_HOL_OEx(U_13928))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),tc_fun(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),U_13928),c_COMBS(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13928,tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool))),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBS(U_13928,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool)),tc_fun(U_13928,tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13928),hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13928),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13928),c_fconj))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_fun(U_13928,U_13928)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool)),tc_fun(tc_fun(U_13928,tc_fun(U_13928,U_13928)),tc_fun(U_13928,tc_fun(U_13928,tc_HOL_Obool))),U_13928),c_COMBB(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool),U_13928)),hAPP(hAPP(c_COMBB(tc_fun(U_13928,tc_HOL_Obool),tc_fun(tc_fun(U_13928,U_13928),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBB(U_13928,tc_HOL_Obool,U_13928)),c_fequal))),c_Orderings_Oord__class_Omin(U_13928)))))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13928,tc_HOL_Obool),tc_fun(U_13928,tc_HOL_Obool)),U_13928),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13928),c_fconj),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13928)),U_13929)))),hAPP(hAPP(c_COMBC(U_13928,tc_fun(U_13928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13928)),U_13930)))))))
    | U_13930 = c_Orderings_Obot__class_Obot(tc_fun(U_13928,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13928),U_13930))
    | U_13929 = c_Orderings_Obot__class_Obot(tc_fun(U_13928,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13928),U_13929))
    | ~ class_Orderings_Olinorder(U_13928) ),
    inference(clausify,[status(thm)],[f_3568_3]) ).

fof(f_3569_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets]) ).

fof(f_3569_2,plain,
    ! [U_13932,U_13931] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13931,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13931,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13931,tc_HOL_Obool),tc_fun(U_13931,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13931,tc_HOL_Obool))),U_13932))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13931),U_13932)) ),
    inference(variable_rename,[status(thm)],[f_3569_1]) ).

fof(f_3569_3,plain,
    ! [U_13932,U_13931] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13931,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13931,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13931,tc_HOL_Obool),tc_fun(U_13931,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13931,tc_HOL_Obool))),U_13932))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13931),U_13932)) ),
    inference(definitional_conversion,[status(esa)],[f_3569_2]) ).

cnf(f_3569_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13931,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13931,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13931,tc_HOL_Obool),tc_fun(U_13931,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13931,tc_HOL_Obool))),U_13932))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13931),U_13932)) ),
    inference(clausify,[status(thm)],[f_3569_3]) ).

fof(f_3570_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))),
    inference(fof_nnf,[status(thm)],[fact_Pow__Compl]) ).

fof(f_3570_2,plain,
    ! [U_13934,U_13933] : hAPP(c_Set_OPow(U_13933),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13933,tc_HOL_Obool)),U_13934)) = hAPP(c_Set_OCollect(tc_fun(U_13933,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13933,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),c_COMBS(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),c_COMBB(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13933,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13933,tc_HOL_Obool)),U_13934)),c_Set_OPow(U_13933))))),
    inference(variable_rename,[status(thm)],[f_3570_1]) ).

fof(f_3570_3,plain,
    ! [U_13933,U_13934] : hAPP(c_Set_OPow(U_13933),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13933,tc_HOL_Obool)),U_13934)) = hAPP(c_Set_OCollect(tc_fun(U_13933,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13933,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),c_COMBS(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),c_COMBB(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13933,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13933,tc_HOL_Obool)),U_13934)),c_Set_OPow(U_13933))))),
    inference(definitional_conversion,[status(esa)],[f_3570_2]) ).

cnf(f_3570_4,plain,
    hAPP(c_Set_OPow(U_13933),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13933,tc_HOL_Obool)),U_13934)) = hAPP(c_Set_OCollect(tc_fun(U_13933,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13933,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),c_COMBS(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13933,tc_HOL_Obool),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_fun(U_13933,tc_HOL_Obool)),tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13933,tc_HOL_Obool)),c_COMBB(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13933,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13933,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13933,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13933,tc_HOL_Obool)),U_13934)),c_Set_OPow(U_13933))))),
    inference(clausify,[status(thm)],[f_3570_3]) ).

fof(f_3571_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__def]) ).

fof(f_3571_2,plain,
    ! [U_13936,U_13935] : hAPP(c_Set_OPow(U_13935),U_13936) = hAPP(c_Set_OCollect(tc_fun(U_13935,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13935,tc_HOL_Obool),tc_fun(U_13935,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13935,tc_HOL_Obool))),U_13936)),
    inference(variable_rename,[status(thm)],[f_3571_1]) ).

fof(f_3571_3,plain,
    ! [U_13935,U_13936] : hAPP(c_Set_OPow(U_13935),U_13936) = hAPP(c_Set_OCollect(tc_fun(U_13935,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13935,tc_HOL_Obool),tc_fun(U_13935,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13935,tc_HOL_Obool))),U_13936)),
    inference(definitional_conversion,[status(esa)],[f_3571_2]) ).

cnf(f_3571_4,plain,
    hAPP(c_Set_OPow(U_13935),U_13936) = hAPP(c_Set_OCollect(tc_fun(U_13935,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13935,tc_HOL_Obool),tc_fun(U_13935,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13935,tc_HOL_Obool))),U_13936)),
    inference(clausify,[status(thm)],[f_3571_3]) ).

fof(f_3572_1,plain,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).

fof(f_3572_2,plain,
    ! [U_13940,U_13939,U_13938,U_13937] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13939),hAPP(c_Set_OCollect(U_13939),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_HOL_Obool),tc_HOL_Obool,U_13939),c_HOL_OEx(U_13937)),hAPP(hAPP(c_COMBC(U_13939,tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_HOL_Obool)),U_13939),c_COMBS(U_13937,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13937),c_fconj)),hAPP(hAPP(c_COMBC(U_13939,tc_fun(U_13937,U_13939),tc_fun(U_13937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13939,tc_HOL_Obool),tc_fun(tc_fun(U_13937,U_13939),tc_fun(U_13937,tc_HOL_Obool)),U_13939),c_COMBB(U_13939,tc_HOL_Obool,U_13937)),c_fequal)),U_13940)))),U_13938)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),hAPP(c_Set_OCollect(U_13937),U_13938))) ),
    inference(variable_rename,[status(thm)],[f_3572_1]) ).

fof(f_3572_3,plain,
    ! [U_13937,U_13938,U_13939,U_13940] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13939),hAPP(c_Set_OCollect(U_13939),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_HOL_Obool),tc_HOL_Obool,U_13939),c_HOL_OEx(U_13937)),hAPP(hAPP(c_COMBC(U_13939,tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_HOL_Obool)),U_13939),c_COMBS(U_13937,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13937),c_fconj)),hAPP(hAPP(c_COMBC(U_13939,tc_fun(U_13937,U_13939),tc_fun(U_13937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13939,tc_HOL_Obool),tc_fun(tc_fun(U_13937,U_13939),tc_fun(U_13937,tc_HOL_Obool)),U_13939),c_COMBB(U_13939,tc_HOL_Obool,U_13937)),c_fequal)),U_13940)))),U_13938)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),hAPP(c_Set_OCollect(U_13937),U_13938))) ),
    inference(definitional_conversion,[status(esa)],[f_3572_2]) ).

cnf(f_3572_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13939),hAPP(c_Set_OCollect(U_13939),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_HOL_Obool),tc_HOL_Obool,U_13939),c_HOL_OEx(U_13937)),hAPP(hAPP(c_COMBC(U_13939,tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_HOL_Obool)),U_13939),c_COMBS(U_13937,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13937,tc_HOL_Obool),tc_fun(U_13937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13937),c_fconj)),hAPP(hAPP(c_COMBC(U_13939,tc_fun(U_13937,U_13939),tc_fun(U_13937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13939,tc_HOL_Obool),tc_fun(tc_fun(U_13937,U_13939),tc_fun(U_13937,tc_HOL_Obool)),U_13939),c_COMBB(U_13939,tc_HOL_Obool,U_13937)),c_fequal)),U_13940)))),U_13938)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),hAPP(c_Set_OCollect(U_13937),U_13938))) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

fof(f_3573_1,plain,
    ! [V_Q_2,T_c,V_P_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
          | ? [B_y] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
              & hBOOL(hAPP(V_P_2,B_y)) ) )
        & ( ! [B_y] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
              | ~ hBOOL(hAPP(V_P_2,B_y)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).

fof(f_3573_2,plain,
    ! [U_13946,U_13945,U_13944,U_13943] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946)))))
          | ? [U_13942] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),U_13942))))
              & hBOOL(hAPP(U_13944,U_13942)) ) )
        & ( ! [U_13941] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),U_13941))))
              | ~ hBOOL(hAPP(U_13944,U_13941)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13943),hAPP(c_Set_OCollect(U_13943),U_13944))) ),
    inference(variable_rename,[status(thm)],[f_3573_1]) ).

fof(f_3573_3,plain,
    ! [U_13946,U_13945,U_13944,U_13943] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),sK320(U_13946,U_13945,U_13944,U_13943)))))
            & hBOOL(hAPP(U_13944,sK320(U_13946,U_13945,U_13944,U_13943))) ) )
        & ( ! [U_13941] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),U_13941))))
              | ~ hBOOL(hAPP(U_13944,U_13941)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13943),hAPP(c_Set_OCollect(U_13943),U_13944))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_13942,sK320(U_13946,U_13945,U_13944,U_13943))],[f_3573_2]) ).

fof(f_3573_4,plain,
    ( ! [U_13943,U_13944,U_13945,U_13946] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),sK320(U_13946,U_13945,U_13944,U_13943)))))
        | ~ sP995(U_13943,U_13944,U_13945,U_13946) )
    & ! [U_13943,U_13944,U_13945,U_13946] :
        ( hBOOL(hAPP(U_13944,sK320(U_13946,U_13945,U_13944,U_13943)))
        | ~ sP995(U_13943,U_13944,U_13945,U_13946) )
    & ! [U_13941,U_13943,U_13944,U_13945,U_13946] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946)))))
        | sP995(U_13943,U_13944,U_13945,U_13946)
        | ~ sP996(U_13941,U_13943,U_13944,U_13945,U_13946) )
    & ! [U_13941,U_13943,U_13944,U_13945,U_13946] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),U_13941))))
        | ~ hBOOL(hAPP(U_13944,U_13941))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946)))))
        | ~ sP996(U_13941,U_13943,U_13944,U_13945,U_13946) )
    & ! [U_13941,U_13943,U_13944,U_13945,U_13946] :
        ( sP996(U_13941,U_13943,U_13944,U_13945,U_13946)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13943),hAPP(c_Set_OCollect(U_13943),U_13944))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP995,sP996])],[f_3573_3]) ).

cnf(f_3573_5,plain,
    ( sP996(U_13941,U_13943,U_13944,U_13945,U_13946)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13943),hAPP(c_Set_OCollect(U_13943),U_13944))) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

cnf(f_3573_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),U_13941))))
    | ~ hBOOL(hAPP(U_13944,U_13941))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946)))))
    | ~ sP996(U_13941,U_13943,U_13944,U_13945,U_13946) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

cnf(f_3573_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_HOL_Obool,U_13945),c_HOL_OEx(U_13943)),hAPP(hAPP(c_COMBB(tc_fun(U_13943,tc_HOL_Obool),tc_fun(U_13943,tc_HOL_Obool),U_13945),hAPP(c_COMBS(U_13943,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13943),c_fconj),U_13944))),U_13946)))))
    | sP995(U_13943,U_13944,U_13945,U_13946)
    | ~ sP996(U_13941,U_13943,U_13944,U_13945,U_13946) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

cnf(f_3573_8,plain,
    ( hBOOL(hAPP(U_13944,sK320(U_13946,U_13945,U_13944,U_13943)))
    | ~ sP995(U_13943,U_13944,U_13945,U_13946) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

cnf(f_3573_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13945),hAPP(c_Set_OCollect(U_13945),hAPP(hAPP(c_COMBC(U_13945,U_13943,tc_HOL_Obool),U_13946),sK320(U_13946,U_13945,U_13944,U_13943)))))
    | ~ sP995(U_13943,U_13944,U_13945,U_13946) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

fof(f_3574_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__apply__notin]) ).

fof(f_3574_2,plain,
    ! [U_13952,U_13951,U_13950,U_13949,U_13948,U_13947] :
      ( hAPP(c_Fun_Ooverride__on(U_13947,U_13950,U_13951,U_13952,U_13949),U_13948) = hAPP(U_13951,U_13948)
      | hBOOL(hAPP(hAPP(c_member(U_13947),U_13948),U_13949)) ),
    inference(variable_rename,[status(thm)],[f_3574_1]) ).

fof(f_3574_3,plain,
    ! [U_13950,U_13951,U_13949,U_13952,U_13948,U_13947] :
      ( hAPP(c_Fun_Ooverride__on(U_13947,U_13950,U_13951,U_13952,U_13949),U_13948) = hAPP(U_13951,U_13948)
      | hBOOL(hAPP(hAPP(c_member(U_13947),U_13948),U_13949)) ),
    inference(definitional_conversion,[status(esa)],[f_3574_2]) ).

cnf(f_3574_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_13947,U_13950,U_13951,U_13952,U_13949),U_13948) = hAPP(U_13951,U_13948)
    | hBOOL(hAPP(hAPP(c_member(U_13947),U_13948),U_13949)) ),
    inference(clausify,[status(thm)],[f_3574_3]) ).

fof(f_3575_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__apply__in]) ).

fof(f_3575_2,plain,
    ! [U_13958,U_13957,U_13956,U_13955,U_13954,U_13953] :
      ( hAPP(c_Fun_Ooverride__on(U_13953,U_13956,U_13957,U_13958,U_13955),U_13954) = hAPP(U_13958,U_13954)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13953),U_13954),U_13955)) ),
    inference(variable_rename,[status(thm)],[f_3575_1]) ).

fof(f_3575_3,plain,
    ! [U_13953,U_13955,U_13954,U_13956,U_13957,U_13958] :
      ( hAPP(c_Fun_Ooverride__on(U_13953,U_13956,U_13957,U_13958,U_13955),U_13954) = hAPP(U_13958,U_13954)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13953),U_13954),U_13955)) ),
    inference(definitional_conversion,[status(esa)],[f_3575_2]) ).

cnf(f_3575_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_13953,U_13956,U_13957,U_13958,U_13955),U_13954) = hAPP(U_13958,U_13954)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13953),U_13954),U_13955)) ),
    inference(clausify,[status(thm)],[f_3575_3]) ).

fof(f_3576_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_override__on__emptyset]) ).

fof(f_3576_2,plain,
    ! [U_13962,U_13961,U_13960,U_13959] : c_Fun_Ooverride__on(U_13959,U_13960,U_13961,U_13962,c_Orderings_Obot__class_Obot(tc_fun(U_13959,tc_HOL_Obool))) = U_13961,
    inference(variable_rename,[status(thm)],[f_3576_1]) ).

fof(f_3576_3,plain,
    ! [U_13960,U_13959,U_13961,U_13962] : c_Fun_Ooverride__on(U_13959,U_13960,U_13961,U_13962,c_Orderings_Obot__class_Obot(tc_fun(U_13959,tc_HOL_Obool))) = U_13961,
    inference(definitional_conversion,[status(esa)],[f_3576_2]) ).

cnf(f_3576_4,plain,
    c_Fun_Ooverride__on(U_13959,U_13960,U_13961,U_13962,c_Orderings_Obot__class_Obot(tc_fun(U_13959,tc_HOL_Obool))) = U_13961,
    inference(clausify,[status(thm)],[f_3576_3]) ).

fof(f_3577_1,plain,
    ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__graph]) ).

fof(f_3577_2,plain,
    ! [U_13964,U_13963] : c_Fun_Oinj__on(tc_fun(U_13963,U_13964),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(U_13963,U_13964)),c_Set_OCollect(tc_prod(U_13963,U_13964))),hAPP(hAPP(c_COMBB(tc_fun(U_13963,tc_fun(U_13964,tc_HOL_Obool)),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(U_13963,U_13964)),c_Product__Type_Oprod_Oprod__case(U_13963,U_13964,tc_HOL_Obool)),hAPP(c_COMBB(U_13964,tc_fun(U_13964,tc_HOL_Obool),U_13963),hAPP(c_COMBC(U_13964,U_13964,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13963,U_13964),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3577_1]) ).

fof(f_3577_3,plain,
    ! [U_13963,U_13964] : c_Fun_Oinj__on(tc_fun(U_13963,U_13964),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(U_13963,U_13964)),c_Set_OCollect(tc_prod(U_13963,U_13964))),hAPP(hAPP(c_COMBB(tc_fun(U_13963,tc_fun(U_13964,tc_HOL_Obool)),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(U_13963,U_13964)),c_Product__Type_Oprod_Oprod__case(U_13963,U_13964,tc_HOL_Obool)),hAPP(c_COMBB(U_13964,tc_fun(U_13964,tc_HOL_Obool),U_13963),hAPP(c_COMBC(U_13964,U_13964,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13963,U_13964),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3577_2]) ).

cnf(f_3577_4,plain,
    c_Fun_Oinj__on(tc_fun(U_13963,U_13964),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(U_13963,U_13964)),c_Set_OCollect(tc_prod(U_13963,U_13964))),hAPP(hAPP(c_COMBB(tc_fun(U_13963,tc_fun(U_13964,tc_HOL_Obool)),tc_fun(tc_prod(U_13963,U_13964),tc_HOL_Obool),tc_fun(U_13963,U_13964)),c_Product__Type_Oprod_Oprod__case(U_13963,U_13964,tc_HOL_Obool)),hAPP(c_COMBB(U_13964,tc_fun(U_13964,tc_HOL_Obool),U_13963),hAPP(c_COMBC(U_13964,U_13964,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13963,U_13964),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3577_3]) ).

fof(f_3578_1,plain,
    ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(f_3578_2,plain,
    ! [U_13965] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13965))),
    inference(variable_rename,[status(thm)],[f_3578_1]) ).

fof(f_3578_3,plain,
    ! [U_13965] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13965))),
    inference(definitional_conversion,[status(esa)],[f_3578_2]) ).

cnf(f_3578_4,plain,
    c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13965))),
    inference(clausify,[status(thm)],[f_3578_3]) ).

fof(f_3579_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__def]) ).

fof(f_3579_2,plain,
    ! [U_13971,U_13970,U_13969,U_13968,U_13967,U_13966] :
      ( ( hAPP(c_Fun_Ooverride__on(U_13966,U_13969,U_13970,U_13971,U_13968),U_13967) = hAPP(U_13970,U_13967)
        | hBOOL(hAPP(hAPP(c_member(U_13966),U_13967),U_13968)) )
      & ( hAPP(c_Fun_Ooverride__on(U_13966,U_13969,U_13970,U_13971,U_13968),U_13967) = hAPP(U_13971,U_13967)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13966),U_13967),U_13968)) ) ),
    inference(variable_rename,[status(thm)],[f_3579_1]) ).

fof(f_3579_3,plain,
    ( ! [U_13983,U_13981,U_13979,U_13977,U_13975,U_13973] :
        ( hAPP(c_Fun_Ooverride__on(U_13973,U_13979,U_13981,U_13983,U_13977),U_13975) = hAPP(U_13981,U_13975)
        | hBOOL(hAPP(hAPP(c_member(U_13973),U_13975),U_13977)) )
    & ! [U_13982,U_13980,U_13978,U_13976,U_13974,U_13972] :
        ( hAPP(c_Fun_Ooverride__on(U_13972,U_13978,U_13980,U_13982,U_13976),U_13974) = hAPP(U_13982,U_13974)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13972),U_13974),U_13976)) ) ),
    inference(miniscope,[status(thm)],[f_3579_2]) ).

fof(f_3579_4,plain,
    ( ! [U_13973,U_13975,U_13977,U_13979,U_13981,U_13983] :
        ( hAPP(c_Fun_Ooverride__on(U_13973,U_13979,U_13981,U_13983,U_13977),U_13975) = hAPP(U_13981,U_13975)
        | hBOOL(hAPP(hAPP(c_member(U_13973),U_13975),U_13977)) )
    & ! [U_13978,U_13972,U_13974,U_13976,U_13980,U_13982] :
        ( hAPP(c_Fun_Ooverride__on(U_13972,U_13978,U_13980,U_13982,U_13976),U_13974) = hAPP(U_13982,U_13974)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13972),U_13974),U_13976)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3579_3]) ).

cnf(f_3579_5,plain,
    ( hAPP(c_Fun_Ooverride__on(U_13972,U_13978,U_13980,U_13982,U_13976),U_13974) = hAPP(U_13982,U_13974)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13972),U_13974),U_13976)) ),
    inference(clausify,[status(thm)],[f_3579_4]) ).

cnf(f_3579_6,plain,
    ( hAPP(c_Fun_Ooverride__on(U_13973,U_13979,U_13981,U_13983,U_13977),U_13975) = hAPP(U_13981,U_13975)
    | hBOOL(hAPP(hAPP(c_member(U_13973),U_13975),U_13977)) ),
    inference(clausify,[status(thm)],[f_3579_4]) ).

fof(f_3580_1,plain,
    ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_finite__psubset__def]) ).

fof(f_3580_2,plain,
    ! [U_13984] : c_Wellfounded_Ofinite__psubset(U_13984) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13984,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13984,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13984,tc_HOL_Obool)),c_COMBS(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13984,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13984,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13984)))),
    inference(variable_rename,[status(thm)],[f_3580_1]) ).

fof(f_3580_3,plain,
    ! [U_13984] : c_Wellfounded_Ofinite__psubset(U_13984) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13984,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13984,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13984,tc_HOL_Obool)),c_COMBS(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13984,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13984,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13984)))),
    inference(definitional_conversion,[status(esa)],[f_3580_2]) ).

cnf(f_3580_4,plain,
    c_Wellfounded_Ofinite__psubset(U_13984) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13984,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13984,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13984,tc_HOL_Obool)),c_COMBS(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13984,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13984,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13984,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13984,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13984)))),
    inference(clausify,[status(thm)],[f_3580_3]) ).

fof(f_3581_1,plain,
    ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_ran__def]) ).

fof(f_3581_2,plain,
    ! [U_13987,U_13986,U_13985] : c_Map_Oran(U_13985,U_13986,U_13987) = hAPP(c_Set_OCollect(U_13986),hAPP(hAPP(c_COMBB(tc_fun(U_13985,tc_HOL_Obool),tc_HOL_Obool,U_13986),c_HOL_OEx(U_13985)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13986),tc_fun(U_13985,tc_HOL_Obool),U_13986),hAPP(c_COMBC(U_13985,tc_Option_Ooption(U_13986),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13986),tc_fun(tc_Option_Ooption(U_13986),tc_HOL_Obool),U_13985),c_fequal),U_13987))),c_Option_Ooption_OSome(U_13986)))),
    inference(variable_rename,[status(thm)],[f_3581_1]) ).

fof(f_3581_3,plain,
    ! [U_13985,U_13986,U_13987] : c_Map_Oran(U_13985,U_13986,U_13987) = hAPP(c_Set_OCollect(U_13986),hAPP(hAPP(c_COMBB(tc_fun(U_13985,tc_HOL_Obool),tc_HOL_Obool,U_13986),c_HOL_OEx(U_13985)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13986),tc_fun(U_13985,tc_HOL_Obool),U_13986),hAPP(c_COMBC(U_13985,tc_Option_Ooption(U_13986),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13986),tc_fun(tc_Option_Ooption(U_13986),tc_HOL_Obool),U_13985),c_fequal),U_13987))),c_Option_Ooption_OSome(U_13986)))),
    inference(definitional_conversion,[status(esa)],[f_3581_2]) ).

cnf(f_3581_4,plain,
    c_Map_Oran(U_13985,U_13986,U_13987) = hAPP(c_Set_OCollect(U_13986),hAPP(hAPP(c_COMBB(tc_fun(U_13985,tc_HOL_Obool),tc_HOL_Obool,U_13986),c_HOL_OEx(U_13985)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13986),tc_fun(U_13985,tc_HOL_Obool),U_13986),hAPP(c_COMBC(U_13985,tc_Option_Ooption(U_13986),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_13986),tc_fun(tc_Option_Ooption(U_13986),tc_HOL_Obool),U_13985),c_fequal),U_13987))),c_Option_Ooption_OSome(U_13986)))),
    inference(clausify,[status(thm)],[f_3581_3]) ).

fof(f_3582_1,plain,
    ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_inv__image__def]) ).

fof(f_3582_2,plain,
    ! [U_13991,U_13990,U_13989,U_13988] : hAPP(hAPP(c_Relation_Oinv__image(U_13988,U_13989),U_13990),U_13991) = hAPP(c_Set_OCollect(tc_prod(U_13989,U_13989)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13989,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13989,tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool)),U_13989),c_COMBC(U_13989,tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_prod(U_13988,U_13988)),tc_fun(U_13989,tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),U_13989),hAPP(c_COMBB(tc_prod(U_13988,U_13988),tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool),U_13989),c_member(tc_prod(U_13988,U_13988)))),hAPP(hAPP(c_COMBC(U_13989,tc_fun(U_13989,U_13988),tc_fun(U_13989,tc_prod(U_13988,U_13988))),hAPP(hAPP(c_COMBB(tc_fun(U_13988,tc_prod(U_13988,U_13988)),tc_fun(tc_fun(U_13989,U_13988),tc_fun(U_13989,tc_prod(U_13988,U_13988))),U_13989),c_COMBB(U_13988,tc_prod(U_13988,U_13988),U_13989)),hAPP(hAPP(c_COMBB(U_13988,tc_fun(U_13988,tc_prod(U_13988,U_13988)),U_13989),c_Product__Type_OPair(U_13988,U_13988)),U_13991))),U_13991)))),U_13990))),
    inference(variable_rename,[status(thm)],[f_3582_1]) ).

fof(f_3582_3,plain,
    ! [U_13988,U_13989,U_13990,U_13991] : hAPP(hAPP(c_Relation_Oinv__image(U_13988,U_13989),U_13990),U_13991) = hAPP(c_Set_OCollect(tc_prod(U_13989,U_13989)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13989,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13989,tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool)),U_13989),c_COMBC(U_13989,tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_prod(U_13988,U_13988)),tc_fun(U_13989,tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),U_13989),hAPP(c_COMBB(tc_prod(U_13988,U_13988),tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool),U_13989),c_member(tc_prod(U_13988,U_13988)))),hAPP(hAPP(c_COMBC(U_13989,tc_fun(U_13989,U_13988),tc_fun(U_13989,tc_prod(U_13988,U_13988))),hAPP(hAPP(c_COMBB(tc_fun(U_13988,tc_prod(U_13988,U_13988)),tc_fun(tc_fun(U_13989,U_13988),tc_fun(U_13989,tc_prod(U_13988,U_13988))),U_13989),c_COMBB(U_13988,tc_prod(U_13988,U_13988),U_13989)),hAPP(hAPP(c_COMBB(U_13988,tc_fun(U_13988,tc_prod(U_13988,U_13988)),U_13989),c_Product__Type_OPair(U_13988,U_13988)),U_13991))),U_13991)))),U_13990))),
    inference(definitional_conversion,[status(esa)],[f_3582_2]) ).

cnf(f_3582_4,plain,
    hAPP(hAPP(c_Relation_Oinv__image(U_13988,U_13989),U_13990),U_13991) = hAPP(c_Set_OCollect(tc_prod(U_13989,U_13989)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13989,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13989,tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool)),U_13989),c_COMBC(U_13989,tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_prod(U_13988,U_13988)),tc_fun(U_13989,tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool)),U_13989),hAPP(c_COMBB(tc_prod(U_13988,U_13988),tc_fun(tc_fun(tc_prod(U_13988,U_13988),tc_HOL_Obool),tc_HOL_Obool),U_13989),c_member(tc_prod(U_13988,U_13988)))),hAPP(hAPP(c_COMBC(U_13989,tc_fun(U_13989,U_13988),tc_fun(U_13989,tc_prod(U_13988,U_13988))),hAPP(hAPP(c_COMBB(tc_fun(U_13988,tc_prod(U_13988,U_13988)),tc_fun(tc_fun(U_13989,U_13988),tc_fun(U_13989,tc_prod(U_13988,U_13988))),U_13989),c_COMBB(U_13988,tc_prod(U_13988,U_13988),U_13989)),hAPP(hAPP(c_COMBB(U_13988,tc_fun(U_13988,tc_prod(U_13988,U_13988)),U_13989),c_Product__Type_OPair(U_13988,U_13988)),U_13991))),U_13991)))),U_13990))),
    inference(clausify,[status(thm)],[f_3582_3]) ).

fof(f_3583_1,plain,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).

fof(f_3583_2,plain,
    ! [U_13992] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13992)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),U_13992),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3583_1]) ).

fof(f_3583_3,plain,
    ! [U_13992] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13992)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),U_13992),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_3583_2]) ).

cnf(f_3583_4,plain,
    hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13992)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),U_13992),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3583_3]) ).

fof(f_3584_1,plain,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(f_3584_2,plain,
    ! [U_13993] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_13993) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),U_13993),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_3584_1]) ).

fof(f_3584_3,plain,
    ! [U_13993] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_13993) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),U_13993),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_3584_2]) ).

cnf(f_3584_4,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),U_13993) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),U_13993),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_3584_3]) ).

fof(f_3585_1,plain,
    ! [V_k_2,V_N_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2)))))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__Max__commute]) ).

fof(f_3585_2,plain,
    ! [U_13996,U_13995,U_13994] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13994),U_13996),c_Big__Operators_Olinorder__class_OMax(U_13994,U_13995)) = c_Big__Operators_Olinorder__class_OMax(U_13994,hAPP(c_Set_OCollect(U_13994),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_HOL_Obool,U_13994),c_HOL_OEx(U_13994)),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_HOL_Obool)),U_13994),c_COMBS(U_13994,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13994),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13994),c_fconj)),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,U_13994),tc_fun(U_13994,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_fun(tc_fun(U_13994,U_13994),tc_fun(U_13994,tc_HOL_Obool)),U_13994),c_COMBB(U_13994,tc_HOL_Obool,U_13994)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13994),U_13996))))),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13994)),U_13995)))))
      | U_13995 = c_Orderings_Obot__class_Obot(tc_fun(U_13994,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13995))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_13994) ),
    inference(variable_rename,[status(thm)],[f_3585_1]) ).

fof(f_3585_3,plain,
    ! [U_13994,U_13995,U_13996] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13994),U_13996),c_Big__Operators_Olinorder__class_OMax(U_13994,U_13995)) = c_Big__Operators_Olinorder__class_OMax(U_13994,hAPP(c_Set_OCollect(U_13994),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_HOL_Obool,U_13994),c_HOL_OEx(U_13994)),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_HOL_Obool)),U_13994),c_COMBS(U_13994,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13994),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13994),c_fconj)),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,U_13994),tc_fun(U_13994,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_fun(tc_fun(U_13994,U_13994),tc_fun(U_13994,tc_HOL_Obool)),U_13994),c_COMBB(U_13994,tc_HOL_Obool,U_13994)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13994),U_13996))))),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13994)),U_13995)))))
      | U_13995 = c_Orderings_Obot__class_Obot(tc_fun(U_13994,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13995))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_13994) ),
    inference(definitional_conversion,[status(esa)],[f_3585_2]) ).

cnf(f_3585_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13994),U_13996),c_Big__Operators_Olinorder__class_OMax(U_13994,U_13995)) = c_Big__Operators_Olinorder__class_OMax(U_13994,hAPP(c_Set_OCollect(U_13994),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_HOL_Obool,U_13994),c_HOL_OEx(U_13994)),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_HOL_Obool)),U_13994),c_COMBS(U_13994,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_fun(U_13994,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13994),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13994),c_fconj)),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,U_13994),tc_fun(U_13994,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13994,tc_HOL_Obool),tc_fun(tc_fun(U_13994,U_13994),tc_fun(U_13994,tc_HOL_Obool)),U_13994),c_COMBB(U_13994,tc_HOL_Obool,U_13994)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13994),U_13996))))),hAPP(hAPP(c_COMBC(U_13994,tc_fun(U_13994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13994)),U_13995)))))
    | U_13995 = c_Orderings_Obot__class_Obot(tc_fun(U_13994,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13995))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_13994) ),
    inference(clausify,[status(thm)],[f_3585_3]) ).

fof(f_3586_1,plain,
    ! [V_k_2,V_N_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2)))))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__Min__commute]) ).

fof(f_3586_2,plain,
    ! [U_13999,U_13998,U_13997] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13997),U_13999),c_Big__Operators_Olinorder__class_OMin(U_13997,U_13998)) = c_Big__Operators_Olinorder__class_OMin(U_13997,hAPP(c_Set_OCollect(U_13997),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_HOL_Obool,U_13997),c_HOL_OEx(U_13997)),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_HOL_Obool)),U_13997),c_COMBS(U_13997,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13997),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13997),c_fconj)),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,U_13997),tc_fun(U_13997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_fun(tc_fun(U_13997,U_13997),tc_fun(U_13997,tc_HOL_Obool)),U_13997),c_COMBB(U_13997,tc_HOL_Obool,U_13997)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13997),U_13999))))),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13997)),U_13998)))))
      | U_13998 = c_Orderings_Obot__class_Obot(tc_fun(U_13997,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),U_13998))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_13997) ),
    inference(variable_rename,[status(thm)],[f_3586_1]) ).

fof(f_3586_3,plain,
    ! [U_13997,U_13998,U_13999] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13997),U_13999),c_Big__Operators_Olinorder__class_OMin(U_13997,U_13998)) = c_Big__Operators_Olinorder__class_OMin(U_13997,hAPP(c_Set_OCollect(U_13997),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_HOL_Obool,U_13997),c_HOL_OEx(U_13997)),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_HOL_Obool)),U_13997),c_COMBS(U_13997,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13997),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13997),c_fconj)),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,U_13997),tc_fun(U_13997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_fun(tc_fun(U_13997,U_13997),tc_fun(U_13997,tc_HOL_Obool)),U_13997),c_COMBB(U_13997,tc_HOL_Obool,U_13997)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13997),U_13999))))),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13997)),U_13998)))))
      | U_13998 = c_Orderings_Obot__class_Obot(tc_fun(U_13997,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),U_13998))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_13997) ),
    inference(definitional_conversion,[status(esa)],[f_3586_2]) ).

cnf(f_3586_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13997),U_13999),c_Big__Operators_Olinorder__class_OMin(U_13997,U_13998)) = c_Big__Operators_Olinorder__class_OMin(U_13997,hAPP(c_Set_OCollect(U_13997),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_HOL_Obool,U_13997),c_HOL_OEx(U_13997)),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_HOL_Obool)),U_13997),c_COMBS(U_13997,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_fun(U_13997,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13997),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13997),c_fconj)),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,U_13997),tc_fun(U_13997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_fun(tc_fun(U_13997,U_13997),tc_fun(U_13997,tc_HOL_Obool)),U_13997),c_COMBB(U_13997,tc_HOL_Obool,U_13997)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13997),U_13999))))),hAPP(hAPP(c_COMBC(U_13997,tc_fun(U_13997,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13997)),U_13998)))))
    | U_13998 = c_Orderings_Obot__class_Obot(tc_fun(U_13997,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),U_13998))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_13997) ),
    inference(clausify,[status(thm)],[f_3586_3]) ).

fof(f_3587_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib]) ).

fof(f_3587_2,plain,
    ! [U_14002,U_14001,U_14000] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14000),c_Big__Operators_Olattice__class_OInf__fin(U_14000,U_14001)),c_Big__Operators_Olattice__class_OInf__fin(U_14000,U_14002)) = c_Big__Operators_Olattice__class_OInf__fin(U_14000,hAPP(c_Set_OCollect(U_14000),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool,U_14000),c_HOL_OEx(U_14000)),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_HOL_Obool),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool,U_14000),c_HOL_OEx(U_14000))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),tc_fun(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),U_14000),c_COMBS(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14000,tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBS(U_14000,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14000),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14000),c_fconj))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_fun(U_14000,U_14000)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool)),tc_fun(tc_fun(U_14000,tc_fun(U_14000,U_14000)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),U_14000),c_COMBB(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool),U_14000)),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_fun(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBB(U_14000,tc_HOL_Obool,U_14000)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_14000)))))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14000)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14000),c_fconj),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14000)),U_14001)))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14000)),U_14002)))))))
      | U_14002 = c_Orderings_Obot__class_Obot(tc_fun(U_14000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14002))
      | U_14001 = c_Orderings_Obot__class_Obot(tc_fun(U_14000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001))
      | ~ class_Lattices_Odistrib__lattice(U_14000) ),
    inference(variable_rename,[status(thm)],[f_3587_1]) ).

fof(f_3587_3,plain,
    ! [U_14000,U_14001,U_14002] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14000),c_Big__Operators_Olattice__class_OInf__fin(U_14000,U_14001)),c_Big__Operators_Olattice__class_OInf__fin(U_14000,U_14002)) = c_Big__Operators_Olattice__class_OInf__fin(U_14000,hAPP(c_Set_OCollect(U_14000),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool,U_14000),c_HOL_OEx(U_14000)),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_HOL_Obool),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool,U_14000),c_HOL_OEx(U_14000))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),tc_fun(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),U_14000),c_COMBS(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14000,tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBS(U_14000,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14000),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14000),c_fconj))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_fun(U_14000,U_14000)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool)),tc_fun(tc_fun(U_14000,tc_fun(U_14000,U_14000)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),U_14000),c_COMBB(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool),U_14000)),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_fun(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBB(U_14000,tc_HOL_Obool,U_14000)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_14000)))))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14000)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14000),c_fconj),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14000)),U_14001)))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14000)),U_14002)))))))
      | U_14002 = c_Orderings_Obot__class_Obot(tc_fun(U_14000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14002))
      | U_14001 = c_Orderings_Obot__class_Obot(tc_fun(U_14000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001))
      | ~ class_Lattices_Odistrib__lattice(U_14000) ),
    inference(definitional_conversion,[status(esa)],[f_3587_2]) ).

cnf(f_3587_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14000),c_Big__Operators_Olattice__class_OInf__fin(U_14000,U_14001)),c_Big__Operators_Olattice__class_OInf__fin(U_14000,U_14002)) = c_Big__Operators_Olattice__class_OInf__fin(U_14000,hAPP(c_Set_OCollect(U_14000),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool,U_14000),c_HOL_OEx(U_14000)),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_HOL_Obool),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool,U_14000),c_HOL_OEx(U_14000))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),tc_fun(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),U_14000),c_COMBS(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14000,tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool))),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBS(U_14000,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool)),tc_fun(U_14000,tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14000),hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14000),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14000),c_fconj))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_fun(U_14000,U_14000)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool)),tc_fun(tc_fun(U_14000,tc_fun(U_14000,U_14000)),tc_fun(U_14000,tc_fun(U_14000,tc_HOL_Obool))),U_14000),c_COMBB(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool),U_14000)),hAPP(hAPP(c_COMBB(tc_fun(U_14000,tc_HOL_Obool),tc_fun(tc_fun(U_14000,U_14000),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBB(U_14000,tc_HOL_Obool,U_14000)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_14000)))))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool)),U_14000),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14000)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14000),c_fconj),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14000)),U_14001)))),hAPP(hAPP(c_COMBC(U_14000,tc_fun(U_14000,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14000)),U_14002)))))))
    | U_14002 = c_Orderings_Obot__class_Obot(tc_fun(U_14000,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14002))
    | U_14001 = c_Orderings_Obot__class_Obot(tc_fun(U_14000,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001))
    | ~ class_Lattices_Odistrib__lattice(U_14000) ),
    inference(clausify,[status(thm)],[f_3587_3]) ).

fof(f_3588_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib]) ).

fof(f_3588_2,plain,
    ! [U_14005,U_14004,U_14003] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14003),U_14005),c_Big__Operators_Olattice__class_OInf__fin(U_14003,U_14004)) = c_Big__Operators_Olattice__class_OInf__fin(U_14003,hAPP(c_Set_OCollect(U_14003),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_HOL_Obool,U_14003),c_HOL_OEx(U_14003)),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_HOL_Obool)),U_14003),c_COMBS(U_14003,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14003),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14003),c_fconj)),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,U_14003),tc_fun(U_14003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_fun(tc_fun(U_14003,U_14003),tc_fun(U_14003,tc_HOL_Obool)),U_14003),c_COMBB(U_14003,tc_HOL_Obool,U_14003)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14003),U_14005))))),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14003)),U_14004)))))
      | U_14004 = c_Orderings_Obot__class_Obot(tc_fun(U_14003,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14003),U_14004))
      | ~ class_Lattices_Odistrib__lattice(U_14003) ),
    inference(variable_rename,[status(thm)],[f_3588_1]) ).

fof(f_3588_3,plain,
    ! [U_14003,U_14005,U_14004] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14003),U_14005),c_Big__Operators_Olattice__class_OInf__fin(U_14003,U_14004)) = c_Big__Operators_Olattice__class_OInf__fin(U_14003,hAPP(c_Set_OCollect(U_14003),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_HOL_Obool,U_14003),c_HOL_OEx(U_14003)),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_HOL_Obool)),U_14003),c_COMBS(U_14003,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14003),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14003),c_fconj)),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,U_14003),tc_fun(U_14003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_fun(tc_fun(U_14003,U_14003),tc_fun(U_14003,tc_HOL_Obool)),U_14003),c_COMBB(U_14003,tc_HOL_Obool,U_14003)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14003),U_14005))))),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14003)),U_14004)))))
      | U_14004 = c_Orderings_Obot__class_Obot(tc_fun(U_14003,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14003),U_14004))
      | ~ class_Lattices_Odistrib__lattice(U_14003) ),
    inference(definitional_conversion,[status(esa)],[f_3588_2]) ).

cnf(f_3588_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14003),U_14005),c_Big__Operators_Olattice__class_OInf__fin(U_14003,U_14004)) = c_Big__Operators_Olattice__class_OInf__fin(U_14003,hAPP(c_Set_OCollect(U_14003),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_HOL_Obool,U_14003),c_HOL_OEx(U_14003)),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_HOL_Obool)),U_14003),c_COMBS(U_14003,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_fun(U_14003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14003),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14003),c_fconj)),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,U_14003),tc_fun(U_14003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14003,tc_HOL_Obool),tc_fun(tc_fun(U_14003,U_14003),tc_fun(U_14003,tc_HOL_Obool)),U_14003),c_COMBB(U_14003,tc_HOL_Obool,U_14003)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14003),U_14005))))),hAPP(hAPP(c_COMBC(U_14003,tc_fun(U_14003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14003)),U_14004)))))
    | U_14004 = c_Orderings_Obot__class_Obot(tc_fun(U_14003,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14003),U_14004))
    | ~ class_Lattices_Odistrib__lattice(U_14003) ),
    inference(clausify,[status(thm)],[f_3588_3]) ).

fof(f_3589_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib]) ).

fof(f_3589_2,plain,
    ! [U_14008,U_14007,U_14006] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14006),U_14008),c_Big__Operators_Olattice__class_OSup__fin(U_14006,U_14007)) = c_Big__Operators_Olattice__class_OSup__fin(U_14006,hAPP(c_Set_OCollect(U_14006),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_HOL_Obool,U_14006),c_HOL_OEx(U_14006)),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_HOL_Obool)),U_14006),c_COMBS(U_14006,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14006),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14006),c_fconj)),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,U_14006),tc_fun(U_14006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_fun(tc_fun(U_14006,U_14006),tc_fun(U_14006,tc_HOL_Obool)),U_14006),c_COMBB(U_14006,tc_HOL_Obool,U_14006)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14006),U_14008))))),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14006)),U_14007)))))
      | U_14007 = c_Orderings_Obot__class_Obot(tc_fun(U_14006,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14006),U_14007))
      | ~ class_Lattices_Odistrib__lattice(U_14006) ),
    inference(variable_rename,[status(thm)],[f_3589_1]) ).

fof(f_3589_3,plain,
    ! [U_14006,U_14007,U_14008] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14006),U_14008),c_Big__Operators_Olattice__class_OSup__fin(U_14006,U_14007)) = c_Big__Operators_Olattice__class_OSup__fin(U_14006,hAPP(c_Set_OCollect(U_14006),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_HOL_Obool,U_14006),c_HOL_OEx(U_14006)),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_HOL_Obool)),U_14006),c_COMBS(U_14006,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14006),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14006),c_fconj)),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,U_14006),tc_fun(U_14006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_fun(tc_fun(U_14006,U_14006),tc_fun(U_14006,tc_HOL_Obool)),U_14006),c_COMBB(U_14006,tc_HOL_Obool,U_14006)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14006),U_14008))))),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14006)),U_14007)))))
      | U_14007 = c_Orderings_Obot__class_Obot(tc_fun(U_14006,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14006),U_14007))
      | ~ class_Lattices_Odistrib__lattice(U_14006) ),
    inference(definitional_conversion,[status(esa)],[f_3589_2]) ).

cnf(f_3589_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14006),U_14008),c_Big__Operators_Olattice__class_OSup__fin(U_14006,U_14007)) = c_Big__Operators_Olattice__class_OSup__fin(U_14006,hAPP(c_Set_OCollect(U_14006),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_HOL_Obool,U_14006),c_HOL_OEx(U_14006)),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_HOL_Obool)),U_14006),c_COMBS(U_14006,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_fun(U_14006,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14006),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14006),c_fconj)),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,U_14006),tc_fun(U_14006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14006,tc_HOL_Obool),tc_fun(tc_fun(U_14006,U_14006),tc_fun(U_14006,tc_HOL_Obool)),U_14006),c_COMBB(U_14006,tc_HOL_Obool,U_14006)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14006),U_14008))))),hAPP(hAPP(c_COMBC(U_14006,tc_fun(U_14006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14006)),U_14007)))))
    | U_14007 = c_Orderings_Obot__class_Obot(tc_fun(U_14006,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14006),U_14007))
    | ~ class_Lattices_Odistrib__lattice(U_14006) ),
    inference(clausify,[status(thm)],[f_3589_3]) ).

fof(f_3590_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib]) ).

fof(f_3590_2,plain,
    ! [U_14011,U_14010,U_14009] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14009),c_Big__Operators_Olattice__class_OSup__fin(U_14009,U_14010)),c_Big__Operators_Olattice__class_OSup__fin(U_14009,U_14011)) = c_Big__Operators_Olattice__class_OSup__fin(U_14009,hAPP(c_Set_OCollect(U_14009),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool,U_14009),c_HOL_OEx(U_14009)),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_HOL_Obool),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool,U_14009),c_HOL_OEx(U_14009))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),tc_fun(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),U_14009),c_COMBS(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14009,tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBS(U_14009,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14009),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14009),c_fconj))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_fun(U_14009,U_14009)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool)),tc_fun(tc_fun(U_14009,tc_fun(U_14009,U_14009)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),U_14009),c_COMBB(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool),U_14009)),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_fun(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBB(U_14009,tc_HOL_Obool,U_14009)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_14009)))))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14009)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14009),c_fconj),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14009)),U_14010)))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14009)),U_14011)))))))
      | U_14011 = c_Orderings_Obot__class_Obot(tc_fun(U_14009,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14009),U_14011))
      | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14009,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14009),U_14010))
      | ~ class_Lattices_Odistrib__lattice(U_14009) ),
    inference(variable_rename,[status(thm)],[f_3590_1]) ).

fof(f_3590_3,plain,
    ! [U_14009,U_14010,U_14011] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14009),c_Big__Operators_Olattice__class_OSup__fin(U_14009,U_14010)),c_Big__Operators_Olattice__class_OSup__fin(U_14009,U_14011)) = c_Big__Operators_Olattice__class_OSup__fin(U_14009,hAPP(c_Set_OCollect(U_14009),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool,U_14009),c_HOL_OEx(U_14009)),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_HOL_Obool),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool,U_14009),c_HOL_OEx(U_14009))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),tc_fun(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),U_14009),c_COMBS(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14009,tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBS(U_14009,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14009),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14009),c_fconj))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_fun(U_14009,U_14009)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool)),tc_fun(tc_fun(U_14009,tc_fun(U_14009,U_14009)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),U_14009),c_COMBB(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool),U_14009)),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_fun(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBB(U_14009,tc_HOL_Obool,U_14009)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_14009)))))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14009)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14009),c_fconj),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14009)),U_14010)))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14009)),U_14011)))))))
      | U_14011 = c_Orderings_Obot__class_Obot(tc_fun(U_14009,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14009),U_14011))
      | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14009,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14009),U_14010))
      | ~ class_Lattices_Odistrib__lattice(U_14009) ),
    inference(definitional_conversion,[status(esa)],[f_3590_2]) ).

cnf(f_3590_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14009),c_Big__Operators_Olattice__class_OSup__fin(U_14009,U_14010)),c_Big__Operators_Olattice__class_OSup__fin(U_14009,U_14011)) = c_Big__Operators_Olattice__class_OSup__fin(U_14009,hAPP(c_Set_OCollect(U_14009),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool,U_14009),c_HOL_OEx(U_14009)),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_HOL_Obool),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool,U_14009),c_HOL_OEx(U_14009))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),tc_fun(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),U_14009),c_COMBS(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14009,tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool))),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBS(U_14009,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool)),tc_fun(U_14009,tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14009),hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14009),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14009),c_fconj))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_fun(U_14009,U_14009)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool)),tc_fun(tc_fun(U_14009,tc_fun(U_14009,U_14009)),tc_fun(U_14009,tc_fun(U_14009,tc_HOL_Obool))),U_14009),c_COMBB(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool),U_14009)),hAPP(hAPP(c_COMBB(tc_fun(U_14009,tc_HOL_Obool),tc_fun(tc_fun(U_14009,U_14009),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBB(U_14009,tc_HOL_Obool,U_14009)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_14009)))))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14009,tc_HOL_Obool),tc_fun(U_14009,tc_HOL_Obool)),U_14009),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14009)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14009),c_fconj),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14009)),U_14010)))),hAPP(hAPP(c_COMBC(U_14009,tc_fun(U_14009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14009)),U_14011)))))))
    | U_14011 = c_Orderings_Obot__class_Obot(tc_fun(U_14009,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14009),U_14011))
    | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14009,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14009),U_14010))
    | ~ class_Lattices_Odistrib__lattice(U_14009) ),
    inference(clausify,[status(thm)],[f_3590_3]) ).

fof(f_3591_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib]) ).

fof(f_3591_2,plain,
    ! [U_14014,U_14013,U_14012] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14012),U_14014),c_Big__Operators_Olattice_OInf__fin(U_14012,c_Orderings_Oord__class_Omin(U_14012),U_14013)) = c_Big__Operators_Olattice_OInf__fin(U_14012,c_Orderings_Oord__class_Omin(U_14012),hAPP(c_Set_OCollect(U_14012),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_HOL_Obool,U_14012),c_HOL_OEx(U_14012)),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_HOL_Obool)),U_14012),c_COMBS(U_14012,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14012),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14012),c_fconj)),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,U_14012),tc_fun(U_14012,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_fun(tc_fun(U_14012,U_14012),tc_fun(U_14012,tc_HOL_Obool)),U_14012),c_COMBB(U_14012,tc_HOL_Obool,U_14012)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_14012),U_14014))))),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14012)),U_14013)))))
      | U_14013 = c_Orderings_Obot__class_Obot(tc_fun(U_14012,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14012),U_14013))
      | ~ class_Orderings_Olinorder(U_14012) ),
    inference(variable_rename,[status(thm)],[f_3591_1]) ).

fof(f_3591_3,plain,
    ! [U_14012,U_14014,U_14013] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14012),U_14014),c_Big__Operators_Olattice_OInf__fin(U_14012,c_Orderings_Oord__class_Omin(U_14012),U_14013)) = c_Big__Operators_Olattice_OInf__fin(U_14012,c_Orderings_Oord__class_Omin(U_14012),hAPP(c_Set_OCollect(U_14012),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_HOL_Obool,U_14012),c_HOL_OEx(U_14012)),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_HOL_Obool)),U_14012),c_COMBS(U_14012,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14012),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14012),c_fconj)),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,U_14012),tc_fun(U_14012,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_fun(tc_fun(U_14012,U_14012),tc_fun(U_14012,tc_HOL_Obool)),U_14012),c_COMBB(U_14012,tc_HOL_Obool,U_14012)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_14012),U_14014))))),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14012)),U_14013)))))
      | U_14013 = c_Orderings_Obot__class_Obot(tc_fun(U_14012,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14012),U_14013))
      | ~ class_Orderings_Olinorder(U_14012) ),
    inference(definitional_conversion,[status(esa)],[f_3591_2]) ).

cnf(f_3591_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14012),U_14014),c_Big__Operators_Olattice_OInf__fin(U_14012,c_Orderings_Oord__class_Omin(U_14012),U_14013)) = c_Big__Operators_Olattice_OInf__fin(U_14012,c_Orderings_Oord__class_Omin(U_14012),hAPP(c_Set_OCollect(U_14012),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_HOL_Obool,U_14012),c_HOL_OEx(U_14012)),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_HOL_Obool)),U_14012),c_COMBS(U_14012,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_fun(U_14012,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14012),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14012),c_fconj)),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,U_14012),tc_fun(U_14012,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14012,tc_HOL_Obool),tc_fun(tc_fun(U_14012,U_14012),tc_fun(U_14012,tc_HOL_Obool)),U_14012),c_COMBB(U_14012,tc_HOL_Obool,U_14012)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_14012),U_14014))))),hAPP(hAPP(c_COMBC(U_14012,tc_fun(U_14012,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14012)),U_14013)))))
    | U_14013 = c_Orderings_Obot__class_Obot(tc_fun(U_14012,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14012),U_14013))
    | ~ class_Orderings_Olinorder(U_14012) ),
    inference(clausify,[status(thm)],[f_3591_3]) ).

fof(f_3592_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib]) ).

fof(f_3592_2,plain,
    ! [U_14017,U_14016,U_14015] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14015),U_14017),c_Big__Operators_Olattice_OSup__fin(U_14015,c_Orderings_Oord__class_Omax(U_14015),U_14016)) = c_Big__Operators_Olattice_OSup__fin(U_14015,c_Orderings_Oord__class_Omax(U_14015),hAPP(c_Set_OCollect(U_14015),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_HOL_Obool,U_14015),c_HOL_OEx(U_14015)),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_HOL_Obool)),U_14015),c_COMBS(U_14015,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14015),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14015),c_fconj)),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,U_14015),tc_fun(U_14015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_fun(tc_fun(U_14015,U_14015),tc_fun(U_14015,tc_HOL_Obool)),U_14015),c_COMBB(U_14015,tc_HOL_Obool,U_14015)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_14015),U_14017))))),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14015)),U_14016)))))
      | U_14016 = c_Orderings_Obot__class_Obot(tc_fun(U_14015,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14015),U_14016))
      | ~ class_Orderings_Olinorder(U_14015) ),
    inference(variable_rename,[status(thm)],[f_3592_1]) ).

fof(f_3592_3,plain,
    ! [U_14015,U_14016,U_14017] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14015),U_14017),c_Big__Operators_Olattice_OSup__fin(U_14015,c_Orderings_Oord__class_Omax(U_14015),U_14016)) = c_Big__Operators_Olattice_OSup__fin(U_14015,c_Orderings_Oord__class_Omax(U_14015),hAPP(c_Set_OCollect(U_14015),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_HOL_Obool,U_14015),c_HOL_OEx(U_14015)),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_HOL_Obool)),U_14015),c_COMBS(U_14015,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14015),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14015),c_fconj)),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,U_14015),tc_fun(U_14015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_fun(tc_fun(U_14015,U_14015),tc_fun(U_14015,tc_HOL_Obool)),U_14015),c_COMBB(U_14015,tc_HOL_Obool,U_14015)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_14015),U_14017))))),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14015)),U_14016)))))
      | U_14016 = c_Orderings_Obot__class_Obot(tc_fun(U_14015,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14015),U_14016))
      | ~ class_Orderings_Olinorder(U_14015) ),
    inference(definitional_conversion,[status(esa)],[f_3592_2]) ).

cnf(f_3592_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14015),U_14017),c_Big__Operators_Olattice_OSup__fin(U_14015,c_Orderings_Oord__class_Omax(U_14015),U_14016)) = c_Big__Operators_Olattice_OSup__fin(U_14015,c_Orderings_Oord__class_Omax(U_14015),hAPP(c_Set_OCollect(U_14015),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_HOL_Obool,U_14015),c_HOL_OEx(U_14015)),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_HOL_Obool)),U_14015),c_COMBS(U_14015,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_fun(U_14015,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14015),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14015),c_fconj)),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,U_14015),tc_fun(U_14015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14015,tc_HOL_Obool),tc_fun(tc_fun(U_14015,U_14015),tc_fun(U_14015,tc_HOL_Obool)),U_14015),c_COMBB(U_14015,tc_HOL_Obool,U_14015)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_14015),U_14017))))),hAPP(hAPP(c_COMBC(U_14015,tc_fun(U_14015,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14015)),U_14016)))))
    | U_14016 = c_Orderings_Obot__class_Obot(tc_fun(U_14015,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14015),U_14016))
    | ~ class_Orderings_Olinorder(U_14015) ),
    inference(clausify,[status(thm)],[f_3592_3]) ).

fof(f_3593_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib]) ).

fof(f_3593_2,plain,
    ! [U_14020,U_14019,U_14018] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14018),c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),U_14019)),c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),U_14020)) = c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),hAPP(c_Set_OCollect(U_14018),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool,U_14018),c_HOL_OEx(U_14018)),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_HOL_Obool),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool,U_14018),c_HOL_OEx(U_14018))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),tc_fun(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),U_14018),c_COMBS(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14018,tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBS(U_14018,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14018),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14018),c_fconj))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_fun(U_14018,U_14018)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool)),tc_fun(tc_fun(U_14018,tc_fun(U_14018,U_14018)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),U_14018),c_COMBB(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool),U_14018)),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_fun(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBB(U_14018,tc_HOL_Obool,U_14018)),c_fequal))),c_Orderings_Oord__class_Omax(U_14018)))))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14018)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14018),c_fconj),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14018)),U_14019)))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14018)),U_14020)))))))
      | U_14020 = c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14018),U_14020))
      | U_14019 = c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14018),U_14019))
      | ~ class_Orderings_Olinorder(U_14018) ),
    inference(variable_rename,[status(thm)],[f_3593_1]) ).

fof(f_3593_3,plain,
    ! [U_14018,U_14019,U_14020] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14018),c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),U_14019)),c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),U_14020)) = c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),hAPP(c_Set_OCollect(U_14018),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool,U_14018),c_HOL_OEx(U_14018)),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_HOL_Obool),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool,U_14018),c_HOL_OEx(U_14018))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),tc_fun(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),U_14018),c_COMBS(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14018,tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBS(U_14018,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14018),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14018),c_fconj))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_fun(U_14018,U_14018)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool)),tc_fun(tc_fun(U_14018,tc_fun(U_14018,U_14018)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),U_14018),c_COMBB(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool),U_14018)),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_fun(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBB(U_14018,tc_HOL_Obool,U_14018)),c_fequal))),c_Orderings_Oord__class_Omax(U_14018)))))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14018)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14018),c_fconj),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14018)),U_14019)))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14018)),U_14020)))))))
      | U_14020 = c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14018),U_14020))
      | U_14019 = c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14018),U_14019))
      | ~ class_Orderings_Olinorder(U_14018) ),
    inference(definitional_conversion,[status(esa)],[f_3593_2]) ).

cnf(f_3593_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14018),c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),U_14019)),c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),U_14020)) = c_Big__Operators_Olattice_OInf__fin(U_14018,c_Orderings_Oord__class_Omin(U_14018),hAPP(c_Set_OCollect(U_14018),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool,U_14018),c_HOL_OEx(U_14018)),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_HOL_Obool),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool,U_14018),c_HOL_OEx(U_14018))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),tc_fun(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),U_14018),c_COMBS(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14018,tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool))),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBS(U_14018,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool)),tc_fun(U_14018,tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14018),hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14018),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14018),c_fconj))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_fun(U_14018,U_14018)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool)),tc_fun(tc_fun(U_14018,tc_fun(U_14018,U_14018)),tc_fun(U_14018,tc_fun(U_14018,tc_HOL_Obool))),U_14018),c_COMBB(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool),U_14018)),hAPP(hAPP(c_COMBB(tc_fun(U_14018,tc_HOL_Obool),tc_fun(tc_fun(U_14018,U_14018),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBB(U_14018,tc_HOL_Obool,U_14018)),c_fequal))),c_Orderings_Oord__class_Omax(U_14018)))))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14018,tc_HOL_Obool),tc_fun(U_14018,tc_HOL_Obool)),U_14018),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14018)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14018),c_fconj),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14018)),U_14019)))),hAPP(hAPP(c_COMBC(U_14018,tc_fun(U_14018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14018)),U_14020)))))))
    | U_14020 = c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14018),U_14020))
    | U_14019 = c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14018),U_14019))
    | ~ class_Orderings_Olinorder(U_14018) ),
    inference(clausify,[status(thm)],[f_3593_3]) ).

fof(f_3594_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oprod__def]) ).

fof(f_3594_2,plain,
    ! [U_14024,U_14023,U_14022,U_14021] : c_Nitpick_Oprod(U_14021,U_14022,U_14023,U_14024) = hAPP(c_Set_OCollect(tc_prod(U_14021,U_14022)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14021,U_14022,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14021,tc_fun(U_14022,tc_HOL_Obool),tc_fun(U_14022,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14022,tc_HOL_Obool),tc_fun(U_14022,tc_HOL_Obool)),U_14021),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14022)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14021),c_fconj),hAPP(hAPP(c_COMBC(U_14021,tc_fun(U_14021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14021)),U_14023)))),hAPP(hAPP(c_COMBC(U_14022,tc_fun(U_14022,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14022)),U_14024)))),
    inference(variable_rename,[status(thm)],[f_3594_1]) ).

fof(f_3594_3,plain,
    ! [U_14023,U_14021,U_14022,U_14024] : c_Nitpick_Oprod(U_14021,U_14022,U_14023,U_14024) = hAPP(c_Set_OCollect(tc_prod(U_14021,U_14022)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14021,U_14022,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14021,tc_fun(U_14022,tc_HOL_Obool),tc_fun(U_14022,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14022,tc_HOL_Obool),tc_fun(U_14022,tc_HOL_Obool)),U_14021),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14022)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14021),c_fconj),hAPP(hAPP(c_COMBC(U_14021,tc_fun(U_14021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14021)),U_14023)))),hAPP(hAPP(c_COMBC(U_14022,tc_fun(U_14022,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14022)),U_14024)))),
    inference(definitional_conversion,[status(esa)],[f_3594_2]) ).

cnf(f_3594_4,plain,
    c_Nitpick_Oprod(U_14021,U_14022,U_14023,U_14024) = hAPP(c_Set_OCollect(tc_prod(U_14021,U_14022)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14021,U_14022,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14021,tc_fun(U_14022,tc_HOL_Obool),tc_fun(U_14022,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14022,tc_HOL_Obool),tc_fun(U_14022,tc_HOL_Obool)),U_14021),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14022)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14021),c_fconj),hAPP(hAPP(c_COMBC(U_14021,tc_fun(U_14021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14021)),U_14023)))),hAPP(hAPP(c_COMBC(U_14022,tc_fun(U_14022,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14022)),U_14024)))),
    inference(clausify,[status(thm)],[f_3594_3]) ).

fof(f_3595_1,plain,
    ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_int__ge__less__than2__def]) ).

fof(f_3595_2,plain,
    ! [U_14025] : c_Int_Oint__ge__less__than2(U_14025) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14025)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3595_1]) ).

fof(f_3595_3,plain,
    ! [U_14025] : c_Int_Oint__ge__less__than2(U_14025) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14025)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_3595_2]) ).

cnf(f_3595_4,plain,
    c_Int_Oint__ge__less__than2(U_14025) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14025)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3595_3]) ).

fof(f_3596_1,plain,
    ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_int__ge__less__than__def]) ).

fof(f_3596_2,plain,
    ! [U_14026] : c_Int_Oint__ge__less__than(U_14026) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14026)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3596_1]) ).

fof(f_3596_3,plain,
    ! [U_14026] : c_Int_Oint__ge__less__than(U_14026) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14026)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_3596_2]) ).

cnf(f_3596_4,plain,
    c_Int_Oint__ge__less__than(U_14026) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14026)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3596_3]) ).

fof(f_3597_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Predicate_Oreflp(T_b,V_r_2)
        | ~ c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Predicate_Oreflp(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reflp__def]) ).

fof(f_3597_2,plain,
    ! [U_14028,U_14027] :
      ( ( c_Predicate_Oreflp(U_14027,U_14028)
        | ~ c_Relation_Orefl__on(U_14027,c_Orderings_Otop__class_Otop(tc_fun(U_14027,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14027,U_14027)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14027,U_14027,tc_HOL_Obool),U_14028))) )
      & ( c_Relation_Orefl__on(U_14027,c_Orderings_Otop__class_Otop(tc_fun(U_14027,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14027,U_14027)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14027,U_14027,tc_HOL_Obool),U_14028)))
        | ~ c_Predicate_Oreflp(U_14027,U_14028) ) ),
    inference(variable_rename,[status(thm)],[f_3597_1]) ).

fof(f_3597_3,plain,
    ( ! [U_14032,U_14030] :
        ( c_Predicate_Oreflp(U_14030,U_14032)
        | ~ c_Relation_Orefl__on(U_14030,c_Orderings_Otop__class_Otop(tc_fun(U_14030,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14030,U_14030)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14030,U_14030,tc_HOL_Obool),U_14032))) )
    & ! [U_14031,U_14029] :
        ( c_Relation_Orefl__on(U_14029,c_Orderings_Otop__class_Otop(tc_fun(U_14029,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14029,U_14029)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14029,U_14029,tc_HOL_Obool),U_14031)))
        | ~ c_Predicate_Oreflp(U_14029,U_14031) ) ),
    inference(miniscope,[status(thm)],[f_3597_2]) ).

fof(f_3597_4,plain,
    ( ! [U_14030,U_14032] :
        ( c_Predicate_Oreflp(U_14030,U_14032)
        | ~ c_Relation_Orefl__on(U_14030,c_Orderings_Otop__class_Otop(tc_fun(U_14030,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14030,U_14030)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14030,U_14030,tc_HOL_Obool),U_14032))) )
    & ! [U_14031,U_14029] :
        ( c_Relation_Orefl__on(U_14029,c_Orderings_Otop__class_Otop(tc_fun(U_14029,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14029,U_14029)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14029,U_14029,tc_HOL_Obool),U_14031)))
        | ~ c_Predicate_Oreflp(U_14029,U_14031) ) ),
    inference(definitional_conversion,[status(esa)],[f_3597_3]) ).

cnf(f_3597_5,plain,
    ( c_Relation_Orefl__on(U_14029,c_Orderings_Otop__class_Otop(tc_fun(U_14029,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14029,U_14029)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14029,U_14029,tc_HOL_Obool),U_14031)))
    | ~ c_Predicate_Oreflp(U_14029,U_14031) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

cnf(f_3597_6,plain,
    ( c_Predicate_Oreflp(U_14030,U_14032)
    | ~ c_Relation_Orefl__on(U_14030,c_Orderings_Otop__class_Otop(tc_fun(U_14030,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14030,U_14030)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14030,U_14030,tc_HOL_Obool),U_14032))) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

fof(f_3598_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2))
      | ~ c_Predicate_Oreflp(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_reflpE]) ).

fof(f_3598_2,plain,
    ! [U_14035,U_14034,U_14033] :
      ( hBOOL(hAPP(hAPP(U_14034,U_14035),U_14035))
      | ~ c_Predicate_Oreflp(U_14033,U_14034) ),
    inference(variable_rename,[status(thm)],[f_3598_1]) ).

fof(f_3598_3,plain,
    ! [U_14035,U_14034] :
      ( ! [U_14033] : ~ c_Predicate_Oreflp(U_14033,U_14034)
      | hBOOL(hAPP(hAPP(U_14034,U_14035),U_14035)) ),
    inference(miniscope,[status(thm)],[f_3598_2]) ).

fof(f_3598_4,plain,
    ! [U_14033,U_14035,U_14034] :
      ( ~ c_Predicate_Oreflp(U_14033,U_14034)
      | hBOOL(hAPP(hAPP(U_14034,U_14035),U_14035)) ),
    inference(definitional_conversion,[status(esa)],[f_3598_3]) ).

cnf(f_3598_5,plain,
    ( ~ c_Predicate_Oreflp(U_14033,U_14034)
    | hBOOL(hAPP(hAPP(U_14034,U_14035),U_14035)) ),
    inference(clausify,[status(thm)],[f_3598_4]) ).

fof(f_3599_1,plain,
    ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))))))
      | ~ c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
      | ~ class_Rings_Osemiring__0(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj]) ).

fof(f_3599_2,plain,
    ! [U_14042,U_14041,U_14040,U_14039,U_14038,U_14037,U_14036] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14036),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14037,U_14036),U_14039),U_14041)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14038,U_14036),U_14040),U_14042)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14036,U_14036),c_Fun_Oid(U_14036)),hAPP(c_Set_OCollect(U_14036),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_HOL_Obool),tc_HOL_Obool,U_14036),c_HOL_OEx(U_14037)),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_HOL_Obool),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_HOL_Obool,U_14037),c_HOL_OEx(U_14038))),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),tc_fun(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),U_14036),c_COMBS(U_14037,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14037,tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14037),c_COMBS(U_14038,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14037),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14038),c_fconj))),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_fun(U_14038,U_14036)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool)),tc_fun(tc_fun(U_14037,tc_fun(U_14038,U_14036)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),U_14036),c_COMBB(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool),U_14037)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,tc_HOL_Obool),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool)),U_14036),c_COMBB(U_14036,tc_HOL_Obool,U_14038)),c_fequal))),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,U_14036),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),U_14037),c_COMBB(U_14036,U_14036,U_14038)),hAPP(hAPP(c_COMBB(U_14036,tc_fun(U_14036,U_14036),U_14037),c_Groups_Otimes__class_Otimes(U_14036)),U_14039))),U_14040)))))),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14037),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14038)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14037),c_fconj),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14037)),U_14041)))),hAPP(hAPP(c_COMBC(U_14038,tc_fun(U_14038,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14038)),U_14042)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_14037,U_14038),U_14036,hAPP(c_Product__Type_Oprod_Oprod__case(U_14037,U_14038,U_14036),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,U_14036),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),U_14037),c_COMBB(U_14036,U_14036,U_14038)),hAPP(hAPP(c_COMBB(U_14036,tc_fun(U_14036,U_14036),U_14037),c_Groups_Otimes__class_Otimes(U_14036)),U_14039))),U_14040)),hAPP(hAPP(c_Product__Type_OSigma(U_14037,U_14038),U_14041),hAPP(c_COMBK(tc_fun(U_14038,tc_HOL_Obool),U_14037),U_14042)))
      | ~ class_Rings_Osemiring__0(U_14036) ),
    inference(variable_rename,[status(thm)],[f_3599_1]) ).

fof(f_3599_3,plain,
    ! [U_14036,U_14037,U_14038,U_14039,U_14040,U_14041,U_14042] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14036),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14037,U_14036),U_14039),U_14041)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14038,U_14036),U_14040),U_14042)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14036,U_14036),c_Fun_Oid(U_14036)),hAPP(c_Set_OCollect(U_14036),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_HOL_Obool),tc_HOL_Obool,U_14036),c_HOL_OEx(U_14037)),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_HOL_Obool),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_HOL_Obool,U_14037),c_HOL_OEx(U_14038))),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),tc_fun(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),U_14036),c_COMBS(U_14037,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14037,tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14037),c_COMBS(U_14038,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14037),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14038),c_fconj))),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_fun(U_14038,U_14036)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool)),tc_fun(tc_fun(U_14037,tc_fun(U_14038,U_14036)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),U_14036),c_COMBB(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool),U_14037)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,tc_HOL_Obool),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool)),U_14036),c_COMBB(U_14036,tc_HOL_Obool,U_14038)),c_fequal))),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,U_14036),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),U_14037),c_COMBB(U_14036,U_14036,U_14038)),hAPP(hAPP(c_COMBB(U_14036,tc_fun(U_14036,U_14036),U_14037),c_Groups_Otimes__class_Otimes(U_14036)),U_14039))),U_14040)))))),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14037),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14038)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14037),c_fconj),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14037)),U_14041)))),hAPP(hAPP(c_COMBC(U_14038,tc_fun(U_14038,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14038)),U_14042)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_14037,U_14038),U_14036,hAPP(c_Product__Type_Oprod_Oprod__case(U_14037,U_14038,U_14036),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,U_14036),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),U_14037),c_COMBB(U_14036,U_14036,U_14038)),hAPP(hAPP(c_COMBB(U_14036,tc_fun(U_14036,U_14036),U_14037),c_Groups_Otimes__class_Otimes(U_14036)),U_14039))),U_14040)),hAPP(hAPP(c_Product__Type_OSigma(U_14037,U_14038),U_14041),hAPP(c_COMBK(tc_fun(U_14038,tc_HOL_Obool),U_14037),U_14042)))
      | ~ class_Rings_Osemiring__0(U_14036) ),
    inference(definitional_conversion,[status(esa)],[f_3599_2]) ).

cnf(f_3599_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14036),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14037,U_14036),U_14039),U_14041)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14038,U_14036),U_14040),U_14042)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14036,U_14036),c_Fun_Oid(U_14036)),hAPP(c_Set_OCollect(U_14036),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_HOL_Obool),tc_HOL_Obool,U_14036),c_HOL_OEx(U_14037)),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_HOL_Obool),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_HOL_Obool,U_14037),c_HOL_OEx(U_14038))),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),tc_fun(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),U_14036),c_COMBS(U_14037,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14037,tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool))),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14037),c_COMBS(U_14038,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool)),tc_fun(U_14037,tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14036),hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14037),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14038),c_fconj))),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_fun(U_14038,U_14036)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool)),tc_fun(tc_fun(U_14037,tc_fun(U_14038,U_14036)),tc_fun(U_14037,tc_fun(U_14038,tc_HOL_Obool))),U_14036),c_COMBB(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool),U_14037)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,tc_HOL_Obool),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,tc_HOL_Obool)),U_14036),c_COMBB(U_14036,tc_HOL_Obool,U_14038)),c_fequal))),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,U_14036),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),U_14037),c_COMBB(U_14036,U_14036,U_14038)),hAPP(hAPP(c_COMBB(U_14036,tc_fun(U_14036,U_14036),U_14037),c_Groups_Otimes__class_Otimes(U_14036)),U_14039))),U_14040)))))),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14037),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14038)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14037),c_fconj),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14037,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14037)),U_14041)))),hAPP(hAPP(c_COMBC(U_14038,tc_fun(U_14038,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14038)),U_14042)))))))
    | ~ c_Fun_Oinj__on(tc_prod(U_14037,U_14038),U_14036,hAPP(c_Product__Type_Oprod_Oprod__case(U_14037,U_14038,U_14036),hAPP(hAPP(c_COMBC(U_14037,tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),hAPP(hAPP(c_COMBB(tc_fun(U_14036,U_14036),tc_fun(tc_fun(U_14038,U_14036),tc_fun(U_14038,U_14036)),U_14037),c_COMBB(U_14036,U_14036,U_14038)),hAPP(hAPP(c_COMBB(U_14036,tc_fun(U_14036,U_14036),U_14037),c_Groups_Otimes__class_Otimes(U_14036)),U_14039))),U_14040)),hAPP(hAPP(c_Product__Type_OSigma(U_14037,U_14038),U_14041),hAPP(c_COMBK(tc_fun(U_14038,tc_HOL_Obool),U_14037),U_14042)))
    | ~ class_Rings_Osemiring__0(U_14036) ),
    inference(clausify,[status(thm)],[f_3599_3]) ).

fof(f_3600_1,plain,
    ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2)
      | ? [B_x] :
          ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) != hAPP(V_k_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen]) ).

fof(f_3600_2,plain,
    ! [U_14049,U_14048,U_14047,U_14046,U_14045,U_14044] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14044,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_Nat_Onat,U_14044),c_Finite__Set_Ocard(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),c_Set_OCollect(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),hAPP(c_COMBS(U_14046,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14046),c_fconj),hAPP(hAPP(c_COMBC(U_14046,tc_fun(U_14046,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14046)),U_14047)))),U_14048)))),U_14045) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14046,tc_Nat_Onat),U_14049),U_14047)
      | ? [U_14043] :
          ( hAPP(c_Finite__Set_Ocard(U_14044),hAPP(c_Set_OCollect(U_14044),hAPP(hAPP(c_COMBS(U_14044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14044),c_fconj),hAPP(hAPP(c_COMBC(U_14044,tc_fun(U_14044,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14044)),U_14045))),hAPP(hAPP(c_COMBC(U_14044,U_14046,tc_HOL_Obool),U_14048),U_14043)))) != hAPP(U_14049,U_14043)
          & hBOOL(hAPP(hAPP(c_member(U_14046),U_14043),U_14047)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14046),U_14047))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045)) ),
    inference(variable_rename,[status(thm)],[f_3600_1]) ).

fof(f_3600_3,plain,
    ! [U_14049,U_14048,U_14047,U_14046,U_14045,U_14044] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14044,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_Nat_Onat,U_14044),c_Finite__Set_Ocard(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),c_Set_OCollect(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),hAPP(c_COMBS(U_14046,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14046),c_fconj),hAPP(hAPP(c_COMBC(U_14046,tc_fun(U_14046,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14046)),U_14047)))),U_14048)))),U_14045) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14046,tc_Nat_Onat),U_14049),U_14047)
      | ( hAPP(c_Finite__Set_Ocard(U_14044),hAPP(c_Set_OCollect(U_14044),hAPP(hAPP(c_COMBS(U_14044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14044),c_fconj),hAPP(hAPP(c_COMBC(U_14044,tc_fun(U_14044,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14044)),U_14045))),hAPP(hAPP(c_COMBC(U_14044,U_14046,tc_HOL_Obool),U_14048),sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))))) != hAPP(U_14049,sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))
        & hBOOL(hAPP(hAPP(c_member(U_14046),sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044)),U_14047)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14046),U_14047))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_14043,sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))],[f_3600_2]) ).

fof(f_3600_4,plain,
    ( ! [U_14044,U_14045,U_14046,U_14047,U_14048,U_14049] :
        ( hAPP(c_Finite__Set_Ocard(U_14044),hAPP(c_Set_OCollect(U_14044),hAPP(hAPP(c_COMBS(U_14044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14044),c_fconj),hAPP(hAPP(c_COMBC(U_14044,tc_fun(U_14044,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14044)),U_14045))),hAPP(hAPP(c_COMBC(U_14044,U_14046,tc_HOL_Obool),U_14048),sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))))) != hAPP(U_14049,sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))
        | ~ sP997(U_14044,U_14045,U_14046,U_14047,U_14048,U_14049) )
    & ! [U_14044,U_14045,U_14046,U_14047,U_14048,U_14049] :
        ( hBOOL(hAPP(hAPP(c_member(U_14046),sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044)),U_14047))
        | ~ sP997(U_14044,U_14045,U_14046,U_14047,U_14048,U_14049) )
    & ! [U_14044,U_14045,U_14046,U_14047,U_14048,U_14049] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14044,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_Nat_Onat,U_14044),c_Finite__Set_Ocard(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),c_Set_OCollect(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),hAPP(c_COMBS(U_14046,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14046),c_fconj),hAPP(hAPP(c_COMBC(U_14046,tc_fun(U_14046,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14046)),U_14047)))),U_14048)))),U_14045) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14046,tc_Nat_Onat),U_14049),U_14047)
        | sP997(U_14044,U_14045,U_14046,U_14047,U_14048,U_14049)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14046),U_14047))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP997])],[f_3600_3]) ).

cnf(f_3600_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14044,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_Nat_Onat,U_14044),c_Finite__Set_Ocard(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),c_Set_OCollect(U_14046)),hAPP(hAPP(c_COMBB(tc_fun(U_14046,tc_HOL_Obool),tc_fun(U_14046,tc_HOL_Obool),U_14044),hAPP(c_COMBS(U_14046,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14046),c_fconj),hAPP(hAPP(c_COMBC(U_14046,tc_fun(U_14046,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14046)),U_14047)))),U_14048)))),U_14045) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14046,tc_Nat_Onat),U_14049),U_14047)
    | sP997(U_14044,U_14045,U_14046,U_14047,U_14048,U_14049)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14046),U_14047))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045)) ),
    inference(clausify,[status(thm)],[f_3600_4]) ).

cnf(f_3600_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14046),sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044)),U_14047))
    | ~ sP997(U_14044,U_14045,U_14046,U_14047,U_14048,U_14049) ),
    inference(clausify,[status(thm)],[f_3600_4]) ).

cnf(f_3600_7,plain,
    ( hAPP(c_Finite__Set_Ocard(U_14044),hAPP(c_Set_OCollect(U_14044),hAPP(hAPP(c_COMBS(U_14044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14044),c_fconj),hAPP(hAPP(c_COMBC(U_14044,tc_fun(U_14044,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14044)),U_14045))),hAPP(hAPP(c_COMBC(U_14044,U_14046,tc_HOL_Obool),U_14048),sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))))) != hAPP(U_14049,sK321(U_14049,U_14048,U_14047,U_14046,U_14045,U_14044))
    | ~ sP997(U_14044,U_14045,U_14046,U_14047,U_14048,U_14049) ),
    inference(clausify,[status(thm)],[f_3600_4]) ).

fof(f_3601_1,plain,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_image__id]) ).

fof(f_3601_2,plain,
    ! [U_14051,U_14050] : hAPP(c_Set_Oimage(U_14050,U_14050,c_Fun_Oid(U_14050)),U_14051) = U_14051,
    inference(variable_rename,[status(thm)],[f_3601_1]) ).

fof(f_3601_3,plain,
    ! [U_14051,U_14050] : hAPP(c_Set_Oimage(U_14050,U_14050,c_Fun_Oid(U_14050)),U_14051) = U_14051,
    inference(definitional_conversion,[status(esa)],[f_3601_2]) ).

cnf(f_3601_4,plain,
    hAPP(c_Set_Oimage(U_14050,U_14050,c_Fun_Oid(U_14050)),U_14051) = U_14051,
    inference(clausify,[status(thm)],[f_3601_3]) ).

fof(f_3602_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_vimage__id]) ).

fof(f_3602_2,plain,
    ! [U_14053,U_14052] : hAPP(c_Set_Ovimage(U_14052,U_14052,c_Fun_Oid(U_14052)),U_14053) = U_14053,
    inference(variable_rename,[status(thm)],[f_3602_1]) ).

fof(f_3602_3,plain,
    ! [U_14052,U_14053] : hAPP(c_Set_Ovimage(U_14052,U_14052,c_Fun_Oid(U_14052)),U_14053) = U_14053,
    inference(definitional_conversion,[status(esa)],[f_3602_2]) ).

cnf(f_3602_4,plain,
    hAPP(c_Set_Ovimage(U_14052,U_14052,c_Fun_Oid(U_14052)),U_14053) = U_14053,
    inference(clausify,[status(thm)],[f_3602_3]) ).

fof(f_3603_1,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__id]) ).

fof(f_3603_2,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_3603_1]) ).

cnf(f_3603_3,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_3603_2]) ).

fof(f_3604_1,plain,
    ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__id]) ).

fof(f_3604_2,plain,
    ! [U_14055,U_14054] : c_Product__Type_Oapsnd(U_14054,U_14054,U_14055,c_Fun_Oid(U_14054)) = c_Fun_Oid(tc_prod(U_14055,U_14054)),
    inference(variable_rename,[status(thm)],[f_3604_1]) ).

fof(f_3604_3,plain,
    ! [U_14054,U_14055] : c_Product__Type_Oapsnd(U_14054,U_14054,U_14055,c_Fun_Oid(U_14054)) = c_Fun_Oid(tc_prod(U_14055,U_14054)),
    inference(definitional_conversion,[status(esa)],[f_3604_2]) ).

cnf(f_3604_4,plain,
    c_Product__Type_Oapsnd(U_14054,U_14054,U_14055,c_Fun_Oid(U_14054)) = c_Fun_Oid(tc_prod(U_14055,U_14054)),
    inference(clausify,[status(thm)],[f_3604_3]) ).

fof(f_3605_1,plain,
    ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_apfst__id]) ).

fof(f_3605_2,plain,
    ! [U_14057,U_14056] : c_Product__Type_Oapfst(U_14056,U_14056,U_14057,c_Fun_Oid(U_14056)) = c_Fun_Oid(tc_prod(U_14056,U_14057)),
    inference(variable_rename,[status(thm)],[f_3605_1]) ).

fof(f_3605_3,plain,
    ! [U_14056,U_14057] : c_Product__Type_Oapfst(U_14056,U_14056,U_14057,c_Fun_Oid(U_14056)) = c_Fun_Oid(tc_prod(U_14056,U_14057)),
    inference(definitional_conversion,[status(esa)],[f_3605_2]) ).

cnf(f_3605_4,plain,
    c_Product__Type_Oapfst(U_14056,U_14056,U_14057,c_Fun_Oid(U_14056)) = c_Fun_Oid(tc_prod(U_14056,U_14057)),
    inference(clausify,[status(thm)],[f_3605_3]) ).

fof(f_3606_1,plain,
    ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
    inference(fof_nnf,[status(thm)],[fact_id__apply]) ).

fof(f_3606_2,plain,
    ! [U_14059,U_14058] : hAPP(c_Fun_Oid(U_14058),U_14059) = U_14059,
    inference(variable_rename,[status(thm)],[f_3606_1]) ).

fof(f_3606_3,plain,
    ! [U_14058,U_14059] : hAPP(c_Fun_Oid(U_14058),U_14059) = U_14059,
    inference(definitional_conversion,[status(esa)],[f_3606_2]) ).

cnf(f_3606_4,plain,
    hAPP(c_Fun_Oid(U_14058),U_14059) = U_14059,
    inference(clausify,[status(thm)],[f_3606_3]) ).

fof(f_3607_1,plain,
    ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
    inference(fof_nnf,[status(thm)],[fact_id__def]) ).

fof(f_3607_2,plain,
    ! [U_14061,U_14060] : hAPP(c_Fun_Oid(U_14060),U_14061) = U_14061,
    inference(variable_rename,[status(thm)],[f_3607_1]) ).

fof(f_3607_3,plain,
    ! [U_14060,U_14061] : hAPP(c_Fun_Oid(U_14060),U_14061) = U_14061,
    inference(definitional_conversion,[status(esa)],[f_3607_2]) ).

cnf(f_3607_4,plain,
    hAPP(c_Fun_Oid(U_14060),U_14061) = U_14061,
    inference(clausify,[status(thm)],[f_3607_3]) ).

fof(f_3608_1,plain,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Oid]) ).

fof(f_3608_2,plain,
    ! [U_14063,U_14062] : c_Product__Type_Omap__pair(U_14062,U_14062,U_14063,U_14063,c_Fun_Oid(U_14062),c_Fun_Oid(U_14063)) = c_Fun_Oid(tc_prod(U_14062,U_14063)),
    inference(variable_rename,[status(thm)],[f_3608_1]) ).

fof(f_3608_3,plain,
    ! [U_14062,U_14063] : c_Product__Type_Omap__pair(U_14062,U_14062,U_14063,U_14063,c_Fun_Oid(U_14062),c_Fun_Oid(U_14063)) = c_Fun_Oid(tc_prod(U_14062,U_14063)),
    inference(definitional_conversion,[status(esa)],[f_3608_2]) ).

cnf(f_3608_4,plain,
    c_Product__Type_Omap__pair(U_14062,U_14062,U_14063,U_14063,c_Fun_Oid(U_14062),c_Fun_Oid(U_14063)) = c_Fun_Oid(tc_prod(U_14062,U_14063)),
    inference(clausify,[status(thm)],[f_3608_3]) ).

fof(f_3609_1,plain,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Oidentity]) ).

fof(f_3609_2,plain,
    ! [U_14065,U_14064] : c_Product__Type_Omap__pair(U_14064,U_14064,U_14065,U_14065,c_COMBI(U_14064),c_COMBI(U_14065)) = c_Fun_Oid(tc_prod(U_14064,U_14065)),
    inference(variable_rename,[status(thm)],[f_3609_1]) ).

fof(f_3609_3,plain,
    ! [U_14064,U_14065] : c_Product__Type_Omap__pair(U_14064,U_14064,U_14065,U_14065,c_COMBI(U_14064),c_COMBI(U_14065)) = c_Fun_Oid(tc_prod(U_14064,U_14065)),
    inference(definitional_conversion,[status(esa)],[f_3609_2]) ).

cnf(f_3609_4,plain,
    c_Product__Type_Omap__pair(U_14064,U_14064,U_14065,U_14065,c_COMBI(U_14064),c_COMBI(U_14065)) = c_Fun_Oid(tc_prod(U_14064,U_14065)),
    inference(clausify,[status(thm)],[f_3609_3]) ).

fof(f_3610_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__id]) ).

fof(f_3610_2,plain,
    ! [U_14067,U_14066] : c_Fun_Oinj__on(U_14066,U_14066,c_Fun_Oid(U_14066),U_14067),
    inference(variable_rename,[status(thm)],[f_3610_1]) ).

fof(f_3610_3,plain,
    ! [U_14066,U_14067] : c_Fun_Oinj__on(U_14066,U_14066,c_Fun_Oid(U_14066),U_14067),
    inference(definitional_conversion,[status(esa)],[f_3610_2]) ).

cnf(f_3610_4,plain,
    c_Fun_Oinj__on(U_14066,U_14066,c_Fun_Oid(U_14066),U_14067),
    inference(clausify,[status(thm)],[f_3610_3]) ).

fof(f_3611_1,plain,
    ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_surj__id]) ).

fof(f_3611_2,plain,
    ! [U_14068] : hAPP(c_Set_Oimage(U_14068,U_14068,c_Fun_Oid(U_14068)),c_Orderings_Otop__class_Otop(tc_fun(U_14068,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14068,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3611_1]) ).

fof(f_3611_3,plain,
    ! [U_14068] : hAPP(c_Set_Oimage(U_14068,U_14068,c_Fun_Oid(U_14068)),c_Orderings_Otop__class_Otop(tc_fun(U_14068,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14068,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3611_2]) ).

cnf(f_3611_4,plain,
    hAPP(c_Set_Oimage(U_14068,U_14068,c_Fun_Oid(U_14068)),c_Orderings_Otop__class_Otop(tc_fun(U_14068,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14068,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3611_3]) ).

fof(f_3612_1,plain,
    ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_apsnd__def]) ).

fof(f_3612_2,plain,
    ! [U_14072,U_14071,U_14070,U_14069] : c_Product__Type_Oapsnd(U_14069,U_14070,U_14071,U_14072) = c_Product__Type_Omap__pair(U_14071,U_14071,U_14069,U_14070,c_Fun_Oid(U_14071),U_14072),
    inference(variable_rename,[status(thm)],[f_3612_1]) ).

fof(f_3612_3,plain,
    ! [U_14069,U_14070,U_14071,U_14072] : c_Product__Type_Oapsnd(U_14069,U_14070,U_14071,U_14072) = c_Product__Type_Omap__pair(U_14071,U_14071,U_14069,U_14070,c_Fun_Oid(U_14071),U_14072),
    inference(definitional_conversion,[status(esa)],[f_3612_2]) ).

cnf(f_3612_4,plain,
    c_Product__Type_Oapsnd(U_14069,U_14070,U_14071,U_14072) = c_Product__Type_Omap__pair(U_14071,U_14071,U_14069,U_14070,c_Fun_Oid(U_14071),U_14072),
    inference(clausify,[status(thm)],[f_3612_3]) ).

fof(f_3613_1,plain,
    ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)),
    inference(fof_nnf,[status(thm)],[fact_apfst__def]) ).

fof(f_3613_2,plain,
    ! [U_14076,U_14075,U_14074,U_14073] : c_Product__Type_Oapfst(U_14073,U_14074,U_14075,U_14076) = c_Product__Type_Omap__pair(U_14073,U_14074,U_14075,U_14075,U_14076,c_Fun_Oid(U_14075)),
    inference(variable_rename,[status(thm)],[f_3613_1]) ).

fof(f_3613_3,plain,
    ! [U_14074,U_14073,U_14075,U_14076] : c_Product__Type_Oapfst(U_14073,U_14074,U_14075,U_14076) = c_Product__Type_Omap__pair(U_14073,U_14074,U_14075,U_14075,U_14076,c_Fun_Oid(U_14075)),
    inference(definitional_conversion,[status(esa)],[f_3613_2]) ).

cnf(f_3613_4,plain,
    c_Product__Type_Oapfst(U_14073,U_14074,U_14075,U_14076) = c_Product__Type_Omap__pair(U_14073,U_14074,U_14075,U_14075,U_14076,c_Fun_Oid(U_14075)),
    inference(clausify,[status(thm)],[f_3613_3]) ).

fof(f_3614_1,plain,
    ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_split__Pair]) ).

fof(f_3614_2,plain,
    ! [U_14078,U_14077] : hAPP(c_Product__Type_Oprod_Oprod__case(U_14077,U_14078,tc_prod(U_14077,U_14078)),c_Product__Type_OPair(U_14077,U_14078)) = c_Fun_Oid(tc_prod(U_14077,U_14078)),
    inference(variable_rename,[status(thm)],[f_3614_1]) ).

fof(f_3614_3,plain,
    ! [U_14077,U_14078] : hAPP(c_Product__Type_Oprod_Oprod__case(U_14077,U_14078,tc_prod(U_14077,U_14078)),c_Product__Type_OPair(U_14077,U_14078)) = c_Fun_Oid(tc_prod(U_14077,U_14078)),
    inference(definitional_conversion,[status(esa)],[f_3614_2]) ).

cnf(f_3614_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_14077,U_14078,tc_prod(U_14077,U_14078)),c_Product__Type_OPair(U_14077,U_14078)) = c_Fun_Oid(tc_prod(U_14077,U_14078)),
    inference(clausify,[status(thm)],[f_3614_3]) ).

fof(f_3615_1,plain,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id]) ).

fof(f_3615_2,plain,
    ! [U_14082,U_14081,U_14080,U_14079] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14080,U_14079),U_14081),U_14082) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14079,U_14079),c_Fun_Oid(U_14079)),hAPP(c_Set_Oimage(U_14080,U_14079,U_14081),U_14082))
      | ~ c_Fun_Oinj__on(U_14080,U_14079,U_14081,U_14082)
      | ~ class_Groups_Ocomm__monoid__add(U_14079) ),
    inference(variable_rename,[status(thm)],[f_3615_1]) ).

fof(f_3615_3,plain,
    ! [U_14079,U_14080,U_14081,U_14082] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14080,U_14079),U_14081),U_14082) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14079,U_14079),c_Fun_Oid(U_14079)),hAPP(c_Set_Oimage(U_14080,U_14079,U_14081),U_14082))
      | ~ c_Fun_Oinj__on(U_14080,U_14079,U_14081,U_14082)
      | ~ class_Groups_Ocomm__monoid__add(U_14079) ),
    inference(definitional_conversion,[status(esa)],[f_3615_2]) ).

cnf(f_3615_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14080,U_14079),U_14081),U_14082) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14079,U_14079),c_Fun_Oid(U_14079)),hAPP(c_Set_Oimage(U_14080,U_14079,U_14081),U_14082))
    | ~ c_Fun_Oinj__on(U_14080,U_14079,U_14081,U_14082)
    | ~ class_Groups_Ocomm__monoid__add(U_14079) ),
    inference(clausify,[status(thm)],[f_3615_3]) ).

fof(f_3616_1,plain,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id]) ).

fof(f_3616_2,plain,
    ! [U_14086,U_14085,U_14084,U_14083] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14084,U_14083),U_14085),U_14086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14083,U_14083),c_Fun_Oid(U_14083)),hAPP(c_Set_Oimage(U_14084,U_14083,U_14085),U_14086))
      | ~ c_Fun_Oinj__on(U_14084,U_14083,U_14085,U_14086)
      | ~ class_Groups_Ocomm__monoid__mult(U_14083) ),
    inference(variable_rename,[status(thm)],[f_3616_1]) ).

fof(f_3616_3,plain,
    ! [U_14085,U_14083,U_14084,U_14086] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14084,U_14083),U_14085),U_14086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14083,U_14083),c_Fun_Oid(U_14083)),hAPP(c_Set_Oimage(U_14084,U_14083,U_14085),U_14086))
      | ~ c_Fun_Oinj__on(U_14084,U_14083,U_14085,U_14086)
      | ~ class_Groups_Ocomm__monoid__mult(U_14083) ),
    inference(definitional_conversion,[status(esa)],[f_3616_2]) ).

cnf(f_3616_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14084,U_14083),U_14085),U_14086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14083,U_14083),c_Fun_Oid(U_14083)),hAPP(c_Set_Oimage(U_14084,U_14083,U_14085),U_14086))
    | ~ c_Fun_Oinj__on(U_14084,U_14083,U_14085,U_14086)
    | ~ class_Groups_Ocomm__monoid__mult(U_14083) ),
    inference(clausify,[status(thm)],[f_3616_3]) ).

fof(f_3617_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | ! [B_n,B_f] : V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) )
      & ( ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image]) ).

fof(f_3617_2,plain,
    ! [U_14092,U_14091] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14091),U_14092))
        | ! [U_14090,U_14089] : U_14092 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14091,U_14089),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14090))) )
      & ( ? [U_14088,U_14087] : U_14092 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14091,U_14087),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14088)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14091),U_14092)) ) ),
    inference(variable_rename,[status(thm)],[f_3617_1]) ).

fof(f_3617_3,plain,
    ( ! [U_14096,U_14094] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14094),U_14096))
        | ! [U_14090,U_14089] : U_14096 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14094,U_14089),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14090))) )
    & ! [U_14095,U_14093] :
        ( ? [U_14088,U_14087] : U_14095 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14093,U_14087),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14088)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14093),U_14095)) ) ),
    inference(miniscope,[status(thm)],[f_3617_2]) ).

fof(f_3617_4,plain,
    ( ! [U_14096,U_14094] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14094),U_14096))
        | ! [U_14090,U_14089] : U_14096 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14094,U_14089),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14090))) )
    & ! [U_14095,U_14093] :
        ( ? [U_14087] : U_14095 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14093,U_14087),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK322(U_14095,U_14093))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14093),U_14095)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_14088,sK322(U_14095,U_14093))],[f_3617_3]) ).

fof(f_3617_5,plain,
    ( ! [U_14096,U_14094] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14094),U_14096))
        | ! [U_14090,U_14089] : U_14096 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14094,U_14089),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14090))) )
    & ! [U_14095,U_14093] :
        ( U_14095 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14093,sK323(U_14095,U_14093)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK322(U_14095,U_14093))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14093),U_14095)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_14087,sK323(U_14095,U_14093))],[f_3617_4]) ).

fof(f_3617_6,plain,
    ( ! [U_14096,U_14089,U_14090,U_14094] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14094),U_14096))
        | U_14096 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14094,U_14089),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14090))) )
    & ! [U_14095,U_14093] :
        ( U_14095 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14093,sK323(U_14095,U_14093)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK322(U_14095,U_14093))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14093),U_14095)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3617_5]) ).

cnf(f_3617_7,plain,
    ( U_14095 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14093,sK323(U_14095,U_14093)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK322(U_14095,U_14093))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14093),U_14095)) ),
    inference(clausify,[status(thm)],[f_3617_6]) ).

cnf(f_3617_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14094),U_14096))
    | U_14096 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14094,U_14089),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14090))) ),
    inference(clausify,[status(thm)],[f_3617_6]) ).

fof(f_3618_1,plain,
    ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__def]) ).

fof(f_3618_2,plain,
    ! [U_14101,U_14100,U_14099,U_14098,U_14097] : hAPP(hAPP(c_Relation_Orel__comp(U_14097,U_14098,U_14099),U_14100),U_14101) = hAPP(c_Set_OCollect(tc_prod(U_14097,U_14099)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14097,U_14099,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_HOL_Obool),U_14097),hAPP(c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_HOL_Obool,U_14099),c_HOL_OEx(U_14098))),hAPP(hAPP(c_COMBC(U_14097,tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),tc_fun(tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool))),U_14097),c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool),U_14099)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBS(U_14098,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14098),c_fconj)),hAPP(hAPP(c_COMBC(U_14097,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBC(U_14098,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14097,U_14098)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_prod(U_14097,U_14098),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14097,U_14098)))),c_Product__Type_OPair(U_14097,U_14098)))),U_14100))))),hAPP(hAPP(c_COMBC(U_14099,tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14099),c_COMBC(U_14098,tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14098,U_14099)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),U_14099),hAPP(c_COMBB(tc_prod(U_14098,U_14099),tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14098,U_14099)))),hAPP(c_COMBC(U_14098,U_14099,tc_prod(U_14098,U_14099)),c_Product__Type_OPair(U_14098,U_14099))))),U_14101))))),
    inference(variable_rename,[status(thm)],[f_3618_1]) ).

fof(f_3618_3,plain,
    ! [U_14097,U_14098,U_14099,U_14100,U_14101] : hAPP(hAPP(c_Relation_Orel__comp(U_14097,U_14098,U_14099),U_14100),U_14101) = hAPP(c_Set_OCollect(tc_prod(U_14097,U_14099)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14097,U_14099,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_HOL_Obool),U_14097),hAPP(c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_HOL_Obool,U_14099),c_HOL_OEx(U_14098))),hAPP(hAPP(c_COMBC(U_14097,tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),tc_fun(tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool))),U_14097),c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool),U_14099)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBS(U_14098,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14098),c_fconj)),hAPP(hAPP(c_COMBC(U_14097,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBC(U_14098,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14097,U_14098)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_prod(U_14097,U_14098),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14097,U_14098)))),c_Product__Type_OPair(U_14097,U_14098)))),U_14100))))),hAPP(hAPP(c_COMBC(U_14099,tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14099),c_COMBC(U_14098,tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14098,U_14099)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),U_14099),hAPP(c_COMBB(tc_prod(U_14098,U_14099),tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14098,U_14099)))),hAPP(c_COMBC(U_14098,U_14099,tc_prod(U_14098,U_14099)),c_Product__Type_OPair(U_14098,U_14099))))),U_14101))))),
    inference(definitional_conversion,[status(esa)],[f_3618_2]) ).

cnf(f_3618_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14097,U_14098,U_14099),U_14100),U_14101) = hAPP(c_Set_OCollect(tc_prod(U_14097,U_14099)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14097,U_14099,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_HOL_Obool),U_14097),hAPP(c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_HOL_Obool,U_14099),c_HOL_OEx(U_14098))),hAPP(hAPP(c_COMBC(U_14097,tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),tc_fun(tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool)),tc_fun(U_14099,tc_fun(U_14098,tc_HOL_Obool))),U_14097),c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool),U_14099)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBS(U_14098,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_HOL_Obool),tc_fun(U_14098,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14098),c_fconj)),hAPP(hAPP(c_COMBC(U_14097,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBC(U_14098,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14097,U_14098)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_prod(U_14097,U_14098),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14097,U_14098)))),c_Product__Type_OPair(U_14097,U_14098)))),U_14100))))),hAPP(hAPP(c_COMBC(U_14099,tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14099),c_COMBC(U_14098,tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14098,U_14099)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool)),U_14099),hAPP(c_COMBB(tc_prod(U_14098,U_14099),tc_fun(tc_fun(tc_prod(U_14098,U_14099),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14098,U_14099)))),hAPP(c_COMBC(U_14098,U_14099,tc_prod(U_14098,U_14099)),c_Product__Type_OPair(U_14098,U_14099))))),U_14101))))),
    inference(clausify,[status(thm)],[f_3618_3]) ).

fof(f_3619_1,plain,
    ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__compI]) ).

fof(f_3619_2,plain,
    ! [U_14109,U_14108,U_14107,U_14106,U_14105,U_14104,U_14103,U_14102] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14102,U_14107)),hAPP(hAPP(c_Product__Type_OPair(U_14102,U_14107),U_14104),U_14108)),hAPP(hAPP(c_Relation_Orel__comp(U_14102,U_14103,U_14107),U_14106),U_14109)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14103,U_14107)),hAPP(hAPP(c_Product__Type_OPair(U_14103,U_14107),U_14105),U_14108)),U_14109))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14102,U_14103)),hAPP(hAPP(c_Product__Type_OPair(U_14102,U_14103),U_14104),U_14105)),U_14106)) ),
    inference(variable_rename,[status(thm)],[f_3619_1]) ).

fof(f_3619_3,plain,
    ! [U_14102,U_14103,U_14104,U_14105,U_14106,U_14107,U_14108,U_14109] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14102,U_14107)),hAPP(hAPP(c_Product__Type_OPair(U_14102,U_14107),U_14104),U_14108)),hAPP(hAPP(c_Relation_Orel__comp(U_14102,U_14103,U_14107),U_14106),U_14109)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14103,U_14107)),hAPP(hAPP(c_Product__Type_OPair(U_14103,U_14107),U_14105),U_14108)),U_14109))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14102,U_14103)),hAPP(hAPP(c_Product__Type_OPair(U_14102,U_14103),U_14104),U_14105)),U_14106)) ),
    inference(definitional_conversion,[status(esa)],[f_3619_2]) ).

cnf(f_3619_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14102,U_14107)),hAPP(hAPP(c_Product__Type_OPair(U_14102,U_14107),U_14104),U_14108)),hAPP(hAPP(c_Relation_Orel__comp(U_14102,U_14103,U_14107),U_14106),U_14109)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14103,U_14107)),hAPP(hAPP(c_Product__Type_OPair(U_14103,U_14107),U_14105),U_14108)),U_14109))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14102,U_14103)),hAPP(hAPP(c_Product__Type_OPair(U_14102,U_14103),U_14104),U_14105)),U_14106)) ),
    inference(clausify,[status(thm)],[f_3619_3]) ).

fof(f_3620_1,plain,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__empty2]) ).

fof(f_3620_2,plain,
    ! [U_14113,U_14112,U_14111,U_14110] : hAPP(hAPP(c_Relation_Orel__comp(U_14110,U_14111,U_14112),U_14113),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14111,U_14112),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14110,U_14112),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3620_1]) ).

fof(f_3620_3,plain,
    ! [U_14111,U_14110,U_14112,U_14113] : hAPP(hAPP(c_Relation_Orel__comp(U_14110,U_14111,U_14112),U_14113),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14111,U_14112),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14110,U_14112),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3620_2]) ).

cnf(f_3620_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14110,U_14111,U_14112),U_14113),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14111,U_14112),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14110,U_14112),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3620_3]) ).

fof(f_3621_1,plain,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__empty1]) ).

fof(f_3621_2,plain,
    ! [U_14117,U_14116,U_14115,U_14114] : hAPP(hAPP(c_Relation_Orel__comp(U_14114,U_14115,U_14116),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14114,U_14115),tc_HOL_Obool))),U_14117) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14114,U_14116),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3621_1]) ).

fof(f_3621_3,plain,
    ! [U_14114,U_14115,U_14116,U_14117] : hAPP(hAPP(c_Relation_Orel__comp(U_14114,U_14115,U_14116),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14114,U_14115),tc_HOL_Obool))),U_14117) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14114,U_14116),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3621_2]) ).

cnf(f_3621_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14114,U_14115,U_14116),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14114,U_14115),tc_HOL_Obool))),U_14117) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14114,U_14116),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3621_3]) ).

fof(f_3622_1,plain,
    ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)),
    inference(fof_nnf,[status(thm)],[fact_O__assoc]) ).

fof(f_3622_2,plain,
    ! [U_14124,U_14123,U_14122,U_14121,U_14120,U_14119,U_14118] : hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14119,U_14120),hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14121,U_14119),U_14122),U_14123)),U_14124) = hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14121,U_14120),U_14122),hAPP(hAPP(c_Relation_Orel__comp(U_14121,U_14119,U_14120),U_14123),U_14124)),
    inference(variable_rename,[status(thm)],[f_3622_1]) ).

fof(f_3622_3,plain,
    ! [U_14118,U_14119,U_14120,U_14121,U_14122,U_14123,U_14124] : hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14119,U_14120),hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14121,U_14119),U_14122),U_14123)),U_14124) = hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14121,U_14120),U_14122),hAPP(hAPP(c_Relation_Orel__comp(U_14121,U_14119,U_14120),U_14123),U_14124)),
    inference(definitional_conversion,[status(esa)],[f_3622_2]) ).

cnf(f_3622_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14119,U_14120),hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14121,U_14119),U_14122),U_14123)),U_14124) = hAPP(hAPP(c_Relation_Orel__comp(U_14118,U_14121,U_14120),U_14122),hAPP(hAPP(c_Relation_Orel__comp(U_14121,U_14119,U_14120),U_14123),U_14124)),
    inference(clausify,[status(thm)],[f_3622_3]) ).

fof(f_3623_1,plain,
    ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__mono]) ).

fof(f_3623_2,plain,
    ! [U_14131,U_14130,U_14129,U_14128,U_14127,U_14126,U_14125] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14125,U_14129),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14125,U_14126,U_14129),U_14127),U_14130)),hAPP(hAPP(c_Relation_Orel__comp(U_14125,U_14126,U_14129),U_14128),U_14131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14126,U_14129),tc_HOL_Obool)),U_14130),U_14131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14125,U_14126),tc_HOL_Obool)),U_14127),U_14128)) ),
    inference(variable_rename,[status(thm)],[f_3623_1]) ).

fof(f_3623_3,plain,
    ! [U_14125,U_14126,U_14127,U_14128,U_14129,U_14130,U_14131] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14125,U_14129),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14125,U_14126,U_14129),U_14127),U_14130)),hAPP(hAPP(c_Relation_Orel__comp(U_14125,U_14126,U_14129),U_14128),U_14131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14126,U_14129),tc_HOL_Obool)),U_14130),U_14131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14125,U_14126),tc_HOL_Obool)),U_14127),U_14128)) ),
    inference(definitional_conversion,[status(esa)],[f_3623_2]) ).

cnf(f_3623_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14125,U_14129),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14125,U_14126,U_14129),U_14127),U_14130)),hAPP(hAPP(c_Relation_Orel__comp(U_14125,U_14126,U_14129),U_14128),U_14131)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14126,U_14129),tc_HOL_Obool)),U_14130),U_14131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14125,U_14126),tc_HOL_Obool)),U_14127),U_14128)) ),
    inference(clausify,[status(thm)],[f_3623_3]) ).

fof(f_3624_1,plain,
    ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib]) ).

fof(f_3624_2,plain,
    ! [U_14137,U_14136,U_14135,U_14134,U_14133,U_14132] : hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14133,U_14134),tc_HOL_Obool)),U_14136),U_14137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14132,U_14134),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),U_14136)),hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),U_14137)),
    inference(variable_rename,[status(thm)],[f_3624_1]) ).

fof(f_3624_3,plain,
    ! [U_14133,U_14132,U_14134,U_14135,U_14136,U_14137] : hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14133,U_14134),tc_HOL_Obool)),U_14136),U_14137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14132,U_14134),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),U_14136)),hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),U_14137)),
    inference(definitional_conversion,[status(esa)],[f_3624_2]) ).

cnf(f_3624_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14133,U_14134),tc_HOL_Obool)),U_14136),U_14137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14132,U_14134),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),U_14136)),hAPP(hAPP(c_Relation_Orel__comp(U_14132,U_14133,U_14134),U_14135),U_14137)),
    inference(clausify,[status(thm)],[f_3624_3]) ).

fof(f_3625_1,plain,
    ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(f_3625_2,plain,
    ! [U_14143,U_14142,U_14141,U_14140,U_14139,U_14138] : hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14138,U_14139),tc_HOL_Obool)),U_14141),U_14142)),U_14143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14138,U_14140),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),U_14141),U_14143)),hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),U_14142),U_14143)),
    inference(variable_rename,[status(thm)],[f_3625_1]) ).

fof(f_3625_3,plain,
    ! [U_14138,U_14139,U_14140,U_14141,U_14142,U_14143] : hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14138,U_14139),tc_HOL_Obool)),U_14141),U_14142)),U_14143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14138,U_14140),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),U_14141),U_14143)),hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),U_14142),U_14143)),
    inference(definitional_conversion,[status(esa)],[f_3625_2]) ).

cnf(f_3625_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14138,U_14139),tc_HOL_Obool)),U_14141),U_14142)),U_14143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14138,U_14140),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),U_14141),U_14143)),hAPP(hAPP(c_Relation_Orel__comp(U_14138,U_14139,U_14140),U_14142),U_14143)),
    inference(clausify,[status(thm)],[f_3625_3]) ).

fof(f_3626_1,plain,
    ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(f_3626_2,plain,
    ! [U_14150,U_14149,U_14148,U_14147,U_14146,U_14145,U_14144] : hAPP(hAPP(c_Relation_Orel__comp(U_14144,U_14145,U_14146),U_14147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14148,tc_fun(tc_prod(U_14145,U_14146),tc_HOL_Obool)),U_14149),U_14150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14148,tc_fun(tc_prod(U_14144,U_14146),tc_HOL_Obool)),U_14149),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14145,U_14146),tc_HOL_Obool),tc_fun(tc_prod(U_14144,U_14146),tc_HOL_Obool),U_14148),hAPP(c_Relation_Orel__comp(U_14144,U_14145,U_14146),U_14147)),U_14150)),
    inference(variable_rename,[status(thm)],[f_3626_1]) ).

fof(f_3626_3,plain,
    ! [U_14144,U_14145,U_14146,U_14147,U_14148,U_14149,U_14150] : hAPP(hAPP(c_Relation_Orel__comp(U_14144,U_14145,U_14146),U_14147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14148,tc_fun(tc_prod(U_14145,U_14146),tc_HOL_Obool)),U_14149),U_14150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14148,tc_fun(tc_prod(U_14144,U_14146),tc_HOL_Obool)),U_14149),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14145,U_14146),tc_HOL_Obool),tc_fun(tc_prod(U_14144,U_14146),tc_HOL_Obool),U_14148),hAPP(c_Relation_Orel__comp(U_14144,U_14145,U_14146),U_14147)),U_14150)),
    inference(definitional_conversion,[status(esa)],[f_3626_2]) ).

cnf(f_3626_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14144,U_14145,U_14146),U_14147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14148,tc_fun(tc_prod(U_14145,U_14146),tc_HOL_Obool)),U_14149),U_14150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14148,tc_fun(tc_prod(U_14144,U_14146),tc_HOL_Obool)),U_14149),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14145,U_14146),tc_HOL_Obool),tc_fun(tc_prod(U_14144,U_14146),tc_HOL_Obool),U_14148),hAPP(c_Relation_Orel__comp(U_14144,U_14145,U_14146),U_14147)),U_14150)),
    inference(clausify,[status(thm)],[f_3626_3]) ).

fof(f_3627_1,plain,
    ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(f_3627_2,plain,
    ! [U_14157,U_14156,U_14155,U_14154,U_14153,U_14152,U_14151] : hAPP(hAPP(c_Relation_Orel__comp(U_14151,U_14152,U_14153),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14154,tc_fun(tc_prod(U_14151,U_14152),tc_HOL_Obool)),U_14155),U_14156)),U_14157) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14154,tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),U_14155),hAPP(hAPP(c_COMBC(U_14154,tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool),tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14151,U_14152),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool),tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),U_14154),c_Relation_Orel__comp(U_14151,U_14152,U_14153)),U_14156)),U_14157)),
    inference(variable_rename,[status(thm)],[f_3627_1]) ).

fof(f_3627_3,plain,
    ! [U_14151,U_14152,U_14153,U_14154,U_14155,U_14156,U_14157] : hAPP(hAPP(c_Relation_Orel__comp(U_14151,U_14152,U_14153),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14154,tc_fun(tc_prod(U_14151,U_14152),tc_HOL_Obool)),U_14155),U_14156)),U_14157) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14154,tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),U_14155),hAPP(hAPP(c_COMBC(U_14154,tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool),tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14151,U_14152),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool),tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),U_14154),c_Relation_Orel__comp(U_14151,U_14152,U_14153)),U_14156)),U_14157)),
    inference(definitional_conversion,[status(esa)],[f_3627_2]) ).

cnf(f_3627_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14151,U_14152,U_14153),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14154,tc_fun(tc_prod(U_14151,U_14152),tc_HOL_Obool)),U_14155),U_14156)),U_14157) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14154,tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),U_14155),hAPP(hAPP(c_COMBC(U_14154,tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool),tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14151,U_14152),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool),tc_fun(tc_prod(U_14151,U_14153),tc_HOL_Obool)),U_14154),c_Relation_Orel__comp(U_14151,U_14152,U_14153)),U_14156)),U_14157)),
    inference(clausify,[status(thm)],[f_3627_3]) ).

fof(f_3628_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL]) ).

fof(f_3628_2,plain,
    ! [U_14161,U_14160,U_14159,U_14158] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool)),U_14159),U_14161)),U_14160) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),U_14161),U_14160) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),U_14159),U_14160) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3628_1]) ).

fof(f_3628_3,plain,
    ! [U_14158,U_14159,U_14160,U_14161] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool)),U_14159),U_14161)),U_14160) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),U_14161),U_14160) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),U_14159),U_14160) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3628_2]) ).

cnf(f_3628_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool)),U_14159),U_14161)),U_14160) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),U_14161),U_14160) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_14158,U_14158,U_14158),U_14159),U_14160) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14158,U_14158),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3628_3]) ).

fof(f_3629_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR]) ).

fof(f_3629_2,plain,
    ! [U_14165,U_14164,U_14163,U_14162] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)),U_14164),U_14165)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),U_14165) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),U_14164) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3629_1]) ).

fof(f_3629_3,plain,
    ! [U_14162,U_14163,U_14164,U_14165] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)),U_14164),U_14165)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),U_14165) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),U_14164) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3629_2]) ).

cnf(f_3629_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)),U_14164),U_14165)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),U_14165) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_14162,U_14162,U_14162),U_14163),U_14164) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3629_3]) ).

fof(f_3630_1,plain,
    ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma]) ).

fof(f_3630_2,plain,
    ! [U_14173,U_14172,U_14171,U_14170,U_14169,U_14168,U_14167,U_14166] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14166,U_14171),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14166,U_14167,U_14171),U_14168),U_14172)),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14171),U_14169),hAPP(c_COMBK(tc_fun(U_14171,tc_HOL_Obool),U_14166),U_14173))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14167,U_14171),tc_HOL_Obool)),U_14172),hAPP(hAPP(c_Product__Type_OSigma(U_14167,U_14171),U_14170),hAPP(c_COMBK(tc_fun(U_14171,tc_HOL_Obool),U_14167),U_14173))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14166,U_14167),tc_HOL_Obool)),U_14168),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14167),U_14169),hAPP(c_COMBK(tc_fun(U_14167,tc_HOL_Obool),U_14166),U_14170)))) ),
    inference(variable_rename,[status(thm)],[f_3630_1]) ).

fof(f_3630_3,plain,
    ! [U_14166,U_14167,U_14168,U_14169,U_14170,U_14171,U_14172,U_14173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14166,U_14171),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14166,U_14167,U_14171),U_14168),U_14172)),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14171),U_14169),hAPP(c_COMBK(tc_fun(U_14171,tc_HOL_Obool),U_14166),U_14173))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14167,U_14171),tc_HOL_Obool)),U_14172),hAPP(hAPP(c_Product__Type_OSigma(U_14167,U_14171),U_14170),hAPP(c_COMBK(tc_fun(U_14171,tc_HOL_Obool),U_14167),U_14173))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14166,U_14167),tc_HOL_Obool)),U_14168),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14167),U_14169),hAPP(c_COMBK(tc_fun(U_14167,tc_HOL_Obool),U_14166),U_14170)))) ),
    inference(definitional_conversion,[status(esa)],[f_3630_2]) ).

cnf(f_3630_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14166,U_14171),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14166,U_14167,U_14171),U_14168),U_14172)),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14171),U_14169),hAPP(c_COMBK(tc_fun(U_14171,tc_HOL_Obool),U_14166),U_14173))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14167,U_14171),tc_HOL_Obool)),U_14172),hAPP(hAPP(c_Product__Type_OSigma(U_14167,U_14171),U_14170),hAPP(c_COMBK(tc_fun(U_14171,tc_HOL_Obool),U_14167),U_14173))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14166,U_14167),tc_HOL_Obool)),U_14168),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14167),U_14169),hAPP(c_COMBK(tc_fun(U_14167,tc_HOL_Obool),U_14166),U_14170)))) ),
    inference(clausify,[status(thm)],[f_3630_3]) ).

fof(f_3631_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__compat]) ).

fof(f_3631_2,plain,
    ! [U_14176,U_14175,U_14174] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_14174,U_14175)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_14174,U_14176)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_14174,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_14174,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_14174,U_14175)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14174,U_14174),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14174,U_14174,U_14174),U_14175),U_14176)),U_14175)) ),
    inference(variable_rename,[status(thm)],[f_3631_1]) ).

fof(f_3631_3,plain,
    ! [U_14174,U_14175,U_14176] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_14174,U_14175)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_14174,U_14176)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_14174,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_14174,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_14174,U_14175)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14174,U_14174),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14174,U_14174,U_14174),U_14175),U_14176)),U_14175)) ),
    inference(definitional_conversion,[status(esa)],[f_3631_2]) ).

cnf(f_3631_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_14174,U_14175)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_14174,U_14176)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_14174,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_14174,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_14174,tc_HOL_Obool),tc_fun(U_14174,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_14174,U_14175)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14174,U_14174),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14174,U_14174,U_14174),U_14175),U_14176)),U_14175)) ),
    inference(clausify,[status(thm)],[f_3631_3]) ).

fof(f_3632_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_min__ext__compat]) ).

fof(f_3632_2,plain,
    ! [U_14179,U_14178,U_14177] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_14177,U_14178)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_14177,U_14179)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_14177,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_14177,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_14177,U_14178)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14177,U_14177),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14177,U_14177,U_14177),U_14178),U_14179)),U_14178)) ),
    inference(variable_rename,[status(thm)],[f_3632_1]) ).

fof(f_3632_3,plain,
    ! [U_14177,U_14178,U_14179] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_14177,U_14178)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_14177,U_14179)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_14177,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_14177,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_14177,U_14178)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14177,U_14177),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14177,U_14177,U_14177),U_14178),U_14179)),U_14178)) ),
    inference(definitional_conversion,[status(esa)],[f_3632_2]) ).

cnf(f_3632_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_14177,U_14178)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_14177,U_14179)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_14177,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_14177,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_14177,tc_HOL_Obool),tc_fun(U_14177,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_14177,U_14178)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14177,U_14177),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14177,U_14177,U_14177),U_14178),U_14179)),U_14178)) ),
    inference(clausify,[status(thm)],[f_3632_3]) ).

fof(f_3633_1,plain,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( ( c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2),V_x_2,V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
        | ~ c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2),V_x_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq]) ).

fof(f_3633_2,plain,
    ! [U_14186,U_14185,U_14184,U_14183,U_14182,U_14181,U_14180] :
      ( ( c_Predicate_Opred__comp(U_14180,U_14181,U_14182,hAPP(hAPP(c_COMBC(U_14180,tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_fun(U_14181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14181,tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_fun(U_14181,tc_HOL_Obool)),U_14180),c_COMBC(U_14181,tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14181,tc_prod(U_14180,U_14181)),tc_fun(U_14181,tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool)),U_14180),hAPP(c_COMBB(tc_prod(U_14180,U_14181),tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool),U_14181),c_member(tc_prod(U_14180,U_14181)))),c_Product__Type_OPair(U_14180,U_14181)))),U_14183),hAPP(hAPP(c_COMBC(U_14181,tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_fun(U_14182,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14182,tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_fun(U_14182,tc_HOL_Obool)),U_14181),c_COMBC(U_14182,tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14182,tc_prod(U_14181,U_14182)),tc_fun(U_14182,tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool)),U_14181),hAPP(c_COMBB(tc_prod(U_14181,U_14182),tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool),U_14182),c_member(tc_prod(U_14181,U_14182)))),c_Product__Type_OPair(U_14181,U_14182)))),U_14184),U_14185,U_14186)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14180,U_14182)),hAPP(hAPP(c_Product__Type_OPair(U_14180,U_14182),U_14185),U_14186)),hAPP(hAPP(c_Relation_Orel__comp(U_14180,U_14181,U_14182),U_14183),U_14184))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14180,U_14182)),hAPP(hAPP(c_Product__Type_OPair(U_14180,U_14182),U_14185),U_14186)),hAPP(hAPP(c_Relation_Orel__comp(U_14180,U_14181,U_14182),U_14183),U_14184)))
        | ~ c_Predicate_Opred__comp(U_14180,U_14181,U_14182,hAPP(hAPP(c_COMBC(U_14180,tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_fun(U_14181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14181,tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_fun(U_14181,tc_HOL_Obool)),U_14180),c_COMBC(U_14181,tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14181,tc_prod(U_14180,U_14181)),tc_fun(U_14181,tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool)),U_14180),hAPP(c_COMBB(tc_prod(U_14180,U_14181),tc_fun(tc_fun(tc_prod(U_14180,U_14181),tc_HOL_Obool),tc_HOL_Obool),U_14181),c_member(tc_prod(U_14180,U_14181)))),c_Product__Type_OPair(U_14180,U_14181)))),U_14183),hAPP(hAPP(c_COMBC(U_14181,tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_fun(U_14182,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14182,tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_fun(U_14182,tc_HOL_Obool)),U_14181),c_COMBC(U_14182,tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14182,tc_prod(U_14181,U_14182)),tc_fun(U_14182,tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool)),U_14181),hAPP(c_COMBB(tc_prod(U_14181,U_14182),tc_fun(tc_fun(tc_prod(U_14181,U_14182),tc_HOL_Obool),tc_HOL_Obool),U_14182),c_member(tc_prod(U_14181,U_14182)))),c_Product__Type_OPair(U_14181,U_14182)))),U_14184),U_14185,U_14186) ) ),
    inference(variable_rename,[status(thm)],[f_3633_1]) ).

fof(f_3633_3,plain,
    ( ! [U_14200,U_14198,U_14196,U_14194,U_14192,U_14190,U_14188] :
        ( c_Predicate_Opred__comp(U_14188,U_14190,U_14192,hAPP(hAPP(c_COMBC(U_14188,tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_fun(U_14190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14190,tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_fun(U_14190,tc_HOL_Obool)),U_14188),c_COMBC(U_14190,tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14190,tc_prod(U_14188,U_14190)),tc_fun(U_14190,tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),U_14188),hAPP(c_COMBB(tc_prod(U_14188,U_14190),tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool),U_14190),c_member(tc_prod(U_14188,U_14190)))),c_Product__Type_OPair(U_14188,U_14190)))),U_14194),hAPP(hAPP(c_COMBC(U_14190,tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_fun(U_14192,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14192,tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_fun(U_14192,tc_HOL_Obool)),U_14190),c_COMBC(U_14192,tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14192,tc_prod(U_14190,U_14192)),tc_fun(U_14192,tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),U_14190),hAPP(c_COMBB(tc_prod(U_14190,U_14192),tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool),U_14192),c_member(tc_prod(U_14190,U_14192)))),c_Product__Type_OPair(U_14190,U_14192)))),U_14196),U_14198,U_14200)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14188,U_14192)),hAPP(hAPP(c_Product__Type_OPair(U_14188,U_14192),U_14198),U_14200)),hAPP(hAPP(c_Relation_Orel__comp(U_14188,U_14190,U_14192),U_14194),U_14196))) )
    & ! [U_14199,U_14197,U_14195,U_14193,U_14191,U_14189,U_14187] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14187,U_14191)),hAPP(hAPP(c_Product__Type_OPair(U_14187,U_14191),U_14197),U_14199)),hAPP(hAPP(c_Relation_Orel__comp(U_14187,U_14189,U_14191),U_14193),U_14195)))
        | ~ c_Predicate_Opred__comp(U_14187,U_14189,U_14191,hAPP(hAPP(c_COMBC(U_14187,tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_fun(U_14189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14189,tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_fun(U_14189,tc_HOL_Obool)),U_14187),c_COMBC(U_14189,tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14189,tc_prod(U_14187,U_14189)),tc_fun(U_14189,tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),U_14187),hAPP(c_COMBB(tc_prod(U_14187,U_14189),tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool),U_14189),c_member(tc_prod(U_14187,U_14189)))),c_Product__Type_OPair(U_14187,U_14189)))),U_14193),hAPP(hAPP(c_COMBC(U_14189,tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_fun(U_14191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14191,tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_fun(U_14191,tc_HOL_Obool)),U_14189),c_COMBC(U_14191,tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14191,tc_prod(U_14189,U_14191)),tc_fun(U_14191,tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),U_14189),hAPP(c_COMBB(tc_prod(U_14189,U_14191),tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool),U_14191),c_member(tc_prod(U_14189,U_14191)))),c_Product__Type_OPair(U_14189,U_14191)))),U_14195),U_14197,U_14199) ) ),
    inference(miniscope,[status(thm)],[f_3633_2]) ).

fof(f_3633_4,plain,
    ( ! [U_14188,U_14190,U_14192,U_14194,U_14196,U_14198,U_14200] :
        ( c_Predicate_Opred__comp(U_14188,U_14190,U_14192,hAPP(hAPP(c_COMBC(U_14188,tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_fun(U_14190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14190,tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_fun(U_14190,tc_HOL_Obool)),U_14188),c_COMBC(U_14190,tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14190,tc_prod(U_14188,U_14190)),tc_fun(U_14190,tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),U_14188),hAPP(c_COMBB(tc_prod(U_14188,U_14190),tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool),U_14190),c_member(tc_prod(U_14188,U_14190)))),c_Product__Type_OPair(U_14188,U_14190)))),U_14194),hAPP(hAPP(c_COMBC(U_14190,tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_fun(U_14192,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14192,tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_fun(U_14192,tc_HOL_Obool)),U_14190),c_COMBC(U_14192,tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14192,tc_prod(U_14190,U_14192)),tc_fun(U_14192,tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),U_14190),hAPP(c_COMBB(tc_prod(U_14190,U_14192),tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool),U_14192),c_member(tc_prod(U_14190,U_14192)))),c_Product__Type_OPair(U_14190,U_14192)))),U_14196),U_14198,U_14200)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14188,U_14192)),hAPP(hAPP(c_Product__Type_OPair(U_14188,U_14192),U_14198),U_14200)),hAPP(hAPP(c_Relation_Orel__comp(U_14188,U_14190,U_14192),U_14194),U_14196))) )
    & ! [U_14193,U_14187,U_14191,U_14189,U_14197,U_14195,U_14199] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14187,U_14191)),hAPP(hAPP(c_Product__Type_OPair(U_14187,U_14191),U_14197),U_14199)),hAPP(hAPP(c_Relation_Orel__comp(U_14187,U_14189,U_14191),U_14193),U_14195)))
        | ~ c_Predicate_Opred__comp(U_14187,U_14189,U_14191,hAPP(hAPP(c_COMBC(U_14187,tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_fun(U_14189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14189,tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_fun(U_14189,tc_HOL_Obool)),U_14187),c_COMBC(U_14189,tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14189,tc_prod(U_14187,U_14189)),tc_fun(U_14189,tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),U_14187),hAPP(c_COMBB(tc_prod(U_14187,U_14189),tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool),U_14189),c_member(tc_prod(U_14187,U_14189)))),c_Product__Type_OPair(U_14187,U_14189)))),U_14193),hAPP(hAPP(c_COMBC(U_14189,tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_fun(U_14191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14191,tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_fun(U_14191,tc_HOL_Obool)),U_14189),c_COMBC(U_14191,tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14191,tc_prod(U_14189,U_14191)),tc_fun(U_14191,tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),U_14189),hAPP(c_COMBB(tc_prod(U_14189,U_14191),tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool),U_14191),c_member(tc_prod(U_14189,U_14191)))),c_Product__Type_OPair(U_14189,U_14191)))),U_14195),U_14197,U_14199) ) ),
    inference(definitional_conversion,[status(esa)],[f_3633_3]) ).

cnf(f_3633_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14187,U_14191)),hAPP(hAPP(c_Product__Type_OPair(U_14187,U_14191),U_14197),U_14199)),hAPP(hAPP(c_Relation_Orel__comp(U_14187,U_14189,U_14191),U_14193),U_14195)))
    | ~ c_Predicate_Opred__comp(U_14187,U_14189,U_14191,hAPP(hAPP(c_COMBC(U_14187,tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_fun(U_14189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14189,tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_fun(U_14189,tc_HOL_Obool)),U_14187),c_COMBC(U_14189,tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14189,tc_prod(U_14187,U_14189)),tc_fun(U_14189,tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool)),U_14187),hAPP(c_COMBB(tc_prod(U_14187,U_14189),tc_fun(tc_fun(tc_prod(U_14187,U_14189),tc_HOL_Obool),tc_HOL_Obool),U_14189),c_member(tc_prod(U_14187,U_14189)))),c_Product__Type_OPair(U_14187,U_14189)))),U_14193),hAPP(hAPP(c_COMBC(U_14189,tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_fun(U_14191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14191,tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_fun(U_14191,tc_HOL_Obool)),U_14189),c_COMBC(U_14191,tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14191,tc_prod(U_14189,U_14191)),tc_fun(U_14191,tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool)),U_14189),hAPP(c_COMBB(tc_prod(U_14189,U_14191),tc_fun(tc_fun(tc_prod(U_14189,U_14191),tc_HOL_Obool),tc_HOL_Obool),U_14191),c_member(tc_prod(U_14189,U_14191)))),c_Product__Type_OPair(U_14189,U_14191)))),U_14195),U_14197,U_14199) ),
    inference(clausify,[status(thm)],[f_3633_4]) ).

cnf(f_3633_6,plain,
    ( c_Predicate_Opred__comp(U_14188,U_14190,U_14192,hAPP(hAPP(c_COMBC(U_14188,tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_fun(U_14190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14190,tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_fun(U_14190,tc_HOL_Obool)),U_14188),c_COMBC(U_14190,tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14190,tc_prod(U_14188,U_14190)),tc_fun(U_14190,tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool)),U_14188),hAPP(c_COMBB(tc_prod(U_14188,U_14190),tc_fun(tc_fun(tc_prod(U_14188,U_14190),tc_HOL_Obool),tc_HOL_Obool),U_14190),c_member(tc_prod(U_14188,U_14190)))),c_Product__Type_OPair(U_14188,U_14190)))),U_14194),hAPP(hAPP(c_COMBC(U_14190,tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_fun(U_14192,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14192,tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_fun(U_14192,tc_HOL_Obool)),U_14190),c_COMBC(U_14192,tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14192,tc_prod(U_14190,U_14192)),tc_fun(U_14192,tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool)),U_14190),hAPP(c_COMBB(tc_prod(U_14190,U_14192),tc_fun(tc_fun(tc_prod(U_14190,U_14192),tc_HOL_Obool),tc_HOL_Obool),U_14192),c_member(tc_prod(U_14190,U_14192)))),c_Product__Type_OPair(U_14190,U_14192)))),U_14196),U_14198,U_14200)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14188,U_14192)),hAPP(hAPP(c_Product__Type_OPair(U_14188,U_14192),U_14198),U_14200)),hAPP(hAPP(c_Relation_Orel__comp(U_14188,U_14190,U_14192),U_14194),U_14196))) ),
    inference(clausify,[status(thm)],[f_3633_4]) ).

fof(f_3634_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pairI]) ).

fof(f_3634_2,plain,
    ! [U_14203,U_14202,U_14201] :
      ( c_FunDef_Oreduction__pair(U_14201,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool),tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool)),U_14202),U_14203))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14201,U_14201,U_14201),U_14202),U_14203)),U_14202))
      | ~ c_Wellfounded_Owf(U_14201,U_14202) ),
    inference(variable_rename,[status(thm)],[f_3634_1]) ).

fof(f_3634_3,plain,
    ! [U_14201,U_14202,U_14203] :
      ( c_FunDef_Oreduction__pair(U_14201,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool),tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool)),U_14202),U_14203))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14201,U_14201,U_14201),U_14202),U_14203)),U_14202))
      | ~ c_Wellfounded_Owf(U_14201,U_14202) ),
    inference(definitional_conversion,[status(esa)],[f_3634_2]) ).

cnf(f_3634_4,plain,
    ( c_FunDef_Oreduction__pair(U_14201,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool),tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool)),U_14202),U_14203))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14201,U_14201),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14201,U_14201,U_14201),U_14202),U_14203)),U_14202))
    | ~ c_Wellfounded_Owf(U_14201,U_14202) ),
    inference(clausify,[status(thm)],[f_3634_3]) ).

fof(f_3635_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).

fof(f_3635_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_3635_1]) ).

cnf(f_3635_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3635_2]) ).

fof(f_3636_1,plain,
    ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
      ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2)
      | ~ hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros]) ).

fof(f_3636_2,plain,
    ! [U_14211,U_14210,U_14209,U_14208,U_14207,U_14206,U_14205,U_14204] :
      ( c_Predicate_Opred__comp(U_14209,U_14210,U_14211,U_14204,U_14207,U_14205,U_14208)
      | ~ hBOOL(hAPP(hAPP(U_14207,U_14206),U_14208))
      | ~ hBOOL(hAPP(hAPP(U_14204,U_14205),U_14206)) ),
    inference(variable_rename,[status(thm)],[f_3636_1]) ).

fof(f_3636_3,plain,
    ! [U_14209,U_14204,U_14205,U_14206,U_14207,U_14208,U_14210,U_14211] :
      ( c_Predicate_Opred__comp(U_14209,U_14210,U_14211,U_14204,U_14207,U_14205,U_14208)
      | ~ hBOOL(hAPP(hAPP(U_14207,U_14206),U_14208))
      | ~ hBOOL(hAPP(hAPP(U_14204,U_14205),U_14206)) ),
    inference(definitional_conversion,[status(esa)],[f_3636_2]) ).

cnf(f_3636_4,plain,
    ( c_Predicate_Opred__comp(U_14209,U_14210,U_14211,U_14204,U_14207,U_14205,U_14208)
    | ~ hBOOL(hAPP(hAPP(U_14207,U_14206),U_14208))
    | ~ hBOOL(hAPP(hAPP(U_14204,U_14205),U_14206)) ),
    inference(clausify,[status(thm)],[f_3636_3]) ).

fof(f_3637_1,plain,
    ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_wf__empty]) ).

fof(f_3637_2,plain,
    ! [U_14212] : c_Wellfounded_Owf(U_14212,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14212,U_14212),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3637_1]) ).

fof(f_3637_3,plain,
    ! [U_14212] : c_Wellfounded_Owf(U_14212,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14212,U_14212),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3637_2]) ).

cnf(f_3637_4,plain,
    c_Wellfounded_Owf(U_14212,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14212,U_14212),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3637_3]) ).

fof(f_3638_1,plain,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__inv__image]) ).

fof(f_3638_2,plain,
    ! [U_14216,U_14215,U_14214,U_14213] :
      ( c_Wellfounded_Owf(U_14215,hAPP(hAPP(c_Relation_Oinv__image(U_14213,U_14215),U_14214),U_14216))
      | ~ c_Wellfounded_Owf(U_14213,U_14214) ),
    inference(variable_rename,[status(thm)],[f_3638_1]) ).

fof(f_3638_3,plain,
    ! [U_14213,U_14214,U_14215,U_14216] :
      ( c_Wellfounded_Owf(U_14215,hAPP(hAPP(c_Relation_Oinv__image(U_14213,U_14215),U_14214),U_14216))
      | ~ c_Wellfounded_Owf(U_14213,U_14214) ),
    inference(definitional_conversion,[status(esa)],[f_3638_2]) ).

cnf(f_3638_4,plain,
    ( c_Wellfounded_Owf(U_14215,hAPP(hAPP(c_Relation_Oinv__image(U_14213,U_14215),U_14214),U_14216))
    | ~ c_Wellfounded_Owf(U_14213,U_14214) ),
    inference(clausify,[status(thm)],[f_3638_3]) ).

fof(f_3639_1,plain,
    ! [V_rb_2,T_c,V_ra_2,T_b] :
      ( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2))
      | ~ c_Wellfounded_Owf(T_c,V_rb_2)
      | ~ c_Wellfounded_Owf(T_b,V_ra_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lex__prod]) ).

fof(f_3639_2,plain,
    ! [U_14220,U_14219,U_14218,U_14217] :
      ( c_Wellfounded_Owf(tc_prod(U_14217,U_14219),c_Wellfounded_Olex__prod(U_14217,U_14219,U_14218,U_14220))
      | ~ c_Wellfounded_Owf(U_14219,U_14220)
      | ~ c_Wellfounded_Owf(U_14217,U_14218) ),
    inference(variable_rename,[status(thm)],[f_3639_1]) ).

fof(f_3639_3,plain,
    ! [U_14219,U_14218,U_14217,U_14220] :
      ( c_Wellfounded_Owf(tc_prod(U_14217,U_14219),c_Wellfounded_Olex__prod(U_14217,U_14219,U_14218,U_14220))
      | ~ c_Wellfounded_Owf(U_14219,U_14220)
      | ~ c_Wellfounded_Owf(U_14217,U_14218) ),
    inference(definitional_conversion,[status(esa)],[f_3639_2]) ).

cnf(f_3639_4,plain,
    ( c_Wellfounded_Owf(tc_prod(U_14217,U_14219),c_Wellfounded_Olex__prod(U_14217,U_14219,U_14218,U_14220))
    | ~ c_Wellfounded_Owf(U_14219,U_14220)
    | ~ c_Wellfounded_Owf(U_14217,U_14218) ),
    inference(clausify,[status(thm)],[f_3639_3]) ).

fof(f_3640_1,plain,
    ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__measure]) ).

fof(f_3640_2,plain,
    ! [U_14222,U_14221] : c_Wellfounded_Owf(U_14221,hAPP(c_Wellfounded_Omeasure(U_14221),U_14222)),
    inference(variable_rename,[status(thm)],[f_3640_1]) ).

fof(f_3640_3,plain,
    ! [U_14222,U_14221] : c_Wellfounded_Owf(U_14221,hAPP(c_Wellfounded_Omeasure(U_14221),U_14222)),
    inference(definitional_conversion,[status(esa)],[f_3640_2]) ).

cnf(f_3640_4,plain,
    c_Wellfounded_Owf(U_14221,hAPP(c_Wellfounded_Omeasure(U_14221),U_14222)),
    inference(clausify,[status(thm)],[f_3640_3]) ).

fof(f_3641_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_R_2)
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) )
      & ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2))
        | ~ c_Wellfounded_Owf(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__comp__self]) ).

fof(f_3641_2,plain,
    ! [U_14224,U_14223] :
      ( ( c_Wellfounded_Owf(U_14223,U_14224)
        | ~ c_Wellfounded_Owf(U_14223,hAPP(hAPP(c_Relation_Orel__comp(U_14223,U_14223,U_14223),U_14224),U_14224)) )
      & ( c_Wellfounded_Owf(U_14223,hAPP(hAPP(c_Relation_Orel__comp(U_14223,U_14223,U_14223),U_14224),U_14224))
        | ~ c_Wellfounded_Owf(U_14223,U_14224) ) ),
    inference(variable_rename,[status(thm)],[f_3641_1]) ).

fof(f_3641_3,plain,
    ( ! [U_14228,U_14226] :
        ( c_Wellfounded_Owf(U_14226,U_14228)
        | ~ c_Wellfounded_Owf(U_14226,hAPP(hAPP(c_Relation_Orel__comp(U_14226,U_14226,U_14226),U_14228),U_14228)) )
    & ! [U_14227,U_14225] :
        ( c_Wellfounded_Owf(U_14225,hAPP(hAPP(c_Relation_Orel__comp(U_14225,U_14225,U_14225),U_14227),U_14227))
        | ~ c_Wellfounded_Owf(U_14225,U_14227) ) ),
    inference(miniscope,[status(thm)],[f_3641_2]) ).

fof(f_3641_4,plain,
    ( ! [U_14226,U_14228] :
        ( c_Wellfounded_Owf(U_14226,U_14228)
        | ~ c_Wellfounded_Owf(U_14226,hAPP(hAPP(c_Relation_Orel__comp(U_14226,U_14226,U_14226),U_14228),U_14228)) )
    & ! [U_14227,U_14225] :
        ( c_Wellfounded_Owf(U_14225,hAPP(hAPP(c_Relation_Orel__comp(U_14225,U_14225,U_14225),U_14227),U_14227))
        | ~ c_Wellfounded_Owf(U_14225,U_14227) ) ),
    inference(definitional_conversion,[status(esa)],[f_3641_3]) ).

cnf(f_3641_5,plain,
    ( c_Wellfounded_Owf(U_14225,hAPP(hAPP(c_Relation_Orel__comp(U_14225,U_14225,U_14225),U_14227),U_14227))
    | ~ c_Wellfounded_Owf(U_14225,U_14227) ),
    inference(clausify,[status(thm)],[f_3641_4]) ).

cnf(f_3641_6,plain,
    ( c_Wellfounded_Owf(U_14226,U_14228)
    | ~ c_Wellfounded_Owf(U_14226,hAPP(hAPP(c_Relation_Orel__comp(U_14226,U_14226,U_14226),U_14228),U_14228)) ),
    inference(clausify,[status(thm)],[f_3641_4]) ).

fof(f_3642_1,plain,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__int__ge__less__than]) ).

fof(f_3642_2,plain,
    ! [U_14229] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_14229)),
    inference(variable_rename,[status(thm)],[f_3642_1]) ).

fof(f_3642_3,plain,
    ! [U_14229] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_14229)),
    inference(definitional_conversion,[status(esa)],[f_3642_2]) ).

cnf(f_3642_4,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_14229)),
    inference(clausify,[status(thm)],[f_3642_3]) ).

fof(f_3643_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__not__refl]) ).

fof(f_3643_2,plain,
    ! [U_14232,U_14231,U_14230] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14230,U_14230)),hAPP(hAPP(c_Product__Type_OPair(U_14230,U_14230),U_14232),U_14232)),U_14231))
      | ~ c_Wellfounded_Owf(U_14230,U_14231) ),
    inference(variable_rename,[status(thm)],[f_3643_1]) ).

fof(f_3643_3,plain,
    ! [U_14230,U_14231,U_14232] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14230,U_14230)),hAPP(hAPP(c_Product__Type_OPair(U_14230,U_14230),U_14232),U_14232)),U_14231))
      | ~ c_Wellfounded_Owf(U_14230,U_14231) ),
    inference(definitional_conversion,[status(esa)],[f_3643_2]) ).

cnf(f_3643_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14230,U_14230)),hAPP(hAPP(c_Product__Type_OPair(U_14230,U_14230),U_14232),U_14232)),U_14231))
    | ~ c_Wellfounded_Owf(U_14230,U_14231) ),
    inference(clausify,[status(thm)],[f_3643_3]) ).

fof(f_3644_1,plain,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__not__sym]) ).

fof(f_3644_2,plain,
    ! [U_14236,U_14235,U_14234,U_14233] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14233,U_14233)),hAPP(hAPP(c_Product__Type_OPair(U_14233,U_14233),U_14236),U_14235)),U_14234))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14233,U_14233)),hAPP(hAPP(c_Product__Type_OPair(U_14233,U_14233),U_14235),U_14236)),U_14234))
      | ~ c_Wellfounded_Owf(U_14233,U_14234) ),
    inference(variable_rename,[status(thm)],[f_3644_1]) ).

fof(f_3644_3,plain,
    ! [U_14233,U_14234,U_14235,U_14236] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14233,U_14233)),hAPP(hAPP(c_Product__Type_OPair(U_14233,U_14233),U_14236),U_14235)),U_14234))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14233,U_14233)),hAPP(hAPP(c_Product__Type_OPair(U_14233,U_14233),U_14235),U_14236)),U_14234))
      | ~ c_Wellfounded_Owf(U_14233,U_14234) ),
    inference(definitional_conversion,[status(esa)],[f_3644_2]) ).

cnf(f_3644_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14233,U_14233)),hAPP(hAPP(c_Product__Type_OPair(U_14233,U_14233),U_14236),U_14235)),U_14234))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14233,U_14233)),hAPP(hAPP(c_Product__Type_OPair(U_14233,U_14233),U_14235),U_14236)),U_14234))
    | ~ c_Wellfounded_Owf(U_14233,U_14234) ),
    inference(clausify,[status(thm)],[f_3644_3]) ).

fof(f_3645_1,plain,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__asym]) ).

fof(f_3645_2,plain,
    ! [U_14240,U_14239,U_14238,U_14237] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14237,U_14237)),hAPP(hAPP(c_Product__Type_OPair(U_14237,U_14237),U_14240),U_14239)),U_14238))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14237,U_14237)),hAPP(hAPP(c_Product__Type_OPair(U_14237,U_14237),U_14239),U_14240)),U_14238))
      | ~ c_Wellfounded_Owf(U_14237,U_14238) ),
    inference(variable_rename,[status(thm)],[f_3645_1]) ).

fof(f_3645_3,plain,
    ! [U_14237,U_14238,U_14239,U_14240] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14237,U_14237)),hAPP(hAPP(c_Product__Type_OPair(U_14237,U_14237),U_14240),U_14239)),U_14238))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14237,U_14237)),hAPP(hAPP(c_Product__Type_OPair(U_14237,U_14237),U_14239),U_14240)),U_14238))
      | ~ c_Wellfounded_Owf(U_14237,U_14238) ),
    inference(definitional_conversion,[status(esa)],[f_3645_2]) ).

cnf(f_3645_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14237,U_14237)),hAPP(hAPP(c_Product__Type_OPair(U_14237,U_14237),U_14240),U_14239)),U_14238))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14237,U_14237)),hAPP(hAPP(c_Product__Type_OPair(U_14237,U_14237),U_14239),U_14240)),U_14238))
    | ~ c_Wellfounded_Owf(U_14237,U_14238) ),
    inference(clausify,[status(thm)],[f_3645_3]) ).

fof(f_3646_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__irrefl]) ).

fof(f_3646_2,plain,
    ! [U_14243,U_14242,U_14241] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14241,U_14241)),hAPP(hAPP(c_Product__Type_OPair(U_14241,U_14241),U_14243),U_14243)),U_14242))
      | ~ c_Wellfounded_Owf(U_14241,U_14242) ),
    inference(variable_rename,[status(thm)],[f_3646_1]) ).

fof(f_3646_3,plain,
    ! [U_14241,U_14242,U_14243] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14241,U_14241)),hAPP(hAPP(c_Product__Type_OPair(U_14241,U_14241),U_14243),U_14243)),U_14242))
      | ~ c_Wellfounded_Owf(U_14241,U_14242) ),
    inference(definitional_conversion,[status(esa)],[f_3646_2]) ).

cnf(f_3646_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14241,U_14241)),hAPP(hAPP(c_Product__Type_OPair(U_14241,U_14241),U_14243),U_14243)),U_14242))
    | ~ c_Wellfounded_Owf(U_14241,U_14242) ),
    inference(clausify,[status(thm)],[f_3646_3]) ).

fof(f_3647_1,plain,
    ! [V_f_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__mlex]) ).

fof(f_3647_2,plain,
    ! [U_14246,U_14245,U_14244] :
      ( c_Wellfounded_Owf(U_14244,c_Wellfounded_Omlex__prod(U_14244,U_14246,U_14245))
      | ~ c_Wellfounded_Owf(U_14244,U_14245) ),
    inference(variable_rename,[status(thm)],[f_3647_1]) ).

fof(f_3647_3,plain,
    ! [U_14244,U_14245,U_14246] :
      ( c_Wellfounded_Owf(U_14244,c_Wellfounded_Omlex__prod(U_14244,U_14246,U_14245))
      | ~ c_Wellfounded_Owf(U_14244,U_14245) ),
    inference(definitional_conversion,[status(esa)],[f_3647_2]) ).

cnf(f_3647_4,plain,
    ( c_Wellfounded_Owf(U_14244,c_Wellfounded_Omlex__prod(U_14244,U_14246,U_14245))
    | ~ c_Wellfounded_Owf(U_14244,U_14245) ),
    inference(clausify,[status(thm)],[f_3647_3]) ).

fof(f_3648_1,plain,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Int2]) ).

fof(f_3648_2,plain,
    ! [U_14249,U_14248,U_14247] :
      ( c_Wellfounded_Owf(U_14247,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool)),U_14249),U_14248))
      | ~ c_Wellfounded_Owf(U_14247,U_14248) ),
    inference(variable_rename,[status(thm)],[f_3648_1]) ).

fof(f_3648_3,plain,
    ! [U_14247,U_14248,U_14249] :
      ( c_Wellfounded_Owf(U_14247,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool)),U_14249),U_14248))
      | ~ c_Wellfounded_Owf(U_14247,U_14248) ),
    inference(definitional_conversion,[status(esa)],[f_3648_2]) ).

cnf(f_3648_4,plain,
    ( c_Wellfounded_Owf(U_14247,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool)),U_14249),U_14248))
    | ~ c_Wellfounded_Owf(U_14247,U_14248) ),
    inference(clausify,[status(thm)],[f_3648_3]) ).

fof(f_3649_1,plain,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Int1]) ).

fof(f_3649_2,plain,
    ! [U_14252,U_14251,U_14250] :
      ( c_Wellfounded_Owf(U_14250,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14250,U_14250),tc_HOL_Obool)),U_14251),U_14252))
      | ~ c_Wellfounded_Owf(U_14250,U_14251) ),
    inference(variable_rename,[status(thm)],[f_3649_1]) ).

fof(f_3649_3,plain,
    ! [U_14250,U_14251,U_14252] :
      ( c_Wellfounded_Owf(U_14250,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14250,U_14250),tc_HOL_Obool)),U_14251),U_14252))
      | ~ c_Wellfounded_Owf(U_14250,U_14251) ),
    inference(definitional_conversion,[status(esa)],[f_3649_2]) ).

cnf(f_3649_4,plain,
    ( c_Wellfounded_Owf(U_14250,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14250,U_14250),tc_HOL_Obool)),U_14251),U_14252))
    | ~ c_Wellfounded_Owf(U_14250,U_14251) ),
    inference(clausify,[status(thm)],[f_3649_3]) ).

fof(f_3650_1,plain,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_p_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__subset]) ).

fof(f_3650_2,plain,
    ! [U_14255,U_14254,U_14253] :
      ( c_Wellfounded_Owf(U_14253,U_14255)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14253,U_14253),tc_HOL_Obool)),U_14255),U_14254))
      | ~ c_Wellfounded_Owf(U_14253,U_14254) ),
    inference(variable_rename,[status(thm)],[f_3650_1]) ).

fof(f_3650_3,plain,
    ! [U_14253,U_14254,U_14255] :
      ( c_Wellfounded_Owf(U_14253,U_14255)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14253,U_14253),tc_HOL_Obool)),U_14255),U_14254))
      | ~ c_Wellfounded_Owf(U_14253,U_14254) ),
    inference(definitional_conversion,[status(esa)],[f_3650_2]) ).

cnf(f_3650_4,plain,
    ( c_Wellfounded_Owf(U_14253,U_14255)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14253,U_14253),tc_HOL_Obool)),U_14255),U_14254))
    | ~ c_Wellfounded_Owf(U_14253,U_14254) ),
    inference(clausify,[status(thm)],[f_3650_3]) ).

fof(f_3651_1,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(fof_nnf,[status(thm)],[fact_wf__pair__less]) ).

fof(f_3651_2,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(definitional_conversion,[status(esa)],[f_3651_1]) ).

cnf(f_3651_3,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3651_2]) ).

fof(f_3652_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__wf]) ).

fof(f_3652_2,plain,
    ! [U_14257,U_14256] :
      ( c_Wellfounded_Owf(tc_fun(U_14256,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_14256,U_14257))
      | ~ c_Wellfounded_Owf(U_14256,U_14257) ),
    inference(variable_rename,[status(thm)],[f_3652_1]) ).

fof(f_3652_3,plain,
    ! [U_14256,U_14257] :
      ( c_Wellfounded_Owf(tc_fun(U_14256,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_14256,U_14257))
      | ~ c_Wellfounded_Owf(U_14256,U_14257) ),
    inference(definitional_conversion,[status(esa)],[f_3652_2]) ).

cnf(f_3652_4,plain,
    ( c_Wellfounded_Owf(tc_fun(U_14256,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_14256,U_14257))
    | ~ c_Wellfounded_Owf(U_14256,U_14257) ),
    inference(clausify,[status(thm)],[f_3652_3]) ).

fof(f_3653_1,plain,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
        | ! [B_b] :
            ( ~ hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
            | ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) )
      & ( ? [B_b] :
            ( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
            & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) )
        | ~ c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations]) ).

fof(f_3653_2,plain,
    ! [U_14266,U_14265,U_14264,U_14263,U_14262,U_14261,U_14260] :
      ( ( c_Predicate_Opred__comp(U_14260,U_14261,U_14262,U_14263,U_14264,U_14265,U_14266)
        | ! [U_14259] :
            ( ~ hBOOL(hAPP(hAPP(U_14264,U_14259),U_14266))
            | ~ hBOOL(hAPP(hAPP(U_14263,U_14265),U_14259)) ) )
      & ( ? [U_14258] :
            ( hBOOL(hAPP(hAPP(U_14264,U_14258),U_14266))
            & hBOOL(hAPP(hAPP(U_14263,U_14265),U_14258)) )
        | ~ c_Predicate_Opred__comp(U_14260,U_14261,U_14262,U_14263,U_14264,U_14265,U_14266) ) ),
    inference(variable_rename,[status(thm)],[f_3653_1]) ).

fof(f_3653_3,plain,
    ( ! [U_14280,U_14278,U_14276,U_14274] :
        ( ! [U_14272,U_14270,U_14268] : c_Predicate_Opred__comp(U_14268,U_14270,U_14272,U_14274,U_14276,U_14278,U_14280)
        | ! [U_14259] :
            ( ~ hBOOL(hAPP(hAPP(U_14276,U_14259),U_14280))
            | ~ hBOOL(hAPP(hAPP(U_14274,U_14278),U_14259)) ) )
    & ! [U_14279,U_14277,U_14275,U_14273] :
        ( ! [U_14271,U_14269,U_14267] : ~ c_Predicate_Opred__comp(U_14267,U_14269,U_14271,U_14273,U_14275,U_14277,U_14279)
        | ? [U_14258] :
            ( hBOOL(hAPP(hAPP(U_14275,U_14258),U_14279))
            & hBOOL(hAPP(hAPP(U_14273,U_14277),U_14258)) ) ) ),
    inference(miniscope,[status(thm)],[f_3653_2]) ).

fof(f_3653_4,plain,
    ( ! [U_14280,U_14278,U_14276,U_14274] :
        ( ! [U_14272,U_14270,U_14268] : c_Predicate_Opred__comp(U_14268,U_14270,U_14272,U_14274,U_14276,U_14278,U_14280)
        | ! [U_14259] :
            ( ~ hBOOL(hAPP(hAPP(U_14276,U_14259),U_14280))
            | ~ hBOOL(hAPP(hAPP(U_14274,U_14278),U_14259)) ) )
    & ! [U_14279,U_14277,U_14275,U_14273] :
        ( ! [U_14271,U_14269,U_14267] : ~ c_Predicate_Opred__comp(U_14267,U_14269,U_14271,U_14273,U_14275,U_14277,U_14279)
        | ( hBOOL(hAPP(hAPP(U_14275,sK324(U_14279,U_14277,U_14275,U_14273)),U_14279))
          & hBOOL(hAPP(hAPP(U_14273,U_14277),sK324(U_14279,U_14277,U_14275,U_14273))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_14258,sK324(U_14279,U_14277,U_14275,U_14273))],[f_3653_3]) ).

fof(f_3653_5,plain,
    ( ! [U_14273,U_14275,U_14279,U_14277] :
        ( hBOOL(hAPP(hAPP(U_14275,sK324(U_14279,U_14277,U_14275,U_14273)),U_14279))
        | ~ sP998(U_14273,U_14275,U_14279,U_14277) )
    & ! [U_14273,U_14275,U_14279,U_14277] :
        ( hBOOL(hAPP(hAPP(U_14273,U_14277),sK324(U_14279,U_14277,U_14275,U_14273)))
        | ~ sP998(U_14273,U_14275,U_14279,U_14277) )
    & ! [U_14270,U_14259,U_14268,U_14278,U_14276,U_14274,U_14272,U_14280] :
        ( c_Predicate_Opred__comp(U_14268,U_14270,U_14272,U_14274,U_14276,U_14278,U_14280)
        | ~ hBOOL(hAPP(hAPP(U_14276,U_14259),U_14280))
        | ~ hBOOL(hAPP(hAPP(U_14274,U_14278),U_14259)) )
    & ! [U_14273,U_14275,U_14279,U_14267,U_14269,U_14277,U_14271] :
        ( ~ c_Predicate_Opred__comp(U_14267,U_14269,U_14271,U_14273,U_14275,U_14277,U_14279)
        | sP998(U_14273,U_14275,U_14279,U_14277) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP998])],[f_3653_4]) ).

cnf(f_3653_6,plain,
    ( ~ c_Predicate_Opred__comp(U_14267,U_14269,U_14271,U_14273,U_14275,U_14277,U_14279)
    | sP998(U_14273,U_14275,U_14279,U_14277) ),
    inference(clausify,[status(thm)],[f_3653_5]) ).

cnf(f_3653_7,plain,
    ( c_Predicate_Opred__comp(U_14268,U_14270,U_14272,U_14274,U_14276,U_14278,U_14280)
    | ~ hBOOL(hAPP(hAPP(U_14276,U_14259),U_14280))
    | ~ hBOOL(hAPP(hAPP(U_14274,U_14278),U_14259)) ),
    inference(clausify,[status(thm)],[f_3653_5]) ).

cnf(f_3653_8,plain,
    ( hBOOL(hAPP(hAPP(U_14273,U_14277),sK324(U_14279,U_14277,U_14275,U_14273)))
    | ~ sP998(U_14273,U_14275,U_14279,U_14277) ),
    inference(clausify,[status(thm)],[f_3653_5]) ).

cnf(f_3653_9,plain,
    ( hBOOL(hAPP(hAPP(U_14275,sK324(U_14279,U_14277,U_14275,U_14273)),U_14279))
    | ~ sP998(U_14273,U_14275,U_14279,U_14277) ),
    inference(clausify,[status(thm)],[f_3653_5]) ).

fof(f_3654_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_min__ext__wf]) ).

fof(f_3654_2,plain,
    ! [U_14282,U_14281] :
      ( c_Wellfounded_Owf(tc_fun(U_14281,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_14281,U_14282))
      | ~ c_Wellfounded_Owf(U_14281,U_14282) ),
    inference(variable_rename,[status(thm)],[f_3654_1]) ).

fof(f_3654_3,plain,
    ! [U_14282,U_14281] :
      ( c_Wellfounded_Owf(tc_fun(U_14281,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_14281,U_14282))
      | ~ c_Wellfounded_Owf(U_14281,U_14282) ),
    inference(definitional_conversion,[status(esa)],[f_3654_2]) ).

cnf(f_3654_4,plain,
    ( c_Wellfounded_Owf(tc_fun(U_14281,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_14281,U_14282))
    | ~ c_Wellfounded_Owf(U_14281,U_14282) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

fof(f_3655_1,plain,
    ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
    inference(fof_nnf,[status(thm)],[fact_wf__finite__psubset]) ).

fof(f_3655_2,plain,
    ! [U_14283] : c_Wellfounded_Owf(tc_fun(U_14283,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_14283)),
    inference(variable_rename,[status(thm)],[f_3655_1]) ).

fof(f_3655_3,plain,
    ! [U_14283] : c_Wellfounded_Owf(tc_fun(U_14283,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_14283)),
    inference(definitional_conversion,[status(esa)],[f_3655_2]) ).

cnf(f_3655_4,plain,
    c_Wellfounded_Owf(tc_fun(U_14283,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_14283)),
    inference(clausify,[status(thm)],[f_3655_3]) ).

fof(f_3656_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_r_2)
        | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) )
      & ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__acc__iff]) ).

fof(f_3656_2,plain,
    ! [U_14287,U_14286] :
      ( ( c_Wellfounded_Owf(U_14286,U_14287)
        | ? [U_14285] : ~ hBOOL(hAPP(hAPP(c_member(U_14286),U_14285),c_Wellfounded_Oacc(U_14286,U_14287))) )
      & ( ! [U_14284] : hBOOL(hAPP(hAPP(c_member(U_14286),U_14284),c_Wellfounded_Oacc(U_14286,U_14287)))
        | ~ c_Wellfounded_Owf(U_14286,U_14287) ) ),
    inference(variable_rename,[status(thm)],[f_3656_1]) ).

fof(f_3656_3,plain,
    ( ! [U_14291,U_14289] :
        ( c_Wellfounded_Owf(U_14289,U_14291)
        | ? [U_14285] : ~ hBOOL(hAPP(hAPP(c_member(U_14289),U_14285),c_Wellfounded_Oacc(U_14289,U_14291))) )
    & ! [U_14290,U_14288] :
        ( ! [U_14284] : hBOOL(hAPP(hAPP(c_member(U_14288),U_14284),c_Wellfounded_Oacc(U_14288,U_14290)))
        | ~ c_Wellfounded_Owf(U_14288,U_14290) ) ),
    inference(miniscope,[status(thm)],[f_3656_2]) ).

fof(f_3656_4,plain,
    ( ! [U_14291,U_14289] :
        ( c_Wellfounded_Owf(U_14289,U_14291)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14289),sK325(U_14291,U_14289)),c_Wellfounded_Oacc(U_14289,U_14291))) )
    & ! [U_14290,U_14288] :
        ( ! [U_14284] : hBOOL(hAPP(hAPP(c_member(U_14288),U_14284),c_Wellfounded_Oacc(U_14288,U_14290)))
        | ~ c_Wellfounded_Owf(U_14288,U_14290) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_14285,sK325(U_14291,U_14289))],[f_3656_3]) ).

fof(f_3656_5,plain,
    ( ! [U_14289,U_14291] :
        ( c_Wellfounded_Owf(U_14289,U_14291)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14289),sK325(U_14291,U_14289)),c_Wellfounded_Oacc(U_14289,U_14291))) )
    & ! [U_14290,U_14284,U_14288] :
        ( hBOOL(hAPP(hAPP(c_member(U_14288),U_14284),c_Wellfounded_Oacc(U_14288,U_14290)))
        | ~ c_Wellfounded_Owf(U_14288,U_14290) ) ),
    inference(definitional_conversion,[status(esa)],[f_3656_4]) ).

cnf(f_3656_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14288),U_14284),c_Wellfounded_Oacc(U_14288,U_14290)))
    | ~ c_Wellfounded_Owf(U_14288,U_14290) ),
    inference(clausify,[status(thm)],[f_3656_5]) ).

cnf(f_3656_7,plain,
    ( c_Wellfounded_Owf(U_14289,U_14291)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14289),sK325(U_14291,U_14289)),c_Wellfounded_Oacc(U_14289,U_14291))) ),
    inference(clausify,[status(thm)],[f_3656_5]) ).

fof(f_3657_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_acc__wfD]) ).

fof(f_3657_2,plain,
    ! [U_14294,U_14293,U_14292] :
      ( hBOOL(hAPP(hAPP(c_member(U_14292),U_14294),c_Wellfounded_Oacc(U_14292,U_14293)))
      | ~ c_Wellfounded_Owf(U_14292,U_14293) ),
    inference(variable_rename,[status(thm)],[f_3657_1]) ).

fof(f_3657_3,plain,
    ! [U_14292,U_14293,U_14294] :
      ( hBOOL(hAPP(hAPP(c_member(U_14292),U_14294),c_Wellfounded_Oacc(U_14292,U_14293)))
      | ~ c_Wellfounded_Owf(U_14292,U_14293) ),
    inference(definitional_conversion,[status(esa)],[f_3657_2]) ).

cnf(f_3657_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14292),U_14294),c_Wellfounded_Oacc(U_14292,U_14293)))
    | ~ c_Wellfounded_Owf(U_14292,U_14293) ),
    inference(clausify,[status(thm)],[f_3657_3]) ).

fof(f_3658_1,plain,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__int__ge__less__than2]) ).

fof(f_3658_2,plain,
    ! [U_14295] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_14295)),
    inference(variable_rename,[status(thm)],[f_3658_1]) ).

fof(f_3658_3,plain,
    ! [U_14295] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_14295)),
    inference(definitional_conversion,[status(esa)],[f_3658_2]) ).

cnf(f_3658_4,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_14295)),
    inference(clausify,[status(thm)],[f_3658_3]) ).

fof(f_3659_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_wf__less]) ).

fof(f_3659_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_3659_1]) ).

cnf(f_3659_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_3659_2]) ).

fof(f_3660_1,plain,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__no__loop]) ).

fof(f_3660_2,plain,
    ! [U_14297,U_14296] :
      ( c_Wellfounded_Owf(U_14296,U_14297)
      | hAPP(hAPP(c_Relation_Orel__comp(U_14296,U_14296,U_14296),U_14297),U_14297) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3660_1]) ).

fof(f_3660_3,plain,
    ! [U_14296,U_14297] :
      ( c_Wellfounded_Owf(U_14296,U_14297)
      | hAPP(hAPP(c_Relation_Orel__comp(U_14296,U_14296,U_14296),U_14297),U_14297) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3660_2]) ).

cnf(f_3660_4,plain,
    ( c_Wellfounded_Owf(U_14296,U_14297)
    | hAPP(hAPP(c_Relation_Orel__comp(U_14296,U_14296,U_14296),U_14297),U_14297) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3660_3]) ).

fof(f_3661_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) )
      & ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2))
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__union__merge]) ).

fof(f_3661_2,plain,
    ! [U_14300,U_14299,U_14298] :
      ( ( c_Wellfounded_Owf(U_14298,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14298,U_14298),tc_HOL_Obool)),U_14299),U_14300))
        | ~ c_Wellfounded_Owf(U_14298,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14298,U_14298),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14298,U_14298),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14298,U_14298,U_14298),U_14299),U_14299)),hAPP(hAPP(c_Relation_Orel__comp(U_14298,U_14298,U_14298),U_14300),U_14299))),U_14300)) )
      & ( c_Wellfounded_Owf(U_14298,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14298,U_14298),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14298,U_14298),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14298,U_14298,U_14298),U_14299),U_14299)),hAPP(hAPP(c_Relation_Orel__comp(U_14298,U_14298,U_14298),U_14300),U_14299))),U_14300))
        | ~ c_Wellfounded_Owf(U_14298,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14298,U_14298),tc_HOL_Obool)),U_14299),U_14300)) ) ),
    inference(variable_rename,[status(thm)],[f_3661_1]) ).

fof(f_3661_3,plain,
    ( ! [U_14306,U_14304,U_14302] :
        ( c_Wellfounded_Owf(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),U_14304),U_14306))
        | ~ c_Wellfounded_Owf(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14302,U_14302,U_14302),U_14304),U_14304)),hAPP(hAPP(c_Relation_Orel__comp(U_14302,U_14302,U_14302),U_14306),U_14304))),U_14306)) )
    & ! [U_14305,U_14303,U_14301] :
        ( c_Wellfounded_Owf(U_14301,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14301,U_14301,U_14301),U_14303),U_14303)),hAPP(hAPP(c_Relation_Orel__comp(U_14301,U_14301,U_14301),U_14305),U_14303))),U_14305))
        | ~ c_Wellfounded_Owf(U_14301,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),U_14303),U_14305)) ) ),
    inference(miniscope,[status(thm)],[f_3661_2]) ).

fof(f_3661_4,plain,
    ( ! [U_14302,U_14304,U_14306] :
        ( c_Wellfounded_Owf(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),U_14304),U_14306))
        | ~ c_Wellfounded_Owf(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14302,U_14302,U_14302),U_14304),U_14304)),hAPP(hAPP(c_Relation_Orel__comp(U_14302,U_14302,U_14302),U_14306),U_14304))),U_14306)) )
    & ! [U_14301,U_14303,U_14305] :
        ( c_Wellfounded_Owf(U_14301,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14301,U_14301,U_14301),U_14303),U_14303)),hAPP(hAPP(c_Relation_Orel__comp(U_14301,U_14301,U_14301),U_14305),U_14303))),U_14305))
        | ~ c_Wellfounded_Owf(U_14301,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),U_14303),U_14305)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3661_3]) ).

cnf(f_3661_5,plain,
    ( c_Wellfounded_Owf(U_14301,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14301,U_14301,U_14301),U_14303),U_14303)),hAPP(hAPP(c_Relation_Orel__comp(U_14301,U_14301,U_14301),U_14305),U_14303))),U_14305))
    | ~ c_Wellfounded_Owf(U_14301,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),U_14303),U_14305)) ),
    inference(clausify,[status(thm)],[f_3661_4]) ).

cnf(f_3661_6,plain,
    ( c_Wellfounded_Owf(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),U_14304),U_14306))
    | ~ c_Wellfounded_Owf(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14302,U_14302,U_14302),U_14304),U_14304)),hAPP(hAPP(c_Relation_Orel__comp(U_14302,U_14302,U_14302),U_14306),U_14304))),U_14306)) ),
    inference(clausify,[status(thm)],[f_3661_4]) ).

fof(f_3662_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_r_2)
        | ? [B_f] :
          ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) )
      & ( ! [B_f] :
          ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain]) ).

fof(f_3662_2,plain,
    ! [U_14312,U_14311] :
      ( ( c_Wellfounded_Owf(U_14311,U_14312)
        | ? [U_14310] :
          ! [U_14309] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14311,U_14311)),hAPP(hAPP(c_Product__Type_OPair(U_14311,U_14311),hAPP(U_14310,hAPP(c_Nat_OSuc,U_14309))),hAPP(U_14310,U_14309))),U_14312)) )
      & ( ! [U_14308] :
          ? [U_14307] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14311,U_14311)),hAPP(hAPP(c_Product__Type_OPair(U_14311,U_14311),hAPP(U_14308,hAPP(c_Nat_OSuc,U_14307))),hAPP(U_14308,U_14307))),U_14312))
        | ~ c_Wellfounded_Owf(U_14311,U_14312) ) ),
    inference(variable_rename,[status(thm)],[f_3662_1]) ).

fof(f_3662_3,plain,
    ( ! [U_14316,U_14314] :
        ( c_Wellfounded_Owf(U_14314,U_14316)
        | ? [U_14310] :
          ! [U_14309] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14314,U_14314)),hAPP(hAPP(c_Product__Type_OPair(U_14314,U_14314),hAPP(U_14310,hAPP(c_Nat_OSuc,U_14309))),hAPP(U_14310,U_14309))),U_14316)) )
    & ! [U_14315,U_14313] :
        ( ! [U_14308] :
          ? [U_14307] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14313,U_14313)),hAPP(hAPP(c_Product__Type_OPair(U_14313,U_14313),hAPP(U_14308,hAPP(c_Nat_OSuc,U_14307))),hAPP(U_14308,U_14307))),U_14315))
        | ~ c_Wellfounded_Owf(U_14313,U_14315) ) ),
    inference(miniscope,[status(thm)],[f_3662_2]) ).

fof(f_3662_4,plain,
    ( ! [U_14316,U_14314] :
        ( c_Wellfounded_Owf(U_14314,U_14316)
        | ? [U_14310] :
          ! [U_14309] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14314,U_14314)),hAPP(hAPP(c_Product__Type_OPair(U_14314,U_14314),hAPP(U_14310,hAPP(c_Nat_OSuc,U_14309))),hAPP(U_14310,U_14309))),U_14316)) )
    & ! [U_14315,U_14313] :
        ( ! [U_14308] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14313,U_14313)),hAPP(hAPP(c_Product__Type_OPair(U_14313,U_14313),hAPP(U_14308,hAPP(c_Nat_OSuc,sK326(U_14315,U_14313,U_14308)))),hAPP(U_14308,sK326(U_14315,U_14313,U_14308)))),U_14315))
        | ~ c_Wellfounded_Owf(U_14313,U_14315) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_14307,sK326(U_14315,U_14313,U_14308))],[f_3662_3]) ).

fof(f_3662_5,plain,
    ( ! [U_14316,U_14314] :
        ( c_Wellfounded_Owf(U_14314,U_14316)
        | ! [U_14309] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14314,U_14314)),hAPP(hAPP(c_Product__Type_OPair(U_14314,U_14314),hAPP(sK327(U_14316,U_14314),hAPP(c_Nat_OSuc,U_14309))),hAPP(sK327(U_14316,U_14314),U_14309))),U_14316)) )
    & ! [U_14315,U_14313] :
        ( ! [U_14308] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14313,U_14313)),hAPP(hAPP(c_Product__Type_OPair(U_14313,U_14313),hAPP(U_14308,hAPP(c_Nat_OSuc,sK326(U_14315,U_14313,U_14308)))),hAPP(U_14308,sK326(U_14315,U_14313,U_14308)))),U_14315))
        | ~ c_Wellfounded_Owf(U_14313,U_14315) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_14310,sK327(U_14316,U_14314))],[f_3662_4]) ).

fof(f_3662_6,plain,
    ( ! [U_14309,U_14314,U_14316] :
        ( c_Wellfounded_Owf(U_14314,U_14316)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14314,U_14314)),hAPP(hAPP(c_Product__Type_OPair(U_14314,U_14314),hAPP(sK327(U_14316,U_14314),hAPP(c_Nat_OSuc,U_14309))),hAPP(sK327(U_14316,U_14314),U_14309))),U_14316)) )
    & ! [U_14315,U_14308,U_14313] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14313,U_14313)),hAPP(hAPP(c_Product__Type_OPair(U_14313,U_14313),hAPP(U_14308,hAPP(c_Nat_OSuc,sK326(U_14315,U_14313,U_14308)))),hAPP(U_14308,sK326(U_14315,U_14313,U_14308)))),U_14315))
        | ~ c_Wellfounded_Owf(U_14313,U_14315) ) ),
    inference(definitional_conversion,[status(esa)],[f_3662_5]) ).

cnf(f_3662_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14313,U_14313)),hAPP(hAPP(c_Product__Type_OPair(U_14313,U_14313),hAPP(U_14308,hAPP(c_Nat_OSuc,sK326(U_14315,U_14313,U_14308)))),hAPP(U_14308,sK326(U_14315,U_14313,U_14308)))),U_14315))
    | ~ c_Wellfounded_Owf(U_14313,U_14315) ),
    inference(clausify,[status(thm)],[f_3662_6]) ).

cnf(f_3662_8,plain,
    ( c_Wellfounded_Owf(U_14314,U_14316)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14314,U_14314)),hAPP(hAPP(c_Product__Type_OPair(U_14314,U_14314),hAPP(sK327(U_14316,U_14314),hAPP(c_Nat_OSuc,U_14309))),hAPP(sK327(U_14316,U_14314),U_14309))),U_14316)) ),
    inference(clausify,[status(thm)],[f_3662_6]) ).

fof(f_3663_1,plain,
    ! [V_A_2,V_R_2,T_b] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfE__pf]) ).

fof(f_3663_2,plain,
    ! [U_14319,U_14318,U_14317] :
      ( U_14319 = c_Orderings_Obot__class_Obot(tc_fun(U_14317,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14317,tc_HOL_Obool)),U_14319),hAPP(c_Relation_OImage(U_14317,U_14317,U_14318),U_14319)))
      | ~ c_Wellfounded_Owf(U_14317,U_14318) ),
    inference(variable_rename,[status(thm)],[f_3663_1]) ).

fof(f_3663_3,plain,
    ! [U_14317,U_14318,U_14319] :
      ( U_14319 = c_Orderings_Obot__class_Obot(tc_fun(U_14317,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14317,tc_HOL_Obool)),U_14319),hAPP(c_Relation_OImage(U_14317,U_14317,U_14318),U_14319)))
      | ~ c_Wellfounded_Owf(U_14317,U_14318) ),
    inference(definitional_conversion,[status(esa)],[f_3663_2]) ).

cnf(f_3663_4,plain,
    ( U_14319 = c_Orderings_Obot__class_Obot(tc_fun(U_14317,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14317,tc_HOL_Obool)),U_14319),hAPP(c_Relation_OImage(U_14317,U_14317,U_14318),U_14319)))
    | ~ c_Wellfounded_Owf(U_14317,U_14318) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

fof(f_3664_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_S_2)
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__union__compatible]) ).

fof(f_3664_2,plain,
    ! [U_14322,U_14321,U_14320] :
      ( c_Wellfounded_Owf(U_14320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),U_14321),U_14322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14320,U_14320,U_14320),U_14321),U_14322)),U_14321))
      | ~ c_Wellfounded_Owf(U_14320,U_14322)
      | ~ c_Wellfounded_Owf(U_14320,U_14321) ),
    inference(variable_rename,[status(thm)],[f_3664_1]) ).

fof(f_3664_3,plain,
    ! [U_14320,U_14321,U_14322] :
      ( c_Wellfounded_Owf(U_14320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),U_14321),U_14322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14320,U_14320,U_14320),U_14321),U_14322)),U_14321))
      | ~ c_Wellfounded_Owf(U_14320,U_14322)
      | ~ c_Wellfounded_Owf(U_14320,U_14321) ),
    inference(definitional_conversion,[status(esa)],[f_3664_2]) ).

cnf(f_3664_4,plain,
    ( c_Wellfounded_Owf(U_14320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),U_14321),U_14322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14320,U_14320,U_14320),U_14321),U_14322)),U_14321))
    | ~ c_Wellfounded_Owf(U_14320,U_14322)
    | ~ c_Wellfounded_Owf(U_14320,U_14321) ),
    inference(clausify,[status(thm)],[f_3664_3]) ).

fof(f_3665_1,plain,
    ! [T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b))))
      | ~ class_Orderings_Owellorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_wf]) ).

fof(f_3665_2,plain,
    ! [U_14323] :
      ( c_Wellfounded_Owf(U_14323,hAPP(c_Set_OCollect(tc_prod(U_14323,U_14323)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14323,U_14323,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_14323))))
      | ~ class_Orderings_Owellorder(U_14323) ),
    inference(variable_rename,[status(thm)],[f_3665_1]) ).

fof(f_3665_3,plain,
    ! [U_14323] :
      ( c_Wellfounded_Owf(U_14323,hAPP(c_Set_OCollect(tc_prod(U_14323,U_14323)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14323,U_14323,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_14323))))
      | ~ class_Orderings_Owellorder(U_14323) ),
    inference(definitional_conversion,[status(esa)],[f_3665_2]) ).

cnf(f_3665_4,plain,
    ( c_Wellfounded_Owf(U_14323,hAPP(c_Set_OCollect(tc_prod(U_14323,U_14323)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14323,U_14323,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_14323))))
    | ~ class_Orderings_Owellorder(U_14323) ),
    inference(clausify,[status(thm)],[f_3665_3]) ).

fof(f_3666_1,plain,
    ! [V_P_2,T_b] :
      ( ( c_FunDef_Oreduction__pair(T_b,V_P_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
        | ~ c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
          & c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
        | ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).

fof(f_3666_2,plain,
    ! [U_14325,U_14324] :
      ( ( c_FunDef_Oreduction__pair(U_14324,U_14325)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14324,U_14324,U_14324),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325)))
        | ~ c_Wellfounded_Owf(U_14324,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14324,U_14324,U_14324),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325)))
          & c_Wellfounded_Owf(U_14324,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool),tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),U_14325)) )
        | ~ c_FunDef_Oreduction__pair(U_14324,U_14325) ) ),
    inference(variable_rename,[status(thm)],[f_3666_1]) ).

fof(f_3666_3,plain,
    ( ! [U_14329,U_14327] :
        ( c_FunDef_Oreduction__pair(U_14327,U_14329)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14327,U_14327,U_14327),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)))
        | ~ c_Wellfounded_Owf(U_14327,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)) )
    & ! [U_14328,U_14326] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14326,U_14326,U_14326),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)))
          & c_Wellfounded_Owf(U_14326,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)) )
        | ~ c_FunDef_Oreduction__pair(U_14326,U_14328) ) ),
    inference(miniscope,[status(thm)],[f_3666_2]) ).

fof(f_3666_4,plain,
    ( ! [U_14328,U_14326] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14326,U_14326,U_14326),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)))
        | ~ sP999(U_14328,U_14326) )
    & ! [U_14328,U_14326] :
        ( c_Wellfounded_Owf(U_14326,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328))
        | ~ sP999(U_14328,U_14326) )
    & ! [U_14329,U_14327] :
        ( c_FunDef_Oreduction__pair(U_14327,U_14329)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14327,U_14327,U_14327),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)))
        | ~ c_Wellfounded_Owf(U_14327,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)) )
    & ! [U_14328,U_14326] :
        ( sP999(U_14328,U_14326)
        | ~ c_FunDef_Oreduction__pair(U_14326,U_14328) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP999])],[f_3666_3]) ).

cnf(f_3666_5,plain,
    ( sP999(U_14328,U_14326)
    | ~ c_FunDef_Oreduction__pair(U_14326,U_14328) ),
    inference(clausify,[status(thm)],[f_3666_4]) ).

cnf(f_3666_6,plain,
    ( c_FunDef_Oreduction__pair(U_14327,U_14329)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14327,U_14327,U_14327),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)))
    | ~ c_Wellfounded_Owf(U_14327,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool),tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool)),U_14329)) ),
    inference(clausify,[status(thm)],[f_3666_4]) ).

cnf(f_3666_7,plain,
    ( c_Wellfounded_Owf(U_14326,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328))
    | ~ sP999(U_14328,U_14326) ),
    inference(clausify,[status(thm)],[f_3666_4]) ).

cnf(f_3666_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14326,U_14326,U_14326),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool),tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14328)))
    | ~ sP999(U_14328,U_14326) ),
    inference(clausify,[status(thm)],[f_3666_4]) ).

fof(f_3667_1,plain,
    ! [V_S_2,V_R_2,V_P_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ c_Wellfounded_Owf(T_b,V_S_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
      | ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).

fof(f_3667_2,plain,
    ! [U_14333,U_14332,U_14331,U_14330] :
      ( c_Wellfounded_Owf(U_14330,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14332),U_14333))
      | ~ c_Wellfounded_Owf(U_14330,U_14333)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14333),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool),tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14331)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14332),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool),tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14331)))
      | ~ c_FunDef_Oreduction__pair(U_14330,U_14331) ),
    inference(variable_rename,[status(thm)],[f_3667_1]) ).

fof(f_3667_3,plain,
    ! [U_14330,U_14331,U_14332,U_14333] :
      ( c_Wellfounded_Owf(U_14330,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14332),U_14333))
      | ~ c_Wellfounded_Owf(U_14330,U_14333)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14333),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool),tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14331)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14332),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool),tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14331)))
      | ~ c_FunDef_Oreduction__pair(U_14330,U_14331) ),
    inference(definitional_conversion,[status(esa)],[f_3667_2]) ).

cnf(f_3667_4,plain,
    ( c_Wellfounded_Owf(U_14330,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14332),U_14333))
    | ~ c_Wellfounded_Owf(U_14330,U_14333)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14333),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool),tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14331)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14332),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool),tc_fun(tc_prod(U_14330,U_14330),tc_HOL_Obool)),U_14331)))
    | ~ c_FunDef_Oreduction__pair(U_14330,U_14331) ),
    inference(clausify,[status(thm)],[f_3667_3]) ).

fof(f_3668_1,plain,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image]) ).

fof(f_3668_2,plain,
    ! [U_14337,U_14336,U_14335,U_14334] :
      ( c_Wellfounded_Owf(U_14336,hAPP(c_Set_Oimage(tc_prod(U_14334,U_14334),tc_prod(U_14336,U_14336),c_Product__Type_Omap__pair(U_14334,U_14336,U_14334,U_14336,U_14337,U_14337)),U_14335))
      | ~ c_Fun_Oinj__on(U_14334,U_14336,U_14337,c_Orderings_Otop__class_Otop(tc_fun(U_14334,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_14334,U_14335) ),
    inference(variable_rename,[status(thm)],[f_3668_1]) ).

fof(f_3668_3,plain,
    ! [U_14336,U_14335,U_14337,U_14334] :
      ( c_Wellfounded_Owf(U_14336,hAPP(c_Set_Oimage(tc_prod(U_14334,U_14334),tc_prod(U_14336,U_14336),c_Product__Type_Omap__pair(U_14334,U_14336,U_14334,U_14336,U_14337,U_14337)),U_14335))
      | ~ c_Fun_Oinj__on(U_14334,U_14336,U_14337,c_Orderings_Otop__class_Otop(tc_fun(U_14334,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_14334,U_14335) ),
    inference(definitional_conversion,[status(esa)],[f_3668_2]) ).

cnf(f_3668_4,plain,
    ( c_Wellfounded_Owf(U_14336,hAPP(c_Set_Oimage(tc_prod(U_14334,U_14334),tc_prod(U_14336,U_14336),c_Product__Type_Omap__pair(U_14334,U_14336,U_14334,U_14336,U_14337,U_14337)),U_14335))
    | ~ c_Fun_Oinj__on(U_14334,U_14336,U_14337,c_Orderings_Otop__class_Otop(tc_fun(U_14334,tc_HOL_Obool)))
    | ~ c_Wellfounded_Owf(U_14334,U_14335) ),
    inference(clausify,[status(thm)],[f_3668_3]) ).

fof(f_3669_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lenlex]) ).

fof(f_3669_2,plain,
    ! [U_14339,U_14338] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_14338),c_List_Olenlex(U_14338,U_14339))
      | ~ c_Wellfounded_Owf(U_14338,U_14339) ),
    inference(variable_rename,[status(thm)],[f_3669_1]) ).

fof(f_3669_3,plain,
    ! [U_14338,U_14339] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_14338),c_List_Olenlex(U_14338,U_14339))
      | ~ c_Wellfounded_Owf(U_14338,U_14339) ),
    inference(definitional_conversion,[status(esa)],[f_3669_2]) ).

cnf(f_3669_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_14338),c_List_Olenlex(U_14338,U_14339))
    | ~ c_Wellfounded_Owf(U_14338,U_14339) ),
    inference(clausify,[status(thm)],[f_3669_3]) ).

fof(f_3670_1,plain,
    ! [T_b,V_g_2,V_f_2,V_P_2] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2)))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(V_P_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).

fof(f_3670_2,plain,
    ! [U_14344,U_14343,U_14342,U_14341] :
      ( c_Wellfounded_Owf(U_14344,hAPP(c_Set_OCollect(tc_prod(U_14344,U_14344)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14344,U_14344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(U_14344,tc_HOL_Obool),U_14344),hAPP(c_COMBS(U_14344,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14344),c_fconj),U_14341))),hAPP(hAPP(c_COMBC(U_14344,tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),U_14344),c_COMBB(U_14344,tc_HOL_Obool,U_14344)),c_fequal)),U_14343)))))
      | ? [U_14340] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_14342,hAPP(U_14343,U_14340))),hAPP(U_14342,U_14340)))
          & hBOOL(hAPP(U_14341,U_14340)) ) ),
    inference(variable_rename,[status(thm)],[f_3670_1]) ).

fof(f_3670_3,plain,
    ! [U_14344,U_14343,U_14342,U_14341] :
      ( c_Wellfounded_Owf(U_14344,hAPP(c_Set_OCollect(tc_prod(U_14344,U_14344)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14344,U_14344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(U_14344,tc_HOL_Obool),U_14344),hAPP(c_COMBS(U_14344,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14344),c_fconj),U_14341))),hAPP(hAPP(c_COMBC(U_14344,tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),U_14344),c_COMBB(U_14344,tc_HOL_Obool,U_14344)),c_fequal)),U_14343)))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_14342,hAPP(U_14343,sK328(U_14344,U_14343,U_14342,U_14341)))),hAPP(U_14342,sK328(U_14344,U_14343,U_14342,U_14341))))
        & hBOOL(hAPP(U_14341,sK328(U_14344,U_14343,U_14342,U_14341))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_14340,sK328(U_14344,U_14343,U_14342,U_14341))],[f_3670_2]) ).

fof(f_3670_4,plain,
    ( ! [U_14341,U_14342,U_14343,U_14344] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_14342,hAPP(U_14343,sK328(U_14344,U_14343,U_14342,U_14341)))),hAPP(U_14342,sK328(U_14344,U_14343,U_14342,U_14341))))
        | ~ sP1000(U_14341,U_14342,U_14343,U_14344) )
    & ! [U_14341,U_14342,U_14343,U_14344] :
        ( hBOOL(hAPP(U_14341,sK328(U_14344,U_14343,U_14342,U_14341)))
        | ~ sP1000(U_14341,U_14342,U_14343,U_14344) )
    & ! [U_14341,U_14342,U_14343,U_14344] :
        ( c_Wellfounded_Owf(U_14344,hAPP(c_Set_OCollect(tc_prod(U_14344,U_14344)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14344,U_14344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(U_14344,tc_HOL_Obool),U_14344),hAPP(c_COMBS(U_14344,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14344),c_fconj),U_14341))),hAPP(hAPP(c_COMBC(U_14344,tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),U_14344),c_COMBB(U_14344,tc_HOL_Obool,U_14344)),c_fequal)),U_14343)))))
        | sP1000(U_14341,U_14342,U_14343,U_14344) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1000])],[f_3670_3]) ).

cnf(f_3670_5,plain,
    ( c_Wellfounded_Owf(U_14344,hAPP(c_Set_OCollect(tc_prod(U_14344,U_14344)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14344,U_14344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(U_14344,tc_HOL_Obool),U_14344),hAPP(c_COMBS(U_14344,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14344),c_fconj),U_14341))),hAPP(hAPP(c_COMBC(U_14344,tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14344,tc_HOL_Obool),tc_fun(tc_fun(U_14344,U_14344),tc_fun(U_14344,tc_HOL_Obool)),U_14344),c_COMBB(U_14344,tc_HOL_Obool,U_14344)),c_fequal)),U_14343)))))
    | sP1000(U_14341,U_14342,U_14343,U_14344) ),
    inference(clausify,[status(thm)],[f_3670_4]) ).

cnf(f_3670_6,plain,
    ( hBOOL(hAPP(U_14341,sK328(U_14344,U_14343,U_14342,U_14341)))
    | ~ sP1000(U_14341,U_14342,U_14343,U_14344) ),
    inference(clausify,[status(thm)],[f_3670_4]) ).

cnf(f_3670_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_14342,hAPP(U_14343,sK328(U_14344,U_14343,U_14342,U_14341)))),hAPP(U_14342,sK328(U_14344,U_14343,U_14342,U_14341))))
    | ~ sP1000(U_14341,U_14342,U_14343,U_14344) ),
    inference(clausify,[status(thm)],[f_3670_4]) ).

fof(f_3671_1,plain,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    inference(fof_nnf,[status(thm)],[fact_pred__nat__def]) ).

fof(f_3671_2,plain,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    inference(definitional_conversion,[status(esa)],[f_3671_1]) ).

cnf(f_3671_3,plain,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    inference(clausify,[status(thm)],[f_3671_2]) ).

fof(f_3672_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lex]) ).

fof(f_3672_2,plain,
    ! [U_14346,U_14345] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_14345),c_List_Olex(U_14345,U_14346))
      | ~ c_Wellfounded_Owf(U_14345,U_14346) ),
    inference(variable_rename,[status(thm)],[f_3672_1]) ).

fof(f_3672_3,plain,
    ! [U_14345,U_14346] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_14345),c_List_Olex(U_14345,U_14346))
      | ~ c_Wellfounded_Owf(U_14345,U_14346) ),
    inference(definitional_conversion,[status(esa)],[f_3672_2]) ).

cnf(f_3672_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_14345),c_List_Olex(U_14345,U_14346))
    | ~ c_Wellfounded_Owf(U_14345,U_14346) ),
    inference(clausify,[status(thm)],[f_3672_3]) ).

fof(f_3673_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).

fof(f_3673_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(definitional_conversion,[status(esa)],[f_3673_1]) ).

cnf(f_3673_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3673_2]) ).

fof(f_3674_1,plain,
    ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_lex__def]) ).

fof(f_3674_2,plain,
    ! [U_14348,U_14347] : c_List_Olex(U_14347,U_14348) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_14347),tc_List_Olist(U_14347)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_14347,U_14348)),
    inference(variable_rename,[status(thm)],[f_3674_1]) ).

fof(f_3674_3,plain,
    ! [U_14347,U_14348] : c_List_Olex(U_14347,U_14348) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_14347),tc_List_Olist(U_14347)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_14347,U_14348)),
    inference(definitional_conversion,[status(esa)],[f_3674_2]) ).

cnf(f_3674_4,plain,
    c_List_Olex(U_14347,U_14348) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_14347),tc_List_Olist(U_14347)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_14347,U_14348)),
    inference(clausify,[status(thm)],[f_3674_3]) ).

fof(f_3675_1,plain,
    ! [V_n_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lexn]) ).

fof(f_3675_2,plain,
    ! [U_14351,U_14350,U_14349] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_14349),hAPP(c_List_Olexn(U_14349,U_14350),U_14351))
      | ~ c_Wellfounded_Owf(U_14349,U_14350) ),
    inference(variable_rename,[status(thm)],[f_3675_1]) ).

fof(f_3675_3,plain,
    ! [U_14349,U_14350,U_14351] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_14349),hAPP(c_List_Olexn(U_14349,U_14350),U_14351))
      | ~ c_Wellfounded_Owf(U_14349,U_14350) ),
    inference(definitional_conversion,[status(esa)],[f_3675_2]) ).

cnf(f_3675_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_14349),hAPP(c_List_Olexn(U_14349,U_14350),U_14351))
    | ~ c_Wellfounded_Owf(U_14349,U_14350) ),
    inference(clausify,[status(thm)],[f_3675_3]) ).

fof(f_3676_1,plain,
    ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(f_3676_2,plain,
    ! [U_14353,U_14352] : hAPP(c_List_Olexn(U_14352,U_14353),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_14352),tc_List_Olist(U_14352)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3676_1]) ).

fof(f_3676_3,plain,
    ! [U_14352,U_14353] : hAPP(c_List_Olexn(U_14352,U_14353),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_14352),tc_List_Olist(U_14352)),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3676_2]) ).

cnf(f_3676_4,plain,
    hAPP(c_List_Olexn(U_14352,U_14353),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_14352),tc_List_Olist(U_14352)),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3676_3]) ).

fof(f_3677_1,plain,
    ! [T_b,V_R_2,T_c,V_P_2] :
      ( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))
      | ? [B_x] :
          ( ~ c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x))
          & hBOOL(hAPP(V_P_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).

fof(f_3677_2,plain,
    ! [U_14358,U_14357,U_14356,U_14355] :
      ( c_Wellfounded_Owf(tc_prod(U_14358,U_14356),c_Recdef_Osame__fst(U_14358,U_14356,U_14355,U_14357))
      | ? [U_14354] :
          ( ~ c_Wellfounded_Owf(U_14356,hAPP(U_14357,U_14354))
          & hBOOL(hAPP(U_14355,U_14354)) ) ),
    inference(variable_rename,[status(thm)],[f_3677_1]) ).

fof(f_3677_3,plain,
    ! [U_14358,U_14357,U_14356,U_14355] :
      ( c_Wellfounded_Owf(tc_prod(U_14358,U_14356),c_Recdef_Osame__fst(U_14358,U_14356,U_14355,U_14357))
      | ( ~ c_Wellfounded_Owf(U_14356,hAPP(U_14357,sK329(U_14358,U_14357,U_14356,U_14355)))
        & hBOOL(hAPP(U_14355,sK329(U_14358,U_14357,U_14356,U_14355))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_14354,sK329(U_14358,U_14357,U_14356,U_14355))],[f_3677_2]) ).

fof(f_3677_4,plain,
    ( ! [U_14355,U_14356,U_14357,U_14358] :
        ( ~ c_Wellfounded_Owf(U_14356,hAPP(U_14357,sK329(U_14358,U_14357,U_14356,U_14355)))
        | ~ sP1001(U_14355,U_14356,U_14357,U_14358) )
    & ! [U_14355,U_14356,U_14357,U_14358] :
        ( hBOOL(hAPP(U_14355,sK329(U_14358,U_14357,U_14356,U_14355)))
        | ~ sP1001(U_14355,U_14356,U_14357,U_14358) )
    & ! [U_14355,U_14356,U_14357,U_14358] :
        ( c_Wellfounded_Owf(tc_prod(U_14358,U_14356),c_Recdef_Osame__fst(U_14358,U_14356,U_14355,U_14357))
        | sP1001(U_14355,U_14356,U_14357,U_14358) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1001])],[f_3677_3]) ).

cnf(f_3677_5,plain,
    ( c_Wellfounded_Owf(tc_prod(U_14358,U_14356),c_Recdef_Osame__fst(U_14358,U_14356,U_14355,U_14357))
    | sP1001(U_14355,U_14356,U_14357,U_14358) ),
    inference(clausify,[status(thm)],[f_3677_4]) ).

cnf(f_3677_6,plain,
    ( hBOOL(hAPP(U_14355,sK329(U_14358,U_14357,U_14356,U_14355)))
    | ~ sP1001(U_14355,U_14356,U_14357,U_14358) ),
    inference(clausify,[status(thm)],[f_3677_4]) ).

cnf(f_3677_7,plain,
    ( ~ c_Wellfounded_Owf(U_14356,hAPP(U_14357,sK329(U_14358,U_14357,U_14356,U_14355)))
    | ~ sP1001(U_14355,U_14356,U_14357,U_14358) ),
    inference(clausify,[status(thm)],[f_3677_4]) ).

fof(f_3678_1,plain,
    ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).

fof(f_3678_2,plain,
    ! [U_14361,U_14360,U_14359] : hAPP(c_Relation_ORange(U_14359,U_14360),hAPP(c_Set_OCollect(tc_prod(U_14359,U_14360)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14359,U_14360,tc_HOL_Obool),U_14361))) = hAPP(c_Set_OCollect(U_14360),hAPP(hAPP(c_COMBB(tc_fun(U_14359,tc_HOL_Obool),tc_HOL_Obool,U_14360),c_HOL_OEx(U_14359)),hAPP(c_COMBC(U_14359,U_14360,tc_HOL_Obool),U_14361))),
    inference(variable_rename,[status(thm)],[f_3678_1]) ).

fof(f_3678_3,plain,
    ! [U_14359,U_14360,U_14361] : hAPP(c_Relation_ORange(U_14359,U_14360),hAPP(c_Set_OCollect(tc_prod(U_14359,U_14360)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14359,U_14360,tc_HOL_Obool),U_14361))) = hAPP(c_Set_OCollect(U_14360),hAPP(hAPP(c_COMBB(tc_fun(U_14359,tc_HOL_Obool),tc_HOL_Obool,U_14360),c_HOL_OEx(U_14359)),hAPP(c_COMBC(U_14359,U_14360,tc_HOL_Obool),U_14361))),
    inference(definitional_conversion,[status(esa)],[f_3678_2]) ).

cnf(f_3678_4,plain,
    hAPP(c_Relation_ORange(U_14359,U_14360),hAPP(c_Set_OCollect(tc_prod(U_14359,U_14360)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14359,U_14360,tc_HOL_Obool),U_14361))) = hAPP(c_Set_OCollect(U_14360),hAPP(hAPP(c_COMBB(tc_fun(U_14359,tc_HOL_Obool),tc_HOL_Obool,U_14360),c_HOL_OEx(U_14359)),hAPP(c_COMBC(U_14359,U_14360,tc_HOL_Obool),U_14361))),
    inference(clausify,[status(thm)],[f_3678_3]) ).

fof(f_3679_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_RangeI]) ).

fof(f_3679_2,plain,
    ! [U_14366,U_14365,U_14364,U_14363,U_14362] :
      ( hBOOL(hAPP(hAPP(c_member(U_14363),U_14365),hAPP(c_Relation_ORange(U_14362,U_14363),U_14366)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14362,U_14363)),hAPP(hAPP(c_Product__Type_OPair(U_14362,U_14363),U_14364),U_14365)),U_14366)) ),
    inference(variable_rename,[status(thm)],[f_3679_1]) ).

fof(f_3679_3,plain,
    ! [U_14362,U_14363,U_14364,U_14365,U_14366] :
      ( hBOOL(hAPP(hAPP(c_member(U_14363),U_14365),hAPP(c_Relation_ORange(U_14362,U_14363),U_14366)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14362,U_14363)),hAPP(hAPP(c_Product__Type_OPair(U_14362,U_14363),U_14364),U_14365)),U_14366)) ),
    inference(definitional_conversion,[status(esa)],[f_3679_2]) ).

cnf(f_3679_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14363),U_14365),hAPP(c_Relation_ORange(U_14362,U_14363),U_14366)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14362,U_14363)),hAPP(hAPP(c_Product__Type_OPair(U_14362,U_14363),U_14364),U_14365)),U_14366)) ),
    inference(clausify,[status(thm)],[f_3679_3]) ).

fof(f_3680_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Range__Id__on]) ).

fof(f_3680_2,plain,
    ! [U_14368,U_14367] : hAPP(c_Relation_ORange(U_14367,U_14367),c_Relation_OId__on(U_14367,U_14368)) = U_14368,
    inference(variable_rename,[status(thm)],[f_3680_1]) ).

fof(f_3680_3,plain,
    ! [U_14367,U_14368] : hAPP(c_Relation_ORange(U_14367,U_14367),c_Relation_OId__on(U_14367,U_14368)) = U_14368,
    inference(definitional_conversion,[status(esa)],[f_3680_2]) ).

cnf(f_3680_4,plain,
    hAPP(c_Relation_ORange(U_14367,U_14367),c_Relation_OId__on(U_14367,U_14368)) = U_14368,
    inference(clausify,[status(thm)],[f_3680_3]) ).

fof(f_3681_1,plain,
    ! [V_r_2,T_b,T_c] :
      ( ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) )
      & ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(T_c,T_b),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Range__empty__iff]) ).

fof(f_3681_2,plain,
    ! [U_14371,U_14370,U_14369] :
      ( ( hAPP(c_Relation_ORange(U_14369,U_14370),U_14371) = c_Orderings_Obot__class_Obot(tc_fun(U_14370,tc_HOL_Obool))
        | U_14371 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14369,U_14370),tc_HOL_Obool)) )
      & ( U_14371 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14369,U_14370),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_14369,U_14370),U_14371) != c_Orderings_Obot__class_Obot(tc_fun(U_14370,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3681_1]) ).

fof(f_3681_3,plain,
    ( ! [U_14377,U_14375,U_14373] :
        ( hAPP(c_Relation_ORange(U_14373,U_14375),U_14377) = c_Orderings_Obot__class_Obot(tc_fun(U_14375,tc_HOL_Obool))
        | U_14377 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14373,U_14375),tc_HOL_Obool)) )
    & ! [U_14376,U_14374,U_14372] :
        ( U_14376 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14372,U_14374),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_14372,U_14374),U_14376) != c_Orderings_Obot__class_Obot(tc_fun(U_14374,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3681_2]) ).

fof(f_3681_4,plain,
    ( ! [U_14373,U_14375,U_14377] :
        ( hAPP(c_Relation_ORange(U_14373,U_14375),U_14377) = c_Orderings_Obot__class_Obot(tc_fun(U_14375,tc_HOL_Obool))
        | U_14377 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14373,U_14375),tc_HOL_Obool)) )
    & ! [U_14374,U_14376,U_14372] :
        ( U_14376 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14372,U_14374),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_14372,U_14374),U_14376) != c_Orderings_Obot__class_Obot(tc_fun(U_14374,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3681_3]) ).

cnf(f_3681_5,plain,
    ( U_14376 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14372,U_14374),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(U_14372,U_14374),U_14376) != c_Orderings_Obot__class_Obot(tc_fun(U_14374,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3681_4]) ).

cnf(f_3681_6,plain,
    ( hAPP(c_Relation_ORange(U_14373,U_14375),U_14377) = c_Orderings_Obot__class_Obot(tc_fun(U_14375,tc_HOL_Obool))
    | U_14377 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14373,U_14375),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3681_4]) ).

fof(f_3682_1,plain,
    ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__empty]) ).

fof(f_3682_2,plain,
    ! [U_14379,U_14378] : hAPP(c_Relation_ORange(U_14378,U_14379),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14378,U_14379),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14379,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3682_1]) ).

fof(f_3682_3,plain,
    ! [U_14378,U_14379] : hAPP(c_Relation_ORange(U_14378,U_14379),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14378,U_14379),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14379,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3682_2]) ).

cnf(f_3682_4,plain,
    hAPP(c_Relation_ORange(U_14378,U_14379),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14378,U_14379),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14379,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3682_3]) ).

fof(f_3683_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__Un__eq]) ).

fof(f_3683_2,plain,
    ! [U_14383,U_14382,U_14381,U_14380] : hAPP(c_Relation_ORange(U_14380,U_14381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14380,U_14381),tc_HOL_Obool)),U_14382),U_14383)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14381,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14380,U_14381),U_14382)),hAPP(c_Relation_ORange(U_14380,U_14381),U_14383)),
    inference(variable_rename,[status(thm)],[f_3683_1]) ).

fof(f_3683_3,plain,
    ! [U_14380,U_14381,U_14382,U_14383] : hAPP(c_Relation_ORange(U_14380,U_14381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14380,U_14381),tc_HOL_Obool)),U_14382),U_14383)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14381,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14380,U_14381),U_14382)),hAPP(c_Relation_ORange(U_14380,U_14381),U_14383)),
    inference(definitional_conversion,[status(esa)],[f_3683_2]) ).

cnf(f_3683_4,plain,
    hAPP(c_Relation_ORange(U_14380,U_14381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14380,U_14381),tc_HOL_Obool)),U_14382),U_14383)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14381,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14380,U_14381),U_14382)),hAPP(c_Relation_ORange(U_14380,U_14381),U_14383)),
    inference(clausify,[status(thm)],[f_3683_3]) ).

fof(f_3684_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Range]) ).

fof(f_3684_2,plain,
    ! [U_14386,U_14385,U_14384] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(c_Relation_ORange(U_14384,U_14385),U_14386)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14384,U_14385)),U_14386)) ),
    inference(variable_rename,[status(thm)],[f_3684_1]) ).

fof(f_3684_3,plain,
    ! [U_14384,U_14385,U_14386] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(c_Relation_ORange(U_14384,U_14385),U_14386)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14384,U_14385)),U_14386)) ),
    inference(definitional_conversion,[status(esa)],[f_3684_2]) ).

cnf(f_3684_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(c_Relation_ORange(U_14384,U_14385),U_14386)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14384,U_14385)),U_14386)) ),
    inference(clausify,[status(thm)],[f_3684_3]) ).

fof(f_3685_1,plain,
    ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_snd__eq__Range]) ).

fof(f_3685_2,plain,
    ! [U_14389,U_14388,U_14387] : hAPP(c_Set_Oimage(tc_prod(U_14387,U_14388),U_14388,c_Product__Type_Osnd(U_14387,U_14388)),U_14389) = hAPP(c_Relation_ORange(U_14387,U_14388),U_14389),
    inference(variable_rename,[status(thm)],[f_3685_1]) ).

fof(f_3685_3,plain,
    ! [U_14387,U_14388,U_14389] : hAPP(c_Set_Oimage(tc_prod(U_14387,U_14388),U_14388,c_Product__Type_Osnd(U_14387,U_14388)),U_14389) = hAPP(c_Relation_ORange(U_14387,U_14388),U_14389),
    inference(definitional_conversion,[status(esa)],[f_3685_2]) ).

cnf(f_3685_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_14387,U_14388),U_14388,c_Product__Type_Osnd(U_14387,U_14388)),U_14389) = hAPP(c_Relation_ORange(U_14387,U_14388),U_14389),
    inference(clausify,[status(thm)],[f_3685_3]) ).

fof(f_3686_1,plain,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
        | ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) )
      & ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Range__iff]) ).

fof(f_3686_2,plain,
    ! [U_14395,U_14394,U_14393,U_14392] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14392),U_14393),hAPP(c_Relation_ORange(U_14394,U_14392),U_14395)))
        | ! [U_14391] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14394,U_14392)),hAPP(hAPP(c_Product__Type_OPair(U_14394,U_14392),U_14391),U_14393)),U_14395)) )
      & ( ? [U_14390] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14394,U_14392)),hAPP(hAPP(c_Product__Type_OPair(U_14394,U_14392),U_14390),U_14393)),U_14395))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14392),U_14393),hAPP(c_Relation_ORange(U_14394,U_14392),U_14395))) ) ),
    inference(variable_rename,[status(thm)],[f_3686_1]) ).

fof(f_3686_3,plain,
    ( ! [U_14403,U_14401,U_14399,U_14397] :
        ( hBOOL(hAPP(hAPP(c_member(U_14397),U_14399),hAPP(c_Relation_ORange(U_14401,U_14397),U_14403)))
        | ! [U_14391] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14401,U_14397)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14397),U_14391),U_14399)),U_14403)) )
    & ! [U_14402,U_14400,U_14398,U_14396] :
        ( ? [U_14390] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14400,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14396),U_14390),U_14398)),U_14402))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14396),U_14398),hAPP(c_Relation_ORange(U_14400,U_14396),U_14402))) ) ),
    inference(miniscope,[status(thm)],[f_3686_2]) ).

fof(f_3686_4,plain,
    ( ! [U_14403,U_14401,U_14399,U_14397] :
        ( hBOOL(hAPP(hAPP(c_member(U_14397),U_14399),hAPP(c_Relation_ORange(U_14401,U_14397),U_14403)))
        | ! [U_14391] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14401,U_14397)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14397),U_14391),U_14399)),U_14403)) )
    & ! [U_14402,U_14400,U_14398,U_14396] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14400,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14396),sK330(U_14402,U_14400,U_14398,U_14396)),U_14398)),U_14402))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14396),U_14398),hAPP(c_Relation_ORange(U_14400,U_14396),U_14402))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_14390,sK330(U_14402,U_14400,U_14398,U_14396))],[f_3686_3]) ).

fof(f_3686_5,plain,
    ( ! [U_14391,U_14397,U_14399,U_14401,U_14403] :
        ( hBOOL(hAPP(hAPP(c_member(U_14397),U_14399),hAPP(c_Relation_ORange(U_14401,U_14397),U_14403)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14401,U_14397)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14397),U_14391),U_14399)),U_14403)) )
    & ! [U_14398,U_14400,U_14402,U_14396] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14400,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14396),sK330(U_14402,U_14400,U_14398,U_14396)),U_14398)),U_14402))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14396),U_14398),hAPP(c_Relation_ORange(U_14400,U_14396),U_14402))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3686_4]) ).

cnf(f_3686_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14400,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14396),sK330(U_14402,U_14400,U_14398,U_14396)),U_14398)),U_14402))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14396),U_14398),hAPP(c_Relation_ORange(U_14400,U_14396),U_14402))) ),
    inference(clausify,[status(thm)],[f_3686_5]) ).

cnf(f_3686_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14397),U_14399),hAPP(c_Relation_ORange(U_14401,U_14397),U_14403)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14401,U_14397)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14397),U_14391),U_14399)),U_14403)) ),
    inference(clausify,[status(thm)],[f_3686_5]) ).

fof(f_3687_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__insert]) ).

fof(f_3687_2,plain,
    ! [U_14408,U_14407,U_14406,U_14405,U_14404] : hAPP(c_Relation_ORange(U_14404,U_14405),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14404,U_14405)),hAPP(hAPP(c_Product__Type_OPair(U_14404,U_14405),U_14406),U_14407)),U_14408)) = hAPP(hAPP(c_Set_Oinsert(U_14405),U_14407),hAPP(c_Relation_ORange(U_14404,U_14405),U_14408)),
    inference(variable_rename,[status(thm)],[f_3687_1]) ).

fof(f_3687_3,plain,
    ! [U_14404,U_14405,U_14406,U_14407,U_14408] : hAPP(c_Relation_ORange(U_14404,U_14405),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14404,U_14405)),hAPP(hAPP(c_Product__Type_OPair(U_14404,U_14405),U_14406),U_14407)),U_14408)) = hAPP(hAPP(c_Set_Oinsert(U_14405),U_14407),hAPP(c_Relation_ORange(U_14404,U_14405),U_14408)),
    inference(definitional_conversion,[status(esa)],[f_3687_2]) ).

cnf(f_3687_4,plain,
    hAPP(c_Relation_ORange(U_14404,U_14405),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14404,U_14405)),hAPP(hAPP(c_Product__Type_OPair(U_14404,U_14405),U_14406),U_14407)),U_14408)) = hAPP(hAPP(c_Set_Oinsert(U_14405),U_14407),hAPP(c_Relation_ORange(U_14404,U_14405),U_14408)),
    inference(clausify,[status(thm)],[f_3687_3]) ).

fof(f_3688_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Range__Int__subset]) ).

fof(f_3688_2,plain,
    ! [U_14412,U_14411,U_14410,U_14409] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14409,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14410,U_14409),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14410,U_14409),tc_HOL_Obool)),U_14411),U_14412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14409,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14410,U_14409),U_14411)),hAPP(c_Relation_ORange(U_14410,U_14409),U_14412)))),
    inference(variable_rename,[status(thm)],[f_3688_1]) ).

fof(f_3688_3,plain,
    ! [U_14409,U_14410,U_14411,U_14412] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14409,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14410,U_14409),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14410,U_14409),tc_HOL_Obool)),U_14411),U_14412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14409,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14410,U_14409),U_14411)),hAPP(c_Relation_ORange(U_14410,U_14409),U_14412)))),
    inference(definitional_conversion,[status(esa)],[f_3688_2]) ).

cnf(f_3688_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14409,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14410,U_14409),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14410,U_14409),tc_HOL_Obool)),U_14411),U_14412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14409,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14410,U_14409),U_14411)),hAPP(c_Relation_ORange(U_14410,U_14409),U_14412)))),
    inference(clausify,[status(thm)],[f_3688_3]) ).

fof(f_3689_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Range__Diff__subset]) ).

fof(f_3689_2,plain,
    ! [U_14416,U_14415,U_14414,U_14413] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14413,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14413,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14414,U_14413),U_14415)),hAPP(c_Relation_ORange(U_14414,U_14413),U_14416))),hAPP(c_Relation_ORange(U_14414,U_14413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14414,U_14413),tc_HOL_Obool)),U_14415),U_14416)))),
    inference(variable_rename,[status(thm)],[f_3689_1]) ).

fof(f_3689_3,plain,
    ! [U_14413,U_14414,U_14415,U_14416] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14413,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14413,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14414,U_14413),U_14415)),hAPP(c_Relation_ORange(U_14414,U_14413),U_14416))),hAPP(c_Relation_ORange(U_14414,U_14413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14414,U_14413),tc_HOL_Obool)),U_14415),U_14416)))),
    inference(definitional_conversion,[status(esa)],[f_3689_2]) ).

cnf(f_3689_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14413,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14413,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_14414,U_14413),U_14415)),hAPP(c_Relation_ORange(U_14414,U_14413),U_14416))),hAPP(c_Relation_ORange(U_14414,U_14413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14414,U_14413),tc_HOL_Obool)),U_14415),U_14416)))),
    inference(clausify,[status(thm)],[f_3689_3]) ).

fof(f_3690_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq]) ).

fof(f_3690_2,plain,
    ! [U_14420,U_14419,U_14418,U_14417] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_14417,U_14418,hAPP(hAPP(c_COMBC(U_14417,tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14418,tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),U_14417),c_COMBC(U_14418,tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14418,tc_prod(U_14417,U_14418)),tc_fun(U_14418,tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool)),U_14417),hAPP(c_COMBB(tc_prod(U_14417,U_14418),tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool),U_14418),c_member(tc_prod(U_14417,U_14418)))),c_Product__Type_OPair(U_14417,U_14418)))),U_14419)),U_14420))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14418),U_14420),hAPP(c_Relation_ORange(U_14417,U_14418),U_14419))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_14418),U_14420),hAPP(c_Relation_ORange(U_14417,U_14418),U_14419)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14417,U_14418,hAPP(hAPP(c_COMBC(U_14417,tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14418,tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),U_14417),c_COMBC(U_14418,tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14418,tc_prod(U_14417,U_14418)),tc_fun(U_14418,tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool)),U_14417),hAPP(c_COMBB(tc_prod(U_14417,U_14418),tc_fun(tc_fun(tc_prod(U_14417,U_14418),tc_HOL_Obool),tc_HOL_Obool),U_14418),c_member(tc_prod(U_14417,U_14418)))),c_Product__Type_OPair(U_14417,U_14418)))),U_14419)),U_14420)) ) ),
    inference(variable_rename,[status(thm)],[f_3690_1]) ).

fof(f_3690_3,plain,
    ( ! [U_14428,U_14426,U_14424,U_14422] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_14422,U_14424,hAPP(hAPP(c_COMBC(U_14422,tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_fun(U_14424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14424,tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_fun(U_14424,tc_HOL_Obool)),U_14422),c_COMBC(U_14424,tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14424,tc_prod(U_14422,U_14424)),tc_fun(U_14424,tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),U_14422),hAPP(c_COMBB(tc_prod(U_14422,U_14424),tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool),U_14424),c_member(tc_prod(U_14422,U_14424)))),c_Product__Type_OPair(U_14422,U_14424)))),U_14426)),U_14428))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14424),U_14428),hAPP(c_Relation_ORange(U_14422,U_14424),U_14426))) )
    & ! [U_14427,U_14425,U_14423,U_14421] :
        ( hBOOL(hAPP(hAPP(c_member(U_14423),U_14427),hAPP(c_Relation_ORange(U_14421,U_14423),U_14425)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14421,U_14423,hAPP(hAPP(c_COMBC(U_14421,tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_fun(U_14423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14423,tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_fun(U_14423,tc_HOL_Obool)),U_14421),c_COMBC(U_14423,tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14423,tc_prod(U_14421,U_14423)),tc_fun(U_14423,tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),U_14421),hAPP(c_COMBB(tc_prod(U_14421,U_14423),tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool),U_14423),c_member(tc_prod(U_14421,U_14423)))),c_Product__Type_OPair(U_14421,U_14423)))),U_14425)),U_14427)) ) ),
    inference(miniscope,[status(thm)],[f_3690_2]) ).

fof(f_3690_4,plain,
    ( ! [U_14422,U_14424,U_14426,U_14428] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_14422,U_14424,hAPP(hAPP(c_COMBC(U_14422,tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_fun(U_14424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14424,tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_fun(U_14424,tc_HOL_Obool)),U_14422),c_COMBC(U_14424,tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14424,tc_prod(U_14422,U_14424)),tc_fun(U_14424,tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),U_14422),hAPP(c_COMBB(tc_prod(U_14422,U_14424),tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool),U_14424),c_member(tc_prod(U_14422,U_14424)))),c_Product__Type_OPair(U_14422,U_14424)))),U_14426)),U_14428))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14424),U_14428),hAPP(c_Relation_ORange(U_14422,U_14424),U_14426))) )
    & ! [U_14425,U_14427,U_14423,U_14421] :
        ( hBOOL(hAPP(hAPP(c_member(U_14423),U_14427),hAPP(c_Relation_ORange(U_14421,U_14423),U_14425)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14421,U_14423,hAPP(hAPP(c_COMBC(U_14421,tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_fun(U_14423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14423,tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_fun(U_14423,tc_HOL_Obool)),U_14421),c_COMBC(U_14423,tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14423,tc_prod(U_14421,U_14423)),tc_fun(U_14423,tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),U_14421),hAPP(c_COMBB(tc_prod(U_14421,U_14423),tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool),U_14423),c_member(tc_prod(U_14421,U_14423)))),c_Product__Type_OPair(U_14421,U_14423)))),U_14425)),U_14427)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3690_3]) ).

cnf(f_3690_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14423),U_14427),hAPP(c_Relation_ORange(U_14421,U_14423),U_14425)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14421,U_14423,hAPP(hAPP(c_COMBC(U_14421,tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_fun(U_14423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14423,tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_fun(U_14423,tc_HOL_Obool)),U_14421),c_COMBC(U_14423,tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14423,tc_prod(U_14421,U_14423)),tc_fun(U_14423,tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool)),U_14421),hAPP(c_COMBB(tc_prod(U_14421,U_14423),tc_fun(tc_fun(tc_prod(U_14421,U_14423),tc_HOL_Obool),tc_HOL_Obool),U_14423),c_member(tc_prod(U_14421,U_14423)))),c_Product__Type_OPair(U_14421,U_14423)))),U_14425)),U_14427)) ),
    inference(clausify,[status(thm)],[f_3690_4]) ).

cnf(f_3690_6,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_14422,U_14424,hAPP(hAPP(c_COMBC(U_14422,tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_fun(U_14424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14424,tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_fun(U_14424,tc_HOL_Obool)),U_14422),c_COMBC(U_14424,tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14424,tc_prod(U_14422,U_14424)),tc_fun(U_14424,tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool)),U_14422),hAPP(c_COMBB(tc_prod(U_14422,U_14424),tc_fun(tc_fun(tc_prod(U_14422,U_14424),tc_HOL_Obool),tc_HOL_Obool),U_14424),c_member(tc_prod(U_14422,U_14424)))),c_Product__Type_OPair(U_14422,U_14424)))),U_14426)),U_14428))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14424),U_14428),hAPP(c_Relation_ORange(U_14422,U_14424),U_14426))) ),
    inference(clausify,[status(thm)],[f_3690_4]) ).

fof(f_3691_1,plain,
    ! [V_r_2,T_c,V_b_2,T_b] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_RangeE]) ).

fof(f_3691_2,plain,
    ! [U_14433,U_14432,U_14431,U_14430] :
      ( ? [U_14429] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14430)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14430),U_14429),U_14431)),U_14433))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(c_Relation_ORange(U_14432,U_14430),U_14433))) ),
    inference(variable_rename,[status(thm)],[f_3691_1]) ).

fof(f_3691_3,plain,
    ! [U_14433,U_14432,U_14431,U_14430] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14430)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14430),sK331(U_14433,U_14432,U_14431,U_14430)),U_14431)),U_14433))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(c_Relation_ORange(U_14432,U_14430),U_14433))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_14429,sK331(U_14433,U_14432,U_14431,U_14430))],[f_3691_2]) ).

fof(f_3691_4,plain,
    ! [U_14430,U_14431,U_14432,U_14433] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14430)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14430),sK331(U_14433,U_14432,U_14431,U_14430)),U_14431)),U_14433))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(c_Relation_ORange(U_14432,U_14430),U_14433))) ),
    inference(definitional_conversion,[status(esa)],[f_3691_3]) ).

cnf(f_3691_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14430)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14430),sK331(U_14433,U_14432,U_14431,U_14430)),U_14431)),U_14433))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(c_Relation_ORange(U_14432,U_14430),U_14433))) ),
    inference(clausify,[status(thm)],[f_3691_4]) ).

fof(f_3692_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros]) ).

fof(f_3692_2,plain,
    ! [U_14438,U_14437,U_14436,U_14435,U_14434] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_14437,U_14438,U_14434),U_14436))
      | ~ hBOOL(hAPP(hAPP(U_14434,U_14435),U_14436)) ),
    inference(variable_rename,[status(thm)],[f_3692_1]) ).

fof(f_3692_3,plain,
    ! [U_14434,U_14436,U_14435,U_14437,U_14438] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_14437,U_14438,U_14434),U_14436))
      | ~ hBOOL(hAPP(hAPP(U_14434,U_14435),U_14436)) ),
    inference(definitional_conversion,[status(esa)],[f_3692_2]) ).

cnf(f_3692_4,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_14437,U_14438,U_14434),U_14436))
    | ~ hBOOL(hAPP(hAPP(U_14434,U_14435),U_14436)) ),
    inference(clausify,[status(thm)],[f_3692_3]) ).

fof(f_3693_1,plain,
    ! [V_a2_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
        | ! [B_a] : ~ hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) )
      & ( ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations]) ).

fof(f_3693_2,plain,
    ! [U_14444,U_14443,U_14442,U_14441] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_14441,U_14442,U_14443),U_14444))
        | ! [U_14440] : ~ hBOOL(hAPP(hAPP(U_14443,U_14440),U_14444)) )
      & ( ? [U_14439] : hBOOL(hAPP(hAPP(U_14443,U_14439),U_14444))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14441,U_14442,U_14443),U_14444)) ) ),
    inference(variable_rename,[status(thm)],[f_3693_1]) ).

fof(f_3693_3,plain,
    ( ! [U_14452,U_14450] :
        ( ! [U_14448,U_14446] : hBOOL(hAPP(c_Predicate_ORangeP(U_14446,U_14448,U_14450),U_14452))
        | ! [U_14440] : ~ hBOOL(hAPP(hAPP(U_14450,U_14440),U_14452)) )
    & ! [U_14451,U_14449] :
        ( ! [U_14447,U_14445] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14445,U_14447,U_14449),U_14451))
        | ? [U_14439] : hBOOL(hAPP(hAPP(U_14449,U_14439),U_14451)) ) ),
    inference(miniscope,[status(thm)],[f_3693_2]) ).

fof(f_3693_4,plain,
    ( ! [U_14452,U_14450] :
        ( ! [U_14448,U_14446] : hBOOL(hAPP(c_Predicate_ORangeP(U_14446,U_14448,U_14450),U_14452))
        | ! [U_14440] : ~ hBOOL(hAPP(hAPP(U_14450,U_14440),U_14452)) )
    & ! [U_14451,U_14449] :
        ( ! [U_14447,U_14445] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14445,U_14447,U_14449),U_14451))
        | hBOOL(hAPP(hAPP(U_14449,sK332(U_14451,U_14449)),U_14451)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_14439,sK332(U_14451,U_14449))],[f_3693_3]) ).

fof(f_3693_5,plain,
    ( ! [U_14452,U_14440,U_14446,U_14448,U_14450] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_14446,U_14448,U_14450),U_14452))
        | ~ hBOOL(hAPP(hAPP(U_14450,U_14440),U_14452)) )
    & ! [U_14449,U_14447,U_14445,U_14451] :
        ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14445,U_14447,U_14449),U_14451))
        | hBOOL(hAPP(hAPP(U_14449,sK332(U_14451,U_14449)),U_14451)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3693_4]) ).

cnf(f_3693_6,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_14445,U_14447,U_14449),U_14451))
    | hBOOL(hAPP(hAPP(U_14449,sK332(U_14451,U_14449)),U_14451)) ),
    inference(clausify,[status(thm)],[f_3693_5]) ).

cnf(f_3693_7,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_14446,U_14448,U_14450),U_14452))
    | ~ hBOOL(hAPP(hAPP(U_14450,U_14440),U_14452)) ),
    inference(clausify,[status(thm)],[f_3693_5]) ).

fof(f_3694_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(T_b,V_s_2)
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Un]) ).

fof(f_3694_2,plain,
    ! [U_14455,U_14454,U_14453] :
      ( c_Wellfounded_Owf(U_14453,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14453,U_14453),tc_HOL_Obool)),U_14454),U_14455))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14453,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14453,U_14453),U_14454)),hAPP(c_Relation_ORange(U_14453,U_14453),U_14455)) != c_Orderings_Obot__class_Obot(tc_fun(U_14453,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_14453,U_14455)
      | ~ c_Wellfounded_Owf(U_14453,U_14454) ),
    inference(variable_rename,[status(thm)],[f_3694_1]) ).

fof(f_3694_3,plain,
    ! [U_14453,U_14454,U_14455] :
      ( c_Wellfounded_Owf(U_14453,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14453,U_14453),tc_HOL_Obool)),U_14454),U_14455))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14453,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14453,U_14453),U_14454)),hAPP(c_Relation_ORange(U_14453,U_14453),U_14455)) != c_Orderings_Obot__class_Obot(tc_fun(U_14453,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_14453,U_14455)
      | ~ c_Wellfounded_Owf(U_14453,U_14454) ),
    inference(definitional_conversion,[status(esa)],[f_3694_2]) ).

cnf(f_3694_4,plain,
    ( c_Wellfounded_Owf(U_14453,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14453,U_14453),tc_HOL_Obool)),U_14454),U_14455))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14453,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14453,U_14453),U_14454)),hAPP(c_Relation_ORange(U_14453,U_14453),U_14455)) != c_Orderings_Obot__class_Obot(tc_fun(U_14453,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(U_14453,U_14455)
    | ~ c_Wellfounded_Owf(U_14453,U_14454) ),
    inference(clausify,[status(thm)],[f_3694_3]) ).

fof(f_3695_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_OwfP(T_b,V_r_2)
        | ~ c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Wellfounded_OwfP(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__def]) ).

fof(f_3695_2,plain,
    ! [U_14457,U_14456] :
      ( ( c_Wellfounded_OwfP(U_14456,U_14457)
        | ~ c_Wellfounded_Owf(U_14456,hAPP(c_Set_OCollect(tc_prod(U_14456,U_14456)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14456,U_14456,tc_HOL_Obool),U_14457))) )
      & ( c_Wellfounded_Owf(U_14456,hAPP(c_Set_OCollect(tc_prod(U_14456,U_14456)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14456,U_14456,tc_HOL_Obool),U_14457)))
        | ~ c_Wellfounded_OwfP(U_14456,U_14457) ) ),
    inference(variable_rename,[status(thm)],[f_3695_1]) ).

fof(f_3695_3,plain,
    ( ! [U_14461,U_14459] :
        ( c_Wellfounded_OwfP(U_14459,U_14461)
        | ~ c_Wellfounded_Owf(U_14459,hAPP(c_Set_OCollect(tc_prod(U_14459,U_14459)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14459,U_14459,tc_HOL_Obool),U_14461))) )
    & ! [U_14460,U_14458] :
        ( c_Wellfounded_Owf(U_14458,hAPP(c_Set_OCollect(tc_prod(U_14458,U_14458)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14458,U_14458,tc_HOL_Obool),U_14460)))
        | ~ c_Wellfounded_OwfP(U_14458,U_14460) ) ),
    inference(miniscope,[status(thm)],[f_3695_2]) ).

fof(f_3695_4,plain,
    ( ! [U_14459,U_14461] :
        ( c_Wellfounded_OwfP(U_14459,U_14461)
        | ~ c_Wellfounded_Owf(U_14459,hAPP(c_Set_OCollect(tc_prod(U_14459,U_14459)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14459,U_14459,tc_HOL_Obool),U_14461))) )
    & ! [U_14458,U_14460] :
        ( c_Wellfounded_Owf(U_14458,hAPP(c_Set_OCollect(tc_prod(U_14458,U_14458)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14458,U_14458,tc_HOL_Obool),U_14460)))
        | ~ c_Wellfounded_OwfP(U_14458,U_14460) ) ),
    inference(definitional_conversion,[status(esa)],[f_3695_3]) ).

cnf(f_3695_5,plain,
    ( c_Wellfounded_Owf(U_14458,hAPP(c_Set_OCollect(tc_prod(U_14458,U_14458)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14458,U_14458,tc_HOL_Obool),U_14460)))
    | ~ c_Wellfounded_OwfP(U_14458,U_14460) ),
    inference(clausify,[status(thm)],[f_3695_4]) ).

cnf(f_3695_6,plain,
    ( c_Wellfounded_OwfP(U_14459,U_14461)
    | ~ c_Wellfounded_Owf(U_14459,hAPP(c_Set_OCollect(tc_prod(U_14459,U_14459)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14459,U_14459,tc_HOL_Obool),U_14461))) ),
    inference(clausify,[status(thm)],[f_3695_4]) ).

fof(f_3696_1,plain,
    ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
    inference(fof_nnf,[status(thm)],[fact_wfP__empty]) ).

fof(f_3696_2,plain,
    ! [U_14462] : c_Wellfounded_OwfP(U_14462,hAPP(c_COMBK(tc_fun(U_14462,tc_HOL_Obool),U_14462),hAPP(c_COMBK(tc_HOL_Obool,U_14462),c_fFalse))),
    inference(variable_rename,[status(thm)],[f_3696_1]) ).

fof(f_3696_3,plain,
    ! [U_14462] : c_Wellfounded_OwfP(U_14462,hAPP(c_COMBK(tc_fun(U_14462,tc_HOL_Obool),U_14462),hAPP(c_COMBK(tc_HOL_Obool,U_14462),c_fFalse))),
    inference(definitional_conversion,[status(esa)],[f_3696_2]) ).

cnf(f_3696_4,plain,
    c_Wellfounded_OwfP(U_14462,hAPP(c_COMBK(tc_fun(U_14462,tc_HOL_Obool),U_14462),hAPP(c_COMBK(tc_HOL_Obool,U_14462),c_fFalse))),
    inference(clausify,[status(thm)],[f_3696_3]) ).

fof(f_3697_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DomainI]) ).

fof(f_3697_2,plain,
    ! [U_14467,U_14466,U_14465,U_14464,U_14463] :
      ( hBOOL(hAPP(hAPP(c_member(U_14463),U_14465),hAPP(c_Relation_ODomain(U_14463,U_14464),U_14467)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14463,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14463,U_14464),U_14465),U_14466)),U_14467)) ),
    inference(variable_rename,[status(thm)],[f_3697_1]) ).

fof(f_3697_3,plain,
    ! [U_14463,U_14464,U_14465,U_14466,U_14467] :
      ( hBOOL(hAPP(hAPP(c_member(U_14463),U_14465),hAPP(c_Relation_ODomain(U_14463,U_14464),U_14467)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14463,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14463,U_14464),U_14465),U_14466)),U_14467)) ),
    inference(definitional_conversion,[status(esa)],[f_3697_2]) ).

cnf(f_3697_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14463),U_14465),hAPP(c_Relation_ODomain(U_14463,U_14464),U_14467)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14463,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14463,U_14464),U_14465),U_14466)),U_14467)) ),
    inference(clausify,[status(thm)],[f_3697_3]) ).

fof(f_3698_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_OwfP(T_b,V_r_2)
        | ? [B_x1] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) )
      & ( ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1))
        | ~ c_Wellfounded_OwfP(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff]) ).

fof(f_3698_2,plain,
    ! [U_14471,U_14470] :
      ( ( c_Wellfounded_OwfP(U_14470,U_14471)
        | ? [U_14469] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_14470,U_14471),U_14469)) )
      & ( ! [U_14468] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_14470,U_14471),U_14468))
        | ~ c_Wellfounded_OwfP(U_14470,U_14471) ) ),
    inference(variable_rename,[status(thm)],[f_3698_1]) ).

fof(f_3698_3,plain,
    ( ! [U_14475,U_14473] :
        ( c_Wellfounded_OwfP(U_14473,U_14475)
        | ? [U_14469] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_14473,U_14475),U_14469)) )
    & ! [U_14474,U_14472] :
        ( ! [U_14468] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_14472,U_14474),U_14468))
        | ~ c_Wellfounded_OwfP(U_14472,U_14474) ) ),
    inference(miniscope,[status(thm)],[f_3698_2]) ).

fof(f_3698_4,plain,
    ( ! [U_14475,U_14473] :
        ( c_Wellfounded_OwfP(U_14473,U_14475)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_14473,U_14475),sK333(U_14475,U_14473))) )
    & ! [U_14474,U_14472] :
        ( ! [U_14468] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_14472,U_14474),U_14468))
        | ~ c_Wellfounded_OwfP(U_14472,U_14474) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_14469,sK333(U_14475,U_14473))],[f_3698_3]) ).

fof(f_3698_5,plain,
    ( ! [U_14473,U_14475] :
        ( c_Wellfounded_OwfP(U_14473,U_14475)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_14473,U_14475),sK333(U_14475,U_14473))) )
    & ! [U_14474,U_14468,U_14472] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_14472,U_14474),U_14468))
        | ~ c_Wellfounded_OwfP(U_14472,U_14474) ) ),
    inference(definitional_conversion,[status(esa)],[f_3698_4]) ).

cnf(f_3698_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_14472,U_14474),U_14468))
    | ~ c_Wellfounded_OwfP(U_14472,U_14474) ),
    inference(clausify,[status(thm)],[f_3698_5]) ).

cnf(f_3698_7,plain,
    ( c_Wellfounded_OwfP(U_14473,U_14475)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_14473,U_14475),sK333(U_14475,U_14473))) ),
    inference(clausify,[status(thm)],[f_3698_5]) ).

fof(f_3699_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2))
      | ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_accp__wfPD]) ).

fof(f_3699_2,plain,
    ! [U_14478,U_14477,U_14476] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_14476,U_14477),U_14478))
      | ~ c_Wellfounded_OwfP(U_14476,U_14477) ),
    inference(variable_rename,[status(thm)],[f_3699_1]) ).

fof(f_3699_3,plain,
    ! [U_14476,U_14477,U_14478] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_14476,U_14477),U_14478))
      | ~ c_Wellfounded_OwfP(U_14476,U_14477) ),
    inference(definitional_conversion,[status(esa)],[f_3699_2]) ).

cnf(f_3699_4,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_14476,U_14477),U_14478))
    | ~ c_Wellfounded_OwfP(U_14476,U_14477) ),
    inference(clausify,[status(thm)],[f_3699_3]) ).

fof(f_3700_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Domain__Id__on]) ).

fof(f_3700_2,plain,
    ! [U_14480,U_14479] : hAPP(c_Relation_ODomain(U_14479,U_14479),c_Relation_OId__on(U_14479,U_14480)) = U_14480,
    inference(variable_rename,[status(thm)],[f_3700_1]) ).

fof(f_3700_3,plain,
    ! [U_14479,U_14480] : hAPP(c_Relation_ODomain(U_14479,U_14479),c_Relation_OId__on(U_14479,U_14480)) = U_14480,
    inference(definitional_conversion,[status(esa)],[f_3700_2]) ).

cnf(f_3700_4,plain,
    hAPP(c_Relation_ODomain(U_14479,U_14479),c_Relation_OId__on(U_14479,U_14480)) = U_14480,
    inference(clausify,[status(thm)],[f_3700_3]) ).

fof(f_3701_1,plain,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_p_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
      | ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__subset]) ).

fof(f_3701_2,plain,
    ! [U_14483,U_14482,U_14481] :
      ( c_Wellfounded_OwfP(U_14481,U_14483)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14481,tc_fun(U_14481,tc_HOL_Obool))),U_14483),U_14482))
      | ~ c_Wellfounded_OwfP(U_14481,U_14482) ),
    inference(variable_rename,[status(thm)],[f_3701_1]) ).

fof(f_3701_3,plain,
    ! [U_14481,U_14482,U_14483] :
      ( c_Wellfounded_OwfP(U_14481,U_14483)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14481,tc_fun(U_14481,tc_HOL_Obool))),U_14483),U_14482))
      | ~ c_Wellfounded_OwfP(U_14481,U_14482) ),
    inference(definitional_conversion,[status(esa)],[f_3701_2]) ).

cnf(f_3701_4,plain,
    ( c_Wellfounded_OwfP(U_14481,U_14483)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14481,tc_fun(U_14481,tc_HOL_Obool))),U_14483),U_14482))
    | ~ c_Wellfounded_OwfP(U_14481,U_14482) ),
    inference(clausify,[status(thm)],[f_3701_3]) ).

fof(f_3702_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) )
      & ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff]) ).

fof(f_3702_2,plain,
    ! [U_14486,U_14485,U_14484] :
      ( ( hAPP(c_Relation_ODomain(U_14484,U_14485),U_14486) = c_Orderings_Obot__class_Obot(tc_fun(U_14484,tc_HOL_Obool))
        | U_14486 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14484,U_14485),tc_HOL_Obool)) )
      & ( U_14486 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14484,U_14485),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_14484,U_14485),U_14486) != c_Orderings_Obot__class_Obot(tc_fun(U_14484,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3702_1]) ).

fof(f_3702_3,plain,
    ( ! [U_14492,U_14490,U_14488] :
        ( hAPP(c_Relation_ODomain(U_14488,U_14490),U_14492) = c_Orderings_Obot__class_Obot(tc_fun(U_14488,tc_HOL_Obool))
        | U_14492 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14488,U_14490),tc_HOL_Obool)) )
    & ! [U_14491,U_14489,U_14487] :
        ( U_14491 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14487,U_14489),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_14487,U_14489),U_14491) != c_Orderings_Obot__class_Obot(tc_fun(U_14487,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3702_2]) ).

fof(f_3702_4,plain,
    ( ! [U_14488,U_14490,U_14492] :
        ( hAPP(c_Relation_ODomain(U_14488,U_14490),U_14492) = c_Orderings_Obot__class_Obot(tc_fun(U_14488,tc_HOL_Obool))
        | U_14492 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14488,U_14490),tc_HOL_Obool)) )
    & ! [U_14491,U_14489,U_14487] :
        ( U_14491 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14487,U_14489),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_14487,U_14489),U_14491) != c_Orderings_Obot__class_Obot(tc_fun(U_14487,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3702_3]) ).

cnf(f_3702_5,plain,
    ( U_14491 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14487,U_14489),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(U_14487,U_14489),U_14491) != c_Orderings_Obot__class_Obot(tc_fun(U_14487,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3702_4]) ).

cnf(f_3702_6,plain,
    ( hAPP(c_Relation_ODomain(U_14488,U_14490),U_14492) = c_Orderings_Obot__class_Obot(tc_fun(U_14488,tc_HOL_Obool))
    | U_14492 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14488,U_14490),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3702_4]) ).

fof(f_3703_1,plain,
    ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__empty]) ).

fof(f_3703_2,plain,
    ! [U_14494,U_14493] : hAPP(c_Relation_ODomain(U_14493,U_14494),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14493,U_14494),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14493,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3703_1]) ).

fof(f_3703_3,plain,
    ! [U_14493,U_14494] : hAPP(c_Relation_ODomain(U_14493,U_14494),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14493,U_14494),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14493,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3703_2]) ).

cnf(f_3703_4,plain,
    hAPP(c_Relation_ODomain(U_14493,U_14494),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14493,U_14494),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14493,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3703_3]) ).

fof(f_3704_1,plain,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__mono]) ).

fof(f_3704_2,plain,
    ! [U_14498,U_14497,U_14496,U_14495] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14495,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14495,U_14496),U_14497)),hAPP(c_Relation_ODomain(U_14495,U_14496),U_14498)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14495,U_14496),tc_HOL_Obool)),U_14497),U_14498)) ),
    inference(variable_rename,[status(thm)],[f_3704_1]) ).

fof(f_3704_3,plain,
    ! [U_14495,U_14496,U_14497,U_14498] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14495,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14495,U_14496),U_14497)),hAPP(c_Relation_ODomain(U_14495,U_14496),U_14498)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14495,U_14496),tc_HOL_Obool)),U_14497),U_14498)) ),
    inference(definitional_conversion,[status(esa)],[f_3704_2]) ).

cnf(f_3704_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14495,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14495,U_14496),U_14497)),hAPP(c_Relation_ODomain(U_14495,U_14496),U_14498)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14495,U_14496),tc_HOL_Obool)),U_14497),U_14498)) ),
    inference(clausify,[status(thm)],[f_3704_3]) ).

fof(f_3705_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Un__eq]) ).

fof(f_3705_2,plain,
    ! [U_14502,U_14501,U_14500,U_14499] : hAPP(c_Relation_ODomain(U_14499,U_14500),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14499,U_14500),tc_HOL_Obool)),U_14501),U_14502)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14499,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14499,U_14500),U_14501)),hAPP(c_Relation_ODomain(U_14499,U_14500),U_14502)),
    inference(variable_rename,[status(thm)],[f_3705_1]) ).

fof(f_3705_3,plain,
    ! [U_14499,U_14500,U_14501,U_14502] : hAPP(c_Relation_ODomain(U_14499,U_14500),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14499,U_14500),tc_HOL_Obool)),U_14501),U_14502)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14499,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14499,U_14500),U_14501)),hAPP(c_Relation_ODomain(U_14499,U_14500),U_14502)),
    inference(definitional_conversion,[status(esa)],[f_3705_2]) ).

cnf(f_3705_4,plain,
    hAPP(c_Relation_ODomain(U_14499,U_14500),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14499,U_14500),tc_HOL_Obool)),U_14501),U_14502)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14499,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14499,U_14500),U_14501)),hAPP(c_Relation_ODomain(U_14499,U_14500),U_14502)),
    inference(clausify,[status(thm)],[f_3705_3]) ).

fof(f_3706_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Domain]) ).

fof(f_3706_2,plain,
    ! [U_14505,U_14504,U_14503] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14503),hAPP(c_Relation_ODomain(U_14503,U_14504),U_14505)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14503,U_14504)),U_14505)) ),
    inference(variable_rename,[status(thm)],[f_3706_1]) ).

fof(f_3706_3,plain,
    ! [U_14503,U_14504,U_14505] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14503),hAPP(c_Relation_ODomain(U_14503,U_14504),U_14505)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14503,U_14504)),U_14505)) ),
    inference(definitional_conversion,[status(esa)],[f_3706_2]) ).

cnf(f_3706_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14503),hAPP(c_Relation_ODomain(U_14503,U_14504),U_14505)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14503,U_14504)),U_14505)) ),
    inference(clausify,[status(thm)],[f_3706_3]) ).

fof(f_3707_1,plain,
    ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_fst__eq__Domain]) ).

fof(f_3707_2,plain,
    ! [U_14508,U_14507,U_14506] : hAPP(c_Set_Oimage(tc_prod(U_14506,U_14507),U_14506,c_Product__Type_Ofst(U_14506,U_14507)),U_14508) = hAPP(c_Relation_ODomain(U_14506,U_14507),U_14508),
    inference(variable_rename,[status(thm)],[f_3707_1]) ).

fof(f_3707_3,plain,
    ! [U_14506,U_14507,U_14508] : hAPP(c_Set_Oimage(tc_prod(U_14506,U_14507),U_14506,c_Product__Type_Ofst(U_14506,U_14507)),U_14508) = hAPP(c_Relation_ODomain(U_14506,U_14507),U_14508),
    inference(definitional_conversion,[status(esa)],[f_3707_2]) ).

cnf(f_3707_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_14506,U_14507),U_14506,c_Product__Type_Ofst(U_14506,U_14507)),U_14508) = hAPP(c_Relation_ODomain(U_14506,U_14507),U_14508),
    inference(clausify,[status(thm)],[f_3707_3]) ).

fof(f_3708_1,plain,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
        | ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) )
      & ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__iff]) ).

fof(f_3708_2,plain,
    ! [U_14514,U_14513,U_14512,U_14511] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14511),U_14512),hAPP(c_Relation_ODomain(U_14511,U_14513),U_14514)))
        | ! [U_14510] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14513),U_14512),U_14510)),U_14514)) )
      & ( ? [U_14509] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14513),U_14512),U_14509)),U_14514))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14511),U_14512),hAPP(c_Relation_ODomain(U_14511,U_14513),U_14514))) ) ),
    inference(variable_rename,[status(thm)],[f_3708_1]) ).

fof(f_3708_3,plain,
    ( ! [U_14522,U_14520,U_14518,U_14516] :
        ( hBOOL(hAPP(hAPP(c_member(U_14516),U_14518),hAPP(c_Relation_ODomain(U_14516,U_14520),U_14522)))
        | ! [U_14510] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14516,U_14520)),hAPP(hAPP(c_Product__Type_OPair(U_14516,U_14520),U_14518),U_14510)),U_14522)) )
    & ! [U_14521,U_14519,U_14517,U_14515] :
        ( ? [U_14509] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14515,U_14519)),hAPP(hAPP(c_Product__Type_OPair(U_14515,U_14519),U_14517),U_14509)),U_14521))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14515),U_14517),hAPP(c_Relation_ODomain(U_14515,U_14519),U_14521))) ) ),
    inference(miniscope,[status(thm)],[f_3708_2]) ).

fof(f_3708_4,plain,
    ( ! [U_14522,U_14520,U_14518,U_14516] :
        ( hBOOL(hAPP(hAPP(c_member(U_14516),U_14518),hAPP(c_Relation_ODomain(U_14516,U_14520),U_14522)))
        | ! [U_14510] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14516,U_14520)),hAPP(hAPP(c_Product__Type_OPair(U_14516,U_14520),U_14518),U_14510)),U_14522)) )
    & ! [U_14521,U_14519,U_14517,U_14515] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14515,U_14519)),hAPP(hAPP(c_Product__Type_OPair(U_14515,U_14519),U_14517),sK334(U_14521,U_14519,U_14517,U_14515))),U_14521))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14515),U_14517),hAPP(c_Relation_ODomain(U_14515,U_14519),U_14521))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_14509,sK334(U_14521,U_14519,U_14517,U_14515))],[f_3708_3]) ).

fof(f_3708_5,plain,
    ( ! [U_14510,U_14516,U_14518,U_14520,U_14522] :
        ( hBOOL(hAPP(hAPP(c_member(U_14516),U_14518),hAPP(c_Relation_ODomain(U_14516,U_14520),U_14522)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14516,U_14520)),hAPP(hAPP(c_Product__Type_OPair(U_14516,U_14520),U_14518),U_14510)),U_14522)) )
    & ! [U_14521,U_14517,U_14515,U_14519] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14515,U_14519)),hAPP(hAPP(c_Product__Type_OPair(U_14515,U_14519),U_14517),sK334(U_14521,U_14519,U_14517,U_14515))),U_14521))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14515),U_14517),hAPP(c_Relation_ODomain(U_14515,U_14519),U_14521))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3708_4]) ).

cnf(f_3708_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14515,U_14519)),hAPP(hAPP(c_Product__Type_OPair(U_14515,U_14519),U_14517),sK334(U_14521,U_14519,U_14517,U_14515))),U_14521))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14515),U_14517),hAPP(c_Relation_ODomain(U_14515,U_14519),U_14521))) ),
    inference(clausify,[status(thm)],[f_3708_5]) ).

cnf(f_3708_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14516),U_14518),hAPP(c_Relation_ODomain(U_14516,U_14520),U_14522)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14516,U_14520)),hAPP(hAPP(c_Product__Type_OPair(U_14516,U_14520),U_14518),U_14510)),U_14522)) ),
    inference(clausify,[status(thm)],[f_3708_5]) ).

fof(f_3709_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__insert]) ).

fof(f_3709_2,plain,
    ! [U_14527,U_14526,U_14525,U_14524,U_14523] : hAPP(c_Relation_ODomain(U_14523,U_14524),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14523,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),U_14525),U_14526)),U_14527)) = hAPP(hAPP(c_Set_Oinsert(U_14523),U_14525),hAPP(c_Relation_ODomain(U_14523,U_14524),U_14527)),
    inference(variable_rename,[status(thm)],[f_3709_1]) ).

fof(f_3709_3,plain,
    ! [U_14523,U_14524,U_14525,U_14526,U_14527] : hAPP(c_Relation_ODomain(U_14523,U_14524),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14523,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),U_14525),U_14526)),U_14527)) = hAPP(hAPP(c_Set_Oinsert(U_14523),U_14525),hAPP(c_Relation_ODomain(U_14523,U_14524),U_14527)),
    inference(definitional_conversion,[status(esa)],[f_3709_2]) ).

cnf(f_3709_4,plain,
    hAPP(c_Relation_ODomain(U_14523,U_14524),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14523,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),U_14525),U_14526)),U_14527)) = hAPP(hAPP(c_Set_Oinsert(U_14523),U_14525),hAPP(c_Relation_ODomain(U_14523,U_14524),U_14527)),
    inference(clausify,[status(thm)],[f_3709_3]) ).

fof(f_3710_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Domain__Int__subset]) ).

fof(f_3710_2,plain,
    ! [U_14531,U_14530,U_14529,U_14528] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14528,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14528,U_14529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14528,U_14529),tc_HOL_Obool)),U_14530),U_14531))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14528,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14528,U_14529),U_14530)),hAPP(c_Relation_ODomain(U_14528,U_14529),U_14531)))),
    inference(variable_rename,[status(thm)],[f_3710_1]) ).

fof(f_3710_3,plain,
    ! [U_14528,U_14529,U_14530,U_14531] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14528,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14528,U_14529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14528,U_14529),tc_HOL_Obool)),U_14530),U_14531))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14528,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14528,U_14529),U_14530)),hAPP(c_Relation_ODomain(U_14528,U_14529),U_14531)))),
    inference(definitional_conversion,[status(esa)],[f_3710_2]) ).

cnf(f_3710_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14528,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14528,U_14529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14528,U_14529),tc_HOL_Obool)),U_14530),U_14531))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14528,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14528,U_14529),U_14530)),hAPP(c_Relation_ODomain(U_14528,U_14529),U_14531)))),
    inference(clausify,[status(thm)],[f_3710_3]) ).

fof(f_3711_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(f_3711_2,plain,
    ! [U_14535,U_14534,U_14533,U_14532] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14532,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14532,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14532,U_14533),U_14534)),hAPP(c_Relation_ODomain(U_14532,U_14533),U_14535))),hAPP(c_Relation_ODomain(U_14532,U_14533),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool)),U_14534),U_14535)))),
    inference(variable_rename,[status(thm)],[f_3711_1]) ).

fof(f_3711_3,plain,
    ! [U_14532,U_14533,U_14534,U_14535] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14532,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14532,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14532,U_14533),U_14534)),hAPP(c_Relation_ODomain(U_14532,U_14533),U_14535))),hAPP(c_Relation_ODomain(U_14532,U_14533),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool)),U_14534),U_14535)))),
    inference(definitional_conversion,[status(esa)],[f_3711_2]) ).

cnf(f_3711_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14532,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14532,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14532,U_14533),U_14534)),hAPP(c_Relation_ODomain(U_14532,U_14533),U_14535))),hAPP(c_Relation_ODomain(U_14532,U_14533),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool)),U_14534),U_14535)))),
    inference(clausify,[status(thm)],[f_3711_3]) ).

fof(f_3712_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__def]) ).

fof(f_3712_2,plain,
    ! [U_14537,U_14536] : hAPP(c_Relation_OField(U_14536),U_14537) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14536,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14536,U_14536),U_14537)),hAPP(c_Relation_ORange(U_14536,U_14536),U_14537)),
    inference(variable_rename,[status(thm)],[f_3712_1]) ).

fof(f_3712_3,plain,
    ! [U_14536,U_14537] : hAPP(c_Relation_OField(U_14536),U_14537) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14536,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14536,U_14536),U_14537)),hAPP(c_Relation_ORange(U_14536,U_14536),U_14537)),
    inference(definitional_conversion,[status(esa)],[f_3712_2]) ).

cnf(f_3712_4,plain,
    hAPP(c_Relation_OField(U_14536),U_14537) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14536,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14536,U_14536),U_14537)),hAPP(c_Relation_ORange(U_14536,U_14536),U_14537)),
    inference(clausify,[status(thm)],[f_3712_3]) ).

fof(f_3713_1,plain,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__in__rel]) ).

fof(f_3713_2,plain,
    ! [U_14539,U_14538] :
      ( c_Wellfounded_OwfP(U_14538,c_FunDef_Oin__rel(U_14538,U_14538,U_14539))
      | ~ c_Wellfounded_Owf(U_14538,U_14539) ),
    inference(variable_rename,[status(thm)],[f_3713_1]) ).

fof(f_3713_3,plain,
    ! [U_14539,U_14538] :
      ( c_Wellfounded_OwfP(U_14538,c_FunDef_Oin__rel(U_14538,U_14538,U_14539))
      | ~ c_Wellfounded_Owf(U_14538,U_14539) ),
    inference(definitional_conversion,[status(esa)],[f_3713_2]) ).

cnf(f_3713_4,plain,
    ( c_Wellfounded_OwfP(U_14538,c_FunDef_Oin__rel(U_14538,U_14538,U_14539))
    | ~ c_Wellfounded_Owf(U_14538,U_14539) ),
    inference(clausify,[status(thm)],[f_3713_3]) ).

fof(f_3714_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) )
      & ( c_Wellfounded_Owf(T_b,V_r_2)
        | ~ c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq]) ).

fof(f_3714_2,plain,
    ! [U_14541,U_14540] :
      ( ( c_Wellfounded_OwfP(U_14540,hAPP(hAPP(c_COMBC(U_14540,tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_fun(U_14540,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14540,tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_fun(U_14540,tc_HOL_Obool)),U_14540),c_COMBC(U_14540,tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14540,tc_prod(U_14540,U_14540)),tc_fun(U_14540,tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool)),U_14540),hAPP(c_COMBB(tc_prod(U_14540,U_14540),tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool),U_14540),c_member(tc_prod(U_14540,U_14540)))),c_Product__Type_OPair(U_14540,U_14540)))),U_14541))
        | ~ c_Wellfounded_Owf(U_14540,U_14541) )
      & ( c_Wellfounded_Owf(U_14540,U_14541)
        | ~ c_Wellfounded_OwfP(U_14540,hAPP(hAPP(c_COMBC(U_14540,tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_fun(U_14540,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14540,tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_fun(U_14540,tc_HOL_Obool)),U_14540),c_COMBC(U_14540,tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14540,tc_prod(U_14540,U_14540)),tc_fun(U_14540,tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool)),U_14540),hAPP(c_COMBB(tc_prod(U_14540,U_14540),tc_fun(tc_fun(tc_prod(U_14540,U_14540),tc_HOL_Obool),tc_HOL_Obool),U_14540),c_member(tc_prod(U_14540,U_14540)))),c_Product__Type_OPair(U_14540,U_14540)))),U_14541)) ) ),
    inference(variable_rename,[status(thm)],[f_3714_1]) ).

fof(f_3714_3,plain,
    ( ! [U_14545,U_14543] :
        ( c_Wellfounded_OwfP(U_14543,hAPP(hAPP(c_COMBC(U_14543,tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_fun(U_14543,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14543,tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_fun(U_14543,tc_HOL_Obool)),U_14543),c_COMBC(U_14543,tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14543,tc_prod(U_14543,U_14543)),tc_fun(U_14543,tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),U_14543),hAPP(c_COMBB(tc_prod(U_14543,U_14543),tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool),U_14543),c_member(tc_prod(U_14543,U_14543)))),c_Product__Type_OPair(U_14543,U_14543)))),U_14545))
        | ~ c_Wellfounded_Owf(U_14543,U_14545) )
    & ! [U_14544,U_14542] :
        ( c_Wellfounded_Owf(U_14542,U_14544)
        | ~ c_Wellfounded_OwfP(U_14542,hAPP(hAPP(c_COMBC(U_14542,tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_fun(U_14542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14542,tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_fun(U_14542,tc_HOL_Obool)),U_14542),c_COMBC(U_14542,tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14542,tc_prod(U_14542,U_14542)),tc_fun(U_14542,tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),U_14542),hAPP(c_COMBB(tc_prod(U_14542,U_14542),tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool),U_14542),c_member(tc_prod(U_14542,U_14542)))),c_Product__Type_OPair(U_14542,U_14542)))),U_14544)) ) ),
    inference(miniscope,[status(thm)],[f_3714_2]) ).

fof(f_3714_4,plain,
    ( ! [U_14545,U_14543] :
        ( c_Wellfounded_OwfP(U_14543,hAPP(hAPP(c_COMBC(U_14543,tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_fun(U_14543,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14543,tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_fun(U_14543,tc_HOL_Obool)),U_14543),c_COMBC(U_14543,tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14543,tc_prod(U_14543,U_14543)),tc_fun(U_14543,tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),U_14543),hAPP(c_COMBB(tc_prod(U_14543,U_14543),tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool),U_14543),c_member(tc_prod(U_14543,U_14543)))),c_Product__Type_OPair(U_14543,U_14543)))),U_14545))
        | ~ c_Wellfounded_Owf(U_14543,U_14545) )
    & ! [U_14544,U_14542] :
        ( c_Wellfounded_Owf(U_14542,U_14544)
        | ~ c_Wellfounded_OwfP(U_14542,hAPP(hAPP(c_COMBC(U_14542,tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_fun(U_14542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14542,tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_fun(U_14542,tc_HOL_Obool)),U_14542),c_COMBC(U_14542,tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14542,tc_prod(U_14542,U_14542)),tc_fun(U_14542,tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),U_14542),hAPP(c_COMBB(tc_prod(U_14542,U_14542),tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool),U_14542),c_member(tc_prod(U_14542,U_14542)))),c_Product__Type_OPair(U_14542,U_14542)))),U_14544)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3714_3]) ).

cnf(f_3714_5,plain,
    ( c_Wellfounded_Owf(U_14542,U_14544)
    | ~ c_Wellfounded_OwfP(U_14542,hAPP(hAPP(c_COMBC(U_14542,tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_fun(U_14542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14542,tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_fun(U_14542,tc_HOL_Obool)),U_14542),c_COMBC(U_14542,tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14542,tc_prod(U_14542,U_14542)),tc_fun(U_14542,tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool)),U_14542),hAPP(c_COMBB(tc_prod(U_14542,U_14542),tc_fun(tc_fun(tc_prod(U_14542,U_14542),tc_HOL_Obool),tc_HOL_Obool),U_14542),c_member(tc_prod(U_14542,U_14542)))),c_Product__Type_OPair(U_14542,U_14542)))),U_14544)) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

cnf(f_3714_6,plain,
    ( c_Wellfounded_OwfP(U_14543,hAPP(hAPP(c_COMBC(U_14543,tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_fun(U_14543,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14543,tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_fun(U_14543,tc_HOL_Obool)),U_14543),c_COMBC(U_14543,tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14543,tc_prod(U_14543,U_14543)),tc_fun(U_14543,tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool)),U_14543),hAPP(c_COMBB(tc_prod(U_14543,U_14543),tc_fun(tc_fun(tc_prod(U_14543,U_14543),tc_HOL_Obool),tc_HOL_Obool),U_14543),c_member(tc_prod(U_14543,U_14543)))),c_Product__Type_OPair(U_14543,U_14543)))),U_14545))
    | ~ c_Wellfounded_Owf(U_14543,U_14545) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

fof(f_3715_1,plain,
    ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).

fof(f_3715_2,plain,
    ! [U_14548,U_14547,U_14546] : hAPP(c_Relation_ODomain(U_14546,U_14547),hAPP(c_Set_OCollect(tc_prod(U_14546,U_14547)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14546,U_14547,tc_HOL_Obool),U_14548))) = hAPP(c_Set_OCollect(U_14546),hAPP(hAPP(c_COMBB(tc_fun(U_14547,tc_HOL_Obool),tc_HOL_Obool,U_14546),c_HOL_OEx(U_14547)),U_14548)),
    inference(variable_rename,[status(thm)],[f_3715_1]) ).

fof(f_3715_3,plain,
    ! [U_14546,U_14547,U_14548] : hAPP(c_Relation_ODomain(U_14546,U_14547),hAPP(c_Set_OCollect(tc_prod(U_14546,U_14547)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14546,U_14547,tc_HOL_Obool),U_14548))) = hAPP(c_Set_OCollect(U_14546),hAPP(hAPP(c_COMBB(tc_fun(U_14547,tc_HOL_Obool),tc_HOL_Obool,U_14546),c_HOL_OEx(U_14547)),U_14548)),
    inference(definitional_conversion,[status(esa)],[f_3715_2]) ).

cnf(f_3715_4,plain,
    hAPP(c_Relation_ODomain(U_14546,U_14547),hAPP(c_Set_OCollect(tc_prod(U_14546,U_14547)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14546,U_14547,tc_HOL_Obool),U_14548))) = hAPP(c_Set_OCollect(U_14546),hAPP(hAPP(c_COMBB(tc_fun(U_14547,tc_HOL_Obool),tc_HOL_Obool,U_14546),c_HOL_OEx(U_14547)),U_14548)),
    inference(clausify,[status(thm)],[f_3715_3]) ).

fof(f_3716_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq]) ).

fof(f_3716_2,plain,
    ! [U_14552,U_14551,U_14550,U_14549] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_14549,U_14550,hAPP(hAPP(c_COMBC(U_14549,tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_fun(U_14550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14550,tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_fun(U_14550,tc_HOL_Obool)),U_14549),c_COMBC(U_14550,tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14550,tc_prod(U_14549,U_14550)),tc_fun(U_14550,tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool)),U_14549),hAPP(c_COMBB(tc_prod(U_14549,U_14550),tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool),U_14550),c_member(tc_prod(U_14549,U_14550)))),c_Product__Type_OPair(U_14549,U_14550)))),U_14551)),U_14552))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14549),U_14552),hAPP(c_Relation_ODomain(U_14549,U_14550),U_14551))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_14549),U_14552),hAPP(c_Relation_ODomain(U_14549,U_14550),U_14551)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14549,U_14550,hAPP(hAPP(c_COMBC(U_14549,tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_fun(U_14550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14550,tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_fun(U_14550,tc_HOL_Obool)),U_14549),c_COMBC(U_14550,tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14550,tc_prod(U_14549,U_14550)),tc_fun(U_14550,tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool)),U_14549),hAPP(c_COMBB(tc_prod(U_14549,U_14550),tc_fun(tc_fun(tc_prod(U_14549,U_14550),tc_HOL_Obool),tc_HOL_Obool),U_14550),c_member(tc_prod(U_14549,U_14550)))),c_Product__Type_OPair(U_14549,U_14550)))),U_14551)),U_14552)) ) ),
    inference(variable_rename,[status(thm)],[f_3716_1]) ).

fof(f_3716_3,plain,
    ( ! [U_14560,U_14558,U_14556,U_14554] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_14554,U_14556,hAPP(hAPP(c_COMBC(U_14554,tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),U_14554),c_COMBC(U_14556,tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_prod(U_14554,U_14556)),tc_fun(U_14556,tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),U_14554),hAPP(c_COMBB(tc_prod(U_14554,U_14556),tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool),U_14556),c_member(tc_prod(U_14554,U_14556)))),c_Product__Type_OPair(U_14554,U_14556)))),U_14558)),U_14560))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14554),U_14560),hAPP(c_Relation_ODomain(U_14554,U_14556),U_14558))) )
    & ! [U_14559,U_14557,U_14555,U_14553] :
        ( hBOOL(hAPP(hAPP(c_member(U_14553),U_14559),hAPP(c_Relation_ODomain(U_14553,U_14555),U_14557)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14553,U_14555,hAPP(hAPP(c_COMBC(U_14553,tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_fun(U_14555,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14555,tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_fun(U_14555,tc_HOL_Obool)),U_14553),c_COMBC(U_14555,tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14555,tc_prod(U_14553,U_14555)),tc_fun(U_14555,tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),U_14553),hAPP(c_COMBB(tc_prod(U_14553,U_14555),tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool),U_14555),c_member(tc_prod(U_14553,U_14555)))),c_Product__Type_OPair(U_14553,U_14555)))),U_14557)),U_14559)) ) ),
    inference(miniscope,[status(thm)],[f_3716_2]) ).

fof(f_3716_4,plain,
    ( ! [U_14554,U_14556,U_14558,U_14560] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_14554,U_14556,hAPP(hAPP(c_COMBC(U_14554,tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),U_14554),c_COMBC(U_14556,tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_prod(U_14554,U_14556)),tc_fun(U_14556,tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),U_14554),hAPP(c_COMBB(tc_prod(U_14554,U_14556),tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool),U_14556),c_member(tc_prod(U_14554,U_14556)))),c_Product__Type_OPair(U_14554,U_14556)))),U_14558)),U_14560))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14554),U_14560),hAPP(c_Relation_ODomain(U_14554,U_14556),U_14558))) )
    & ! [U_14555,U_14559,U_14553,U_14557] :
        ( hBOOL(hAPP(hAPP(c_member(U_14553),U_14559),hAPP(c_Relation_ODomain(U_14553,U_14555),U_14557)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14553,U_14555,hAPP(hAPP(c_COMBC(U_14553,tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_fun(U_14555,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14555,tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_fun(U_14555,tc_HOL_Obool)),U_14553),c_COMBC(U_14555,tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14555,tc_prod(U_14553,U_14555)),tc_fun(U_14555,tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),U_14553),hAPP(c_COMBB(tc_prod(U_14553,U_14555),tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool),U_14555),c_member(tc_prod(U_14553,U_14555)))),c_Product__Type_OPair(U_14553,U_14555)))),U_14557)),U_14559)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3716_3]) ).

cnf(f_3716_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14553),U_14559),hAPP(c_Relation_ODomain(U_14553,U_14555),U_14557)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14553,U_14555,hAPP(hAPP(c_COMBC(U_14553,tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_fun(U_14555,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14555,tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_fun(U_14555,tc_HOL_Obool)),U_14553),c_COMBC(U_14555,tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14555,tc_prod(U_14553,U_14555)),tc_fun(U_14555,tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool)),U_14553),hAPP(c_COMBB(tc_prod(U_14553,U_14555),tc_fun(tc_fun(tc_prod(U_14553,U_14555),tc_HOL_Obool),tc_HOL_Obool),U_14555),c_member(tc_prod(U_14553,U_14555)))),c_Product__Type_OPair(U_14553,U_14555)))),U_14557)),U_14559)) ),
    inference(clausify,[status(thm)],[f_3716_4]) ).

cnf(f_3716_6,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_14554,U_14556,hAPP(hAPP(c_COMBC(U_14554,tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),U_14554),c_COMBC(U_14556,tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_prod(U_14554,U_14556)),tc_fun(U_14556,tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool)),U_14554),hAPP(c_COMBB(tc_prod(U_14554,U_14556),tc_fun(tc_fun(tc_prod(U_14554,U_14556),tc_HOL_Obool),tc_HOL_Obool),U_14556),c_member(tc_prod(U_14554,U_14556)))),c_Product__Type_OPair(U_14554,U_14556)))),U_14558)),U_14560))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14554),U_14560),hAPP(c_Relation_ODomain(U_14554,U_14556),U_14558))) ),
    inference(clausify,[status(thm)],[f_3716_4]) ).

fof(f_3717_1,plain,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DomainE]) ).

fof(f_3717_2,plain,
    ! [U_14565,U_14564,U_14563,U_14562] :
      ( ? [U_14561] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14564)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14564),U_14563),U_14561)),U_14565))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14562),U_14563),hAPP(c_Relation_ODomain(U_14562,U_14564),U_14565))) ),
    inference(variable_rename,[status(thm)],[f_3717_1]) ).

fof(f_3717_3,plain,
    ! [U_14565,U_14564,U_14563,U_14562] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14564)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14564),U_14563),sK335(U_14565,U_14564,U_14563,U_14562))),U_14565))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14562),U_14563),hAPP(c_Relation_ODomain(U_14562,U_14564),U_14565))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_14561,sK335(U_14565,U_14564,U_14563,U_14562))],[f_3717_2]) ).

fof(f_3717_4,plain,
    ! [U_14562,U_14563,U_14564,U_14565] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14564)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14564),U_14563),sK335(U_14565,U_14564,U_14563,U_14562))),U_14565))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14562),U_14563),hAPP(c_Relation_ODomain(U_14562,U_14564),U_14565))) ),
    inference(definitional_conversion,[status(esa)],[f_3717_3]) ).

cnf(f_3717_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14564)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14564),U_14563),sK335(U_14565,U_14564,U_14563,U_14562))),U_14565))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14562),U_14563),hAPP(c_Relation_ODomain(U_14562,U_14564),U_14565))) ),
    inference(clausify,[status(thm)],[f_3717_4]) ).

fof(f_3718_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros]) ).

fof(f_3718_2,plain,
    ! [U_14570,U_14569,U_14568,U_14567,U_14566] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_14569,U_14570,U_14566),U_14567))
      | ~ hBOOL(hAPP(hAPP(U_14566,U_14567),U_14568)) ),
    inference(variable_rename,[status(thm)],[f_3718_1]) ).

fof(f_3718_3,plain,
    ! [U_14566,U_14567,U_14568,U_14569,U_14570] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_14569,U_14570,U_14566),U_14567))
      | ~ hBOOL(hAPP(hAPP(U_14566,U_14567),U_14568)) ),
    inference(definitional_conversion,[status(esa)],[f_3718_2]) ).

cnf(f_3718_4,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_14569,U_14570,U_14566),U_14567))
    | ~ hBOOL(hAPP(hAPP(U_14566,U_14567),U_14568)) ),
    inference(clausify,[status(thm)],[f_3718_3]) ).

fof(f_3719_1,plain,
    ! [V_a1_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
        | ! [B_x1] : ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations]) ).

fof(f_3719_2,plain,
    ! [U_14576,U_14575,U_14574,U_14573] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_14573,U_14574,U_14575),U_14576))
        | ! [U_14572] : ~ hBOOL(hAPP(hAPP(U_14575,U_14576),U_14572)) )
      & ( ? [U_14571] : hBOOL(hAPP(hAPP(U_14575,U_14576),U_14571))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14573,U_14574,U_14575),U_14576)) ) ),
    inference(variable_rename,[status(thm)],[f_3719_1]) ).

fof(f_3719_3,plain,
    ( ! [U_14584,U_14582] :
        ( ! [U_14580,U_14578] : hBOOL(hAPP(c_Predicate_ODomainP(U_14578,U_14580,U_14582),U_14584))
        | ! [U_14572] : ~ hBOOL(hAPP(hAPP(U_14582,U_14584),U_14572)) )
    & ! [U_14583,U_14581] :
        ( ! [U_14579,U_14577] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14577,U_14579,U_14581),U_14583))
        | ? [U_14571] : hBOOL(hAPP(hAPP(U_14581,U_14583),U_14571)) ) ),
    inference(miniscope,[status(thm)],[f_3719_2]) ).

fof(f_3719_4,plain,
    ( ! [U_14584,U_14582] :
        ( ! [U_14580,U_14578] : hBOOL(hAPP(c_Predicate_ODomainP(U_14578,U_14580,U_14582),U_14584))
        | ! [U_14572] : ~ hBOOL(hAPP(hAPP(U_14582,U_14584),U_14572)) )
    & ! [U_14583,U_14581] :
        ( ! [U_14579,U_14577] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14577,U_14579,U_14581),U_14583))
        | hBOOL(hAPP(hAPP(U_14581,U_14583),sK336(U_14583,U_14581))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_14571,sK336(U_14583,U_14581))],[f_3719_3]) ).

fof(f_3719_5,plain,
    ( ! [U_14584,U_14572,U_14578,U_14580,U_14582] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_14578,U_14580,U_14582),U_14584))
        | ~ hBOOL(hAPP(hAPP(U_14582,U_14584),U_14572)) )
    & ! [U_14581,U_14579,U_14577,U_14583] :
        ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14577,U_14579,U_14581),U_14583))
        | hBOOL(hAPP(hAPP(U_14581,U_14583),sK336(U_14583,U_14581))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3719_4]) ).

cnf(f_3719_6,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14577,U_14579,U_14581),U_14583))
    | hBOOL(hAPP(hAPP(U_14581,U_14583),sK336(U_14583,U_14581))) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

cnf(f_3719_7,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_14578,U_14580,U_14582),U_14584))
    | ~ hBOOL(hAPP(hAPP(U_14582,U_14584),U_14572)) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

fof(f_3720_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
      | ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP]) ).

fof(f_3720_2,plain,
    ! [U_14586,U_14585] :
      ( c_Wellfounded_Oacyclic(U_14585,hAPP(c_Set_OCollect(tc_prod(U_14585,U_14585)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14585,U_14585,tc_HOL_Obool),U_14586)))
      | ~ c_Wellfounded_OwfP(U_14585,U_14586) ),
    inference(variable_rename,[status(thm)],[f_3720_1]) ).

fof(f_3720_3,plain,
    ! [U_14585,U_14586] :
      ( c_Wellfounded_Oacyclic(U_14585,hAPP(c_Set_OCollect(tc_prod(U_14585,U_14585)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14585,U_14585,tc_HOL_Obool),U_14586)))
      | ~ c_Wellfounded_OwfP(U_14585,U_14586) ),
    inference(definitional_conversion,[status(esa)],[f_3720_2]) ).

cnf(f_3720_4,plain,
    ( c_Wellfounded_Oacyclic(U_14585,hAPP(c_Set_OCollect(tc_prod(U_14585,U_14585)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14585,U_14585,tc_HOL_Obool),U_14586)))
    | ~ c_Wellfounded_OwfP(U_14585,U_14586) ),
    inference(clausify,[status(thm)],[f_3720_3]) ).

fof(f_3721_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(f_3721_2,plain,
    ! [U_14591,U_14590,U_14589,U_14588] :
      ( ? [U_14587] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),hAPP(c_Set_OCollect(U_14588),hAPP(hAPP(c_COMBS(U_14588,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14588),c_fconj),hAPP(hAPP(c_COMBC(U_14588,tc_fun(U_14588,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14588)),U_14589))),hAPP(hAPP(c_COMBC(U_14588,U_14590,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14590,tc_fun(U_14590,tc_HOL_Obool),U_14588),c_fequal),U_14591)),hAPP(U_14591,U_14587))))))
          & hBOOL(hAPP(hAPP(c_member(U_14588),U_14587),U_14589)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14590),hAPP(c_Set_Oimage(U_14588,U_14590,U_14591),U_14589)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),U_14589)) ),
    inference(variable_rename,[status(thm)],[f_3721_1]) ).

fof(f_3721_3,plain,
    ! [U_14591,U_14590,U_14589,U_14588] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),hAPP(c_Set_OCollect(U_14588),hAPP(hAPP(c_COMBS(U_14588,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14588),c_fconj),hAPP(hAPP(c_COMBC(U_14588,tc_fun(U_14588,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14588)),U_14589))),hAPP(hAPP(c_COMBC(U_14588,U_14590,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14590,tc_fun(U_14590,tc_HOL_Obool),U_14588),c_fequal),U_14591)),hAPP(U_14591,sK337(U_14591,U_14590,U_14589,U_14588)))))))
        & hBOOL(hAPP(hAPP(c_member(U_14588),sK337(U_14591,U_14590,U_14589,U_14588)),U_14589)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14590),hAPP(c_Set_Oimage(U_14588,U_14590,U_14591),U_14589)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),U_14589)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_14587,sK337(U_14591,U_14590,U_14589,U_14588))],[f_3721_2]) ).

fof(f_3721_4,plain,
    ( ! [U_14588,U_14589,U_14590,U_14591] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),hAPP(c_Set_OCollect(U_14588),hAPP(hAPP(c_COMBS(U_14588,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14588),c_fconj),hAPP(hAPP(c_COMBC(U_14588,tc_fun(U_14588,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14588)),U_14589))),hAPP(hAPP(c_COMBC(U_14588,U_14590,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14590,tc_fun(U_14590,tc_HOL_Obool),U_14588),c_fequal),U_14591)),hAPP(U_14591,sK337(U_14591,U_14590,U_14589,U_14588)))))))
        | ~ sP1002(U_14588,U_14589,U_14590,U_14591) )
    & ! [U_14588,U_14589,U_14590,U_14591] :
        ( hBOOL(hAPP(hAPP(c_member(U_14588),sK337(U_14591,U_14590,U_14589,U_14588)),U_14589))
        | ~ sP1002(U_14588,U_14589,U_14590,U_14591) )
    & ! [U_14588,U_14589,U_14590,U_14591] :
        ( sP1002(U_14588,U_14589,U_14590,U_14591)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14590),hAPP(c_Set_Oimage(U_14588,U_14590,U_14591),U_14589)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),U_14589)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1002])],[f_3721_3]) ).

cnf(f_3721_5,plain,
    ( sP1002(U_14588,U_14589,U_14590,U_14591)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14590),hAPP(c_Set_Oimage(U_14588,U_14590,U_14591),U_14589)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),U_14589)) ),
    inference(clausify,[status(thm)],[f_3721_4]) ).

cnf(f_3721_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14588),sK337(U_14591,U_14590,U_14589,U_14588)),U_14589))
    | ~ sP1002(U_14588,U_14589,U_14590,U_14591) ),
    inference(clausify,[status(thm)],[f_3721_4]) ).

cnf(f_3721_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14588),hAPP(c_Set_OCollect(U_14588),hAPP(hAPP(c_COMBS(U_14588,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14588),c_fconj),hAPP(hAPP(c_COMBC(U_14588,tc_fun(U_14588,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14588)),U_14589))),hAPP(hAPP(c_COMBC(U_14588,U_14590,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14590,tc_fun(U_14590,tc_HOL_Obool),U_14588),c_fequal),U_14591)),hAPP(U_14591,sK337(U_14591,U_14590,U_14589,U_14588)))))))
    | ~ sP1002(U_14588,U_14589,U_14590,U_14591) ),
    inference(clausify,[status(thm)],[f_3721_4]) ).

fof(f_3722_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__acyclic]) ).

fof(f_3722_2,plain,
    ! [U_14593,U_14592] :
      ( c_Wellfounded_Oacyclic(U_14592,U_14593)
      | ~ c_Wellfounded_Owf(U_14592,U_14593) ),
    inference(variable_rename,[status(thm)],[f_3722_1]) ).

fof(f_3722_3,plain,
    ! [U_14592,U_14593] :
      ( c_Wellfounded_Oacyclic(U_14592,U_14593)
      | ~ c_Wellfounded_Owf(U_14592,U_14593) ),
    inference(definitional_conversion,[status(esa)],[f_3722_2]) ).

cnf(f_3722_4,plain,
    ( c_Wellfounded_Oacyclic(U_14592,U_14593)
    | ~ c_Wellfounded_Owf(U_14592,U_14593) ),
    inference(clausify,[status(thm)],[f_3722_3]) ).

fof(f_3723_1,plain,
    ! [V_r_2,V_s_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Wellfounded_Oacyclic(T_b,V_s_2) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__subset]) ).

fof(f_3723_2,plain,
    ! [U_14596,U_14595,U_14594] :
      ( c_Wellfounded_Oacyclic(U_14594,U_14596)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14594,U_14594),tc_HOL_Obool)),U_14596),U_14595))
      | ~ c_Wellfounded_Oacyclic(U_14594,U_14595) ),
    inference(variable_rename,[status(thm)],[f_3723_1]) ).

fof(f_3723_3,plain,
    ! [U_14596,U_14595,U_14594] :
      ( c_Wellfounded_Oacyclic(U_14594,U_14596)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14594,U_14594),tc_HOL_Obool)),U_14596),U_14595))
      | ~ c_Wellfounded_Oacyclic(U_14594,U_14595) ),
    inference(definitional_conversion,[status(esa)],[f_3723_2]) ).

cnf(f_3723_4,plain,
    ( c_Wellfounded_Oacyclic(U_14594,U_14596)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14594,U_14594),tc_HOL_Obool)),U_14596),U_14595))
    | ~ c_Wellfounded_Oacyclic(U_14594,U_14595) ),
    inference(clausify,[status(thm)],[f_3723_3]) ).

fof(f_3724_1,plain,
    ! [V_r_2,T_b] :
      ( ( ( c_Wellfounded_Owf(T_b,V_r_2)
          | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
        & ( c_Wellfounded_Oacyclic(T_b,V_r_2)
          | ~ c_Wellfounded_Owf(T_b,V_r_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite]) ).

fof(f_3724_2,plain,
    ! [U_14598,U_14597] :
      ( ( ( c_Wellfounded_Owf(U_14597,U_14598)
          | ~ c_Wellfounded_Oacyclic(U_14597,U_14598) )
        & ( c_Wellfounded_Oacyclic(U_14597,U_14598)
          | ~ c_Wellfounded_Owf(U_14597,U_14598) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14597,U_14597)),U_14598)) ),
    inference(variable_rename,[status(thm)],[f_3724_1]) ).

fof(f_3724_3,plain,
    ( ! [U_14598,U_14597] :
        ( c_Wellfounded_Owf(U_14597,U_14598)
        | ~ c_Wellfounded_Oacyclic(U_14597,U_14598)
        | ~ sP1003(U_14598,U_14597) )
    & ! [U_14598,U_14597] :
        ( c_Wellfounded_Oacyclic(U_14597,U_14598)
        | ~ c_Wellfounded_Owf(U_14597,U_14598)
        | ~ sP1003(U_14598,U_14597) )
    & ! [U_14598,U_14597] :
        ( sP1003(U_14598,U_14597)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14597,U_14597)),U_14598)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1003])],[f_3724_2]) ).

cnf(f_3724_4,plain,
    ( sP1003(U_14598,U_14597)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14597,U_14597)),U_14598)) ),
    inference(clausify,[status(thm)],[f_3724_3]) ).

cnf(f_3724_5,plain,
    ( c_Wellfounded_Oacyclic(U_14597,U_14598)
    | ~ c_Wellfounded_Owf(U_14597,U_14598)
    | ~ sP1003(U_14598,U_14597) ),
    inference(clausify,[status(thm)],[f_3724_3]) ).

cnf(f_3724_6,plain,
    ( c_Wellfounded_Owf(U_14597,U_14598)
    | ~ c_Wellfounded_Oacyclic(U_14597,U_14598)
    | ~ sP1003(U_14598,U_14597) ),
    inference(clausify,[status(thm)],[f_3724_3]) ).

fof(f_3725_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
      | ~ c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf]) ).

fof(f_3725_2,plain,
    ! [U_14600,U_14599] :
      ( c_Wellfounded_Owf(U_14599,U_14600)
      | ~ c_Wellfounded_Oacyclic(U_14599,U_14600)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14599,U_14599)),U_14600)) ),
    inference(variable_rename,[status(thm)],[f_3725_1]) ).

fof(f_3725_3,plain,
    ! [U_14600,U_14599] :
      ( c_Wellfounded_Owf(U_14599,U_14600)
      | ~ c_Wellfounded_Oacyclic(U_14599,U_14600)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14599,U_14599)),U_14600)) ),
    inference(definitional_conversion,[status(esa)],[f_3725_2]) ).

cnf(f_3725_4,plain,
    ( c_Wellfounded_Owf(U_14599,U_14600)
    | ~ c_Wellfounded_Oacyclic(U_14599,U_14600)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14599,U_14599)),U_14600)) ),
    inference(clausify,[status(thm)],[f_3725_3]) ).

fof(f_3726_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Nitpick_Owf_H(T_b,V_r_2)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
          & c_Wellfounded_Oacyclic(T_b,V_r_2) )
        | ~ c_Nitpick_Owf_H(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def]) ).

fof(f_3726_2,plain,
    ! [U_14602,U_14601] :
      ( ( c_Nitpick_Owf_H(U_14601,U_14602)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14601,U_14601)),U_14602)) )
        | ~ c_Wellfounded_Oacyclic(U_14601,U_14602) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14601,U_14601)),U_14602)) )
          & c_Wellfounded_Oacyclic(U_14601,U_14602) )
        | ~ c_Nitpick_Owf_H(U_14601,U_14602) ) ),
    inference(variable_rename,[status(thm)],[f_3726_1]) ).

fof(f_3726_3,plain,
    ( ! [U_14606,U_14604] :
        ( c_Nitpick_Owf_H(U_14604,U_14606)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14604,U_14604)),U_14606)) )
        | ~ c_Wellfounded_Oacyclic(U_14604,U_14606) )
    & ! [U_14605,U_14603] :
        ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14603,U_14603)),U_14605)) )
          & c_Wellfounded_Oacyclic(U_14603,U_14605) )
        | ~ c_Nitpick_Owf_H(U_14603,U_14605) ) ),
    inference(miniscope,[status(thm)],[f_3726_2]) ).

fof(f_3726_4,plain,
    ( ! [U_14606,U_14604] :
        ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ sP1005(U_14606,U_14604) )
    & ! [U_14606,U_14604] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14604,U_14604)),U_14606))
        | ~ sP1005(U_14606,U_14604) )
    & ! [U_14603,U_14605] :
        ( c_Nitpick_Ounknown(tc_HOL_Obool)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14603,U_14603)),U_14605))
        | ~ sP1004(U_14603,U_14605) )
    & ! [U_14603,U_14605] :
        ( c_Wellfounded_Oacyclic(U_14603,U_14605)
        | ~ sP1004(U_14603,U_14605) )
    & ! [U_14606,U_14604] :
        ( c_Nitpick_Owf_H(U_14604,U_14606)
        | sP1005(U_14606,U_14604)
        | ~ c_Wellfounded_Oacyclic(U_14604,U_14606) )
    & ! [U_14603,U_14605] :
        ( sP1004(U_14603,U_14605)
        | ~ c_Nitpick_Owf_H(U_14603,U_14605) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1004,sP1005])],[f_3726_3]) ).

cnf(f_3726_5,plain,
    ( sP1004(U_14603,U_14605)
    | ~ c_Nitpick_Owf_H(U_14603,U_14605) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_6,plain,
    ( c_Nitpick_Owf_H(U_14604,U_14606)
    | sP1005(U_14606,U_14604)
    | ~ c_Wellfounded_Oacyclic(U_14604,U_14606) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_7,plain,
    ( c_Wellfounded_Oacyclic(U_14603,U_14605)
    | ~ sP1004(U_14603,U_14605) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_8,plain,
    ( c_Nitpick_Ounknown(tc_HOL_Obool)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14603,U_14603)),U_14605))
    | ~ sP1004(U_14603,U_14605) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14604,U_14604)),U_14606))
    | ~ sP1005(U_14606,U_14604) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_10,plain,
    ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ sP1005(U_14606,U_14604) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

fof(f_3727_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__def_H]) ).

fof(f_3727_2,plain,
    ! [U_14613,U_14612,U_14611] :
      ( ( c_Relation_Orefl__on(U_14611,U_14612,U_14613)
        | ? [U_14610] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14611,U_14611)),hAPP(hAPP(c_Product__Type_OPair(U_14611,U_14611),U_14610),U_14610)),U_14613))
            & hBOOL(hAPP(hAPP(c_member(U_14611),U_14610),U_14612)) )
        | ? [U_14609] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14611,U_14611,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14611,tc_fun(U_14611,tc_HOL_Obool),tc_fun(U_14611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14611,tc_HOL_Obool),tc_fun(U_14611,tc_HOL_Obool)),U_14611),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14611),c_fconj),hAPP(hAPP(c_COMBC(U_14611,tc_fun(U_14611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14611)),U_14612)))),hAPP(hAPP(c_COMBC(U_14611,tc_fun(U_14611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14611)),U_14612))),U_14609))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14611,U_14611)),U_14609),U_14613)) ) )
      & ( ( ! [U_14608] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14611,U_14611)),hAPP(hAPP(c_Product__Type_OPair(U_14611,U_14611),U_14608),U_14608)),U_14613))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14611),U_14608),U_14612)) )
          & ! [U_14607] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14611,U_14611,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14611,tc_fun(U_14611,tc_HOL_Obool),tc_fun(U_14611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14611,tc_HOL_Obool),tc_fun(U_14611,tc_HOL_Obool)),U_14611),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14611),c_fconj),hAPP(hAPP(c_COMBC(U_14611,tc_fun(U_14611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14611)),U_14612)))),hAPP(hAPP(c_COMBC(U_14611,tc_fun(U_14611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14611)),U_14612))),U_14607))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14611,U_14611)),U_14607),U_14613)) ) )
        | ~ c_Relation_Orefl__on(U_14611,U_14612,U_14613) ) ),
    inference(variable_rename,[status(thm)],[f_3727_1]) ).

fof(f_3727_3,plain,
    ( ! [U_14619,U_14617,U_14615] :
        ( c_Relation_Orefl__on(U_14615,U_14617,U_14619)
        | ? [U_14610] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),hAPP(hAPP(c_Product__Type_OPair(U_14615,U_14615),U_14610),U_14610)),U_14619))
            & hBOOL(hAPP(hAPP(c_member(U_14615),U_14610),U_14617)) )
        | ? [U_14609] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14615,U_14615,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),U_14615),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14615)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14615),c_fconj),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617)))),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617))),U_14609))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),U_14609),U_14619)) ) )
    & ! [U_14618,U_14616,U_14614] :
        ( ( ! [U_14608] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),hAPP(hAPP(c_Product__Type_OPair(U_14614,U_14614),U_14608),U_14608)),U_14618))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14614),U_14608),U_14616)) )
          & ! [U_14607] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14614,U_14614,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),U_14614),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14614)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14614),c_fconj),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616)))),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616))),U_14607))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),U_14607),U_14618)) ) )
        | ~ c_Relation_Orefl__on(U_14614,U_14616,U_14618) ) ),
    inference(miniscope,[status(thm)],[f_3727_2]) ).

fof(f_3727_4,plain,
    ( ! [U_14619,U_14617,U_14615] :
        ( c_Relation_Orefl__on(U_14615,U_14617,U_14619)
        | ? [U_14610] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),hAPP(hAPP(c_Product__Type_OPair(U_14615,U_14615),U_14610),U_14610)),U_14619))
            & hBOOL(hAPP(hAPP(c_member(U_14615),U_14610),U_14617)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14615,U_14615,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),U_14615),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14615)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14615),c_fconj),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617)))),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617))),sK338(U_14619,U_14617,U_14615)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),sK338(U_14619,U_14617,U_14615)),U_14619)) ) )
    & ! [U_14618,U_14616,U_14614] :
        ( ( ! [U_14608] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),hAPP(hAPP(c_Product__Type_OPair(U_14614,U_14614),U_14608),U_14608)),U_14618))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14614),U_14608),U_14616)) )
          & ! [U_14607] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14614,U_14614,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),U_14614),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14614)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14614),c_fconj),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616)))),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616))),U_14607))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),U_14607),U_14618)) ) )
        | ~ c_Relation_Orefl__on(U_14614,U_14616,U_14618) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_14609,sK338(U_14619,U_14617,U_14615))],[f_3727_3]) ).

fof(f_3727_5,plain,
    ( ! [U_14619,U_14617,U_14615] :
        ( c_Relation_Orefl__on(U_14615,U_14617,U_14619)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),hAPP(hAPP(c_Product__Type_OPair(U_14615,U_14615),sK339(U_14619,U_14617,U_14615)),sK339(U_14619,U_14617,U_14615))),U_14619))
          & hBOOL(hAPP(hAPP(c_member(U_14615),sK339(U_14619,U_14617,U_14615)),U_14617)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14615,U_14615,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),U_14615),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14615)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14615),c_fconj),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617)))),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617))),sK338(U_14619,U_14617,U_14615)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),sK338(U_14619,U_14617,U_14615)),U_14619)) ) )
    & ! [U_14618,U_14616,U_14614] :
        ( ( ! [U_14608] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),hAPP(hAPP(c_Product__Type_OPair(U_14614,U_14614),U_14608),U_14608)),U_14618))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14614),U_14608),U_14616)) )
          & ! [U_14607] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14614,U_14614,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),U_14614),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14614)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14614),c_fconj),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616)))),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616))),U_14607))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),U_14607),U_14618)) ) )
        | ~ c_Relation_Orefl__on(U_14614,U_14616,U_14618) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_14610,sK339(U_14619,U_14617,U_14615))],[f_3727_4]) ).

fof(f_3727_6,plain,
    ( ! [U_14615,U_14617,U_14619] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),hAPP(hAPP(c_Product__Type_OPair(U_14615,U_14615),sK339(U_14619,U_14617,U_14615)),sK339(U_14619,U_14617,U_14615))),U_14619))
        | ~ sP1008(U_14615,U_14617,U_14619) )
    & ! [U_14615,U_14617,U_14619] :
        ( hBOOL(hAPP(hAPP(c_member(U_14615),sK339(U_14619,U_14617,U_14615)),U_14617))
        | ~ sP1008(U_14615,U_14617,U_14619) )
    & ! [U_14615,U_14617,U_14619] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14615,U_14615,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),U_14615),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14615)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14615),c_fconj),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617)))),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617))),sK338(U_14619,U_14617,U_14615)))
        | ~ sP1007(U_14615,U_14617,U_14619) )
    & ! [U_14615,U_14617,U_14619] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),sK338(U_14619,U_14617,U_14615)),U_14619))
        | ~ sP1007(U_14615,U_14617,U_14619) )
    & ! [U_14608,U_14607,U_14618,U_14614,U_14616] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),hAPP(hAPP(c_Product__Type_OPair(U_14614,U_14614),U_14608),U_14608)),U_14618))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14614),U_14608),U_14616))
        | ~ sP1006(U_14608,U_14607,U_14618,U_14614,U_14616) )
    & ! [U_14608,U_14607,U_14618,U_14614,U_14616] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14614,U_14614,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),U_14614),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14614)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14614),c_fconj),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616)))),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616))),U_14607))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),U_14607),U_14618))
        | ~ sP1006(U_14608,U_14607,U_14618,U_14614,U_14616) )
    & ! [U_14615,U_14617,U_14619] :
        ( c_Relation_Orefl__on(U_14615,U_14617,U_14619)
        | sP1008(U_14615,U_14617,U_14619)
        | sP1007(U_14615,U_14617,U_14619) )
    & ! [U_14608,U_14607,U_14618,U_14614,U_14616] :
        ( sP1006(U_14608,U_14607,U_14618,U_14614,U_14616)
        | ~ c_Relation_Orefl__on(U_14614,U_14616,U_14618) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1006,sP1007,sP1008])],[f_3727_5]) ).

cnf(f_3727_7,plain,
    ( sP1006(U_14608,U_14607,U_14618,U_14614,U_14616)
    | ~ c_Relation_Orefl__on(U_14614,U_14616,U_14618) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_8,plain,
    ( c_Relation_Orefl__on(U_14615,U_14617,U_14619)
    | sP1008(U_14615,U_14617,U_14619)
    | sP1007(U_14615,U_14617,U_14619) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14614,U_14614,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14614,tc_HOL_Obool),tc_fun(U_14614,tc_HOL_Obool)),U_14614),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14614)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14614),c_fconj),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616)))),hAPP(hAPP(c_COMBC(U_14614,tc_fun(U_14614,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14614)),U_14616))),U_14607))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),U_14607),U_14618))
    | ~ sP1006(U_14608,U_14607,U_14618,U_14614,U_14616) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14614,U_14614)),hAPP(hAPP(c_Product__Type_OPair(U_14614,U_14614),U_14608),U_14608)),U_14618))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14614),U_14608),U_14616))
    | ~ sP1006(U_14608,U_14607,U_14618,U_14614,U_14616) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),sK338(U_14619,U_14617,U_14615)),U_14619))
    | ~ sP1007(U_14615,U_14617,U_14619) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14615,U_14615,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14615,tc_HOL_Obool),tc_fun(U_14615,tc_HOL_Obool)),U_14615),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14615)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14615),c_fconj),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617)))),hAPP(hAPP(c_COMBC(U_14615,tc_fun(U_14615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14615)),U_14617))),sK338(U_14619,U_14617,U_14615)))
    | ~ sP1007(U_14615,U_14617,U_14619) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14615),sK339(U_14619,U_14617,U_14615)),U_14617))
    | ~ sP1008(U_14615,U_14617,U_14619) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14615,U_14615)),hAPP(hAPP(c_Product__Type_OPair(U_14615,U_14615),sK339(U_14619,U_14617,U_14615)),sK339(U_14619,U_14617,U_14615))),U_14619))
    | ~ sP1008(U_14615,U_14617,U_14619) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

fof(f_3728_1,plain,
    ! [V_P_2,T_b,B_x] :
      ( hBOOL(hAPP(V_P_2,B_x))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_ball__empty]) ).

fof(f_3728_2,plain,
    ! [U_14622,U_14621,U_14620] :
      ( hBOOL(hAPP(U_14622,U_14620))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14621),U_14620),c_Orderings_Obot__class_Obot(tc_fun(U_14621,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3728_1]) ).

fof(f_3728_3,plain,
    ! [U_14621,U_14620,U_14622] :
      ( hBOOL(hAPP(U_14622,U_14620))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14621),U_14620),c_Orderings_Obot__class_Obot(tc_fun(U_14621,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3728_2]) ).

cnf(f_3728_4,plain,
    ( hBOOL(hAPP(U_14622,U_14620))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14621),U_14620),c_Orderings_Obot__class_Obot(tc_fun(U_14621,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3728_3]) ).

fof(f_3729_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_A_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_A_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__def]) ).

fof(f_3729_2,plain,
    ! [U_14627,U_14626,U_14625] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_14625,U_14626),U_14627))
        | ? [U_14624] :
            ( ~ hBOOL(hAPP(U_14626,U_14624))
            & hBOOL(hAPP(hAPP(c_member(U_14625),U_14624),U_14627)) ) )
      & ( ! [U_14623] :
            ( hBOOL(hAPP(U_14626,U_14623))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14625),U_14623),U_14627)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14625,U_14626),U_14627)) ) ),
    inference(variable_rename,[status(thm)],[f_3729_1]) ).

fof(f_3729_3,plain,
    ( ! [U_14633,U_14631,U_14629] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_14629,U_14631),U_14633))
        | ? [U_14624] :
            ( ~ hBOOL(hAPP(U_14631,U_14624))
            & hBOOL(hAPP(hAPP(c_member(U_14629),U_14624),U_14633)) ) )
    & ! [U_14632,U_14630,U_14628] :
        ( ! [U_14623] :
            ( hBOOL(hAPP(U_14630,U_14623))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14628),U_14623),U_14632)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14628,U_14630),U_14632)) ) ),
    inference(miniscope,[status(thm)],[f_3729_2]) ).

fof(f_3729_4,plain,
    ( ! [U_14633,U_14631,U_14629] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_14629,U_14631),U_14633))
        | ( ~ hBOOL(hAPP(U_14631,sK340(U_14633,U_14631,U_14629)))
          & hBOOL(hAPP(hAPP(c_member(U_14629),sK340(U_14633,U_14631,U_14629)),U_14633)) ) )
    & ! [U_14632,U_14630,U_14628] :
        ( ! [U_14623] :
            ( hBOOL(hAPP(U_14630,U_14623))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14628),U_14623),U_14632)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14628,U_14630),U_14632)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_14624,sK340(U_14633,U_14631,U_14629))],[f_3729_3]) ).

fof(f_3729_5,plain,
    ( ! [U_14631,U_14629,U_14633] :
        ( ~ hBOOL(hAPP(U_14631,sK340(U_14633,U_14631,U_14629)))
        | ~ sP1009(U_14631,U_14629,U_14633) )
    & ! [U_14631,U_14629,U_14633] :
        ( hBOOL(hAPP(hAPP(c_member(U_14629),sK340(U_14633,U_14631,U_14629)),U_14633))
        | ~ sP1009(U_14631,U_14629,U_14633) )
    & ! [U_14631,U_14629,U_14633] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_14629,U_14631),U_14633))
        | sP1009(U_14631,U_14629,U_14633) )
    & ! [U_14630,U_14632,U_14623,U_14628] :
        ( hBOOL(hAPP(U_14630,U_14623))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14628),U_14623),U_14632))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14628,U_14630),U_14632)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1009])],[f_3729_4]) ).

cnf(f_3729_6,plain,
    ( hBOOL(hAPP(U_14630,U_14623))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14628),U_14623),U_14632))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14628,U_14630),U_14632)) ),
    inference(clausify,[status(thm)],[f_3729_5]) ).

cnf(f_3729_7,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_14629,U_14631),U_14633))
    | sP1009(U_14631,U_14629,U_14633) ),
    inference(clausify,[status(thm)],[f_3729_5]) ).

cnf(f_3729_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14629),sK340(U_14633,U_14631,U_14629)),U_14633))
    | ~ sP1009(U_14631,U_14629,U_14633) ),
    inference(clausify,[status(thm)],[f_3729_5]) ).

cnf(f_3729_9,plain,
    ( ~ hBOOL(hAPP(U_14631,sK340(U_14633,U_14631,U_14629)))
    | ~ sP1009(U_14631,U_14629,U_14633) ),
    inference(clausify,[status(thm)],[f_3729_5]) ).

fof(f_3730_1,plain,
    ! [V_f_2,V_r_2,T_c,T_b] :
      ( ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) )
        | ~ c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_congruent__def]) ).

fof(f_3730_2,plain,
    ! [U_14639,U_14638,U_14637,U_14636] :
      ( ( c_Equiv__Relations_Ocongruent(U_14636,U_14637,U_14638,U_14639)
        | ? [U_14635] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14636,U_14636,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14636,tc_fun(U_14636,U_14637),tc_fun(U_14636,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14637,tc_HOL_Obool),tc_fun(tc_fun(U_14636,U_14637),tc_fun(U_14636,tc_HOL_Obool)),U_14636),c_COMBB(U_14637,tc_HOL_Obool,U_14636)),hAPP(hAPP(c_COMBB(U_14637,tc_fun(U_14637,tc_HOL_Obool),U_14636),c_fequal),U_14639))),U_14639)),U_14635))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14636,U_14636)),U_14635),U_14638)) ) )
      & ( ! [U_14634] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14636,U_14636,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14636,tc_fun(U_14636,U_14637),tc_fun(U_14636,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14637,tc_HOL_Obool),tc_fun(tc_fun(U_14636,U_14637),tc_fun(U_14636,tc_HOL_Obool)),U_14636),c_COMBB(U_14637,tc_HOL_Obool,U_14636)),hAPP(hAPP(c_COMBB(U_14637,tc_fun(U_14637,tc_HOL_Obool),U_14636),c_fequal),U_14639))),U_14639)),U_14634))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14636,U_14636)),U_14634),U_14638)) )
        | ~ c_Equiv__Relations_Ocongruent(U_14636,U_14637,U_14638,U_14639) ) ),
    inference(variable_rename,[status(thm)],[f_3730_1]) ).

fof(f_3730_3,plain,
    ( ! [U_14647,U_14645,U_14643,U_14641] :
        ( c_Equiv__Relations_Ocongruent(U_14641,U_14643,U_14645,U_14647)
        | ? [U_14635] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14641,U_14641,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14641,tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14643,tc_HOL_Obool),tc_fun(tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),U_14641),c_COMBB(U_14643,tc_HOL_Obool,U_14641)),hAPP(hAPP(c_COMBB(U_14643,tc_fun(U_14643,tc_HOL_Obool),U_14641),c_fequal),U_14647))),U_14647)),U_14635))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14641,U_14641)),U_14635),U_14645)) ) )
    & ! [U_14646,U_14644,U_14642,U_14640] :
        ( ! [U_14634] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14640,U_14640,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14640,tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14642,tc_HOL_Obool),tc_fun(tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),U_14640),c_COMBB(U_14642,tc_HOL_Obool,U_14640)),hAPP(hAPP(c_COMBB(U_14642,tc_fun(U_14642,tc_HOL_Obool),U_14640),c_fequal),U_14646))),U_14646)),U_14634))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14640,U_14640)),U_14634),U_14644)) )
        | ~ c_Equiv__Relations_Ocongruent(U_14640,U_14642,U_14644,U_14646) ) ),
    inference(miniscope,[status(thm)],[f_3730_2]) ).

fof(f_3730_4,plain,
    ( ! [U_14647,U_14645,U_14643,U_14641] :
        ( c_Equiv__Relations_Ocongruent(U_14641,U_14643,U_14645,U_14647)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14641,U_14641,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14641,tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14643,tc_HOL_Obool),tc_fun(tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),U_14641),c_COMBB(U_14643,tc_HOL_Obool,U_14641)),hAPP(hAPP(c_COMBB(U_14643,tc_fun(U_14643,tc_HOL_Obool),U_14641),c_fequal),U_14647))),U_14647)),sK341(U_14647,U_14645,U_14643,U_14641)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14641,U_14641)),sK341(U_14647,U_14645,U_14643,U_14641)),U_14645)) ) )
    & ! [U_14646,U_14644,U_14642,U_14640] :
        ( ! [U_14634] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14640,U_14640,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14640,tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14642,tc_HOL_Obool),tc_fun(tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),U_14640),c_COMBB(U_14642,tc_HOL_Obool,U_14640)),hAPP(hAPP(c_COMBB(U_14642,tc_fun(U_14642,tc_HOL_Obool),U_14640),c_fequal),U_14646))),U_14646)),U_14634))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14640,U_14640)),U_14634),U_14644)) )
        | ~ c_Equiv__Relations_Ocongruent(U_14640,U_14642,U_14644,U_14646) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_14635,sK341(U_14647,U_14645,U_14643,U_14641))],[f_3730_3]) ).

fof(f_3730_5,plain,
    ( ! [U_14641,U_14645,U_14647,U_14643] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14641,U_14641,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14641,tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14643,tc_HOL_Obool),tc_fun(tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),U_14641),c_COMBB(U_14643,tc_HOL_Obool,U_14641)),hAPP(hAPP(c_COMBB(U_14643,tc_fun(U_14643,tc_HOL_Obool),U_14641),c_fequal),U_14647))),U_14647)),sK341(U_14647,U_14645,U_14643,U_14641)))
        | ~ sP1010(U_14641,U_14645,U_14647,U_14643) )
    & ! [U_14641,U_14645,U_14647,U_14643] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14641,U_14641)),sK341(U_14647,U_14645,U_14643,U_14641)),U_14645))
        | ~ sP1010(U_14641,U_14645,U_14647,U_14643) )
    & ! [U_14641,U_14645,U_14647,U_14643] :
        ( c_Equiv__Relations_Ocongruent(U_14641,U_14643,U_14645,U_14647)
        | sP1010(U_14641,U_14645,U_14647,U_14643) )
    & ! [U_14634,U_14642,U_14640,U_14646,U_14644] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14640,U_14640,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14640,tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14642,tc_HOL_Obool),tc_fun(tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),U_14640),c_COMBB(U_14642,tc_HOL_Obool,U_14640)),hAPP(hAPP(c_COMBB(U_14642,tc_fun(U_14642,tc_HOL_Obool),U_14640),c_fequal),U_14646))),U_14646)),U_14634))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14640,U_14640)),U_14634),U_14644))
        | ~ c_Equiv__Relations_Ocongruent(U_14640,U_14642,U_14644,U_14646) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1010])],[f_3730_4]) ).

cnf(f_3730_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14640,U_14640,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14640,tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14642,tc_HOL_Obool),tc_fun(tc_fun(U_14640,U_14642),tc_fun(U_14640,tc_HOL_Obool)),U_14640),c_COMBB(U_14642,tc_HOL_Obool,U_14640)),hAPP(hAPP(c_COMBB(U_14642,tc_fun(U_14642,tc_HOL_Obool),U_14640),c_fequal),U_14646))),U_14646)),U_14634))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14640,U_14640)),U_14634),U_14644))
    | ~ c_Equiv__Relations_Ocongruent(U_14640,U_14642,U_14644,U_14646) ),
    inference(clausify,[status(thm)],[f_3730_5]) ).

cnf(f_3730_7,plain,
    ( c_Equiv__Relations_Ocongruent(U_14641,U_14643,U_14645,U_14647)
    | sP1010(U_14641,U_14645,U_14647,U_14643) ),
    inference(clausify,[status(thm)],[f_3730_5]) ).

cnf(f_3730_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14641,U_14641)),sK341(U_14647,U_14645,U_14643,U_14641)),U_14645))
    | ~ sP1010(U_14641,U_14645,U_14647,U_14643) ),
    inference(clausify,[status(thm)],[f_3730_5]) ).

cnf(f_3730_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14641,U_14641,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14641,tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14643,tc_HOL_Obool),tc_fun(tc_fun(U_14641,U_14643),tc_fun(U_14641,tc_HOL_Obool)),U_14641),c_COMBB(U_14643,tc_HOL_Obool,U_14641)),hAPP(hAPP(c_COMBB(U_14643,tc_fun(U_14643,tc_HOL_Obool),U_14641),c_fequal),U_14647))),U_14647)),sK341(U_14647,U_14645,U_14643,U_14641)))
    | ~ sP1010(U_14641,U_14645,U_14647,U_14643) ),
    inference(clausify,[status(thm)],[f_3730_5]) ).

fof(f_3731_1,plain,
    ! [V_x_2] :
    ? [B_y] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
      & V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) ),
    inference(fof_nnf,[status(thm)],[fact_Abs__Integ__cases]) ).

fof(f_3731_2,plain,
    ! [U_14649] :
    ? [U_14648] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14648),c_Int_OInteg))
      & U_14649 = hAPP(c_Int_OAbs__Integ,U_14648) ),
    inference(variable_rename,[status(thm)],[f_3731_1]) ).

fof(f_3731_3,plain,
    ! [U_14649] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK342(U_14649)),c_Int_OInteg))
      & U_14649 = hAPP(c_Int_OAbs__Integ,sK342(U_14649)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_14648,sK342(U_14649))],[f_3731_2]) ).

fof(f_3731_4,plain,
    ( ! [U_14649] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK342(U_14649)),c_Int_OInteg))
    & ! [U_14649] : U_14649 = hAPP(c_Int_OAbs__Integ,sK342(U_14649)) ),
    inference(definitional_conversion,[status(esa)],[f_3731_3]) ).

cnf(f_3731_5,plain,
    U_14649 = hAPP(c_Int_OAbs__Integ,sK342(U_14649)),
    inference(clausify,[status(thm)],[f_3731_4]) ).

cnf(f_3731_6,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK342(U_14649)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3731_4]) ).

fof(f_3732_1,plain,
    ! [V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct]) ).

fof(f_3732_2,plain,
    ! [U_14652,U_14651] :
      ( hBOOL(hAPP(U_14651,U_14652))
      | ? [U_14650] :
          ( ~ hBOOL(hAPP(U_14651,hAPP(c_Int_OAbs__Integ,U_14650)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14650),c_Int_OInteg)) ) ),
    inference(variable_rename,[status(thm)],[f_3732_1]) ).

fof(f_3732_3,plain,
    ! [U_14652,U_14651] :
      ( hBOOL(hAPP(U_14651,U_14652))
      | ( ~ hBOOL(hAPP(U_14651,hAPP(c_Int_OAbs__Integ,sK343(U_14652,U_14651))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK343(U_14652,U_14651)),c_Int_OInteg)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_14650,sK343(U_14652,U_14651))],[f_3732_2]) ).

fof(f_3732_4,plain,
    ( ! [U_14651,U_14652] :
        ( ~ hBOOL(hAPP(U_14651,hAPP(c_Int_OAbs__Integ,sK343(U_14652,U_14651))))
        | ~ sP1011(U_14651,U_14652) )
    & ! [U_14651,U_14652] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK343(U_14652,U_14651)),c_Int_OInteg))
        | ~ sP1011(U_14651,U_14652) )
    & ! [U_14651,U_14652] :
        ( hBOOL(hAPP(U_14651,U_14652))
        | sP1011(U_14651,U_14652) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1011])],[f_3732_3]) ).

cnf(f_3732_5,plain,
    ( hBOOL(hAPP(U_14651,U_14652))
    | sP1011(U_14651,U_14652) ),
    inference(clausify,[status(thm)],[f_3732_4]) ).

cnf(f_3732_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK343(U_14652,U_14651)),c_Int_OInteg))
    | ~ sP1011(U_14651,U_14652) ),
    inference(clausify,[status(thm)],[f_3732_4]) ).

cnf(f_3732_7,plain,
    ( ~ hBOOL(hAPP(U_14651,hAPP(c_Int_OAbs__Integ,sK343(U_14652,U_14651))))
    | ~ sP1011(U_14651,U_14652) ),
    inference(clausify,[status(thm)],[f_3732_4]) ).

fof(f_3733_1,plain,
    ! [V_n_2,V_tsa_2,T_b] :
      ( ! [B_x] :
          ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
      | ? [B_x] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x)
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_triples__valid__Suc]) ).

fof(f_3733_2,plain,
    ! [U_14657,U_14656,U_14655] :
      ( ! [U_14654] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_14655,U_14657,U_14654)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),U_14654),U_14656)) )
      | ? [U_14653] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14655,hAPP(c_Nat_OSuc,U_14657),U_14653)
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),U_14653),U_14656)) ) ),
    inference(variable_rename,[status(thm)],[f_3733_1]) ).

fof(f_3733_3,plain,
    ! [U_14657,U_14656,U_14655] :
      ( ! [U_14654] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_14655,U_14657,U_14654)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),U_14654),U_14656)) )
      | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14655,hAPP(c_Nat_OSuc,U_14657),sK344(U_14657,U_14656,U_14655))
        & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),sK344(U_14657,U_14656,U_14655)),U_14656)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_14653,sK344(U_14657,U_14656,U_14655))],[f_3733_2]) ).

fof(f_3733_4,plain,
    ( ! [U_14655,U_14656,U_14657] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14655,hAPP(c_Nat_OSuc,U_14657),sK344(U_14657,U_14656,U_14655))
        | ~ sP1012(U_14655,U_14656,U_14657) )
    & ! [U_14655,U_14656,U_14657] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),sK344(U_14657,U_14656,U_14655)),U_14656))
        | ~ sP1012(U_14655,U_14656,U_14657) )
    & ! [U_14655,U_14654,U_14656,U_14657] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_14655,U_14657,U_14654)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),U_14654),U_14656))
        | sP1012(U_14655,U_14656,U_14657) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1012])],[f_3733_3]) ).

cnf(f_3733_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_14655,U_14657,U_14654)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),U_14654),U_14656))
    | sP1012(U_14655,U_14656,U_14657) ),
    inference(clausify,[status(thm)],[f_3733_4]) ).

cnf(f_3733_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14655)),sK344(U_14657,U_14656,U_14655)),U_14656))
    | ~ sP1012(U_14655,U_14656,U_14657) ),
    inference(clausify,[status(thm)],[f_3733_4]) ).

cnf(f_3733_7,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14655,hAPP(c_Nat_OSuc,U_14657),sK344(U_14657,U_14656,U_14655))
    | ~ sP1012(U_14655,U_14656,U_14657) ),
    inference(clausify,[status(thm)],[f_3733_4]) ).

fof(f_3734_1,plain,
    ! [V_tsa_2,V_Ga_2,T_b] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
        | ? [B_n] :
            ( ? [B_x] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
            & ! [B_x] :
                ( c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) ) ) )
      & ( ! [B_n] :
            ( ! [B_x] :
                ( c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
            | ? [B_x] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__valids__def]) ).

fof(f_3734_2,plain,
    ! [U_14666,U_14665,U_14664] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(U_14664,U_14665,U_14666)
        | ? [U_14663] :
            ( ? [U_14662] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14664,U_14663,U_14662)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14664)),U_14662),U_14666)) )
            & ! [U_14661] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14664,U_14663,U_14661)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14664)),U_14661),U_14665)) ) ) )
      & ( ! [U_14660] :
            ( ! [U_14659] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14664,U_14660,U_14659)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14664)),U_14659),U_14666)) )
            | ? [U_14658] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14664,U_14660,U_14658)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14664)),U_14658),U_14665)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14664,U_14665,U_14666) ) ),
    inference(variable_rename,[status(thm)],[f_3734_1]) ).

fof(f_3734_3,plain,
    ( ! [U_14672,U_14670,U_14668] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14668,U_14670,U_14672)
        | ? [U_14663] :
            ( ? [U_14662] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14668,U_14663,U_14662)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14662),U_14672)) )
            & ! [U_14661] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14668,U_14663,U_14661)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14661),U_14670)) ) ) )
    & ! [U_14671,U_14669,U_14667] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14659)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14659),U_14671)) )
            | ? [U_14658] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14658)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14658),U_14669)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14667,U_14669,U_14671) ) ),
    inference(miniscope,[status(thm)],[f_3734_2]) ).

fof(f_3734_4,plain,
    ( ! [U_14672,U_14670,U_14668] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14668,U_14670,U_14672)
        | ? [U_14663] :
            ( ? [U_14662] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14668,U_14663,U_14662)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14662),U_14672)) )
            & ! [U_14661] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14668,U_14663,U_14661)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14661),U_14670)) ) ) )
    & ! [U_14671,U_14669,U_14667] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14659)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14659),U_14671)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,sK345(U_14671,U_14669,U_14667,U_14660))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),sK345(U_14671,U_14669,U_14667,U_14660)),U_14669)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14667,U_14669,U_14671) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_14658,sK345(U_14671,U_14669,U_14667,U_14660))],[f_3734_3]) ).

fof(f_3734_5,plain,
    ( ! [U_14672,U_14670,U_14668] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14668,U_14670,U_14672)
        | ( ? [U_14662] :
              ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),U_14662)
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14662),U_14672)) )
          & ! [U_14661] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),U_14661)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14661),U_14670)) ) ) )
    & ! [U_14671,U_14669,U_14667] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14659)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14659),U_14671)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,sK345(U_14671,U_14669,U_14667,U_14660))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),sK345(U_14671,U_14669,U_14667,U_14660)),U_14669)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14667,U_14669,U_14671) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_14663,sK346(U_14672,U_14670,U_14668))],[f_3734_4]) ).

fof(f_3734_6,plain,
    ( ! [U_14672,U_14670,U_14668] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14668,U_14670,U_14672)
        | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),sK347(U_14672,U_14670,U_14668))
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),sK347(U_14672,U_14670,U_14668)),U_14672))
          & ! [U_14661] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),U_14661)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14661),U_14670)) ) ) )
    & ! [U_14671,U_14669,U_14667] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14659)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14659),U_14671)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,sK345(U_14671,U_14669,U_14667,U_14660))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),sK345(U_14671,U_14669,U_14667,U_14660)),U_14669)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14667,U_14669,U_14671) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_14662,sK347(U_14672,U_14670,U_14668))],[f_3734_5]) ).

fof(f_3734_7,plain,
    ( ! [U_14672,U_14668,U_14661,U_14670] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),sK347(U_14672,U_14670,U_14668))
        | ~ sP1014(U_14672,U_14668,U_14661,U_14670) )
    & ! [U_14672,U_14668,U_14661,U_14670] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),sK347(U_14672,U_14670,U_14668)),U_14672))
        | ~ sP1014(U_14672,U_14668,U_14661,U_14670) )
    & ! [U_14672,U_14668,U_14661,U_14670] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),U_14661)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14661),U_14670))
        | ~ sP1014(U_14672,U_14668,U_14661,U_14670) )
    & ! [U_14660,U_14669,U_14671,U_14667] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,sK345(U_14671,U_14669,U_14667,U_14660))
        | ~ sP1013(U_14660,U_14669,U_14671,U_14667) )
    & ! [U_14660,U_14669,U_14671,U_14667] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),sK345(U_14671,U_14669,U_14667,U_14660)),U_14669))
        | ~ sP1013(U_14660,U_14669,U_14671,U_14667) )
    & ! [U_14672,U_14668,U_14661,U_14670] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14668,U_14670,U_14672)
        | sP1014(U_14672,U_14668,U_14661,U_14670) )
    & ! [U_14660,U_14659,U_14669,U_14671,U_14667] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14659)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14659),U_14671))
        | sP1013(U_14660,U_14669,U_14671,U_14667)
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14667,U_14669,U_14671) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1013,sP1014])],[f_3734_6]) ).

cnf(f_3734_8,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,U_14659)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),U_14659),U_14671))
    | sP1013(U_14660,U_14669,U_14671,U_14667)
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14667,U_14669,U_14671) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

cnf(f_3734_9,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_14668,U_14670,U_14672)
    | sP1014(U_14672,U_14668,U_14661,U_14670) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

cnf(f_3734_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14667)),sK345(U_14671,U_14669,U_14667,U_14660)),U_14669))
    | ~ sP1013(U_14660,U_14669,U_14671,U_14667) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

cnf(f_3734_11,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14667,U_14660,sK345(U_14671,U_14669,U_14667,U_14660))
    | ~ sP1013(U_14660,U_14669,U_14671,U_14667) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

cnf(f_3734_12,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),U_14661)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),U_14661),U_14670))
    | ~ sP1014(U_14672,U_14668,U_14661,U_14670) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

cnf(f_3734_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14668)),sK347(U_14672,U_14670,U_14668)),U_14672))
    | ~ sP1014(U_14672,U_14668,U_14661,U_14670) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

cnf(f_3734_14,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14668,sK346(U_14672,U_14670,U_14668),sK347(U_14672,U_14670,U_14668))
    | ~ sP1014(U_14672,U_14668,U_14661,U_14670) ),
    inference(clausify,[status(thm)],[f_3734_7]) ).

fof(f_3735_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_a] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UN__I]) ).

fof(f_3735_2,plain,
    ! [U_14677,U_14676,U_14675,U_14674] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14674,tc_fun(U_14676,tc_HOL_Obool)),U_14675),U_14677)))
      | ? [U_14673] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(U_14677,U_14673)))
          & hBOOL(hAPP(hAPP(c_member(U_14674),U_14673),U_14675)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14674),U_14675)) ),
    inference(variable_rename,[status(thm)],[f_3735_1]) ).

fof(f_3735_3,plain,
    ! [U_14677,U_14676,U_14675,U_14674] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14674,tc_fun(U_14676,tc_HOL_Obool)),U_14675),U_14677)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(U_14677,sK348(U_14677,U_14676,U_14675,U_14674))))
        & hBOOL(hAPP(hAPP(c_member(U_14674),sK348(U_14677,U_14676,U_14675,U_14674)),U_14675)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14674),U_14675)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_14673,sK348(U_14677,U_14676,U_14675,U_14674))],[f_3735_2]) ).

fof(f_3735_4,plain,
    ( ! [U_14675,U_14676,U_14674,U_14677] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(U_14677,sK348(U_14677,U_14676,U_14675,U_14674))))
        | ~ sP1015(U_14675,U_14676,U_14674,U_14677) )
    & ! [U_14675,U_14676,U_14674,U_14677] :
        ( hBOOL(hAPP(hAPP(c_member(U_14674),sK348(U_14677,U_14676,U_14675,U_14674)),U_14675))
        | ~ sP1015(U_14675,U_14676,U_14674,U_14677) )
    & ! [U_14675,U_14676,U_14674,U_14677] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14674,tc_fun(U_14676,tc_HOL_Obool)),U_14675),U_14677)))
        | sP1015(U_14675,U_14676,U_14674,U_14677)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14674),U_14675)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1015])],[f_3735_3]) ).

cnf(f_3735_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14674,tc_fun(U_14676,tc_HOL_Obool)),U_14675),U_14677)))
    | sP1015(U_14675,U_14676,U_14674,U_14677)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14674),U_14675)) ),
    inference(clausify,[status(thm)],[f_3735_4]) ).

cnf(f_3735_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14674),sK348(U_14677,U_14676,U_14675,U_14674)),U_14675))
    | ~ sP1015(U_14675,U_14676,U_14674,U_14677) ),
    inference(clausify,[status(thm)],[f_3735_4]) ).

cnf(f_3735_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14676),hAPP(U_14677,sK348(U_14677,U_14676,U_14675,U_14674))))
    | ~ sP1015(U_14675,U_14676,U_14674,U_14677) ),
    inference(clausify,[status(thm)],[f_3735_4]) ).

fof(f_3736_1,plain,
    ! [V_k_2,V_N_2] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__diff__nat]) ).

fof(f_3736_2,plain,
    ! [U_14680,U_14679] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_14680),U_14679)
      | ? [U_14678] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14680),U_14678))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_14678),U_14679)) ) ),
    inference(variable_rename,[status(thm)],[f_3736_1]) ).

fof(f_3736_3,plain,
    ! [U_14680,U_14679] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_14680),U_14679)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14680),sK349(U_14680,U_14679)))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK349(U_14680,U_14679)),U_14679)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_14678,sK349(U_14680,U_14679))],[f_3736_2]) ).

fof(f_3736_4,plain,
    ( ! [U_14680,U_14679] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14680),sK349(U_14680,U_14679)))
        | ~ sP1016(U_14680,U_14679) )
    & ! [U_14680,U_14679] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK349(U_14680,U_14679)),U_14679))
        | ~ sP1016(U_14680,U_14679) )
    & ! [U_14680,U_14679] :
        ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_14680),U_14679)
        | sP1016(U_14680,U_14679) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1016])],[f_3736_3]) ).

cnf(f_3736_5,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_14680),U_14679)
    | sP1016(U_14680,U_14679) ),
    inference(clausify,[status(thm)],[f_3736_4]) ).

cnf(f_3736_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK349(U_14680,U_14679)),U_14679))
    | ~ sP1016(U_14680,U_14679) ),
    inference(clausify,[status(thm)],[f_3736_4]) ).

cnf(f_3736_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14680),sK349(U_14680,U_14679)))
    | ~ sP1016(U_14680,U_14679) ),
    inference(clausify,[status(thm)],[f_3736_4]) ).

fof(f_3737_1,plain,
    ! [T_b,V_r_2,T_c] :
      ( c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))
      | ? [B_i,B_j] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) )
      | ? [B_i] : ~ c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__SUP]) ).

fof(f_3737_2,plain,
    ! [U_14686,U_14685,U_14684] :
      ( c_Wellfounded_OwfP(U_14684,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14686,tc_fun(U_14684,tc_fun(U_14684,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14686,tc_HOL_Obool))),U_14685))
      | ? [U_14683,U_14682] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),c_Predicate_ODomainP(U_14684,U_14684,hAPP(U_14685,U_14683))),c_Predicate_ORangeP(U_14684,U_14684,hAPP(U_14685,U_14682))) != c_Orderings_Obot__class_Obot(tc_fun(U_14684,tc_HOL_Obool))
          & hAPP(U_14685,U_14683) != hAPP(U_14685,U_14682) )
      | ? [U_14681] : ~ c_Wellfounded_OwfP(U_14684,hAPP(U_14685,U_14681)) ),
    inference(variable_rename,[status(thm)],[f_3737_1]) ).

fof(f_3737_3,plain,
    ! [U_14686,U_14685,U_14684] :
      ( c_Wellfounded_OwfP(U_14684,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14686,tc_fun(U_14684,tc_fun(U_14684,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14686,tc_HOL_Obool))),U_14685))
      | ? [U_14683,U_14682] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),c_Predicate_ODomainP(U_14684,U_14684,hAPP(U_14685,U_14683))),c_Predicate_ORangeP(U_14684,U_14684,hAPP(U_14685,U_14682))) != c_Orderings_Obot__class_Obot(tc_fun(U_14684,tc_HOL_Obool))
          & hAPP(U_14685,U_14683) != hAPP(U_14685,U_14682) )
      | ~ c_Wellfounded_OwfP(U_14684,hAPP(U_14685,sK350(U_14686,U_14685,U_14684))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_14681,sK350(U_14686,U_14685,U_14684))],[f_3737_2]) ).

fof(f_3737_4,plain,
    ! [U_14686,U_14685,U_14684] :
      ( c_Wellfounded_OwfP(U_14684,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14686,tc_fun(U_14684,tc_fun(U_14684,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14686,tc_HOL_Obool))),U_14685))
      | ? [U_14682] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),c_Predicate_ODomainP(U_14684,U_14684,hAPP(U_14685,sK351(U_14686,U_14685,U_14684)))),c_Predicate_ORangeP(U_14684,U_14684,hAPP(U_14685,U_14682))) != c_Orderings_Obot__class_Obot(tc_fun(U_14684,tc_HOL_Obool))
          & hAPP(U_14685,sK351(U_14686,U_14685,U_14684)) != hAPP(U_14685,U_14682) )
      | ~ c_Wellfounded_OwfP(U_14684,hAPP(U_14685,sK350(U_14686,U_14685,U_14684))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_14683,sK351(U_14686,U_14685,U_14684))],[f_3737_3]) ).

fof(f_3737_5,plain,
    ! [U_14686,U_14685,U_14684] :
      ( c_Wellfounded_OwfP(U_14684,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14686,tc_fun(U_14684,tc_fun(U_14684,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14686,tc_HOL_Obool))),U_14685))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),c_Predicate_ODomainP(U_14684,U_14684,hAPP(U_14685,sK351(U_14686,U_14685,U_14684)))),c_Predicate_ORangeP(U_14684,U_14684,hAPP(U_14685,sK352(U_14686,U_14685,U_14684)))) != c_Orderings_Obot__class_Obot(tc_fun(U_14684,tc_HOL_Obool))
        & hAPP(U_14685,sK351(U_14686,U_14685,U_14684)) != hAPP(U_14685,sK352(U_14686,U_14685,U_14684)) )
      | ~ c_Wellfounded_OwfP(U_14684,hAPP(U_14685,sK350(U_14686,U_14685,U_14684))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_14682,sK352(U_14686,U_14685,U_14684))],[f_3737_4]) ).

fof(f_3737_6,plain,
    ( ! [U_14684,U_14685,U_14686] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),c_Predicate_ODomainP(U_14684,U_14684,hAPP(U_14685,sK351(U_14686,U_14685,U_14684)))),c_Predicate_ORangeP(U_14684,U_14684,hAPP(U_14685,sK352(U_14686,U_14685,U_14684)))) != c_Orderings_Obot__class_Obot(tc_fun(U_14684,tc_HOL_Obool))
        | ~ sP1017(U_14684,U_14685,U_14686) )
    & ! [U_14684,U_14685,U_14686] :
        ( hAPP(U_14685,sK351(U_14686,U_14685,U_14684)) != hAPP(U_14685,sK352(U_14686,U_14685,U_14684))
        | ~ sP1017(U_14684,U_14685,U_14686) )
    & ! [U_14684,U_14685,U_14686] :
        ( c_Wellfounded_OwfP(U_14684,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14686,tc_fun(U_14684,tc_fun(U_14684,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14686,tc_HOL_Obool))),U_14685))
        | sP1017(U_14684,U_14685,U_14686)
        | ~ c_Wellfounded_OwfP(U_14684,hAPP(U_14685,sK350(U_14686,U_14685,U_14684))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1017])],[f_3737_5]) ).

cnf(f_3737_7,plain,
    ( c_Wellfounded_OwfP(U_14684,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14686,tc_fun(U_14684,tc_fun(U_14684,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14686,tc_HOL_Obool))),U_14685))
    | sP1017(U_14684,U_14685,U_14686)
    | ~ c_Wellfounded_OwfP(U_14684,hAPP(U_14685,sK350(U_14686,U_14685,U_14684))) ),
    inference(clausify,[status(thm)],[f_3737_6]) ).

cnf(f_3737_8,plain,
    ( hAPP(U_14685,sK351(U_14686,U_14685,U_14684)) != hAPP(U_14685,sK352(U_14686,U_14685,U_14684))
    | ~ sP1017(U_14684,U_14685,U_14686) ),
    inference(clausify,[status(thm)],[f_3737_6]) ).

cnf(f_3737_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),c_Predicate_ODomainP(U_14684,U_14684,hAPP(U_14685,sK351(U_14686,U_14685,U_14684)))),c_Predicate_ORangeP(U_14684,U_14684,hAPP(U_14685,sK352(U_14686,U_14685,U_14684)))) != c_Orderings_Obot__class_Obot(tc_fun(U_14684,tc_HOL_Obool))
    | ~ sP1017(U_14684,U_14685,U_14686) ),
    inference(clausify,[status(thm)],[f_3737_6]) ).

fof(f_3738_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__map__freshness]) ).

fof(f_3738_2,plain,
    ! [U_14690,U_14689,U_14688] :
      ( ? [U_14687] : hAPP(U_14690,U_14687) = c_Option_Ooption_ONone(U_14689)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Orderings_Otop__class_Otop(tc_fun(U_14688,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Map_Odom(U_14688,U_14689,U_14690))) ),
    inference(variable_rename,[status(thm)],[f_3738_1]) ).

fof(f_3738_3,plain,
    ! [U_14690,U_14689,U_14688] :
      ( hAPP(U_14690,sK353(U_14690,U_14689,U_14688)) = c_Option_Ooption_ONone(U_14689)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Orderings_Otop__class_Otop(tc_fun(U_14688,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Map_Odom(U_14688,U_14689,U_14690))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_14687,sK353(U_14690,U_14689,U_14688))],[f_3738_2]) ).

fof(f_3738_4,plain,
    ! [U_14689,U_14688,U_14690] :
      ( hAPP(U_14690,sK353(U_14690,U_14689,U_14688)) = c_Option_Ooption_ONone(U_14689)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Orderings_Otop__class_Otop(tc_fun(U_14688,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Map_Odom(U_14688,U_14689,U_14690))) ),
    inference(definitional_conversion,[status(esa)],[f_3738_3]) ).

cnf(f_3738_5,plain,
    ( hAPP(U_14690,sK353(U_14690,U_14689,U_14688)) = c_Option_Ooption_ONone(U_14689)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Orderings_Otop__class_Otop(tc_fun(U_14688,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14688),c_Map_Odom(U_14688,U_14689,U_14690))) ),
    inference(clausify,[status(thm)],[f_3738_4]) ).

fof(f_3739_1,plain,
    ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y)))
          & V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitE]) ).

fof(f_3739_2,plain,
    ! [U_14698,U_14697,U_14696,U_14695,U_14694,U_14693] :
      ( ? [U_14692,U_14691] :
          ( hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(U_14697,U_14692),U_14691)))
          & U_14698 = hAPP(hAPP(c_Product__Type_OPair(U_14695,U_14696),U_14692),U_14691) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14695,U_14696,tc_fun(U_14693,tc_HOL_Obool)),U_14697),U_14698))) ),
    inference(variable_rename,[status(thm)],[f_3739_1]) ).

fof(f_3739_3,plain,
    ! [U_14698,U_14697,U_14696,U_14695,U_14694,U_14693] :
      ( ? [U_14691] :
          ( hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(U_14697,sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),U_14691)))
          & U_14698 = hAPP(hAPP(c_Product__Type_OPair(U_14695,U_14696),sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),U_14691) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14695,U_14696,tc_fun(U_14693,tc_HOL_Obool)),U_14697),U_14698))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_14692,sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))],[f_3739_2]) ).

fof(f_3739_4,plain,
    ! [U_14698,U_14697,U_14696,U_14695,U_14694,U_14693] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(U_14697,sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))))
        & U_14698 = hAPP(hAPP(c_Product__Type_OPair(U_14695,U_14696),sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14695,U_14696,tc_fun(U_14693,tc_HOL_Obool)),U_14697),U_14698))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_14691,sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))],[f_3739_3]) ).

fof(f_3739_5,plain,
    ( ! [U_14693,U_14694,U_14695,U_14696,U_14697,U_14698] :
        ( hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(U_14697,sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))))
        | ~ sP1018(U_14693,U_14694,U_14695,U_14696,U_14697,U_14698) )
    & ! [U_14693,U_14694,U_14695,U_14696,U_14697,U_14698] :
        ( U_14698 = hAPP(hAPP(c_Product__Type_OPair(U_14695,U_14696),sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))
        | ~ sP1018(U_14693,U_14694,U_14695,U_14696,U_14697,U_14698) )
    & ! [U_14693,U_14694,U_14695,U_14696,U_14697,U_14698] :
        ( sP1018(U_14693,U_14694,U_14695,U_14696,U_14697,U_14698)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14695,U_14696,tc_fun(U_14693,tc_HOL_Obool)),U_14697),U_14698))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1018])],[f_3739_4]) ).

cnf(f_3739_6,plain,
    ( sP1018(U_14693,U_14694,U_14695,U_14696,U_14697,U_14698)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14695,U_14696,tc_fun(U_14693,tc_HOL_Obool)),U_14697),U_14698))) ),
    inference(clausify,[status(thm)],[f_3739_5]) ).

cnf(f_3739_7,plain,
    ( U_14698 = hAPP(hAPP(c_Product__Type_OPair(U_14695,U_14696),sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))
    | ~ sP1018(U_14693,U_14694,U_14695,U_14696,U_14697,U_14698) ),
    inference(clausify,[status(thm)],[f_3739_5]) ).

cnf(f_3739_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14693),U_14694),hAPP(hAPP(U_14697,sK354(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693)),sK355(U_14698,U_14697,U_14696,U_14695,U_14694,U_14693))))
    | ~ sP1018(U_14693,U_14694,U_14695,U_14696,U_14697,U_14698) ),
    inference(clausify,[status(thm)],[f_3739_5]) ).

fof(f_3740_1,plain,
    ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b)))
          & V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI2]) ).

fof(f_3740_2,plain,
    ! [U_14706,U_14705,U_14704,U_14703,U_14702,U_14701] :
      ( hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14702,U_14703,tc_fun(U_14704,tc_HOL_Obool)),U_14706),U_14701)))
      | ? [U_14700,U_14699] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(U_14706,U_14700),U_14699)))
          & U_14701 = hAPP(hAPP(c_Product__Type_OPair(U_14702,U_14703),U_14700),U_14699) ) ),
    inference(variable_rename,[status(thm)],[f_3740_1]) ).

fof(f_3740_3,plain,
    ! [U_14706,U_14705,U_14704,U_14703,U_14702,U_14701] :
      ( hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14702,U_14703,tc_fun(U_14704,tc_HOL_Obool)),U_14706),U_14701)))
      | ? [U_14699] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(U_14706,sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),U_14699)))
          & U_14701 = hAPP(hAPP(c_Product__Type_OPair(U_14702,U_14703),sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),U_14699) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_14700,sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))],[f_3740_2]) ).

fof(f_3740_4,plain,
    ! [U_14706,U_14705,U_14704,U_14703,U_14702,U_14701] :
      ( hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14702,U_14703,tc_fun(U_14704,tc_HOL_Obool)),U_14706),U_14701)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(U_14706,sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))))
        & U_14701 = hAPP(hAPP(c_Product__Type_OPair(U_14702,U_14703),sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_14699,sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))],[f_3740_3]) ).

fof(f_3740_5,plain,
    ( ! [U_14701,U_14702,U_14703,U_14704,U_14705,U_14706] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(U_14706,sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))))
        | ~ sP1019(U_14701,U_14702,U_14703,U_14704,U_14705,U_14706) )
    & ! [U_14701,U_14702,U_14703,U_14704,U_14705,U_14706] :
        ( U_14701 = hAPP(hAPP(c_Product__Type_OPair(U_14702,U_14703),sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))
        | ~ sP1019(U_14701,U_14702,U_14703,U_14704,U_14705,U_14706) )
    & ! [U_14701,U_14702,U_14703,U_14704,U_14705,U_14706] :
        ( hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14702,U_14703,tc_fun(U_14704,tc_HOL_Obool)),U_14706),U_14701)))
        | sP1019(U_14701,U_14702,U_14703,U_14704,U_14705,U_14706) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1019])],[f_3740_4]) ).

cnf(f_3740_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14702,U_14703,tc_fun(U_14704,tc_HOL_Obool)),U_14706),U_14701)))
    | sP1019(U_14701,U_14702,U_14703,U_14704,U_14705,U_14706) ),
    inference(clausify,[status(thm)],[f_3740_5]) ).

cnf(f_3740_7,plain,
    ( U_14701 = hAPP(hAPP(c_Product__Type_OPair(U_14702,U_14703),sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))
    | ~ sP1019(U_14701,U_14702,U_14703,U_14704,U_14705,U_14706) ),
    inference(clausify,[status(thm)],[f_3740_5]) ).

cnf(f_3740_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14704),U_14705),hAPP(hAPP(U_14706,sK356(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701)),sK357(U_14706,U_14705,U_14704,U_14703,U_14702,U_14701))))
    | ~ sP1019(U_14701,U_14702,U_14703,U_14704,U_14705,U_14706) ),
    inference(clausify,[status(thm)],[f_3740_5]) ).

fof(f_3741_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Times]) ).

fof(f_3741_2,plain,
    ! [U_14712,U_14711,U_14710,U_14709,U_14708,U_14707] : hAPP(c_Set_Ovimage(U_14707,tc_prod(U_14708,U_14709),U_14710),hAPP(hAPP(c_Product__Type_OSigma(U_14708,U_14709),U_14711),hAPP(c_COMBK(tc_fun(U_14709,tc_HOL_Obool),U_14708),U_14712))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14707,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14707,U_14708,hAPP(c_Fun_Ocomp(tc_prod(U_14708,U_14709),U_14708,U_14707,c_Product__Type_Ofst(U_14708,U_14709)),U_14710)),U_14711)),hAPP(c_Set_Ovimage(U_14707,U_14709,hAPP(c_Fun_Ocomp(tc_prod(U_14708,U_14709),U_14709,U_14707,c_Product__Type_Osnd(U_14708,U_14709)),U_14710)),U_14712)),
    inference(variable_rename,[status(thm)],[f_3741_1]) ).

fof(f_3741_3,plain,
    ! [U_14707,U_14708,U_14709,U_14710,U_14711,U_14712] : hAPP(c_Set_Ovimage(U_14707,tc_prod(U_14708,U_14709),U_14710),hAPP(hAPP(c_Product__Type_OSigma(U_14708,U_14709),U_14711),hAPP(c_COMBK(tc_fun(U_14709,tc_HOL_Obool),U_14708),U_14712))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14707,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14707,U_14708,hAPP(c_Fun_Ocomp(tc_prod(U_14708,U_14709),U_14708,U_14707,c_Product__Type_Ofst(U_14708,U_14709)),U_14710)),U_14711)),hAPP(c_Set_Ovimage(U_14707,U_14709,hAPP(c_Fun_Ocomp(tc_prod(U_14708,U_14709),U_14709,U_14707,c_Product__Type_Osnd(U_14708,U_14709)),U_14710)),U_14712)),
    inference(definitional_conversion,[status(esa)],[f_3741_2]) ).

cnf(f_3741_4,plain,
    hAPP(c_Set_Ovimage(U_14707,tc_prod(U_14708,U_14709),U_14710),hAPP(hAPP(c_Product__Type_OSigma(U_14708,U_14709),U_14711),hAPP(c_COMBK(tc_fun(U_14709,tc_HOL_Obool),U_14708),U_14712))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14707,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14707,U_14708,hAPP(c_Fun_Ocomp(tc_prod(U_14708,U_14709),U_14708,U_14707,c_Product__Type_Ofst(U_14708,U_14709)),U_14710)),U_14711)),hAPP(c_Set_Ovimage(U_14707,U_14709,hAPP(c_Fun_Ocomp(tc_prod(U_14708,U_14709),U_14709,U_14707,c_Product__Type_Osnd(U_14708,U_14709)),U_14710)),U_14712)),
    inference(clausify,[status(thm)],[f_3741_3]) ).

fof(f_3742_1,plain,
    ! [V_n_2,V_A_2,V_f_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != hAPP(c_Nat_OSuc,V_n_2) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__SucD]) ).

fof(f_3742_2,plain,
    ! [U_14717,U_14716,U_14715,U_14714] :
      ( ? [U_14713] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14715,U_14713)))
          & hBOOL(hAPP(hAPP(c_member(U_14714),U_14713),U_14716)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14714,tc_Nat_Onat),U_14715),U_14716) != hAPP(c_Nat_OSuc,U_14717) ),
    inference(variable_rename,[status(thm)],[f_3742_1]) ).

fof(f_3742_3,plain,
    ! [U_14717,U_14716,U_14715,U_14714] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14715,sK358(U_14717,U_14716,U_14715,U_14714))))
        & hBOOL(hAPP(hAPP(c_member(U_14714),sK358(U_14717,U_14716,U_14715,U_14714)),U_14716)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14714,tc_Nat_Onat),U_14715),U_14716) != hAPP(c_Nat_OSuc,U_14717) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_14713,sK358(U_14717,U_14716,U_14715,U_14714))],[f_3742_2]) ).

fof(f_3742_4,plain,
    ( ! [U_14714,U_14715,U_14716,U_14717] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14715,sK358(U_14717,U_14716,U_14715,U_14714))))
        | ~ sP1020(U_14714,U_14715,U_14716,U_14717) )
    & ! [U_14714,U_14715,U_14716,U_14717] :
        ( hBOOL(hAPP(hAPP(c_member(U_14714),sK358(U_14717,U_14716,U_14715,U_14714)),U_14716))
        | ~ sP1020(U_14714,U_14715,U_14716,U_14717) )
    & ! [U_14714,U_14715,U_14716,U_14717] :
        ( sP1020(U_14714,U_14715,U_14716,U_14717)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14714,tc_Nat_Onat),U_14715),U_14716) != hAPP(c_Nat_OSuc,U_14717) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1020])],[f_3742_3]) ).

cnf(f_3742_5,plain,
    ( sP1020(U_14714,U_14715,U_14716,U_14717)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14714,tc_Nat_Onat),U_14715),U_14716) != hAPP(c_Nat_OSuc,U_14717) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

cnf(f_3742_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14714),sK358(U_14717,U_14716,U_14715,U_14714)),U_14716))
    | ~ sP1020(U_14714,U_14715,U_14716,U_14717) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

cnf(f_3742_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14715,sK358(U_14717,U_14716,U_14715,U_14714))))
    | ~ sP1020(U_14714,U_14715,U_14716,U_14717) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

fof(f_3743_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_o__id]) ).

fof(f_3743_2,plain,
    ! [U_14720,U_14719,U_14718] : hAPP(c_Fun_Ocomp(U_14718,U_14719,U_14718,U_14720),c_Fun_Oid(U_14718)) = U_14720,
    inference(variable_rename,[status(thm)],[f_3743_1]) ).

fof(f_3743_3,plain,
    ! [U_14719,U_14718,U_14720] : hAPP(c_Fun_Ocomp(U_14718,U_14719,U_14718,U_14720),c_Fun_Oid(U_14718)) = U_14720,
    inference(definitional_conversion,[status(esa)],[f_3743_2]) ).

cnf(f_3743_4,plain,
    hAPP(c_Fun_Ocomp(U_14718,U_14719,U_14718,U_14720),c_Fun_Oid(U_14718)) = U_14720,
    inference(clausify,[status(thm)],[f_3743_3]) ).

fof(f_3744_1,plain,
    ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
    inference(fof_nnf,[status(thm)],[fact_id__o]) ).

fof(f_3744_2,plain,
    ! [U_14723,U_14722,U_14721] : hAPP(c_Fun_Ocomp(U_14721,U_14721,U_14722,c_Fun_Oid(U_14721)),U_14723) = U_14723,
    inference(variable_rename,[status(thm)],[f_3744_1]) ).

fof(f_3744_3,plain,
    ! [U_14721,U_14722,U_14723] : hAPP(c_Fun_Ocomp(U_14721,U_14721,U_14722,c_Fun_Oid(U_14721)),U_14723) = U_14723,
    inference(definitional_conversion,[status(esa)],[f_3744_2]) ).

cnf(f_3744_4,plain,
    hAPP(c_Fun_Ocomp(U_14721,U_14721,U_14722,c_Fun_Oid(U_14721)),U_14723) = U_14723,
    inference(clausify,[status(thm)],[f_3744_3]) ).

fof(f_3745_1,plain,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest]) ).

fof(f_3745_2,plain,
    ! [U_14730,U_14729,U_14728,U_14727,U_14726,U_14725,U_14724] :
      ( hAPP(U_14727,hAPP(U_14728,U_14730)) = hAPP(U_14729,U_14730)
      | hAPP(c_Fun_Ocomp(U_14724,U_14725,U_14726,U_14727),U_14728) != hAPP(c_Fun_Ocomp(U_14725,U_14725,U_14726,c_Fun_Oid(U_14725)),U_14729) ),
    inference(variable_rename,[status(thm)],[f_3745_1]) ).

fof(f_3745_3,plain,
    ! [U_14730,U_14729,U_14728,U_14727] :
      ( ! [U_14726,U_14725,U_14724] : hAPP(c_Fun_Ocomp(U_14724,U_14725,U_14726,U_14727),U_14728) != hAPP(c_Fun_Ocomp(U_14725,U_14725,U_14726,c_Fun_Oid(U_14725)),U_14729)
      | hAPP(U_14727,hAPP(U_14728,U_14730)) = hAPP(U_14729,U_14730) ),
    inference(miniscope,[status(thm)],[f_3745_2]) ).

fof(f_3745_4,plain,
    ! [U_14724,U_14725,U_14726,U_14727,U_14728,U_14729,U_14730] :
      ( hAPP(c_Fun_Ocomp(U_14724,U_14725,U_14726,U_14727),U_14728) != hAPP(c_Fun_Ocomp(U_14725,U_14725,U_14726,c_Fun_Oid(U_14725)),U_14729)
      | hAPP(U_14727,hAPP(U_14728,U_14730)) = hAPP(U_14729,U_14730) ),
    inference(definitional_conversion,[status(esa)],[f_3745_3]) ).

cnf(f_3745_5,plain,
    ( hAPP(c_Fun_Ocomp(U_14724,U_14725,U_14726,U_14727),U_14728) != hAPP(c_Fun_Ocomp(U_14725,U_14725,U_14726,c_Fun_Oid(U_14725)),U_14729)
    | hAPP(U_14727,hAPP(U_14728,U_14730)) = hAPP(U_14729,U_14730) ),
    inference(clausify,[status(thm)],[f_3745_4]) ).

fof(f_3746_1,plain,
    ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_image__compose]) ).

fof(f_3746_2,plain,
    ! [U_14736,U_14735,U_14734,U_14733,U_14732,U_14731] : hAPP(c_Set_Oimage(U_14731,U_14732,hAPP(c_Fun_Ocomp(U_14733,U_14732,U_14731,U_14734),U_14735)),U_14736) = hAPP(c_Set_Oimage(U_14733,U_14732,U_14734),hAPP(c_Set_Oimage(U_14731,U_14733,U_14735),U_14736)),
    inference(variable_rename,[status(thm)],[f_3746_1]) ).

fof(f_3746_3,plain,
    ! [U_14731,U_14732,U_14733,U_14734,U_14735,U_14736] : hAPP(c_Set_Oimage(U_14731,U_14732,hAPP(c_Fun_Ocomp(U_14733,U_14732,U_14731,U_14734),U_14735)),U_14736) = hAPP(c_Set_Oimage(U_14733,U_14732,U_14734),hAPP(c_Set_Oimage(U_14731,U_14733,U_14735),U_14736)),
    inference(definitional_conversion,[status(esa)],[f_3746_2]) ).

cnf(f_3746_4,plain,
    hAPP(c_Set_Oimage(U_14731,U_14732,hAPP(c_Fun_Ocomp(U_14733,U_14732,U_14731,U_14734),U_14735)),U_14736) = hAPP(c_Set_Oimage(U_14733,U_14732,U_14734),hAPP(c_Set_Oimage(U_14731,U_14733,U_14735),U_14736)),
    inference(clausify,[status(thm)],[f_3746_3]) ).

fof(f_3747_1,plain,
    ! [V_g_2,T_d,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_comp__surj]) ).

fof(f_3747_2,plain,
    ! [U_14741,U_14740,U_14739,U_14738,U_14737] :
      ( hAPP(c_Set_Oimage(U_14737,U_14740,hAPP(c_Fun_Ocomp(U_14738,U_14740,U_14737,U_14741),U_14739)),c_Orderings_Otop__class_Otop(tc_fun(U_14737,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14740,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14738,U_14740,U_14741),c_Orderings_Otop__class_Otop(tc_fun(U_14738,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14740,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14737,U_14738,U_14739),c_Orderings_Otop__class_Otop(tc_fun(U_14737,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14738,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3747_1]) ).

fof(f_3747_3,plain,
    ! [U_14737,U_14738,U_14739,U_14740,U_14741] :
      ( hAPP(c_Set_Oimage(U_14737,U_14740,hAPP(c_Fun_Ocomp(U_14738,U_14740,U_14737,U_14741),U_14739)),c_Orderings_Otop__class_Otop(tc_fun(U_14737,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14740,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14738,U_14740,U_14741),c_Orderings_Otop__class_Otop(tc_fun(U_14738,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14740,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14737,U_14738,U_14739),c_Orderings_Otop__class_Otop(tc_fun(U_14737,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14738,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3747_2]) ).

cnf(f_3747_4,plain,
    ( hAPP(c_Set_Oimage(U_14737,U_14740,hAPP(c_Fun_Ocomp(U_14738,U_14740,U_14737,U_14741),U_14739)),c_Orderings_Otop__class_Otop(tc_fun(U_14737,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14740,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14738,U_14740,U_14741),c_Orderings_Otop__class_Otop(tc_fun(U_14738,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14740,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14737,U_14738,U_14739),c_Orderings_Otop__class_Otop(tc_fun(U_14737,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14738,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3747_3]) ).

fof(f_3748_1,plain,
    ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__compose]) ).

fof(f_3748_2,plain,
    ! [U_14747,U_14746,U_14745,U_14744,U_14743,U_14742] : hAPP(c_Set_Ovimage(U_14742,U_14743,hAPP(c_Fun_Ocomp(U_14744,U_14743,U_14742,U_14745),U_14746)),U_14747) = hAPP(c_Set_Ovimage(U_14742,U_14744,U_14746),hAPP(c_Set_Ovimage(U_14744,U_14743,U_14745),U_14747)),
    inference(variable_rename,[status(thm)],[f_3748_1]) ).

fof(f_3748_3,plain,
    ! [U_14743,U_14742,U_14744,U_14745,U_14746,U_14747] : hAPP(c_Set_Ovimage(U_14742,U_14743,hAPP(c_Fun_Ocomp(U_14744,U_14743,U_14742,U_14745),U_14746)),U_14747) = hAPP(c_Set_Ovimage(U_14742,U_14744,U_14746),hAPP(c_Set_Ovimage(U_14744,U_14743,U_14745),U_14747)),
    inference(definitional_conversion,[status(esa)],[f_3748_2]) ).

cnf(f_3748_4,plain,
    hAPP(c_Set_Ovimage(U_14742,U_14743,hAPP(c_Fun_Ocomp(U_14744,U_14743,U_14742,U_14745),U_14746)),U_14747) = hAPP(c_Set_Ovimage(U_14742,U_14744,U_14746),hAPP(c_Set_Ovimage(U_14744,U_14743,U_14745),U_14747)),
    inference(clausify,[status(thm)],[f_3748_3]) ).

fof(f_3749_1,plain,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__comp]) ).

fof(f_3749_2,plain,
    ! [U_14754,U_14753,U_14752,U_14751,U_14750,U_14749,U_14748] : hAPP(c_Fun_Ocomp(U_14748,U_14749,U_14750,U_14751),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14750,U_14748),U_14752),U_14753),U_14754)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14750,U_14749),hAPP(c_Fun_Ocomp(U_14748,U_14749,U_14750,U_14751),U_14752)),U_14753),hAPP(U_14751,U_14754)),
    inference(variable_rename,[status(thm)],[f_3749_1]) ).

fof(f_3749_3,plain,
    ! [U_14748,U_14749,U_14750,U_14751,U_14752,U_14753,U_14754] : hAPP(c_Fun_Ocomp(U_14748,U_14749,U_14750,U_14751),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14750,U_14748),U_14752),U_14753),U_14754)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14750,U_14749),hAPP(c_Fun_Ocomp(U_14748,U_14749,U_14750,U_14751),U_14752)),U_14753),hAPP(U_14751,U_14754)),
    inference(definitional_conversion,[status(esa)],[f_3749_2]) ).

cnf(f_3749_4,plain,
    hAPP(c_Fun_Ocomp(U_14748,U_14749,U_14750,U_14751),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14750,U_14748),U_14752),U_14753),U_14754)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14750,U_14749),hAPP(c_Fun_Ocomp(U_14748,U_14749,U_14750,U_14751),U_14752)),U_14753),hAPP(U_14751,U_14754)),
    inference(clausify,[status(thm)],[f_3749_3]) ).

fof(f_3750_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_apfst__compose]) ).

fof(f_3750_2,plain,
    ! [U_14761,U_14760,U_14759,U_14758,U_14757,U_14756,U_14755] : hAPP(c_Product__Type_Oapfst(U_14755,U_14756,U_14757,U_14758),hAPP(c_Product__Type_Oapfst(U_14759,U_14755,U_14757,U_14760),U_14761)) = hAPP(c_Product__Type_Oapfst(U_14759,U_14756,U_14757,hAPP(c_Fun_Ocomp(U_14755,U_14756,U_14759,U_14758),U_14760)),U_14761),
    inference(variable_rename,[status(thm)],[f_3750_1]) ).

fof(f_3750_3,plain,
    ! [U_14755,U_14756,U_14757,U_14758,U_14759,U_14760,U_14761] : hAPP(c_Product__Type_Oapfst(U_14755,U_14756,U_14757,U_14758),hAPP(c_Product__Type_Oapfst(U_14759,U_14755,U_14757,U_14760),U_14761)) = hAPP(c_Product__Type_Oapfst(U_14759,U_14756,U_14757,hAPP(c_Fun_Ocomp(U_14755,U_14756,U_14759,U_14758),U_14760)),U_14761),
    inference(definitional_conversion,[status(esa)],[f_3750_2]) ).

cnf(f_3750_4,plain,
    hAPP(c_Product__Type_Oapfst(U_14755,U_14756,U_14757,U_14758),hAPP(c_Product__Type_Oapfst(U_14759,U_14755,U_14757,U_14760),U_14761)) = hAPP(c_Product__Type_Oapfst(U_14759,U_14756,U_14757,hAPP(c_Fun_Ocomp(U_14755,U_14756,U_14759,U_14758),U_14760)),U_14761),
    inference(clausify,[status(thm)],[f_3750_3]) ).

fof(f_3751_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_apsnd__compose]) ).

fof(f_3751_2,plain,
    ! [U_14768,U_14767,U_14766,U_14765,U_14764,U_14763,U_14762] : hAPP(c_Product__Type_Oapsnd(U_14762,U_14763,U_14764,U_14765),hAPP(c_Product__Type_Oapsnd(U_14766,U_14762,U_14764,U_14767),U_14768)) = hAPP(c_Product__Type_Oapsnd(U_14766,U_14763,U_14764,hAPP(c_Fun_Ocomp(U_14762,U_14763,U_14766,U_14765),U_14767)),U_14768),
    inference(variable_rename,[status(thm)],[f_3751_1]) ).

fof(f_3751_3,plain,
    ! [U_14763,U_14762,U_14764,U_14765,U_14766,U_14767,U_14768] : hAPP(c_Product__Type_Oapsnd(U_14762,U_14763,U_14764,U_14765),hAPP(c_Product__Type_Oapsnd(U_14766,U_14762,U_14764,U_14767),U_14768)) = hAPP(c_Product__Type_Oapsnd(U_14766,U_14763,U_14764,hAPP(c_Fun_Ocomp(U_14762,U_14763,U_14766,U_14765),U_14767)),U_14768),
    inference(definitional_conversion,[status(esa)],[f_3751_2]) ).

cnf(f_3751_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_14762,U_14763,U_14764,U_14765),hAPP(c_Product__Type_Oapsnd(U_14766,U_14762,U_14764,U_14767),U_14768)) = hAPP(c_Product__Type_Oapsnd(U_14766,U_14763,U_14764,hAPP(c_Fun_Ocomp(U_14762,U_14763,U_14766,U_14765),U_14767)),U_14768),
    inference(clausify,[status(thm)],[f_3751_3]) ).

fof(f_3752_1,plain,
    ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
      ( hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2)
      | hAPP(V_f_2,hAPP(V_g_2,V_x_2)) != hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) ),
    inference(fof_nnf,[status(thm)],[fact_comp__cong]) ).

fof(f_3752_2,plain,
    ! [U_14779,U_14778,U_14777,U_14776,U_14775,U_14774,U_14773,U_14772,U_14771,U_14770,U_14769] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_14775,U_14776,U_14777,U_14769),U_14770),U_14771) = hAPP(hAPP(c_Fun_Ocomp(U_14778,U_14776,U_14779,U_14772),U_14773),U_14774)
      | hAPP(U_14769,hAPP(U_14770,U_14771)) != hAPP(U_14772,hAPP(U_14773,U_14774)) ),
    inference(variable_rename,[status(thm)],[f_3752_1]) ).

fof(f_3752_3,plain,
    ! [U_14769,U_14770,U_14771,U_14772,U_14773,U_14774,U_14775,U_14776,U_14777,U_14778,U_14779] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_14775,U_14776,U_14777,U_14769),U_14770),U_14771) = hAPP(hAPP(c_Fun_Ocomp(U_14778,U_14776,U_14779,U_14772),U_14773),U_14774)
      | hAPP(U_14769,hAPP(U_14770,U_14771)) != hAPP(U_14772,hAPP(U_14773,U_14774)) ),
    inference(definitional_conversion,[status(esa)],[f_3752_2]) ).

cnf(f_3752_4,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(U_14775,U_14776,U_14777,U_14769),U_14770),U_14771) = hAPP(hAPP(c_Fun_Ocomp(U_14778,U_14776,U_14779,U_14772),U_14773),U_14774)
    | hAPP(U_14769,hAPP(U_14770,U_14771)) != hAPP(U_14772,hAPP(U_14773,U_14774)) ),
    inference(clausify,[status(thm)],[f_3752_3]) ).

fof(f_3753_1,plain,
    ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v))
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__elim]) ).

fof(f_3753_2,plain,
    ! [U_14788,U_14787,U_14786,U_14785,U_14784,U_14783,U_14782,U_14781] :
      ( ! [U_14780] : hAPP(U_14784,hAPP(U_14785,U_14780)) = hAPP(U_14787,hAPP(U_14788,U_14780))
      | hAPP(c_Fun_Ocomp(U_14781,U_14782,U_14783,U_14784),U_14785) != hAPP(c_Fun_Ocomp(U_14786,U_14782,U_14783,U_14787),U_14788) ),
    inference(variable_rename,[status(thm)],[f_3753_1]) ).

fof(f_3753_3,plain,
    ! [U_14788,U_14787,U_14786,U_14785,U_14784] :
      ( ! [U_14783,U_14782,U_14781] : hAPP(c_Fun_Ocomp(U_14781,U_14782,U_14783,U_14784),U_14785) != hAPP(c_Fun_Ocomp(U_14786,U_14782,U_14783,U_14787),U_14788)
      | ! [U_14780] : hAPP(U_14784,hAPP(U_14785,U_14780)) = hAPP(U_14787,hAPP(U_14788,U_14780)) ),
    inference(miniscope,[status(thm)],[f_3753_2]) ).

fof(f_3753_4,plain,
    ! [U_14780,U_14782,U_14781,U_14783,U_14784,U_14785,U_14786,U_14787,U_14788] :
      ( hAPP(c_Fun_Ocomp(U_14781,U_14782,U_14783,U_14784),U_14785) != hAPP(c_Fun_Ocomp(U_14786,U_14782,U_14783,U_14787),U_14788)
      | hAPP(U_14784,hAPP(U_14785,U_14780)) = hAPP(U_14787,hAPP(U_14788,U_14780)) ),
    inference(definitional_conversion,[status(esa)],[f_3753_3]) ).

cnf(f_3753_5,plain,
    ( hAPP(c_Fun_Ocomp(U_14781,U_14782,U_14783,U_14784),U_14785) != hAPP(c_Fun_Ocomp(U_14786,U_14782,U_14783,U_14787),U_14788)
    | hAPP(U_14784,hAPP(U_14785,U_14780)) = hAPP(U_14787,hAPP(U_14788,U_14780)) ),
    inference(clausify,[status(thm)],[f_3753_4]) ).

fof(f_3754_1,plain,
    ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2))
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest]) ).

fof(f_3754_2,plain,
    ! [U_14797,U_14796,U_14795,U_14794,U_14793,U_14792,U_14791,U_14790,U_14789] :
      ( hAPP(U_14792,hAPP(U_14793,U_14797)) = hAPP(U_14795,hAPP(U_14796,U_14797))
      | hAPP(c_Fun_Ocomp(U_14789,U_14790,U_14791,U_14792),U_14793) != hAPP(c_Fun_Ocomp(U_14794,U_14790,U_14791,U_14795),U_14796) ),
    inference(variable_rename,[status(thm)],[f_3754_1]) ).

fof(f_3754_3,plain,
    ! [U_14797,U_14796,U_14795,U_14794,U_14793,U_14792] :
      ( ! [U_14791,U_14790,U_14789] : hAPP(c_Fun_Ocomp(U_14789,U_14790,U_14791,U_14792),U_14793) != hAPP(c_Fun_Ocomp(U_14794,U_14790,U_14791,U_14795),U_14796)
      | hAPP(U_14792,hAPP(U_14793,U_14797)) = hAPP(U_14795,hAPP(U_14796,U_14797)) ),
    inference(miniscope,[status(thm)],[f_3754_2]) ).

fof(f_3754_4,plain,
    ! [U_14790,U_14789,U_14791,U_14792,U_14793,U_14794,U_14795,U_14796,U_14797] :
      ( hAPP(c_Fun_Ocomp(U_14789,U_14790,U_14791,U_14792),U_14793) != hAPP(c_Fun_Ocomp(U_14794,U_14790,U_14791,U_14795),U_14796)
      | hAPP(U_14792,hAPP(U_14793,U_14797)) = hAPP(U_14795,hAPP(U_14796,U_14797)) ),
    inference(definitional_conversion,[status(esa)],[f_3754_3]) ).

cnf(f_3754_5,plain,
    ( hAPP(c_Fun_Ocomp(U_14789,U_14790,U_14791,U_14792),U_14793) != hAPP(c_Fun_Ocomp(U_14794,U_14790,U_14791,U_14795),U_14796)
    | hAPP(U_14792,hAPP(U_14793,U_14797)) = hAPP(U_14795,hAPP(U_14796,U_14797)) ),
    inference(clausify,[status(thm)],[f_3754_4]) ).

fof(f_3755_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_o__apply]) ).

fof(f_3755_2,plain,
    ! [U_14803,U_14802,U_14801,U_14800,U_14799,U_14798] : hAPP(hAPP(c_Fun_Ocomp(U_14798,U_14799,U_14800,U_14801),U_14802),U_14803) = hAPP(U_14801,hAPP(U_14802,U_14803)),
    inference(variable_rename,[status(thm)],[f_3755_1]) ).

fof(f_3755_3,plain,
    ! [U_14799,U_14798,U_14800,U_14801,U_14802,U_14803] : hAPP(hAPP(c_Fun_Ocomp(U_14798,U_14799,U_14800,U_14801),U_14802),U_14803) = hAPP(U_14801,hAPP(U_14802,U_14803)),
    inference(definitional_conversion,[status(esa)],[f_3755_2]) ).

cnf(f_3755_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_14798,U_14799,U_14800,U_14801),U_14802),U_14803) = hAPP(U_14801,hAPP(U_14802,U_14803)),
    inference(clausify,[status(thm)],[f_3755_3]) ).

fof(f_3756_1,plain,
    ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2),
    inference(fof_nnf,[status(thm)],[fact_o__assoc]) ).

fof(f_3756_2,plain,
    ! [U_14810,U_14809,U_14808,U_14807,U_14806,U_14805,U_14804] : hAPP(c_Fun_Ocomp(U_14804,U_14805,U_14806,U_14807),hAPP(c_Fun_Ocomp(U_14808,U_14804,U_14806,U_14809),U_14810)) = hAPP(c_Fun_Ocomp(U_14808,U_14805,U_14806,hAPP(c_Fun_Ocomp(U_14804,U_14805,U_14808,U_14807),U_14809)),U_14810),
    inference(variable_rename,[status(thm)],[f_3756_1]) ).

fof(f_3756_3,plain,
    ! [U_14804,U_14805,U_14806,U_14807,U_14808,U_14809,U_14810] : hAPP(c_Fun_Ocomp(U_14804,U_14805,U_14806,U_14807),hAPP(c_Fun_Ocomp(U_14808,U_14804,U_14806,U_14809),U_14810)) = hAPP(c_Fun_Ocomp(U_14808,U_14805,U_14806,hAPP(c_Fun_Ocomp(U_14804,U_14805,U_14808,U_14807),U_14809)),U_14810),
    inference(definitional_conversion,[status(esa)],[f_3756_2]) ).

cnf(f_3756_4,plain,
    hAPP(c_Fun_Ocomp(U_14804,U_14805,U_14806,U_14807),hAPP(c_Fun_Ocomp(U_14808,U_14804,U_14806,U_14809),U_14810)) = hAPP(c_Fun_Ocomp(U_14808,U_14805,U_14806,hAPP(c_Fun_Ocomp(U_14804,U_14805,U_14808,U_14807),U_14809)),U_14810),
    inference(clausify,[status(thm)],[f_3756_3]) ).

fof(f_3757_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_o__def]) ).

fof(f_3757_2,plain,
    ! [U_14816,U_14815,U_14814,U_14813,U_14812,U_14811] : hAPP(hAPP(c_Fun_Ocomp(U_14811,U_14812,U_14813,U_14814),U_14815),U_14816) = hAPP(U_14814,hAPP(U_14815,U_14816)),
    inference(variable_rename,[status(thm)],[f_3757_1]) ).

fof(f_3757_3,plain,
    ! [U_14811,U_14812,U_14813,U_14814,U_14815,U_14816] : hAPP(hAPP(c_Fun_Ocomp(U_14811,U_14812,U_14813,U_14814),U_14815),U_14816) = hAPP(U_14814,hAPP(U_14815,U_14816)),
    inference(definitional_conversion,[status(esa)],[f_3757_2]) ).

cnf(f_3757_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_14811,U_14812,U_14813,U_14814),U_14815),U_14816) = hAPP(U_14814,hAPP(U_14815,U_14816)),
    inference(clausify,[status(thm)],[f_3757_3]) ).

fof(f_3758_1,plain,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != V_c_2 ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs]) ).

fof(f_3758_2,plain,
    ! [U_14823,U_14822,U_14821,U_14820,U_14819,U_14818,U_14817] :
      ( hAPP(U_14820,hAPP(U_14821,U_14823)) = hAPP(U_14822,U_14823)
      | hAPP(c_Fun_Ocomp(U_14817,U_14818,U_14819,U_14820),U_14821) != U_14822 ),
    inference(variable_rename,[status(thm)],[f_3758_1]) ).

fof(f_3758_3,plain,
    ! [U_14823,U_14822,U_14821,U_14820] :
      ( ! [U_14819,U_14818,U_14817] : hAPP(c_Fun_Ocomp(U_14817,U_14818,U_14819,U_14820),U_14821) != U_14822
      | hAPP(U_14820,hAPP(U_14821,U_14823)) = hAPP(U_14822,U_14823) ),
    inference(miniscope,[status(thm)],[f_3758_2]) ).

fof(f_3758_4,plain,
    ! [U_14818,U_14817,U_14819,U_14820,U_14821,U_14822,U_14823] :
      ( hAPP(c_Fun_Ocomp(U_14817,U_14818,U_14819,U_14820),U_14821) != U_14822
      | hAPP(U_14820,hAPP(U_14821,U_14823)) = hAPP(U_14822,U_14823) ),
    inference(definitional_conversion,[status(esa)],[f_3758_3]) ).

cnf(f_3758_5,plain,
    ( hAPP(c_Fun_Ocomp(U_14817,U_14818,U_14819,U_14820),U_14821) != U_14822
    | hAPP(U_14820,hAPP(U_14821,U_14823)) = hAPP(U_14822,U_14823) ),
    inference(clausify,[status(thm)],[f_3758_4]) ).

fof(f_3759_1,plain,
    ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
    inference(fof_nnf,[status(thm)],[fact_K__record__comp]) ).

fof(f_3759_2,plain,
    ! [U_14829,U_14828,U_14827,U_14826,U_14825,U_14824] : hAPP(hAPP(c_Fun_Ocomp(U_14824,U_14825,U_14826,hAPP(c_COMBK(U_14825,U_14824),U_14827)),U_14828),U_14829) = U_14827,
    inference(variable_rename,[status(thm)],[f_3759_1]) ).

fof(f_3759_3,plain,
    ! [U_14824,U_14825,U_14826,U_14827,U_14828,U_14829] : hAPP(hAPP(c_Fun_Ocomp(U_14824,U_14825,U_14826,hAPP(c_COMBK(U_14825,U_14824),U_14827)),U_14828),U_14829) = U_14827,
    inference(definitional_conversion,[status(esa)],[f_3759_2]) ).

cnf(f_3759_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_14824,U_14825,U_14826,hAPP(c_COMBK(U_14825,U_14824),U_14827)),U_14828),U_14829) = U_14827,
    inference(clausify,[status(thm)],[f_3759_3]) ).

fof(f_3760_1,plain,
    ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(f_3760_2,plain,
    ! [U_14839,U_14838,U_14837,U_14836,U_14835,U_14834,U_14833,U_14832,U_14831,U_14830] : hAPP(c_Fun_Ocomp(tc_prod(U_14830,U_14831),tc_prod(U_14832,U_14833),tc_prod(U_14834,U_14835),c_Product__Type_Omap__pair(U_14830,U_14832,U_14831,U_14833,U_14836,U_14837)),c_Product__Type_Omap__pair(U_14834,U_14830,U_14835,U_14831,U_14838,U_14839)) = c_Product__Type_Omap__pair(U_14834,U_14832,U_14835,U_14833,hAPP(c_Fun_Ocomp(U_14830,U_14832,U_14834,U_14836),U_14838),hAPP(c_Fun_Ocomp(U_14831,U_14833,U_14835,U_14837),U_14839)),
    inference(variable_rename,[status(thm)],[f_3760_1]) ).

fof(f_3760_3,plain,
    ! [U_14830,U_14831,U_14832,U_14833,U_14834,U_14835,U_14836,U_14837,U_14838,U_14839] : hAPP(c_Fun_Ocomp(tc_prod(U_14830,U_14831),tc_prod(U_14832,U_14833),tc_prod(U_14834,U_14835),c_Product__Type_Omap__pair(U_14830,U_14832,U_14831,U_14833,U_14836,U_14837)),c_Product__Type_Omap__pair(U_14834,U_14830,U_14835,U_14831,U_14838,U_14839)) = c_Product__Type_Omap__pair(U_14834,U_14832,U_14835,U_14833,hAPP(c_Fun_Ocomp(U_14830,U_14832,U_14834,U_14836),U_14838),hAPP(c_Fun_Ocomp(U_14831,U_14833,U_14835,U_14837),U_14839)),
    inference(definitional_conversion,[status(esa)],[f_3760_2]) ).

cnf(f_3760_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14830,U_14831),tc_prod(U_14832,U_14833),tc_prod(U_14834,U_14835),c_Product__Type_Omap__pair(U_14830,U_14832,U_14831,U_14833,U_14836,U_14837)),c_Product__Type_Omap__pair(U_14834,U_14830,U_14835,U_14831,U_14838,U_14839)) = c_Product__Type_Omap__pair(U_14834,U_14832,U_14835,U_14833,hAPP(c_Fun_Ocomp(U_14830,U_14832,U_14834,U_14836),U_14838),hAPP(c_Fun_Ocomp(U_14831,U_14833,U_14835,U_14837),U_14839)),
    inference(clausify,[status(thm)],[f_3760_3]) ).

fof(f_3761_1,plain,
    ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__compose]) ).

fof(f_3761_2,plain,
    ! [U_14849,U_14848,U_14847,U_14846,U_14845,U_14844,U_14843,U_14842,U_14841,U_14840] : c_Product__Type_Omap__pair(U_14840,U_14841,U_14842,U_14843,hAPP(c_Fun_Ocomp(U_14844,U_14841,U_14840,U_14845),U_14846),hAPP(c_Fun_Ocomp(U_14847,U_14843,U_14842,U_14848),U_14849)) = hAPP(c_Fun_Ocomp(tc_prod(U_14844,U_14847),tc_prod(U_14841,U_14843),tc_prod(U_14840,U_14842),c_Product__Type_Omap__pair(U_14844,U_14841,U_14847,U_14843,U_14845,U_14848)),c_Product__Type_Omap__pair(U_14840,U_14844,U_14842,U_14847,U_14846,U_14849)),
    inference(variable_rename,[status(thm)],[f_3761_1]) ).

fof(f_3761_3,plain,
    ! [U_14840,U_14841,U_14842,U_14843,U_14844,U_14845,U_14846,U_14847,U_14848,U_14849] : c_Product__Type_Omap__pair(U_14840,U_14841,U_14842,U_14843,hAPP(c_Fun_Ocomp(U_14844,U_14841,U_14840,U_14845),U_14846),hAPP(c_Fun_Ocomp(U_14847,U_14843,U_14842,U_14848),U_14849)) = hAPP(c_Fun_Ocomp(tc_prod(U_14844,U_14847),tc_prod(U_14841,U_14843),tc_prod(U_14840,U_14842),c_Product__Type_Omap__pair(U_14844,U_14841,U_14847,U_14843,U_14845,U_14848)),c_Product__Type_Omap__pair(U_14840,U_14844,U_14842,U_14847,U_14846,U_14849)),
    inference(definitional_conversion,[status(esa)],[f_3761_2]) ).

cnf(f_3761_4,plain,
    c_Product__Type_Omap__pair(U_14840,U_14841,U_14842,U_14843,hAPP(c_Fun_Ocomp(U_14844,U_14841,U_14840,U_14845),U_14846),hAPP(c_Fun_Ocomp(U_14847,U_14843,U_14842,U_14848),U_14849)) = hAPP(c_Fun_Ocomp(tc_prod(U_14844,U_14847),tc_prod(U_14841,U_14843),tc_prod(U_14840,U_14842),c_Product__Type_Omap__pair(U_14844,U_14841,U_14847,U_14843,U_14845,U_14848)),c_Product__Type_Omap__pair(U_14840,U_14844,U_14842,U_14847,U_14846,U_14849)),
    inference(clausify,[status(thm)],[f_3761_3]) ).

fof(f_3762_1,plain,
    ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(f_3762_2,plain,
    ! [U_14860,U_14859,U_14858,U_14857,U_14856,U_14855,U_14854,U_14853,U_14852,U_14851,U_14850] : hAPP(c_Product__Type_Omap__pair(U_14850,U_14851,U_14852,U_14853,U_14854,U_14855),hAPP(c_Product__Type_Omap__pair(U_14856,U_14850,U_14857,U_14852,U_14858,U_14859),U_14860)) = hAPP(c_Product__Type_Omap__pair(U_14856,U_14851,U_14857,U_14853,hAPP(c_Fun_Ocomp(U_14850,U_14851,U_14856,U_14854),U_14858),hAPP(c_Fun_Ocomp(U_14852,U_14853,U_14857,U_14855),U_14859)),U_14860),
    inference(variable_rename,[status(thm)],[f_3762_1]) ).

fof(f_3762_3,plain,
    ! [U_14850,U_14851,U_14852,U_14853,U_14854,U_14855,U_14856,U_14857,U_14858,U_14859,U_14860] : hAPP(c_Product__Type_Omap__pair(U_14850,U_14851,U_14852,U_14853,U_14854,U_14855),hAPP(c_Product__Type_Omap__pair(U_14856,U_14850,U_14857,U_14852,U_14858,U_14859),U_14860)) = hAPP(c_Product__Type_Omap__pair(U_14856,U_14851,U_14857,U_14853,hAPP(c_Fun_Ocomp(U_14850,U_14851,U_14856,U_14854),U_14858),hAPP(c_Fun_Ocomp(U_14852,U_14853,U_14857,U_14855),U_14859)),U_14860),
    inference(definitional_conversion,[status(esa)],[f_3762_2]) ).

cnf(f_3762_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_14850,U_14851,U_14852,U_14853,U_14854,U_14855),hAPP(c_Product__Type_Omap__pair(U_14856,U_14850,U_14857,U_14852,U_14858,U_14859),U_14860)) = hAPP(c_Product__Type_Omap__pair(U_14856,U_14851,U_14857,U_14853,hAPP(c_Fun_Ocomp(U_14850,U_14851,U_14856,U_14854),U_14858),hAPP(c_Fun_Ocomp(U_14852,U_14853,U_14857,U_14855),U_14859)),U_14860),
    inference(clausify,[status(thm)],[f_3762_3]) ).

fof(f_3763_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem]) ).

fof(f_3763_2,plain,
    ! [U_14864,U_14863,U_14862,U_14861] :
      ( hAPP(c_Fun_Ocomp(U_14862,U_14862,U_14862,hAPP(U_14863,U_14864)),hAPP(U_14863,U_14864)) = hAPP(U_14863,U_14864)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_14861,U_14862,U_14863) ),
    inference(variable_rename,[status(thm)],[f_3763_1]) ).

fof(f_3763_3,plain,
    ! [U_14864,U_14863,U_14862] :
      ( ! [U_14861] : ~ c_Finite__Set_Ofun__left__comm__idem(U_14861,U_14862,U_14863)
      | hAPP(c_Fun_Ocomp(U_14862,U_14862,U_14862,hAPP(U_14863,U_14864)),hAPP(U_14863,U_14864)) = hAPP(U_14863,U_14864) ),
    inference(miniscope,[status(thm)],[f_3763_2]) ).

fof(f_3763_4,plain,
    ! [U_14861,U_14863,U_14862,U_14864] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(U_14861,U_14862,U_14863)
      | hAPP(c_Fun_Ocomp(U_14862,U_14862,U_14862,hAPP(U_14863,U_14864)),hAPP(U_14863,U_14864)) = hAPP(U_14863,U_14864) ),
    inference(definitional_conversion,[status(esa)],[f_3763_3]) ).

cnf(f_3763_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_14861,U_14862,U_14863)
    | hAPP(c_Fun_Ocomp(U_14862,U_14862,U_14862,hAPP(U_14863,U_14864)),hAPP(U_14863,U_14864)) = hAPP(U_14863,U_14864) ),
    inference(clausify,[status(thm)],[f_3763_4]) ).

fof(f_3764_1,plain,
    ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
          | ~ c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) )
        & ( c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2)
          | ~ c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff]) ).

fof(f_3764_2,plain,
    ! [U_14870,U_14869,U_14868,U_14867,U_14866,U_14865] :
      ( ( ( c_Fun_Oinj__on(U_14866,U_14869,U_14870,hAPP(c_Set_Oimage(U_14865,U_14866,U_14867),U_14868))
          | ~ c_Fun_Oinj__on(U_14865,U_14869,hAPP(c_Fun_Ocomp(U_14866,U_14869,U_14865,U_14870),U_14867),U_14868) )
        & ( c_Fun_Oinj__on(U_14865,U_14869,hAPP(c_Fun_Ocomp(U_14866,U_14869,U_14865,U_14870),U_14867),U_14868)
          | ~ c_Fun_Oinj__on(U_14866,U_14869,U_14870,hAPP(c_Set_Oimage(U_14865,U_14866,U_14867),U_14868)) ) )
      | ~ c_Fun_Oinj__on(U_14865,U_14866,U_14867,U_14868) ),
    inference(variable_rename,[status(thm)],[f_3764_1]) ).

fof(f_3764_3,plain,
    ( ! [U_14865,U_14866,U_14867,U_14868,U_14869,U_14870] :
        ( c_Fun_Oinj__on(U_14866,U_14869,U_14870,hAPP(c_Set_Oimage(U_14865,U_14866,U_14867),U_14868))
        | ~ c_Fun_Oinj__on(U_14865,U_14869,hAPP(c_Fun_Ocomp(U_14866,U_14869,U_14865,U_14870),U_14867),U_14868)
        | ~ sP1021(U_14865,U_14866,U_14867,U_14868,U_14869,U_14870) )
    & ! [U_14865,U_14866,U_14867,U_14868,U_14869,U_14870] :
        ( c_Fun_Oinj__on(U_14865,U_14869,hAPP(c_Fun_Ocomp(U_14866,U_14869,U_14865,U_14870),U_14867),U_14868)
        | ~ c_Fun_Oinj__on(U_14866,U_14869,U_14870,hAPP(c_Set_Oimage(U_14865,U_14866,U_14867),U_14868))
        | ~ sP1021(U_14865,U_14866,U_14867,U_14868,U_14869,U_14870) )
    & ! [U_14865,U_14866,U_14867,U_14868,U_14869,U_14870] :
        ( sP1021(U_14865,U_14866,U_14867,U_14868,U_14869,U_14870)
        | ~ c_Fun_Oinj__on(U_14865,U_14866,U_14867,U_14868) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1021])],[f_3764_2]) ).

cnf(f_3764_4,plain,
    ( sP1021(U_14865,U_14866,U_14867,U_14868,U_14869,U_14870)
    | ~ c_Fun_Oinj__on(U_14865,U_14866,U_14867,U_14868) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

cnf(f_3764_5,plain,
    ( c_Fun_Oinj__on(U_14865,U_14869,hAPP(c_Fun_Ocomp(U_14866,U_14869,U_14865,U_14870),U_14867),U_14868)
    | ~ c_Fun_Oinj__on(U_14866,U_14869,U_14870,hAPP(c_Set_Oimage(U_14865,U_14866,U_14867),U_14868))
    | ~ sP1021(U_14865,U_14866,U_14867,U_14868,U_14869,U_14870) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

cnf(f_3764_6,plain,
    ( c_Fun_Oinj__on(U_14866,U_14869,U_14870,hAPP(c_Set_Oimage(U_14865,U_14866,U_14867),U_14868))
    | ~ c_Fun_Oinj__on(U_14865,U_14869,hAPP(c_Fun_Ocomp(U_14866,U_14869,U_14865,U_14870),U_14867),U_14868)
    | ~ sP1021(U_14865,U_14866,U_14867,U_14868,U_14869,U_14870) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

fof(f_3765_1,plain,
    ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_comp__inj__on]) ).

fof(f_3765_2,plain,
    ! [U_14876,U_14875,U_14874,U_14873,U_14872,U_14871] :
      ( c_Fun_Oinj__on(U_14871,U_14875,hAPP(c_Fun_Ocomp(U_14872,U_14875,U_14871,U_14876),U_14873),U_14874)
      | ~ c_Fun_Oinj__on(U_14872,U_14875,U_14876,hAPP(c_Set_Oimage(U_14871,U_14872,U_14873),U_14874))
      | ~ c_Fun_Oinj__on(U_14871,U_14872,U_14873,U_14874) ),
    inference(variable_rename,[status(thm)],[f_3765_1]) ).

fof(f_3765_3,plain,
    ! [U_14871,U_14872,U_14874,U_14876,U_14873,U_14875] :
      ( c_Fun_Oinj__on(U_14871,U_14875,hAPP(c_Fun_Ocomp(U_14872,U_14875,U_14871,U_14876),U_14873),U_14874)
      | ~ c_Fun_Oinj__on(U_14872,U_14875,U_14876,hAPP(c_Set_Oimage(U_14871,U_14872,U_14873),U_14874))
      | ~ c_Fun_Oinj__on(U_14871,U_14872,U_14873,U_14874) ),
    inference(definitional_conversion,[status(esa)],[f_3765_2]) ).

cnf(f_3765_4,plain,
    ( c_Fun_Oinj__on(U_14871,U_14875,hAPP(c_Fun_Ocomp(U_14872,U_14875,U_14871,U_14876),U_14873),U_14874)
    | ~ c_Fun_Oinj__on(U_14872,U_14875,U_14876,hAPP(c_Set_Oimage(U_14871,U_14872,U_14873),U_14874))
    | ~ c_Fun_Oinj__on(U_14871,U_14872,U_14873,U_14874) ),
    inference(clausify,[status(thm)],[f_3765_3]) ).

fof(f_3766_1,plain,
    ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imageI]) ).

fof(f_3766_2,plain,
    ! [U_14882,U_14881,U_14880,U_14879,U_14878,U_14877] :
      ( c_Fun_Oinj__on(U_14879,U_14878,U_14880,hAPP(c_Set_Oimage(U_14877,U_14879,U_14881),U_14882))
      | ~ c_Fun_Oinj__on(U_14877,U_14878,hAPP(c_Fun_Ocomp(U_14879,U_14878,U_14877,U_14880),U_14881),U_14882) ),
    inference(variable_rename,[status(thm)],[f_3766_1]) ).

fof(f_3766_3,plain,
    ! [U_14879,U_14877,U_14878,U_14880,U_14881,U_14882] :
      ( c_Fun_Oinj__on(U_14879,U_14878,U_14880,hAPP(c_Set_Oimage(U_14877,U_14879,U_14881),U_14882))
      | ~ c_Fun_Oinj__on(U_14877,U_14878,hAPP(c_Fun_Ocomp(U_14879,U_14878,U_14877,U_14880),U_14881),U_14882) ),
    inference(definitional_conversion,[status(esa)],[f_3766_2]) ).

cnf(f_3766_4,plain,
    ( c_Fun_Oinj__on(U_14879,U_14878,U_14880,hAPP(c_Set_Oimage(U_14877,U_14879,U_14881),U_14882))
    | ~ c_Fun_Oinj__on(U_14877,U_14878,hAPP(c_Fun_Ocomp(U_14879,U_14878,U_14877,U_14880),U_14881),U_14882) ),
    inference(clausify,[status(thm)],[f_3766_3]) ).

fof(f_3767_1,plain,
    ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2]) ).

fof(f_3767_2,plain,
    ! [U_14888,U_14887,U_14886,U_14885,U_14884,U_14883] :
      ( c_Fun_Oinj__on(U_14883,U_14885,U_14887,U_14888)
      | ~ c_Fun_Oinj__on(U_14883,U_14884,hAPP(c_Fun_Ocomp(U_14885,U_14884,U_14883,U_14886),U_14887),U_14888) ),
    inference(variable_rename,[status(thm)],[f_3767_1]) ).

fof(f_3767_3,plain,
    ! [U_14884,U_14885,U_14883,U_14886,U_14887,U_14888] :
      ( c_Fun_Oinj__on(U_14883,U_14885,U_14887,U_14888)
      | ~ c_Fun_Oinj__on(U_14883,U_14884,hAPP(c_Fun_Ocomp(U_14885,U_14884,U_14883,U_14886),U_14887),U_14888) ),
    inference(definitional_conversion,[status(esa)],[f_3767_2]) ).

cnf(f_3767_4,plain,
    ( c_Fun_Oinj__on(U_14883,U_14885,U_14887,U_14888)
    | ~ c_Fun_Oinj__on(U_14883,U_14884,hAPP(c_Fun_Ocomp(U_14885,U_14884,U_14883,U_14886),U_14887),U_14888) ),
    inference(clausify,[status(thm)],[f_3767_3]) ).

fof(f_3768_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__comp]) ).

fof(f_3768_2,plain,
    ! [U_14893,U_14892,U_14891,U_14890,U_14889] :
      ( c_Fun_Oinj__on(U_14892,U_14890,hAPP(c_Fun_Ocomp(U_14889,U_14890,U_14892,U_14891),U_14893),c_Orderings_Otop__class_Otop(tc_fun(U_14892,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_14892,U_14889,U_14893,c_Orderings_Otop__class_Otop(tc_fun(U_14892,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_14889,U_14890,U_14891,c_Orderings_Otop__class_Otop(tc_fun(U_14889,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3768_1]) ).

fof(f_3768_3,plain,
    ! [U_14890,U_14889,U_14891,U_14892,U_14893] :
      ( c_Fun_Oinj__on(U_14892,U_14890,hAPP(c_Fun_Ocomp(U_14889,U_14890,U_14892,U_14891),U_14893),c_Orderings_Otop__class_Otop(tc_fun(U_14892,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_14892,U_14889,U_14893,c_Orderings_Otop__class_Otop(tc_fun(U_14892,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_14889,U_14890,U_14891,c_Orderings_Otop__class_Otop(tc_fun(U_14889,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3768_2]) ).

cnf(f_3768_4,plain,
    ( c_Fun_Oinj__on(U_14892,U_14890,hAPP(c_Fun_Ocomp(U_14889,U_14890,U_14892,U_14891),U_14893),c_Orderings_Otop__class_Otop(tc_fun(U_14892,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_14892,U_14889,U_14893,c_Orderings_Otop__class_Otop(tc_fun(U_14892,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_14889,U_14890,U_14891,c_Orderings_Otop__class_Otop(tc_fun(U_14889,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3768_3]) ).

fof(f_3769_1,plain,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex]) ).

fof(f_3769_2,plain,
    ! [U_14899,U_14898,U_14897,U_14896,U_14895,U_14894] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14896,U_14894),U_14899),hAPP(c_Set_Oimage(U_14895,U_14896,U_14897),U_14898)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14895,U_14894),hAPP(c_Fun_Ocomp(U_14896,U_14894,U_14895,U_14899),U_14897)),U_14898)
      | ~ c_Fun_Oinj__on(U_14895,U_14896,U_14897,U_14898)
      | ~ class_Groups_Ocomm__monoid__add(U_14894) ),
    inference(variable_rename,[status(thm)],[f_3769_1]) ).

fof(f_3769_3,plain,
    ! [U_14895,U_14894,U_14896,U_14897,U_14898,U_14899] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14896,U_14894),U_14899),hAPP(c_Set_Oimage(U_14895,U_14896,U_14897),U_14898)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14895,U_14894),hAPP(c_Fun_Ocomp(U_14896,U_14894,U_14895,U_14899),U_14897)),U_14898)
      | ~ c_Fun_Oinj__on(U_14895,U_14896,U_14897,U_14898)
      | ~ class_Groups_Ocomm__monoid__add(U_14894) ),
    inference(definitional_conversion,[status(esa)],[f_3769_2]) ).

cnf(f_3769_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14896,U_14894),U_14899),hAPP(c_Set_Oimage(U_14895,U_14896,U_14897),U_14898)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14895,U_14894),hAPP(c_Fun_Ocomp(U_14896,U_14894,U_14895,U_14899),U_14897)),U_14898)
    | ~ c_Fun_Oinj__on(U_14895,U_14896,U_14897,U_14898)
    | ~ class_Groups_Ocomm__monoid__add(U_14894) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

fof(f_3770_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)
      | V_g_2 != hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
      | V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong]) ).

fof(f_3770_2,plain,
    ! [U_14907,U_14906,U_14905,U_14904,U_14903,U_14902,U_14901,U_14900] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14902,U_14900),U_14907),U_14905) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14901,U_14900),U_14906),U_14904)
      | U_14906 != hAPP(c_Fun_Ocomp(U_14902,U_14900,U_14901,U_14907),U_14903)
      | U_14905 != hAPP(c_Set_Oimage(U_14901,U_14902,U_14903),U_14904)
      | ~ c_Fun_Oinj__on(U_14901,U_14902,U_14903,U_14904)
      | ~ class_Groups_Ocomm__monoid__mult(U_14900) ),
    inference(variable_rename,[status(thm)],[f_3770_1]) ).

fof(f_3770_3,plain,
    ! [U_14900,U_14901,U_14902,U_14903,U_14904,U_14905,U_14906,U_14907] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14902,U_14900),U_14907),U_14905) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14901,U_14900),U_14906),U_14904)
      | U_14906 != hAPP(c_Fun_Ocomp(U_14902,U_14900,U_14901,U_14907),U_14903)
      | U_14905 != hAPP(c_Set_Oimage(U_14901,U_14902,U_14903),U_14904)
      | ~ c_Fun_Oinj__on(U_14901,U_14902,U_14903,U_14904)
      | ~ class_Groups_Ocomm__monoid__mult(U_14900) ),
    inference(definitional_conversion,[status(esa)],[f_3770_2]) ).

cnf(f_3770_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14902,U_14900),U_14907),U_14905) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14901,U_14900),U_14906),U_14904)
    | U_14906 != hAPP(c_Fun_Ocomp(U_14902,U_14900,U_14901,U_14907),U_14903)
    | U_14905 != hAPP(c_Set_Oimage(U_14901,U_14902,U_14903),U_14904)
    | ~ c_Fun_Oinj__on(U_14901,U_14902,U_14903,U_14904)
    | ~ class_Groups_Ocomm__monoid__mult(U_14900) ),
    inference(clausify,[status(thm)],[f_3770_3]) ).

fof(f_3771_1,plain,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex]) ).

fof(f_3771_2,plain,
    ! [U_14913,U_14912,U_14911,U_14910,U_14909,U_14908] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14910,U_14908),U_14913),hAPP(c_Set_Oimage(U_14909,U_14910,U_14911),U_14912)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14909,U_14908),hAPP(c_Fun_Ocomp(U_14910,U_14908,U_14909,U_14913),U_14911)),U_14912)
      | ~ c_Fun_Oinj__on(U_14909,U_14910,U_14911,U_14912)
      | ~ class_Groups_Ocomm__monoid__mult(U_14908) ),
    inference(variable_rename,[status(thm)],[f_3771_1]) ).

fof(f_3771_3,plain,
    ! [U_14909,U_14910,U_14911,U_14908,U_14912,U_14913] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14910,U_14908),U_14913),hAPP(c_Set_Oimage(U_14909,U_14910,U_14911),U_14912)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14909,U_14908),hAPP(c_Fun_Ocomp(U_14910,U_14908,U_14909,U_14913),U_14911)),U_14912)
      | ~ c_Fun_Oinj__on(U_14909,U_14910,U_14911,U_14912)
      | ~ class_Groups_Ocomm__monoid__mult(U_14908) ),
    inference(definitional_conversion,[status(esa)],[f_3771_2]) ).

cnf(f_3771_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14910,U_14908),U_14913),hAPP(c_Set_Oimage(U_14909,U_14910,U_14911),U_14912)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14909,U_14908),hAPP(c_Fun_Ocomp(U_14910,U_14908,U_14909,U_14913),U_14911)),U_14912)
    | ~ c_Fun_Oinj__on(U_14909,U_14910,U_14911,U_14912)
    | ~ class_Groups_Ocomm__monoid__mult(U_14908) ),
    inference(clausify,[status(thm)],[f_3771_3]) ).

fof(f_3772_1,plain,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex]) ).

fof(f_3772_2,plain,
    ! [U_14918,U_14917,U_14916,U_14915,U_14914] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14915,U_14914),U_14918),hAPP(c_Set_Oimage(U_14915,U_14915,U_14917),U_14916)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14915,U_14914),hAPP(c_Fun_Ocomp(U_14915,U_14914,U_14915,U_14918),U_14917)),U_14916)
      | ~ c_Fun_Oinj__on(U_14915,U_14915,U_14917,U_14916)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14915),U_14916))
      | ~ class_Groups_Ocomm__monoid__add(U_14914) ),
    inference(variable_rename,[status(thm)],[f_3772_1]) ).

fof(f_3772_3,plain,
    ! [U_14915,U_14914,U_14916,U_14917,U_14918] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14915,U_14914),U_14918),hAPP(c_Set_Oimage(U_14915,U_14915,U_14917),U_14916)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14915,U_14914),hAPP(c_Fun_Ocomp(U_14915,U_14914,U_14915,U_14918),U_14917)),U_14916)
      | ~ c_Fun_Oinj__on(U_14915,U_14915,U_14917,U_14916)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14915),U_14916))
      | ~ class_Groups_Ocomm__monoid__add(U_14914) ),
    inference(definitional_conversion,[status(esa)],[f_3772_2]) ).

cnf(f_3772_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14915,U_14914),U_14918),hAPP(c_Set_Oimage(U_14915,U_14915,U_14917),U_14916)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14915,U_14914),hAPP(c_Fun_Ocomp(U_14915,U_14914,U_14915,U_14918),U_14917)),U_14916)
    | ~ c_Fun_Oinj__on(U_14915,U_14915,U_14917,U_14916)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14915),U_14916))
    | ~ class_Groups_Ocomm__monoid__add(U_14914) ),
    inference(clausify,[status(thm)],[f_3772_3]) ).

fof(f_3773_1,plain,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex]) ).

fof(f_3773_2,plain,
    ! [U_14923,U_14922,U_14921,U_14920,U_14919] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14920,U_14919),U_14923),hAPP(c_Set_Oimage(U_14920,U_14920,U_14922),U_14921)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14920,U_14919),hAPP(c_Fun_Ocomp(U_14920,U_14919,U_14920,U_14923),U_14922)),U_14921)
      | ~ c_Fun_Oinj__on(U_14920,U_14920,U_14922,U_14921)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14920),U_14921))
      | ~ class_Groups_Ocomm__monoid__mult(U_14919) ),
    inference(variable_rename,[status(thm)],[f_3773_1]) ).

fof(f_3773_3,plain,
    ! [U_14920,U_14919,U_14921,U_14922,U_14923] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14920,U_14919),U_14923),hAPP(c_Set_Oimage(U_14920,U_14920,U_14922),U_14921)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14920,U_14919),hAPP(c_Fun_Ocomp(U_14920,U_14919,U_14920,U_14923),U_14922)),U_14921)
      | ~ c_Fun_Oinj__on(U_14920,U_14920,U_14922,U_14921)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14920),U_14921))
      | ~ class_Groups_Ocomm__monoid__mult(U_14919) ),
    inference(definitional_conversion,[status(esa)],[f_3773_2]) ).

cnf(f_3773_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14920,U_14919),U_14923),hAPP(c_Set_Oimage(U_14920,U_14920,U_14922),U_14921)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14920,U_14919),hAPP(c_Fun_Ocomp(U_14920,U_14919,U_14920,U_14923),U_14922)),U_14921)
    | ~ c_Fun_Oinj__on(U_14920,U_14920,U_14922,U_14921)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14920),U_14921))
    | ~ class_Groups_Ocomm__monoid__mult(U_14919) ),
    inference(clausify,[status(thm)],[f_3773_3]) ).

fof(f_3774_1,plain,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp]) ).

fof(f_3774_2,plain,
    ! [U_14930,U_14929,U_14928,U_14927,U_14926,U_14925,U_14924] :
      ( hAPP(c_Fun_Othe__inv__into(U_14927,U_14925,U_14929,hAPP(c_Fun_Ocomp(U_14924,U_14925,U_14927,U_14926),U_14928)),U_14930) = hAPP(hAPP(c_Fun_Ocomp(U_14924,U_14927,U_14925,c_Fun_Othe__inv__into(U_14927,U_14924,U_14929,U_14928)),c_Fun_Othe__inv__into(U_14924,U_14925,hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929),U_14926)),U_14930)
      | ~ hBOOL(hAPP(hAPP(c_member(U_14925),U_14930),hAPP(c_Set_Oimage(U_14924,U_14925,U_14926),hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929))))
      | ~ c_Fun_Oinj__on(U_14927,U_14924,U_14928,U_14929)
      | ~ c_Fun_Oinj__on(U_14924,U_14925,U_14926,hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929)) ),
    inference(variable_rename,[status(thm)],[f_3774_1]) ).

fof(f_3774_3,plain,
    ! [U_14924,U_14925,U_14926,U_14927,U_14928,U_14929,U_14930] :
      ( hAPP(c_Fun_Othe__inv__into(U_14927,U_14925,U_14929,hAPP(c_Fun_Ocomp(U_14924,U_14925,U_14927,U_14926),U_14928)),U_14930) = hAPP(hAPP(c_Fun_Ocomp(U_14924,U_14927,U_14925,c_Fun_Othe__inv__into(U_14927,U_14924,U_14929,U_14928)),c_Fun_Othe__inv__into(U_14924,U_14925,hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929),U_14926)),U_14930)
      | ~ hBOOL(hAPP(hAPP(c_member(U_14925),U_14930),hAPP(c_Set_Oimage(U_14924,U_14925,U_14926),hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929))))
      | ~ c_Fun_Oinj__on(U_14927,U_14924,U_14928,U_14929)
      | ~ c_Fun_Oinj__on(U_14924,U_14925,U_14926,hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929)) ),
    inference(definitional_conversion,[status(esa)],[f_3774_2]) ).

cnf(f_3774_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_14927,U_14925,U_14929,hAPP(c_Fun_Ocomp(U_14924,U_14925,U_14927,U_14926),U_14928)),U_14930) = hAPP(hAPP(c_Fun_Ocomp(U_14924,U_14927,U_14925,c_Fun_Othe__inv__into(U_14927,U_14924,U_14929,U_14928)),c_Fun_Othe__inv__into(U_14924,U_14925,hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929),U_14926)),U_14930)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14925),U_14930),hAPP(c_Set_Oimage(U_14924,U_14925,U_14926),hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929))))
    | ~ c_Fun_Oinj__on(U_14927,U_14924,U_14928,U_14929)
    | ~ c_Fun_Oinj__on(U_14924,U_14925,U_14926,hAPP(c_Set_Oimage(U_14927,U_14924,U_14928),U_14929)) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

fof(f_3775_1,plain,
    ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__reindex]) ).

fof(f_3775_2,plain,
    ! [U_14937,U_14936,U_14935,U_14934,U_14933,U_14932,U_14931] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14931,U_14934,c_Groups_Otimes__class_Otimes(U_14931)),U_14936),U_14937),hAPP(c_Set_Oimage(U_14932,U_14934,U_14935),U_14933)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14931,U_14932,c_Groups_Otimes__class_Otimes(U_14931)),hAPP(c_Fun_Ocomp(U_14934,U_14931,U_14932,U_14936),U_14935)),U_14937),U_14933)
      | ~ c_Fun_Oinj__on(U_14932,U_14934,U_14935,U_14933)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),U_14933))
      | ~ class_Groups_Oab__semigroup__mult(U_14931) ),
    inference(variable_rename,[status(thm)],[f_3775_1]) ).

fof(f_3775_3,plain,
    ! [U_14931,U_14932,U_14933,U_14934,U_14935,U_14936,U_14937] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14931,U_14934,c_Groups_Otimes__class_Otimes(U_14931)),U_14936),U_14937),hAPP(c_Set_Oimage(U_14932,U_14934,U_14935),U_14933)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14931,U_14932,c_Groups_Otimes__class_Otimes(U_14931)),hAPP(c_Fun_Ocomp(U_14934,U_14931,U_14932,U_14936),U_14935)),U_14937),U_14933)
      | ~ c_Fun_Oinj__on(U_14932,U_14934,U_14935,U_14933)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),U_14933))
      | ~ class_Groups_Oab__semigroup__mult(U_14931) ),
    inference(definitional_conversion,[status(esa)],[f_3775_2]) ).

cnf(f_3775_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14931,U_14934,c_Groups_Otimes__class_Otimes(U_14931)),U_14936),U_14937),hAPP(c_Set_Oimage(U_14932,U_14934,U_14935),U_14933)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14931,U_14932,c_Groups_Otimes__class_Otimes(U_14931)),hAPP(c_Fun_Ocomp(U_14934,U_14931,U_14932,U_14936),U_14935)),U_14937),U_14933)
    | ~ c_Fun_Oinj__on(U_14932,U_14934,U_14935,U_14933)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),U_14933))
    | ~ class_Groups_Oab__semigroup__mult(U_14931) ),
    inference(clausify,[status(thm)],[f_3775_3]) ).

fof(f_3776_1,plain,
    ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(f_3776_2,plain,
    ! [U_14938] : c_Nitpick_Odenom(U_14938) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14938,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14938)),
    inference(variable_rename,[status(thm)],[f_3776_1]) ).

fof(f_3776_3,plain,
    ! [U_14938] : c_Nitpick_Odenom(U_14938) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14938,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14938)),
    inference(definitional_conversion,[status(esa)],[f_3776_2]) ).

cnf(f_3776_4,plain,
    c_Nitpick_Odenom(U_14938) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14938,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14938)),
    inference(clausify,[status(thm)],[f_3776_3]) ).

fof(f_3777_1,plain,
    ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(f_3777_2,plain,
    ! [U_14939] : c_Nitpick_Onum(U_14939) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14939,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14939)),
    inference(variable_rename,[status(thm)],[f_3777_1]) ).

fof(f_3777_3,plain,
    ! [U_14939] : c_Nitpick_Onum(U_14939) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14939,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14939)),
    inference(definitional_conversion,[status(esa)],[f_3777_2]) ).

cnf(f_3777_4,plain,
    c_Nitpick_Onum(U_14939) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14939,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14939)),
    inference(clausify,[status(thm)],[f_3777_3]) ).

fof(f_3778_1,plain,
    ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
    inference(fof_nnf,[status(thm)],[fact_UN__o]) ).

fof(f_3778_2,plain,
    ! [U_14945,U_14944,U_14943,U_14942,U_14941,U_14940] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14940,tc_fun(U_14941,tc_HOL_Obool)),U_14942),hAPP(c_Fun_Ocomp(U_14943,tc_fun(U_14941,tc_HOL_Obool),U_14940,U_14944),U_14945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14943,tc_fun(U_14941,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14940,U_14943,U_14945),U_14942)),U_14944),
    inference(variable_rename,[status(thm)],[f_3778_1]) ).

fof(f_3778_3,plain,
    ! [U_14940,U_14941,U_14942,U_14943,U_14944,U_14945] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14940,tc_fun(U_14941,tc_HOL_Obool)),U_14942),hAPP(c_Fun_Ocomp(U_14943,tc_fun(U_14941,tc_HOL_Obool),U_14940,U_14944),U_14945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14943,tc_fun(U_14941,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14940,U_14943,U_14945),U_14942)),U_14944),
    inference(definitional_conversion,[status(esa)],[f_3778_2]) ).

cnf(f_3778_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14940,tc_fun(U_14941,tc_HOL_Obool)),U_14942),hAPP(c_Fun_Ocomp(U_14943,tc_fun(U_14941,tc_HOL_Obool),U_14940,U_14944),U_14945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14943,tc_fun(U_14941,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14940,U_14943,U_14945),U_14942)),U_14944),
    inference(clausify,[status(thm)],[f_3778_3]) ).

fof(f_3779_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(f_3779_2,plain,
    ! [U_14951,U_14950,U_14949,U_14948,U_14947,U_14946] : hAPP(c_Fun_Ocomp(tc_prod(U_14946,U_14947),U_14947,tc_prod(U_14948,U_14949),c_Product__Type_Osnd(U_14946,U_14947)),c_Product__Type_Omap__pair(U_14948,U_14946,U_14949,U_14947,U_14950,U_14951)) = hAPP(c_Fun_Ocomp(U_14949,U_14947,tc_prod(U_14948,U_14949),U_14951),c_Product__Type_Osnd(U_14948,U_14949)),
    inference(variable_rename,[status(thm)],[f_3779_1]) ).

fof(f_3779_3,plain,
    ! [U_14946,U_14947,U_14948,U_14949,U_14950,U_14951] : hAPP(c_Fun_Ocomp(tc_prod(U_14946,U_14947),U_14947,tc_prod(U_14948,U_14949),c_Product__Type_Osnd(U_14946,U_14947)),c_Product__Type_Omap__pair(U_14948,U_14946,U_14949,U_14947,U_14950,U_14951)) = hAPP(c_Fun_Ocomp(U_14949,U_14947,tc_prod(U_14948,U_14949),U_14951),c_Product__Type_Osnd(U_14948,U_14949)),
    inference(definitional_conversion,[status(esa)],[f_3779_2]) ).

cnf(f_3779_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14946,U_14947),U_14947,tc_prod(U_14948,U_14949),c_Product__Type_Osnd(U_14946,U_14947)),c_Product__Type_Omap__pair(U_14948,U_14946,U_14949,U_14947,U_14950,U_14951)) = hAPP(c_Fun_Ocomp(U_14949,U_14947,tc_prod(U_14948,U_14949),U_14951),c_Product__Type_Osnd(U_14948,U_14949)),
    inference(clausify,[status(thm)],[f_3779_3]) ).

fof(f_3780_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(f_3780_2,plain,
    ! [U_14957,U_14956,U_14955,U_14954,U_14953,U_14952] : hAPP(c_Fun_Ocomp(tc_prod(U_14952,U_14953),U_14952,tc_prod(U_14954,U_14955),c_Product__Type_Ofst(U_14952,U_14953)),c_Product__Type_Omap__pair(U_14954,U_14952,U_14955,U_14953,U_14956,U_14957)) = hAPP(c_Fun_Ocomp(U_14954,U_14952,tc_prod(U_14954,U_14955),U_14956),c_Product__Type_Ofst(U_14954,U_14955)),
    inference(variable_rename,[status(thm)],[f_3780_1]) ).

fof(f_3780_3,plain,
    ! [U_14952,U_14953,U_14954,U_14955,U_14956,U_14957] : hAPP(c_Fun_Ocomp(tc_prod(U_14952,U_14953),U_14952,tc_prod(U_14954,U_14955),c_Product__Type_Ofst(U_14952,U_14953)),c_Product__Type_Omap__pair(U_14954,U_14952,U_14955,U_14953,U_14956,U_14957)) = hAPP(c_Fun_Ocomp(U_14954,U_14952,tc_prod(U_14954,U_14955),U_14956),c_Product__Type_Ofst(U_14954,U_14955)),
    inference(definitional_conversion,[status(esa)],[f_3780_2]) ).

cnf(f_3780_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14952,U_14953),U_14952,tc_prod(U_14954,U_14955),c_Product__Type_Ofst(U_14952,U_14953)),c_Product__Type_Omap__pair(U_14954,U_14952,U_14955,U_14953,U_14956,U_14957)) = hAPP(c_Fun_Ocomp(U_14954,U_14952,tc_prod(U_14954,U_14955),U_14956),c_Product__Type_Ofst(U_14954,U_14955)),
    inference(clausify,[status(thm)],[f_3780_3]) ).

fof(f_3781_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_split__comp]) ).

fof(f_3781_2,plain,
    ! [U_14964,U_14963,U_14962,U_14961,U_14960,U_14959,U_14958] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14958,U_14959,U_14960),hAPP(c_Fun_Ocomp(U_14961,tc_fun(U_14959,U_14960),U_14958,U_14962),U_14963)),U_14964) = hAPP(hAPP(U_14962,hAPP(U_14963,hAPP(c_Product__Type_Ofst(U_14958,U_14959),U_14964))),hAPP(c_Product__Type_Osnd(U_14958,U_14959),U_14964)),
    inference(variable_rename,[status(thm)],[f_3781_1]) ).

fof(f_3781_3,plain,
    ! [U_14958,U_14959,U_14960,U_14961,U_14962,U_14963,U_14964] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14958,U_14959,U_14960),hAPP(c_Fun_Ocomp(U_14961,tc_fun(U_14959,U_14960),U_14958,U_14962),U_14963)),U_14964) = hAPP(hAPP(U_14962,hAPP(U_14963,hAPP(c_Product__Type_Ofst(U_14958,U_14959),U_14964))),hAPP(c_Product__Type_Osnd(U_14958,U_14959),U_14964)),
    inference(definitional_conversion,[status(esa)],[f_3781_2]) ).

cnf(f_3781_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14958,U_14959,U_14960),hAPP(c_Fun_Ocomp(U_14961,tc_fun(U_14959,U_14960),U_14958,U_14962),U_14963)),U_14964) = hAPP(hAPP(U_14962,hAPP(U_14963,hAPP(c_Product__Type_Ofst(U_14958,U_14959),U_14964))),hAPP(c_Product__Type_Osnd(U_14958,U_14959),U_14964)),
    inference(clausify,[status(thm)],[f_3781_3]) ).

fof(f_3782_1,plain,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    inference(fof_nnf,[status(thm)],[fact_number__of__code__numeral__def]) ).

fof(f_3782_2,plain,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    inference(definitional_conversion,[status(esa)],[f_3782_1]) ).

cnf(f_3782_3,plain,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    inference(clausify,[status(thm)],[f_3782_2]) ).

fof(f_3783_1,plain,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    inference(fof_nnf,[status(thm)],[fact_int__of__def]) ).

fof(f_3783_2,plain,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    inference(definitional_conversion,[status(esa)],[f_3783_1]) ).

cnf(f_3783_3,plain,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    inference(clausify,[status(thm)],[f_3783_2]) ).

fof(f_3784_1,plain,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Loop__sound__lemma]) ).

fof(f_3784_2,plain,
    ! [U_14969,U_14968,U_14967,U_14966,U_14965] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_14965,U_14966,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14965)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14965),U_14967),c_Com_Ocom_OWhile(U_14968,U_14969)),c_Hoare__Mirabelle_Opeek__and(U_14965,U_14967,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14968)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14965),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14965,U_14966,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14965)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14965),c_Hoare__Mirabelle_Opeek__and(U_14965,U_14967,U_14968)),U_14969),U_14967)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14965),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3784_1]) ).

fof(f_3784_3,plain,
    ! [U_14965,U_14966,U_14967,U_14968,U_14969] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_14965,U_14966,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14965)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14965),U_14967),c_Com_Ocom_OWhile(U_14968,U_14969)),c_Hoare__Mirabelle_Opeek__and(U_14965,U_14967,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14968)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14965),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14965,U_14966,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14965)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14965),c_Hoare__Mirabelle_Opeek__and(U_14965,U_14967,U_14968)),U_14969),U_14967)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14965),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3784_2]) ).

cnf(f_3784_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_14965,U_14966,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14965)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14965),U_14967),c_Com_Ocom_OWhile(U_14968,U_14969)),c_Hoare__Mirabelle_Opeek__and(U_14965,U_14967,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14968)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14965),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14965,U_14966,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14965)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14965),c_Hoare__Mirabelle_Opeek__and(U_14965,U_14967,U_14968)),U_14969),U_14967)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14965),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3784_3]) ).

fof(f_3785_1,plain,
    ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf]) ).

fof(f_3785_2,plain,
    ! [U_14976,U_14975,U_14974,U_14973,U_14972,U_14971,U_14970] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),U_14972),c_Com_Ocom_OCond(U_14973,U_14974,U_14976)),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),c_Hoare__Mirabelle_Opeek__and(U_14970,U_14972,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14973))),U_14976),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),c_Hoare__Mirabelle_Opeek__and(U_14970,U_14972,U_14973)),U_14974),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3785_1]) ).

fof(f_3785_3,plain,
    ! [U_14970,U_14971,U_14972,U_14973,U_14974,U_14975,U_14976] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),U_14972),c_Com_Ocom_OCond(U_14973,U_14974,U_14976)),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),c_Hoare__Mirabelle_Opeek__and(U_14970,U_14972,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14973))),U_14976),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),c_Hoare__Mirabelle_Opeek__and(U_14970,U_14972,U_14973)),U_14974),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3785_2]) ).

cnf(f_3785_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),U_14972),c_Com_Ocom_OCond(U_14973,U_14974,U_14976)),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),c_Hoare__Mirabelle_Opeek__and(U_14970,U_14972,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14973))),U_14976),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14970,U_14971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14970)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14970),c_Hoare__Mirabelle_Opeek__and(U_14970,U_14972,U_14973)),U_14974),U_14975)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14970),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

fof(f_3786_1,plain,
    ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2))
        | ~ hBOOL(hAPP(V_p_2,V_s_2))
        | ~ hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) )
      & ( ( hBOOL(hAPP(V_p_2,V_s_2))
          & hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_peek__and__def]) ).

fof(f_3786_2,plain,
    ! [U_14981,U_14980,U_14979,U_14978,U_14977] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14977,U_14978,U_14979),U_14980),U_14981))
        | ~ hBOOL(hAPP(U_14979,U_14981))
        | ~ hBOOL(hAPP(hAPP(U_14978,U_14980),U_14981)) )
      & ( ( hBOOL(hAPP(U_14979,U_14981))
          & hBOOL(hAPP(hAPP(U_14978,U_14980),U_14981)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14977,U_14978,U_14979),U_14980),U_14981)) ) ),
    inference(variable_rename,[status(thm)],[f_3786_1]) ).

fof(f_3786_3,plain,
    ( ! [U_14991,U_14989,U_14987,U_14985] :
        ( ! [U_14983] : hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14983,U_14985,U_14987),U_14989),U_14991))
        | ~ hBOOL(hAPP(U_14987,U_14991))
        | ~ hBOOL(hAPP(hAPP(U_14985,U_14989),U_14991)) )
    & ! [U_14990,U_14988,U_14986,U_14984] :
        ( ! [U_14982] : ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14982,U_14984,U_14986),U_14988),U_14990))
        | ( hBOOL(hAPP(U_14986,U_14990))
          & hBOOL(hAPP(hAPP(U_14984,U_14988),U_14990)) ) ) ),
    inference(miniscope,[status(thm)],[f_3786_2]) ).

fof(f_3786_4,plain,
    ( ! [U_14986,U_14988,U_14984,U_14990] :
        ( hBOOL(hAPP(U_14986,U_14990))
        | ~ sP1022(U_14986,U_14988,U_14984,U_14990) )
    & ! [U_14986,U_14988,U_14984,U_14990] :
        ( hBOOL(hAPP(hAPP(U_14984,U_14988),U_14990))
        | ~ sP1022(U_14986,U_14988,U_14984,U_14990) )
    & ! [U_14987,U_14985,U_14983,U_14989,U_14991] :
        ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14983,U_14985,U_14987),U_14989),U_14991))
        | ~ hBOOL(hAPP(U_14987,U_14991))
        | ~ hBOOL(hAPP(hAPP(U_14985,U_14989),U_14991)) )
    & ! [U_14986,U_14988,U_14984,U_14982,U_14990] :
        ( ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14982,U_14984,U_14986),U_14988),U_14990))
        | sP1022(U_14986,U_14988,U_14984,U_14990) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1022])],[f_3786_3]) ).

cnf(f_3786_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14982,U_14984,U_14986),U_14988),U_14990))
    | sP1022(U_14986,U_14988,U_14984,U_14990) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_6,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_14983,U_14985,U_14987),U_14989),U_14991))
    | ~ hBOOL(hAPP(U_14987,U_14991))
    | ~ hBOOL(hAPP(hAPP(U_14985,U_14989),U_14991)) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_7,plain,
    ( hBOOL(hAPP(hAPP(U_14984,U_14988),U_14990))
    | ~ sP1022(U_14986,U_14988,U_14984,U_14990) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_8,plain,
    ( hBOOL(hAPP(U_14986,U_14990))
    | ~ sP1022(U_14986,U_14988,U_14984,U_14990) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

fof(f_3787_1,plain,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Loop]) ).

fof(f_3787_2,plain,
    ! [U_14996,U_14995,U_14994,U_14993,U_14992] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14992,U_14993,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14992),U_14994),c_Com_Ocom_OWhile(U_14995,U_14996)),c_Hoare__Mirabelle_Opeek__and(U_14992,U_14994,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14995)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14992),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14992,U_14993,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14992),c_Hoare__Mirabelle_Opeek__and(U_14992,U_14994,U_14995)),U_14996),U_14994)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14992),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3787_1]) ).

fof(f_3787_3,plain,
    ! [U_14993,U_14994,U_14992,U_14995,U_14996] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14992,U_14993,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14992),U_14994),c_Com_Ocom_OWhile(U_14995,U_14996)),c_Hoare__Mirabelle_Opeek__and(U_14992,U_14994,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14995)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14992),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14992,U_14993,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14992),c_Hoare__Mirabelle_Opeek__and(U_14992,U_14994,U_14995)),U_14996),U_14994)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14992),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3787_2]) ).

cnf(f_3787_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_14992,U_14993,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14992),U_14994),c_Com_Ocom_OWhile(U_14995,U_14996)),c_Hoare__Mirabelle_Opeek__and(U_14992,U_14994,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_14995)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14992),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14992,U_14993,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14992),c_Hoare__Mirabelle_Opeek__and(U_14992,U_14994,U_14995)),U_14996),U_14994)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14992),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3787_3]) ).

fof(f_3788_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oremove]) ).

fof(f_3788_2,plain,
    ! [U_15002,U_15001,U_15000,U_14999,U_14998,U_14997] :
      ( hAPP(U_15000,U_15001) = hAPP(c_Fun_Ocomp(U_14998,U_14998,U_14998,hAPP(U_15000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14997,tc_HOL_Obool)),U_15001),hAPP(hAPP(c_Set_Oinsert(U_14997),U_15002),c_Orderings_Obot__class_Obot(tc_fun(U_14997,tc_HOL_Obool)))))),hAPP(U_14999,U_15002))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14997),U_15002),U_15001))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14997),U_15001))
      | ~ c_Finite__Set_Ofolding(U_14997,U_14998,U_14999,U_15000) ),
    inference(variable_rename,[status(thm)],[f_3788_1]) ).

fof(f_3788_3,plain,
    ! [U_14997,U_14998,U_14999,U_15000,U_15001,U_15002] :
      ( hAPP(U_15000,U_15001) = hAPP(c_Fun_Ocomp(U_14998,U_14998,U_14998,hAPP(U_15000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14997,tc_HOL_Obool)),U_15001),hAPP(hAPP(c_Set_Oinsert(U_14997),U_15002),c_Orderings_Obot__class_Obot(tc_fun(U_14997,tc_HOL_Obool)))))),hAPP(U_14999,U_15002))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14997),U_15002),U_15001))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14997),U_15001))
      | ~ c_Finite__Set_Ofolding(U_14997,U_14998,U_14999,U_15000) ),
    inference(definitional_conversion,[status(esa)],[f_3788_2]) ).

cnf(f_3788_4,plain,
    ( hAPP(U_15000,U_15001) = hAPP(c_Fun_Ocomp(U_14998,U_14998,U_14998,hAPP(U_15000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14997,tc_HOL_Obool)),U_15001),hAPP(hAPP(c_Set_Oinsert(U_14997),U_15002),c_Orderings_Obot__class_Obot(tc_fun(U_14997,tc_HOL_Obool)))))),hAPP(U_14999,U_15002))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14997),U_15002),U_15001))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14997),U_15001))
    | ~ c_Finite__Set_Ofolding(U_14997,U_14998,U_14999,U_15000) ),
    inference(clausify,[status(thm)],[f_3788_3]) ).

fof(f_3789_1,plain,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex]) ).

fof(f_3789_2,plain,
    ! [U_15010,U_15009,U_15008,U_15007,U_15006,U_15005,U_15004,U_15003] :
      ( hAPP(hAPP(U_15007,U_15010),hAPP(c_Set_Oimage(U_15004,U_15004,U_15009),U_15008)) = hAPP(hAPP(U_15007,hAPP(c_Fun_Ocomp(U_15004,U_15003,U_15004,U_15010),U_15009)),U_15008)
      | ~ c_Fun_Oinj__on(U_15004,U_15004,U_15009,U_15008)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15004),U_15008))
      | ~ c_Finite__Set_Ofolding__image(U_15003,U_15004,U_15005,U_15006,U_15007) ),
    inference(variable_rename,[status(thm)],[f_3789_1]) ).

fof(f_3789_3,plain,
    ! [U_15004,U_15005,U_15006,U_15003,U_15007,U_15008,U_15009,U_15010] :
      ( hAPP(hAPP(U_15007,U_15010),hAPP(c_Set_Oimage(U_15004,U_15004,U_15009),U_15008)) = hAPP(hAPP(U_15007,hAPP(c_Fun_Ocomp(U_15004,U_15003,U_15004,U_15010),U_15009)),U_15008)
      | ~ c_Fun_Oinj__on(U_15004,U_15004,U_15009,U_15008)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15004),U_15008))
      | ~ c_Finite__Set_Ofolding__image(U_15003,U_15004,U_15005,U_15006,U_15007) ),
    inference(definitional_conversion,[status(esa)],[f_3789_2]) ).

cnf(f_3789_4,plain,
    ( hAPP(hAPP(U_15007,U_15010),hAPP(c_Set_Oimage(U_15004,U_15004,U_15009),U_15008)) = hAPP(hAPP(U_15007,hAPP(c_Fun_Ocomp(U_15004,U_15003,U_15004,U_15010),U_15009)),U_15008)
    | ~ c_Fun_Oinj__on(U_15004,U_15004,U_15009,U_15008)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15004),U_15008))
    | ~ c_Finite__Set_Ofolding__image(U_15003,U_15004,U_15005,U_15006,U_15007) ),
    inference(clausify,[status(thm)],[f_3789_3]) ).

fof(f_3790_1,plain,
    ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp]) ).

fof(f_3790_2,plain,
    ! [U_15018,U_15017,U_15016,U_15015,U_15014,U_15013,U_15012,U_15011] :
      ( hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),U_15018)) = hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),U_15018))
      | ~ c_Finite__Set_Ofolding(U_15011,U_15012,U_15013,U_15014) ),
    inference(variable_rename,[status(thm)],[f_3790_1]) ).

fof(f_3790_3,plain,
    ! [U_15018,U_15017,U_15016,U_15015,U_15014,U_15013,U_15012] :
      ( ! [U_15011] : ~ c_Finite__Set_Ofolding(U_15011,U_15012,U_15013,U_15014)
      | hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),U_15018)) = hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),U_15018)) ),
    inference(miniscope,[status(thm)],[f_3790_2]) ).

fof(f_3790_4,plain,
    ! [U_15011,U_15012,U_15013,U_15014,U_15015,U_15016,U_15017,U_15018] :
      ( ~ c_Finite__Set_Ofolding(U_15011,U_15012,U_15013,U_15014)
      | hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),U_15018)) = hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),U_15018)) ),
    inference(definitional_conversion,[status(esa)],[f_3790_3]) ).

cnf(f_3790_5,plain,
    ( ~ c_Finite__Set_Ofolding(U_15011,U_15012,U_15013,U_15014)
    | hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),U_15018)) = hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15017)),hAPP(c_Fun_Ocomp(U_15012,U_15012,U_15015,hAPP(U_15013,U_15016)),U_15018)) ),
    inference(clausify,[status(thm)],[f_3790_4]) ).

fof(f_3791_1,plain,
    ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp]) ).

fof(f_3791_2,plain,
    ! [U_15024,U_15023,U_15022,U_15021,U_15020,U_15019] :
      ( hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15023)),hAPP(U_15021,U_15024)) = hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15024)),hAPP(U_15021,U_15023))
      | ~ c_Finite__Set_Ofolding(U_15019,U_15020,U_15021,U_15022) ),
    inference(variable_rename,[status(thm)],[f_3791_1]) ).

fof(f_3791_3,plain,
    ! [U_15024,U_15023,U_15022,U_15021,U_15020] :
      ( ! [U_15019] : ~ c_Finite__Set_Ofolding(U_15019,U_15020,U_15021,U_15022)
      | hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15023)),hAPP(U_15021,U_15024)) = hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15024)),hAPP(U_15021,U_15023)) ),
    inference(miniscope,[status(thm)],[f_3791_2]) ).

fof(f_3791_4,plain,
    ! [U_15019,U_15021,U_15020,U_15022,U_15023,U_15024] :
      ( ~ c_Finite__Set_Ofolding(U_15019,U_15020,U_15021,U_15022)
      | hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15023)),hAPP(U_15021,U_15024)) = hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15024)),hAPP(U_15021,U_15023)) ),
    inference(definitional_conversion,[status(esa)],[f_3791_3]) ).

cnf(f_3791_5,plain,
    ( ~ c_Finite__Set_Ofolding(U_15019,U_15020,U_15021,U_15022)
    | hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15023)),hAPP(U_15021,U_15024)) = hAPP(c_Fun_Ocomp(U_15020,U_15020,U_15020,hAPP(U_15021,U_15024)),hAPP(U_15021,U_15023)) ),
    inference(clausify,[status(thm)],[f_3791_4]) ).

fof(f_3792_1,plain,
    ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2)
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J]) ).

fof(f_3792_2,plain,
    ! [U_15035,U_15034,U_15033,U_15032,U_15031,U_15030,U_15029,U_15028,U_15027,U_15026,U_15025] :
      ( hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15031,U_15032),hAPP(c_Fun_Ocomp(U_15033,U_15029,U_15031,U_15034),U_15035)) = hAPP(c_Fun_Ocomp(U_15033,U_15030,U_15031,hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15033,U_15032),U_15034)),U_15035)
      | ~ c_Finite__Set_Ofolding(U_15025,U_15026,U_15027,U_15028) ),
    inference(variable_rename,[status(thm)],[f_3792_1]) ).

fof(f_3792_3,plain,
    ( ! [U_15035,U_15034,U_15033,U_15032,U_15031,U_15030,U_15029] : hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15031,U_15032),hAPP(c_Fun_Ocomp(U_15033,U_15029,U_15031,U_15034),U_15035)) = hAPP(c_Fun_Ocomp(U_15033,U_15030,U_15031,hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15033,U_15032),U_15034)),U_15035)
    | ! [U_15028,U_15027,U_15026,U_15025] : ~ c_Finite__Set_Ofolding(U_15025,U_15026,U_15027,U_15028) ),
    inference(miniscope,[status(thm)],[f_3792_2]) ).

fof(f_3792_4,plain,
    ! [U_15025,U_15027,U_15026,U_15028,U_15029,U_15030,U_15031,U_15032,U_15033,U_15034,U_15035] :
      ( hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15031,U_15032),hAPP(c_Fun_Ocomp(U_15033,U_15029,U_15031,U_15034),U_15035)) = hAPP(c_Fun_Ocomp(U_15033,U_15030,U_15031,hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15033,U_15032),U_15034)),U_15035)
      | ~ c_Finite__Set_Ofolding(U_15025,U_15026,U_15027,U_15028) ),
    inference(definitional_conversion,[status(esa)],[f_3792_3]) ).

cnf(f_3792_5,plain,
    ( hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15031,U_15032),hAPP(c_Fun_Ocomp(U_15033,U_15029,U_15031,U_15034),U_15035)) = hAPP(c_Fun_Ocomp(U_15033,U_15030,U_15031,hAPP(c_Fun_Ocomp(U_15029,U_15030,U_15033,U_15032),U_15034)),U_15035)
    | ~ c_Finite__Set_Ofolding(U_15025,U_15026,U_15027,U_15028) ),
    inference(clausify,[status(thm)],[f_3792_4]) ).

fof(f_3793_1,plain,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib]) ).

fof(f_3793_2,plain,
    ! [U_15043,U_15042,U_15041,U_15040,U_15039,U_15038,U_15037,U_15036] :
      ( hAPP(hAPP(U_15040,hAPP(hAPP(c_COMBS(U_15037,U_15036,U_15036),hAPP(hAPP(c_COMBB(U_15036,tc_fun(U_15036,U_15036),U_15037),U_15038),U_15042)),U_15043)),U_15041) = hAPP(hAPP(U_15038,hAPP(hAPP(U_15040,U_15042),U_15041)),hAPP(hAPP(U_15040,U_15043),U_15041))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15037),U_15041))
      | ~ c_Finite__Set_Ofolding__image(U_15036,U_15037,U_15038,U_15039,U_15040) ),
    inference(variable_rename,[status(thm)],[f_3793_1]) ).

fof(f_3793_3,plain,
    ! [U_15036,U_15037,U_15038,U_15039,U_15040,U_15041,U_15042,U_15043] :
      ( hAPP(hAPP(U_15040,hAPP(hAPP(c_COMBS(U_15037,U_15036,U_15036),hAPP(hAPP(c_COMBB(U_15036,tc_fun(U_15036,U_15036),U_15037),U_15038),U_15042)),U_15043)),U_15041) = hAPP(hAPP(U_15038,hAPP(hAPP(U_15040,U_15042),U_15041)),hAPP(hAPP(U_15040,U_15043),U_15041))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15037),U_15041))
      | ~ c_Finite__Set_Ofolding__image(U_15036,U_15037,U_15038,U_15039,U_15040) ),
    inference(definitional_conversion,[status(esa)],[f_3793_2]) ).

cnf(f_3793_4,plain,
    ( hAPP(hAPP(U_15040,hAPP(hAPP(c_COMBS(U_15037,U_15036,U_15036),hAPP(hAPP(c_COMBB(U_15036,tc_fun(U_15036,U_15036),U_15037),U_15038),U_15042)),U_15043)),U_15041) = hAPP(hAPP(U_15038,hAPP(hAPP(U_15040,U_15042),U_15041)),hAPP(hAPP(U_15040,U_15043),U_15041))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15037),U_15041))
    | ~ c_Finite__Set_Ofolding__image(U_15036,U_15037,U_15038,U_15039,U_15040) ),
    inference(clausify,[status(thm)],[f_3793_3]) ).

fof(f_3794_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H]) ).

fof(f_3794_2,plain,
    ! [U_15049,U_15048,U_15047,U_15046,U_15045,U_15044] :
      ( hAPP(c_Fun_Ocomp(U_15045,U_15045,U_15045,hAPP(U_15046,U_15049)),hAPP(U_15047,U_15048)) = hAPP(c_Fun_Ocomp(U_15045,U_15045,U_15045,hAPP(U_15047,U_15048)),hAPP(U_15046,U_15049))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15044),U_15048))
      | ~ c_Finite__Set_Ofolding(U_15044,U_15045,U_15046,U_15047) ),
    inference(variable_rename,[status(thm)],[f_3794_1]) ).

fof(f_3794_3,plain,
    ! [U_15045,U_15044,U_15046,U_15047,U_15048,U_15049] :
      ( hAPP(c_Fun_Ocomp(U_15045,U_15045,U_15045,hAPP(U_15046,U_15049)),hAPP(U_15047,U_15048)) = hAPP(c_Fun_Ocomp(U_15045,U_15045,U_15045,hAPP(U_15047,U_15048)),hAPP(U_15046,U_15049))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15044),U_15048))
      | ~ c_Finite__Set_Ofolding(U_15044,U_15045,U_15046,U_15047) ),
    inference(definitional_conversion,[status(esa)],[f_3794_2]) ).

cnf(f_3794_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15045,U_15045,U_15045,hAPP(U_15046,U_15049)),hAPP(U_15047,U_15048)) = hAPP(c_Fun_Ocomp(U_15045,U_15045,U_15045,hAPP(U_15047,U_15048)),hAPP(U_15046,U_15049))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15044),U_15048))
    | ~ c_Finite__Set_Ofolding(U_15044,U_15045,U_15046,U_15047) ),
    inference(clausify,[status(thm)],[f_3794_3]) ).

fof(f_3795_1,plain,
    ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H]) ).

fof(f_3795_2,plain,
    ! [U_15057,U_15056,U_15055,U_15054,U_15053,U_15052,U_15051,U_15050] :
      ( hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15052,U_15056)),hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15053,U_15054)),U_15057)) = hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15053,U_15054)),hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15052,U_15056)),U_15057))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15050),U_15054))
      | ~ c_Finite__Set_Ofolding(U_15050,U_15051,U_15052,U_15053) ),
    inference(variable_rename,[status(thm)],[f_3795_1]) ).

fof(f_3795_3,plain,
    ! [U_15051,U_15050,U_15052,U_15053,U_15054,U_15055,U_15056,U_15057] :
      ( hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15052,U_15056)),hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15053,U_15054)),U_15057)) = hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15053,U_15054)),hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15052,U_15056)),U_15057))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15050),U_15054))
      | ~ c_Finite__Set_Ofolding(U_15050,U_15051,U_15052,U_15053) ),
    inference(definitional_conversion,[status(esa)],[f_3795_2]) ).

cnf(f_3795_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15052,U_15056)),hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15053,U_15054)),U_15057)) = hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15053,U_15054)),hAPP(c_Fun_Ocomp(U_15051,U_15051,U_15055,hAPP(U_15052,U_15056)),U_15057))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15050),U_15054))
    | ~ c_Finite__Set_Ofolding(U_15050,U_15051,U_15052,U_15053) ),
    inference(clausify,[status(thm)],[f_3795_3]) ).

fof(f_3796_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H]) ).

fof(f_3796_2,plain,
    ! [U_15063,U_15062,U_15061,U_15060,U_15059,U_15058] :
      ( hAPP(c_Fun_Ocomp(U_15059,U_15059,U_15059,hAPP(U_15061,U_15063)),hAPP(U_15061,U_15062)) = hAPP(c_Fun_Ocomp(U_15059,U_15059,U_15059,hAPP(U_15061,U_15062)),hAPP(U_15061,U_15063))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15058),U_15063))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15058),U_15062))
      | ~ c_Finite__Set_Ofolding(U_15058,U_15059,U_15060,U_15061) ),
    inference(variable_rename,[status(thm)],[f_3796_1]) ).

fof(f_3796_3,plain,
    ! [U_15059,U_15060,U_15058,U_15061,U_15062,U_15063] :
      ( hAPP(c_Fun_Ocomp(U_15059,U_15059,U_15059,hAPP(U_15061,U_15063)),hAPP(U_15061,U_15062)) = hAPP(c_Fun_Ocomp(U_15059,U_15059,U_15059,hAPP(U_15061,U_15062)),hAPP(U_15061,U_15063))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15058),U_15063))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15058),U_15062))
      | ~ c_Finite__Set_Ofolding(U_15058,U_15059,U_15060,U_15061) ),
    inference(definitional_conversion,[status(esa)],[f_3796_2]) ).

cnf(f_3796_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15059,U_15059,U_15059,hAPP(U_15061,U_15063)),hAPP(U_15061,U_15062)) = hAPP(c_Fun_Ocomp(U_15059,U_15059,U_15059,hAPP(U_15061,U_15062)),hAPP(U_15061,U_15063))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15058),U_15063))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15058),U_15062))
    | ~ c_Finite__Set_Ofolding(U_15058,U_15059,U_15060,U_15061) ),
    inference(clausify,[status(thm)],[f_3796_3]) ).

fof(f_3797_1,plain,
    ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H]) ).

fof(f_3797_2,plain,
    ! [U_15071,U_15070,U_15069,U_15068,U_15067,U_15066,U_15065,U_15064] :
      ( hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15069)),hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15068)),U_15071)) = hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15068)),hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15069)),U_15071))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15064),U_15069))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15064),U_15068))
      | ~ c_Finite__Set_Ofolding(U_15064,U_15065,U_15066,U_15067) ),
    inference(variable_rename,[status(thm)],[f_3797_1]) ).

fof(f_3797_3,plain,
    ! [U_15064,U_15066,U_15065,U_15067,U_15068,U_15069,U_15070,U_15071] :
      ( hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15069)),hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15068)),U_15071)) = hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15068)),hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15069)),U_15071))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15064),U_15069))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15064),U_15068))
      | ~ c_Finite__Set_Ofolding(U_15064,U_15065,U_15066,U_15067) ),
    inference(definitional_conversion,[status(esa)],[f_3797_2]) ).

cnf(f_3797_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15069)),hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15068)),U_15071)) = hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15068)),hAPP(c_Fun_Ocomp(U_15065,U_15065,U_15070,hAPP(U_15067,U_15069)),U_15071))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15064),U_15069))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15064),U_15068))
    | ~ c_Finite__Set_Ofolding(U_15064,U_15065,U_15066,U_15067) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

fof(f_3798_1,plain,
    ! [V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c)
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oempty]) ).

fof(f_3798_2,plain,
    ! [U_15075,U_15074,U_15073,U_15072] :
      ( hAPP(U_15075,c_Orderings_Obot__class_Obot(tc_fun(U_15072,tc_HOL_Obool))) = c_Fun_Oid(U_15073)
      | ~ c_Finite__Set_Ofolding(U_15072,U_15073,U_15074,U_15075) ),
    inference(variable_rename,[status(thm)],[f_3798_1]) ).

fof(f_3798_3,plain,
    ! [U_15074,U_15075,U_15073,U_15072] :
      ( hAPP(U_15075,c_Orderings_Obot__class_Obot(tc_fun(U_15072,tc_HOL_Obool))) = c_Fun_Oid(U_15073)
      | ~ c_Finite__Set_Ofolding(U_15072,U_15073,U_15074,U_15075) ),
    inference(definitional_conversion,[status(esa)],[f_3798_2]) ).

cnf(f_3798_4,plain,
    ( hAPP(U_15075,c_Orderings_Obot__class_Obot(tc_fun(U_15072,tc_HOL_Obool))) = c_Fun_Oid(U_15073)
    | ~ c_Finite__Set_Ofolding(U_15072,U_15073,U_15074,U_15075) ),
    inference(clausify,[status(thm)],[f_3798_3]) ).

fof(f_3799_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold]) ).

fof(f_3799_2,plain,
    ! [U_15082,U_15081,U_15080,U_15079,U_15078,U_15077,U_15076] :
      ( hAPP(hAPP(U_15080,U_15082),U_15081) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15076,U_15077,U_15078),U_15082),U_15079),U_15081)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15077),U_15081))
      | ~ c_Finite__Set_Ofolding__image(U_15076,U_15077,U_15078,U_15079,U_15080) ),
    inference(variable_rename,[status(thm)],[f_3799_1]) ).

fof(f_3799_3,plain,
    ! [U_15076,U_15077,U_15078,U_15079,U_15080,U_15081,U_15082] :
      ( hAPP(hAPP(U_15080,U_15082),U_15081) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15076,U_15077,U_15078),U_15082),U_15079),U_15081)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15077),U_15081))
      | ~ c_Finite__Set_Ofolding__image(U_15076,U_15077,U_15078,U_15079,U_15080) ),
    inference(definitional_conversion,[status(esa)],[f_3799_2]) ).

cnf(f_3799_4,plain,
    ( hAPP(hAPP(U_15080,U_15082),U_15081) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15076,U_15077,U_15078),U_15082),U_15079),U_15081)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15077),U_15081))
    | ~ c_Finite__Set_Ofolding__image(U_15076,U_15077,U_15078,U_15079,U_15080) ),
    inference(clausify,[status(thm)],[f_3799_3]) ).

fof(f_3800_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oinsert]) ).

fof(f_3800_2,plain,
    ! [U_15088,U_15087,U_15086,U_15085,U_15084,U_15083] :
      ( hAPP(U_15086,hAPP(hAPP(c_Set_Oinsert(U_15083),U_15088),U_15087)) = hAPP(c_Fun_Ocomp(U_15084,U_15084,U_15084,hAPP(U_15086,U_15087)),hAPP(U_15085,U_15088))
      | hBOOL(hAPP(hAPP(c_member(U_15083),U_15088),U_15087))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15083),U_15087))
      | ~ c_Finite__Set_Ofolding(U_15083,U_15084,U_15085,U_15086) ),
    inference(variable_rename,[status(thm)],[f_3800_1]) ).

fof(f_3800_3,plain,
    ! [U_15084,U_15085,U_15083,U_15086,U_15087,U_15088] :
      ( hAPP(U_15086,hAPP(hAPP(c_Set_Oinsert(U_15083),U_15088),U_15087)) = hAPP(c_Fun_Ocomp(U_15084,U_15084,U_15084,hAPP(U_15086,U_15087)),hAPP(U_15085,U_15088))
      | hBOOL(hAPP(hAPP(c_member(U_15083),U_15088),U_15087))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15083),U_15087))
      | ~ c_Finite__Set_Ofolding(U_15083,U_15084,U_15085,U_15086) ),
    inference(definitional_conversion,[status(esa)],[f_3800_2]) ).

cnf(f_3800_4,plain,
    ( hAPP(U_15086,hAPP(hAPP(c_Set_Oinsert(U_15083),U_15088),U_15087)) = hAPP(c_Fun_Ocomp(U_15084,U_15084,U_15084,hAPP(U_15086,U_15087)),hAPP(U_15085,U_15088))
    | hBOOL(hAPP(hAPP(c_member(U_15083),U_15088),U_15087))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15083),U_15087))
    | ~ c_Finite__Set_Ofolding(U_15083,U_15084,U_15085,U_15086) ),
    inference(clausify,[status(thm)],[f_3800_3]) ).

fof(f_3801_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter]) ).

fof(f_3801_2,plain,
    ! [U_15094,U_15093,U_15092,U_15091,U_15090,U_15089] :
      ( hAPP(c_Fun_Ocomp(U_15090,U_15090,U_15090,hAPP(U_15092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15089,tc_HOL_Obool)),U_15093),U_15094))),hAPP(U_15092,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15089,tc_HOL_Obool)),U_15093),U_15094))) = hAPP(c_Fun_Ocomp(U_15090,U_15090,U_15090,hAPP(U_15092,U_15093)),hAPP(U_15092,U_15094))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15089),U_15094))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15089),U_15093))
      | ~ c_Finite__Set_Ofolding(U_15089,U_15090,U_15091,U_15092) ),
    inference(variable_rename,[status(thm)],[f_3801_1]) ).

fof(f_3801_3,plain,
    ! [U_15089,U_15090,U_15091,U_15092,U_15093,U_15094] :
      ( hAPP(c_Fun_Ocomp(U_15090,U_15090,U_15090,hAPP(U_15092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15089,tc_HOL_Obool)),U_15093),U_15094))),hAPP(U_15092,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15089,tc_HOL_Obool)),U_15093),U_15094))) = hAPP(c_Fun_Ocomp(U_15090,U_15090,U_15090,hAPP(U_15092,U_15093)),hAPP(U_15092,U_15094))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15089),U_15094))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15089),U_15093))
      | ~ c_Finite__Set_Ofolding(U_15089,U_15090,U_15091,U_15092) ),
    inference(definitional_conversion,[status(esa)],[f_3801_2]) ).

cnf(f_3801_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15090,U_15090,U_15090,hAPP(U_15092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15089,tc_HOL_Obool)),U_15093),U_15094))),hAPP(U_15092,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15089,tc_HOL_Obool)),U_15093),U_15094))) = hAPP(c_Fun_Ocomp(U_15090,U_15090,U_15090,hAPP(U_15092,U_15093)),hAPP(U_15092,U_15094))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15089),U_15094))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15089),U_15093))
    | ~ c_Finite__Set_Ofolding(U_15089,U_15090,U_15091,U_15092) ),
    inference(clausify,[status(thm)],[f_3801_3]) ).

fof(f_3802_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove]) ).

fof(f_3802_2,plain,
    ! [U_15100,U_15099,U_15098,U_15097,U_15096,U_15095] :
      ( hAPP(U_15098,hAPP(hAPP(c_Set_Oinsert(U_15095),U_15100),U_15099)) = hAPP(c_Fun_Ocomp(U_15096,U_15096,U_15096,hAPP(U_15098,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15095,tc_HOL_Obool)),U_15099),hAPP(hAPP(c_Set_Oinsert(U_15095),U_15100),c_Orderings_Obot__class_Obot(tc_fun(U_15095,tc_HOL_Obool)))))),hAPP(U_15097,U_15100))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15095),U_15099))
      | ~ c_Finite__Set_Ofolding(U_15095,U_15096,U_15097,U_15098) ),
    inference(variable_rename,[status(thm)],[f_3802_1]) ).

fof(f_3802_3,plain,
    ! [U_15095,U_15097,U_15098,U_15096,U_15099,U_15100] :
      ( hAPP(U_15098,hAPP(hAPP(c_Set_Oinsert(U_15095),U_15100),U_15099)) = hAPP(c_Fun_Ocomp(U_15096,U_15096,U_15096,hAPP(U_15098,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15095,tc_HOL_Obool)),U_15099),hAPP(hAPP(c_Set_Oinsert(U_15095),U_15100),c_Orderings_Obot__class_Obot(tc_fun(U_15095,tc_HOL_Obool)))))),hAPP(U_15097,U_15100))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15095),U_15099))
      | ~ c_Finite__Set_Ofolding(U_15095,U_15096,U_15097,U_15098) ),
    inference(definitional_conversion,[status(esa)],[f_3802_2]) ).

cnf(f_3802_4,plain,
    ( hAPP(U_15098,hAPP(hAPP(c_Set_Oinsert(U_15095),U_15100),U_15099)) = hAPP(c_Fun_Ocomp(U_15096,U_15096,U_15096,hAPP(U_15098,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15095,tc_HOL_Obool)),U_15099),hAPP(hAPP(c_Set_Oinsert(U_15095),U_15100),c_Orderings_Obot__class_Obot(tc_fun(U_15095,tc_HOL_Obool)))))),hAPP(U_15097,U_15100))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15095),U_15099))
    | ~ c_Finite__Set_Ofolding(U_15095,U_15096,U_15097,U_15098) ),
    inference(clausify,[status(thm)],[f_3802_3]) ).

fof(f_3803_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ounion]) ).

fof(f_3803_2,plain,
    ! [U_15106,U_15105,U_15104,U_15103,U_15102,U_15101] :
      ( hAPP(U_15104,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15101,tc_HOL_Obool)),U_15105),U_15106)) = hAPP(c_Fun_Ocomp(U_15102,U_15102,U_15102,hAPP(U_15104,U_15105)),hAPP(U_15104,U_15106))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15101,tc_HOL_Obool)),U_15105),U_15106) != c_Orderings_Obot__class_Obot(tc_fun(U_15101,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15101),U_15106))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15101),U_15105))
      | ~ c_Finite__Set_Ofolding(U_15101,U_15102,U_15103,U_15104) ),
    inference(variable_rename,[status(thm)],[f_3803_1]) ).

fof(f_3803_3,plain,
    ! [U_15101,U_15102,U_15103,U_15104,U_15105,U_15106] :
      ( hAPP(U_15104,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15101,tc_HOL_Obool)),U_15105),U_15106)) = hAPP(c_Fun_Ocomp(U_15102,U_15102,U_15102,hAPP(U_15104,U_15105)),hAPP(U_15104,U_15106))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15101,tc_HOL_Obool)),U_15105),U_15106) != c_Orderings_Obot__class_Obot(tc_fun(U_15101,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15101),U_15106))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15101),U_15105))
      | ~ c_Finite__Set_Ofolding(U_15101,U_15102,U_15103,U_15104) ),
    inference(definitional_conversion,[status(esa)],[f_3803_2]) ).

cnf(f_3803_4,plain,
    ( hAPP(U_15104,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15101,tc_HOL_Obool)),U_15105),U_15106)) = hAPP(c_Fun_Ocomp(U_15102,U_15102,U_15102,hAPP(U_15104,U_15105)),hAPP(U_15104,U_15106))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15101,tc_HOL_Obool)),U_15105),U_15106) != c_Orderings_Obot__class_Obot(tc_fun(U_15101,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15101),U_15106))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15101),U_15105))
    | ~ c_Finite__Set_Ofolding(U_15101,U_15102,U_15103,U_15104) ),
    inference(clausify,[status(thm)],[f_3803_3]) ).

fof(f_3804_1,plain,
    ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2)
      | ? [B_x] :
          ( ? [B_y] :
              ( hAPP(V_h_2,hAPP(V_f_2,B_x)) != c_Groups_Ozero__class_Ozero(T_d)
              & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
              & B_x != B_y
              & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__nonzero]) ).

fof(f_3804_2,plain,
    ! [U_15114,U_15113,U_15112,U_15111,U_15110,U_15109] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15114,U_15109),U_15113),hAPP(c_Set_Oimage(U_15110,U_15114,U_15112),U_15111)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15110,U_15109),hAPP(c_Fun_Ocomp(U_15114,U_15109,U_15110,U_15113),U_15112)),U_15111)
      | ? [U_15108] :
          ( ? [U_15107] :
              ( hAPP(U_15113,hAPP(U_15112,U_15108)) != c_Groups_Ozero__class_Ozero(U_15109)
              & hAPP(U_15112,U_15108) = hAPP(U_15112,U_15107)
              & U_15108 != U_15107
              & hBOOL(hAPP(hAPP(c_member(U_15110),U_15107),U_15111)) )
          & hBOOL(hAPP(hAPP(c_member(U_15110),U_15108),U_15111)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15110),U_15111))
      | ~ class_Groups_Ocomm__monoid__add(U_15109) ),
    inference(variable_rename,[status(thm)],[f_3804_1]) ).

fof(f_3804_3,plain,
    ! [U_15114,U_15113,U_15112,U_15111,U_15110,U_15109] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15114,U_15109),U_15113),hAPP(c_Set_Oimage(U_15110,U_15114,U_15112),U_15111)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15110,U_15109),hAPP(c_Fun_Ocomp(U_15114,U_15109,U_15110,U_15113),U_15112)),U_15111)
      | ( ? [U_15107] :
            ( hAPP(U_15113,hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))) != c_Groups_Ozero__class_Ozero(U_15109)
            & hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)) = hAPP(U_15112,U_15107)
            & sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109) != U_15107
            & hBOOL(hAPP(hAPP(c_member(U_15110),U_15107),U_15111)) )
        & hBOOL(hAPP(hAPP(c_member(U_15110),sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15110),U_15111))
      | ~ class_Groups_Ocomm__monoid__add(U_15109) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_15108,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))],[f_3804_2]) ).

fof(f_3804_4,plain,
    ! [U_15114,U_15113,U_15112,U_15111,U_15110,U_15109] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15114,U_15109),U_15113),hAPP(c_Set_Oimage(U_15110,U_15114,U_15112),U_15111)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15110,U_15109),hAPP(c_Fun_Ocomp(U_15114,U_15109,U_15110,U_15113),U_15112)),U_15111)
      | ( hAPP(U_15113,hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))) != c_Groups_Ozero__class_Ozero(U_15109)
        & hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)) = hAPP(U_15112,sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))
        & sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109) != sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)
        & hBOOL(hAPP(hAPP(c_member(U_15110),sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111))
        & hBOOL(hAPP(hAPP(c_member(U_15110),sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15110),U_15111))
      | ~ class_Groups_Ocomm__monoid__add(U_15109) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_15107,sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))],[f_3804_3]) ).

fof(f_3804_5,plain,
    ( ! [U_15109,U_15110,U_15111,U_15112,U_15113,U_15114] :
        ( hAPP(U_15113,hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))) != c_Groups_Ozero__class_Ozero(U_15109)
        | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) )
    & ! [U_15109,U_15110,U_15111,U_15112,U_15113,U_15114] :
        ( hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)) = hAPP(U_15112,sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))
        | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) )
    & ! [U_15109,U_15110,U_15111,U_15112,U_15113,U_15114] :
        ( sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109) != sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)
        | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) )
    & ! [U_15109,U_15110,U_15111,U_15112,U_15113,U_15114] :
        ( hBOOL(hAPP(hAPP(c_member(U_15110),sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111))
        | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) )
    & ! [U_15109,U_15110,U_15111,U_15112,U_15113,U_15114] :
        ( hBOOL(hAPP(hAPP(c_member(U_15110),sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111))
        | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) )
    & ! [U_15109,U_15110,U_15111,U_15112,U_15113,U_15114] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15114,U_15109),U_15113),hAPP(c_Set_Oimage(U_15110,U_15114,U_15112),U_15111)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15110,U_15109),hAPP(c_Fun_Ocomp(U_15114,U_15109,U_15110,U_15113),U_15112)),U_15111)
        | sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15110),U_15111))
        | ~ class_Groups_Ocomm__monoid__add(U_15109) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1023])],[f_3804_4]) ).

cnf(f_3804_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15114,U_15109),U_15113),hAPP(c_Set_Oimage(U_15110,U_15114,U_15112),U_15111)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15110,U_15109),hAPP(c_Fun_Ocomp(U_15114,U_15109,U_15110,U_15113),U_15112)),U_15111)
    | sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15110),U_15111))
    | ~ class_Groups_Ocomm__monoid__add(U_15109) ),
    inference(clausify,[status(thm)],[f_3804_5]) ).

cnf(f_3804_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15110),sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111))
    | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) ),
    inference(clausify,[status(thm)],[f_3804_5]) ).

cnf(f_3804_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15110),sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)),U_15111))
    | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) ),
    inference(clausify,[status(thm)],[f_3804_5]) ).

cnf(f_3804_9,plain,
    ( sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109) != sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)
    | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) ),
    inference(clausify,[status(thm)],[f_3804_5]) ).

cnf(f_3804_10,plain,
    ( hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109)) = hAPP(U_15112,sK360(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))
    | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) ),
    inference(clausify,[status(thm)],[f_3804_5]) ).

cnf(f_3804_11,plain,
    ( hAPP(U_15113,hAPP(U_15112,sK359(U_15114,U_15113,U_15112,U_15111,U_15110,U_15109))) != c_Groups_Ozero__class_Ozero(U_15109)
    | ~ sP1023(U_15109,U_15110,U_15111,U_15112,U_15113,U_15114) ),
    inference(clausify,[status(thm)],[f_3804_5]) ).

fof(f_3805_1,plain,
    ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Omap__def]) ).

fof(f_3805_2,plain,
    ! [U_15118,U_15117,U_15116,U_15115] : c_Random__Sequence_Omap(U_15115,U_15116,U_15117,U_15118) = c_Random__Sequence_Obind(U_15115,U_15116,U_15118,hAPP(c_Fun_Ocomp(U_15116,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_15116)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_15115,c_Random__Sequence_Osingle(U_15116)),U_15117)),
    inference(variable_rename,[status(thm)],[f_3805_1]) ).

fof(f_3805_3,plain,
    ! [U_15116,U_15117,U_15118,U_15115] : c_Random__Sequence_Omap(U_15115,U_15116,U_15117,U_15118) = c_Random__Sequence_Obind(U_15115,U_15116,U_15118,hAPP(c_Fun_Ocomp(U_15116,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_15116)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_15115,c_Random__Sequence_Osingle(U_15116)),U_15117)),
    inference(definitional_conversion,[status(esa)],[f_3805_2]) ).

cnf(f_3805_4,plain,
    c_Random__Sequence_Omap(U_15115,U_15116,U_15117,U_15118) = c_Random__Sequence_Obind(U_15115,U_15116,U_15118,hAPP(c_Fun_Ocomp(U_15116,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_15116)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_15115,c_Random__Sequence_Osingle(U_15116)),U_15117)),
    inference(clausify,[status(thm)],[f_3805_3]) ).

fof(f_3806_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem]) ).

fof(f_3806_2,plain,
    ! [U_15124,U_15123,U_15122,U_15121,U_15120,U_15119] :
      ( hAPP(U_15122,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15119,tc_HOL_Obool)),U_15123),U_15124)) = hAPP(c_Fun_Ocomp(U_15120,U_15120,U_15120,hAPP(U_15122,U_15123)),hAPP(U_15122,U_15124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15119),U_15124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15119),U_15123))
      | ~ c_Finite__Set_Ofolding__idem(U_15119,U_15120,U_15121,U_15122) ),
    inference(variable_rename,[status(thm)],[f_3806_1]) ).

fof(f_3806_3,plain,
    ! [U_15119,U_15122,U_15120,U_15121,U_15123,U_15124] :
      ( hAPP(U_15122,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15119,tc_HOL_Obool)),U_15123),U_15124)) = hAPP(c_Fun_Ocomp(U_15120,U_15120,U_15120,hAPP(U_15122,U_15123)),hAPP(U_15122,U_15124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15119),U_15124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15119),U_15123))
      | ~ c_Finite__Set_Ofolding__idem(U_15119,U_15120,U_15121,U_15122) ),
    inference(definitional_conversion,[status(esa)],[f_3806_2]) ).

cnf(f_3806_4,plain,
    ( hAPP(U_15122,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15119,tc_HOL_Obool)),U_15123),U_15124)) = hAPP(c_Fun_Ocomp(U_15120,U_15120,U_15120,hAPP(U_15122,U_15123)),hAPP(U_15122,U_15124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15119),U_15124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15119),U_15123))
    | ~ c_Finite__Set_Ofolding__idem(U_15119,U_15120,U_15121,U_15122) ),
    inference(clausify,[status(thm)],[f_3806_3]) ).

fof(f_3807_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem]) ).

fof(f_3807_2,plain,
    ! [U_15130,U_15129,U_15128,U_15127,U_15126,U_15125] :
      ( hAPP(c_Fun_Ocomp(U_15126,U_15126,U_15126,hAPP(U_15128,U_15129)),hAPP(U_15128,U_15130)) = hAPP(U_15128,U_15129)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15125,tc_HOL_Obool)),U_15130),U_15129))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
      | ~ c_Finite__Set_Ofolding__idem(U_15125,U_15126,U_15127,U_15128) ),
    inference(variable_rename,[status(thm)],[f_3807_1]) ).

fof(f_3807_3,plain,
    ! [U_15128,U_15126,U_15127,U_15125,U_15129,U_15130] :
      ( hAPP(c_Fun_Ocomp(U_15126,U_15126,U_15126,hAPP(U_15128,U_15129)),hAPP(U_15128,U_15130)) = hAPP(U_15128,U_15129)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15125,tc_HOL_Obool)),U_15130),U_15129))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
      | ~ c_Finite__Set_Ofolding__idem(U_15125,U_15126,U_15127,U_15128) ),
    inference(definitional_conversion,[status(esa)],[f_3807_2]) ).

cnf(f_3807_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15126,U_15126,U_15126,hAPP(U_15128,U_15129)),hAPP(U_15128,U_15130)) = hAPP(U_15128,U_15129)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15125,tc_HOL_Obool)),U_15130),U_15129))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
    | ~ c_Finite__Set_Ofolding__idem(U_15125,U_15126,U_15127,U_15128) ),
    inference(clausify,[status(thm)],[f_3807_3]) ).

fof(f_3808_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2)
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp]) ).

fof(f_3808_2,plain,
    ! [U_15135,U_15134,U_15133,U_15132,U_15131] :
      ( hAPP(c_Fun_Ocomp(U_15132,U_15132,U_15132,hAPP(U_15133,U_15135)),hAPP(U_15133,U_15135)) = hAPP(U_15133,U_15135)
      | ~ c_Finite__Set_Ofolding__idem(U_15131,U_15132,U_15133,U_15134) ),
    inference(variable_rename,[status(thm)],[f_3808_1]) ).

fof(f_3808_3,plain,
    ! [U_15135,U_15134,U_15133,U_15132] :
      ( ! [U_15131] : ~ c_Finite__Set_Ofolding__idem(U_15131,U_15132,U_15133,U_15134)
      | hAPP(c_Fun_Ocomp(U_15132,U_15132,U_15132,hAPP(U_15133,U_15135)),hAPP(U_15133,U_15135)) = hAPP(U_15133,U_15135) ),
    inference(miniscope,[status(thm)],[f_3808_2]) ).

fof(f_3808_4,plain,
    ! [U_15131,U_15132,U_15135,U_15133,U_15134] :
      ( ~ c_Finite__Set_Ofolding__idem(U_15131,U_15132,U_15133,U_15134)
      | hAPP(c_Fun_Ocomp(U_15132,U_15132,U_15132,hAPP(U_15133,U_15135)),hAPP(U_15133,U_15135)) = hAPP(U_15133,U_15135) ),
    inference(definitional_conversion,[status(esa)],[f_3808_3]) ).

cnf(f_3808_5,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_15131,U_15132,U_15133,U_15134)
    | hAPP(c_Fun_Ocomp(U_15132,U_15132,U_15132,hAPP(U_15133,U_15135)),hAPP(U_15133,U_15135)) = hAPP(U_15133,U_15135) ),
    inference(clausify,[status(thm)],[f_3808_4]) ).

fof(f_3809_1,plain,
    ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp]) ).

fof(f_3809_2,plain,
    ! [U_15142,U_15141,U_15140,U_15139,U_15138,U_15137,U_15136] :
      ( hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142)) = hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142)
      | ~ c_Finite__Set_Ofolding__idem(U_15136,U_15137,U_15138,U_15139) ),
    inference(variable_rename,[status(thm)],[f_3809_1]) ).

fof(f_3809_3,plain,
    ! [U_15142,U_15141,U_15140,U_15139,U_15138,U_15137] :
      ( ! [U_15136] : ~ c_Finite__Set_Ofolding__idem(U_15136,U_15137,U_15138,U_15139)
      | hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142)) = hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142) ),
    inference(miniscope,[status(thm)],[f_3809_2]) ).

fof(f_3809_4,plain,
    ! [U_15136,U_15137,U_15138,U_15139,U_15140,U_15141,U_15142] :
      ( ~ c_Finite__Set_Ofolding__idem(U_15136,U_15137,U_15138,U_15139)
      | hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142)) = hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142) ),
    inference(definitional_conversion,[status(esa)],[f_3809_3]) ).

cnf(f_3809_5,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_15136,U_15137,U_15138,U_15139)
    | hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142)) = hAPP(c_Fun_Ocomp(U_15137,U_15137,U_15140,hAPP(U_15138,U_15141)),U_15142) ),
    inference(clausify,[status(thm)],[f_3809_4]) ).

fof(f_3810_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem]) ).

fof(f_3810_2,plain,
    ! [U_15148,U_15147,U_15146,U_15145,U_15144,U_15143] :
      ( hAPP(c_Fun_Ocomp(U_15144,U_15144,U_15144,hAPP(U_15146,U_15147)),hAPP(U_15145,U_15148)) = hAPP(U_15146,U_15147)
      | ~ hBOOL(hAPP(hAPP(c_member(U_15143),U_15148),U_15147))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15143),U_15147))
      | ~ c_Finite__Set_Ofolding__idem(U_15143,U_15144,U_15145,U_15146) ),
    inference(variable_rename,[status(thm)],[f_3810_1]) ).

fof(f_3810_3,plain,
    ! [U_15144,U_15143,U_15145,U_15146,U_15147,U_15148] :
      ( hAPP(c_Fun_Ocomp(U_15144,U_15144,U_15144,hAPP(U_15146,U_15147)),hAPP(U_15145,U_15148)) = hAPP(U_15146,U_15147)
      | ~ hBOOL(hAPP(hAPP(c_member(U_15143),U_15148),U_15147))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15143),U_15147))
      | ~ c_Finite__Set_Ofolding__idem(U_15143,U_15144,U_15145,U_15146) ),
    inference(definitional_conversion,[status(esa)],[f_3810_2]) ).

cnf(f_3810_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15144,U_15144,U_15144,hAPP(U_15146,U_15147)),hAPP(U_15145,U_15148)) = hAPP(U_15146,U_15147)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15143),U_15148),U_15147))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15143),U_15147))
    | ~ c_Finite__Set_Ofolding__idem(U_15143,U_15144,U_15145,U_15146) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

fof(f_3811_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem]) ).

fof(f_3811_2,plain,
    ! [U_15154,U_15153,U_15152,U_15151,U_15150,U_15149] :
      ( hAPP(U_15152,hAPP(hAPP(c_Set_Oinsert(U_15149),U_15154),U_15153)) = hAPP(c_Fun_Ocomp(U_15150,U_15150,U_15150,hAPP(U_15152,U_15153)),hAPP(U_15151,U_15154))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15149),U_15153))
      | ~ c_Finite__Set_Ofolding__idem(U_15149,U_15150,U_15151,U_15152) ),
    inference(variable_rename,[status(thm)],[f_3811_1]) ).

fof(f_3811_3,plain,
    ! [U_15151,U_15149,U_15150,U_15152,U_15153,U_15154] :
      ( hAPP(U_15152,hAPP(hAPP(c_Set_Oinsert(U_15149),U_15154),U_15153)) = hAPP(c_Fun_Ocomp(U_15150,U_15150,U_15150,hAPP(U_15152,U_15153)),hAPP(U_15151,U_15154))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15149),U_15153))
      | ~ c_Finite__Set_Ofolding__idem(U_15149,U_15150,U_15151,U_15152) ),
    inference(definitional_conversion,[status(esa)],[f_3811_2]) ).

cnf(f_3811_4,plain,
    ( hAPP(U_15152,hAPP(hAPP(c_Set_Oinsert(U_15149),U_15154),U_15153)) = hAPP(c_Fun_Ocomp(U_15150,U_15150,U_15150,hAPP(U_15152,U_15153)),hAPP(U_15151,U_15154))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15149),U_15153))
    | ~ c_Finite__Set_Ofolding__idem(U_15149,U_15150,U_15151,U_15152) ),
    inference(clausify,[status(thm)],[f_3811_3]) ).

fof(f_3812_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_strong__setprod__reindex__cong]) ).

fof(f_3812_2,plain,
    ! [U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15158,U_15156),U_15163),U_15161) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15157,U_15156),U_15162),U_15160)
      | ? [U_15155] :
          ( hAPP(U_15162,U_15155) != hAPP(hAPP(c_Fun_Ocomp(U_15158,U_15156,U_15157,U_15163),U_15159),U_15155)
          & hBOOL(hAPP(hAPP(c_member(U_15157),U_15155),U_15160)) )
      | U_15161 != hAPP(c_Set_Oimage(U_15157,U_15158,U_15159),U_15160)
      | ~ c_Fun_Oinj__on(U_15157,U_15158,U_15159,U_15160)
      | ~ class_Groups_Ocomm__monoid__mult(U_15156) ),
    inference(variable_rename,[status(thm)],[f_3812_1]) ).

fof(f_3812_3,plain,
    ! [U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15158,U_15156),U_15163),U_15161) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15157,U_15156),U_15162),U_15160)
      | ( hAPP(U_15162,sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156)) != hAPP(hAPP(c_Fun_Ocomp(U_15158,U_15156,U_15157,U_15163),U_15159),sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156))
        & hBOOL(hAPP(hAPP(c_member(U_15157),sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156)),U_15160)) )
      | U_15161 != hAPP(c_Set_Oimage(U_15157,U_15158,U_15159),U_15160)
      | ~ c_Fun_Oinj__on(U_15157,U_15158,U_15159,U_15160)
      | ~ class_Groups_Ocomm__monoid__mult(U_15156) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_15155,sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156))],[f_3812_2]) ).

fof(f_3812_4,plain,
    ( ! [U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163] :
        ( hAPP(U_15162,sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156)) != hAPP(hAPP(c_Fun_Ocomp(U_15158,U_15156,U_15157,U_15163),U_15159),sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156))
        | ~ sP1024(U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163) )
    & ! [U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163] :
        ( hBOOL(hAPP(hAPP(c_member(U_15157),sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156)),U_15160))
        | ~ sP1024(U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163) )
    & ! [U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15158,U_15156),U_15163),U_15161) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15157,U_15156),U_15162),U_15160)
        | sP1024(U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163)
        | U_15161 != hAPP(c_Set_Oimage(U_15157,U_15158,U_15159),U_15160)
        | ~ c_Fun_Oinj__on(U_15157,U_15158,U_15159,U_15160)
        | ~ class_Groups_Ocomm__monoid__mult(U_15156) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1024])],[f_3812_3]) ).

cnf(f_3812_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15158,U_15156),U_15163),U_15161) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15157,U_15156),U_15162),U_15160)
    | sP1024(U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163)
    | U_15161 != hAPP(c_Set_Oimage(U_15157,U_15158,U_15159),U_15160)
    | ~ c_Fun_Oinj__on(U_15157,U_15158,U_15159,U_15160)
    | ~ class_Groups_Ocomm__monoid__mult(U_15156) ),
    inference(clausify,[status(thm)],[f_3812_4]) ).

cnf(f_3812_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15157),sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156)),U_15160))
    | ~ sP1024(U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163) ),
    inference(clausify,[status(thm)],[f_3812_4]) ).

cnf(f_3812_7,plain,
    ( hAPP(U_15162,sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156)) != hAPP(hAPP(c_Fun_Ocomp(U_15158,U_15156,U_15157,U_15163),U_15159),sK361(U_15163,U_15162,U_15161,U_15160,U_15159,U_15158,U_15157,U_15156))
    | ~ sP1024(U_15156,U_15157,U_15158,U_15159,U_15160,U_15161,U_15162,U_15163) ),
    inference(clausify,[status(thm)],[f_3812_4]) ).

fof(f_3813_1,plain,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_neg__map__def]) ).

fof(f_3813_2,plain,
    ! [U_15167,U_15166,U_15165,U_15164] : c_New__Random__Sequence_Oneg__map(U_15164,U_15165,U_15166,U_15167) = c_New__Random__Sequence_Oneg__bind(U_15164,U_15165,U_15167,hAPP(c_Fun_Ocomp(U_15165,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_15165)))))),U_15164,c_New__Random__Sequence_Oneg__single(U_15165)),U_15166)),
    inference(variable_rename,[status(thm)],[f_3813_1]) ).

fof(f_3813_3,plain,
    ! [U_15167,U_15164,U_15166,U_15165] : c_New__Random__Sequence_Oneg__map(U_15164,U_15165,U_15166,U_15167) = c_New__Random__Sequence_Oneg__bind(U_15164,U_15165,U_15167,hAPP(c_Fun_Ocomp(U_15165,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_15165)))))),U_15164,c_New__Random__Sequence_Oneg__single(U_15165)),U_15166)),
    inference(definitional_conversion,[status(esa)],[f_3813_2]) ).

cnf(f_3813_4,plain,
    c_New__Random__Sequence_Oneg__map(U_15164,U_15165,U_15166,U_15167) = c_New__Random__Sequence_Oneg__bind(U_15164,U_15165,U_15167,hAPP(c_Fun_Ocomp(U_15165,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_15165)))))),U_15164,c_New__Random__Sequence_Oneg__single(U_15165)),U_15166)),
    inference(clausify,[status(thm)],[f_3813_3]) ).

fof(f_3814_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_neg__single__def]) ).

fof(f_3814_2,plain,
    ! [U_15172,U_15171,U_15170,U_15169,U_15168] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15168),U_15169),U_15170),U_15171),U_15172) = c_New__DSequence_Oneg__single(U_15168,U_15169),
    inference(variable_rename,[status(thm)],[f_3814_1]) ).

fof(f_3814_3,plain,
    ! [U_15169,U_15170,U_15168,U_15171,U_15172] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15168),U_15169),U_15170),U_15171),U_15172) = c_New__DSequence_Oneg__single(U_15168,U_15169),
    inference(definitional_conversion,[status(esa)],[f_3814_2]) ).

cnf(f_3814_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15168),U_15169),U_15170),U_15171),U_15172) = c_New__DSequence_Oneg__single(U_15168,U_15169),
    inference(clausify,[status(thm)],[f_3814_3]) ).

fof(f_3815_1,plain,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__map__def]) ).

fof(f_3815_2,plain,
    ! [U_15176,U_15175,U_15174,U_15173] : c_New__Random__Sequence_Opos__map(U_15173,U_15174,U_15175,U_15176) = c_New__Random__Sequence_Opos__bind(U_15173,U_15174,U_15176,hAPP(c_Fun_Ocomp(U_15174,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_15174))))),U_15173,c_New__Random__Sequence_Opos__single(U_15174)),U_15175)),
    inference(variable_rename,[status(thm)],[f_3815_1]) ).

fof(f_3815_3,plain,
    ! [U_15173,U_15174,U_15175,U_15176] : c_New__Random__Sequence_Opos__map(U_15173,U_15174,U_15175,U_15176) = c_New__Random__Sequence_Opos__bind(U_15173,U_15174,U_15176,hAPP(c_Fun_Ocomp(U_15174,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_15174))))),U_15173,c_New__Random__Sequence_Opos__single(U_15174)),U_15175)),
    inference(definitional_conversion,[status(esa)],[f_3815_2]) ).

cnf(f_3815_4,plain,
    c_New__Random__Sequence_Opos__map(U_15173,U_15174,U_15175,U_15176) = c_New__Random__Sequence_Opos__bind(U_15173,U_15174,U_15176,hAPP(c_Fun_Ocomp(U_15174,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_15174))))),U_15173,c_New__Random__Sequence_Opos__single(U_15174)),U_15175)),
    inference(clausify,[status(thm)],[f_3815_3]) ).

fof(f_3816_1,plain,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).

fof(f_3816_2,plain,
    ! [U_15179,U_15178,U_15177] : hAPP(c_New__DSequence_Oneg__single(U_15177,U_15178),U_15179) = c_Lazy__Sequence_Ohb__single(U_15177,U_15178),
    inference(variable_rename,[status(thm)],[f_3816_1]) ).

fof(f_3816_3,plain,
    ! [U_15177,U_15178,U_15179] : hAPP(c_New__DSequence_Oneg__single(U_15177,U_15178),U_15179) = c_Lazy__Sequence_Ohb__single(U_15177,U_15178),
    inference(definitional_conversion,[status(esa)],[f_3816_2]) ).

cnf(f_3816_4,plain,
    hAPP(c_New__DSequence_Oneg__single(U_15177,U_15178),U_15179) = c_Lazy__Sequence_Ohb__single(U_15177,U_15178),
    inference(clausify,[status(thm)],[f_3816_3]) ).

fof(f_3817_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_pos__single__def]) ).

fof(f_3817_2,plain,
    ! [U_15184,U_15183,U_15182,U_15181,U_15180] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15180),U_15181),U_15182),U_15183),U_15184) = c_New__DSequence_Opos__single(U_15180,U_15181),
    inference(variable_rename,[status(thm)],[f_3817_1]) ).

fof(f_3817_3,plain,
    ! [U_15180,U_15181,U_15182,U_15183,U_15184] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15180),U_15181),U_15182),U_15183),U_15184) = c_New__DSequence_Opos__single(U_15180,U_15181),
    inference(definitional_conversion,[status(esa)],[f_3817_2]) ).

cnf(f_3817_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15180),U_15181),U_15182),U_15183),U_15184) = c_New__DSequence_Opos__single(U_15180,U_15181),
    inference(clausify,[status(thm)],[f_3817_3]) ).

fof(f_3818_1,plain,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Osingle(T_a,V_x),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(f_3818_2,plain,
    ! [U_15187,U_15186,U_15185] : hAPP(c_New__DSequence_Opos__single(U_15185,U_15186),U_15187) = c_Lazy__Sequence_Osingle(U_15185,U_15186),
    inference(variable_rename,[status(thm)],[f_3818_1]) ).

fof(f_3818_3,plain,
    ! [U_15185,U_15186,U_15187] : hAPP(c_New__DSequence_Opos__single(U_15185,U_15186),U_15187) = c_Lazy__Sequence_Osingle(U_15185,U_15186),
    inference(definitional_conversion,[status(esa)],[f_3818_2]) ).

cnf(f_3818_4,plain,
    hAPP(c_New__DSequence_Opos__single(U_15185,U_15186),U_15187) = c_Lazy__Sequence_Osingle(U_15185,U_15186),
    inference(clausify,[status(thm)],[f_3818_3]) ).

fof(f_3819_1,plain,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    inference(fof_nnf,[status(thm)],[fact_Eps__split]) ).

fof(f_3819_2,plain,
    ! [U_15190,U_15189,U_15188] : c_Hilbert__Choice_OEps(tc_prod(U_15188,U_15189),hAPP(c_Product__Type_Oprod_Oprod__case(U_15188,U_15189,tc_HOL_Obool),U_15190)) = c_Hilbert__Choice_OEps(tc_prod(U_15188,U_15189),hAPP(hAPP(c_COMBS(tc_prod(U_15188,U_15189),U_15189,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15188,tc_fun(U_15189,tc_HOL_Obool),tc_prod(U_15188,U_15189)),U_15190),c_Product__Type_Ofst(U_15188,U_15189))),c_Product__Type_Osnd(U_15188,U_15189))),
    inference(variable_rename,[status(thm)],[f_3819_1]) ).

fof(f_3819_3,plain,
    ! [U_15188,U_15189,U_15190] : c_Hilbert__Choice_OEps(tc_prod(U_15188,U_15189),hAPP(c_Product__Type_Oprod_Oprod__case(U_15188,U_15189,tc_HOL_Obool),U_15190)) = c_Hilbert__Choice_OEps(tc_prod(U_15188,U_15189),hAPP(hAPP(c_COMBS(tc_prod(U_15188,U_15189),U_15189,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15188,tc_fun(U_15189,tc_HOL_Obool),tc_prod(U_15188,U_15189)),U_15190),c_Product__Type_Ofst(U_15188,U_15189))),c_Product__Type_Osnd(U_15188,U_15189))),
    inference(definitional_conversion,[status(esa)],[f_3819_2]) ).

cnf(f_3819_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_15188,U_15189),hAPP(c_Product__Type_Oprod_Oprod__case(U_15188,U_15189,tc_HOL_Obool),U_15190)) = c_Hilbert__Choice_OEps(tc_prod(U_15188,U_15189),hAPP(hAPP(c_COMBS(tc_prod(U_15188,U_15189),U_15189,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15188,tc_fun(U_15189,tc_HOL_Obool),tc_prod(U_15188,U_15189)),U_15190),c_Product__Type_Ofst(U_15188,U_15189))),c_Product__Type_Osnd(U_15188,U_15189))),
    inference(clausify,[status(thm)],[f_3819_3]) ).

fof(f_3820_1,plain,
    ! [T_b,V_c_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_c_2))
      | V_c_2 != c_Hilbert__Choice_OEps(T_b,V_P_2)
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_exE__some]) ).

fof(f_3820_2,plain,
    ! [U_15194,U_15193,U_15192] :
      ( hBOOL(hAPP(U_15192,U_15193))
      | U_15193 != c_Hilbert__Choice_OEps(U_15194,U_15192)
      | ! [U_15191] : ~ hBOOL(hAPP(U_15192,U_15191)) ),
    inference(variable_rename,[status(thm)],[f_3820_1]) ).

fof(f_3820_3,plain,
    ! [U_15192,U_15191,U_15193,U_15194] :
      ( hBOOL(hAPP(U_15192,U_15193))
      | U_15193 != c_Hilbert__Choice_OEps(U_15194,U_15192)
      | ~ hBOOL(hAPP(U_15192,U_15191)) ),
    inference(definitional_conversion,[status(esa)],[f_3820_2]) ).

cnf(f_3820_4,plain,
    ( hBOOL(hAPP(U_15192,U_15193))
    | U_15193 != c_Hilbert__Choice_OEps(U_15194,U_15192)
    | ~ hBOOL(hAPP(U_15192,U_15191)) ),
    inference(clausify,[status(thm)],[f_3820_3]) ).

fof(f_3821_1,plain,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(f_3821_2,plain,
    ! [U_15196,U_15195] : c_Hilbert__Choice_OEps(U_15195,hAPP(c_fequal,U_15196)) = U_15196,
    inference(variable_rename,[status(thm)],[f_3821_1]) ).

fof(f_3821_3,plain,
    ! [U_15195,U_15196] : c_Hilbert__Choice_OEps(U_15195,hAPP(c_fequal,U_15196)) = U_15196,
    inference(definitional_conversion,[status(esa)],[f_3821_2]) ).

cnf(f_3821_4,plain,
    c_Hilbert__Choice_OEps(U_15195,hAPP(c_fequal,U_15196)) = U_15196,
    inference(clausify,[status(thm)],[f_3821_3]) ).

fof(f_3822_1,plain,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_some__eq__trivial]) ).

fof(f_3822_2,plain,
    ! [U_15198,U_15197] : c_Hilbert__Choice_OEps(U_15197,hAPP(hAPP(c_COMBC(U_15197,U_15197,tc_HOL_Obool),c_fequal),U_15198)) = U_15198,
    inference(variable_rename,[status(thm)],[f_3822_1]) ).

fof(f_3822_3,plain,
    ! [U_15197,U_15198] : c_Hilbert__Choice_OEps(U_15197,hAPP(hAPP(c_COMBC(U_15197,U_15197,tc_HOL_Obool),c_fequal),U_15198)) = U_15198,
    inference(definitional_conversion,[status(esa)],[f_3822_2]) ).

cnf(f_3822_4,plain,
    c_Hilbert__Choice_OEps(U_15197,hAPP(hAPP(c_COMBC(U_15197,U_15197,tc_HOL_Obool),c_fequal),U_15198)) = U_15198,
    inference(clausify,[status(thm)],[f_3822_3]) ).

fof(f_3823_1,plain,
    ! [T_b,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ~ hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).

fof(f_3823_2,plain,
    ! [U_15202,U_15201] :
      ( ( hBOOL(hAPP(U_15201,c_Hilbert__Choice_OEps(U_15202,U_15201)))
        | ! [U_15200] : ~ hBOOL(hAPP(U_15201,U_15200)) )
      & ( ? [U_15199] : hBOOL(hAPP(U_15201,U_15199))
        | ~ hBOOL(hAPP(U_15201,c_Hilbert__Choice_OEps(U_15202,U_15201))) ) ),
    inference(variable_rename,[status(thm)],[f_3823_1]) ).

fof(f_3823_3,plain,
    ( ! [U_15206,U_15204] :
        ( hBOOL(hAPP(U_15204,c_Hilbert__Choice_OEps(U_15206,U_15204)))
        | ! [U_15200] : ~ hBOOL(hAPP(U_15204,U_15200)) )
    & ! [U_15205,U_15203] :
        ( ? [U_15199] : hBOOL(hAPP(U_15203,U_15199))
        | ~ hBOOL(hAPP(U_15203,c_Hilbert__Choice_OEps(U_15205,U_15203))) ) ),
    inference(miniscope,[status(thm)],[f_3823_2]) ).

fof(f_3823_4,plain,
    ( ! [U_15206,U_15204] :
        ( hBOOL(hAPP(U_15204,c_Hilbert__Choice_OEps(U_15206,U_15204)))
        | ! [U_15200] : ~ hBOOL(hAPP(U_15204,U_15200)) )
    & ! [U_15205,U_15203] :
        ( hBOOL(hAPP(U_15203,sK362(U_15205,U_15203)))
        | ~ hBOOL(hAPP(U_15203,c_Hilbert__Choice_OEps(U_15205,U_15203))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_15199,sK362(U_15205,U_15203))],[f_3823_3]) ).

fof(f_3823_5,plain,
    ( ! [U_15200,U_15204,U_15206] :
        ( hBOOL(hAPP(U_15204,c_Hilbert__Choice_OEps(U_15206,U_15204)))
        | ~ hBOOL(hAPP(U_15204,U_15200)) )
    & ! [U_15205,U_15203] :
        ( hBOOL(hAPP(U_15203,sK362(U_15205,U_15203)))
        | ~ hBOOL(hAPP(U_15203,c_Hilbert__Choice_OEps(U_15205,U_15203))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3823_4]) ).

cnf(f_3823_6,plain,
    ( hBOOL(hAPP(U_15203,sK362(U_15205,U_15203)))
    | ~ hBOOL(hAPP(U_15203,c_Hilbert__Choice_OEps(U_15205,U_15203))) ),
    inference(clausify,[status(thm)],[f_3823_5]) ).

cnf(f_3823_7,plain,
    ( hBOOL(hAPP(U_15204,c_Hilbert__Choice_OEps(U_15206,U_15204)))
    | ~ hBOOL(hAPP(U_15204,U_15200)) ),
    inference(clausify,[status(thm)],[f_3823_5]) ).

fof(f_3824_1,plain,
    ! [T_b,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).

fof(f_3824_2,plain,
    ! [U_15209,U_15208] :
      ( hBOOL(hAPP(U_15208,c_Hilbert__Choice_OEps(U_15209,U_15208)))
      | ! [U_15207] : ~ hBOOL(hAPP(U_15208,U_15207)) ),
    inference(variable_rename,[status(thm)],[f_3824_1]) ).

fof(f_3824_3,plain,
    ! [U_15207,U_15208,U_15209] :
      ( hBOOL(hAPP(U_15208,c_Hilbert__Choice_OEps(U_15209,U_15208)))
      | ~ hBOOL(hAPP(U_15208,U_15207)) ),
    inference(definitional_conversion,[status(esa)],[f_3824_2]) ).

cnf(f_3824_4,plain,
    ( hBOOL(hAPP(U_15208,c_Hilbert__Choice_OEps(U_15209,U_15208)))
    | ~ hBOOL(hAPP(U_15208,U_15207)) ),
    inference(clausify,[status(thm)],[f_3824_3]) ).

fof(f_3825_1,plain,
    ! [T_b,B_P] :
      ( hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P)))
      | ! [B_x] : ~ hBOOL(hAPP(B_P,B_x)) ),
    inference(fof_nnf,[status(thm)],[fact_tfl__some]) ).

fof(f_3825_2,plain,
    ! [U_15212,U_15211] :
      ( hBOOL(hAPP(U_15211,c_Hilbert__Choice_OEps(U_15212,U_15211)))
      | ! [U_15210] : ~ hBOOL(hAPP(U_15211,U_15210)) ),
    inference(variable_rename,[status(thm)],[f_3825_1]) ).

fof(f_3825_3,plain,
    ! [U_15210,U_15211,U_15212] :
      ( hBOOL(hAPP(U_15211,c_Hilbert__Choice_OEps(U_15212,U_15211)))
      | ~ hBOOL(hAPP(U_15211,U_15210)) ),
    inference(definitional_conversion,[status(esa)],[f_3825_2]) ).

cnf(f_3825_4,plain,
    ( hBOOL(hAPP(U_15211,c_Hilbert__Choice_OEps(U_15212,U_15211)))
    | ~ hBOOL(hAPP(U_15211,U_15210)) ),
    inference(clausify,[status(thm)],[f_3825_3]) ).

fof(f_3826_1,plain,
    ! [T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_someI]) ).

fof(f_3826_2,plain,
    ! [U_15215,U_15214,U_15213] :
      ( hBOOL(hAPP(U_15213,c_Hilbert__Choice_OEps(U_15215,U_15213)))
      | ~ hBOOL(hAPP(U_15213,U_15214)) ),
    inference(variable_rename,[status(thm)],[f_3826_1]) ).

fof(f_3826_3,plain,
    ! [U_15213,U_15214,U_15215] :
      ( hBOOL(hAPP(U_15213,c_Hilbert__Choice_OEps(U_15215,U_15213)))
      | ~ hBOOL(hAPP(U_15213,U_15214)) ),
    inference(definitional_conversion,[status(esa)],[f_3826_2]) ).

cnf(f_3826_4,plain,
    ( hBOOL(hAPP(U_15213,c_Hilbert__Choice_OEps(U_15215,U_15213)))
    | ~ hBOOL(hAPP(U_15213,U_15214)) ),
    inference(clausify,[status(thm)],[f_3826_3]) ).

fof(f_3827_1,plain,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).

fof(f_3827_2,plain,
    ! [U_15218,U_15217,U_15216] : c_Hilbert__Choice_OEps(tc_prod(U_15216,U_15217),U_15218) = c_Hilbert__Choice_OEps(tc_prod(U_15216,U_15217),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15217,tc_prod(U_15216,U_15217)),tc_fun(U_15217,tc_HOL_Obool),U_15216),hAPP(c_COMBB(tc_prod(U_15216,U_15217),tc_HOL_Obool,U_15217),U_15218)),c_Product__Type_OPair(U_15216,U_15217)))),
    inference(variable_rename,[status(thm)],[f_3827_1]) ).

fof(f_3827_3,plain,
    ! [U_15216,U_15217,U_15218] : c_Hilbert__Choice_OEps(tc_prod(U_15216,U_15217),U_15218) = c_Hilbert__Choice_OEps(tc_prod(U_15216,U_15217),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15217,tc_prod(U_15216,U_15217)),tc_fun(U_15217,tc_HOL_Obool),U_15216),hAPP(c_COMBB(tc_prod(U_15216,U_15217),tc_HOL_Obool,U_15217),U_15218)),c_Product__Type_OPair(U_15216,U_15217)))),
    inference(definitional_conversion,[status(esa)],[f_3827_2]) ).

cnf(f_3827_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_15216,U_15217),U_15218) = c_Hilbert__Choice_OEps(tc_prod(U_15216,U_15217),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15217,tc_prod(U_15216,U_15217)),tc_fun(U_15217,tc_HOL_Obool),U_15216),hAPP(c_COMBB(tc_prod(U_15216,U_15217),tc_HOL_Obool,U_15217),U_15218)),c_Product__Type_OPair(U_15216,U_15217)))),
    inference(clausify,[status(thm)],[f_3827_3]) ).

fof(f_3828_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_Eps__split__eq]) ).

fof(f_3828_2,plain,
    ! [U_15222,U_15221,U_15220,U_15219] : c_Hilbert__Choice_OEps(tc_prod(U_15219,U_15220),hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(c_fequal,U_15221)))),hAPP(c_fequal,U_15222)))) = hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15220),U_15221),U_15222),
    inference(variable_rename,[status(thm)],[f_3828_1]) ).

fof(f_3828_3,plain,
    ! [U_15219,U_15220,U_15221,U_15222] : c_Hilbert__Choice_OEps(tc_prod(U_15219,U_15220),hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(c_fequal,U_15221)))),hAPP(c_fequal,U_15222)))) = hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15220),U_15221),U_15222),
    inference(definitional_conversion,[status(esa)],[f_3828_2]) ).

cnf(f_3828_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_15219,U_15220),hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(c_fequal,U_15221)))),hAPP(c_fequal,U_15222)))) = hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15220),U_15221),U_15222),
    inference(clausify,[status(thm)],[f_3828_3]) ).

fof(f_3829_1,plain,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
      | ? [B_A] :
          ( B_A != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfI__pf]) ).

fof(f_3829_2,plain,
    ! [U_15225,U_15224] :
      ( c_Wellfounded_Owf(U_15224,U_15225)
      | ? [U_15223] :
          ( U_15223 != c_Orderings_Obot__class_Obot(tc_fun(U_15224,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15224,tc_HOL_Obool)),U_15223),hAPP(c_Relation_OImage(U_15224,U_15224,U_15225),U_15223))) ) ),
    inference(variable_rename,[status(thm)],[f_3829_1]) ).

fof(f_3829_3,plain,
    ! [U_15225,U_15224] :
      ( c_Wellfounded_Owf(U_15224,U_15225)
      | ( sK363(U_15225,U_15224) != c_Orderings_Obot__class_Obot(tc_fun(U_15224,tc_HOL_Obool))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15224,tc_HOL_Obool)),sK363(U_15225,U_15224)),hAPP(c_Relation_OImage(U_15224,U_15224,U_15225),sK363(U_15225,U_15224)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_15223,sK363(U_15225,U_15224))],[f_3829_2]) ).

fof(f_3829_4,plain,
    ( ! [U_15224,U_15225] :
        ( sK363(U_15225,U_15224) != c_Orderings_Obot__class_Obot(tc_fun(U_15224,tc_HOL_Obool))
        | ~ sP1025(U_15224,U_15225) )
    & ! [U_15224,U_15225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15224,tc_HOL_Obool)),sK363(U_15225,U_15224)),hAPP(c_Relation_OImage(U_15224,U_15224,U_15225),sK363(U_15225,U_15224))))
        | ~ sP1025(U_15224,U_15225) )
    & ! [U_15224,U_15225] :
        ( c_Wellfounded_Owf(U_15224,U_15225)
        | sP1025(U_15224,U_15225) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1025])],[f_3829_3]) ).

cnf(f_3829_5,plain,
    ( c_Wellfounded_Owf(U_15224,U_15225)
    | sP1025(U_15224,U_15225) ),
    inference(clausify,[status(thm)],[f_3829_4]) ).

cnf(f_3829_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15224,tc_HOL_Obool)),sK363(U_15225,U_15224)),hAPP(c_Relation_OImage(U_15224,U_15224,U_15225),sK363(U_15225,U_15224))))
    | ~ sP1025(U_15224,U_15225) ),
    inference(clausify,[status(thm)],[f_3829_4]) ).

cnf(f_3829_7,plain,
    ( sK363(U_15225,U_15224) != c_Orderings_Obot__class_Obot(tc_fun(U_15224,tc_HOL_Obool))
    | ~ sP1025(U_15224,U_15225) ),
    inference(clausify,[status(thm)],[f_3829_4]) ).

fof(f_3830_1,plain,
    ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Sigma__mono]) ).

fof(f_3830_2,plain,
    ! [U_15232,U_15231,U_15230,U_15229,U_15228,U_15227] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15227,U_15230),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15228),U_15231)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15229),U_15232)))
      | ? [U_15226] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15230,tc_HOL_Obool)),hAPP(U_15231,U_15226)),hAPP(U_15232,U_15226)))
          & hBOOL(hAPP(hAPP(c_member(U_15227),U_15226),U_15228)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15227,tc_HOL_Obool)),U_15228),U_15229)) ),
    inference(variable_rename,[status(thm)],[f_3830_1]) ).

fof(f_3830_3,plain,
    ! [U_15232,U_15231,U_15230,U_15229,U_15228,U_15227] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15227,U_15230),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15228),U_15231)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15229),U_15232)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15230,tc_HOL_Obool)),hAPP(U_15231,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))),hAPP(U_15232,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))))
        & hBOOL(hAPP(hAPP(c_member(U_15227),sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227)),U_15228)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15227,tc_HOL_Obool)),U_15228),U_15229)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_15226,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))],[f_3830_2]) ).

fof(f_3830_4,plain,
    ( ! [U_15227,U_15228,U_15229,U_15230,U_15231,U_15232] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15230,tc_HOL_Obool)),hAPP(U_15231,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))),hAPP(U_15232,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))))
        | ~ sP1026(U_15227,U_15228,U_15229,U_15230,U_15231,U_15232) )
    & ! [U_15227,U_15228,U_15229,U_15230,U_15231,U_15232] :
        ( hBOOL(hAPP(hAPP(c_member(U_15227),sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227)),U_15228))
        | ~ sP1026(U_15227,U_15228,U_15229,U_15230,U_15231,U_15232) )
    & ! [U_15227,U_15228,U_15229,U_15230,U_15231,U_15232] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15227,U_15230),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15228),U_15231)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15229),U_15232)))
        | sP1026(U_15227,U_15228,U_15229,U_15230,U_15231,U_15232)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15227,tc_HOL_Obool)),U_15228),U_15229)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1026])],[f_3830_3]) ).

cnf(f_3830_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15227,U_15230),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15228),U_15231)),hAPP(hAPP(c_Product__Type_OSigma(U_15227,U_15230),U_15229),U_15232)))
    | sP1026(U_15227,U_15228,U_15229,U_15230,U_15231,U_15232)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15227,tc_HOL_Obool)),U_15228),U_15229)) ),
    inference(clausify,[status(thm)],[f_3830_4]) ).

cnf(f_3830_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15227),sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227)),U_15228))
    | ~ sP1026(U_15227,U_15228,U_15229,U_15230,U_15231,U_15232) ),
    inference(clausify,[status(thm)],[f_3830_4]) ).

cnf(f_3830_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15230,tc_HOL_Obool)),hAPP(U_15231,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))),hAPP(U_15232,sK364(U_15232,U_15231,U_15230,U_15229,U_15228,U_15227))))
    | ~ sP1026(U_15227,U_15228,U_15229,U_15230,U_15231,U_15232) ),
    inference(clausify,[status(thm)],[f_3830_4]) ).

fof(f_3831_1,plain,
    ! [V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acc_OaccI]) ).

fof(f_3831_2,plain,
    ! [U_15236,U_15235,U_15234] :
      ( hBOOL(hAPP(hAPP(c_member(U_15234),U_15235),c_Wellfounded_Oacc(U_15234,U_15236)))
      | ? [U_15233] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_15234),U_15233),c_Wellfounded_Oacc(U_15234,U_15236)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15234),U_15233),U_15235)),U_15236)) ) ),
    inference(variable_rename,[status(thm)],[f_3831_1]) ).

fof(f_3831_3,plain,
    ! [U_15236,U_15235,U_15234] :
      ( hBOOL(hAPP(hAPP(c_member(U_15234),U_15235),c_Wellfounded_Oacc(U_15234,U_15236)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_15234),sK365(U_15236,U_15235,U_15234)),c_Wellfounded_Oacc(U_15234,U_15236)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15234),sK365(U_15236,U_15235,U_15234)),U_15235)),U_15236)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_15233,sK365(U_15236,U_15235,U_15234))],[f_3831_2]) ).

fof(f_3831_4,plain,
    ( ! [U_15234,U_15235,U_15236] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_15234),sK365(U_15236,U_15235,U_15234)),c_Wellfounded_Oacc(U_15234,U_15236)))
        | ~ sP1027(U_15234,U_15235,U_15236) )
    & ! [U_15234,U_15235,U_15236] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15234),sK365(U_15236,U_15235,U_15234)),U_15235)),U_15236))
        | ~ sP1027(U_15234,U_15235,U_15236) )
    & ! [U_15234,U_15235,U_15236] :
        ( hBOOL(hAPP(hAPP(c_member(U_15234),U_15235),c_Wellfounded_Oacc(U_15234,U_15236)))
        | sP1027(U_15234,U_15235,U_15236) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1027])],[f_3831_3]) ).

cnf(f_3831_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15234),U_15235),c_Wellfounded_Oacc(U_15234,U_15236)))
    | sP1027(U_15234,U_15235,U_15236) ),
    inference(clausify,[status(thm)],[f_3831_4]) ).

cnf(f_3831_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15234),sK365(U_15236,U_15235,U_15234)),U_15235)),U_15236))
    | ~ sP1027(U_15234,U_15235,U_15236) ),
    inference(clausify,[status(thm)],[f_3831_4]) ).

cnf(f_3831_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15234),sK365(U_15236,U_15235,U_15234)),c_Wellfounded_Oacc(U_15234,U_15236)))
    | ~ sP1027(U_15234,U_15235,U_15236) ),
    inference(clausify,[status(thm)],[f_3831_4]) ).

fof(f_3832_1,plain,
    ! [V_R_2,V_x_2,T_b] :
      ( ? [B_z] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_not__acc__down]) ).

fof(f_3832_2,plain,
    ! [U_15240,U_15239,U_15238] :
      ( ? [U_15237] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_15238),U_15237),c_Wellfounded_Oacc(U_15238,U_15240)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),U_15237),U_15239)),U_15240)) )
      | hBOOL(hAPP(hAPP(c_member(U_15238),U_15239),c_Wellfounded_Oacc(U_15238,U_15240))) ),
    inference(variable_rename,[status(thm)],[f_3832_1]) ).

fof(f_3832_3,plain,
    ! [U_15240,U_15239,U_15238] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_15238),sK366(U_15240,U_15239,U_15238)),c_Wellfounded_Oacc(U_15238,U_15240)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),sK366(U_15240,U_15239,U_15238)),U_15239)),U_15240)) )
      | hBOOL(hAPP(hAPP(c_member(U_15238),U_15239),c_Wellfounded_Oacc(U_15238,U_15240))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_15237,sK366(U_15240,U_15239,U_15238))],[f_3832_2]) ).

fof(f_3832_4,plain,
    ( ! [U_15238,U_15239,U_15240] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_15238),sK366(U_15240,U_15239,U_15238)),c_Wellfounded_Oacc(U_15238,U_15240)))
        | ~ sP1028(U_15238,U_15239,U_15240) )
    & ! [U_15238,U_15239,U_15240] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),sK366(U_15240,U_15239,U_15238)),U_15239)),U_15240))
        | ~ sP1028(U_15238,U_15239,U_15240) )
    & ! [U_15238,U_15239,U_15240] :
        ( sP1028(U_15238,U_15239,U_15240)
        | hBOOL(hAPP(hAPP(c_member(U_15238),U_15239),c_Wellfounded_Oacc(U_15238,U_15240))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1028])],[f_3832_3]) ).

cnf(f_3832_5,plain,
    ( sP1028(U_15238,U_15239,U_15240)
    | hBOOL(hAPP(hAPP(c_member(U_15238),U_15239),c_Wellfounded_Oacc(U_15238,U_15240))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),sK366(U_15240,U_15239,U_15238)),U_15239)),U_15240))
    | ~ sP1028(U_15238,U_15239,U_15240) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15238),sK366(U_15240,U_15239,U_15238)),c_Wellfounded_Oacc(U_15238,U_15240)))
    | ~ sP1028(U_15238,U_15239,U_15240) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

fof(f_3833_1,plain,
    ! [V_f_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__1]) ).

fof(f_3833_2,plain,
    ! [U_15245,U_15244,U_15243,U_15242] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15242,U_15243,c_Groups_Otimes__class_Otimes(U_15242)),U_15245),c_Groups_Oone__class_Oone(U_15242)),U_15244) = c_Groups_Oone__class_Oone(U_15242)
      | ? [U_15241] :
          ( hAPP(U_15245,U_15241) != c_Groups_Oone__class_Oone(U_15242)
          & hBOOL(hAPP(hAPP(c_member(U_15243),U_15241),U_15244)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15243),U_15244))
      | ~ class_Groups_Ocomm__monoid__mult(U_15242) ),
    inference(variable_rename,[status(thm)],[f_3833_1]) ).

fof(f_3833_3,plain,
    ! [U_15245,U_15244,U_15243,U_15242] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15242,U_15243,c_Groups_Otimes__class_Otimes(U_15242)),U_15245),c_Groups_Oone__class_Oone(U_15242)),U_15244) = c_Groups_Oone__class_Oone(U_15242)
      | ( hAPP(U_15245,sK367(U_15245,U_15244,U_15243,U_15242)) != c_Groups_Oone__class_Oone(U_15242)
        & hBOOL(hAPP(hAPP(c_member(U_15243),sK367(U_15245,U_15244,U_15243,U_15242)),U_15244)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15243),U_15244))
      | ~ class_Groups_Ocomm__monoid__mult(U_15242) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_15241,sK367(U_15245,U_15244,U_15243,U_15242))],[f_3833_2]) ).

fof(f_3833_4,plain,
    ( ! [U_15242,U_15243,U_15244,U_15245] :
        ( hAPP(U_15245,sK367(U_15245,U_15244,U_15243,U_15242)) != c_Groups_Oone__class_Oone(U_15242)
        | ~ sP1029(U_15242,U_15243,U_15244,U_15245) )
    & ! [U_15242,U_15243,U_15244,U_15245] :
        ( hBOOL(hAPP(hAPP(c_member(U_15243),sK367(U_15245,U_15244,U_15243,U_15242)),U_15244))
        | ~ sP1029(U_15242,U_15243,U_15244,U_15245) )
    & ! [U_15242,U_15243,U_15244,U_15245] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15242,U_15243,c_Groups_Otimes__class_Otimes(U_15242)),U_15245),c_Groups_Oone__class_Oone(U_15242)),U_15244) = c_Groups_Oone__class_Oone(U_15242)
        | sP1029(U_15242,U_15243,U_15244,U_15245)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15243),U_15244))
        | ~ class_Groups_Ocomm__monoid__mult(U_15242) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1029])],[f_3833_3]) ).

cnf(f_3833_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15242,U_15243,c_Groups_Otimes__class_Otimes(U_15242)),U_15245),c_Groups_Oone__class_Oone(U_15242)),U_15244) = c_Groups_Oone__class_Oone(U_15242)
    | sP1029(U_15242,U_15243,U_15244,U_15245)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15243),U_15244))
    | ~ class_Groups_Ocomm__monoid__mult(U_15242) ),
    inference(clausify,[status(thm)],[f_3833_4]) ).

cnf(f_3833_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15243),sK367(U_15245,U_15244,U_15243,U_15242)),U_15244))
    | ~ sP1029(U_15242,U_15243,U_15244,U_15245) ),
    inference(clausify,[status(thm)],[f_3833_4]) ).

cnf(f_3833_7,plain,
    ( hAPP(U_15245,sK367(U_15245,U_15244,U_15243,U_15242)) != c_Groups_Oone__class_Oone(U_15242)
    | ~ sP1029(U_15242,U_15243,U_15244,U_15245) ),
    inference(clausify,[status(thm)],[f_3833_4]) ).

fof(f_3834_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oneutral]) ).

fof(f_3834_2,plain,
    ! [U_15248,U_15247] :
      ( hAPP(c_Finite__Set_Ocard(U_15247),U_15248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_15246] : hBOOL(hAPP(hAPP(c_member(U_15247),U_15246),U_15248)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15247),U_15248)) ),
    inference(variable_rename,[status(thm)],[f_3834_1]) ).

fof(f_3834_3,plain,
    ! [U_15248,U_15247] :
      ( hAPP(c_Finite__Set_Ocard(U_15247),U_15248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_15247),sK368(U_15248,U_15247)),U_15248)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15247),U_15248)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_15246,sK368(U_15248,U_15247))],[f_3834_2]) ).

fof(f_3834_4,plain,
    ( ! [U_15248,U_15247] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1030(U_15248,U_15247) )
    & ! [U_15248,U_15247] :
        ( hBOOL(hAPP(hAPP(c_member(U_15247),sK368(U_15248,U_15247)),U_15248))
        | ~ sP1030(U_15248,U_15247) )
    & ! [U_15248,U_15247] :
        ( hAPP(c_Finite__Set_Ocard(U_15247),U_15248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1030(U_15248,U_15247)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15247),U_15248)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1030])],[f_3834_3]) ).

cnf(f_3834_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_15247),U_15248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1030(U_15248,U_15247)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15247),U_15248)) ),
    inference(clausify,[status(thm)],[f_3834_4]) ).

cnf(f_3834_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15247),sK368(U_15248,U_15247)),U_15248))
    | ~ sP1030(U_15248,U_15247) ),
    inference(clausify,[status(thm)],[f_3834_4]) ).

cnf(f_3834_7,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1030(U_15248,U_15247) ),
    inference(clausify,[status(thm)],[f_3834_4]) ).

fof(f_3835_1,plain,
    ! [V_R_2,V_a2_2,V_a1_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
        | ? [B_x] :
            ( ! [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext_Osimps]) ).

fof(f_3835_2,plain,
    ! [U_15256,U_15255,U_15254,U_15253] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15253,tc_HOL_Obool),tc_fun(U_15253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15253,tc_HOL_Obool),tc_fun(U_15253,tc_HOL_Obool)),U_15254),U_15255)),c_Wellfounded_Omax__ext(U_15253,U_15256)))
        | ? [U_15252] :
            ( ! [U_15251] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15253,U_15253)),hAPP(hAPP(c_Product__Type_OPair(U_15253,U_15253),U_15252),U_15251)),U_15256))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15253),U_15251),U_15255)) )
            & hBOOL(hAPP(hAPP(c_member(U_15253),U_15252),U_15254)) )
        | U_15255 = c_Orderings_Obot__class_Obot(tc_fun(U_15253,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15253),U_15255))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15253),U_15254)) )
      & ( ( ! [U_15250] :
              ( ? [U_15249] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15253,U_15253)),hAPP(hAPP(c_Product__Type_OPair(U_15253,U_15253),U_15250),U_15249)),U_15256))
                  & hBOOL(hAPP(hAPP(c_member(U_15253),U_15249),U_15255)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15253),U_15250),U_15254)) )
          & U_15255 != c_Orderings_Obot__class_Obot(tc_fun(U_15253,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15253),U_15255))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15253),U_15254)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15253,tc_HOL_Obool),tc_fun(U_15253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15253,tc_HOL_Obool),tc_fun(U_15253,tc_HOL_Obool)),U_15254),U_15255)),c_Wellfounded_Omax__ext(U_15253,U_15256))) ) ),
    inference(variable_rename,[status(thm)],[f_3835_1]) ).

fof(f_3835_3,plain,
    ( ! [U_15264,U_15262,U_15260,U_15258] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool)),U_15260),U_15262)),c_Wellfounded_Omax__ext(U_15258,U_15264)))
        | ? [U_15252] :
            ( ! [U_15251] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15258,U_15258)),hAPP(hAPP(c_Product__Type_OPair(U_15258,U_15258),U_15252),U_15251)),U_15264))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15258),U_15251),U_15262)) )
            & hBOOL(hAPP(hAPP(c_member(U_15258),U_15252),U_15260)) )
        | U_15262 = c_Orderings_Obot__class_Obot(tc_fun(U_15258,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15262))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15260)) )
    & ! [U_15263,U_15261,U_15259,U_15257] :
        ( ( ! [U_15250] :
              ( ? [U_15249] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15257,U_15257)),hAPP(hAPP(c_Product__Type_OPair(U_15257,U_15257),U_15250),U_15249)),U_15263))
                  & hBOOL(hAPP(hAPP(c_member(U_15257),U_15249),U_15261)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15257),U_15250),U_15259)) )
          & U_15261 != c_Orderings_Obot__class_Obot(tc_fun(U_15257,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15261))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15259)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool)),U_15259),U_15261)),c_Wellfounded_Omax__ext(U_15257,U_15263))) ) ),
    inference(miniscope,[status(thm)],[f_3835_2]) ).

fof(f_3835_4,plain,
    ( ! [U_15264,U_15262,U_15260,U_15258] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool)),U_15260),U_15262)),c_Wellfounded_Omax__ext(U_15258,U_15264)))
        | ? [U_15252] :
            ( ! [U_15251] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15258,U_15258)),hAPP(hAPP(c_Product__Type_OPair(U_15258,U_15258),U_15252),U_15251)),U_15264))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15258),U_15251),U_15262)) )
            & hBOOL(hAPP(hAPP(c_member(U_15258),U_15252),U_15260)) )
        | U_15262 = c_Orderings_Obot__class_Obot(tc_fun(U_15258,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15262))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15260)) )
    & ! [U_15263,U_15261,U_15259,U_15257] :
        ( ( ! [U_15250] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15257,U_15257)),hAPP(hAPP(c_Product__Type_OPair(U_15257,U_15257),U_15250),sK369(U_15263,U_15261,U_15259,U_15257,U_15250))),U_15263))
                & hBOOL(hAPP(hAPP(c_member(U_15257),sK369(U_15263,U_15261,U_15259,U_15257,U_15250)),U_15261)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15257),U_15250),U_15259)) )
          & U_15261 != c_Orderings_Obot__class_Obot(tc_fun(U_15257,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15261))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15259)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool)),U_15259),U_15261)),c_Wellfounded_Omax__ext(U_15257,U_15263))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_15249,sK369(U_15263,U_15261,U_15259,U_15257,U_15250))],[f_3835_3]) ).

fof(f_3835_5,plain,
    ( ! [U_15264,U_15262,U_15260,U_15258] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool)),U_15260),U_15262)),c_Wellfounded_Omax__ext(U_15258,U_15264)))
        | ( ! [U_15251] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15258,U_15258)),hAPP(hAPP(c_Product__Type_OPair(U_15258,U_15258),sK370(U_15264,U_15262,U_15260,U_15258)),U_15251)),U_15264))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15258),U_15251),U_15262)) )
          & hBOOL(hAPP(hAPP(c_member(U_15258),sK370(U_15264,U_15262,U_15260,U_15258)),U_15260)) )
        | U_15262 = c_Orderings_Obot__class_Obot(tc_fun(U_15258,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15262))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15260)) )
    & ! [U_15263,U_15261,U_15259,U_15257] :
        ( ( ! [U_15250] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15257,U_15257)),hAPP(hAPP(c_Product__Type_OPair(U_15257,U_15257),U_15250),sK369(U_15263,U_15261,U_15259,U_15257,U_15250))),U_15263))
                & hBOOL(hAPP(hAPP(c_member(U_15257),sK369(U_15263,U_15261,U_15259,U_15257,U_15250)),U_15261)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15257),U_15250),U_15259)) )
          & U_15261 != c_Orderings_Obot__class_Obot(tc_fun(U_15257,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15261))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15259)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool)),U_15259),U_15261)),c_Wellfounded_Omax__ext(U_15257,U_15263))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_15252,sK370(U_15264,U_15262,U_15260,U_15258))],[f_3835_4]) ).

fof(f_3835_6,plain,
    ( ! [U_15264,U_15260,U_15262,U_15251,U_15258] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15258,U_15258)),hAPP(hAPP(c_Product__Type_OPair(U_15258,U_15258),sK370(U_15264,U_15262,U_15260,U_15258)),U_15251)),U_15264))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15258),U_15251),U_15262))
        | ~ sP1033(U_15264,U_15260,U_15262,U_15251,U_15258) )
    & ! [U_15264,U_15260,U_15262,U_15251,U_15258] :
        ( hBOOL(hAPP(hAPP(c_member(U_15258),sK370(U_15264,U_15262,U_15260,U_15258)),U_15260))
        | ~ sP1033(U_15264,U_15260,U_15262,U_15251,U_15258) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15257,U_15257)),hAPP(hAPP(c_Product__Type_OPair(U_15257,U_15257),U_15250),sK369(U_15263,U_15261,U_15259,U_15257,U_15250))),U_15263))
        | ~ sP1031(U_15250,U_15257,U_15259,U_15263,U_15261) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( hBOOL(hAPP(hAPP(c_member(U_15257),sK369(U_15263,U_15261,U_15259,U_15257,U_15250)),U_15261))
        | ~ sP1031(U_15250,U_15257,U_15259,U_15263,U_15261) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( sP1031(U_15250,U_15257,U_15259,U_15263,U_15261)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15257),U_15250),U_15259))
        | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( U_15261 != c_Orderings_Obot__class_Obot(tc_fun(U_15257,tc_HOL_Obool))
        | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15261))
        | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15259))
        | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) )
    & ! [U_15264,U_15260,U_15262,U_15251,U_15258] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool)),U_15260),U_15262)),c_Wellfounded_Omax__ext(U_15258,U_15264)))
        | sP1033(U_15264,U_15260,U_15262,U_15251,U_15258)
        | U_15262 = c_Orderings_Obot__class_Obot(tc_fun(U_15258,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15262))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15260)) )
    & ! [U_15250,U_15257,U_15259,U_15263,U_15261] :
        ( sP1032(U_15250,U_15257,U_15259,U_15263,U_15261)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool)),U_15259),U_15261)),c_Wellfounded_Omax__ext(U_15257,U_15263))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1031,sP1032,sP1033])],[f_3835_5]) ).

cnf(f_3835_7,plain,
    ( sP1032(U_15250,U_15257,U_15259,U_15263,U_15261)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15257,tc_HOL_Obool),tc_fun(U_15257,tc_HOL_Obool)),U_15259),U_15261)),c_Wellfounded_Omax__ext(U_15257,U_15263))) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15258,tc_HOL_Obool),tc_fun(U_15258,tc_HOL_Obool)),U_15260),U_15262)),c_Wellfounded_Omax__ext(U_15258,U_15264)))
    | sP1033(U_15264,U_15260,U_15262,U_15251,U_15258)
    | U_15262 = c_Orderings_Obot__class_Obot(tc_fun(U_15258,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15262))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15258),U_15260)) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15259))
    | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15261))
    | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_11,plain,
    ( U_15261 != c_Orderings_Obot__class_Obot(tc_fun(U_15257,tc_HOL_Obool))
    | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_12,plain,
    ( sP1031(U_15250,U_15257,U_15259,U_15263,U_15261)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15257),U_15250),U_15259))
    | ~ sP1032(U_15250,U_15257,U_15259,U_15263,U_15261) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15257),sK369(U_15263,U_15261,U_15259,U_15257,U_15250)),U_15261))
    | ~ sP1031(U_15250,U_15257,U_15259,U_15263,U_15261) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15257,U_15257)),hAPP(hAPP(c_Product__Type_OPair(U_15257,U_15257),U_15250),sK369(U_15263,U_15261,U_15259,U_15257,U_15250))),U_15263))
    | ~ sP1031(U_15250,U_15257,U_15259,U_15263,U_15261) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15258),sK370(U_15264,U_15262,U_15260,U_15258)),U_15260))
    | ~ sP1033(U_15264,U_15260,U_15262,U_15251,U_15258) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

cnf(f_3835_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15258,U_15258)),hAPP(hAPP(c_Product__Type_OPair(U_15258,U_15258),sK370(U_15264,U_15262,U_15260,U_15258)),U_15251)),U_15264))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15258),U_15251),U_15262))
    | ~ sP1033(U_15264,U_15260,U_15262,U_15251,U_15258) ),
    inference(clausify,[status(thm)],[f_3835_6]) ).

fof(f_3836_1,plain,
    ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2)
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != hAPP(V_h_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__cong]) ).

fof(f_3836_2,plain,
    ! [U_15271,U_15270,U_15269,U_15268,U_15267,U_15266] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15269),U_15271),U_15268) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15270),U_15271),U_15268)
      | ? [U_15265] :
          ( hAPP(U_15269,U_15265) != hAPP(U_15270,U_15265)
          & hBOOL(hAPP(hAPP(c_member(U_15267),U_15265),U_15268)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15267),U_15268))
      | ~ class_Groups_Oab__semigroup__mult(U_15266) ),
    inference(variable_rename,[status(thm)],[f_3836_1]) ).

fof(f_3836_3,plain,
    ! [U_15271,U_15270,U_15269,U_15268,U_15267,U_15266] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15269),U_15271),U_15268) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15270),U_15271),U_15268)
      | ( hAPP(U_15269,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266)) != hAPP(U_15270,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266))
        & hBOOL(hAPP(hAPP(c_member(U_15267),sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266)),U_15268)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15267),U_15268))
      | ~ class_Groups_Oab__semigroup__mult(U_15266) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_15265,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266))],[f_3836_2]) ).

fof(f_3836_4,plain,
    ( ! [U_15267,U_15266,U_15271,U_15269,U_15268,U_15270] :
        ( hAPP(U_15269,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266)) != hAPP(U_15270,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266))
        | ~ sP1034(U_15267,U_15266,U_15271,U_15269,U_15268,U_15270) )
    & ! [U_15267,U_15266,U_15271,U_15269,U_15268,U_15270] :
        ( hBOOL(hAPP(hAPP(c_member(U_15267),sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266)),U_15268))
        | ~ sP1034(U_15267,U_15266,U_15271,U_15269,U_15268,U_15270) )
    & ! [U_15267,U_15266,U_15271,U_15269,U_15268,U_15270] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15269),U_15271),U_15268) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15270),U_15271),U_15268)
        | sP1034(U_15267,U_15266,U_15271,U_15269,U_15268,U_15270)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15267),U_15268))
        | ~ class_Groups_Oab__semigroup__mult(U_15266) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1034])],[f_3836_3]) ).

cnf(f_3836_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15269),U_15271),U_15268) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15266,U_15267,c_Groups_Otimes__class_Otimes(U_15266)),U_15270),U_15271),U_15268)
    | sP1034(U_15267,U_15266,U_15271,U_15269,U_15268,U_15270)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15267),U_15268))
    | ~ class_Groups_Oab__semigroup__mult(U_15266) ),
    inference(clausify,[status(thm)],[f_3836_4]) ).

cnf(f_3836_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15267),sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266)),U_15268))
    | ~ sP1034(U_15267,U_15266,U_15271,U_15269,U_15268,U_15270) ),
    inference(clausify,[status(thm)],[f_3836_4]) ).

cnf(f_3836_7,plain,
    ( hAPP(U_15269,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266)) != hAPP(U_15270,sK371(U_15271,U_15270,U_15269,U_15268,U_15267,U_15266))
    | ~ sP1034(U_15267,U_15266,U_15271,U_15269,U_15268,U_15270) ),
    inference(clausify,[status(thm)],[f_3836_4]) ).

fof(f_3837_1,plain,
    ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ class_Rings_Ocomm__semiring__1(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset2]) ).

fof(f_3837_2,plain,
    ! [U_15278,U_15277,U_15276,U_15275,U_15274,U_15273] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15277),U_15276)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15278),U_15275)))
      | ? [U_15272] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(U_15277,U_15272)),hAPP(U_15278,U_15272)))
          & hBOOL(hAPP(hAPP(c_member(U_15274),U_15272),U_15276)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15274,tc_HOL_Obool)),U_15276),U_15275))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15274),U_15275))
      | ~ class_Rings_Ocomm__semiring__1(U_15273) ),
    inference(variable_rename,[status(thm)],[f_3837_1]) ).

fof(f_3837_3,plain,
    ! [U_15278,U_15277,U_15276,U_15275,U_15274,U_15273] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15277),U_15276)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15278),U_15275)))
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(U_15277,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))),hAPP(U_15278,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))))
        & hBOOL(hAPP(hAPP(c_member(U_15274),sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273)),U_15276)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15274,tc_HOL_Obool)),U_15276),U_15275))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15274),U_15275))
      | ~ class_Rings_Ocomm__semiring__1(U_15273) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_15272,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))],[f_3837_2]) ).

fof(f_3837_4,plain,
    ( ! [U_15274,U_15275,U_15273,U_15276,U_15277,U_15278] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(U_15277,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))),hAPP(U_15278,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))))
        | ~ sP1035(U_15274,U_15275,U_15273,U_15276,U_15277,U_15278) )
    & ! [U_15274,U_15275,U_15273,U_15276,U_15277,U_15278] :
        ( hBOOL(hAPP(hAPP(c_member(U_15274),sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273)),U_15276))
        | ~ sP1035(U_15274,U_15275,U_15273,U_15276,U_15277,U_15278) )
    & ! [U_15274,U_15275,U_15273,U_15276,U_15277,U_15278] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15277),U_15276)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15278),U_15275)))
        | sP1035(U_15274,U_15275,U_15273,U_15276,U_15277,U_15278)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15274,tc_HOL_Obool)),U_15276),U_15275))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15274),U_15275))
        | ~ class_Rings_Ocomm__semiring__1(U_15273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1035])],[f_3837_3]) ).

cnf(f_3837_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15277),U_15276)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15274,U_15273),U_15278),U_15275)))
    | sP1035(U_15274,U_15275,U_15273,U_15276,U_15277,U_15278)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15274,tc_HOL_Obool)),U_15276),U_15275))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15274),U_15275))
    | ~ class_Rings_Ocomm__semiring__1(U_15273) ),
    inference(clausify,[status(thm)],[f_3837_4]) ).

cnf(f_3837_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15274),sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273)),U_15276))
    | ~ sP1035(U_15274,U_15275,U_15273,U_15276,U_15277,U_15278) ),
    inference(clausify,[status(thm)],[f_3837_4]) ).

cnf(f_3837_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15273),hAPP(U_15277,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))),hAPP(U_15278,sK372(U_15278,U_15277,U_15276,U_15275,U_15274,U_15273))))
    | ~ sP1035(U_15274,U_15275,U_15273,U_15276,U_15277,U_15278) ),
    inference(clausify,[status(thm)],[f_3837_4]) ).

fof(f_3838_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__eqI]) ).

fof(f_3838_2,plain,
    ! [U_15282,U_15281,U_15280] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15280,U_15281) = U_15282
      | ~ hBOOL(hAPP(hAPP(c_member(U_15280),U_15282),U_15281))
      | ? [U_15279] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15280),U_15279),U_15282))
          & hBOOL(hAPP(hAPP(c_member(U_15280),U_15279),U_15281)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15280),U_15281))
      | ~ class_Orderings_Olinorder(U_15280) ),
    inference(variable_rename,[status(thm)],[f_3838_1]) ).

fof(f_3838_3,plain,
    ! [U_15282,U_15281,U_15280] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15280,U_15281) = U_15282
      | ~ hBOOL(hAPP(hAPP(c_member(U_15280),U_15282),U_15281))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15280),sK373(U_15282,U_15281,U_15280)),U_15282))
        & hBOOL(hAPP(hAPP(c_member(U_15280),sK373(U_15282,U_15281,U_15280)),U_15281)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15280),U_15281))
      | ~ class_Orderings_Olinorder(U_15280) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_15279,sK373(U_15282,U_15281,U_15280))],[f_3838_2]) ).

fof(f_3838_4,plain,
    ( ! [U_15280,U_15281,U_15282] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15280),sK373(U_15282,U_15281,U_15280)),U_15282))
        | ~ sP1036(U_15280,U_15281,U_15282) )
    & ! [U_15280,U_15281,U_15282] :
        ( hBOOL(hAPP(hAPP(c_member(U_15280),sK373(U_15282,U_15281,U_15280)),U_15281))
        | ~ sP1036(U_15280,U_15281,U_15282) )
    & ! [U_15280,U_15281,U_15282] :
        ( c_Big__Operators_Olinorder__class_OMax(U_15280,U_15281) = U_15282
        | ~ hBOOL(hAPP(hAPP(c_member(U_15280),U_15282),U_15281))
        | sP1036(U_15280,U_15281,U_15282)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15280),U_15281))
        | ~ class_Orderings_Olinorder(U_15280) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1036])],[f_3838_3]) ).

cnf(f_3838_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15280,U_15281) = U_15282
    | ~ hBOOL(hAPP(hAPP(c_member(U_15280),U_15282),U_15281))
    | sP1036(U_15280,U_15281,U_15282)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15280),U_15281))
    | ~ class_Orderings_Olinorder(U_15280) ),
    inference(clausify,[status(thm)],[f_3838_4]) ).

cnf(f_3838_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15280),sK373(U_15282,U_15281,U_15280)),U_15281))
    | ~ sP1036(U_15280,U_15281,U_15282) ),
    inference(clausify,[status(thm)],[f_3838_4]) ).

cnf(f_3838_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15280),sK373(U_15282,U_15281,U_15280)),U_15282))
    | ~ sP1036(U_15280,U_15281,U_15282) ),
    inference(clausify,[status(thm)],[f_3838_4]) ).

fof(f_3839_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__eqI]) ).

fof(f_3839_2,plain,
    ! [U_15286,U_15285,U_15284] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15284,U_15285) = U_15286
      | ~ hBOOL(hAPP(hAPP(c_member(U_15284),U_15286),U_15285))
      | ? [U_15283] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15284),U_15286),U_15283))
          & hBOOL(hAPP(hAPP(c_member(U_15284),U_15283),U_15285)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15284),U_15285))
      | ~ class_Orderings_Olinorder(U_15284) ),
    inference(variable_rename,[status(thm)],[f_3839_1]) ).

fof(f_3839_3,plain,
    ! [U_15286,U_15285,U_15284] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15284,U_15285) = U_15286
      | ~ hBOOL(hAPP(hAPP(c_member(U_15284),U_15286),U_15285))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15284),U_15286),sK374(U_15286,U_15285,U_15284)))
        & hBOOL(hAPP(hAPP(c_member(U_15284),sK374(U_15286,U_15285,U_15284)),U_15285)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15284),U_15285))
      | ~ class_Orderings_Olinorder(U_15284) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_15283,sK374(U_15286,U_15285,U_15284))],[f_3839_2]) ).

fof(f_3839_4,plain,
    ( ! [U_15285,U_15286,U_15284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15284),U_15286),sK374(U_15286,U_15285,U_15284)))
        | ~ sP1037(U_15285,U_15286,U_15284) )
    & ! [U_15285,U_15286,U_15284] :
        ( hBOOL(hAPP(hAPP(c_member(U_15284),sK374(U_15286,U_15285,U_15284)),U_15285))
        | ~ sP1037(U_15285,U_15286,U_15284) )
    & ! [U_15285,U_15286,U_15284] :
        ( c_Big__Operators_Olinorder__class_OMin(U_15284,U_15285) = U_15286
        | ~ hBOOL(hAPP(hAPP(c_member(U_15284),U_15286),U_15285))
        | sP1037(U_15285,U_15286,U_15284)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15284),U_15285))
        | ~ class_Orderings_Olinorder(U_15284) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1037])],[f_3839_3]) ).

cnf(f_3839_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15284,U_15285) = U_15286
    | ~ hBOOL(hAPP(hAPP(c_member(U_15284),U_15286),U_15285))
    | sP1037(U_15285,U_15286,U_15284)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15284),U_15285))
    | ~ class_Orderings_Olinorder(U_15284) ),
    inference(clausify,[status(thm)],[f_3839_4]) ).

cnf(f_3839_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15284),sK374(U_15286,U_15285,U_15284)),U_15285))
    | ~ sP1037(U_15285,U_15286,U_15284) ),
    inference(clausify,[status(thm)],[f_3839_4]) ).

cnf(f_3839_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15284),U_15286),sK374(U_15286,U_15285,U_15284)))
    | ~ sP1037(U_15285,U_15286,U_15284) ),
    inference(clausify,[status(thm)],[f_3839_4]) ).

fof(f_3840_1,plain,
    ! [V_f_2,V_r_2,T_b] :
      ( ? [B_k] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE]) ).

fof(f_3840_2,plain,
    ! [U_15290,U_15289,U_15288] :
      ( ? [U_15287] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15288,U_15288)),hAPP(hAPP(c_Product__Type_OPair(U_15288,U_15288),hAPP(U_15290,hAPP(c_Nat_OSuc,U_15287))),hAPP(U_15290,U_15287))),U_15289))
      | ~ c_Wellfounded_Owf(U_15288,U_15289) ),
    inference(variable_rename,[status(thm)],[f_3840_1]) ).

fof(f_3840_3,plain,
    ! [U_15290,U_15289,U_15288] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15288,U_15288)),hAPP(hAPP(c_Product__Type_OPair(U_15288,U_15288),hAPP(U_15290,hAPP(c_Nat_OSuc,sK375(U_15290,U_15289,U_15288)))),hAPP(U_15290,sK375(U_15290,U_15289,U_15288)))),U_15289))
      | ~ c_Wellfounded_Owf(U_15288,U_15289) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_15287,sK375(U_15290,U_15289,U_15288))],[f_3840_2]) ).

fof(f_3840_4,plain,
    ! [U_15289,U_15288,U_15290] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15288,U_15288)),hAPP(hAPP(c_Product__Type_OPair(U_15288,U_15288),hAPP(U_15290,hAPP(c_Nat_OSuc,sK375(U_15290,U_15289,U_15288)))),hAPP(U_15290,sK375(U_15290,U_15289,U_15288)))),U_15289))
      | ~ c_Wellfounded_Owf(U_15288,U_15289) ),
    inference(definitional_conversion,[status(esa)],[f_3840_3]) ).

cnf(f_3840_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15288,U_15288)),hAPP(hAPP(c_Product__Type_OPair(U_15288,U_15288),hAPP(U_15290,hAPP(c_Nat_OSuc,sK375(U_15290,U_15289,U_15288)))),hAPP(U_15290,sK375(U_15290,U_15289,U_15288)))),U_15289))
    | ~ c_Wellfounded_Owf(U_15288,U_15289) ),
    inference(clausify,[status(thm)],[f_3840_4]) ).

fof(f_3841_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2)
      | ? [B_a] :
          ( hAPP(V_g_2,B_a) != hAPP(V_h_2,hAPP(V_f_2,B_a))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
      | V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong]) ).

fof(f_3841_2,plain,
    ! [U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15294,U_15292),U_15299),U_15297) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15293,U_15292),U_15298),U_15296)
      | ? [U_15291] :
          ( hAPP(U_15298,U_15291) != hAPP(U_15299,hAPP(U_15295,U_15291))
          & hBOOL(hAPP(hAPP(c_member(U_15293),U_15291),U_15296)) )
      | U_15297 != hAPP(c_Set_Oimage(U_15293,U_15294,U_15295),U_15296)
      | ~ c_Fun_Oinj__on(U_15293,U_15294,U_15295,U_15296)
      | ~ class_Groups_Ocomm__monoid__add(U_15292) ),
    inference(variable_rename,[status(thm)],[f_3841_1]) ).

fof(f_3841_3,plain,
    ! [U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15294,U_15292),U_15299),U_15297) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15293,U_15292),U_15298),U_15296)
      | ( hAPP(U_15298,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)) != hAPP(U_15299,hAPP(U_15295,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)))
        & hBOOL(hAPP(hAPP(c_member(U_15293),sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)),U_15296)) )
      | U_15297 != hAPP(c_Set_Oimage(U_15293,U_15294,U_15295),U_15296)
      | ~ c_Fun_Oinj__on(U_15293,U_15294,U_15295,U_15296)
      | ~ class_Groups_Ocomm__monoid__add(U_15292) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_15291,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292))],[f_3841_2]) ).

fof(f_3841_4,plain,
    ( ! [U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299] :
        ( hAPP(U_15298,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)) != hAPP(U_15299,hAPP(U_15295,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)))
        | ~ sP1038(U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299) )
    & ! [U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299] :
        ( hBOOL(hAPP(hAPP(c_member(U_15293),sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)),U_15296))
        | ~ sP1038(U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299) )
    & ! [U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15294,U_15292),U_15299),U_15297) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15293,U_15292),U_15298),U_15296)
        | sP1038(U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299)
        | U_15297 != hAPP(c_Set_Oimage(U_15293,U_15294,U_15295),U_15296)
        | ~ c_Fun_Oinj__on(U_15293,U_15294,U_15295,U_15296)
        | ~ class_Groups_Ocomm__monoid__add(U_15292) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1038])],[f_3841_3]) ).

cnf(f_3841_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15294,U_15292),U_15299),U_15297) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15293,U_15292),U_15298),U_15296)
    | sP1038(U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299)
    | U_15297 != hAPP(c_Set_Oimage(U_15293,U_15294,U_15295),U_15296)
    | ~ c_Fun_Oinj__on(U_15293,U_15294,U_15295,U_15296)
    | ~ class_Groups_Ocomm__monoid__add(U_15292) ),
    inference(clausify,[status(thm)],[f_3841_4]) ).

cnf(f_3841_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15293),sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)),U_15296))
    | ~ sP1038(U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299) ),
    inference(clausify,[status(thm)],[f_3841_4]) ).

cnf(f_3841_7,plain,
    ( hAPP(U_15298,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)) != hAPP(U_15299,hAPP(U_15295,sK376(U_15299,U_15298,U_15297,U_15296,U_15295,U_15294,U_15293,U_15292)))
    | ~ sP1038(U_15292,U_15293,U_15294,U_15295,U_15296,U_15297,U_15298,U_15299) ),
    inference(clausify,[status(thm)],[f_3841_4]) ).

fof(f_3842_1,plain,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) )
      | V_b_2 != V_d_2
      | V_a_2 != V_c_2
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).

fof(f_3842_2,plain,
    ! [U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15303),U_15305)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15304),U_15306))
      | ? [U_15300] :
          ( hAPP(U_15307,U_15300) != hAPP(U_15308,U_15300)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15302),U_15300),U_15306))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15302),U_15304),U_15300)) )
      | U_15305 != U_15306
      | U_15303 != U_15304
      | ~ class_Orderings_Oord(U_15302)
      | ~ class_Groups_Ocomm__monoid__add(U_15301) ),
    inference(variable_rename,[status(thm)],[f_3842_1]) ).

fof(f_3842_3,plain,
    ! [U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15303),U_15305)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15304),U_15306))
      | ( hAPP(U_15307,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)) != hAPP(U_15308,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15302),sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)),U_15306))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15302),U_15304),sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301))) )
      | U_15305 != U_15306
      | U_15303 != U_15304
      | ~ class_Orderings_Oord(U_15302)
      | ~ class_Groups_Ocomm__monoid__add(U_15301) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_15300,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301))],[f_3842_2]) ).

fof(f_3842_4,plain,
    ( ! [U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308] :
        ( hAPP(U_15307,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)) != hAPP(U_15308,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301))
        | ~ sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308) )
    & ! [U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15302),sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)),U_15306))
        | ~ sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308) )
    & ! [U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15302),U_15304),sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)))
        | ~ sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308) )
    & ! [U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15303),U_15305)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15304),U_15306))
        | sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308)
        | U_15305 != U_15306
        | U_15303 != U_15304
        | ~ class_Orderings_Oord(U_15302)
        | ~ class_Groups_Ocomm__monoid__add(U_15301) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1039])],[f_3842_3]) ).

cnf(f_3842_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15303),U_15305)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15302,U_15301),U_15308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15302,U_15304),U_15306))
    | sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308)
    | U_15305 != U_15306
    | U_15303 != U_15304
    | ~ class_Orderings_Oord(U_15302)
    | ~ class_Groups_Ocomm__monoid__add(U_15301) ),
    inference(clausify,[status(thm)],[f_3842_4]) ).

cnf(f_3842_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15302),U_15304),sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)))
    | ~ sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308) ),
    inference(clausify,[status(thm)],[f_3842_4]) ).

cnf(f_3842_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15302),sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)),U_15306))
    | ~ sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308) ),
    inference(clausify,[status(thm)],[f_3842_4]) ).

cnf(f_3842_8,plain,
    ( hAPP(U_15307,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301)) != hAPP(U_15308,sK377(U_15308,U_15307,U_15306,U_15305,U_15304,U_15303,U_15302,U_15301))
    | ~ sP1039(U_15301,U_15302,U_15304,U_15305,U_15303,U_15306,U_15307,U_15308) ),
    inference(clausify,[status(thm)],[f_3842_4]) ).

fof(f_3843_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq]) ).

fof(f_3843_2,plain,
    ! [U_15310,U_15309] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15309),U_15310)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15309),U_15310)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15309),U_15310))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15309),U_15310)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3843_1]) ).

fof(f_3843_3,plain,
    ( ! [U_15314,U_15312] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15312),U_15314)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15312),U_15314)) )
    & ! [U_15313,U_15311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15311),U_15313))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15311),U_15313)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3843_2]) ).

fof(f_3843_4,plain,
    ( ! [U_15314,U_15312] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15312),U_15314)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15312),U_15314)) )
    & ! [U_15313,U_15311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15311),U_15313))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15311),U_15313)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3843_3]) ).

cnf(f_3843_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15311),U_15313))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15311),U_15313)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3843_4]) ).

cnf(f_3843_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15312),U_15314)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15312),U_15314)) ),
    inference(clausify,[status(thm)],[f_3843_4]) ).

fof(f_3844_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(f_3844_2,plain,
    ! [U_15317,U_15316,U_15315] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15315,c_Orderings_Oord__class_Omax(U_15315),hAPP(hAPP(c_Set_Oinsert(U_15315),U_15317),U_15316)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15315,U_15315,c_Orderings_Oord__class_Omax(U_15315)),U_15317),U_15316)
      | hBOOL(hAPP(hAPP(c_member(U_15315),U_15317),U_15316))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15315),U_15316))
      | ~ class_Orderings_Olinorder(U_15315) ),
    inference(variable_rename,[status(thm)],[f_3844_1]) ).

fof(f_3844_3,plain,
    ! [U_15315,U_15316,U_15317] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15315,c_Orderings_Oord__class_Omax(U_15315),hAPP(hAPP(c_Set_Oinsert(U_15315),U_15317),U_15316)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15315,U_15315,c_Orderings_Oord__class_Omax(U_15315)),U_15317),U_15316)
      | hBOOL(hAPP(hAPP(c_member(U_15315),U_15317),U_15316))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15315),U_15316))
      | ~ class_Orderings_Olinorder(U_15315) ),
    inference(definitional_conversion,[status(esa)],[f_3844_2]) ).

cnf(f_3844_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_15315,c_Orderings_Oord__class_Omax(U_15315),hAPP(hAPP(c_Set_Oinsert(U_15315),U_15317),U_15316)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15315,U_15315,c_Orderings_Oord__class_Omax(U_15315)),U_15317),U_15316)
    | hBOOL(hAPP(hAPP(c_member(U_15315),U_15317),U_15316))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15315),U_15316))
    | ~ class_Orderings_Olinorder(U_15315) ),
    inference(clausify,[status(thm)],[f_3844_3]) ).

fof(f_3845_1,plain,
    ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_fold__empty]) ).

fof(f_3845_2,plain,
    ! [U_15321,U_15320,U_15319,U_15318] : hAPP(hAPP(c_Finite__Set_Ofold(U_15318,U_15319,U_15320),U_15321),c_Orderings_Obot__class_Obot(tc_fun(U_15318,tc_HOL_Obool))) = U_15321,
    inference(variable_rename,[status(thm)],[f_3845_1]) ).

fof(f_3845_3,plain,
    ! [U_15319,U_15318,U_15320,U_15321] : hAPP(hAPP(c_Finite__Set_Ofold(U_15318,U_15319,U_15320),U_15321),c_Orderings_Obot__class_Obot(tc_fun(U_15318,tc_HOL_Obool))) = U_15321,
    inference(definitional_conversion,[status(esa)],[f_3845_2]) ).

cnf(f_3845_4,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_15318,U_15319,U_15320),U_15321),c_Orderings_Obot__class_Obot(tc_fun(U_15318,tc_HOL_Obool))) = U_15321,
    inference(clausify,[status(thm)],[f_3845_3]) ).

fof(f_3846_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__image__def]) ).

fof(f_3846_2,plain,
    ! [U_15325,U_15324,U_15323,U_15322] : hAPP(c_Finite__Set_Ofold__image(U_15322,U_15323,U_15324),U_15325) = c_Finite__Set_Ofold(U_15323,U_15322,hAPP(hAPP(c_COMBB(U_15322,tc_fun(U_15322,U_15322),U_15323),U_15324),U_15325)),
    inference(variable_rename,[status(thm)],[f_3846_1]) ).

fof(f_3846_3,plain,
    ! [U_15322,U_15323,U_15324,U_15325] : hAPP(c_Finite__Set_Ofold__image(U_15322,U_15323,U_15324),U_15325) = c_Finite__Set_Ofold(U_15323,U_15322,hAPP(hAPP(c_COMBB(U_15322,tc_fun(U_15322,U_15322),U_15323),U_15324),U_15325)),
    inference(definitional_conversion,[status(esa)],[f_3846_2]) ).

cnf(f_3846_4,plain,
    hAPP(c_Finite__Set_Ofold__image(U_15322,U_15323,U_15324),U_15325) = c_Finite__Set_Ofold(U_15323,U_15322,hAPP(hAPP(c_COMBB(U_15322,tc_fun(U_15322,U_15322),U_15323),U_15324),U_15325)),
    inference(clausify,[status(thm)],[f_3846_3]) ).

fof(f_3847_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__trancl]) ).

fof(f_3847_2,plain,
    ! [U_15327,U_15326] :
      ( c_Wellfounded_Owf(U_15326,c_Transitive__Closure_Otrancl(U_15326,U_15327))
      | ~ c_Wellfounded_Owf(U_15326,U_15327) ),
    inference(variable_rename,[status(thm)],[f_3847_1]) ).

fof(f_3847_3,plain,
    ! [U_15327,U_15326] :
      ( c_Wellfounded_Owf(U_15326,c_Transitive__Closure_Otrancl(U_15326,U_15327))
      | ~ c_Wellfounded_Owf(U_15326,U_15327) ),
    inference(definitional_conversion,[status(esa)],[f_3847_2]) ).

cnf(f_3847_4,plain,
    ( c_Wellfounded_Owf(U_15326,c_Transitive__Closure_Otrancl(U_15326,U_15327))
    | ~ c_Wellfounded_Owf(U_15326,U_15327) ),
    inference(clausify,[status(thm)],[f_3847_3]) ).

fof(f_3848_1,plain,
    ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold]) ).

fof(f_3848_2,plain,
    ! [U_15333,U_15332,U_15331,U_15330,U_15329,U_15328] :
      ( hAPP(hAPP(U_15331,U_15332),U_15333) = hAPP(hAPP(c_Finite__Set_Ofold(U_15328,U_15329,U_15330),U_15333),U_15332)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15328),U_15332))
      | ~ c_Finite__Set_Ofolding(U_15328,U_15329,U_15330,U_15331) ),
    inference(variable_rename,[status(thm)],[f_3848_1]) ).

fof(f_3848_3,plain,
    ! [U_15328,U_15329,U_15330,U_15331,U_15332,U_15333] :
      ( hAPP(hAPP(U_15331,U_15332),U_15333) = hAPP(hAPP(c_Finite__Set_Ofold(U_15328,U_15329,U_15330),U_15333),U_15332)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15328),U_15332))
      | ~ c_Finite__Set_Ofolding(U_15328,U_15329,U_15330,U_15331) ),
    inference(definitional_conversion,[status(esa)],[f_3848_2]) ).

cnf(f_3848_4,plain,
    ( hAPP(hAPP(U_15331,U_15332),U_15333) = hAPP(hAPP(c_Finite__Set_Ofold(U_15328,U_15329,U_15330),U_15333),U_15332)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15328),U_15332))
    | ~ c_Finite__Set_Ofolding(U_15328,U_15329,U_15330,U_15331) ),
    inference(clausify,[status(thm)],[f_3848_3]) ).

fof(f_3849_1,plain,
    ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__def]) ).

fof(f_3849_2,plain,
    ! [U_15338,U_15337,U_15336,U_15335,U_15334] : hAPP(hAPP(c_Finite__Set_Ofold(U_15334,U_15335,U_15336),U_15337),U_15338) = c_HOL_OThe(U_15335,c_Finite__Set_Ofold__graph(U_15334,U_15335,U_15336,U_15337,U_15338)),
    inference(variable_rename,[status(thm)],[f_3849_1]) ).

fof(f_3849_3,plain,
    ! [U_15335,U_15334,U_15336,U_15337,U_15338] : hAPP(hAPP(c_Finite__Set_Ofold(U_15334,U_15335,U_15336),U_15337),U_15338) = c_HOL_OThe(U_15335,c_Finite__Set_Ofold__graph(U_15334,U_15335,U_15336,U_15337,U_15338)),
    inference(definitional_conversion,[status(esa)],[f_3849_2]) ).

cnf(f_3849_4,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_15334,U_15335,U_15336),U_15337),U_15338) = c_HOL_OThe(U_15335,c_Finite__Set_Ofold__graph(U_15334,U_15335,U_15336,U_15337,U_15338)),
    inference(clausify,[status(thm)],[f_3849_3]) ).

fof(f_3850_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_union__fold__insert]) ).

fof(f_3850_2,plain,
    ! [U_15341,U_15340,U_15339] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15339,tc_HOL_Obool)),U_15340),U_15341) = hAPP(hAPP(c_Finite__Set_Ofold(U_15339,tc_fun(U_15339,tc_HOL_Obool),c_Set_Oinsert(U_15339)),U_15341),U_15340)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15339),U_15340)) ),
    inference(variable_rename,[status(thm)],[f_3850_1]) ).

fof(f_3850_3,plain,
    ! [U_15339,U_15340,U_15341] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15339,tc_HOL_Obool)),U_15340),U_15341) = hAPP(hAPP(c_Finite__Set_Ofold(U_15339,tc_fun(U_15339,tc_HOL_Obool),c_Set_Oinsert(U_15339)),U_15341),U_15340)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15339),U_15340)) ),
    inference(definitional_conversion,[status(esa)],[f_3850_2]) ).

cnf(f_3850_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15339,tc_HOL_Obool)),U_15340),U_15341) = hAPP(hAPP(c_Finite__Set_Ofold(U_15339,tc_fun(U_15339,tc_HOL_Obool),c_Set_Oinsert(U_15339)),U_15341),U_15340)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15339),U_15340)) ),
    inference(clausify,[status(thm)],[f_3850_3]) ).

fof(f_3851_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__sup__insert]) ).

fof(f_3851_2,plain,
    ! [U_15345,U_15344,U_15343,U_15342] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15342,U_15342,c_Lattices_Osemilattice__sup__class_Osup(U_15342)),U_15344),hAPP(hAPP(c_Set_Oinsert(U_15342),U_15345),U_15343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15342),U_15345),hAPP(hAPP(c_Finite__Set_Ofold(U_15342,U_15342,c_Lattices_Osemilattice__sup__class_Osup(U_15342)),U_15344),U_15343))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15342),U_15343))
      | ~ class_Lattices_Osemilattice__sup(U_15342) ),
    inference(variable_rename,[status(thm)],[f_3851_1]) ).

fof(f_3851_3,plain,
    ! [U_15342,U_15343,U_15344,U_15345] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15342,U_15342,c_Lattices_Osemilattice__sup__class_Osup(U_15342)),U_15344),hAPP(hAPP(c_Set_Oinsert(U_15342),U_15345),U_15343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15342),U_15345),hAPP(hAPP(c_Finite__Set_Ofold(U_15342,U_15342,c_Lattices_Osemilattice__sup__class_Osup(U_15342)),U_15344),U_15343))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15342),U_15343))
      | ~ class_Lattices_Osemilattice__sup(U_15342) ),
    inference(definitional_conversion,[status(esa)],[f_3851_2]) ).

cnf(f_3851_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15342,U_15342,c_Lattices_Osemilattice__sup__class_Osup(U_15342)),U_15344),hAPP(hAPP(c_Set_Oinsert(U_15342),U_15345),U_15343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15342),U_15345),hAPP(hAPP(c_Finite__Set_Ofold(U_15342,U_15342,c_Lattices_Osemilattice__sup__class_Osup(U_15342)),U_15344),U_15343))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15342),U_15343))
    | ~ class_Lattices_Osemilattice__sup(U_15342) ),
    inference(clausify,[status(thm)],[f_3851_3]) ).

fof(f_3852_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__inf__insert]) ).

fof(f_3852_2,plain,
    ! [U_15349,U_15348,U_15347,U_15346] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15346,U_15346,c_Lattices_Osemilattice__inf__class_Oinf(U_15346)),U_15348),hAPP(hAPP(c_Set_Oinsert(U_15346),U_15349),U_15347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15346),U_15349),hAPP(hAPP(c_Finite__Set_Ofold(U_15346,U_15346,c_Lattices_Osemilattice__inf__class_Oinf(U_15346)),U_15348),U_15347))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15346),U_15347))
      | ~ class_Lattices_Osemilattice__inf(U_15346) ),
    inference(variable_rename,[status(thm)],[f_3852_1]) ).

fof(f_3852_3,plain,
    ! [U_15346,U_15347,U_15348,U_15349] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15346,U_15346,c_Lattices_Osemilattice__inf__class_Oinf(U_15346)),U_15348),hAPP(hAPP(c_Set_Oinsert(U_15346),U_15349),U_15347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15346),U_15349),hAPP(hAPP(c_Finite__Set_Ofold(U_15346,U_15346,c_Lattices_Osemilattice__inf__class_Oinf(U_15346)),U_15348),U_15347))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15346),U_15347))
      | ~ class_Lattices_Osemilattice__inf(U_15346) ),
    inference(definitional_conversion,[status(esa)],[f_3852_2]) ).

cnf(f_3852_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15346,U_15346,c_Lattices_Osemilattice__inf__class_Oinf(U_15346)),U_15348),hAPP(hAPP(c_Set_Oinsert(U_15346),U_15349),U_15347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15346),U_15349),hAPP(hAPP(c_Finite__Set_Ofold(U_15346,U_15346,c_Lattices_Osemilattice__inf__class_Oinf(U_15346)),U_15348),U_15347))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15346),U_15347))
    | ~ class_Lattices_Osemilattice__inf(U_15346) ),
    inference(clausify,[status(thm)],[f_3852_3]) ).

fof(f_3853_1,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_less__than__def]) ).

fof(f_3853_2,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(definitional_conversion,[status(esa)],[f_3853_1]) ).

cnf(f_3853_3,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3853_2]) ).

fof(f_3854_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert]) ).

fof(f_3854_2,plain,
    ! [U_15353,U_15352,U_15351,U_15350] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15350,U_15350,c_Orderings_Oord__class_Omin(U_15350)),U_15352),hAPP(hAPP(c_Set_Oinsert(U_15350),U_15353),U_15351)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15350),U_15353),hAPP(hAPP(c_Finite__Set_Ofold(U_15350,U_15350,c_Orderings_Oord__class_Omin(U_15350)),U_15352),U_15351))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15350),U_15351))
      | ~ class_Orderings_Olinorder(U_15350) ),
    inference(variable_rename,[status(thm)],[f_3854_1]) ).

fof(f_3854_3,plain,
    ! [U_15350,U_15351,U_15352,U_15353] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15350,U_15350,c_Orderings_Oord__class_Omin(U_15350)),U_15352),hAPP(hAPP(c_Set_Oinsert(U_15350),U_15353),U_15351)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15350),U_15353),hAPP(hAPP(c_Finite__Set_Ofold(U_15350,U_15350,c_Orderings_Oord__class_Omin(U_15350)),U_15352),U_15351))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15350),U_15351))
      | ~ class_Orderings_Olinorder(U_15350) ),
    inference(definitional_conversion,[status(esa)],[f_3854_2]) ).

cnf(f_3854_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15350,U_15350,c_Orderings_Oord__class_Omin(U_15350)),U_15352),hAPP(hAPP(c_Set_Oinsert(U_15350),U_15353),U_15351)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15350),U_15353),hAPP(hAPP(c_Finite__Set_Ofold(U_15350,U_15350,c_Orderings_Oord__class_Omin(U_15350)),U_15352),U_15351))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15350),U_15351))
    | ~ class_Orderings_Olinorder(U_15350) ),
    inference(clausify,[status(thm)],[f_3854_3]) ).

fof(f_3855_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert]) ).

fof(f_3855_2,plain,
    ! [U_15357,U_15356,U_15355,U_15354] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15354,U_15354,c_Orderings_Oord__class_Omax(U_15354)),U_15356),hAPP(hAPP(c_Set_Oinsert(U_15354),U_15357),U_15355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15354),U_15357),hAPP(hAPP(c_Finite__Set_Ofold(U_15354,U_15354,c_Orderings_Oord__class_Omax(U_15354)),U_15356),U_15355))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15354),U_15355))
      | ~ class_Orderings_Olinorder(U_15354) ),
    inference(variable_rename,[status(thm)],[f_3855_1]) ).

fof(f_3855_3,plain,
    ! [U_15354,U_15355,U_15356,U_15357] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15354,U_15354,c_Orderings_Oord__class_Omax(U_15354)),U_15356),hAPP(hAPP(c_Set_Oinsert(U_15354),U_15357),U_15355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15354),U_15357),hAPP(hAPP(c_Finite__Set_Ofold(U_15354,U_15354,c_Orderings_Oord__class_Omax(U_15354)),U_15356),U_15355))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15354),U_15355))
      | ~ class_Orderings_Olinorder(U_15354) ),
    inference(definitional_conversion,[status(esa)],[f_3855_2]) ).

cnf(f_3855_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15354,U_15354,c_Orderings_Oord__class_Omax(U_15354)),U_15356),hAPP(hAPP(c_Set_Oinsert(U_15354),U_15357),U_15355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15354),U_15357),hAPP(hAPP(c_Finite__Set_Ofold(U_15354,U_15354,c_Orderings_Oord__class_Omax(U_15354)),U_15356),U_15355))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15354),U_15355))
    | ~ class_Orderings_Olinorder(U_15354) ),
    inference(clausify,[status(thm)],[f_3855_3]) ).

fof(f_3856_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,V_r_2)
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) )
      & ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__def]) ).

fof(f_3856_2,plain,
    ! [U_15361,U_15360] :
      ( ( c_Wellfounded_Oacyclic(U_15360,U_15361)
        | ? [U_15359] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15360,U_15360)),hAPP(hAPP(c_Product__Type_OPair(U_15360,U_15360),U_15359),U_15359)),c_Transitive__Closure_Otrancl(U_15360,U_15361))) )
      & ( ! [U_15358] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15360,U_15360)),hAPP(hAPP(c_Product__Type_OPair(U_15360,U_15360),U_15358),U_15358)),c_Transitive__Closure_Otrancl(U_15360,U_15361)))
        | ~ c_Wellfounded_Oacyclic(U_15360,U_15361) ) ),
    inference(variable_rename,[status(thm)],[f_3856_1]) ).

fof(f_3856_3,plain,
    ( ! [U_15365,U_15363] :
        ( c_Wellfounded_Oacyclic(U_15363,U_15365)
        | ? [U_15359] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15363,U_15363)),hAPP(hAPP(c_Product__Type_OPair(U_15363,U_15363),U_15359),U_15359)),c_Transitive__Closure_Otrancl(U_15363,U_15365))) )
    & ! [U_15364,U_15362] :
        ( ! [U_15358] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15362,U_15362)),hAPP(hAPP(c_Product__Type_OPair(U_15362,U_15362),U_15358),U_15358)),c_Transitive__Closure_Otrancl(U_15362,U_15364)))
        | ~ c_Wellfounded_Oacyclic(U_15362,U_15364) ) ),
    inference(miniscope,[status(thm)],[f_3856_2]) ).

fof(f_3856_4,plain,
    ( ! [U_15365,U_15363] :
        ( c_Wellfounded_Oacyclic(U_15363,U_15365)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15363,U_15363)),hAPP(hAPP(c_Product__Type_OPair(U_15363,U_15363),sK378(U_15365,U_15363)),sK378(U_15365,U_15363))),c_Transitive__Closure_Otrancl(U_15363,U_15365))) )
    & ! [U_15364,U_15362] :
        ( ! [U_15358] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15362,U_15362)),hAPP(hAPP(c_Product__Type_OPair(U_15362,U_15362),U_15358),U_15358)),c_Transitive__Closure_Otrancl(U_15362,U_15364)))
        | ~ c_Wellfounded_Oacyclic(U_15362,U_15364) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_15359,sK378(U_15365,U_15363))],[f_3856_3]) ).

fof(f_3856_5,plain,
    ( ! [U_15363,U_15365] :
        ( c_Wellfounded_Oacyclic(U_15363,U_15365)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15363,U_15363)),hAPP(hAPP(c_Product__Type_OPair(U_15363,U_15363),sK378(U_15365,U_15363)),sK378(U_15365,U_15363))),c_Transitive__Closure_Otrancl(U_15363,U_15365))) )
    & ! [U_15364,U_15358,U_15362] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15362,U_15362)),hAPP(hAPP(c_Product__Type_OPair(U_15362,U_15362),U_15358),U_15358)),c_Transitive__Closure_Otrancl(U_15362,U_15364)))
        | ~ c_Wellfounded_Oacyclic(U_15362,U_15364) ) ),
    inference(definitional_conversion,[status(esa)],[f_3856_4]) ).

cnf(f_3856_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15362,U_15362)),hAPP(hAPP(c_Product__Type_OPair(U_15362,U_15362),U_15358),U_15358)),c_Transitive__Closure_Otrancl(U_15362,U_15364)))
    | ~ c_Wellfounded_Oacyclic(U_15362,U_15364) ),
    inference(clausify,[status(thm)],[f_3856_5]) ).

cnf(f_3856_7,plain,
    ( c_Wellfounded_Oacyclic(U_15363,U_15365)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15363,U_15363)),hAPP(hAPP(c_Product__Type_OPair(U_15363,U_15363),sK378(U_15365,U_15363)),sK378(U_15365,U_15363))),c_Transitive__Closure_Otrancl(U_15363,U_15365))) ),
    inference(clausify,[status(thm)],[f_3856_5]) ).

fof(f_3857_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem]) ).

fof(f_3857_2,plain,
    ! [U_15371,U_15370,U_15369,U_15368,U_15367,U_15366] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15366,U_15367,U_15368),U_15370),hAPP(hAPP(c_Set_Oinsert(U_15366),U_15371),U_15369)) = hAPP(hAPP(U_15368,U_15371),hAPP(hAPP(c_Finite__Set_Ofold(U_15366,U_15367,U_15368),U_15370),U_15369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15366),U_15369))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15366,U_15367,U_15368) ),
    inference(variable_rename,[status(thm)],[f_3857_1]) ).

fof(f_3857_3,plain,
    ! [U_15366,U_15367,U_15368,U_15369,U_15370,U_15371] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15366,U_15367,U_15368),U_15370),hAPP(hAPP(c_Set_Oinsert(U_15366),U_15371),U_15369)) = hAPP(hAPP(U_15368,U_15371),hAPP(hAPP(c_Finite__Set_Ofold(U_15366,U_15367,U_15368),U_15370),U_15369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15366),U_15369))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15366,U_15367,U_15368) ),
    inference(definitional_conversion,[status(esa)],[f_3857_2]) ).

cnf(f_3857_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15366,U_15367,U_15368),U_15370),hAPP(hAPP(c_Set_Oinsert(U_15366),U_15371),U_15369)) = hAPP(hAPP(U_15368,U_15371),hAPP(hAPP(c_Finite__Set_Ofold(U_15366,U_15367,U_15368),U_15370),U_15369))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15366),U_15369))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15366,U_15367,U_15368) ),
    inference(clausify,[status(thm)],[f_3857_3]) ).

fof(f_3858_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2]) ).

fof(f_3858_2,plain,
    ! [U_15377,U_15376,U_15375,U_15374,U_15373,U_15372] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15372,U_15373,U_15374),U_15376),hAPP(hAPP(c_Set_Oinsert(U_15372),U_15377),U_15375)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15372,U_15373,U_15374),hAPP(hAPP(U_15374,U_15377),U_15376)),U_15375)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15372),U_15375))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15372,U_15373,U_15374) ),
    inference(variable_rename,[status(thm)],[f_3858_1]) ).

fof(f_3858_3,plain,
    ! [U_15372,U_15373,U_15374,U_15375,U_15376,U_15377] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15372,U_15373,U_15374),U_15376),hAPP(hAPP(c_Set_Oinsert(U_15372),U_15377),U_15375)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15372,U_15373,U_15374),hAPP(hAPP(U_15374,U_15377),U_15376)),U_15375)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15372),U_15375))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15372,U_15373,U_15374) ),
    inference(definitional_conversion,[status(esa)],[f_3858_2]) ).

cnf(f_3858_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15372,U_15373,U_15374),U_15376),hAPP(hAPP(c_Set_Oinsert(U_15372),U_15377),U_15375)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15372,U_15373,U_15374),hAPP(hAPP(U_15374,U_15377),U_15376)),U_15375)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15372),U_15375))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15372,U_15373,U_15374) ),
    inference(clausify,[status(thm)],[f_3858_3]) ).

fof(f_3859_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup]) ).

fof(f_3859_2,plain,
    ! [U_15382,U_15381,U_15380,U_15379,U_15378] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15378),U_15381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15379,U_15378),U_15380),U_15382)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15379,U_15378,hAPP(hAPP(c_COMBB(U_15378,tc_fun(U_15378,U_15378),U_15379),c_Lattices_Osemilattice__sup__class_Osup(U_15378)),U_15382)),U_15381),U_15380)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),U_15380))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15378) ),
    inference(variable_rename,[status(thm)],[f_3859_1]) ).

fof(f_3859_3,plain,
    ! [U_15378,U_15379,U_15380,U_15381,U_15382] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15378),U_15381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15379,U_15378),U_15380),U_15382)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15379,U_15378,hAPP(hAPP(c_COMBB(U_15378,tc_fun(U_15378,U_15378),U_15379),c_Lattices_Osemilattice__sup__class_Osup(U_15378)),U_15382)),U_15381),U_15380)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),U_15380))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15378) ),
    inference(definitional_conversion,[status(esa)],[f_3859_2]) ).

cnf(f_3859_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15378),U_15381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15379,U_15378),U_15380),U_15382)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15379,U_15378,hAPP(hAPP(c_COMBB(U_15378,tc_fun(U_15378,U_15378),U_15379),c_Lattices_Osemilattice__sup__class_Osup(U_15378)),U_15382)),U_15381),U_15380)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),U_15380))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15378) ),
    inference(clausify,[status(thm)],[f_3859_3]) ).

fof(f_3860_1,plain,
    ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H]) ).

fof(f_3860_2,plain,
    ! [U_15387,U_15386,U_15385,U_15384,U_15383] :
      ( hAPP(U_15385,hAPP(hAPP(c_Set_Oinsert(U_15383),U_15387),U_15386)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15383,U_15383,U_15384),U_15387),U_15386)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15383),U_15386))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15383,U_15384,U_15385) ),
    inference(variable_rename,[status(thm)],[f_3860_1]) ).

fof(f_3860_3,plain,
    ! [U_15383,U_15384,U_15385,U_15386,U_15387] :
      ( hAPP(U_15385,hAPP(hAPP(c_Set_Oinsert(U_15383),U_15387),U_15386)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15383,U_15383,U_15384),U_15387),U_15386)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15383),U_15386))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15383,U_15384,U_15385) ),
    inference(definitional_conversion,[status(esa)],[f_3860_2]) ).

cnf(f_3860_4,plain,
    ( hAPP(U_15385,hAPP(hAPP(c_Set_Oinsert(U_15383),U_15387),U_15386)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15383,U_15383,U_15384),U_15387),U_15386)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15383),U_15386))
    | ~ c_Finite__Set_Ofolding__one__idem(U_15383,U_15384,U_15385) ),
    inference(clausify,[status(thm)],[f_3860_3]) ).

fof(f_3861_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup]) ).

fof(f_3861_2,plain,
    ! [U_15391,U_15390,U_15389,U_15388] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15388),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15388),U_15390),U_15391)),hAPP(hAPP(c_Finite__Set_Ofold(U_15388,U_15388,c_Lattices_Osemilattice__sup__class_Osup(U_15388)),U_15391),U_15389)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),U_15389))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15388),U_15389))
      | ~ class_Lattices_Osemilattice__sup(U_15388) ),
    inference(variable_rename,[status(thm)],[f_3861_1]) ).

fof(f_3861_3,plain,
    ! [U_15388,U_15389,U_15390,U_15391] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15388),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15388),U_15390),U_15391)),hAPP(hAPP(c_Finite__Set_Ofold(U_15388,U_15388,c_Lattices_Osemilattice__sup__class_Osup(U_15388)),U_15391),U_15389)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),U_15389))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15388),U_15389))
      | ~ class_Lattices_Osemilattice__sup(U_15388) ),
    inference(definitional_conversion,[status(esa)],[f_3861_2]) ).

cnf(f_3861_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15388),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15388),U_15390),U_15391)),hAPP(hAPP(c_Finite__Set_Ofold(U_15388,U_15388,c_Lattices_Osemilattice__sup__class_Osup(U_15388)),U_15391),U_15389)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),U_15389))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15388),U_15389))
    | ~ class_Lattices_Osemilattice__sup(U_15388) ),
    inference(clausify,[status(thm)],[f_3861_3]) ).

fof(f_3862_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf]) ).

fof(f_3862_2,plain,
    ! [U_15395,U_15394,U_15393,U_15392] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15392),hAPP(hAPP(c_Finite__Set_Ofold(U_15392,U_15392,c_Lattices_Osemilattice__inf__class_Oinf(U_15392)),U_15395),U_15393)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15392),U_15394),U_15395)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15392),U_15394),U_15393))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15392),U_15393))
      | ~ class_Lattices_Osemilattice__inf(U_15392) ),
    inference(variable_rename,[status(thm)],[f_3862_1]) ).

fof(f_3862_3,plain,
    ! [U_15392,U_15393,U_15394,U_15395] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15392),hAPP(hAPP(c_Finite__Set_Ofold(U_15392,U_15392,c_Lattices_Osemilattice__inf__class_Oinf(U_15392)),U_15395),U_15393)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15392),U_15394),U_15395)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15392),U_15394),U_15393))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15392),U_15393))
      | ~ class_Lattices_Osemilattice__inf(U_15392) ),
    inference(definitional_conversion,[status(esa)],[f_3862_2]) ).

cnf(f_3862_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15392),hAPP(hAPP(c_Finite__Set_Ofold(U_15392,U_15392,c_Lattices_Osemilattice__inf__class_Oinf(U_15392)),U_15395),U_15393)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15392),U_15394),U_15395)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15392),U_15394),U_15393))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15392),U_15393))
    | ~ class_Lattices_Osemilattice__inf(U_15392) ),
    inference(clausify,[status(thm)],[f_3862_3]) ).

fof(f_3863_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf]) ).

fof(f_3863_2,plain,
    ! [U_15399,U_15398,U_15397,U_15396] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15396),hAPP(hAPP(c_Finite__Set_Ofold(U_15396,U_15396,c_Orderings_Oord__class_Omin(U_15396)),U_15399),U_15397)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15396),U_15398),U_15399)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15396),U_15398),U_15397))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15396),U_15397))
      | ~ class_Orderings_Olinorder(U_15396) ),
    inference(variable_rename,[status(thm)],[f_3863_1]) ).

fof(f_3863_3,plain,
    ! [U_15396,U_15397,U_15398,U_15399] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15396),hAPP(hAPP(c_Finite__Set_Ofold(U_15396,U_15396,c_Orderings_Oord__class_Omin(U_15396)),U_15399),U_15397)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15396),U_15398),U_15399)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15396),U_15398),U_15397))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15396),U_15397))
      | ~ class_Orderings_Olinorder(U_15396) ),
    inference(definitional_conversion,[status(esa)],[f_3863_2]) ).

cnf(f_3863_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15396),hAPP(hAPP(c_Finite__Set_Ofold(U_15396,U_15396,c_Orderings_Oord__class_Omin(U_15396)),U_15399),U_15397)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15396),U_15398),U_15399)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15396),U_15398),U_15397))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15396),U_15397))
    | ~ class_Orderings_Olinorder(U_15396) ),
    inference(clausify,[status(thm)],[f_3863_3]) ).

fof(f_3864_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup]) ).

fof(f_3864_2,plain,
    ! [U_15403,U_15402,U_15401,U_15400] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15400),U_15402),U_15403)),hAPP(hAPP(c_Finite__Set_Ofold(U_15400,U_15400,c_Orderings_Oord__class_Omax(U_15400)),U_15403),U_15401)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15400),U_15402),U_15401))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15400),U_15401))
      | ~ class_Orderings_Olinorder(U_15400) ),
    inference(variable_rename,[status(thm)],[f_3864_1]) ).

fof(f_3864_3,plain,
    ! [U_15400,U_15401,U_15402,U_15403] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15400),U_15402),U_15403)),hAPP(hAPP(c_Finite__Set_Ofold(U_15400,U_15400,c_Orderings_Oord__class_Omax(U_15400)),U_15403),U_15401)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15400),U_15402),U_15401))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15400),U_15401))
      | ~ class_Orderings_Olinorder(U_15400) ),
    inference(definitional_conversion,[status(esa)],[f_3864_2]) ).

cnf(f_3864_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15400),U_15402),U_15403)),hAPP(hAPP(c_Finite__Set_Ofold(U_15400,U_15400,c_Orderings_Oord__class_Omax(U_15400)),U_15403),U_15401)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15400),U_15402),U_15401))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15400),U_15401))
    | ~ class_Orderings_Olinorder(U_15400) ),
    inference(clausify,[status(thm)],[f_3864_3]) ).

fof(f_3865_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem]) ).

fof(f_3865_2,plain,
    ! [U_15406,U_15405,U_15404] :
      ( hAPP(c_Finite__Set_Ofold1(U_15404,c_Groups_Otimes__class_Otimes(U_15404)),hAPP(hAPP(c_Set_Oinsert(U_15404),U_15406),U_15405)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15404,U_15404,c_Groups_Otimes__class_Otimes(U_15404)),U_15406),U_15405)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15404),U_15405))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15404) ),
    inference(variable_rename,[status(thm)],[f_3865_1]) ).

fof(f_3865_3,plain,
    ! [U_15406,U_15405,U_15404] :
      ( hAPP(c_Finite__Set_Ofold1(U_15404,c_Groups_Otimes__class_Otimes(U_15404)),hAPP(hAPP(c_Set_Oinsert(U_15404),U_15406),U_15405)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15404,U_15404,c_Groups_Otimes__class_Otimes(U_15404)),U_15406),U_15405)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15404),U_15405))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15404) ),
    inference(definitional_conversion,[status(esa)],[f_3865_2]) ).

cnf(f_3865_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_15404,c_Groups_Otimes__class_Otimes(U_15404)),hAPP(hAPP(c_Set_Oinsert(U_15404),U_15406),U_15405)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15404,U_15404,c_Groups_Otimes__class_Otimes(U_15404)),U_15406),U_15405)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15404),U_15405))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_15404) ),
    inference(clausify,[status(thm)],[f_3865_3]) ).

fof(f_3866_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H]) ).

fof(f_3866_2,plain,
    ! [U_15409,U_15408,U_15407] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15407,hAPP(hAPP(c_Set_Oinsert(U_15407),U_15409),U_15408)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15407,U_15407,c_Lattices_Osemilattice__sup__class_Osup(U_15407)),U_15409),U_15408)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15407),U_15408))
      | ~ class_Lattices_Olattice(U_15407) ),
    inference(variable_rename,[status(thm)],[f_3866_1]) ).

fof(f_3866_3,plain,
    ! [U_15407,U_15408,U_15409] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15407,hAPP(hAPP(c_Set_Oinsert(U_15407),U_15409),U_15408)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15407,U_15407,c_Lattices_Osemilattice__sup__class_Osup(U_15407)),U_15409),U_15408)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15407),U_15408))
      | ~ class_Lattices_Olattice(U_15407) ),
    inference(definitional_conversion,[status(esa)],[f_3866_2]) ).

cnf(f_3866_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_15407,hAPP(hAPP(c_Set_Oinsert(U_15407),U_15409),U_15408)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15407,U_15407,c_Lattices_Osemilattice__sup__class_Osup(U_15407)),U_15409),U_15408)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15407),U_15408))
    | ~ class_Lattices_Olattice(U_15407) ),
    inference(clausify,[status(thm)],[f_3866_3]) ).

fof(f_3867_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H]) ).

fof(f_3867_2,plain,
    ! [U_15412,U_15411,U_15410] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15410,hAPP(hAPP(c_Set_Oinsert(U_15410),U_15412),U_15411)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15410,U_15410,c_Lattices_Osemilattice__inf__class_Oinf(U_15410)),U_15412),U_15411)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15410),U_15411))
      | ~ class_Lattices_Olattice(U_15410) ),
    inference(variable_rename,[status(thm)],[f_3867_1]) ).

fof(f_3867_3,plain,
    ! [U_15410,U_15411,U_15412] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15410,hAPP(hAPP(c_Set_Oinsert(U_15410),U_15412),U_15411)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15410,U_15410,c_Lattices_Osemilattice__inf__class_Oinf(U_15410)),U_15412),U_15411)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15410),U_15411))
      | ~ class_Lattices_Olattice(U_15410) ),
    inference(definitional_conversion,[status(esa)],[f_3867_2]) ).

cnf(f_3867_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_15410,hAPP(hAPP(c_Set_Oinsert(U_15410),U_15412),U_15411)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15410,U_15410,c_Lattices_Osemilattice__inf__class_Oinf(U_15410)),U_15412),U_15411)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15410),U_15411))
    | ~ class_Lattices_Olattice(U_15410) ),
    inference(clausify,[status(thm)],[f_3867_3]) ).

fof(f_3868_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H]) ).

fof(f_3868_2,plain,
    ! [U_15415,U_15414,U_15413] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15413,hAPP(hAPP(c_Set_Oinsert(U_15413),U_15415),U_15414)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15413,U_15413,c_Orderings_Oord__class_Omin(U_15413)),U_15415),U_15414)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15413),U_15414))
      | ~ class_Orderings_Olinorder(U_15413) ),
    inference(variable_rename,[status(thm)],[f_3868_1]) ).

fof(f_3868_3,plain,
    ! [U_15413,U_15414,U_15415] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15413,hAPP(hAPP(c_Set_Oinsert(U_15413),U_15415),U_15414)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15413,U_15413,c_Orderings_Oord__class_Omin(U_15413)),U_15415),U_15414)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15413),U_15414))
      | ~ class_Orderings_Olinorder(U_15413) ),
    inference(definitional_conversion,[status(esa)],[f_3868_2]) ).

cnf(f_3868_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15413,hAPP(hAPP(c_Set_Oinsert(U_15413),U_15415),U_15414)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15413,U_15413,c_Orderings_Oord__class_Omin(U_15413)),U_15415),U_15414)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15413),U_15414))
    | ~ class_Orderings_Olinorder(U_15413) ),
    inference(clausify,[status(thm)],[f_3868_3]) ).

fof(f_3869_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H]) ).

fof(f_3869_2,plain,
    ! [U_15418,U_15417,U_15416] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15416,hAPP(hAPP(c_Set_Oinsert(U_15416),U_15418),U_15417)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15416,U_15416,c_Orderings_Oord__class_Omax(U_15416)),U_15418),U_15417)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15416),U_15417))
      | ~ class_Orderings_Olinorder(U_15416) ),
    inference(variable_rename,[status(thm)],[f_3869_1]) ).

fof(f_3869_3,plain,
    ! [U_15416,U_15417,U_15418] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15416,hAPP(hAPP(c_Set_Oinsert(U_15416),U_15418),U_15417)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15416,U_15416,c_Orderings_Oord__class_Omax(U_15416)),U_15418),U_15417)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15416),U_15417))
      | ~ class_Orderings_Olinorder(U_15416) ),
    inference(definitional_conversion,[status(esa)],[f_3869_2]) ).

cnf(f_3869_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15416,hAPP(hAPP(c_Set_Oinsert(U_15416),U_15418),U_15417)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15416,U_15416,c_Orderings_Oord__class_Omax(U_15416)),U_15418),U_15417)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15416),U_15417))
    | ~ class_Orderings_Olinorder(U_15416) ),
    inference(clausify,[status(thm)],[f_3869_3]) ).

fof(f_3870_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H]) ).

fof(f_3870_2,plain,
    ! [U_15421,U_15420,U_15419] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15419,c_Orderings_Oord__class_Omin(U_15419),hAPP(hAPP(c_Set_Oinsert(U_15419),U_15421),U_15420)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15419,U_15419,c_Orderings_Oord__class_Omin(U_15419)),U_15421),U_15420)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15419),U_15420))
      | ~ class_Orderings_Olinorder(U_15419) ),
    inference(variable_rename,[status(thm)],[f_3870_1]) ).

fof(f_3870_3,plain,
    ! [U_15419,U_15420,U_15421] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15419,c_Orderings_Oord__class_Omin(U_15419),hAPP(hAPP(c_Set_Oinsert(U_15419),U_15421),U_15420)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15419,U_15419,c_Orderings_Oord__class_Omin(U_15419)),U_15421),U_15420)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15419),U_15420))
      | ~ class_Orderings_Olinorder(U_15419) ),
    inference(definitional_conversion,[status(esa)],[f_3870_2]) ).

cnf(f_3870_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_15419,c_Orderings_Oord__class_Omin(U_15419),hAPP(hAPP(c_Set_Oinsert(U_15419),U_15421),U_15420)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15419,U_15419,c_Orderings_Oord__class_Omin(U_15419)),U_15421),U_15420)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15419),U_15420))
    | ~ class_Orderings_Olinorder(U_15419) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

fof(f_3871_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H]) ).

fof(f_3871_2,plain,
    ! [U_15424,U_15423,U_15422] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15422,c_Orderings_Oord__class_Omax(U_15422),hAPP(hAPP(c_Set_Oinsert(U_15422),U_15424),U_15423)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15422,U_15422,c_Orderings_Oord__class_Omax(U_15422)),U_15424),U_15423)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15422),U_15423))
      | ~ class_Orderings_Olinorder(U_15422) ),
    inference(variable_rename,[status(thm)],[f_3871_1]) ).

fof(f_3871_3,plain,
    ! [U_15422,U_15423,U_15424] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15422,c_Orderings_Oord__class_Omax(U_15422),hAPP(hAPP(c_Set_Oinsert(U_15422),U_15424),U_15423)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15422,U_15422,c_Orderings_Oord__class_Omax(U_15422)),U_15424),U_15423)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15422),U_15423))
      | ~ class_Orderings_Olinorder(U_15422) ),
    inference(definitional_conversion,[status(esa)],[f_3871_2]) ).

cnf(f_3871_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_15422,c_Orderings_Oord__class_Omax(U_15422),hAPP(hAPP(c_Set_Oinsert(U_15422),U_15424),U_15423)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15422,U_15422,c_Orderings_Oord__class_Omax(U_15422)),U_15424),U_15423)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15422),U_15423))
    | ~ class_Orderings_Olinorder(U_15422) ),
    inference(clausify,[status(thm)],[f_3871_3]) ).

fof(f_3872_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_minus__fold__remove]) ).

fof(f_3872_2,plain,
    ! [U_15427,U_15426,U_15425] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15425,tc_HOL_Obool)),U_15427),U_15426) = hAPP(hAPP(c_Finite__Set_Ofold(U_15425,tc_fun(U_15425,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_HOL_Obool),tc_fun(tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),U_15425),hAPP(c_COMBC(tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15425,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15425,tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),c_Set_Oinsert(U_15425)),c_Orderings_Obot__class_Obot(tc_fun(U_15425,tc_HOL_Obool))))),U_15427),U_15426)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15425),U_15426)) ),
    inference(variable_rename,[status(thm)],[f_3872_1]) ).

fof(f_3872_3,plain,
    ! [U_15425,U_15426,U_15427] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15425,tc_HOL_Obool)),U_15427),U_15426) = hAPP(hAPP(c_Finite__Set_Ofold(U_15425,tc_fun(U_15425,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_HOL_Obool),tc_fun(tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),U_15425),hAPP(c_COMBC(tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15425,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15425,tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),c_Set_Oinsert(U_15425)),c_Orderings_Obot__class_Obot(tc_fun(U_15425,tc_HOL_Obool))))),U_15427),U_15426)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15425),U_15426)) ),
    inference(definitional_conversion,[status(esa)],[f_3872_2]) ).

cnf(f_3872_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15425,tc_HOL_Obool)),U_15427),U_15426) = hAPP(hAPP(c_Finite__Set_Ofold(U_15425,tc_fun(U_15425,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_HOL_Obool),tc_fun(tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),U_15425),hAPP(c_COMBC(tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15425,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15425,tc_fun(U_15425,tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),c_Set_Oinsert(U_15425)),c_Orderings_Obot__class_Obot(tc_fun(U_15425,tc_HOL_Obool))))),U_15427),U_15426)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15425),U_15426)) ),
    inference(clausify,[status(thm)],[f_3872_3]) ).

fof(f_3873_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(f_3873_2,plain,
    ! [U_15432,U_15431,U_15430,U_15429,U_15428] :
      ( hAPP(U_15430,hAPP(hAPP(c_Set_Oinsert(U_15428),U_15432),U_15431)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15428,U_15428,U_15429),U_15432),U_15431)
      | hBOOL(hAPP(hAPP(c_member(U_15428),U_15432),U_15431))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15428),U_15431))
      | ~ c_Finite__Set_Ofolding__one(U_15428,U_15429,U_15430) ),
    inference(variable_rename,[status(thm)],[f_3873_1]) ).

fof(f_3873_3,plain,
    ! [U_15428,U_15429,U_15430,U_15431,U_15432] :
      ( hAPP(U_15430,hAPP(hAPP(c_Set_Oinsert(U_15428),U_15432),U_15431)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15428,U_15428,U_15429),U_15432),U_15431)
      | hBOOL(hAPP(hAPP(c_member(U_15428),U_15432),U_15431))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15428),U_15431))
      | ~ c_Finite__Set_Ofolding__one(U_15428,U_15429,U_15430) ),
    inference(definitional_conversion,[status(esa)],[f_3873_2]) ).

cnf(f_3873_4,plain,
    ( hAPP(U_15430,hAPP(hAPP(c_Set_Oinsert(U_15428),U_15432),U_15431)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15428,U_15428,U_15429),U_15432),U_15431)
    | hBOOL(hAPP(hAPP(c_member(U_15428),U_15432),U_15431))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15428),U_15431))
    | ~ c_Finite__Set_Ofolding__one(U_15428,U_15429,U_15430) ),
    inference(clausify,[status(thm)],[f_3873_3]) ).

fof(f_3874_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup]) ).

fof(f_3874_2,plain,
    ! [U_15436,U_15435,U_15434,U_15433] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15434,U_15433),U_15435),U_15436) = hAPP(hAPP(c_Finite__Set_Ofold(U_15434,U_15433,hAPP(hAPP(c_COMBB(U_15433,tc_fun(U_15433,U_15433),U_15434),c_Lattices_Osemilattice__sup__class_Osup(U_15433)),U_15436)),c_Orderings_Obot__class_Obot(U_15433)),U_15435)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15434),U_15435))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15433) ),
    inference(variable_rename,[status(thm)],[f_3874_1]) ).

fof(f_3874_3,plain,
    ! [U_15433,U_15434,U_15435,U_15436] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15434,U_15433),U_15435),U_15436) = hAPP(hAPP(c_Finite__Set_Ofold(U_15434,U_15433,hAPP(hAPP(c_COMBB(U_15433,tc_fun(U_15433,U_15433),U_15434),c_Lattices_Osemilattice__sup__class_Osup(U_15433)),U_15436)),c_Orderings_Obot__class_Obot(U_15433)),U_15435)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15434),U_15435))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15433) ),
    inference(definitional_conversion,[status(esa)],[f_3874_2]) ).

cnf(f_3874_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15434,U_15433),U_15435),U_15436) = hAPP(hAPP(c_Finite__Set_Ofold(U_15434,U_15433,hAPP(hAPP(c_COMBB(U_15433,tc_fun(U_15433,U_15433),U_15434),c_Lattices_Osemilattice__sup__class_Osup(U_15433)),U_15436)),c_Orderings_Obot__class_Obot(U_15433)),U_15435)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15434),U_15435))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15433) ),
    inference(clausify,[status(thm)],[f_3874_3]) ).

fof(f_3875_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold]) ).

fof(f_3875_2,plain,
    ! [U_15439,U_15438,U_15437] :
      ( hAPP(c_Finite__Set_Ofold1(U_15437,c_Groups_Otimes__class_Otimes(U_15437)),hAPP(hAPP(c_Set_Oinsert(U_15437),U_15439),U_15438)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15437,U_15437,c_Groups_Otimes__class_Otimes(U_15437)),U_15439),U_15438)
      | hBOOL(hAPP(hAPP(c_member(U_15437),U_15439),U_15438))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15437),U_15438))
      | ~ class_Groups_Oab__semigroup__mult(U_15437) ),
    inference(variable_rename,[status(thm)],[f_3875_1]) ).

fof(f_3875_3,plain,
    ! [U_15437,U_15438,U_15439] :
      ( hAPP(c_Finite__Set_Ofold1(U_15437,c_Groups_Otimes__class_Otimes(U_15437)),hAPP(hAPP(c_Set_Oinsert(U_15437),U_15439),U_15438)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15437,U_15437,c_Groups_Otimes__class_Otimes(U_15437)),U_15439),U_15438)
      | hBOOL(hAPP(hAPP(c_member(U_15437),U_15439),U_15438))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15437),U_15438))
      | ~ class_Groups_Oab__semigroup__mult(U_15437) ),
    inference(definitional_conversion,[status(esa)],[f_3875_2]) ).

cnf(f_3875_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_15437,c_Groups_Otimes__class_Otimes(U_15437)),hAPP(hAPP(c_Set_Oinsert(U_15437),U_15439),U_15438)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15437,U_15437,c_Groups_Otimes__class_Otimes(U_15437)),U_15439),U_15438)
    | hBOOL(hAPP(hAPP(c_member(U_15437),U_15439),U_15438))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15437),U_15438))
    | ~ class_Groups_Oab__semigroup__mult(U_15437) ),
    inference(clausify,[status(thm)],[f_3875_3]) ).

fof(f_3876_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(f_3876_2,plain,
    ! [U_15442,U_15441,U_15440] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15440,hAPP(hAPP(c_Set_Oinsert(U_15440),U_15442),U_15441)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15440,U_15440,c_Lattices_Osemilattice__sup__class_Osup(U_15440)),U_15442),U_15441)
      | hBOOL(hAPP(hAPP(c_member(U_15440),U_15442),U_15441))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15440),U_15441))
      | ~ class_Lattices_Olattice(U_15440) ),
    inference(variable_rename,[status(thm)],[f_3876_1]) ).

fof(f_3876_3,plain,
    ! [U_15440,U_15441,U_15442] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15440,hAPP(hAPP(c_Set_Oinsert(U_15440),U_15442),U_15441)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15440,U_15440,c_Lattices_Osemilattice__sup__class_Osup(U_15440)),U_15442),U_15441)
      | hBOOL(hAPP(hAPP(c_member(U_15440),U_15442),U_15441))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15440),U_15441))
      | ~ class_Lattices_Olattice(U_15440) ),
    inference(definitional_conversion,[status(esa)],[f_3876_2]) ).

cnf(f_3876_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_15440,hAPP(hAPP(c_Set_Oinsert(U_15440),U_15442),U_15441)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15440,U_15440,c_Lattices_Osemilattice__sup__class_Osup(U_15440)),U_15442),U_15441)
    | hBOOL(hAPP(hAPP(c_member(U_15440),U_15442),U_15441))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15440),U_15441))
    | ~ class_Lattices_Olattice(U_15440) ),
    inference(clausify,[status(thm)],[f_3876_3]) ).

fof(f_3877_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(f_3877_2,plain,
    ! [U_15445,U_15444,U_15443] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15443,hAPP(hAPP(c_Set_Oinsert(U_15443),U_15445),U_15444)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15443,U_15443,c_Lattices_Osemilattice__inf__class_Oinf(U_15443)),U_15445),U_15444)
      | hBOOL(hAPP(hAPP(c_member(U_15443),U_15445),U_15444))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15443),U_15444))
      | ~ class_Lattices_Olattice(U_15443) ),
    inference(variable_rename,[status(thm)],[f_3877_1]) ).

fof(f_3877_3,plain,
    ! [U_15443,U_15444,U_15445] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15443,hAPP(hAPP(c_Set_Oinsert(U_15443),U_15445),U_15444)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15443,U_15443,c_Lattices_Osemilattice__inf__class_Oinf(U_15443)),U_15445),U_15444)
      | hBOOL(hAPP(hAPP(c_member(U_15443),U_15445),U_15444))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15443),U_15444))
      | ~ class_Lattices_Olattice(U_15443) ),
    inference(definitional_conversion,[status(esa)],[f_3877_2]) ).

cnf(f_3877_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_15443,hAPP(hAPP(c_Set_Oinsert(U_15443),U_15445),U_15444)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15443,U_15443,c_Lattices_Osemilattice__inf__class_Oinf(U_15443)),U_15445),U_15444)
    | hBOOL(hAPP(hAPP(c_member(U_15443),U_15445),U_15444))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15443),U_15444))
    | ~ class_Lattices_Olattice(U_15443) ),
    inference(clausify,[status(thm)],[f_3877_3]) ).

fof(f_3878_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(f_3878_2,plain,
    ! [U_15448,U_15447,U_15446] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15446,hAPP(hAPP(c_Set_Oinsert(U_15446),U_15448),U_15447)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15446,U_15446,c_Orderings_Oord__class_Omin(U_15446)),U_15448),U_15447)
      | hBOOL(hAPP(hAPP(c_member(U_15446),U_15448),U_15447))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15446),U_15447))
      | ~ class_Orderings_Olinorder(U_15446) ),
    inference(variable_rename,[status(thm)],[f_3878_1]) ).

fof(f_3878_3,plain,
    ! [U_15446,U_15447,U_15448] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15446,hAPP(hAPP(c_Set_Oinsert(U_15446),U_15448),U_15447)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15446,U_15446,c_Orderings_Oord__class_Omin(U_15446)),U_15448),U_15447)
      | hBOOL(hAPP(hAPP(c_member(U_15446),U_15448),U_15447))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15446),U_15447))
      | ~ class_Orderings_Olinorder(U_15446) ),
    inference(definitional_conversion,[status(esa)],[f_3878_2]) ).

cnf(f_3878_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15446,hAPP(hAPP(c_Set_Oinsert(U_15446),U_15448),U_15447)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15446,U_15446,c_Orderings_Oord__class_Omin(U_15446)),U_15448),U_15447)
    | hBOOL(hAPP(hAPP(c_member(U_15446),U_15448),U_15447))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15446),U_15447))
    | ~ class_Orderings_Olinorder(U_15446) ),
    inference(clausify,[status(thm)],[f_3878_3]) ).

fof(f_3879_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(f_3879_2,plain,
    ! [U_15451,U_15450,U_15449] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15449,hAPP(hAPP(c_Set_Oinsert(U_15449),U_15451),U_15450)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15449,U_15449,c_Orderings_Oord__class_Omax(U_15449)),U_15451),U_15450)
      | hBOOL(hAPP(hAPP(c_member(U_15449),U_15451),U_15450))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15449),U_15450))
      | ~ class_Orderings_Olinorder(U_15449) ),
    inference(variable_rename,[status(thm)],[f_3879_1]) ).

fof(f_3879_3,plain,
    ! [U_15449,U_15450,U_15451] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15449,hAPP(hAPP(c_Set_Oinsert(U_15449),U_15451),U_15450)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15449,U_15449,c_Orderings_Oord__class_Omax(U_15449)),U_15451),U_15450)
      | hBOOL(hAPP(hAPP(c_member(U_15449),U_15451),U_15450))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15449),U_15450))
      | ~ class_Orderings_Olinorder(U_15449) ),
    inference(definitional_conversion,[status(esa)],[f_3879_2]) ).

cnf(f_3879_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15449,hAPP(hAPP(c_Set_Oinsert(U_15449),U_15451),U_15450)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15449,U_15449,c_Orderings_Oord__class_Omax(U_15449)),U_15451),U_15450)
    | hBOOL(hAPP(hAPP(c_member(U_15449),U_15451),U_15450))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15449),U_15450))
    | ~ class_Orderings_Olinorder(U_15449) ),
    inference(clausify,[status(thm)],[f_3879_3]) ).

fof(f_3880_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(f_3880_2,plain,
    ! [U_15454,U_15453,U_15452] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15452,c_Orderings_Oord__class_Omin(U_15452),hAPP(hAPP(c_Set_Oinsert(U_15452),U_15454),U_15453)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15452,U_15452,c_Orderings_Oord__class_Omin(U_15452)),U_15454),U_15453)
      | hBOOL(hAPP(hAPP(c_member(U_15452),U_15454),U_15453))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15452),U_15453))
      | ~ class_Orderings_Olinorder(U_15452) ),
    inference(variable_rename,[status(thm)],[f_3880_1]) ).

fof(f_3880_3,plain,
    ! [U_15452,U_15453,U_15454] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15452,c_Orderings_Oord__class_Omin(U_15452),hAPP(hAPP(c_Set_Oinsert(U_15452),U_15454),U_15453)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15452,U_15452,c_Orderings_Oord__class_Omin(U_15452)),U_15454),U_15453)
      | hBOOL(hAPP(hAPP(c_member(U_15452),U_15454),U_15453))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15452),U_15453))
      | ~ class_Orderings_Olinorder(U_15452) ),
    inference(definitional_conversion,[status(esa)],[f_3880_2]) ).

cnf(f_3880_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_15452,c_Orderings_Oord__class_Omin(U_15452),hAPP(hAPP(c_Set_Oinsert(U_15452),U_15454),U_15453)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15452,U_15452,c_Orderings_Oord__class_Omin(U_15452)),U_15454),U_15453)
    | hBOOL(hAPP(hAPP(c_member(U_15452),U_15454),U_15453))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15452),U_15453))
    | ~ class_Orderings_Olinorder(U_15452) ),
    inference(clausify,[status(thm)],[f_3880_3]) ).

fof(f_3881_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl]) ).

fof(f_3881_2,plain,
    ! [U_15458,U_15457,U_15456,U_15455] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15456),U_15457)),c_Transitive__Closure_Otrancl(U_15455,U_15458)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15456),U_15457)),U_15458)) ),
    inference(variable_rename,[status(thm)],[f_3881_1]) ).

fof(f_3881_3,plain,
    ! [U_15456,U_15455,U_15457,U_15458] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15456),U_15457)),c_Transitive__Closure_Otrancl(U_15455,U_15458)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15456),U_15457)),U_15458)) ),
    inference(definitional_conversion,[status(esa)],[f_3881_2]) ).

cnf(f_3881_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15456),U_15457)),c_Transitive__Closure_Otrancl(U_15455,U_15458)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15456),U_15457)),U_15458)) ),
    inference(clausify,[status(thm)],[f_3881_3]) ).

fof(f_3882_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(f_3882_2,plain,
    ! [U_15460,U_15459] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15459,U_15459),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15459,U_15460)),hAPP(hAPP(c_Product__Type_OSigma(U_15459,U_15459),hAPP(c_Relation_OField(U_15459),U_15460)),hAPP(c_COMBK(tc_fun(U_15459,tc_HOL_Obool),U_15459),hAPP(c_Relation_OField(U_15459),U_15460))))),
    inference(variable_rename,[status(thm)],[f_3882_1]) ).

fof(f_3882_3,plain,
    ! [U_15459,U_15460] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15459,U_15459),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15459,U_15460)),hAPP(hAPP(c_Product__Type_OSigma(U_15459,U_15459),hAPP(c_Relation_OField(U_15459),U_15460)),hAPP(c_COMBK(tc_fun(U_15459,tc_HOL_Obool),U_15459),hAPP(c_Relation_OField(U_15459),U_15460))))),
    inference(definitional_conversion,[status(esa)],[f_3882_2]) ).

cnf(f_3882_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15459,U_15459),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15459,U_15460)),hAPP(hAPP(c_Product__Type_OSigma(U_15459,U_15459),hAPP(c_Relation_OField(U_15459),U_15460)),hAPP(c_COMBK(tc_fun(U_15459,tc_HOL_Obool),U_15459),hAPP(c_Relation_OField(U_15459),U_15460))))),
    inference(clausify,[status(thm)],[f_3882_3]) ).

fof(f_3883_1,plain,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H]) ).

fof(f_3883_2,plain,
    ! [U_15463,U_15462,U_15461] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15462),c_Transitive__Closure_Otrancl(U_15461,U_15463)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15462),U_15463)) ),
    inference(variable_rename,[status(thm)],[f_3883_1]) ).

fof(f_3883_3,plain,
    ! [U_15461,U_15462,U_15463] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15462),c_Transitive__Closure_Otrancl(U_15461,U_15463)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15462),U_15463)) ),
    inference(definitional_conversion,[status(esa)],[f_3883_2]) ).

cnf(f_3883_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15462),c_Transitive__Closure_Otrancl(U_15461,U_15463)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15462),U_15463)) ),
    inference(clausify,[status(thm)],[f_3883_3]) ).

fof(f_3884_1,plain,
    ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_trancl__empty]) ).

fof(f_3884_2,plain,
    ! [U_15464] : c_Transitive__Closure_Otrancl(U_15464,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15464,U_15464),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15464,U_15464),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3884_1]) ).

fof(f_3884_3,plain,
    ! [U_15464] : c_Transitive__Closure_Otrancl(U_15464,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15464,U_15464),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15464,U_15464),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3884_2]) ).

cnf(f_3884_4,plain,
    c_Transitive__Closure_Otrancl(U_15464,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15464,U_15464),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15464,U_15464),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3884_3]) ).

fof(f_3885_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__domain]) ).

fof(f_3885_2,plain,
    ! [U_15466,U_15465] : hAPP(c_Relation_ODomain(U_15465,U_15465),c_Transitive__Closure_Otrancl(U_15465,U_15466)) = hAPP(c_Relation_ODomain(U_15465,U_15465),U_15466),
    inference(variable_rename,[status(thm)],[f_3885_1]) ).

fof(f_3885_3,plain,
    ! [U_15465,U_15466] : hAPP(c_Relation_ODomain(U_15465,U_15465),c_Transitive__Closure_Otrancl(U_15465,U_15466)) = hAPP(c_Relation_ODomain(U_15465,U_15465),U_15466),
    inference(definitional_conversion,[status(esa)],[f_3885_2]) ).

cnf(f_3885_4,plain,
    hAPP(c_Relation_ODomain(U_15465,U_15465),c_Transitive__Closure_Otrancl(U_15465,U_15466)) = hAPP(c_Relation_ODomain(U_15465,U_15465),U_15466),
    inference(clausify,[status(thm)],[f_3885_3]) ).

fof(f_3886_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__range]) ).

fof(f_3886_2,plain,
    ! [U_15468,U_15467] : hAPP(c_Relation_ORange(U_15467,U_15467),c_Transitive__Closure_Otrancl(U_15467,U_15468)) = hAPP(c_Relation_ORange(U_15467,U_15467),U_15468),
    inference(variable_rename,[status(thm)],[f_3886_1]) ).

fof(f_3886_3,plain,
    ! [U_15467,U_15468] : hAPP(c_Relation_ORange(U_15467,U_15467),c_Transitive__Closure_Otrancl(U_15467,U_15468)) = hAPP(c_Relation_ORange(U_15467,U_15467),U_15468),
    inference(definitional_conversion,[status(esa)],[f_3886_2]) ).

cnf(f_3886_4,plain,
    hAPP(c_Relation_ORange(U_15467,U_15467),c_Transitive__Closure_Otrancl(U_15467,U_15468)) = hAPP(c_Relation_ORange(U_15467,U_15467),U_15468),
    inference(clausify,[status(thm)],[f_3886_3]) ).

fof(f_3887_1,plain,
    ! [V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__trancl]) ).

fof(f_3887_2,plain,
    ! [U_15470,U_15469] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15469,U_15469)),c_Transitive__Closure_Otrancl(U_15469,U_15470)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15469,U_15469)),U_15470)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15469,U_15469)),U_15470))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15469,U_15469)),c_Transitive__Closure_Otrancl(U_15469,U_15470))) ) ),
    inference(variable_rename,[status(thm)],[f_3887_1]) ).

fof(f_3887_3,plain,
    ( ! [U_15474,U_15472] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15472,U_15472)),c_Transitive__Closure_Otrancl(U_15472,U_15474)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15472,U_15472)),U_15474)) )
    & ! [U_15473,U_15471] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15471,U_15471)),U_15473))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15471,U_15471)),c_Transitive__Closure_Otrancl(U_15471,U_15473))) ) ),
    inference(miniscope,[status(thm)],[f_3887_2]) ).

fof(f_3887_4,plain,
    ( ! [U_15472,U_15474] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15472,U_15472)),c_Transitive__Closure_Otrancl(U_15472,U_15474)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15472,U_15472)),U_15474)) )
    & ! [U_15473,U_15471] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15471,U_15471)),U_15473))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15471,U_15471)),c_Transitive__Closure_Otrancl(U_15471,U_15473))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3887_3]) ).

cnf(f_3887_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15471,U_15471)),U_15473))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15471,U_15471)),c_Transitive__Closure_Otrancl(U_15471,U_15473))) ),
    inference(clausify,[status(thm)],[f_3887_4]) ).

cnf(f_3887_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15472,U_15472)),c_Transitive__Closure_Otrancl(U_15472,U_15474)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15472,U_15472)),U_15474)) ),
    inference(clausify,[status(thm)],[f_3887_4]) ).

fof(f_3888_1,plain,
    ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl]) ).

fof(f_3888_2,plain,
    ! [U_15479,U_15478,U_15477,U_15476,U_15475] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15476),U_15479)),c_Transitive__Closure_Otrancl(U_15475,U_15478)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15477),U_15479)),U_15478))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15476),U_15477)),U_15478)) ),
    inference(variable_rename,[status(thm)],[f_3888_1]) ).

fof(f_3888_3,plain,
    ! [U_15475,U_15476,U_15477,U_15478,U_15479] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15476),U_15479)),c_Transitive__Closure_Otrancl(U_15475,U_15478)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15477),U_15479)),U_15478))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15476),U_15477)),U_15478)) ),
    inference(definitional_conversion,[status(esa)],[f_3888_2]) ).

cnf(f_3888_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15476),U_15479)),c_Transitive__Closure_Otrancl(U_15475,U_15478)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15477),U_15479)),U_15478))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15475),U_15476),U_15477)),U_15478)) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

fof(f_3889_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2]) ).

fof(f_3889_2,plain,
    ! [U_15484,U_15483,U_15482,U_15481,U_15480] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15484)),c_Transitive__Closure_Otrancl(U_15480,U_15483)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15482),U_15484)),c_Transitive__Closure_Otrancl(U_15480,U_15483)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15482)),U_15483)) ),
    inference(variable_rename,[status(thm)],[f_3889_1]) ).

fof(f_3889_3,plain,
    ! [U_15480,U_15481,U_15482,U_15483,U_15484] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15484)),c_Transitive__Closure_Otrancl(U_15480,U_15483)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15482),U_15484)),c_Transitive__Closure_Otrancl(U_15480,U_15483)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15482)),U_15483)) ),
    inference(definitional_conversion,[status(esa)],[f_3889_2]) ).

cnf(f_3889_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15484)),c_Transitive__Closure_Otrancl(U_15480,U_15483)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15482),U_15484)),c_Transitive__Closure_Otrancl(U_15480,U_15483)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15482)),U_15483)) ),
    inference(clausify,[status(thm)],[f_3889_3]) ).

fof(f_3890_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl]) ).

fof(f_3890_2,plain,
    ! [U_15489,U_15488,U_15487,U_15486,U_15485] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15486),U_15489)),c_Transitive__Closure_Otrancl(U_15485,U_15488)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15487),U_15489)),U_15488))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15486),U_15487)),c_Transitive__Closure_Otrancl(U_15485,U_15488))) ),
    inference(variable_rename,[status(thm)],[f_3890_1]) ).

fof(f_3890_3,plain,
    ! [U_15485,U_15486,U_15487,U_15488,U_15489] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15486),U_15489)),c_Transitive__Closure_Otrancl(U_15485,U_15488)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15487),U_15489)),U_15488))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15486),U_15487)),c_Transitive__Closure_Otrancl(U_15485,U_15488))) ),
    inference(definitional_conversion,[status(esa)],[f_3890_2]) ).

cnf(f_3890_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15486),U_15489)),c_Transitive__Closure_Otrancl(U_15485,U_15488)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15487),U_15489)),U_15488))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15486),U_15487)),c_Transitive__Closure_Otrancl(U_15485,U_15488))) ),
    inference(clausify,[status(thm)],[f_3890_3]) ).

fof(f_3891_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__trans]) ).

fof(f_3891_2,plain,
    ! [U_15494,U_15493,U_15492,U_15491,U_15490] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15491),U_15494)),c_Transitive__Closure_Otrancl(U_15490,U_15493)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15492),U_15494)),c_Transitive__Closure_Otrancl(U_15490,U_15493)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15491),U_15492)),c_Transitive__Closure_Otrancl(U_15490,U_15493))) ),
    inference(variable_rename,[status(thm)],[f_3891_1]) ).

fof(f_3891_3,plain,
    ! [U_15490,U_15491,U_15492,U_15493,U_15494] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15491),U_15494)),c_Transitive__Closure_Otrancl(U_15490,U_15493)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15492),U_15494)),c_Transitive__Closure_Otrancl(U_15490,U_15493)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15491),U_15492)),c_Transitive__Closure_Otrancl(U_15490,U_15493))) ),
    inference(definitional_conversion,[status(esa)],[f_3891_2]) ).

cnf(f_3891_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15491),U_15494)),c_Transitive__Closure_Otrancl(U_15490,U_15493)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15492),U_15494)),c_Transitive__Closure_Otrancl(U_15490,U_15493)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15490,U_15490)),hAPP(hAPP(c_Product__Type_OPair(U_15490,U_15490),U_15491),U_15492)),c_Transitive__Closure_Otrancl(U_15490,U_15493))) ),
    inference(clausify,[status(thm)],[f_3891_3]) ).

fof(f_3892_1,plain,
    ! [V_s_2,V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__mono]) ).

fof(f_3892_2,plain,
    ! [U_15498,U_15497,U_15496,U_15495] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15495,U_15495)),U_15496),c_Transitive__Closure_Otrancl(U_15495,U_15498)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15495,U_15495),tc_HOL_Obool)),U_15497),U_15498))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15495,U_15495)),U_15496),c_Transitive__Closure_Otrancl(U_15495,U_15497))) ),
    inference(variable_rename,[status(thm)],[f_3892_1]) ).

fof(f_3892_3,plain,
    ! [U_15495,U_15496,U_15497,U_15498] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15495,U_15495)),U_15496),c_Transitive__Closure_Otrancl(U_15495,U_15498)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15495,U_15495),tc_HOL_Obool)),U_15497),U_15498))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15495,U_15495)),U_15496),c_Transitive__Closure_Otrancl(U_15495,U_15497))) ),
    inference(definitional_conversion,[status(esa)],[f_3892_2]) ).

cnf(f_3892_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15495,U_15495)),U_15496),c_Transitive__Closure_Otrancl(U_15495,U_15498)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15495,U_15495),tc_HOL_Obool)),U_15497),U_15498))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15495,U_15495)),U_15496),c_Transitive__Closure_Otrancl(U_15495,U_15497))) ),
    inference(clausify,[status(thm)],[f_3892_3]) ).

fof(f_3893_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold]) ).

fof(f_3893_2,plain,
    ! [U_15500,U_15499] : c_Transitive__Closure_Otrancl(U_15499,U_15500) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15499,U_15499),tc_HOL_Obool)),U_15500),hAPP(hAPP(c_Relation_Orel__comp(U_15499,U_15499,U_15499),c_Transitive__Closure_Otrancl(U_15499,U_15500)),U_15500)),
    inference(variable_rename,[status(thm)],[f_3893_1]) ).

fof(f_3893_3,plain,
    ! [U_15499,U_15500] : c_Transitive__Closure_Otrancl(U_15499,U_15500) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15499,U_15499),tc_HOL_Obool)),U_15500),hAPP(hAPP(c_Relation_Orel__comp(U_15499,U_15499,U_15499),c_Transitive__Closure_Otrancl(U_15499,U_15500)),U_15500)),
    inference(definitional_conversion,[status(esa)],[f_3893_2]) ).

cnf(f_3893_4,plain,
    c_Transitive__Closure_Otrancl(U_15499,U_15500) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15499,U_15499),tc_HOL_Obool)),U_15500),hAPP(hAPP(c_Relation_Orel__comp(U_15499,U_15499,U_15499),c_Transitive__Closure_Otrancl(U_15499,U_15500)),U_15500)),
    inference(clausify,[status(thm)],[f_3893_3]) ).

fof(f_3894_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma]) ).

fof(f_3894_2,plain,
    ! [U_15503,U_15502,U_15501] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15501,U_15501),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15501,U_15502)),hAPP(hAPP(c_Product__Type_OSigma(U_15501,U_15501),U_15503),hAPP(c_COMBK(tc_fun(U_15501,tc_HOL_Obool),U_15501),U_15503))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15501,U_15501),tc_HOL_Obool)),U_15502),hAPP(hAPP(c_Product__Type_OSigma(U_15501,U_15501),U_15503),hAPP(c_COMBK(tc_fun(U_15501,tc_HOL_Obool),U_15501),U_15503)))) ),
    inference(variable_rename,[status(thm)],[f_3894_1]) ).

fof(f_3894_3,plain,
    ! [U_15501,U_15502,U_15503] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15501,U_15501),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15501,U_15502)),hAPP(hAPP(c_Product__Type_OSigma(U_15501,U_15501),U_15503),hAPP(c_COMBK(tc_fun(U_15501,tc_HOL_Obool),U_15501),U_15503))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15501,U_15501),tc_HOL_Obool)),U_15502),hAPP(hAPP(c_Product__Type_OSigma(U_15501,U_15501),U_15503),hAPP(c_COMBK(tc_fun(U_15501,tc_HOL_Obool),U_15501),U_15503)))) ),
    inference(definitional_conversion,[status(esa)],[f_3894_2]) ).

cnf(f_3894_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15501,U_15501),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15501,U_15502)),hAPP(hAPP(c_Product__Type_OSigma(U_15501,U_15501),U_15503),hAPP(c_COMBK(tc_fun(U_15501,tc_HOL_Obool),U_15501),U_15503))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15501,U_15501),tc_HOL_Obool)),U_15502),hAPP(hAPP(c_Product__Type_OSigma(U_15501,U_15501),U_15503),hAPP(c_COMBK(tc_fun(U_15501,tc_HOL_Obool),U_15501),U_15503)))) ),
    inference(clausify,[status(thm)],[f_3894_3]) ).

fof(f_3895_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset]) ).

fof(f_3895_2,plain,
    ! [U_15506,U_15505,U_15504] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15504,U_15505)),U_15506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15504,U_15504,U_15504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15504,U_15505)),U_15506)),U_15505)),U_15506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),U_15505),U_15506)) ),
    inference(variable_rename,[status(thm)],[f_3895_1]) ).

fof(f_3895_3,plain,
    ! [U_15504,U_15505,U_15506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15504,U_15505)),U_15506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15504,U_15504,U_15504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15504,U_15505)),U_15506)),U_15505)),U_15506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),U_15505),U_15506)) ),
    inference(definitional_conversion,[status(esa)],[f_3895_2]) ).

cnf(f_3895_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15504,U_15505)),U_15506))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15504,U_15504,U_15504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15504,U_15505)),U_15506)),U_15505)),U_15506))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15504,U_15504),tc_HOL_Obool)),U_15505),U_15506)) ),
    inference(clausify,[status(thm)],[f_3895_3]) ).

fof(f_3896_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec]) ).

fof(f_3896_2,plain,
    ! [U_15512,U_15511,U_15510,U_15509,U_15508,U_15507] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15507,U_15508,U_15509),U_15512),U_15510) = hAPP(hAPP(U_15509,U_15511),hAPP(hAPP(c_Finite__Set_Ofold(U_15507,U_15508,U_15509),U_15512),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15507,tc_HOL_Obool)),U_15510),hAPP(hAPP(c_Set_Oinsert(U_15507),U_15511),c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15507),U_15511),U_15510))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15507),U_15510))
      | ~ c_Finite__Set_Ofun__left__comm(U_15507,U_15508,U_15509) ),
    inference(variable_rename,[status(thm)],[f_3896_1]) ).

fof(f_3896_3,plain,
    ! [U_15507,U_15508,U_15509,U_15510,U_15511,U_15512] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15507,U_15508,U_15509),U_15512),U_15510) = hAPP(hAPP(U_15509,U_15511),hAPP(hAPP(c_Finite__Set_Ofold(U_15507,U_15508,U_15509),U_15512),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15507,tc_HOL_Obool)),U_15510),hAPP(hAPP(c_Set_Oinsert(U_15507),U_15511),c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15507),U_15511),U_15510))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15507),U_15510))
      | ~ c_Finite__Set_Ofun__left__comm(U_15507,U_15508,U_15509) ),
    inference(definitional_conversion,[status(esa)],[f_3896_2]) ).

cnf(f_3896_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15507,U_15508,U_15509),U_15512),U_15510) = hAPP(hAPP(U_15509,U_15511),hAPP(hAPP(c_Finite__Set_Ofold(U_15507,U_15508,U_15509),U_15512),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15507,tc_HOL_Obool)),U_15510),hAPP(hAPP(c_Set_Oinsert(U_15507),U_15511),c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15507),U_15511),U_15510))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15507),U_15510))
    | ~ c_Finite__Set_Ofun__left__comm(U_15507,U_15508,U_15509) ),
    inference(clausify,[status(thm)],[f_3896_3]) ).

fof(f_3897_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove]) ).

fof(f_3897_2,plain,
    ! [U_15518,U_15517,U_15516,U_15515,U_15514,U_15513] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15513,U_15514,U_15515),U_15517),hAPP(hAPP(c_Set_Oinsert(U_15513),U_15518),U_15516)) = hAPP(hAPP(U_15515,U_15518),hAPP(hAPP(c_Finite__Set_Ofold(U_15513,U_15514,U_15515),U_15517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15513,tc_HOL_Obool)),U_15516),hAPP(hAPP(c_Set_Oinsert(U_15513),U_15518),c_Orderings_Obot__class_Obot(tc_fun(U_15513,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15513),U_15516))
      | ~ c_Finite__Set_Ofun__left__comm(U_15513,U_15514,U_15515) ),
    inference(variable_rename,[status(thm)],[f_3897_1]) ).

fof(f_3897_3,plain,
    ! [U_15513,U_15514,U_15515,U_15516,U_15517,U_15518] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15513,U_15514,U_15515),U_15517),hAPP(hAPP(c_Set_Oinsert(U_15513),U_15518),U_15516)) = hAPP(hAPP(U_15515,U_15518),hAPP(hAPP(c_Finite__Set_Ofold(U_15513,U_15514,U_15515),U_15517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15513,tc_HOL_Obool)),U_15516),hAPP(hAPP(c_Set_Oinsert(U_15513),U_15518),c_Orderings_Obot__class_Obot(tc_fun(U_15513,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15513),U_15516))
      | ~ c_Finite__Set_Ofun__left__comm(U_15513,U_15514,U_15515) ),
    inference(definitional_conversion,[status(esa)],[f_3897_2]) ).

cnf(f_3897_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15513,U_15514,U_15515),U_15517),hAPP(hAPP(c_Set_Oinsert(U_15513),U_15518),U_15516)) = hAPP(hAPP(U_15515,U_15518),hAPP(hAPP(c_Finite__Set_Ofold(U_15513,U_15514,U_15515),U_15517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15513,tc_HOL_Obool)),U_15516),hAPP(hAPP(c_Set_Oinsert(U_15513),U_15518),c_Orderings_Obot__class_Obot(tc_fun(U_15513,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15513),U_15516))
    | ~ c_Finite__Set_Ofun__left__comm(U_15513,U_15514,U_15515) ),
    inference(clausify,[status(thm)],[f_3897_3]) ).

fof(f_3898_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( V_y_2 = V_x_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ]) ).

fof(f_3898_2,plain,
    ! [U_15525,U_15524,U_15523,U_15522,U_15521,U_15520,U_15519] :
      ( U_15525 = U_15524
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15519,U_15520,U_15521,U_15522,U_15523),U_15525))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15519,U_15520,U_15521,U_15522,U_15523),U_15524))
      | ~ c_Finite__Set_Ofun__left__comm(U_15519,U_15520,U_15521) ),
    inference(variable_rename,[status(thm)],[f_3898_1]) ).

fof(f_3898_3,plain,
    ! [U_15521,U_15520,U_15519,U_15522,U_15523,U_15524,U_15525] :
      ( U_15525 = U_15524
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15519,U_15520,U_15521,U_15522,U_15523),U_15525))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15519,U_15520,U_15521,U_15522,U_15523),U_15524))
      | ~ c_Finite__Set_Ofun__left__comm(U_15519,U_15520,U_15521) ),
    inference(definitional_conversion,[status(esa)],[f_3898_2]) ).

cnf(f_3898_4,plain,
    ( U_15525 = U_15524
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15519,U_15520,U_15521,U_15522,U_15523),U_15525))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15519,U_15520,U_15521,U_15522,U_15523),U_15524))
    | ~ c_Finite__Set_Ofun__left__comm(U_15519,U_15520,U_15521) ),
    inference(clausify,[status(thm)],[f_3898_3]) ).

fof(f_3899_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply]) ).

fof(f_3899_2,plain,
    ! [U_15530,U_15529,U_15528,U_15527,U_15526] :
      ( c_Finite__Set_Ofun__left__comm(U_15529,U_15527,hAPP(hAPP(c_COMBB(U_15526,tc_fun(U_15527,U_15527),U_15529),U_15528),U_15530))
      | ~ c_Finite__Set_Ofun__left__comm(U_15526,U_15527,U_15528) ),
    inference(variable_rename,[status(thm)],[f_3899_1]) ).

fof(f_3899_3,plain,
    ! [U_15529,U_15530,U_15528,U_15527,U_15526] :
      ( c_Finite__Set_Ofun__left__comm(U_15529,U_15527,hAPP(hAPP(c_COMBB(U_15526,tc_fun(U_15527,U_15527),U_15529),U_15528),U_15530))
      | ~ c_Finite__Set_Ofun__left__comm(U_15526,U_15527,U_15528) ),
    inference(definitional_conversion,[status(esa)],[f_3899_2]) ).

cnf(f_3899_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_15529,U_15527,hAPP(hAPP(c_COMBB(U_15526,tc_fun(U_15527,U_15527),U_15529),U_15528),U_15530))
    | ~ c_Finite__Set_Ofun__left__comm(U_15526,U_15527,U_15528) ),
    inference(clausify,[status(thm)],[f_3899_3]) ).

fof(f_3900_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm]) ).

fof(f_3900_2,plain,
    ! [U_15536,U_15535,U_15534,U_15533,U_15532,U_15531] :
      ( hAPP(hAPP(U_15533,U_15534),hAPP(hAPP(U_15533,U_15535),U_15536)) = hAPP(hAPP(U_15533,U_15535),hAPP(hAPP(U_15533,U_15534),U_15536))
      | ~ c_Finite__Set_Ofun__left__comm(U_15531,U_15532,U_15533) ),
    inference(variable_rename,[status(thm)],[f_3900_1]) ).

fof(f_3900_3,plain,
    ! [U_15536,U_15535,U_15534,U_15533] :
      ( ! [U_15532,U_15531] : ~ c_Finite__Set_Ofun__left__comm(U_15531,U_15532,U_15533)
      | hAPP(hAPP(U_15533,U_15534),hAPP(hAPP(U_15533,U_15535),U_15536)) = hAPP(hAPP(U_15533,U_15535),hAPP(hAPP(U_15533,U_15534),U_15536)) ),
    inference(miniscope,[status(thm)],[f_3900_2]) ).

fof(f_3900_4,plain,
    ! [U_15532,U_15533,U_15531,U_15534,U_15535,U_15536] :
      ( ~ c_Finite__Set_Ofun__left__comm(U_15531,U_15532,U_15533)
      | hAPP(hAPP(U_15533,U_15534),hAPP(hAPP(U_15533,U_15535),U_15536)) = hAPP(hAPP(U_15533,U_15535),hAPP(hAPP(U_15533,U_15534),U_15536)) ),
    inference(definitional_conversion,[status(esa)],[f_3900_3]) ).

cnf(f_3900_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_15531,U_15532,U_15533)
    | hAPP(hAPP(U_15533,U_15534),hAPP(hAPP(U_15533,U_15535),U_15536)) = hAPP(hAPP(U_15533,U_15535),hAPP(hAPP(U_15533,U_15534),U_15536)) ),
    inference(clausify,[status(thm)],[f_3900_4]) ).

fof(f_3901_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm]) ).

fof(f_3901_2,plain,
    ! [U_15537] :
      ( c_Finite__Set_Ofun__left__comm(U_15537,U_15537,c_Groups_Otimes__class_Otimes(U_15537))
      | ~ class_Groups_Oab__semigroup__mult(U_15537) ),
    inference(variable_rename,[status(thm)],[f_3901_1]) ).

fof(f_3901_3,plain,
    ! [U_15537] :
      ( c_Finite__Set_Ofun__left__comm(U_15537,U_15537,c_Groups_Otimes__class_Otimes(U_15537))
      | ~ class_Groups_Oab__semigroup__mult(U_15537) ),
    inference(definitional_conversion,[status(esa)],[f_3901_2]) ).

cnf(f_3901_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_15537,U_15537,c_Groups_Otimes__class_Otimes(U_15537))
    | ~ class_Groups_Oab__semigroup__mult(U_15537) ),
    inference(clausify,[status(thm)],[f_3901_3]) ).

fof(f_3902_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm]) ).

fof(f_3902_2,plain,
    ! [U_15542,U_15541,U_15540,U_15539,U_15538] :
      ( hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15541)),hAPP(U_15540,U_15542)) = hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15542)),hAPP(U_15540,U_15541))
      | ~ c_Finite__Set_Ofun__left__comm(U_15538,U_15539,U_15540) ),
    inference(variable_rename,[status(thm)],[f_3902_1]) ).

fof(f_3902_3,plain,
    ! [U_15542,U_15541,U_15540,U_15539] :
      ( ! [U_15538] : ~ c_Finite__Set_Ofun__left__comm(U_15538,U_15539,U_15540)
      | hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15541)),hAPP(U_15540,U_15542)) = hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15542)),hAPP(U_15540,U_15541)) ),
    inference(miniscope,[status(thm)],[f_3902_2]) ).

fof(f_3902_4,plain,
    ! [U_15538,U_15539,U_15540,U_15541,U_15542] :
      ( ~ c_Finite__Set_Ofun__left__comm(U_15538,U_15539,U_15540)
      | hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15541)),hAPP(U_15540,U_15542)) = hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15542)),hAPP(U_15540,U_15541)) ),
    inference(definitional_conversion,[status(esa)],[f_3902_3]) ).

cnf(f_3902_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_15538,U_15539,U_15540)
    | hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15541)),hAPP(U_15540,U_15542)) = hAPP(c_Fun_Ocomp(U_15539,U_15539,U_15539,hAPP(U_15540,U_15542)),hAPP(U_15540,U_15541)) ),
    inference(clausify,[status(thm)],[f_3902_4]) ).

fof(f_3903_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm]) ).

fof(f_3903_2,plain,
    ! [U_15548,U_15547,U_15546,U_15545,U_15544,U_15543] :
      ( hAPP(hAPP(U_15545,U_15547),hAPP(hAPP(c_Finite__Set_Ofold(U_15543,U_15544,U_15545),U_15548),U_15546)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15543,U_15544,U_15545),hAPP(hAPP(U_15545,U_15547),U_15548)),U_15546)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15543),U_15546))
      | ~ c_Finite__Set_Ofun__left__comm(U_15543,U_15544,U_15545) ),
    inference(variable_rename,[status(thm)],[f_3903_1]) ).

fof(f_3903_3,plain,
    ! [U_15543,U_15544,U_15545,U_15546,U_15547,U_15548] :
      ( hAPP(hAPP(U_15545,U_15547),hAPP(hAPP(c_Finite__Set_Ofold(U_15543,U_15544,U_15545),U_15548),U_15546)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15543,U_15544,U_15545),hAPP(hAPP(U_15545,U_15547),U_15548)),U_15546)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15543),U_15546))
      | ~ c_Finite__Set_Ofun__left__comm(U_15543,U_15544,U_15545) ),
    inference(definitional_conversion,[status(esa)],[f_3903_2]) ).

cnf(f_3903_4,plain,
    ( hAPP(hAPP(U_15545,U_15547),hAPP(hAPP(c_Finite__Set_Ofold(U_15543,U_15544,U_15545),U_15548),U_15546)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15543,U_15544,U_15545),hAPP(hAPP(U_15545,U_15547),U_15548)),U_15546)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15543),U_15546))
    | ~ c_Finite__Set_Ofun__left__comm(U_15543,U_15544,U_15545) ),
    inference(clausify,[status(thm)],[f_3903_3]) ).

fof(f_3904_1,plain,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality]) ).

fof(f_3904_2,plain,
    ! [U_15554,U_15553,U_15552,U_15551,U_15550,U_15549] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15549,U_15550,U_15551),U_15552),U_15553) = U_15554
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15549,U_15550,U_15551,U_15552,U_15553),U_15554))
      | ~ c_Finite__Set_Ofun__left__comm(U_15549,U_15550,U_15551) ),
    inference(variable_rename,[status(thm)],[f_3904_1]) ).

fof(f_3904_3,plain,
    ! [U_15549,U_15550,U_15551,U_15552,U_15553,U_15554] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15549,U_15550,U_15551),U_15552),U_15553) = U_15554
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15549,U_15550,U_15551,U_15552,U_15553),U_15554))
      | ~ c_Finite__Set_Ofun__left__comm(U_15549,U_15550,U_15551) ),
    inference(definitional_conversion,[status(esa)],[f_3904_2]) ).

cnf(f_3904_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15549,U_15550,U_15551),U_15552),U_15553) = U_15554
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15549,U_15550,U_15551,U_15552,U_15553),U_15554))
    | ~ c_Finite__Set_Ofun__left__comm(U_15549,U_15550,U_15551) ),
    inference(clausify,[status(thm)],[f_3904_3]) ).

fof(f_3905_1,plain,
    ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold]) ).

fof(f_3905_2,plain,
    ! [U_15559,U_15558,U_15557,U_15556,U_15555] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15555,U_15556,U_15557,U_15559,U_15558),hAPP(hAPP(c_Finite__Set_Ofold(U_15555,U_15556,U_15557),U_15559),U_15558)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15555),U_15558))
      | ~ c_Finite__Set_Ofun__left__comm(U_15555,U_15556,U_15557) ),
    inference(variable_rename,[status(thm)],[f_3905_1]) ).

fof(f_3905_3,plain,
    ! [U_15555,U_15556,U_15557,U_15558,U_15559] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15555,U_15556,U_15557,U_15559,U_15558),hAPP(hAPP(c_Finite__Set_Ofold(U_15555,U_15556,U_15557),U_15559),U_15558)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15555),U_15558))
      | ~ c_Finite__Set_Ofun__left__comm(U_15555,U_15556,U_15557) ),
    inference(definitional_conversion,[status(esa)],[f_3905_2]) ).

cnf(f_3905_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15555,U_15556,U_15557,U_15559,U_15558),hAPP(hAPP(c_Finite__Set_Ofold(U_15555,U_15556,U_15557),U_15559),U_15558)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15555),U_15558))
    | ~ c_Finite__Set_Ofun__left__comm(U_15555,U_15556,U_15557) ),
    inference(clausify,[status(thm)],[f_3905_3]) ).

fof(f_3906_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(f_3906_2,plain,
    ! [U_15565,U_15564,U_15563,U_15562,U_15561,U_15560] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15560,U_15561,U_15562),U_15565),hAPP(hAPP(c_Set_Oinsert(U_15560),U_15564),U_15563)) = hAPP(hAPP(U_15562,U_15564),hAPP(hAPP(c_Finite__Set_Ofold(U_15560,U_15561,U_15562),U_15565),U_15563))
      | hBOOL(hAPP(hAPP(c_member(U_15560),U_15564),U_15563))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15560),U_15563))
      | ~ c_Finite__Set_Ofun__left__comm(U_15560,U_15561,U_15562) ),
    inference(variable_rename,[status(thm)],[f_3906_1]) ).

fof(f_3906_3,plain,
    ! [U_15560,U_15561,U_15562,U_15563,U_15564,U_15565] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15560,U_15561,U_15562),U_15565),hAPP(hAPP(c_Set_Oinsert(U_15560),U_15564),U_15563)) = hAPP(hAPP(U_15562,U_15564),hAPP(hAPP(c_Finite__Set_Ofold(U_15560,U_15561,U_15562),U_15565),U_15563))
      | hBOOL(hAPP(hAPP(c_member(U_15560),U_15564),U_15563))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15560),U_15563))
      | ~ c_Finite__Set_Ofun__left__comm(U_15560,U_15561,U_15562) ),
    inference(definitional_conversion,[status(esa)],[f_3906_2]) ).

cnf(f_3906_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15560,U_15561,U_15562),U_15565),hAPP(hAPP(c_Set_Oinsert(U_15560),U_15564),U_15563)) = hAPP(hAPP(U_15562,U_15564),hAPP(hAPP(c_Finite__Set_Ofold(U_15560,U_15561,U_15562),U_15565),U_15563))
    | hBOOL(hAPP(hAPP(c_member(U_15560),U_15564),U_15563))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15560),U_15563))
    | ~ c_Finite__Set_Ofun__left__comm(U_15560,U_15561,U_15562) ),
    inference(clausify,[status(thm)],[f_3906_3]) ).

fof(f_3907_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(f_3907_2,plain,
    ! [U_15571,U_15570,U_15569,U_15568,U_15567,U_15566] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15566,U_15567,U_15568),U_15571),hAPP(hAPP(c_Set_Oinsert(U_15566),U_15570),U_15569)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15566,U_15567,U_15568),hAPP(hAPP(U_15568,U_15570),U_15571)),U_15569)
      | hBOOL(hAPP(hAPP(c_member(U_15566),U_15570),U_15569))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15566),U_15569))
      | ~ c_Finite__Set_Ofun__left__comm(U_15566,U_15567,U_15568) ),
    inference(variable_rename,[status(thm)],[f_3907_1]) ).

fof(f_3907_3,plain,
    ! [U_15566,U_15567,U_15568,U_15569,U_15570,U_15571] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15566,U_15567,U_15568),U_15571),hAPP(hAPP(c_Set_Oinsert(U_15566),U_15570),U_15569)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15566,U_15567,U_15568),hAPP(hAPP(U_15568,U_15570),U_15571)),U_15569)
      | hBOOL(hAPP(hAPP(c_member(U_15566),U_15570),U_15569))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15566),U_15569))
      | ~ c_Finite__Set_Ofun__left__comm(U_15566,U_15567,U_15568) ),
    inference(definitional_conversion,[status(esa)],[f_3907_2]) ).

cnf(f_3907_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15566,U_15567,U_15568),U_15571),hAPP(hAPP(c_Set_Oinsert(U_15566),U_15570),U_15569)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15566,U_15567,U_15568),hAPP(hAPP(U_15568,U_15570),U_15571)),U_15569)
    | hBOOL(hAPP(hAPP(c_member(U_15566),U_15570),U_15569))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15566),U_15569))
    | ~ c_Finite__Set_Ofun__left__comm(U_15566,U_15567,U_15568) ),
    inference(clausify,[status(thm)],[f_3907_3]) ).

fof(f_3908_1,plain,
    ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( ? [B_y_H] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
          & V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux]) ).

fof(f_3908_2,plain,
    ! [U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573] :
      ( ? [U_15572] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15573,tc_HOL_Obool)),U_15577),hAPP(hAPP(c_Set_Oinsert(U_15573),U_15579),c_Orderings_Obot__class_Obot(tc_fun(U_15573,tc_HOL_Obool))))),U_15572))
          & U_15578 = hAPP(hAPP(U_15575,U_15579),U_15572) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15573),U_15579),U_15577))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,U_15577),U_15578))
      | ~ c_Finite__Set_Ofun__left__comm(U_15573,U_15574,U_15575) ),
    inference(variable_rename,[status(thm)],[f_3908_1]) ).

fof(f_3908_3,plain,
    ! [U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15573,tc_HOL_Obool)),U_15577),hAPP(hAPP(c_Set_Oinsert(U_15573),U_15579),c_Orderings_Obot__class_Obot(tc_fun(U_15573,tc_HOL_Obool))))),sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573)))
        & U_15578 = hAPP(hAPP(U_15575,U_15579),sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15573),U_15579),U_15577))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,U_15577),U_15578))
      | ~ c_Finite__Set_Ofun__left__comm(U_15573,U_15574,U_15575) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_15572,sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573))],[f_3908_2]) ).

fof(f_3908_4,plain,
    ( ! [U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15573,tc_HOL_Obool)),U_15577),hAPP(hAPP(c_Set_Oinsert(U_15573),U_15579),c_Orderings_Obot__class_Obot(tc_fun(U_15573,tc_HOL_Obool))))),sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573)))
        | ~ sP1040(U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579) )
    & ! [U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579] :
        ( U_15578 = hAPP(hAPP(U_15575,U_15579),sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573))
        | ~ sP1040(U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579) )
    & ! [U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579] :
        ( sP1040(U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15573),U_15579),U_15577))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,U_15577),U_15578))
        | ~ c_Finite__Set_Ofun__left__comm(U_15573,U_15574,U_15575) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1040])],[f_3908_3]) ).

cnf(f_3908_5,plain,
    ( sP1040(U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15573),U_15579),U_15577))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,U_15577),U_15578))
    | ~ c_Finite__Set_Ofun__left__comm(U_15573,U_15574,U_15575) ),
    inference(clausify,[status(thm)],[f_3908_4]) ).

cnf(f_3908_6,plain,
    ( U_15578 = hAPP(hAPP(U_15575,U_15579),sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573))
    | ~ sP1040(U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579) ),
    inference(clausify,[status(thm)],[f_3908_4]) ).

cnf(f_3908_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15573,U_15574,U_15575,U_15576,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15573,tc_HOL_Obool)),U_15577),hAPP(hAPP(c_Set_Oinsert(U_15573),U_15579),c_Orderings_Obot__class_Obot(tc_fun(U_15573,tc_HOL_Obool))))),sK379(U_15579,U_15578,U_15577,U_15576,U_15575,U_15574,U_15573)))
    | ~ sP1040(U_15573,U_15574,U_15575,U_15576,U_15577,U_15578,U_15579) ),
    inference(clausify,[status(thm)],[f_3908_4]) ).

fof(f_3909_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
    inference(fof_nnf,[status(thm)],[fact_trancl__insert]) ).

fof(f_3909_2,plain,
    ! [U_15583,U_15582,U_15581,U_15580] : c_Transitive__Closure_Otrancl(U_15580,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15580,U_15580)),hAPP(hAPP(c_Product__Type_OPair(U_15580,U_15580),U_15581),U_15582)),U_15583)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15580,U_15583)),hAPP(c_Set_OCollect(tc_prod(U_15580,U_15580)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15580,U_15580,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15580,tc_fun(U_15580,tc_HOL_Obool),tc_fun(U_15580,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15580,tc_HOL_Obool),tc_fun(U_15580,tc_HOL_Obool)),U_15580),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15580)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15580),c_fconj),hAPP(hAPP(c_COMBC(U_15580,tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15580,U_15580),tc_fun(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),U_15580),c_member(tc_prod(U_15580,U_15580))),hAPP(hAPP(c_COMBC(U_15580,U_15580,tc_prod(U_15580,U_15580)),c_Product__Type_OPair(U_15580,U_15580)),U_15581))),c_Transitive__Closure_Ortrancl(U_15580,U_15583))))),hAPP(hAPP(c_COMBC(U_15580,tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15580,U_15580),tc_fun(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),U_15580),c_member(tc_prod(U_15580,U_15580))),hAPP(c_Product__Type_OPair(U_15580,U_15580),U_15582))),c_Transitive__Closure_Ortrancl(U_15580,U_15583)))))),
    inference(variable_rename,[status(thm)],[f_3909_1]) ).

fof(f_3909_3,plain,
    ! [U_15580,U_15581,U_15582,U_15583] : c_Transitive__Closure_Otrancl(U_15580,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15580,U_15580)),hAPP(hAPP(c_Product__Type_OPair(U_15580,U_15580),U_15581),U_15582)),U_15583)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15580,U_15583)),hAPP(c_Set_OCollect(tc_prod(U_15580,U_15580)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15580,U_15580,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15580,tc_fun(U_15580,tc_HOL_Obool),tc_fun(U_15580,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15580,tc_HOL_Obool),tc_fun(U_15580,tc_HOL_Obool)),U_15580),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15580)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15580),c_fconj),hAPP(hAPP(c_COMBC(U_15580,tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15580,U_15580),tc_fun(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),U_15580),c_member(tc_prod(U_15580,U_15580))),hAPP(hAPP(c_COMBC(U_15580,U_15580,tc_prod(U_15580,U_15580)),c_Product__Type_OPair(U_15580,U_15580)),U_15581))),c_Transitive__Closure_Ortrancl(U_15580,U_15583))))),hAPP(hAPP(c_COMBC(U_15580,tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15580,U_15580),tc_fun(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),U_15580),c_member(tc_prod(U_15580,U_15580))),hAPP(c_Product__Type_OPair(U_15580,U_15580),U_15582))),c_Transitive__Closure_Ortrancl(U_15580,U_15583)))))),
    inference(definitional_conversion,[status(esa)],[f_3909_2]) ).

cnf(f_3909_4,plain,
    c_Transitive__Closure_Otrancl(U_15580,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15580,U_15580)),hAPP(hAPP(c_Product__Type_OPair(U_15580,U_15580),U_15581),U_15582)),U_15583)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15580,U_15583)),hAPP(c_Set_OCollect(tc_prod(U_15580,U_15580)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15580,U_15580,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15580,tc_fun(U_15580,tc_HOL_Obool),tc_fun(U_15580,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15580,tc_HOL_Obool),tc_fun(U_15580,tc_HOL_Obool)),U_15580),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15580)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15580),c_fconj),hAPP(hAPP(c_COMBC(U_15580,tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15580,U_15580),tc_fun(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),U_15580),c_member(tc_prod(U_15580,U_15580))),hAPP(hAPP(c_COMBC(U_15580,U_15580,tc_prod(U_15580,U_15580)),c_Product__Type_OPair(U_15580,U_15580)),U_15581))),c_Transitive__Closure_Ortrancl(U_15580,U_15583))))),hAPP(hAPP(c_COMBC(U_15580,tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15580,U_15580),tc_fun(tc_fun(tc_prod(U_15580,U_15580),tc_HOL_Obool),tc_HOL_Obool),U_15580),c_member(tc_prod(U_15580,U_15580))),hAPP(c_Product__Type_OPair(U_15580,U_15580),U_15582))),c_Transitive__Closure_Ortrancl(U_15580,U_15583)))))),
    inference(clausify,[status(thm)],[f_3909_3]) ).

fof(f_3910_1,plain,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl]) ).

fof(f_3910_2,plain,
    ! [U_15586,U_15585,U_15584] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15584,U_15584)),U_15585),c_Transitive__Closure_Ortrancl(U_15584,U_15586)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15584,U_15584)),U_15585),U_15586)) ),
    inference(variable_rename,[status(thm)],[f_3910_1]) ).

fof(f_3910_3,plain,
    ! [U_15584,U_15585,U_15586] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15584,U_15584)),U_15585),c_Transitive__Closure_Ortrancl(U_15584,U_15586)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15584,U_15584)),U_15585),U_15586)) ),
    inference(definitional_conversion,[status(esa)],[f_3910_2]) ).

cnf(f_3910_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15584,U_15584)),U_15585),c_Transitive__Closure_Ortrancl(U_15584,U_15586)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15584,U_15584)),U_15585),U_15586)) ),
    inference(clausify,[status(thm)],[f_3910_3]) ).

fof(f_3911_1,plain,
    ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

fof(f_3911_2,plain,
    ! [U_15589,U_15588,U_15587] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15587,U_15587)),hAPP(hAPP(c_Product__Type_OPair(U_15587,U_15587),U_15588),U_15588)),c_Transitive__Closure_Ortrancl(U_15587,U_15589))),
    inference(variable_rename,[status(thm)],[f_3911_1]) ).

fof(f_3911_3,plain,
    ! [U_15587,U_15588,U_15589] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15587,U_15587)),hAPP(hAPP(c_Product__Type_OPair(U_15587,U_15587),U_15588),U_15588)),c_Transitive__Closure_Ortrancl(U_15587,U_15589))),
    inference(definitional_conversion,[status(esa)],[f_3911_2]) ).

cnf(f_3911_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_15587,U_15587)),hAPP(hAPP(c_Product__Type_OPair(U_15587,U_15587),U_15588),U_15588)),c_Transitive__Closure_Ortrancl(U_15587,U_15589))),
    inference(clausify,[status(thm)],[f_3911_3]) ).

fof(f_3912_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl]) ).

fof(f_3912_2,plain,
    ! [U_15593,U_15592,U_15591,U_15590] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15590,U_15590)),hAPP(hAPP(c_Product__Type_OPair(U_15590,U_15590),U_15591),U_15592)),c_Transitive__Closure_Ortrancl(U_15590,U_15593)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15590,U_15590)),hAPP(hAPP(c_Product__Type_OPair(U_15590,U_15590),U_15591),U_15592)),c_Transitive__Closure_Otrancl(U_15590,U_15593))) ),
    inference(variable_rename,[status(thm)],[f_3912_1]) ).

fof(f_3912_3,plain,
    ! [U_15590,U_15591,U_15592,U_15593] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15590,U_15590)),hAPP(hAPP(c_Product__Type_OPair(U_15590,U_15590),U_15591),U_15592)),c_Transitive__Closure_Ortrancl(U_15590,U_15593)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15590,U_15590)),hAPP(hAPP(c_Product__Type_OPair(U_15590,U_15590),U_15591),U_15592)),c_Transitive__Closure_Otrancl(U_15590,U_15593))) ),
    inference(definitional_conversion,[status(esa)],[f_3912_2]) ).

cnf(f_3912_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15590,U_15590)),hAPP(hAPP(c_Product__Type_OPair(U_15590,U_15590),U_15591),U_15592)),c_Transitive__Closure_Ortrancl(U_15590,U_15593)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15590,U_15590)),hAPP(hAPP(c_Product__Type_OPair(U_15590,U_15590),U_15591),U_15592)),c_Transitive__Closure_Otrancl(U_15590,U_15593))) ),
    inference(clausify,[status(thm)],[f_3912_3]) ).

fof(f_3913_1,plain,
    ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__rtrancl]) ).

fof(f_3913_2,plain,
    ! [U_15595,U_15594] : hAPP(c_Relation_ODomain(U_15594,U_15594),c_Transitive__Closure_Ortrancl(U_15594,U_15595)) = c_Orderings_Otop__class_Otop(tc_fun(U_15594,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3913_1]) ).

fof(f_3913_3,plain,
    ! [U_15594,U_15595] : hAPP(c_Relation_ODomain(U_15594,U_15594),c_Transitive__Closure_Ortrancl(U_15594,U_15595)) = c_Orderings_Otop__class_Otop(tc_fun(U_15594,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3913_2]) ).

cnf(f_3913_4,plain,
    hAPP(c_Relation_ODomain(U_15594,U_15594),c_Transitive__Closure_Ortrancl(U_15594,U_15595)) = c_Orderings_Otop__class_Otop(tc_fun(U_15594,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3913_3]) ).

fof(f_3914_1,plain,
    ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__rtrancl]) ).

fof(f_3914_2,plain,
    ! [U_15597,U_15596] : hAPP(c_Relation_ORange(U_15596,U_15596),c_Transitive__Closure_Ortrancl(U_15596,U_15597)) = c_Orderings_Otop__class_Otop(tc_fun(U_15596,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3914_1]) ).

fof(f_3914_3,plain,
    ! [U_15596,U_15597] : hAPP(c_Relation_ORange(U_15596,U_15596),c_Transitive__Closure_Ortrancl(U_15596,U_15597)) = c_Orderings_Otop__class_Otop(tc_fun(U_15596,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3914_2]) ).

cnf(f_3914_4,plain,
    hAPP(c_Relation_ORange(U_15596,U_15596),c_Transitive__Closure_Ortrancl(U_15596,U_15597)) = c_Orderings_Otop__class_Otop(tc_fun(U_15596,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3914_3]) ).

fof(f_3915_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(f_3915_2,plain,
    ! [U_15599,U_15598] : hAPP(hAPP(c_Relation_Orel__comp(U_15598,U_15598,U_15598),c_Transitive__Closure_Ortrancl(U_15598,U_15599)),c_Transitive__Closure_Ortrancl(U_15598,U_15599)) = c_Transitive__Closure_Ortrancl(U_15598,U_15599),
    inference(variable_rename,[status(thm)],[f_3915_1]) ).

fof(f_3915_3,plain,
    ! [U_15598,U_15599] : hAPP(hAPP(c_Relation_Orel__comp(U_15598,U_15598,U_15598),c_Transitive__Closure_Ortrancl(U_15598,U_15599)),c_Transitive__Closure_Ortrancl(U_15598,U_15599)) = c_Transitive__Closure_Ortrancl(U_15598,U_15599),
    inference(definitional_conversion,[status(esa)],[f_3915_2]) ).

cnf(f_3915_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15598,U_15598,U_15598),c_Transitive__Closure_Ortrancl(U_15598,U_15599)),c_Transitive__Closure_Ortrancl(U_15598,U_15599)) = c_Transitive__Closure_Ortrancl(U_15598,U_15599),
    inference(clausify,[status(thm)],[f_3915_3]) ).

fof(f_3916_1,plain,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

fof(f_3916_2,plain,
    ! [U_15601,U_15600] : hAPP(hAPP(c_Relation_Orel__comp(U_15600,U_15600,U_15600),U_15601),c_Transitive__Closure_Ortrancl(U_15600,U_15601)) = hAPP(hAPP(c_Relation_Orel__comp(U_15600,U_15600,U_15600),c_Transitive__Closure_Ortrancl(U_15600,U_15601)),U_15601),
    inference(variable_rename,[status(thm)],[f_3916_1]) ).

fof(f_3916_3,plain,
    ! [U_15600,U_15601] : hAPP(hAPP(c_Relation_Orel__comp(U_15600,U_15600,U_15600),U_15601),c_Transitive__Closure_Ortrancl(U_15600,U_15601)) = hAPP(hAPP(c_Relation_Orel__comp(U_15600,U_15600,U_15600),c_Transitive__Closure_Ortrancl(U_15600,U_15601)),U_15601),
    inference(definitional_conversion,[status(esa)],[f_3916_2]) ).

cnf(f_3916_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15600,U_15600,U_15600),U_15601),c_Transitive__Closure_Ortrancl(U_15600,U_15601)) = hAPP(hAPP(c_Relation_Orel__comp(U_15600,U_15600,U_15600),c_Transitive__Closure_Ortrancl(U_15600,U_15601)),U_15601),
    inference(clausify,[status(thm)],[f_3916_3]) ).

fof(f_3917_1,plain,
    ! [V_S_2,V_R_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI]) ).

fof(f_3917_2,plain,
    ! [U_15605,U_15604,U_15603,U_15602] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15602,U_15602),tc_HOL_Obool)),U_15604),U_15605))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,U_15605)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,U_15604))) ) ),
    inference(variable_rename,[status(thm)],[f_3917_1]) ).

fof(f_3917_3,plain,
    ( ! [U_15602,U_15603,U_15604,U_15605] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,U_15605)))
        | ~ sP1041(U_15602,U_15603,U_15604,U_15605) )
    & ! [U_15602,U_15603,U_15604,U_15605] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,U_15604)))
        | ~ sP1041(U_15602,U_15603,U_15604,U_15605) )
    & ! [U_15602,U_15603,U_15604,U_15605] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15602,U_15602),tc_HOL_Obool)),U_15604),U_15605))))
        | sP1041(U_15602,U_15603,U_15604,U_15605) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1041])],[f_3917_2]) ).

cnf(f_3917_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15602,U_15602),tc_HOL_Obool)),U_15604),U_15605))))
    | sP1041(U_15602,U_15603,U_15604,U_15605) ),
    inference(clausify,[status(thm)],[f_3917_3]) ).

cnf(f_3917_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,U_15604)))
    | ~ sP1041(U_15602,U_15603,U_15604,U_15605) ),
    inference(clausify,[status(thm)],[f_3917_3]) ).

cnf(f_3917_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15602,U_15602)),U_15603),c_Transitive__Closure_Ortrancl(U_15602,U_15605)))
    | ~ sP1041(U_15602,U_15603,U_15604,U_15605) ),
    inference(clausify,[status(thm)],[f_3917_3]) ).

fof(f_3918_1,plain,
    ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

fof(f_3918_2,plain,
    ! [U_15608,U_15607,U_15606] : c_Transitive__Closure_Ortrancl(U_15606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15606,U_15606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15606,U_15607)),c_Transitive__Closure_Ortrancl(U_15606,U_15608))) = c_Transitive__Closure_Ortrancl(U_15606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15606,U_15606),tc_HOL_Obool)),U_15607),U_15608)),
    inference(variable_rename,[status(thm)],[f_3918_1]) ).

fof(f_3918_3,plain,
    ! [U_15606,U_15607,U_15608] : c_Transitive__Closure_Ortrancl(U_15606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15606,U_15606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15606,U_15607)),c_Transitive__Closure_Ortrancl(U_15606,U_15608))) = c_Transitive__Closure_Ortrancl(U_15606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15606,U_15606),tc_HOL_Obool)),U_15607),U_15608)),
    inference(definitional_conversion,[status(esa)],[f_3918_2]) ).

cnf(f_3918_4,plain,
    c_Transitive__Closure_Ortrancl(U_15606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15606,U_15606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15606,U_15607)),c_Transitive__Closure_Ortrancl(U_15606,U_15608))) = c_Transitive__Closure_Ortrancl(U_15606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15606,U_15606),tc_HOL_Obool)),U_15607),U_15608)),
    inference(clausify,[status(thm)],[f_3918_3]) ).

fof(f_3919_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__mono]) ).

fof(f_3919_2,plain,
    ! [U_15611,U_15610,U_15609] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15609,U_15609),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15609,U_15610)),c_Transitive__Closure_Ortrancl(U_15609,U_15611)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15609,U_15609),tc_HOL_Obool)),U_15610),U_15611)) ),
    inference(variable_rename,[status(thm)],[f_3919_1]) ).

fof(f_3919_3,plain,
    ! [U_15609,U_15610,U_15611] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15609,U_15609),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15609,U_15610)),c_Transitive__Closure_Ortrancl(U_15609,U_15611)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15609,U_15609),tc_HOL_Obool)),U_15610),U_15611)) ),
    inference(definitional_conversion,[status(esa)],[f_3919_2]) ).

cnf(f_3919_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15609,U_15609),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15609,U_15610)),c_Transitive__Closure_Ortrancl(U_15609,U_15611)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15609,U_15609),tc_HOL_Obool)),U_15610),U_15611)) ),
    inference(clausify,[status(thm)],[f_3919_3]) ).

fof(f_3920_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__subset]) ).

fof(f_3920_2,plain,
    ! [U_15614,U_15613,U_15612] :
      ( c_Transitive__Closure_Ortrancl(U_15612,U_15614) = c_Transitive__Closure_Ortrancl(U_15612,U_15613)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15612,U_15612),tc_HOL_Obool)),U_15614),c_Transitive__Closure_Ortrancl(U_15612,U_15613)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15612,U_15612),tc_HOL_Obool)),U_15613),U_15614)) ),
    inference(variable_rename,[status(thm)],[f_3920_1]) ).

fof(f_3920_3,plain,
    ! [U_15612,U_15613,U_15614] :
      ( c_Transitive__Closure_Ortrancl(U_15612,U_15614) = c_Transitive__Closure_Ortrancl(U_15612,U_15613)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15612,U_15612),tc_HOL_Obool)),U_15614),c_Transitive__Closure_Ortrancl(U_15612,U_15613)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15612,U_15612),tc_HOL_Obool)),U_15613),U_15614)) ),
    inference(definitional_conversion,[status(esa)],[f_3920_2]) ).

cnf(f_3920_4,plain,
    ( c_Transitive__Closure_Ortrancl(U_15612,U_15614) = c_Transitive__Closure_Ortrancl(U_15612,U_15613)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15612,U_15612),tc_HOL_Obool)),U_15614),c_Transitive__Closure_Ortrancl(U_15612,U_15613)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15612,U_15612),tc_HOL_Obool)),U_15613),U_15614)) ),
    inference(clausify,[status(thm)],[f_3920_3]) ).

fof(f_3921_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl]) ).

fof(f_3921_2,plain,
    ! [U_15617,U_15616,U_15615] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15615,U_15615),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15615,U_15616)),c_Transitive__Closure_Ortrancl(U_15615,U_15617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15615,U_15615),tc_HOL_Obool)),U_15616),c_Transitive__Closure_Ortrancl(U_15615,U_15617))) ),
    inference(variable_rename,[status(thm)],[f_3921_1]) ).

fof(f_3921_3,plain,
    ! [U_15615,U_15616,U_15617] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15615,U_15615),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15615,U_15616)),c_Transitive__Closure_Ortrancl(U_15615,U_15617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15615,U_15615),tc_HOL_Obool)),U_15616),c_Transitive__Closure_Ortrancl(U_15615,U_15617))) ),
    inference(definitional_conversion,[status(esa)],[f_3921_2]) ).

cnf(f_3921_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15615,U_15615),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15615,U_15616)),c_Transitive__Closure_Ortrancl(U_15615,U_15617)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15615,U_15615),tc_HOL_Obool)),U_15616),c_Transitive__Closure_Ortrancl(U_15615,U_15617))) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

fof(f_3922_1,plain,
    ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(f_3922_2,plain,
    ! [U_15620,U_15619,U_15618] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15618,U_15619)),c_Transitive__Closure_Ortrancl(U_15618,U_15620))),c_Transitive__Closure_Ortrancl(U_15618,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),U_15619),U_15620)))),
    inference(variable_rename,[status(thm)],[f_3922_1]) ).

fof(f_3922_3,plain,
    ! [U_15618,U_15619,U_15620] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15618,U_15619)),c_Transitive__Closure_Ortrancl(U_15618,U_15620))),c_Transitive__Closure_Ortrancl(U_15618,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),U_15619),U_15620)))),
    inference(definitional_conversion,[status(esa)],[f_3922_2]) ).

cnf(f_3922_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15618,U_15619)),c_Transitive__Closure_Ortrancl(U_15618,U_15620))),c_Transitive__Closure_Ortrancl(U_15618,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15618,U_15618),tc_HOL_Obool)),U_15619),U_15620)))),
    inference(clausify,[status(thm)],[f_3922_3]) ).

fof(f_3923_1,plain,
    ! [V_X_2,V_r_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl]) ).

fof(f_3923_2,plain,
    ! [U_15623,U_15622,U_15621] :
      ( hAPP(c_Relation_OImage(U_15621,U_15621,c_Transitive__Closure_Ortrancl(U_15621,U_15622)),U_15623) = U_15623
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15621,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15621,U_15621,U_15622),U_15623)),U_15623)) ),
    inference(variable_rename,[status(thm)],[f_3923_1]) ).

fof(f_3923_3,plain,
    ! [U_15621,U_15622,U_15623] :
      ( hAPP(c_Relation_OImage(U_15621,U_15621,c_Transitive__Closure_Ortrancl(U_15621,U_15622)),U_15623) = U_15623
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15621,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15621,U_15621,U_15622),U_15623)),U_15623)) ),
    inference(definitional_conversion,[status(esa)],[f_3923_2]) ).

cnf(f_3923_4,plain,
    ( hAPP(c_Relation_OImage(U_15621,U_15621,c_Transitive__Closure_Ortrancl(U_15621,U_15622)),U_15623) = U_15623
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15621,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15621,U_15621,U_15622),U_15623)),U_15623)) ),
    inference(clausify,[status(thm)],[f_3923_3]) ).

fof(f_3924_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp]) ).

fof(f_3924_2,plain,
    ! [U_15625,U_15624] : c_Transitive__Closure_Ortrancl(U_15624,c_Transitive__Closure_Ortrancl(U_15624,U_15625)) = c_Transitive__Closure_Ortrancl(U_15624,U_15625),
    inference(variable_rename,[status(thm)],[f_3924_1]) ).

fof(f_3924_3,plain,
    ! [U_15624,U_15625] : c_Transitive__Closure_Ortrancl(U_15624,c_Transitive__Closure_Ortrancl(U_15624,U_15625)) = c_Transitive__Closure_Ortrancl(U_15624,U_15625),
    inference(definitional_conversion,[status(esa)],[f_3924_2]) ).

cnf(f_3924_4,plain,
    c_Transitive__Closure_Ortrancl(U_15624,c_Transitive__Closure_Ortrancl(U_15624,U_15625)) = c_Transitive__Closure_Ortrancl(U_15624,U_15625),
    inference(clausify,[status(thm)],[f_3924_3]) ).

fof(f_3925_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trans]) ).

fof(f_3925_2,plain,
    ! [U_15630,U_15629,U_15628,U_15627,U_15626] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15627),U_15630)),c_Transitive__Closure_Ortrancl(U_15626,U_15629)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15628),U_15630)),c_Transitive__Closure_Ortrancl(U_15626,U_15629)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15627),U_15628)),c_Transitive__Closure_Ortrancl(U_15626,U_15629))) ),
    inference(variable_rename,[status(thm)],[f_3925_1]) ).

fof(f_3925_3,plain,
    ! [U_15626,U_15627,U_15628,U_15629,U_15630] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15627),U_15630)),c_Transitive__Closure_Ortrancl(U_15626,U_15629)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15628),U_15630)),c_Transitive__Closure_Ortrancl(U_15626,U_15629)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15627),U_15628)),c_Transitive__Closure_Ortrancl(U_15626,U_15629))) ),
    inference(definitional_conversion,[status(esa)],[f_3925_2]) ).

cnf(f_3925_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15627),U_15630)),c_Transitive__Closure_Ortrancl(U_15626,U_15629)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15628),U_15630)),c_Transitive__Closure_Ortrancl(U_15626,U_15629)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15626,U_15626)),hAPP(hAPP(c_Product__Type_OPair(U_15626,U_15626),U_15627),U_15628)),c_Transitive__Closure_Ortrancl(U_15626,U_15629))) ),
    inference(clausify,[status(thm)],[f_3925_3]) ).

fof(f_3926_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl]) ).

fof(f_3926_2,plain,
    ! [U_15635,U_15634,U_15633,U_15632,U_15631] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15632),U_15635)),c_Transitive__Closure_Ortrancl(U_15631,U_15634)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15633),U_15635)),U_15634))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15632),U_15633)),c_Transitive__Closure_Ortrancl(U_15631,U_15634))) ),
    inference(variable_rename,[status(thm)],[f_3926_1]) ).

fof(f_3926_3,plain,
    ! [U_15631,U_15632,U_15633,U_15634,U_15635] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15632),U_15635)),c_Transitive__Closure_Ortrancl(U_15631,U_15634)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15633),U_15635)),U_15634))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15632),U_15633)),c_Transitive__Closure_Ortrancl(U_15631,U_15634))) ),
    inference(definitional_conversion,[status(esa)],[f_3926_2]) ).

cnf(f_3926_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15632),U_15635)),c_Transitive__Closure_Ortrancl(U_15631,U_15634)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15633),U_15635)),U_15634))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15631,U_15631)),hAPP(hAPP(c_Product__Type_OPair(U_15631,U_15631),U_15632),U_15633)),c_Transitive__Closure_Ortrancl(U_15631,U_15634))) ),
    inference(clausify,[status(thm)],[f_3926_3]) ).

fof(f_3927_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl]) ).

fof(f_3927_2,plain,
    ! [U_15640,U_15639,U_15638,U_15637,U_15636] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15637),U_15640)),c_Transitive__Closure_Ortrancl(U_15636,U_15639)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15638),U_15640)),c_Transitive__Closure_Ortrancl(U_15636,U_15639)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15637),U_15638)),U_15639)) ),
    inference(variable_rename,[status(thm)],[f_3927_1]) ).

fof(f_3927_3,plain,
    ! [U_15636,U_15637,U_15638,U_15639,U_15640] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15637),U_15640)),c_Transitive__Closure_Ortrancl(U_15636,U_15639)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15638),U_15640)),c_Transitive__Closure_Ortrancl(U_15636,U_15639)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15637),U_15638)),U_15639)) ),
    inference(definitional_conversion,[status(esa)],[f_3927_2]) ).

cnf(f_3927_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15637),U_15640)),c_Transitive__Closure_Ortrancl(U_15636,U_15639)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15638),U_15640)),c_Transitive__Closure_Ortrancl(U_15636,U_15639)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15636,U_15636)),hAPP(hAPP(c_Product__Type_OPair(U_15636,U_15636),U_15637),U_15638)),U_15639)) ),
    inference(clausify,[status(thm)],[f_3927_3]) ).

fof(f_3928_1,plain,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_refl__rtrancl]) ).

fof(f_3928_2,plain,
    ! [U_15642,U_15641] : c_Relation_Orefl__on(U_15641,c_Orderings_Otop__class_Otop(tc_fun(U_15641,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15641,U_15642)),
    inference(variable_rename,[status(thm)],[f_3928_1]) ).

fof(f_3928_3,plain,
    ! [U_15641,U_15642] : c_Relation_Orefl__on(U_15641,c_Orderings_Otop__class_Otop(tc_fun(U_15641,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15641,U_15642)),
    inference(definitional_conversion,[status(esa)],[f_3928_2]) ).

cnf(f_3928_4,plain,
    c_Relation_Orefl__on(U_15641,c_Orderings_Otop__class_Otop(tc_fun(U_15641,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15641,U_15642)),
    inference(clausify,[status(thm)],[f_3928_3]) ).

fof(f_3929_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(f_3929_2,plain,
    ! [U_15644,U_15643] : c_Transitive__Closure_Otrancl(U_15643,c_Transitive__Closure_Ortrancl(U_15643,U_15644)) = c_Transitive__Closure_Ortrancl(U_15643,U_15644),
    inference(variable_rename,[status(thm)],[f_3929_1]) ).

fof(f_3929_3,plain,
    ! [U_15643,U_15644] : c_Transitive__Closure_Otrancl(U_15643,c_Transitive__Closure_Ortrancl(U_15643,U_15644)) = c_Transitive__Closure_Ortrancl(U_15643,U_15644),
    inference(definitional_conversion,[status(esa)],[f_3929_2]) ).

cnf(f_3929_4,plain,
    c_Transitive__Closure_Otrancl(U_15643,c_Transitive__Closure_Ortrancl(U_15643,U_15644)) = c_Transitive__Closure_Ortrancl(U_15643,U_15644),
    inference(clausify,[status(thm)],[f_3929_3]) ).

fof(f_3930_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(f_3930_2,plain,
    ! [U_15646,U_15645] : c_Transitive__Closure_Ortrancl(U_15645,c_Transitive__Closure_Otrancl(U_15645,U_15646)) = c_Transitive__Closure_Ortrancl(U_15645,U_15646),
    inference(variable_rename,[status(thm)],[f_3930_1]) ).

fof(f_3930_3,plain,
    ! [U_15645,U_15646] : c_Transitive__Closure_Ortrancl(U_15645,c_Transitive__Closure_Otrancl(U_15645,U_15646)) = c_Transitive__Closure_Ortrancl(U_15645,U_15646),
    inference(definitional_conversion,[status(esa)],[f_3930_2]) ).

cnf(f_3930_4,plain,
    c_Transitive__Closure_Ortrancl(U_15645,c_Transitive__Closure_Otrancl(U_15645,U_15646)) = c_Transitive__Closure_Ortrancl(U_15645,U_15646),
    inference(clausify,[status(thm)],[f_3930_3]) ).

fof(f_3931_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold__left]) ).

fof(f_3931_2,plain,
    ! [U_15648,U_15647] : c_Transitive__Closure_Otrancl(U_15647,U_15648) = hAPP(hAPP(c_Relation_Orel__comp(U_15647,U_15647,U_15647),U_15648),c_Transitive__Closure_Ortrancl(U_15647,U_15648)),
    inference(variable_rename,[status(thm)],[f_3931_1]) ).

fof(f_3931_3,plain,
    ! [U_15647,U_15648] : c_Transitive__Closure_Otrancl(U_15647,U_15648) = hAPP(hAPP(c_Relation_Orel__comp(U_15647,U_15647,U_15647),U_15648),c_Transitive__Closure_Ortrancl(U_15647,U_15648)),
    inference(definitional_conversion,[status(esa)],[f_3931_2]) ).

cnf(f_3931_4,plain,
    c_Transitive__Closure_Otrancl(U_15647,U_15648) = hAPP(hAPP(c_Relation_Orel__comp(U_15647,U_15647,U_15647),U_15648),c_Transitive__Closure_Ortrancl(U_15647,U_15648)),
    inference(clausify,[status(thm)],[f_3931_3]) ).

fof(f_3932_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold__right]) ).

fof(f_3932_2,plain,
    ! [U_15650,U_15649] : c_Transitive__Closure_Otrancl(U_15649,U_15650) = hAPP(hAPP(c_Relation_Orel__comp(U_15649,U_15649,U_15649),c_Transitive__Closure_Ortrancl(U_15649,U_15650)),U_15650),
    inference(variable_rename,[status(thm)],[f_3932_1]) ).

fof(f_3932_3,plain,
    ! [U_15649,U_15650] : c_Transitive__Closure_Otrancl(U_15649,U_15650) = hAPP(hAPP(c_Relation_Orel__comp(U_15649,U_15649,U_15649),c_Transitive__Closure_Ortrancl(U_15649,U_15650)),U_15650),
    inference(definitional_conversion,[status(esa)],[f_3932_2]) ).

cnf(f_3932_4,plain,
    c_Transitive__Closure_Otrancl(U_15649,U_15650) = hAPP(hAPP(c_Relation_Orel__comp(U_15649,U_15649,U_15649),c_Transitive__Closure_Ortrancl(U_15649,U_15650)),U_15650),
    inference(clausify,[status(thm)],[f_3932_3]) ).

fof(f_3933_1,plain,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl]) ).

fof(f_3933_2,plain,
    ! [U_15655,U_15654,U_15653,U_15652,U_15651] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15652),U_15655)),c_Transitive__Closure_Otrancl(U_15651,U_15654)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15653),U_15655)),c_Transitive__Closure_Otrancl(U_15651,U_15654)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15652),U_15653)),c_Transitive__Closure_Ortrancl(U_15651,U_15654))) ),
    inference(variable_rename,[status(thm)],[f_3933_1]) ).

fof(f_3933_3,plain,
    ! [U_15651,U_15652,U_15653,U_15654,U_15655] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15652),U_15655)),c_Transitive__Closure_Otrancl(U_15651,U_15654)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15653),U_15655)),c_Transitive__Closure_Otrancl(U_15651,U_15654)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15652),U_15653)),c_Transitive__Closure_Ortrancl(U_15651,U_15654))) ),
    inference(definitional_conversion,[status(esa)],[f_3933_2]) ).

cnf(f_3933_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15652),U_15655)),c_Transitive__Closure_Otrancl(U_15651,U_15654)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15653),U_15655)),c_Transitive__Closure_Otrancl(U_15651,U_15654)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),U_15652),U_15653)),c_Transitive__Closure_Ortrancl(U_15651,U_15654))) ),
    inference(clausify,[status(thm)],[f_3933_3]) ).

fof(f_3934_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl]) ).

fof(f_3934_2,plain,
    ! [U_15660,U_15659,U_15658,U_15657,U_15656] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15657),U_15660)),c_Transitive__Closure_Otrancl(U_15656,U_15659)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15658),U_15660)),c_Transitive__Closure_Ortrancl(U_15656,U_15659)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15657),U_15658)),c_Transitive__Closure_Otrancl(U_15656,U_15659))) ),
    inference(variable_rename,[status(thm)],[f_3934_1]) ).

fof(f_3934_3,plain,
    ! [U_15656,U_15657,U_15658,U_15659,U_15660] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15657),U_15660)),c_Transitive__Closure_Otrancl(U_15656,U_15659)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15658),U_15660)),c_Transitive__Closure_Ortrancl(U_15656,U_15659)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15657),U_15658)),c_Transitive__Closure_Otrancl(U_15656,U_15659))) ),
    inference(definitional_conversion,[status(esa)],[f_3934_2]) ).

cnf(f_3934_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15657),U_15660)),c_Transitive__Closure_Otrancl(U_15656,U_15659)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15658),U_15660)),c_Transitive__Closure_Ortrancl(U_15656,U_15659)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15656,U_15656)),hAPP(hAPP(c_Product__Type_OPair(U_15656,U_15656),U_15657),U_15658)),c_Transitive__Closure_Otrancl(U_15656,U_15659))) ),
    inference(clausify,[status(thm)],[f_3934_3]) ).

fof(f_3935_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1]) ).

fof(f_3935_2,plain,
    ! [U_15665,U_15664,U_15663,U_15662,U_15661] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15662),U_15665)),c_Transitive__Closure_Otrancl(U_15661,U_15664)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15663),U_15665)),U_15664))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15662),U_15663)),c_Transitive__Closure_Ortrancl(U_15661,U_15664))) ),
    inference(variable_rename,[status(thm)],[f_3935_1]) ).

fof(f_3935_3,plain,
    ! [U_15661,U_15662,U_15663,U_15664,U_15665] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15662),U_15665)),c_Transitive__Closure_Otrancl(U_15661,U_15664)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15663),U_15665)),U_15664))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15662),U_15663)),c_Transitive__Closure_Ortrancl(U_15661,U_15664))) ),
    inference(definitional_conversion,[status(esa)],[f_3935_2]) ).

cnf(f_3935_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15662),U_15665)),c_Transitive__Closure_Otrancl(U_15661,U_15664)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15663),U_15665)),U_15664))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15661,U_15661)),hAPP(hAPP(c_Product__Type_OPair(U_15661,U_15661),U_15662),U_15663)),c_Transitive__Closure_Ortrancl(U_15661,U_15664))) ),
    inference(clausify,[status(thm)],[f_3935_3]) ).

fof(f_3936_1,plain,
    ! [V_R_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
        & V_a_2 != V_b_2 )
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtranclD]) ).

fof(f_3936_2,plain,
    ! [U_15669,U_15668,U_15667,U_15666] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15666,U_15666)),hAPP(hAPP(c_Product__Type_OPair(U_15666,U_15666),U_15667),U_15668)),c_Transitive__Closure_Otrancl(U_15666,U_15669)))
        & U_15667 != U_15668 )
      | U_15667 = U_15668
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15666,U_15666)),hAPP(hAPP(c_Product__Type_OPair(U_15666,U_15666),U_15667),U_15668)),c_Transitive__Closure_Ortrancl(U_15666,U_15669))) ),
    inference(variable_rename,[status(thm)],[f_3936_1]) ).

fof(f_3936_3,plain,
    ( ! [U_15666,U_15667,U_15668,U_15669] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15666,U_15666)),hAPP(hAPP(c_Product__Type_OPair(U_15666,U_15666),U_15667),U_15668)),c_Transitive__Closure_Otrancl(U_15666,U_15669)))
        | ~ sP1042(U_15666,U_15667,U_15668,U_15669) )
    & ! [U_15666,U_15667,U_15668,U_15669] :
        ( U_15667 != U_15668
        | ~ sP1042(U_15666,U_15667,U_15668,U_15669) )
    & ! [U_15666,U_15667,U_15668,U_15669] :
        ( sP1042(U_15666,U_15667,U_15668,U_15669)
        | U_15667 = U_15668
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15666,U_15666)),hAPP(hAPP(c_Product__Type_OPair(U_15666,U_15666),U_15667),U_15668)),c_Transitive__Closure_Ortrancl(U_15666,U_15669))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1042])],[f_3936_2]) ).

cnf(f_3936_4,plain,
    ( sP1042(U_15666,U_15667,U_15668,U_15669)
    | U_15667 = U_15668
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15666,U_15666)),hAPP(hAPP(c_Product__Type_OPair(U_15666,U_15666),U_15667),U_15668)),c_Transitive__Closure_Ortrancl(U_15666,U_15669))) ),
    inference(clausify,[status(thm)],[f_3936_3]) ).

cnf(f_3936_5,plain,
    ( U_15667 != U_15668
    | ~ sP1042(U_15666,U_15667,U_15668,U_15669) ),
    inference(clausify,[status(thm)],[f_3936_3]) ).

cnf(f_3936_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15666,U_15666)),hAPP(hAPP(c_Product__Type_OPair(U_15666,U_15666),U_15667),U_15668)),c_Transitive__Closure_Otrancl(U_15666,U_15669)))
    | ~ sP1042(U_15666,U_15667,U_15668,U_15669) ),
    inference(clausify,[status(thm)],[f_3936_3]) ).

fof(f_3937_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2]) ).

fof(f_3937_2,plain,
    ! [U_15674,U_15673,U_15672,U_15671,U_15670] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15671),U_15674)),c_Transitive__Closure_Otrancl(U_15670,U_15673)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15672),U_15674)),c_Transitive__Closure_Ortrancl(U_15670,U_15673)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15671),U_15672)),U_15673)) ),
    inference(variable_rename,[status(thm)],[f_3937_1]) ).

fof(f_3937_3,plain,
    ! [U_15670,U_15671,U_15672,U_15673,U_15674] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15671),U_15674)),c_Transitive__Closure_Otrancl(U_15670,U_15673)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15672),U_15674)),c_Transitive__Closure_Ortrancl(U_15670,U_15673)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15671),U_15672)),U_15673)) ),
    inference(definitional_conversion,[status(esa)],[f_3937_2]) ).

cnf(f_3937_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15671),U_15674)),c_Transitive__Closure_Otrancl(U_15670,U_15673)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15672),U_15674)),c_Transitive__Closure_Ortrancl(U_15670,U_15673)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15670,U_15670)),hAPP(hAPP(c_Product__Type_OPair(U_15670,U_15670),U_15671),U_15672)),U_15673)) ),
    inference(clausify,[status(thm)],[f_3937_3]) ).

fof(f_3938_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
            | V_x_2 = V_y_2 )
          & V_x_2 != V_y_2 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
          & V_x_2 != V_y_2 )
        | V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl]) ).

fof(f_3938_2,plain,
    ! [U_15678,U_15677,U_15676,U_15675] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),U_15676),U_15677)),c_Transitive__Closure_Ortrancl(U_15675,U_15678)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),U_15676),U_15677)),c_Transitive__Closure_Otrancl(U_15675,U_15678)))
            | U_15676 = U_15677 )
          & U_15676 != U_15677 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),U_15676),U_15677)),c_Transitive__Closure_Otrancl(U_15675,U_15678)))
          & U_15676 != U_15677 )
        | U_15676 = U_15677
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),U_15676),U_15677)),c_Transitive__Closure_Ortrancl(U_15675,U_15678))) ) ),
    inference(variable_rename,[status(thm)],[f_3938_1]) ).

fof(f_3938_3,plain,
    ( ! [U_15686,U_15684,U_15682,U_15680] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15680,U_15680)),hAPP(hAPP(c_Product__Type_OPair(U_15680,U_15680),U_15682),U_15684)),c_Transitive__Closure_Ortrancl(U_15680,U_15686)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15680,U_15680)),hAPP(hAPP(c_Product__Type_OPair(U_15680,U_15680),U_15682),U_15684)),c_Transitive__Closure_Otrancl(U_15680,U_15686)))
            | U_15682 = U_15684 )
          & U_15682 != U_15684 ) )
    & ! [U_15685,U_15683,U_15681,U_15679] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15679,U_15679)),hAPP(hAPP(c_Product__Type_OPair(U_15679,U_15679),U_15681),U_15683)),c_Transitive__Closure_Otrancl(U_15679,U_15685)))
          & U_15681 != U_15683 )
        | U_15681 = U_15683
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15679,U_15679)),hAPP(hAPP(c_Product__Type_OPair(U_15679,U_15679),U_15681),U_15683)),c_Transitive__Closure_Ortrancl(U_15679,U_15685))) ) ),
    inference(miniscope,[status(thm)],[f_3938_2]) ).

fof(f_3938_4,plain,
    ( ! [U_15682,U_15680,U_15684,U_15686] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15680,U_15680)),hAPP(hAPP(c_Product__Type_OPair(U_15680,U_15680),U_15682),U_15684)),c_Transitive__Closure_Otrancl(U_15680,U_15686)))
        | U_15682 = U_15684
        | ~ sP1044(U_15682,U_15680,U_15684,U_15686) )
    & ! [U_15682,U_15680,U_15684,U_15686] :
        ( U_15682 != U_15684
        | ~ sP1044(U_15682,U_15680,U_15684,U_15686) )
    & ! [U_15683,U_15679,U_15681,U_15685] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15679,U_15679)),hAPP(hAPP(c_Product__Type_OPair(U_15679,U_15679),U_15681),U_15683)),c_Transitive__Closure_Otrancl(U_15679,U_15685)))
        | ~ sP1043(U_15683,U_15679,U_15681,U_15685) )
    & ! [U_15683,U_15679,U_15681,U_15685] :
        ( U_15681 != U_15683
        | ~ sP1043(U_15683,U_15679,U_15681,U_15685) )
    & ! [U_15682,U_15680,U_15684,U_15686] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15680,U_15680)),hAPP(hAPP(c_Product__Type_OPair(U_15680,U_15680),U_15682),U_15684)),c_Transitive__Closure_Ortrancl(U_15680,U_15686)))
        | sP1044(U_15682,U_15680,U_15684,U_15686) )
    & ! [U_15683,U_15679,U_15681,U_15685] :
        ( sP1043(U_15683,U_15679,U_15681,U_15685)
        | U_15681 = U_15683
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15679,U_15679)),hAPP(hAPP(c_Product__Type_OPair(U_15679,U_15679),U_15681),U_15683)),c_Transitive__Closure_Ortrancl(U_15679,U_15685))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1043,sP1044])],[f_3938_3]) ).

cnf(f_3938_5,plain,
    ( sP1043(U_15683,U_15679,U_15681,U_15685)
    | U_15681 = U_15683
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15679,U_15679)),hAPP(hAPP(c_Product__Type_OPair(U_15679,U_15679),U_15681),U_15683)),c_Transitive__Closure_Ortrancl(U_15679,U_15685))) ),
    inference(clausify,[status(thm)],[f_3938_4]) ).

cnf(f_3938_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15680,U_15680)),hAPP(hAPP(c_Product__Type_OPair(U_15680,U_15680),U_15682),U_15684)),c_Transitive__Closure_Ortrancl(U_15680,U_15686)))
    | sP1044(U_15682,U_15680,U_15684,U_15686) ),
    inference(clausify,[status(thm)],[f_3938_4]) ).

cnf(f_3938_7,plain,
    ( U_15681 != U_15683
    | ~ sP1043(U_15683,U_15679,U_15681,U_15685) ),
    inference(clausify,[status(thm)],[f_3938_4]) ).

cnf(f_3938_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15679,U_15679)),hAPP(hAPP(c_Product__Type_OPair(U_15679,U_15679),U_15681),U_15683)),c_Transitive__Closure_Otrancl(U_15679,U_15685)))
    | ~ sP1043(U_15683,U_15679,U_15681,U_15685) ),
    inference(clausify,[status(thm)],[f_3938_4]) ).

cnf(f_3938_9,plain,
    ( U_15682 != U_15684
    | ~ sP1044(U_15682,U_15680,U_15684,U_15686) ),
    inference(clausify,[status(thm)],[f_3938_4]) ).

cnf(f_3938_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15680,U_15680)),hAPP(hAPP(c_Product__Type_OPair(U_15680,U_15680),U_15682),U_15684)),c_Transitive__Closure_Otrancl(U_15680,U_15686)))
    | U_15682 = U_15684
    | ~ sP1044(U_15682,U_15680,U_15684,U_15686) ),
    inference(clausify,[status(thm)],[f_3938_4]) ).

fof(f_3939_1,plain,
    ! [V_y_2,V_R_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(f_3939_2,plain,
    ! [U_15690,U_15689,U_15688,U_15687] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15687,U_15687)),hAPP(hAPP(c_Product__Type_OPair(U_15687,U_15687),U_15688),U_15690)),c_Transitive__Closure_Ortrancl(U_15687,U_15689)))
          | U_15688 != U_15690 )
        & ( U_15688 = U_15690
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15687,U_15687)),hAPP(hAPP(c_Product__Type_OPair(U_15687,U_15687),U_15688),U_15690)),c_Transitive__Closure_Ortrancl(U_15687,U_15689))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_15687),U_15688),hAPP(c_Relation_ODomain(U_15687,U_15687),U_15689))) ),
    inference(variable_rename,[status(thm)],[f_3939_1]) ).

fof(f_3939_3,plain,
    ( ! [U_15687,U_15689,U_15688,U_15690] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15687,U_15687)),hAPP(hAPP(c_Product__Type_OPair(U_15687,U_15687),U_15688),U_15690)),c_Transitive__Closure_Ortrancl(U_15687,U_15689)))
        | U_15688 != U_15690
        | ~ sP1045(U_15687,U_15689,U_15688,U_15690) )
    & ! [U_15687,U_15689,U_15688,U_15690] :
        ( U_15688 = U_15690
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15687,U_15687)),hAPP(hAPP(c_Product__Type_OPair(U_15687,U_15687),U_15688),U_15690)),c_Transitive__Closure_Ortrancl(U_15687,U_15689)))
        | ~ sP1045(U_15687,U_15689,U_15688,U_15690) )
    & ! [U_15687,U_15689,U_15688,U_15690] :
        ( sP1045(U_15687,U_15689,U_15688,U_15690)
        | hBOOL(hAPP(hAPP(c_member(U_15687),U_15688),hAPP(c_Relation_ODomain(U_15687,U_15687),U_15689))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1045])],[f_3939_2]) ).

cnf(f_3939_4,plain,
    ( sP1045(U_15687,U_15689,U_15688,U_15690)
    | hBOOL(hAPP(hAPP(c_member(U_15687),U_15688),hAPP(c_Relation_ODomain(U_15687,U_15687),U_15689))) ),
    inference(clausify,[status(thm)],[f_3939_3]) ).

cnf(f_3939_5,plain,
    ( U_15688 = U_15690
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15687,U_15687)),hAPP(hAPP(c_Product__Type_OPair(U_15687,U_15687),U_15688),U_15690)),c_Transitive__Closure_Ortrancl(U_15687,U_15689)))
    | ~ sP1045(U_15687,U_15689,U_15688,U_15690) ),
    inference(clausify,[status(thm)],[f_3939_3]) ).

cnf(f_3939_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15687,U_15687)),hAPP(hAPP(c_Product__Type_OPair(U_15687,U_15687),U_15688),U_15690)),c_Transitive__Closure_Ortrancl(U_15687,U_15689)))
    | U_15688 != U_15690
    | ~ sP1045(U_15687,U_15689,U_15688,U_15690) ),
    inference(clausify,[status(thm)],[f_3939_3]) ).

fof(f_3940_1,plain,
    ! [V_b_2,V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downwards]) ).

fof(f_3940_2,plain,
    ! [U_15694,U_15693,U_15692,U_15691] :
      ( hBOOL(hAPP(hAPP(c_member(U_15691),U_15694),c_Wellfounded_Oacc(U_15691,U_15693)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15691,U_15691)),hAPP(hAPP(c_Product__Type_OPair(U_15691,U_15691),U_15694),U_15692)),c_Transitive__Closure_Ortrancl(U_15691,U_15693)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15691),U_15692),c_Wellfounded_Oacc(U_15691,U_15693))) ),
    inference(variable_rename,[status(thm)],[f_3940_1]) ).

fof(f_3940_3,plain,
    ! [U_15691,U_15692,U_15693,U_15694] :
      ( hBOOL(hAPP(hAPP(c_member(U_15691),U_15694),c_Wellfounded_Oacc(U_15691,U_15693)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15691,U_15691)),hAPP(hAPP(c_Product__Type_OPair(U_15691,U_15691),U_15694),U_15692)),c_Transitive__Closure_Ortrancl(U_15691,U_15693)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15691),U_15692),c_Wellfounded_Oacc(U_15691,U_15693))) ),
    inference(definitional_conversion,[status(esa)],[f_3940_2]) ).

cnf(f_3940_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15691),U_15694),c_Wellfounded_Oacc(U_15691,U_15693)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15691,U_15691)),hAPP(hAPP(c_Product__Type_OPair(U_15691,U_15691),U_15694),U_15692)),c_Transitive__Closure_Ortrancl(U_15691,U_15693)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15691),U_15692),c_Wellfounded_Oacc(U_15691,U_15693))) ),
    inference(clausify,[status(thm)],[f_3940_3]) ).

fof(f_3941_1,plain,
    ! [V_r_2,V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux]) ).

fof(f_3941_2,plain,
    ! [U_15698,U_15697,U_15696,U_15695] :
      ( hBOOL(hAPP(hAPP(c_member(U_15695),U_15696),c_Wellfounded_Oacc(U_15695,U_15698)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15695),U_15697),c_Wellfounded_Oacc(U_15695,U_15698)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15695,U_15695)),hAPP(hAPP(c_Product__Type_OPair(U_15695,U_15695),U_15696),U_15697)),c_Transitive__Closure_Ortrancl(U_15695,U_15698))) ),
    inference(variable_rename,[status(thm)],[f_3941_1]) ).

fof(f_3941_3,plain,
    ! [U_15695,U_15696,U_15697,U_15698] :
      ( hBOOL(hAPP(hAPP(c_member(U_15695),U_15696),c_Wellfounded_Oacc(U_15695,U_15698)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15695),U_15697),c_Wellfounded_Oacc(U_15695,U_15698)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15695,U_15695)),hAPP(hAPP(c_Product__Type_OPair(U_15695,U_15695),U_15696),U_15697)),c_Transitive__Closure_Ortrancl(U_15695,U_15698))) ),
    inference(definitional_conversion,[status(esa)],[f_3941_2]) ).

cnf(f_3941_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15695),U_15696),c_Wellfounded_Oacc(U_15695,U_15698)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15695),U_15697),c_Wellfounded_Oacc(U_15695,U_15698)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15695,U_15695)),hAPP(hAPP(c_Product__Type_OPair(U_15695,U_15695),U_15696),U_15697)),c_Transitive__Closure_Ortrancl(U_15695,U_15698))) ),
    inference(clausify,[status(thm)],[f_3941_3]) ).

fof(f_3942_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
          & c_Wellfounded_Owf(T_b,V_r_2) )
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__insert]) ).

fof(f_3942_2,plain,
    ! [U_15702,U_15701,U_15700,U_15699] :
      ( ( c_Wellfounded_Owf(U_15699,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15699,U_15699)),hAPP(hAPP(c_Product__Type_OPair(U_15699,U_15699),U_15700),U_15701)),U_15702))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15699,U_15699)),hAPP(hAPP(c_Product__Type_OPair(U_15699,U_15699),U_15701),U_15700)),c_Transitive__Closure_Ortrancl(U_15699,U_15702)))
        | ~ c_Wellfounded_Owf(U_15699,U_15702) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15699,U_15699)),hAPP(hAPP(c_Product__Type_OPair(U_15699,U_15699),U_15701),U_15700)),c_Transitive__Closure_Ortrancl(U_15699,U_15702)))
          & c_Wellfounded_Owf(U_15699,U_15702) )
        | ~ c_Wellfounded_Owf(U_15699,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15699,U_15699)),hAPP(hAPP(c_Product__Type_OPair(U_15699,U_15699),U_15700),U_15701)),U_15702)) ) ),
    inference(variable_rename,[status(thm)],[f_3942_1]) ).

fof(f_3942_3,plain,
    ( ! [U_15710,U_15708,U_15706,U_15704] :
        ( c_Wellfounded_Owf(U_15704,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15704,U_15704)),hAPP(hAPP(c_Product__Type_OPair(U_15704,U_15704),U_15706),U_15708)),U_15710))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15704,U_15704)),hAPP(hAPP(c_Product__Type_OPair(U_15704,U_15704),U_15708),U_15706)),c_Transitive__Closure_Ortrancl(U_15704,U_15710)))
        | ~ c_Wellfounded_Owf(U_15704,U_15710) )
    & ! [U_15709,U_15707,U_15705,U_15703] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15703,U_15703)),hAPP(hAPP(c_Product__Type_OPair(U_15703,U_15703),U_15707),U_15705)),c_Transitive__Closure_Ortrancl(U_15703,U_15709)))
          & c_Wellfounded_Owf(U_15703,U_15709) )
        | ~ c_Wellfounded_Owf(U_15703,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15703,U_15703)),hAPP(hAPP(c_Product__Type_OPair(U_15703,U_15703),U_15705),U_15707)),U_15709)) ) ),
    inference(miniscope,[status(thm)],[f_3942_2]) ).

fof(f_3942_4,plain,
    ( ! [U_15705,U_15707,U_15703,U_15709] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15703,U_15703)),hAPP(hAPP(c_Product__Type_OPair(U_15703,U_15703),U_15707),U_15705)),c_Transitive__Closure_Ortrancl(U_15703,U_15709)))
        | ~ sP1046(U_15705,U_15707,U_15703,U_15709) )
    & ! [U_15705,U_15707,U_15703,U_15709] :
        ( c_Wellfounded_Owf(U_15703,U_15709)
        | ~ sP1046(U_15705,U_15707,U_15703,U_15709) )
    & ! [U_15706,U_15704,U_15710,U_15708] :
        ( c_Wellfounded_Owf(U_15704,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15704,U_15704)),hAPP(hAPP(c_Product__Type_OPair(U_15704,U_15704),U_15706),U_15708)),U_15710))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15704,U_15704)),hAPP(hAPP(c_Product__Type_OPair(U_15704,U_15704),U_15708),U_15706)),c_Transitive__Closure_Ortrancl(U_15704,U_15710)))
        | ~ c_Wellfounded_Owf(U_15704,U_15710) )
    & ! [U_15705,U_15707,U_15703,U_15709] :
        ( sP1046(U_15705,U_15707,U_15703,U_15709)
        | ~ c_Wellfounded_Owf(U_15703,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15703,U_15703)),hAPP(hAPP(c_Product__Type_OPair(U_15703,U_15703),U_15705),U_15707)),U_15709)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1046])],[f_3942_3]) ).

cnf(f_3942_5,plain,
    ( sP1046(U_15705,U_15707,U_15703,U_15709)
    | ~ c_Wellfounded_Owf(U_15703,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15703,U_15703)),hAPP(hAPP(c_Product__Type_OPair(U_15703,U_15703),U_15705),U_15707)),U_15709)) ),
    inference(clausify,[status(thm)],[f_3942_4]) ).

cnf(f_3942_6,plain,
    ( c_Wellfounded_Owf(U_15704,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15704,U_15704)),hAPP(hAPP(c_Product__Type_OPair(U_15704,U_15704),U_15706),U_15708)),U_15710))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15704,U_15704)),hAPP(hAPP(c_Product__Type_OPair(U_15704,U_15704),U_15708),U_15706)),c_Transitive__Closure_Ortrancl(U_15704,U_15710)))
    | ~ c_Wellfounded_Owf(U_15704,U_15710) ),
    inference(clausify,[status(thm)],[f_3942_4]) ).

cnf(f_3942_7,plain,
    ( c_Wellfounded_Owf(U_15703,U_15709)
    | ~ sP1046(U_15705,U_15707,U_15703,U_15709) ),
    inference(clausify,[status(thm)],[f_3942_4]) ).

cnf(f_3942_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15703,U_15703)),hAPP(hAPP(c_Product__Type_OPair(U_15703,U_15703),U_15707),U_15705)),c_Transitive__Closure_Ortrancl(U_15703,U_15709)))
    | ~ sP1046(U_15705,U_15707,U_15703,U_15709) ),
    inference(clausify,[status(thm)],[f_3942_4]) ).

fof(f_3943_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
          & c_Wellfounded_Oacyclic(T_b,V_r_2) )
        | ~ c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__insert]) ).

fof(f_3943_2,plain,
    ! [U_15714,U_15713,U_15712,U_15711] :
      ( ( c_Wellfounded_Oacyclic(U_15711,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15711,U_15711)),hAPP(hAPP(c_Product__Type_OPair(U_15711,U_15711),U_15712),U_15713)),U_15714))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15711,U_15711)),hAPP(hAPP(c_Product__Type_OPair(U_15711,U_15711),U_15713),U_15712)),c_Transitive__Closure_Ortrancl(U_15711,U_15714)))
        | ~ c_Wellfounded_Oacyclic(U_15711,U_15714) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15711,U_15711)),hAPP(hAPP(c_Product__Type_OPair(U_15711,U_15711),U_15713),U_15712)),c_Transitive__Closure_Ortrancl(U_15711,U_15714)))
          & c_Wellfounded_Oacyclic(U_15711,U_15714) )
        | ~ c_Wellfounded_Oacyclic(U_15711,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15711,U_15711)),hAPP(hAPP(c_Product__Type_OPair(U_15711,U_15711),U_15712),U_15713)),U_15714)) ) ),
    inference(variable_rename,[status(thm)],[f_3943_1]) ).

fof(f_3943_3,plain,
    ( ! [U_15722,U_15720,U_15718,U_15716] :
        ( c_Wellfounded_Oacyclic(U_15716,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15716,U_15716)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15716),U_15718),U_15720)),U_15722))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15716)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15716),U_15720),U_15718)),c_Transitive__Closure_Ortrancl(U_15716,U_15722)))
        | ~ c_Wellfounded_Oacyclic(U_15716,U_15722) )
    & ! [U_15721,U_15719,U_15717,U_15715] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15715,U_15715)),hAPP(hAPP(c_Product__Type_OPair(U_15715,U_15715),U_15719),U_15717)),c_Transitive__Closure_Ortrancl(U_15715,U_15721)))
          & c_Wellfounded_Oacyclic(U_15715,U_15721) )
        | ~ c_Wellfounded_Oacyclic(U_15715,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15715,U_15715)),hAPP(hAPP(c_Product__Type_OPair(U_15715,U_15715),U_15717),U_15719)),U_15721)) ) ),
    inference(miniscope,[status(thm)],[f_3943_2]) ).

fof(f_3943_4,plain,
    ( ! [U_15715,U_15717,U_15719,U_15721] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15715,U_15715)),hAPP(hAPP(c_Product__Type_OPair(U_15715,U_15715),U_15719),U_15717)),c_Transitive__Closure_Ortrancl(U_15715,U_15721)))
        | ~ sP1047(U_15715,U_15717,U_15719,U_15721) )
    & ! [U_15715,U_15717,U_15719,U_15721] :
        ( c_Wellfounded_Oacyclic(U_15715,U_15721)
        | ~ sP1047(U_15715,U_15717,U_15719,U_15721) )
    & ! [U_15716,U_15722,U_15718,U_15720] :
        ( c_Wellfounded_Oacyclic(U_15716,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15716,U_15716)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15716),U_15718),U_15720)),U_15722))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15716)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15716),U_15720),U_15718)),c_Transitive__Closure_Ortrancl(U_15716,U_15722)))
        | ~ c_Wellfounded_Oacyclic(U_15716,U_15722) )
    & ! [U_15715,U_15717,U_15719,U_15721] :
        ( sP1047(U_15715,U_15717,U_15719,U_15721)
        | ~ c_Wellfounded_Oacyclic(U_15715,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15715,U_15715)),hAPP(hAPP(c_Product__Type_OPair(U_15715,U_15715),U_15717),U_15719)),U_15721)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1047])],[f_3943_3]) ).

cnf(f_3943_5,plain,
    ( sP1047(U_15715,U_15717,U_15719,U_15721)
    | ~ c_Wellfounded_Oacyclic(U_15715,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15715,U_15715)),hAPP(hAPP(c_Product__Type_OPair(U_15715,U_15715),U_15717),U_15719)),U_15721)) ),
    inference(clausify,[status(thm)],[f_3943_4]) ).

cnf(f_3943_6,plain,
    ( c_Wellfounded_Oacyclic(U_15716,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15716,U_15716)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15716),U_15718),U_15720)),U_15722))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15716)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15716),U_15720),U_15718)),c_Transitive__Closure_Ortrancl(U_15716,U_15722)))
    | ~ c_Wellfounded_Oacyclic(U_15716,U_15722) ),
    inference(clausify,[status(thm)],[f_3943_4]) ).

cnf(f_3943_7,plain,
    ( c_Wellfounded_Oacyclic(U_15715,U_15721)
    | ~ sP1047(U_15715,U_15717,U_15719,U_15721) ),
    inference(clausify,[status(thm)],[f_3943_4]) ).

cnf(f_3943_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15715,U_15715)),hAPP(hAPP(c_Product__Type_OPair(U_15715,U_15715),U_15719),U_15717)),c_Transitive__Closure_Ortrancl(U_15715,U_15721)))
    | ~ sP1047(U_15715,U_15717,U_15719,U_15721) ),
    inference(clausify,[status(thm)],[f_3943_4]) ).

fof(f_3944_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le]) ).

fof(f_3944_2,plain,
    ! [U_15724,U_15723] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15723),U_15724)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15723),U_15724)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15723),U_15724))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15723),U_15724)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3944_1]) ).

fof(f_3944_3,plain,
    ( ! [U_15728,U_15726] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15726),U_15728)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15726),U_15728)) )
    & ! [U_15727,U_15725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15725),U_15727))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15725),U_15727)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3944_2]) ).

fof(f_3944_4,plain,
    ( ! [U_15726,U_15728] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15726),U_15728)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15726),U_15728)) )
    & ! [U_15725,U_15727] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15725),U_15727))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15725),U_15727)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3944_3]) ).

cnf(f_3944_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15725),U_15727))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15725),U_15727)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3944_4]) ).

cnf(f_3944_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_15726),U_15728)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15726),U_15728)) ),
    inference(clausify,[status(thm)],[f_3944_4]) ).

fof(f_3945_1,plain,
    ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux]) ).

fof(f_3945_2,plain,
    ! [U_15733,U_15732,U_15731,U_15730,U_15729] :
      ( hBOOL(hAPP(hAPP(c_member(U_15729),U_15730),U_15733))
      | U_15730 = U_15731
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15729,U_15729),tc_HOL_Obool)),U_15732),hAPP(hAPP(c_Product__Type_OSigma(U_15729,U_15729),U_15733),hAPP(c_COMBK(tc_fun(U_15729,tc_HOL_Obool),U_15729),U_15733))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15729,U_15729)),hAPP(hAPP(c_Product__Type_OPair(U_15729,U_15729),U_15730),U_15731)),c_Transitive__Closure_Ortrancl(U_15729,U_15732))) ),
    inference(variable_rename,[status(thm)],[f_3945_1]) ).

fof(f_3945_3,plain,
    ! [U_15729,U_15730,U_15731,U_15732,U_15733] :
      ( hBOOL(hAPP(hAPP(c_member(U_15729),U_15730),U_15733))
      | U_15730 = U_15731
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15729,U_15729),tc_HOL_Obool)),U_15732),hAPP(hAPP(c_Product__Type_OSigma(U_15729,U_15729),U_15733),hAPP(c_COMBK(tc_fun(U_15729,tc_HOL_Obool),U_15729),U_15733))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15729,U_15729)),hAPP(hAPP(c_Product__Type_OPair(U_15729,U_15729),U_15730),U_15731)),c_Transitive__Closure_Ortrancl(U_15729,U_15732))) ),
    inference(definitional_conversion,[status(esa)],[f_3945_2]) ).

cnf(f_3945_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15729),U_15730),U_15733))
    | U_15730 = U_15731
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15729,U_15729),tc_HOL_Obool)),U_15732),hAPP(hAPP(c_Product__Type_OSigma(U_15729,U_15729),U_15733),hAPP(c_COMBK(tc_fun(U_15729,tc_HOL_Obool),U_15729),U_15733))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15729,U_15729)),hAPP(hAPP(c_Product__Type_OPair(U_15729,U_15729),U_15730),U_15731)),c_Transitive__Closure_Ortrancl(U_15729,U_15732))) ),
    inference(clausify,[status(thm)],[f_3945_3]) ).

fof(f_3946_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_irrefl__tranclI]) ).

fof(f_3946_2,plain,
    ! [U_15736,U_15735,U_15734] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15734,U_15734)),hAPP(hAPP(c_Product__Type_OPair(U_15734,U_15734),U_15736),U_15736)),c_Transitive__Closure_Otrancl(U_15734,U_15735)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15734,U_15734),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15734,U_15734),U_15735)),c_Transitive__Closure_Ortrancl(U_15734,U_15735)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15734,U_15734),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3946_1]) ).

fof(f_3946_3,plain,
    ! [U_15734,U_15735,U_15736] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15734,U_15734)),hAPP(hAPP(c_Product__Type_OPair(U_15734,U_15734),U_15736),U_15736)),c_Transitive__Closure_Otrancl(U_15734,U_15735)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15734,U_15734),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15734,U_15734),U_15735)),c_Transitive__Closure_Ortrancl(U_15734,U_15735)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15734,U_15734),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3946_2]) ).

cnf(f_3946_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15734,U_15734)),hAPP(hAPP(c_Product__Type_OPair(U_15734,U_15734),U_15736),U_15736)),c_Transitive__Closure_Otrancl(U_15734,U_15735)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15734,U_15734),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15734,U_15734),U_15735)),c_Transitive__Closure_Ortrancl(U_15734,U_15735)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15734,U_15734),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3946_3]) ).

fof(f_3947_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf]) ).

fof(f_3947_2,plain,
    ! [U_15740,U_15739,U_15738,U_15737] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15738,U_15737),U_15739),U_15740) = hAPP(hAPP(c_Finite__Set_Ofold(U_15738,U_15737,hAPP(hAPP(c_COMBB(U_15737,tc_fun(U_15737,U_15737),U_15738),c_Lattices_Osemilattice__inf__class_Oinf(U_15737)),U_15740)),c_Orderings_Otop__class_Otop(U_15737)),U_15739)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15738),U_15739))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15737) ),
    inference(variable_rename,[status(thm)],[f_3947_1]) ).

fof(f_3947_3,plain,
    ! [U_15737,U_15738,U_15739,U_15740] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15738,U_15737),U_15739),U_15740) = hAPP(hAPP(c_Finite__Set_Ofold(U_15738,U_15737,hAPP(hAPP(c_COMBB(U_15737,tc_fun(U_15737,U_15737),U_15738),c_Lattices_Osemilattice__inf__class_Oinf(U_15737)),U_15740)),c_Orderings_Otop__class_Otop(U_15737)),U_15739)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15738),U_15739))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15737) ),
    inference(definitional_conversion,[status(esa)],[f_3947_2]) ).

cnf(f_3947_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15738,U_15737),U_15739),U_15740) = hAPP(hAPP(c_Finite__Set_Ofold(U_15738,U_15737,hAPP(hAPP(c_COMBB(U_15737,tc_fun(U_15737,U_15737),U_15738),c_Lattices_Osemilattice__inf__class_Oinf(U_15737)),U_15740)),c_Orderings_Otop__class_Otop(U_15737)),U_15739)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15738),U_15739))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15737) ),
    inference(clausify,[status(thm)],[f_3947_3]) ).

fof(f_3948_1,plain,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).

fof(f_3948_2,plain,
    ! [U_15748,U_15747,U_15746,U_15745,U_15744,U_15743,U_15742,U_15741] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15741),U_15748),U_15744))
      | hBOOL(hAPP(hAPP(hAPP(U_15745,U_15748),U_15746),U_15747))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15741,tc_fun(U_15742,tc_fun(U_15743,tc_HOL_Obool))),U_15744),U_15745),U_15746),U_15747)) ),
    inference(variable_rename,[status(thm)],[f_3948_1]) ).

fof(f_3948_3,plain,
    ! [U_15741,U_15742,U_15743,U_15744,U_15745,U_15746,U_15747,U_15748] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15741),U_15748),U_15744))
      | hBOOL(hAPP(hAPP(hAPP(U_15745,U_15748),U_15746),U_15747))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15741,tc_fun(U_15742,tc_fun(U_15743,tc_HOL_Obool))),U_15744),U_15745),U_15746),U_15747)) ),
    inference(definitional_conversion,[status(esa)],[f_3948_2]) ).

cnf(f_3948_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15741),U_15748),U_15744))
    | hBOOL(hAPP(hAPP(hAPP(U_15745,U_15748),U_15746),U_15747))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15741,tc_fun(U_15742,tc_fun(U_15743,tc_HOL_Obool))),U_15744),U_15745),U_15746),U_15747)) ),
    inference(clausify,[status(thm)],[f_3948_3]) ).

fof(f_3949_1,plain,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).

fof(f_3949_2,plain,
    ! [U_15756,U_15755,U_15754,U_15753,U_15752,U_15751,U_15750,U_15749] :
      ( hBOOL(hAPP(hAPP(hAPP(U_15753,U_15756),U_15754),U_15755))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15749),U_15756),U_15752))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15749,tc_fun(U_15750,tc_fun(U_15751,tc_HOL_Obool))),U_15752),U_15753),U_15754),U_15755)) ),
    inference(variable_rename,[status(thm)],[f_3949_1]) ).

fof(f_3949_3,plain,
    ! [U_15749,U_15750,U_15751,U_15752,U_15753,U_15754,U_15755,U_15756] :
      ( hBOOL(hAPP(hAPP(hAPP(U_15753,U_15756),U_15754),U_15755))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15749),U_15756),U_15752))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15749,tc_fun(U_15750,tc_fun(U_15751,tc_HOL_Obool))),U_15752),U_15753),U_15754),U_15755)) ),
    inference(definitional_conversion,[status(esa)],[f_3949_2]) ).

cnf(f_3949_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_15753,U_15756),U_15754),U_15755))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15749),U_15756),U_15752))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15749,tc_fun(U_15750,tc_fun(U_15751,tc_HOL_Obool))),U_15752),U_15753),U_15754),U_15755)) ),
    inference(clausify,[status(thm)],[f_3949_3]) ).

fof(f_3950_1,plain,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_INT__D]) ).

fof(f_3950_2,plain,
    ! [U_15762,U_15761,U_15760,U_15759,U_15758,U_15757] :
      ( hBOOL(hAPP(hAPP(c_member(U_15757),U_15758),hAPP(U_15761,U_15762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15759),U_15762),U_15760))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15757),U_15758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15759,tc_fun(U_15757,tc_HOL_Obool)),U_15760),U_15761))) ),
    inference(variable_rename,[status(thm)],[f_3950_1]) ).

fof(f_3950_3,plain,
    ! [U_15757,U_15758,U_15759,U_15760,U_15761,U_15762] :
      ( hBOOL(hAPP(hAPP(c_member(U_15757),U_15758),hAPP(U_15761,U_15762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15759),U_15762),U_15760))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15757),U_15758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15759,tc_fun(U_15757,tc_HOL_Obool)),U_15760),U_15761))) ),
    inference(definitional_conversion,[status(esa)],[f_3950_2]) ).

cnf(f_3950_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15757),U_15758),hAPP(U_15761,U_15762)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15759),U_15762),U_15760))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15757),U_15758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15759,tc_fun(U_15757,tc_HOL_Obool)),U_15760),U_15761))) ),
    inference(clausify,[status(thm)],[f_3950_3]) ).

fof(f_3951_1,plain,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_INT__E]) ).

fof(f_3951_2,plain,
    ! [U_15768,U_15767,U_15766,U_15765,U_15764,U_15763] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15765),U_15768),U_15766))
      | hBOOL(hAPP(hAPP(c_member(U_15763),U_15764),hAPP(U_15767,U_15768)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15763),U_15764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15765,tc_fun(U_15763,tc_HOL_Obool)),U_15766),U_15767))) ),
    inference(variable_rename,[status(thm)],[f_3951_1]) ).

fof(f_3951_3,plain,
    ! [U_15763,U_15764,U_15765,U_15766,U_15767,U_15768] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15765),U_15768),U_15766))
      | hBOOL(hAPP(hAPP(c_member(U_15763),U_15764),hAPP(U_15767,U_15768)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15763),U_15764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15765,tc_fun(U_15763,tc_HOL_Obool)),U_15766),U_15767))) ),
    inference(definitional_conversion,[status(esa)],[f_3951_2]) ).

cnf(f_3951_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15765),U_15768),U_15766))
    | hBOOL(hAPP(hAPP(c_member(U_15763),U_15764),hAPP(U_15767,U_15768)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15763),U_15764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15765,tc_fun(U_15763,tc_HOL_Obool)),U_15766),U_15767))) ),
    inference(clausify,[status(thm)],[f_3951_3]) ).

fof(f_3952_1,plain,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__D]) ).

fof(f_3952_2,plain,
    ! [U_15774,U_15773,U_15772,U_15771,U_15770,U_15769] :
      ( hBOOL(hAPP(hAPP(U_15772,U_15774),U_15773))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15769),U_15774),U_15771))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15769,tc_fun(U_15770,tc_HOL_Obool)),U_15771),U_15772),U_15773)) ),
    inference(variable_rename,[status(thm)],[f_3952_1]) ).

fof(f_3952_3,plain,
    ! [U_15769,U_15770,U_15771,U_15772,U_15773,U_15774] :
      ( hBOOL(hAPP(hAPP(U_15772,U_15774),U_15773))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15769),U_15774),U_15771))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15769,tc_fun(U_15770,tc_HOL_Obool)),U_15771),U_15772),U_15773)) ),
    inference(definitional_conversion,[status(esa)],[f_3952_2]) ).

cnf(f_3952_4,plain,
    ( hBOOL(hAPP(hAPP(U_15772,U_15774),U_15773))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15769),U_15774),U_15771))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15769,tc_fun(U_15770,tc_HOL_Obool)),U_15771),U_15772),U_15773)) ),
    inference(clausify,[status(thm)],[f_3952_3]) ).

fof(f_3953_1,plain,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__E]) ).

fof(f_3953_2,plain,
    ! [U_15780,U_15779,U_15778,U_15777,U_15776,U_15775] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15775),U_15780),U_15777))
      | hBOOL(hAPP(hAPP(U_15778,U_15780),U_15779))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15775,tc_fun(U_15776,tc_HOL_Obool)),U_15777),U_15778),U_15779)) ),
    inference(variable_rename,[status(thm)],[f_3953_1]) ).

fof(f_3953_3,plain,
    ! [U_15775,U_15776,U_15777,U_15778,U_15779,U_15780] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15775),U_15780),U_15777))
      | hBOOL(hAPP(hAPP(U_15778,U_15780),U_15779))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15775,tc_fun(U_15776,tc_HOL_Obool)),U_15777),U_15778),U_15779)) ),
    inference(definitional_conversion,[status(esa)],[f_3953_2]) ).

cnf(f_3953_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15775),U_15780),U_15777))
    | hBOOL(hAPP(hAPP(U_15778,U_15780),U_15779))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15775,tc_fun(U_15776,tc_HOL_Obool)),U_15777),U_15778),U_15779)) ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

fof(f_3954_1,plain,
    ! [V_A_2,T_c,V_I_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)))
      | ! [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__INT]) ).

fof(f_3954_2,plain,
    ! [U_15785,U_15784,U_15783,U_15782] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15782,tc_fun(U_15784,tc_HOL_Obool)),U_15783),U_15785)))
      | ! [U_15781] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15784),hAPP(U_15785,U_15781)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_15782),U_15781),U_15783)) ) ),
    inference(variable_rename,[status(thm)],[f_3954_1]) ).

fof(f_3954_3,plain,
    ! [U_15782,U_15781,U_15783,U_15784,U_15785] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15782,tc_fun(U_15784,tc_HOL_Obool)),U_15783),U_15785)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15784),hAPP(U_15785,U_15781)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15782),U_15781),U_15783)) ),
    inference(definitional_conversion,[status(esa)],[f_3954_2]) ).

cnf(f_3954_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15782,tc_fun(U_15784,tc_HOL_Obool)),U_15783),U_15785)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15784),hAPP(U_15785,U_15781)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15782),U_15781),U_15783)) ),
    inference(clausify,[status(thm)],[f_3954_3]) ).

fof(f_3955_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converse]) ).

fof(f_3955_2,plain,
    ! [U_15787,U_15786] : c_Transitive__Closure_Ortrancl(U_15786,hAPP(c_Relation_Oconverse(U_15786,U_15786),U_15787)) = hAPP(c_Relation_Oconverse(U_15786,U_15786),c_Transitive__Closure_Ortrancl(U_15786,U_15787)),
    inference(variable_rename,[status(thm)],[f_3955_1]) ).

fof(f_3955_3,plain,
    ! [U_15787,U_15786] : c_Transitive__Closure_Ortrancl(U_15786,hAPP(c_Relation_Oconverse(U_15786,U_15786),U_15787)) = hAPP(c_Relation_Oconverse(U_15786,U_15786),c_Transitive__Closure_Ortrancl(U_15786,U_15787)),
    inference(definitional_conversion,[status(esa)],[f_3955_2]) ).

cnf(f_3955_4,plain,
    c_Transitive__Closure_Ortrancl(U_15786,hAPP(c_Relation_Oconverse(U_15786,U_15786),U_15787)) = hAPP(c_Relation_Oconverse(U_15786,U_15786),c_Transitive__Closure_Ortrancl(U_15786,U_15787)),
    inference(clausify,[status(thm)],[f_3955_3]) ).

fof(f_3956_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__converse]) ).

fof(f_3956_2,plain,
    ! [U_15789,U_15788] : c_Transitive__Closure_Otrancl(U_15788,hAPP(c_Relation_Oconverse(U_15788,U_15788),U_15789)) = hAPP(c_Relation_Oconverse(U_15788,U_15788),c_Transitive__Closure_Otrancl(U_15788,U_15789)),
    inference(variable_rename,[status(thm)],[f_3956_1]) ).

fof(f_3956_3,plain,
    ! [U_15788,U_15789] : c_Transitive__Closure_Otrancl(U_15788,hAPP(c_Relation_Oconverse(U_15788,U_15788),U_15789)) = hAPP(c_Relation_Oconverse(U_15788,U_15788),c_Transitive__Closure_Otrancl(U_15788,U_15789)),
    inference(definitional_conversion,[status(esa)],[f_3956_2]) ).

cnf(f_3956_4,plain,
    c_Transitive__Closure_Otrancl(U_15788,hAPP(c_Relation_Oconverse(U_15788,U_15788),U_15789)) = hAPP(c_Relation_Oconverse(U_15788,U_15788),c_Transitive__Closure_Otrancl(U_15788,U_15789)),
    inference(clausify,[status(thm)],[f_3956_3]) ).

fof(f_3957_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl]) ).

fof(f_3957_2,plain,
    ! [U_15791,U_15790] :
      ( c_Wellfounded_Owf(U_15790,hAPP(c_Relation_Oconverse(U_15790,U_15790),c_Transitive__Closure_Otrancl(U_15790,U_15791)))
      | ~ c_Wellfounded_Owf(U_15790,hAPP(c_Relation_Oconverse(U_15790,U_15790),U_15791)) ),
    inference(variable_rename,[status(thm)],[f_3957_1]) ).

fof(f_3957_3,plain,
    ! [U_15790,U_15791] :
      ( c_Wellfounded_Owf(U_15790,hAPP(c_Relation_Oconverse(U_15790,U_15790),c_Transitive__Closure_Otrancl(U_15790,U_15791)))
      | ~ c_Wellfounded_Owf(U_15790,hAPP(c_Relation_Oconverse(U_15790,U_15790),U_15791)) ),
    inference(definitional_conversion,[status(esa)],[f_3957_2]) ).

cnf(f_3957_4,plain,
    ( c_Wellfounded_Owf(U_15790,hAPP(c_Relation_Oconverse(U_15790,U_15790),c_Transitive__Closure_Otrancl(U_15790,U_15791)))
    | ~ c_Wellfounded_Owf(U_15790,hAPP(c_Relation_Oconverse(U_15790,U_15790),U_15791)) ),
    inference(clausify,[status(thm)],[f_3957_3]) ).

fof(f_3958_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Range__converse]) ).

fof(f_3958_2,plain,
    ! [U_15794,U_15793,U_15792] : hAPP(c_Relation_ORange(U_15792,U_15793),hAPP(c_Relation_Oconverse(U_15793,U_15792),U_15794)) = hAPP(c_Relation_ODomain(U_15793,U_15792),U_15794),
    inference(variable_rename,[status(thm)],[f_3958_1]) ).

fof(f_3958_3,plain,
    ! [U_15792,U_15793,U_15794] : hAPP(c_Relation_ORange(U_15792,U_15793),hAPP(c_Relation_Oconverse(U_15793,U_15792),U_15794)) = hAPP(c_Relation_ODomain(U_15793,U_15792),U_15794),
    inference(definitional_conversion,[status(esa)],[f_3958_2]) ).

cnf(f_3958_4,plain,
    hAPP(c_Relation_ORange(U_15792,U_15793),hAPP(c_Relation_Oconverse(U_15793,U_15792),U_15794)) = hAPP(c_Relation_ODomain(U_15793,U_15792),U_15794),
    inference(clausify,[status(thm)],[f_3958_3]) ).

fof(f_3959_1,plain,
    ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Domain__converse]) ).

fof(f_3959_2,plain,
    ! [U_15797,U_15796,U_15795] : hAPP(c_Relation_ODomain(U_15795,U_15796),hAPP(c_Relation_Oconverse(U_15796,U_15795),U_15797)) = hAPP(c_Relation_ORange(U_15796,U_15795),U_15797),
    inference(variable_rename,[status(thm)],[f_3959_1]) ).

fof(f_3959_3,plain,
    ! [U_15795,U_15796,U_15797] : hAPP(c_Relation_ODomain(U_15795,U_15796),hAPP(c_Relation_Oconverse(U_15796,U_15795),U_15797)) = hAPP(c_Relation_ORange(U_15796,U_15795),U_15797),
    inference(definitional_conversion,[status(esa)],[f_3959_2]) ).

cnf(f_3959_4,plain,
    hAPP(c_Relation_ODomain(U_15795,U_15796),hAPP(c_Relation_Oconverse(U_15796,U_15795),U_15797)) = hAPP(c_Relation_ORange(U_15796,U_15795),U_15797),
    inference(clausify,[status(thm)],[f_3959_3]) ).

fof(f_3960_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__def]) ).

fof(f_3960_2,plain,
    ! [U_15800,U_15799,U_15798] : hAPP(c_Relation_ORange(U_15798,U_15799),U_15800) = hAPP(c_Relation_ODomain(U_15799,U_15798),hAPP(c_Relation_Oconverse(U_15798,U_15799),U_15800)),
    inference(variable_rename,[status(thm)],[f_3960_1]) ).

fof(f_3960_3,plain,
    ! [U_15798,U_15799,U_15800] : hAPP(c_Relation_ORange(U_15798,U_15799),U_15800) = hAPP(c_Relation_ODomain(U_15799,U_15798),hAPP(c_Relation_Oconverse(U_15798,U_15799),U_15800)),
    inference(definitional_conversion,[status(esa)],[f_3960_2]) ).

cnf(f_3960_4,plain,
    hAPP(c_Relation_ORange(U_15798,U_15799),U_15800) = hAPP(c_Relation_ODomain(U_15799,U_15798),hAPP(c_Relation_Oconverse(U_15798,U_15799),U_15800)),
    inference(clausify,[status(thm)],[f_3960_3]) ).

fof(f_3961_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__INT]) ).

fof(f_3961_2,plain,
    ! [U_15806,U_15805,U_15804,U_15803,U_15802,U_15801] : hAPP(c_Set_Ovimage(U_15801,U_15802,U_15803),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15804,tc_fun(U_15802,tc_HOL_Obool)),U_15805),U_15806)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15804,tc_fun(U_15801,tc_HOL_Obool)),U_15805),hAPP(hAPP(c_COMBB(tc_fun(U_15802,tc_HOL_Obool),tc_fun(U_15801,tc_HOL_Obool),U_15804),c_Set_Ovimage(U_15801,U_15802,U_15803)),U_15806)),
    inference(variable_rename,[status(thm)],[f_3961_1]) ).

fof(f_3961_3,plain,
    ! [U_15801,U_15802,U_15803,U_15804,U_15805,U_15806] : hAPP(c_Set_Ovimage(U_15801,U_15802,U_15803),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15804,tc_fun(U_15802,tc_HOL_Obool)),U_15805),U_15806)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15804,tc_fun(U_15801,tc_HOL_Obool)),U_15805),hAPP(hAPP(c_COMBB(tc_fun(U_15802,tc_HOL_Obool),tc_fun(U_15801,tc_HOL_Obool),U_15804),c_Set_Ovimage(U_15801,U_15802,U_15803)),U_15806)),
    inference(definitional_conversion,[status(esa)],[f_3961_2]) ).

cnf(f_3961_4,plain,
    hAPP(c_Set_Ovimage(U_15801,U_15802,U_15803),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15804,tc_fun(U_15802,tc_HOL_Obool)),U_15805),U_15806)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15804,tc_fun(U_15801,tc_HOL_Obool)),U_15805),hAPP(hAPP(c_COMBB(tc_fun(U_15802,tc_HOL_Obool),tc_fun(U_15801,tc_HOL_Obool),U_15804),c_Set_Ovimage(U_15801,U_15802,U_15803)),U_15806)),
    inference(clausify,[status(thm)],[f_3961_3]) ).

fof(f_3962_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
      & ( c_Wellfounded_Oacyclic(T_b,V_r_2)
        | ~ c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__converse]) ).

fof(f_3962_2,plain,
    ! [U_15808,U_15807] :
      ( ( c_Wellfounded_Oacyclic(U_15807,hAPP(c_Relation_Oconverse(U_15807,U_15807),U_15808))
        | ~ c_Wellfounded_Oacyclic(U_15807,U_15808) )
      & ( c_Wellfounded_Oacyclic(U_15807,U_15808)
        | ~ c_Wellfounded_Oacyclic(U_15807,hAPP(c_Relation_Oconverse(U_15807,U_15807),U_15808)) ) ),
    inference(variable_rename,[status(thm)],[f_3962_1]) ).

fof(f_3962_3,plain,
    ( ! [U_15812,U_15810] :
        ( c_Wellfounded_Oacyclic(U_15810,hAPP(c_Relation_Oconverse(U_15810,U_15810),U_15812))
        | ~ c_Wellfounded_Oacyclic(U_15810,U_15812) )
    & ! [U_15811,U_15809] :
        ( c_Wellfounded_Oacyclic(U_15809,U_15811)
        | ~ c_Wellfounded_Oacyclic(U_15809,hAPP(c_Relation_Oconverse(U_15809,U_15809),U_15811)) ) ),
    inference(miniscope,[status(thm)],[f_3962_2]) ).

fof(f_3962_4,plain,
    ( ! [U_15810,U_15812] :
        ( c_Wellfounded_Oacyclic(U_15810,hAPP(c_Relation_Oconverse(U_15810,U_15810),U_15812))
        | ~ c_Wellfounded_Oacyclic(U_15810,U_15812) )
    & ! [U_15811,U_15809] :
        ( c_Wellfounded_Oacyclic(U_15809,U_15811)
        | ~ c_Wellfounded_Oacyclic(U_15809,hAPP(c_Relation_Oconverse(U_15809,U_15809),U_15811)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3962_3]) ).

cnf(f_3962_5,plain,
    ( c_Wellfounded_Oacyclic(U_15809,U_15811)
    | ~ c_Wellfounded_Oacyclic(U_15809,hAPP(c_Relation_Oconverse(U_15809,U_15809),U_15811)) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

cnf(f_3962_6,plain,
    ( c_Wellfounded_Oacyclic(U_15810,hAPP(c_Relation_Oconverse(U_15810,U_15810),U_15812))
    | ~ c_Wellfounded_Oacyclic(U_15810,U_15812) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

fof(f_3963_1,plain,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).

fof(f_3963_2,plain,
    ! [U_15816,U_15815,U_15814,U_15813] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15814,tc_fun(U_15815,tc_HOL_Obool)),U_15813),hAPP(c_COMBK(tc_fun(U_15815,tc_HOL_Obool),U_15814),U_15816)) = U_15816
        | U_15813 = c_Orderings_Obot__class_Obot(tc_fun(U_15814,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15814,tc_fun(U_15815,tc_HOL_Obool)),U_15813),hAPP(c_COMBK(tc_fun(U_15815,tc_HOL_Obool),U_15814),U_15816)) = c_Orderings_Otop__class_Otop(tc_fun(U_15815,tc_HOL_Obool))
        | U_15813 != c_Orderings_Obot__class_Obot(tc_fun(U_15814,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3963_1]) ).

fof(f_3963_3,plain,
    ( ! [U_15824,U_15822,U_15820,U_15818] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15820,tc_fun(U_15822,tc_HOL_Obool)),U_15818),hAPP(c_COMBK(tc_fun(U_15822,tc_HOL_Obool),U_15820),U_15824)) = U_15824
        | U_15818 = c_Orderings_Obot__class_Obot(tc_fun(U_15820,tc_HOL_Obool)) )
    & ! [U_15823,U_15821,U_15819,U_15817] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15819,tc_fun(U_15821,tc_HOL_Obool)),U_15817),hAPP(c_COMBK(tc_fun(U_15821,tc_HOL_Obool),U_15819),U_15823)) = c_Orderings_Otop__class_Otop(tc_fun(U_15821,tc_HOL_Obool))
        | U_15817 != c_Orderings_Obot__class_Obot(tc_fun(U_15819,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3963_2]) ).

fof(f_3963_4,plain,
    ( ! [U_15818,U_15820,U_15822,U_15824] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15820,tc_fun(U_15822,tc_HOL_Obool)),U_15818),hAPP(c_COMBK(tc_fun(U_15822,tc_HOL_Obool),U_15820),U_15824)) = U_15824
        | U_15818 = c_Orderings_Obot__class_Obot(tc_fun(U_15820,tc_HOL_Obool)) )
    & ! [U_15821,U_15823,U_15819,U_15817] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15819,tc_fun(U_15821,tc_HOL_Obool)),U_15817),hAPP(c_COMBK(tc_fun(U_15821,tc_HOL_Obool),U_15819),U_15823)) = c_Orderings_Otop__class_Otop(tc_fun(U_15821,tc_HOL_Obool))
        | U_15817 != c_Orderings_Obot__class_Obot(tc_fun(U_15819,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3963_3]) ).

cnf(f_3963_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15819,tc_fun(U_15821,tc_HOL_Obool)),U_15817),hAPP(c_COMBK(tc_fun(U_15821,tc_HOL_Obool),U_15819),U_15823)) = c_Orderings_Otop__class_Otop(tc_fun(U_15821,tc_HOL_Obool))
    | U_15817 != c_Orderings_Obot__class_Obot(tc_fun(U_15819,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3963_4]) ).

cnf(f_3963_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15820,tc_fun(U_15822,tc_HOL_Obool)),U_15818),hAPP(c_COMBK(tc_fun(U_15822,tc_HOL_Obool),U_15820),U_15824)) = U_15824
    | U_15818 = c_Orderings_Obot__class_Obot(tc_fun(U_15820,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3963_4]) ).

fof(f_3964_1,plain,
    ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_INT__empty]) ).

fof(f_3964_2,plain,
    ! [U_15827,U_15826,U_15825] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15825,tc_fun(U_15826,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15825,tc_HOL_Obool))),U_15827) = c_Orderings_Otop__class_Otop(tc_fun(U_15826,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3964_1]) ).

fof(f_3964_3,plain,
    ! [U_15825,U_15826,U_15827] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15825,tc_fun(U_15826,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15825,tc_HOL_Obool))),U_15827) = c_Orderings_Otop__class_Otop(tc_fun(U_15826,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3964_2]) ).

cnf(f_3964_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15825,tc_fun(U_15826,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15825,tc_HOL_Obool))),U_15827) = c_Orderings_Otop__class_Otop(tc_fun(U_15826,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3964_3]) ).

fof(f_3965_1,plain,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INF__const]) ).

fof(f_3965_2,plain,
    ! [U_15831,U_15830,U_15829,U_15828] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15830,U_15828),U_15829),hAPP(c_COMBK(U_15828,U_15830),U_15831)) = U_15831
      | U_15829 = c_Orderings_Obot__class_Obot(tc_fun(U_15830,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15828) ),
    inference(variable_rename,[status(thm)],[f_3965_1]) ).

fof(f_3965_3,plain,
    ! [U_15828,U_15829,U_15830,U_15831] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15830,U_15828),U_15829),hAPP(c_COMBK(U_15828,U_15830),U_15831)) = U_15831
      | U_15829 = c_Orderings_Obot__class_Obot(tc_fun(U_15830,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15828) ),
    inference(definitional_conversion,[status(esa)],[f_3965_2]) ).

cnf(f_3965_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15830,U_15828),U_15829),hAPP(c_COMBK(U_15828,U_15830),U_15831)) = U_15831
    | U_15829 = c_Orderings_Obot__class_Obot(tc_fun(U_15830,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15828) ),
    inference(clausify,[status(thm)],[f_3965_3]) ).

fof(f_3966_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J]) ).

fof(f_3966_2,plain,
    ! [U_15836,U_15835,U_15834,U_15833,U_15832] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15834,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15833,tc_fun(U_15834,tc_HOL_Obool)),U_15832),U_15835)),U_15836) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15833,tc_fun(U_15834,tc_HOL_Obool)),U_15832),hAPP(hAPP(c_COMBC(U_15833,tc_fun(U_15834,tc_HOL_Obool),tc_fun(U_15834,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15834,tc_HOL_Obool),tc_fun(tc_fun(U_15834,tc_HOL_Obool),tc_fun(U_15834,tc_HOL_Obool)),U_15833),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15834,tc_HOL_Obool))),U_15835)),U_15836))
        | U_15832 = c_Orderings_Obot__class_Obot(tc_fun(U_15833,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15834,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15833,tc_fun(U_15834,tc_HOL_Obool)),U_15832),U_15835)),U_15836) = U_15836
        | U_15832 != c_Orderings_Obot__class_Obot(tc_fun(U_15833,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3966_1]) ).

fof(f_3966_3,plain,
    ( ! [U_15846,U_15844,U_15842,U_15840,U_15838] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15842,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15840,tc_fun(U_15842,tc_HOL_Obool)),U_15838),U_15844)),U_15846) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15840,tc_fun(U_15842,tc_HOL_Obool)),U_15838),hAPP(hAPP(c_COMBC(U_15840,tc_fun(U_15842,tc_HOL_Obool),tc_fun(U_15842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15842,tc_HOL_Obool),tc_fun(tc_fun(U_15842,tc_HOL_Obool),tc_fun(U_15842,tc_HOL_Obool)),U_15840),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15842,tc_HOL_Obool))),U_15844)),U_15846))
        | U_15838 = c_Orderings_Obot__class_Obot(tc_fun(U_15840,tc_HOL_Obool)) )
    & ! [U_15845,U_15843,U_15841,U_15839,U_15837] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15841,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15839,tc_fun(U_15841,tc_HOL_Obool)),U_15837),U_15843)),U_15845) = U_15845
        | U_15837 != c_Orderings_Obot__class_Obot(tc_fun(U_15839,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3966_2]) ).

fof(f_3966_4,plain,
    ( ! [U_15846,U_15838,U_15840,U_15842,U_15844] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15842,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15840,tc_fun(U_15842,tc_HOL_Obool)),U_15838),U_15844)),U_15846) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15840,tc_fun(U_15842,tc_HOL_Obool)),U_15838),hAPP(hAPP(c_COMBC(U_15840,tc_fun(U_15842,tc_HOL_Obool),tc_fun(U_15842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15842,tc_HOL_Obool),tc_fun(tc_fun(U_15842,tc_HOL_Obool),tc_fun(U_15842,tc_HOL_Obool)),U_15840),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15842,tc_HOL_Obool))),U_15844)),U_15846))
        | U_15838 = c_Orderings_Obot__class_Obot(tc_fun(U_15840,tc_HOL_Obool)) )
    & ! [U_15839,U_15843,U_15837,U_15845,U_15841] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15841,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15839,tc_fun(U_15841,tc_HOL_Obool)),U_15837),U_15843)),U_15845) = U_15845
        | U_15837 != c_Orderings_Obot__class_Obot(tc_fun(U_15839,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3966_3]) ).

cnf(f_3966_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15841,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15839,tc_fun(U_15841,tc_HOL_Obool)),U_15837),U_15843)),U_15845) = U_15845
    | U_15837 != c_Orderings_Obot__class_Obot(tc_fun(U_15839,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3966_4]) ).

cnf(f_3966_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15842,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15840,tc_fun(U_15842,tc_HOL_Obool)),U_15838),U_15844)),U_15846) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15840,tc_fun(U_15842,tc_HOL_Obool)),U_15838),hAPP(hAPP(c_COMBC(U_15840,tc_fun(U_15842,tc_HOL_Obool),tc_fun(U_15842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15842,tc_HOL_Obool),tc_fun(tc_fun(U_15842,tc_HOL_Obool),tc_fun(U_15842,tc_HOL_Obool)),U_15840),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15842,tc_HOL_Obool))),U_15844)),U_15846))
    | U_15838 = c_Orderings_Obot__class_Obot(tc_fun(U_15840,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3966_4]) ).

fof(f_3967_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J]) ).

fof(f_3967_2,plain,
    ! [U_15851,U_15850,U_15849,U_15848,U_15847] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15849,tc_HOL_Obool)),U_15850),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15848,tc_fun(U_15849,tc_HOL_Obool)),U_15847),U_15851)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15848,tc_fun(U_15849,tc_HOL_Obool)),U_15847),hAPP(hAPP(c_COMBB(tc_fun(U_15849,tc_HOL_Obool),tc_fun(U_15849,tc_HOL_Obool),U_15848),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15849,tc_HOL_Obool)),U_15850)),U_15851))
        | U_15847 = c_Orderings_Obot__class_Obot(tc_fun(U_15848,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15849,tc_HOL_Obool)),U_15850),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15848,tc_fun(U_15849,tc_HOL_Obool)),U_15847),U_15851)) = U_15850
        | U_15847 != c_Orderings_Obot__class_Obot(tc_fun(U_15848,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3967_1]) ).

fof(f_3967_3,plain,
    ( ! [U_15861,U_15859,U_15857,U_15855,U_15853] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15857,tc_HOL_Obool)),U_15859),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15855,tc_fun(U_15857,tc_HOL_Obool)),U_15853),U_15861)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15855,tc_fun(U_15857,tc_HOL_Obool)),U_15853),hAPP(hAPP(c_COMBB(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool),U_15855),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15857,tc_HOL_Obool)),U_15859)),U_15861))
        | U_15853 = c_Orderings_Obot__class_Obot(tc_fun(U_15855,tc_HOL_Obool)) )
    & ! [U_15860,U_15858,U_15856,U_15854,U_15852] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15856,tc_HOL_Obool)),U_15858),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15854,tc_fun(U_15856,tc_HOL_Obool)),U_15852),U_15860)) = U_15858
        | U_15852 != c_Orderings_Obot__class_Obot(tc_fun(U_15854,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3967_2]) ).

fof(f_3967_4,plain,
    ( ! [U_15853,U_15855,U_15857,U_15859,U_15861] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15857,tc_HOL_Obool)),U_15859),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15855,tc_fun(U_15857,tc_HOL_Obool)),U_15853),U_15861)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15855,tc_fun(U_15857,tc_HOL_Obool)),U_15853),hAPP(hAPP(c_COMBB(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool),U_15855),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15857,tc_HOL_Obool)),U_15859)),U_15861))
        | U_15853 = c_Orderings_Obot__class_Obot(tc_fun(U_15855,tc_HOL_Obool)) )
    & ! [U_15854,U_15858,U_15856,U_15852,U_15860] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15856,tc_HOL_Obool)),U_15858),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15854,tc_fun(U_15856,tc_HOL_Obool)),U_15852),U_15860)) = U_15858
        | U_15852 != c_Orderings_Obot__class_Obot(tc_fun(U_15854,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3967_3]) ).

cnf(f_3967_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15856,tc_HOL_Obool)),U_15858),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15854,tc_fun(U_15856,tc_HOL_Obool)),U_15852),U_15860)) = U_15858
    | U_15852 != c_Orderings_Obot__class_Obot(tc_fun(U_15854,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3967_4]) ).

cnf(f_3967_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15857,tc_HOL_Obool)),U_15859),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15855,tc_fun(U_15857,tc_HOL_Obool)),U_15853),U_15861)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15855,tc_fun(U_15857,tc_HOL_Obool)),U_15853),hAPP(hAPP(c_COMBB(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool),U_15855),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15857,tc_HOL_Obool)),U_15859)),U_15861))
    | U_15853 = c_Orderings_Obot__class_Obot(tc_fun(U_15855,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3967_4]) ).

fof(f_3968_1,plain,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__rel__comp]) ).

fof(f_3968_2,plain,
    ! [U_15866,U_15865,U_15864,U_15863,U_15862] : hAPP(c_Relation_Oconverse(U_15862,U_15863),hAPP(hAPP(c_Relation_Orel__comp(U_15862,U_15864,U_15863),U_15865),U_15866)) = hAPP(hAPP(c_Relation_Orel__comp(U_15863,U_15864,U_15862),hAPP(c_Relation_Oconverse(U_15864,U_15863),U_15866)),hAPP(c_Relation_Oconverse(U_15862,U_15864),U_15865)),
    inference(variable_rename,[status(thm)],[f_3968_1]) ).

fof(f_3968_3,plain,
    ! [U_15862,U_15863,U_15864,U_15865,U_15866] : hAPP(c_Relation_Oconverse(U_15862,U_15863),hAPP(hAPP(c_Relation_Orel__comp(U_15862,U_15864,U_15863),U_15865),U_15866)) = hAPP(hAPP(c_Relation_Orel__comp(U_15863,U_15864,U_15862),hAPP(c_Relation_Oconverse(U_15864,U_15863),U_15866)),hAPP(c_Relation_Oconverse(U_15862,U_15864),U_15865)),
    inference(definitional_conversion,[status(esa)],[f_3968_2]) ).

cnf(f_3968_4,plain,
    hAPP(c_Relation_Oconverse(U_15862,U_15863),hAPP(hAPP(c_Relation_Orel__comp(U_15862,U_15864,U_15863),U_15865),U_15866)) = hAPP(hAPP(c_Relation_Orel__comp(U_15863,U_15864,U_15862),hAPP(c_Relation_Oconverse(U_15864,U_15863),U_15866)),hAPP(c_Relation_Oconverse(U_15862,U_15864),U_15865)),
    inference(clausify,[status(thm)],[f_3968_3]) ).

fof(f_3969_1,plain,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__Un]) ).

fof(f_3969_2,plain,
    ! [U_15871,U_15870,U_15869,U_15868,U_15867] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15867,tc_HOL_Obool)),U_15869),U_15870)),U_15871) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15868,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),U_15869),U_15871)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),U_15870),U_15871)),
    inference(variable_rename,[status(thm)],[f_3969_1]) ).

fof(f_3969_3,plain,
    ! [U_15867,U_15868,U_15869,U_15870,U_15871] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15867,tc_HOL_Obool)),U_15869),U_15870)),U_15871) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15868,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),U_15869),U_15871)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),U_15870),U_15871)),
    inference(definitional_conversion,[status(esa)],[f_3969_2]) ).

cnf(f_3969_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15867,tc_HOL_Obool)),U_15869),U_15870)),U_15871) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15868,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),U_15869),U_15871)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15867,tc_fun(U_15868,tc_HOL_Obool)),U_15870),U_15871)),
    inference(clausify,[status(thm)],[f_3969_3]) ).

fof(f_3970_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__insert]) ).

fof(f_3970_2,plain,
    ! [U_15876,U_15875,U_15874,U_15873,U_15872] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15872,tc_fun(U_15873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_15872),U_15874),U_15875)),U_15876) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15873,tc_HOL_Obool)),hAPP(U_15876,U_15874)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15872,tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15876)),
    inference(variable_rename,[status(thm)],[f_3970_1]) ).

fof(f_3970_3,plain,
    ! [U_15872,U_15873,U_15874,U_15875,U_15876] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15872,tc_fun(U_15873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_15872),U_15874),U_15875)),U_15876) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15873,tc_HOL_Obool)),hAPP(U_15876,U_15874)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15872,tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15876)),
    inference(definitional_conversion,[status(esa)],[f_3970_2]) ).

cnf(f_3970_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15872,tc_fun(U_15873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_15872),U_15874),U_15875)),U_15876) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15873,tc_HOL_Obool)),hAPP(U_15876,U_15874)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15872,tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15876)),
    inference(clausify,[status(thm)],[f_3970_3]) ).

fof(f_3971_1,plain,
    ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__INF__iff]) ).

fof(f_3971_2,plain,
    ! [U_15883,U_15882,U_15881,U_15880,U_15879] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883)))
          | ? [U_15878] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,U_15878)))
              & hBOOL(hAPP(hAPP(c_member(U_15881),U_15878),U_15882)) ) )
        & ( ! [U_15877] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,U_15877)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15881),U_15877),U_15882)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15879) ),
    inference(variable_rename,[status(thm)],[f_3971_1]) ).

fof(f_3971_3,plain,
    ! [U_15883,U_15882,U_15881,U_15880,U_15879] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,sK380(U_15883,U_15882,U_15881,U_15880,U_15879))))
            & hBOOL(hAPP(hAPP(c_member(U_15881),sK380(U_15883,U_15882,U_15881,U_15880,U_15879)),U_15882)) ) )
        & ( ! [U_15877] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,U_15877)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15881),U_15877),U_15882)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15879) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_15878,sK380(U_15883,U_15882,U_15881,U_15880,U_15879))],[f_3971_2]) ).

fof(f_3971_4,plain,
    ( ! [U_15879,U_15880,U_15881,U_15882,U_15883] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,sK380(U_15883,U_15882,U_15881,U_15880,U_15879))))
        | ~ sP1048(U_15879,U_15880,U_15881,U_15882,U_15883) )
    & ! [U_15879,U_15880,U_15881,U_15882,U_15883] :
        ( hBOOL(hAPP(hAPP(c_member(U_15881),sK380(U_15883,U_15882,U_15881,U_15880,U_15879)),U_15882))
        | ~ sP1048(U_15879,U_15880,U_15881,U_15882,U_15883) )
    & ! [U_15877,U_15879,U_15880,U_15881,U_15882,U_15883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883)))
        | sP1048(U_15879,U_15880,U_15881,U_15882,U_15883)
        | ~ sP1049(U_15877,U_15879,U_15880,U_15881,U_15882,U_15883) )
    & ! [U_15877,U_15879,U_15880,U_15881,U_15882,U_15883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,U_15877)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15881),U_15877),U_15882))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883)))
        | ~ sP1049(U_15877,U_15879,U_15880,U_15881,U_15882,U_15883) )
    & ! [U_15877,U_15879,U_15880,U_15881,U_15882,U_15883] :
        ( sP1049(U_15877,U_15879,U_15880,U_15881,U_15882,U_15883)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_15879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1048,sP1049])],[f_3971_3]) ).

cnf(f_3971_5,plain,
    ( sP1049(U_15877,U_15879,U_15880,U_15881,U_15882,U_15883)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15879) ),
    inference(clausify,[status(thm)],[f_3971_4]) ).

cnf(f_3971_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,U_15877)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15881),U_15877),U_15882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883)))
    | ~ sP1049(U_15877,U_15879,U_15880,U_15881,U_15882,U_15883) ),
    inference(clausify,[status(thm)],[f_3971_4]) ).

cnf(f_3971_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15881,U_15879),U_15882),U_15883)))
    | sP1048(U_15879,U_15880,U_15881,U_15882,U_15883)
    | ~ sP1049(U_15877,U_15879,U_15880,U_15881,U_15882,U_15883) ),
    inference(clausify,[status(thm)],[f_3971_4]) ).

cnf(f_3971_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15881),sK380(U_15883,U_15882,U_15881,U_15880,U_15879)),U_15882))
    | ~ sP1048(U_15879,U_15880,U_15881,U_15882,U_15883) ),
    inference(clausify,[status(thm)],[f_3971_4]) ).

cnf(f_3971_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15880),hAPP(U_15883,sK380(U_15883,U_15882,U_15881,U_15880,U_15879))))
    | ~ sP1048(U_15879,U_15880,U_15881,U_15882,U_15883) ),
    inference(clausify,[status(thm)],[f_3971_4]) ).

fof(f_3972_1,plain,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib]) ).

fof(f_3972_2,plain,
    ! [U_15889,U_15888,U_15887,U_15886,U_15885,U_15884] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15884,tc_fun(U_15887,tc_HOL_Obool)),U_15886),hAPP(hAPP(c_COMBB(tc_fun(U_15887,tc_HOL_Obool),tc_fun(U_15887,tc_HOL_Obool),U_15884),hAPP(c_Set_Oinsert(U_15887),U_15888)),U_15889)) = hAPP(hAPP(c_Set_Oinsert(U_15887),U_15888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15884,tc_fun(U_15887,tc_HOL_Obool)),U_15886),U_15889))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15884),U_15885),U_15886)) ),
    inference(variable_rename,[status(thm)],[f_3972_1]) ).

fof(f_3972_3,plain,
    ! [U_15889,U_15888,U_15884,U_15885,U_15886,U_15887] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15884,tc_fun(U_15887,tc_HOL_Obool)),U_15886),hAPP(hAPP(c_COMBB(tc_fun(U_15887,tc_HOL_Obool),tc_fun(U_15887,tc_HOL_Obool),U_15884),hAPP(c_Set_Oinsert(U_15887),U_15888)),U_15889)) = hAPP(hAPP(c_Set_Oinsert(U_15887),U_15888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15884,tc_fun(U_15887,tc_HOL_Obool)),U_15886),U_15889))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15884),U_15885),U_15886)) ),
    inference(definitional_conversion,[status(esa)],[f_3972_2]) ).

cnf(f_3972_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15884,tc_fun(U_15887,tc_HOL_Obool)),U_15886),hAPP(hAPP(c_COMBB(tc_fun(U_15887,tc_HOL_Obool),tc_fun(U_15887,tc_HOL_Obool),U_15884),hAPP(c_Set_Oinsert(U_15887),U_15888)),U_15889)) = hAPP(hAPP(c_Set_Oinsert(U_15887),U_15888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15884,tc_fun(U_15887,tc_HOL_Obool)),U_15886),U_15889))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15884),U_15885),U_15886)) ),
    inference(clausify,[status(thm)],[f_3972_3]) ).

fof(f_3973_1,plain,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__lower]) ).

fof(f_3973_2,plain,
    ! [U_15894,U_15893,U_15892,U_15891,U_15890] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15893,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15890,tc_fun(U_15893,tc_HOL_Obool)),U_15892),U_15894)),hAPP(U_15894,U_15891)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15890),U_15891),U_15892)) ),
    inference(variable_rename,[status(thm)],[f_3973_1]) ).

fof(f_3973_3,plain,
    ! [U_15891,U_15890,U_15892,U_15893,U_15894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15893,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15890,tc_fun(U_15893,tc_HOL_Obool)),U_15892),U_15894)),hAPP(U_15894,U_15891)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15890),U_15891),U_15892)) ),
    inference(definitional_conversion,[status(esa)],[f_3973_2]) ).

cnf(f_3973_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15893,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15890,tc_fun(U_15893,tc_HOL_Obool)),U_15892),U_15894)),hAPP(U_15894,U_15891)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15890),U_15891),U_15892)) ),
    inference(clausify,[status(thm)],[f_3973_3]) ).

fof(f_3974_1,plain,
    ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(f_3974_2,plain,
    ! [U_15899,U_15898,U_15897,U_15896,U_15895] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15895,tc_fun(U_15896,tc_HOL_Obool)),U_15897),hAPP(hAPP(c_COMBB(tc_fun(U_15896,tc_HOL_Obool),tc_fun(U_15896,tc_HOL_Obool),U_15895),hAPP(c_Set_Oinsert(U_15896),U_15898)),U_15899)) = hAPP(hAPP(c_Set_Oinsert(U_15896),U_15898),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15895,tc_fun(U_15896,tc_HOL_Obool)),U_15897),U_15899)),
    inference(variable_rename,[status(thm)],[f_3974_1]) ).

fof(f_3974_3,plain,
    ! [U_15895,U_15896,U_15897,U_15898,U_15899] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15895,tc_fun(U_15896,tc_HOL_Obool)),U_15897),hAPP(hAPP(c_COMBB(tc_fun(U_15896,tc_HOL_Obool),tc_fun(U_15896,tc_HOL_Obool),U_15895),hAPP(c_Set_Oinsert(U_15896),U_15898)),U_15899)) = hAPP(hAPP(c_Set_Oinsert(U_15896),U_15898),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15895,tc_fun(U_15896,tc_HOL_Obool)),U_15897),U_15899)),
    inference(definitional_conversion,[status(esa)],[f_3974_2]) ).

cnf(f_3974_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15895,tc_fun(U_15896,tc_HOL_Obool)),U_15897),hAPP(hAPP(c_COMBB(tc_fun(U_15896,tc_HOL_Obool),tc_fun(U_15896,tc_HOL_Obool),U_15895),hAPP(c_Set_Oinsert(U_15896),U_15898)),U_15899)) = hAPP(hAPP(c_Set_Oinsert(U_15896),U_15898),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15895,tc_fun(U_15896,tc_HOL_Obool)),U_15897),U_15899)),
    inference(clausify,[status(thm)],[f_3974_3]) ).

fof(f_3975_1,plain,
    ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(f_3975_2,plain,
    ! [U_15904,U_15903,U_15902,U_15901,U_15900] : hAPP(hAPP(c_Set_Oinsert(U_15900),U_15901),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15902,tc_fun(U_15900,tc_HOL_Obool)),U_15903),U_15904)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15902,tc_fun(U_15900,tc_HOL_Obool)),U_15903),hAPP(hAPP(c_COMBB(tc_fun(U_15900,tc_HOL_Obool),tc_fun(U_15900,tc_HOL_Obool),U_15902),hAPP(c_Set_Oinsert(U_15900),U_15901)),U_15904)),
    inference(variable_rename,[status(thm)],[f_3975_1]) ).

fof(f_3975_3,plain,
    ! [U_15900,U_15901,U_15902,U_15903,U_15904] : hAPP(hAPP(c_Set_Oinsert(U_15900),U_15901),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15902,tc_fun(U_15900,tc_HOL_Obool)),U_15903),U_15904)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15902,tc_fun(U_15900,tc_HOL_Obool)),U_15903),hAPP(hAPP(c_COMBB(tc_fun(U_15900,tc_HOL_Obool),tc_fun(U_15900,tc_HOL_Obool),U_15902),hAPP(c_Set_Oinsert(U_15900),U_15901)),U_15904)),
    inference(definitional_conversion,[status(esa)],[f_3975_2]) ).

cnf(f_3975_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_15900),U_15901),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15902,tc_fun(U_15900,tc_HOL_Obool)),U_15903),U_15904)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15902,tc_fun(U_15900,tc_HOL_Obool)),U_15903),hAPP(hAPP(c_COMBB(tc_fun(U_15900,tc_HOL_Obool),tc_fun(U_15900,tc_HOL_Obool),U_15902),hAPP(c_Set_Oinsert(U_15900),U_15901)),U_15904)),
    inference(clausify,[status(thm)],[f_3975_3]) ).

fof(f_3976_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__Un]) ).

fof(f_3976_2,plain,
    ! [U_15908,U_15907,U_15906,U_15905] : hAPP(c_Relation_Oconverse(U_15905,U_15906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15905,U_15906),tc_HOL_Obool)),U_15907),U_15908)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15906,U_15905),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15905,U_15906),U_15907)),hAPP(c_Relation_Oconverse(U_15905,U_15906),U_15908)),
    inference(variable_rename,[status(thm)],[f_3976_1]) ).

fof(f_3976_3,plain,
    ! [U_15905,U_15906,U_15907,U_15908] : hAPP(c_Relation_Oconverse(U_15905,U_15906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15905,U_15906),tc_HOL_Obool)),U_15907),U_15908)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15906,U_15905),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15905,U_15906),U_15907)),hAPP(c_Relation_Oconverse(U_15905,U_15906),U_15908)),
    inference(definitional_conversion,[status(esa)],[f_3976_2]) ).

cnf(f_3976_4,plain,
    hAPP(c_Relation_Oconverse(U_15905,U_15906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15905,U_15906),tc_HOL_Obool)),U_15907),U_15908)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15906,U_15905),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15905,U_15906),U_15907)),hAPP(c_Relation_Oconverse(U_15905,U_15906),U_15908)),
    inference(clausify,[status(thm)],[f_3976_3]) ).

fof(f_3977_1,plain,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__subset__iff]) ).

fof(f_3977_2,plain,
    ! [U_15915,U_15914,U_15913,U_15912,U_15911] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15911,tc_HOL_Obool)),U_15912),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15913,tc_fun(U_15911,tc_HOL_Obool)),U_15914),U_15915)))
        | ? [U_15910] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15911,tc_HOL_Obool)),U_15912),hAPP(U_15915,U_15910)))
            & hBOOL(hAPP(hAPP(c_member(U_15913),U_15910),U_15914)) ) )
      & ( ! [U_15909] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15911,tc_HOL_Obool)),U_15912),hAPP(U_15915,U_15909)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15913),U_15909),U_15914)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15911,tc_HOL_Obool)),U_15912),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15913,tc_fun(U_15911,tc_HOL_Obool)),U_15914),U_15915))) ) ),
    inference(variable_rename,[status(thm)],[f_3977_1]) ).

fof(f_3977_3,plain,
    ( ! [U_15925,U_15923,U_15921,U_15919,U_15917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15921,tc_fun(U_15917,tc_HOL_Obool)),U_15923),U_15925)))
        | ? [U_15910] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(U_15925,U_15910)))
            & hBOOL(hAPP(hAPP(c_member(U_15921),U_15910),U_15923)) ) )
    & ! [U_15924,U_15922,U_15920,U_15918,U_15916] :
        ( ! [U_15909] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(U_15924,U_15909)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15920),U_15909),U_15922)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15920,tc_fun(U_15916,tc_HOL_Obool)),U_15922),U_15924))) ) ),
    inference(miniscope,[status(thm)],[f_3977_2]) ).

fof(f_3977_4,plain,
    ( ! [U_15925,U_15923,U_15921,U_15919,U_15917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15921,tc_fun(U_15917,tc_HOL_Obool)),U_15923),U_15925)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(U_15925,sK381(U_15925,U_15923,U_15921,U_15919,U_15917))))
          & hBOOL(hAPP(hAPP(c_member(U_15921),sK381(U_15925,U_15923,U_15921,U_15919,U_15917)),U_15923)) ) )
    & ! [U_15924,U_15922,U_15920,U_15918,U_15916] :
        ( ! [U_15909] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(U_15924,U_15909)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15920),U_15909),U_15922)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15920,tc_fun(U_15916,tc_HOL_Obool)),U_15922),U_15924))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_15910,sK381(U_15925,U_15923,U_15921,U_15919,U_15917))],[f_3977_3]) ).

fof(f_3977_5,plain,
    ( ! [U_15919,U_15917,U_15923,U_15925,U_15921] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(U_15925,sK381(U_15925,U_15923,U_15921,U_15919,U_15917))))
        | ~ sP1050(U_15919,U_15917,U_15923,U_15925,U_15921) )
    & ! [U_15919,U_15917,U_15923,U_15925,U_15921] :
        ( hBOOL(hAPP(hAPP(c_member(U_15921),sK381(U_15925,U_15923,U_15921,U_15919,U_15917)),U_15923))
        | ~ sP1050(U_15919,U_15917,U_15923,U_15925,U_15921) )
    & ! [U_15919,U_15917,U_15923,U_15925,U_15921] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15921,tc_fun(U_15917,tc_HOL_Obool)),U_15923),U_15925)))
        | sP1050(U_15919,U_15917,U_15923,U_15925,U_15921) )
    & ! [U_15920,U_15918,U_15909,U_15916,U_15924,U_15922] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(U_15924,U_15909)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15920),U_15909),U_15922))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15920,tc_fun(U_15916,tc_HOL_Obool)),U_15922),U_15924))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1050])],[f_3977_4]) ).

cnf(f_3977_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(U_15924,U_15909)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15920),U_15909),U_15922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15916,tc_HOL_Obool)),U_15918),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15920,tc_fun(U_15916,tc_HOL_Obool)),U_15922),U_15924))) ),
    inference(clausify,[status(thm)],[f_3977_5]) ).

cnf(f_3977_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15921,tc_fun(U_15917,tc_HOL_Obool)),U_15923),U_15925)))
    | sP1050(U_15919,U_15917,U_15923,U_15925,U_15921) ),
    inference(clausify,[status(thm)],[f_3977_5]) ).

cnf(f_3977_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15921),sK381(U_15925,U_15923,U_15921,U_15919,U_15917)),U_15923))
    | ~ sP1050(U_15919,U_15917,U_15923,U_15925,U_15921) ),
    inference(clausify,[status(thm)],[f_3977_5]) ).

cnf(f_3977_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15917,tc_HOL_Obool)),U_15919),hAPP(U_15925,sK381(U_15925,U_15923,U_15921,U_15919,U_15917))))
    | ~ sP1050(U_15919,U_15917,U_15923,U_15925,U_15921) ),
    inference(clausify,[status(thm)],[f_3977_5]) ).

fof(f_3978_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(f_3978_2,plain,
    ! [U_15930,U_15929,U_15928,U_15927,U_15926] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15926,tc_fun(U_15927,tc_HOL_Obool)),U_15928),hAPP(hAPP(c_COMBB(tc_fun(U_15927,tc_HOL_Obool),tc_fun(U_15927,tc_HOL_Obool),U_15926),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15927,tc_HOL_Obool)),U_15929)),U_15930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15927,tc_HOL_Obool)),U_15929),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15926,tc_fun(U_15927,tc_HOL_Obool)),U_15928),U_15930)),
    inference(variable_rename,[status(thm)],[f_3978_1]) ).

fof(f_3978_3,plain,
    ! [U_15927,U_15926,U_15928,U_15929,U_15930] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15926,tc_fun(U_15927,tc_HOL_Obool)),U_15928),hAPP(hAPP(c_COMBB(tc_fun(U_15927,tc_HOL_Obool),tc_fun(U_15927,tc_HOL_Obool),U_15926),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15927,tc_HOL_Obool)),U_15929)),U_15930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15927,tc_HOL_Obool)),U_15929),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15926,tc_fun(U_15927,tc_HOL_Obool)),U_15928),U_15930)),
    inference(definitional_conversion,[status(esa)],[f_3978_2]) ).

cnf(f_3978_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15926,tc_fun(U_15927,tc_HOL_Obool)),U_15928),hAPP(hAPP(c_COMBB(tc_fun(U_15927,tc_HOL_Obool),tc_fun(U_15927,tc_HOL_Obool),U_15926),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15927,tc_HOL_Obool)),U_15929)),U_15930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15927,tc_HOL_Obool)),U_15929),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15926,tc_fun(U_15927,tc_HOL_Obool)),U_15928),U_15930)),
    inference(clausify,[status(thm)],[f_3978_3]) ).

fof(f_3979_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(f_3979_2,plain,
    ! [U_15935,U_15934,U_15933,U_15932,U_15931] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15931,tc_fun(U_15932,tc_HOL_Obool)),U_15933),hAPP(hAPP(c_COMBC(U_15931,tc_fun(U_15932,tc_HOL_Obool),tc_fun(U_15932,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15932,tc_HOL_Obool),tc_fun(tc_fun(U_15932,tc_HOL_Obool),tc_fun(U_15932,tc_HOL_Obool)),U_15931),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15932,tc_HOL_Obool))),U_15934)),U_15935)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15932,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15931,tc_fun(U_15932,tc_HOL_Obool)),U_15933),U_15934)),U_15935),
    inference(variable_rename,[status(thm)],[f_3979_1]) ).

fof(f_3979_3,plain,
    ! [U_15931,U_15932,U_15933,U_15934,U_15935] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15931,tc_fun(U_15932,tc_HOL_Obool)),U_15933),hAPP(hAPP(c_COMBC(U_15931,tc_fun(U_15932,tc_HOL_Obool),tc_fun(U_15932,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15932,tc_HOL_Obool),tc_fun(tc_fun(U_15932,tc_HOL_Obool),tc_fun(U_15932,tc_HOL_Obool)),U_15931),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15932,tc_HOL_Obool))),U_15934)),U_15935)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15932,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15931,tc_fun(U_15932,tc_HOL_Obool)),U_15933),U_15934)),U_15935),
    inference(definitional_conversion,[status(esa)],[f_3979_2]) ).

cnf(f_3979_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15931,tc_fun(U_15932,tc_HOL_Obool)),U_15933),hAPP(hAPP(c_COMBC(U_15931,tc_fun(U_15932,tc_HOL_Obool),tc_fun(U_15932,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15932,tc_HOL_Obool),tc_fun(tc_fun(U_15932,tc_HOL_Obool),tc_fun(U_15932,tc_HOL_Obool)),U_15931),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15932,tc_HOL_Obool))),U_15934)),U_15935)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15932,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15931,tc_fun(U_15932,tc_HOL_Obool)),U_15933),U_15934)),U_15935),
    inference(clausify,[status(thm)],[f_3979_3]) ).

fof(f_3980_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(f_3980_2,plain,
    ! [U_15940,U_15939,U_15938,U_15937,U_15936] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15936,tc_HOL_Obool)),U_15937),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15938,tc_fun(U_15936,tc_HOL_Obool)),U_15939),U_15940)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15938,tc_fun(U_15936,tc_HOL_Obool)),U_15939),hAPP(hAPP(c_COMBB(tc_fun(U_15936,tc_HOL_Obool),tc_fun(U_15936,tc_HOL_Obool),U_15938),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15936,tc_HOL_Obool)),U_15937)),U_15940)),
    inference(variable_rename,[status(thm)],[f_3980_1]) ).

fof(f_3980_3,plain,
    ! [U_15936,U_15937,U_15938,U_15939,U_15940] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15936,tc_HOL_Obool)),U_15937),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15938,tc_fun(U_15936,tc_HOL_Obool)),U_15939),U_15940)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15938,tc_fun(U_15936,tc_HOL_Obool)),U_15939),hAPP(hAPP(c_COMBB(tc_fun(U_15936,tc_HOL_Obool),tc_fun(U_15936,tc_HOL_Obool),U_15938),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15936,tc_HOL_Obool)),U_15937)),U_15940)),
    inference(definitional_conversion,[status(esa)],[f_3980_2]) ).

cnf(f_3980_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15936,tc_HOL_Obool)),U_15937),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15938,tc_fun(U_15936,tc_HOL_Obool)),U_15939),U_15940)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15938,tc_fun(U_15936,tc_HOL_Obool)),U_15939),hAPP(hAPP(c_COMBB(tc_fun(U_15936,tc_HOL_Obool),tc_fun(U_15936,tc_HOL_Obool),U_15938),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15936,tc_HOL_Obool)),U_15937)),U_15940)),
    inference(clausify,[status(thm)],[f_3980_3]) ).

fof(f_3981_1,plain,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib]) ).

fof(f_3981_2,plain,
    ! [U_15945,U_15944,U_15943,U_15942,U_15941] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15941,tc_HOL_Obool)),U_15942),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15943,tc_fun(U_15941,tc_HOL_Obool)),U_15944),U_15945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15943,tc_fun(U_15941,tc_HOL_Obool)),U_15944),hAPP(hAPP(c_COMBB(tc_fun(U_15941,tc_HOL_Obool),tc_fun(U_15941,tc_HOL_Obool),U_15943),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15941,tc_HOL_Obool)),U_15942)),U_15945)),
    inference(variable_rename,[status(thm)],[f_3981_1]) ).

fof(f_3981_3,plain,
    ! [U_15941,U_15942,U_15943,U_15944,U_15945] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15941,tc_HOL_Obool)),U_15942),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15943,tc_fun(U_15941,tc_HOL_Obool)),U_15944),U_15945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15943,tc_fun(U_15941,tc_HOL_Obool)),U_15944),hAPP(hAPP(c_COMBB(tc_fun(U_15941,tc_HOL_Obool),tc_fun(U_15941,tc_HOL_Obool),U_15943),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15941,tc_HOL_Obool)),U_15942)),U_15945)),
    inference(definitional_conversion,[status(esa)],[f_3981_2]) ).

cnf(f_3981_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15941,tc_HOL_Obool)),U_15942),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15943,tc_fun(U_15941,tc_HOL_Obool)),U_15944),U_15945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15943,tc_fun(U_15941,tc_HOL_Obool)),U_15944),hAPP(hAPP(c_COMBB(tc_fun(U_15941,tc_HOL_Obool),tc_fun(U_15941,tc_HOL_Obool),U_15943),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15941,tc_HOL_Obool)),U_15942)),U_15945)),
    inference(clausify,[status(thm)],[f_3981_3]) ).

fof(f_3982_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(f_3982_2,plain,
    ! [U_15950,U_15949,U_15948,U_15947,U_15946] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15946,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15947,tc_fun(U_15946,tc_HOL_Obool)),U_15948),U_15949)),U_15950) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15947,tc_fun(U_15946,tc_HOL_Obool)),U_15948),hAPP(hAPP(c_COMBC(U_15947,tc_fun(U_15946,tc_HOL_Obool),tc_fun(U_15946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15946,tc_HOL_Obool),tc_fun(tc_fun(U_15946,tc_HOL_Obool),tc_fun(U_15946,tc_HOL_Obool)),U_15947),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15946,tc_HOL_Obool))),U_15949)),U_15950)),
    inference(variable_rename,[status(thm)],[f_3982_1]) ).

fof(f_3982_3,plain,
    ! [U_15946,U_15947,U_15948,U_15949,U_15950] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15946,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15947,tc_fun(U_15946,tc_HOL_Obool)),U_15948),U_15949)),U_15950) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15947,tc_fun(U_15946,tc_HOL_Obool)),U_15948),hAPP(hAPP(c_COMBC(U_15947,tc_fun(U_15946,tc_HOL_Obool),tc_fun(U_15946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15946,tc_HOL_Obool),tc_fun(tc_fun(U_15946,tc_HOL_Obool),tc_fun(U_15946,tc_HOL_Obool)),U_15947),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15946,tc_HOL_Obool))),U_15949)),U_15950)),
    inference(definitional_conversion,[status(esa)],[f_3982_2]) ).

cnf(f_3982_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15946,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15947,tc_fun(U_15946,tc_HOL_Obool)),U_15948),U_15949)),U_15950) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15947,tc_fun(U_15946,tc_HOL_Obool)),U_15948),hAPP(hAPP(c_COMBC(U_15947,tc_fun(U_15946,tc_HOL_Obool),tc_fun(U_15946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15946,tc_HOL_Obool),tc_fun(tc_fun(U_15946,tc_HOL_Obool),tc_fun(U_15946,tc_HOL_Obool)),U_15947),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15946,tc_HOL_Obool))),U_15949)),U_15950)),
    inference(clausify,[status(thm)],[f_3982_3]) ).

fof(f_3983_1,plain,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib2]) ).

fof(f_3983_2,plain,
    ! [U_15957,U_15956,U_15955,U_15954,U_15953,U_15952,U_15951] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15952,tc_fun(U_15951,tc_HOL_Obool)),U_15953),U_15954)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15955,tc_fun(U_15951,tc_HOL_Obool)),U_15956),U_15957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15952,tc_fun(U_15951,tc_HOL_Obool)),U_15953),hAPP(hAPP(c_COMBB(tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15951,tc_HOL_Obool),U_15952),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15955,tc_fun(U_15951,tc_HOL_Obool)),U_15956)),hAPP(hAPP(c_COMBC(U_15952,tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool)),tc_fun(tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool))),U_15952),c_COMBB(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool),U_15955)),hAPP(hAPP(c_COMBB(tc_fun(U_15951,tc_HOL_Obool),tc_fun(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool)),U_15952),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15951,tc_HOL_Obool))),U_15954))),U_15957))),
    inference(variable_rename,[status(thm)],[f_3983_1]) ).

fof(f_3983_3,plain,
    ! [U_15951,U_15952,U_15953,U_15954,U_15955,U_15956,U_15957] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15952,tc_fun(U_15951,tc_HOL_Obool)),U_15953),U_15954)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15955,tc_fun(U_15951,tc_HOL_Obool)),U_15956),U_15957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15952,tc_fun(U_15951,tc_HOL_Obool)),U_15953),hAPP(hAPP(c_COMBB(tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15951,tc_HOL_Obool),U_15952),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15955,tc_fun(U_15951,tc_HOL_Obool)),U_15956)),hAPP(hAPP(c_COMBC(U_15952,tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool)),tc_fun(tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool))),U_15952),c_COMBB(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool),U_15955)),hAPP(hAPP(c_COMBB(tc_fun(U_15951,tc_HOL_Obool),tc_fun(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool)),U_15952),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15951,tc_HOL_Obool))),U_15954))),U_15957))),
    inference(definitional_conversion,[status(esa)],[f_3983_2]) ).

cnf(f_3983_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15952,tc_fun(U_15951,tc_HOL_Obool)),U_15953),U_15954)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15955,tc_fun(U_15951,tc_HOL_Obool)),U_15956),U_15957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15952,tc_fun(U_15951,tc_HOL_Obool)),U_15953),hAPP(hAPP(c_COMBB(tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15951,tc_HOL_Obool),U_15952),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15955,tc_fun(U_15951,tc_HOL_Obool)),U_15956)),hAPP(hAPP(c_COMBC(U_15952,tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool)),tc_fun(tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool)),tc_fun(U_15955,tc_fun(U_15951,tc_HOL_Obool))),U_15952),c_COMBB(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool),U_15955)),hAPP(hAPP(c_COMBB(tc_fun(U_15951,tc_HOL_Obool),tc_fun(tc_fun(U_15951,tc_HOL_Obool),tc_fun(U_15951,tc_HOL_Obool)),U_15952),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15951,tc_HOL_Obool))),U_15954))),U_15957))),
    inference(clausify,[status(thm)],[f_3983_3]) ).

fof(f_3984_1,plain,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__INT__subset]) ).

fof(f_3984_2,plain,
    ! [U_15963,U_15962,U_15961,U_15960,U_15959,U_15958] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15958,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15959,U_15958,U_15960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15961,tc_fun(U_15959,tc_HOL_Obool)),U_15962),U_15963))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15961,tc_fun(U_15958,tc_HOL_Obool)),U_15962),hAPP(hAPP(c_COMBB(tc_fun(U_15959,tc_HOL_Obool),tc_fun(U_15958,tc_HOL_Obool),U_15961),c_Relation_OImage(U_15959,U_15958,U_15960)),U_15963)))),
    inference(variable_rename,[status(thm)],[f_3984_1]) ).

fof(f_3984_3,plain,
    ! [U_15958,U_15959,U_15960,U_15961,U_15962,U_15963] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15958,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15959,U_15958,U_15960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15961,tc_fun(U_15959,tc_HOL_Obool)),U_15962),U_15963))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15961,tc_fun(U_15958,tc_HOL_Obool)),U_15962),hAPP(hAPP(c_COMBB(tc_fun(U_15959,tc_HOL_Obool),tc_fun(U_15958,tc_HOL_Obool),U_15961),c_Relation_OImage(U_15959,U_15958,U_15960)),U_15963)))),
    inference(definitional_conversion,[status(esa)],[f_3984_2]) ).

cnf(f_3984_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15958,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15959,U_15958,U_15960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15961,tc_fun(U_15959,tc_HOL_Obool)),U_15962),U_15963))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15961,tc_fun(U_15958,tc_HOL_Obool)),U_15962),hAPP(hAPP(c_COMBB(tc_fun(U_15959,tc_HOL_Obool),tc_fun(U_15958,tc_HOL_Obool),U_15961),c_Relation_OImage(U_15959,U_15958,U_15960)),U_15963)))),
    inference(clausify,[status(thm)],[f_3984_3]) ).

fof(f_3985_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__INT__eq]) ).

fof(f_3985_2,plain,
    ! [U_15967,U_15966,U_15965,U_15964] : hAPP(c_Set_OPow(U_15964),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15965,tc_fun(U_15964,tc_HOL_Obool)),U_15966),U_15967)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15965,tc_fun(tc_fun(U_15964,tc_HOL_Obool),tc_HOL_Obool)),U_15966),hAPP(hAPP(c_COMBB(tc_fun(U_15964,tc_HOL_Obool),tc_fun(tc_fun(U_15964,tc_HOL_Obool),tc_HOL_Obool),U_15965),c_Set_OPow(U_15964)),U_15967)),
    inference(variable_rename,[status(thm)],[f_3985_1]) ).

fof(f_3985_3,plain,
    ! [U_15964,U_15965,U_15966,U_15967] : hAPP(c_Set_OPow(U_15964),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15965,tc_fun(U_15964,tc_HOL_Obool)),U_15966),U_15967)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15965,tc_fun(tc_fun(U_15964,tc_HOL_Obool),tc_HOL_Obool)),U_15966),hAPP(hAPP(c_COMBB(tc_fun(U_15964,tc_HOL_Obool),tc_fun(tc_fun(U_15964,tc_HOL_Obool),tc_HOL_Obool),U_15965),c_Set_OPow(U_15964)),U_15967)),
    inference(definitional_conversion,[status(esa)],[f_3985_2]) ).

cnf(f_3985_4,plain,
    hAPP(c_Set_OPow(U_15964),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15965,tc_fun(U_15964,tc_HOL_Obool)),U_15966),U_15967)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15965,tc_fun(tc_fun(U_15964,tc_HOL_Obool),tc_HOL_Obool)),U_15966),hAPP(hAPP(c_COMBB(tc_fun(U_15964,tc_HOL_Obool),tc_fun(tc_fun(U_15964,tc_HOL_Obool),tc_HOL_Obool),U_15965),c_Set_OPow(U_15964)),U_15967)),
    inference(clausify,[status(thm)],[f_3985_3]) ).

fof(f_3986_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2),
    inference(fof_nnf,[status(thm)],[fact_converse__Id__on]) ).

fof(f_3986_2,plain,
    ! [U_15969,U_15968] : hAPP(c_Relation_Oconverse(U_15968,U_15968),c_Relation_OId__on(U_15968,U_15969)) = c_Relation_OId__on(U_15968,U_15969),
    inference(variable_rename,[status(thm)],[f_3986_1]) ).

fof(f_3986_3,plain,
    ! [U_15968,U_15969] : hAPP(c_Relation_Oconverse(U_15968,U_15968),c_Relation_OId__on(U_15968,U_15969)) = c_Relation_OId__on(U_15968,U_15969),
    inference(definitional_conversion,[status(esa)],[f_3986_2]) ).

cnf(f_3986_4,plain,
    hAPP(c_Relation_Oconverse(U_15968,U_15968),c_Relation_OId__on(U_15968,U_15969)) = c_Relation_OId__on(U_15968,U_15969),
    inference(clausify,[status(thm)],[f_3986_3]) ).

fof(f_3987_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Field__converse]) ).

fof(f_3987_2,plain,
    ! [U_15971,U_15970] : hAPP(c_Relation_OField(U_15970),hAPP(c_Relation_Oconverse(U_15970,U_15970),U_15971)) = hAPP(c_Relation_OField(U_15970),U_15971),
    inference(variable_rename,[status(thm)],[f_3987_1]) ).

fof(f_3987_3,plain,
    ! [U_15970,U_15971] : hAPP(c_Relation_OField(U_15970),hAPP(c_Relation_Oconverse(U_15970,U_15970),U_15971)) = hAPP(c_Relation_OField(U_15970),U_15971),
    inference(definitional_conversion,[status(esa)],[f_3987_2]) ).

cnf(f_3987_4,plain,
    hAPP(c_Relation_OField(U_15970),hAPP(c_Relation_Oconverse(U_15970,U_15970),U_15971)) = hAPP(c_Relation_OField(U_15970),U_15971),
    inference(clausify,[status(thm)],[f_3987_3]) ).

fof(f_3988_1,plain,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__INTER]) ).

fof(f_3988_2,plain,
    ! [U_15976,U_15975,U_15974,U_15973,U_15972] : hAPP(c_Relation_Oconverse(U_15972,U_15973),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15974,tc_fun(tc_prod(U_15972,U_15973),tc_HOL_Obool)),U_15975),U_15976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15974,tc_fun(tc_prod(U_15973,U_15972),tc_HOL_Obool)),U_15975),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15972,U_15973),tc_HOL_Obool),tc_fun(tc_prod(U_15973,U_15972),tc_HOL_Obool),U_15974),c_Relation_Oconverse(U_15972,U_15973)),U_15976)),
    inference(variable_rename,[status(thm)],[f_3988_1]) ).

fof(f_3988_3,plain,
    ! [U_15972,U_15973,U_15974,U_15975,U_15976] : hAPP(c_Relation_Oconverse(U_15972,U_15973),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15974,tc_fun(tc_prod(U_15972,U_15973),tc_HOL_Obool)),U_15975),U_15976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15974,tc_fun(tc_prod(U_15973,U_15972),tc_HOL_Obool)),U_15975),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15972,U_15973),tc_HOL_Obool),tc_fun(tc_prod(U_15973,U_15972),tc_HOL_Obool),U_15974),c_Relation_Oconverse(U_15972,U_15973)),U_15976)),
    inference(definitional_conversion,[status(esa)],[f_3988_2]) ).

cnf(f_3988_4,plain,
    hAPP(c_Relation_Oconverse(U_15972,U_15973),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15974,tc_fun(tc_prod(U_15972,U_15973),tc_HOL_Obool)),U_15975),U_15976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15974,tc_fun(tc_prod(U_15973,U_15972),tc_HOL_Obool)),U_15975),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15972,U_15973),tc_HOL_Obool),tc_fun(tc_prod(U_15973,U_15972),tc_HOL_Obool),U_15974),c_Relation_Oconverse(U_15972,U_15973)),U_15976)),
    inference(clausify,[status(thm)],[f_3988_3]) ).

fof(f_3989_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
    inference(fof_nnf,[status(thm)],[fact_converse__converse]) ).

fof(f_3989_2,plain,
    ! [U_15979,U_15978,U_15977] : hAPP(c_Relation_Oconverse(U_15977,U_15978),hAPP(c_Relation_Oconverse(U_15978,U_15977),U_15979)) = U_15979,
    inference(variable_rename,[status(thm)],[f_3989_1]) ).

fof(f_3989_3,plain,
    ! [U_15977,U_15978,U_15979] : hAPP(c_Relation_Oconverse(U_15977,U_15978),hAPP(c_Relation_Oconverse(U_15978,U_15977),U_15979)) = U_15979,
    inference(definitional_conversion,[status(esa)],[f_3989_2]) ).

cnf(f_3989_4,plain,
    hAPP(c_Relation_Oconverse(U_15977,U_15978),hAPP(c_Relation_Oconverse(U_15978,U_15977),U_15979)) = U_15979,
    inference(clausify,[status(thm)],[f_3989_3]) ).

fof(f_3990_1,plain,
    ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_converse__inv__image]) ).

fof(f_3990_2,plain,
    ! [U_15983,U_15982,U_15981,U_15980] : hAPP(c_Relation_Oconverse(U_15980,U_15980),hAPP(hAPP(c_Relation_Oinv__image(U_15981,U_15980),U_15982),U_15983)) = hAPP(hAPP(c_Relation_Oinv__image(U_15981,U_15980),hAPP(c_Relation_Oconverse(U_15981,U_15981),U_15982)),U_15983),
    inference(variable_rename,[status(thm)],[f_3990_1]) ).

fof(f_3990_3,plain,
    ! [U_15980,U_15981,U_15982,U_15983] : hAPP(c_Relation_Oconverse(U_15980,U_15980),hAPP(hAPP(c_Relation_Oinv__image(U_15981,U_15980),U_15982),U_15983)) = hAPP(hAPP(c_Relation_Oinv__image(U_15981,U_15980),hAPP(c_Relation_Oconverse(U_15981,U_15981),U_15982)),U_15983),
    inference(definitional_conversion,[status(esa)],[f_3990_2]) ).

cnf(f_3990_4,plain,
    hAPP(c_Relation_Oconverse(U_15980,U_15980),hAPP(hAPP(c_Relation_Oinv__image(U_15981,U_15980),U_15982),U_15983)) = hAPP(hAPP(c_Relation_Oinv__image(U_15981,U_15980),hAPP(c_Relation_Oconverse(U_15981,U_15981),U_15982)),U_15983),
    inference(clausify,[status(thm)],[f_3990_3]) ).

fof(f_3991_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__commute]) ).

fof(f_3991_2,plain,
    ! [U_15989,U_15988,U_15987,U_15986,U_15985,U_15984] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15985,U_15984),U_15986),hAPP(hAPP(c_COMBB(tc_fun(U_15987,U_15984),U_15984,U_15985),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15987,U_15984),U_15988)),U_15989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15987,U_15984),U_15988),hAPP(hAPP(c_COMBB(tc_fun(U_15985,U_15984),U_15984,U_15987),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15985,U_15984),U_15986)),hAPP(c_COMBC(U_15985,U_15987,U_15984),U_15989)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15984) ),
    inference(variable_rename,[status(thm)],[f_3991_1]) ).

fof(f_3991_3,plain,
    ! [U_15984,U_15985,U_15986,U_15987,U_15988,U_15989] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15985,U_15984),U_15986),hAPP(hAPP(c_COMBB(tc_fun(U_15987,U_15984),U_15984,U_15985),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15987,U_15984),U_15988)),U_15989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15987,U_15984),U_15988),hAPP(hAPP(c_COMBB(tc_fun(U_15985,U_15984),U_15984,U_15987),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15985,U_15984),U_15986)),hAPP(c_COMBC(U_15985,U_15987,U_15984),U_15989)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15984) ),
    inference(definitional_conversion,[status(esa)],[f_3991_2]) ).

cnf(f_3991_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15985,U_15984),U_15986),hAPP(hAPP(c_COMBB(tc_fun(U_15987,U_15984),U_15984,U_15985),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15987,U_15984),U_15988)),U_15989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15987,U_15984),U_15988),hAPP(hAPP(c_COMBB(tc_fun(U_15985,U_15984),U_15984,U_15987),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15985,U_15984),U_15986)),hAPP(c_COMBC(U_15985,U_15987,U_15984),U_15989)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15984) ),
    inference(clausify,[status(thm)],[f_3991_3]) ).

fof(f_3992_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__apply]) ).

fof(f_3992_2,plain,
    ! [U_15995,U_15994,U_15993,U_15992,U_15991,U_15990] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15991,tc_fun(U_15992,U_15990)),U_15993),U_15994),U_15995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15991,U_15990),U_15993),hAPP(hAPP(c_COMBC(U_15991,U_15992,U_15990),U_15994),U_15995))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15990) ),
    inference(variable_rename,[status(thm)],[f_3992_1]) ).

fof(f_3992_3,plain,
    ! [U_15990,U_15991,U_15992,U_15993,U_15994,U_15995] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15991,tc_fun(U_15992,U_15990)),U_15993),U_15994),U_15995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15991,U_15990),U_15993),hAPP(hAPP(c_COMBC(U_15991,U_15992,U_15990),U_15994),U_15995))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15990) ),
    inference(definitional_conversion,[status(esa)],[f_3992_2]) ).

cnf(f_3992_4,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15991,tc_fun(U_15992,U_15990)),U_15993),U_15994),U_15995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15991,U_15990),U_15993),hAPP(hAPP(c_COMBC(U_15991,U_15992,U_15990),U_15994),U_15995))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15990) ),
    inference(clausify,[status(thm)],[f_3992_3]) ).

fof(f_3993_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__Int__distrib]) ).

fof(f_3993_2,plain,
    ! [U_16000,U_15999,U_15998,U_15997,U_15996] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),hAPP(hAPP(c_COMBS(U_15996,tc_fun(U_15997,tc_HOL_Obool),tc_fun(U_15997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15997,tc_HOL_Obool),tc_fun(tc_fun(U_15997,tc_HOL_Obool),tc_fun(U_15997,tc_HOL_Obool)),U_15996),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15997,tc_HOL_Obool))),U_15999)),U_16000)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15997,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),U_15999)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),U_16000)),
    inference(variable_rename,[status(thm)],[f_3993_1]) ).

fof(f_3993_3,plain,
    ! [U_15996,U_15997,U_15998,U_15999,U_16000] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),hAPP(hAPP(c_COMBS(U_15996,tc_fun(U_15997,tc_HOL_Obool),tc_fun(U_15997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15997,tc_HOL_Obool),tc_fun(tc_fun(U_15997,tc_HOL_Obool),tc_fun(U_15997,tc_HOL_Obool)),U_15996),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15997,tc_HOL_Obool))),U_15999)),U_16000)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15997,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),U_15999)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),U_16000)),
    inference(definitional_conversion,[status(esa)],[f_3993_2]) ).

cnf(f_3993_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),hAPP(hAPP(c_COMBS(U_15996,tc_fun(U_15997,tc_HOL_Obool),tc_fun(U_15997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15997,tc_HOL_Obool),tc_fun(tc_fun(U_15997,tc_HOL_Obool),tc_fun(U_15997,tc_HOL_Obool)),U_15996),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15997,tc_HOL_Obool))),U_15999)),U_16000)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15997,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),U_15999)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15996,tc_fun(U_15997,tc_HOL_Obool)),U_15998),U_16000)),
    inference(clausify,[status(thm)],[f_3993_3]) ).

fof(f_3994_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__Int]) ).

fof(f_3994_2,plain,
    ! [U_16004,U_16003,U_16002,U_16001] : hAPP(c_Relation_Oconverse(U_16001,U_16002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16001,U_16002),tc_HOL_Obool)),U_16003),U_16004)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16002,U_16001),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16001,U_16002),U_16003)),hAPP(c_Relation_Oconverse(U_16001,U_16002),U_16004)),
    inference(variable_rename,[status(thm)],[f_3994_1]) ).

fof(f_3994_3,plain,
    ! [U_16001,U_16002,U_16003,U_16004] : hAPP(c_Relation_Oconverse(U_16001,U_16002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16001,U_16002),tc_HOL_Obool)),U_16003),U_16004)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16002,U_16001),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16001,U_16002),U_16003)),hAPP(c_Relation_Oconverse(U_16001,U_16002),U_16004)),
    inference(definitional_conversion,[status(esa)],[f_3994_2]) ).

cnf(f_3994_4,plain,
    hAPP(c_Relation_Oconverse(U_16001,U_16002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16001,U_16002),tc_HOL_Obool)),U_16003),U_16004)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16002,U_16001),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16001,U_16002),U_16003)),hAPP(c_Relation_Oconverse(U_16001,U_16002),U_16004)),
    inference(clausify,[status(thm)],[f_3994_3]) ).

fof(f_3995_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J]) ).

fof(f_3995_2,plain,
    ! [U_16010,U_16009,U_16008,U_16007] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(U_16007,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16008,tc_fun(U_16007,tc_HOL_Obool)),U_16009),U_16010)
        | ? [U_16006] :
            ( hAPP(U_16010,U_16006) != c_Orderings_Otop__class_Otop(tc_fun(U_16007,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16008),U_16006),U_16009)) ) )
      & ( ! [U_16005] :
            ( hAPP(U_16010,U_16005) = c_Orderings_Otop__class_Otop(tc_fun(U_16007,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16008),U_16005),U_16009)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16007,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16008,tc_fun(U_16007,tc_HOL_Obool)),U_16009),U_16010) ) ),
    inference(variable_rename,[status(thm)],[f_3995_1]) ).

fof(f_3995_3,plain,
    ( ! [U_16018,U_16016,U_16014,U_16012] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16014,tc_fun(U_16012,tc_HOL_Obool)),U_16016),U_16018)
        | ? [U_16006] :
            ( hAPP(U_16018,U_16006) != c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16014),U_16006),U_16016)) ) )
    & ! [U_16017,U_16015,U_16013,U_16011] :
        ( ! [U_16005] :
            ( hAPP(U_16017,U_16005) = c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16013),U_16005),U_16015)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16013,tc_fun(U_16011,tc_HOL_Obool)),U_16015),U_16017) ) ),
    inference(miniscope,[status(thm)],[f_3995_2]) ).

fof(f_3995_4,plain,
    ( ! [U_16018,U_16016,U_16014,U_16012] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16014,tc_fun(U_16012,tc_HOL_Obool)),U_16016),U_16018)
        | ( hAPP(U_16018,sK382(U_16018,U_16016,U_16014,U_16012)) != c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_16014),sK382(U_16018,U_16016,U_16014,U_16012)),U_16016)) ) )
    & ! [U_16017,U_16015,U_16013,U_16011] :
        ( ! [U_16005] :
            ( hAPP(U_16017,U_16005) = c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16013),U_16005),U_16015)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16013,tc_fun(U_16011,tc_HOL_Obool)),U_16015),U_16017) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_16006,sK382(U_16018,U_16016,U_16014,U_16012))],[f_3995_3]) ).

fof(f_3995_5,plain,
    ( ! [U_16012,U_16018,U_16014,U_16016] :
        ( hAPP(U_16018,sK382(U_16018,U_16016,U_16014,U_16012)) != c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool))
        | ~ sP1051(U_16012,U_16018,U_16014,U_16016) )
    & ! [U_16012,U_16018,U_16014,U_16016] :
        ( hBOOL(hAPP(hAPP(c_member(U_16014),sK382(U_16018,U_16016,U_16014,U_16012)),U_16016))
        | ~ sP1051(U_16012,U_16018,U_16014,U_16016) )
    & ! [U_16012,U_16018,U_16014,U_16016] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16014,tc_fun(U_16012,tc_HOL_Obool)),U_16016),U_16018)
        | sP1051(U_16012,U_16018,U_16014,U_16016) )
    & ! [U_16017,U_16013,U_16005,U_16011,U_16015] :
        ( hAPP(U_16017,U_16005) = c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16013),U_16005),U_16015))
        | c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16013,tc_fun(U_16011,tc_HOL_Obool)),U_16015),U_16017) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1051])],[f_3995_4]) ).

cnf(f_3995_6,plain,
    ( hAPP(U_16017,U_16005) = c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16013),U_16005),U_16015))
    | c_Orderings_Otop__class_Otop(tc_fun(U_16011,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16013,tc_fun(U_16011,tc_HOL_Obool)),U_16015),U_16017) ),
    inference(clausify,[status(thm)],[f_3995_5]) ).

cnf(f_3995_7,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16014,tc_fun(U_16012,tc_HOL_Obool)),U_16016),U_16018)
    | sP1051(U_16012,U_16018,U_16014,U_16016) ),
    inference(clausify,[status(thm)],[f_3995_5]) ).

cnf(f_3995_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16014),sK382(U_16018,U_16016,U_16014,U_16012)),U_16016))
    | ~ sP1051(U_16012,U_16018,U_16014,U_16016) ),
    inference(clausify,[status(thm)],[f_3995_5]) ).

cnf(f_3995_9,plain,
    ( hAPP(U_16018,sK382(U_16018,U_16016,U_16014,U_16012)) != c_Orderings_Otop__class_Otop(tc_fun(U_16012,tc_HOL_Obool))
    | ~ sP1051(U_16012,U_16018,U_16014,U_16016) ),
    inference(clausify,[status(thm)],[f_3995_5]) ).

fof(f_3996_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J]) ).

fof(f_3996_2,plain,
    ! [U_16024,U_16023,U_16022,U_16021] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16021,tc_fun(U_16022,tc_HOL_Obool)),U_16023),U_16024) = c_Orderings_Otop__class_Otop(tc_fun(U_16022,tc_HOL_Obool))
        | ? [U_16020] :
            ( hAPP(U_16024,U_16020) != c_Orderings_Otop__class_Otop(tc_fun(U_16022,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16021),U_16020),U_16023)) ) )
      & ( ! [U_16019] :
            ( hAPP(U_16024,U_16019) = c_Orderings_Otop__class_Otop(tc_fun(U_16022,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16021),U_16019),U_16023)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16021,tc_fun(U_16022,tc_HOL_Obool)),U_16023),U_16024) != c_Orderings_Otop__class_Otop(tc_fun(U_16022,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3996_1]) ).

fof(f_3996_3,plain,
    ( ! [U_16032,U_16030,U_16028,U_16026] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16026,tc_fun(U_16028,tc_HOL_Obool)),U_16030),U_16032) = c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
        | ? [U_16020] :
            ( hAPP(U_16032,U_16020) != c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16026),U_16020),U_16030)) ) )
    & ! [U_16031,U_16029,U_16027,U_16025] :
        ( ! [U_16019] :
            ( hAPP(U_16031,U_16019) = c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16025),U_16019),U_16029)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16025,tc_fun(U_16027,tc_HOL_Obool)),U_16029),U_16031) != c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3996_2]) ).

fof(f_3996_4,plain,
    ( ! [U_16032,U_16030,U_16028,U_16026] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16026,tc_fun(U_16028,tc_HOL_Obool)),U_16030),U_16032) = c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
        | ( hAPP(U_16032,sK383(U_16032,U_16030,U_16028,U_16026)) != c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_16026),sK383(U_16032,U_16030,U_16028,U_16026)),U_16030)) ) )
    & ! [U_16031,U_16029,U_16027,U_16025] :
        ( ! [U_16019] :
            ( hAPP(U_16031,U_16019) = c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16025),U_16019),U_16029)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16025,tc_fun(U_16027,tc_HOL_Obool)),U_16029),U_16031) != c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_16020,sK383(U_16032,U_16030,U_16028,U_16026))],[f_3996_3]) ).

fof(f_3996_5,plain,
    ( ! [U_16028,U_16030,U_16026,U_16032] :
        ( hAPP(U_16032,sK383(U_16032,U_16030,U_16028,U_16026)) != c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
        | ~ sP1052(U_16028,U_16030,U_16026,U_16032) )
    & ! [U_16028,U_16030,U_16026,U_16032] :
        ( hBOOL(hAPP(hAPP(c_member(U_16026),sK383(U_16032,U_16030,U_16028,U_16026)),U_16030))
        | ~ sP1052(U_16028,U_16030,U_16026,U_16032) )
    & ! [U_16028,U_16030,U_16026,U_16032] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16026,tc_fun(U_16028,tc_HOL_Obool)),U_16030),U_16032) = c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
        | sP1052(U_16028,U_16030,U_16026,U_16032) )
    & ! [U_16019,U_16029,U_16027,U_16031,U_16025] :
        ( hAPP(U_16031,U_16019) = c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16025),U_16019),U_16029))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16025,tc_fun(U_16027,tc_HOL_Obool)),U_16029),U_16031) != c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1052])],[f_3996_4]) ).

cnf(f_3996_6,plain,
    ( hAPP(U_16031,U_16019) = c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16025),U_16019),U_16029))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16025,tc_fun(U_16027,tc_HOL_Obool)),U_16029),U_16031) != c_Orderings_Otop__class_Otop(tc_fun(U_16027,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3996_5]) ).

cnf(f_3996_7,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16026,tc_fun(U_16028,tc_HOL_Obool)),U_16030),U_16032) = c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
    | sP1052(U_16028,U_16030,U_16026,U_16032) ),
    inference(clausify,[status(thm)],[f_3996_5]) ).

cnf(f_3996_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16026),sK383(U_16032,U_16030,U_16028,U_16026)),U_16030))
    | ~ sP1052(U_16028,U_16030,U_16026,U_16032) ),
    inference(clausify,[status(thm)],[f_3996_5]) ).

cnf(f_3996_9,plain,
    ( hAPP(U_16032,sK383(U_16032,U_16030,U_16028,U_16026)) != c_Orderings_Otop__class_Otop(tc_fun(U_16028,tc_HOL_Obool))
    | ~ sP1052(U_16028,U_16030,U_16026,U_16032) ),
    inference(clausify,[status(thm)],[f_3996_5]) ).

fof(f_3997_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__converse]) ).

fof(f_3997_2,plain,
    ! [U_16035,U_16034,U_16033] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16033,U_16034)),hAPP(c_Relation_Oconverse(U_16034,U_16033),U_16035)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16034,U_16033)),U_16035)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16034,U_16033)),U_16035))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16033,U_16034)),hAPP(c_Relation_Oconverse(U_16034,U_16033),U_16035))) ) ),
    inference(variable_rename,[status(thm)],[f_3997_1]) ).

fof(f_3997_3,plain,
    ( ! [U_16041,U_16039,U_16037] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16037,U_16039)),hAPP(c_Relation_Oconverse(U_16039,U_16037),U_16041)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16039,U_16037)),U_16041)) )
    & ! [U_16040,U_16038,U_16036] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16038,U_16036)),U_16040))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16036,U_16038)),hAPP(c_Relation_Oconverse(U_16038,U_16036),U_16040))) ) ),
    inference(miniscope,[status(thm)],[f_3997_2]) ).

fof(f_3997_4,plain,
    ( ! [U_16037,U_16039,U_16041] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16037,U_16039)),hAPP(c_Relation_Oconverse(U_16039,U_16037),U_16041)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16039,U_16037)),U_16041)) )
    & ! [U_16038,U_16040,U_16036] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16038,U_16036)),U_16040))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16036,U_16038)),hAPP(c_Relation_Oconverse(U_16038,U_16036),U_16040))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3997_3]) ).

cnf(f_3997_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16038,U_16036)),U_16040))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16036,U_16038)),hAPP(c_Relation_Oconverse(U_16038,U_16036),U_16040))) ),
    inference(clausify,[status(thm)],[f_3997_4]) ).

cnf(f_3997_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16037,U_16039)),hAPP(c_Relation_Oconverse(U_16039,U_16037),U_16041)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16039,U_16037)),U_16041)) ),
    inference(clausify,[status(thm)],[f_3997_4]) ).

fof(f_3998_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2]) ).

fof(f_3998_2,plain,
    ! [U_16047,U_16046,U_16045,U_16044,U_16043,U_16042] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16042,tc_fun(U_16043,tc_fun(U_16044,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16042,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_fun(U_16043,tc_fun(U_16044,tc_HOL_Obool)),U_16042),hAPP(c_COMBC(U_16043,tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_fun(U_16044,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16044,tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_fun(U_16044,tc_HOL_Obool)),U_16043),c_COMBC(U_16044,tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16044,tc_prod(U_16043,U_16044)),tc_fun(U_16044,tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool)),U_16043),hAPP(c_COMBB(tc_prod(U_16043,U_16044),tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool),U_16044),c_member(tc_prod(U_16043,U_16044)))),c_Product__Type_OPair(U_16043,U_16044))))),U_16045)),U_16046),U_16047))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16043,U_16044)),hAPP(hAPP(c_Product__Type_OPair(U_16043,U_16044),U_16046),U_16047)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16042,tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16042,tc_HOL_Obool))),U_16045))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16043,U_16044)),hAPP(hAPP(c_Product__Type_OPair(U_16043,U_16044),U_16046),U_16047)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16042,tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16042,tc_HOL_Obool))),U_16045)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16042,tc_fun(U_16043,tc_fun(U_16044,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16042,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_fun(U_16043,tc_fun(U_16044,tc_HOL_Obool)),U_16042),hAPP(c_COMBC(U_16043,tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_fun(U_16044,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16044,tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_fun(U_16044,tc_HOL_Obool)),U_16043),c_COMBC(U_16044,tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16044,tc_prod(U_16043,U_16044)),tc_fun(U_16044,tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool)),U_16043),hAPP(c_COMBB(tc_prod(U_16043,U_16044),tc_fun(tc_fun(tc_prod(U_16043,U_16044),tc_HOL_Obool),tc_HOL_Obool),U_16044),c_member(tc_prod(U_16043,U_16044)))),c_Product__Type_OPair(U_16043,U_16044))))),U_16045)),U_16046),U_16047)) ) ),
    inference(variable_rename,[status(thm)],[f_3998_1]) ).

fof(f_3998_3,plain,
    ( ! [U_16059,U_16057,U_16055,U_16053,U_16051,U_16049] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16049,tc_fun(U_16051,tc_fun(U_16053,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16049,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16051,tc_fun(U_16053,tc_HOL_Obool)),U_16049),hAPP(c_COMBC(U_16051,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16053,tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16053,tc_HOL_Obool)),U_16051),c_COMBC(U_16053,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16053,tc_prod(U_16051,U_16053)),tc_fun(U_16053,tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),U_16051),hAPP(c_COMBB(tc_prod(U_16051,U_16053),tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool),U_16053),c_member(tc_prod(U_16051,U_16053)))),c_Product__Type_OPair(U_16051,U_16053))))),U_16055)),U_16057),U_16059))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16051,U_16053)),hAPP(hAPP(c_Product__Type_OPair(U_16051,U_16053),U_16057),U_16059)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16049,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16049,tc_HOL_Obool))),U_16055))) )
    & ! [U_16058,U_16056,U_16054,U_16052,U_16050,U_16048] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16052)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16052),U_16056),U_16058)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16048,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16048,tc_HOL_Obool))),U_16054)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16048,tc_fun(U_16050,tc_fun(U_16052,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16048,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16050,tc_fun(U_16052,tc_HOL_Obool)),U_16048),hAPP(c_COMBC(U_16050,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16052,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16052,tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16052,tc_HOL_Obool)),U_16050),c_COMBC(U_16052,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16052,tc_prod(U_16050,U_16052)),tc_fun(U_16052,tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),U_16050),hAPP(c_COMBB(tc_prod(U_16050,U_16052),tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool),U_16052),c_member(tc_prod(U_16050,U_16052)))),c_Product__Type_OPair(U_16050,U_16052))))),U_16054)),U_16056),U_16058)) ) ),
    inference(miniscope,[status(thm)],[f_3998_2]) ).

fof(f_3998_4,plain,
    ( ! [U_16059,U_16049,U_16051,U_16053,U_16055,U_16057] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16049,tc_fun(U_16051,tc_fun(U_16053,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16049,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16051,tc_fun(U_16053,tc_HOL_Obool)),U_16049),hAPP(c_COMBC(U_16051,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16053,tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16053,tc_HOL_Obool)),U_16051),c_COMBC(U_16053,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16053,tc_prod(U_16051,U_16053)),tc_fun(U_16053,tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),U_16051),hAPP(c_COMBB(tc_prod(U_16051,U_16053),tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool),U_16053),c_member(tc_prod(U_16051,U_16053)))),c_Product__Type_OPair(U_16051,U_16053))))),U_16055)),U_16057),U_16059))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16051,U_16053)),hAPP(hAPP(c_Product__Type_OPair(U_16051,U_16053),U_16057),U_16059)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16049,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16049,tc_HOL_Obool))),U_16055))) )
    & ! [U_16050,U_16054,U_16052,U_16048,U_16056,U_16058] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16052)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16052),U_16056),U_16058)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16048,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16048,tc_HOL_Obool))),U_16054)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16048,tc_fun(U_16050,tc_fun(U_16052,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16048,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16050,tc_fun(U_16052,tc_HOL_Obool)),U_16048),hAPP(c_COMBC(U_16050,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16052,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16052,tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16052,tc_HOL_Obool)),U_16050),c_COMBC(U_16052,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16052,tc_prod(U_16050,U_16052)),tc_fun(U_16052,tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),U_16050),hAPP(c_COMBB(tc_prod(U_16050,U_16052),tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool),U_16052),c_member(tc_prod(U_16050,U_16052)))),c_Product__Type_OPair(U_16050,U_16052))))),U_16054)),U_16056),U_16058)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3998_3]) ).

cnf(f_3998_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16052)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16052),U_16056),U_16058)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16048,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16048,tc_HOL_Obool))),U_16054)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16048,tc_fun(U_16050,tc_fun(U_16052,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16048,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16050,tc_fun(U_16052,tc_HOL_Obool)),U_16048),hAPP(c_COMBC(U_16050,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16052,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16052,tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_fun(U_16052,tc_HOL_Obool)),U_16050),c_COMBC(U_16052,tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16052,tc_prod(U_16050,U_16052)),tc_fun(U_16052,tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool)),U_16050),hAPP(c_COMBB(tc_prod(U_16050,U_16052),tc_fun(tc_fun(tc_prod(U_16050,U_16052),tc_HOL_Obool),tc_HOL_Obool),U_16052),c_member(tc_prod(U_16050,U_16052)))),c_Product__Type_OPair(U_16050,U_16052))))),U_16054)),U_16056),U_16058)) ),
    inference(clausify,[status(thm)],[f_3998_4]) ).

cnf(f_3998_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16049,tc_fun(U_16051,tc_fun(U_16053,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16049,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16051,tc_fun(U_16053,tc_HOL_Obool)),U_16049),hAPP(c_COMBC(U_16051,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16053,tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_fun(U_16053,tc_HOL_Obool)),U_16051),c_COMBC(U_16053,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16053,tc_prod(U_16051,U_16053)),tc_fun(U_16053,tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool)),U_16051),hAPP(c_COMBB(tc_prod(U_16051,U_16053),tc_fun(tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool),tc_HOL_Obool),U_16053),c_member(tc_prod(U_16051,U_16053)))),c_Product__Type_OPair(U_16051,U_16053))))),U_16055)),U_16057),U_16059))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16051,U_16053)),hAPP(hAPP(c_Product__Type_OPair(U_16051,U_16053),U_16057),U_16059)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16049,tc_fun(tc_prod(U_16051,U_16053),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16049,tc_HOL_Obool))),U_16055))) ),
    inference(clausify,[status(thm)],[f_3998_4]) ).

fof(f_3999_1,plain,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__iff]) ).

fof(f_3999_2,plain,
    ! [U_16066,U_16065,U_16064,U_16063,U_16062] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_16062),U_16063),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16064,tc_fun(U_16062,tc_HOL_Obool)),U_16065),U_16066)))
        | ? [U_16061] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_16062),U_16063),hAPP(U_16066,U_16061)))
            & hBOOL(hAPP(hAPP(c_member(U_16064),U_16061),U_16065)) ) )
      & ( ! [U_16060] :
            ( hBOOL(hAPP(hAPP(c_member(U_16062),U_16063),hAPP(U_16066,U_16060)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16064),U_16060),U_16065)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16062),U_16063),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16064,tc_fun(U_16062,tc_HOL_Obool)),U_16065),U_16066))) ) ),
    inference(variable_rename,[status(thm)],[f_3999_1]) ).

fof(f_3999_3,plain,
    ( ! [U_16076,U_16074,U_16072,U_16070,U_16068] :
        ( hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16072,tc_fun(U_16068,tc_HOL_Obool)),U_16074),U_16076)))
        | ? [U_16061] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(U_16076,U_16061)))
            & hBOOL(hAPP(hAPP(c_member(U_16072),U_16061),U_16074)) ) )
    & ! [U_16075,U_16073,U_16071,U_16069,U_16067] :
        ( ! [U_16060] :
            ( hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(U_16075,U_16060)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16071),U_16060),U_16073)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16071,tc_fun(U_16067,tc_HOL_Obool)),U_16073),U_16075))) ) ),
    inference(miniscope,[status(thm)],[f_3999_2]) ).

fof(f_3999_4,plain,
    ( ! [U_16076,U_16074,U_16072,U_16070,U_16068] :
        ( hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16072,tc_fun(U_16068,tc_HOL_Obool)),U_16074),U_16076)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(U_16076,sK384(U_16076,U_16074,U_16072,U_16070,U_16068))))
          & hBOOL(hAPP(hAPP(c_member(U_16072),sK384(U_16076,U_16074,U_16072,U_16070,U_16068)),U_16074)) ) )
    & ! [U_16075,U_16073,U_16071,U_16069,U_16067] :
        ( ! [U_16060] :
            ( hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(U_16075,U_16060)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16071),U_16060),U_16073)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16071,tc_fun(U_16067,tc_HOL_Obool)),U_16073),U_16075))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_16061,sK384(U_16076,U_16074,U_16072,U_16070,U_16068))],[f_3999_3]) ).

fof(f_3999_5,plain,
    ( ! [U_16068,U_16070,U_16074,U_16076,U_16072] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(U_16076,sK384(U_16076,U_16074,U_16072,U_16070,U_16068))))
        | ~ sP1053(U_16068,U_16070,U_16074,U_16076,U_16072) )
    & ! [U_16068,U_16070,U_16074,U_16076,U_16072] :
        ( hBOOL(hAPP(hAPP(c_member(U_16072),sK384(U_16076,U_16074,U_16072,U_16070,U_16068)),U_16074))
        | ~ sP1053(U_16068,U_16070,U_16074,U_16076,U_16072) )
    & ! [U_16068,U_16070,U_16074,U_16076,U_16072] :
        ( hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16072,tc_fun(U_16068,tc_HOL_Obool)),U_16074),U_16076)))
        | sP1053(U_16068,U_16070,U_16074,U_16076,U_16072) )
    & ! [U_16067,U_16071,U_16075,U_16073,U_16060,U_16069] :
        ( hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(U_16075,U_16060)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16071),U_16060),U_16073))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16071,tc_fun(U_16067,tc_HOL_Obool)),U_16073),U_16075))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1053])],[f_3999_4]) ).

cnf(f_3999_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(U_16075,U_16060)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16071),U_16060),U_16073))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16067),U_16069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16071,tc_fun(U_16067,tc_HOL_Obool)),U_16073),U_16075))) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16072,tc_fun(U_16068,tc_HOL_Obool)),U_16074),U_16076)))
    | sP1053(U_16068,U_16070,U_16074,U_16076,U_16072) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16072),sK384(U_16076,U_16074,U_16072,U_16070,U_16068)),U_16074))
    | ~ sP1053(U_16068,U_16070,U_16074,U_16076,U_16072) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16068),U_16070),hAPP(U_16076,sK384(U_16076,U_16074,U_16072,U_16070,U_16068))))
    | ~ sP1053(U_16068,U_16070,U_16074,U_16076,U_16072) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

fof(f_4000_1,plain,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__absorb]) ).

fof(f_4000_2,plain,
    ! [U_16081,U_16080,U_16079,U_16078,U_16077] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16080,tc_HOL_Obool)),hAPP(U_16081,U_16078)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16077,tc_fun(U_16080,tc_HOL_Obool)),U_16079),U_16081)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16077,tc_fun(U_16080,tc_HOL_Obool)),U_16079),U_16081)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16077),U_16078),U_16079)) ),
    inference(variable_rename,[status(thm)],[f_4000_1]) ).

fof(f_4000_3,plain,
    ! [U_16079,U_16081,U_16080,U_16078,U_16077] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16080,tc_HOL_Obool)),hAPP(U_16081,U_16078)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16077,tc_fun(U_16080,tc_HOL_Obool)),U_16079),U_16081)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16077,tc_fun(U_16080,tc_HOL_Obool)),U_16079),U_16081)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16077),U_16078),U_16079)) ),
    inference(definitional_conversion,[status(esa)],[f_4000_2]) ).

cnf(f_4000_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16080,tc_HOL_Obool)),hAPP(U_16081,U_16078)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16077,tc_fun(U_16080,tc_HOL_Obool)),U_16079),U_16081)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16077,tc_fun(U_16080,tc_HOL_Obool)),U_16079),U_16081)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16077),U_16078),U_16079)) ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

fof(f_4001_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF__INT__eq]) ).

fof(f_4001_2,plain,
    ! [U_16085,U_16084,U_16083,U_16082] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16082,tc_fun(U_16083,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16082,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16083,tc_HOL_Obool),tc_fun(U_16083,tc_HOL_Obool),U_16082),hAPP(c_COMBC(U_16083,tc_fun(U_16083,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16083))),U_16084)),U_16085))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16083),U_16085),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16082,tc_fun(U_16083,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16082,tc_HOL_Obool))),U_16084))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_16083),U_16085),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16082,tc_fun(U_16083,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16082,tc_HOL_Obool))),U_16084)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16082,tc_fun(U_16083,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16082,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16083,tc_HOL_Obool),tc_fun(U_16083,tc_HOL_Obool),U_16082),hAPP(c_COMBC(U_16083,tc_fun(U_16083,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16083))),U_16084)),U_16085)) ) ),
    inference(variable_rename,[status(thm)],[f_4001_1]) ).

fof(f_4001_3,plain,
    ( ! [U_16093,U_16091,U_16089,U_16087] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16087,tc_fun(U_16089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16087,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16089,tc_HOL_Obool),tc_fun(U_16089,tc_HOL_Obool),U_16087),hAPP(c_COMBC(U_16089,tc_fun(U_16089,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16089))),U_16091)),U_16093))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16089),U_16093),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16087,tc_fun(U_16089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16087,tc_HOL_Obool))),U_16091))) )
    & ! [U_16092,U_16090,U_16088,U_16086] :
        ( hBOOL(hAPP(hAPP(c_member(U_16088),U_16092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16086,tc_fun(U_16088,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16086,tc_HOL_Obool))),U_16090)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16086,tc_fun(U_16088,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16086,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16088,tc_HOL_Obool),tc_fun(U_16088,tc_HOL_Obool),U_16086),hAPP(c_COMBC(U_16088,tc_fun(U_16088,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16088))),U_16090)),U_16092)) ) ),
    inference(miniscope,[status(thm)],[f_4001_2]) ).

fof(f_4001_4,plain,
    ( ! [U_16087,U_16089,U_16091,U_16093] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16087,tc_fun(U_16089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16087,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16089,tc_HOL_Obool),tc_fun(U_16089,tc_HOL_Obool),U_16087),hAPP(c_COMBC(U_16089,tc_fun(U_16089,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16089))),U_16091)),U_16093))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16089),U_16093),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16087,tc_fun(U_16089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16087,tc_HOL_Obool))),U_16091))) )
    & ! [U_16088,U_16092,U_16086,U_16090] :
        ( hBOOL(hAPP(hAPP(c_member(U_16088),U_16092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16086,tc_fun(U_16088,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16086,tc_HOL_Obool))),U_16090)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16086,tc_fun(U_16088,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16086,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16088,tc_HOL_Obool),tc_fun(U_16088,tc_HOL_Obool),U_16086),hAPP(c_COMBC(U_16088,tc_fun(U_16088,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16088))),U_16090)),U_16092)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4001_3]) ).

cnf(f_4001_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16088),U_16092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16086,tc_fun(U_16088,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16086,tc_HOL_Obool))),U_16090)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16086,tc_fun(U_16088,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16086,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16088,tc_HOL_Obool),tc_fun(U_16088,tc_HOL_Obool),U_16086),hAPP(c_COMBC(U_16088,tc_fun(U_16088,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16088))),U_16090)),U_16092)) ),
    inference(clausify,[status(thm)],[f_4001_4]) ).

cnf(f_4001_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16087,tc_fun(U_16089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16087,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16089,tc_HOL_Obool),tc_fun(U_16089,tc_HOL_Obool),U_16087),hAPP(c_COMBC(U_16089,tc_fun(U_16089,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16089))),U_16091)),U_16093))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16089),U_16093),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16087,tc_fun(U_16089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16087,tc_HOL_Obool))),U_16091))) ),
    inference(clausify,[status(thm)],[f_4001_4]) ).

fof(f_4002_1,plain,
    ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__less__iff]) ).

fof(f_4002_2,plain,
    ! [U_16100,U_16099,U_16098,U_16097,U_16096] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100))
          | ! [U_16095] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,U_16095)),U_16100))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16097),U_16095),U_16098)) ) )
        & ( ? [U_16094] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,U_16094)),U_16100))
              & hBOOL(hAPP(hAPP(c_member(U_16097),U_16094),U_16098)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100)) ) )
      | ~ class_Orderings_Olinorder(U_16096)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16096) ),
    inference(variable_rename,[status(thm)],[f_4002_1]) ).

fof(f_4002_3,plain,
    ! [U_16100,U_16099,U_16098,U_16097,U_16096] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100))
          | ! [U_16095] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,U_16095)),U_16100))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16097),U_16095),U_16098)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,sK385(U_16100,U_16099,U_16098,U_16097,U_16096))),U_16100))
            & hBOOL(hAPP(hAPP(c_member(U_16097),sK385(U_16100,U_16099,U_16098,U_16097,U_16096)),U_16098)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100)) ) )
      | ~ class_Orderings_Olinorder(U_16096)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16096) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_16094,sK385(U_16100,U_16099,U_16098,U_16097,U_16096))],[f_4002_2]) ).

fof(f_4002_4,plain,
    ( ! [U_16096,U_16097,U_16098,U_16099,U_16100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,sK385(U_16100,U_16099,U_16098,U_16097,U_16096))),U_16100))
        | ~ sP1054(U_16096,U_16097,U_16098,U_16099,U_16100) )
    & ! [U_16096,U_16097,U_16098,U_16099,U_16100] :
        ( hBOOL(hAPP(hAPP(c_member(U_16097),sK385(U_16100,U_16099,U_16098,U_16097,U_16096)),U_16098))
        | ~ sP1054(U_16096,U_16097,U_16098,U_16099,U_16100) )
    & ! [U_16095,U_16096,U_16097,U_16098,U_16099,U_16100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,U_16095)),U_16100))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16097),U_16095),U_16098))
        | ~ sP1055(U_16095,U_16096,U_16097,U_16098,U_16099,U_16100) )
    & ! [U_16095,U_16096,U_16097,U_16098,U_16099,U_16100] :
        ( sP1054(U_16096,U_16097,U_16098,U_16099,U_16100)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100))
        | ~ sP1055(U_16095,U_16096,U_16097,U_16098,U_16099,U_16100) )
    & ! [U_16095,U_16096,U_16097,U_16098,U_16099,U_16100] :
        ( sP1055(U_16095,U_16096,U_16097,U_16098,U_16099,U_16100)
        | ~ class_Orderings_Olinorder(U_16096)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16096) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1054,sP1055])],[f_4002_3]) ).

cnf(f_4002_5,plain,
    ( sP1055(U_16095,U_16096,U_16097,U_16098,U_16099,U_16100)
    | ~ class_Orderings_Olinorder(U_16096)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16096) ),
    inference(clausify,[status(thm)],[f_4002_4]) ).

cnf(f_4002_6,plain,
    ( sP1054(U_16096,U_16097,U_16098,U_16099,U_16100)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100))
    | ~ sP1055(U_16095,U_16096,U_16097,U_16098,U_16099,U_16100) ),
    inference(clausify,[status(thm)],[f_4002_4]) ).

cnf(f_4002_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16097,U_16096),U_16098),U_16099)),U_16100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,U_16095)),U_16100))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16097),U_16095),U_16098))
    | ~ sP1055(U_16095,U_16096,U_16097,U_16098,U_16099,U_16100) ),
    inference(clausify,[status(thm)],[f_4002_4]) ).

cnf(f_4002_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16097),sK385(U_16100,U_16099,U_16098,U_16097,U_16096)),U_16098))
    | ~ sP1054(U_16096,U_16097,U_16098,U_16099,U_16100) ),
    inference(clausify,[status(thm)],[f_4002_4]) ).

cnf(f_4002_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16096),hAPP(U_16099,sK385(U_16100,U_16099,U_16098,U_16097,U_16096))),U_16100))
    | ~ sP1054(U_16096,U_16097,U_16098,U_16099,U_16100) ),
    inference(clausify,[status(thm)],[f_4002_4]) ).

fof(f_4003_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_converse__iff]) ).

fof(f_4003_2,plain,
    ! [U_16105,U_16104,U_16103,U_16102,U_16101] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16101,U_16102)),hAPP(hAPP(c_Product__Type_OPair(U_16101,U_16102),U_16103),U_16104)),hAPP(c_Relation_Oconverse(U_16102,U_16101),U_16105)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16102,U_16101)),hAPP(hAPP(c_Product__Type_OPair(U_16102,U_16101),U_16104),U_16103)),U_16105)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16102,U_16101)),hAPP(hAPP(c_Product__Type_OPair(U_16102,U_16101),U_16104),U_16103)),U_16105))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16101,U_16102)),hAPP(hAPP(c_Product__Type_OPair(U_16101,U_16102),U_16103),U_16104)),hAPP(c_Relation_Oconverse(U_16102,U_16101),U_16105))) ) ),
    inference(variable_rename,[status(thm)],[f_4003_1]) ).

fof(f_4003_3,plain,
    ( ! [U_16115,U_16113,U_16111,U_16109,U_16107] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16107,U_16109)),hAPP(hAPP(c_Product__Type_OPair(U_16107,U_16109),U_16111),U_16113)),hAPP(c_Relation_Oconverse(U_16109,U_16107),U_16115)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16109,U_16107)),hAPP(hAPP(c_Product__Type_OPair(U_16109,U_16107),U_16113),U_16111)),U_16115)) )
    & ! [U_16114,U_16112,U_16110,U_16108,U_16106] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16108,U_16106)),hAPP(hAPP(c_Product__Type_OPair(U_16108,U_16106),U_16112),U_16110)),U_16114))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16106,U_16108)),hAPP(hAPP(c_Product__Type_OPair(U_16106,U_16108),U_16110),U_16112)),hAPP(c_Relation_Oconverse(U_16108,U_16106),U_16114))) ) ),
    inference(miniscope,[status(thm)],[f_4003_2]) ).

fof(f_4003_4,plain,
    ( ! [U_16107,U_16109,U_16111,U_16113,U_16115] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16107,U_16109)),hAPP(hAPP(c_Product__Type_OPair(U_16107,U_16109),U_16111),U_16113)),hAPP(c_Relation_Oconverse(U_16109,U_16107),U_16115)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16109,U_16107)),hAPP(hAPP(c_Product__Type_OPair(U_16109,U_16107),U_16113),U_16111)),U_16115)) )
    & ! [U_16108,U_16110,U_16112,U_16106,U_16114] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16108,U_16106)),hAPP(hAPP(c_Product__Type_OPair(U_16108,U_16106),U_16112),U_16110)),U_16114))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16106,U_16108)),hAPP(hAPP(c_Product__Type_OPair(U_16106,U_16108),U_16110),U_16112)),hAPP(c_Relation_Oconverse(U_16108,U_16106),U_16114))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4003_3]) ).

cnf(f_4003_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16108,U_16106)),hAPP(hAPP(c_Product__Type_OPair(U_16108,U_16106),U_16112),U_16110)),U_16114))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16106,U_16108)),hAPP(hAPP(c_Product__Type_OPair(U_16106,U_16108),U_16110),U_16112)),hAPP(c_Relation_Oconverse(U_16108,U_16106),U_16114))) ),
    inference(clausify,[status(thm)],[f_4003_4]) ).

cnf(f_4003_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16107,U_16109)),hAPP(hAPP(c_Product__Type_OPair(U_16107,U_16109),U_16111),U_16113)),hAPP(c_Relation_Oconverse(U_16109,U_16107),U_16115)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16109,U_16107)),hAPP(hAPP(c_Product__Type_OPair(U_16109,U_16107),U_16113),U_16111)),U_16115)) ),
    inference(clausify,[status(thm)],[f_4003_4]) ).

fof(f_4004_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_converseI]) ).

fof(f_4004_2,plain,
    ! [U_16120,U_16119,U_16118,U_16117,U_16116] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16117,U_16116)),hAPP(hAPP(c_Product__Type_OPair(U_16117,U_16116),U_16119),U_16118)),hAPP(c_Relation_Oconverse(U_16116,U_16117),U_16120)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16116,U_16117)),hAPP(hAPP(c_Product__Type_OPair(U_16116,U_16117),U_16118),U_16119)),U_16120)) ),
    inference(variable_rename,[status(thm)],[f_4004_1]) ).

fof(f_4004_3,plain,
    ! [U_16116,U_16117,U_16118,U_16119,U_16120] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16117,U_16116)),hAPP(hAPP(c_Product__Type_OPair(U_16117,U_16116),U_16119),U_16118)),hAPP(c_Relation_Oconverse(U_16116,U_16117),U_16120)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16116,U_16117)),hAPP(hAPP(c_Product__Type_OPair(U_16116,U_16117),U_16118),U_16119)),U_16120)) ),
    inference(definitional_conversion,[status(esa)],[f_4004_2]) ).

cnf(f_4004_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16117,U_16116)),hAPP(hAPP(c_Product__Type_OPair(U_16117,U_16116),U_16119),U_16118)),hAPP(c_Relation_Oconverse(U_16116,U_16117),U_16120)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16116,U_16117)),hAPP(hAPP(c_Product__Type_OPair(U_16116,U_16117),U_16118),U_16119)),U_16120)) ),
    inference(clausify,[status(thm)],[f_4004_3]) ).

fof(f_4005_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converseD]) ).

fof(f_4005_2,plain,
    ! [U_16125,U_16124,U_16123,U_16122,U_16121] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16122,U_16121)),hAPP(hAPP(c_Product__Type_OPair(U_16122,U_16121),U_16124),U_16123)),U_16125))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16121,U_16122)),hAPP(hAPP(c_Product__Type_OPair(U_16121,U_16122),U_16123),U_16124)),hAPP(c_Relation_Oconverse(U_16122,U_16121),U_16125))) ),
    inference(variable_rename,[status(thm)],[f_4005_1]) ).

fof(f_4005_3,plain,
    ! [U_16121,U_16122,U_16123,U_16124,U_16125] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16122,U_16121)),hAPP(hAPP(c_Product__Type_OPair(U_16122,U_16121),U_16124),U_16123)),U_16125))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16121,U_16122)),hAPP(hAPP(c_Product__Type_OPair(U_16121,U_16122),U_16123),U_16124)),hAPP(c_Relation_Oconverse(U_16122,U_16121),U_16125))) ),
    inference(definitional_conversion,[status(esa)],[f_4005_2]) ).

cnf(f_4005_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16122,U_16121)),hAPP(hAPP(c_Product__Type_OPair(U_16122,U_16121),U_16124),U_16123)),U_16125))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16121,U_16122)),hAPP(hAPP(c_Product__Type_OPair(U_16121,U_16122),U_16123),U_16124)),hAPP(c_Relation_Oconverse(U_16122,U_16121),U_16125))) ),
    inference(clausify,[status(thm)],[f_4005_3]) ).

fof(f_4006_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) )
      & ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__converse]) ).

fof(f_4006_2,plain,
    ! [U_16128,U_16127,U_16126] :
      ( ( c_Relation_Orefl__on(U_16126,U_16127,hAPP(c_Relation_Oconverse(U_16126,U_16126),U_16128))
        | ~ c_Relation_Orefl__on(U_16126,U_16127,U_16128) )
      & ( c_Relation_Orefl__on(U_16126,U_16127,U_16128)
        | ~ c_Relation_Orefl__on(U_16126,U_16127,hAPP(c_Relation_Oconverse(U_16126,U_16126),U_16128)) ) ),
    inference(variable_rename,[status(thm)],[f_4006_1]) ).

fof(f_4006_3,plain,
    ( ! [U_16134,U_16132,U_16130] :
        ( c_Relation_Orefl__on(U_16130,U_16132,hAPP(c_Relation_Oconverse(U_16130,U_16130),U_16134))
        | ~ c_Relation_Orefl__on(U_16130,U_16132,U_16134) )
    & ! [U_16133,U_16131,U_16129] :
        ( c_Relation_Orefl__on(U_16129,U_16131,U_16133)
        | ~ c_Relation_Orefl__on(U_16129,U_16131,hAPP(c_Relation_Oconverse(U_16129,U_16129),U_16133)) ) ),
    inference(miniscope,[status(thm)],[f_4006_2]) ).

fof(f_4006_4,plain,
    ( ! [U_16134,U_16132,U_16130] :
        ( c_Relation_Orefl__on(U_16130,U_16132,hAPP(c_Relation_Oconverse(U_16130,U_16130),U_16134))
        | ~ c_Relation_Orefl__on(U_16130,U_16132,U_16134) )
    & ! [U_16131,U_16129,U_16133] :
        ( c_Relation_Orefl__on(U_16129,U_16131,U_16133)
        | ~ c_Relation_Orefl__on(U_16129,U_16131,hAPP(c_Relation_Oconverse(U_16129,U_16129),U_16133)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4006_3]) ).

cnf(f_4006_5,plain,
    ( c_Relation_Orefl__on(U_16129,U_16131,U_16133)
    | ~ c_Relation_Orefl__on(U_16129,U_16131,hAPP(c_Relation_Oconverse(U_16129,U_16129),U_16133)) ),
    inference(clausify,[status(thm)],[f_4006_4]) ).

cnf(f_4006_6,plain,
    ( c_Relation_Orefl__on(U_16130,U_16132,hAPP(c_Relation_Oconverse(U_16130,U_16130),U_16134))
    | ~ c_Relation_Orefl__on(U_16130,U_16132,U_16134) ),
    inference(clausify,[status(thm)],[f_4006_4]) ).

fof(f_4007_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(f_4007_2,plain,
    ! [U_16140,U_16139,U_16138,U_16137,U_16136,U_16135] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16135,tc_fun(U_16136,tc_HOL_Obool)),U_16137),hAPP(hAPP(c_COMBB(U_16138,tc_fun(U_16136,tc_HOL_Obool),U_16135),U_16139),U_16140)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16138,tc_fun(U_16136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16135,U_16138,U_16140),U_16137)),U_16139),
    inference(variable_rename,[status(thm)],[f_4007_1]) ).

fof(f_4007_3,plain,
    ! [U_16135,U_16136,U_16137,U_16138,U_16139,U_16140] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16135,tc_fun(U_16136,tc_HOL_Obool)),U_16137),hAPP(hAPP(c_COMBB(U_16138,tc_fun(U_16136,tc_HOL_Obool),U_16135),U_16139),U_16140)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16138,tc_fun(U_16136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16135,U_16138,U_16140),U_16137)),U_16139),
    inference(definitional_conversion,[status(esa)],[f_4007_2]) ).

cnf(f_4007_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16135,tc_fun(U_16136,tc_HOL_Obool)),U_16137),hAPP(hAPP(c_COMBB(U_16138,tc_fun(U_16136,tc_HOL_Obool),U_16135),U_16139),U_16140)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16138,tc_fun(U_16136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16135,U_16138,U_16140),U_16137)),U_16139),
    inference(clausify,[status(thm)],[f_4007_3]) ).

fof(f_4008_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(f_4008_2,plain,
    ! [U_16146,U_16145,U_16144,U_16143,U_16142,U_16141] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16141,tc_fun(U_16142,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16143,U_16141,U_16144),U_16145)),U_16146) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16143,tc_fun(U_16142,tc_HOL_Obool)),U_16145),hAPP(hAPP(c_COMBB(U_16141,tc_fun(U_16142,tc_HOL_Obool),U_16143),U_16146),U_16144)),
    inference(variable_rename,[status(thm)],[f_4008_1]) ).

fof(f_4008_3,plain,
    ! [U_16141,U_16142,U_16143,U_16144,U_16145,U_16146] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16141,tc_fun(U_16142,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16143,U_16141,U_16144),U_16145)),U_16146) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16143,tc_fun(U_16142,tc_HOL_Obool)),U_16145),hAPP(hAPP(c_COMBB(U_16141,tc_fun(U_16142,tc_HOL_Obool),U_16143),U_16146),U_16144)),
    inference(definitional_conversion,[status(esa)],[f_4008_2]) ).

cnf(f_4008_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16141,tc_fun(U_16142,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16143,U_16141,U_16144),U_16145)),U_16146) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16143,tc_fun(U_16142,tc_HOL_Obool)),U_16145),hAPP(hAPP(c_COMBB(U_16141,tc_fun(U_16142,tc_HOL_Obool),U_16143),U_16146),U_16144)),
    inference(clausify,[status(thm)],[f_4008_3]) ).

fof(f_4009_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__INT]) ).

fof(f_4009_2,plain,
    ! [U_16150,U_16149,U_16148,U_16147] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16147,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16148,tc_fun(U_16147,tc_HOL_Obool)),U_16149),U_16150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16148,tc_fun(U_16147,tc_HOL_Obool)),U_16149),hAPP(hAPP(c_COMBB(tc_fun(U_16147,tc_HOL_Obool),tc_fun(U_16147,tc_HOL_Obool),U_16148),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16147,tc_HOL_Obool))),U_16150)),
    inference(variable_rename,[status(thm)],[f_4009_1]) ).

fof(f_4009_3,plain,
    ! [U_16147,U_16148,U_16149,U_16150] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16147,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16148,tc_fun(U_16147,tc_HOL_Obool)),U_16149),U_16150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16148,tc_fun(U_16147,tc_HOL_Obool)),U_16149),hAPP(hAPP(c_COMBB(tc_fun(U_16147,tc_HOL_Obool),tc_fun(U_16147,tc_HOL_Obool),U_16148),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16147,tc_HOL_Obool))),U_16150)),
    inference(definitional_conversion,[status(esa)],[f_4009_2]) ).

cnf(f_4009_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16147,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16148,tc_fun(U_16147,tc_HOL_Obool)),U_16149),U_16150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16148,tc_fun(U_16147,tc_HOL_Obool)),U_16149),hAPP(hAPP(c_COMBB(tc_fun(U_16147,tc_HOL_Obool),tc_fun(U_16147,tc_HOL_Obool),U_16148),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16147,tc_HOL_Obool))),U_16150)),
    inference(clausify,[status(thm)],[f_4009_3]) ).

fof(f_4010_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__UN]) ).

fof(f_4010_2,plain,
    ! [U_16154,U_16153,U_16152,U_16151] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16151,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16152,tc_fun(U_16151,tc_HOL_Obool)),U_16153),U_16154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16152,tc_fun(U_16151,tc_HOL_Obool)),U_16153),hAPP(hAPP(c_COMBB(tc_fun(U_16151,tc_HOL_Obool),tc_fun(U_16151,tc_HOL_Obool),U_16152),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16151,tc_HOL_Obool))),U_16154)),
    inference(variable_rename,[status(thm)],[f_4010_1]) ).

fof(f_4010_3,plain,
    ! [U_16152,U_16151,U_16153,U_16154] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16151,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16152,tc_fun(U_16151,tc_HOL_Obool)),U_16153),U_16154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16152,tc_fun(U_16151,tc_HOL_Obool)),U_16153),hAPP(hAPP(c_COMBB(tc_fun(U_16151,tc_HOL_Obool),tc_fun(U_16151,tc_HOL_Obool),U_16152),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16151,tc_HOL_Obool))),U_16154)),
    inference(definitional_conversion,[status(esa)],[f_4010_2]) ).

cnf(f_4010_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16151,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16152,tc_fun(U_16151,tc_HOL_Obool)),U_16153),U_16154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16152,tc_fun(U_16151,tc_HOL_Obool)),U_16153),hAPP(hAPP(c_COMBB(tc_fun(U_16151,tc_HOL_Obool),tc_fun(U_16151,tc_HOL_Obool),U_16152),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16151,tc_HOL_Obool))),U_16154)),
    inference(clausify,[status(thm)],[f_4010_3]) ).

fof(f_4011_1,plain,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__UNION]) ).

fof(f_4011_2,plain,
    ! [U_16159,U_16158,U_16157,U_16156,U_16155] : hAPP(c_Relation_Oconverse(U_16155,U_16156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16157,tc_fun(tc_prod(U_16155,U_16156),tc_HOL_Obool)),U_16158),U_16159)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16157,tc_fun(tc_prod(U_16156,U_16155),tc_HOL_Obool)),U_16158),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16155,U_16156),tc_HOL_Obool),tc_fun(tc_prod(U_16156,U_16155),tc_HOL_Obool),U_16157),c_Relation_Oconverse(U_16155,U_16156)),U_16159)),
    inference(variable_rename,[status(thm)],[f_4011_1]) ).

fof(f_4011_3,plain,
    ! [U_16155,U_16156,U_16157,U_16158,U_16159] : hAPP(c_Relation_Oconverse(U_16155,U_16156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16157,tc_fun(tc_prod(U_16155,U_16156),tc_HOL_Obool)),U_16158),U_16159)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16157,tc_fun(tc_prod(U_16156,U_16155),tc_HOL_Obool)),U_16158),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16155,U_16156),tc_HOL_Obool),tc_fun(tc_prod(U_16156,U_16155),tc_HOL_Obool),U_16157),c_Relation_Oconverse(U_16155,U_16156)),U_16159)),
    inference(definitional_conversion,[status(esa)],[f_4011_2]) ).

cnf(f_4011_4,plain,
    hAPP(c_Relation_Oconverse(U_16155,U_16156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16157,tc_fun(tc_prod(U_16155,U_16156),tc_HOL_Obool)),U_16158),U_16159)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16157,tc_fun(tc_prod(U_16156,U_16155),tc_HOL_Obool)),U_16158),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16155,U_16156),tc_HOL_Obool),tc_fun(tc_prod(U_16156,U_16155),tc_HOL_Obool),U_16157),c_Relation_Oconverse(U_16155,U_16156)),U_16159)),
    inference(clausify,[status(thm)],[f_4011_3]) ).

fof(f_4012_1,plain,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(f_4012_2,plain,
    ! [U_16165,U_16164,U_16163,U_16162,U_16161,U_16160] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16160,tc_fun(U_16161,tc_HOL_Obool)),U_16162),hAPP(hAPP(c_COMBC(U_16160,tc_fun(U_16163,tc_fun(U_16161,tc_HOL_Obool)),tc_fun(U_16161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16163,tc_HOL_Obool),tc_fun(tc_fun(U_16163,tc_fun(U_16161,tc_HOL_Obool)),tc_fun(U_16161,tc_HOL_Obool)),U_16160),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16163,tc_fun(U_16161,tc_HOL_Obool))),U_16164)),U_16165)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16163,tc_fun(U_16161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16160,tc_fun(U_16163,tc_HOL_Obool)),U_16162),U_16164)),U_16165),
    inference(variable_rename,[status(thm)],[f_4012_1]) ).

fof(f_4012_3,plain,
    ! [U_16160,U_16161,U_16162,U_16163,U_16164,U_16165] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16160,tc_fun(U_16161,tc_HOL_Obool)),U_16162),hAPP(hAPP(c_COMBC(U_16160,tc_fun(U_16163,tc_fun(U_16161,tc_HOL_Obool)),tc_fun(U_16161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16163,tc_HOL_Obool),tc_fun(tc_fun(U_16163,tc_fun(U_16161,tc_HOL_Obool)),tc_fun(U_16161,tc_HOL_Obool)),U_16160),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16163,tc_fun(U_16161,tc_HOL_Obool))),U_16164)),U_16165)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16163,tc_fun(U_16161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16160,tc_fun(U_16163,tc_HOL_Obool)),U_16162),U_16164)),U_16165),
    inference(definitional_conversion,[status(esa)],[f_4012_2]) ).

cnf(f_4012_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16160,tc_fun(U_16161,tc_HOL_Obool)),U_16162),hAPP(hAPP(c_COMBC(U_16160,tc_fun(U_16163,tc_fun(U_16161,tc_HOL_Obool)),tc_fun(U_16161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16163,tc_HOL_Obool),tc_fun(tc_fun(U_16163,tc_fun(U_16161,tc_HOL_Obool)),tc_fun(U_16161,tc_HOL_Obool)),U_16160),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16163,tc_fun(U_16161,tc_HOL_Obool))),U_16164)),U_16165)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16163,tc_fun(U_16161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16160,tc_fun(U_16163,tc_HOL_Obool)),U_16162),U_16164)),U_16165),
    inference(clausify,[status(thm)],[f_4012_3]) ).

fof(f_4013_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(f_4013_2,plain,
    ! [U_16171,U_16170,U_16169,U_16168,U_16167,U_16166] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16166,tc_fun(U_16167,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16168,tc_fun(U_16166,tc_HOL_Obool)),U_16169),U_16170)),U_16171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16168,tc_fun(U_16167,tc_HOL_Obool)),U_16169),hAPP(hAPP(c_COMBC(U_16168,tc_fun(U_16166,tc_fun(U_16167,tc_HOL_Obool)),tc_fun(U_16167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16166,tc_HOL_Obool),tc_fun(tc_fun(U_16166,tc_fun(U_16167,tc_HOL_Obool)),tc_fun(U_16167,tc_HOL_Obool)),U_16168),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16166,tc_fun(U_16167,tc_HOL_Obool))),U_16170)),U_16171)),
    inference(variable_rename,[status(thm)],[f_4013_1]) ).

fof(f_4013_3,plain,
    ! [U_16166,U_16167,U_16168,U_16169,U_16170,U_16171] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16166,tc_fun(U_16167,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16168,tc_fun(U_16166,tc_HOL_Obool)),U_16169),U_16170)),U_16171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16168,tc_fun(U_16167,tc_HOL_Obool)),U_16169),hAPP(hAPP(c_COMBC(U_16168,tc_fun(U_16166,tc_fun(U_16167,tc_HOL_Obool)),tc_fun(U_16167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16166,tc_HOL_Obool),tc_fun(tc_fun(U_16166,tc_fun(U_16167,tc_HOL_Obool)),tc_fun(U_16167,tc_HOL_Obool)),U_16168),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16166,tc_fun(U_16167,tc_HOL_Obool))),U_16170)),U_16171)),
    inference(definitional_conversion,[status(esa)],[f_4013_2]) ).

cnf(f_4013_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16166,tc_fun(U_16167,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16168,tc_fun(U_16166,tc_HOL_Obool)),U_16169),U_16170)),U_16171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16168,tc_fun(U_16167,tc_HOL_Obool)),U_16169),hAPP(hAPP(c_COMBC(U_16168,tc_fun(U_16166,tc_fun(U_16167,tc_HOL_Obool)),tc_fun(U_16167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16166,tc_HOL_Obool),tc_fun(tc_fun(U_16166,tc_fun(U_16167,tc_HOL_Obool)),tc_fun(U_16167,tc_HOL_Obool)),U_16168),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16166,tc_fun(U_16167,tc_HOL_Obool))),U_16170)),U_16171)),
    inference(clausify,[status(thm)],[f_4013_3]) ).

fof(f_4014_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(f_4014_2,plain,
    ! [U_16176,U_16175,U_16174,U_16173,U_16172] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16172,tc_fun(U_16173,tc_HOL_Obool)),U_16174),hAPP(hAPP(c_COMBB(tc_fun(U_16173,tc_HOL_Obool),tc_fun(U_16173,tc_HOL_Obool),U_16172),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16173,tc_HOL_Obool)),U_16175)),U_16176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16173,tc_HOL_Obool)),U_16175),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16173,tc_HOL_Obool)),U_16174),U_16176)),
    inference(variable_rename,[status(thm)],[f_4014_1]) ).

fof(f_4014_3,plain,
    ! [U_16172,U_16173,U_16174,U_16175,U_16176] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16172,tc_fun(U_16173,tc_HOL_Obool)),U_16174),hAPP(hAPP(c_COMBB(tc_fun(U_16173,tc_HOL_Obool),tc_fun(U_16173,tc_HOL_Obool),U_16172),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16173,tc_HOL_Obool)),U_16175)),U_16176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16173,tc_HOL_Obool)),U_16175),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16173,tc_HOL_Obool)),U_16174),U_16176)),
    inference(definitional_conversion,[status(esa)],[f_4014_2]) ).

cnf(f_4014_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16172,tc_fun(U_16173,tc_HOL_Obool)),U_16174),hAPP(hAPP(c_COMBB(tc_fun(U_16173,tc_HOL_Obool),tc_fun(U_16173,tc_HOL_Obool),U_16172),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16173,tc_HOL_Obool)),U_16175)),U_16176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16173,tc_HOL_Obool)),U_16175),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16173,tc_HOL_Obool)),U_16174),U_16176)),
    inference(clausify,[status(thm)],[f_4014_3]) ).

fof(f_4015_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(f_4015_2,plain,
    ! [U_16181,U_16180,U_16179,U_16178,U_16177] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16177,tc_HOL_Obool)),U_16178),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16179,tc_fun(U_16177,tc_HOL_Obool)),U_16180),U_16181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16179,tc_fun(U_16177,tc_HOL_Obool)),U_16180),hAPP(hAPP(c_COMBB(tc_fun(U_16177,tc_HOL_Obool),tc_fun(U_16177,tc_HOL_Obool),U_16179),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16177,tc_HOL_Obool)),U_16178)),U_16181)),
    inference(variable_rename,[status(thm)],[f_4015_1]) ).

fof(f_4015_3,plain,
    ! [U_16177,U_16178,U_16179,U_16180,U_16181] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16177,tc_HOL_Obool)),U_16178),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16179,tc_fun(U_16177,tc_HOL_Obool)),U_16180),U_16181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16179,tc_fun(U_16177,tc_HOL_Obool)),U_16180),hAPP(hAPP(c_COMBB(tc_fun(U_16177,tc_HOL_Obool),tc_fun(U_16177,tc_HOL_Obool),U_16179),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16177,tc_HOL_Obool)),U_16178)),U_16181)),
    inference(definitional_conversion,[status(esa)],[f_4015_2]) ).

cnf(f_4015_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16177,tc_HOL_Obool)),U_16178),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16179,tc_fun(U_16177,tc_HOL_Obool)),U_16180),U_16181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16179,tc_fun(U_16177,tc_HOL_Obool)),U_16180),hAPP(hAPP(c_COMBB(tc_fun(U_16177,tc_HOL_Obool),tc_fun(U_16177,tc_HOL_Obool),U_16179),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16177,tc_HOL_Obool)),U_16178)),U_16181)),
    inference(clausify,[status(thm)],[f_4015_3]) ).

fof(f_4016_1,plain,
    ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).

fof(f_4016_2,plain,
    ! [U_16185,U_16184,U_16183,U_16182] : hAPP(c_Set_OCollect(U_16182),hAPP(hAPP(c_COMBB(tc_fun(U_16183,tc_HOL_Obool),tc_HOL_Obool,U_16182),c_HOL_OAll(U_16183)),hAPP(hAPP(c_COMBB(tc_fun(U_16183,tc_HOL_Obool),tc_fun(U_16183,tc_HOL_Obool),U_16182),hAPP(c_COMBS(U_16183,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16183),c_fimplies),hAPP(hAPP(c_COMBC(U_16183,tc_fun(U_16183,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16183)),U_16184)))),U_16185))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16182,tc_HOL_Obool)),U_16184),hAPP(hAPP(c_COMBB(tc_fun(U_16182,tc_HOL_Obool),tc_fun(U_16182,tc_HOL_Obool),U_16183),c_Set_OCollect(U_16182)),hAPP(c_COMBC(U_16182,U_16183,tc_HOL_Obool),U_16185))),
    inference(variable_rename,[status(thm)],[f_4016_1]) ).

fof(f_4016_3,plain,
    ! [U_16182,U_16183,U_16184,U_16185] : hAPP(c_Set_OCollect(U_16182),hAPP(hAPP(c_COMBB(tc_fun(U_16183,tc_HOL_Obool),tc_HOL_Obool,U_16182),c_HOL_OAll(U_16183)),hAPP(hAPP(c_COMBB(tc_fun(U_16183,tc_HOL_Obool),tc_fun(U_16183,tc_HOL_Obool),U_16182),hAPP(c_COMBS(U_16183,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16183),c_fimplies),hAPP(hAPP(c_COMBC(U_16183,tc_fun(U_16183,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16183)),U_16184)))),U_16185))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16182,tc_HOL_Obool)),U_16184),hAPP(hAPP(c_COMBB(tc_fun(U_16182,tc_HOL_Obool),tc_fun(U_16182,tc_HOL_Obool),U_16183),c_Set_OCollect(U_16182)),hAPP(c_COMBC(U_16182,U_16183,tc_HOL_Obool),U_16185))),
    inference(definitional_conversion,[status(esa)],[f_4016_2]) ).

cnf(f_4016_4,plain,
    hAPP(c_Set_OCollect(U_16182),hAPP(hAPP(c_COMBB(tc_fun(U_16183,tc_HOL_Obool),tc_HOL_Obool,U_16182),c_HOL_OAll(U_16183)),hAPP(hAPP(c_COMBB(tc_fun(U_16183,tc_HOL_Obool),tc_fun(U_16183,tc_HOL_Obool),U_16182),hAPP(c_COMBS(U_16183,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16183),c_fimplies),hAPP(hAPP(c_COMBC(U_16183,tc_fun(U_16183,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16183)),U_16184)))),U_16185))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16182,tc_HOL_Obool)),U_16184),hAPP(hAPP(c_COMBB(tc_fun(U_16182,tc_HOL_Obool),tc_fun(U_16182,tc_HOL_Obool),U_16183),c_Set_OCollect(U_16182)),hAPP(c_COMBC(U_16182,U_16183,tc_HOL_Obool),U_16185))),
    inference(clausify,[status(thm)],[f_4016_3]) ).

fof(f_4017_1,plain,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
    inference(fof_nnf,[status(thm)],[fact_INFI__bool__eq]) ).

fof(f_4017_2,plain,
    ! [U_16186] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16186,tc_HOL_Obool) = c_Set_OBall(U_16186),
    inference(variable_rename,[status(thm)],[f_4017_1]) ).

fof(f_4017_3,plain,
    ! [U_16186] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16186,tc_HOL_Obool) = c_Set_OBall(U_16186),
    inference(definitional_conversion,[status(esa)],[f_4017_2]) ).

cnf(f_4017_4,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16186,tc_HOL_Obool) = c_Set_OBall(U_16186),
    inference(clausify,[status(thm)],[f_4017_3]) ).

fof(f_4018_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq]) ).

fof(f_4018_2,plain,
    ! [U_16189,U_16188,U_16187] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_16187,U_16187,U_16187),hAPP(c_Relation_Oconverse(U_16187,U_16187),U_16189)),U_16189) = U_16189
      | ~ c_Equiv__Relations_Oequiv(U_16187,U_16188,U_16189) ),
    inference(variable_rename,[status(thm)],[f_4018_1]) ).

fof(f_4018_3,plain,
    ! [U_16187,U_16188,U_16189] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_16187,U_16187,U_16187),hAPP(c_Relation_Oconverse(U_16187,U_16187),U_16189)),U_16189) = U_16189
      | ~ c_Equiv__Relations_Oequiv(U_16187,U_16188,U_16189) ),
    inference(definitional_conversion,[status(esa)],[f_4018_2]) ).

cnf(f_4018_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_16187,U_16187,U_16187),hAPP(c_Relation_Oconverse(U_16187,U_16187),U_16189)),U_16189) = U_16189
    | ~ c_Equiv__Relations_Oequiv(U_16187,U_16188,U_16189) ),
    inference(clausify,[status(thm)],[f_4018_3]) ).

fof(f_4019_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INF__subset]) ).

fof(f_4019_2,plain,
    ! [U_16194,U_16193,U_16192,U_16191,U_16190] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16190),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16191,U_16190),U_16193),U_16194)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16191,U_16190),U_16192),U_16194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16191,tc_HOL_Obool)),U_16192),U_16193))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16190) ),
    inference(variable_rename,[status(thm)],[f_4019_1]) ).

fof(f_4019_3,plain,
    ! [U_16190,U_16191,U_16192,U_16193,U_16194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16190),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16191,U_16190),U_16193),U_16194)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16191,U_16190),U_16192),U_16194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16191,tc_HOL_Obool)),U_16192),U_16193))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16190) ),
    inference(definitional_conversion,[status(esa)],[f_4019_2]) ).

cnf(f_4019_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16190),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16191,U_16190),U_16193),U_16194)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16191,U_16190),U_16192),U_16194)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16191,tc_HOL_Obool)),U_16192),U_16193))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16190) ),
    inference(clausify,[status(thm)],[f_4019_3]) ).

fof(f_4020_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_INTER__def]) ).

fof(f_4020_2,plain,
    ! [U_16198,U_16197,U_16196,U_16195] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(U_16196,tc_HOL_Obool)),U_16197),U_16198) = hAPP(c_Set_OCollect(U_16196),hAPP(hAPP(c_COMBB(tc_fun(U_16195,tc_HOL_Obool),tc_HOL_Obool,U_16196),c_HOL_OAll(U_16195)),hAPP(hAPP(c_COMBB(tc_fun(U_16195,tc_HOL_Obool),tc_fun(U_16195,tc_HOL_Obool),U_16196),hAPP(c_COMBS(U_16195,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16195),c_fimplies),hAPP(hAPP(c_COMBC(U_16195,tc_fun(U_16195,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16195)),U_16197)))),hAPP(hAPP(c_COMBC(U_16196,tc_fun(U_16195,tc_fun(U_16196,tc_HOL_Obool)),tc_fun(U_16195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16196,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16195,tc_fun(U_16196,tc_HOL_Obool)),tc_fun(U_16195,tc_HOL_Obool)),U_16196),c_COMBB(tc_fun(U_16196,tc_HOL_Obool),tc_HOL_Obool,U_16195)),c_member(U_16196))),U_16198)))),
    inference(variable_rename,[status(thm)],[f_4020_1]) ).

fof(f_4020_3,plain,
    ! [U_16195,U_16196,U_16197,U_16198] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(U_16196,tc_HOL_Obool)),U_16197),U_16198) = hAPP(c_Set_OCollect(U_16196),hAPP(hAPP(c_COMBB(tc_fun(U_16195,tc_HOL_Obool),tc_HOL_Obool,U_16196),c_HOL_OAll(U_16195)),hAPP(hAPP(c_COMBB(tc_fun(U_16195,tc_HOL_Obool),tc_fun(U_16195,tc_HOL_Obool),U_16196),hAPP(c_COMBS(U_16195,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16195),c_fimplies),hAPP(hAPP(c_COMBC(U_16195,tc_fun(U_16195,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16195)),U_16197)))),hAPP(hAPP(c_COMBC(U_16196,tc_fun(U_16195,tc_fun(U_16196,tc_HOL_Obool)),tc_fun(U_16195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16196,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16195,tc_fun(U_16196,tc_HOL_Obool)),tc_fun(U_16195,tc_HOL_Obool)),U_16196),c_COMBB(tc_fun(U_16196,tc_HOL_Obool),tc_HOL_Obool,U_16195)),c_member(U_16196))),U_16198)))),
    inference(definitional_conversion,[status(esa)],[f_4020_2]) ).

cnf(f_4020_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(U_16196,tc_HOL_Obool)),U_16197),U_16198) = hAPP(c_Set_OCollect(U_16196),hAPP(hAPP(c_COMBB(tc_fun(U_16195,tc_HOL_Obool),tc_HOL_Obool,U_16196),c_HOL_OAll(U_16195)),hAPP(hAPP(c_COMBB(tc_fun(U_16195,tc_HOL_Obool),tc_fun(U_16195,tc_HOL_Obool),U_16196),hAPP(c_COMBS(U_16195,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16195),c_fimplies),hAPP(hAPP(c_COMBC(U_16195,tc_fun(U_16195,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16195)),U_16197)))),hAPP(hAPP(c_COMBC(U_16196,tc_fun(U_16195,tc_fun(U_16196,tc_HOL_Obool)),tc_fun(U_16195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16196,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16195,tc_fun(U_16196,tc_HOL_Obool)),tc_fun(U_16195,tc_HOL_Obool)),U_16196),c_COMBB(tc_fun(U_16196,tc_HOL_Obool),tc_HOL_Obool,U_16195)),c_member(U_16196))),U_16198)))),
    inference(clausify,[status(thm)],[f_4020_3]) ).

fof(f_4021_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J]) ).

fof(f_4021_2,plain,
    ! [U_16203,U_16202,U_16201,U_16200,U_16199] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16200,tc_fun(U_16201,tc_HOL_Obool)),U_16199),hAPP(hAPP(c_COMBB(tc_fun(U_16201,tc_HOL_Obool),tc_fun(U_16201,tc_HOL_Obool),U_16200),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16201,tc_HOL_Obool)),U_16202)),U_16203)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16201,tc_HOL_Obool)),U_16202),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16200,tc_fun(U_16201,tc_HOL_Obool)),U_16199),U_16203))
        | U_16199 = c_Orderings_Obot__class_Obot(tc_fun(U_16200,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16200,tc_fun(U_16201,tc_HOL_Obool)),U_16199),hAPP(hAPP(c_COMBB(tc_fun(U_16201,tc_HOL_Obool),tc_fun(U_16201,tc_HOL_Obool),U_16200),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16201,tc_HOL_Obool)),U_16202)),U_16203)) = c_Orderings_Otop__class_Otop(tc_fun(U_16201,tc_HOL_Obool))
        | U_16199 != c_Orderings_Obot__class_Obot(tc_fun(U_16200,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4021_1]) ).

fof(f_4021_3,plain,
    ( ! [U_16213,U_16211,U_16209,U_16207,U_16205] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16209,tc_HOL_Obool)),U_16205),hAPP(hAPP(c_COMBB(tc_fun(U_16209,tc_HOL_Obool),tc_fun(U_16209,tc_HOL_Obool),U_16207),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16209,tc_HOL_Obool)),U_16211)),U_16213)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16209,tc_HOL_Obool)),U_16211),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16209,tc_HOL_Obool)),U_16205),U_16213))
        | U_16205 = c_Orderings_Obot__class_Obot(tc_fun(U_16207,tc_HOL_Obool)) )
    & ! [U_16212,U_16210,U_16208,U_16206,U_16204] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16206,tc_fun(U_16208,tc_HOL_Obool)),U_16204),hAPP(hAPP(c_COMBB(tc_fun(U_16208,tc_HOL_Obool),tc_fun(U_16208,tc_HOL_Obool),U_16206),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16208,tc_HOL_Obool)),U_16210)),U_16212)) = c_Orderings_Otop__class_Otop(tc_fun(U_16208,tc_HOL_Obool))
        | U_16204 != c_Orderings_Obot__class_Obot(tc_fun(U_16206,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4021_2]) ).

fof(f_4021_4,plain,
    ( ! [U_16205,U_16207,U_16209,U_16211,U_16213] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16209,tc_HOL_Obool)),U_16205),hAPP(hAPP(c_COMBB(tc_fun(U_16209,tc_HOL_Obool),tc_fun(U_16209,tc_HOL_Obool),U_16207),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16209,tc_HOL_Obool)),U_16211)),U_16213)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16209,tc_HOL_Obool)),U_16211),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16209,tc_HOL_Obool)),U_16205),U_16213))
        | U_16205 = c_Orderings_Obot__class_Obot(tc_fun(U_16207,tc_HOL_Obool)) )
    & ! [U_16210,U_16206,U_16204,U_16208,U_16212] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16206,tc_fun(U_16208,tc_HOL_Obool)),U_16204),hAPP(hAPP(c_COMBB(tc_fun(U_16208,tc_HOL_Obool),tc_fun(U_16208,tc_HOL_Obool),U_16206),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16208,tc_HOL_Obool)),U_16210)),U_16212)) = c_Orderings_Otop__class_Otop(tc_fun(U_16208,tc_HOL_Obool))
        | U_16204 != c_Orderings_Obot__class_Obot(tc_fun(U_16206,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4021_3]) ).

cnf(f_4021_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16206,tc_fun(U_16208,tc_HOL_Obool)),U_16204),hAPP(hAPP(c_COMBB(tc_fun(U_16208,tc_HOL_Obool),tc_fun(U_16208,tc_HOL_Obool),U_16206),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16208,tc_HOL_Obool)),U_16210)),U_16212)) = c_Orderings_Otop__class_Otop(tc_fun(U_16208,tc_HOL_Obool))
    | U_16204 != c_Orderings_Obot__class_Obot(tc_fun(U_16206,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4021_4]) ).

cnf(f_4021_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16209,tc_HOL_Obool)),U_16205),hAPP(hAPP(c_COMBB(tc_fun(U_16209,tc_HOL_Obool),tc_fun(U_16209,tc_HOL_Obool),U_16207),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16209,tc_HOL_Obool)),U_16211)),U_16213)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16209,tc_HOL_Obool)),U_16211),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16209,tc_HOL_Obool)),U_16205),U_16213))
    | U_16205 = c_Orderings_Obot__class_Obot(tc_fun(U_16207,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4021_4]) ).

fof(f_4022_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J]) ).

fof(f_4022_2,plain,
    ! [U_16218,U_16217,U_16216,U_16215,U_16214] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),U_16214),hAPP(hAPP(c_COMBC(U_16215,tc_fun(U_16216,tc_HOL_Obool),tc_fun(U_16216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16216,tc_HOL_Obool),tc_fun(tc_fun(U_16216,tc_HOL_Obool),tc_fun(U_16216,tc_HOL_Obool)),U_16215),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16216,tc_HOL_Obool))),U_16217)),U_16218)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16216,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),U_16214),U_16217)),U_16218)
        | U_16214 = c_Orderings_Obot__class_Obot(tc_fun(U_16215,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),U_16214),hAPP(hAPP(c_COMBC(U_16215,tc_fun(U_16216,tc_HOL_Obool),tc_fun(U_16216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16216,tc_HOL_Obool),tc_fun(tc_fun(U_16216,tc_HOL_Obool),tc_fun(U_16216,tc_HOL_Obool)),U_16215),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16216,tc_HOL_Obool))),U_16217)),U_16218)) = c_Orderings_Otop__class_Otop(tc_fun(U_16216,tc_HOL_Obool))
        | U_16214 != c_Orderings_Obot__class_Obot(tc_fun(U_16215,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4022_1]) ).

fof(f_4022_3,plain,
    ( ! [U_16228,U_16226,U_16224,U_16222,U_16220] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16224,tc_HOL_Obool)),U_16220),hAPP(hAPP(c_COMBC(U_16222,tc_fun(U_16224,tc_HOL_Obool),tc_fun(U_16224,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16224,tc_HOL_Obool),tc_fun(tc_fun(U_16224,tc_HOL_Obool),tc_fun(U_16224,tc_HOL_Obool)),U_16222),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16224,tc_HOL_Obool))),U_16226)),U_16228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16224,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16224,tc_HOL_Obool)),U_16220),U_16226)),U_16228)
        | U_16220 = c_Orderings_Obot__class_Obot(tc_fun(U_16222,tc_HOL_Obool)) )
    & ! [U_16227,U_16225,U_16223,U_16221,U_16219] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16221,tc_fun(U_16223,tc_HOL_Obool)),U_16219),hAPP(hAPP(c_COMBC(U_16221,tc_fun(U_16223,tc_HOL_Obool),tc_fun(U_16223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16223,tc_HOL_Obool),tc_fun(tc_fun(U_16223,tc_HOL_Obool),tc_fun(U_16223,tc_HOL_Obool)),U_16221),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16223,tc_HOL_Obool))),U_16225)),U_16227)) = c_Orderings_Otop__class_Otop(tc_fun(U_16223,tc_HOL_Obool))
        | U_16219 != c_Orderings_Obot__class_Obot(tc_fun(U_16221,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4022_2]) ).

fof(f_4022_4,plain,
    ( ! [U_16220,U_16222,U_16224,U_16226,U_16228] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16224,tc_HOL_Obool)),U_16220),hAPP(hAPP(c_COMBC(U_16222,tc_fun(U_16224,tc_HOL_Obool),tc_fun(U_16224,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16224,tc_HOL_Obool),tc_fun(tc_fun(U_16224,tc_HOL_Obool),tc_fun(U_16224,tc_HOL_Obool)),U_16222),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16224,tc_HOL_Obool))),U_16226)),U_16228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16224,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16224,tc_HOL_Obool)),U_16220),U_16226)),U_16228)
        | U_16220 = c_Orderings_Obot__class_Obot(tc_fun(U_16222,tc_HOL_Obool)) )
    & ! [U_16225,U_16221,U_16219,U_16223,U_16227] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16221,tc_fun(U_16223,tc_HOL_Obool)),U_16219),hAPP(hAPP(c_COMBC(U_16221,tc_fun(U_16223,tc_HOL_Obool),tc_fun(U_16223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16223,tc_HOL_Obool),tc_fun(tc_fun(U_16223,tc_HOL_Obool),tc_fun(U_16223,tc_HOL_Obool)),U_16221),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16223,tc_HOL_Obool))),U_16225)),U_16227)) = c_Orderings_Otop__class_Otop(tc_fun(U_16223,tc_HOL_Obool))
        | U_16219 != c_Orderings_Obot__class_Obot(tc_fun(U_16221,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4022_3]) ).

cnf(f_4022_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16221,tc_fun(U_16223,tc_HOL_Obool)),U_16219),hAPP(hAPP(c_COMBC(U_16221,tc_fun(U_16223,tc_HOL_Obool),tc_fun(U_16223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16223,tc_HOL_Obool),tc_fun(tc_fun(U_16223,tc_HOL_Obool),tc_fun(U_16223,tc_HOL_Obool)),U_16221),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16223,tc_HOL_Obool))),U_16225)),U_16227)) = c_Orderings_Otop__class_Otop(tc_fun(U_16223,tc_HOL_Obool))
    | U_16219 != c_Orderings_Obot__class_Obot(tc_fun(U_16221,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4022_4]) ).

cnf(f_4022_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16224,tc_HOL_Obool)),U_16220),hAPP(hAPP(c_COMBC(U_16222,tc_fun(U_16224,tc_HOL_Obool),tc_fun(U_16224,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16224,tc_HOL_Obool),tc_fun(tc_fun(U_16224,tc_HOL_Obool),tc_fun(U_16224,tc_HOL_Obool)),U_16222),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16224,tc_HOL_Obool))),U_16226)),U_16228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16224,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16224,tc_HOL_Obool)),U_16220),U_16226)),U_16228)
    | U_16220 = c_Orderings_Obot__class_Obot(tc_fun(U_16222,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4022_4]) ).

fof(f_4023_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2)
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J]) ).

fof(f_4023_2,plain,
    ! [U_16233,U_16232,U_16231,U_16230,U_16229] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16231,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16230,tc_fun(U_16231,tc_HOL_Obool)),U_16229),U_16232)),U_16233) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16230,tc_fun(U_16231,tc_HOL_Obool)),U_16229),hAPP(hAPP(c_COMBC(U_16230,tc_fun(U_16231,tc_HOL_Obool),tc_fun(U_16231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16231,tc_HOL_Obool),tc_fun(tc_fun(U_16231,tc_HOL_Obool),tc_fun(U_16231,tc_HOL_Obool)),U_16230),c_Groups_Ominus__class_Ominus(tc_fun(U_16231,tc_HOL_Obool))),U_16232)),U_16233))
        | U_16229 = c_Orderings_Obot__class_Obot(tc_fun(U_16230,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16231,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16230,tc_fun(U_16231,tc_HOL_Obool)),U_16229),U_16232)),U_16233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16231,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16231,tc_HOL_Obool))),U_16233)
        | U_16229 != c_Orderings_Obot__class_Obot(tc_fun(U_16230,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4023_1]) ).

fof(f_4023_3,plain,
    ( ! [U_16243,U_16241,U_16239,U_16237,U_16235] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16239,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16239,tc_HOL_Obool)),U_16235),U_16241)),U_16243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16239,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_COMBC(U_16237,tc_fun(U_16239,tc_HOL_Obool),tc_fun(U_16239,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16239,tc_HOL_Obool),tc_fun(tc_fun(U_16239,tc_HOL_Obool),tc_fun(U_16239,tc_HOL_Obool)),U_16237),c_Groups_Ominus__class_Ominus(tc_fun(U_16239,tc_HOL_Obool))),U_16241)),U_16243))
        | U_16235 = c_Orderings_Obot__class_Obot(tc_fun(U_16237,tc_HOL_Obool)) )
    & ! [U_16242,U_16240,U_16238,U_16236,U_16234] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16238,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16238,tc_HOL_Obool)),U_16234),U_16240)),U_16242) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16238,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16238,tc_HOL_Obool))),U_16242)
        | U_16234 != c_Orderings_Obot__class_Obot(tc_fun(U_16236,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4023_2]) ).

fof(f_4023_4,plain,
    ( ! [U_16235,U_16237,U_16239,U_16241,U_16243] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16239,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16239,tc_HOL_Obool)),U_16235),U_16241)),U_16243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16239,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_COMBC(U_16237,tc_fun(U_16239,tc_HOL_Obool),tc_fun(U_16239,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16239,tc_HOL_Obool),tc_fun(tc_fun(U_16239,tc_HOL_Obool),tc_fun(U_16239,tc_HOL_Obool)),U_16237),c_Groups_Ominus__class_Ominus(tc_fun(U_16239,tc_HOL_Obool))),U_16241)),U_16243))
        | U_16235 = c_Orderings_Obot__class_Obot(tc_fun(U_16237,tc_HOL_Obool)) )
    & ! [U_16240,U_16236,U_16234,U_16242,U_16238] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16238,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16238,tc_HOL_Obool)),U_16234),U_16240)),U_16242) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16238,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16238,tc_HOL_Obool))),U_16242)
        | U_16234 != c_Orderings_Obot__class_Obot(tc_fun(U_16236,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4023_3]) ).

cnf(f_4023_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16238,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16238,tc_HOL_Obool)),U_16234),U_16240)),U_16242) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16238,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16238,tc_HOL_Obool))),U_16242)
    | U_16234 != c_Orderings_Obot__class_Obot(tc_fun(U_16236,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4023_4]) ).

cnf(f_4023_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16239,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16239,tc_HOL_Obool)),U_16235),U_16241)),U_16243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16239,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_COMBC(U_16237,tc_fun(U_16239,tc_HOL_Obool),tc_fun(U_16239,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16239,tc_HOL_Obool),tc_fun(tc_fun(U_16239,tc_HOL_Obool),tc_fun(U_16239,tc_HOL_Obool)),U_16237),c_Groups_Ominus__class_Ominus(tc_fun(U_16239,tc_HOL_Obool))),U_16241)),U_16243))
    | U_16235 = c_Orderings_Obot__class_Obot(tc_fun(U_16237,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4023_4]) ).

fof(f_4024_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J]) ).

fof(f_4024_2,plain,
    ! [U_16248,U_16247,U_16246,U_16245,U_16244] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16245,tc_fun(U_16246,tc_HOL_Obool)),U_16244),hAPP(hAPP(c_COMBC(U_16245,tc_fun(U_16246,tc_HOL_Obool),tc_fun(U_16246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16246,tc_HOL_Obool),tc_fun(tc_fun(U_16246,tc_HOL_Obool),tc_fun(U_16246,tc_HOL_Obool)),U_16245),c_Groups_Ominus__class_Ominus(tc_fun(U_16246,tc_HOL_Obool))),U_16247)),U_16248)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16246,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16245,tc_fun(U_16246,tc_HOL_Obool)),U_16244),U_16247)),U_16248)
        | U_16244 = c_Orderings_Obot__class_Obot(tc_fun(U_16245,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16245,tc_fun(U_16246,tc_HOL_Obool)),U_16244),hAPP(hAPP(c_COMBC(U_16245,tc_fun(U_16246,tc_HOL_Obool),tc_fun(U_16246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16246,tc_HOL_Obool),tc_fun(tc_fun(U_16246,tc_HOL_Obool),tc_fun(U_16246,tc_HOL_Obool)),U_16245),c_Groups_Ominus__class_Ominus(tc_fun(U_16246,tc_HOL_Obool))),U_16247)),U_16248)) = c_Orderings_Otop__class_Otop(tc_fun(U_16246,tc_HOL_Obool))
        | U_16244 != c_Orderings_Obot__class_Obot(tc_fun(U_16245,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4024_1]) ).

fof(f_4024_3,plain,
    ( ! [U_16258,U_16256,U_16254,U_16252,U_16250] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16252,tc_fun(U_16254,tc_HOL_Obool)),U_16250),hAPP(hAPP(c_COMBC(U_16252,tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16254,tc_HOL_Obool),tc_fun(tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool)),U_16252),c_Groups_Ominus__class_Ominus(tc_fun(U_16254,tc_HOL_Obool))),U_16256)),U_16258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16252,tc_fun(U_16254,tc_HOL_Obool)),U_16250),U_16256)),U_16258)
        | U_16250 = c_Orderings_Obot__class_Obot(tc_fun(U_16252,tc_HOL_Obool)) )
    & ! [U_16257,U_16255,U_16253,U_16251,U_16249] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16251,tc_fun(U_16253,tc_HOL_Obool)),U_16249),hAPP(hAPP(c_COMBC(U_16251,tc_fun(U_16253,tc_HOL_Obool),tc_fun(U_16253,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16253,tc_HOL_Obool),tc_fun(tc_fun(U_16253,tc_HOL_Obool),tc_fun(U_16253,tc_HOL_Obool)),U_16251),c_Groups_Ominus__class_Ominus(tc_fun(U_16253,tc_HOL_Obool))),U_16255)),U_16257)) = c_Orderings_Otop__class_Otop(tc_fun(U_16253,tc_HOL_Obool))
        | U_16249 != c_Orderings_Obot__class_Obot(tc_fun(U_16251,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4024_2]) ).

fof(f_4024_4,plain,
    ( ! [U_16250,U_16252,U_16254,U_16256,U_16258] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16252,tc_fun(U_16254,tc_HOL_Obool)),U_16250),hAPP(hAPP(c_COMBC(U_16252,tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16254,tc_HOL_Obool),tc_fun(tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool)),U_16252),c_Groups_Ominus__class_Ominus(tc_fun(U_16254,tc_HOL_Obool))),U_16256)),U_16258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16252,tc_fun(U_16254,tc_HOL_Obool)),U_16250),U_16256)),U_16258)
        | U_16250 = c_Orderings_Obot__class_Obot(tc_fun(U_16252,tc_HOL_Obool)) )
    & ! [U_16253,U_16255,U_16251,U_16249,U_16257] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16251,tc_fun(U_16253,tc_HOL_Obool)),U_16249),hAPP(hAPP(c_COMBC(U_16251,tc_fun(U_16253,tc_HOL_Obool),tc_fun(U_16253,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16253,tc_HOL_Obool),tc_fun(tc_fun(U_16253,tc_HOL_Obool),tc_fun(U_16253,tc_HOL_Obool)),U_16251),c_Groups_Ominus__class_Ominus(tc_fun(U_16253,tc_HOL_Obool))),U_16255)),U_16257)) = c_Orderings_Otop__class_Otop(tc_fun(U_16253,tc_HOL_Obool))
        | U_16249 != c_Orderings_Obot__class_Obot(tc_fun(U_16251,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4024_3]) ).

cnf(f_4024_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16251,tc_fun(U_16253,tc_HOL_Obool)),U_16249),hAPP(hAPP(c_COMBC(U_16251,tc_fun(U_16253,tc_HOL_Obool),tc_fun(U_16253,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16253,tc_HOL_Obool),tc_fun(tc_fun(U_16253,tc_HOL_Obool),tc_fun(U_16253,tc_HOL_Obool)),U_16251),c_Groups_Ominus__class_Ominus(tc_fun(U_16253,tc_HOL_Obool))),U_16255)),U_16257)) = c_Orderings_Otop__class_Otop(tc_fun(U_16253,tc_HOL_Obool))
    | U_16249 != c_Orderings_Obot__class_Obot(tc_fun(U_16251,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4024_4]) ).

cnf(f_4024_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16252,tc_fun(U_16254,tc_HOL_Obool)),U_16250),hAPP(hAPP(c_COMBC(U_16252,tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16254,tc_HOL_Obool),tc_fun(tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool)),U_16252),c_Groups_Ominus__class_Ominus(tc_fun(U_16254,tc_HOL_Obool))),U_16256)),U_16258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16252,tc_fun(U_16254,tc_HOL_Obool)),U_16250),U_16256)),U_16258)
    | U_16250 = c_Orderings_Obot__class_Obot(tc_fun(U_16252,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4024_4]) ).

fof(f_4025_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J]) ).

fof(f_4025_2,plain,
    ! [U_16263,U_16262,U_16261,U_16260,U_16259] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16261,tc_HOL_Obool)),U_16262),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16260,tc_fun(U_16261,tc_HOL_Obool)),U_16259),U_16263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16260,tc_fun(U_16261,tc_HOL_Obool)),U_16259),hAPP(hAPP(c_COMBB(tc_fun(U_16261,tc_HOL_Obool),tc_fun(U_16261,tc_HOL_Obool),U_16260),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16261,tc_HOL_Obool)),U_16262)),U_16263))
        | U_16259 = c_Orderings_Obot__class_Obot(tc_fun(U_16260,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16261,tc_HOL_Obool)),U_16262),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16260,tc_fun(U_16261,tc_HOL_Obool)),U_16259),U_16263)) = U_16262
        | U_16259 != c_Orderings_Obot__class_Obot(tc_fun(U_16260,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4025_1]) ).

fof(f_4025_3,plain,
    ( ! [U_16273,U_16271,U_16269,U_16267,U_16265] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16269,tc_HOL_Obool)),U_16271),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16267,tc_fun(U_16269,tc_HOL_Obool)),U_16265),U_16273)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16267,tc_fun(U_16269,tc_HOL_Obool)),U_16265),hAPP(hAPP(c_COMBB(tc_fun(U_16269,tc_HOL_Obool),tc_fun(U_16269,tc_HOL_Obool),U_16267),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16269,tc_HOL_Obool)),U_16271)),U_16273))
        | U_16265 = c_Orderings_Obot__class_Obot(tc_fun(U_16267,tc_HOL_Obool)) )
    & ! [U_16272,U_16270,U_16268,U_16266,U_16264] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16268,tc_HOL_Obool)),U_16270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16266,tc_fun(U_16268,tc_HOL_Obool)),U_16264),U_16272)) = U_16270
        | U_16264 != c_Orderings_Obot__class_Obot(tc_fun(U_16266,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4025_2]) ).

fof(f_4025_4,plain,
    ( ! [U_16265,U_16267,U_16269,U_16271,U_16273] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16269,tc_HOL_Obool)),U_16271),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16267,tc_fun(U_16269,tc_HOL_Obool)),U_16265),U_16273)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16267,tc_fun(U_16269,tc_HOL_Obool)),U_16265),hAPP(hAPP(c_COMBB(tc_fun(U_16269,tc_HOL_Obool),tc_fun(U_16269,tc_HOL_Obool),U_16267),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16269,tc_HOL_Obool)),U_16271)),U_16273))
        | U_16265 = c_Orderings_Obot__class_Obot(tc_fun(U_16267,tc_HOL_Obool)) )
    & ! [U_16266,U_16270,U_16268,U_16264,U_16272] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16268,tc_HOL_Obool)),U_16270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16266,tc_fun(U_16268,tc_HOL_Obool)),U_16264),U_16272)) = U_16270
        | U_16264 != c_Orderings_Obot__class_Obot(tc_fun(U_16266,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4025_3]) ).

cnf(f_4025_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16268,tc_HOL_Obool)),U_16270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16266,tc_fun(U_16268,tc_HOL_Obool)),U_16264),U_16272)) = U_16270
    | U_16264 != c_Orderings_Obot__class_Obot(tc_fun(U_16266,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4025_4]) ).

cnf(f_4025_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16269,tc_HOL_Obool)),U_16271),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16267,tc_fun(U_16269,tc_HOL_Obool)),U_16265),U_16273)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16267,tc_fun(U_16269,tc_HOL_Obool)),U_16265),hAPP(hAPP(c_COMBB(tc_fun(U_16269,tc_HOL_Obool),tc_fun(U_16269,tc_HOL_Obool),U_16267),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16269,tc_HOL_Obool)),U_16271)),U_16273))
    | U_16265 = c_Orderings_Obot__class_Obot(tc_fun(U_16267,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4025_4]) ).

fof(f_4026_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI]) ).

fof(f_4026_2,plain,
    ! [U_16277,U_16276,U_16275,U_16274] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16274,U_16274)),hAPP(hAPP(c_Product__Type_OPair(U_16274,U_16274),U_16276),U_16275)),c_Transitive__Closure_Ortrancl(U_16274,hAPP(c_Relation_Oconverse(U_16274,U_16274),U_16277))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16274,U_16274)),hAPP(hAPP(c_Product__Type_OPair(U_16274,U_16274),U_16275),U_16276)),c_Transitive__Closure_Ortrancl(U_16274,U_16277))) ),
    inference(variable_rename,[status(thm)],[f_4026_1]) ).

fof(f_4026_3,plain,
    ! [U_16274,U_16275,U_16276,U_16277] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16274,U_16274)),hAPP(hAPP(c_Product__Type_OPair(U_16274,U_16274),U_16276),U_16275)),c_Transitive__Closure_Ortrancl(U_16274,hAPP(c_Relation_Oconverse(U_16274,U_16274),U_16277))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16274,U_16274)),hAPP(hAPP(c_Product__Type_OPair(U_16274,U_16274),U_16275),U_16276)),c_Transitive__Closure_Ortrancl(U_16274,U_16277))) ),
    inference(definitional_conversion,[status(esa)],[f_4026_2]) ).

cnf(f_4026_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16274,U_16274)),hAPP(hAPP(c_Product__Type_OPair(U_16274,U_16274),U_16276),U_16275)),c_Transitive__Closure_Ortrancl(U_16274,hAPP(c_Relation_Oconverse(U_16274,U_16274),U_16277))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16274,U_16274)),hAPP(hAPP(c_Product__Type_OPair(U_16274,U_16274),U_16275),U_16276)),c_Transitive__Closure_Ortrancl(U_16274,U_16277))) ),
    inference(clausify,[status(thm)],[f_4026_3]) ).

fof(f_4027_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD]) ).

fof(f_4027_2,plain,
    ! [U_16281,U_16280,U_16279,U_16278] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16278,U_16278)),hAPP(hAPP(c_Product__Type_OPair(U_16278,U_16278),U_16280),U_16279)),c_Transitive__Closure_Ortrancl(U_16278,U_16281)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16278,U_16278)),hAPP(hAPP(c_Product__Type_OPair(U_16278,U_16278),U_16279),U_16280)),c_Transitive__Closure_Ortrancl(U_16278,hAPP(c_Relation_Oconverse(U_16278,U_16278),U_16281)))) ),
    inference(variable_rename,[status(thm)],[f_4027_1]) ).

fof(f_4027_3,plain,
    ! [U_16278,U_16279,U_16280,U_16281] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16278,U_16278)),hAPP(hAPP(c_Product__Type_OPair(U_16278,U_16278),U_16280),U_16279)),c_Transitive__Closure_Ortrancl(U_16278,U_16281)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16278,U_16278)),hAPP(hAPP(c_Product__Type_OPair(U_16278,U_16278),U_16279),U_16280)),c_Transitive__Closure_Ortrancl(U_16278,hAPP(c_Relation_Oconverse(U_16278,U_16278),U_16281)))) ),
    inference(definitional_conversion,[status(esa)],[f_4027_2]) ).

cnf(f_4027_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16278,U_16278)),hAPP(hAPP(c_Product__Type_OPair(U_16278,U_16278),U_16280),U_16279)),c_Transitive__Closure_Ortrancl(U_16278,U_16281)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16278,U_16278)),hAPP(hAPP(c_Product__Type_OPair(U_16278,U_16278),U_16279),U_16280)),c_Transitive__Closure_Ortrancl(U_16278,hAPP(c_Relation_Oconverse(U_16278,U_16278),U_16281)))) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

fof(f_4028_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__converseI]) ).

fof(f_4028_2,plain,
    ! [U_16285,U_16284,U_16283,U_16282] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16282,U_16282)),hAPP(hAPP(c_Product__Type_OPair(U_16282,U_16282),U_16283),U_16284)),c_Transitive__Closure_Otrancl(U_16282,hAPP(c_Relation_Oconverse(U_16282,U_16282),U_16285))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16282,U_16282)),hAPP(hAPP(c_Product__Type_OPair(U_16282,U_16282),U_16283),U_16284)),hAPP(c_Relation_Oconverse(U_16282,U_16282),c_Transitive__Closure_Otrancl(U_16282,U_16285)))) ),
    inference(variable_rename,[status(thm)],[f_4028_1]) ).

fof(f_4028_3,plain,
    ! [U_16282,U_16283,U_16284,U_16285] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16282,U_16282)),hAPP(hAPP(c_Product__Type_OPair(U_16282,U_16282),U_16283),U_16284)),c_Transitive__Closure_Otrancl(U_16282,hAPP(c_Relation_Oconverse(U_16282,U_16282),U_16285))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16282,U_16282)),hAPP(hAPP(c_Product__Type_OPair(U_16282,U_16282),U_16283),U_16284)),hAPP(c_Relation_Oconverse(U_16282,U_16282),c_Transitive__Closure_Otrancl(U_16282,U_16285)))) ),
    inference(definitional_conversion,[status(esa)],[f_4028_2]) ).

cnf(f_4028_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16282,U_16282)),hAPP(hAPP(c_Product__Type_OPair(U_16282,U_16282),U_16283),U_16284)),c_Transitive__Closure_Otrancl(U_16282,hAPP(c_Relation_Oconverse(U_16282,U_16282),U_16285))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16282,U_16282)),hAPP(hAPP(c_Product__Type_OPair(U_16282,U_16282),U_16283),U_16284)),hAPP(c_Relation_Oconverse(U_16282,U_16282),c_Transitive__Closure_Otrancl(U_16282,U_16285)))) ),
    inference(clausify,[status(thm)],[f_4028_3]) ).

fof(f_4029_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__converseD]) ).

fof(f_4029_2,plain,
    ! [U_16289,U_16288,U_16287,U_16286] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16286,U_16286)),hAPP(hAPP(c_Product__Type_OPair(U_16286,U_16286),U_16287),U_16288)),hAPP(c_Relation_Oconverse(U_16286,U_16286),c_Transitive__Closure_Otrancl(U_16286,U_16289))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16286,U_16286)),hAPP(hAPP(c_Product__Type_OPair(U_16286,U_16286),U_16287),U_16288)),c_Transitive__Closure_Otrancl(U_16286,hAPP(c_Relation_Oconverse(U_16286,U_16286),U_16289)))) ),
    inference(variable_rename,[status(thm)],[f_4029_1]) ).

fof(f_4029_3,plain,
    ! [U_16286,U_16287,U_16288,U_16289] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16286,U_16286)),hAPP(hAPP(c_Product__Type_OPair(U_16286,U_16286),U_16287),U_16288)),hAPP(c_Relation_Oconverse(U_16286,U_16286),c_Transitive__Closure_Otrancl(U_16286,U_16289))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16286,U_16286)),hAPP(hAPP(c_Product__Type_OPair(U_16286,U_16286),U_16287),U_16288)),c_Transitive__Closure_Otrancl(U_16286,hAPP(c_Relation_Oconverse(U_16286,U_16286),U_16289)))) ),
    inference(definitional_conversion,[status(esa)],[f_4029_2]) ).

cnf(f_4029_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16286,U_16286)),hAPP(hAPP(c_Product__Type_OPair(U_16286,U_16286),U_16287),U_16288)),hAPP(c_Relation_Oconverse(U_16286,U_16286),c_Transitive__Closure_Otrancl(U_16286,U_16289))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16286,U_16286)),hAPP(hAPP(c_Product__Type_OPair(U_16286,U_16286),U_16287),U_16288)),c_Transitive__Closure_Otrancl(U_16286,hAPP(c_Relation_Oconverse(U_16286,U_16286),U_16289)))) ),
    inference(clausify,[status(thm)],[f_4029_3]) ).

fof(f_4030_1,plain,
    ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__subset__eq]) ).

fof(f_4030_2,plain,
    ! [U_16294,U_16293,U_16292,U_16291,U_16290] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16290,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16291,U_16290,U_16292),U_16293)),U_16294))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16291,tc_HOL_Obool)),U_16293),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16291,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16290,U_16291,hAPP(c_Relation_Oconverse(U_16291,U_16290),U_16292)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16290,tc_HOL_Obool)),U_16294))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16291,tc_HOL_Obool)),U_16293),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16291,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16290,U_16291,hAPP(c_Relation_Oconverse(U_16291,U_16290),U_16292)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16290,tc_HOL_Obool)),U_16294)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16290,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16291,U_16290,U_16292),U_16293)),U_16294)) ) ),
    inference(variable_rename,[status(thm)],[f_4030_1]) ).

fof(f_4030_3,plain,
    ( ! [U_16304,U_16302,U_16300,U_16298,U_16296] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16296,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16298,U_16296,U_16300),U_16302)),U_16304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16298,tc_HOL_Obool)),U_16302),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16298,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16296,U_16298,hAPP(c_Relation_Oconverse(U_16298,U_16296),U_16300)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16296,tc_HOL_Obool)),U_16304))))) )
    & ! [U_16303,U_16301,U_16299,U_16297,U_16295] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16297,tc_HOL_Obool)),U_16301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16297,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16295,U_16297,hAPP(c_Relation_Oconverse(U_16297,U_16295),U_16299)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16295,tc_HOL_Obool)),U_16303)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16295,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16297,U_16295,U_16299),U_16301)),U_16303)) ) ),
    inference(miniscope,[status(thm)],[f_4030_2]) ).

fof(f_4030_4,plain,
    ( ! [U_16296,U_16298,U_16300,U_16302,U_16304] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16296,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16298,U_16296,U_16300),U_16302)),U_16304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16298,tc_HOL_Obool)),U_16302),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16298,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16296,U_16298,hAPP(c_Relation_Oconverse(U_16298,U_16296),U_16300)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16296,tc_HOL_Obool)),U_16304))))) )
    & ! [U_16301,U_16297,U_16295,U_16299,U_16303] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16297,tc_HOL_Obool)),U_16301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16297,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16295,U_16297,hAPP(c_Relation_Oconverse(U_16297,U_16295),U_16299)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16295,tc_HOL_Obool)),U_16303)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16295,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16297,U_16295,U_16299),U_16301)),U_16303)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4030_3]) ).

cnf(f_4030_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16297,tc_HOL_Obool)),U_16301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16297,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16295,U_16297,hAPP(c_Relation_Oconverse(U_16297,U_16295),U_16299)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16295,tc_HOL_Obool)),U_16303)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16295,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16297,U_16295,U_16299),U_16301)),U_16303)) ),
    inference(clausify,[status(thm)],[f_4030_4]) ).

cnf(f_4030_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16296,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16298,U_16296,U_16300),U_16302)),U_16304))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16298,tc_HOL_Obool)),U_16302),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16298,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16296,U_16298,hAPP(c_Relation_Oconverse(U_16298,U_16296),U_16300)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16296,tc_HOL_Obool)),U_16304))))) ),
    inference(clausify,[status(thm)],[f_4030_4]) ).

fof(f_4031_1,plain,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INF__leI]) ).

fof(f_4031_2,plain,
    ! [U_16309,U_16308,U_16307,U_16306,U_16305] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16306,U_16305),U_16308),U_16309)),hAPP(U_16309,U_16307)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16306),U_16307),U_16308))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16305) ),
    inference(variable_rename,[status(thm)],[f_4031_1]) ).

fof(f_4031_3,plain,
    ! [U_16307,U_16305,U_16306,U_16308,U_16309] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16306,U_16305),U_16308),U_16309)),hAPP(U_16309,U_16307)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16306),U_16307),U_16308))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16305) ),
    inference(definitional_conversion,[status(esa)],[f_4031_2]) ).

cnf(f_4031_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16306,U_16305),U_16308),U_16309)),hAPP(U_16309,U_16307)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16306),U_16307),U_16308))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16305) ),
    inference(clausify,[status(thm)],[f_4031_3]) ).

fof(f_4032_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset]) ).

fof(f_4032_2,plain,
    ! [U_16312,U_16311,U_16310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16310,U_16310),tc_HOL_Obool)),U_16312),hAPP(hAPP(c_Relation_Orel__comp(U_16310,U_16310,U_16310),hAPP(c_Relation_Oconverse(U_16310,U_16310),U_16312)),U_16312)))
      | ~ c_Relation_Orefl__on(U_16310,U_16311,U_16312) ),
    inference(variable_rename,[status(thm)],[f_4032_1]) ).

fof(f_4032_3,plain,
    ! [U_16310,U_16311,U_16312] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16310,U_16310),tc_HOL_Obool)),U_16312),hAPP(hAPP(c_Relation_Orel__comp(U_16310,U_16310,U_16310),hAPP(c_Relation_Oconverse(U_16310,U_16310),U_16312)),U_16312)))
      | ~ c_Relation_Orefl__on(U_16310,U_16311,U_16312) ),
    inference(definitional_conversion,[status(esa)],[f_4032_2]) ).

cnf(f_4032_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16310,U_16310),tc_HOL_Obool)),U_16312),hAPP(hAPP(c_Relation_Orel__comp(U_16310,U_16310,U_16310),hAPP(c_Relation_Oconverse(U_16310,U_16310),U_16312)),U_16312)))
    | ~ c_Relation_Orefl__on(U_16310,U_16311,U_16312) ),
    inference(clausify,[status(thm)],[f_4032_3]) ).

fof(f_4033_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
      | hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) != V_A_2
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) != V_r_2 ),
    inference(fof_nnf,[status(thm)],[fact_comp__equivI]) ).

fof(f_4033_2,plain,
    ! [U_16315,U_16314,U_16313] :
      ( c_Equiv__Relations_Oequiv(U_16313,U_16315,U_16314)
      | hAPP(c_Relation_ODomain(U_16313,U_16313),U_16314) != U_16315
      | hAPP(hAPP(c_Relation_Orel__comp(U_16313,U_16313,U_16313),hAPP(c_Relation_Oconverse(U_16313,U_16313),U_16314)),U_16314) != U_16314 ),
    inference(variable_rename,[status(thm)],[f_4033_1]) ).

fof(f_4033_3,plain,
    ! [U_16313,U_16314,U_16315] :
      ( c_Equiv__Relations_Oequiv(U_16313,U_16315,U_16314)
      | hAPP(c_Relation_ODomain(U_16313,U_16313),U_16314) != U_16315
      | hAPP(hAPP(c_Relation_Orel__comp(U_16313,U_16313,U_16313),hAPP(c_Relation_Oconverse(U_16313,U_16313),U_16314)),U_16314) != U_16314 ),
    inference(definitional_conversion,[status(esa)],[f_4033_2]) ).

cnf(f_4033_4,plain,
    ( c_Equiv__Relations_Oequiv(U_16313,U_16315,U_16314)
    | hAPP(c_Relation_ODomain(U_16313,U_16313),U_16314) != U_16315
    | hAPP(hAPP(c_Relation_Orel__comp(U_16313,U_16313,U_16313),hAPP(c_Relation_Oconverse(U_16313,U_16313),U_16314)),U_16314) != U_16314 ),
    inference(clausify,[status(thm)],[f_4033_3]) ).

fof(f_4034_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
      | ~ c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse]) ).

fof(f_4034_2,plain,
    ! [U_16317,U_16316] :
      ( c_Wellfounded_Owf(U_16316,hAPP(c_Relation_Oconverse(U_16316,U_16316),U_16317))
      | ~ c_Wellfounded_Oacyclic(U_16316,U_16317)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16316,U_16316)),U_16317)) ),
    inference(variable_rename,[status(thm)],[f_4034_1]) ).

fof(f_4034_3,plain,
    ! [U_16316,U_16317] :
      ( c_Wellfounded_Owf(U_16316,hAPP(c_Relation_Oconverse(U_16316,U_16316),U_16317))
      | ~ c_Wellfounded_Oacyclic(U_16316,U_16317)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16316,U_16316)),U_16317)) ),
    inference(definitional_conversion,[status(esa)],[f_4034_2]) ).

cnf(f_4034_4,plain,
    ( c_Wellfounded_Owf(U_16316,hAPP(c_Relation_Oconverse(U_16316,U_16316),U_16317))
    | ~ c_Wellfounded_Oacyclic(U_16316,U_16317)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16316,U_16316)),U_16317)) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

fof(f_4035_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_INT__greaterThan__UNIV]) ).

fof(f_4035_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4035_1]) ).

cnf(f_4035_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4035_2]) ).

fof(f_4036_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J]) ).

fof(f_4036_2,plain,
    ! [U_16322,U_16321,U_16320,U_16319,U_16318] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16319,tc_fun(U_16320,tc_HOL_Obool)),U_16318),hAPP(hAPP(c_COMBB(tc_fun(U_16320,tc_HOL_Obool),tc_fun(U_16320,tc_HOL_Obool),U_16319),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16320,tc_HOL_Obool)),U_16321)),U_16322)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16320,tc_HOL_Obool)),U_16321),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16319,tc_fun(U_16320,tc_HOL_Obool)),U_16318),U_16322))
        | U_16318 = c_Orderings_Obot__class_Obot(tc_fun(U_16319,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16319,tc_fun(U_16320,tc_HOL_Obool)),U_16318),hAPP(hAPP(c_COMBB(tc_fun(U_16320,tc_HOL_Obool),tc_fun(U_16320,tc_HOL_Obool),U_16319),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16320,tc_HOL_Obool)),U_16321)),U_16322)) = c_Orderings_Otop__class_Otop(tc_fun(U_16320,tc_HOL_Obool))
        | U_16318 != c_Orderings_Obot__class_Obot(tc_fun(U_16319,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4036_1]) ).

fof(f_4036_3,plain,
    ( ! [U_16332,U_16330,U_16328,U_16326,U_16324] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16326,tc_fun(U_16328,tc_HOL_Obool)),U_16324),hAPP(hAPP(c_COMBB(tc_fun(U_16328,tc_HOL_Obool),tc_fun(U_16328,tc_HOL_Obool),U_16326),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16328,tc_HOL_Obool)),U_16330)),U_16332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16328,tc_HOL_Obool)),U_16330),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16326,tc_fun(U_16328,tc_HOL_Obool)),U_16324),U_16332))
        | U_16324 = c_Orderings_Obot__class_Obot(tc_fun(U_16326,tc_HOL_Obool)) )
    & ! [U_16331,U_16329,U_16327,U_16325,U_16323] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16327,tc_HOL_Obool)),U_16323),hAPP(hAPP(c_COMBB(tc_fun(U_16327,tc_HOL_Obool),tc_fun(U_16327,tc_HOL_Obool),U_16325),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16327,tc_HOL_Obool)),U_16329)),U_16331)) = c_Orderings_Otop__class_Otop(tc_fun(U_16327,tc_HOL_Obool))
        | U_16323 != c_Orderings_Obot__class_Obot(tc_fun(U_16325,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4036_2]) ).

fof(f_4036_4,plain,
    ( ! [U_16324,U_16326,U_16328,U_16330,U_16332] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16326,tc_fun(U_16328,tc_HOL_Obool)),U_16324),hAPP(hAPP(c_COMBB(tc_fun(U_16328,tc_HOL_Obool),tc_fun(U_16328,tc_HOL_Obool),U_16326),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16328,tc_HOL_Obool)),U_16330)),U_16332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16328,tc_HOL_Obool)),U_16330),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16326,tc_fun(U_16328,tc_HOL_Obool)),U_16324),U_16332))
        | U_16324 = c_Orderings_Obot__class_Obot(tc_fun(U_16326,tc_HOL_Obool)) )
    & ! [U_16325,U_16329,U_16323,U_16327,U_16331] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16327,tc_HOL_Obool)),U_16323),hAPP(hAPP(c_COMBB(tc_fun(U_16327,tc_HOL_Obool),tc_fun(U_16327,tc_HOL_Obool),U_16325),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16327,tc_HOL_Obool)),U_16329)),U_16331)) = c_Orderings_Otop__class_Otop(tc_fun(U_16327,tc_HOL_Obool))
        | U_16323 != c_Orderings_Obot__class_Obot(tc_fun(U_16325,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4036_3]) ).

cnf(f_4036_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16327,tc_HOL_Obool)),U_16323),hAPP(hAPP(c_COMBB(tc_fun(U_16327,tc_HOL_Obool),tc_fun(U_16327,tc_HOL_Obool),U_16325),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16327,tc_HOL_Obool)),U_16329)),U_16331)) = c_Orderings_Otop__class_Otop(tc_fun(U_16327,tc_HOL_Obool))
    | U_16323 != c_Orderings_Obot__class_Obot(tc_fun(U_16325,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4036_4]) ).

cnf(f_4036_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16326,tc_fun(U_16328,tc_HOL_Obool)),U_16324),hAPP(hAPP(c_COMBB(tc_fun(U_16328,tc_HOL_Obool),tc_fun(U_16328,tc_HOL_Obool),U_16326),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16328,tc_HOL_Obool)),U_16330)),U_16332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16328,tc_HOL_Obool)),U_16330),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16326,tc_fun(U_16328,tc_HOL_Obool)),U_16324),U_16332))
    | U_16324 = c_Orderings_Obot__class_Obot(tc_fun(U_16326,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4036_4]) ).

fof(f_4037_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_converse__def]) ).

fof(f_4037_2,plain,
    ! [U_16335,U_16334,U_16333] : hAPP(c_Relation_Oconverse(U_16333,U_16334),U_16335) = hAPP(c_Set_OCollect(tc_prod(U_16334,U_16333)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16334,U_16333,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16334,tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_fun(U_16333,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16333,tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_fun(U_16333,tc_HOL_Obool)),U_16334),c_COMBC(U_16333,tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16333,tc_prod(U_16333,U_16334)),tc_fun(U_16333,tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),U_16334),hAPP(c_COMBB(tc_prod(U_16333,U_16334),tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool),U_16333),c_member(tc_prod(U_16333,U_16334)))),hAPP(c_COMBC(U_16333,U_16334,tc_prod(U_16333,U_16334)),c_Product__Type_OPair(U_16333,U_16334))))),U_16335))),
    inference(variable_rename,[status(thm)],[f_4037_1]) ).

fof(f_4037_3,plain,
    ! [U_16333,U_16334,U_16335] : hAPP(c_Relation_Oconverse(U_16333,U_16334),U_16335) = hAPP(c_Set_OCollect(tc_prod(U_16334,U_16333)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16334,U_16333,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16334,tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_fun(U_16333,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16333,tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_fun(U_16333,tc_HOL_Obool)),U_16334),c_COMBC(U_16333,tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16333,tc_prod(U_16333,U_16334)),tc_fun(U_16333,tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),U_16334),hAPP(c_COMBB(tc_prod(U_16333,U_16334),tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool),U_16333),c_member(tc_prod(U_16333,U_16334)))),hAPP(c_COMBC(U_16333,U_16334,tc_prod(U_16333,U_16334)),c_Product__Type_OPair(U_16333,U_16334))))),U_16335))),
    inference(definitional_conversion,[status(esa)],[f_4037_2]) ).

cnf(f_4037_4,plain,
    hAPP(c_Relation_Oconverse(U_16333,U_16334),U_16335) = hAPP(c_Set_OCollect(tc_prod(U_16334,U_16333)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16334,U_16333,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16334,tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_fun(U_16333,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16333,tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_fun(U_16333,tc_HOL_Obool)),U_16334),c_COMBC(U_16333,tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16333,tc_prod(U_16333,U_16334)),tc_fun(U_16333,tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool)),U_16334),hAPP(c_COMBB(tc_prod(U_16333,U_16334),tc_fun(tc_fun(tc_prod(U_16333,U_16334),tc_HOL_Obool),tc_HOL_Obool),U_16333),c_member(tc_prod(U_16333,U_16334)))),hAPP(c_COMBC(U_16333,U_16334,tc_prod(U_16333,U_16334)),c_Product__Type_OPair(U_16333,U_16334))))),U_16335))),
    inference(clausify,[status(thm)],[f_4037_3]) ).

fof(f_4038_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf]) ).

fof(f_4038_2,plain,
    ! [U_16340,U_16339,U_16338,U_16337,U_16336] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16336),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16337,U_16336),U_16338),U_16340)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16337,U_16336,hAPP(hAPP(c_COMBB(U_16336,tc_fun(U_16336,U_16336),U_16337),c_Lattices_Osemilattice__inf__class_Oinf(U_16336)),U_16340)),U_16339),U_16338)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16337),U_16338))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16336) ),
    inference(variable_rename,[status(thm)],[f_4038_1]) ).

fof(f_4038_3,plain,
    ! [U_16336,U_16337,U_16338,U_16339,U_16340] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16336),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16337,U_16336),U_16338),U_16340)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16337,U_16336,hAPP(hAPP(c_COMBB(U_16336,tc_fun(U_16336,U_16336),U_16337),c_Lattices_Osemilattice__inf__class_Oinf(U_16336)),U_16340)),U_16339),U_16338)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16337),U_16338))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16336) ),
    inference(definitional_conversion,[status(esa)],[f_4038_2]) ).

cnf(f_4038_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16336),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16337,U_16336),U_16338),U_16340)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16337,U_16336,hAPP(hAPP(c_COMBB(U_16336,tc_fun(U_16336,U_16336),U_16337),c_Lattices_Osemilattice__inf__class_Oinf(U_16336)),U_16340)),U_16339),U_16338)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16337),U_16338))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16336) ),
    inference(clausify,[status(thm)],[f_4038_3]) ).

fof(f_4039_1,plain,
    ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_sequence__trans]) ).

fof(f_4039_2,plain,
    ! [U_16346,U_16345,U_16344,U_16343,U_16342] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16345),U_16346))),hAPP(U_16343,U_16345))),c_Transitive__Closure_Ortrancl(U_16342,U_16344)))
      | ? [U_16341] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(c_Nat_OSuc,U_16341))),hAPP(U_16343,U_16341))),c_Transitive__Closure_Ortrancl(U_16342,U_16344))) ),
    inference(variable_rename,[status(thm)],[f_4039_1]) ).

fof(f_4039_3,plain,
    ! [U_16346,U_16345,U_16344,U_16343,U_16342] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16345),U_16346))),hAPP(U_16343,U_16345))),c_Transitive__Closure_Ortrancl(U_16342,U_16344)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(c_Nat_OSuc,sK386(U_16346,U_16345,U_16344,U_16343,U_16342)))),hAPP(U_16343,sK386(U_16346,U_16345,U_16344,U_16343,U_16342)))),c_Transitive__Closure_Ortrancl(U_16342,U_16344))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_16341,sK386(U_16346,U_16345,U_16344,U_16343,U_16342))],[f_4039_2]) ).

fof(f_4039_4,plain,
    ! [U_16342,U_16343,U_16344,U_16345,U_16346] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16345),U_16346))),hAPP(U_16343,U_16345))),c_Transitive__Closure_Ortrancl(U_16342,U_16344)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(c_Nat_OSuc,sK386(U_16346,U_16345,U_16344,U_16343,U_16342)))),hAPP(U_16343,sK386(U_16346,U_16345,U_16344,U_16343,U_16342)))),c_Transitive__Closure_Ortrancl(U_16342,U_16344))) ),
    inference(definitional_conversion,[status(esa)],[f_4039_3]) ).

cnf(f_4039_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16345),U_16346))),hAPP(U_16343,U_16345))),c_Transitive__Closure_Ortrancl(U_16342,U_16344)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16342,U_16342)),hAPP(hAPP(c_Product__Type_OPair(U_16342,U_16342),hAPP(U_16343,hAPP(c_Nat_OSuc,sK386(U_16346,U_16345,U_16344,U_16343,U_16342)))),hAPP(U_16343,sK386(U_16346,U_16345,U_16344,U_16343,U_16342)))),c_Transitive__Closure_Ortrancl(U_16342,U_16344))) ),
    inference(clausify,[status(thm)],[f_4039_4]) ).

fof(f_4040_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq]) ).

fof(f_4040_2,plain,
    ! [U_16350,U_16349,U_16348,U_16347] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16347,tc_fun(U_16347,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16347,tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_fun(U_16347,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16347,tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_fun(U_16347,tc_HOL_Obool)),U_16347),c_COMBC(U_16347,tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16347,tc_prod(U_16347,U_16347)),tc_fun(U_16347,tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool)),U_16347),hAPP(c_COMBB(tc_prod(U_16347,U_16347),tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool),U_16347),c_member(tc_prod(U_16347,U_16347)))),c_Product__Type_OPair(U_16347,U_16347)))),U_16348)),c_fequal),U_16349),U_16350))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16347,U_16347)),hAPP(hAPP(c_Product__Type_OPair(U_16347,U_16347),U_16349),U_16350)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool)),U_16348),c_Relation_OId(U_16347)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16347,U_16347)),hAPP(hAPP(c_Product__Type_OPair(U_16347,U_16347),U_16349),U_16350)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool)),U_16348),c_Relation_OId(U_16347))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16347,tc_fun(U_16347,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16347,tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_fun(U_16347,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16347,tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_fun(U_16347,tc_HOL_Obool)),U_16347),c_COMBC(U_16347,tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16347,tc_prod(U_16347,U_16347)),tc_fun(U_16347,tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool)),U_16347),hAPP(c_COMBB(tc_prod(U_16347,U_16347),tc_fun(tc_fun(tc_prod(U_16347,U_16347),tc_HOL_Obool),tc_HOL_Obool),U_16347),c_member(tc_prod(U_16347,U_16347)))),c_Product__Type_OPair(U_16347,U_16347)))),U_16348)),c_fequal),U_16349),U_16350)) ) ),
    inference(variable_rename,[status(thm)],[f_4040_1]) ).

fof(f_4040_3,plain,
    ( ! [U_16358,U_16356,U_16354,U_16352] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16352,tc_fun(U_16352,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16352,tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_fun(U_16352,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16352,tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_fun(U_16352,tc_HOL_Obool)),U_16352),c_COMBC(U_16352,tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16352,tc_prod(U_16352,U_16352)),tc_fun(U_16352,tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),U_16352),hAPP(c_COMBB(tc_prod(U_16352,U_16352),tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool),U_16352),c_member(tc_prod(U_16352,U_16352)))),c_Product__Type_OPair(U_16352,U_16352)))),U_16354)),c_fequal),U_16356),U_16358))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16352,U_16352)),hAPP(hAPP(c_Product__Type_OPair(U_16352,U_16352),U_16356),U_16358)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool)),U_16354),c_Relation_OId(U_16352)))) )
    & ! [U_16357,U_16355,U_16353,U_16351] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16351,U_16351)),hAPP(hAPP(c_Product__Type_OPair(U_16351,U_16351),U_16355),U_16357)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool)),U_16353),c_Relation_OId(U_16351))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16351,tc_fun(U_16351,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16351,tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_fun(U_16351,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16351,tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_fun(U_16351,tc_HOL_Obool)),U_16351),c_COMBC(U_16351,tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16351,tc_prod(U_16351,U_16351)),tc_fun(U_16351,tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),U_16351),hAPP(c_COMBB(tc_prod(U_16351,U_16351),tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool),U_16351),c_member(tc_prod(U_16351,U_16351)))),c_Product__Type_OPair(U_16351,U_16351)))),U_16353)),c_fequal),U_16355),U_16357)) ) ),
    inference(miniscope,[status(thm)],[f_4040_2]) ).

fof(f_4040_4,plain,
    ( ! [U_16352,U_16354,U_16356,U_16358] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16352,tc_fun(U_16352,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16352,tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_fun(U_16352,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16352,tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_fun(U_16352,tc_HOL_Obool)),U_16352),c_COMBC(U_16352,tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16352,tc_prod(U_16352,U_16352)),tc_fun(U_16352,tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),U_16352),hAPP(c_COMBB(tc_prod(U_16352,U_16352),tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool),U_16352),c_member(tc_prod(U_16352,U_16352)))),c_Product__Type_OPair(U_16352,U_16352)))),U_16354)),c_fequal),U_16356),U_16358))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16352,U_16352)),hAPP(hAPP(c_Product__Type_OPair(U_16352,U_16352),U_16356),U_16358)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool)),U_16354),c_Relation_OId(U_16352)))) )
    & ! [U_16353,U_16357,U_16351,U_16355] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16351,U_16351)),hAPP(hAPP(c_Product__Type_OPair(U_16351,U_16351),U_16355),U_16357)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool)),U_16353),c_Relation_OId(U_16351))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16351,tc_fun(U_16351,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16351,tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_fun(U_16351,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16351,tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_fun(U_16351,tc_HOL_Obool)),U_16351),c_COMBC(U_16351,tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16351,tc_prod(U_16351,U_16351)),tc_fun(U_16351,tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),U_16351),hAPP(c_COMBB(tc_prod(U_16351,U_16351),tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool),U_16351),c_member(tc_prod(U_16351,U_16351)))),c_Product__Type_OPair(U_16351,U_16351)))),U_16353)),c_fequal),U_16355),U_16357)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4040_3]) ).

cnf(f_4040_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16351,U_16351)),hAPP(hAPP(c_Product__Type_OPair(U_16351,U_16351),U_16355),U_16357)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool)),U_16353),c_Relation_OId(U_16351))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16351,tc_fun(U_16351,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16351,tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_fun(U_16351,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16351,tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_fun(U_16351,tc_HOL_Obool)),U_16351),c_COMBC(U_16351,tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16351,tc_prod(U_16351,U_16351)),tc_fun(U_16351,tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool)),U_16351),hAPP(c_COMBB(tc_prod(U_16351,U_16351),tc_fun(tc_fun(tc_prod(U_16351,U_16351),tc_HOL_Obool),tc_HOL_Obool),U_16351),c_member(tc_prod(U_16351,U_16351)))),c_Product__Type_OPair(U_16351,U_16351)))),U_16353)),c_fequal),U_16355),U_16357)) ),
    inference(clausify,[status(thm)],[f_4040_4]) ).

cnf(f_4040_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16352,tc_fun(U_16352,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16352,tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_fun(U_16352,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16352,tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_fun(U_16352,tc_HOL_Obool)),U_16352),c_COMBC(U_16352,tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16352,tc_prod(U_16352,U_16352)),tc_fun(U_16352,tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool)),U_16352),hAPP(c_COMBB(tc_prod(U_16352,U_16352),tc_fun(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool),tc_HOL_Obool),U_16352),c_member(tc_prod(U_16352,U_16352)))),c_Product__Type_OPair(U_16352,U_16352)))),U_16354)),c_fequal),U_16356),U_16358))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16352,U_16352)),hAPP(hAPP(c_Product__Type_OPair(U_16352,U_16352),U_16356),U_16358)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16352,U_16352),tc_HOL_Obool)),U_16354),c_Relation_OId(U_16352)))) ),
    inference(clausify,[status(thm)],[f_4040_4]) ).

fof(f_4041_1,plain,
    ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
    inference(fof_nnf,[status(thm)],[fact_IdI]) ).

fof(f_4041_2,plain,
    ! [U_16360,U_16359] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16359,U_16359)),hAPP(hAPP(c_Product__Type_OPair(U_16359,U_16359),U_16360),U_16360)),c_Relation_OId(U_16359))),
    inference(variable_rename,[status(thm)],[f_4041_1]) ).

fof(f_4041_3,plain,
    ! [U_16359,U_16360] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16359,U_16359)),hAPP(hAPP(c_Product__Type_OPair(U_16359,U_16359),U_16360),U_16360)),c_Relation_OId(U_16359))),
    inference(definitional_conversion,[status(esa)],[f_4041_2]) ).

cnf(f_4041_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_16359,U_16359)),hAPP(hAPP(c_Product__Type_OPair(U_16359,U_16359),U_16360),U_16360)),c_Relation_OId(U_16359))),
    inference(clausify,[status(thm)],[f_4041_3]) ).

fof(f_4042_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__iff]) ).

fof(f_4042_2,plain,
    ! [U_16367,U_16366,U_16365,U_16364,U_16363] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16363,tc_fun(U_16364,tc_HOL_Obool)),U_16365),U_16366),U_16367))
        | ? [U_16362] :
            ( ~ hBOOL(hAPP(hAPP(U_16366,U_16362),U_16367))
            & hBOOL(hAPP(hAPP(c_member(U_16363),U_16362),U_16365)) ) )
      & ( ! [U_16361] :
            ( hBOOL(hAPP(hAPP(U_16366,U_16361),U_16367))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16363),U_16361),U_16365)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16363,tc_fun(U_16364,tc_HOL_Obool)),U_16365),U_16366),U_16367)) ) ),
    inference(variable_rename,[status(thm)],[f_4042_1]) ).

fof(f_4042_3,plain,
    ( ! [U_16377,U_16375,U_16373,U_16371,U_16369] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16369,tc_fun(U_16371,tc_HOL_Obool)),U_16373),U_16375),U_16377))
        | ? [U_16362] :
            ( ~ hBOOL(hAPP(hAPP(U_16375,U_16362),U_16377))
            & hBOOL(hAPP(hAPP(c_member(U_16369),U_16362),U_16373)) ) )
    & ! [U_16376,U_16374,U_16372,U_16370,U_16368] :
        ( ! [U_16361] :
            ( hBOOL(hAPP(hAPP(U_16374,U_16361),U_16376))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16368),U_16361),U_16372)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16370,tc_HOL_Obool)),U_16372),U_16374),U_16376)) ) ),
    inference(miniscope,[status(thm)],[f_4042_2]) ).

fof(f_4042_4,plain,
    ( ! [U_16377,U_16375,U_16373,U_16371,U_16369] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16369,tc_fun(U_16371,tc_HOL_Obool)),U_16373),U_16375),U_16377))
        | ( ~ hBOOL(hAPP(hAPP(U_16375,sK387(U_16377,U_16375,U_16373,U_16371,U_16369)),U_16377))
          & hBOOL(hAPP(hAPP(c_member(U_16369),sK387(U_16377,U_16375,U_16373,U_16371,U_16369)),U_16373)) ) )
    & ! [U_16376,U_16374,U_16372,U_16370,U_16368] :
        ( ! [U_16361] :
            ( hBOOL(hAPP(hAPP(U_16374,U_16361),U_16376))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16368),U_16361),U_16372)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16370,tc_HOL_Obool)),U_16372),U_16374),U_16376)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_16362,sK387(U_16377,U_16375,U_16373,U_16371,U_16369))],[f_4042_3]) ).

fof(f_4042_5,plain,
    ( ! [U_16373,U_16369,U_16371,U_16375,U_16377] :
        ( ~ hBOOL(hAPP(hAPP(U_16375,sK387(U_16377,U_16375,U_16373,U_16371,U_16369)),U_16377))
        | ~ sP1056(U_16373,U_16369,U_16371,U_16375,U_16377) )
    & ! [U_16373,U_16369,U_16371,U_16375,U_16377] :
        ( hBOOL(hAPP(hAPP(c_member(U_16369),sK387(U_16377,U_16375,U_16373,U_16371,U_16369)),U_16373))
        | ~ sP1056(U_16373,U_16369,U_16371,U_16375,U_16377) )
    & ! [U_16373,U_16369,U_16371,U_16375,U_16377] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16369,tc_fun(U_16371,tc_HOL_Obool)),U_16373),U_16375),U_16377))
        | sP1056(U_16373,U_16369,U_16371,U_16375,U_16377) )
    & ! [U_16361,U_16372,U_16374,U_16368,U_16370,U_16376] :
        ( hBOOL(hAPP(hAPP(U_16374,U_16361),U_16376))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16368),U_16361),U_16372))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16370,tc_HOL_Obool)),U_16372),U_16374),U_16376)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1056])],[f_4042_4]) ).

cnf(f_4042_6,plain,
    ( hBOOL(hAPP(hAPP(U_16374,U_16361),U_16376))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16368),U_16361),U_16372))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16370,tc_HOL_Obool)),U_16372),U_16374),U_16376)) ),
    inference(clausify,[status(thm)],[f_4042_5]) ).

cnf(f_4042_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16369,tc_fun(U_16371,tc_HOL_Obool)),U_16373),U_16375),U_16377))
    | sP1056(U_16373,U_16369,U_16371,U_16375,U_16377) ),
    inference(clausify,[status(thm)],[f_4042_5]) ).

cnf(f_4042_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16369),sK387(U_16377,U_16375,U_16373,U_16371,U_16369)),U_16373))
    | ~ sP1056(U_16373,U_16369,U_16371,U_16375,U_16377) ),
    inference(clausify,[status(thm)],[f_4042_5]) ).

cnf(f_4042_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_16375,sK387(U_16377,U_16375,U_16373,U_16371,U_16369)),U_16377))
    | ~ sP1056(U_16373,U_16369,U_16371,U_16375,U_16377) ),
    inference(clausify,[status(thm)],[f_4042_5]) ).

fof(f_4043_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).

fof(f_4043_2,plain,
    ! [U_16386,U_16385,U_16384,U_16383,U_16382,U_16381,U_16380] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16380,tc_fun(U_16381,tc_fun(U_16382,tc_HOL_Obool))),U_16383),U_16384),U_16385),U_16386))
        | ? [U_16379] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_16384,U_16379),U_16385),U_16386))
            & hBOOL(hAPP(hAPP(c_member(U_16380),U_16379),U_16383)) ) )
      & ( ! [U_16378] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16384,U_16378),U_16385),U_16386))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16380),U_16378),U_16383)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16380,tc_fun(U_16381,tc_fun(U_16382,tc_HOL_Obool))),U_16383),U_16384),U_16385),U_16386)) ) ),
    inference(variable_rename,[status(thm)],[f_4043_1]) ).

fof(f_4043_3,plain,
    ( ! [U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16388,tc_fun(U_16390,tc_fun(U_16392,tc_HOL_Obool))),U_16394),U_16396),U_16398),U_16400))
        | ? [U_16379] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_16396,U_16379),U_16398),U_16400))
            & hBOOL(hAPP(hAPP(c_member(U_16388),U_16379),U_16394)) ) )
    & ! [U_16399,U_16397,U_16395,U_16393,U_16391,U_16389,U_16387] :
        ( ! [U_16378] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16395,U_16378),U_16397),U_16399))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16387),U_16378),U_16393)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16387,tc_fun(U_16389,tc_fun(U_16391,tc_HOL_Obool))),U_16393),U_16395),U_16397),U_16399)) ) ),
    inference(miniscope,[status(thm)],[f_4043_2]) ).

fof(f_4043_4,plain,
    ( ! [U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16388,tc_fun(U_16390,tc_fun(U_16392,tc_HOL_Obool))),U_16394),U_16396),U_16398),U_16400))
        | ( ~ hBOOL(hAPP(hAPP(hAPP(U_16396,sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388)),U_16398),U_16400))
          & hBOOL(hAPP(hAPP(c_member(U_16388),sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388)),U_16394)) ) )
    & ! [U_16399,U_16397,U_16395,U_16393,U_16391,U_16389,U_16387] :
        ( ! [U_16378] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16395,U_16378),U_16397),U_16399))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16387),U_16378),U_16393)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16387,tc_fun(U_16389,tc_fun(U_16391,tc_HOL_Obool))),U_16393),U_16395),U_16397),U_16399)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_16379,sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388))],[f_4043_3]) ).

fof(f_4043_5,plain,
    ( ! [U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(U_16396,sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388)),U_16398),U_16400))
        | ~ sP1057(U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400) )
    & ! [U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400] :
        ( hBOOL(hAPP(hAPP(c_member(U_16388),sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388)),U_16394))
        | ~ sP1057(U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400) )
    & ! [U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16388,tc_fun(U_16390,tc_fun(U_16392,tc_HOL_Obool))),U_16394),U_16396),U_16398),U_16400))
        | sP1057(U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400) )
    & ! [U_16378,U_16391,U_16387,U_16389,U_16395,U_16399,U_16393,U_16397] :
        ( hBOOL(hAPP(hAPP(hAPP(U_16395,U_16378),U_16397),U_16399))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16387),U_16378),U_16393))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16387,tc_fun(U_16389,tc_fun(U_16391,tc_HOL_Obool))),U_16393),U_16395),U_16397),U_16399)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1057])],[f_4043_4]) ).

cnf(f_4043_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_16395,U_16378),U_16397),U_16399))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16387),U_16378),U_16393))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16387,tc_fun(U_16389,tc_fun(U_16391,tc_HOL_Obool))),U_16393),U_16395),U_16397),U_16399)) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

cnf(f_4043_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16388,tc_fun(U_16390,tc_fun(U_16392,tc_HOL_Obool))),U_16394),U_16396),U_16398),U_16400))
    | sP1057(U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

cnf(f_4043_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16388),sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388)),U_16394))
    | ~ sP1057(U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

cnf(f_4043_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_16396,sK388(U_16400,U_16398,U_16396,U_16394,U_16392,U_16390,U_16388)),U_16398),U_16400))
    | ~ sP1057(U_16388,U_16394,U_16390,U_16392,U_16398,U_16396,U_16400) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

fof(f_4044_1,plain,
    ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
    inference(fof_nnf,[status(thm)],[fact_converse__Id]) ).

fof(f_4044_2,plain,
    ! [U_16401] : hAPP(c_Relation_Oconverse(U_16401,U_16401),c_Relation_OId(U_16401)) = c_Relation_OId(U_16401),
    inference(variable_rename,[status(thm)],[f_4044_1]) ).

fof(f_4044_3,plain,
    ! [U_16401] : hAPP(c_Relation_Oconverse(U_16401,U_16401),c_Relation_OId(U_16401)) = c_Relation_OId(U_16401),
    inference(definitional_conversion,[status(esa)],[f_4044_2]) ).

cnf(f_4044_4,plain,
    hAPP(c_Relation_Oconverse(U_16401,U_16401),c_Relation_OId(U_16401)) = c_Relation_OId(U_16401),
    inference(clausify,[status(thm)],[f_4044_3]) ).

fof(f_4045_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Image__Id]) ).

fof(f_4045_2,plain,
    ! [U_16403,U_16402] : hAPP(c_Relation_OImage(U_16402,U_16402,c_Relation_OId(U_16402)),U_16403) = U_16403,
    inference(variable_rename,[status(thm)],[f_4045_1]) ).

fof(f_4045_3,plain,
    ! [U_16403,U_16402] : hAPP(c_Relation_OImage(U_16402,U_16402,c_Relation_OId(U_16402)),U_16403) = U_16403,
    inference(definitional_conversion,[status(esa)],[f_4045_2]) ).

cnf(f_4045_4,plain,
    hAPP(c_Relation_OImage(U_16402,U_16402,c_Relation_OId(U_16402)),U_16403) = U_16403,
    inference(clausify,[status(thm)],[f_4045_3]) ).

fof(f_4046_1,plain,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_R__O__Id]) ).

fof(f_4046_2,plain,
    ! [U_16406,U_16405,U_16404] : hAPP(hAPP(c_Relation_Orel__comp(U_16404,U_16405,U_16405),U_16406),c_Relation_OId(U_16405)) = U_16406,
    inference(variable_rename,[status(thm)],[f_4046_1]) ).

fof(f_4046_3,plain,
    ! [U_16404,U_16405,U_16406] : hAPP(hAPP(c_Relation_Orel__comp(U_16404,U_16405,U_16405),U_16406),c_Relation_OId(U_16405)) = U_16406,
    inference(definitional_conversion,[status(esa)],[f_4046_2]) ).

cnf(f_4046_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_16404,U_16405,U_16405),U_16406),c_Relation_OId(U_16405)) = U_16406,
    inference(clausify,[status(thm)],[f_4046_3]) ).

fof(f_4047_1,plain,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_Id__O__R]) ).

fof(f_4047_2,plain,
    ! [U_16409,U_16408,U_16407] : hAPP(hAPP(c_Relation_Orel__comp(U_16407,U_16407,U_16408),c_Relation_OId(U_16407)),U_16409) = U_16409,
    inference(variable_rename,[status(thm)],[f_4047_1]) ).

fof(f_4047_3,plain,
    ! [U_16407,U_16408,U_16409] : hAPP(hAPP(c_Relation_Orel__comp(U_16407,U_16407,U_16408),c_Relation_OId(U_16407)),U_16409) = U_16409,
    inference(definitional_conversion,[status(esa)],[f_4047_2]) ).

cnf(f_4047_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_16407,U_16407,U_16408),c_Relation_OId(U_16407)),U_16409) = U_16409,
    inference(clausify,[status(thm)],[f_4047_3]) ).

fof(f_4048_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
        | V_a_2 != V_b_2 )
      & ( V_a_2 = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv]) ).

fof(f_4048_2,plain,
    ! [U_16412,U_16411,U_16410] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16410,U_16410)),hAPP(hAPP(c_Product__Type_OPair(U_16410,U_16410),U_16411),U_16412)),c_Relation_OId(U_16410)))
        | U_16411 != U_16412 )
      & ( U_16411 = U_16412
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16410,U_16410)),hAPP(hAPP(c_Product__Type_OPair(U_16410,U_16410),U_16411),U_16412)),c_Relation_OId(U_16410))) ) ),
    inference(variable_rename,[status(thm)],[f_4048_1]) ).

fof(f_4048_3,plain,
    ( ! [U_16418,U_16416] :
        ( ! [U_16414] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16414,U_16414)),hAPP(hAPP(c_Product__Type_OPair(U_16414,U_16414),U_16416),U_16418)),c_Relation_OId(U_16414)))
        | U_16416 != U_16418 )
    & ! [U_16417,U_16415] :
        ( ! [U_16413] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16413,U_16413)),hAPP(hAPP(c_Product__Type_OPair(U_16413,U_16413),U_16415),U_16417)),c_Relation_OId(U_16413)))
        | U_16415 = U_16417 ) ),
    inference(miniscope,[status(thm)],[f_4048_2]) ).

fof(f_4048_4,plain,
    ( ! [U_16414,U_16416,U_16418] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16414,U_16414)),hAPP(hAPP(c_Product__Type_OPair(U_16414,U_16414),U_16416),U_16418)),c_Relation_OId(U_16414)))
        | U_16416 != U_16418 )
    & ! [U_16417,U_16415,U_16413] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16413,U_16413)),hAPP(hAPP(c_Product__Type_OPair(U_16413,U_16413),U_16415),U_16417)),c_Relation_OId(U_16413)))
        | U_16415 = U_16417 ) ),
    inference(definitional_conversion,[status(esa)],[f_4048_3]) ).

cnf(f_4048_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16413,U_16413)),hAPP(hAPP(c_Product__Type_OPair(U_16413,U_16413),U_16415),U_16417)),c_Relation_OId(U_16413)))
    | U_16415 = U_16417 ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

cnf(f_4048_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16414,U_16414)),hAPP(hAPP(c_Product__Type_OPair(U_16414,U_16414),U_16416),U_16418)),c_Relation_OId(U_16414)))
    | U_16416 != U_16418 ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

fof(f_4049_1,plain,
    ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Id]) ).

fof(f_4049_2,plain,
    ! [U_16419] : hAPP(c_Relation_ODomain(U_16419,U_16419),c_Relation_OId(U_16419)) = c_Orderings_Otop__class_Otop(tc_fun(U_16419,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4049_1]) ).

fof(f_4049_3,plain,
    ! [U_16419] : hAPP(c_Relation_ODomain(U_16419,U_16419),c_Relation_OId(U_16419)) = c_Orderings_Otop__class_Otop(tc_fun(U_16419,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4049_2]) ).

cnf(f_4049_4,plain,
    hAPP(c_Relation_ODomain(U_16419,U_16419),c_Relation_OId(U_16419)) = c_Orderings_Otop__class_Otop(tc_fun(U_16419,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4049_3]) ).

fof(f_4050_1,plain,
    ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__empty]) ).

fof(f_4050_2,plain,
    ! [U_16420] : c_Transitive__Closure_Ortrancl(U_16420,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16420,U_16420),tc_HOL_Obool))) = c_Relation_OId(U_16420),
    inference(variable_rename,[status(thm)],[f_4050_1]) ).

fof(f_4050_3,plain,
    ! [U_16420] : c_Transitive__Closure_Ortrancl(U_16420,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16420,U_16420),tc_HOL_Obool))) = c_Relation_OId(U_16420),
    inference(definitional_conversion,[status(esa)],[f_4050_2]) ).

cnf(f_4050_4,plain,
    c_Transitive__Closure_Ortrancl(U_16420,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16420,U_16420),tc_HOL_Obool))) = c_Relation_OId(U_16420),
    inference(clausify,[status(thm)],[f_4050_3]) ).

fof(f_4051_1,plain,
    ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__Id]) ).

fof(f_4051_2,plain,
    ! [U_16421] : hAPP(c_Relation_ORange(U_16421,U_16421),c_Relation_OId(U_16421)) = c_Orderings_Otop__class_Otop(tc_fun(U_16421,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4051_1]) ).

fof(f_4051_3,plain,
    ! [U_16421] : hAPP(c_Relation_ORange(U_16421,U_16421),c_Relation_OId(U_16421)) = c_Orderings_Otop__class_Otop(tc_fun(U_16421,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4051_2]) ).

cnf(f_4051_4,plain,
    hAPP(c_Relation_ORange(U_16421,U_16421),c_Relation_OId(U_16421)) = c_Orderings_Otop__class_Otop(tc_fun(U_16421,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4051_3]) ).

fof(f_4052_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(f_4052_2,plain,
    ! [U_16423,U_16422] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16422,U_16422),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16422,U_16423)),c_Relation_OId(U_16422)) = c_Transitive__Closure_Ortrancl(U_16422,U_16423),
    inference(variable_rename,[status(thm)],[f_4052_1]) ).

fof(f_4052_3,plain,
    ! [U_16422,U_16423] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16422,U_16422),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16422,U_16423)),c_Relation_OId(U_16422)) = c_Transitive__Closure_Ortrancl(U_16422,U_16423),
    inference(definitional_conversion,[status(esa)],[f_4052_2]) ).

cnf(f_4052_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16422,U_16422),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16422,U_16423)),c_Relation_OId(U_16422)) = c_Transitive__Closure_Ortrancl(U_16422,U_16423),
    inference(clausify,[status(thm)],[f_4052_3]) ).

fof(f_4053_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(f_4053_2,plain,
    ! [U_16425,U_16424] : c_Transitive__Closure_Ortrancl(U_16424,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16424,U_16424),tc_HOL_Obool)),U_16425),c_Relation_OId(U_16424))) = c_Transitive__Closure_Ortrancl(U_16424,U_16425),
    inference(variable_rename,[status(thm)],[f_4053_1]) ).

fof(f_4053_3,plain,
    ! [U_16424,U_16425] : c_Transitive__Closure_Ortrancl(U_16424,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16424,U_16424),tc_HOL_Obool)),U_16425),c_Relation_OId(U_16424))) = c_Transitive__Closure_Ortrancl(U_16424,U_16425),
    inference(definitional_conversion,[status(esa)],[f_4053_2]) ).

cnf(f_4053_4,plain,
    c_Transitive__Closure_Ortrancl(U_16424,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16424,U_16424),tc_HOL_Obool)),U_16425),c_Relation_OId(U_16424))) = c_Transitive__Closure_Ortrancl(U_16424,U_16425),
    inference(clausify,[status(thm)],[f_4053_3]) ).

fof(f_4054_1,plain,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_refl__Id]) ).

fof(f_4054_2,plain,
    ! [U_16426] : c_Relation_Orefl__on(U_16426,c_Orderings_Otop__class_Otop(tc_fun(U_16426,tc_HOL_Obool)),c_Relation_OId(U_16426)),
    inference(variable_rename,[status(thm)],[f_4054_1]) ).

fof(f_4054_3,plain,
    ! [U_16426] : c_Relation_Orefl__on(U_16426,c_Orderings_Otop__class_Otop(tc_fun(U_16426,tc_HOL_Obool)),c_Relation_OId(U_16426)),
    inference(definitional_conversion,[status(esa)],[f_4054_2]) ).

cnf(f_4054_4,plain,
    c_Relation_Orefl__on(U_16426,c_Orderings_Otop__class_Otop(tc_fun(U_16426,tc_HOL_Obool)),c_Relation_OId(U_16426)),
    inference(clausify,[status(thm)],[f_4054_3]) ).

fof(f_4055_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(f_4055_2,plain,
    ! [U_16428,U_16427] : c_Transitive__Closure_Ortrancl(U_16427,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16427,U_16427),tc_HOL_Obool)),U_16428),c_Relation_OId(U_16427))) = c_Transitive__Closure_Ortrancl(U_16427,U_16428),
    inference(variable_rename,[status(thm)],[f_4055_1]) ).

fof(f_4055_3,plain,
    ! [U_16427,U_16428] : c_Transitive__Closure_Ortrancl(U_16427,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16427,U_16427),tc_HOL_Obool)),U_16428),c_Relation_OId(U_16427))) = c_Transitive__Closure_Ortrancl(U_16427,U_16428),
    inference(definitional_conversion,[status(esa)],[f_4055_2]) ).

cnf(f_4055_4,plain,
    c_Transitive__Closure_Ortrancl(U_16427,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16427,U_16427),tc_HOL_Obool)),U_16428),c_Relation_OId(U_16427))) = c_Transitive__Closure_Ortrancl(U_16427,U_16428),
    inference(clausify,[status(thm)],[f_4055_3]) ).

fof(f_4056_1,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_pair__leq__def]) ).

fof(f_4056_2,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4056_1]) ).

cnf(f_4056_3,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4056_2]) ).

fof(f_4057_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__reflcl]) ).

fof(f_4057_2,plain,
    ! [U_16430,U_16429] : c_Transitive__Closure_Otrancl(U_16429,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16429,U_16429),tc_HOL_Obool)),U_16430),c_Relation_OId(U_16429))) = c_Transitive__Closure_Ortrancl(U_16429,U_16430),
    inference(variable_rename,[status(thm)],[f_4057_1]) ).

fof(f_4057_3,plain,
    ! [U_16429,U_16430] : c_Transitive__Closure_Otrancl(U_16429,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16429,U_16429),tc_HOL_Obool)),U_16430),c_Relation_OId(U_16429))) = c_Transitive__Closure_Ortrancl(U_16429,U_16430),
    inference(definitional_conversion,[status(esa)],[f_4057_2]) ).

cnf(f_4057_4,plain,
    c_Transitive__Closure_Otrancl(U_16429,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16429,U_16429),tc_HOL_Obool)),U_16430),c_Relation_OId(U_16429))) = c_Transitive__Closure_Ortrancl(U_16429,U_16430),
    inference(clausify,[status(thm)],[f_4057_3]) ).

fof(f_4058_1,plain,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_reflcl__trancl]) ).

fof(f_4058_2,plain,
    ! [U_16432,U_16431] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16431,U_16431),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_16431,U_16432)),c_Relation_OId(U_16431)) = c_Transitive__Closure_Ortrancl(U_16431,U_16432),
    inference(variable_rename,[status(thm)],[f_4058_1]) ).

fof(f_4058_3,plain,
    ! [U_16431,U_16432] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16431,U_16431),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_16431,U_16432)),c_Relation_OId(U_16431)) = c_Transitive__Closure_Ortrancl(U_16431,U_16432),
    inference(definitional_conversion,[status(esa)],[f_4058_2]) ).

cnf(f_4058_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16431,U_16431),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_16431,U_16432)),c_Relation_OId(U_16431)) = c_Transitive__Closure_Ortrancl(U_16431,U_16432),
    inference(clausify,[status(thm)],[f_4058_3]) ).

fof(f_4059_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__unfold]) ).

fof(f_4059_2,plain,
    ! [U_16434,U_16433] : c_Transitive__Closure_Ortrancl(U_16433,U_16434) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16433,U_16433),tc_HOL_Obool)),c_Relation_OId(U_16433)),hAPP(hAPP(c_Relation_Orel__comp(U_16433,U_16433,U_16433),c_Transitive__Closure_Ortrancl(U_16433,U_16434)),U_16434)),
    inference(variable_rename,[status(thm)],[f_4059_1]) ).

fof(f_4059_3,plain,
    ! [U_16433,U_16434] : c_Transitive__Closure_Ortrancl(U_16433,U_16434) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16433,U_16433),tc_HOL_Obool)),c_Relation_OId(U_16433)),hAPP(hAPP(c_Relation_Orel__comp(U_16433,U_16433,U_16433),c_Transitive__Closure_Ortrancl(U_16433,U_16434)),U_16434)),
    inference(definitional_conversion,[status(esa)],[f_4059_2]) ).

cnf(f_4059_4,plain,
    c_Transitive__Closure_Ortrancl(U_16433,U_16434) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16433,U_16433),tc_HOL_Obool)),c_Relation_OId(U_16433)),hAPP(hAPP(c_Relation_Orel__comp(U_16433,U_16433,U_16433),c_Transitive__Closure_Ortrancl(U_16433,U_16434)),U_16434)),
    inference(clausify,[status(thm)],[f_4059_3]) ).

fof(f_4060_1,plain,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    inference(fof_nnf,[status(thm)],[fact_refl__reflcl]) ).

fof(f_4060_2,plain,
    ! [U_16436,U_16435] : c_Relation_Orefl__on(U_16435,c_Orderings_Otop__class_Otop(tc_fun(U_16435,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16435,U_16435),tc_HOL_Obool)),U_16436),c_Relation_OId(U_16435))),
    inference(variable_rename,[status(thm)],[f_4060_1]) ).

fof(f_4060_3,plain,
    ! [U_16435,U_16436] : c_Relation_Orefl__on(U_16435,c_Orderings_Otop__class_Otop(tc_fun(U_16435,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16435,U_16435),tc_HOL_Obool)),U_16436),c_Relation_OId(U_16435))),
    inference(definitional_conversion,[status(esa)],[f_4060_2]) ).

cnf(f_4060_4,plain,
    c_Relation_Orefl__on(U_16435,c_Orderings_Otop__class_Otop(tc_fun(U_16435,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16435,U_16435),tc_HOL_Obool)),U_16436),c_Relation_OId(U_16435))),
    inference(clausify,[status(thm)],[f_4060_3]) ).

fof(f_4061_1,plain,
    ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
    inference(fof_nnf,[status(thm)],[fact_Id__def]) ).

fof(f_4061_2,plain,
    ! [U_16437] : c_Relation_OId(U_16437) = hAPP(c_Set_OCollect(tc_prod(U_16437,U_16437)),hAPP(hAPP(c_COMBB(tc_fun(U_16437,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16437,U_16437)),c_HOL_OEx(U_16437)),hAPP(hAPP(c_COMBC(tc_prod(U_16437,U_16437),tc_fun(U_16437,tc_prod(U_16437,U_16437)),tc_fun(U_16437,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16437,U_16437),tc_HOL_Obool),tc_fun(tc_fun(U_16437,tc_prod(U_16437,U_16437)),tc_fun(U_16437,tc_HOL_Obool)),tc_prod(U_16437,U_16437)),c_COMBB(tc_prod(U_16437,U_16437),tc_HOL_Obool,U_16437)),c_fequal)),hAPP(hAPP(c_COMBS(U_16437,U_16437,tc_prod(U_16437,U_16437)),c_Product__Type_OPair(U_16437,U_16437)),c_COMBI(U_16437))))),
    inference(variable_rename,[status(thm)],[f_4061_1]) ).

fof(f_4061_3,plain,
    ! [U_16437] : c_Relation_OId(U_16437) = hAPP(c_Set_OCollect(tc_prod(U_16437,U_16437)),hAPP(hAPP(c_COMBB(tc_fun(U_16437,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16437,U_16437)),c_HOL_OEx(U_16437)),hAPP(hAPP(c_COMBC(tc_prod(U_16437,U_16437),tc_fun(U_16437,tc_prod(U_16437,U_16437)),tc_fun(U_16437,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16437,U_16437),tc_HOL_Obool),tc_fun(tc_fun(U_16437,tc_prod(U_16437,U_16437)),tc_fun(U_16437,tc_HOL_Obool)),tc_prod(U_16437,U_16437)),c_COMBB(tc_prod(U_16437,U_16437),tc_HOL_Obool,U_16437)),c_fequal)),hAPP(hAPP(c_COMBS(U_16437,U_16437,tc_prod(U_16437,U_16437)),c_Product__Type_OPair(U_16437,U_16437)),c_COMBI(U_16437))))),
    inference(definitional_conversion,[status(esa)],[f_4061_2]) ).

cnf(f_4061_4,plain,
    c_Relation_OId(U_16437) = hAPP(c_Set_OCollect(tc_prod(U_16437,U_16437)),hAPP(hAPP(c_COMBB(tc_fun(U_16437,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16437,U_16437)),c_HOL_OEx(U_16437)),hAPP(hAPP(c_COMBC(tc_prod(U_16437,U_16437),tc_fun(U_16437,tc_prod(U_16437,U_16437)),tc_fun(U_16437,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16437,U_16437),tc_HOL_Obool),tc_fun(tc_fun(U_16437,tc_prod(U_16437,U_16437)),tc_fun(U_16437,tc_HOL_Obool)),tc_prod(U_16437,U_16437)),c_COMBB(tc_prod(U_16437,U_16437),tc_HOL_Obool,U_16437)),c_fequal)),hAPP(hAPP(c_COMBS(U_16437,U_16437,tc_prod(U_16437,U_16437)),c_Product__Type_OPair(U_16437,U_16437)),c_COMBI(U_16437))))),
    inference(clausify,[status(thm)],[f_4061_3]) ).

fof(f_4062_1,plain,
    ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    inference(fof_nnf,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(f_4062_2,plain,
    ! [U_16439,U_16438] : c_Relation_Oirrefl(U_16438,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16438,U_16438),tc_HOL_Obool)),U_16439),c_Relation_OId(U_16438))),
    inference(variable_rename,[status(thm)],[f_4062_1]) ).

fof(f_4062_3,plain,
    ! [U_16438,U_16439] : c_Relation_Oirrefl(U_16438,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16438,U_16438),tc_HOL_Obool)),U_16439),c_Relation_OId(U_16438))),
    inference(definitional_conversion,[status(esa)],[f_4062_2]) ).

cnf(f_4062_4,plain,
    c_Relation_Oirrefl(U_16438,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16438,U_16438),tc_HOL_Obool)),U_16439),c_Relation_OId(U_16438))),
    inference(clausify,[status(thm)],[f_4062_3]) ).

fof(f_4063_1,plain,
    ! [V_r_2,V_s_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset]) ).

fof(f_4063_2,plain,
    ! [U_16442,U_16441,U_16440] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16440,U_16442)),U_16441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_16440,U_16440,U_16440),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16440,U_16442)),U_16441)),U_16442)),U_16441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Relation_OId(U_16440)),U_16441)) ),
    inference(variable_rename,[status(thm)],[f_4063_1]) ).

fof(f_4063_3,plain,
    ! [U_16440,U_16441,U_16442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16440,U_16442)),U_16441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_16440,U_16440,U_16440),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16440,U_16442)),U_16441)),U_16442)),U_16441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Relation_OId(U_16440)),U_16441)) ),
    inference(definitional_conversion,[status(esa)],[f_4063_2]) ).

cnf(f_4063_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16440,U_16442)),U_16441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_16440,U_16440,U_16440),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16440,U_16442)),U_16441)),U_16442)),U_16441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16440,U_16440),tc_HOL_Obool)),c_Relation_OId(U_16440)),U_16441)) ),
    inference(clausify,[status(thm)],[f_4063_3]) ).

fof(f_4064_1,plain,
    ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
      ( hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__INT__eq]) ).

fof(f_4064_2,plain,
    ! [U_16448,U_16447,U_16446,U_16445,U_16444,U_16443] :
      ( hAPP(c_Relation_OImage(U_16444,U_16443,U_16445),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16444,tc_HOL_Obool)),U_16446),U_16448)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16443,tc_HOL_Obool)),U_16446),hAPP(hAPP(c_COMBB(tc_fun(U_16444,tc_HOL_Obool),tc_fun(U_16443,tc_HOL_Obool),U_16447),c_Relation_OImage(U_16444,U_16443,U_16445)),U_16448))
      | U_16446 = c_Orderings_Obot__class_Obot(tc_fun(U_16447,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_16443,U_16444,hAPP(c_Relation_Oconverse(U_16444,U_16443),U_16445)) ),
    inference(variable_rename,[status(thm)],[f_4064_1]) ).

fof(f_4064_3,plain,
    ! [U_16443,U_16444,U_16445,U_16446,U_16447,U_16448] :
      ( hAPP(c_Relation_OImage(U_16444,U_16443,U_16445),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16444,tc_HOL_Obool)),U_16446),U_16448)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16443,tc_HOL_Obool)),U_16446),hAPP(hAPP(c_COMBB(tc_fun(U_16444,tc_HOL_Obool),tc_fun(U_16443,tc_HOL_Obool),U_16447),c_Relation_OImage(U_16444,U_16443,U_16445)),U_16448))
      | U_16446 = c_Orderings_Obot__class_Obot(tc_fun(U_16447,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_16443,U_16444,hAPP(c_Relation_Oconverse(U_16444,U_16443),U_16445)) ),
    inference(definitional_conversion,[status(esa)],[f_4064_2]) ).

cnf(f_4064_4,plain,
    ( hAPP(c_Relation_OImage(U_16444,U_16443,U_16445),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16444,tc_HOL_Obool)),U_16446),U_16448)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16443,tc_HOL_Obool)),U_16446),hAPP(hAPP(c_COMBB(tc_fun(U_16444,tc_HOL_Obool),tc_fun(U_16443,tc_HOL_Obool),U_16447),c_Relation_OImage(U_16444,U_16443,U_16445)),U_16448))
    | U_16446 = c_Orderings_Obot__class_Obot(tc_fun(U_16447,tc_HOL_Obool))
    | ~ c_Relation_Osingle__valued(U_16443,U_16444,hAPP(c_Relation_Oconverse(U_16444,U_16443),U_16445)) ),
    inference(clausify,[status(thm)],[f_4064_3]) ).

fof(f_4065_1,plain,
    ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2))
          & hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_image__INT]) ).

fof(f_4065_2,plain,
    ! [U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450] :
      ( hAPP(c_Set_Oimage(U_16450,U_16451,U_16452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16450,tc_HOL_Obool)),U_16455),U_16456)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16451,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16450,tc_HOL_Obool),tc_fun(U_16451,tc_HOL_Obool),U_16454),c_Set_Oimage(U_16450,U_16451,U_16452)),U_16456))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16454),U_16457),U_16455))
      | ? [U_16449] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16450,tc_HOL_Obool)),hAPP(U_16456,U_16449)),U_16453))
          & hBOOL(hAPP(hAPP(c_member(U_16454),U_16449),U_16455)) )
      | ~ c_Fun_Oinj__on(U_16450,U_16451,U_16452,U_16453) ),
    inference(variable_rename,[status(thm)],[f_4065_1]) ).

fof(f_4065_3,plain,
    ! [U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450] :
      ( hAPP(c_Set_Oimage(U_16450,U_16451,U_16452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16450,tc_HOL_Obool)),U_16455),U_16456)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16451,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16450,tc_HOL_Obool),tc_fun(U_16451,tc_HOL_Obool),U_16454),c_Set_Oimage(U_16450,U_16451,U_16452)),U_16456))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16454),U_16457),U_16455))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16450,tc_HOL_Obool)),hAPP(U_16456,sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450))),U_16453))
        & hBOOL(hAPP(hAPP(c_member(U_16454),sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450)),U_16455)) )
      | ~ c_Fun_Oinj__on(U_16450,U_16451,U_16452,U_16453) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_16449,sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450))],[f_4065_2]) ).

fof(f_4065_4,plain,
    ( ! [U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16450,tc_HOL_Obool)),hAPP(U_16456,sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450))),U_16453))
        | ~ sP1058(U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457) )
    & ! [U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457] :
        ( hBOOL(hAPP(hAPP(c_member(U_16454),sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450)),U_16455))
        | ~ sP1058(U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457) )
    & ! [U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457] :
        ( hAPP(c_Set_Oimage(U_16450,U_16451,U_16452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16450,tc_HOL_Obool)),U_16455),U_16456)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16451,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16450,tc_HOL_Obool),tc_fun(U_16451,tc_HOL_Obool),U_16454),c_Set_Oimage(U_16450,U_16451,U_16452)),U_16456))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16454),U_16457),U_16455))
        | sP1058(U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457)
        | ~ c_Fun_Oinj__on(U_16450,U_16451,U_16452,U_16453) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1058])],[f_4065_3]) ).

cnf(f_4065_5,plain,
    ( hAPP(c_Set_Oimage(U_16450,U_16451,U_16452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16450,tc_HOL_Obool)),U_16455),U_16456)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16451,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16450,tc_HOL_Obool),tc_fun(U_16451,tc_HOL_Obool),U_16454),c_Set_Oimage(U_16450,U_16451,U_16452)),U_16456))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16454),U_16457),U_16455))
    | sP1058(U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457)
    | ~ c_Fun_Oinj__on(U_16450,U_16451,U_16452,U_16453) ),
    inference(clausify,[status(thm)],[f_4065_4]) ).

cnf(f_4065_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16454),sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450)),U_16455))
    | ~ sP1058(U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457) ),
    inference(clausify,[status(thm)],[f_4065_4]) ).

cnf(f_4065_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16450,tc_HOL_Obool)),hAPP(U_16456,sK389(U_16457,U_16456,U_16455,U_16454,U_16453,U_16452,U_16451,U_16450))),U_16453))
    | ~ sP1058(U_16450,U_16451,U_16452,U_16453,U_16454,U_16455,U_16456,U_16457) ),
    inference(clausify,[status(thm)],[f_4065_4]) ).

fof(f_4066_1,plain,
    ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_single__valued__Id]) ).

fof(f_4066_2,plain,
    ! [U_16458] : c_Relation_Osingle__valued(U_16458,U_16458,c_Relation_OId(U_16458)),
    inference(variable_rename,[status(thm)],[f_4066_1]) ).

fof(f_4066_3,plain,
    ! [U_16458] : c_Relation_Osingle__valued(U_16458,U_16458,c_Relation_OId(U_16458)),
    inference(definitional_conversion,[status(esa)],[f_4066_2]) ).

cnf(f_4066_4,plain,
    c_Relation_Osingle__valued(U_16458,U_16458,c_Relation_OId(U_16458)),
    inference(clausify,[status(thm)],[f_4066_3]) ).

fof(f_4067_1,plain,
    ! [V_s_2,T_d,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))
      | ~ c_Relation_Osingle__valued(T_c,T_d,V_s_2)
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp]) ).

fof(f_4067_2,plain,
    ! [U_16463,U_16462,U_16461,U_16460,U_16459] :
      ( c_Relation_Osingle__valued(U_16459,U_16462,hAPP(hAPP(c_Relation_Orel__comp(U_16459,U_16460,U_16462),U_16461),U_16463))
      | ~ c_Relation_Osingle__valued(U_16460,U_16462,U_16463)
      | ~ c_Relation_Osingle__valued(U_16459,U_16460,U_16461) ),
    inference(variable_rename,[status(thm)],[f_4067_1]) ).

fof(f_4067_3,plain,
    ! [U_16461,U_16463,U_16459,U_16462,U_16460] :
      ( c_Relation_Osingle__valued(U_16459,U_16462,hAPP(hAPP(c_Relation_Orel__comp(U_16459,U_16460,U_16462),U_16461),U_16463))
      | ~ c_Relation_Osingle__valued(U_16460,U_16462,U_16463)
      | ~ c_Relation_Osingle__valued(U_16459,U_16460,U_16461) ),
    inference(definitional_conversion,[status(esa)],[f_4067_2]) ).

cnf(f_4067_4,plain,
    ( c_Relation_Osingle__valued(U_16459,U_16462,hAPP(hAPP(c_Relation_Orel__comp(U_16459,U_16460,U_16462),U_16461),U_16463))
    | ~ c_Relation_Osingle__valued(U_16460,U_16462,U_16463)
    | ~ c_Relation_Osingle__valued(U_16459,U_16460,U_16461) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

fof(f_4068_1,plain,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_s_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__subset]) ).

fof(f_4068_2,plain,
    ! [U_16467,U_16466,U_16465,U_16464] :
      ( c_Relation_Osingle__valued(U_16464,U_16465,U_16466)
      | ~ c_Relation_Osingle__valued(U_16464,U_16465,U_16467)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16464,U_16465),tc_HOL_Obool)),U_16466),U_16467)) ),
    inference(variable_rename,[status(thm)],[f_4068_1]) ).

fof(f_4068_3,plain,
    ! [U_16465,U_16464,U_16466,U_16467] :
      ( c_Relation_Osingle__valued(U_16464,U_16465,U_16466)
      | ~ c_Relation_Osingle__valued(U_16464,U_16465,U_16467)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16464,U_16465),tc_HOL_Obool)),U_16466),U_16467)) ),
    inference(definitional_conversion,[status(esa)],[f_4068_2]) ).

cnf(f_4068_4,plain,
    ( c_Relation_Osingle__valued(U_16464,U_16465,U_16466)
    | ~ c_Relation_Osingle__valued(U_16464,U_16465,U_16467)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16464,U_16465),tc_HOL_Obool)),U_16466),U_16467)) ),
    inference(clausify,[status(thm)],[f_4068_3]) ).

fof(f_4069_1,plain,
    ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_single__valued__Id__on]) ).

fof(f_4069_2,plain,
    ! [U_16469,U_16468] : c_Relation_Osingle__valued(U_16468,U_16468,c_Relation_OId__on(U_16468,U_16469)),
    inference(variable_rename,[status(thm)],[f_4069_1]) ).

fof(f_4069_3,plain,
    ! [U_16468,U_16469] : c_Relation_Osingle__valued(U_16468,U_16468,c_Relation_OId__on(U_16468,U_16469)),
    inference(definitional_conversion,[status(esa)],[f_4069_2]) ).

cnf(f_4069_4,plain,
    c_Relation_Osingle__valued(U_16468,U_16468,c_Relation_OId__on(U_16468,U_16469)),
    inference(clausify,[status(thm)],[f_4069_3]) ).

fof(f_4070_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
        | ? [B_x,B_y] :
            ( ? [B_z] :
                ( B_y != B_z
                & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) ) )
      & ( ! [B_x,B_y] :
            ( ! [B_z] :
                ( B_y = B_z
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) )
        | ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__def]) ).

fof(f_4070_2,plain,
    ! [U_16478,U_16477,U_16476] :
      ( ( c_Relation_Osingle__valued(U_16476,U_16477,U_16478)
        | ? [U_16475,U_16474] :
            ( ? [U_16473] :
                ( U_16474 != U_16473
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16476,U_16477)),hAPP(hAPP(c_Product__Type_OPair(U_16476,U_16477),U_16475),U_16473)),U_16478)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16476,U_16477)),hAPP(hAPP(c_Product__Type_OPair(U_16476,U_16477),U_16475),U_16474)),U_16478)) ) )
      & ( ! [U_16472,U_16471] :
            ( ! [U_16470] :
                ( U_16471 = U_16470
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16476,U_16477)),hAPP(hAPP(c_Product__Type_OPair(U_16476,U_16477),U_16472),U_16470)),U_16478)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16476,U_16477)),hAPP(hAPP(c_Product__Type_OPair(U_16476,U_16477),U_16472),U_16471)),U_16478)) )
        | ~ c_Relation_Osingle__valued(U_16476,U_16477,U_16478) ) ),
    inference(variable_rename,[status(thm)],[f_4070_1]) ).

fof(f_4070_3,plain,
    ( ! [U_16484,U_16482,U_16480] :
        ( c_Relation_Osingle__valued(U_16480,U_16482,U_16484)
        | ? [U_16475,U_16474] :
            ( ? [U_16473] :
                ( U_16474 != U_16473
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),U_16475),U_16473)),U_16484)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),U_16475),U_16474)),U_16484)) ) )
    & ! [U_16483,U_16481,U_16479] :
        ( ! [U_16472,U_16471] :
            ( ! [U_16470] :
                ( U_16471 = U_16470
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16470)),U_16483)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16471)),U_16483)) )
        | ~ c_Relation_Osingle__valued(U_16479,U_16481,U_16483) ) ),
    inference(miniscope,[status(thm)],[f_4070_2]) ).

fof(f_4070_4,plain,
    ( ! [U_16484,U_16482,U_16480] :
        ( c_Relation_Osingle__valued(U_16480,U_16482,U_16484)
        | ? [U_16474] :
            ( ? [U_16473] :
                ( U_16474 != U_16473
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),U_16473)),U_16484)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),U_16474)),U_16484)) ) )
    & ! [U_16483,U_16481,U_16479] :
        ( ! [U_16472,U_16471] :
            ( ! [U_16470] :
                ( U_16471 = U_16470
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16470)),U_16483)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16471)),U_16483)) )
        | ~ c_Relation_Osingle__valued(U_16479,U_16481,U_16483) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_16475,sK390(U_16484,U_16482,U_16480))],[f_4070_3]) ).

fof(f_4070_5,plain,
    ( ! [U_16484,U_16482,U_16480] :
        ( c_Relation_Osingle__valued(U_16480,U_16482,U_16484)
        | ( ? [U_16473] :
              ( sK391(U_16484,U_16482,U_16480) != U_16473
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),U_16473)),U_16484)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK391(U_16484,U_16482,U_16480))),U_16484)) ) )
    & ! [U_16483,U_16481,U_16479] :
        ( ! [U_16472,U_16471] :
            ( ! [U_16470] :
                ( U_16471 = U_16470
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16470)),U_16483)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16471)),U_16483)) )
        | ~ c_Relation_Osingle__valued(U_16479,U_16481,U_16483) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_16474,sK391(U_16484,U_16482,U_16480))],[f_4070_4]) ).

fof(f_4070_6,plain,
    ( ! [U_16484,U_16482,U_16480] :
        ( c_Relation_Osingle__valued(U_16480,U_16482,U_16484)
        | ( sK391(U_16484,U_16482,U_16480) != sK392(U_16484,U_16482,U_16480)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK392(U_16484,U_16482,U_16480))),U_16484))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK391(U_16484,U_16482,U_16480))),U_16484)) ) )
    & ! [U_16483,U_16481,U_16479] :
        ( ! [U_16472,U_16471] :
            ( ! [U_16470] :
                ( U_16471 = U_16470
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16470)),U_16483)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16471)),U_16483)) )
        | ~ c_Relation_Osingle__valued(U_16479,U_16481,U_16483) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_16473,sK392(U_16484,U_16482,U_16480))],[f_4070_5]) ).

fof(f_4070_7,plain,
    ( ! [U_16480,U_16482,U_16484] :
        ( sK391(U_16484,U_16482,U_16480) != sK392(U_16484,U_16482,U_16480)
        | ~ sP1059(U_16480,U_16482,U_16484) )
    & ! [U_16480,U_16482,U_16484] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK392(U_16484,U_16482,U_16480))),U_16484))
        | ~ sP1059(U_16480,U_16482,U_16484) )
    & ! [U_16480,U_16482,U_16484] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK391(U_16484,U_16482,U_16480))),U_16484))
        | ~ sP1059(U_16480,U_16482,U_16484) )
    & ! [U_16480,U_16482,U_16484] :
        ( c_Relation_Osingle__valued(U_16480,U_16482,U_16484)
        | sP1059(U_16480,U_16482,U_16484) )
    & ! [U_16483,U_16470,U_16481,U_16471,U_16472,U_16479] :
        ( U_16471 = U_16470
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16470)),U_16483))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16471)),U_16483))
        | ~ c_Relation_Osingle__valued(U_16479,U_16481,U_16483) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1059])],[f_4070_6]) ).

cnf(f_4070_8,plain,
    ( U_16471 = U_16470
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16470)),U_16483))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16479,U_16481)),hAPP(hAPP(c_Product__Type_OPair(U_16479,U_16481),U_16472),U_16471)),U_16483))
    | ~ c_Relation_Osingle__valued(U_16479,U_16481,U_16483) ),
    inference(clausify,[status(thm)],[f_4070_7]) ).

cnf(f_4070_9,plain,
    ( c_Relation_Osingle__valued(U_16480,U_16482,U_16484)
    | sP1059(U_16480,U_16482,U_16484) ),
    inference(clausify,[status(thm)],[f_4070_7]) ).

cnf(f_4070_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK391(U_16484,U_16482,U_16480))),U_16484))
    | ~ sP1059(U_16480,U_16482,U_16484) ),
    inference(clausify,[status(thm)],[f_4070_7]) ).

cnf(f_4070_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16480,U_16482)),hAPP(hAPP(c_Product__Type_OPair(U_16480,U_16482),sK390(U_16484,U_16482,U_16480)),sK392(U_16484,U_16482,U_16480))),U_16484))
    | ~ sP1059(U_16480,U_16482,U_16484) ),
    inference(clausify,[status(thm)],[f_4070_7]) ).

cnf(f_4070_12,plain,
    ( sK391(U_16484,U_16482,U_16480) != sK392(U_16484,U_16482,U_16480)
    | ~ sP1059(U_16480,U_16482,U_16484) ),
    inference(clausify,[status(thm)],[f_4070_7]) ).

fof(f_4071_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( V_y_2 = V_z_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valuedD]) ).

fof(f_4071_2,plain,
    ! [U_16490,U_16489,U_16488,U_16487,U_16486,U_16485] :
      ( U_16489 = U_16490
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16485,U_16486)),hAPP(hAPP(c_Product__Type_OPair(U_16485,U_16486),U_16488),U_16490)),U_16487))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16485,U_16486)),hAPP(hAPP(c_Product__Type_OPair(U_16485,U_16486),U_16488),U_16489)),U_16487))
      | ~ c_Relation_Osingle__valued(U_16485,U_16486,U_16487) ),
    inference(variable_rename,[status(thm)],[f_4071_1]) ).

fof(f_4071_3,plain,
    ! [U_16486,U_16485,U_16488,U_16487,U_16489,U_16490] :
      ( U_16489 = U_16490
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16485,U_16486)),hAPP(hAPP(c_Product__Type_OPair(U_16485,U_16486),U_16488),U_16490)),U_16487))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16485,U_16486)),hAPP(hAPP(c_Product__Type_OPair(U_16485,U_16486),U_16488),U_16489)),U_16487))
      | ~ c_Relation_Osingle__valued(U_16485,U_16486,U_16487) ),
    inference(definitional_conversion,[status(esa)],[f_4071_2]) ).

cnf(f_4071_4,plain,
    ( U_16489 = U_16490
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16485,U_16486)),hAPP(hAPP(c_Product__Type_OPair(U_16485,U_16486),U_16488),U_16490)),U_16487))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16485,U_16486)),hAPP(hAPP(c_Product__Type_OPair(U_16485,U_16486),U_16488),U_16489)),U_16487))
    | ~ c_Relation_Osingle__valued(U_16485,U_16486,U_16487) ),
    inference(clausify,[status(thm)],[f_4071_3]) ).

fof(f_4072_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ c_Relation_Osingle__valued(T_b,T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__confluent]) ).

fof(f_4072_2,plain,
    ! [U_16495,U_16494,U_16493,U_16492,U_16491] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16495),U_16494)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16494),U_16495)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16493),U_16495)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16493),U_16494)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | ~ c_Relation_Osingle__valued(U_16491,U_16491,U_16492) ),
    inference(variable_rename,[status(thm)],[f_4072_1]) ).

fof(f_4072_3,plain,
    ! [U_16491,U_16492,U_16493,U_16494,U_16495] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16495),U_16494)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16494),U_16495)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16493),U_16495)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16493),U_16494)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
      | ~ c_Relation_Osingle__valued(U_16491,U_16491,U_16492) ),
    inference(definitional_conversion,[status(esa)],[f_4072_2]) ).

cnf(f_4072_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16495),U_16494)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16494),U_16495)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16493),U_16495)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16491,U_16491)),hAPP(hAPP(c_Product__Type_OPair(U_16491,U_16491),U_16493),U_16494)),c_Transitive__Closure_Ortrancl(U_16491,U_16492)))
    | ~ c_Relation_Osingle__valued(U_16491,U_16491,U_16492) ),
    inference(clausify,[status(thm)],[f_4072_3]) ).

fof(f_4073_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
      ( hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2))
      | ~ c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__Int__eq]) ).

fof(f_4073_2,plain,
    ! [U_16500,U_16499,U_16498,U_16497,U_16496] :
      ( hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16497,tc_HOL_Obool)),U_16499),U_16500)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16496,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),U_16499)),hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),U_16500))
      | ~ c_Relation_Osingle__valued(U_16496,U_16497,hAPP(c_Relation_Oconverse(U_16497,U_16496),U_16498)) ),
    inference(variable_rename,[status(thm)],[f_4073_1]) ).

fof(f_4073_3,plain,
    ! [U_16496,U_16498,U_16497,U_16499,U_16500] :
      ( hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16497,tc_HOL_Obool)),U_16499),U_16500)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16496,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),U_16499)),hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),U_16500))
      | ~ c_Relation_Osingle__valued(U_16496,U_16497,hAPP(c_Relation_Oconverse(U_16497,U_16496),U_16498)) ),
    inference(definitional_conversion,[status(esa)],[f_4073_2]) ).

cnf(f_4073_4,plain,
    ( hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16497,tc_HOL_Obool)),U_16499),U_16500)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16496,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),U_16499)),hAPP(c_Relation_OImage(U_16497,U_16496,U_16498),U_16500))
    | ~ c_Relation_Osingle__valued(U_16496,U_16497,hAPP(c_Relation_Oconverse(U_16497,U_16496),U_16498)) ),
    inference(clausify,[status(thm)],[f_4073_3]) ).

fof(f_4074_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
        | ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) )
      & ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id]) ).

fof(f_4074_2,plain,
    ! [U_16503,U_16502,U_16501] :
      ( ( c_Relation_Ototal__on(U_16501,U_16502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16501,U_16501),tc_HOL_Obool)),U_16503),c_Relation_OId(U_16501)))
        | ~ c_Relation_Ototal__on(U_16501,U_16502,U_16503) )
      & ( c_Relation_Ototal__on(U_16501,U_16502,U_16503)
        | ~ c_Relation_Ototal__on(U_16501,U_16502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16501,U_16501),tc_HOL_Obool)),U_16503),c_Relation_OId(U_16501))) ) ),
    inference(variable_rename,[status(thm)],[f_4074_1]) ).

fof(f_4074_3,plain,
    ( ! [U_16509,U_16507,U_16505] :
        ( c_Relation_Ototal__on(U_16505,U_16507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16505,U_16505),tc_HOL_Obool)),U_16509),c_Relation_OId(U_16505)))
        | ~ c_Relation_Ototal__on(U_16505,U_16507,U_16509) )
    & ! [U_16508,U_16506,U_16504] :
        ( c_Relation_Ototal__on(U_16504,U_16506,U_16508)
        | ~ c_Relation_Ototal__on(U_16504,U_16506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16504,U_16504),tc_HOL_Obool)),U_16508),c_Relation_OId(U_16504))) ) ),
    inference(miniscope,[status(thm)],[f_4074_2]) ).

fof(f_4074_4,plain,
    ( ! [U_16507,U_16505,U_16509] :
        ( c_Relation_Ototal__on(U_16505,U_16507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16505,U_16505),tc_HOL_Obool)),U_16509),c_Relation_OId(U_16505)))
        | ~ c_Relation_Ototal__on(U_16505,U_16507,U_16509) )
    & ! [U_16506,U_16504,U_16508] :
        ( c_Relation_Ototal__on(U_16504,U_16506,U_16508)
        | ~ c_Relation_Ototal__on(U_16504,U_16506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16504,U_16504),tc_HOL_Obool)),U_16508),c_Relation_OId(U_16504))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4074_3]) ).

cnf(f_4074_5,plain,
    ( c_Relation_Ototal__on(U_16504,U_16506,U_16508)
    | ~ c_Relation_Ototal__on(U_16504,U_16506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16504,U_16504),tc_HOL_Obool)),U_16508),c_Relation_OId(U_16504))) ),
    inference(clausify,[status(thm)],[f_4074_4]) ).

cnf(f_4074_6,plain,
    ( c_Relation_Ototal__on(U_16505,U_16507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16505,U_16505),tc_HOL_Obool)),U_16509),c_Relation_OId(U_16505)))
    | ~ c_Relation_Ototal__on(U_16505,U_16507,U_16509) ),
    inference(clausify,[status(thm)],[f_4074_4]) ).

fof(f_4075_1,plain,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow]) ).

fof(f_4075_2,plain,
    ! [U_16512,U_16511,U_16510] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16510,U_16510)),U_16511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool),tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16510,U_16510),tc_HOL_Obool)),U_16512))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16510,U_16510)),U_16511),c_Transitive__Closure_Ortrancl(U_16510,U_16512))) ),
    inference(variable_rename,[status(thm)],[f_4075_1]) ).

fof(f_4075_3,plain,
    ! [U_16510,U_16511,U_16512] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16510,U_16510)),U_16511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool),tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16510,U_16510),tc_HOL_Obool)),U_16512))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16510,U_16510)),U_16511),c_Transitive__Closure_Ortrancl(U_16510,U_16512))) ),
    inference(definitional_conversion,[status(esa)],[f_4075_2]) ).

cnf(f_4075_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16510,U_16510)),U_16511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool),tc_fun(tc_prod(U_16510,U_16510),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16510,U_16510),tc_HOL_Obool)),U_16512))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16510,U_16510)),U_16511),c_Transitive__Closure_Ortrancl(U_16510,U_16512))) ),
    inference(clausify,[status(thm)],[f_4075_3]) ).

fof(f_4076_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
    inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(f_4076_2,plain,
    ! [U_16514,U_16513] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16513,U_16513),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16514) = c_Relation_OId(U_16513),
    inference(variable_rename,[status(thm)],[f_4076_1]) ).

fof(f_4076_3,plain,
    ! [U_16513,U_16514] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16513,U_16513),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16514) = c_Relation_OId(U_16513),
    inference(definitional_conversion,[status(esa)],[f_4076_2]) ).

cnf(f_4076_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16513,U_16513),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16514) = c_Relation_OId(U_16513),
    inference(clausify,[status(thm)],[f_4076_3]) ).

fof(f_4077_1,plain,
    ! [V_n_2,V_R_2,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
      | ~ c_Relation_Osingle__valued(T_b,T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow]) ).

fof(f_4077_2,plain,
    ! [U_16517,U_16516,U_16515] :
      ( c_Relation_Osingle__valued(U_16515,U_16515,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16515,U_16515),tc_HOL_Obool),U_16517),U_16516))
      | ~ c_Relation_Osingle__valued(U_16515,U_16515,U_16516) ),
    inference(variable_rename,[status(thm)],[f_4077_1]) ).

fof(f_4077_3,plain,
    ! [U_16515,U_16516,U_16517] :
      ( c_Relation_Osingle__valued(U_16515,U_16515,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16515,U_16515),tc_HOL_Obool),U_16517),U_16516))
      | ~ c_Relation_Osingle__valued(U_16515,U_16515,U_16516) ),
    inference(definitional_conversion,[status(esa)],[f_4077_2]) ).

cnf(f_4077_4,plain,
    ( c_Relation_Osingle__valued(U_16515,U_16515,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16515,U_16515),tc_HOL_Obool),U_16517),U_16516))
    | ~ c_Relation_Osingle__valued(U_16515,U_16515,U_16516) ),
    inference(clausify,[status(thm)],[f_4077_3]) ).

fof(f_4078_1,plain,
    ! [V_R_2,V_n_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl]) ).

fof(f_4078_2,plain,
    ! [U_16521,U_16520,U_16519,U_16518] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16518,U_16518)),U_16519),c_Transitive__Closure_Ortrancl(U_16518,U_16521)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16518,U_16518)),U_16519),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16518,U_16518),tc_HOL_Obool),U_16520),U_16521))) ),
    inference(variable_rename,[status(thm)],[f_4078_1]) ).

fof(f_4078_3,plain,
    ! [U_16518,U_16519,U_16520,U_16521] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16518,U_16518)),U_16519),c_Transitive__Closure_Ortrancl(U_16518,U_16521)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16518,U_16518)),U_16519),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16518,U_16518),tc_HOL_Obool),U_16520),U_16521))) ),
    inference(definitional_conversion,[status(esa)],[f_4078_2]) ).

cnf(f_4078_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16518,U_16518)),U_16519),c_Transitive__Closure_Ortrancl(U_16518,U_16521)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16518,U_16518)),U_16519),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16518,U_16518),tc_HOL_Obool),U_16520),U_16521))) ),
    inference(clausify,[status(thm)],[f_4078_3]) ).

fof(f_4079_1,plain,
    ! [V_R_2,V_p_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
        | ! [B_n] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) )
      & ( ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__power]) ).

fof(f_4079_2,plain,
    ! [U_16526,U_16525,U_16524] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16524,U_16524)),U_16525),c_Transitive__Closure_Ortrancl(U_16524,U_16526)))
        | ! [U_16523] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16524,U_16524)),U_16525),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16524,U_16524),tc_HOL_Obool),U_16523),U_16526))) )
      & ( ? [U_16522] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16524,U_16524)),U_16525),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16524,U_16524),tc_HOL_Obool),U_16522),U_16526)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16524,U_16524)),U_16525),c_Transitive__Closure_Ortrancl(U_16524,U_16526))) ) ),
    inference(variable_rename,[status(thm)],[f_4079_1]) ).

fof(f_4079_3,plain,
    ( ! [U_16532,U_16530,U_16528] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),c_Transitive__Closure_Ortrancl(U_16528,U_16532)))
        | ! [U_16523] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16528,U_16528),tc_HOL_Obool),U_16523),U_16532))) )
    & ! [U_16531,U_16529,U_16527] :
        ( ? [U_16522] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16527,U_16527),tc_HOL_Obool),U_16522),U_16531)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),c_Transitive__Closure_Ortrancl(U_16527,U_16531))) ) ),
    inference(miniscope,[status(thm)],[f_4079_2]) ).

fof(f_4079_4,plain,
    ( ! [U_16532,U_16530,U_16528] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),c_Transitive__Closure_Ortrancl(U_16528,U_16532)))
        | ! [U_16523] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16528,U_16528),tc_HOL_Obool),U_16523),U_16532))) )
    & ! [U_16531,U_16529,U_16527] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16527,U_16527),tc_HOL_Obool),sK393(U_16531,U_16529,U_16527)),U_16531)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),c_Transitive__Closure_Ortrancl(U_16527,U_16531))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_16522,sK393(U_16531,U_16529,U_16527))],[f_4079_3]) ).

fof(f_4079_5,plain,
    ( ! [U_16523,U_16528,U_16530,U_16532] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),c_Transitive__Closure_Ortrancl(U_16528,U_16532)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16528,U_16528),tc_HOL_Obool),U_16523),U_16532))) )
    & ! [U_16529,U_16527,U_16531] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16527,U_16527),tc_HOL_Obool),sK393(U_16531,U_16529,U_16527)),U_16531)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),c_Transitive__Closure_Ortrancl(U_16527,U_16531))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4079_4]) ).

cnf(f_4079_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16527,U_16527),tc_HOL_Obool),sK393(U_16531,U_16529,U_16527)),U_16531)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16527,U_16527)),U_16529),c_Transitive__Closure_Ortrancl(U_16527,U_16531))) ),
    inference(clausify,[status(thm)],[f_4079_5]) ).

cnf(f_4079_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),c_Transitive__Closure_Ortrancl(U_16528,U_16532)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16528,U_16528)),U_16530),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16528,U_16528),tc_HOL_Obool),U_16523),U_16532))) ),
    inference(clausify,[status(thm)],[f_4079_5]) ).

fof(f_4080_1,plain,
    ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_comp__funpow]) ).

fof(f_4080_2,plain,
    ! [U_16536,U_16535,U_16534,U_16533] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_16533,U_16534),tc_fun(U_16533,U_16534)),U_16535),c_Fun_Ocomp(U_16534,U_16534,U_16533,U_16536)) = c_Fun_Ocomp(U_16534,U_16534,U_16533,hAPP(hAPP(c_Nat_Ocompow(U_16534,U_16534),U_16535),U_16536)),
    inference(variable_rename,[status(thm)],[f_4080_1]) ).

fof(f_4080_3,plain,
    ! [U_16534,U_16533,U_16535,U_16536] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_16533,U_16534),tc_fun(U_16533,U_16534)),U_16535),c_Fun_Ocomp(U_16534,U_16534,U_16533,U_16536)) = c_Fun_Ocomp(U_16534,U_16534,U_16533,hAPP(hAPP(c_Nat_Ocompow(U_16534,U_16534),U_16535),U_16536)),
    inference(definitional_conversion,[status(esa)],[f_4080_2]) ).

cnf(f_4080_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_16533,U_16534),tc_fun(U_16533,U_16534)),U_16535),c_Fun_Ocomp(U_16534,U_16534,U_16533,U_16536)) = c_Fun_Ocomp(U_16534,U_16534,U_16533,hAPP(hAPP(c_Nat_Ocompow(U_16534,U_16534),U_16535),U_16536)),
    inference(clausify,[status(thm)],[f_4080_3]) ).

fof(f_4081_1,plain,
    ! [V_R_2,V_n_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
      | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__exp]) ).

fof(f_4081_2,plain,
    ! [U_16539,U_16538,U_16537] :
      ( c_Wellfounded_Owf(U_16537,U_16539)
      | ~ c_Wellfounded_Owf(U_16537,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16537,U_16537),tc_HOL_Obool),U_16538),U_16539)) ),
    inference(variable_rename,[status(thm)],[f_4081_1]) ).

fof(f_4081_3,plain,
    ! [U_16538,U_16537,U_16539] :
      ( c_Wellfounded_Owf(U_16537,U_16539)
      | ~ c_Wellfounded_Owf(U_16537,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16537,U_16537),tc_HOL_Obool),U_16538),U_16539)) ),
    inference(definitional_conversion,[status(esa)],[f_4081_2]) ).

cnf(f_4081_4,plain,
    ( c_Wellfounded_Owf(U_16537,U_16539)
    | ~ c_Wellfounded_Owf(U_16537,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16537,U_16537),tc_HOL_Obool),U_16538),U_16539)) ),
    inference(clausify,[status(thm)],[f_4081_3]) ).

fof(f_4082_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_funpow__mult]) ).

fof(f_4082_2,plain,
    ! [U_16543,U_16542,U_16541,U_16540] : hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),U_16541),hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),U_16542),U_16543)) = hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16542),U_16541)),U_16543),
    inference(variable_rename,[status(thm)],[f_4082_1]) ).

fof(f_4082_3,plain,
    ! [U_16540,U_16541,U_16542,U_16543] : hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),U_16541),hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),U_16542),U_16543)) = hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16542),U_16541)),U_16543),
    inference(definitional_conversion,[status(esa)],[f_4082_2]) ).

cnf(f_4082_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),U_16541),hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),U_16542),U_16543)) = hAPP(hAPP(c_Nat_Ocompow(U_16540,U_16540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16542),U_16541)),U_16543),
    inference(clausify,[status(thm)],[f_4082_3]) ).

fof(f_4083_1,plain,
    ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow__swap1]) ).

fof(f_4083_2,plain,
    ! [U_16547,U_16546,U_16545,U_16544] : hAPP(U_16544,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16545,U_16545),U_16546),U_16544),U_16547)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16545,U_16545),U_16546),U_16544),hAPP(U_16544,U_16547)),
    inference(variable_rename,[status(thm)],[f_4083_1]) ).

fof(f_4083_3,plain,
    ! [U_16544,U_16545,U_16546,U_16547] : hAPP(U_16544,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16545,U_16545),U_16546),U_16544),U_16547)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16545,U_16545),U_16546),U_16544),hAPP(U_16544,U_16547)),
    inference(definitional_conversion,[status(esa)],[f_4083_2]) ).

cnf(f_4083_4,plain,
    hAPP(U_16544,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16545,U_16545),U_16546),U_16544),U_16547)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16545,U_16545),U_16546),U_16544),hAPP(U_16544,U_16547)),
    inference(clausify,[status(thm)],[f_4083_3]) ).

fof(f_4084_1,plain,
    ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(f_4084_2,plain,
    ! [U_16550,U_16549,U_16548] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16548,U_16548),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16549)),U_16550) = hAPP(hAPP(c_Relation_Orel__comp(U_16548,U_16548,U_16548),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16548,U_16548),tc_HOL_Obool),U_16549),U_16550)),U_16550),
    inference(variable_rename,[status(thm)],[f_4084_1]) ).

fof(f_4084_3,plain,
    ! [U_16549,U_16548,U_16550] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16548,U_16548),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16549)),U_16550) = hAPP(hAPP(c_Relation_Orel__comp(U_16548,U_16548,U_16548),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16548,U_16548),tc_HOL_Obool),U_16549),U_16550)),U_16550),
    inference(definitional_conversion,[status(esa)],[f_4084_2]) ).

cnf(f_4084_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16548,U_16548),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16549)),U_16550) = hAPP(hAPP(c_Relation_Orel__comp(U_16548,U_16548,U_16548),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16548,U_16548),tc_HOL_Obool),U_16549),U_16550)),U_16550),
    inference(clausify,[status(thm)],[f_4084_3]) ).

fof(f_4085_1,plain,
    ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__commute]) ).

fof(f_4085_2,plain,
    ! [U_16553,U_16552,U_16551] : hAPP(hAPP(c_Relation_Orel__comp(U_16551,U_16551,U_16551),U_16552),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16551,U_16551),tc_HOL_Obool),U_16553),U_16552)) = hAPP(hAPP(c_Relation_Orel__comp(U_16551,U_16551,U_16551),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16551,U_16551),tc_HOL_Obool),U_16553),U_16552)),U_16552),
    inference(variable_rename,[status(thm)],[f_4085_1]) ).

fof(f_4085_3,plain,
    ! [U_16551,U_16552,U_16553] : hAPP(hAPP(c_Relation_Orel__comp(U_16551,U_16551,U_16551),U_16552),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16551,U_16551),tc_HOL_Obool),U_16553),U_16552)) = hAPP(hAPP(c_Relation_Orel__comp(U_16551,U_16551,U_16551),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16551,U_16551),tc_HOL_Obool),U_16553),U_16552)),U_16552),
    inference(definitional_conversion,[status(esa)],[f_4085_2]) ).

cnf(f_4085_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_16551,U_16551,U_16551),U_16552),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16551,U_16551),tc_HOL_Obool),U_16553),U_16552)) = hAPP(hAPP(c_Relation_Orel__comp(U_16551,U_16551,U_16551),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16551,U_16551),tc_HOL_Obool),U_16553),U_16552)),U_16552),
    inference(clausify,[status(thm)],[f_4085_3]) ).

fof(f_4086_1,plain,
    ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__add]) ).

fof(f_4086_2,plain,
    ! [U_16557,U_16556,U_16555,U_16554] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16555),U_16556)),U_16557) = hAPP(hAPP(c_Relation_Orel__comp(U_16554,U_16554,U_16554),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),U_16555),U_16557)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),U_16556),U_16557)),
    inference(variable_rename,[status(thm)],[f_4086_1]) ).

fof(f_4086_3,plain,
    ! [U_16554,U_16555,U_16556,U_16557] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16555),U_16556)),U_16557) = hAPP(hAPP(c_Relation_Orel__comp(U_16554,U_16554,U_16554),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),U_16555),U_16557)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),U_16556),U_16557)),
    inference(definitional_conversion,[status(esa)],[f_4086_2]) ).

cnf(f_4086_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16555),U_16556)),U_16557) = hAPP(hAPP(c_Relation_Orel__comp(U_16554,U_16554,U_16554),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),U_16555),U_16557)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16554,U_16554),tc_HOL_Obool),U_16556),U_16557)),
    inference(clausify,[status(thm)],[f_4086_3]) ).

fof(f_4087_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_rel__pow__1]) ).

fof(f_4087_2,plain,
    ! [U_16559,U_16558] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16558,U_16558),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_16559) = U_16559,
    inference(variable_rename,[status(thm)],[f_4087_1]) ).

fof(f_4087_3,plain,
    ! [U_16559,U_16558] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16558,U_16558),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_16559) = U_16559,
    inference(definitional_conversion,[status(esa)],[f_4087_2]) ).

cnf(f_4087_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16558,U_16558),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_16559) = U_16559,
    inference(clausify,[status(thm)],[f_4087_3]) ).

fof(f_4088_1,plain,
    ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_total__on__empty]) ).

fof(f_4088_2,plain,
    ! [U_16561,U_16560] : c_Relation_Ototal__on(U_16560,c_Orderings_Obot__class_Obot(tc_fun(U_16560,tc_HOL_Obool)),U_16561),
    inference(variable_rename,[status(thm)],[f_4088_1]) ).

fof(f_4088_3,plain,
    ! [U_16560,U_16561] : c_Relation_Ototal__on(U_16560,c_Orderings_Obot__class_Obot(tc_fun(U_16560,tc_HOL_Obool)),U_16561),
    inference(definitional_conversion,[status(esa)],[f_4088_2]) ).

cnf(f_4088_4,plain,
    c_Relation_Ototal__on(U_16560,c_Orderings_Obot__class_Obot(tc_fun(U_16560,tc_HOL_Obool)),U_16561),
    inference(clausify,[status(thm)],[f_4088_3]) ).

fof(f_4089_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) )
      & ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__converse]) ).

fof(f_4089_2,plain,
    ! [U_16564,U_16563,U_16562] :
      ( ( c_Relation_Ototal__on(U_16562,U_16563,hAPP(c_Relation_Oconverse(U_16562,U_16562),U_16564))
        | ~ c_Relation_Ototal__on(U_16562,U_16563,U_16564) )
      & ( c_Relation_Ototal__on(U_16562,U_16563,U_16564)
        | ~ c_Relation_Ototal__on(U_16562,U_16563,hAPP(c_Relation_Oconverse(U_16562,U_16562),U_16564)) ) ),
    inference(variable_rename,[status(thm)],[f_4089_1]) ).

fof(f_4089_3,plain,
    ( ! [U_16570,U_16568,U_16566] :
        ( c_Relation_Ototal__on(U_16566,U_16568,hAPP(c_Relation_Oconverse(U_16566,U_16566),U_16570))
        | ~ c_Relation_Ototal__on(U_16566,U_16568,U_16570) )
    & ! [U_16569,U_16567,U_16565] :
        ( c_Relation_Ototal__on(U_16565,U_16567,U_16569)
        | ~ c_Relation_Ototal__on(U_16565,U_16567,hAPP(c_Relation_Oconverse(U_16565,U_16565),U_16569)) ) ),
    inference(miniscope,[status(thm)],[f_4089_2]) ).

fof(f_4089_4,plain,
    ( ! [U_16570,U_16568,U_16566] :
        ( c_Relation_Ototal__on(U_16566,U_16568,hAPP(c_Relation_Oconverse(U_16566,U_16566),U_16570))
        | ~ c_Relation_Ototal__on(U_16566,U_16568,U_16570) )
    & ! [U_16567,U_16565,U_16569] :
        ( c_Relation_Ototal__on(U_16565,U_16567,U_16569)
        | ~ c_Relation_Ototal__on(U_16565,U_16567,hAPP(c_Relation_Oconverse(U_16565,U_16565),U_16569)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4089_3]) ).

cnf(f_4089_5,plain,
    ( c_Relation_Ototal__on(U_16565,U_16567,U_16569)
    | ~ c_Relation_Ototal__on(U_16565,U_16567,hAPP(c_Relation_Oconverse(U_16565,U_16565),U_16569)) ),
    inference(clausify,[status(thm)],[f_4089_4]) ).

cnf(f_4089_6,plain,
    ( c_Relation_Ototal__on(U_16566,U_16568,hAPP(c_Relation_Oconverse(U_16566,U_16566),U_16570))
    | ~ c_Relation_Ototal__on(U_16566,U_16568,U_16570) ),
    inference(clausify,[status(thm)],[f_4089_4]) ).

fof(f_4090_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E]) ).

fof(f_4090_2,plain,
    ! [U_16574,U_16573,U_16572,U_16571] :
      ( U_16572 = U_16573
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16571,U_16571)),hAPP(hAPP(c_Product__Type_OPair(U_16571,U_16571),U_16572),U_16573)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16571,U_16571),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16574))) ),
    inference(variable_rename,[status(thm)],[f_4090_1]) ).

fof(f_4090_3,plain,
    ! [U_16574,U_16573,U_16572] :
      ( ! [U_16571] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16571,U_16571)),hAPP(hAPP(c_Product__Type_OPair(U_16571,U_16571),U_16572),U_16573)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16571,U_16571),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16574)))
      | U_16572 = U_16573 ),
    inference(miniscope,[status(thm)],[f_4090_2]) ).

fof(f_4090_4,plain,
    ! [U_16571,U_16572,U_16573,U_16574] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16571,U_16571)),hAPP(hAPP(c_Product__Type_OPair(U_16571,U_16571),U_16572),U_16573)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16571,U_16571),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16574)))
      | U_16572 = U_16573 ),
    inference(definitional_conversion,[status(esa)],[f_4090_3]) ).

cnf(f_4090_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16571,U_16571)),hAPP(hAPP(c_Product__Type_OPair(U_16571,U_16571),U_16572),U_16573)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16571,U_16571),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16574)))
    | U_16572 = U_16573 ),
    inference(clausify,[status(thm)],[f_4090_4]) ).

fof(f_4091_1,plain,
    ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__0__I]) ).

fof(f_4091_2,plain,
    ! [U_16577,U_16576,U_16575] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16575,U_16575)),hAPP(hAPP(c_Product__Type_OPair(U_16575,U_16575),U_16576),U_16576)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16575,U_16575),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16577))),
    inference(variable_rename,[status(thm)],[f_4091_1]) ).

fof(f_4091_3,plain,
    ! [U_16575,U_16576,U_16577] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16575,U_16575)),hAPP(hAPP(c_Product__Type_OPair(U_16575,U_16575),U_16576),U_16576)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16575,U_16575),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16577))),
    inference(definitional_conversion,[status(esa)],[f_4091_2]) ).

cnf(f_4091_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_16575,U_16575)),hAPP(hAPP(c_Product__Type_OPair(U_16575,U_16575),U_16576),U_16576)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16575,U_16575),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16577))),
    inference(clausify,[status(thm)],[f_4091_3]) ).

fof(f_4092_1,plain,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I]) ).

fof(f_4092_2,plain,
    ! [U_16583,U_16582,U_16581,U_16580,U_16579,U_16578] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16579),U_16583)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16578,U_16578),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16581)),U_16582)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16580),U_16583)),U_16582))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16579),U_16580)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16578,U_16578),tc_HOL_Obool),U_16581),U_16582))) ),
    inference(variable_rename,[status(thm)],[f_4092_1]) ).

fof(f_4092_3,plain,
    ! [U_16578,U_16579,U_16580,U_16581,U_16582,U_16583] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16579),U_16583)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16578,U_16578),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16581)),U_16582)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16580),U_16583)),U_16582))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16579),U_16580)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16578,U_16578),tc_HOL_Obool),U_16581),U_16582))) ),
    inference(definitional_conversion,[status(esa)],[f_4092_2]) ).

cnf(f_4092_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16579),U_16583)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16578,U_16578),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16581)),U_16582)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16580),U_16583)),U_16582))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16578,U_16578)),hAPP(hAPP(c_Product__Type_OPair(U_16578,U_16578),U_16579),U_16580)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16578,U_16578),tc_HOL_Obool),U_16581),U_16582))) ),
    inference(clausify,[status(thm)],[f_4092_3]) ).

fof(f_4093_1,plain,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2]) ).

fof(f_4093_2,plain,
    ! [U_16589,U_16588,U_16587,U_16586,U_16585,U_16584] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16585),U_16588)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16584,U_16584),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16589)),U_16587)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16586),U_16588)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16584,U_16584),tc_HOL_Obool),U_16589),U_16587)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16585),U_16586)),U_16587)) ),
    inference(variable_rename,[status(thm)],[f_4093_1]) ).

fof(f_4093_3,plain,
    ! [U_16584,U_16585,U_16586,U_16587,U_16588,U_16589] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16585),U_16588)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16584,U_16584),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16589)),U_16587)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16586),U_16588)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16584,U_16584),tc_HOL_Obool),U_16589),U_16587)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16585),U_16586)),U_16587)) ),
    inference(definitional_conversion,[status(esa)],[f_4093_2]) ).

cnf(f_4093_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16585),U_16588)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16584,U_16584),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16589)),U_16587)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16586),U_16588)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16584,U_16584),tc_HOL_Obool),U_16589),U_16587)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16584,U_16584)),hAPP(hAPP(c_Product__Type_OPair(U_16584,U_16584),U_16585),U_16586)),U_16587)) ),
    inference(clausify,[status(thm)],[f_4093_3]) ).

fof(f_4094_1,plain,
    ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(f_4094_2,plain,
    ! [U_16592,U_16591,U_16590] : hAPP(hAPP(c_Nat_Ocompow(U_16590,U_16590),hAPP(c_Nat_OSuc,U_16591)),U_16592) = hAPP(c_Fun_Ocomp(U_16590,U_16590,U_16590,U_16592),hAPP(hAPP(c_Nat_Ocompow(U_16590,U_16590),U_16591),U_16592)),
    inference(variable_rename,[status(thm)],[f_4094_1]) ).

fof(f_4094_3,plain,
    ! [U_16591,U_16590,U_16592] : hAPP(hAPP(c_Nat_Ocompow(U_16590,U_16590),hAPP(c_Nat_OSuc,U_16591)),U_16592) = hAPP(c_Fun_Ocomp(U_16590,U_16590,U_16590,U_16592),hAPP(hAPP(c_Nat_Ocompow(U_16590,U_16590),U_16591),U_16592)),
    inference(definitional_conversion,[status(esa)],[f_4094_2]) ).

cnf(f_4094_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16590,U_16590),hAPP(c_Nat_OSuc,U_16591)),U_16592) = hAPP(c_Fun_Ocomp(U_16590,U_16590,U_16590,U_16592),hAPP(hAPP(c_Nat_Ocompow(U_16590,U_16590),U_16591),U_16592)),
    inference(clausify,[status(thm)],[f_4094_3]) ).

fof(f_4095_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow__add]) ).

fof(f_4095_2,plain,
    ! [U_16596,U_16595,U_16594,U_16593] : hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16594),U_16595)),U_16596) = hAPP(c_Fun_Ocomp(U_16593,U_16593,U_16593,hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),U_16594),U_16596)),hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),U_16595),U_16596)),
    inference(variable_rename,[status(thm)],[f_4095_1]) ).

fof(f_4095_3,plain,
    ! [U_16593,U_16594,U_16595,U_16596] : hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16594),U_16595)),U_16596) = hAPP(c_Fun_Ocomp(U_16593,U_16593,U_16593,hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),U_16594),U_16596)),hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),U_16595),U_16596)),
    inference(definitional_conversion,[status(esa)],[f_4095_2]) ).

cnf(f_4095_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16594),U_16595)),U_16596) = hAPP(c_Fun_Ocomp(U_16593,U_16593,U_16593,hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),U_16594),U_16596)),hAPP(hAPP(c_Nat_Ocompow(U_16593,U_16593),U_16595),U_16596)),
    inference(clausify,[status(thm)],[f_4095_3]) ).

fof(f_4096_1,plain,
    ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
    inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(f_4096_2,plain,
    ! [U_16598,U_16597] : hAPP(hAPP(c_Nat_Ocompow(U_16597,U_16597),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16598) = c_Fun_Oid(U_16597),
    inference(variable_rename,[status(thm)],[f_4096_1]) ).

fof(f_4096_3,plain,
    ! [U_16598,U_16597] : hAPP(hAPP(c_Nat_Ocompow(U_16597,U_16597),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16598) = c_Fun_Oid(U_16597),
    inference(definitional_conversion,[status(esa)],[f_4096_2]) ).

cnf(f_4096_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16597,U_16597),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16598) = c_Fun_Oid(U_16597),
    inference(clausify,[status(thm)],[f_4096_3]) ).

fof(f_4097_1,plain,
    ! [V_R_2,V_p_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
        | ! [B_n] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) )
      & ( ? [B_n] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__power]) ).

fof(f_4097_2,plain,
    ! [U_16603,U_16602,U_16601] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16601,U_16601)),U_16602),c_Transitive__Closure_Otrancl(U_16601,U_16603)))
        | ! [U_16600] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16601,U_16601)),U_16602),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16601,U_16601),tc_HOL_Obool),U_16600),U_16603)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16600)) ) )
      & ( ? [U_16599] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16601,U_16601)),U_16602),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16601,U_16601),tc_HOL_Obool),U_16599),U_16603)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16599)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16601,U_16601)),U_16602),c_Transitive__Closure_Otrancl(U_16601,U_16603))) ) ),
    inference(variable_rename,[status(thm)],[f_4097_1]) ).

fof(f_4097_3,plain,
    ( ! [U_16609,U_16607,U_16605] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),c_Transitive__Closure_Otrancl(U_16605,U_16609)))
        | ! [U_16600] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16605,U_16605),tc_HOL_Obool),U_16600),U_16609)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16600)) ) )
    & ! [U_16608,U_16606,U_16604] :
        ( ? [U_16599] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16604,U_16604),tc_HOL_Obool),U_16599),U_16608)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16599)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),c_Transitive__Closure_Otrancl(U_16604,U_16608))) ) ),
    inference(miniscope,[status(thm)],[f_4097_2]) ).

fof(f_4097_4,plain,
    ( ! [U_16609,U_16607,U_16605] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),c_Transitive__Closure_Otrancl(U_16605,U_16609)))
        | ! [U_16600] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16605,U_16605),tc_HOL_Obool),U_16600),U_16609)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16600)) ) )
    & ! [U_16608,U_16606,U_16604] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16604,U_16604),tc_HOL_Obool),sK394(U_16608,U_16606,U_16604)),U_16608)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK394(U_16608,U_16606,U_16604))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),c_Transitive__Closure_Otrancl(U_16604,U_16608))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_16599,sK394(U_16608,U_16606,U_16604))],[f_4097_3]) ).

fof(f_4097_5,plain,
    ( ! [U_16606,U_16604,U_16608] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16604,U_16604),tc_HOL_Obool),sK394(U_16608,U_16606,U_16604)),U_16608)))
        | ~ sP1060(U_16606,U_16604,U_16608) )
    & ! [U_16606,U_16604,U_16608] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK394(U_16608,U_16606,U_16604)))
        | ~ sP1060(U_16606,U_16604,U_16608) )
    & ! [U_16600,U_16607,U_16605,U_16609] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),c_Transitive__Closure_Otrancl(U_16605,U_16609)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16605,U_16605),tc_HOL_Obool),U_16600),U_16609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16600)) )
    & ! [U_16606,U_16604,U_16608] :
        ( sP1060(U_16606,U_16604,U_16608)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),c_Transitive__Closure_Otrancl(U_16604,U_16608))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1060])],[f_4097_4]) ).

cnf(f_4097_6,plain,
    ( sP1060(U_16606,U_16604,U_16608)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),c_Transitive__Closure_Otrancl(U_16604,U_16608))) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

cnf(f_4097_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),c_Transitive__Closure_Otrancl(U_16605,U_16609)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16605,U_16605)),U_16607),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16605,U_16605),tc_HOL_Obool),U_16600),U_16609)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16600)) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

cnf(f_4097_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK394(U_16608,U_16606,U_16604)))
    | ~ sP1060(U_16606,U_16604,U_16608) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

cnf(f_4097_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16604,U_16604)),U_16606),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16604,U_16604),tc_HOL_Obool),sK394(U_16608,U_16606,U_16604)),U_16608)))
    | ~ sP1060(U_16606,U_16604,U_16608) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

fof(f_4098_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
        | ? [B_x] :
            ( ? [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
                & B_x != B_xa
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
                | B_x = B_xa
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__def]) ).

fof(f_4098_2,plain,
    ! [U_16616,U_16615,U_16614] :
      ( ( c_Relation_Ototal__on(U_16614,U_16615,U_16616)
        | ? [U_16613] :
            ( ? [U_16612] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16614,U_16614)),hAPP(hAPP(c_Product__Type_OPair(U_16614,U_16614),U_16612),U_16613)),U_16616))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16614,U_16614)),hAPP(hAPP(c_Product__Type_OPair(U_16614,U_16614),U_16613),U_16612)),U_16616))
                & U_16613 != U_16612
                & hBOOL(hAPP(hAPP(c_member(U_16614),U_16612),U_16615)) )
            & hBOOL(hAPP(hAPP(c_member(U_16614),U_16613),U_16615)) ) )
      & ( ! [U_16611] :
            ( ! [U_16610] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16614,U_16614)),hAPP(hAPP(c_Product__Type_OPair(U_16614,U_16614),U_16610),U_16611)),U_16616))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16614,U_16614)),hAPP(hAPP(c_Product__Type_OPair(U_16614,U_16614),U_16611),U_16610)),U_16616))
                | U_16611 = U_16610
                | ~ hBOOL(hAPP(hAPP(c_member(U_16614),U_16610),U_16615)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16614),U_16611),U_16615)) )
        | ~ c_Relation_Ototal__on(U_16614,U_16615,U_16616) ) ),
    inference(variable_rename,[status(thm)],[f_4098_1]) ).

fof(f_4098_3,plain,
    ( ! [U_16622,U_16620,U_16618] :
        ( c_Relation_Ototal__on(U_16618,U_16620,U_16622)
        | ? [U_16613] :
            ( ? [U_16612] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),U_16612),U_16613)),U_16622))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),U_16613),U_16612)),U_16622))
                & U_16613 != U_16612
                & hBOOL(hAPP(hAPP(c_member(U_16618),U_16612),U_16620)) )
            & hBOOL(hAPP(hAPP(c_member(U_16618),U_16613),U_16620)) ) )
    & ! [U_16621,U_16619,U_16617] :
        ( ! [U_16611] :
            ( ! [U_16610] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16610),U_16611)),U_16621))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16611),U_16610)),U_16621))
                | U_16611 = U_16610
                | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16610),U_16619)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16611),U_16619)) )
        | ~ c_Relation_Ototal__on(U_16617,U_16619,U_16621) ) ),
    inference(miniscope,[status(thm)],[f_4098_2]) ).

fof(f_4098_4,plain,
    ( ! [U_16622,U_16620,U_16618] :
        ( c_Relation_Ototal__on(U_16618,U_16620,U_16622)
        | ( ? [U_16612] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),U_16612),sK395(U_16622,U_16620,U_16618))),U_16622))
              & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK395(U_16622,U_16620,U_16618)),U_16612)),U_16622))
              & sK395(U_16622,U_16620,U_16618) != U_16612
              & hBOOL(hAPP(hAPP(c_member(U_16618),U_16612),U_16620)) )
          & hBOOL(hAPP(hAPP(c_member(U_16618),sK395(U_16622,U_16620,U_16618)),U_16620)) ) )
    & ! [U_16621,U_16619,U_16617] :
        ( ! [U_16611] :
            ( ! [U_16610] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16610),U_16611)),U_16621))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16611),U_16610)),U_16621))
                | U_16611 = U_16610
                | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16610),U_16619)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16611),U_16619)) )
        | ~ c_Relation_Ototal__on(U_16617,U_16619,U_16621) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_16613,sK395(U_16622,U_16620,U_16618))],[f_4098_3]) ).

fof(f_4098_5,plain,
    ( ! [U_16622,U_16620,U_16618] :
        ( c_Relation_Ototal__on(U_16618,U_16620,U_16622)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK396(U_16622,U_16620,U_16618)),sK395(U_16622,U_16620,U_16618))),U_16622))
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK395(U_16622,U_16620,U_16618)),sK396(U_16622,U_16620,U_16618))),U_16622))
          & sK395(U_16622,U_16620,U_16618) != sK396(U_16622,U_16620,U_16618)
          & hBOOL(hAPP(hAPP(c_member(U_16618),sK396(U_16622,U_16620,U_16618)),U_16620))
          & hBOOL(hAPP(hAPP(c_member(U_16618),sK395(U_16622,U_16620,U_16618)),U_16620)) ) )
    & ! [U_16621,U_16619,U_16617] :
        ( ! [U_16611] :
            ( ! [U_16610] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16610),U_16611)),U_16621))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16611),U_16610)),U_16621))
                | U_16611 = U_16610
                | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16610),U_16619)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16611),U_16619)) )
        | ~ c_Relation_Ototal__on(U_16617,U_16619,U_16621) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_16612,sK396(U_16622,U_16620,U_16618))],[f_4098_4]) ).

fof(f_4098_6,plain,
    ( ! [U_16620,U_16618,U_16622] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK396(U_16622,U_16620,U_16618)),sK395(U_16622,U_16620,U_16618))),U_16622))
        | ~ sP1061(U_16620,U_16618,U_16622) )
    & ! [U_16620,U_16618,U_16622] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK395(U_16622,U_16620,U_16618)),sK396(U_16622,U_16620,U_16618))),U_16622))
        | ~ sP1061(U_16620,U_16618,U_16622) )
    & ! [U_16620,U_16618,U_16622] :
        ( sK395(U_16622,U_16620,U_16618) != sK396(U_16622,U_16620,U_16618)
        | ~ sP1061(U_16620,U_16618,U_16622) )
    & ! [U_16620,U_16618,U_16622] :
        ( hBOOL(hAPP(hAPP(c_member(U_16618),sK396(U_16622,U_16620,U_16618)),U_16620))
        | ~ sP1061(U_16620,U_16618,U_16622) )
    & ! [U_16620,U_16618,U_16622] :
        ( hBOOL(hAPP(hAPP(c_member(U_16618),sK395(U_16622,U_16620,U_16618)),U_16620))
        | ~ sP1061(U_16620,U_16618,U_16622) )
    & ! [U_16620,U_16618,U_16622] :
        ( c_Relation_Ototal__on(U_16618,U_16620,U_16622)
        | sP1061(U_16620,U_16618,U_16622) )
    & ! [U_16617,U_16621,U_16619,U_16610,U_16611] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16610),U_16611)),U_16621))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16611),U_16610)),U_16621))
        | U_16611 = U_16610
        | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16610),U_16619))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16611),U_16619))
        | ~ c_Relation_Ototal__on(U_16617,U_16619,U_16621) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1061])],[f_4098_5]) ).

cnf(f_4098_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16610),U_16611)),U_16621))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16617,U_16617)),hAPP(hAPP(c_Product__Type_OPair(U_16617,U_16617),U_16611),U_16610)),U_16621))
    | U_16611 = U_16610
    | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16610),U_16619))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16617),U_16611),U_16619))
    | ~ c_Relation_Ototal__on(U_16617,U_16619,U_16621) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

cnf(f_4098_8,plain,
    ( c_Relation_Ototal__on(U_16618,U_16620,U_16622)
    | sP1061(U_16620,U_16618,U_16622) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

cnf(f_4098_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16618),sK395(U_16622,U_16620,U_16618)),U_16620))
    | ~ sP1061(U_16620,U_16618,U_16622) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

cnf(f_4098_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16618),sK396(U_16622,U_16620,U_16618)),U_16620))
    | ~ sP1061(U_16620,U_16618,U_16622) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

cnf(f_4098_11,plain,
    ( sK395(U_16622,U_16620,U_16618) != sK396(U_16622,U_16620,U_16618)
    | ~ sP1061(U_16620,U_16618,U_16622) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

cnf(f_4098_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK395(U_16622,U_16620,U_16618)),sK396(U_16622,U_16620,U_16618))),U_16622))
    | ~ sP1061(U_16620,U_16618,U_16622) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

cnf(f_4098_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16618,U_16618)),hAPP(hAPP(c_Product__Type_OPair(U_16618,U_16618),sK396(U_16622,U_16620,U_16618)),sK395(U_16622,U_16620,U_16618))),U_16622))
    | ~ sP1061(U_16620,U_16618,U_16622) ),
    inference(clausify,[status(thm)],[f_4098_6]) ).

fof(f_4099_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(f_4099_2,plain,
    ! [U_16624,U_16623] : c_Transitive__Closure_Ortrancl(U_16623,U_16624) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool),tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16623,U_16623),tc_HOL_Obool)),U_16624)),
    inference(variable_rename,[status(thm)],[f_4099_1]) ).

fof(f_4099_3,plain,
    ! [U_16624,U_16623] : c_Transitive__Closure_Ortrancl(U_16623,U_16624) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool),tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16623,U_16623),tc_HOL_Obool)),U_16624)),
    inference(definitional_conversion,[status(esa)],[f_4099_2]) ).

cnf(f_4099_4,plain,
    c_Transitive__Closure_Ortrancl(U_16623,U_16624) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool),tc_fun(tc_prod(U_16623,U_16623),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16623,U_16623),tc_HOL_Obool)),U_16624)),
    inference(clausify,[status(thm)],[f_4099_3]) ).

fof(f_4100_1,plain,
    ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
    inference(fof_nnf,[status(thm)],[fact_funpow__code__def]) ).

fof(f_4100_2,plain,
    ! [U_16625] : c_Nat_Ofunpow(U_16625) = c_Nat_Ocompow(U_16625,U_16625),
    inference(variable_rename,[status(thm)],[f_4100_1]) ).

fof(f_4100_3,plain,
    ! [U_16625] : c_Nat_Ofunpow(U_16625) = c_Nat_Ocompow(U_16625,U_16625),
    inference(definitional_conversion,[status(esa)],[f_4100_2]) ).

cnf(f_4100_4,plain,
    c_Nat_Ofunpow(U_16625) = c_Nat_Ocompow(U_16625,U_16625),
    inference(clausify,[status(thm)],[f_4100_3]) ).

fof(f_4101_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y,B_m] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
          & V_n_2 = hAPP(c_Nat_OSuc,B_m) )
      | ( V_x_2 = V_z_2
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__E2]) ).

fof(f_4101_2,plain,
    ! [U_16632,U_16631,U_16630,U_16629,U_16628] :
      ( ? [U_16627,U_16626] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16627),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16626),U_16632)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),U_16627)),U_16632))
          & U_16631 = hAPP(c_Nat_OSuc,U_16626) )
      | ( U_16629 = U_16630
        & U_16631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16631),U_16632))) ),
    inference(variable_rename,[status(thm)],[f_4101_1]) ).

fof(f_4101_3,plain,
    ! [U_16632,U_16631,U_16630,U_16629,U_16628] :
      ( ? [U_16626] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),sK397(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16626),U_16632)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),sK397(U_16632,U_16631,U_16630,U_16629,U_16628))),U_16632))
          & U_16631 = hAPP(c_Nat_OSuc,U_16626) )
      | ( U_16629 = U_16630
        & U_16631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16631),U_16632))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_16627,sK397(U_16632,U_16631,U_16630,U_16629,U_16628))],[f_4101_2]) ).

fof(f_4101_4,plain,
    ! [U_16632,U_16631,U_16630,U_16629,U_16628] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),sK397(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),sK398(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16632)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),sK397(U_16632,U_16631,U_16630,U_16629,U_16628))),U_16632))
        & U_16631 = hAPP(c_Nat_OSuc,sK398(U_16632,U_16631,U_16630,U_16629,U_16628)) )
      | ( U_16629 = U_16630
        & U_16631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16631),U_16632))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_16626,sK398(U_16632,U_16631,U_16630,U_16629,U_16628))],[f_4101_3]) ).

fof(f_4101_5,plain,
    ( ! [U_16628,U_16629,U_16630,U_16631,U_16632] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),sK397(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),sK398(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16632)))
        | ~ sP1063(U_16628,U_16629,U_16630,U_16631,U_16632) )
    & ! [U_16628,U_16629,U_16630,U_16631,U_16632] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),sK397(U_16632,U_16631,U_16630,U_16629,U_16628))),U_16632))
        | ~ sP1063(U_16628,U_16629,U_16630,U_16631,U_16632) )
    & ! [U_16628,U_16629,U_16630,U_16631,U_16632] :
        ( U_16631 = hAPP(c_Nat_OSuc,sK398(U_16632,U_16631,U_16630,U_16629,U_16628))
        | ~ sP1063(U_16628,U_16629,U_16630,U_16631,U_16632) )
    & ! [U_16629,U_16630,U_16631] :
        ( U_16629 = U_16630
        | ~ sP1062(U_16629,U_16630,U_16631) )
    & ! [U_16629,U_16630,U_16631] :
        ( U_16631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1062(U_16629,U_16630,U_16631) )
    & ! [U_16628,U_16629,U_16630,U_16631,U_16632] :
        ( sP1063(U_16628,U_16629,U_16630,U_16631,U_16632)
        | sP1062(U_16629,U_16630,U_16631)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16631),U_16632))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1062,sP1063])],[f_4101_4]) ).

cnf(f_4101_6,plain,
    ( sP1063(U_16628,U_16629,U_16630,U_16631,U_16632)
    | sP1062(U_16629,U_16630,U_16631)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),U_16631),U_16632))) ),
    inference(clausify,[status(thm)],[f_4101_5]) ).

cnf(f_4101_7,plain,
    ( U_16631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1062(U_16629,U_16630,U_16631) ),
    inference(clausify,[status(thm)],[f_4101_5]) ).

cnf(f_4101_8,plain,
    ( U_16629 = U_16630
    | ~ sP1062(U_16629,U_16630,U_16631) ),
    inference(clausify,[status(thm)],[f_4101_5]) ).

cnf(f_4101_9,plain,
    ( U_16631 = hAPP(c_Nat_OSuc,sK398(U_16632,U_16631,U_16630,U_16629,U_16628))
    | ~ sP1063(U_16628,U_16629,U_16630,U_16631,U_16632) ),
    inference(clausify,[status(thm)],[f_4101_5]) ).

cnf(f_4101_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),U_16629),sK397(U_16632,U_16631,U_16630,U_16629,U_16628))),U_16632))
    | ~ sP1063(U_16628,U_16629,U_16630,U_16631,U_16632) ),
    inference(clausify,[status(thm)],[f_4101_5]) ).

cnf(f_4101_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16628,U_16628)),hAPP(hAPP(c_Product__Type_OPair(U_16628,U_16628),sK397(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16628,U_16628),tc_HOL_Obool),sK398(U_16632,U_16631,U_16630,U_16629,U_16628)),U_16632)))
    | ~ sP1063(U_16628,U_16629,U_16630,U_16631,U_16632) ),
    inference(clausify,[status(thm)],[f_4101_5]) ).

fof(f_4102_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y,B_m] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
          & V_n_2 = hAPP(c_Nat_OSuc,B_m) )
      | ( V_x_2 = V_z_2
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__E]) ).

fof(f_4102_2,plain,
    ! [U_16639,U_16638,U_16637,U_16636,U_16635] :
      ( ? [U_16634,U_16633] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16634),U_16637)),U_16639))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),U_16634)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16633),U_16639)))
          & U_16638 = hAPP(c_Nat_OSuc,U_16633) )
      | ( U_16636 = U_16637
        & U_16638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),U_16637)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16638),U_16639))) ),
    inference(variable_rename,[status(thm)],[f_4102_1]) ).

fof(f_4102_3,plain,
    ! [U_16639,U_16638,U_16637,U_16636,U_16635] :
      ( ? [U_16633] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),sK399(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16637)),U_16639))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),sK399(U_16639,U_16638,U_16637,U_16636,U_16635))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16633),U_16639)))
          & U_16638 = hAPP(c_Nat_OSuc,U_16633) )
      | ( U_16636 = U_16637
        & U_16638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),U_16637)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16638),U_16639))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_16634,sK399(U_16639,U_16638,U_16637,U_16636,U_16635))],[f_4102_2]) ).

fof(f_4102_4,plain,
    ! [U_16639,U_16638,U_16637,U_16636,U_16635] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),sK399(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16637)),U_16639))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),sK399(U_16639,U_16638,U_16637,U_16636,U_16635))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),sK400(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16639)))
        & U_16638 = hAPP(c_Nat_OSuc,sK400(U_16639,U_16638,U_16637,U_16636,U_16635)) )
      | ( U_16636 = U_16637
        & U_16638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),U_16637)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16638),U_16639))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_16633,sK400(U_16639,U_16638,U_16637,U_16636,U_16635))],[f_4102_3]) ).

fof(f_4102_5,plain,
    ( ! [U_16637,U_16635,U_16636,U_16638,U_16639] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),sK399(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16637)),U_16639))
        | ~ sP1065(U_16637,U_16635,U_16636,U_16638,U_16639) )
    & ! [U_16637,U_16635,U_16636,U_16638,U_16639] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),sK399(U_16639,U_16638,U_16637,U_16636,U_16635))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),sK400(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16639)))
        | ~ sP1065(U_16637,U_16635,U_16636,U_16638,U_16639) )
    & ! [U_16637,U_16635,U_16636,U_16638,U_16639] :
        ( U_16638 = hAPP(c_Nat_OSuc,sK400(U_16639,U_16638,U_16637,U_16636,U_16635))
        | ~ sP1065(U_16637,U_16635,U_16636,U_16638,U_16639) )
    & ! [U_16637,U_16636,U_16638] :
        ( U_16636 = U_16637
        | ~ sP1064(U_16637,U_16636,U_16638) )
    & ! [U_16637,U_16636,U_16638] :
        ( U_16638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1064(U_16637,U_16636,U_16638) )
    & ! [U_16637,U_16635,U_16636,U_16638,U_16639] :
        ( sP1065(U_16637,U_16635,U_16636,U_16638,U_16639)
        | sP1064(U_16637,U_16636,U_16638)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),U_16637)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16638),U_16639))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1064,sP1065])],[f_4102_4]) ).

cnf(f_4102_6,plain,
    ( sP1065(U_16637,U_16635,U_16636,U_16638,U_16639)
    | sP1064(U_16637,U_16636,U_16638)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),U_16637)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),U_16638),U_16639))) ),
    inference(clausify,[status(thm)],[f_4102_5]) ).

cnf(f_4102_7,plain,
    ( U_16638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1064(U_16637,U_16636,U_16638) ),
    inference(clausify,[status(thm)],[f_4102_5]) ).

cnf(f_4102_8,plain,
    ( U_16636 = U_16637
    | ~ sP1064(U_16637,U_16636,U_16638) ),
    inference(clausify,[status(thm)],[f_4102_5]) ).

cnf(f_4102_9,plain,
    ( U_16638 = hAPP(c_Nat_OSuc,sK400(U_16639,U_16638,U_16637,U_16636,U_16635))
    | ~ sP1065(U_16637,U_16635,U_16636,U_16638,U_16639) ),
    inference(clausify,[status(thm)],[f_4102_5]) ).

cnf(f_4102_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),U_16636),sK399(U_16639,U_16638,U_16637,U_16636,U_16635))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16635,U_16635),tc_HOL_Obool),sK400(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16639)))
    | ~ sP1065(U_16637,U_16635,U_16636,U_16638,U_16639) ),
    inference(clausify,[status(thm)],[f_4102_5]) ).

cnf(f_4102_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16635,U_16635)),hAPP(hAPP(c_Product__Type_OPair(U_16635,U_16635),sK399(U_16639,U_16638,U_16637,U_16636,U_16635)),U_16637)),U_16639))
    | ~ sP1065(U_16637,U_16635,U_16636,U_16638,U_16639) ),
    inference(clausify,[status(thm)],[f_4102_5]) ).

fof(f_4103_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf]) ).

fof(f_4103_2,plain,
    ! [U_16641,U_16640] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16640,U_16641) = hAPP(hAPP(c_Finite__Set_Ofold(U_16640,U_16640,c_Lattices_Osemilattice__inf__class_Oinf(U_16640)),c_Orderings_Otop__class_Otop(U_16640)),U_16641)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16640),U_16641))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16640) ),
    inference(variable_rename,[status(thm)],[f_4103_1]) ).

fof(f_4103_3,plain,
    ! [U_16641,U_16640] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16640,U_16641) = hAPP(hAPP(c_Finite__Set_Ofold(U_16640,U_16640,c_Lattices_Osemilattice__inf__class_Oinf(U_16640)),c_Orderings_Otop__class_Otop(U_16640)),U_16641)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16640),U_16641))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16640) ),
    inference(definitional_conversion,[status(esa)],[f_4103_2]) ).

cnf(f_4103_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16640,U_16641) = hAPP(hAPP(c_Finite__Set_Ofold(U_16640,U_16640,c_Lattices_Osemilattice__inf__class_Oinf(U_16640)),c_Orderings_Otop__class_Otop(U_16640)),U_16641)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16640),U_16641))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16640) ),
    inference(clausify,[status(thm)],[f_4103_3]) ).

fof(f_4104_1,plain,
    ! [V_M_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2)))
      | ! [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Inter]) ).

fof(f_4104_2,plain,
    ! [U_16644,U_16643] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16643,tc_HOL_Obool),U_16644)))
      | ! [U_16642] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),U_16642))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16643,tc_HOL_Obool)),U_16642),U_16644)) ) ),
    inference(variable_rename,[status(thm)],[f_4104_1]) ).

fof(f_4104_3,plain,
    ! [U_16642,U_16644,U_16643] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16643,tc_HOL_Obool),U_16644)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),U_16642))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16643,tc_HOL_Obool)),U_16642),U_16644)) ),
    inference(definitional_conversion,[status(esa)],[f_4104_2]) ).

cnf(f_4104_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16643,tc_HOL_Obool),U_16644)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),U_16642))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16643,tc_HOL_Obool)),U_16642),U_16644)) ),
    inference(clausify,[status(thm)],[f_4104_3]) ).

fof(f_4105_1,plain,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_InterE]) ).

fof(f_4105_2,plain,
    ! [U_16648,U_16647,U_16646,U_16645] :
      ( hBOOL(hAPP(hAPP(c_member(U_16645),U_16646),U_16648))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16645,tc_HOL_Obool)),U_16648),U_16647))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16645),U_16646),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16645,tc_HOL_Obool),U_16647))) ),
    inference(variable_rename,[status(thm)],[f_4105_1]) ).

fof(f_4105_3,plain,
    ! [U_16645,U_16646,U_16647,U_16648] :
      ( hBOOL(hAPP(hAPP(c_member(U_16645),U_16646),U_16648))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16645,tc_HOL_Obool)),U_16648),U_16647))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16645),U_16646),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16645,tc_HOL_Obool),U_16647))) ),
    inference(definitional_conversion,[status(esa)],[f_4105_2]) ).

cnf(f_4105_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16645),U_16646),U_16648))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16645,tc_HOL_Obool)),U_16648),U_16647))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16645),U_16646),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16645,tc_HOL_Obool),U_16647))) ),
    inference(clausify,[status(thm)],[f_4105_3]) ).

fof(f_4106_1,plain,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_InterD]) ).

fof(f_4106_2,plain,
    ! [U_16652,U_16651,U_16650,U_16649] :
      ( hBOOL(hAPP(hAPP(c_member(U_16649),U_16650),U_16652))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16649,tc_HOL_Obool)),U_16652),U_16651))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16649),U_16650),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16649,tc_HOL_Obool),U_16651))) ),
    inference(variable_rename,[status(thm)],[f_4106_1]) ).

fof(f_4106_3,plain,
    ! [U_16649,U_16650,U_16651,U_16652] :
      ( hBOOL(hAPP(hAPP(c_member(U_16649),U_16650),U_16652))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16649,tc_HOL_Obool)),U_16652),U_16651))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16649),U_16650),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16649,tc_HOL_Obool),U_16651))) ),
    inference(definitional_conversion,[status(esa)],[f_4106_2]) ).

cnf(f_4106_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16649),U_16650),U_16652))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16649,tc_HOL_Obool)),U_16652),U_16651))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16649),U_16650),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16649,tc_HOL_Obool),U_16651))) ),
    inference(clausify,[status(thm)],[f_4106_3]) ).

fof(f_4107_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Inter]) ).

fof(f_4107_2,plain,
    ! [U_16655,U_16654,U_16653] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16653,tc_HOL_Obool)),U_16654),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16653,tc_HOL_Obool),U_16655)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16653,tc_HOL_Obool),tc_fun(U_16653,tc_HOL_Obool)),U_16655),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16653,tc_HOL_Obool)),U_16654)),
    inference(variable_rename,[status(thm)],[f_4107_1]) ).

fof(f_4107_3,plain,
    ! [U_16653,U_16654,U_16655] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16653,tc_HOL_Obool)),U_16654),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16653,tc_HOL_Obool),U_16655)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16653,tc_HOL_Obool),tc_fun(U_16653,tc_HOL_Obool)),U_16655),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16653,tc_HOL_Obool)),U_16654)),
    inference(definitional_conversion,[status(esa)],[f_4107_2]) ).

cnf(f_4107_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16653,tc_HOL_Obool)),U_16654),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16653,tc_HOL_Obool),U_16655)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16653,tc_HOL_Obool),tc_fun(U_16653,tc_HOL_Obool)),U_16655),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16653,tc_HOL_Obool)),U_16654)),
    inference(clausify,[status(thm)],[f_4107_3]) ).

fof(f_4108_1,plain,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Inter__insert]) ).

fof(f_4108_2,plain,
    ! [U_16658,U_16657,U_16656] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16656,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16656,tc_HOL_Obool)),U_16657),U_16658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16656,tc_HOL_Obool)),U_16657),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16656,tc_HOL_Obool),U_16658)),
    inference(variable_rename,[status(thm)],[f_4108_1]) ).

fof(f_4108_3,plain,
    ! [U_16656,U_16657,U_16658] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16656,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16656,tc_HOL_Obool)),U_16657),U_16658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16656,tc_HOL_Obool)),U_16657),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16656,tc_HOL_Obool),U_16658)),
    inference(definitional_conversion,[status(esa)],[f_4108_2]) ).

cnf(f_4108_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16656,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16656,tc_HOL_Obool)),U_16657),U_16658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16656,tc_HOL_Obool)),U_16657),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16656,tc_HOL_Obool),U_16658)),
    inference(clausify,[status(thm)],[f_4108_3]) ).

fof(f_4109_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__lower]) ).

fof(f_4109_2,plain,
    ! [U_16661,U_16660,U_16659] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16659,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16659,tc_HOL_Obool),U_16661)),U_16660))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16659,tc_HOL_Obool)),U_16660),U_16661)) ),
    inference(variable_rename,[status(thm)],[f_4109_1]) ).

fof(f_4109_3,plain,
    ! [U_16659,U_16660,U_16661] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16659,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16659,tc_HOL_Obool),U_16661)),U_16660))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16659,tc_HOL_Obool)),U_16660),U_16661)) ),
    inference(definitional_conversion,[status(esa)],[f_4109_2]) ).

cnf(f_4109_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16659,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16659,tc_HOL_Obool),U_16661)),U_16660))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16659,tc_HOL_Obool)),U_16660),U_16661)) ),
    inference(clausify,[status(thm)],[f_4109_3]) ).

fof(f_4110_1,plain,
    ! [V_a_2,V_S_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__less__iff]) ).

fof(f_4110_2,plain,
    ! [U_16666,U_16665,U_16664] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666))
          | ! [U_16663] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),U_16663),U_16666))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16664),U_16663),U_16665)) ) )
        & ( ? [U_16662] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),U_16662),U_16666))
              & hBOOL(hAPP(hAPP(c_member(U_16664),U_16662),U_16665)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666)) ) )
      | ~ class_Orderings_Olinorder(U_16664)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16664) ),
    inference(variable_rename,[status(thm)],[f_4110_1]) ).

fof(f_4110_3,plain,
    ! [U_16666,U_16665,U_16664] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666))
          | ! [U_16663] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),U_16663),U_16666))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16664),U_16663),U_16665)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),sK401(U_16666,U_16665,U_16664)),U_16666))
            & hBOOL(hAPP(hAPP(c_member(U_16664),sK401(U_16666,U_16665,U_16664)),U_16665)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666)) ) )
      | ~ class_Orderings_Olinorder(U_16664)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16664) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_16662,sK401(U_16666,U_16665,U_16664))],[f_4110_2]) ).

fof(f_4110_4,plain,
    ( ! [U_16664,U_16665,U_16666] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),sK401(U_16666,U_16665,U_16664)),U_16666))
        | ~ sP1066(U_16664,U_16665,U_16666) )
    & ! [U_16664,U_16665,U_16666] :
        ( hBOOL(hAPP(hAPP(c_member(U_16664),sK401(U_16666,U_16665,U_16664)),U_16665))
        | ~ sP1066(U_16664,U_16665,U_16666) )
    & ! [U_16663,U_16664,U_16665,U_16666] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),U_16663),U_16666))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16664),U_16663),U_16665))
        | ~ sP1067(U_16663,U_16664,U_16665,U_16666) )
    & ! [U_16663,U_16664,U_16665,U_16666] :
        ( sP1066(U_16664,U_16665,U_16666)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666))
        | ~ sP1067(U_16663,U_16664,U_16665,U_16666) )
    & ! [U_16663,U_16664,U_16665,U_16666] :
        ( sP1067(U_16663,U_16664,U_16665,U_16666)
        | ~ class_Orderings_Olinorder(U_16664)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16664) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1066,sP1067])],[f_4110_3]) ).

cnf(f_4110_5,plain,
    ( sP1067(U_16663,U_16664,U_16665,U_16666)
    | ~ class_Orderings_Olinorder(U_16664)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16664) ),
    inference(clausify,[status(thm)],[f_4110_4]) ).

cnf(f_4110_6,plain,
    ( sP1066(U_16664,U_16665,U_16666)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666))
    | ~ sP1067(U_16663,U_16664,U_16665,U_16666) ),
    inference(clausify,[status(thm)],[f_4110_4]) ).

cnf(f_4110_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),c_Complete__Lattice_OInf__class_OInf(U_16664,U_16665)),U_16666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),U_16663),U_16666))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16664),U_16663),U_16665))
    | ~ sP1067(U_16663,U_16664,U_16665,U_16666) ),
    inference(clausify,[status(thm)],[f_4110_4]) ).

cnf(f_4110_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16664),sK401(U_16666,U_16665,U_16664)),U_16665))
    | ~ sP1066(U_16664,U_16665,U_16666) ),
    inference(clausify,[status(thm)],[f_4110_4]) ).

cnf(f_4110_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16664),sK401(U_16666,U_16665,U_16664)),U_16666))
    | ~ sP1066(U_16664,U_16665,U_16666) ),
    inference(clausify,[status(thm)],[f_4110_4]) ).

fof(f_4111_1,plain,
    ! [V_A_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__Inf__iff]) ).

fof(f_4111_2,plain,
    ! [U_16671,U_16670,U_16669] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671)))
          | ? [U_16668] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),U_16668))
              & hBOOL(hAPP(hAPP(c_member(U_16669),U_16668),U_16671)) ) )
        & ( ! [U_16667] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),U_16667))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16667),U_16671)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16669) ),
    inference(variable_rename,[status(thm)],[f_4111_1]) ).

fof(f_4111_3,plain,
    ! [U_16671,U_16670,U_16669] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),sK402(U_16671,U_16670,U_16669)))
            & hBOOL(hAPP(hAPP(c_member(U_16669),sK402(U_16671,U_16670,U_16669)),U_16671)) ) )
        & ( ! [U_16667] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),U_16667))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16667),U_16671)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16669) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_16668,sK402(U_16671,U_16670,U_16669))],[f_4111_2]) ).

fof(f_4111_4,plain,
    ( ! [U_16669,U_16670,U_16671] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),sK402(U_16671,U_16670,U_16669)))
        | ~ sP1068(U_16669,U_16670,U_16671) )
    & ! [U_16669,U_16670,U_16671] :
        ( hBOOL(hAPP(hAPP(c_member(U_16669),sK402(U_16671,U_16670,U_16669)),U_16671))
        | ~ sP1068(U_16669,U_16670,U_16671) )
    & ! [U_16669,U_16670,U_16671,U_16667] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671)))
        | sP1068(U_16669,U_16670,U_16671)
        | ~ sP1069(U_16669,U_16670,U_16671,U_16667) )
    & ! [U_16669,U_16670,U_16671,U_16667] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),U_16667))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16667),U_16671))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671)))
        | ~ sP1069(U_16669,U_16670,U_16671,U_16667) )
    & ! [U_16669,U_16670,U_16671,U_16667] :
        ( sP1069(U_16669,U_16670,U_16671,U_16667)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16669) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1068,sP1069])],[f_4111_3]) ).

cnf(f_4111_5,plain,
    ( sP1069(U_16669,U_16670,U_16671,U_16667)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16669) ),
    inference(clausify,[status(thm)],[f_4111_4]) ).

cnf(f_4111_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),U_16667))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16667),U_16671))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671)))
    | ~ sP1069(U_16669,U_16670,U_16671,U_16667) ),
    inference(clausify,[status(thm)],[f_4111_4]) ).

cnf(f_4111_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),c_Complete__Lattice_OInf__class_OInf(U_16669,U_16671)))
    | sP1068(U_16669,U_16670,U_16671)
    | ~ sP1069(U_16669,U_16670,U_16671,U_16667) ),
    inference(clausify,[status(thm)],[f_4111_4]) ).

cnf(f_4111_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16669),sK402(U_16671,U_16670,U_16669)),U_16671))
    | ~ sP1068(U_16669,U_16670,U_16671) ),
    inference(clausify,[status(thm)],[f_4111_4]) ).

cnf(f_4111_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16669),U_16670),sK402(U_16671,U_16670,U_16669)))
    | ~ sP1068(U_16669,U_16670,U_16671) ),
    inference(clausify,[status(thm)],[f_4111_4]) ).

fof(f_4112_1,plain,
    ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_Inter__eq]) ).

fof(f_4112_2,plain,
    ! [U_16673,U_16672] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16672,tc_HOL_Obool),U_16673) = hAPP(c_Set_OCollect(U_16672),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_16672),c_HOL_OAll(tc_fun(U_16672,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),U_16672),hAPP(c_COMBS(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_16672,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_16672,tc_HOL_Obool),tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_16672,tc_HOL_Obool))),U_16673)))),c_member(U_16672)))),
    inference(variable_rename,[status(thm)],[f_4112_1]) ).

fof(f_4112_3,plain,
    ! [U_16673,U_16672] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16672,tc_HOL_Obool),U_16673) = hAPP(c_Set_OCollect(U_16672),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_16672),c_HOL_OAll(tc_fun(U_16672,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),U_16672),hAPP(c_COMBS(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_16672,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_16672,tc_HOL_Obool),tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_16672,tc_HOL_Obool))),U_16673)))),c_member(U_16672)))),
    inference(definitional_conversion,[status(esa)],[f_4112_2]) ).

cnf(f_4112_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16672,tc_HOL_Obool),U_16673) = hAPP(c_Set_OCollect(U_16672),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_16672),c_HOL_OAll(tc_fun(U_16672,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),U_16672),hAPP(c_COMBS(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_16672,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_16672,tc_HOL_Obool),tc_fun(tc_fun(U_16672,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_16672,tc_HOL_Obool))),U_16673)))),c_member(U_16672)))),
    inference(clausify,[status(thm)],[f_4112_3]) ).

fof(f_4113_1,plain,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Inter__empty]) ).

fof(f_4113_2,plain,
    ! [U_16674] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16674,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16674,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16674,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4113_1]) ).

fof(f_4113_3,plain,
    ! [U_16674] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16674,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16674,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16674,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4113_2]) ).

cnf(f_4113_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16674,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16674,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16674,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4113_3]) ).

fof(f_4114_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono]) ).

fof(f_4114_2,plain,
    ! [U_16677,U_16676,U_16675] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16675,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16675,tc_HOL_Obool),U_16677)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16675,tc_HOL_Obool),U_16676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16675,tc_HOL_Obool),tc_HOL_Obool)),U_16676),U_16677)) ),
    inference(variable_rename,[status(thm)],[f_4114_1]) ).

fof(f_4114_3,plain,
    ! [U_16675,U_16676,U_16677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16675,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16675,tc_HOL_Obool),U_16677)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16675,tc_HOL_Obool),U_16676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16675,tc_HOL_Obool),tc_HOL_Obool)),U_16676),U_16677)) ),
    inference(definitional_conversion,[status(esa)],[f_4114_2]) ).

cnf(f_4114_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16675,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16675,tc_HOL_Obool),U_16677)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16675,tc_HOL_Obool),U_16676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16675,tc_HOL_Obool),tc_HOL_Obool)),U_16676),U_16677)) ),
    inference(clausify,[status(thm)],[f_4114_3]) ).

fof(f_4115_1,plain,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Inter__UNIV]) ).

fof(f_4115_2,plain,
    ! [U_16678] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16678,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16678,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16678,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4115_1]) ).

fof(f_4115_3,plain,
    ! [U_16678] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16678,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16678,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16678,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4115_2]) ).

cnf(f_4115_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16678,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16678,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16678,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4115_3]) ).

fof(f_4116_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__lower]) ).

fof(f_4116_2,plain,
    ! [U_16681,U_16680,U_16679] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16679),c_Complete__Lattice_OInf__class_OInf(U_16679,U_16681)),U_16680))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16679),U_16680),U_16681))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16679) ),
    inference(variable_rename,[status(thm)],[f_4116_1]) ).

fof(f_4116_3,plain,
    ! [U_16679,U_16680,U_16681] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16679),c_Complete__Lattice_OInf__class_OInf(U_16679,U_16681)),U_16680))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16679),U_16680),U_16681))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16679) ),
    inference(definitional_conversion,[status(esa)],[f_4116_2]) ).

cnf(f_4116_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16679),c_Complete__Lattice_OInf__class_OInf(U_16679,U_16681)),U_16680))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16679),U_16680),U_16681))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16679) ),
    inference(clausify,[status(thm)],[f_4116_3]) ).

fof(f_4117_1,plain,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(f_4117_2,plain,
    ! [U_16684,U_16683,U_16682] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16682,tc_HOL_Obool),tc_HOL_Obool)),U_16683),U_16684)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),U_16683)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),U_16684)),
    inference(variable_rename,[status(thm)],[f_4117_1]) ).

fof(f_4117_3,plain,
    ! [U_16682,U_16683,U_16684] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16682,tc_HOL_Obool),tc_HOL_Obool)),U_16683),U_16684)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),U_16683)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),U_16684)),
    inference(definitional_conversion,[status(esa)],[f_4117_2]) ).

cnf(f_4117_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16682,tc_HOL_Obool),tc_HOL_Obool)),U_16683),U_16684)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),U_16683)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16682,tc_HOL_Obool),U_16684)),
    inference(clausify,[status(thm)],[f_4117_3]) ).

fof(f_4118_1,plain,
    ! [V_a_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__singleton]) ).

fof(f_4118_2,plain,
    ! [U_16686,U_16685] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16685,hAPP(hAPP(c_Set_Oinsert(U_16685),U_16686),c_Orderings_Obot__class_Obot(tc_fun(U_16685,tc_HOL_Obool)))) = U_16686
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16685) ),
    inference(variable_rename,[status(thm)],[f_4118_1]) ).

fof(f_4118_3,plain,
    ! [U_16685,U_16686] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16685,hAPP(hAPP(c_Set_Oinsert(U_16685),U_16686),c_Orderings_Obot__class_Obot(tc_fun(U_16685,tc_HOL_Obool)))) = U_16686
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16685) ),
    inference(definitional_conversion,[status(esa)],[f_4118_2]) ).

cnf(f_4118_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16685,hAPP(hAPP(c_Set_Oinsert(U_16685),U_16686),c_Orderings_Obot__class_Obot(tc_fun(U_16685,tc_HOL_Obool)))) = U_16686
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16685) ),
    inference(clausify,[status(thm)],[f_4118_3]) ).

fof(f_4119_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__empty]) ).

fof(f_4119_2,plain,
    ! [U_16687] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16687,c_Orderings_Obot__class_Obot(tc_fun(U_16687,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16687)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16687) ),
    inference(variable_rename,[status(thm)],[f_4119_1]) ).

fof(f_4119_3,plain,
    ! [U_16687] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16687,c_Orderings_Obot__class_Obot(tc_fun(U_16687,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16687)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16687) ),
    inference(definitional_conversion,[status(esa)],[f_4119_2]) ).

cnf(f_4119_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16687,c_Orderings_Obot__class_Obot(tc_fun(U_16687,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16687)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16687) ),
    inference(clausify,[status(thm)],[f_4119_3]) ).

fof(f_4120_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__UNIV]) ).

fof(f_4120_2,plain,
    ! [U_16688] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16688,c_Orderings_Otop__class_Otop(tc_fun(U_16688,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16688)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16688) ),
    inference(variable_rename,[status(thm)],[f_4120_1]) ).

fof(f_4120_3,plain,
    ! [U_16688] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16688,c_Orderings_Otop__class_Otop(tc_fun(U_16688,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16688)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16688) ),
    inference(definitional_conversion,[status(esa)],[f_4120_2]) ).

cnf(f_4120_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16688,c_Orderings_Otop__class_Otop(tc_fun(U_16688,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16688)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16688) ),
    inference(clausify,[status(thm)],[f_4120_3]) ).

fof(f_4121_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__insert]) ).

fof(f_4121_2,plain,
    ! [U_16691,U_16690,U_16689] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16689,hAPP(hAPP(c_Set_Oinsert(U_16689),U_16690),U_16691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16689),U_16690),c_Complete__Lattice_OInf__class_OInf(U_16689,U_16691))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16689) ),
    inference(variable_rename,[status(thm)],[f_4121_1]) ).

fof(f_4121_3,plain,
    ! [U_16689,U_16690,U_16691] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16689,hAPP(hAPP(c_Set_Oinsert(U_16689),U_16690),U_16691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16689),U_16690),c_Complete__Lattice_OInf__class_OInf(U_16689,U_16691))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16689) ),
    inference(definitional_conversion,[status(esa)],[f_4121_2]) ).

cnf(f_4121_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16689,hAPP(hAPP(c_Set_Oinsert(U_16689),U_16690),U_16691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16689),U_16690),c_Complete__Lattice_OInf__class_OInf(U_16689,U_16691))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16689) ),
    inference(clausify,[status(thm)],[f_4121_3]) ).

fof(f_4122_1,plain,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Inter__image__eq]) ).

fof(f_4122_2,plain,
    ! [U_16695,U_16694,U_16693,U_16692] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16692,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16693,tc_fun(U_16692,tc_HOL_Obool),U_16694),U_16695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16693,tc_fun(U_16692,tc_HOL_Obool)),U_16695),U_16694),
    inference(variable_rename,[status(thm)],[f_4122_1]) ).

fof(f_4122_3,plain,
    ! [U_16692,U_16693,U_16694,U_16695] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16692,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16693,tc_fun(U_16692,tc_HOL_Obool),U_16694),U_16695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16693,tc_fun(U_16692,tc_HOL_Obool)),U_16695),U_16694),
    inference(definitional_conversion,[status(esa)],[f_4122_2]) ).

cnf(f_4122_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16692,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16693,tc_fun(U_16692,tc_HOL_Obool),U_16694),U_16695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16693,tc_fun(U_16692,tc_HOL_Obool)),U_16695),U_16694),
    inference(clausify,[status(thm)],[f_4122_3]) ).

fof(f_4123_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(f_4123_2,plain,
    ! [U_16699,U_16698,U_16697,U_16696] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16696,tc_fun(U_16697,tc_HOL_Obool)),U_16698),U_16699) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16697,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16696,tc_fun(U_16697,tc_HOL_Obool),U_16699),U_16698)),
    inference(variable_rename,[status(thm)],[f_4123_1]) ).

fof(f_4123_3,plain,
    ! [U_16696,U_16697,U_16698,U_16699] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16696,tc_fun(U_16697,tc_HOL_Obool)),U_16698),U_16699) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16697,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16696,tc_fun(U_16697,tc_HOL_Obool),U_16699),U_16698)),
    inference(definitional_conversion,[status(esa)],[f_4123_2]) ).

cnf(f_4123_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16696,tc_fun(U_16697,tc_HOL_Obool)),U_16698),U_16699) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16697,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16696,tc_fun(U_16697,tc_HOL_Obool),U_16699),U_16698)),
    inference(clausify,[status(thm)],[f_4123_3]) ).

fof(f_4124_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Int__eq__Inter]) ).

fof(f_4124_2,plain,
    ! [U_16702,U_16701,U_16700] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16700,tc_HOL_Obool)),U_16701),U_16702) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16700,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16700,tc_HOL_Obool)),U_16701),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16700,tc_HOL_Obool)),U_16702),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16700,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4124_1]) ).

fof(f_4124_3,plain,
    ! [U_16700,U_16701,U_16702] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16700,tc_HOL_Obool)),U_16701),U_16702) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16700,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16700,tc_HOL_Obool)),U_16701),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16700,tc_HOL_Obool)),U_16702),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16700,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4124_2]) ).

cnf(f_4124_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16700,tc_HOL_Obool)),U_16701),U_16702) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16700,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16700,tc_HOL_Obool)),U_16701),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16700,tc_HOL_Obool)),U_16702),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16700,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4124_3]) ).

fof(f_4125_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__Inter__image]) ).

fof(f_4125_2,plain,
    ! [U_16707,U_16706,U_16705,U_16704,U_16703] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16703,tc_fun(U_16704,tc_HOL_Obool)),U_16705),hAPP(hAPP(c_COMBS(U_16703,tc_fun(U_16704,tc_HOL_Obool),tc_fun(U_16704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16704,tc_HOL_Obool),tc_fun(tc_fun(U_16704,tc_HOL_Obool),tc_fun(U_16704,tc_HOL_Obool)),U_16703),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16704,tc_HOL_Obool))),U_16706)),U_16707)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16704,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16704,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16703,tc_fun(U_16704,tc_HOL_Obool),U_16706),U_16705))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16704,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16703,tc_fun(U_16704,tc_HOL_Obool),U_16707),U_16705))),
    inference(variable_rename,[status(thm)],[f_4125_1]) ).

fof(f_4125_3,plain,
    ! [U_16703,U_16704,U_16705,U_16706,U_16707] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16703,tc_fun(U_16704,tc_HOL_Obool)),U_16705),hAPP(hAPP(c_COMBS(U_16703,tc_fun(U_16704,tc_HOL_Obool),tc_fun(U_16704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16704,tc_HOL_Obool),tc_fun(tc_fun(U_16704,tc_HOL_Obool),tc_fun(U_16704,tc_HOL_Obool)),U_16703),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16704,tc_HOL_Obool))),U_16706)),U_16707)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16704,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16704,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16703,tc_fun(U_16704,tc_HOL_Obool),U_16706),U_16705))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16704,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16703,tc_fun(U_16704,tc_HOL_Obool),U_16707),U_16705))),
    inference(definitional_conversion,[status(esa)],[f_4125_2]) ).

cnf(f_4125_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16703,tc_fun(U_16704,tc_HOL_Obool)),U_16705),hAPP(hAPP(c_COMBS(U_16703,tc_fun(U_16704,tc_HOL_Obool),tc_fun(U_16704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16704,tc_HOL_Obool),tc_fun(tc_fun(U_16704,tc_HOL_Obool),tc_fun(U_16704,tc_HOL_Obool)),U_16703),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16704,tc_HOL_Obool))),U_16706)),U_16707)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16704,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16704,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16703,tc_fun(U_16704,tc_HOL_Obool),U_16706),U_16705))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16704,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16703,tc_fun(U_16704,tc_HOL_Obool),U_16707),U_16705))),
    inference(clausify,[status(thm)],[f_4125_3]) ).

fof(f_4126_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Inter__Un__subset]) ).

fof(f_4126_2,plain,
    ! [U_16710,U_16709,U_16708] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16708,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16708,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),U_16709)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),U_16710))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16708,tc_HOL_Obool),tc_HOL_Obool)),U_16709),U_16710)))),
    inference(variable_rename,[status(thm)],[f_4126_1]) ).

fof(f_4126_3,plain,
    ! [U_16708,U_16709,U_16710] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16708,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16708,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),U_16709)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),U_16710))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16708,tc_HOL_Obool),tc_HOL_Obool)),U_16709),U_16710)))),
    inference(definitional_conversion,[status(esa)],[f_4126_2]) ).

cnf(f_4126_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16708,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16708,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),U_16709)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),U_16710))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16708,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16708,tc_HOL_Obool),tc_HOL_Obool)),U_16709),U_16710)))),
    inference(clausify,[status(thm)],[f_4126_3]) ).

fof(f_4127_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__binary]) ).

fof(f_4127_2,plain,
    ! [U_16713,U_16712,U_16711] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16711,hAPP(hAPP(c_Set_Oinsert(U_16711),U_16712),hAPP(hAPP(c_Set_Oinsert(U_16711),U_16713),c_Orderings_Obot__class_Obot(tc_fun(U_16711,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16711),U_16712),U_16713)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16711) ),
    inference(variable_rename,[status(thm)],[f_4127_1]) ).

fof(f_4127_3,plain,
    ! [U_16711,U_16712,U_16713] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16711,hAPP(hAPP(c_Set_Oinsert(U_16711),U_16712),hAPP(hAPP(c_Set_Oinsert(U_16711),U_16713),c_Orderings_Obot__class_Obot(tc_fun(U_16711,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16711),U_16712),U_16713)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16711) ),
    inference(definitional_conversion,[status(esa)],[f_4127_2]) ).

cnf(f_4127_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16711,hAPP(hAPP(c_Set_Oinsert(U_16711),U_16712),hAPP(hAPP(c_Set_Oinsert(U_16711),U_16713),c_Orderings_Obot__class_Obot(tc_fun(U_16711,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16711),U_16712),U_16713)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16711) ),
    inference(clausify,[status(thm)],[f_4127_3]) ).

fof(f_4128_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf]) ).

fof(f_4128_2,plain,
    ! [U_16716,U_16715,U_16714] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16714),U_16716),c_Complete__Lattice_OInf__class_OInf(U_16714,U_16715)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16714,U_16714,c_Lattices_Osemilattice__inf__class_Oinf(U_16714)),U_16716),U_16715)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16714),U_16715))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16714) ),
    inference(variable_rename,[status(thm)],[f_4128_1]) ).

fof(f_4128_3,plain,
    ! [U_16714,U_16715,U_16716] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16714),U_16716),c_Complete__Lattice_OInf__class_OInf(U_16714,U_16715)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16714,U_16714,c_Lattices_Osemilattice__inf__class_Oinf(U_16714)),U_16716),U_16715)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16714),U_16715))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16714) ),
    inference(definitional_conversion,[status(esa)],[f_4128_2]) ).

cnf(f_4128_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16714),U_16716),c_Complete__Lattice_OInf__class_OInf(U_16714,U_16715)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16714,U_16714,c_Lattices_Osemilattice__inf__class_Oinf(U_16714)),U_16716),U_16715)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16714),U_16715))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16714) ),
    inference(clausify,[status(thm)],[f_4128_3]) ).

fof(f_4129_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf]) ).

fof(f_4129_2,plain,
    ! [U_16718,U_16717] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16717,U_16718) = c_Complete__Lattice_OInf__class_OInf(U_16717,U_16718)
      | U_16718 = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16717),U_16718))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16717) ),
    inference(variable_rename,[status(thm)],[f_4129_1]) ).

fof(f_4129_3,plain,
    ! [U_16717,U_16718] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16717,U_16718) = c_Complete__Lattice_OInf__class_OInf(U_16717,U_16718)
      | U_16718 = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16717),U_16718))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16717) ),
    inference(definitional_conversion,[status(esa)],[f_4129_2]) ).

cnf(f_4129_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_16717,U_16718) = c_Complete__Lattice_OInf__class_OInf(U_16717,U_16718)
    | U_16718 = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16717),U_16718))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16717) ),
    inference(clausify,[status(thm)],[f_4129_3]) ).

fof(f_4130_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__Inf]) ).

fof(f_4130_2,plain,
    ! [U_16720,U_16719] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16719,U_16720) = c_Complete__Lattice_OInf__class_OInf(U_16719,hAPP(c_Set_OCollect(U_16719),hAPP(hAPP(c_COMBB(tc_fun(U_16719,tc_HOL_Obool),tc_HOL_Obool,U_16719),c_HOL_OAll(U_16719)),hAPP(hAPP(c_COMBB(tc_fun(U_16719,tc_HOL_Obool),tc_fun(U_16719,tc_HOL_Obool),U_16719),hAPP(c_COMBS(U_16719,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16719),c_fimplies),hAPP(hAPP(c_COMBC(U_16719,tc_fun(U_16719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16719)),U_16720)))),hAPP(c_COMBC(U_16719,U_16719,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_16719))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16719) ),
    inference(variable_rename,[status(thm)],[f_4130_1]) ).

fof(f_4130_3,plain,
    ! [U_16719,U_16720] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16719,U_16720) = c_Complete__Lattice_OInf__class_OInf(U_16719,hAPP(c_Set_OCollect(U_16719),hAPP(hAPP(c_COMBB(tc_fun(U_16719,tc_HOL_Obool),tc_HOL_Obool,U_16719),c_HOL_OAll(U_16719)),hAPP(hAPP(c_COMBB(tc_fun(U_16719,tc_HOL_Obool),tc_fun(U_16719,tc_HOL_Obool),U_16719),hAPP(c_COMBS(U_16719,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16719),c_fimplies),hAPP(hAPP(c_COMBC(U_16719,tc_fun(U_16719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16719)),U_16720)))),hAPP(c_COMBC(U_16719,U_16719,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_16719))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16719) ),
    inference(definitional_conversion,[status(esa)],[f_4130_2]) ).

cnf(f_4130_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16719,U_16720) = c_Complete__Lattice_OInf__class_OInf(U_16719,hAPP(c_Set_OCollect(U_16719),hAPP(hAPP(c_COMBB(tc_fun(U_16719,tc_HOL_Obool),tc_HOL_Obool,U_16719),c_HOL_OAll(U_16719)),hAPP(hAPP(c_COMBB(tc_fun(U_16719,tc_HOL_Obool),tc_fun(U_16719,tc_HOL_Obool),U_16719),hAPP(c_COMBS(U_16719,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16719),c_fimplies),hAPP(hAPP(c_COMBC(U_16719,tc_fun(U_16719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16719)),U_16720)))),hAPP(c_COMBC(U_16719,U_16719,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_16719))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16719) ),
    inference(clausify,[status(thm)],[f_4130_3]) ).

fof(f_4131_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__Sup]) ).

fof(f_4131_2,plain,
    ! [U_16722,U_16721] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16721,U_16722) = c_Complete__Lattice_OSup__class_OSup(U_16721,hAPP(c_Set_OCollect(U_16721),hAPP(hAPP(c_COMBB(tc_fun(U_16721,tc_HOL_Obool),tc_HOL_Obool,U_16721),c_HOL_OAll(U_16721)),hAPP(hAPP(c_COMBB(tc_fun(U_16721,tc_HOL_Obool),tc_fun(U_16721,tc_HOL_Obool),U_16721),hAPP(c_COMBS(U_16721,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16721),c_fimplies),hAPP(hAPP(c_COMBC(U_16721,tc_fun(U_16721,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16721)),U_16722)))),c_Orderings_Oord__class_Oless__eq(U_16721)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16721) ),
    inference(variable_rename,[status(thm)],[f_4131_1]) ).

fof(f_4131_3,plain,
    ! [U_16721,U_16722] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16721,U_16722) = c_Complete__Lattice_OSup__class_OSup(U_16721,hAPP(c_Set_OCollect(U_16721),hAPP(hAPP(c_COMBB(tc_fun(U_16721,tc_HOL_Obool),tc_HOL_Obool,U_16721),c_HOL_OAll(U_16721)),hAPP(hAPP(c_COMBB(tc_fun(U_16721,tc_HOL_Obool),tc_fun(U_16721,tc_HOL_Obool),U_16721),hAPP(c_COMBS(U_16721,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16721),c_fimplies),hAPP(hAPP(c_COMBC(U_16721,tc_fun(U_16721,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16721)),U_16722)))),c_Orderings_Oord__class_Oless__eq(U_16721)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16721) ),
    inference(definitional_conversion,[status(esa)],[f_4131_2]) ).

cnf(f_4131_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16721,U_16722) = c_Complete__Lattice_OSup__class_OSup(U_16721,hAPP(c_Set_OCollect(U_16721),hAPP(hAPP(c_COMBB(tc_fun(U_16721,tc_HOL_Obool),tc_HOL_Obool,U_16721),c_HOL_OAll(U_16721)),hAPP(hAPP(c_COMBB(tc_fun(U_16721,tc_HOL_Obool),tc_fun(U_16721,tc_HOL_Obool),U_16721),hAPP(c_COMBS(U_16721,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16721),c_fimplies),hAPP(hAPP(c_COMBC(U_16721,tc_fun(U_16721,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16721)),U_16722)))),c_Orderings_Oord__class_Oless__eq(U_16721)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16721) ),
    inference(clausify,[status(thm)],[f_4131_3]) ).

fof(f_4132_1,plain,
    ! [V_A_2,V_C_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnionI]) ).

fof(f_4132_2,plain,
    ! [U_16726,U_16725,U_16724,U_16723] :
      ( hBOOL(hAPP(hAPP(c_member(U_16723),U_16726),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16723,tc_HOL_Obool),U_16725)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16723),U_16726),U_16724))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16723,tc_HOL_Obool)),U_16724),U_16725)) ),
    inference(variable_rename,[status(thm)],[f_4132_1]) ).

fof(f_4132_3,plain,
    ! [U_16723,U_16724,U_16725,U_16726] :
      ( hBOOL(hAPP(hAPP(c_member(U_16723),U_16726),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16723,tc_HOL_Obool),U_16725)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16723),U_16726),U_16724))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16723,tc_HOL_Obool)),U_16724),U_16725)) ),
    inference(definitional_conversion,[status(esa)],[f_4132_2]) ).

cnf(f_4132_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16723),U_16726),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16723,tc_HOL_Obool),U_16725)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16723),U_16726),U_16724))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16723,tc_HOL_Obool)),U_16724),U_16725)) ),
    inference(clausify,[status(thm)],[f_4132_3]) ).

fof(f_4133_1,plain,
    ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Inter__def]) ).

fof(f_4133_2,plain,
    ! [U_16728,U_16727] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16727,tc_HOL_Obool),U_16728) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16727,tc_HOL_Obool),tc_fun(U_16727,tc_HOL_Obool)),U_16728),c_COMBI(tc_fun(U_16727,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4133_1]) ).

fof(f_4133_3,plain,
    ! [U_16728,U_16727] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16727,tc_HOL_Obool),U_16728) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16727,tc_HOL_Obool),tc_fun(U_16727,tc_HOL_Obool)),U_16728),c_COMBI(tc_fun(U_16727,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4133_2]) ).

cnf(f_4133_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16727,tc_HOL_Obool),U_16728) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16727,tc_HOL_Obool),tc_fun(U_16727,tc_HOL_Obool)),U_16728),c_COMBI(tc_fun(U_16727,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4133_3]) ).

fof(f_4134_1,plain,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Union2]) ).

fof(f_4134_2,plain,
    ! [U_16731,U_16730,U_16729] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16729,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16729,tc_HOL_Obool),U_16730)),U_16731) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool)),U_16730),hAPP(hAPP(c_COMBC(tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16729,tc_HOL_Obool))),U_16731)),
    inference(variable_rename,[status(thm)],[f_4134_1]) ).

fof(f_4134_3,plain,
    ! [U_16729,U_16730,U_16731] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16729,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16729,tc_HOL_Obool),U_16730)),U_16731) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool)),U_16730),hAPP(hAPP(c_COMBC(tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16729,tc_HOL_Obool))),U_16731)),
    inference(definitional_conversion,[status(esa)],[f_4134_2]) ).

cnf(f_4134_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16729,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16729,tc_HOL_Obool),U_16730)),U_16731) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool)),U_16730),hAPP(hAPP(c_COMBC(tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool),tc_fun(U_16729,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16729,tc_HOL_Obool))),U_16731)),
    inference(clausify,[status(thm)],[f_4134_3]) ).

fof(f_4135_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Union]) ).

fof(f_4135_2,plain,
    ! [U_16734,U_16733,U_16732] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16732,tc_HOL_Obool)),U_16733),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16732,tc_HOL_Obool),U_16734)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16732,tc_HOL_Obool),tc_fun(U_16732,tc_HOL_Obool)),U_16734),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16732,tc_HOL_Obool)),U_16733)),
    inference(variable_rename,[status(thm)],[f_4135_1]) ).

fof(f_4135_3,plain,
    ! [U_16732,U_16733,U_16734] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16732,tc_HOL_Obool)),U_16733),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16732,tc_HOL_Obool),U_16734)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16732,tc_HOL_Obool),tc_fun(U_16732,tc_HOL_Obool)),U_16734),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16732,tc_HOL_Obool)),U_16733)),
    inference(definitional_conversion,[status(esa)],[f_4135_2]) ).

cnf(f_4135_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16732,tc_HOL_Obool)),U_16733),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16732,tc_HOL_Obool),U_16734)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16732,tc_HOL_Obool),tc_fun(U_16732,tc_HOL_Obool)),U_16734),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16732,tc_HOL_Obool)),U_16733)),
    inference(clausify,[status(thm)],[f_4135_3]) ).

fof(f_4136_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(f_4136_2,plain,
    ! [U_16738,U_16737,U_16736,U_16735] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16735,tc_fun(U_16736,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16735,tc_HOL_Obool),U_16737)),U_16738) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16735,tc_HOL_Obool),tc_fun(U_16736,tc_HOL_Obool)),U_16737),hAPP(hAPP(c_COMBC(tc_fun(U_16735,tc_HOL_Obool),tc_fun(U_16735,tc_fun(U_16736,tc_HOL_Obool)),tc_fun(U_16736,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16735,tc_fun(U_16736,tc_HOL_Obool))),U_16738)),
    inference(variable_rename,[status(thm)],[f_4136_1]) ).

fof(f_4136_3,plain,
    ! [U_16735,U_16736,U_16737,U_16738] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16735,tc_fun(U_16736,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16735,tc_HOL_Obool),U_16737)),U_16738) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16735,tc_HOL_Obool),tc_fun(U_16736,tc_HOL_Obool)),U_16737),hAPP(hAPP(c_COMBC(tc_fun(U_16735,tc_HOL_Obool),tc_fun(U_16735,tc_fun(U_16736,tc_HOL_Obool)),tc_fun(U_16736,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16735,tc_fun(U_16736,tc_HOL_Obool))),U_16738)),
    inference(definitional_conversion,[status(esa)],[f_4136_2]) ).

cnf(f_4136_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16735,tc_fun(U_16736,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16735,tc_HOL_Obool),U_16737)),U_16738) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16735,tc_HOL_Obool),tc_fun(U_16736,tc_HOL_Obool)),U_16737),hAPP(hAPP(c_COMBC(tc_fun(U_16735,tc_HOL_Obool),tc_fun(U_16735,tc_fun(U_16736,tc_HOL_Obool)),tc_fun(U_16736,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16735,tc_fun(U_16736,tc_HOL_Obool))),U_16738)),
    inference(clausify,[status(thm)],[f_4136_3]) ).

fof(f_4137_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(f_4137_2,plain,
    ! [U_16742,U_16741,U_16740,U_16739] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16739,tc_HOL_Obool),tc_fun(U_16740,tc_HOL_Obool)),U_16741),hAPP(hAPP(c_COMBC(tc_fun(U_16739,tc_HOL_Obool),tc_fun(U_16739,tc_fun(U_16740,tc_HOL_Obool)),tc_fun(U_16740,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16739,tc_fun(U_16740,tc_HOL_Obool))),U_16742)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16739,tc_fun(U_16740,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16739,tc_HOL_Obool),U_16741)),U_16742),
    inference(variable_rename,[status(thm)],[f_4137_1]) ).

fof(f_4137_3,plain,
    ! [U_16739,U_16740,U_16741,U_16742] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16739,tc_HOL_Obool),tc_fun(U_16740,tc_HOL_Obool)),U_16741),hAPP(hAPP(c_COMBC(tc_fun(U_16739,tc_HOL_Obool),tc_fun(U_16739,tc_fun(U_16740,tc_HOL_Obool)),tc_fun(U_16740,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16739,tc_fun(U_16740,tc_HOL_Obool))),U_16742)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16739,tc_fun(U_16740,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16739,tc_HOL_Obool),U_16741)),U_16742),
    inference(definitional_conversion,[status(esa)],[f_4137_2]) ).

cnf(f_4137_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16739,tc_HOL_Obool),tc_fun(U_16740,tc_HOL_Obool)),U_16741),hAPP(hAPP(c_COMBC(tc_fun(U_16739,tc_HOL_Obool),tc_fun(U_16739,tc_fun(U_16740,tc_HOL_Obool)),tc_fun(U_16740,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16739,tc_fun(U_16740,tc_HOL_Obool))),U_16742)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16739,tc_fun(U_16740,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16739,tc_HOL_Obool),U_16741)),U_16742),
    inference(clausify,[status(thm)],[f_4137_3]) ).

fof(f_4138_1,plain,
    ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Union]) ).

fof(f_4138_2,plain,
    ! [U_16746,U_16745,U_16744,U_16743] : hAPP(hAPP(c_Product__Type_OSigma(U_16743,U_16744),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16743,tc_HOL_Obool),U_16745)),U_16746) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16743,tc_HOL_Obool),tc_fun(tc_prod(U_16743,U_16744),tc_HOL_Obool)),U_16745),hAPP(hAPP(c_COMBC(tc_fun(U_16743,tc_HOL_Obool),tc_fun(U_16743,tc_fun(U_16744,tc_HOL_Obool)),tc_fun(tc_prod(U_16743,U_16744),tc_HOL_Obool)),c_Product__Type_OSigma(U_16743,U_16744)),U_16746)),
    inference(variable_rename,[status(thm)],[f_4138_1]) ).

fof(f_4138_3,plain,
    ! [U_16743,U_16744,U_16745,U_16746] : hAPP(hAPP(c_Product__Type_OSigma(U_16743,U_16744),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16743,tc_HOL_Obool),U_16745)),U_16746) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16743,tc_HOL_Obool),tc_fun(tc_prod(U_16743,U_16744),tc_HOL_Obool)),U_16745),hAPP(hAPP(c_COMBC(tc_fun(U_16743,tc_HOL_Obool),tc_fun(U_16743,tc_fun(U_16744,tc_HOL_Obool)),tc_fun(tc_prod(U_16743,U_16744),tc_HOL_Obool)),c_Product__Type_OSigma(U_16743,U_16744)),U_16746)),
    inference(definitional_conversion,[status(esa)],[f_4138_2]) ).

cnf(f_4138_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_16743,U_16744),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16743,tc_HOL_Obool),U_16745)),U_16746) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16743,tc_HOL_Obool),tc_fun(tc_prod(U_16743,U_16744),tc_HOL_Obool)),U_16745),hAPP(hAPP(c_COMBC(tc_fun(U_16743,tc_HOL_Obool),tc_fun(U_16743,tc_fun(U_16744,tc_HOL_Obool)),tc_fun(tc_prod(U_16743,U_16744),tc_HOL_Obool)),c_Product__Type_OSigma(U_16743,U_16744)),U_16746)),
    inference(clausify,[status(thm)],[f_4138_3]) ).

fof(f_4139_1,plain,
    ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Union]) ).

fof(f_4139_2,plain,
    ! [U_16750,U_16749,U_16748,U_16747] : hAPP(c_Set_Oimage(U_16747,U_16748,U_16749),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16747,tc_HOL_Obool),U_16750)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16747,tc_HOL_Obool),tc_fun(U_16748,tc_HOL_Obool)),U_16750),c_Set_Oimage(U_16747,U_16748,U_16749)),
    inference(variable_rename,[status(thm)],[f_4139_1]) ).

fof(f_4139_3,plain,
    ! [U_16747,U_16748,U_16749,U_16750] : hAPP(c_Set_Oimage(U_16747,U_16748,U_16749),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16747,tc_HOL_Obool),U_16750)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16747,tc_HOL_Obool),tc_fun(U_16748,tc_HOL_Obool)),U_16750),c_Set_Oimage(U_16747,U_16748,U_16749)),
    inference(definitional_conversion,[status(esa)],[f_4139_2]) ).

cnf(f_4139_4,plain,
    hAPP(c_Set_Oimage(U_16747,U_16748,U_16749),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16747,tc_HOL_Obool),U_16750)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16747,tc_HOL_Obool),tc_fun(U_16748,tc_HOL_Obool)),U_16750),c_Set_Oimage(U_16747,U_16748,U_16749)),
    inference(clausify,[status(thm)],[f_4139_3]) ).

fof(f_4140_1,plain,
    ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
    inference(fof_nnf,[status(thm)],[fact_Range__Union]) ).

fof(f_4140_2,plain,
    ! [U_16753,U_16752,U_16751] : hAPP(c_Relation_ORange(U_16751,U_16752),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16751,U_16752),tc_HOL_Obool),U_16753)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16751,U_16752),tc_HOL_Obool),tc_fun(U_16752,tc_HOL_Obool)),U_16753),c_Relation_ORange(U_16751,U_16752)),
    inference(variable_rename,[status(thm)],[f_4140_1]) ).

fof(f_4140_3,plain,
    ! [U_16751,U_16752,U_16753] : hAPP(c_Relation_ORange(U_16751,U_16752),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16751,U_16752),tc_HOL_Obool),U_16753)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16751,U_16752),tc_HOL_Obool),tc_fun(U_16752,tc_HOL_Obool)),U_16753),c_Relation_ORange(U_16751,U_16752)),
    inference(definitional_conversion,[status(esa)],[f_4140_2]) ).

cnf(f_4140_4,plain,
    hAPP(c_Relation_ORange(U_16751,U_16752),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16751,U_16752),tc_HOL_Obool),U_16753)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16751,U_16752),tc_HOL_Obool),tc_fun(U_16752,tc_HOL_Obool)),U_16753),c_Relation_ORange(U_16751,U_16752)),
    inference(clausify,[status(thm)],[f_4140_3]) ).

fof(f_4141_1,plain,
    ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Union]) ).

fof(f_4141_2,plain,
    ! [U_16756,U_16755,U_16754] : hAPP(c_Relation_ODomain(U_16754,U_16755),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16754,U_16755),tc_HOL_Obool),U_16756)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16754,U_16755),tc_HOL_Obool),tc_fun(U_16754,tc_HOL_Obool)),U_16756),c_Relation_ODomain(U_16754,U_16755)),
    inference(variable_rename,[status(thm)],[f_4141_1]) ).

fof(f_4141_3,plain,
    ! [U_16754,U_16755,U_16756] : hAPP(c_Relation_ODomain(U_16754,U_16755),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16754,U_16755),tc_HOL_Obool),U_16756)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16754,U_16755),tc_HOL_Obool),tc_fun(U_16754,tc_HOL_Obool)),U_16756),c_Relation_ODomain(U_16754,U_16755)),
    inference(definitional_conversion,[status(esa)],[f_4141_2]) ).

cnf(f_4141_4,plain,
    hAPP(c_Relation_ODomain(U_16754,U_16755),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16754,U_16755),tc_HOL_Obool),U_16756)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16754,U_16755),tc_HOL_Obool),tc_fun(U_16754,tc_HOL_Obool)),U_16756),c_Relation_ODomain(U_16754,U_16755)),
    inference(clausify,[status(thm)],[f_4141_3]) ).

fof(f_4142_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Union]) ).

fof(f_4142_2,plain,
    ! [U_16760,U_16759,U_16758,U_16757] : hAPP(c_Set_Ovimage(U_16757,U_16758,U_16759),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16758,tc_HOL_Obool),U_16760)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16758,tc_HOL_Obool),tc_fun(U_16757,tc_HOL_Obool)),U_16760),c_Set_Ovimage(U_16757,U_16758,U_16759)),
    inference(variable_rename,[status(thm)],[f_4142_1]) ).

fof(f_4142_3,plain,
    ! [U_16757,U_16758,U_16759,U_16760] : hAPP(c_Set_Ovimage(U_16757,U_16758,U_16759),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16758,tc_HOL_Obool),U_16760)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16758,tc_HOL_Obool),tc_fun(U_16757,tc_HOL_Obool)),U_16760),c_Set_Ovimage(U_16757,U_16758,U_16759)),
    inference(definitional_conversion,[status(esa)],[f_4142_2]) ).

cnf(f_4142_4,plain,
    hAPP(c_Set_Ovimage(U_16757,U_16758,U_16759),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16758,tc_HOL_Obool),U_16760)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16758,tc_HOL_Obool),tc_fun(U_16757,tc_HOL_Obool)),U_16760),c_Set_Ovimage(U_16757,U_16758,U_16759)),
    inference(clausify,[status(thm)],[f_4142_3]) ).

fof(f_4143_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(f_4143_2,plain,
    ! [U_16764,U_16763,U_16762,U_16761] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16761,tc_HOL_Obool),tc_fun(U_16762,tc_HOL_Obool)),U_16763),hAPP(hAPP(c_COMBC(tc_fun(U_16761,tc_HOL_Obool),tc_fun(U_16761,tc_fun(U_16762,tc_HOL_Obool)),tc_fun(U_16762,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16761,tc_fun(U_16762,tc_HOL_Obool))),U_16764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16761,tc_fun(U_16762,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16761,tc_HOL_Obool),U_16763)),U_16764),
    inference(variable_rename,[status(thm)],[f_4143_1]) ).

fof(f_4143_3,plain,
    ! [U_16761,U_16762,U_16763,U_16764] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16761,tc_HOL_Obool),tc_fun(U_16762,tc_HOL_Obool)),U_16763),hAPP(hAPP(c_COMBC(tc_fun(U_16761,tc_HOL_Obool),tc_fun(U_16761,tc_fun(U_16762,tc_HOL_Obool)),tc_fun(U_16762,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16761,tc_fun(U_16762,tc_HOL_Obool))),U_16764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16761,tc_fun(U_16762,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16761,tc_HOL_Obool),U_16763)),U_16764),
    inference(definitional_conversion,[status(esa)],[f_4143_2]) ).

cnf(f_4143_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16761,tc_HOL_Obool),tc_fun(U_16762,tc_HOL_Obool)),U_16763),hAPP(hAPP(c_COMBC(tc_fun(U_16761,tc_HOL_Obool),tc_fun(U_16761,tc_fun(U_16762,tc_HOL_Obool)),tc_fun(U_16762,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16761,tc_fun(U_16762,tc_HOL_Obool))),U_16764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16761,tc_fun(U_16762,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16761,tc_HOL_Obool),U_16763)),U_16764),
    inference(clausify,[status(thm)],[f_4143_3]) ).

fof(f_4144_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(f_4144_2,plain,
    ! [U_16768,U_16767,U_16766,U_16765] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16765,tc_fun(U_16766,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16765,tc_HOL_Obool),U_16767)),U_16768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16765,tc_HOL_Obool),tc_fun(U_16766,tc_HOL_Obool)),U_16767),hAPP(hAPP(c_COMBC(tc_fun(U_16765,tc_HOL_Obool),tc_fun(U_16765,tc_fun(U_16766,tc_HOL_Obool)),tc_fun(U_16766,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16765,tc_fun(U_16766,tc_HOL_Obool))),U_16768)),
    inference(variable_rename,[status(thm)],[f_4144_1]) ).

fof(f_4144_3,plain,
    ! [U_16765,U_16766,U_16767,U_16768] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16765,tc_fun(U_16766,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16765,tc_HOL_Obool),U_16767)),U_16768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16765,tc_HOL_Obool),tc_fun(U_16766,tc_HOL_Obool)),U_16767),hAPP(hAPP(c_COMBC(tc_fun(U_16765,tc_HOL_Obool),tc_fun(U_16765,tc_fun(U_16766,tc_HOL_Obool)),tc_fun(U_16766,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16765,tc_fun(U_16766,tc_HOL_Obool))),U_16768)),
    inference(definitional_conversion,[status(esa)],[f_4144_2]) ).

cnf(f_4144_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16765,tc_fun(U_16766,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16765,tc_HOL_Obool),U_16767)),U_16768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16765,tc_HOL_Obool),tc_fun(U_16766,tc_HOL_Obool)),U_16767),hAPP(hAPP(c_COMBC(tc_fun(U_16765,tc_HOL_Obool),tc_fun(U_16765,tc_fun(U_16766,tc_HOL_Obool)),tc_fun(U_16766,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16765,tc_fun(U_16766,tc_HOL_Obool))),U_16768)),
    inference(clausify,[status(thm)],[f_4144_3]) ).

fof(f_4145_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_subset__Pow__Union]) ).

fof(f_4145_2,plain,
    ! [U_16770,U_16769] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16769,tc_HOL_Obool),tc_HOL_Obool)),U_16770),hAPP(c_Set_OPow(U_16769),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16769,tc_HOL_Obool),U_16770)))),
    inference(variable_rename,[status(thm)],[f_4145_1]) ).

fof(f_4145_3,plain,
    ! [U_16769,U_16770] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16769,tc_HOL_Obool),tc_HOL_Obool)),U_16770),hAPP(c_Set_OPow(U_16769),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16769,tc_HOL_Obool),U_16770)))),
    inference(definitional_conversion,[status(esa)],[f_4145_2]) ).

cnf(f_4145_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16769,tc_HOL_Obool),tc_HOL_Obool)),U_16770),hAPP(c_Set_OPow(U_16769),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16769,tc_HOL_Obool),U_16770)))),
    inference(clausify,[status(thm)],[f_4145_3]) ).

fof(f_4146_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnionD]) ).

fof(f_4146_2,plain,
    ! [U_16772,U_16771] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16771,tc_HOL_Obool)),U_16772))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16771),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16771,tc_HOL_Obool),U_16772))) ),
    inference(variable_rename,[status(thm)],[f_4146_1]) ).

fof(f_4146_3,plain,
    ! [U_16771,U_16772] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16771,tc_HOL_Obool)),U_16772))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16771),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16771,tc_HOL_Obool),U_16772))) ),
    inference(definitional_conversion,[status(esa)],[f_4146_2]) ).

cnf(f_4146_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16771,tc_HOL_Obool)),U_16772))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16771),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16771,tc_HOL_Obool),U_16772))) ),
    inference(clausify,[status(thm)],[f_4146_3]) ).

fof(f_4147_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Union__mono]) ).

fof(f_4147_2,plain,
    ! [U_16775,U_16774,U_16773] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16773,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16773,tc_HOL_Obool),U_16774)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16773,tc_HOL_Obool),U_16775)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16773,tc_HOL_Obool),tc_HOL_Obool)),U_16774),U_16775)) ),
    inference(variable_rename,[status(thm)],[f_4147_1]) ).

fof(f_4147_3,plain,
    ! [U_16773,U_16774,U_16775] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16773,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16773,tc_HOL_Obool),U_16774)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16773,tc_HOL_Obool),U_16775)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16773,tc_HOL_Obool),tc_HOL_Obool)),U_16774),U_16775)) ),
    inference(definitional_conversion,[status(esa)],[f_4147_2]) ).

cnf(f_4147_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16773,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16773,tc_HOL_Obool),U_16774)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16773,tc_HOL_Obool),U_16775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16773,tc_HOL_Obool),tc_HOL_Obool)),U_16774),U_16775)) ),
    inference(clausify,[status(thm)],[f_4147_3]) ).

fof(f_4148_1,plain,
    ! [V_A_2,V_C_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) ) )
      & ( ! [B_x] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Union__disjoint]) ).

fof(f_4148_2,plain,
    ! [U_16780,U_16779,U_16778] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16778,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16778,tc_HOL_Obool),U_16779)),U_16780) = c_Orderings_Obot__class_Obot(tc_fun(U_16778,tc_HOL_Obool))
        | ? [U_16777] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16778,tc_HOL_Obool)),U_16777),U_16780) != c_Orderings_Obot__class_Obot(tc_fun(U_16778,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16778,tc_HOL_Obool)),U_16777),U_16779)) ) )
      & ( ! [U_16776] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16778,tc_HOL_Obool)),U_16776),U_16780) = c_Orderings_Obot__class_Obot(tc_fun(U_16778,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16778,tc_HOL_Obool)),U_16776),U_16779)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16778,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16778,tc_HOL_Obool),U_16779)),U_16780) != c_Orderings_Obot__class_Obot(tc_fun(U_16778,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4148_1]) ).

fof(f_4148_3,plain,
    ( ! [U_16786,U_16784,U_16782] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16782,tc_HOL_Obool),U_16784)),U_16786) = c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
        | ? [U_16777] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),U_16777),U_16786) != c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16782,tc_HOL_Obool)),U_16777),U_16784)) ) )
    & ! [U_16785,U_16783,U_16781] :
        ( ! [U_16776] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16785) = c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16783)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16781,tc_HOL_Obool),U_16783)),U_16785) != c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4148_2]) ).

fof(f_4148_4,plain,
    ( ! [U_16786,U_16784,U_16782] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16782,tc_HOL_Obool),U_16784)),U_16786) = c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
        | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),sK403(U_16786,U_16784,U_16782)),U_16786) != c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16782,tc_HOL_Obool)),sK403(U_16786,U_16784,U_16782)),U_16784)) ) )
    & ! [U_16785,U_16783,U_16781] :
        ( ! [U_16776] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16785) = c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16783)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16781,tc_HOL_Obool),U_16783)),U_16785) != c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_16777,sK403(U_16786,U_16784,U_16782))],[f_4148_3]) ).

fof(f_4148_5,plain,
    ( ! [U_16786,U_16784,U_16782] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),sK403(U_16786,U_16784,U_16782)),U_16786) != c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
        | ~ sP1070(U_16786,U_16784,U_16782) )
    & ! [U_16786,U_16784,U_16782] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16782,tc_HOL_Obool)),sK403(U_16786,U_16784,U_16782)),U_16784))
        | ~ sP1070(U_16786,U_16784,U_16782) )
    & ! [U_16786,U_16784,U_16782] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16782,tc_HOL_Obool),U_16784)),U_16786) = c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
        | sP1070(U_16786,U_16784,U_16782) )
    & ! [U_16783,U_16776,U_16781,U_16785] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16785) = c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16783))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16781,tc_HOL_Obool),U_16783)),U_16785) != c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1070])],[f_4148_4]) ).

cnf(f_4148_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16785) = c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16781,tc_HOL_Obool)),U_16776),U_16783))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16781,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16781,tc_HOL_Obool),U_16783)),U_16785) != c_Orderings_Obot__class_Obot(tc_fun(U_16781,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4148_5]) ).

cnf(f_4148_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16782,tc_HOL_Obool),U_16784)),U_16786) = c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
    | sP1070(U_16786,U_16784,U_16782) ),
    inference(clausify,[status(thm)],[f_4148_5]) ).

cnf(f_4148_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16782,tc_HOL_Obool)),sK403(U_16786,U_16784,U_16782)),U_16784))
    | ~ sP1070(U_16786,U_16784,U_16782) ),
    inference(clausify,[status(thm)],[f_4148_5]) ).

cnf(f_4148_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16782,tc_HOL_Obool)),sK403(U_16786,U_16784,U_16782)),U_16786) != c_Orderings_Obot__class_Obot(tc_fun(U_16782,tc_HOL_Obool))
    | ~ sP1070(U_16786,U_16784,U_16782) ),
    inference(clausify,[status(thm)],[f_4148_5]) ).

fof(f_4149_1,plain,
    ! [V_b_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__le__iff]) ).

fof(f_4149_2,plain,
    ! [U_16791,U_16790,U_16789] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791))
          | ? [U_16788] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),U_16788),U_16791))
              & hBOOL(hAPP(hAPP(c_member(U_16789),U_16788),U_16790)) ) )
        & ( ! [U_16787] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),U_16787),U_16791))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16789),U_16787),U_16790)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16789) ),
    inference(variable_rename,[status(thm)],[f_4149_1]) ).

fof(f_4149_3,plain,
    ! [U_16791,U_16790,U_16789] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),sK404(U_16791,U_16790,U_16789)),U_16791))
            & hBOOL(hAPP(hAPP(c_member(U_16789),sK404(U_16791,U_16790,U_16789)),U_16790)) ) )
        & ( ! [U_16787] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),U_16787),U_16791))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16789),U_16787),U_16790)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16789) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_16788,sK404(U_16791,U_16790,U_16789))],[f_4149_2]) ).

fof(f_4149_4,plain,
    ( ! [U_16789,U_16790,U_16791] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),sK404(U_16791,U_16790,U_16789)),U_16791))
        | ~ sP1071(U_16789,U_16790,U_16791) )
    & ! [U_16789,U_16790,U_16791] :
        ( hBOOL(hAPP(hAPP(c_member(U_16789),sK404(U_16791,U_16790,U_16789)),U_16790))
        | ~ sP1071(U_16789,U_16790,U_16791) )
    & ! [U_16787,U_16789,U_16790,U_16791] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791))
        | sP1071(U_16789,U_16790,U_16791)
        | ~ sP1072(U_16787,U_16789,U_16790,U_16791) )
    & ! [U_16787,U_16789,U_16790,U_16791] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),U_16787),U_16791))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16789),U_16787),U_16790))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791))
        | ~ sP1072(U_16787,U_16789,U_16790,U_16791) )
    & ! [U_16787,U_16789,U_16790,U_16791] :
        ( sP1072(U_16787,U_16789,U_16790,U_16791)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16789) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1071,sP1072])],[f_4149_3]) ).

cnf(f_4149_5,plain,
    ( sP1072(U_16787,U_16789,U_16790,U_16791)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16789) ),
    inference(clausify,[status(thm)],[f_4149_4]) ).

cnf(f_4149_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),U_16787),U_16791))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16789),U_16787),U_16790))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791))
    | ~ sP1072(U_16787,U_16789,U_16790,U_16791) ),
    inference(clausify,[status(thm)],[f_4149_4]) ).

cnf(f_4149_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),c_Complete__Lattice_OSup__class_OSup(U_16789,U_16790)),U_16791))
    | sP1071(U_16789,U_16790,U_16791)
    | ~ sP1072(U_16787,U_16789,U_16790,U_16791) ),
    inference(clausify,[status(thm)],[f_4149_4]) ).

cnf(f_4149_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16789),sK404(U_16791,U_16790,U_16789)),U_16790))
    | ~ sP1071(U_16789,U_16790,U_16791) ),
    inference(clausify,[status(thm)],[f_4149_4]) ).

cnf(f_4149_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16789),sK404(U_16791,U_16790,U_16789)),U_16791))
    | ~ sP1071(U_16789,U_16790,U_16791) ),
    inference(clausify,[status(thm)],[f_4149_4]) ).

fof(f_4150_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Union__upper]) ).

fof(f_4150_2,plain,
    ! [U_16794,U_16793,U_16792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16792,tc_HOL_Obool)),U_16793),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16792,tc_HOL_Obool),U_16794)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16792,tc_HOL_Obool)),U_16793),U_16794)) ),
    inference(variable_rename,[status(thm)],[f_4150_1]) ).

fof(f_4150_3,plain,
    ! [U_16794,U_16793,U_16792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16792,tc_HOL_Obool)),U_16793),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16792,tc_HOL_Obool),U_16794)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16792,tc_HOL_Obool)),U_16793),U_16794)) ),
    inference(definitional_conversion,[status(esa)],[f_4150_2]) ).

cnf(f_4150_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16792,tc_HOL_Obool)),U_16793),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16792,tc_HOL_Obool),U_16794)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16792,tc_HOL_Obool)),U_16793),U_16794)) ),
    inference(clausify,[status(thm)],[f_4150_3]) ).

fof(f_4151_1,plain,
    ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Union__Pow__eq]) ).

fof(f_4151_2,plain,
    ! [U_16796,U_16795] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16795,tc_HOL_Obool),hAPP(c_Set_OPow(U_16795),U_16796)) = U_16796,
    inference(variable_rename,[status(thm)],[f_4151_1]) ).

fof(f_4151_3,plain,
    ! [U_16795,U_16796] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16795,tc_HOL_Obool),hAPP(c_Set_OPow(U_16795),U_16796)) = U_16796,
    inference(definitional_conversion,[status(esa)],[f_4151_2]) ).

cnf(f_4151_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16795,tc_HOL_Obool),hAPP(c_Set_OPow(U_16795),U_16796)) = U_16796,
    inference(clausify,[status(thm)],[f_4151_3]) ).

fof(f_4152_1,plain,
    ! [V_S_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__Sup__iff]) ).

fof(f_4152_2,plain,
    ! [U_16801,U_16800,U_16799] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801)))
          | ! [U_16798] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),U_16798))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16799),U_16798),U_16801)) ) )
        & ( ? [U_16797] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),U_16797))
              & hBOOL(hAPP(hAPP(c_member(U_16799),U_16797),U_16801)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801))) ) )
      | ~ class_Orderings_Olinorder(U_16799)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16799) ),
    inference(variable_rename,[status(thm)],[f_4152_1]) ).

fof(f_4152_3,plain,
    ! [U_16801,U_16800,U_16799] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801)))
          | ! [U_16798] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),U_16798))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16799),U_16798),U_16801)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),sK405(U_16801,U_16800,U_16799)))
            & hBOOL(hAPP(hAPP(c_member(U_16799),sK405(U_16801,U_16800,U_16799)),U_16801)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801))) ) )
      | ~ class_Orderings_Olinorder(U_16799)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16799) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_16797,sK405(U_16801,U_16800,U_16799))],[f_4152_2]) ).

fof(f_4152_4,plain,
    ( ! [U_16799,U_16800,U_16801] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),sK405(U_16801,U_16800,U_16799)))
        | ~ sP1073(U_16799,U_16800,U_16801) )
    & ! [U_16799,U_16800,U_16801] :
        ( hBOOL(hAPP(hAPP(c_member(U_16799),sK405(U_16801,U_16800,U_16799)),U_16801))
        | ~ sP1073(U_16799,U_16800,U_16801) )
    & ! [U_16798,U_16799,U_16800,U_16801] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),U_16798))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16799),U_16798),U_16801))
        | ~ sP1074(U_16798,U_16799,U_16800,U_16801) )
    & ! [U_16798,U_16799,U_16800,U_16801] :
        ( sP1073(U_16799,U_16800,U_16801)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801)))
        | ~ sP1074(U_16798,U_16799,U_16800,U_16801) )
    & ! [U_16798,U_16799,U_16800,U_16801] :
        ( sP1074(U_16798,U_16799,U_16800,U_16801)
        | ~ class_Orderings_Olinorder(U_16799)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16799) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1073,sP1074])],[f_4152_3]) ).

cnf(f_4152_5,plain,
    ( sP1074(U_16798,U_16799,U_16800,U_16801)
    | ~ class_Orderings_Olinorder(U_16799)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16799) ),
    inference(clausify,[status(thm)],[f_4152_4]) ).

cnf(f_4152_6,plain,
    ( sP1073(U_16799,U_16800,U_16801)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801)))
    | ~ sP1074(U_16798,U_16799,U_16800,U_16801) ),
    inference(clausify,[status(thm)],[f_4152_4]) ).

cnf(f_4152_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),c_Complete__Lattice_OSup__class_OSup(U_16799,U_16801)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),U_16798))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16799),U_16798),U_16801))
    | ~ sP1074(U_16798,U_16799,U_16800,U_16801) ),
    inference(clausify,[status(thm)],[f_4152_4]) ).

cnf(f_4152_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16799),sK405(U_16801,U_16800,U_16799)),U_16801))
    | ~ sP1073(U_16799,U_16800,U_16801) ),
    inference(clausify,[status(thm)],[f_4152_4]) ).

cnf(f_4152_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16799),U_16800),sK405(U_16801,U_16800,U_16799)))
    | ~ sP1073(U_16799,U_16800,U_16801) ),
    inference(clausify,[status(thm)],[f_4152_4]) ).

fof(f_4153_1,plain,
    ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__Union]) ).

fof(f_4153_2,plain,
    ! [U_16803,U_16802] : hAPP(c_Relation_OField(U_16802),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16802,U_16802),tc_HOL_Obool),U_16803)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_16802,U_16802),tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool),c_Relation_OField(U_16802)),U_16803)),
    inference(variable_rename,[status(thm)],[f_4153_1]) ).

fof(f_4153_3,plain,
    ! [U_16803,U_16802] : hAPP(c_Relation_OField(U_16802),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16802,U_16802),tc_HOL_Obool),U_16803)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_16802,U_16802),tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool),c_Relation_OField(U_16802)),U_16803)),
    inference(definitional_conversion,[status(esa)],[f_4153_2]) ).

cnf(f_4153_4,plain,
    hAPP(c_Relation_OField(U_16802),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16802,U_16802),tc_HOL_Obool),U_16803)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_16802,U_16802),tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool),c_Relation_OField(U_16802)),U_16803)),
    inference(clausify,[status(thm)],[f_4153_3]) ).

fof(f_4154_1,plain,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Union__empty]) ).

fof(f_4154_2,plain,
    ! [U_16804] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16804,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16804,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16804,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4154_1]) ).

fof(f_4154_3,plain,
    ! [U_16804] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16804,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16804,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16804,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4154_2]) ).

cnf(f_4154_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16804,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16804,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16804,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4154_3]) ).

fof(f_4155_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_Union__quotient]) ).

fof(f_4155_2,plain,
    ! [U_16807,U_16806,U_16805] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16805,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_16805),U_16806),U_16807)) = U_16806
      | ~ c_Equiv__Relations_Oequiv(U_16805,U_16806,U_16807) ),
    inference(variable_rename,[status(thm)],[f_4155_1]) ).

fof(f_4155_3,plain,
    ! [U_16805,U_16806,U_16807] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16805,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_16805),U_16806),U_16807)) = U_16806
      | ~ c_Equiv__Relations_Oequiv(U_16805,U_16806,U_16807) ),
    inference(definitional_conversion,[status(esa)],[f_4155_2]) ).

cnf(f_4155_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16805,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_16805),U_16806),U_16807)) = U_16806
    | ~ c_Equiv__Relations_Oequiv(U_16805,U_16806,U_16807) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

fof(f_4156_1,plain,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Union__Un__distrib]) ).

fof(f_4156_2,plain,
    ! [U_16810,U_16809,U_16808] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16808,tc_HOL_Obool),tc_HOL_Obool)),U_16809),U_16810)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16808,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),U_16809)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),U_16810)),
    inference(variable_rename,[status(thm)],[f_4156_1]) ).

fof(f_4156_3,plain,
    ! [U_16808,U_16809,U_16810] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16808,tc_HOL_Obool),tc_HOL_Obool)),U_16809),U_16810)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16808,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),U_16809)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),U_16810)),
    inference(definitional_conversion,[status(esa)],[f_4156_2]) ).

cnf(f_4156_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16808,tc_HOL_Obool),tc_HOL_Obool)),U_16809),U_16810)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16808,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),U_16809)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16808,tc_HOL_Obool),U_16810)),
    inference(clausify,[status(thm)],[f_4156_3]) ).

fof(f_4157_1,plain,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Union__UNIV]) ).

fof(f_4157_2,plain,
    ! [U_16811] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16811,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16811,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16811,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4157_1]) ).

fof(f_4157_3,plain,
    ! [U_16811] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16811,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16811,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16811,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4157_2]) ).

cnf(f_4157_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16811,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16811,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16811,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4157_3]) ).

fof(f_4158_1,plain,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Union__insert]) ).

fof(f_4158_2,plain,
    ! [U_16814,U_16813,U_16812] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16812,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16812,tc_HOL_Obool)),U_16813),U_16814)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16812,tc_HOL_Obool)),U_16813),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16812,tc_HOL_Obool),U_16814)),
    inference(variable_rename,[status(thm)],[f_4158_1]) ).

fof(f_4158_3,plain,
    ! [U_16812,U_16813,U_16814] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16812,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16812,tc_HOL_Obool)),U_16813),U_16814)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16812,tc_HOL_Obool)),U_16813),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16812,tc_HOL_Obool),U_16814)),
    inference(definitional_conversion,[status(esa)],[f_4158_2]) ).

cnf(f_4158_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16812,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16812,tc_HOL_Obool)),U_16813),U_16814)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16812,tc_HOL_Obool)),U_16813),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16812,tc_HOL_Obool),U_16814)),
    inference(clausify,[status(thm)],[f_4158_3]) ).

fof(f_4159_1,plain,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Union__image__eq]) ).

fof(f_4159_2,plain,
    ! [U_16818,U_16817,U_16816,U_16815] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16815,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16816,tc_fun(U_16815,tc_HOL_Obool),U_16817),U_16818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16816,tc_fun(U_16815,tc_HOL_Obool)),U_16818),U_16817),
    inference(variable_rename,[status(thm)],[f_4159_1]) ).

fof(f_4159_3,plain,
    ! [U_16815,U_16816,U_16817,U_16818] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16815,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16816,tc_fun(U_16815,tc_HOL_Obool),U_16817),U_16818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16816,tc_fun(U_16815,tc_HOL_Obool)),U_16818),U_16817),
    inference(definitional_conversion,[status(esa)],[f_4159_2]) ).

cnf(f_4159_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16815,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16816,tc_fun(U_16815,tc_HOL_Obool),U_16817),U_16818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16816,tc_fun(U_16815,tc_HOL_Obool)),U_16818),U_16817),
    inference(clausify,[status(thm)],[f_4159_3]) ).

fof(f_4160_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(f_4160_2,plain,
    ! [U_16822,U_16821,U_16820,U_16819] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16819,tc_fun(U_16820,tc_HOL_Obool)),U_16821),U_16822) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16820,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16819,tc_fun(U_16820,tc_HOL_Obool),U_16822),U_16821)),
    inference(variable_rename,[status(thm)],[f_4160_1]) ).

fof(f_4160_3,plain,
    ! [U_16819,U_16820,U_16821,U_16822] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16819,tc_fun(U_16820,tc_HOL_Obool)),U_16821),U_16822) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16820,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16819,tc_fun(U_16820,tc_HOL_Obool),U_16822),U_16821)),
    inference(definitional_conversion,[status(esa)],[f_4160_2]) ).

cnf(f_4160_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16819,tc_fun(U_16820,tc_HOL_Obool)),U_16821),U_16822) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16820,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16819,tc_fun(U_16820,tc_HOL_Obool),U_16822),U_16821)),
    inference(clausify,[status(thm)],[f_4160_3]) ).

fof(f_4161_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__upper]) ).

fof(f_4161_2,plain,
    ! [U_16825,U_16824,U_16823] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16823),U_16824),c_Complete__Lattice_OSup__class_OSup(U_16823,U_16825)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16823),U_16824),U_16825))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16823) ),
    inference(variable_rename,[status(thm)],[f_4161_1]) ).

fof(f_4161_3,plain,
    ! [U_16823,U_16824,U_16825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16823),U_16824),c_Complete__Lattice_OSup__class_OSup(U_16823,U_16825)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16823),U_16824),U_16825))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16823) ),
    inference(definitional_conversion,[status(esa)],[f_4161_2]) ).

cnf(f_4161_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16823),U_16824),c_Complete__Lattice_OSup__class_OSup(U_16823,U_16825)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16823),U_16824),U_16825))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16823) ),
    inference(clausify,[status(thm)],[f_4161_3]) ).

fof(f_4162_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__empty]) ).

fof(f_4162_2,plain,
    ! [U_16826] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16826,c_Orderings_Obot__class_Obot(tc_fun(U_16826,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16826)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16826) ),
    inference(variable_rename,[status(thm)],[f_4162_1]) ).

fof(f_4162_3,plain,
    ! [U_16826] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16826,c_Orderings_Obot__class_Obot(tc_fun(U_16826,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16826)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16826) ),
    inference(definitional_conversion,[status(esa)],[f_4162_2]) ).

cnf(f_4162_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16826,c_Orderings_Obot__class_Obot(tc_fun(U_16826,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16826)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16826) ),
    inference(clausify,[status(thm)],[f_4162_3]) ).

fof(f_4163_1,plain,
    ! [V_a_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__singleton]) ).

fof(f_4163_2,plain,
    ! [U_16828,U_16827] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16827,hAPP(hAPP(c_Set_Oinsert(U_16827),U_16828),c_Orderings_Obot__class_Obot(tc_fun(U_16827,tc_HOL_Obool)))) = U_16828
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16827) ),
    inference(variable_rename,[status(thm)],[f_4163_1]) ).

fof(f_4163_3,plain,
    ! [U_16827,U_16828] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16827,hAPP(hAPP(c_Set_Oinsert(U_16827),U_16828),c_Orderings_Obot__class_Obot(tc_fun(U_16827,tc_HOL_Obool)))) = U_16828
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16827) ),
    inference(definitional_conversion,[status(esa)],[f_4163_2]) ).

cnf(f_4163_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16827,hAPP(hAPP(c_Set_Oinsert(U_16827),U_16828),c_Orderings_Obot__class_Obot(tc_fun(U_16827,tc_HOL_Obool)))) = U_16828
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16827) ),
    inference(clausify,[status(thm)],[f_4163_3]) ).

fof(f_4164_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__insert]) ).

fof(f_4164_2,plain,
    ! [U_16831,U_16830,U_16829] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16829,hAPP(hAPP(c_Set_Oinsert(U_16829),U_16830),U_16831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16829),U_16830),c_Complete__Lattice_OSup__class_OSup(U_16829,U_16831))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16829) ),
    inference(variable_rename,[status(thm)],[f_4164_1]) ).

fof(f_4164_3,plain,
    ! [U_16829,U_16830,U_16831] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16829,hAPP(hAPP(c_Set_Oinsert(U_16829),U_16830),U_16831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16829),U_16830),c_Complete__Lattice_OSup__class_OSup(U_16829,U_16831))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16829) ),
    inference(definitional_conversion,[status(esa)],[f_4164_2]) ).

cnf(f_4164_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16829,hAPP(hAPP(c_Set_Oinsert(U_16829),U_16830),U_16831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16829),U_16830),c_Complete__Lattice_OSup__class_OSup(U_16829,U_16831))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16829) ),
    inference(clausify,[status(thm)],[f_4164_3]) ).

fof(f_4165_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__UNIV]) ).

fof(f_4165_2,plain,
    ! [U_16832] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16832,c_Orderings_Otop__class_Otop(tc_fun(U_16832,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16832)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16832) ),
    inference(variable_rename,[status(thm)],[f_4165_1]) ).

fof(f_4165_3,plain,
    ! [U_16832] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16832,c_Orderings_Otop__class_Otop(tc_fun(U_16832,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16832)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16832) ),
    inference(definitional_conversion,[status(esa)],[f_4165_2]) ).

cnf(f_4165_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16832,c_Orderings_Otop__class_Otop(tc_fun(U_16832,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16832)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16832) ),
    inference(clausify,[status(thm)],[f_4165_3]) ).

fof(f_4166_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Un__eq__Union]) ).

fof(f_4166_2,plain,
    ! [U_16835,U_16834,U_16833] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16833,tc_HOL_Obool)),U_16834),U_16835) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16833,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16833,tc_HOL_Obool)),U_16834),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16833,tc_HOL_Obool)),U_16835),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16833,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4166_1]) ).

fof(f_4166_3,plain,
    ! [U_16833,U_16834,U_16835] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16833,tc_HOL_Obool)),U_16834),U_16835) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16833,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16833,tc_HOL_Obool)),U_16834),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16833,tc_HOL_Obool)),U_16835),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16833,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4166_2]) ).

cnf(f_4166_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16833,tc_HOL_Obool)),U_16834),U_16835) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16833,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16833,tc_HOL_Obool)),U_16834),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16833,tc_HOL_Obool)),U_16835),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16833,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4166_3]) ).

fof(f_4167_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__Union__image]) ).

fof(f_4167_2,plain,
    ! [U_16840,U_16839,U_16838,U_16837,U_16836] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16836,tc_fun(U_16837,tc_HOL_Obool)),U_16838),hAPP(hAPP(c_COMBS(U_16836,tc_fun(U_16837,tc_HOL_Obool),tc_fun(U_16837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16837,tc_HOL_Obool),tc_fun(tc_fun(U_16837,tc_HOL_Obool),tc_fun(U_16837,tc_HOL_Obool)),U_16836),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16837,tc_HOL_Obool))),U_16839)),U_16840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16837,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16837,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16836,tc_fun(U_16837,tc_HOL_Obool),U_16839),U_16838))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16837,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16836,tc_fun(U_16837,tc_HOL_Obool),U_16840),U_16838))),
    inference(variable_rename,[status(thm)],[f_4167_1]) ).

fof(f_4167_3,plain,
    ! [U_16836,U_16837,U_16838,U_16839,U_16840] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16836,tc_fun(U_16837,tc_HOL_Obool)),U_16838),hAPP(hAPP(c_COMBS(U_16836,tc_fun(U_16837,tc_HOL_Obool),tc_fun(U_16837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16837,tc_HOL_Obool),tc_fun(tc_fun(U_16837,tc_HOL_Obool),tc_fun(U_16837,tc_HOL_Obool)),U_16836),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16837,tc_HOL_Obool))),U_16839)),U_16840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16837,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16837,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16836,tc_fun(U_16837,tc_HOL_Obool),U_16839),U_16838))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16837,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16836,tc_fun(U_16837,tc_HOL_Obool),U_16840),U_16838))),
    inference(definitional_conversion,[status(esa)],[f_4167_2]) ).

cnf(f_4167_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16836,tc_fun(U_16837,tc_HOL_Obool)),U_16838),hAPP(hAPP(c_COMBS(U_16836,tc_fun(U_16837,tc_HOL_Obool),tc_fun(U_16837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16837,tc_HOL_Obool),tc_fun(tc_fun(U_16837,tc_HOL_Obool),tc_fun(U_16837,tc_HOL_Obool)),U_16836),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16837,tc_HOL_Obool))),U_16839)),U_16840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16837,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16837,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16836,tc_fun(U_16837,tc_HOL_Obool),U_16839),U_16838))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16837,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16836,tc_fun(U_16837,tc_HOL_Obool),U_16840),U_16838))),
    inference(clausify,[status(thm)],[f_4167_3]) ).

fof(f_4168_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Union__Int__subset]) ).

fof(f_4168_2,plain,
    ! [U_16843,U_16842,U_16841] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16841,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16841,tc_HOL_Obool),tc_HOL_Obool)),U_16842),U_16843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16841,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),U_16842)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),U_16843)))),
    inference(variable_rename,[status(thm)],[f_4168_1]) ).

fof(f_4168_3,plain,
    ! [U_16841,U_16842,U_16843] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16841,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16841,tc_HOL_Obool),tc_HOL_Obool)),U_16842),U_16843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16841,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),U_16842)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),U_16843)))),
    inference(definitional_conversion,[status(esa)],[f_4168_2]) ).

cnf(f_4168_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16841,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16841,tc_HOL_Obool),tc_HOL_Obool)),U_16842),U_16843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16841,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),U_16842)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16841,tc_HOL_Obool),U_16843)))),
    inference(clausify,[status(thm)],[f_4168_3]) ).

fof(f_4169_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__binary]) ).

fof(f_4169_2,plain,
    ! [U_16846,U_16845,U_16844] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16844,hAPP(hAPP(c_Set_Oinsert(U_16844),U_16845),hAPP(hAPP(c_Set_Oinsert(U_16844),U_16846),c_Orderings_Obot__class_Obot(tc_fun(U_16844,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16844),U_16845),U_16846)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16844) ),
    inference(variable_rename,[status(thm)],[f_4169_1]) ).

fof(f_4169_3,plain,
    ! [U_16844,U_16845,U_16846] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16844,hAPP(hAPP(c_Set_Oinsert(U_16844),U_16845),hAPP(hAPP(c_Set_Oinsert(U_16844),U_16846),c_Orderings_Obot__class_Obot(tc_fun(U_16844,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16844),U_16845),U_16846)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16844) ),
    inference(definitional_conversion,[status(esa)],[f_4169_2]) ).

cnf(f_4169_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16844,hAPP(hAPP(c_Set_Oinsert(U_16844),U_16845),hAPP(hAPP(c_Set_Oinsert(U_16844),U_16846),c_Orderings_Obot__class_Obot(tc_fun(U_16844,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16844),U_16845),U_16846)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16844) ),
    inference(clausify,[status(thm)],[f_4169_3]) ).

fof(f_4170_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup]) ).

fof(f_4170_2,plain,
    ! [U_16849,U_16848,U_16847] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16847),U_16849),c_Complete__Lattice_OSup__class_OSup(U_16847,U_16848)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16847,U_16847,c_Lattices_Osemilattice__sup__class_Osup(U_16847)),U_16849),U_16848)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16847),U_16848))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16847) ),
    inference(variable_rename,[status(thm)],[f_4170_1]) ).

fof(f_4170_3,plain,
    ! [U_16847,U_16848,U_16849] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16847),U_16849),c_Complete__Lattice_OSup__class_OSup(U_16847,U_16848)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16847,U_16847,c_Lattices_Osemilattice__sup__class_Osup(U_16847)),U_16849),U_16848)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16847),U_16848))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16847) ),
    inference(definitional_conversion,[status(esa)],[f_4170_2]) ).

cnf(f_4170_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16847),U_16849),c_Complete__Lattice_OSup__class_OSup(U_16847,U_16848)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16847,U_16847,c_Lattices_Osemilattice__sup__class_Osup(U_16847)),U_16849),U_16848)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16847),U_16848))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16847) ),
    inference(clausify,[status(thm)],[f_4170_3]) ).

fof(f_4171_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup]) ).

fof(f_4171_2,plain,
    ! [U_16851,U_16850] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16850,U_16851) = c_Complete__Lattice_OSup__class_OSup(U_16850,U_16851)
      | U_16851 = c_Orderings_Obot__class_Obot(tc_fun(U_16850,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16850),U_16851))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16850) ),
    inference(variable_rename,[status(thm)],[f_4171_1]) ).

fof(f_4171_3,plain,
    ! [U_16850,U_16851] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16850,U_16851) = c_Complete__Lattice_OSup__class_OSup(U_16850,U_16851)
      | U_16851 = c_Orderings_Obot__class_Obot(tc_fun(U_16850,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16850),U_16851))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16850) ),
    inference(definitional_conversion,[status(esa)],[f_4171_2]) ).

cnf(f_4171_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_16850,U_16851) = c_Complete__Lattice_OSup__class_OSup(U_16850,U_16851)
    | U_16851 = c_Orderings_Obot__class_Obot(tc_fun(U_16850,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16850),U_16851))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16850) ),
    inference(clausify,[status(thm)],[f_4171_3]) ).

fof(f_4172_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup]) ).

fof(f_4172_2,plain,
    ! [U_16853,U_16852] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16852,U_16853) = hAPP(hAPP(c_Finite__Set_Ofold(U_16852,U_16852,c_Lattices_Osemilattice__sup__class_Osup(U_16852)),c_Orderings_Obot__class_Obot(U_16852)),U_16853)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16852),U_16853))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16852) ),
    inference(variable_rename,[status(thm)],[f_4172_1]) ).

fof(f_4172_3,plain,
    ! [U_16853,U_16852] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16852,U_16853) = hAPP(hAPP(c_Finite__Set_Ofold(U_16852,U_16852,c_Lattices_Osemilattice__sup__class_Osup(U_16852)),c_Orderings_Obot__class_Obot(U_16852)),U_16853)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16852),U_16853))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16852) ),
    inference(definitional_conversion,[status(esa)],[f_4172_2]) ).

cnf(f_4172_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16852,U_16853) = hAPP(hAPP(c_Finite__Set_Ofold(U_16852,U_16852,c_Lattices_Osemilattice__sup__class_Osup(U_16852)),c_Orderings_Obot__class_Obot(U_16852)),U_16853)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16852),U_16853))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16852) ),
    inference(clausify,[status(thm)],[f_4172_3]) ).

fof(f_4173_1,plain,
    ! [V_f_2,T_c,T_b,V_S_2] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2))
      | ? [B_A] :
          ( ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) )
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Inter]) ).

fof(f_4173_2,plain,
    ! [U_16858,U_16857,U_16856,U_16855] :
      ( c_Fun_Oinj__on(U_16856,U_16857,U_16858,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16856,tc_HOL_Obool),U_16855))
      | ? [U_16854] :
          ( ~ c_Fun_Oinj__on(U_16856,U_16857,U_16858,U_16854)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16856,tc_HOL_Obool)),U_16854),U_16855)) )
      | U_16855 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16856,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4173_1]) ).

fof(f_4173_3,plain,
    ! [U_16858,U_16857,U_16856,U_16855] :
      ( c_Fun_Oinj__on(U_16856,U_16857,U_16858,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16856,tc_HOL_Obool),U_16855))
      | ( ~ c_Fun_Oinj__on(U_16856,U_16857,U_16858,sK406(U_16858,U_16857,U_16856,U_16855))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16856,tc_HOL_Obool)),sK406(U_16858,U_16857,U_16856,U_16855)),U_16855)) )
      | U_16855 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16856,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_16854,sK406(U_16858,U_16857,U_16856,U_16855))],[f_4173_2]) ).

fof(f_4173_4,plain,
    ( ! [U_16855,U_16856,U_16857,U_16858] :
        ( ~ c_Fun_Oinj__on(U_16856,U_16857,U_16858,sK406(U_16858,U_16857,U_16856,U_16855))
        | ~ sP1075(U_16855,U_16856,U_16857,U_16858) )
    & ! [U_16855,U_16856,U_16857,U_16858] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16856,tc_HOL_Obool)),sK406(U_16858,U_16857,U_16856,U_16855)),U_16855))
        | ~ sP1075(U_16855,U_16856,U_16857,U_16858) )
    & ! [U_16855,U_16856,U_16857,U_16858] :
        ( c_Fun_Oinj__on(U_16856,U_16857,U_16858,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16856,tc_HOL_Obool),U_16855))
        | sP1075(U_16855,U_16856,U_16857,U_16858)
        | U_16855 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16856,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1075])],[f_4173_3]) ).

cnf(f_4173_5,plain,
    ( c_Fun_Oinj__on(U_16856,U_16857,U_16858,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16856,tc_HOL_Obool),U_16855))
    | sP1075(U_16855,U_16856,U_16857,U_16858)
    | U_16855 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16856,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4173_4]) ).

cnf(f_4173_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16856,tc_HOL_Obool)),sK406(U_16858,U_16857,U_16856,U_16855)),U_16855))
    | ~ sP1075(U_16855,U_16856,U_16857,U_16858) ),
    inference(clausify,[status(thm)],[f_4173_4]) ).

cnf(f_4173_7,plain,
    ( ~ c_Fun_Oinj__on(U_16856,U_16857,U_16858,sK406(U_16858,U_16857,U_16856,U_16855))
    | ~ sP1075(U_16855,U_16856,U_16857,U_16858) ),
    inference(clausify,[status(thm)],[f_4173_4]) ).

fof(f_4174_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
      | ? [B_X] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__subset]) ).

fof(f_4174_2,plain,
    ! [U_16862,U_16861,U_16860] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16861)),U_16862))
      | U_16861 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool))
      | ? [U_16859] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),U_16859),U_16862))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),U_16859),U_16861)) ) ),
    inference(variable_rename,[status(thm)],[f_4174_1]) ).

fof(f_4174_3,plain,
    ! [U_16862,U_16861,U_16860] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16861)),U_16862))
      | U_16861 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),sK407(U_16862,U_16861,U_16860)),U_16862))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),sK407(U_16862,U_16861,U_16860)),U_16861)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_16859,sK407(U_16862,U_16861,U_16860))],[f_4174_2]) ).

fof(f_4174_4,plain,
    ( ! [U_16861,U_16860,U_16862] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),sK407(U_16862,U_16861,U_16860)),U_16862))
        | ~ sP1076(U_16861,U_16860,U_16862) )
    & ! [U_16861,U_16860,U_16862] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),sK407(U_16862,U_16861,U_16860)),U_16861))
        | ~ sP1076(U_16861,U_16860,U_16862) )
    & ! [U_16861,U_16860,U_16862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16861)),U_16862))
        | U_16861 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool))
        | sP1076(U_16861,U_16860,U_16862) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1076])],[f_4174_3]) ).

cnf(f_4174_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16861)),U_16862))
    | U_16861 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool))
    | sP1076(U_16861,U_16860,U_16862) ),
    inference(clausify,[status(thm)],[f_4174_4]) ).

cnf(f_4174_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),sK407(U_16862,U_16861,U_16860)),U_16861))
    | ~ sP1076(U_16861,U_16860,U_16862) ),
    inference(clausify,[status(thm)],[f_4174_4]) ).

cnf(f_4174_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16860,tc_HOL_Obool)),sK407(U_16862,U_16861,U_16860)),U_16862))
    | ~ sP1076(U_16861,U_16860,U_16862) ),
    inference(clausify,[status(thm)],[f_4174_4]) ).

fof(f_4175_1,plain,
    ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Union__def]) ).

fof(f_4175_2,plain,
    ! [U_16864,U_16863] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16863,tc_HOL_Obool),U_16864) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16863,tc_HOL_Obool),tc_fun(U_16863,tc_HOL_Obool)),U_16864),c_COMBI(tc_fun(U_16863,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4175_1]) ).

fof(f_4175_3,plain,
    ! [U_16864,U_16863] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16863,tc_HOL_Obool),U_16864) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16863,tc_HOL_Obool),tc_fun(U_16863,tc_HOL_Obool)),U_16864),c_COMBI(tc_fun(U_16863,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4175_2]) ).

cnf(f_4175_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16863,tc_HOL_Obool),U_16864) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16863,tc_HOL_Obool),tc_fun(U_16863,tc_HOL_Obool)),U_16864),c_COMBI(tc_fun(U_16863,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4175_3]) ).

fof(f_4176_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
      | ? [B_M] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Union]) ).

fof(f_4176_2,plain,
    ! [U_16867,U_16866] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16866,tc_HOL_Obool),U_16867)))
      | ? [U_16865] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),U_16865))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16866,tc_HOL_Obool)),U_16865),U_16867)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16866,tc_HOL_Obool)),U_16867)) ),
    inference(variable_rename,[status(thm)],[f_4176_1]) ).

fof(f_4176_3,plain,
    ! [U_16867,U_16866] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16866,tc_HOL_Obool),U_16867)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),sK408(U_16867,U_16866)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16866,tc_HOL_Obool)),sK408(U_16867,U_16866)),U_16867)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16866,tc_HOL_Obool)),U_16867)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_16865,sK408(U_16867,U_16866))],[f_4176_2]) ).

fof(f_4176_4,plain,
    ( ! [U_16866,U_16867] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),sK408(U_16867,U_16866)))
        | ~ sP1077(U_16866,U_16867) )
    & ! [U_16866,U_16867] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16866,tc_HOL_Obool)),sK408(U_16867,U_16866)),U_16867))
        | ~ sP1077(U_16866,U_16867) )
    & ! [U_16866,U_16867] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16866,tc_HOL_Obool),U_16867)))
        | sP1077(U_16866,U_16867)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16866,tc_HOL_Obool)),U_16867)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1077])],[f_4176_3]) ).

cnf(f_4176_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16866,tc_HOL_Obool),U_16867)))
    | sP1077(U_16866,U_16867)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16866,tc_HOL_Obool)),U_16867)) ),
    inference(clausify,[status(thm)],[f_4176_4]) ).

cnf(f_4176_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16866,tc_HOL_Obool)),sK408(U_16867,U_16866)),U_16867))
    | ~ sP1077(U_16866,U_16867) ),
    inference(clausify,[status(thm)],[f_4176_4]) ).

cnf(f_4176_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16866),sK408(U_16867,U_16866)))
    | ~ sP1077(U_16866,U_16867) ),
    inference(clausify,[status(thm)],[f_4176_4]) ).

fof(f_4177_1,plain,
    ! [V_F_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ? [B_x] :
          ( ? [B_xa] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & B_x != B_xa
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__partition]) ).

fof(f_4177_2,plain,
    ! [U_16872,U_16871,U_16870] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),U_16871),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16870,tc_HOL_Obool),U_16872)) = c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
      | ? [U_16869] :
          ( ? [U_16868] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),U_16869),U_16868) != c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
              & U_16869 != U_16868
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16868),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16869),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)) ),
    inference(variable_rename,[status(thm)],[f_4177_1]) ).

fof(f_4177_3,plain,
    ! [U_16872,U_16871,U_16870] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),U_16871),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16870,tc_HOL_Obool),U_16872)) = c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
      | ( ? [U_16868] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),U_16868) != c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
            & sK409(U_16872,U_16871,U_16870) != U_16868
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16868),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872))) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_16869,sK409(U_16872,U_16871,U_16870))],[f_4177_2]) ).

fof(f_4177_4,plain,
    ! [U_16872,U_16871,U_16870] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),U_16871),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16870,tc_HOL_Obool),U_16872)) = c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),sK410(U_16872,U_16871,U_16870)) != c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
        & sK409(U_16872,U_16871,U_16870) != sK410(U_16872,U_16871,U_16870)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK410(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_16868,sK410(U_16872,U_16871,U_16870))],[f_4177_3]) ).

fof(f_4177_5,plain,
    ( ! [U_16870,U_16871,U_16872] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),sK410(U_16872,U_16871,U_16870)) != c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
        | ~ sP1078(U_16870,U_16871,U_16872) )
    & ! [U_16870,U_16871,U_16872] :
        ( sK409(U_16872,U_16871,U_16870) != sK410(U_16872,U_16871,U_16870)
        | ~ sP1078(U_16870,U_16871,U_16872) )
    & ! [U_16870,U_16871,U_16872] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK410(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)))
        | ~ sP1078(U_16870,U_16871,U_16872) )
    & ! [U_16870,U_16871,U_16872] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)))
        | ~ sP1078(U_16870,U_16871,U_16872) )
    & ! [U_16870,U_16871,U_16872] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),U_16871),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16870,tc_HOL_Obool),U_16872)) = c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
        | sP1078(U_16870,U_16871,U_16872)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1078])],[f_4177_4]) ).

cnf(f_4177_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),U_16871),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16870,tc_HOL_Obool),U_16872)) = c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
    | sP1078(U_16870,U_16871,U_16872)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)) ),
    inference(clausify,[status(thm)],[f_4177_5]) ).

cnf(f_4177_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)))
    | ~ sP1078(U_16870,U_16871,U_16872) ),
    inference(clausify,[status(thm)],[f_4177_5]) ).

cnf(f_4177_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16870,tc_HOL_Obool)),sK410(U_16872,U_16871,U_16870)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16870,tc_HOL_Obool)),U_16871),U_16872)))
    | ~ sP1078(U_16870,U_16871,U_16872) ),
    inference(clausify,[status(thm)],[f_4177_5]) ).

cnf(f_4177_9,plain,
    ( sK409(U_16872,U_16871,U_16870) != sK410(U_16872,U_16871,U_16870)
    | ~ sP1078(U_16870,U_16871,U_16872) ),
    inference(clausify,[status(thm)],[f_4177_5]) ).

cnf(f_4177_10,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16870,tc_HOL_Obool)),sK409(U_16872,U_16871,U_16870)),sK410(U_16872,U_16871,U_16870)) != c_Orderings_Obot__class_Obot(tc_fun(U_16870,tc_HOL_Obool))
    | ~ sP1078(U_16870,U_16871,U_16872) ),
    inference(clausify,[status(thm)],[f_4177_5]) ).

fof(f_4178_1,plain,
    ! [V_k_2,V_C_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))
      | ? [B_c1] :
          ( ? [B_c2] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & B_c1 != B_c2
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) )
      | ? [B_c] :
          ( hAPP(c_Finite__Set_Ocard(T_b),B_c) != V_k_2
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__partition]) ).

fof(f_4178_2,plain,
    ! [U_16878,U_16877,U_16876] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16878),hAPP(c_Finite__Set_Ocard(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) = hAPP(c_Finite__Set_Ocard(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877))
      | ? [U_16875] :
          ( ? [U_16874] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16876,tc_HOL_Obool)),U_16875),U_16874) != c_Orderings_Obot__class_Obot(tc_fun(U_16876,tc_HOL_Obool))
              & U_16875 != U_16874
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),U_16874),U_16877)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),U_16875),U_16877)) )
      | ? [U_16873] :
          ( hAPP(c_Finite__Set_Ocard(U_16876),U_16873) != U_16878
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),U_16873),U_16877)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) ),
    inference(variable_rename,[status(thm)],[f_4178_1]) ).

fof(f_4178_3,plain,
    ! [U_16878,U_16877,U_16876] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16878),hAPP(c_Finite__Set_Ocard(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) = hAPP(c_Finite__Set_Ocard(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877))
      | ? [U_16875] :
          ( ? [U_16874] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16876,tc_HOL_Obool)),U_16875),U_16874) != c_Orderings_Obot__class_Obot(tc_fun(U_16876,tc_HOL_Obool))
              & U_16875 != U_16874
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),U_16874),U_16877)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),U_16875),U_16877)) )
      | ( hAPP(c_Finite__Set_Ocard(U_16876),sK411(U_16878,U_16877,U_16876)) != U_16878
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK411(U_16878,U_16877,U_16876)),U_16877)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_16873,sK411(U_16878,U_16877,U_16876))],[f_4178_2]) ).

fof(f_4178_4,plain,
    ! [U_16878,U_16877,U_16876] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16878),hAPP(c_Finite__Set_Ocard(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) = hAPP(c_Finite__Set_Ocard(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877))
      | ( ? [U_16874] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),U_16874) != c_Orderings_Obot__class_Obot(tc_fun(U_16876,tc_HOL_Obool))
            & sK412(U_16878,U_16877,U_16876) != U_16874
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),U_16874),U_16877)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),U_16877)) )
      | ( hAPP(c_Finite__Set_Ocard(U_16876),sK411(U_16878,U_16877,U_16876)) != U_16878
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK411(U_16878,U_16877,U_16876)),U_16877)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_16875,sK412(U_16878,U_16877,U_16876))],[f_4178_3]) ).

fof(f_4178_5,plain,
    ! [U_16878,U_16877,U_16876] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16878),hAPP(c_Finite__Set_Ocard(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) = hAPP(c_Finite__Set_Ocard(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),sK413(U_16878,U_16877,U_16876)) != c_Orderings_Obot__class_Obot(tc_fun(U_16876,tc_HOL_Obool))
        & sK412(U_16878,U_16877,U_16876) != sK413(U_16878,U_16877,U_16876)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK413(U_16878,U_16877,U_16876)),U_16877))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),U_16877)) )
      | ( hAPP(c_Finite__Set_Ocard(U_16876),sK411(U_16878,U_16877,U_16876)) != U_16878
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK411(U_16878,U_16877,U_16876)),U_16877)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_16874,sK413(U_16878,U_16877,U_16876))],[f_4178_4]) ).

fof(f_4178_6,plain,
    ( ! [U_16876,U_16877,U_16878] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),sK413(U_16878,U_16877,U_16876)) != c_Orderings_Obot__class_Obot(tc_fun(U_16876,tc_HOL_Obool))
        | ~ sP1080(U_16876,U_16877,U_16878) )
    & ! [U_16876,U_16877,U_16878] :
        ( sK412(U_16878,U_16877,U_16876) != sK413(U_16878,U_16877,U_16876)
        | ~ sP1080(U_16876,U_16877,U_16878) )
    & ! [U_16876,U_16877,U_16878] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK413(U_16878,U_16877,U_16876)),U_16877))
        | ~ sP1080(U_16876,U_16877,U_16878) )
    & ! [U_16876,U_16877,U_16878] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),U_16877))
        | ~ sP1080(U_16876,U_16877,U_16878) )
    & ! [U_16876,U_16877,U_16878] :
        ( hAPP(c_Finite__Set_Ocard(U_16876),sK411(U_16878,U_16877,U_16876)) != U_16878
        | ~ sP1079(U_16876,U_16877,U_16878) )
    & ! [U_16876,U_16877,U_16878] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK411(U_16878,U_16877,U_16876)),U_16877))
        | ~ sP1079(U_16876,U_16877,U_16878) )
    & ! [U_16876,U_16877,U_16878] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16878),hAPP(c_Finite__Set_Ocard(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) = hAPP(c_Finite__Set_Ocard(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877))
        | sP1080(U_16876,U_16877,U_16878)
        | sP1079(U_16876,U_16877,U_16878)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1079,sP1080])],[f_4178_5]) ).

cnf(f_4178_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16878),hAPP(c_Finite__Set_Ocard(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) = hAPP(c_Finite__Set_Ocard(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877))
    | sP1080(U_16876,U_16877,U_16878)
    | sP1079(U_16876,U_16877,U_16878)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16876),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16876,tc_HOL_Obool),U_16877)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16876,tc_HOL_Obool)),U_16877)) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

cnf(f_4178_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK411(U_16878,U_16877,U_16876)),U_16877))
    | ~ sP1079(U_16876,U_16877,U_16878) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

cnf(f_4178_9,plain,
    ( hAPP(c_Finite__Set_Ocard(U_16876),sK411(U_16878,U_16877,U_16876)) != U_16878
    | ~ sP1079(U_16876,U_16877,U_16878) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

cnf(f_4178_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),U_16877))
    | ~ sP1080(U_16876,U_16877,U_16878) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

cnf(f_4178_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16876,tc_HOL_Obool)),sK413(U_16878,U_16877,U_16876)),U_16877))
    | ~ sP1080(U_16876,U_16877,U_16878) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

cnf(f_4178_12,plain,
    ( sK412(U_16878,U_16877,U_16876) != sK413(U_16878,U_16877,U_16876)
    | ~ sP1080(U_16876,U_16877,U_16878) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

cnf(f_4178_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16876,tc_HOL_Obool)),sK412(U_16878,U_16877,U_16876)),sK413(U_16878,U_16877,U_16876)) != c_Orderings_Obot__class_Obot(tc_fun(U_16876,tc_HOL_Obool))
    | ~ sP1080(U_16876,U_16877,U_16878) ),
    inference(clausify,[status(thm)],[f_4178_6]) ).

fof(f_4179_1,plain,
    ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
      ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))
      | ? [B_i] :
          ( ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) )
      | V_I_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__INTER]) ).

fof(f_4179_2,plain,
    ! [U_16885,U_16884,U_16883,U_16882,U_16881,U_16880] :
      ( c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16881,tc_fun(U_16882,tc_HOL_Obool)),U_16880),U_16885))
      | ? [U_16879] :
          ( ~ c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(U_16885,U_16879))
          & hBOOL(hAPP(hAPP(c_member(U_16881),U_16879),U_16880)) )
      | U_16880 = c_Orderings_Obot__class_Obot(tc_fun(U_16881,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4179_1]) ).

fof(f_4179_3,plain,
    ! [U_16885,U_16884,U_16883,U_16882,U_16881,U_16880] :
      ( c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16881,tc_fun(U_16882,tc_HOL_Obool)),U_16880),U_16885))
      | ( ~ c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(U_16885,sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880)))
        & hBOOL(hAPP(hAPP(c_member(U_16881),sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880)),U_16880)) )
      | U_16880 = c_Orderings_Obot__class_Obot(tc_fun(U_16881,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_16879,sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880))],[f_4179_2]) ).

fof(f_4179_4,plain,
    ( ! [U_16882,U_16883,U_16881,U_16885,U_16880,U_16884] :
        ( ~ c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(U_16885,sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880)))
        | ~ sP1081(U_16882,U_16883,U_16881,U_16885,U_16880,U_16884) )
    & ! [U_16882,U_16883,U_16881,U_16885,U_16880,U_16884] :
        ( hBOOL(hAPP(hAPP(c_member(U_16881),sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880)),U_16880))
        | ~ sP1081(U_16882,U_16883,U_16881,U_16885,U_16880,U_16884) )
    & ! [U_16882,U_16883,U_16881,U_16885,U_16880,U_16884] :
        ( c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16881,tc_fun(U_16882,tc_HOL_Obool)),U_16880),U_16885))
        | sP1081(U_16882,U_16883,U_16881,U_16885,U_16880,U_16884)
        | U_16880 = c_Orderings_Obot__class_Obot(tc_fun(U_16881,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1081])],[f_4179_3]) ).

cnf(f_4179_5,plain,
    ( c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16881,tc_fun(U_16882,tc_HOL_Obool)),U_16880),U_16885))
    | sP1081(U_16882,U_16883,U_16881,U_16885,U_16880,U_16884)
    | U_16880 = c_Orderings_Obot__class_Obot(tc_fun(U_16881,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4179_4]) ).

cnf(f_4179_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16881),sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880)),U_16880))
    | ~ sP1081(U_16882,U_16883,U_16881,U_16885,U_16880,U_16884) ),
    inference(clausify,[status(thm)],[f_4179_4]) ).

cnf(f_4179_7,plain,
    ( ~ c_Fun_Oinj__on(U_16882,U_16883,U_16884,hAPP(U_16885,sK414(U_16885,U_16884,U_16883,U_16882,U_16881,U_16880)))
    | ~ sP1081(U_16882,U_16883,U_16881,U_16885,U_16880,U_16884) ),
    inference(clausify,[status(thm)],[f_4179_4]) ).

fof(f_4180_1,plain,
    ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y))
          & V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(f_4180_2,plain,
    ! [U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887] :
      ( ? [U_16886] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,U_16892),U_16886))
          & U_16893 = hAPP(hAPP(U_16889,U_16891),U_16886) )
      | hBOOL(hAPP(hAPP(c_member(U_16887),U_16891),U_16892))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,hAPP(hAPP(c_Set_Oinsert(U_16887),U_16891),U_16892)),U_16893))
      | ~ c_Finite__Set_Ofun__left__comm(U_16887,U_16888,U_16889) ),
    inference(variable_rename,[status(thm)],[f_4180_1]) ).

fof(f_4180_3,plain,
    ! [U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,U_16892),sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887)))
        & U_16893 = hAPP(hAPP(U_16889,U_16891),sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887)) )
      | hBOOL(hAPP(hAPP(c_member(U_16887),U_16891),U_16892))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,hAPP(hAPP(c_Set_Oinsert(U_16887),U_16891),U_16892)),U_16893))
      | ~ c_Finite__Set_Ofun__left__comm(U_16887,U_16888,U_16889) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_16886,sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887))],[f_4180_2]) ).

fof(f_4180_4,plain,
    ( ! [U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,U_16892),sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887)))
        | ~ sP1082(U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889) )
    & ! [U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889] :
        ( U_16893 = hAPP(hAPP(U_16889,U_16891),sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887))
        | ~ sP1082(U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889) )
    & ! [U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889] :
        ( sP1082(U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889)
        | hBOOL(hAPP(hAPP(c_member(U_16887),U_16891),U_16892))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,hAPP(hAPP(c_Set_Oinsert(U_16887),U_16891),U_16892)),U_16893))
        | ~ c_Finite__Set_Ofun__left__comm(U_16887,U_16888,U_16889) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1082])],[f_4180_3]) ).

cnf(f_4180_5,plain,
    ( sP1082(U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889)
    | hBOOL(hAPP(hAPP(c_member(U_16887),U_16891),U_16892))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,hAPP(hAPP(c_Set_Oinsert(U_16887),U_16891),U_16892)),U_16893))
    | ~ c_Finite__Set_Ofun__left__comm(U_16887,U_16888,U_16889) ),
    inference(clausify,[status(thm)],[f_4180_4]) ).

cnf(f_4180_6,plain,
    ( U_16893 = hAPP(hAPP(U_16889,U_16891),sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887))
    | ~ sP1082(U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889) ),
    inference(clausify,[status(thm)],[f_4180_4]) ).

cnf(f_4180_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16887,U_16888,U_16889,U_16890,U_16892),sK415(U_16893,U_16892,U_16891,U_16890,U_16889,U_16888,U_16887)))
    | ~ sP1082(U_16891,U_16892,U_16893,U_16888,U_16887,U_16890,U_16889) ),
    inference(clausify,[status(thm)],[f_4180_4]) ).

fof(f_4181_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acyclicI]) ).

fof(f_4181_2,plain,
    ! [U_16896,U_16895] :
      ( c_Wellfounded_Oacyclic(U_16895,U_16896)
      | ? [U_16894] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16895,U_16895)),hAPP(hAPP(c_Product__Type_OPair(U_16895,U_16895),U_16894),U_16894)),c_Transitive__Closure_Otrancl(U_16895,U_16896))) ),
    inference(variable_rename,[status(thm)],[f_4181_1]) ).

fof(f_4181_3,plain,
    ! [U_16896,U_16895] :
      ( c_Wellfounded_Oacyclic(U_16895,U_16896)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16895,U_16895)),hAPP(hAPP(c_Product__Type_OPair(U_16895,U_16895),sK416(U_16896,U_16895)),sK416(U_16896,U_16895))),c_Transitive__Closure_Otrancl(U_16895,U_16896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_16894,sK416(U_16896,U_16895))],[f_4181_2]) ).

fof(f_4181_4,plain,
    ! [U_16896,U_16895] :
      ( c_Wellfounded_Oacyclic(U_16895,U_16896)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16895,U_16895)),hAPP(hAPP(c_Product__Type_OPair(U_16895,U_16895),sK416(U_16896,U_16895)),sK416(U_16896,U_16895))),c_Transitive__Closure_Otrancl(U_16895,U_16896))) ),
    inference(definitional_conversion,[status(esa)],[f_4181_3]) ).

cnf(f_4181_5,plain,
    ( c_Wellfounded_Oacyclic(U_16895,U_16896)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16895,U_16895)),hAPP(hAPP(c_Product__Type_OPair(U_16895,U_16895),sK416(U_16896,U_16895)),sK416(U_16896,U_16895))),c_Transitive__Closure_Otrancl(U_16895,U_16896))) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

fof(f_4182_1,plain,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
      | ? [B_x] :
          ( ? [B_y] :
              ( B_x != B_y
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).

fof(f_4182_2,plain,
    ! [U_16903,U_16902,U_16901,U_16900,U_16899] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
      | ? [U_16898] :
          ( ? [U_16897] :
              ( U_16898 != U_16897
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16898),U_16897)),U_16903)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16898)),c_Transitive__Closure_Ortrancl(U_16899,U_16902))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16899,U_16899),tc_HOL_Obool)),U_16902),U_16903)))) ),
    inference(variable_rename,[status(thm)],[f_4182_1]) ).

fof(f_4182_3,plain,
    ! [U_16903,U_16902,U_16901,U_16900,U_16899] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
      | ( ? [U_16897] :
            ( sK417(U_16903,U_16902,U_16901,U_16900,U_16899) != U_16897
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),sK417(U_16903,U_16902,U_16901,U_16900,U_16899)),U_16897)),U_16903)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),sK417(U_16903,U_16902,U_16901,U_16900,U_16899))),c_Transitive__Closure_Ortrancl(U_16899,U_16902))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16899,U_16899),tc_HOL_Obool)),U_16902),U_16903)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_16898,sK417(U_16903,U_16902,U_16901,U_16900,U_16899))],[f_4182_2]) ).

fof(f_4182_4,plain,
    ! [U_16903,U_16902,U_16901,U_16900,U_16899] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
      | ( sK417(U_16903,U_16902,U_16901,U_16900,U_16899) != sK418(U_16903,U_16902,U_16901,U_16900,U_16899)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),sK417(U_16903,U_16902,U_16901,U_16900,U_16899)),sK418(U_16903,U_16902,U_16901,U_16900,U_16899))),U_16903))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),sK417(U_16903,U_16902,U_16901,U_16900,U_16899))),c_Transitive__Closure_Ortrancl(U_16899,U_16902))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16899,U_16899),tc_HOL_Obool)),U_16902),U_16903)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_16897,sK418(U_16903,U_16902,U_16901,U_16900,U_16899))],[f_4182_3]) ).

fof(f_4182_5,plain,
    ( ! [U_16899,U_16900,U_16901,U_16902,U_16903] :
        ( sK417(U_16903,U_16902,U_16901,U_16900,U_16899) != sK418(U_16903,U_16902,U_16901,U_16900,U_16899)
        | ~ sP1083(U_16899,U_16900,U_16901,U_16902,U_16903) )
    & ! [U_16899,U_16900,U_16901,U_16902,U_16903] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),sK417(U_16903,U_16902,U_16901,U_16900,U_16899)),sK418(U_16903,U_16902,U_16901,U_16900,U_16899))),U_16903))
        | ~ sP1083(U_16899,U_16900,U_16901,U_16902,U_16903) )
    & ! [U_16899,U_16900,U_16901,U_16902,U_16903] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),sK417(U_16903,U_16902,U_16901,U_16900,U_16899))),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
        | ~ sP1083(U_16899,U_16900,U_16901,U_16902,U_16903) )
    & ! [U_16899,U_16900,U_16901,U_16902,U_16903] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
        | sP1083(U_16899,U_16900,U_16901,U_16902,U_16903)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16899,U_16899),tc_HOL_Obool)),U_16902),U_16903)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1083])],[f_4182_4]) ).

cnf(f_4182_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
    | sP1083(U_16899,U_16900,U_16901,U_16902,U_16903)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),U_16901)),c_Transitive__Closure_Ortrancl(U_16899,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16899,U_16899),tc_HOL_Obool)),U_16902),U_16903)))) ),
    inference(clausify,[status(thm)],[f_4182_5]) ).

cnf(f_4182_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),U_16900),sK417(U_16903,U_16902,U_16901,U_16900,U_16899))),c_Transitive__Closure_Ortrancl(U_16899,U_16902)))
    | ~ sP1083(U_16899,U_16900,U_16901,U_16902,U_16903) ),
    inference(clausify,[status(thm)],[f_4182_5]) ).

cnf(f_4182_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16899,U_16899)),hAPP(hAPP(c_Product__Type_OPair(U_16899,U_16899),sK417(U_16903,U_16902,U_16901,U_16900,U_16899)),sK418(U_16903,U_16902,U_16901,U_16900,U_16899))),U_16903))
    | ~ sP1083(U_16899,U_16900,U_16901,U_16902,U_16903) ),
    inference(clausify,[status(thm)],[f_4182_5]) ).

cnf(f_4182_9,plain,
    ( sK417(U_16903,U_16902,U_16901,U_16900,U_16899) != sK418(U_16903,U_16902,U_16901,U_16900,U_16899)
    | ~ sP1083(U_16899,U_16900,U_16901,U_16902,U_16903) ),
    inference(clausify,[status(thm)],[f_4182_5]) ).

fof(f_4183_1,plain,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
      | ? [B_x] :
          ( ? [B_y] :
              ( B_y != B_x
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).

fof(f_4183_2,plain,
    ! [U_16910,U_16909,U_16908,U_16907,U_16906] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
      | ? [U_16905] :
          ( ? [U_16904] :
              ( U_16904 != U_16905
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16904),U_16905)),U_16910)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16905),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16906,U_16906),tc_HOL_Obool)),U_16909),U_16910)))) ),
    inference(variable_rename,[status(thm)],[f_4183_1]) ).

fof(f_4183_3,plain,
    ! [U_16910,U_16909,U_16908,U_16907,U_16906] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
      | ( ? [U_16904] :
            ( U_16904 != sK419(U_16910,U_16909,U_16908,U_16907,U_16906)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16904),sK419(U_16910,U_16909,U_16908,U_16907,U_16906))),U_16910)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK419(U_16910,U_16909,U_16908,U_16907,U_16906)),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16906,U_16906),tc_HOL_Obool)),U_16909),U_16910)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_16905,sK419(U_16910,U_16909,U_16908,U_16907,U_16906))],[f_4183_2]) ).

fof(f_4183_4,plain,
    ! [U_16910,U_16909,U_16908,U_16907,U_16906] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
      | ( sK420(U_16910,U_16909,U_16908,U_16907,U_16906) != sK419(U_16910,U_16909,U_16908,U_16907,U_16906)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK420(U_16910,U_16909,U_16908,U_16907,U_16906)),sK419(U_16910,U_16909,U_16908,U_16907,U_16906))),U_16910))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK419(U_16910,U_16909,U_16908,U_16907,U_16906)),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16906,U_16906),tc_HOL_Obool)),U_16909),U_16910)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_16904,sK420(U_16910,U_16909,U_16908,U_16907,U_16906))],[f_4183_3]) ).

fof(f_4183_5,plain,
    ( ! [U_16908,U_16907,U_16906,U_16909,U_16910] :
        ( sK420(U_16910,U_16909,U_16908,U_16907,U_16906) != sK419(U_16910,U_16909,U_16908,U_16907,U_16906)
        | ~ sP1084(U_16908,U_16907,U_16906,U_16909,U_16910) )
    & ! [U_16908,U_16907,U_16906,U_16909,U_16910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK420(U_16910,U_16909,U_16908,U_16907,U_16906)),sK419(U_16910,U_16909,U_16908,U_16907,U_16906))),U_16910))
        | ~ sP1084(U_16908,U_16907,U_16906,U_16909,U_16910) )
    & ! [U_16908,U_16907,U_16906,U_16909,U_16910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK419(U_16910,U_16909,U_16908,U_16907,U_16906)),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
        | ~ sP1084(U_16908,U_16907,U_16906,U_16909,U_16910) )
    & ! [U_16908,U_16907,U_16906,U_16909,U_16910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
        | sP1084(U_16908,U_16907,U_16906,U_16909,U_16910)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16906,U_16906),tc_HOL_Obool)),U_16909),U_16910)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1084])],[f_4183_4]) ).

cnf(f_4183_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
    | sP1084(U_16908,U_16907,U_16906,U_16909,U_16910)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),U_16907),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16906,U_16906),tc_HOL_Obool)),U_16909),U_16910)))) ),
    inference(clausify,[status(thm)],[f_4183_5]) ).

cnf(f_4183_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK419(U_16910,U_16909,U_16908,U_16907,U_16906)),U_16908)),c_Transitive__Closure_Ortrancl(U_16906,U_16909)))
    | ~ sP1084(U_16908,U_16907,U_16906,U_16909,U_16910) ),
    inference(clausify,[status(thm)],[f_4183_5]) ).

cnf(f_4183_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16906,U_16906)),hAPP(hAPP(c_Product__Type_OPair(U_16906,U_16906),sK420(U_16910,U_16909,U_16908,U_16907,U_16906)),sK419(U_16910,U_16909,U_16908,U_16907,U_16906))),U_16910))
    | ~ sP1084(U_16908,U_16907,U_16906,U_16909,U_16910) ),
    inference(clausify,[status(thm)],[f_4183_5]) ).

cnf(f_4183_9,plain,
    ( sK420(U_16910,U_16909,U_16908,U_16907,U_16906) != sK419(U_16910,U_16909,U_16908,U_16907,U_16906)
    | ~ sP1084(U_16908,U_16907,U_16906,U_16909,U_16910) ),
    inference(clausify,[status(thm)],[f_4183_5]) ).

fof(f_4184_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__E]) ).

fof(f_4184_2,plain,
    ! [U_16916,U_16915,U_16914,U_16913,U_16912] :
      ( ? [U_16911] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16911),U_16914)),U_16916))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),U_16911)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),U_16915),U_16916))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16915)),U_16916))) ),
    inference(variable_rename,[status(thm)],[f_4184_1]) ).

fof(f_4184_3,plain,
    ! [U_16916,U_16915,U_16914,U_16913,U_16912] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),sK421(U_16916,U_16915,U_16914,U_16913,U_16912)),U_16914)),U_16916))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),sK421(U_16916,U_16915,U_16914,U_16913,U_16912))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),U_16915),U_16916))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16915)),U_16916))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_16911,sK421(U_16916,U_16915,U_16914,U_16913,U_16912))],[f_4184_2]) ).

fof(f_4184_4,plain,
    ( ! [U_16912,U_16913,U_16914,U_16915,U_16916] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),sK421(U_16916,U_16915,U_16914,U_16913,U_16912)),U_16914)),U_16916))
        | ~ sP1085(U_16912,U_16913,U_16914,U_16915,U_16916) )
    & ! [U_16912,U_16913,U_16914,U_16915,U_16916] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),sK421(U_16916,U_16915,U_16914,U_16913,U_16912))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),U_16915),U_16916)))
        | ~ sP1085(U_16912,U_16913,U_16914,U_16915,U_16916) )
    & ! [U_16912,U_16913,U_16914,U_16915,U_16916] :
        ( sP1085(U_16912,U_16913,U_16914,U_16915,U_16916)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16915)),U_16916))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1085])],[f_4184_3]) ).

cnf(f_4184_5,plain,
    ( sP1085(U_16912,U_16913,U_16914,U_16915,U_16916)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16915)),U_16916))) ),
    inference(clausify,[status(thm)],[f_4184_4]) ).

cnf(f_4184_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),U_16913),sK421(U_16916,U_16915,U_16914,U_16913,U_16912))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16912,U_16912),tc_HOL_Obool),U_16915),U_16916)))
    | ~ sP1085(U_16912,U_16913,U_16914,U_16915,U_16916) ),
    inference(clausify,[status(thm)],[f_4184_4]) ).

cnf(f_4184_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16912,U_16912)),hAPP(hAPP(c_Product__Type_OPair(U_16912,U_16912),sK421(U_16916,U_16915,U_16914,U_16913,U_16912)),U_16914)),U_16916))
    | ~ sP1085(U_16912,U_16913,U_16914,U_16915,U_16916) ),
    inference(clausify,[status(thm)],[f_4184_4]) ).

fof(f_4185_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__E2]) ).

fof(f_4185_2,plain,
    ! [U_16922,U_16921,U_16920,U_16919,U_16918] :
      ( ? [U_16917] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16917),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16921),U_16922)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),U_16917)),U_16922)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16921)),U_16922))) ),
    inference(variable_rename,[status(thm)],[f_4185_1]) ).

fof(f_4185_3,plain,
    ! [U_16922,U_16921,U_16920,U_16919,U_16918] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),sK422(U_16922,U_16921,U_16920,U_16919,U_16918)),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16921),U_16922)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),sK422(U_16922,U_16921,U_16920,U_16919,U_16918))),U_16922)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16921)),U_16922))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_16917,sK422(U_16922,U_16921,U_16920,U_16919,U_16918))],[f_4185_2]) ).

fof(f_4185_4,plain,
    ( ! [U_16918,U_16919,U_16920,U_16921,U_16922] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),sK422(U_16922,U_16921,U_16920,U_16919,U_16918)),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16921),U_16922)))
        | ~ sP1086(U_16918,U_16919,U_16920,U_16921,U_16922) )
    & ! [U_16918,U_16919,U_16920,U_16921,U_16922] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),sK422(U_16922,U_16921,U_16920,U_16919,U_16918))),U_16922))
        | ~ sP1086(U_16918,U_16919,U_16920,U_16921,U_16922) )
    & ! [U_16918,U_16919,U_16920,U_16921,U_16922] :
        ( sP1086(U_16918,U_16919,U_16920,U_16921,U_16922)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16921)),U_16922))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1086])],[f_4185_3]) ).

cnf(f_4185_5,plain,
    ( sP1086(U_16918,U_16919,U_16920,U_16921,U_16922)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16921)),U_16922))) ),
    inference(clausify,[status(thm)],[f_4185_4]) ).

cnf(f_4185_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),U_16919),sK422(U_16922,U_16921,U_16920,U_16919,U_16918))),U_16922))
    | ~ sP1086(U_16918,U_16919,U_16920,U_16921,U_16922) ),
    inference(clausify,[status(thm)],[f_4185_4]) ).

cnf(f_4185_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16918,U_16918)),hAPP(hAPP(c_Product__Type_OPair(U_16918,U_16918),sK422(U_16922,U_16921,U_16920,U_16919,U_16918)),U_16920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16921),U_16922)))
    | ~ sP1086(U_16918,U_16919,U_16920,U_16921,U_16922) ),
    inference(clausify,[status(thm)],[f_4185_4]) ).

fof(f_4186_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__D2]) ).

fof(f_4186_2,plain,
    ! [U_16928,U_16927,U_16926,U_16925,U_16924] :
      ( ? [U_16923] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16923),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),U_16927),U_16928)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),U_16923)),U_16928)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16927)),U_16928))) ),
    inference(variable_rename,[status(thm)],[f_4186_1]) ).

fof(f_4186_3,plain,
    ! [U_16928,U_16927,U_16926,U_16925,U_16924] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),sK423(U_16928,U_16927,U_16926,U_16925,U_16924)),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),U_16927),U_16928)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),sK423(U_16928,U_16927,U_16926,U_16925,U_16924))),U_16928)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16927)),U_16928))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_16923,sK423(U_16928,U_16927,U_16926,U_16925,U_16924))],[f_4186_2]) ).

fof(f_4186_4,plain,
    ( ! [U_16924,U_16925,U_16926,U_16927,U_16928] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),sK423(U_16928,U_16927,U_16926,U_16925,U_16924)),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),U_16927),U_16928)))
        | ~ sP1087(U_16924,U_16925,U_16926,U_16927,U_16928) )
    & ! [U_16924,U_16925,U_16926,U_16927,U_16928] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),sK423(U_16928,U_16927,U_16926,U_16925,U_16924))),U_16928))
        | ~ sP1087(U_16924,U_16925,U_16926,U_16927,U_16928) )
    & ! [U_16924,U_16925,U_16926,U_16927,U_16928] :
        ( sP1087(U_16924,U_16925,U_16926,U_16927,U_16928)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16927)),U_16928))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1087])],[f_4186_3]) ).

cnf(f_4186_5,plain,
    ( sP1087(U_16924,U_16925,U_16926,U_16927,U_16928)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16927)),U_16928))) ),
    inference(clausify,[status(thm)],[f_4186_4]) ).

cnf(f_4186_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),U_16925),sK423(U_16928,U_16927,U_16926,U_16925,U_16924))),U_16928))
    | ~ sP1087(U_16924,U_16925,U_16926,U_16927,U_16928) ),
    inference(clausify,[status(thm)],[f_4186_4]) ).

cnf(f_4186_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16924,U_16924)),hAPP(hAPP(c_Product__Type_OPair(U_16924,U_16924),sK423(U_16928,U_16927,U_16926,U_16925,U_16924)),U_16926)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16924,U_16924),tc_HOL_Obool),U_16927),U_16928)))
    | ~ sP1087(U_16924,U_16925,U_16926,U_16927,U_16928) ),
    inference(clausify,[status(thm)],[f_4186_4]) ).

fof(f_4187_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_tranclD2]) ).

fof(f_4187_2,plain,
    ! [U_16933,U_16932,U_16931,U_16930] :
      ( ? [U_16929] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16929),U_16932)),U_16933))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),U_16929)),c_Transitive__Closure_Ortrancl(U_16930,U_16933))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),U_16932)),c_Transitive__Closure_Otrancl(U_16930,U_16933))) ),
    inference(variable_rename,[status(thm)],[f_4187_1]) ).

fof(f_4187_3,plain,
    ! [U_16933,U_16932,U_16931,U_16930] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),sK424(U_16933,U_16932,U_16931,U_16930)),U_16932)),U_16933))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),sK424(U_16933,U_16932,U_16931,U_16930))),c_Transitive__Closure_Ortrancl(U_16930,U_16933))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),U_16932)),c_Transitive__Closure_Otrancl(U_16930,U_16933))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_16929,sK424(U_16933,U_16932,U_16931,U_16930))],[f_4187_2]) ).

fof(f_4187_4,plain,
    ( ! [U_16930,U_16931,U_16932,U_16933] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),sK424(U_16933,U_16932,U_16931,U_16930)),U_16932)),U_16933))
        | ~ sP1088(U_16930,U_16931,U_16932,U_16933) )
    & ! [U_16930,U_16931,U_16932,U_16933] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),sK424(U_16933,U_16932,U_16931,U_16930))),c_Transitive__Closure_Ortrancl(U_16930,U_16933)))
        | ~ sP1088(U_16930,U_16931,U_16932,U_16933) )
    & ! [U_16930,U_16931,U_16932,U_16933] :
        ( sP1088(U_16930,U_16931,U_16932,U_16933)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),U_16932)),c_Transitive__Closure_Otrancl(U_16930,U_16933))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1088])],[f_4187_3]) ).

cnf(f_4187_5,plain,
    ( sP1088(U_16930,U_16931,U_16932,U_16933)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),U_16932)),c_Transitive__Closure_Otrancl(U_16930,U_16933))) ),
    inference(clausify,[status(thm)],[f_4187_4]) ).

cnf(f_4187_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),U_16931),sK424(U_16933,U_16932,U_16931,U_16930))),c_Transitive__Closure_Ortrancl(U_16930,U_16933)))
    | ~ sP1088(U_16930,U_16931,U_16932,U_16933) ),
    inference(clausify,[status(thm)],[f_4187_4]) ).

cnf(f_4187_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16930,U_16930)),hAPP(hAPP(c_Product__Type_OPair(U_16930,U_16930),sK424(U_16933,U_16932,U_16931,U_16930)),U_16932)),U_16933))
    | ~ sP1088(U_16930,U_16931,U_16932,U_16933) ),
    inference(clausify,[status(thm)],[f_4187_4]) ).

fof(f_4188_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_tranclD]) ).

fof(f_4188_2,plain,
    ! [U_16938,U_16937,U_16936,U_16935] :
      ( ? [U_16934] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16934),U_16937)),c_Transitive__Closure_Ortrancl(U_16935,U_16938)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),U_16934)),U_16938)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),U_16937)),c_Transitive__Closure_Otrancl(U_16935,U_16938))) ),
    inference(variable_rename,[status(thm)],[f_4188_1]) ).

fof(f_4188_3,plain,
    ! [U_16938,U_16937,U_16936,U_16935] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),sK425(U_16938,U_16937,U_16936,U_16935)),U_16937)),c_Transitive__Closure_Ortrancl(U_16935,U_16938)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),sK425(U_16938,U_16937,U_16936,U_16935))),U_16938)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),U_16937)),c_Transitive__Closure_Otrancl(U_16935,U_16938))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_16934,sK425(U_16938,U_16937,U_16936,U_16935))],[f_4188_2]) ).

fof(f_4188_4,plain,
    ( ! [U_16935,U_16936,U_16937,U_16938] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),sK425(U_16938,U_16937,U_16936,U_16935)),U_16937)),c_Transitive__Closure_Ortrancl(U_16935,U_16938)))
        | ~ sP1089(U_16935,U_16936,U_16937,U_16938) )
    & ! [U_16935,U_16936,U_16937,U_16938] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),sK425(U_16938,U_16937,U_16936,U_16935))),U_16938))
        | ~ sP1089(U_16935,U_16936,U_16937,U_16938) )
    & ! [U_16935,U_16936,U_16937,U_16938] :
        ( sP1089(U_16935,U_16936,U_16937,U_16938)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),U_16937)),c_Transitive__Closure_Otrancl(U_16935,U_16938))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1089])],[f_4188_3]) ).

cnf(f_4188_5,plain,
    ( sP1089(U_16935,U_16936,U_16937,U_16938)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),U_16937)),c_Transitive__Closure_Otrancl(U_16935,U_16938))) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

cnf(f_4188_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),U_16936),sK425(U_16938,U_16937,U_16936,U_16935))),U_16938))
    | ~ sP1089(U_16935,U_16936,U_16937,U_16938) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

cnf(f_4188_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16935,U_16935)),hAPP(hAPP(c_Product__Type_OPair(U_16935,U_16935),sK425(U_16938,U_16937,U_16936,U_16935)),U_16937)),c_Transitive__Closure_Ortrancl(U_16935,U_16938)))
    | ~ sP1089(U_16935,U_16936,U_16937,U_16938) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

fof(f_4189_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).

fof(f_4189_2,plain,
    ! [U_16943,U_16942,U_16941,U_16940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),hAPP(hAPP(c_Finite__Set_Ofold(U_16940,U_16940,c_Orderings_Oord__class_Omax(U_16940)),U_16943),U_16941)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16940),U_16942),U_16943)))
      | ? [U_16939] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),U_16939),U_16942))
          & hBOOL(hAPP(hAPP(c_member(U_16940),U_16939),U_16941)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16940),U_16941))
      | ~ class_Orderings_Olinorder(U_16940) ),
    inference(variable_rename,[status(thm)],[f_4189_1]) ).

fof(f_4189_3,plain,
    ! [U_16943,U_16942,U_16941,U_16940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),hAPP(hAPP(c_Finite__Set_Ofold(U_16940,U_16940,c_Orderings_Oord__class_Omax(U_16940)),U_16943),U_16941)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16940),U_16942),U_16943)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),sK426(U_16943,U_16942,U_16941,U_16940)),U_16942))
        & hBOOL(hAPP(hAPP(c_member(U_16940),sK426(U_16943,U_16942,U_16941,U_16940)),U_16941)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16940),U_16941))
      | ~ class_Orderings_Olinorder(U_16940) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_16939,sK426(U_16943,U_16942,U_16941,U_16940))],[f_4189_2]) ).

fof(f_4189_4,plain,
    ( ! [U_16940,U_16941,U_16942,U_16943] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),sK426(U_16943,U_16942,U_16941,U_16940)),U_16942))
        | ~ sP1090(U_16940,U_16941,U_16942,U_16943) )
    & ! [U_16940,U_16941,U_16942,U_16943] :
        ( hBOOL(hAPP(hAPP(c_member(U_16940),sK426(U_16943,U_16942,U_16941,U_16940)),U_16941))
        | ~ sP1090(U_16940,U_16941,U_16942,U_16943) )
    & ! [U_16940,U_16941,U_16942,U_16943] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),hAPP(hAPP(c_Finite__Set_Ofold(U_16940,U_16940,c_Orderings_Oord__class_Omax(U_16940)),U_16943),U_16941)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16940),U_16942),U_16943)))
        | sP1090(U_16940,U_16941,U_16942,U_16943)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16940),U_16941))
        | ~ class_Orderings_Olinorder(U_16940) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1090])],[f_4189_3]) ).

cnf(f_4189_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),hAPP(hAPP(c_Finite__Set_Ofold(U_16940,U_16940,c_Orderings_Oord__class_Omax(U_16940)),U_16943),U_16941)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16940),U_16942),U_16943)))
    | sP1090(U_16940,U_16941,U_16942,U_16943)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16940),U_16941))
    | ~ class_Orderings_Olinorder(U_16940) ),
    inference(clausify,[status(thm)],[f_4189_4]) ).

cnf(f_4189_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16940),sK426(U_16943,U_16942,U_16941,U_16940)),U_16941))
    | ~ sP1090(U_16940,U_16941,U_16942,U_16943) ),
    inference(clausify,[status(thm)],[f_4189_4]) ).

cnf(f_4189_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16940),sK426(U_16943,U_16942,U_16941,U_16940)),U_16942))
    | ~ sP1090(U_16940,U_16941,U_16942,U_16943) ),
    inference(clausify,[status(thm)],[f_4189_4]) ).

fof(f_4190_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).

fof(f_4190_2,plain,
    ! [U_16948,U_16947,U_16946,U_16945] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16945),U_16947),U_16948)),hAPP(hAPP(c_Finite__Set_Ofold(U_16945,U_16945,c_Orderings_Oord__class_Omin(U_16945)),U_16948),U_16946)))
      | ? [U_16944] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),U_16947),U_16944))
          & hBOOL(hAPP(hAPP(c_member(U_16945),U_16944),U_16946)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16945),U_16946))
      | ~ class_Orderings_Olinorder(U_16945) ),
    inference(variable_rename,[status(thm)],[f_4190_1]) ).

fof(f_4190_3,plain,
    ! [U_16948,U_16947,U_16946,U_16945] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16945),U_16947),U_16948)),hAPP(hAPP(c_Finite__Set_Ofold(U_16945,U_16945,c_Orderings_Oord__class_Omin(U_16945)),U_16948),U_16946)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),U_16947),sK427(U_16948,U_16947,U_16946,U_16945)))
        & hBOOL(hAPP(hAPP(c_member(U_16945),sK427(U_16948,U_16947,U_16946,U_16945)),U_16946)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16945),U_16946))
      | ~ class_Orderings_Olinorder(U_16945) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_16944,sK427(U_16948,U_16947,U_16946,U_16945))],[f_4190_2]) ).

fof(f_4190_4,plain,
    ( ! [U_16945,U_16946,U_16947,U_16948] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),U_16947),sK427(U_16948,U_16947,U_16946,U_16945)))
        | ~ sP1091(U_16945,U_16946,U_16947,U_16948) )
    & ! [U_16945,U_16946,U_16947,U_16948] :
        ( hBOOL(hAPP(hAPP(c_member(U_16945),sK427(U_16948,U_16947,U_16946,U_16945)),U_16946))
        | ~ sP1091(U_16945,U_16946,U_16947,U_16948) )
    & ! [U_16945,U_16946,U_16947,U_16948] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16945),U_16947),U_16948)),hAPP(hAPP(c_Finite__Set_Ofold(U_16945,U_16945,c_Orderings_Oord__class_Omin(U_16945)),U_16948),U_16946)))
        | sP1091(U_16945,U_16946,U_16947,U_16948)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16945),U_16946))
        | ~ class_Orderings_Olinorder(U_16945) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1091])],[f_4190_3]) ).

cnf(f_4190_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16945),U_16947),U_16948)),hAPP(hAPP(c_Finite__Set_Ofold(U_16945,U_16945,c_Orderings_Oord__class_Omin(U_16945)),U_16948),U_16946)))
    | sP1091(U_16945,U_16946,U_16947,U_16948)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16945),U_16946))
    | ~ class_Orderings_Olinorder(U_16945) ),
    inference(clausify,[status(thm)],[f_4190_4]) ).

cnf(f_4190_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16945),sK427(U_16948,U_16947,U_16946,U_16945)),U_16946))
    | ~ sP1091(U_16945,U_16946,U_16947,U_16948) ),
    inference(clausify,[status(thm)],[f_4190_4]) ).

cnf(f_4190_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16945),U_16947),sK427(U_16948,U_16947,U_16946,U_16945)))
    | ~ sP1091(U_16945,U_16946,U_16947,U_16948) ),
    inference(clausify,[status(thm)],[f_4190_4]) ).

fof(f_4191_1,plain,
    ! [V_A_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
      | ? [B_X] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_InterI]) ).

fof(f_4191_2,plain,
    ! [U_16952,U_16951,U_16950] :
      ( hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16950,tc_HOL_Obool),U_16951)))
      | ? [U_16949] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),U_16949))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16950,tc_HOL_Obool)),U_16949),U_16951)) ) ),
    inference(variable_rename,[status(thm)],[f_4191_1]) ).

fof(f_4191_3,plain,
    ! [U_16952,U_16951,U_16950] :
      ( hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16950,tc_HOL_Obool),U_16951)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),sK428(U_16952,U_16951,U_16950)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16950,tc_HOL_Obool)),sK428(U_16952,U_16951,U_16950)),U_16951)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_16949,sK428(U_16952,U_16951,U_16950))],[f_4191_2]) ).

fof(f_4191_4,plain,
    ( ! [U_16951,U_16952,U_16950] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),sK428(U_16952,U_16951,U_16950)))
        | ~ sP1092(U_16951,U_16952,U_16950) )
    & ! [U_16951,U_16952,U_16950] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16950,tc_HOL_Obool)),sK428(U_16952,U_16951,U_16950)),U_16951))
        | ~ sP1092(U_16951,U_16952,U_16950) )
    & ! [U_16951,U_16952,U_16950] :
        ( hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16950,tc_HOL_Obool),U_16951)))
        | sP1092(U_16951,U_16952,U_16950) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1092])],[f_4191_3]) ).

cnf(f_4191_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16950,tc_HOL_Obool),U_16951)))
    | sP1092(U_16951,U_16952,U_16950) ),
    inference(clausify,[status(thm)],[f_4191_4]) ).

cnf(f_4191_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16950,tc_HOL_Obool)),sK428(U_16952,U_16951,U_16950)),U_16951))
    | ~ sP1092(U_16951,U_16952,U_16950) ),
    inference(clausify,[status(thm)],[f_4191_4]) ).

cnf(f_4191_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16950),U_16952),sK428(U_16952,U_16951,U_16950)))
    | ~ sP1092(U_16951,U_16952,U_16950) ),
    inference(clausify,[status(thm)],[f_4191_4]) ).

fof(f_4192_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).

fof(f_4192_2,plain,
    ! [U_16957,U_16956,U_16955,U_16954] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16954),U_16956),U_16957)),hAPP(hAPP(c_Finite__Set_Ofold(U_16954,U_16954,c_Lattices_Osemilattice__inf__class_Oinf(U_16954)),U_16957),U_16955)))
      | ? [U_16953] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),U_16956),U_16953))
          & hBOOL(hAPP(hAPP(c_member(U_16954),U_16953),U_16955)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16954),U_16955))
      | ~ class_Lattices_Osemilattice__inf(U_16954) ),
    inference(variable_rename,[status(thm)],[f_4192_1]) ).

fof(f_4192_3,plain,
    ! [U_16957,U_16956,U_16955,U_16954] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16954),U_16956),U_16957)),hAPP(hAPP(c_Finite__Set_Ofold(U_16954,U_16954,c_Lattices_Osemilattice__inf__class_Oinf(U_16954)),U_16957),U_16955)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),U_16956),sK429(U_16957,U_16956,U_16955,U_16954)))
        & hBOOL(hAPP(hAPP(c_member(U_16954),sK429(U_16957,U_16956,U_16955,U_16954)),U_16955)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16954),U_16955))
      | ~ class_Lattices_Osemilattice__inf(U_16954) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_16953,sK429(U_16957,U_16956,U_16955,U_16954))],[f_4192_2]) ).

fof(f_4192_4,plain,
    ( ! [U_16954,U_16955,U_16956,U_16957] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),U_16956),sK429(U_16957,U_16956,U_16955,U_16954)))
        | ~ sP1093(U_16954,U_16955,U_16956,U_16957) )
    & ! [U_16954,U_16955,U_16956,U_16957] :
        ( hBOOL(hAPP(hAPP(c_member(U_16954),sK429(U_16957,U_16956,U_16955,U_16954)),U_16955))
        | ~ sP1093(U_16954,U_16955,U_16956,U_16957) )
    & ! [U_16954,U_16955,U_16956,U_16957] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16954),U_16956),U_16957)),hAPP(hAPP(c_Finite__Set_Ofold(U_16954,U_16954,c_Lattices_Osemilattice__inf__class_Oinf(U_16954)),U_16957),U_16955)))
        | sP1093(U_16954,U_16955,U_16956,U_16957)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16954),U_16955))
        | ~ class_Lattices_Osemilattice__inf(U_16954) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1093])],[f_4192_3]) ).

cnf(f_4192_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16954),U_16956),U_16957)),hAPP(hAPP(c_Finite__Set_Ofold(U_16954,U_16954,c_Lattices_Osemilattice__inf__class_Oinf(U_16954)),U_16957),U_16955)))
    | sP1093(U_16954,U_16955,U_16956,U_16957)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16954),U_16955))
    | ~ class_Lattices_Osemilattice__inf(U_16954) ),
    inference(clausify,[status(thm)],[f_4192_4]) ).

cnf(f_4192_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16954),sK429(U_16957,U_16956,U_16955,U_16954)),U_16955))
    | ~ sP1093(U_16954,U_16955,U_16956,U_16957) ),
    inference(clausify,[status(thm)],[f_4192_4]) ).

cnf(f_4192_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16954),U_16956),sK429(U_16957,U_16956,U_16955,U_16954)))
    | ~ sP1093(U_16954,U_16955,U_16956,U_16957) ),
    inference(clausify,[status(thm)],[f_4192_4]) ).

fof(f_4193_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).

fof(f_4193_2,plain,
    ! [U_16962,U_16961,U_16960,U_16959] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),hAPP(hAPP(c_Finite__Set_Ofold(U_16959,U_16959,c_Lattices_Osemilattice__sup__class_Osup(U_16959)),U_16962),U_16960)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16959),U_16961),U_16962)))
      | ? [U_16958] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),U_16958),U_16961))
          & hBOOL(hAPP(hAPP(c_member(U_16959),U_16958),U_16960)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16959),U_16960))
      | ~ class_Lattices_Osemilattice__sup(U_16959) ),
    inference(variable_rename,[status(thm)],[f_4193_1]) ).

fof(f_4193_3,plain,
    ! [U_16962,U_16961,U_16960,U_16959] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),hAPP(hAPP(c_Finite__Set_Ofold(U_16959,U_16959,c_Lattices_Osemilattice__sup__class_Osup(U_16959)),U_16962),U_16960)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16959),U_16961),U_16962)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),sK430(U_16962,U_16961,U_16960,U_16959)),U_16961))
        & hBOOL(hAPP(hAPP(c_member(U_16959),sK430(U_16962,U_16961,U_16960,U_16959)),U_16960)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16959),U_16960))
      | ~ class_Lattices_Osemilattice__sup(U_16959) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_16958,sK430(U_16962,U_16961,U_16960,U_16959))],[f_4193_2]) ).

fof(f_4193_4,plain,
    ( ! [U_16959,U_16960,U_16961,U_16962] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),sK430(U_16962,U_16961,U_16960,U_16959)),U_16961))
        | ~ sP1094(U_16959,U_16960,U_16961,U_16962) )
    & ! [U_16959,U_16960,U_16961,U_16962] :
        ( hBOOL(hAPP(hAPP(c_member(U_16959),sK430(U_16962,U_16961,U_16960,U_16959)),U_16960))
        | ~ sP1094(U_16959,U_16960,U_16961,U_16962) )
    & ! [U_16959,U_16960,U_16961,U_16962] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),hAPP(hAPP(c_Finite__Set_Ofold(U_16959,U_16959,c_Lattices_Osemilattice__sup__class_Osup(U_16959)),U_16962),U_16960)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16959),U_16961),U_16962)))
        | sP1094(U_16959,U_16960,U_16961,U_16962)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16959),U_16960))
        | ~ class_Lattices_Osemilattice__sup(U_16959) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1094])],[f_4193_3]) ).

cnf(f_4193_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),hAPP(hAPP(c_Finite__Set_Ofold(U_16959,U_16959,c_Lattices_Osemilattice__sup__class_Osup(U_16959)),U_16962),U_16960)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16959),U_16961),U_16962)))
    | sP1094(U_16959,U_16960,U_16961,U_16962)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16959),U_16960))
    | ~ class_Lattices_Osemilattice__sup(U_16959) ),
    inference(clausify,[status(thm)],[f_4193_4]) ).

cnf(f_4193_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16959),sK430(U_16962,U_16961,U_16960,U_16959)),U_16960))
    | ~ sP1094(U_16959,U_16960,U_16961,U_16962) ),
    inference(clausify,[status(thm)],[f_4193_4]) ).

cnf(f_4193_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16959),sK430(U_16962,U_16961,U_16960,U_16959)),U_16961))
    | ~ sP1094(U_16959,U_16960,U_16961,U_16962) ),
    inference(clausify,[status(thm)],[f_4193_4]) ).

fof(f_4194_1,plain,
    ! [V_p_2,T_b] :
      ( ? [B_x] : V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) ),
    inference(fof_nnf,[status(thm)],[fact_IdE]) ).

fof(f_4194_2,plain,
    ! [U_16965,U_16964] :
      ( ? [U_16963] : U_16965 = hAPP(hAPP(c_Product__Type_OPair(U_16964,U_16964),U_16963),U_16963)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),c_Relation_OId(U_16964))) ),
    inference(variable_rename,[status(thm)],[f_4194_1]) ).

fof(f_4194_3,plain,
    ! [U_16965,U_16964] :
      ( U_16965 = hAPP(hAPP(c_Product__Type_OPair(U_16964,U_16964),sK431(U_16965,U_16964)),sK431(U_16965,U_16964))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),c_Relation_OId(U_16964))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_16963,sK431(U_16965,U_16964))],[f_4194_2]) ).

fof(f_4194_4,plain,
    ! [U_16965,U_16964] :
      ( U_16965 = hAPP(hAPP(c_Product__Type_OPair(U_16964,U_16964),sK431(U_16965,U_16964)),sK431(U_16965,U_16964))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),c_Relation_OId(U_16964))) ),
    inference(definitional_conversion,[status(esa)],[f_4194_3]) ).

cnf(f_4194_5,plain,
    ( U_16965 = hAPP(hAPP(c_Product__Type_OPair(U_16964,U_16964),sK431(U_16965,U_16964)),sK431(U_16965,U_16964))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),c_Relation_OId(U_16964))) ),
    inference(clausify,[status(thm)],[f_4194_4]) ).

fof(f_4195_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_r_2)
        | ? [B_Q] :
            ( ! [B_x] :
                ( ? [B_y] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) )
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
            & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) )
      & ( ! [B_Q] :
            ( ? [B_x] :
                ( ! [B_y] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) )
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
            | ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
        | ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__eq__minimal]) ).

fof(f_4195_2,plain,
    ! [U_16975,U_16974] :
      ( ( c_Wellfounded_Owf(U_16974,U_16975)
        | ? [U_16973] :
            ( ! [U_16972] :
                ( ? [U_16971] :
                    ( hBOOL(hAPP(hAPP(c_member(U_16974),U_16971),U_16973))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16974,U_16974)),hAPP(hAPP(c_Product__Type_OPair(U_16974,U_16974),U_16971),U_16972)),U_16975)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_16974),U_16972),U_16973)) )
            & ? [U_16970] : hBOOL(hAPP(hAPP(c_member(U_16974),U_16970),U_16973)) ) )
      & ( ! [U_16969] :
            ( ? [U_16968] :
                ( ! [U_16967] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_16974),U_16967),U_16969))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16974,U_16974)),hAPP(hAPP(c_Product__Type_OPair(U_16974,U_16974),U_16967),U_16968)),U_16975)) )
                & hBOOL(hAPP(hAPP(c_member(U_16974),U_16968),U_16969)) )
            | ! [U_16966] : ~ hBOOL(hAPP(hAPP(c_member(U_16974),U_16966),U_16969)) )
        | ~ c_Wellfounded_Owf(U_16974,U_16975) ) ),
    inference(variable_rename,[status(thm)],[f_4195_1]) ).

fof(f_4195_3,plain,
    ( ! [U_16979,U_16977] :
        ( c_Wellfounded_Owf(U_16977,U_16979)
        | ? [U_16973] :
            ( ! [U_16972] :
                ( ? [U_16971] :
                    ( hBOOL(hAPP(hAPP(c_member(U_16977),U_16971),U_16973))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16971),U_16972)),U_16979)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),U_16973)) )
            & ? [U_16970] : hBOOL(hAPP(hAPP(c_member(U_16977),U_16970),U_16973)) ) )
    & ! [U_16978,U_16976] :
        ( ! [U_16969] :
            ( ? [U_16968] :
                ( ! [U_16967] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),U_16968)),U_16978)) )
                & hBOOL(hAPP(hAPP(c_member(U_16976),U_16968),U_16969)) )
            | ! [U_16966] : ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969)) )
        | ~ c_Wellfounded_Owf(U_16976,U_16978) ) ),
    inference(miniscope,[status(thm)],[f_4195_2]) ).

fof(f_4195_4,plain,
    ( ! [U_16979,U_16977] :
        ( c_Wellfounded_Owf(U_16977,U_16979)
        | ? [U_16973] :
            ( ! [U_16972] :
                ( ? [U_16971] :
                    ( hBOOL(hAPP(hAPP(c_member(U_16977),U_16971),U_16973))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16971),U_16972)),U_16979)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),U_16973)) )
            & ? [U_16970] : hBOOL(hAPP(hAPP(c_member(U_16977),U_16970),U_16973)) ) )
    & ! [U_16978,U_16976] :
        ( ! [U_16969] :
            ( ( ! [U_16967] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),sK432(U_16978,U_16976,U_16969))),U_16978)) )
              & hBOOL(hAPP(hAPP(c_member(U_16976),sK432(U_16978,U_16976,U_16969)),U_16969)) )
            | ! [U_16966] : ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969)) )
        | ~ c_Wellfounded_Owf(U_16976,U_16978) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_16968,sK432(U_16978,U_16976,U_16969))],[f_4195_3]) ).

fof(f_4195_5,plain,
    ( ! [U_16979,U_16977] :
        ( c_Wellfounded_Owf(U_16977,U_16979)
        | ( ! [U_16972] :
              ( ? [U_16971] :
                  ( hBOOL(hAPP(hAPP(c_member(U_16977),U_16971),sK433(U_16979,U_16977)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16971),U_16972)),U_16979)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),sK433(U_16979,U_16977))) )
          & ? [U_16970] : hBOOL(hAPP(hAPP(c_member(U_16977),U_16970),sK433(U_16979,U_16977))) ) )
    & ! [U_16978,U_16976] :
        ( ! [U_16969] :
            ( ( ! [U_16967] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),sK432(U_16978,U_16976,U_16969))),U_16978)) )
              & hBOOL(hAPP(hAPP(c_member(U_16976),sK432(U_16978,U_16976,U_16969)),U_16969)) )
            | ! [U_16966] : ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969)) )
        | ~ c_Wellfounded_Owf(U_16976,U_16978) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_16973,sK433(U_16979,U_16977))],[f_4195_4]) ).

fof(f_4195_6,plain,
    ( ! [U_16979,U_16977] :
        ( c_Wellfounded_Owf(U_16977,U_16979)
        | ( ! [U_16972] :
              ( ? [U_16971] :
                  ( hBOOL(hAPP(hAPP(c_member(U_16977),U_16971),sK433(U_16979,U_16977)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16971),U_16972)),U_16979)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),sK433(U_16979,U_16977))) )
          & hBOOL(hAPP(hAPP(c_member(U_16977),sK434(U_16979,U_16977)),sK433(U_16979,U_16977))) ) )
    & ! [U_16978,U_16976] :
        ( ! [U_16969] :
            ( ( ! [U_16967] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),sK432(U_16978,U_16976,U_16969))),U_16978)) )
              & hBOOL(hAPP(hAPP(c_member(U_16976),sK432(U_16978,U_16976,U_16969)),U_16969)) )
            | ! [U_16966] : ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969)) )
        | ~ c_Wellfounded_Owf(U_16976,U_16978) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_16970,sK434(U_16979,U_16977))],[f_4195_5]) ).

fof(f_4195_7,plain,
    ( ! [U_16979,U_16977] :
        ( c_Wellfounded_Owf(U_16977,U_16979)
        | ( ! [U_16972] :
              ( ( hBOOL(hAPP(hAPP(c_member(U_16977),sK435(U_16979,U_16977,U_16972)),sK433(U_16979,U_16977)))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),sK435(U_16979,U_16977,U_16972)),U_16972)),U_16979)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),sK433(U_16979,U_16977))) )
          & hBOOL(hAPP(hAPP(c_member(U_16977),sK434(U_16979,U_16977)),sK433(U_16979,U_16977))) ) )
    & ! [U_16978,U_16976] :
        ( ! [U_16969] :
            ( ( ! [U_16967] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),sK432(U_16978,U_16976,U_16969))),U_16978)) )
              & hBOOL(hAPP(hAPP(c_member(U_16976),sK432(U_16978,U_16976,U_16969)),U_16969)) )
            | ! [U_16966] : ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969)) )
        | ~ c_Wellfounded_Owf(U_16976,U_16978) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_16971,sK435(U_16979,U_16977,U_16972))],[f_4195_6]) ).

fof(f_4195_8,plain,
    ( ! [U_16977,U_16972,U_16979] :
        ( hBOOL(hAPP(hAPP(c_member(U_16977),sK435(U_16979,U_16977,U_16972)),sK433(U_16979,U_16977)))
        | ~ sP1096(U_16977,U_16972,U_16979) )
    & ! [U_16977,U_16972,U_16979] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),sK435(U_16979,U_16977,U_16972)),U_16972)),U_16979))
        | ~ sP1096(U_16977,U_16972,U_16979) )
    & ! [U_16977,U_16972,U_16979] :
        ( sP1096(U_16977,U_16972,U_16979)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),sK433(U_16979,U_16977)))
        | ~ sP1097(U_16977,U_16972,U_16979) )
    & ! [U_16977,U_16972,U_16979] :
        ( hBOOL(hAPP(hAPP(c_member(U_16977),sK434(U_16979,U_16977)),sK433(U_16979,U_16977)))
        | ~ sP1097(U_16977,U_16972,U_16979) )
    & ! [U_16967,U_16969,U_16976,U_16978] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),sK432(U_16978,U_16976,U_16969))),U_16978))
        | ~ sP1095(U_16967,U_16969,U_16976,U_16978) )
    & ! [U_16967,U_16969,U_16976,U_16978] :
        ( hBOOL(hAPP(hAPP(c_member(U_16976),sK432(U_16978,U_16976,U_16969)),U_16969))
        | ~ sP1095(U_16967,U_16969,U_16976,U_16978) )
    & ! [U_16977,U_16972,U_16979] :
        ( c_Wellfounded_Owf(U_16977,U_16979)
        | sP1097(U_16977,U_16972,U_16979) )
    & ! [U_16966,U_16967,U_16969,U_16976,U_16978] :
        ( sP1095(U_16967,U_16969,U_16976,U_16978)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969))
        | ~ c_Wellfounded_Owf(U_16976,U_16978) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1095,sP1096,sP1097])],[f_4195_7]) ).

cnf(f_4195_9,plain,
    ( sP1095(U_16967,U_16969,U_16976,U_16978)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16966),U_16969))
    | ~ c_Wellfounded_Owf(U_16976,U_16978) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_10,plain,
    ( c_Wellfounded_Owf(U_16977,U_16979)
    | sP1097(U_16977,U_16972,U_16979) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16976),sK432(U_16978,U_16976,U_16969)),U_16969))
    | ~ sP1095(U_16967,U_16969,U_16976,U_16978) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16976),U_16967),U_16969))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16976,U_16976)),hAPP(hAPP(c_Product__Type_OPair(U_16976,U_16976),U_16967),sK432(U_16978,U_16976,U_16969))),U_16978))
    | ~ sP1095(U_16967,U_16969,U_16976,U_16978) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16977),sK434(U_16979,U_16977)),sK433(U_16979,U_16977)))
    | ~ sP1097(U_16977,U_16972,U_16979) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_14,plain,
    ( sP1096(U_16977,U_16972,U_16979)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16972),sK433(U_16979,U_16977)))
    | ~ sP1097(U_16977,U_16972,U_16979) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),sK435(U_16979,U_16977,U_16972)),U_16972)),U_16979))
    | ~ sP1096(U_16977,U_16972,U_16979) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

cnf(f_4195_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16977),sK435(U_16979,U_16977,U_16972)),sK433(U_16979,U_16977)))
    | ~ sP1096(U_16977,U_16972,U_16979) ),
    inference(clausify,[status(thm)],[f_4195_8]) ).

fof(f_4196_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem]) ).

fof(f_4196_2,plain,
    ! [U_16987,U_16986,U_16985,U_16984,U_16983,U_16982,U_16981,U_16980] :
      ( hAPP(U_16985,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16981,tc_HOL_Obool)),U_16986),U_16987)) = hAPP(hAPP(U_16982,hAPP(U_16985,U_16986)),hAPP(U_16985,U_16987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16986))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16980,U_16981,U_16982,U_16983,U_16984,U_16985) ),
    inference(variable_rename,[status(thm)],[f_4196_1]) ).

fof(f_4196_3,plain,
    ! [U_16987,U_16986,U_16985,U_16984,U_16983,U_16982,U_16981] :
      ( ! [U_16980] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16980,U_16981,U_16982,U_16983,U_16984,U_16985)
      | hAPP(U_16985,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16981,tc_HOL_Obool)),U_16986),U_16987)) = hAPP(hAPP(U_16982,hAPP(U_16985,U_16986)),hAPP(U_16985,U_16987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16986)) ),
    inference(miniscope,[status(thm)],[f_4196_2]) ).

fof(f_4196_4,plain,
    ! [U_16986,U_16985,U_16982,U_16980,U_16981,U_16987,U_16983,U_16984] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16980,U_16981,U_16982,U_16983,U_16984,U_16985)
      | hAPP(U_16985,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16981,tc_HOL_Obool)),U_16986),U_16987)) = hAPP(hAPP(U_16982,hAPP(U_16985,U_16986)),hAPP(U_16985,U_16987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16986)) ),
    inference(definitional_conversion,[status(esa)],[f_4196_3]) ).

cnf(f_4196_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16980,U_16981,U_16982,U_16983,U_16984,U_16985)
    | hAPP(U_16985,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16981,tc_HOL_Obool)),U_16986),U_16987)) = hAPP(hAPP(U_16982,hAPP(U_16985,U_16986)),hAPP(U_16985,U_16987))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16987))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16981),U_16986)) ),
    inference(clausify,[status(thm)],[f_4196_4]) ).

fof(f_4197_1,plain,
    ! [V_P_H_2,V_P_2] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2))
      | ? [B_x] :
          ( ( ( ~ hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(V_P_H_2,B_x)) )
            | ( ~ hBOOL(hAPP(V_P_H_2,B_x))
              & hBOOL(hAPP(V_P_2,B_x)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong]) ).

fof(f_4197_2,plain,
    ! [U_16990,U_16989] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16989)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16990))
      | ? [U_16988] :
          ( ( ( ~ hBOOL(hAPP(U_16989,U_16988))
              & hBOOL(hAPP(U_16990,U_16988)) )
            | ( ~ hBOOL(hAPP(U_16990,U_16988))
              & hBOOL(hAPP(U_16989,U_16988)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_16988)) ) ),
    inference(variable_rename,[status(thm)],[f_4197_1]) ).

fof(f_4197_3,plain,
    ! [U_16990,U_16989] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16989)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16990))
      | ( ( ( ~ hBOOL(hAPP(U_16989,sK436(U_16990,U_16989)))
            & hBOOL(hAPP(U_16990,sK436(U_16990,U_16989))) )
          | ( ~ hBOOL(hAPP(U_16990,sK436(U_16990,U_16989)))
            & hBOOL(hAPP(U_16989,sK436(U_16990,U_16989))) ) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK436(U_16990,U_16989))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_16988,sK436(U_16990,U_16989))],[f_4197_2]) ).

fof(f_4197_4,plain,
    ( ! [U_16990,U_16989] :
        ( ~ hBOOL(hAPP(U_16989,sK436(U_16990,U_16989)))
        | ~ sP1099(U_16990,U_16989) )
    & ! [U_16990,U_16989] :
        ( hBOOL(hAPP(U_16990,sK436(U_16990,U_16989)))
        | ~ sP1099(U_16990,U_16989) )
    & ! [U_16990,U_16989] :
        ( ~ hBOOL(hAPP(U_16990,sK436(U_16990,U_16989)))
        | ~ sP1098(U_16990,U_16989) )
    & ! [U_16990,U_16989] :
        ( hBOOL(hAPP(U_16989,sK436(U_16990,U_16989)))
        | ~ sP1098(U_16990,U_16989) )
    & ! [U_16990,U_16989] :
        ( sP1099(U_16990,U_16989)
        | sP1098(U_16990,U_16989)
        | ~ sP1100(U_16990,U_16989) )
    & ! [U_16990,U_16989] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK436(U_16990,U_16989)))
        | ~ sP1100(U_16990,U_16989) )
    & ! [U_16990,U_16989] :
        ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16989)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16990))
        | sP1100(U_16990,U_16989) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1098,sP1099,sP1100])],[f_4197_3]) ).

cnf(f_4197_5,plain,
    ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16989)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_16990))
    | sP1100(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

cnf(f_4197_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK436(U_16990,U_16989)))
    | ~ sP1100(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

cnf(f_4197_7,plain,
    ( sP1099(U_16990,U_16989)
    | sP1098(U_16990,U_16989)
    | ~ sP1100(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

cnf(f_4197_8,plain,
    ( hBOOL(hAPP(U_16989,sK436(U_16990,U_16989)))
    | ~ sP1098(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

cnf(f_4197_9,plain,
    ( ~ hBOOL(hAPP(U_16990,sK436(U_16990,U_16989)))
    | ~ sP1098(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

cnf(f_4197_10,plain,
    ( hBOOL(hAPP(U_16990,sK436(U_16990,U_16989)))
    | ~ sP1099(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

cnf(f_4197_11,plain,
    ( ~ hBOOL(hAPP(U_16989,sK436(U_16990,U_16989)))
    | ~ sP1099(U_16990,U_16989) ),
    inference(clausify,[status(thm)],[f_4197_4]) ).

fof(f_4198_1,plain,
    ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem]) ).

fof(f_4198_2,plain,
    ! [U_16997,U_16996,U_16995,U_16994,U_16993,U_16992,U_16991] :
      ( hAPP(hAPP(U_16993,U_16997),U_16997) = U_16997
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16991,U_16992,U_16993,U_16994,U_16995,U_16996) ),
    inference(variable_rename,[status(thm)],[f_4198_1]) ).

fof(f_4198_3,plain,
    ! [U_16997,U_16996,U_16995,U_16994,U_16993] :
      ( ! [U_16992,U_16991] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16991,U_16992,U_16993,U_16994,U_16995,U_16996)
      | hAPP(hAPP(U_16993,U_16997),U_16997) = U_16997 ),
    inference(miniscope,[status(thm)],[f_4198_2]) ).

fof(f_4198_4,plain,
    ! [U_16993,U_16994,U_16996,U_16992,U_16991,U_16995,U_16997] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16991,U_16992,U_16993,U_16994,U_16995,U_16996)
      | hAPP(hAPP(U_16993,U_16997),U_16997) = U_16997 ),
    inference(definitional_conversion,[status(esa)],[f_4198_3]) ).

cnf(f_4198_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16991,U_16992,U_16993,U_16994,U_16995,U_16996)
    | hAPP(hAPP(U_16993,U_16997),U_16997) = U_16997 ),
    inference(clausify,[status(thm)],[f_4198_4]) ).

fof(f_4199_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem]) ).

fof(f_4199_2,plain,
    ! [U_17005,U_17004,U_17003,U_17002,U_17001,U_17000,U_16999,U_16998] :
      ( hAPP(hAPP(U_17000,hAPP(U_17002,U_17005)),hAPP(U_17003,U_17004)) = hAPP(U_17003,U_17004)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_17005),U_17004))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16999),U_17004))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16998,U_16999,U_17000,U_17001,U_17002,U_17003) ),
    inference(variable_rename,[status(thm)],[f_4199_1]) ).

fof(f_4199_3,plain,
    ! [U_17005,U_17004,U_17003,U_17002,U_17001,U_17000,U_16999] :
      ( ! [U_16998] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16998,U_16999,U_17000,U_17001,U_17002,U_17003)
      | hAPP(hAPP(U_17000,hAPP(U_17002,U_17005)),hAPP(U_17003,U_17004)) = hAPP(U_17003,U_17004)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_17005),U_17004))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16999),U_17004)) ),
    inference(miniscope,[status(thm)],[f_4199_2]) ).

fof(f_4199_4,plain,
    ! [U_16999,U_16998,U_17000,U_17001,U_17002,U_17003,U_17004,U_17005] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16998,U_16999,U_17000,U_17001,U_17002,U_17003)
      | hAPP(hAPP(U_17000,hAPP(U_17002,U_17005)),hAPP(U_17003,U_17004)) = hAPP(U_17003,U_17004)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_17005),U_17004))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16999),U_17004)) ),
    inference(definitional_conversion,[status(esa)],[f_4199_3]) ).

cnf(f_4199_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16998,U_16999,U_17000,U_17001,U_17002,U_17003)
    | hAPP(hAPP(U_17000,hAPP(U_17002,U_17005)),hAPP(U_17003,U_17004)) = hAPP(U_17003,U_17004)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_17005),U_17004))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16999),U_17004)) ),
    inference(clausify,[status(thm)],[f_4199_4]) ).

fof(f_4200_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem]) ).

fof(f_4200_2,plain,
    ! [U_17013,U_17012,U_17011,U_17010,U_17009,U_17008,U_17007,U_17006] :
      ( hAPP(U_17011,hAPP(hAPP(c_Set_Oinsert(U_17007),U_17013),U_17012)) = hAPP(hAPP(U_17008,hAPP(U_17010,U_17013)),hAPP(U_17011,U_17012))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17007),U_17012))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17006,U_17007,U_17008,U_17009,U_17010,U_17011) ),
    inference(variable_rename,[status(thm)],[f_4200_1]) ).

fof(f_4200_3,plain,
    ! [U_17013,U_17012,U_17011,U_17010,U_17009,U_17008,U_17007] :
      ( ! [U_17006] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17006,U_17007,U_17008,U_17009,U_17010,U_17011)
      | hAPP(U_17011,hAPP(hAPP(c_Set_Oinsert(U_17007),U_17013),U_17012)) = hAPP(hAPP(U_17008,hAPP(U_17010,U_17013)),hAPP(U_17011,U_17012))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17007),U_17012)) ),
    inference(miniscope,[status(thm)],[f_4200_2]) ).

fof(f_4200_4,plain,
    ! [U_17007,U_17006,U_17008,U_17009,U_17010,U_17011,U_17012,U_17013] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17006,U_17007,U_17008,U_17009,U_17010,U_17011)
      | hAPP(U_17011,hAPP(hAPP(c_Set_Oinsert(U_17007),U_17013),U_17012)) = hAPP(hAPP(U_17008,hAPP(U_17010,U_17013)),hAPP(U_17011,U_17012))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17007),U_17012)) ),
    inference(definitional_conversion,[status(esa)],[f_4200_3]) ).

cnf(f_4200_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17006,U_17007,U_17008,U_17009,U_17010,U_17011)
    | hAPP(U_17011,hAPP(hAPP(c_Set_Oinsert(U_17007),U_17013),U_17012)) = hAPP(hAPP(U_17008,hAPP(U_17010,U_17013)),hAPP(U_17011,U_17012))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17007),U_17012)) ),
    inference(clausify,[status(thm)],[f_4200_4]) ).

fof(f_4201_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem]) ).

fof(f_4201_2,plain,
    ! [U_17021,U_17020,U_17019,U_17018,U_17017,U_17016,U_17015,U_17014] :
      ( hAPP(hAPP(U_17016,hAPP(U_17019,U_17021)),hAPP(U_17019,U_17020)) = hAPP(U_17019,U_17020)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17015,tc_HOL_Obool)),U_17021),U_17020))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17015),U_17020))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17014,U_17015,U_17016,U_17017,U_17018,U_17019) ),
    inference(variable_rename,[status(thm)],[f_4201_1]) ).

fof(f_4201_3,plain,
    ! [U_17021,U_17020,U_17019,U_17018,U_17017,U_17016,U_17015] :
      ( ! [U_17014] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17014,U_17015,U_17016,U_17017,U_17018,U_17019)
      | hAPP(hAPP(U_17016,hAPP(U_17019,U_17021)),hAPP(U_17019,U_17020)) = hAPP(U_17019,U_17020)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17015,tc_HOL_Obool)),U_17021),U_17020))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17015),U_17020)) ),
    inference(miniscope,[status(thm)],[f_4201_2]) ).

fof(f_4201_4,plain,
    ! [U_17014,U_17015,U_17016,U_17017,U_17018,U_17019,U_17020,U_17021] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17014,U_17015,U_17016,U_17017,U_17018,U_17019)
      | hAPP(hAPP(U_17016,hAPP(U_17019,U_17021)),hAPP(U_17019,U_17020)) = hAPP(U_17019,U_17020)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17015,tc_HOL_Obool)),U_17021),U_17020))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17015),U_17020)) ),
    inference(definitional_conversion,[status(esa)],[f_4201_3]) ).

cnf(f_4201_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17014,U_17015,U_17016,U_17017,U_17018,U_17019)
    | hAPP(hAPP(U_17016,hAPP(U_17019,U_17021)),hAPP(U_17019,U_17020)) = hAPP(U_17019,U_17020)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17015,tc_HOL_Obool)),U_17021),U_17020))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17015),U_17020)) ),
    inference(clausify,[status(thm)],[f_4201_4]) ).

fof(f_4202_1,plain,
    ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Q_2,B_x))
          & hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono]) ).

fof(f_4202_2,plain,
    ! [U_17027,U_17026,U_17025,U_17024,U_17023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17024),hAPP(c_Set_OCollect(U_17023),U_17026))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17025),hAPP(c_Set_OCollect(U_17023),U_17027))))
      | ? [U_17022] :
          ( ~ hBOOL(hAPP(U_17027,U_17022))
          & hBOOL(hAPP(U_17026,U_17022))
          & hBOOL(hAPP(hAPP(c_member(U_17023),U_17022),U_17024)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),U_17024),U_17025)) ),
    inference(variable_rename,[status(thm)],[f_4202_1]) ).

fof(f_4202_3,plain,
    ! [U_17027,U_17026,U_17025,U_17024,U_17023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17024),hAPP(c_Set_OCollect(U_17023),U_17026))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17025),hAPP(c_Set_OCollect(U_17023),U_17027))))
      | ( ~ hBOOL(hAPP(U_17027,sK437(U_17027,U_17026,U_17025,U_17024,U_17023)))
        & hBOOL(hAPP(U_17026,sK437(U_17027,U_17026,U_17025,U_17024,U_17023)))
        & hBOOL(hAPP(hAPP(c_member(U_17023),sK437(U_17027,U_17026,U_17025,U_17024,U_17023)),U_17024)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),U_17024),U_17025)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_17022,sK437(U_17027,U_17026,U_17025,U_17024,U_17023))],[f_4202_2]) ).

fof(f_4202_4,plain,
    ( ! [U_17023,U_17024,U_17025,U_17026,U_17027] :
        ( ~ hBOOL(hAPP(U_17027,sK437(U_17027,U_17026,U_17025,U_17024,U_17023)))
        | ~ sP1101(U_17023,U_17024,U_17025,U_17026,U_17027) )
    & ! [U_17023,U_17024,U_17025,U_17026,U_17027] :
        ( hBOOL(hAPP(U_17026,sK437(U_17027,U_17026,U_17025,U_17024,U_17023)))
        | ~ sP1101(U_17023,U_17024,U_17025,U_17026,U_17027) )
    & ! [U_17023,U_17024,U_17025,U_17026,U_17027] :
        ( hBOOL(hAPP(hAPP(c_member(U_17023),sK437(U_17027,U_17026,U_17025,U_17024,U_17023)),U_17024))
        | ~ sP1101(U_17023,U_17024,U_17025,U_17026,U_17027) )
    & ! [U_17023,U_17024,U_17025,U_17026,U_17027] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17024),hAPP(c_Set_OCollect(U_17023),U_17026))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17025),hAPP(c_Set_OCollect(U_17023),U_17027))))
        | sP1101(U_17023,U_17024,U_17025,U_17026,U_17027)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),U_17024),U_17025)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1101])],[f_4202_3]) ).

cnf(f_4202_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17024),hAPP(c_Set_OCollect(U_17023),U_17026))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17023,tc_HOL_Obool)),U_17025),hAPP(c_Set_OCollect(U_17023),U_17027))))
    | sP1101(U_17023,U_17024,U_17025,U_17026,U_17027)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17023,tc_HOL_Obool)),U_17024),U_17025)) ),
    inference(clausify,[status(thm)],[f_4202_4]) ).

cnf(f_4202_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17023),sK437(U_17027,U_17026,U_17025,U_17024,U_17023)),U_17024))
    | ~ sP1101(U_17023,U_17024,U_17025,U_17026,U_17027) ),
    inference(clausify,[status(thm)],[f_4202_4]) ).

cnf(f_4202_7,plain,
    ( hBOOL(hAPP(U_17026,sK437(U_17027,U_17026,U_17025,U_17024,U_17023)))
    | ~ sP1101(U_17023,U_17024,U_17025,U_17026,U_17027) ),
    inference(clausify,[status(thm)],[f_4202_4]) ).

cnf(f_4202_8,plain,
    ( ~ hBOOL(hAPP(U_17027,sK437(U_17027,U_17026,U_17025,U_17024,U_17023)))
    | ~ sP1101(U_17023,U_17024,U_17025,U_17026,U_17027) ),
    inference(clausify,[status(thm)],[f_4202_4]) ).

fof(f_4203_1,plain,
    ! [V_C_2,V_A_2,T_b] :
      ( ? [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UnionE]) ).

fof(f_4203_2,plain,
    ! [U_17031,U_17030,U_17029] :
      ( ? [U_17028] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17029,tc_HOL_Obool)),U_17028),U_17031))
          & hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),U_17028)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17029,tc_HOL_Obool),U_17031))) ),
    inference(variable_rename,[status(thm)],[f_4203_1]) ).

fof(f_4203_3,plain,
    ! [U_17031,U_17030,U_17029] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17029,tc_HOL_Obool)),sK438(U_17031,U_17030,U_17029)),U_17031))
        & hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),sK438(U_17031,U_17030,U_17029))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17029,tc_HOL_Obool),U_17031))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_17028,sK438(U_17031,U_17030,U_17029))],[f_4203_2]) ).

fof(f_4203_4,plain,
    ( ! [U_17030,U_17029,U_17031] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17029,tc_HOL_Obool)),sK438(U_17031,U_17030,U_17029)),U_17031))
        | ~ sP1102(U_17030,U_17029,U_17031) )
    & ! [U_17030,U_17029,U_17031] :
        ( hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),sK438(U_17031,U_17030,U_17029)))
        | ~ sP1102(U_17030,U_17029,U_17031) )
    & ! [U_17030,U_17029,U_17031] :
        ( sP1102(U_17030,U_17029,U_17031)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17029,tc_HOL_Obool),U_17031))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1102])],[f_4203_3]) ).

cnf(f_4203_5,plain,
    ( sP1102(U_17030,U_17029,U_17031)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17029,tc_HOL_Obool),U_17031))) ),
    inference(clausify,[status(thm)],[f_4203_4]) ).

cnf(f_4203_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17029),U_17030),sK438(U_17031,U_17030,U_17029)))
    | ~ sP1102(U_17030,U_17029,U_17031) ),
    inference(clausify,[status(thm)],[f_4203_4]) ).

cnf(f_4203_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17029,tc_HOL_Obool)),sK438(U_17031,U_17030,U_17029)),U_17031))
    | ~ sP1102(U_17030,U_17029,U_17031) ),
    inference(clausify,[status(thm)],[f_4203_4]) ).

fof(f_4204_1,plain,
    ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
      ( c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__upd__left]) ).

fof(f_4204_2,plain,
    ! [U_17037,U_17036,U_17035,U_17034,U_17033,U_17032] :
      ( c_Map_Omap__add(U_17032,U_17034,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17032,tc_Option_Ooption(U_17034)),U_17036),U_17033),hAPP(c_Option_Ooption_OSome(U_17034),U_17037)),U_17035) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17032,tc_Option_Ooption(U_17034)),c_Map_Omap__add(U_17032,U_17034,U_17036,U_17035)),U_17033),hAPP(c_Option_Ooption_OSome(U_17034),U_17037))
      | hBOOL(hAPP(hAPP(c_member(U_17032),U_17033),c_Map_Odom(U_17032,U_17034,U_17035))) ),
    inference(variable_rename,[status(thm)],[f_4204_1]) ).

fof(f_4204_3,plain,
    ! [U_17032,U_17033,U_17034,U_17035,U_17036,U_17037] :
      ( c_Map_Omap__add(U_17032,U_17034,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17032,tc_Option_Ooption(U_17034)),U_17036),U_17033),hAPP(c_Option_Ooption_OSome(U_17034),U_17037)),U_17035) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17032,tc_Option_Ooption(U_17034)),c_Map_Omap__add(U_17032,U_17034,U_17036,U_17035)),U_17033),hAPP(c_Option_Ooption_OSome(U_17034),U_17037))
      | hBOOL(hAPP(hAPP(c_member(U_17032),U_17033),c_Map_Odom(U_17032,U_17034,U_17035))) ),
    inference(definitional_conversion,[status(esa)],[f_4204_2]) ).

cnf(f_4204_4,plain,
    ( c_Map_Omap__add(U_17032,U_17034,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17032,tc_Option_Ooption(U_17034)),U_17036),U_17033),hAPP(c_Option_Ooption_OSome(U_17034),U_17037)),U_17035) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17032,tc_Option_Ooption(U_17034)),c_Map_Omap__add(U_17032,U_17034,U_17036,U_17035)),U_17033),hAPP(c_Option_Ooption_OSome(U_17034),U_17037))
    | hBOOL(hAPP(hAPP(c_member(U_17032),U_17033),c_Map_Odom(U_17032,U_17034,U_17035))) ),
    inference(clausify,[status(thm)],[f_4204_3]) ).

fof(f_4205_1,plain,
    ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
      ( ? [B_x,B_y,B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
          & V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__compE]) ).

fof(f_4205_2,plain,
    ! [U_17046,U_17045,U_17044,U_17043,U_17042,U_17041] :
      ( ? [U_17040,U_17039,U_17038] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17044,U_17042)),hAPP(hAPP(c_Product__Type_OPair(U_17044,U_17042),U_17039),U_17038)),U_17046))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17044)),hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17044),U_17040),U_17039)),U_17045))
          & U_17043 = hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17042),U_17040),U_17038) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17042)),U_17043),hAPP(hAPP(c_Relation_Orel__comp(U_17041,U_17044,U_17042),U_17045),U_17046))) ),
    inference(variable_rename,[status(thm)],[f_4205_1]) ).

fof(f_4205_3,plain,
    ! [U_17046,U_17045,U_17044,U_17043,U_17042,U_17041] :
      ( ? [U_17039,U_17038] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17044,U_17042)),hAPP(hAPP(c_Product__Type_OPair(U_17044,U_17042),U_17039),U_17038)),U_17046))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17044)),hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17044),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),U_17039)),U_17045))
          & U_17043 = hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17042),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),U_17038) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17042)),U_17043),hAPP(hAPP(c_Relation_Orel__comp(U_17041,U_17044,U_17042),U_17045),U_17046))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_17040,sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))],[f_4205_2]) ).

fof(f_4205_4,plain,
    ! [U_17046,U_17045,U_17044,U_17043,U_17042,U_17041] :
      ( ? [U_17038] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17044,U_17042)),hAPP(hAPP(c_Product__Type_OPair(U_17044,U_17042),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),U_17038)),U_17046))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17044)),hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17044),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17045))
          & U_17043 = hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17042),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),U_17038) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17042)),U_17043),hAPP(hAPP(c_Relation_Orel__comp(U_17041,U_17044,U_17042),U_17045),U_17046))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_17039,sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))],[f_4205_3]) ).

fof(f_4205_5,plain,
    ! [U_17046,U_17045,U_17044,U_17043,U_17042,U_17041] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17044,U_17042)),hAPP(hAPP(c_Product__Type_OPair(U_17044,U_17042),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17046))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17044)),hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17044),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17045))
        & U_17043 = hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17042),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17042)),U_17043),hAPP(hAPP(c_Relation_Orel__comp(U_17041,U_17044,U_17042),U_17045),U_17046))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_17038,sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))],[f_4205_4]) ).

fof(f_4205_6,plain,
    ( ! [U_17041,U_17042,U_17043,U_17044,U_17045,U_17046] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17044,U_17042)),hAPP(hAPP(c_Product__Type_OPair(U_17044,U_17042),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17046))
        | ~ sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046) )
    & ! [U_17041,U_17042,U_17043,U_17044,U_17045,U_17046] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17044)),hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17044),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17045))
        | ~ sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046) )
    & ! [U_17041,U_17042,U_17043,U_17044,U_17045,U_17046] :
        ( U_17043 = hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17042),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))
        | ~ sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046) )
    & ! [U_17041,U_17042,U_17043,U_17044,U_17045,U_17046] :
        ( sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17042)),U_17043),hAPP(hAPP(c_Relation_Orel__comp(U_17041,U_17044,U_17042),U_17045),U_17046))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1103])],[f_4205_5]) ).

cnf(f_4205_7,plain,
    ( sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17042)),U_17043),hAPP(hAPP(c_Relation_Orel__comp(U_17041,U_17044,U_17042),U_17045),U_17046))) ),
    inference(clausify,[status(thm)],[f_4205_6]) ).

cnf(f_4205_8,plain,
    ( U_17043 = hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17042),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))
    | ~ sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046) ),
    inference(clausify,[status(thm)],[f_4205_6]) ).

cnf(f_4205_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17041,U_17044)),hAPP(hAPP(c_Product__Type_OPair(U_17041,U_17044),sK439(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17045))
    | ~ sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046) ),
    inference(clausify,[status(thm)],[f_4205_6]) ).

cnf(f_4205_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17044,U_17042)),hAPP(hAPP(c_Product__Type_OPair(U_17044,U_17042),sK440(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041)),sK441(U_17046,U_17045,U_17044,U_17043,U_17042,U_17041))),U_17046))
    | ~ sP1103(U_17041,U_17042,U_17043,U_17044,U_17045,U_17046) ),
    inference(clausify,[status(thm)],[f_4205_6]) ).

fof(f_4206_1,plain,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
      ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
        & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) )
      | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
      | hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__SomeD]) ).

fof(f_4206_2,plain,
    ! [U_17052,U_17051,U_17050,U_17049,U_17048,U_17047] :
      ( ( hAPP(U_17049,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
        & hAPP(U_17050,U_17051) = c_Option_Ooption_ONone(U_17048) )
      | hAPP(U_17050,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
      | hAPP(c_Map_Omap__add(U_17047,U_17048,U_17049,U_17050),U_17051) != hAPP(c_Option_Ooption_OSome(U_17048),U_17052) ),
    inference(variable_rename,[status(thm)],[f_4206_1]) ).

fof(f_4206_3,plain,
    ! [U_17052,U_17051,U_17050,U_17049,U_17048] :
      ( ! [U_17047] : hAPP(c_Map_Omap__add(U_17047,U_17048,U_17049,U_17050),U_17051) != hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
      | ( hAPP(U_17049,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
        & hAPP(U_17050,U_17051) = c_Option_Ooption_ONone(U_17048) )
      | hAPP(U_17050,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052) ),
    inference(miniscope,[status(thm)],[f_4206_2]) ).

fof(f_4206_4,plain,
    ( ! [U_17049,U_17048,U_17051,U_17050,U_17052] :
        ( hAPP(U_17049,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
        | ~ sP1104(U_17049,U_17048,U_17051,U_17050,U_17052) )
    & ! [U_17049,U_17048,U_17051,U_17050,U_17052] :
        ( hAPP(U_17050,U_17051) = c_Option_Ooption_ONone(U_17048)
        | ~ sP1104(U_17049,U_17048,U_17051,U_17050,U_17052) )
    & ! [U_17049,U_17047,U_17048,U_17051,U_17050,U_17052] :
        ( hAPP(c_Map_Omap__add(U_17047,U_17048,U_17049,U_17050),U_17051) != hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
        | sP1104(U_17049,U_17048,U_17051,U_17050,U_17052)
        | hAPP(U_17050,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1104])],[f_4206_3]) ).

cnf(f_4206_5,plain,
    ( hAPP(c_Map_Omap__add(U_17047,U_17048,U_17049,U_17050),U_17051) != hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
    | sP1104(U_17049,U_17048,U_17051,U_17050,U_17052)
    | hAPP(U_17050,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052) ),
    inference(clausify,[status(thm)],[f_4206_4]) ).

cnf(f_4206_6,plain,
    ( hAPP(U_17050,U_17051) = c_Option_Ooption_ONone(U_17048)
    | ~ sP1104(U_17049,U_17048,U_17051,U_17050,U_17052) ),
    inference(clausify,[status(thm)],[f_4206_4]) ).

cnf(f_4206_7,plain,
    ( hAPP(U_17049,U_17051) = hAPP(c_Option_Ooption_OSome(U_17048),U_17052)
    | ~ sP1104(U_17049,U_17048,U_17051,U_17050,U_17052) ),
    inference(clausify,[status(thm)],[f_4206_4]) ).

fof(f_4207_1,plain,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
      ( ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
        | ( ( hAPP(V_m_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
            | hAPP(V_n_2,V_k_2) != c_Option_Ooption_ONone(T_b) )
          & hAPP(V_n_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) )
      & ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) )
        | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
        | hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff]) ).

fof(f_4207_2,plain,
    ! [U_17058,U_17057,U_17056,U_17055,U_17054,U_17053] :
      ( ( hAPP(c_Map_Omap__add(U_17053,U_17054,U_17055,U_17056),U_17057) = hAPP(c_Option_Ooption_OSome(U_17054),U_17058)
        | ( ( hAPP(U_17055,U_17057) != hAPP(c_Option_Ooption_OSome(U_17054),U_17058)
            | hAPP(U_17056,U_17057) != c_Option_Ooption_ONone(U_17054) )
          & hAPP(U_17056,U_17057) != hAPP(c_Option_Ooption_OSome(U_17054),U_17058) ) )
      & ( ( hAPP(U_17055,U_17057) = hAPP(c_Option_Ooption_OSome(U_17054),U_17058)
          & hAPP(U_17056,U_17057) = c_Option_Ooption_ONone(U_17054) )
        | hAPP(U_17056,U_17057) = hAPP(c_Option_Ooption_OSome(U_17054),U_17058)
        | hAPP(c_Map_Omap__add(U_17053,U_17054,U_17055,U_17056),U_17057) != hAPP(c_Option_Ooption_OSome(U_17054),U_17058) ) ),
    inference(variable_rename,[status(thm)],[f_4207_1]) ).

fof(f_4207_3,plain,
    ( ! [U_17070,U_17068,U_17066,U_17064,U_17062] :
        ( ! [U_17060] : hAPP(c_Map_Omap__add(U_17060,U_17062,U_17064,U_17066),U_17068) = hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
        | ( ( hAPP(U_17064,U_17068) != hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
            | hAPP(U_17066,U_17068) != c_Option_Ooption_ONone(U_17062) )
          & hAPP(U_17066,U_17068) != hAPP(c_Option_Ooption_OSome(U_17062),U_17070) ) )
    & ! [U_17069,U_17067,U_17065,U_17063,U_17061] :
        ( ! [U_17059] : hAPP(c_Map_Omap__add(U_17059,U_17061,U_17063,U_17065),U_17067) != hAPP(c_Option_Ooption_OSome(U_17061),U_17069)
        | ( hAPP(U_17063,U_17067) = hAPP(c_Option_Ooption_OSome(U_17061),U_17069)
          & hAPP(U_17065,U_17067) = c_Option_Ooption_ONone(U_17061) )
        | hAPP(U_17065,U_17067) = hAPP(c_Option_Ooption_OSome(U_17061),U_17069) ) ),
    inference(miniscope,[status(thm)],[f_4207_2]) ).

fof(f_4207_4,plain,
    ( ! [U_17070,U_17064,U_17062,U_17066,U_17068] :
        ( hAPP(U_17064,U_17068) != hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
        | hAPP(U_17066,U_17068) != c_Option_Ooption_ONone(U_17062)
        | ~ sP1106(U_17070,U_17064,U_17062,U_17066,U_17068) )
    & ! [U_17070,U_17064,U_17062,U_17066,U_17068] :
        ( hAPP(U_17066,U_17068) != hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
        | ~ sP1106(U_17070,U_17064,U_17062,U_17066,U_17068) )
    & ! [U_17065,U_17061,U_17063,U_17069,U_17067] :
        ( hAPP(U_17063,U_17067) = hAPP(c_Option_Ooption_OSome(U_17061),U_17069)
        | ~ sP1105(U_17065,U_17061,U_17063,U_17069,U_17067) )
    & ! [U_17065,U_17061,U_17063,U_17069,U_17067] :
        ( hAPP(U_17065,U_17067) = c_Option_Ooption_ONone(U_17061)
        | ~ sP1105(U_17065,U_17061,U_17063,U_17069,U_17067) )
    & ! [U_17070,U_17064,U_17060,U_17062,U_17066,U_17068] :
        ( hAPP(c_Map_Omap__add(U_17060,U_17062,U_17064,U_17066),U_17068) = hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
        | sP1106(U_17070,U_17064,U_17062,U_17066,U_17068) )
    & ! [U_17065,U_17059,U_17061,U_17063,U_17069,U_17067] :
        ( hAPP(c_Map_Omap__add(U_17059,U_17061,U_17063,U_17065),U_17067) != hAPP(c_Option_Ooption_OSome(U_17061),U_17069)
        | sP1105(U_17065,U_17061,U_17063,U_17069,U_17067)
        | hAPP(U_17065,U_17067) = hAPP(c_Option_Ooption_OSome(U_17061),U_17069) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1105,sP1106])],[f_4207_3]) ).

cnf(f_4207_5,plain,
    ( hAPP(c_Map_Omap__add(U_17059,U_17061,U_17063,U_17065),U_17067) != hAPP(c_Option_Ooption_OSome(U_17061),U_17069)
    | sP1105(U_17065,U_17061,U_17063,U_17069,U_17067)
    | hAPP(U_17065,U_17067) = hAPP(c_Option_Ooption_OSome(U_17061),U_17069) ),
    inference(clausify,[status(thm)],[f_4207_4]) ).

cnf(f_4207_6,plain,
    ( hAPP(c_Map_Omap__add(U_17060,U_17062,U_17064,U_17066),U_17068) = hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
    | sP1106(U_17070,U_17064,U_17062,U_17066,U_17068) ),
    inference(clausify,[status(thm)],[f_4207_4]) ).

cnf(f_4207_7,plain,
    ( hAPP(U_17065,U_17067) = c_Option_Ooption_ONone(U_17061)
    | ~ sP1105(U_17065,U_17061,U_17063,U_17069,U_17067) ),
    inference(clausify,[status(thm)],[f_4207_4]) ).

cnf(f_4207_8,plain,
    ( hAPP(U_17063,U_17067) = hAPP(c_Option_Ooption_OSome(U_17061),U_17069)
    | ~ sP1105(U_17065,U_17061,U_17063,U_17069,U_17067) ),
    inference(clausify,[status(thm)],[f_4207_4]) ).

cnf(f_4207_9,plain,
    ( hAPP(U_17066,U_17068) != hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
    | ~ sP1106(U_17070,U_17064,U_17062,U_17066,U_17068) ),
    inference(clausify,[status(thm)],[f_4207_4]) ).

cnf(f_4207_10,plain,
    ( hAPP(U_17064,U_17068) != hAPP(c_Option_Ooption_OSome(U_17062),U_17070)
    | hAPP(U_17066,U_17068) != c_Option_Ooption_ONone(U_17062)
    | ~ sP1106(U_17070,U_17064,U_17062,U_17066,U_17068) ),
    inference(clausify,[status(thm)],[f_4207_4]) ).

fof(f_4208_1,plain,
    ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_map__add__def]) ).

fof(f_4208_2,plain,
    ! [U_17075,U_17074,U_17073,U_17072,U_17071] : hAPP(c_Map_Omap__add(U_17071,U_17072,U_17073,U_17074),U_17075) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17072),U_17072,hAPP(U_17073,U_17075),c_Option_Ooption_OSome(U_17072)),hAPP(U_17074,U_17075)),
    inference(variable_rename,[status(thm)],[f_4208_1]) ).

fof(f_4208_3,plain,
    ! [U_17073,U_17075,U_17074,U_17072,U_17071] : hAPP(c_Map_Omap__add(U_17071,U_17072,U_17073,U_17074),U_17075) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17072),U_17072,hAPP(U_17073,U_17075),c_Option_Ooption_OSome(U_17072)),hAPP(U_17074,U_17075)),
    inference(definitional_conversion,[status(esa)],[f_4208_2]) ).

cnf(f_4208_4,plain,
    hAPP(c_Map_Omap__add(U_17071,U_17072,U_17073,U_17074),U_17075) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17072),U_17072,hAPP(U_17073,U_17075),c_Option_Ooption_OSome(U_17072)),hAPP(U_17074,U_17075)),
    inference(clausify,[status(thm)],[f_4208_3]) ).

fof(f_4209_1,plain,
    ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_map__add__empty]) ).

fof(f_4209_2,plain,
    ! [U_17078,U_17077,U_17076] : c_Map_Omap__add(U_17076,U_17077,U_17078,hAPP(c_COMBK(tc_Option_Ooption(U_17077),U_17076),c_Option_Ooption_ONone(U_17077))) = U_17078,
    inference(variable_rename,[status(thm)],[f_4209_1]) ).

fof(f_4209_3,plain,
    ! [U_17077,U_17078,U_17076] : c_Map_Omap__add(U_17076,U_17077,U_17078,hAPP(c_COMBK(tc_Option_Ooption(U_17077),U_17076),c_Option_Ooption_ONone(U_17077))) = U_17078,
    inference(definitional_conversion,[status(esa)],[f_4209_2]) ).

cnf(f_4209_4,plain,
    c_Map_Omap__add(U_17076,U_17077,U_17078,hAPP(c_COMBK(tc_Option_Ooption(U_17077),U_17076),c_Option_Ooption_ONone(U_17077))) = U_17078,
    inference(clausify,[status(thm)],[f_4209_3]) ).

fof(f_4210_1,plain,
    ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_empty__map__add]) ).

fof(f_4210_2,plain,
    ! [U_17081,U_17080,U_17079] : c_Map_Omap__add(U_17079,U_17080,hAPP(c_COMBK(tc_Option_Ooption(U_17080),U_17079),c_Option_Ooption_ONone(U_17080)),U_17081) = U_17081,
    inference(variable_rename,[status(thm)],[f_4210_1]) ).

fof(f_4210_3,plain,
    ! [U_17079,U_17080,U_17081] : c_Map_Omap__add(U_17079,U_17080,hAPP(c_COMBK(tc_Option_Ooption(U_17080),U_17079),c_Option_Ooption_ONone(U_17080)),U_17081) = U_17081,
    inference(definitional_conversion,[status(esa)],[f_4210_2]) ).

cnf(f_4210_4,plain,
    c_Map_Omap__add(U_17079,U_17080,hAPP(c_COMBK(tc_Option_Ooption(U_17080),U_17079),c_Option_Ooption_ONone(U_17080)),U_17081) = U_17081,
    inference(clausify,[status(thm)],[f_4210_3]) ).

fof(f_4211_1,plain,
    ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
      ( ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
        | hAPP(V_m_2,V_k_2) != c_Option_Ooption_ONone(T_b)
        | hAPP(V_n_2,V_k_2) != c_Option_Ooption_ONone(T_b) )
      & ( ( hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) )
        | hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) != c_Option_Ooption_ONone(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__None]) ).

fof(f_4211_2,plain,
    ! [U_17086,U_17085,U_17084,U_17083,U_17082] :
      ( ( hAPP(c_Map_Omap__add(U_17082,U_17083,U_17084,U_17085),U_17086) = c_Option_Ooption_ONone(U_17083)
        | hAPP(U_17084,U_17086) != c_Option_Ooption_ONone(U_17083)
        | hAPP(U_17085,U_17086) != c_Option_Ooption_ONone(U_17083) )
      & ( ( hAPP(U_17084,U_17086) = c_Option_Ooption_ONone(U_17083)
          & hAPP(U_17085,U_17086) = c_Option_Ooption_ONone(U_17083) )
        | hAPP(c_Map_Omap__add(U_17082,U_17083,U_17084,U_17085),U_17086) != c_Option_Ooption_ONone(U_17083) ) ),
    inference(variable_rename,[status(thm)],[f_4211_1]) ).

fof(f_4211_3,plain,
    ( ! [U_17096,U_17094,U_17092,U_17090] :
        ( ! [U_17088] : hAPP(c_Map_Omap__add(U_17088,U_17090,U_17092,U_17094),U_17096) = c_Option_Ooption_ONone(U_17090)
        | hAPP(U_17092,U_17096) != c_Option_Ooption_ONone(U_17090)
        | hAPP(U_17094,U_17096) != c_Option_Ooption_ONone(U_17090) )
    & ! [U_17095,U_17093,U_17091,U_17089] :
        ( ! [U_17087] : hAPP(c_Map_Omap__add(U_17087,U_17089,U_17091,U_17093),U_17095) != c_Option_Ooption_ONone(U_17089)
        | ( hAPP(U_17091,U_17095) = c_Option_Ooption_ONone(U_17089)
          & hAPP(U_17093,U_17095) = c_Option_Ooption_ONone(U_17089) ) ) ),
    inference(miniscope,[status(thm)],[f_4211_2]) ).

fof(f_4211_4,plain,
    ( ! [U_17089,U_17091,U_17093,U_17095] :
        ( hAPP(U_17091,U_17095) = c_Option_Ooption_ONone(U_17089)
        | ~ sP1107(U_17089,U_17091,U_17093,U_17095) )
    & ! [U_17089,U_17091,U_17093,U_17095] :
        ( hAPP(U_17093,U_17095) = c_Option_Ooption_ONone(U_17089)
        | ~ sP1107(U_17089,U_17091,U_17093,U_17095) )
    & ! [U_17090,U_17088,U_17092,U_17096,U_17094] :
        ( hAPP(c_Map_Omap__add(U_17088,U_17090,U_17092,U_17094),U_17096) = c_Option_Ooption_ONone(U_17090)
        | hAPP(U_17092,U_17096) != c_Option_Ooption_ONone(U_17090)
        | hAPP(U_17094,U_17096) != c_Option_Ooption_ONone(U_17090) )
    & ! [U_17087,U_17089,U_17091,U_17093,U_17095] :
        ( hAPP(c_Map_Omap__add(U_17087,U_17089,U_17091,U_17093),U_17095) != c_Option_Ooption_ONone(U_17089)
        | sP1107(U_17089,U_17091,U_17093,U_17095) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1107])],[f_4211_3]) ).

cnf(f_4211_5,plain,
    ( hAPP(c_Map_Omap__add(U_17087,U_17089,U_17091,U_17093),U_17095) != c_Option_Ooption_ONone(U_17089)
    | sP1107(U_17089,U_17091,U_17093,U_17095) ),
    inference(clausify,[status(thm)],[f_4211_4]) ).

cnf(f_4211_6,plain,
    ( hAPP(c_Map_Omap__add(U_17088,U_17090,U_17092,U_17094),U_17096) = c_Option_Ooption_ONone(U_17090)
    | hAPP(U_17092,U_17096) != c_Option_Ooption_ONone(U_17090)
    | hAPP(U_17094,U_17096) != c_Option_Ooption_ONone(U_17090) ),
    inference(clausify,[status(thm)],[f_4211_4]) ).

cnf(f_4211_7,plain,
    ( hAPP(U_17093,U_17095) = c_Option_Ooption_ONone(U_17089)
    | ~ sP1107(U_17089,U_17091,U_17093,U_17095) ),
    inference(clausify,[status(thm)],[f_4211_4]) ).

cnf(f_4211_8,plain,
    ( hAPP(U_17091,U_17095) = c_Option_Ooption_ONone(U_17089)
    | ~ sP1107(U_17089,U_17091,U_17093,U_17095) ),
    inference(clausify,[status(thm)],[f_4211_4]) ).

fof(f_4212_1,plain,
    ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2),
    inference(fof_nnf,[status(thm)],[fact_map__add__assoc]) ).

fof(f_4212_2,plain,
    ! [U_17101,U_17100,U_17099,U_17098,U_17097] : c_Map_Omap__add(U_17097,U_17098,U_17099,c_Map_Omap__add(U_17097,U_17098,U_17100,U_17101)) = c_Map_Omap__add(U_17097,U_17098,c_Map_Omap__add(U_17097,U_17098,U_17099,U_17100),U_17101),
    inference(variable_rename,[status(thm)],[f_4212_1]) ).

fof(f_4212_3,plain,
    ! [U_17099,U_17098,U_17100,U_17101,U_17097] : c_Map_Omap__add(U_17097,U_17098,U_17099,c_Map_Omap__add(U_17097,U_17098,U_17100,U_17101)) = c_Map_Omap__add(U_17097,U_17098,c_Map_Omap__add(U_17097,U_17098,U_17099,U_17100),U_17101),
    inference(definitional_conversion,[status(esa)],[f_4212_2]) ).

cnf(f_4212_4,plain,
    c_Map_Omap__add(U_17097,U_17098,U_17099,c_Map_Omap__add(U_17097,U_17098,U_17100,U_17101)) = c_Map_Omap__add(U_17097,U_17098,c_Map_Omap__add(U_17097,U_17098,U_17099,U_17100),U_17101),
    inference(clausify,[status(thm)],[f_4212_3]) ).

fof(f_4213_1,plain,
    ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
      ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
      | hAPP(V_n_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__find__right]) ).

fof(f_4213_2,plain,
    ! [U_17107,U_17106,U_17105,U_17104,U_17103,U_17102] :
      ( hAPP(c_Map_Omap__add(U_17106,U_17104,U_17107,U_17102),U_17103) = hAPP(c_Option_Ooption_OSome(U_17104),U_17105)
      | hAPP(U_17102,U_17103) != hAPP(c_Option_Ooption_OSome(U_17104),U_17105) ),
    inference(variable_rename,[status(thm)],[f_4213_1]) ).

fof(f_4213_3,plain,
    ! [U_17103,U_17102,U_17104,U_17105,U_17106,U_17107] :
      ( hAPP(c_Map_Omap__add(U_17106,U_17104,U_17107,U_17102),U_17103) = hAPP(c_Option_Ooption_OSome(U_17104),U_17105)
      | hAPP(U_17102,U_17103) != hAPP(c_Option_Ooption_OSome(U_17104),U_17105) ),
    inference(definitional_conversion,[status(esa)],[f_4213_2]) ).

cnf(f_4213_4,plain,
    ( hAPP(c_Map_Omap__add(U_17106,U_17104,U_17107,U_17102),U_17103) = hAPP(c_Option_Ooption_OSome(U_17104),U_17105)
    | hAPP(U_17102,U_17103) != hAPP(c_Option_Ooption_OSome(U_17104),U_17105) ),
    inference(clausify,[status(thm)],[f_4213_3]) ).

fof(f_4214_1,plain,
    ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
      ( hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I2_J]) ).

fof(f_4214_2,plain,
    ! [U_17112,U_17111,U_17110,U_17109,U_17108] :
      ( hAPP(c_Map_Omap__add(U_17108,U_17110,U_17111,U_17112),U_17109) = hAPP(U_17112,U_17109)
      | hBOOL(hAPP(hAPP(c_member(U_17108),U_17109),c_Map_Odom(U_17108,U_17110,U_17111))) ),
    inference(variable_rename,[status(thm)],[f_4214_1]) ).

fof(f_4214_3,plain,
    ! [U_17108,U_17109,U_17110,U_17111,U_17112] :
      ( hAPP(c_Map_Omap__add(U_17108,U_17110,U_17111,U_17112),U_17109) = hAPP(U_17112,U_17109)
      | hBOOL(hAPP(hAPP(c_member(U_17108),U_17109),c_Map_Odom(U_17108,U_17110,U_17111))) ),
    inference(definitional_conversion,[status(esa)],[f_4214_2]) ).

cnf(f_4214_4,plain,
    ( hAPP(c_Map_Omap__add(U_17108,U_17110,U_17111,U_17112),U_17109) = hAPP(U_17112,U_17109)
    | hBOOL(hAPP(hAPP(c_member(U_17108),U_17109),c_Map_Odom(U_17108,U_17110,U_17111))) ),
    inference(clausify,[status(thm)],[f_4214_3]) ).

fof(f_4215_1,plain,
    ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
      ( hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I3_J]) ).

fof(f_4215_2,plain,
    ! [U_17117,U_17116,U_17115,U_17114,U_17113] :
      ( hAPP(c_Map_Omap__add(U_17113,U_17115,U_17117,U_17116),U_17114) = hAPP(U_17117,U_17114)
      | hBOOL(hAPP(hAPP(c_member(U_17113),U_17114),c_Map_Odom(U_17113,U_17115,U_17116))) ),
    inference(variable_rename,[status(thm)],[f_4215_1]) ).

fof(f_4215_3,plain,
    ! [U_17113,U_17114,U_17115,U_17116,U_17117] :
      ( hAPP(c_Map_Omap__add(U_17113,U_17115,U_17117,U_17116),U_17114) = hAPP(U_17117,U_17114)
      | hBOOL(hAPP(hAPP(c_member(U_17113),U_17114),c_Map_Odom(U_17113,U_17115,U_17116))) ),
    inference(definitional_conversion,[status(esa)],[f_4215_2]) ).

cnf(f_4215_4,plain,
    ( hAPP(c_Map_Omap__add(U_17113,U_17115,U_17117,U_17116),U_17114) = hAPP(U_17117,U_17114)
    | hBOOL(hAPP(hAPP(c_member(U_17113),U_17114),c_Map_Odom(U_17113,U_17115,U_17116))) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

fof(f_4216_1,plain,
    ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
      ( hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I1_J]) ).

fof(f_4216_2,plain,
    ! [U_17122,U_17121,U_17120,U_17119,U_17118] :
      ( hAPP(c_Map_Omap__add(U_17118,U_17120,U_17122,U_17121),U_17119) = hAPP(U_17121,U_17119)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17118),U_17119),c_Map_Odom(U_17118,U_17120,U_17121))) ),
    inference(variable_rename,[status(thm)],[f_4216_1]) ).

fof(f_4216_3,plain,
    ! [U_17118,U_17119,U_17120,U_17121,U_17122] :
      ( hAPP(c_Map_Omap__add(U_17118,U_17120,U_17122,U_17121),U_17119) = hAPP(U_17121,U_17119)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17118),U_17119),c_Map_Odom(U_17118,U_17120,U_17121))) ),
    inference(definitional_conversion,[status(esa)],[f_4216_2]) ).

cnf(f_4216_4,plain,
    ( hAPP(c_Map_Omap__add(U_17118,U_17120,U_17122,U_17121),U_17119) = hAPP(U_17121,U_17119)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17118),U_17119),c_Map_Odom(U_17118,U_17120,U_17121))) ),
    inference(clausify,[status(thm)],[f_4216_3]) ).

fof(f_4217_1,plain,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_map__add__upd]) ).

fof(f_4217_2,plain,
    ! [U_17128,U_17127,U_17126,U_17125,U_17124,U_17123] : c_Map_Omap__add(U_17123,U_17124,U_17125,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17123,tc_Option_Ooption(U_17124)),U_17126),U_17127),hAPP(c_Option_Ooption_OSome(U_17124),U_17128))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17123,tc_Option_Ooption(U_17124)),c_Map_Omap__add(U_17123,U_17124,U_17125,U_17126)),U_17127),hAPP(c_Option_Ooption_OSome(U_17124),U_17128)),
    inference(variable_rename,[status(thm)],[f_4217_1]) ).

fof(f_4217_3,plain,
    ! [U_17123,U_17124,U_17125,U_17126,U_17127,U_17128] : c_Map_Omap__add(U_17123,U_17124,U_17125,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17123,tc_Option_Ooption(U_17124)),U_17126),U_17127),hAPP(c_Option_Ooption_OSome(U_17124),U_17128))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17123,tc_Option_Ooption(U_17124)),c_Map_Omap__add(U_17123,U_17124,U_17125,U_17126)),U_17127),hAPP(c_Option_Ooption_OSome(U_17124),U_17128)),
    inference(definitional_conversion,[status(esa)],[f_4217_2]) ).

cnf(f_4217_4,plain,
    c_Map_Omap__add(U_17123,U_17124,U_17125,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17123,tc_Option_Ooption(U_17124)),U_17126),U_17127),hAPP(c_Option_Ooption_OSome(U_17124),U_17128))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17123,tc_Option_Ooption(U_17124)),c_Map_Omap__add(U_17123,U_17124,U_17125,U_17126)),U_17127),hAPP(c_Option_Ooption_OSome(U_17124),U_17128)),
    inference(clausify,[status(thm)],[f_4217_3]) ).

fof(f_4218_1,plain,
    ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)),
    inference(fof_nnf,[status(thm)],[fact_dom__map__add]) ).

fof(f_4218_2,plain,
    ! [U_17132,U_17131,U_17130,U_17129] : c_Map_Odom(U_17129,U_17130,c_Map_Omap__add(U_17129,U_17130,U_17131,U_17132)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17129,tc_HOL_Obool)),c_Map_Odom(U_17129,U_17130,U_17132)),c_Map_Odom(U_17129,U_17130,U_17131)),
    inference(variable_rename,[status(thm)],[f_4218_1]) ).

fof(f_4218_3,plain,
    ! [U_17129,U_17130,U_17131,U_17132] : c_Map_Odom(U_17129,U_17130,c_Map_Omap__add(U_17129,U_17130,U_17131,U_17132)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17129,tc_HOL_Obool)),c_Map_Odom(U_17129,U_17130,U_17132)),c_Map_Odom(U_17129,U_17130,U_17131)),
    inference(definitional_conversion,[status(esa)],[f_4218_2]) ).

cnf(f_4218_4,plain,
    c_Map_Odom(U_17129,U_17130,c_Map_Omap__add(U_17129,U_17130,U_17131,U_17132)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17129,tc_HOL_Obool)),c_Map_Odom(U_17129,U_17130,U_17132)),c_Map_Odom(U_17129,U_17130,U_17131)),
    inference(clausify,[status(thm)],[f_4218_3]) ).

fof(f_4219_1,plain,
    ! [V_m_H_2,V_m_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2))
        | ~ c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) )
      & ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2))
        | ~ c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom]) ).

fof(f_4219_2,plain,
    ! [U_17136,U_17135,U_17134,U_17133] :
      ( ( c_Fun_Oinj__on(U_17133,tc_Option_Ooption(U_17134),c_Map_Omap__add(U_17133,U_17134,U_17135,U_17136),c_Map_Odom(U_17133,U_17134,U_17136))
        | ~ c_Fun_Oinj__on(U_17133,tc_Option_Ooption(U_17134),U_17136,c_Map_Odom(U_17133,U_17134,U_17136)) )
      & ( c_Fun_Oinj__on(U_17133,tc_Option_Ooption(U_17134),U_17136,c_Map_Odom(U_17133,U_17134,U_17136))
        | ~ c_Fun_Oinj__on(U_17133,tc_Option_Ooption(U_17134),c_Map_Omap__add(U_17133,U_17134,U_17135,U_17136),c_Map_Odom(U_17133,U_17134,U_17136)) ) ),
    inference(variable_rename,[status(thm)],[f_4219_1]) ).

fof(f_4219_3,plain,
    ( ! [U_17144,U_17142,U_17140,U_17138] :
        ( c_Fun_Oinj__on(U_17138,tc_Option_Ooption(U_17140),c_Map_Omap__add(U_17138,U_17140,U_17142,U_17144),c_Map_Odom(U_17138,U_17140,U_17144))
        | ~ c_Fun_Oinj__on(U_17138,tc_Option_Ooption(U_17140),U_17144,c_Map_Odom(U_17138,U_17140,U_17144)) )
    & ! [U_17143,U_17141,U_17139,U_17137] :
        ( c_Fun_Oinj__on(U_17137,tc_Option_Ooption(U_17139),U_17143,c_Map_Odom(U_17137,U_17139,U_17143))
        | ~ c_Fun_Oinj__on(U_17137,tc_Option_Ooption(U_17139),c_Map_Omap__add(U_17137,U_17139,U_17141,U_17143),c_Map_Odom(U_17137,U_17139,U_17143)) ) ),
    inference(miniscope,[status(thm)],[f_4219_2]) ).

fof(f_4219_4,plain,
    ( ! [U_17142,U_17140,U_17138,U_17144] :
        ( c_Fun_Oinj__on(U_17138,tc_Option_Ooption(U_17140),c_Map_Omap__add(U_17138,U_17140,U_17142,U_17144),c_Map_Odom(U_17138,U_17140,U_17144))
        | ~ c_Fun_Oinj__on(U_17138,tc_Option_Ooption(U_17140),U_17144,c_Map_Odom(U_17138,U_17140,U_17144)) )
    & ! [U_17139,U_17137,U_17143,U_17141] :
        ( c_Fun_Oinj__on(U_17137,tc_Option_Ooption(U_17139),U_17143,c_Map_Odom(U_17137,U_17139,U_17143))
        | ~ c_Fun_Oinj__on(U_17137,tc_Option_Ooption(U_17139),c_Map_Omap__add(U_17137,U_17139,U_17141,U_17143),c_Map_Odom(U_17137,U_17139,U_17143)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4219_3]) ).

cnf(f_4219_5,plain,
    ( c_Fun_Oinj__on(U_17137,tc_Option_Ooption(U_17139),U_17143,c_Map_Odom(U_17137,U_17139,U_17143))
    | ~ c_Fun_Oinj__on(U_17137,tc_Option_Ooption(U_17139),c_Map_Omap__add(U_17137,U_17139,U_17141,U_17143),c_Map_Odom(U_17137,U_17139,U_17143)) ),
    inference(clausify,[status(thm)],[f_4219_4]) ).

cnf(f_4219_6,plain,
    ( c_Fun_Oinj__on(U_17138,tc_Option_Ooption(U_17140),c_Map_Omap__add(U_17138,U_17140,U_17142,U_17144),c_Map_Odom(U_17138,U_17140,U_17144))
    | ~ c_Fun_Oinj__on(U_17138,tc_Option_Ooption(U_17140),U_17144,c_Map_Odom(U_17138,U_17140,U_17144)) ),
    inference(clausify,[status(thm)],[f_4219_4]) ).

fof(f_4220_1,plain,
    ! [V_m2_2,V_m1_2,T_c,T_b] :
      ( c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__comm]) ).

fof(f_4220_2,plain,
    ! [U_17148,U_17147,U_17146,U_17145] :
      ( c_Map_Omap__add(U_17145,U_17146,U_17147,U_17148) = c_Map_Omap__add(U_17145,U_17146,U_17148,U_17147)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17145,tc_HOL_Obool)),c_Map_Odom(U_17145,U_17146,U_17147)),c_Map_Odom(U_17145,U_17146,U_17148)) != c_Orderings_Obot__class_Obot(tc_fun(U_17145,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4220_1]) ).

fof(f_4220_3,plain,
    ! [U_17146,U_17145,U_17147,U_17148] :
      ( c_Map_Omap__add(U_17145,U_17146,U_17147,U_17148) = c_Map_Omap__add(U_17145,U_17146,U_17148,U_17147)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17145,tc_HOL_Obool)),c_Map_Odom(U_17145,U_17146,U_17147)),c_Map_Odom(U_17145,U_17146,U_17148)) != c_Orderings_Obot__class_Obot(tc_fun(U_17145,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_4220_2]) ).

cnf(f_4220_4,plain,
    ( c_Map_Omap__add(U_17145,U_17146,U_17147,U_17148) = c_Map_Omap__add(U_17145,U_17146,U_17148,U_17147)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17145,tc_HOL_Obool)),c_Map_Odom(U_17145,U_17146,U_17147)),c_Map_Odom(U_17145,U_17146,U_17148)) != c_Orderings_Obot__class_Obot(tc_fun(U_17145,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4220_3]) ).

fof(f_4221_1,plain,
    ! [V_l_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,c_Map_Omap__of(T_c,T_b,V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__map__of__map__add]) ).

fof(f_4221_2,plain,
    ! [U_17152,U_17151,U_17150,U_17149] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17149)),hAPP(c_Set_Oimage(U_17150,tc_Option_Ooption(U_17149),c_Map_Omap__add(U_17150,U_17149,U_17151,c_Map_Omap__of(U_17150,U_17149,U_17152))),c_Orderings_Otop__class_Otop(tc_fun(U_17150,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17149)),hAPP(c_Set_Oimage(U_17150,tc_Option_Ooption(U_17149),U_17151),c_Orderings_Otop__class_Otop(tc_fun(U_17150,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_4221_1]) ).

fof(f_4221_3,plain,
    ! [U_17149,U_17150,U_17151,U_17152] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17149)),hAPP(c_Set_Oimage(U_17150,tc_Option_Ooption(U_17149),c_Map_Omap__add(U_17150,U_17149,U_17151,c_Map_Omap__of(U_17150,U_17149,U_17152))),c_Orderings_Otop__class_Otop(tc_fun(U_17150,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17149)),hAPP(c_Set_Oimage(U_17150,tc_Option_Ooption(U_17149),U_17151),c_Orderings_Otop__class_Otop(tc_fun(U_17150,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_4221_2]) ).

cnf(f_4221_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17149)),hAPP(c_Set_Oimage(U_17150,tc_Option_Ooption(U_17149),c_Map_Omap__add(U_17150,U_17149,U_17151,c_Map_Omap__of(U_17150,U_17149,U_17152))),c_Orderings_Otop__class_Otop(tc_fun(U_17150,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17149)),hAPP(c_Set_Oimage(U_17150,tc_Option_Ooption(U_17149),U_17151),c_Orderings_Otop__class_Otop(tc_fun(U_17150,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_4221_3]) ).

fof(f_4222_1,plain,
    ! [V_r_2,V_yx_2,T_c,T_b] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2))
          & V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converseE]) ).

fof(f_4222_2,plain,
    ! [U_17158,U_17157,U_17156,U_17155] :
      ( ? [U_17154,U_17153] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17156,U_17155)),hAPP(hAPP(c_Product__Type_OPair(U_17156,U_17155),U_17154),U_17153)),U_17158))
          & U_17157 = hAPP(hAPP(c_Product__Type_OPair(U_17155,U_17156),U_17153),U_17154) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17155,U_17156)),U_17157),hAPP(c_Relation_Oconverse(U_17156,U_17155),U_17158))) ),
    inference(variable_rename,[status(thm)],[f_4222_1]) ).

fof(f_4222_3,plain,
    ! [U_17158,U_17157,U_17156,U_17155] :
      ( ? [U_17153] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17156,U_17155)),hAPP(hAPP(c_Product__Type_OPair(U_17156,U_17155),sK442(U_17158,U_17157,U_17156,U_17155)),U_17153)),U_17158))
          & U_17157 = hAPP(hAPP(c_Product__Type_OPair(U_17155,U_17156),U_17153),sK442(U_17158,U_17157,U_17156,U_17155)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17155,U_17156)),U_17157),hAPP(c_Relation_Oconverse(U_17156,U_17155),U_17158))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_17154,sK442(U_17158,U_17157,U_17156,U_17155))],[f_4222_2]) ).

fof(f_4222_4,plain,
    ! [U_17158,U_17157,U_17156,U_17155] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17156,U_17155)),hAPP(hAPP(c_Product__Type_OPair(U_17156,U_17155),sK442(U_17158,U_17157,U_17156,U_17155)),sK443(U_17158,U_17157,U_17156,U_17155))),U_17158))
        & U_17157 = hAPP(hAPP(c_Product__Type_OPair(U_17155,U_17156),sK443(U_17158,U_17157,U_17156,U_17155)),sK442(U_17158,U_17157,U_17156,U_17155)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17155,U_17156)),U_17157),hAPP(c_Relation_Oconverse(U_17156,U_17155),U_17158))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_17153,sK443(U_17158,U_17157,U_17156,U_17155))],[f_4222_3]) ).

fof(f_4222_5,plain,
    ( ! [U_17155,U_17156,U_17157,U_17158] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17156,U_17155)),hAPP(hAPP(c_Product__Type_OPair(U_17156,U_17155),sK442(U_17158,U_17157,U_17156,U_17155)),sK443(U_17158,U_17157,U_17156,U_17155))),U_17158))
        | ~ sP1108(U_17155,U_17156,U_17157,U_17158) )
    & ! [U_17155,U_17156,U_17157,U_17158] :
        ( U_17157 = hAPP(hAPP(c_Product__Type_OPair(U_17155,U_17156),sK443(U_17158,U_17157,U_17156,U_17155)),sK442(U_17158,U_17157,U_17156,U_17155))
        | ~ sP1108(U_17155,U_17156,U_17157,U_17158) )
    & ! [U_17155,U_17156,U_17157,U_17158] :
        ( sP1108(U_17155,U_17156,U_17157,U_17158)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17155,U_17156)),U_17157),hAPP(c_Relation_Oconverse(U_17156,U_17155),U_17158))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1108])],[f_4222_4]) ).

cnf(f_4222_6,plain,
    ( sP1108(U_17155,U_17156,U_17157,U_17158)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17155,U_17156)),U_17157),hAPP(c_Relation_Oconverse(U_17156,U_17155),U_17158))) ),
    inference(clausify,[status(thm)],[f_4222_5]) ).

cnf(f_4222_7,plain,
    ( U_17157 = hAPP(hAPP(c_Product__Type_OPair(U_17155,U_17156),sK443(U_17158,U_17157,U_17156,U_17155)),sK442(U_17158,U_17157,U_17156,U_17155))
    | ~ sP1108(U_17155,U_17156,U_17157,U_17158) ),
    inference(clausify,[status(thm)],[f_4222_5]) ).

cnf(f_4222_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17156,U_17155)),hAPP(hAPP(c_Product__Type_OPair(U_17156,U_17155),sK442(U_17158,U_17157,U_17156,U_17155)),sK443(U_17158,U_17157,U_17156,U_17155))),U_17158))
    | ~ sP1108(U_17155,U_17156,U_17157,U_17158) ),
    inference(clausify,[status(thm)],[f_4222_5]) ).

fof(f_4223_1,plain,
    ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_l_2)))),
    inference(fof_nnf,[status(thm)],[fact_finite__dom__map__of]) ).

fof(f_4223_2,plain,
    ! [U_17161,U_17160,U_17159] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17159),c_Map_Odom(U_17159,U_17160,c_Map_Omap__of(U_17159,U_17160,U_17161)))),
    inference(variable_rename,[status(thm)],[f_4223_1]) ).

fof(f_4223_3,plain,
    ! [U_17161,U_17159,U_17160] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17159),c_Map_Odom(U_17159,U_17160,c_Map_Omap__of(U_17159,U_17160,U_17161)))),
    inference(definitional_conversion,[status(esa)],[f_4223_2]) ).

cnf(f_4223_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17159),c_Map_Odom(U_17159,U_17160,c_Map_Omap__of(U_17159,U_17160,U_17161)))),
    inference(clausify,[status(thm)],[f_4223_3]) ).

fof(f_4224_1,plain,
    ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__of(T_c,T_b,V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_finite__range__map__of]) ).

fof(f_4224_2,plain,
    ! [U_17164,U_17163,U_17162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17162)),hAPP(c_Set_Oimage(U_17163,tc_Option_Ooption(U_17162),c_Map_Omap__of(U_17163,U_17162,U_17164)),c_Orderings_Otop__class_Otop(tc_fun(U_17163,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4224_1]) ).

fof(f_4224_3,plain,
    ! [U_17162,U_17163,U_17164] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17162)),hAPP(c_Set_Oimage(U_17163,tc_Option_Ooption(U_17162),c_Map_Omap__of(U_17163,U_17162,U_17164)),c_Orderings_Otop__class_Otop(tc_fun(U_17163,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4224_2]) ).

cnf(f_4224_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17162)),hAPP(c_Set_Oimage(U_17163,tc_Option_Ooption(U_17162),c_Map_Omap__of(U_17163,U_17162,U_17164)),c_Orderings_Otop__class_Otop(tc_fun(U_17163,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4224_3]) ).

fof(f_4225_1,plain,
    ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2),
    inference(fof_nnf,[status(thm)],[fact_map__add__map__of__foldr]) ).

fof(f_4225_2,plain,
    ! [U_17168,U_17167,U_17166,U_17165] : c_Map_Omap__add(U_17165,U_17166,U_17167,c_Map_Omap__of(U_17165,U_17166,U_17168)) = c_List_Ofoldr(tc_prod(U_17165,U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17165,U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),hAPP(hAPP(c_COMBC(U_17165,tc_fun(U_17166,tc_Option_Ooption(U_17166)),tc_fun(U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),tc_fun(tc_fun(U_17166,tc_Option_Ooption(U_17166)),tc_fun(U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))))),U_17165),c_COMBB(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))),U_17166)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),tc_fun(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),U_17165),c_COMBC(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),hAPP(c_COMBC(tc_fun(U_17165,tc_Option_Ooption(U_17166)),U_17165,tc_fun(tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),c_Fun_Ofun__upd(U_17165,tc_Option_Ooption(U_17166)))))),c_Option_Ooption_OSome(U_17166))),U_17168,U_17167),
    inference(variable_rename,[status(thm)],[f_4225_1]) ).

fof(f_4225_3,plain,
    ! [U_17165,U_17166,U_17167,U_17168] : c_Map_Omap__add(U_17165,U_17166,U_17167,c_Map_Omap__of(U_17165,U_17166,U_17168)) = c_List_Ofoldr(tc_prod(U_17165,U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17165,U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),hAPP(hAPP(c_COMBC(U_17165,tc_fun(U_17166,tc_Option_Ooption(U_17166)),tc_fun(U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),tc_fun(tc_fun(U_17166,tc_Option_Ooption(U_17166)),tc_fun(U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))))),U_17165),c_COMBB(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))),U_17166)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),tc_fun(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),U_17165),c_COMBC(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),hAPP(c_COMBC(tc_fun(U_17165,tc_Option_Ooption(U_17166)),U_17165,tc_fun(tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),c_Fun_Ofun__upd(U_17165,tc_Option_Ooption(U_17166)))))),c_Option_Ooption_OSome(U_17166))),U_17168,U_17167),
    inference(definitional_conversion,[status(esa)],[f_4225_2]) ).

cnf(f_4225_4,plain,
    c_Map_Omap__add(U_17165,U_17166,U_17167,c_Map_Omap__of(U_17165,U_17166,U_17168)) = c_List_Ofoldr(tc_prod(U_17165,U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17165,U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),hAPP(hAPP(c_COMBC(U_17165,tc_fun(U_17166,tc_Option_Ooption(U_17166)),tc_fun(U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),tc_fun(tc_fun(U_17166,tc_Option_Ooption(U_17166)),tc_fun(U_17166,tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))))),U_17165),c_COMBB(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166))),U_17166)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),tc_fun(tc_Option_Ooption(U_17166),tc_fun(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),U_17165),c_COMBC(tc_fun(U_17165,tc_Option_Ooption(U_17166)),tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),hAPP(c_COMBC(tc_fun(U_17165,tc_Option_Ooption(U_17166)),U_17165,tc_fun(tc_Option_Ooption(U_17166),tc_fun(U_17165,tc_Option_Ooption(U_17166)))),c_Fun_Ofun__upd(U_17165,tc_Option_Ooption(U_17166)))))),c_Option_Ooption_OSome(U_17166))),U_17168,U_17167),
    inference(clausify,[status(thm)],[f_4225_3]) ).

fof(f_4226_1,plain,
    ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_]) ).

fof(f_4226_2,plain,
    ! [U_17171,U_17170,U_17169] : c_Smallcheck_Oorelse(U_17169,U_17170,U_17171) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17169),U_17169,U_17171,c_Option_Ooption_OSome(U_17169)),U_17170),
    inference(variable_rename,[status(thm)],[f_4226_1]) ).

fof(f_4226_3,plain,
    ! [U_17170,U_17169,U_17171] : c_Smallcheck_Oorelse(U_17169,U_17170,U_17171) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17169),U_17169,U_17171,c_Option_Ooption_OSome(U_17169)),U_17170),
    inference(definitional_conversion,[status(esa)],[f_4226_2]) ).

cnf(f_4226_4,plain,
    c_Smallcheck_Oorelse(U_17169,U_17170,U_17171) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17169),U_17169,U_17171,c_Option_Ooption_OSome(U_17169)),U_17170),
    inference(clausify,[status(thm)],[f_4226_3]) ).

fof(f_4227_1,plain,
    ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))),
    inference(fof_nnf,[status(thm)],[fact_full__small__int__def]) ).

fof(f_4227_2,plain,
    ! [U_17173,U_17172] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17172,U_17173) = c_Smallcheck_Ofull__small_H(U_17172,hAPP(c_Code__Numeral_Oint__of,U_17173),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17173))),
    inference(variable_rename,[status(thm)],[f_4227_1]) ).

fof(f_4227_3,plain,
    ! [U_17172,U_17173] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17172,U_17173) = c_Smallcheck_Ofull__small_H(U_17172,hAPP(c_Code__Numeral_Oint__of,U_17173),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17173))),
    inference(definitional_conversion,[status(esa)],[f_4227_2]) ).

cnf(f_4227_4,plain,
    c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17172,U_17173) = c_Smallcheck_Ofull__small_H(U_17172,hAPP(c_Code__Numeral_Oint__of,U_17173),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17173))),
    inference(clausify,[status(thm)],[f_4227_3]) ).

fof(f_4228_1,plain,
    ! [V_f_2,V_i_2,V_d_2] :
      ( ( c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) )
      & ( c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_small_H_Osimps]) ).

fof(f_4228_2,plain,
    ! [U_17176,U_17175,U_17174] :
      ( ( c_Smallcheck_Osmall_H(U_17176,U_17174,U_17175) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17176,U_17174,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17175),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17176,U_17175))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17174),U_17175)) )
      & ( c_Smallcheck_Osmall_H(U_17176,U_17174,U_17175) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17174),U_17175)) ) ),
    inference(variable_rename,[status(thm)],[f_4228_1]) ).

fof(f_4228_3,plain,
    ( ! [U_17182,U_17180,U_17178] :
        ( c_Smallcheck_Osmall_H(U_17182,U_17178,U_17180) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17182,U_17178,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17180),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17182,U_17180))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17178),U_17180)) )
    & ! [U_17181,U_17179,U_17177] :
        ( c_Smallcheck_Osmall_H(U_17181,U_17177,U_17179) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17177),U_17179)) ) ),
    inference(miniscope,[status(thm)],[f_4228_2]) ).

fof(f_4228_4,plain,
    ( ! [U_17180,U_17182,U_17178] :
        ( c_Smallcheck_Osmall_H(U_17182,U_17178,U_17180) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17182,U_17178,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17180),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17182,U_17180))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17178),U_17180)) )
    & ! [U_17177,U_17181,U_17179] :
        ( c_Smallcheck_Osmall_H(U_17181,U_17177,U_17179) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17177),U_17179)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4228_3]) ).

cnf(f_4228_5,plain,
    ( c_Smallcheck_Osmall_H(U_17181,U_17177,U_17179) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17177),U_17179)) ),
    inference(clausify,[status(thm)],[f_4228_4]) ).

cnf(f_4228_6,plain,
    ( c_Smallcheck_Osmall_H(U_17182,U_17178,U_17180) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17182,U_17178,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17180),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17182,U_17180))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17178),U_17180)) ),
    inference(clausify,[status(thm)],[f_4228_4]) ).

fof(f_4229_1,plain,
    ! [V_i_2,V_d_2,V_f_2] :
      ( ( ( c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) )
        & ( c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_small_H_Opsimps]) ).

fof(f_4229_2,plain,
    ! [U_17185,U_17184,U_17183] :
      ( ( ( c_Smallcheck_Osmall_H(U_17183,U_17184,U_17185) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17183,U_17184,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17185),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17183,U_17185))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17184),U_17185)) )
        & ( c_Smallcheck_Osmall_H(U_17183,U_17184,U_17185) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17184),U_17185)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17183),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17184),U_17185)))) ),
    inference(variable_rename,[status(thm)],[f_4229_1]) ).

fof(f_4229_3,plain,
    ( ! [U_17183,U_17184,U_17185] :
        ( c_Smallcheck_Osmall_H(U_17183,U_17184,U_17185) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17183,U_17184,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17185),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17183,U_17185))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17184),U_17185))
        | ~ sP1109(U_17183,U_17184,U_17185) )
    & ! [U_17183,U_17184,U_17185] :
        ( c_Smallcheck_Osmall_H(U_17183,U_17184,U_17185) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17184),U_17185))
        | ~ sP1109(U_17183,U_17184,U_17185) )
    & ! [U_17183,U_17184,U_17185] :
        ( sP1109(U_17183,U_17184,U_17185)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17183),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17184),U_17185)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1109])],[f_4229_2]) ).

cnf(f_4229_4,plain,
    ( sP1109(U_17183,U_17184,U_17185)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17183),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17184),U_17185)))) ),
    inference(clausify,[status(thm)],[f_4229_3]) ).

cnf(f_4229_5,plain,
    ( c_Smallcheck_Osmall_H(U_17183,U_17184,U_17185) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17184),U_17185))
    | ~ sP1109(U_17183,U_17184,U_17185) ),
    inference(clausify,[status(thm)],[f_4229_3]) ).

cnf(f_4229_6,plain,
    ( c_Smallcheck_Osmall_H(U_17183,U_17184,U_17185) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(U_17183,U_17184,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17185),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17183,U_17185))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17184),U_17185))
    | ~ sP1109(U_17183,U_17184,U_17185) ),
    inference(clausify,[status(thm)],[f_4229_3]) ).

fof(f_4230_1,plain,
    ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))),
    inference(fof_nnf,[status(thm)],[fact_small__int__def]) ).

fof(f_4230_2,plain,
    ! [U_17187,U_17186] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17186),U_17187) = c_Smallcheck_Osmall_H(U_17186,hAPP(c_Code__Numeral_Oint__of,U_17187),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17187))),
    inference(variable_rename,[status(thm)],[f_4230_1]) ).

fof(f_4230_3,plain,
    ! [U_17187,U_17186] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17186),U_17187) = c_Smallcheck_Osmall_H(U_17186,hAPP(c_Code__Numeral_Oint__of,U_17187),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17187))),
    inference(definitional_conversion,[status(esa)],[f_4230_2]) ).

cnf(f_4230_4,plain,
    hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17186),U_17187) = c_Smallcheck_Osmall_H(U_17186,hAPP(c_Code__Numeral_Oint__of,U_17187),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17187))),
    inference(clausify,[status(thm)],[f_4230_3]) ).

fof(f_4231_1,plain,
    ! [V_d_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2)
      | ~ class_Smallcheck_Osmall(T_b)
      | ~ class_Smallcheck_Osmall(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_small__prod__def]) ).

fof(f_4231_2,plain,
    ! [U_17191,U_17190,U_17189,U_17188] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17189,U_17188)),U_17190),U_17191) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17189),hAPP(hAPP(c_COMBC(U_17189,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17188,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17189),c_Smallcheck_Osmall__class_Osmall(U_17188)),hAPP(hAPP(c_COMBB(tc_fun(U_17188,tc_prod(U_17189,U_17188)),tc_fun(U_17188,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17189),hAPP(c_COMBB(tc_prod(U_17189,U_17188),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17188),U_17190)),c_Product__Type_OPair(U_17189,U_17188)))),U_17191)),U_17191)
      | ~ class_Smallcheck_Osmall(U_17189)
      | ~ class_Smallcheck_Osmall(U_17188) ),
    inference(variable_rename,[status(thm)],[f_4231_1]) ).

fof(f_4231_3,plain,
    ! [U_17189,U_17188,U_17190,U_17191] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17189,U_17188)),U_17190),U_17191) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17189),hAPP(hAPP(c_COMBC(U_17189,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17188,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17189),c_Smallcheck_Osmall__class_Osmall(U_17188)),hAPP(hAPP(c_COMBB(tc_fun(U_17188,tc_prod(U_17189,U_17188)),tc_fun(U_17188,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17189),hAPP(c_COMBB(tc_prod(U_17189,U_17188),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17188),U_17190)),c_Product__Type_OPair(U_17189,U_17188)))),U_17191)),U_17191)
      | ~ class_Smallcheck_Osmall(U_17189)
      | ~ class_Smallcheck_Osmall(U_17188) ),
    inference(definitional_conversion,[status(esa)],[f_4231_2]) ).

cnf(f_4231_4,plain,
    ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17189,U_17188)),U_17190),U_17191) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17189),hAPP(hAPP(c_COMBC(U_17189,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17188,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17189),c_Smallcheck_Osmall__class_Osmall(U_17188)),hAPP(hAPP(c_COMBB(tc_fun(U_17188,tc_prod(U_17189,U_17188)),tc_fun(U_17188,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17189),hAPP(c_COMBB(tc_prod(U_17189,U_17188),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17188),U_17190)),c_Product__Type_OPair(U_17189,U_17188)))),U_17191)),U_17191)
    | ~ class_Smallcheck_Osmall(U_17189)
    | ~ class_Smallcheck_Osmall(U_17188) ),
    inference(clausify,[status(thm)],[f_4231_3]) ).

fof(f_4232_1,plain,
    ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2))
      | ? [B_f,B_d,B_i] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i))
          & ( hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(B_f,B_i) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_small_H_Opinduct]) ).

fof(f_4232_2,plain,
    ! [U_17198,U_17197,U_17196,U_17195] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17195),U_17196),U_17197))
      | ? [U_17194,U_17193,U_17192] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17198,U_17194),U_17193),U_17192))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17194),U_17193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17192),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(U_17194,U_17192) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17193),U_17192)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17194),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17193),U_17192)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17195),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17196),U_17197)))) ),
    inference(variable_rename,[status(thm)],[f_4232_1]) ).

fof(f_4232_3,plain,
    ! [U_17198,U_17197,U_17196,U_17195] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17195),U_17196),U_17197))
      | ? [U_17193,U_17192] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),U_17193),U_17192))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),U_17193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17192),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK444(U_17198,U_17197,U_17196,U_17195),U_17192) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17193),U_17192)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),sK444(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17193),U_17192)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17195),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17196),U_17197)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_17194,sK444(U_17198,U_17197,U_17196,U_17195))],[f_4232_2]) ).

fof(f_4232_4,plain,
    ! [U_17198,U_17197,U_17196,U_17195] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17195),U_17196),U_17197))
      | ? [U_17192] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),U_17192))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17192),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK444(U_17198,U_17197,U_17196,U_17195),U_17192) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),U_17192)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),sK444(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),U_17192)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17195),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17196),U_17197)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_17193,sK445(U_17198,U_17197,U_17196,U_17195))],[f_4232_3]) ).

fof(f_4232_5,plain,
    ! [U_17198,U_17197,U_17196,U_17195] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17195),U_17196),U_17197))
      | ( ~ hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))
        & ( hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK446(U_17198,U_17197,U_17196,U_17195)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hAPP(sK444(U_17198,U_17197,U_17196,U_17195),sK446(U_17198,U_17197,U_17196,U_17195)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),sK444(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195))))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17195),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17196),U_17197)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_17192,sK446(U_17198,U_17197,U_17196,U_17195))],[f_4232_4]) ).

fof(f_4232_6,plain,
    ( ! [U_17195,U_17196,U_17197,U_17198] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))
        | ~ sP1110(U_17195,U_17196,U_17197,U_17198) )
    & ! [U_17195,U_17196,U_17197,U_17198] :
        ( hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK446(U_17198,U_17197,U_17196,U_17195)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hAPP(sK444(U_17198,U_17197,U_17196,U_17195),sK446(U_17198,U_17197,U_17196,U_17195)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))
        | ~ sP1110(U_17195,U_17196,U_17197,U_17198) )
    & ! [U_17195,U_17196,U_17197,U_17198] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),sK444(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))))
        | ~ sP1110(U_17195,U_17196,U_17197,U_17198) )
    & ! [U_17195,U_17196,U_17197,U_17198] :
        ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17195),U_17196),U_17197))
        | sP1110(U_17195,U_17196,U_17197,U_17198)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17195),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17196),U_17197)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1110])],[f_4232_5]) ).

cnf(f_4232_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_17198,U_17195),U_17196),U_17197))
    | sP1110(U_17195,U_17196,U_17197,U_17198)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),U_17195),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17196),U_17197)))) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_8,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),sK444(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))))
    | ~ sP1110(U_17195,U_17196,U_17197,U_17198) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK446(U_17198,U_17197,U_17196,U_17195)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hAPP(sK444(U_17198,U_17197,U_17196,U_17195),sK446(U_17198,U_17197,U_17196,U_17195)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))
    | ~ sP1110(U_17195,U_17196,U_17197,U_17198) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_10,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_17198,sK444(U_17198,U_17197,U_17196,U_17195)),sK445(U_17198,U_17197,U_17196,U_17195)),sK446(U_17198,U_17197,U_17196,U_17195)))
    | ~ sP1110(U_17195,U_17196,U_17197,U_17198) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

fof(f_4233_1,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(fof_nnf,[status(thm)],[fact_body__def]) ).

fof(f_4233_2,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(definitional_conversion,[status(esa)],[f_4233_1]) ).

cnf(f_4233_3,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(clausify,[status(thm)],[f_4233_2]) ).

fof(f_4234_1,plain,
    ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
      ( hAPP(c_Map_Omap__of(T_c,T_d,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
      | hAPP(c_Map_Omap__of(T_b,T_d,V_t_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__mapk__SomeI]) ).

fof(f_4234_2,plain,
    ! [U_17205,U_17204,U_17203,U_17202,U_17201,U_17200,U_17199] :
      ( hAPP(c_Map_Omap__of(U_17200,U_17202,hAPP(hAPP(c_List_Omap(tc_prod(U_17199,U_17202),tc_prod(U_17200,U_17202)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17199,U_17202,tc_prod(U_17200,U_17202)),hAPP(hAPP(c_COMBB(U_17200,tc_fun(U_17202,tc_prod(U_17200,U_17202)),U_17199),c_Product__Type_OPair(U_17200,U_17202)),U_17201))),U_17203)),hAPP(U_17201,U_17204)) = hAPP(c_Option_Ooption_OSome(U_17202),U_17205)
      | hAPP(c_Map_Omap__of(U_17199,U_17202,U_17203),U_17204) != hAPP(c_Option_Ooption_OSome(U_17202),U_17205)
      | ~ c_Fun_Oinj__on(U_17199,U_17200,U_17201,c_Orderings_Otop__class_Otop(tc_fun(U_17199,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4234_1]) ).

fof(f_4234_3,plain,
    ! [U_17202,U_17201,U_17199,U_17200,U_17203,U_17204,U_17205] :
      ( hAPP(c_Map_Omap__of(U_17200,U_17202,hAPP(hAPP(c_List_Omap(tc_prod(U_17199,U_17202),tc_prod(U_17200,U_17202)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17199,U_17202,tc_prod(U_17200,U_17202)),hAPP(hAPP(c_COMBB(U_17200,tc_fun(U_17202,tc_prod(U_17200,U_17202)),U_17199),c_Product__Type_OPair(U_17200,U_17202)),U_17201))),U_17203)),hAPP(U_17201,U_17204)) = hAPP(c_Option_Ooption_OSome(U_17202),U_17205)
      | hAPP(c_Map_Omap__of(U_17199,U_17202,U_17203),U_17204) != hAPP(c_Option_Ooption_OSome(U_17202),U_17205)
      | ~ c_Fun_Oinj__on(U_17199,U_17200,U_17201,c_Orderings_Otop__class_Otop(tc_fun(U_17199,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4234_2]) ).

cnf(f_4234_4,plain,
    ( hAPP(c_Map_Omap__of(U_17200,U_17202,hAPP(hAPP(c_List_Omap(tc_prod(U_17199,U_17202),tc_prod(U_17200,U_17202)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17199,U_17202,tc_prod(U_17200,U_17202)),hAPP(hAPP(c_COMBB(U_17200,tc_fun(U_17202,tc_prod(U_17200,U_17202)),U_17199),c_Product__Type_OPair(U_17200,U_17202)),U_17201))),U_17203)),hAPP(U_17201,U_17204)) = hAPP(c_Option_Ooption_OSome(U_17202),U_17205)
    | hAPP(c_Map_Omap__of(U_17199,U_17202,U_17203),U_17204) != hAPP(c_Option_Ooption_OSome(U_17202),U_17205)
    | ~ c_Fun_Oinj__on(U_17199,U_17200,U_17201,c_Orderings_Otop__class_Otop(tc_fun(U_17199,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4234_3]) ).

fof(f_4235_1,plain,
    ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_map__comp__def]) ).

fof(f_4235_2,plain,
    ! [U_17211,U_17210,U_17209,U_17208,U_17207,U_17206] : c_Map_Omap__comp(U_17206,U_17207,U_17208,U_17209,U_17210,U_17211) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17207),U_17206,c_Option_Ooption_ONone(U_17207),U_17209),hAPP(U_17210,U_17211)),
    inference(variable_rename,[status(thm)],[f_4235_1]) ).

fof(f_4235_3,plain,
    ! [U_17206,U_17207,U_17208,U_17209,U_17210,U_17211] : c_Map_Omap__comp(U_17206,U_17207,U_17208,U_17209,U_17210,U_17211) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17207),U_17206,c_Option_Ooption_ONone(U_17207),U_17209),hAPP(U_17210,U_17211)),
    inference(definitional_conversion,[status(esa)],[f_4235_2]) ).

cnf(f_4235_4,plain,
    c_Map_Omap__comp(U_17206,U_17207,U_17208,U_17209,U_17210,U_17211) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17207),U_17206,c_Option_Ooption_ONone(U_17207),U_17209),hAPP(U_17210,U_17211)),
    inference(clausify,[status(thm)],[f_4235_3]) ).

fof(f_4236_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__mapI]) ).

fof(f_4236_2,plain,
    ! [U_17214,U_17213,U_17212] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17212),tc_List_Olist(U_17213),hAPP(c_List_Omap(U_17212,U_17213),U_17214),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17212),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17212,U_17213,U_17214,c_Orderings_Otop__class_Otop(tc_fun(U_17212,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4236_1]) ).

fof(f_4236_3,plain,
    ! [U_17212,U_17213,U_17214] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17212),tc_List_Olist(U_17213),hAPP(c_List_Omap(U_17212,U_17213),U_17214),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17212),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17212,U_17213,U_17214,c_Orderings_Otop__class_Otop(tc_fun(U_17212,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4236_2]) ).

cnf(f_4236_4,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17212),tc_List_Olist(U_17213),hAPP(c_List_Omap(U_17212,U_17213),U_17214),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17212),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17212,U_17213,U_17214,c_Orderings_Otop__class_Otop(tc_fun(U_17212,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4236_3]) ).

fof(f_4237_1,plain,
    ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
      ( c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d)
      | hAPP(V_m2_2,V_k_2) != c_Option_Ooption_ONone(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I1_J]) ).

fof(f_4237_2,plain,
    ! [U_17220,U_17219,U_17218,U_17217,U_17216,U_17215] :
      ( c_Map_Omap__comp(U_17217,U_17218,U_17219,U_17220,U_17215,U_17216) = c_Option_Ooption_ONone(U_17218)
      | hAPP(U_17215,U_17216) != c_Option_Ooption_ONone(U_17217) ),
    inference(variable_rename,[status(thm)],[f_4237_1]) ).

fof(f_4237_3,plain,
    ! [U_17216,U_17217,U_17215,U_17218,U_17219,U_17220] :
      ( c_Map_Omap__comp(U_17217,U_17218,U_17219,U_17220,U_17215,U_17216) = c_Option_Ooption_ONone(U_17218)
      | hAPP(U_17215,U_17216) != c_Option_Ooption_ONone(U_17217) ),
    inference(definitional_conversion,[status(esa)],[f_4237_2]) ).

cnf(f_4237_4,plain,
    ( c_Map_Omap__comp(U_17217,U_17218,U_17219,U_17220,U_17215,U_17216) = c_Option_Ooption_ONone(U_17218)
    | hAPP(U_17215,U_17216) != c_Option_Ooption_ONone(U_17217) ),
    inference(clausify,[status(thm)],[f_4237_3]) ).

fof(f_4238_1,plain,
    ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
      ( ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
        | ! [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) != hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
            | hAPP(V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_c),B_k_H) ) )
      & ( ? [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
            & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) )
        | c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__Some__iff]) ).

fof(f_4238_2,plain,
    ! [U_17229,U_17228,U_17227,U_17226,U_17225,U_17224,U_17223] :
      ( ( c_Map_Omap__comp(U_17223,U_17224,U_17225,U_17226,U_17227,U_17228) = hAPP(c_Option_Ooption_OSome(U_17224),U_17229)
        | ! [U_17222] :
            ( hAPP(U_17226,U_17222) != hAPP(c_Option_Ooption_OSome(U_17224),U_17229)
            | hAPP(U_17227,U_17228) != hAPP(c_Option_Ooption_OSome(U_17223),U_17222) ) )
      & ( ? [U_17221] :
            ( hAPP(U_17226,U_17221) = hAPP(c_Option_Ooption_OSome(U_17224),U_17229)
            & hAPP(U_17227,U_17228) = hAPP(c_Option_Ooption_OSome(U_17223),U_17221) )
        | c_Map_Omap__comp(U_17223,U_17224,U_17225,U_17226,U_17227,U_17228) != hAPP(c_Option_Ooption_OSome(U_17224),U_17229) ) ),
    inference(variable_rename,[status(thm)],[f_4238_1]) ).

fof(f_4238_3,plain,
    ( ! [U_17243,U_17241,U_17239,U_17237,U_17235,U_17233,U_17231] :
        ( c_Map_Omap__comp(U_17231,U_17233,U_17235,U_17237,U_17239,U_17241) = hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
        | ! [U_17222] :
            ( hAPP(U_17237,U_17222) != hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
            | hAPP(U_17239,U_17241) != hAPP(c_Option_Ooption_OSome(U_17231),U_17222) ) )
    & ! [U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230] :
        ( ? [U_17221] :
            ( hAPP(U_17236,U_17221) = hAPP(c_Option_Ooption_OSome(U_17232),U_17242)
            & hAPP(U_17238,U_17240) = hAPP(c_Option_Ooption_OSome(U_17230),U_17221) )
        | c_Map_Omap__comp(U_17230,U_17232,U_17234,U_17236,U_17238,U_17240) != hAPP(c_Option_Ooption_OSome(U_17232),U_17242) ) ),
    inference(miniscope,[status(thm)],[f_4238_2]) ).

fof(f_4238_4,plain,
    ( ! [U_17243,U_17241,U_17239,U_17237,U_17235,U_17233,U_17231] :
        ( c_Map_Omap__comp(U_17231,U_17233,U_17235,U_17237,U_17239,U_17241) = hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
        | ! [U_17222] :
            ( hAPP(U_17237,U_17222) != hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
            | hAPP(U_17239,U_17241) != hAPP(c_Option_Ooption_OSome(U_17231),U_17222) ) )
    & ! [U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230] :
        ( ( hAPP(U_17236,sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230)) = hAPP(c_Option_Ooption_OSome(U_17232),U_17242)
          & hAPP(U_17238,U_17240) = hAPP(c_Option_Ooption_OSome(U_17230),sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230)) )
        | c_Map_Omap__comp(U_17230,U_17232,U_17234,U_17236,U_17238,U_17240) != hAPP(c_Option_Ooption_OSome(U_17232),U_17242) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_17221,sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230))],[f_4238_3]) ).

fof(f_4238_5,plain,
    ( ! [U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242] :
        ( hAPP(U_17236,sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230)) = hAPP(c_Option_Ooption_OSome(U_17232),U_17242)
        | ~ sP1111(U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242) )
    & ! [U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242] :
        ( hAPP(U_17238,U_17240) = hAPP(c_Option_Ooption_OSome(U_17230),sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230))
        | ~ sP1111(U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242) )
    & ! [U_17235,U_17243,U_17233,U_17222,U_17231,U_17237,U_17241,U_17239] :
        ( c_Map_Omap__comp(U_17231,U_17233,U_17235,U_17237,U_17239,U_17241) = hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
        | hAPP(U_17237,U_17222) != hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
        | hAPP(U_17239,U_17241) != hAPP(c_Option_Ooption_OSome(U_17231),U_17222) )
    & ! [U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242] :
        ( sP1111(U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242)
        | c_Map_Omap__comp(U_17230,U_17232,U_17234,U_17236,U_17238,U_17240) != hAPP(c_Option_Ooption_OSome(U_17232),U_17242) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1111])],[f_4238_4]) ).

cnf(f_4238_6,plain,
    ( sP1111(U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242)
    | c_Map_Omap__comp(U_17230,U_17232,U_17234,U_17236,U_17238,U_17240) != hAPP(c_Option_Ooption_OSome(U_17232),U_17242) ),
    inference(clausify,[status(thm)],[f_4238_5]) ).

cnf(f_4238_7,plain,
    ( c_Map_Omap__comp(U_17231,U_17233,U_17235,U_17237,U_17239,U_17241) = hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
    | hAPP(U_17237,U_17222) != hAPP(c_Option_Ooption_OSome(U_17233),U_17243)
    | hAPP(U_17239,U_17241) != hAPP(c_Option_Ooption_OSome(U_17231),U_17222) ),
    inference(clausify,[status(thm)],[f_4238_5]) ).

cnf(f_4238_8,plain,
    ( hAPP(U_17238,U_17240) = hAPP(c_Option_Ooption_OSome(U_17230),sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230))
    | ~ sP1111(U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242) ),
    inference(clausify,[status(thm)],[f_4238_5]) ).

cnf(f_4238_9,plain,
    ( hAPP(U_17236,sK447(U_17242,U_17240,U_17238,U_17236,U_17234,U_17232,U_17230)) = hAPP(c_Option_Ooption_OSome(U_17232),U_17242)
    | ~ sP1111(U_17236,U_17232,U_17230,U_17234,U_17238,U_17240,U_17242) ),
    inference(clausify,[status(thm)],[f_4238_5]) ).

fof(f_4239_1,plain,
    ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
      ( c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2)
      | hAPP(V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I2_J]) ).

fof(f_4239_2,plain,
    ! [U_17250,U_17249,U_17248,U_17247,U_17246,U_17245,U_17244] :
      ( c_Map_Omap__comp(U_17246,U_17248,U_17249,U_17250,U_17244,U_17245) = hAPP(U_17250,U_17247)
      | hAPP(U_17244,U_17245) != hAPP(c_Option_Ooption_OSome(U_17246),U_17247) ),
    inference(variable_rename,[status(thm)],[f_4239_1]) ).

fof(f_4239_3,plain,
    ! [U_17248,U_17246,U_17244,U_17245,U_17249,U_17247,U_17250] :
      ( c_Map_Omap__comp(U_17246,U_17248,U_17249,U_17250,U_17244,U_17245) = hAPP(U_17250,U_17247)
      | hAPP(U_17244,U_17245) != hAPP(c_Option_Ooption_OSome(U_17246),U_17247) ),
    inference(definitional_conversion,[status(esa)],[f_4239_2]) ).

cnf(f_4239_4,plain,
    ( c_Map_Omap__comp(U_17246,U_17248,U_17249,U_17250,U_17244,U_17245) = hAPP(U_17250,U_17247)
    | hAPP(U_17244,U_17245) != hAPP(c_Option_Ooption_OSome(U_17246),U_17247) ),
    inference(clausify,[status(thm)],[f_4239_3]) ).

fof(f_4240_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( V_xs_2 = V_ys_2
      | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__injective]) ).

fof(f_4240_2,plain,
    ! [U_17255,U_17254,U_17253,U_17252,U_17251] :
      ( U_17254 = U_17255
      | ~ c_Fun_Oinj__on(U_17251,U_17252,U_17253,c_Orderings_Otop__class_Otop(tc_fun(U_17251,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17251,U_17252),U_17253),U_17254) != hAPP(hAPP(c_List_Omap(U_17251,U_17252),U_17253),U_17255) ),
    inference(variable_rename,[status(thm)],[f_4240_1]) ).

fof(f_4240_3,plain,
    ! [U_17251,U_17252,U_17253,U_17254,U_17255] :
      ( U_17254 = U_17255
      | ~ c_Fun_Oinj__on(U_17251,U_17252,U_17253,c_Orderings_Otop__class_Otop(tc_fun(U_17251,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17251,U_17252),U_17253),U_17254) != hAPP(hAPP(c_List_Omap(U_17251,U_17252),U_17253),U_17255) ),
    inference(definitional_conversion,[status(esa)],[f_4240_2]) ).

cnf(f_4240_4,plain,
    ( U_17254 = U_17255
    | ~ c_Fun_Oinj__on(U_17251,U_17252,U_17253,c_Orderings_Otop__class_Otop(tc_fun(U_17251,tc_HOL_Obool)))
    | hAPP(hAPP(c_List_Omap(U_17251,U_17252),U_17253),U_17254) != hAPP(hAPP(c_List_Omap(U_17251,U_17252),U_17253),U_17255) ),
    inference(clausify,[status(thm)],[f_4240_3]) ).

fof(f_4241_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__mapD]) ).

fof(f_4241_2,plain,
    ! [U_17258,U_17257,U_17256] :
      ( c_Fun_Oinj__on(U_17256,U_17257,U_17258,c_Orderings_Otop__class_Otop(tc_fun(U_17256,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17256),tc_List_Olist(U_17257),hAPP(c_List_Omap(U_17256,U_17257),U_17258),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17256),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4241_1]) ).

fof(f_4241_3,plain,
    ! [U_17256,U_17257,U_17258] :
      ( c_Fun_Oinj__on(U_17256,U_17257,U_17258,c_Orderings_Otop__class_Otop(tc_fun(U_17256,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17256),tc_List_Olist(U_17257),hAPP(c_List_Omap(U_17256,U_17257),U_17258),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17256),tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4241_2]) ).

cnf(f_4241_4,plain,
    ( c_Fun_Oinj__on(U_17256,U_17257,U_17258,c_Orderings_Otop__class_Otop(tc_fun(U_17256,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17256),tc_List_Olist(U_17257),hAPP(c_List_Omap(U_17256,U_17257),U_17258),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17256),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4241_3]) ).

fof(f_4242_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__map__eq__map]) ).

fof(f_4242_2,plain,
    ! [U_17263,U_17262,U_17261,U_17260,U_17259] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17262) = hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17263)
          | U_17262 != U_17263 )
        & ( U_17262 = U_17263
          | hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17262) != hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17263) ) )
      | ~ c_Fun_Oinj__on(U_17259,U_17260,U_17261,c_Orderings_Otop__class_Otop(tc_fun(U_17259,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4242_1]) ).

fof(f_4242_3,plain,
    ( ! [U_17259,U_17260,U_17261,U_17262,U_17263] :
        ( hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17262) = hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17263)
        | U_17262 != U_17263
        | ~ sP1112(U_17259,U_17260,U_17261,U_17262,U_17263) )
    & ! [U_17259,U_17260,U_17261,U_17262,U_17263] :
        ( U_17262 = U_17263
        | hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17262) != hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17263)
        | ~ sP1112(U_17259,U_17260,U_17261,U_17262,U_17263) )
    & ! [U_17259,U_17260,U_17261,U_17262,U_17263] :
        ( sP1112(U_17259,U_17260,U_17261,U_17262,U_17263)
        | ~ c_Fun_Oinj__on(U_17259,U_17260,U_17261,c_Orderings_Otop__class_Otop(tc_fun(U_17259,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1112])],[f_4242_2]) ).

cnf(f_4242_4,plain,
    ( sP1112(U_17259,U_17260,U_17261,U_17262,U_17263)
    | ~ c_Fun_Oinj__on(U_17259,U_17260,U_17261,c_Orderings_Otop__class_Otop(tc_fun(U_17259,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4242_3]) ).

cnf(f_4242_5,plain,
    ( U_17262 = U_17263
    | hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17262) != hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17263)
    | ~ sP1112(U_17259,U_17260,U_17261,U_17262,U_17263) ),
    inference(clausify,[status(thm)],[f_4242_3]) ).

cnf(f_4242_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17262) = hAPP(hAPP(c_List_Omap(U_17259,U_17260),U_17261),U_17263)
    | U_17262 != U_17263
    | ~ sP1112(U_17259,U_17260,U_17261,U_17262,U_17263) ),
    inference(clausify,[status(thm)],[f_4242_3]) ).

fof(f_4243_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__map]) ).

fof(f_4243_2,plain,
    ! [U_17266,U_17265,U_17264] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(U_17264),tc_List_Olist(U_17265),hAPP(c_List_Omap(U_17264,U_17265),U_17266),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17264),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17264,U_17265,U_17266,c_Orderings_Otop__class_Otop(tc_fun(U_17264,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(U_17264,U_17265,U_17266,c_Orderings_Otop__class_Otop(tc_fun(U_17264,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17264),tc_List_Olist(U_17265),hAPP(c_List_Omap(U_17264,U_17265),U_17266),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17264),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4243_1]) ).

fof(f_4243_3,plain,
    ( ! [U_17272,U_17270,U_17268] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17268),tc_List_Olist(U_17270),hAPP(c_List_Omap(U_17268,U_17270),U_17272),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17268),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17268,U_17270,U_17272,c_Orderings_Otop__class_Otop(tc_fun(U_17268,tc_HOL_Obool))) )
    & ! [U_17271,U_17269,U_17267] :
        ( c_Fun_Oinj__on(U_17267,U_17269,U_17271,c_Orderings_Otop__class_Otop(tc_fun(U_17267,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17267),tc_List_Olist(U_17269),hAPP(c_List_Omap(U_17267,U_17269),U_17271),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17267),tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4243_2]) ).

fof(f_4243_4,plain,
    ( ! [U_17272,U_17270,U_17268] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17268),tc_List_Olist(U_17270),hAPP(c_List_Omap(U_17268,U_17270),U_17272),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17268),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17268,U_17270,U_17272,c_Orderings_Otop__class_Otop(tc_fun(U_17268,tc_HOL_Obool))) )
    & ! [U_17269,U_17267,U_17271] :
        ( c_Fun_Oinj__on(U_17267,U_17269,U_17271,c_Orderings_Otop__class_Otop(tc_fun(U_17267,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17267),tc_List_Olist(U_17269),hAPP(c_List_Omap(U_17267,U_17269),U_17271),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17267),tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4243_3]) ).

cnf(f_4243_5,plain,
    ( c_Fun_Oinj__on(U_17267,U_17269,U_17271,c_Orderings_Otop__class_Otop(tc_fun(U_17267,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17267),tc_List_Olist(U_17269),hAPP(c_List_Omap(U_17267,U_17269),U_17271),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17267),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4243_4]) ).

cnf(f_4243_6,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17268),tc_List_Olist(U_17270),hAPP(c_List_Omap(U_17268,U_17270),U_17272),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17268),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17268,U_17270,U_17272,c_Orderings_Otop__class_Otop(tc_fun(U_17268,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4243_4]) ).

fof(f_4244_1,plain,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_map__ident]) ).

fof(f_4244_2,plain,
    ! [U_17274,U_17273] : hAPP(hAPP(c_List_Omap(U_17273,U_17273),c_COMBI(U_17273)),U_17274) = U_17274,
    inference(variable_rename,[status(thm)],[f_4244_1]) ).

fof(f_4244_3,plain,
    ! [U_17273,U_17274] : hAPP(hAPP(c_List_Omap(U_17273,U_17273),c_COMBI(U_17273)),U_17274) = U_17274,
    inference(definitional_conversion,[status(esa)],[f_4244_2]) ).

cnf(f_4244_4,plain,
    hAPP(hAPP(c_List_Omap(U_17273,U_17273),c_COMBI(U_17273)),U_17274) = U_17274,
    inference(clausify,[status(thm)],[f_4244_3]) ).

fof(f_4245_1,plain,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(f_4245_2,plain,
    ! [U_17275] : hAPP(c_List_Omap(U_17275,U_17275),c_COMBI(U_17275)) = c_Fun_Oid(tc_List_Olist(U_17275)),
    inference(variable_rename,[status(thm)],[f_4245_1]) ).

fof(f_4245_3,plain,
    ! [U_17275] : hAPP(c_List_Omap(U_17275,U_17275),c_COMBI(U_17275)) = c_Fun_Oid(tc_List_Olist(U_17275)),
    inference(definitional_conversion,[status(esa)],[f_4245_2]) ).

cnf(f_4245_4,plain,
    hAPP(c_List_Omap(U_17275,U_17275),c_COMBI(U_17275)) = c_Fun_Oid(tc_List_Olist(U_17275)),
    inference(clausify,[status(thm)],[f_4245_3]) ).

fof(f_4246_1,plain,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Oid]) ).

fof(f_4246_2,plain,
    ! [U_17276] : hAPP(c_List_Omap(U_17276,U_17276),c_Fun_Oid(U_17276)) = c_Fun_Oid(tc_List_Olist(U_17276)),
    inference(variable_rename,[status(thm)],[f_4246_1]) ).

fof(f_4246_3,plain,
    ! [U_17276] : hAPP(c_List_Omap(U_17276,U_17276),c_Fun_Oid(U_17276)) = c_Fun_Oid(tc_List_Olist(U_17276)),
    inference(definitional_conversion,[status(esa)],[f_4246_2]) ).

cnf(f_4246_4,plain,
    hAPP(c_List_Omap(U_17276,U_17276),c_Fun_Oid(U_17276)) = c_Fun_Oid(tc_List_Olist(U_17276)),
    inference(clausify,[status(thm)],[f_4246_3]) ).

fof(f_4247_1,plain,
    ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_map__map]) ).

fof(f_4247_2,plain,
    ! [U_17282,U_17281,U_17280,U_17279,U_17278,U_17277] : hAPP(hAPP(c_List_Omap(U_17277,U_17278),U_17279),hAPP(hAPP(c_List_Omap(U_17280,U_17277),U_17281),U_17282)) = hAPP(hAPP(c_List_Omap(U_17280,U_17278),hAPP(c_Fun_Ocomp(U_17277,U_17278,U_17280,U_17279),U_17281)),U_17282),
    inference(variable_rename,[status(thm)],[f_4247_1]) ).

fof(f_4247_3,plain,
    ! [U_17277,U_17278,U_17279,U_17280,U_17281,U_17282] : hAPP(hAPP(c_List_Omap(U_17277,U_17278),U_17279),hAPP(hAPP(c_List_Omap(U_17280,U_17277),U_17281),U_17282)) = hAPP(hAPP(c_List_Omap(U_17280,U_17278),hAPP(c_Fun_Ocomp(U_17277,U_17278,U_17280,U_17279),U_17281)),U_17282),
    inference(definitional_conversion,[status(esa)],[f_4247_2]) ).

cnf(f_4247_4,plain,
    hAPP(hAPP(c_List_Omap(U_17277,U_17278),U_17279),hAPP(hAPP(c_List_Omap(U_17280,U_17277),U_17281),U_17282)) = hAPP(hAPP(c_List_Omap(U_17280,U_17278),hAPP(c_Fun_Ocomp(U_17277,U_17278,U_17280,U_17279),U_17281)),U_17282),
    inference(clausify,[status(thm)],[f_4247_3]) ).

fof(f_4248_1,plain,
    ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(f_4248_2,plain,
    ! [U_17288,U_17287,U_17286,U_17285,U_17284,U_17283] : hAPP(hAPP(c_List_Omap(U_17283,U_17284),U_17285),hAPP(hAPP(c_List_Omap(U_17286,U_17283),U_17287),U_17288)) = hAPP(hAPP(c_List_Omap(U_17286,U_17284),hAPP(c_Fun_Ocomp(U_17283,U_17284,U_17286,U_17285),U_17287)),U_17288),
    inference(variable_rename,[status(thm)],[f_4248_1]) ).

fof(f_4248_3,plain,
    ! [U_17283,U_17284,U_17285,U_17286,U_17287,U_17288] : hAPP(hAPP(c_List_Omap(U_17283,U_17284),U_17285),hAPP(hAPP(c_List_Omap(U_17286,U_17283),U_17287),U_17288)) = hAPP(hAPP(c_List_Omap(U_17286,U_17284),hAPP(c_Fun_Ocomp(U_17283,U_17284,U_17286,U_17285),U_17287)),U_17288),
    inference(definitional_conversion,[status(esa)],[f_4248_2]) ).

cnf(f_4248_4,plain,
    hAPP(hAPP(c_List_Omap(U_17283,U_17284),U_17285),hAPP(hAPP(c_List_Omap(U_17286,U_17283),U_17287),U_17288)) = hAPP(hAPP(c_List_Omap(U_17286,U_17284),hAPP(c_Fun_Ocomp(U_17283,U_17284,U_17286,U_17285),U_17287)),U_17288),
    inference(clausify,[status(thm)],[f_4248_3]) ).

fof(f_4249_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_map__comp__map]) ).

fof(f_4249_2,plain,
    ! [U_17293,U_17292,U_17291,U_17290,U_17289] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17289),tc_List_Olist(U_17290),tc_List_Olist(U_17291),hAPP(c_List_Omap(U_17289,U_17290),U_17292)),hAPP(c_List_Omap(U_17291,U_17289),U_17293)) = hAPP(c_List_Omap(U_17291,U_17290),hAPP(c_Fun_Ocomp(U_17289,U_17290,U_17291,U_17292),U_17293)),
    inference(variable_rename,[status(thm)],[f_4249_1]) ).

fof(f_4249_3,plain,
    ! [U_17289,U_17290,U_17291,U_17292,U_17293] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17289),tc_List_Olist(U_17290),tc_List_Olist(U_17291),hAPP(c_List_Omap(U_17289,U_17290),U_17292)),hAPP(c_List_Omap(U_17291,U_17289),U_17293)) = hAPP(c_List_Omap(U_17291,U_17290),hAPP(c_Fun_Ocomp(U_17289,U_17290,U_17291,U_17292),U_17293)),
    inference(definitional_conversion,[status(esa)],[f_4249_2]) ).

cnf(f_4249_4,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17289),tc_List_Olist(U_17290),tc_List_Olist(U_17291),hAPP(c_List_Omap(U_17289,U_17290),U_17292)),hAPP(c_List_Omap(U_17291,U_17289),U_17293)) = hAPP(c_List_Omap(U_17291,U_17290),hAPP(c_Fun_Ocomp(U_17289,U_17290,U_17291,U_17292),U_17293)),
    inference(clausify,[status(thm)],[f_4249_3]) ).

fof(f_4250_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(f_4250_2,plain,
    ! [U_17298,U_17297,U_17296,U_17295,U_17294] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17294),tc_List_Olist(U_17295),tc_List_Olist(U_17296),hAPP(c_List_Omap(U_17294,U_17295),U_17297)),hAPP(c_List_Omap(U_17296,U_17294),U_17298)) = hAPP(c_List_Omap(U_17296,U_17295),hAPP(c_Fun_Ocomp(U_17294,U_17295,U_17296,U_17297),U_17298)),
    inference(variable_rename,[status(thm)],[f_4250_1]) ).

fof(f_4250_3,plain,
    ! [U_17294,U_17295,U_17296,U_17297,U_17298] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17294),tc_List_Olist(U_17295),tc_List_Olist(U_17296),hAPP(c_List_Omap(U_17294,U_17295),U_17297)),hAPP(c_List_Omap(U_17296,U_17294),U_17298)) = hAPP(c_List_Omap(U_17296,U_17295),hAPP(c_Fun_Ocomp(U_17294,U_17295,U_17296,U_17297),U_17298)),
    inference(definitional_conversion,[status(esa)],[f_4250_2]) ).

cnf(f_4250_4,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17294),tc_List_Olist(U_17295),tc_List_Olist(U_17296),hAPP(c_List_Omap(U_17294,U_17295),U_17297)),hAPP(c_List_Omap(U_17296,U_17294),U_17298)) = hAPP(c_List_Omap(U_17296,U_17295),hAPP(c_Fun_Ocomp(U_17294,U_17295,U_17296,U_17297),U_17298)),
    inference(clausify,[status(thm)],[f_4250_3]) ).

fof(f_4251_1,plain,
    ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_foldr__map]) ).

fof(f_4251_2,plain,
    ! [U_17305,U_17304,U_17303,U_17302,U_17301,U_17300,U_17299] : c_List_Ofoldr(U_17299,U_17300,U_17301,hAPP(hAPP(c_List_Omap(U_17302,U_17299),U_17303),U_17304),U_17305) = c_List_Ofoldr(U_17302,U_17300,hAPP(c_Fun_Ocomp(U_17299,tc_fun(U_17300,U_17300),U_17302,U_17301),U_17303),U_17304,U_17305),
    inference(variable_rename,[status(thm)],[f_4251_1]) ).

fof(f_4251_3,plain,
    ! [U_17300,U_17299,U_17301,U_17302,U_17303,U_17304,U_17305] : c_List_Ofoldr(U_17299,U_17300,U_17301,hAPP(hAPP(c_List_Omap(U_17302,U_17299),U_17303),U_17304),U_17305) = c_List_Ofoldr(U_17302,U_17300,hAPP(c_Fun_Ocomp(U_17299,tc_fun(U_17300,U_17300),U_17302,U_17301),U_17303),U_17304,U_17305),
    inference(definitional_conversion,[status(esa)],[f_4251_2]) ).

cnf(f_4251_4,plain,
    c_List_Ofoldr(U_17299,U_17300,U_17301,hAPP(hAPP(c_List_Omap(U_17302,U_17299),U_17303),U_17304),U_17305) = c_List_Ofoldr(U_17302,U_17300,hAPP(c_Fun_Ocomp(U_17299,tc_fun(U_17300,U_17300),U_17302,U_17301),U_17303),U_17304,U_17305),
    inference(clausify,[status(thm)],[f_4251_3]) ).

fof(f_4252_1,plain,
    ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_map__comp__empty_I1_J]) ).

fof(f_4252_2,plain,
    ! [U_17310,U_17309,U_17308,U_17307,U_17306] : c_Map_Omap__comp(U_17306,U_17307,U_17308,U_17309,hAPP(c_COMBK(tc_Option_Ooption(U_17306),U_17308),c_Option_Ooption_ONone(U_17306)),U_17310) = c_Option_Ooption_ONone(U_17307),
    inference(variable_rename,[status(thm)],[f_4252_1]) ).

fof(f_4252_3,plain,
    ! [U_17308,U_17307,U_17306,U_17309,U_17310] : c_Map_Omap__comp(U_17306,U_17307,U_17308,U_17309,hAPP(c_COMBK(tc_Option_Ooption(U_17306),U_17308),c_Option_Ooption_ONone(U_17306)),U_17310) = c_Option_Ooption_ONone(U_17307),
    inference(definitional_conversion,[status(esa)],[f_4252_2]) ).

cnf(f_4252_4,plain,
    c_Map_Omap__comp(U_17306,U_17307,U_17308,U_17309,hAPP(c_COMBK(tc_Option_Ooption(U_17306),U_17308),c_Option_Ooption_ONone(U_17306)),U_17310) = c_Option_Ooption_ONone(U_17307),
    inference(clausify,[status(thm)],[f_4252_3]) ).

fof(f_4253_1,plain,
    ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_map__comp__empty_I2_J]) ).

fof(f_4253_2,plain,
    ! [U_17315,U_17314,U_17313,U_17312,U_17311] : c_Map_Omap__comp(U_17311,U_17312,U_17313,hAPP(c_COMBK(tc_Option_Ooption(U_17312),U_17311),c_Option_Ooption_ONone(U_17312)),U_17314,U_17315) = c_Option_Ooption_ONone(U_17312),
    inference(variable_rename,[status(thm)],[f_4253_1]) ).

fof(f_4253_3,plain,
    ! [U_17311,U_17312,U_17313,U_17314,U_17315] : c_Map_Omap__comp(U_17311,U_17312,U_17313,hAPP(c_COMBK(tc_Option_Ooption(U_17312),U_17311),c_Option_Ooption_ONone(U_17312)),U_17314,U_17315) = c_Option_Ooption_ONone(U_17312),
    inference(definitional_conversion,[status(esa)],[f_4253_2]) ).

cnf(f_4253_4,plain,
    c_Map_Omap__comp(U_17311,U_17312,U_17313,hAPP(c_COMBK(tc_Option_Ooption(U_17312),U_17311),c_Option_Ooption_ONone(U_17312)),U_17314,U_17315) = c_Option_Ooption_ONone(U_17312),
    inference(clausify,[status(thm)],[f_4253_3]) ).

fof(f_4254_1,plain,
    ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
      ( ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
        | ( ! [B_k_H] :
              ( hAPP(V_m1_2,B_k_H) != c_Option_Ooption_ONone(T_b)
              | hAPP(V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_c),B_k_H) )
          & hAPP(V_m2_2,V_k_2) != c_Option_Ooption_ONone(T_c) ) )
      & ( ? [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b)
            & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) )
        | hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
        | c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) != c_Option_Ooption_ONone(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__None__iff]) ).

fof(f_4254_2,plain,
    ! [U_17323,U_17322,U_17321,U_17320,U_17319,U_17318] :
      ( ( c_Map_Omap__comp(U_17318,U_17319,U_17320,U_17321,U_17322,U_17323) = c_Option_Ooption_ONone(U_17319)
        | ( ! [U_17317] :
              ( hAPP(U_17321,U_17317) != c_Option_Ooption_ONone(U_17319)
              | hAPP(U_17322,U_17323) != hAPP(c_Option_Ooption_OSome(U_17318),U_17317) )
          & hAPP(U_17322,U_17323) != c_Option_Ooption_ONone(U_17318) ) )
      & ( ? [U_17316] :
            ( hAPP(U_17321,U_17316) = c_Option_Ooption_ONone(U_17319)
            & hAPP(U_17322,U_17323) = hAPP(c_Option_Ooption_OSome(U_17318),U_17316) )
        | hAPP(U_17322,U_17323) = c_Option_Ooption_ONone(U_17318)
        | c_Map_Omap__comp(U_17318,U_17319,U_17320,U_17321,U_17322,U_17323) != c_Option_Ooption_ONone(U_17319) ) ),
    inference(variable_rename,[status(thm)],[f_4254_1]) ).

fof(f_4254_3,plain,
    ( ! [U_17335,U_17333,U_17331,U_17329,U_17327,U_17325] :
        ( c_Map_Omap__comp(U_17325,U_17327,U_17329,U_17331,U_17333,U_17335) = c_Option_Ooption_ONone(U_17327)
        | ( ! [U_17317] :
              ( hAPP(U_17331,U_17317) != c_Option_Ooption_ONone(U_17327)
              | hAPP(U_17333,U_17335) != hAPP(c_Option_Ooption_OSome(U_17325),U_17317) )
          & hAPP(U_17333,U_17335) != c_Option_Ooption_ONone(U_17325) ) )
    & ! [U_17334,U_17332,U_17330,U_17328,U_17326,U_17324] :
        ( ? [U_17316] :
            ( hAPP(U_17330,U_17316) = c_Option_Ooption_ONone(U_17326)
            & hAPP(U_17332,U_17334) = hAPP(c_Option_Ooption_OSome(U_17324),U_17316) )
        | hAPP(U_17332,U_17334) = c_Option_Ooption_ONone(U_17324)
        | c_Map_Omap__comp(U_17324,U_17326,U_17328,U_17330,U_17332,U_17334) != c_Option_Ooption_ONone(U_17326) ) ),
    inference(miniscope,[status(thm)],[f_4254_2]) ).

fof(f_4254_4,plain,
    ( ! [U_17335,U_17333,U_17331,U_17329,U_17327,U_17325] :
        ( c_Map_Omap__comp(U_17325,U_17327,U_17329,U_17331,U_17333,U_17335) = c_Option_Ooption_ONone(U_17327)
        | ( ! [U_17317] :
              ( hAPP(U_17331,U_17317) != c_Option_Ooption_ONone(U_17327)
              | hAPP(U_17333,U_17335) != hAPP(c_Option_Ooption_OSome(U_17325),U_17317) )
          & hAPP(U_17333,U_17335) != c_Option_Ooption_ONone(U_17325) ) )
    & ! [U_17334,U_17332,U_17330,U_17328,U_17326,U_17324] :
        ( ( hAPP(U_17330,sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324)) = c_Option_Ooption_ONone(U_17326)
          & hAPP(U_17332,U_17334) = hAPP(c_Option_Ooption_OSome(U_17324),sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324)) )
        | hAPP(U_17332,U_17334) = c_Option_Ooption_ONone(U_17324)
        | c_Map_Omap__comp(U_17324,U_17326,U_17328,U_17330,U_17332,U_17334) != c_Option_Ooption_ONone(U_17326) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_17316,sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324))],[f_4254_3]) ).

fof(f_4254_5,plain,
    ( ! [U_17327,U_17331,U_17317,U_17325,U_17333,U_17335] :
        ( hAPP(U_17331,U_17317) != c_Option_Ooption_ONone(U_17327)
        | hAPP(U_17333,U_17335) != hAPP(c_Option_Ooption_OSome(U_17325),U_17317)
        | ~ sP1114(U_17327,U_17331,U_17317,U_17325,U_17333,U_17335) )
    & ! [U_17327,U_17331,U_17317,U_17325,U_17333,U_17335] :
        ( hAPP(U_17333,U_17335) != c_Option_Ooption_ONone(U_17325)
        | ~ sP1114(U_17327,U_17331,U_17317,U_17325,U_17333,U_17335) )
    & ! [U_17326,U_17328,U_17332,U_17324,U_17330,U_17334] :
        ( hAPP(U_17330,sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324)) = c_Option_Ooption_ONone(U_17326)
        | ~ sP1113(U_17326,U_17328,U_17332,U_17324,U_17330,U_17334) )
    & ! [U_17326,U_17328,U_17332,U_17324,U_17330,U_17334] :
        ( hAPP(U_17332,U_17334) = hAPP(c_Option_Ooption_OSome(U_17324),sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324))
        | ~ sP1113(U_17326,U_17328,U_17332,U_17324,U_17330,U_17334) )
    & ! [U_17327,U_17329,U_17331,U_17317,U_17325,U_17333,U_17335] :
        ( c_Map_Omap__comp(U_17325,U_17327,U_17329,U_17331,U_17333,U_17335) = c_Option_Ooption_ONone(U_17327)
        | sP1114(U_17327,U_17331,U_17317,U_17325,U_17333,U_17335) )
    & ! [U_17326,U_17328,U_17332,U_17324,U_17330,U_17334] :
        ( sP1113(U_17326,U_17328,U_17332,U_17324,U_17330,U_17334)
        | hAPP(U_17332,U_17334) = c_Option_Ooption_ONone(U_17324)
        | c_Map_Omap__comp(U_17324,U_17326,U_17328,U_17330,U_17332,U_17334) != c_Option_Ooption_ONone(U_17326) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1113,sP1114])],[f_4254_4]) ).

cnf(f_4254_6,plain,
    ( sP1113(U_17326,U_17328,U_17332,U_17324,U_17330,U_17334)
    | hAPP(U_17332,U_17334) = c_Option_Ooption_ONone(U_17324)
    | c_Map_Omap__comp(U_17324,U_17326,U_17328,U_17330,U_17332,U_17334) != c_Option_Ooption_ONone(U_17326) ),
    inference(clausify,[status(thm)],[f_4254_5]) ).

cnf(f_4254_7,plain,
    ( c_Map_Omap__comp(U_17325,U_17327,U_17329,U_17331,U_17333,U_17335) = c_Option_Ooption_ONone(U_17327)
    | sP1114(U_17327,U_17331,U_17317,U_17325,U_17333,U_17335) ),
    inference(clausify,[status(thm)],[f_4254_5]) ).

cnf(f_4254_8,plain,
    ( hAPP(U_17332,U_17334) = hAPP(c_Option_Ooption_OSome(U_17324),sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324))
    | ~ sP1113(U_17326,U_17328,U_17332,U_17324,U_17330,U_17334) ),
    inference(clausify,[status(thm)],[f_4254_5]) ).

cnf(f_4254_9,plain,
    ( hAPP(U_17330,sK448(U_17334,U_17332,U_17330,U_17328,U_17326,U_17324)) = c_Option_Ooption_ONone(U_17326)
    | ~ sP1113(U_17326,U_17328,U_17332,U_17324,U_17330,U_17334) ),
    inference(clausify,[status(thm)],[f_4254_5]) ).

cnf(f_4254_10,plain,
    ( hAPP(U_17333,U_17335) != c_Option_Ooption_ONone(U_17325)
    | ~ sP1114(U_17327,U_17331,U_17317,U_17325,U_17333,U_17335) ),
    inference(clausify,[status(thm)],[f_4254_5]) ).

cnf(f_4254_11,plain,
    ( hAPP(U_17331,U_17317) != c_Option_Ooption_ONone(U_17327)
    | hAPP(U_17333,U_17335) != hAPP(c_Option_Ooption_OSome(U_17325),U_17317)
    | ~ sP1114(U_17327,U_17331,U_17317,U_17325,U_17333,U_17335) ),
    inference(clausify,[status(thm)],[f_4254_5]) ).

fof(f_4255_1,plain,
    ! [V_xs_2,V_f_2,T_d,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),c_Map_Omap__of(T_b,T_d,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__of__map]) ).

fof(f_4255_2,plain,
    ! [U_17340,U_17339,U_17338,U_17337,U_17336] : c_Map_Omap__of(U_17336,U_17337,hAPP(hAPP(c_List_Omap(tc_prod(U_17336,U_17338),tc_prod(U_17336,U_17337)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17336,U_17338,tc_prod(U_17336,U_17337)),hAPP(hAPP(c_COMBC(U_17336,tc_fun(U_17338,U_17337),tc_fun(U_17338,tc_prod(U_17336,U_17337))),hAPP(hAPP(c_COMBB(tc_fun(U_17337,tc_prod(U_17336,U_17337)),tc_fun(tc_fun(U_17338,U_17337),tc_fun(U_17338,tc_prod(U_17336,U_17337))),U_17336),c_COMBB(U_17337,tc_prod(U_17336,U_17337),U_17338)),c_Product__Type_OPair(U_17336,U_17337))),U_17339))),U_17340)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17338),tc_Option_Ooption(U_17337),U_17336,hAPP(c_Option_Omap(U_17338,U_17337),U_17339)),c_Map_Omap__of(U_17336,U_17338,U_17340)),
    inference(variable_rename,[status(thm)],[f_4255_1]) ).

fof(f_4255_3,plain,
    ! [U_17336,U_17337,U_17338,U_17339,U_17340] : c_Map_Omap__of(U_17336,U_17337,hAPP(hAPP(c_List_Omap(tc_prod(U_17336,U_17338),tc_prod(U_17336,U_17337)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17336,U_17338,tc_prod(U_17336,U_17337)),hAPP(hAPP(c_COMBC(U_17336,tc_fun(U_17338,U_17337),tc_fun(U_17338,tc_prod(U_17336,U_17337))),hAPP(hAPP(c_COMBB(tc_fun(U_17337,tc_prod(U_17336,U_17337)),tc_fun(tc_fun(U_17338,U_17337),tc_fun(U_17338,tc_prod(U_17336,U_17337))),U_17336),c_COMBB(U_17337,tc_prod(U_17336,U_17337),U_17338)),c_Product__Type_OPair(U_17336,U_17337))),U_17339))),U_17340)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17338),tc_Option_Ooption(U_17337),U_17336,hAPP(c_Option_Omap(U_17338,U_17337),U_17339)),c_Map_Omap__of(U_17336,U_17338,U_17340)),
    inference(definitional_conversion,[status(esa)],[f_4255_2]) ).

cnf(f_4255_4,plain,
    c_Map_Omap__of(U_17336,U_17337,hAPP(hAPP(c_List_Omap(tc_prod(U_17336,U_17338),tc_prod(U_17336,U_17337)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17336,U_17338,tc_prod(U_17336,U_17337)),hAPP(hAPP(c_COMBC(U_17336,tc_fun(U_17338,U_17337),tc_fun(U_17338,tc_prod(U_17336,U_17337))),hAPP(hAPP(c_COMBB(tc_fun(U_17337,tc_prod(U_17336,U_17337)),tc_fun(tc_fun(U_17338,U_17337),tc_fun(U_17338,tc_prod(U_17336,U_17337))),U_17336),c_COMBB(U_17337,tc_prod(U_17336,U_17337),U_17338)),c_Product__Type_OPair(U_17336,U_17337))),U_17339))),U_17340)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17338),tc_Option_Ooption(U_17337),U_17336,hAPP(c_Option_Omap(U_17338,U_17337),U_17339)),c_Map_Omap__of(U_17336,U_17338,U_17340)),
    inference(clausify,[status(thm)],[f_4255_3]) ).

fof(f_4256_1,plain,
    ! [V_m_2,T_c,V_xs_2,T_b] :
      ( c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2
      | hAPP(c_List_Oset(T_b),V_xs_2) != c_Map_Odom(T_b,T_c,V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__map__keys]) ).

fof(f_4256_2,plain,
    ! [U_17344,U_17343,U_17342,U_17341] :
      ( c_Map_Omap__of(U_17341,U_17343,hAPP(hAPP(c_List_Omap(U_17341,tc_prod(U_17341,U_17343)),hAPP(hAPP(c_COMBS(U_17341,U_17343,tc_prod(U_17341,U_17343)),c_Product__Type_OPair(U_17341,U_17343)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17343),U_17343,U_17341),c_Option_Othe(U_17343)),U_17344))),U_17342)) = U_17344
      | hAPP(c_List_Oset(U_17341),U_17342) != c_Map_Odom(U_17341,U_17343,U_17344) ),
    inference(variable_rename,[status(thm)],[f_4256_1]) ).

fof(f_4256_3,plain,
    ! [U_17341,U_17342,U_17343,U_17344] :
      ( c_Map_Omap__of(U_17341,U_17343,hAPP(hAPP(c_List_Omap(U_17341,tc_prod(U_17341,U_17343)),hAPP(hAPP(c_COMBS(U_17341,U_17343,tc_prod(U_17341,U_17343)),c_Product__Type_OPair(U_17341,U_17343)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17343),U_17343,U_17341),c_Option_Othe(U_17343)),U_17344))),U_17342)) = U_17344
      | hAPP(c_List_Oset(U_17341),U_17342) != c_Map_Odom(U_17341,U_17343,U_17344) ),
    inference(definitional_conversion,[status(esa)],[f_4256_2]) ).

cnf(f_4256_4,plain,
    ( c_Map_Omap__of(U_17341,U_17343,hAPP(hAPP(c_List_Omap(U_17341,tc_prod(U_17341,U_17343)),hAPP(hAPP(c_COMBS(U_17341,U_17343,tc_prod(U_17341,U_17343)),c_Product__Type_OPair(U_17341,U_17343)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17343),U_17343,U_17341),c_Option_Othe(U_17343)),U_17344))),U_17342)) = U_17344
    | hAPP(c_List_Oset(U_17341),U_17342) != c_Map_Odom(U_17341,U_17343,U_17344) ),
    inference(clausify,[status(thm)],[f_4256_3]) ).

fof(f_4257_1,plain,
    ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__set]) ).

fof(f_4257_2,plain,
    ! [U_17346,U_17345] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17345),hAPP(c_List_Oset(U_17345),U_17346))),
    inference(variable_rename,[status(thm)],[f_4257_1]) ).

fof(f_4257_3,plain,
    ! [U_17345,U_17346] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17345),hAPP(c_List_Oset(U_17345),U_17346))),
    inference(definitional_conversion,[status(esa)],[f_4257_2]) ).

cnf(f_4257_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17345),hAPP(c_List_Oset(U_17345),U_17346))),
    inference(clausify,[status(thm)],[f_4257_3]) ).

fof(f_4258_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_set__map]) ).

fof(f_4258_2,plain,
    ! [U_17350,U_17349,U_17348,U_17347] : hAPP(c_List_Oset(U_17347),hAPP(hAPP(c_List_Omap(U_17348,U_17347),U_17349),U_17350)) = hAPP(c_Set_Oimage(U_17348,U_17347,U_17349),hAPP(c_List_Oset(U_17348),U_17350)),
    inference(variable_rename,[status(thm)],[f_4258_1]) ).

fof(f_4258_3,plain,
    ! [U_17347,U_17348,U_17349,U_17350] : hAPP(c_List_Oset(U_17347),hAPP(hAPP(c_List_Omap(U_17348,U_17347),U_17349),U_17350)) = hAPP(c_Set_Oimage(U_17348,U_17347,U_17349),hAPP(c_List_Oset(U_17348),U_17350)),
    inference(definitional_conversion,[status(esa)],[f_4258_2]) ).

cnf(f_4258_4,plain,
    hAPP(c_List_Oset(U_17347),hAPP(hAPP(c_List_Omap(U_17348,U_17347),U_17349),U_17350)) = hAPP(c_Set_Oimage(U_17348,U_17347,U_17349),hAPP(c_List_Oset(U_17348),U_17350)),
    inference(clausify,[status(thm)],[f_4258_3]) ).

fof(f_4259_1,plain,
    ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
        | ? [B_x] :
            ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) )
        | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__eq__conv]) ).

fof(f_4259_2,plain,
    ! [U_17357,U_17356,U_17355,U_17354,U_17353] :
      ( ( hAPP(hAPP(c_List_Omap(U_17353,U_17354),U_17355),U_17356) = hAPP(hAPP(c_List_Omap(U_17353,U_17354),U_17357),U_17356)
        | ? [U_17352] :
            ( hAPP(U_17355,U_17352) != hAPP(U_17357,U_17352)
            & hBOOL(hAPP(hAPP(c_member(U_17353),U_17352),hAPP(c_List_Oset(U_17353),U_17356))) ) )
      & ( ! [U_17351] :
            ( hAPP(U_17355,U_17351) = hAPP(U_17357,U_17351)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17353),U_17351),hAPP(c_List_Oset(U_17353),U_17356))) )
        | hAPP(hAPP(c_List_Omap(U_17353,U_17354),U_17355),U_17356) != hAPP(hAPP(c_List_Omap(U_17353,U_17354),U_17357),U_17356) ) ),
    inference(variable_rename,[status(thm)],[f_4259_1]) ).

fof(f_4259_3,plain,
    ( ! [U_17367,U_17365,U_17363,U_17361,U_17359] :
        ( hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17363),U_17365) = hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17367),U_17365)
        | ? [U_17352] :
            ( hAPP(U_17363,U_17352) != hAPP(U_17367,U_17352)
            & hBOOL(hAPP(hAPP(c_member(U_17359),U_17352),hAPP(c_List_Oset(U_17359),U_17365))) ) )
    & ! [U_17366,U_17364,U_17362,U_17360,U_17358] :
        ( ! [U_17351] :
            ( hAPP(U_17362,U_17351) = hAPP(U_17366,U_17351)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17358),U_17351),hAPP(c_List_Oset(U_17358),U_17364))) )
        | hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17362),U_17364) != hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17366),U_17364) ) ),
    inference(miniscope,[status(thm)],[f_4259_2]) ).

fof(f_4259_4,plain,
    ( ! [U_17367,U_17365,U_17363,U_17361,U_17359] :
        ( hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17363),U_17365) = hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17367),U_17365)
        | ( hAPP(U_17363,sK449(U_17367,U_17365,U_17363,U_17361,U_17359)) != hAPP(U_17367,sK449(U_17367,U_17365,U_17363,U_17361,U_17359))
          & hBOOL(hAPP(hAPP(c_member(U_17359),sK449(U_17367,U_17365,U_17363,U_17361,U_17359)),hAPP(c_List_Oset(U_17359),U_17365))) ) )
    & ! [U_17366,U_17364,U_17362,U_17360,U_17358] :
        ( ! [U_17351] :
            ( hAPP(U_17362,U_17351) = hAPP(U_17366,U_17351)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17358),U_17351),hAPP(c_List_Oset(U_17358),U_17364))) )
        | hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17362),U_17364) != hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17366),U_17364) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_17352,sK449(U_17367,U_17365,U_17363,U_17361,U_17359))],[f_4259_3]) ).

fof(f_4259_5,plain,
    ( ! [U_17361,U_17359,U_17363,U_17367,U_17365] :
        ( hAPP(U_17363,sK449(U_17367,U_17365,U_17363,U_17361,U_17359)) != hAPP(U_17367,sK449(U_17367,U_17365,U_17363,U_17361,U_17359))
        | ~ sP1115(U_17361,U_17359,U_17363,U_17367,U_17365) )
    & ! [U_17361,U_17359,U_17363,U_17367,U_17365] :
        ( hBOOL(hAPP(hAPP(c_member(U_17359),sK449(U_17367,U_17365,U_17363,U_17361,U_17359)),hAPP(c_List_Oset(U_17359),U_17365)))
        | ~ sP1115(U_17361,U_17359,U_17363,U_17367,U_17365) )
    & ! [U_17361,U_17359,U_17363,U_17367,U_17365] :
        ( hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17363),U_17365) = hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17367),U_17365)
        | sP1115(U_17361,U_17359,U_17363,U_17367,U_17365) )
    & ! [U_17362,U_17360,U_17351,U_17364,U_17358,U_17366] :
        ( hAPP(U_17362,U_17351) = hAPP(U_17366,U_17351)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17358),U_17351),hAPP(c_List_Oset(U_17358),U_17364)))
        | hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17362),U_17364) != hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17366),U_17364) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1115])],[f_4259_4]) ).

cnf(f_4259_6,plain,
    ( hAPP(U_17362,U_17351) = hAPP(U_17366,U_17351)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17358),U_17351),hAPP(c_List_Oset(U_17358),U_17364)))
    | hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17362),U_17364) != hAPP(hAPP(c_List_Omap(U_17358,U_17360),U_17366),U_17364) ),
    inference(clausify,[status(thm)],[f_4259_5]) ).

cnf(f_4259_7,plain,
    ( hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17363),U_17365) = hAPP(hAPP(c_List_Omap(U_17359,U_17361),U_17367),U_17365)
    | sP1115(U_17361,U_17359,U_17363,U_17367,U_17365) ),
    inference(clausify,[status(thm)],[f_4259_5]) ).

cnf(f_4259_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17359),sK449(U_17367,U_17365,U_17363,U_17361,U_17359)),hAPP(c_List_Oset(U_17359),U_17365)))
    | ~ sP1115(U_17361,U_17359,U_17363,U_17367,U_17365) ),
    inference(clausify,[status(thm)],[f_4259_5]) ).

cnf(f_4259_9,plain,
    ( hAPP(U_17363,sK449(U_17367,U_17365,U_17363,U_17361,U_17359)) != hAPP(U_17367,sK449(U_17367,U_17365,U_17363,U_17361,U_17359))
    | ~ sP1115(U_17361,U_17359,U_17363,U_17367,U_17365) ),
    inference(clausify,[status(thm)],[f_4259_5]) ).

fof(f_4260_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Ocomp]) ).

fof(f_4260_2,plain,
    ! [U_17372,U_17371,U_17370,U_17369,U_17368] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17368),tc_Option_Ooption(U_17369),tc_Option_Ooption(U_17370),hAPP(c_Option_Omap(U_17368,U_17369),U_17371)),hAPP(c_Option_Omap(U_17370,U_17368),U_17372)) = hAPP(c_Option_Omap(U_17370,U_17369),hAPP(c_Fun_Ocomp(U_17368,U_17369,U_17370,U_17371),U_17372)),
    inference(variable_rename,[status(thm)],[f_4260_1]) ).

fof(f_4260_3,plain,
    ! [U_17369,U_17370,U_17368,U_17371,U_17372] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17368),tc_Option_Ooption(U_17369),tc_Option_Ooption(U_17370),hAPP(c_Option_Omap(U_17368,U_17369),U_17371)),hAPP(c_Option_Omap(U_17370,U_17368),U_17372)) = hAPP(c_Option_Omap(U_17370,U_17369),hAPP(c_Fun_Ocomp(U_17368,U_17369,U_17370,U_17371),U_17372)),
    inference(definitional_conversion,[status(esa)],[f_4260_2]) ).

cnf(f_4260_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17368),tc_Option_Ooption(U_17369),tc_Option_Ooption(U_17370),hAPP(c_Option_Omap(U_17368,U_17369),U_17371)),hAPP(c_Option_Omap(U_17370,U_17368),U_17372)) = hAPP(c_Option_Omap(U_17370,U_17369),hAPP(c_Fun_Ocomp(U_17368,U_17369,U_17370,U_17371),U_17372)),
    inference(clausify,[status(thm)],[f_4260_3]) ).

fof(f_4261_1,plain,
    ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Ocompositionality]) ).

fof(f_4261_2,plain,
    ! [U_17378,U_17377,U_17376,U_17375,U_17374,U_17373] : hAPP(hAPP(c_Option_Omap(U_17373,U_17374),U_17375),hAPP(hAPP(c_Option_Omap(U_17376,U_17373),U_17377),U_17378)) = hAPP(hAPP(c_Option_Omap(U_17376,U_17374),hAPP(c_Fun_Ocomp(U_17373,U_17374,U_17376,U_17375),U_17377)),U_17378),
    inference(variable_rename,[status(thm)],[f_4261_1]) ).

fof(f_4261_3,plain,
    ! [U_17373,U_17374,U_17375,U_17376,U_17377,U_17378] : hAPP(hAPP(c_Option_Omap(U_17373,U_17374),U_17375),hAPP(hAPP(c_Option_Omap(U_17376,U_17373),U_17377),U_17378)) = hAPP(hAPP(c_Option_Omap(U_17376,U_17374),hAPP(c_Fun_Ocomp(U_17373,U_17374,U_17376,U_17375),U_17377)),U_17378),
    inference(definitional_conversion,[status(esa)],[f_4261_2]) ).

cnf(f_4261_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17373,U_17374),U_17375),hAPP(hAPP(c_Option_Omap(U_17376,U_17373),U_17377),U_17378)) = hAPP(hAPP(c_Option_Omap(U_17376,U_17374),hAPP(c_Fun_Ocomp(U_17373,U_17374,U_17376,U_17375),U_17377)),U_17378),
    inference(clausify,[status(thm)],[f_4261_3]) ).

fof(f_4262_1,plain,
    ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2),
    inference(fof_nnf,[status(thm)],[fact_option__map__comp]) ).

fof(f_4262_2,plain,
    ! [U_17384,U_17383,U_17382,U_17381,U_17380,U_17379] : hAPP(hAPP(c_Option_Omap(U_17379,U_17380),U_17381),hAPP(hAPP(c_Option_Omap(U_17382,U_17379),U_17383),U_17384)) = hAPP(hAPP(c_Option_Omap(U_17382,U_17380),hAPP(c_Fun_Ocomp(U_17379,U_17380,U_17382,U_17381),U_17383)),U_17384),
    inference(variable_rename,[status(thm)],[f_4262_1]) ).

fof(f_4262_3,plain,
    ! [U_17379,U_17380,U_17381,U_17382,U_17383,U_17384] : hAPP(hAPP(c_Option_Omap(U_17379,U_17380),U_17381),hAPP(hAPP(c_Option_Omap(U_17382,U_17379),U_17383),U_17384)) = hAPP(hAPP(c_Option_Omap(U_17382,U_17380),hAPP(c_Fun_Ocomp(U_17379,U_17380,U_17382,U_17381),U_17383)),U_17384),
    inference(definitional_conversion,[status(esa)],[f_4262_2]) ).

cnf(f_4262_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17379,U_17380),U_17381),hAPP(hAPP(c_Option_Omap(U_17382,U_17379),U_17383),U_17384)) = hAPP(hAPP(c_Option_Omap(U_17382,U_17380),hAPP(c_Fun_Ocomp(U_17379,U_17380,U_17382,U_17381),U_17383)),U_17384),
    inference(clausify,[status(thm)],[f_4262_3]) ).

fof(f_4263_1,plain,
    ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Oidentity]) ).

fof(f_4263_2,plain,
    ! [U_17385] : hAPP(c_Option_Omap(U_17385,U_17385),c_COMBI(U_17385)) = c_Fun_Oid(tc_Option_Ooption(U_17385)),
    inference(variable_rename,[status(thm)],[f_4263_1]) ).

fof(f_4263_3,plain,
    ! [U_17385] : hAPP(c_Option_Omap(U_17385,U_17385),c_COMBI(U_17385)) = c_Fun_Oid(tc_Option_Ooption(U_17385)),
    inference(definitional_conversion,[status(esa)],[f_4263_2]) ).

cnf(f_4263_4,plain,
    hAPP(c_Option_Omap(U_17385,U_17385),c_COMBI(U_17385)) = c_Fun_Oid(tc_Option_Ooption(U_17385)),
    inference(clausify,[status(thm)],[f_4263_3]) ).

fof(f_4264_1,plain,
    ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Oid]) ).

fof(f_4264_2,plain,
    ! [U_17386] : hAPP(c_Option_Omap(U_17386,U_17386),c_Fun_Oid(U_17386)) = c_Fun_Oid(tc_Option_Ooption(U_17386)),
    inference(variable_rename,[status(thm)],[f_4264_1]) ).

fof(f_4264_3,plain,
    ! [U_17386] : hAPP(c_Option_Omap(U_17386,U_17386),c_Fun_Oid(U_17386)) = c_Fun_Oid(tc_Option_Ooption(U_17386)),
    inference(definitional_conversion,[status(esa)],[f_4264_2]) ).

cnf(f_4264_4,plain,
    hAPP(c_Option_Omap(U_17386,U_17386),c_Fun_Oid(U_17386)) = c_Fun_Oid(tc_Option_Ooption(U_17386)),
    inference(clausify,[status(thm)],[f_4264_3]) ).

fof(f_4265_1,plain,
    ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__listI]) ).

fof(f_4265_2,plain,
    ! [U_17387] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17387)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17387),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4265_1]) ).

fof(f_4265_3,plain,
    ! [U_17387] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17387)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17387),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_4265_2]) ).

cnf(f_4265_4,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17387)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17387),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4265_3]) ).

fof(f_4266_1,plain,
    ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2),
    inference(fof_nnf,[status(thm)],[fact_dom__option__map]) ).

fof(f_4266_2,plain,
    ! [U_17392,U_17391,U_17390,U_17389,U_17388] : c_Map_Odom(U_17388,U_17389,hAPP(hAPP(c_COMBS(U_17388,tc_Option_Ooption(U_17390),tc_Option_Ooption(U_17389)),hAPP(hAPP(c_COMBB(tc_fun(U_17390,U_17389),tc_fun(tc_Option_Ooption(U_17390),tc_Option_Ooption(U_17389)),U_17388),c_Option_Omap(U_17390,U_17389)),U_17391)),U_17392)) = c_Map_Odom(U_17388,U_17390,U_17392),
    inference(variable_rename,[status(thm)],[f_4266_1]) ).

fof(f_4266_3,plain,
    ! [U_17388,U_17389,U_17390,U_17391,U_17392] : c_Map_Odom(U_17388,U_17389,hAPP(hAPP(c_COMBS(U_17388,tc_Option_Ooption(U_17390),tc_Option_Ooption(U_17389)),hAPP(hAPP(c_COMBB(tc_fun(U_17390,U_17389),tc_fun(tc_Option_Ooption(U_17390),tc_Option_Ooption(U_17389)),U_17388),c_Option_Omap(U_17390,U_17389)),U_17391)),U_17392)) = c_Map_Odom(U_17388,U_17390,U_17392),
    inference(definitional_conversion,[status(esa)],[f_4266_2]) ).

cnf(f_4266_4,plain,
    c_Map_Odom(U_17388,U_17389,hAPP(hAPP(c_COMBS(U_17388,tc_Option_Ooption(U_17390),tc_Option_Ooption(U_17389)),hAPP(hAPP(c_COMBB(tc_fun(U_17390,U_17389),tc_fun(tc_Option_Ooption(U_17390),tc_Option_Ooption(U_17389)),U_17388),c_Option_Omap(U_17390,U_17389)),U_17391)),U_17392)) = c_Map_Odom(U_17388,U_17390,U_17392),
    inference(clausify,[status(thm)],[f_4266_3]) ).

fof(f_4267_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_option__map__Some]) ).

fof(f_4267_2,plain,
    ! [U_17396,U_17395,U_17394,U_17393] : hAPP(hAPP(c_Option_Omap(U_17393,U_17394),U_17395),hAPP(c_Option_Ooption_OSome(U_17393),U_17396)) = hAPP(c_Option_Ooption_OSome(U_17394),hAPP(U_17395,U_17396)),
    inference(variable_rename,[status(thm)],[f_4267_1]) ).

fof(f_4267_3,plain,
    ! [U_17393,U_17394,U_17395,U_17396] : hAPP(hAPP(c_Option_Omap(U_17393,U_17394),U_17395),hAPP(c_Option_Ooption_OSome(U_17393),U_17396)) = hAPP(c_Option_Ooption_OSome(U_17394),hAPP(U_17395,U_17396)),
    inference(definitional_conversion,[status(esa)],[f_4267_2]) ).

cnf(f_4267_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17393,U_17394),U_17395),hAPP(c_Option_Ooption_OSome(U_17393),U_17396)) = hAPP(c_Option_Ooption_OSome(U_17394),hAPP(U_17395,U_17396)),
    inference(clausify,[status(thm)],[f_4267_3]) ).

fof(f_4268_1,plain,
    ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
        | ! [B_z] :
            ( hAPP(V_f_2,B_z) != V_y_2
            | V_xo_2 != hAPP(c_Option_Ooption_OSome(T_c),B_z) ) )
      & ( ? [B_z] :
            ( hAPP(V_f_2,B_z) = V_y_2
            & V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z) )
        | hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_option__map__eq__Some]) ).

fof(f_4268_2,plain,
    ! [U_17403,U_17402,U_17401,U_17400,U_17399] :
      ( ( hAPP(hAPP(c_Option_Omap(U_17399,U_17400),U_17401),U_17402) = hAPP(c_Option_Ooption_OSome(U_17400),U_17403)
        | ! [U_17398] :
            ( hAPP(U_17401,U_17398) != U_17403
            | U_17402 != hAPP(c_Option_Ooption_OSome(U_17399),U_17398) ) )
      & ( ? [U_17397] :
            ( hAPP(U_17401,U_17397) = U_17403
            & U_17402 = hAPP(c_Option_Ooption_OSome(U_17399),U_17397) )
        | hAPP(hAPP(c_Option_Omap(U_17399,U_17400),U_17401),U_17402) != hAPP(c_Option_Ooption_OSome(U_17400),U_17403) ) ),
    inference(variable_rename,[status(thm)],[f_4268_1]) ).

fof(f_4268_3,plain,
    ( ! [U_17413,U_17411,U_17409,U_17407,U_17405] :
        ( hAPP(hAPP(c_Option_Omap(U_17405,U_17407),U_17409),U_17411) = hAPP(c_Option_Ooption_OSome(U_17407),U_17413)
        | ! [U_17398] :
            ( hAPP(U_17409,U_17398) != U_17413
            | U_17411 != hAPP(c_Option_Ooption_OSome(U_17405),U_17398) ) )
    & ! [U_17412,U_17410,U_17408,U_17406,U_17404] :
        ( ? [U_17397] :
            ( hAPP(U_17408,U_17397) = U_17412
            & U_17410 = hAPP(c_Option_Ooption_OSome(U_17404),U_17397) )
        | hAPP(hAPP(c_Option_Omap(U_17404,U_17406),U_17408),U_17410) != hAPP(c_Option_Ooption_OSome(U_17406),U_17412) ) ),
    inference(miniscope,[status(thm)],[f_4268_2]) ).

fof(f_4268_4,plain,
    ( ! [U_17413,U_17411,U_17409,U_17407,U_17405] :
        ( hAPP(hAPP(c_Option_Omap(U_17405,U_17407),U_17409),U_17411) = hAPP(c_Option_Ooption_OSome(U_17407),U_17413)
        | ! [U_17398] :
            ( hAPP(U_17409,U_17398) != U_17413
            | U_17411 != hAPP(c_Option_Ooption_OSome(U_17405),U_17398) ) )
    & ! [U_17412,U_17410,U_17408,U_17406,U_17404] :
        ( ( hAPP(U_17408,sK450(U_17412,U_17410,U_17408,U_17406,U_17404)) = U_17412
          & U_17410 = hAPP(c_Option_Ooption_OSome(U_17404),sK450(U_17412,U_17410,U_17408,U_17406,U_17404)) )
        | hAPP(hAPP(c_Option_Omap(U_17404,U_17406),U_17408),U_17410) != hAPP(c_Option_Ooption_OSome(U_17406),U_17412) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_17397,sK450(U_17412,U_17410,U_17408,U_17406,U_17404))],[f_4268_3]) ).

fof(f_4268_5,plain,
    ( ! [U_17410,U_17406,U_17404,U_17408,U_17412] :
        ( hAPP(U_17408,sK450(U_17412,U_17410,U_17408,U_17406,U_17404)) = U_17412
        | ~ sP1116(U_17410,U_17406,U_17404,U_17408,U_17412) )
    & ! [U_17410,U_17406,U_17404,U_17408,U_17412] :
        ( U_17410 = hAPP(c_Option_Ooption_OSome(U_17404),sK450(U_17412,U_17410,U_17408,U_17406,U_17404))
        | ~ sP1116(U_17410,U_17406,U_17404,U_17408,U_17412) )
    & ! [U_17409,U_17407,U_17411,U_17398,U_17413,U_17405] :
        ( hAPP(hAPP(c_Option_Omap(U_17405,U_17407),U_17409),U_17411) = hAPP(c_Option_Ooption_OSome(U_17407),U_17413)
        | hAPP(U_17409,U_17398) != U_17413
        | U_17411 != hAPP(c_Option_Ooption_OSome(U_17405),U_17398) )
    & ! [U_17410,U_17406,U_17404,U_17408,U_17412] :
        ( sP1116(U_17410,U_17406,U_17404,U_17408,U_17412)
        | hAPP(hAPP(c_Option_Omap(U_17404,U_17406),U_17408),U_17410) != hAPP(c_Option_Ooption_OSome(U_17406),U_17412) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1116])],[f_4268_4]) ).

cnf(f_4268_6,plain,
    ( sP1116(U_17410,U_17406,U_17404,U_17408,U_17412)
    | hAPP(hAPP(c_Option_Omap(U_17404,U_17406),U_17408),U_17410) != hAPP(c_Option_Ooption_OSome(U_17406),U_17412) ),
    inference(clausify,[status(thm)],[f_4268_5]) ).

cnf(f_4268_7,plain,
    ( hAPP(hAPP(c_Option_Omap(U_17405,U_17407),U_17409),U_17411) = hAPP(c_Option_Ooption_OSome(U_17407),U_17413)
    | hAPP(U_17409,U_17398) != U_17413
    | U_17411 != hAPP(c_Option_Ooption_OSome(U_17405),U_17398) ),
    inference(clausify,[status(thm)],[f_4268_5]) ).

cnf(f_4268_8,plain,
    ( U_17410 = hAPP(c_Option_Ooption_OSome(U_17404),sK450(U_17412,U_17410,U_17408,U_17406,U_17404))
    | ~ sP1116(U_17410,U_17406,U_17404,U_17408,U_17412) ),
    inference(clausify,[status(thm)],[f_4268_5]) ).

cnf(f_4268_9,plain,
    ( hAPP(U_17408,sK450(U_17412,U_17410,U_17408,U_17406,U_17404)) = U_17412
    | ~ sP1116(U_17410,U_17406,U_17404,U_17408,U_17412) ),
    inference(clausify,[status(thm)],[f_4268_5]) ).

fof(f_4269_1,plain,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_option__map__None]) ).

fof(f_4269_2,plain,
    ! [U_17416,U_17415,U_17414] : hAPP(hAPP(c_Option_Omap(U_17414,U_17415),U_17416),c_Option_Ooption_ONone(U_17414)) = c_Option_Ooption_ONone(U_17415),
    inference(variable_rename,[status(thm)],[f_4269_1]) ).

fof(f_4269_3,plain,
    ! [U_17416,U_17415,U_17414] : hAPP(hAPP(c_Option_Omap(U_17414,U_17415),U_17416),c_Option_Ooption_ONone(U_17414)) = c_Option_Ooption_ONone(U_17415),
    inference(definitional_conversion,[status(esa)],[f_4269_2]) ).

cnf(f_4269_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17414,U_17415),U_17416),c_Option_Ooption_ONone(U_17414)) = c_Option_Ooption_ONone(U_17415),
    inference(clausify,[status(thm)],[f_4269_3]) ).

fof(f_4270_1,plain,
    ! [V_opt_2,V_f_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
        | V_opt_2 != c_Option_Ooption_ONone(T_c) )
      & ( V_opt_2 = c_Option_Ooption_ONone(T_c)
        | hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) != c_Option_Ooption_ONone(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_option__map__is__None]) ).

fof(f_4270_2,plain,
    ! [U_17420,U_17419,U_17418,U_17417] :
      ( ( hAPP(hAPP(c_Option_Omap(U_17417,U_17418),U_17419),U_17420) = c_Option_Ooption_ONone(U_17418)
        | U_17420 != c_Option_Ooption_ONone(U_17417) )
      & ( U_17420 = c_Option_Ooption_ONone(U_17417)
        | hAPP(hAPP(c_Option_Omap(U_17417,U_17418),U_17419),U_17420) != c_Option_Ooption_ONone(U_17418) ) ),
    inference(variable_rename,[status(thm)],[f_4270_1]) ).

fof(f_4270_3,plain,
    ( ! [U_17428,U_17426,U_17424,U_17422] :
        ( hAPP(hAPP(c_Option_Omap(U_17422,U_17424),U_17426),U_17428) = c_Option_Ooption_ONone(U_17424)
        | U_17428 != c_Option_Ooption_ONone(U_17422) )
    & ! [U_17427,U_17425,U_17423,U_17421] :
        ( U_17427 = c_Option_Ooption_ONone(U_17421)
        | hAPP(hAPP(c_Option_Omap(U_17421,U_17423),U_17425),U_17427) != c_Option_Ooption_ONone(U_17423) ) ),
    inference(miniscope,[status(thm)],[f_4270_2]) ).

fof(f_4270_4,plain,
    ( ! [U_17422,U_17428,U_17424,U_17426] :
        ( hAPP(hAPP(c_Option_Omap(U_17422,U_17424),U_17426),U_17428) = c_Option_Ooption_ONone(U_17424)
        | U_17428 != c_Option_Ooption_ONone(U_17422) )
    & ! [U_17423,U_17425,U_17427,U_17421] :
        ( U_17427 = c_Option_Ooption_ONone(U_17421)
        | hAPP(hAPP(c_Option_Omap(U_17421,U_17423),U_17425),U_17427) != c_Option_Ooption_ONone(U_17423) ) ),
    inference(definitional_conversion,[status(esa)],[f_4270_3]) ).

cnf(f_4270_5,plain,
    ( U_17427 = c_Option_Ooption_ONone(U_17421)
    | hAPP(hAPP(c_Option_Omap(U_17421,U_17423),U_17425),U_17427) != c_Option_Ooption_ONone(U_17423) ),
    inference(clausify,[status(thm)],[f_4270_4]) ).

cnf(f_4270_6,plain,
    ( hAPP(hAPP(c_Option_Omap(U_17422,U_17424),U_17426),U_17428) = c_Option_Ooption_ONone(U_17424)
    | U_17428 != c_Option_Ooption_ONone(U_17422) ),
    inference(clausify,[status(thm)],[f_4270_4]) ).

fof(f_4271_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_option__map__o__empty]) ).

fof(f_4271_2,plain,
    ! [U_17433,U_17432,U_17431,U_17430,U_17429] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17429),tc_Option_Ooption(U_17430),U_17431,hAPP(c_Option_Omap(U_17429,U_17430),U_17432)),hAPP(c_COMBK(tc_Option_Ooption(U_17429),U_17431),c_Option_Ooption_ONone(U_17429))),U_17433) = c_Option_Ooption_ONone(U_17430),
    inference(variable_rename,[status(thm)],[f_4271_1]) ).

fof(f_4271_3,plain,
    ! [U_17429,U_17430,U_17431,U_17432,U_17433] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17429),tc_Option_Ooption(U_17430),U_17431,hAPP(c_Option_Omap(U_17429,U_17430),U_17432)),hAPP(c_COMBK(tc_Option_Ooption(U_17429),U_17431),c_Option_Ooption_ONone(U_17429))),U_17433) = c_Option_Ooption_ONone(U_17430),
    inference(definitional_conversion,[status(esa)],[f_4271_2]) ).

cnf(f_4271_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17429),tc_Option_Ooption(U_17430),U_17431,hAPP(c_Option_Omap(U_17429,U_17430),U_17432)),hAPP(c_COMBK(tc_Option_Ooption(U_17429),U_17431),c_Option_Ooption_ONone(U_17429))),U_17433) = c_Option_Ooption_ONone(U_17430),
    inference(clausify,[status(thm)],[f_4271_3]) ).

fof(f_4272_1,plain,
    ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))),
    inference(fof_nnf,[status(thm)],[fact_option__map__o__map__upd]) ).

fof(f_4272_2,plain,
    ! [U_17440,U_17439,U_17438,U_17437,U_17436,U_17435,U_17434] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17434),tc_Option_Ooption(U_17435),U_17436,hAPP(c_Option_Omap(U_17434,U_17435),U_17437)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17436,tc_Option_Ooption(U_17434)),U_17438),U_17439),hAPP(c_Option_Ooption_OSome(U_17434),U_17440))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17436,tc_Option_Ooption(U_17435)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17434),tc_Option_Ooption(U_17435),U_17436,hAPP(c_Option_Omap(U_17434,U_17435),U_17437)),U_17438)),U_17439),hAPP(c_Option_Ooption_OSome(U_17435),hAPP(U_17437,U_17440))),
    inference(variable_rename,[status(thm)],[f_4272_1]) ).

fof(f_4272_3,plain,
    ! [U_17434,U_17435,U_17436,U_17437,U_17438,U_17439,U_17440] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17434),tc_Option_Ooption(U_17435),U_17436,hAPP(c_Option_Omap(U_17434,U_17435),U_17437)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17436,tc_Option_Ooption(U_17434)),U_17438),U_17439),hAPP(c_Option_Ooption_OSome(U_17434),U_17440))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17436,tc_Option_Ooption(U_17435)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17434),tc_Option_Ooption(U_17435),U_17436,hAPP(c_Option_Omap(U_17434,U_17435),U_17437)),U_17438)),U_17439),hAPP(c_Option_Ooption_OSome(U_17435),hAPP(U_17437,U_17440))),
    inference(definitional_conversion,[status(esa)],[f_4272_2]) ).

cnf(f_4272_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17434),tc_Option_Ooption(U_17435),U_17436,hAPP(c_Option_Omap(U_17434,U_17435),U_17437)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17436,tc_Option_Ooption(U_17434)),U_17438),U_17439),hAPP(c_Option_Ooption_OSome(U_17434),U_17440))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17436,tc_Option_Ooption(U_17435)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17434),tc_Option_Ooption(U_17435),U_17436,hAPP(c_Option_Omap(U_17434,U_17435),U_17437)),U_17438)),U_17439),hAPP(c_Option_Ooption_OSome(U_17435),hAPP(U_17437,U_17440))),
    inference(clausify,[status(thm)],[f_4272_3]) ).

fof(f_4273_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( V_xs_2 = V_ys_2
      | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
      | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__inj__on]) ).

fof(f_4273_2,plain,
    ! [U_17445,U_17444,U_17443,U_17442,U_17441] :
      ( U_17444 = U_17445
      | ~ c_Fun_Oinj__on(U_17441,U_17442,U_17443,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17441,tc_HOL_Obool)),hAPP(c_List_Oset(U_17441),U_17444)),hAPP(c_List_Oset(U_17441),U_17445)))
      | hAPP(hAPP(c_List_Omap(U_17441,U_17442),U_17443),U_17444) != hAPP(hAPP(c_List_Omap(U_17441,U_17442),U_17443),U_17445) ),
    inference(variable_rename,[status(thm)],[f_4273_1]) ).

fof(f_4273_3,plain,
    ! [U_17441,U_17442,U_17443,U_17444,U_17445] :
      ( U_17444 = U_17445
      | ~ c_Fun_Oinj__on(U_17441,U_17442,U_17443,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17441,tc_HOL_Obool)),hAPP(c_List_Oset(U_17441),U_17444)),hAPP(c_List_Oset(U_17441),U_17445)))
      | hAPP(hAPP(c_List_Omap(U_17441,U_17442),U_17443),U_17444) != hAPP(hAPP(c_List_Omap(U_17441,U_17442),U_17443),U_17445) ),
    inference(definitional_conversion,[status(esa)],[f_4273_2]) ).

cnf(f_4273_4,plain,
    ( U_17444 = U_17445
    | ~ c_Fun_Oinj__on(U_17441,U_17442,U_17443,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17441,tc_HOL_Obool)),hAPP(c_List_Oset(U_17441),U_17444)),hAPP(c_List_Oset(U_17441),U_17445)))
    | hAPP(hAPP(c_List_Omap(U_17441,U_17442),U_17443),U_17444) != hAPP(hAPP(c_List_Omap(U_17441,U_17442),U_17443),U_17445) ),
    inference(clausify,[status(thm)],[f_4273_3]) ).

fof(f_4274_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map]) ).

fof(f_4274_2,plain,
    ! [U_17450,U_17449,U_17448,U_17447,U_17446] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17449) = hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17450)
          | U_17449 != U_17450 )
        & ( U_17449 = U_17450
          | hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17449) != hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17450) ) )
      | ~ c_Fun_Oinj__on(U_17446,U_17447,U_17448,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17446,tc_HOL_Obool)),hAPP(c_List_Oset(U_17446),U_17449)),hAPP(c_List_Oset(U_17446),U_17450))) ),
    inference(variable_rename,[status(thm)],[f_4274_1]) ).

fof(f_4274_3,plain,
    ( ! [U_17446,U_17447,U_17448,U_17449,U_17450] :
        ( hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17449) = hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17450)
        | U_17449 != U_17450
        | ~ sP1117(U_17446,U_17447,U_17448,U_17449,U_17450) )
    & ! [U_17446,U_17447,U_17448,U_17449,U_17450] :
        ( U_17449 = U_17450
        | hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17449) != hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17450)
        | ~ sP1117(U_17446,U_17447,U_17448,U_17449,U_17450) )
    & ! [U_17446,U_17447,U_17448,U_17449,U_17450] :
        ( sP1117(U_17446,U_17447,U_17448,U_17449,U_17450)
        | ~ c_Fun_Oinj__on(U_17446,U_17447,U_17448,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17446,tc_HOL_Obool)),hAPP(c_List_Oset(U_17446),U_17449)),hAPP(c_List_Oset(U_17446),U_17450))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1117])],[f_4274_2]) ).

cnf(f_4274_4,plain,
    ( sP1117(U_17446,U_17447,U_17448,U_17449,U_17450)
    | ~ c_Fun_Oinj__on(U_17446,U_17447,U_17448,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17446,tc_HOL_Obool)),hAPP(c_List_Oset(U_17446),U_17449)),hAPP(c_List_Oset(U_17446),U_17450))) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

cnf(f_4274_5,plain,
    ( U_17449 = U_17450
    | hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17449) != hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17450)
    | ~ sP1117(U_17446,U_17447,U_17448,U_17449,U_17450) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

cnf(f_4274_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17449) = hAPP(hAPP(c_List_Omap(U_17446,U_17447),U_17448),U_17450)
    | U_17449 != U_17450
    | ~ sP1117(U_17446,U_17447,U_17448,U_17449,U_17450) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

fof(f_4275_1,plain,
    ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__fun__upd]) ).

fof(f_4275_2,plain,
    ! [U_17456,U_17455,U_17454,U_17453,U_17452,U_17451] :
      ( hAPP(hAPP(c_List_Omap(U_17451,U_17454),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17451,U_17454),U_17455),U_17452),U_17456)),U_17453) = hAPP(hAPP(c_List_Omap(U_17451,U_17454),U_17455),U_17453)
      | hBOOL(hAPP(hAPP(c_member(U_17451),U_17452),hAPP(c_List_Oset(U_17451),U_17453))) ),
    inference(variable_rename,[status(thm)],[f_4275_1]) ).

fof(f_4275_3,plain,
    ! [U_17452,U_17451,U_17453,U_17454,U_17455,U_17456] :
      ( hAPP(hAPP(c_List_Omap(U_17451,U_17454),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17451,U_17454),U_17455),U_17452),U_17456)),U_17453) = hAPP(hAPP(c_List_Omap(U_17451,U_17454),U_17455),U_17453)
      | hBOOL(hAPP(hAPP(c_member(U_17451),U_17452),hAPP(c_List_Oset(U_17451),U_17453))) ),
    inference(definitional_conversion,[status(esa)],[f_4275_2]) ).

cnf(f_4275_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17451,U_17454),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17451,U_17454),U_17455),U_17452),U_17456)),U_17453) = hAPP(hAPP(c_List_Omap(U_17451,U_17454),U_17455),U_17453)
    | hBOOL(hAPP(hAPP(c_member(U_17451),U_17452),hAPP(c_List_Oset(U_17451),U_17453))) ),
    inference(clausify,[status(thm)],[f_4275_3]) ).

fof(f_4276_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__mapI]) ).

fof(f_4276_2,plain,
    ! [U_17460,U_17459,U_17458,U_17457] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17457),tc_List_Olist(U_17458),hAPP(c_List_Omap(U_17457,U_17458),U_17459),U_17460)
      | ~ c_Fun_Oinj__on(U_17457,U_17458,U_17459,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17457,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17457),tc_fun(U_17457,tc_HOL_Obool),c_List_Oset(U_17457)),U_17460))) ),
    inference(variable_rename,[status(thm)],[f_4276_1]) ).

fof(f_4276_3,plain,
    ! [U_17457,U_17458,U_17459,U_17460] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17457),tc_List_Olist(U_17458),hAPP(c_List_Omap(U_17457,U_17458),U_17459),U_17460)
      | ~ c_Fun_Oinj__on(U_17457,U_17458,U_17459,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17457,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17457),tc_fun(U_17457,tc_HOL_Obool),c_List_Oset(U_17457)),U_17460))) ),
    inference(definitional_conversion,[status(esa)],[f_4276_2]) ).

cnf(f_4276_4,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17457),tc_List_Olist(U_17458),hAPP(c_List_Omap(U_17457,U_17458),U_17459),U_17460)
    | ~ c_Fun_Oinj__on(U_17457,U_17458,U_17459,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17457,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17457),tc_fun(U_17457,tc_HOL_Obool),c_List_Oset(U_17457)),U_17460))) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

fof(f_4277_1,plain,
    ! [V_ys_2,V_xs_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2))
      | c_Map_Omap__of(T_b,T_c,V_xs_2) != c_Map_Omap__of(T_b,T_c,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom]) ).

fof(f_4277_2,plain,
    ! [U_17464,U_17463,U_17462,U_17461] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17461,U_17462),U_17461,c_Product__Type_Ofst(U_17461,U_17462)),hAPP(c_List_Oset(tc_prod(U_17461,U_17462)),U_17463)) = hAPP(c_Set_Oimage(tc_prod(U_17461,U_17462),U_17461,c_Product__Type_Ofst(U_17461,U_17462)),hAPP(c_List_Oset(tc_prod(U_17461,U_17462)),U_17464))
      | c_Map_Omap__of(U_17461,U_17462,U_17463) != c_Map_Omap__of(U_17461,U_17462,U_17464) ),
    inference(variable_rename,[status(thm)],[f_4277_1]) ).

fof(f_4277_3,plain,
    ! [U_17461,U_17462,U_17463,U_17464] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17461,U_17462),U_17461,c_Product__Type_Ofst(U_17461,U_17462)),hAPP(c_List_Oset(tc_prod(U_17461,U_17462)),U_17463)) = hAPP(c_Set_Oimage(tc_prod(U_17461,U_17462),U_17461,c_Product__Type_Ofst(U_17461,U_17462)),hAPP(c_List_Oset(tc_prod(U_17461,U_17462)),U_17464))
      | c_Map_Omap__of(U_17461,U_17462,U_17463) != c_Map_Omap__of(U_17461,U_17462,U_17464) ),
    inference(definitional_conversion,[status(esa)],[f_4277_2]) ).

cnf(f_4277_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_17461,U_17462),U_17461,c_Product__Type_Ofst(U_17461,U_17462)),hAPP(c_List_Oset(tc_prod(U_17461,U_17462)),U_17463)) = hAPP(c_Set_Oimage(tc_prod(U_17461,U_17462),U_17461,c_Product__Type_Ofst(U_17461,U_17462)),hAPP(c_List_Oset(tc_prod(U_17461,U_17462)),U_17464))
    | c_Map_Omap__of(U_17461,U_17462,U_17463) != c_Map_Omap__of(U_17461,U_17462,U_17464) ),
    inference(clausify,[status(thm)],[f_4277_3]) ).

fof(f_4278_1,plain,
    ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))
      | hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD]) ).

fof(f_4278_2,plain,
    ! [U_17469,U_17468,U_17467,U_17466,U_17465] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17465,U_17466)),hAPP(hAPP(c_Product__Type_OPair(U_17465,U_17466),U_17468),U_17469)),hAPP(c_List_Oset(tc_prod(U_17465,U_17466)),U_17467)))
      | hAPP(c_Map_Omap__of(U_17465,U_17466,U_17467),U_17468) != hAPP(c_Option_Ooption_OSome(U_17466),U_17469) ),
    inference(variable_rename,[status(thm)],[f_4278_1]) ).

fof(f_4278_3,plain,
    ! [U_17465,U_17466,U_17467,U_17468,U_17469] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17465,U_17466)),hAPP(hAPP(c_Product__Type_OPair(U_17465,U_17466),U_17468),U_17469)),hAPP(c_List_Oset(tc_prod(U_17465,U_17466)),U_17467)))
      | hAPP(c_Map_Omap__of(U_17465,U_17466,U_17467),U_17468) != hAPP(c_Option_Ooption_OSome(U_17466),U_17469) ),
    inference(definitional_conversion,[status(esa)],[f_4278_2]) ).

cnf(f_4278_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17465,U_17466)),hAPP(hAPP(c_Product__Type_OPair(U_17465,U_17466),U_17468),U_17469)),hAPP(c_List_Oset(tc_prod(U_17465,U_17466)),U_17467)))
    | hAPP(c_Map_Omap__of(U_17465,U_17466,U_17467),U_17468) != hAPP(c_Option_Ooption_OSome(U_17466),U_17469) ),
    inference(clausify,[status(thm)],[f_4278_3]) ).

fof(f_4279_1,plain,
    ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2)))
      | hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__SomeD]) ).

fof(f_4279_2,plain,
    ! [U_17474,U_17473,U_17472,U_17471,U_17470] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17470,U_17471)),hAPP(hAPP(c_Product__Type_OPair(U_17470,U_17471),U_17473),U_17474)),hAPP(c_List_Oset(tc_prod(U_17470,U_17471)),U_17472)))
      | hAPP(c_Map_Omap__of(U_17470,U_17471,U_17472),U_17473) != hAPP(c_Option_Ooption_OSome(U_17471),U_17474) ),
    inference(variable_rename,[status(thm)],[f_4279_1]) ).

fof(f_4279_3,plain,
    ! [U_17470,U_17471,U_17472,U_17473,U_17474] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17470,U_17471)),hAPP(hAPP(c_Product__Type_OPair(U_17470,U_17471),U_17473),U_17474)),hAPP(c_List_Oset(tc_prod(U_17470,U_17471)),U_17472)))
      | hAPP(c_Map_Omap__of(U_17470,U_17471,U_17472),U_17473) != hAPP(c_Option_Ooption_OSome(U_17471),U_17474) ),
    inference(definitional_conversion,[status(esa)],[f_4279_2]) ).

cnf(f_4279_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17470,U_17471)),hAPP(hAPP(c_Product__Type_OPair(U_17470,U_17471),U_17473),U_17474)),hAPP(c_List_Oset(tc_prod(U_17470,U_17471)),U_17472)))
    | hAPP(c_Map_Omap__of(U_17470,U_17471,U_17472),U_17473) != hAPP(c_Option_Ooption_OSome(U_17471),U_17474) ),
    inference(clausify,[status(thm)],[f_4279_3]) ).

fof(f_4280_1,plain,
    ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)),
    inference(fof_nnf,[status(thm)],[fact_dom__map__of__conv__image__fst]) ).

fof(f_4280_2,plain,
    ! [U_17477,U_17476,U_17475] : c_Map_Odom(U_17475,U_17476,c_Map_Omap__of(U_17475,U_17476,U_17477)) = hAPP(c_Set_Oimage(tc_prod(U_17475,U_17476),U_17475,c_Product__Type_Ofst(U_17475,U_17476)),hAPP(c_List_Oset(tc_prod(U_17475,U_17476)),U_17477)),
    inference(variable_rename,[status(thm)],[f_4280_1]) ).

fof(f_4280_3,plain,
    ! [U_17475,U_17476,U_17477] : c_Map_Odom(U_17475,U_17476,c_Map_Omap__of(U_17475,U_17476,U_17477)) = hAPP(c_Set_Oimage(tc_prod(U_17475,U_17476),U_17475,c_Product__Type_Ofst(U_17475,U_17476)),hAPP(c_List_Oset(tc_prod(U_17475,U_17476)),U_17477)),
    inference(definitional_conversion,[status(esa)],[f_4280_2]) ).

cnf(f_4280_4,plain,
    c_Map_Odom(U_17475,U_17476,c_Map_Omap__of(U_17475,U_17476,U_17477)) = hAPP(c_Set_Oimage(tc_prod(U_17475,U_17476),U_17475,c_Product__Type_Ofst(U_17475,U_17476)),hAPP(c_List_Oset(tc_prod(U_17475,U_17476)),U_17477)),
    inference(clausify,[status(thm)],[f_4280_3]) ).

fof(f_4281_1,plain,
    ! [V_x_2,V_xys_2,T_b,T_c] :
      ( ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
        | hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2))))
        | hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) != c_Option_Ooption_ONone(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eq__None__iff]) ).

fof(f_4281_2,plain,
    ! [U_17481,U_17480,U_17479,U_17478] :
      ( ( hAPP(c_Map_Omap__of(U_17478,U_17479,U_17480),U_17481) = c_Option_Ooption_ONone(U_17479)
        | hBOOL(hAPP(hAPP(c_member(U_17478),U_17481),hAPP(c_Set_Oimage(tc_prod(U_17478,U_17479),U_17478,c_Product__Type_Ofst(U_17478,U_17479)),hAPP(c_List_Oset(tc_prod(U_17478,U_17479)),U_17480)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_17478),U_17481),hAPP(c_Set_Oimage(tc_prod(U_17478,U_17479),U_17478,c_Product__Type_Ofst(U_17478,U_17479)),hAPP(c_List_Oset(tc_prod(U_17478,U_17479)),U_17480))))
        | hAPP(c_Map_Omap__of(U_17478,U_17479,U_17480),U_17481) != c_Option_Ooption_ONone(U_17479) ) ),
    inference(variable_rename,[status(thm)],[f_4281_1]) ).

fof(f_4281_3,plain,
    ( ! [U_17489,U_17487,U_17485,U_17483] :
        ( hAPP(c_Map_Omap__of(U_17483,U_17485,U_17487),U_17489) = c_Option_Ooption_ONone(U_17485)
        | hBOOL(hAPP(hAPP(c_member(U_17483),U_17489),hAPP(c_Set_Oimage(tc_prod(U_17483,U_17485),U_17483,c_Product__Type_Ofst(U_17483,U_17485)),hAPP(c_List_Oset(tc_prod(U_17483,U_17485)),U_17487)))) )
    & ! [U_17488,U_17486,U_17484,U_17482] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17482),U_17488),hAPP(c_Set_Oimage(tc_prod(U_17482,U_17484),U_17482,c_Product__Type_Ofst(U_17482,U_17484)),hAPP(c_List_Oset(tc_prod(U_17482,U_17484)),U_17486))))
        | hAPP(c_Map_Omap__of(U_17482,U_17484,U_17486),U_17488) != c_Option_Ooption_ONone(U_17484) ) ),
    inference(miniscope,[status(thm)],[f_4281_2]) ).

fof(f_4281_4,plain,
    ( ! [U_17483,U_17485,U_17487,U_17489] :
        ( hAPP(c_Map_Omap__of(U_17483,U_17485,U_17487),U_17489) = c_Option_Ooption_ONone(U_17485)
        | hBOOL(hAPP(hAPP(c_member(U_17483),U_17489),hAPP(c_Set_Oimage(tc_prod(U_17483,U_17485),U_17483,c_Product__Type_Ofst(U_17483,U_17485)),hAPP(c_List_Oset(tc_prod(U_17483,U_17485)),U_17487)))) )
    & ! [U_17484,U_17482,U_17486,U_17488] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17482),U_17488),hAPP(c_Set_Oimage(tc_prod(U_17482,U_17484),U_17482,c_Product__Type_Ofst(U_17482,U_17484)),hAPP(c_List_Oset(tc_prod(U_17482,U_17484)),U_17486))))
        | hAPP(c_Map_Omap__of(U_17482,U_17484,U_17486),U_17488) != c_Option_Ooption_ONone(U_17484) ) ),
    inference(definitional_conversion,[status(esa)],[f_4281_3]) ).

cnf(f_4281_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17482),U_17488),hAPP(c_Set_Oimage(tc_prod(U_17482,U_17484),U_17482,c_Product__Type_Ofst(U_17482,U_17484)),hAPP(c_List_Oset(tc_prod(U_17482,U_17484)),U_17486))))
    | hAPP(c_Map_Omap__of(U_17482,U_17484,U_17486),U_17488) != c_Option_Ooption_ONone(U_17484) ),
    inference(clausify,[status(thm)],[f_4281_4]) ).

cnf(f_4281_6,plain,
    ( hAPP(c_Map_Omap__of(U_17483,U_17485,U_17487),U_17489) = c_Option_Ooption_ONone(U_17485)
    | hBOOL(hAPP(hAPP(c_member(U_17483),U_17489),hAPP(c_Set_Oimage(tc_prod(U_17483,U_17485),U_17483,c_Product__Type_Ofst(U_17483,U_17485)),hAPP(c_List_Oset(tc_prod(U_17483,U_17485)),U_17487)))) ),
    inference(clausify,[status(thm)],[f_4281_4]) ).

fof(f_4282_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap__def]) ).

fof(f_4282_2,plain,
    ! [U_17492,U_17491,U_17490] : hAPP(c_Option_Omap(U_17490,U_17491),U_17492) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17491),U_17490,c_Option_Ooption_ONone(U_17491),hAPP(hAPP(c_COMBB(U_17491,tc_Option_Ooption(U_17491),U_17490),c_Option_Ooption_OSome(U_17491)),U_17492)),
    inference(variable_rename,[status(thm)],[f_4282_1]) ).

fof(f_4282_3,plain,
    ! [U_17490,U_17491,U_17492] : hAPP(c_Option_Omap(U_17490,U_17491),U_17492) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17491),U_17490,c_Option_Ooption_ONone(U_17491),hAPP(hAPP(c_COMBB(U_17491,tc_Option_Ooption(U_17491),U_17490),c_Option_Ooption_OSome(U_17491)),U_17492)),
    inference(definitional_conversion,[status(esa)],[f_4282_2]) ).

cnf(f_4282_4,plain,
    hAPP(c_Option_Omap(U_17490,U_17491),U_17492) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17491),U_17490,c_Option_Ooption_ONone(U_17491),hAPP(hAPP(c_COMBB(U_17491,tc_Option_Ooption(U_17491),U_17490),c_Option_Ooption_OSome(U_17491)),U_17492)),
    inference(clausify,[status(thm)],[f_4282_3]) ).

fof(f_4283_1,plain,
    ( ( c_Com_OWT__bodies
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) )
      | ~ c_Com_OWT__bodies ) ),
    inference(fof_nnf,[status(thm)],[fact_WT__bodies__def]) ).

fof(f_4283_2,plain,
    ( ( c_Com_OWT__bodies
      | ? [U_17494] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),U_17494))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17494),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_17493] :
          ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),U_17493))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17493),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) )
      | ~ c_Com_OWT__bodies ) ),
    inference(variable_rename,[status(thm)],[f_4283_1]) ).

fof(f_4283_3,plain,
    ( ( c_Com_OWT__bodies
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sK451))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK451),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_17493] :
          ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),U_17493))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17493),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) )
      | ~ c_Com_OWT__bodies ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_17494,sK451)],[f_4283_2]) ).

fof(f_4283_4,plain,
    ( ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sK451))
      | ~ sP1118 )
    & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK451),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
      | ~ sP1118 )
    & ( c_Com_OWT__bodies
      | sP1118 )
    & ! [U_17493] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),U_17493))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17493),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
        | ~ c_Com_OWT__bodies ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1118])],[f_4283_3]) ).

cnf(f_4283_5,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),U_17493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17493),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_4283_4]) ).

cnf(f_4283_6,plain,
    ( c_Com_OWT__bodies
    | sP1118 ),
    inference(clausify,[status(thm)],[f_4283_4]) ).

cnf(f_4283_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK451),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ sP1118 ),
    inference(clausify,[status(thm)],[f_4283_4]) ).

cnf(f_4283_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sK451))
    | ~ sP1118 ),
    inference(clausify,[status(thm)],[f_4283_4]) ).

fof(f_4284_1,plain,
    ! [V_ks_2,V_f_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)),
    inference(fof_nnf,[status(thm)],[fact_map__of__map__restrict]) ).

fof(f_4284_2,plain,
    ! [U_17498,U_17497,U_17496,U_17495] : c_Map_Omap__of(U_17495,U_17496,hAPP(hAPP(c_List_Omap(U_17495,tc_prod(U_17495,U_17496)),hAPP(hAPP(c_COMBS(U_17495,U_17496,tc_prod(U_17495,U_17496)),c_Product__Type_OPair(U_17495,U_17496)),U_17497)),U_17498)) = c_Map_Orestrict__map(U_17495,U_17496,hAPP(c_Fun_Ocomp(U_17496,tc_Option_Ooption(U_17496),U_17495,c_Option_Ooption_OSome(U_17496)),U_17497),hAPP(c_List_Oset(U_17495),U_17498)),
    inference(variable_rename,[status(thm)],[f_4284_1]) ).

fof(f_4284_3,plain,
    ! [U_17495,U_17496,U_17497,U_17498] : c_Map_Omap__of(U_17495,U_17496,hAPP(hAPP(c_List_Omap(U_17495,tc_prod(U_17495,U_17496)),hAPP(hAPP(c_COMBS(U_17495,U_17496,tc_prod(U_17495,U_17496)),c_Product__Type_OPair(U_17495,U_17496)),U_17497)),U_17498)) = c_Map_Orestrict__map(U_17495,U_17496,hAPP(c_Fun_Ocomp(U_17496,tc_Option_Ooption(U_17496),U_17495,c_Option_Ooption_OSome(U_17496)),U_17497),hAPP(c_List_Oset(U_17495),U_17498)),
    inference(definitional_conversion,[status(esa)],[f_4284_2]) ).

cnf(f_4284_4,plain,
    c_Map_Omap__of(U_17495,U_17496,hAPP(hAPP(c_List_Omap(U_17495,tc_prod(U_17495,U_17496)),hAPP(hAPP(c_COMBS(U_17495,U_17496,tc_prod(U_17495,U_17496)),c_Product__Type_OPair(U_17495,U_17496)),U_17497)),U_17498)) = c_Map_Orestrict__map(U_17495,U_17496,hAPP(c_Fun_Ocomp(U_17496,tc_Option_Ooption(U_17496),U_17495,c_Option_Ooption_OSome(U_17496)),U_17497),hAPP(c_List_Oset(U_17495),U_17498)),
    inference(clausify,[status(thm)],[f_4284_3]) ).

fof(f_4285_1,plain,
    ! [V_al_2,T_c,T_b] :
      ( c_Map_Oran(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ran__distinct]) ).

fof(f_4285_2,plain,
    ! [U_17501,U_17500,U_17499] :
      ( c_Map_Oran(U_17499,U_17500,c_Map_Omap__of(U_17499,U_17500,U_17501)) = hAPP(c_Set_Oimage(tc_prod(U_17499,U_17500),U_17500,c_Product__Type_Osnd(U_17499,U_17500)),hAPP(c_List_Oset(tc_prod(U_17499,U_17500)),U_17501))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17499),hAPP(hAPP(c_List_Omap(tc_prod(U_17499,U_17500),U_17499),c_Product__Type_Ofst(U_17499,U_17500)),U_17501))) ),
    inference(variable_rename,[status(thm)],[f_4285_1]) ).

fof(f_4285_3,plain,
    ! [U_17501,U_17499,U_17500] :
      ( c_Map_Oran(U_17499,U_17500,c_Map_Omap__of(U_17499,U_17500,U_17501)) = hAPP(c_Set_Oimage(tc_prod(U_17499,U_17500),U_17500,c_Product__Type_Osnd(U_17499,U_17500)),hAPP(c_List_Oset(tc_prod(U_17499,U_17500)),U_17501))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17499),hAPP(hAPP(c_List_Omap(tc_prod(U_17499,U_17500),U_17499),c_Product__Type_Ofst(U_17499,U_17500)),U_17501))) ),
    inference(definitional_conversion,[status(esa)],[f_4285_2]) ).

cnf(f_4285_4,plain,
    ( c_Map_Oran(U_17499,U_17500,c_Map_Omap__of(U_17499,U_17500,U_17501)) = hAPP(c_Set_Oimage(tc_prod(U_17499,U_17500),U_17500,c_Product__Type_Osnd(U_17499,U_17500)),hAPP(c_List_Oset(tc_prod(U_17499,U_17500)),U_17501))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17499),hAPP(hAPP(c_List_Omap(tc_prod(U_17499,U_17500),U_17499),c_Product__Type_Ofst(U_17499,U_17500)),U_17501))) ),
    inference(clausify,[status(thm)],[f_4285_3]) ).

fof(f_4286_1,plain,
    ! [V_xs_2,T_c,T_b] :
      ( hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),c_Map_Omap__of(T_b,T_c,V_xs_2)))),c_Option_Ooption_OSome(T_c))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_set__map__of__compr]) ).

fof(f_4286_2,plain,
    ! [U_17504,U_17503,U_17502] :
      ( hAPP(c_List_Oset(tc_prod(U_17502,U_17503)),U_17504) = hAPP(c_Set_OCollect(tc_prod(U_17502,U_17503)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17502,U_17503,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17502,tc_fun(U_17503,tc_Option_Ooption(U_17503)),tc_fun(U_17503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17503),tc_HOL_Obool),tc_fun(tc_fun(U_17503,tc_Option_Ooption(U_17503)),tc_fun(U_17503,tc_HOL_Obool)),U_17502),c_COMBB(tc_Option_Ooption(U_17503),tc_HOL_Obool,U_17503)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17503),tc_fun(tc_Option_Ooption(U_17503),tc_HOL_Obool),U_17502),c_fequal),c_Map_Omap__of(U_17502,U_17503,U_17504)))),c_Option_Ooption_OSome(U_17503))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17502),hAPP(hAPP(c_List_Omap(tc_prod(U_17502,U_17503),U_17502),c_Product__Type_Ofst(U_17502,U_17503)),U_17504))) ),
    inference(variable_rename,[status(thm)],[f_4286_1]) ).

fof(f_4286_3,plain,
    ! [U_17502,U_17503,U_17504] :
      ( hAPP(c_List_Oset(tc_prod(U_17502,U_17503)),U_17504) = hAPP(c_Set_OCollect(tc_prod(U_17502,U_17503)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17502,U_17503,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17502,tc_fun(U_17503,tc_Option_Ooption(U_17503)),tc_fun(U_17503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17503),tc_HOL_Obool),tc_fun(tc_fun(U_17503,tc_Option_Ooption(U_17503)),tc_fun(U_17503,tc_HOL_Obool)),U_17502),c_COMBB(tc_Option_Ooption(U_17503),tc_HOL_Obool,U_17503)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17503),tc_fun(tc_Option_Ooption(U_17503),tc_HOL_Obool),U_17502),c_fequal),c_Map_Omap__of(U_17502,U_17503,U_17504)))),c_Option_Ooption_OSome(U_17503))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17502),hAPP(hAPP(c_List_Omap(tc_prod(U_17502,U_17503),U_17502),c_Product__Type_Ofst(U_17502,U_17503)),U_17504))) ),
    inference(definitional_conversion,[status(esa)],[f_4286_2]) ).

cnf(f_4286_4,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17502,U_17503)),U_17504) = hAPP(c_Set_OCollect(tc_prod(U_17502,U_17503)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17502,U_17503,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17502,tc_fun(U_17503,tc_Option_Ooption(U_17503)),tc_fun(U_17503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17503),tc_HOL_Obool),tc_fun(tc_fun(U_17503,tc_Option_Ooption(U_17503)),tc_fun(U_17503,tc_HOL_Obool)),U_17502),c_COMBB(tc_Option_Ooption(U_17503),tc_HOL_Obool,U_17503)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17503),tc_fun(tc_Option_Ooption(U_17503),tc_HOL_Obool),U_17502),c_fequal),c_Map_Omap__of(U_17502,U_17503,U_17504)))),c_Option_Ooption_OSome(U_17503))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17502),hAPP(hAPP(c_List_Omap(tc_prod(U_17502,U_17503),U_17502),c_Product__Type_Ofst(U_17502,U_17503)),U_17504))) ),
    inference(clausify,[status(thm)],[f_4286_3]) ).

fof(f_4287_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
        | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) )
      & ( ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
          & hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__map]) ).

fof(f_4287_2,plain,
    ! [U_17508,U_17507,U_17506,U_17505] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17505),hAPP(hAPP(c_List_Omap(U_17506,U_17505),U_17507),U_17508)))
        | ~ c_Fun_Oinj__on(U_17506,U_17505,U_17507,hAPP(c_List_Oset(U_17506),U_17508))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17506),U_17508)) )
      & ( ( c_Fun_Oinj__on(U_17506,U_17505,U_17507,hAPP(c_List_Oset(U_17506),U_17508))
          & hBOOL(hAPP(c_List_Odistinct(U_17506),U_17508)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17505),hAPP(hAPP(c_List_Omap(U_17506,U_17505),U_17507),U_17508))) ) ),
    inference(variable_rename,[status(thm)],[f_4287_1]) ).

fof(f_4287_3,plain,
    ( ! [U_17516,U_17514,U_17512,U_17510] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17510),hAPP(hAPP(c_List_Omap(U_17512,U_17510),U_17514),U_17516)))
        | ~ c_Fun_Oinj__on(U_17512,U_17510,U_17514,hAPP(c_List_Oset(U_17512),U_17516))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17512),U_17516)) )
    & ! [U_17515,U_17513,U_17511,U_17509] :
        ( ( c_Fun_Oinj__on(U_17511,U_17509,U_17513,hAPP(c_List_Oset(U_17511),U_17515))
          & hBOOL(hAPP(c_List_Odistinct(U_17511),U_17515)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17509),hAPP(hAPP(c_List_Omap(U_17511,U_17509),U_17513),U_17515))) ) ),
    inference(miniscope,[status(thm)],[f_4287_2]) ).

fof(f_4287_4,plain,
    ( ! [U_17511,U_17513,U_17509,U_17515] :
        ( c_Fun_Oinj__on(U_17511,U_17509,U_17513,hAPP(c_List_Oset(U_17511),U_17515))
        | ~ sP1119(U_17511,U_17513,U_17509,U_17515) )
    & ! [U_17511,U_17513,U_17509,U_17515] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17511),U_17515))
        | ~ sP1119(U_17511,U_17513,U_17509,U_17515) )
    & ! [U_17512,U_17510,U_17516,U_17514] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17510),hAPP(hAPP(c_List_Omap(U_17512,U_17510),U_17514),U_17516)))
        | ~ c_Fun_Oinj__on(U_17512,U_17510,U_17514,hAPP(c_List_Oset(U_17512),U_17516))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17512),U_17516)) )
    & ! [U_17511,U_17513,U_17509,U_17515] :
        ( sP1119(U_17511,U_17513,U_17509,U_17515)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17509),hAPP(hAPP(c_List_Omap(U_17511,U_17509),U_17513),U_17515))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1119])],[f_4287_3]) ).

cnf(f_4287_5,plain,
    ( sP1119(U_17511,U_17513,U_17509,U_17515)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17509),hAPP(hAPP(c_List_Omap(U_17511,U_17509),U_17513),U_17515))) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

cnf(f_4287_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17510),hAPP(hAPP(c_List_Omap(U_17512,U_17510),U_17514),U_17516)))
    | ~ c_Fun_Oinj__on(U_17512,U_17510,U_17514,hAPP(c_List_Oset(U_17512),U_17516))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17512),U_17516)) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

cnf(f_4287_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17511),U_17515))
    | ~ sP1119(U_17511,U_17513,U_17509,U_17515) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

cnf(f_4287_8,plain,
    ( c_Fun_Oinj__on(U_17511,U_17509,U_17513,hAPP(c_List_Oset(U_17511),U_17515))
    | ~ sP1119(U_17511,U_17513,U_17509,U_17515) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

fof(f_4288_1,plain,
    ! [V_ys_2,V_xs_2,T_c,T_b] :
      ( ( ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
          | hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) != hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) )
        & ( hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)
          | c_Map_Omap__of(T_b,T_c,V_xs_2) != c_Map_Omap__of(T_b,T_c,V_ys_2) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__inject__set]) ).

fof(f_4288_2,plain,
    ! [U_17520,U_17519,U_17518,U_17517] :
      ( ( ( c_Map_Omap__of(U_17517,U_17518,U_17519) = c_Map_Omap__of(U_17517,U_17518,U_17520)
          | hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17519) != hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17520) )
        & ( hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17519) = hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17520)
          | c_Map_Omap__of(U_17517,U_17518,U_17519) != c_Map_Omap__of(U_17517,U_17518,U_17520) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),hAPP(hAPP(c_List_Omap(tc_prod(U_17517,U_17518),U_17517),c_Product__Type_Ofst(U_17517,U_17518)),U_17520)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),hAPP(hAPP(c_List_Omap(tc_prod(U_17517,U_17518),U_17517),c_Product__Type_Ofst(U_17517,U_17518)),U_17519))) ),
    inference(variable_rename,[status(thm)],[f_4288_1]) ).

fof(f_4288_3,plain,
    ( ! [U_17517,U_17518,U_17519,U_17520] :
        ( c_Map_Omap__of(U_17517,U_17518,U_17519) = c_Map_Omap__of(U_17517,U_17518,U_17520)
        | hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17519) != hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17520)
        | ~ sP1120(U_17517,U_17518,U_17519,U_17520) )
    & ! [U_17517,U_17518,U_17519,U_17520] :
        ( hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17519) = hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17520)
        | c_Map_Omap__of(U_17517,U_17518,U_17519) != c_Map_Omap__of(U_17517,U_17518,U_17520)
        | ~ sP1120(U_17517,U_17518,U_17519,U_17520) )
    & ! [U_17517,U_17518,U_17519,U_17520] :
        ( sP1120(U_17517,U_17518,U_17519,U_17520)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),hAPP(hAPP(c_List_Omap(tc_prod(U_17517,U_17518),U_17517),c_Product__Type_Ofst(U_17517,U_17518)),U_17520)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),hAPP(hAPP(c_List_Omap(tc_prod(U_17517,U_17518),U_17517),c_Product__Type_Ofst(U_17517,U_17518)),U_17519))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1120])],[f_4288_2]) ).

cnf(f_4288_4,plain,
    ( sP1120(U_17517,U_17518,U_17519,U_17520)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),hAPP(hAPP(c_List_Omap(tc_prod(U_17517,U_17518),U_17517),c_Product__Type_Ofst(U_17517,U_17518)),U_17520)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),hAPP(hAPP(c_List_Omap(tc_prod(U_17517,U_17518),U_17517),c_Product__Type_Ofst(U_17517,U_17518)),U_17519))) ),
    inference(clausify,[status(thm)],[f_4288_3]) ).

cnf(f_4288_5,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17519) = hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17520)
    | c_Map_Omap__of(U_17517,U_17518,U_17519) != c_Map_Omap__of(U_17517,U_17518,U_17520)
    | ~ sP1120(U_17517,U_17518,U_17519,U_17520) ),
    inference(clausify,[status(thm)],[f_4288_3]) ).

cnf(f_4288_6,plain,
    ( c_Map_Omap__of(U_17517,U_17518,U_17519) = c_Map_Omap__of(U_17517,U_17518,U_17520)
    | hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17519) != hAPP(c_List_Oset(tc_prod(U_17517,U_17518)),U_17520)
    | ~ sP1120(U_17517,U_17518,U_17519,U_17520) ),
    inference(clausify,[status(thm)],[f_4288_3]) ).

fof(f_4289_1,plain,
    ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
      ( ( ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
          | hAPP(c_Option_Ooption_OSome(T_c),V_y_2) != hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Some__eq__map__of__iff]) ).

fof(f_4289_2,plain,
    ! [U_17525,U_17524,U_17523,U_17522,U_17521] :
      ( ( ( hAPP(c_Option_Ooption_OSome(U_17522),U_17524) = hAPP(c_Map_Omap__of(U_17521,U_17522,U_17523),U_17525)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17521,U_17522)),hAPP(hAPP(c_Product__Type_OPair(U_17521,U_17522),U_17525),U_17524)),hAPP(c_List_Oset(tc_prod(U_17521,U_17522)),U_17523))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17521,U_17522)),hAPP(hAPP(c_Product__Type_OPair(U_17521,U_17522),U_17525),U_17524)),hAPP(c_List_Oset(tc_prod(U_17521,U_17522)),U_17523)))
          | hAPP(c_Option_Ooption_OSome(U_17522),U_17524) != hAPP(c_Map_Omap__of(U_17521,U_17522,U_17523),U_17525) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17521),hAPP(hAPP(c_List_Omap(tc_prod(U_17521,U_17522),U_17521),c_Product__Type_Ofst(U_17521,U_17522)),U_17523))) ),
    inference(variable_rename,[status(thm)],[f_4289_1]) ).

fof(f_4289_3,plain,
    ( ! [U_17521,U_17522,U_17523,U_17524,U_17525] :
        ( hAPP(c_Option_Ooption_OSome(U_17522),U_17524) = hAPP(c_Map_Omap__of(U_17521,U_17522,U_17523),U_17525)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17521,U_17522)),hAPP(hAPP(c_Product__Type_OPair(U_17521,U_17522),U_17525),U_17524)),hAPP(c_List_Oset(tc_prod(U_17521,U_17522)),U_17523)))
        | ~ sP1121(U_17521,U_17522,U_17523,U_17524,U_17525) )
    & ! [U_17521,U_17522,U_17523,U_17524,U_17525] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17521,U_17522)),hAPP(hAPP(c_Product__Type_OPair(U_17521,U_17522),U_17525),U_17524)),hAPP(c_List_Oset(tc_prod(U_17521,U_17522)),U_17523)))
        | hAPP(c_Option_Ooption_OSome(U_17522),U_17524) != hAPP(c_Map_Omap__of(U_17521,U_17522,U_17523),U_17525)
        | ~ sP1121(U_17521,U_17522,U_17523,U_17524,U_17525) )
    & ! [U_17521,U_17522,U_17523,U_17524,U_17525] :
        ( sP1121(U_17521,U_17522,U_17523,U_17524,U_17525)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17521),hAPP(hAPP(c_List_Omap(tc_prod(U_17521,U_17522),U_17521),c_Product__Type_Ofst(U_17521,U_17522)),U_17523))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1121])],[f_4289_2]) ).

cnf(f_4289_4,plain,
    ( sP1121(U_17521,U_17522,U_17523,U_17524,U_17525)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17521),hAPP(hAPP(c_List_Omap(tc_prod(U_17521,U_17522),U_17521),c_Product__Type_Ofst(U_17521,U_17522)),U_17523))) ),
    inference(clausify,[status(thm)],[f_4289_3]) ).

cnf(f_4289_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17521,U_17522)),hAPP(hAPP(c_Product__Type_OPair(U_17521,U_17522),U_17525),U_17524)),hAPP(c_List_Oset(tc_prod(U_17521,U_17522)),U_17523)))
    | hAPP(c_Option_Ooption_OSome(U_17522),U_17524) != hAPP(c_Map_Omap__of(U_17521,U_17522,U_17523),U_17525)
    | ~ sP1121(U_17521,U_17522,U_17523,U_17524,U_17525) ),
    inference(clausify,[status(thm)],[f_4289_3]) ).

cnf(f_4289_6,plain,
    ( hAPP(c_Option_Ooption_OSome(U_17522),U_17524) = hAPP(c_Map_Omap__of(U_17521,U_17522,U_17523),U_17525)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17521,U_17522)),hAPP(hAPP(c_Product__Type_OPair(U_17521,U_17522),U_17525),U_17524)),hAPP(c_List_Oset(tc_prod(U_17521,U_17522)),U_17523)))
    | ~ sP1121(U_17521,U_17522,U_17523,U_17524,U_17525) ),
    inference(clausify,[status(thm)],[f_4289_3]) ).

fof(f_4290_1,plain,
    ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
      ( ( ( hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
          | hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) != hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eq__Some__iff]) ).

fof(f_4290_2,plain,
    ! [U_17530,U_17529,U_17528,U_17527,U_17526] :
      ( ( ( hAPP(c_Map_Omap__of(U_17526,U_17527,U_17528),U_17529) = hAPP(c_Option_Ooption_OSome(U_17527),U_17530)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17526,U_17527)),hAPP(hAPP(c_Product__Type_OPair(U_17526,U_17527),U_17529),U_17530)),hAPP(c_List_Oset(tc_prod(U_17526,U_17527)),U_17528))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17526,U_17527)),hAPP(hAPP(c_Product__Type_OPair(U_17526,U_17527),U_17529),U_17530)),hAPP(c_List_Oset(tc_prod(U_17526,U_17527)),U_17528)))
          | hAPP(c_Map_Omap__of(U_17526,U_17527,U_17528),U_17529) != hAPP(c_Option_Ooption_OSome(U_17527),U_17530) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17526),hAPP(hAPP(c_List_Omap(tc_prod(U_17526,U_17527),U_17526),c_Product__Type_Ofst(U_17526,U_17527)),U_17528))) ),
    inference(variable_rename,[status(thm)],[f_4290_1]) ).

fof(f_4290_3,plain,
    ( ! [U_17528,U_17526,U_17527,U_17529,U_17530] :
        ( hAPP(c_Map_Omap__of(U_17526,U_17527,U_17528),U_17529) = hAPP(c_Option_Ooption_OSome(U_17527),U_17530)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17526,U_17527)),hAPP(hAPP(c_Product__Type_OPair(U_17526,U_17527),U_17529),U_17530)),hAPP(c_List_Oset(tc_prod(U_17526,U_17527)),U_17528)))
        | ~ sP1122(U_17528,U_17526,U_17527,U_17529,U_17530) )
    & ! [U_17528,U_17526,U_17527,U_17529,U_17530] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17526,U_17527)),hAPP(hAPP(c_Product__Type_OPair(U_17526,U_17527),U_17529),U_17530)),hAPP(c_List_Oset(tc_prod(U_17526,U_17527)),U_17528)))
        | hAPP(c_Map_Omap__of(U_17526,U_17527,U_17528),U_17529) != hAPP(c_Option_Ooption_OSome(U_17527),U_17530)
        | ~ sP1122(U_17528,U_17526,U_17527,U_17529,U_17530) )
    & ! [U_17528,U_17526,U_17527,U_17529,U_17530] :
        ( sP1122(U_17528,U_17526,U_17527,U_17529,U_17530)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17526),hAPP(hAPP(c_List_Omap(tc_prod(U_17526,U_17527),U_17526),c_Product__Type_Ofst(U_17526,U_17527)),U_17528))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1122])],[f_4290_2]) ).

cnf(f_4290_4,plain,
    ( sP1122(U_17528,U_17526,U_17527,U_17529,U_17530)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17526),hAPP(hAPP(c_List_Omap(tc_prod(U_17526,U_17527),U_17526),c_Product__Type_Ofst(U_17526,U_17527)),U_17528))) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

cnf(f_4290_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17526,U_17527)),hAPP(hAPP(c_Product__Type_OPair(U_17526,U_17527),U_17529),U_17530)),hAPP(c_List_Oset(tc_prod(U_17526,U_17527)),U_17528)))
    | hAPP(c_Map_Omap__of(U_17526,U_17527,U_17528),U_17529) != hAPP(c_Option_Ooption_OSome(U_17527),U_17530)
    | ~ sP1122(U_17528,U_17526,U_17527,U_17529,U_17530) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

cnf(f_4290_6,plain,
    ( hAPP(c_Map_Omap__of(U_17526,U_17527,U_17528),U_17529) = hAPP(c_Option_Ooption_OSome(U_17527),U_17530)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17526,U_17527)),hAPP(hAPP(c_Product__Type_OPair(U_17526,U_17527),U_17529),U_17530)),hAPP(c_List_Oset(tc_prod(U_17526,U_17527)),U_17528)))
    | ~ sP1122(U_17528,U_17526,U_17527,U_17529,U_17530) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

fof(f_4291_1,plain,
    ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
      ( hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeI]) ).

fof(f_4291_2,plain,
    ! [U_17535,U_17534,U_17533,U_17532,U_17531] :
      ( hAPP(c_Map_Omap__of(U_17531,U_17532,U_17533),U_17534) = hAPP(c_Option_Ooption_OSome(U_17532),U_17535)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17531,U_17532)),hAPP(hAPP(c_Product__Type_OPair(U_17531,U_17532),U_17534),U_17535)),hAPP(c_List_Oset(tc_prod(U_17531,U_17532)),U_17533)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17531),hAPP(hAPP(c_List_Omap(tc_prod(U_17531,U_17532),U_17531),c_Product__Type_Ofst(U_17531,U_17532)),U_17533))) ),
    inference(variable_rename,[status(thm)],[f_4291_1]) ).

fof(f_4291_3,plain,
    ! [U_17533,U_17531,U_17532,U_17534,U_17535] :
      ( hAPP(c_Map_Omap__of(U_17531,U_17532,U_17533),U_17534) = hAPP(c_Option_Ooption_OSome(U_17532),U_17535)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17531,U_17532)),hAPP(hAPP(c_Product__Type_OPair(U_17531,U_17532),U_17534),U_17535)),hAPP(c_List_Oset(tc_prod(U_17531,U_17532)),U_17533)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17531),hAPP(hAPP(c_List_Omap(tc_prod(U_17531,U_17532),U_17531),c_Product__Type_Ofst(U_17531,U_17532)),U_17533))) ),
    inference(definitional_conversion,[status(esa)],[f_4291_2]) ).

cnf(f_4291_4,plain,
    ( hAPP(c_Map_Omap__of(U_17531,U_17532,U_17533),U_17534) = hAPP(c_Option_Ooption_OSome(U_17532),U_17535)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17531,U_17532)),hAPP(hAPP(c_Product__Type_OPair(U_17531,U_17532),U_17534),U_17535)),hAPP(c_List_Oset(tc_prod(U_17531,U_17532)),U_17533)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17531),hAPP(hAPP(c_List_Omap(tc_prod(U_17531,U_17532),U_17531),c_Product__Type_Ofst(U_17531,U_17532)),U_17533))) ),
    inference(clausify,[status(thm)],[f_4291_3]) ).

fof(f_4292_1,plain,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__upto]) ).

fof(f_4292_2,plain,
    ! [U_17537,U_17536] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17536,U_17537) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17536),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17537),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_4292_1]) ).

fof(f_4292_3,plain,
    ! [U_17537,U_17536] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17536,U_17537) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17536),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17537),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_4292_2]) ).

cnf(f_4292_4,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17536,U_17537) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17536),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17537),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_4292_3]) ).

fof(f_4293_1,plain,
    ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
      ( ? [B_x] : hAPP(c_Map_Omap__of(T_b,T_c,V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2))) ),
    inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI]) ).

fof(f_4293_2,plain,
    ! [U_17543,U_17542,U_17541,U_17540,U_17539] :
      ( ? [U_17538] : hAPP(c_Map_Omap__of(U_17539,U_17540,U_17543),U_17541) = hAPP(c_Option_Ooption_OSome(U_17540),U_17538)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17539,U_17540)),hAPP(hAPP(c_Product__Type_OPair(U_17539,U_17540),U_17541),U_17542)),hAPP(c_List_Oset(tc_prod(U_17539,U_17540)),U_17543))) ),
    inference(variable_rename,[status(thm)],[f_4293_1]) ).

fof(f_4293_3,plain,
    ! [U_17543,U_17542,U_17541,U_17540,U_17539] :
      ( hAPP(c_Map_Omap__of(U_17539,U_17540,U_17543),U_17541) = hAPP(c_Option_Ooption_OSome(U_17540),sK452(U_17543,U_17542,U_17541,U_17540,U_17539))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17539,U_17540)),hAPP(hAPP(c_Product__Type_OPair(U_17539,U_17540),U_17541),U_17542)),hAPP(c_List_Oset(tc_prod(U_17539,U_17540)),U_17543))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_17538,sK452(U_17543,U_17542,U_17541,U_17540,U_17539))],[f_4293_2]) ).

fof(f_4293_4,plain,
    ! [U_17539,U_17540,U_17541,U_17542,U_17543] :
      ( hAPP(c_Map_Omap__of(U_17539,U_17540,U_17543),U_17541) = hAPP(c_Option_Ooption_OSome(U_17540),sK452(U_17543,U_17542,U_17541,U_17540,U_17539))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17539,U_17540)),hAPP(hAPP(c_Product__Type_OPair(U_17539,U_17540),U_17541),U_17542)),hAPP(c_List_Oset(tc_prod(U_17539,U_17540)),U_17543))) ),
    inference(definitional_conversion,[status(esa)],[f_4293_3]) ).

cnf(f_4293_5,plain,
    ( hAPP(c_Map_Omap__of(U_17539,U_17540,U_17543),U_17541) = hAPP(c_Option_Ooption_OSome(U_17540),sK452(U_17543,U_17542,U_17541,U_17540,U_17539))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17539,U_17540)),hAPP(hAPP(c_Product__Type_OPair(U_17539,U_17540),U_17541),U_17542)),hAPP(c_List_Oset(tc_prod(U_17539,U_17540)),U_17543))) ),
    inference(clausify,[status(thm)],[f_4293_4]) ).

fof(f_4294_1,plain,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__upto]) ).

fof(f_4294_2,plain,
    ! [U_17545,U_17544] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17544,U_17545) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17544,U_17545)),
    inference(variable_rename,[status(thm)],[f_4294_1]) ).

fof(f_4294_3,plain,
    ! [U_17545,U_17544] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17544,U_17545) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17544,U_17545)),
    inference(definitional_conversion,[status(esa)],[f_4294_2]) ).

cnf(f_4294_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17544,U_17545) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17544,U_17545)),
    inference(clausify,[status(thm)],[f_4294_3]) ).

fof(f_4295_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),
    inference(fof_nnf,[status(thm)],[fact_set__upto]) ).

fof(f_4295_2,plain,
    ! [U_17547,U_17546] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17546,U_17547)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17546,U_17547),
    inference(variable_rename,[status(thm)],[f_4295_1]) ).

fof(f_4295_3,plain,
    ! [U_17546,U_17547] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17546,U_17547)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17546,U_17547),
    inference(definitional_conversion,[status(esa)],[f_4295_2]) ).

cnf(f_4295_4,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17546,U_17547)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17546,U_17547),
    inference(clausify,[status(thm)],[f_4295_3]) ).

fof(f_4296_1,plain,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))),
    inference(fof_nnf,[status(thm)],[fact_distinct__upto]) ).

fof(f_4296_2,plain,
    ! [U_17549,U_17548] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17548,U_17549))),
    inference(variable_rename,[status(thm)],[f_4296_1]) ).

fof(f_4296_3,plain,
    ! [U_17548,U_17549] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17548,U_17549))),
    inference(definitional_conversion,[status(esa)],[f_4296_2]) ).

cnf(f_4296_4,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17548,U_17549))),
    inference(clausify,[status(thm)],[f_4296_3]) ).

fof(f_4297_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__upto]) ).

fof(f_4297_2,plain,
    ! [U_17551,U_17550] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17550),U_17551) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17550,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17551),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_4297_1]) ).

fof(f_4297_3,plain,
    ! [U_17550,U_17551] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17550),U_17551) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17550,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17551),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_4297_2]) ).

cnf(f_4297_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17550),U_17551) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17550,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17551),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_4297_3]) ).

fof(f_4298_1,plain,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__upto]) ).

fof(f_4298_2,plain,
    ! [U_17553,U_17552] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17552,U_17553) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17552),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17553)),
    inference(variable_rename,[status(thm)],[f_4298_1]) ).

fof(f_4298_3,plain,
    ! [U_17552,U_17553] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17552,U_17553) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17552),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17553)),
    inference(definitional_conversion,[status(esa)],[f_4298_2]) ).

cnf(f_4298_4,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17552,U_17553) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17552),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17553)),
    inference(clausify,[status(thm)],[f_4298_3]) ).

fof(f_4299_1,plain,
    ! [V_l_2] :
      ( ( c_List_Onat__list(V_l_2)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2))
        | ~ c_List_Onat__list(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__list__def]) ).

fof(f_4299_2,plain,
    ! [U_17554] :
      ( ( c_List_Onat__list(U_17554)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17554)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17554))
        | ~ c_List_Onat__list(U_17554) ) ),
    inference(variable_rename,[status(thm)],[f_4299_1]) ).

fof(f_4299_3,plain,
    ( ! [U_17556] :
        ( c_List_Onat__list(U_17556)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17556)) )
    & ! [U_17555] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17555))
        | ~ c_List_Onat__list(U_17555) ) ),
    inference(miniscope,[status(thm)],[f_4299_2]) ).

fof(f_4299_4,plain,
    ( ! [U_17556] :
        ( c_List_Onat__list(U_17556)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17556)) )
    & ! [U_17555] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17555))
        | ~ c_List_Onat__list(U_17555) ) ),
    inference(definitional_conversion,[status(esa)],[f_4299_3]) ).

cnf(f_4299_5,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17555))
    | ~ c_List_Onat__list(U_17555) ),
    inference(clausify,[status(thm)],[f_4299_4]) ).

cnf(f_4299_6,plain,
    ( c_List_Onat__list(U_17556)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17556)) ),
    inference(clausify,[status(thm)],[f_4299_4]) ).

fof(f_4300_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__remove1__eq]) ).

fof(f_4300_2,plain,
    ! [U_17559,U_17558,U_17557] :
      ( hAPP(c_List_Oset(U_17557),c_List_Oremove1(U_17557,U_17559,U_17558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17557,tc_HOL_Obool)),hAPP(c_List_Oset(U_17557),U_17558)),hAPP(hAPP(c_Set_Oinsert(U_17557),U_17559),c_Orderings_Obot__class_Obot(tc_fun(U_17557,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17557),U_17558)) ),
    inference(variable_rename,[status(thm)],[f_4300_1]) ).

fof(f_4300_3,plain,
    ! [U_17557,U_17558,U_17559] :
      ( hAPP(c_List_Oset(U_17557),c_List_Oremove1(U_17557,U_17559,U_17558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17557,tc_HOL_Obool)),hAPP(c_List_Oset(U_17557),U_17558)),hAPP(hAPP(c_Set_Oinsert(U_17557),U_17559),c_Orderings_Obot__class_Obot(tc_fun(U_17557,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17557),U_17558)) ),
    inference(definitional_conversion,[status(esa)],[f_4300_2]) ).

cnf(f_4300_4,plain,
    ( hAPP(c_List_Oset(U_17557),c_List_Oremove1(U_17557,U_17559,U_17558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17557,tc_HOL_Obool)),hAPP(c_List_Oset(U_17557),U_17558)),hAPP(hAPP(c_Set_Oinsert(U_17557),U_17559),c_Orderings_Obot__class_Obot(tc_fun(U_17557,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17557),U_17558)) ),
    inference(clausify,[status(thm)],[f_4300_3]) ).

fof(f_4301_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__idem]) ).

fof(f_4301_2,plain,
    ! [U_17562,U_17561,U_17560] :
      ( c_List_Oremove1(U_17560,U_17561,U_17562) = U_17562
      | hBOOL(hAPP(hAPP(c_member(U_17560),U_17561),hAPP(c_List_Oset(U_17560),U_17562))) ),
    inference(variable_rename,[status(thm)],[f_4301_1]) ).

fof(f_4301_3,plain,
    ! [U_17560,U_17561,U_17562] :
      ( c_List_Oremove1(U_17560,U_17561,U_17562) = U_17562
      | hBOOL(hAPP(hAPP(c_member(U_17560),U_17561),hAPP(c_List_Oset(U_17560),U_17562))) ),
    inference(definitional_conversion,[status(esa)],[f_4301_2]) ).

cnf(f_4301_4,plain,
    ( c_List_Oremove1(U_17560,U_17561,U_17562) = U_17562
    | hBOOL(hAPP(hAPP(c_member(U_17560),U_17561),hAPP(c_List_Oset(U_17560),U_17562))) ),
    inference(clausify,[status(thm)],[f_4301_3]) ).

fof(f_4302_1,plain,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2))))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_notin__set__remove1]) ).

fof(f_4302_2,plain,
    ! [U_17566,U_17565,U_17564,U_17563] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17563),U_17564),hAPP(c_List_Oset(U_17563),c_List_Oremove1(U_17563,U_17566,U_17565))))
      | hBOOL(hAPP(hAPP(c_member(U_17563),U_17564),hAPP(c_List_Oset(U_17563),U_17565))) ),
    inference(variable_rename,[status(thm)],[f_4302_1]) ).

fof(f_4302_3,plain,
    ! [U_17563,U_17564,U_17565,U_17566] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17563),U_17564),hAPP(c_List_Oset(U_17563),c_List_Oremove1(U_17563,U_17566,U_17565))))
      | hBOOL(hAPP(hAPP(c_member(U_17563),U_17564),hAPP(c_List_Oset(U_17563),U_17565))) ),
    inference(definitional_conversion,[status(esa)],[f_4302_2]) ).

cnf(f_4302_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17563),U_17564),hAPP(c_List_Oset(U_17563),c_List_Oremove1(U_17563,U_17566,U_17565))))
    | hBOOL(hAPP(hAPP(c_member(U_17563),U_17564),hAPP(c_List_Oset(U_17563),U_17565))) ),
    inference(clausify,[status(thm)],[f_4302_3]) ).

fof(f_4303_1,plain,
    ! [V_xs_2,T_b,V_b_2,V_a_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2)))) ) )
      | V_a_2 = V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_in__set__remove1]) ).

fof(f_4303_2,plain,
    ! [U_17570,U_17569,U_17568,U_17567] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),c_List_Oremove1(U_17569,U_17568,U_17570))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),U_17570))) )
        & ( hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),U_17570)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),c_List_Oremove1(U_17569,U_17568,U_17570)))) ) )
      | U_17567 = U_17568 ),
    inference(variable_rename,[status(thm)],[f_4303_1]) ).

fof(f_4303_3,plain,
    ( ! [U_17568,U_17567,U_17569,U_17570] :
        ( hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),c_List_Oremove1(U_17569,U_17568,U_17570))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),U_17570)))
        | ~ sP1123(U_17568,U_17567,U_17569,U_17570) )
    & ! [U_17568,U_17567,U_17569,U_17570] :
        ( hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),U_17570)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),c_List_Oremove1(U_17569,U_17568,U_17570))))
        | ~ sP1123(U_17568,U_17567,U_17569,U_17570) )
    & ! [U_17568,U_17567,U_17569,U_17570] :
        ( sP1123(U_17568,U_17567,U_17569,U_17570)
        | U_17567 = U_17568 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1123])],[f_4303_2]) ).

cnf(f_4303_4,plain,
    ( sP1123(U_17568,U_17567,U_17569,U_17570)
    | U_17567 = U_17568 ),
    inference(clausify,[status(thm)],[f_4303_3]) ).

cnf(f_4303_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),U_17570)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),c_List_Oremove1(U_17569,U_17568,U_17570))))
    | ~ sP1123(U_17568,U_17567,U_17569,U_17570) ),
    inference(clausify,[status(thm)],[f_4303_3]) ).

cnf(f_4303_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),c_List_Oremove1(U_17569,U_17568,U_17570))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17569),U_17567),hAPP(c_List_Oset(U_17569),U_17570)))
    | ~ sP1123(U_17568,U_17567,U_17569,U_17570) ),
    inference(clausify,[status(thm)],[f_4303_3]) ).

fof(f_4304_1,plain,
    ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__remove1__subset]) ).

fof(f_4304_2,plain,
    ! [U_17573,U_17572,U_17571] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17571,tc_HOL_Obool)),hAPP(c_List_Oset(U_17571),c_List_Oremove1(U_17571,U_17572,U_17573))),hAPP(c_List_Oset(U_17571),U_17573))),
    inference(variable_rename,[status(thm)],[f_4304_1]) ).

fof(f_4304_3,plain,
    ! [U_17573,U_17572,U_17571] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17571,tc_HOL_Obool)),hAPP(c_List_Oset(U_17571),c_List_Oremove1(U_17571,U_17572,U_17573))),hAPP(c_List_Oset(U_17571),U_17573))),
    inference(definitional_conversion,[status(esa)],[f_4304_2]) ).

cnf(f_4304_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17571,tc_HOL_Obool)),hAPP(c_List_Oset(U_17571),c_List_Oremove1(U_17571,U_17572,U_17573))),hAPP(c_List_Oset(U_17571),U_17573))),
    inference(clausify,[status(thm)],[f_4304_3]) ).

fof(f_4305_1,plain,
    ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)),
    inference(fof_nnf,[status(thm)],[fact_remove1__commute]) ).

fof(f_4305_2,plain,
    ! [U_17577,U_17576,U_17575,U_17574] : c_List_Oremove1(U_17574,U_17575,c_List_Oremove1(U_17574,U_17576,U_17577)) = c_List_Oremove1(U_17574,U_17576,c_List_Oremove1(U_17574,U_17575,U_17577)),
    inference(variable_rename,[status(thm)],[f_4305_1]) ).

fof(f_4305_3,plain,
    ! [U_17574,U_17575,U_17576,U_17577] : c_List_Oremove1(U_17574,U_17575,c_List_Oremove1(U_17574,U_17576,U_17577)) = c_List_Oremove1(U_17574,U_17576,c_List_Oremove1(U_17574,U_17575,U_17577)),
    inference(definitional_conversion,[status(esa)],[f_4305_2]) ).

cnf(f_4305_4,plain,
    c_List_Oremove1(U_17574,U_17575,c_List_Oremove1(U_17574,U_17576,U_17577)) = c_List_Oremove1(U_17574,U_17576,c_List_Oremove1(U_17574,U_17575,U_17577)),
    inference(clausify,[status(thm)],[f_4305_3]) ).

fof(f_4306_1,plain,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remove1]) ).

fof(f_4306_2,plain,
    ! [U_17580,U_17579,U_17578] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17578),c_List_Oremove1(U_17578,U_17580,U_17579)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17578),U_17579)) ),
    inference(variable_rename,[status(thm)],[f_4306_1]) ).

fof(f_4306_3,plain,
    ! [U_17578,U_17579,U_17580] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17578),c_List_Oremove1(U_17578,U_17580,U_17579)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17578),U_17579)) ),
    inference(definitional_conversion,[status(esa)],[f_4306_2]) ).

cnf(f_4306_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17578),c_List_Oremove1(U_17578,U_17580,U_17579)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17578),U_17579)) ),
    inference(clausify,[status(thm)],[f_4306_3]) ).

fof(f_4307_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove]) ).

fof(f_4307_2,plain,
    ! [U_17583,U_17582,U_17581] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17581,tc_HOL_Obool)),U_17582),hAPP(hAPP(c_Set_Oinsert(U_17581),U_17583),c_Orderings_Obot__class_Obot(tc_fun(U_17581,tc_HOL_Obool))))) = c_List_Oremove1(U_17581,U_17583,c_List_Olinorder__class_Osorted__list__of__set(U_17581,U_17582))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17581),U_17582))
      | ~ class_Orderings_Olinorder(U_17581) ),
    inference(variable_rename,[status(thm)],[f_4307_1]) ).

fof(f_4307_3,plain,
    ! [U_17581,U_17582,U_17583] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17581,tc_HOL_Obool)),U_17582),hAPP(hAPP(c_Set_Oinsert(U_17581),U_17583),c_Orderings_Obot__class_Obot(tc_fun(U_17581,tc_HOL_Obool))))) = c_List_Oremove1(U_17581,U_17583,c_List_Olinorder__class_Osorted__list__of__set(U_17581,U_17582))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17581),U_17582))
      | ~ class_Orderings_Olinorder(U_17581) ),
    inference(definitional_conversion,[status(esa)],[f_4307_2]) ).

cnf(f_4307_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17581,tc_HOL_Obool)),U_17582),hAPP(hAPP(c_Set_Oinsert(U_17581),U_17583),c_Orderings_Obot__class_Obot(tc_fun(U_17581,tc_HOL_Obool))))) = c_List_Oremove1(U_17581,U_17583,c_List_Olinorder__class_Osorted__list__of__set(U_17581,U_17582))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17581),U_17582))
    | ~ class_Orderings_Olinorder(U_17581) ),
    inference(clausify,[status(thm)],[f_4307_3]) ).

fof(f_4308_1,plain,
    ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
      ( ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__map]) ).

fof(f_4308_2,plain,
    ! [U_17588,U_17587,U_17586,U_17585,U_17584] :
      ( ( hAPP(c_Map_Omap__of(U_17584,U_17587,hAPP(hAPP(c_List_Ozip(U_17584,U_17587),U_17586),hAPP(hAPP(c_List_Omap(U_17584,U_17587),U_17588),U_17586))),U_17585) = c_Option_Ooption_ONone(U_17587)
        | hBOOL(hAPP(hAPP(c_member(U_17584),U_17585),hAPP(c_List_Oset(U_17584),U_17586))) )
      & ( hAPP(c_Map_Omap__of(U_17584,U_17587,hAPP(hAPP(c_List_Ozip(U_17584,U_17587),U_17586),hAPP(hAPP(c_List_Omap(U_17584,U_17587),U_17588),U_17586))),U_17585) = hAPP(c_Option_Ooption_OSome(U_17587),hAPP(U_17588,U_17585))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17584),U_17585),hAPP(c_List_Oset(U_17584),U_17586))) ) ),
    inference(variable_rename,[status(thm)],[f_4308_1]) ).

fof(f_4308_3,plain,
    ( ! [U_17598,U_17596,U_17594,U_17592,U_17590] :
        ( hAPP(c_Map_Omap__of(U_17590,U_17596,hAPP(hAPP(c_List_Ozip(U_17590,U_17596),U_17594),hAPP(hAPP(c_List_Omap(U_17590,U_17596),U_17598),U_17594))),U_17592) = c_Option_Ooption_ONone(U_17596)
        | hBOOL(hAPP(hAPP(c_member(U_17590),U_17592),hAPP(c_List_Oset(U_17590),U_17594))) )
    & ! [U_17597,U_17595,U_17593,U_17591,U_17589] :
        ( hAPP(c_Map_Omap__of(U_17589,U_17595,hAPP(hAPP(c_List_Ozip(U_17589,U_17595),U_17593),hAPP(hAPP(c_List_Omap(U_17589,U_17595),U_17597),U_17593))),U_17591) = hAPP(c_Option_Ooption_OSome(U_17595),hAPP(U_17597,U_17591))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17589),U_17591),hAPP(c_List_Oset(U_17589),U_17593))) ) ),
    inference(miniscope,[status(thm)],[f_4308_2]) ).

fof(f_4308_4,plain,
    ( ! [U_17590,U_17592,U_17594,U_17596,U_17598] :
        ( hAPP(c_Map_Omap__of(U_17590,U_17596,hAPP(hAPP(c_List_Ozip(U_17590,U_17596),U_17594),hAPP(hAPP(c_List_Omap(U_17590,U_17596),U_17598),U_17594))),U_17592) = c_Option_Ooption_ONone(U_17596)
        | hBOOL(hAPP(hAPP(c_member(U_17590),U_17592),hAPP(c_List_Oset(U_17590),U_17594))) )
    & ! [U_17593,U_17591,U_17595,U_17589,U_17597] :
        ( hAPP(c_Map_Omap__of(U_17589,U_17595,hAPP(hAPP(c_List_Ozip(U_17589,U_17595),U_17593),hAPP(hAPP(c_List_Omap(U_17589,U_17595),U_17597),U_17593))),U_17591) = hAPP(c_Option_Ooption_OSome(U_17595),hAPP(U_17597,U_17591))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17589),U_17591),hAPP(c_List_Oset(U_17589),U_17593))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4308_3]) ).

cnf(f_4308_5,plain,
    ( hAPP(c_Map_Omap__of(U_17589,U_17595,hAPP(hAPP(c_List_Ozip(U_17589,U_17595),U_17593),hAPP(hAPP(c_List_Omap(U_17589,U_17595),U_17597),U_17593))),U_17591) = hAPP(c_Option_Ooption_OSome(U_17595),hAPP(U_17597,U_17591))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17589),U_17591),hAPP(c_List_Oset(U_17589),U_17593))) ),
    inference(clausify,[status(thm)],[f_4308_4]) ).

cnf(f_4308_6,plain,
    ( hAPP(c_Map_Omap__of(U_17590,U_17596,hAPP(hAPP(c_List_Ozip(U_17590,U_17596),U_17594),hAPP(hAPP(c_List_Omap(U_17590,U_17596),U_17598),U_17594))),U_17592) = c_Option_Ooption_ONone(U_17596)
    | hBOOL(hAPP(hAPP(c_member(U_17590),U_17592),hAPP(c_List_Oset(U_17590),U_17594))) ),
    inference(clausify,[status(thm)],[f_4308_4]) ).

fof(f_4309_1,plain,
    ! [V_xs,T_b,V_ys,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__zipI2]) ).

fof(f_4309_2,plain,
    ! [U_17602,U_17601,U_17600,U_17599] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17601,U_17599)),hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17599),U_17600)) ),
    inference(variable_rename,[status(thm)],[f_4309_1]) ).

fof(f_4309_3,plain,
    ! [U_17599,U_17600,U_17601,U_17602] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17601,U_17599)),hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17599),U_17600)) ),
    inference(definitional_conversion,[status(esa)],[f_4309_2]) ).

cnf(f_4309_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17601,U_17599)),hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17599),U_17600)) ),
    inference(clausify,[status(thm)],[f_4309_3]) ).

fof(f_4310_1,plain,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__zipI1]) ).

fof(f_4310_2,plain,
    ! [U_17606,U_17605,U_17604,U_17603] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17603,U_17605)),hAPP(hAPP(c_List_Ozip(U_17603,U_17605),U_17604),U_17606)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17603),U_17604)) ),
    inference(variable_rename,[status(thm)],[f_4310_1]) ).

fof(f_4310_3,plain,
    ! [U_17603,U_17604,U_17605,U_17606] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17603,U_17605)),hAPP(hAPP(c_List_Ozip(U_17603,U_17605),U_17604),U_17606)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17603),U_17604)) ),
    inference(definitional_conversion,[status(esa)],[f_4310_2]) ).

cnf(f_4310_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17603,U_17605)),hAPP(hAPP(c_List_Ozip(U_17603,U_17605),U_17604),U_17606)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17603),U_17604)) ),
    inference(clausify,[status(thm)],[f_4310_3]) ).

fof(f_4311_1,plain,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_zip__same__conv__map]) ).

fof(f_4311_2,plain,
    ! [U_17608,U_17607] : hAPP(hAPP(c_List_Ozip(U_17607,U_17607),U_17608),U_17608) = hAPP(hAPP(c_List_Omap(U_17607,tc_prod(U_17607,U_17607)),hAPP(hAPP(c_COMBS(U_17607,U_17607,tc_prod(U_17607,U_17607)),c_Product__Type_OPair(U_17607,U_17607)),c_COMBI(U_17607))),U_17608),
    inference(variable_rename,[status(thm)],[f_4311_1]) ).

fof(f_4311_3,plain,
    ! [U_17607,U_17608] : hAPP(hAPP(c_List_Ozip(U_17607,U_17607),U_17608),U_17608) = hAPP(hAPP(c_List_Omap(U_17607,tc_prod(U_17607,U_17607)),hAPP(hAPP(c_COMBS(U_17607,U_17607,tc_prod(U_17607,U_17607)),c_Product__Type_OPair(U_17607,U_17607)),c_COMBI(U_17607))),U_17608),
    inference(definitional_conversion,[status(esa)],[f_4311_2]) ).

cnf(f_4311_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17607,U_17607),U_17608),U_17608) = hAPP(hAPP(c_List_Omap(U_17607,tc_prod(U_17607,U_17607)),hAPP(hAPP(c_COMBS(U_17607,U_17607,tc_prod(U_17607,U_17607)),c_Product__Type_OPair(U_17607,U_17607)),c_COMBI(U_17607))),U_17608),
    inference(clausify,[status(thm)],[f_4311_3]) ).

fof(f_4312_1,plain,
    ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2,
    inference(fof_nnf,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(f_4312_2,plain,
    ! [U_17611,U_17610,U_17609] : hAPP(hAPP(c_List_Ozip(U_17609,U_17610),hAPP(hAPP(c_List_Omap(tc_prod(U_17609,U_17610),U_17609),c_Product__Type_Ofst(U_17609,U_17610)),U_17611)),hAPP(hAPP(c_List_Omap(tc_prod(U_17609,U_17610),U_17610),c_Product__Type_Osnd(U_17609,U_17610)),U_17611)) = U_17611,
    inference(variable_rename,[status(thm)],[f_4312_1]) ).

fof(f_4312_3,plain,
    ! [U_17609,U_17610,U_17611] : hAPP(hAPP(c_List_Ozip(U_17609,U_17610),hAPP(hAPP(c_List_Omap(tc_prod(U_17609,U_17610),U_17609),c_Product__Type_Ofst(U_17609,U_17610)),U_17611)),hAPP(hAPP(c_List_Omap(tc_prod(U_17609,U_17610),U_17610),c_Product__Type_Osnd(U_17609,U_17610)),U_17611)) = U_17611,
    inference(definitional_conversion,[status(esa)],[f_4312_2]) ).

cnf(f_4312_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17609,U_17610),hAPP(hAPP(c_List_Omap(tc_prod(U_17609,U_17610),U_17609),c_Product__Type_Ofst(U_17609,U_17610)),U_17611)),hAPP(hAPP(c_List_Omap(tc_prod(U_17609,U_17610),U_17610),c_Product__Type_Osnd(U_17609,U_17610)),U_17611)) = U_17611,
    inference(clausify,[status(thm)],[f_4312_3]) ).

fof(f_4313_1,plain,
    ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__zip__map]) ).

fof(f_4313_2,plain,
    ! [U_17619,U_17618,U_17617,U_17616,U_17615,U_17614,U_17613,U_17612] : hAPP(hAPP(c_List_Omap(tc_prod(U_17612,U_17613),U_17614),U_17615),hAPP(hAPP(c_List_Ozip(U_17612,U_17613),hAPP(hAPP(c_List_Omap(U_17616,U_17612),U_17617),U_17618)),U_17619)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17616,U_17613),U_17614),hAPP(c_Product__Type_Oprod_Oprod__case(U_17616,U_17613,U_17614),hAPP(hAPP(c_COMBB(tc_fun(U_17613,tc_prod(U_17612,U_17613)),tc_fun(U_17613,U_17614),U_17616),hAPP(c_COMBB(tc_prod(U_17612,U_17613),U_17614,U_17613),U_17615)),hAPP(hAPP(c_COMBB(U_17612,tc_fun(U_17613,tc_prod(U_17612,U_17613)),U_17616),c_Product__Type_OPair(U_17612,U_17613)),U_17617)))),hAPP(hAPP(c_List_Ozip(U_17616,U_17613),U_17618),U_17619)),
    inference(variable_rename,[status(thm)],[f_4313_1]) ).

fof(f_4313_3,plain,
    ! [U_17612,U_17613,U_17614,U_17615,U_17616,U_17617,U_17618,U_17619] : hAPP(hAPP(c_List_Omap(tc_prod(U_17612,U_17613),U_17614),U_17615),hAPP(hAPP(c_List_Ozip(U_17612,U_17613),hAPP(hAPP(c_List_Omap(U_17616,U_17612),U_17617),U_17618)),U_17619)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17616,U_17613),U_17614),hAPP(c_Product__Type_Oprod_Oprod__case(U_17616,U_17613,U_17614),hAPP(hAPP(c_COMBB(tc_fun(U_17613,tc_prod(U_17612,U_17613)),tc_fun(U_17613,U_17614),U_17616),hAPP(c_COMBB(tc_prod(U_17612,U_17613),U_17614,U_17613),U_17615)),hAPP(hAPP(c_COMBB(U_17612,tc_fun(U_17613,tc_prod(U_17612,U_17613)),U_17616),c_Product__Type_OPair(U_17612,U_17613)),U_17617)))),hAPP(hAPP(c_List_Ozip(U_17616,U_17613),U_17618),U_17619)),
    inference(definitional_conversion,[status(esa)],[f_4313_2]) ).

cnf(f_4313_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17612,U_17613),U_17614),U_17615),hAPP(hAPP(c_List_Ozip(U_17612,U_17613),hAPP(hAPP(c_List_Omap(U_17616,U_17612),U_17617),U_17618)),U_17619)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17616,U_17613),U_17614),hAPP(c_Product__Type_Oprod_Oprod__case(U_17616,U_17613,U_17614),hAPP(hAPP(c_COMBB(tc_fun(U_17613,tc_prod(U_17612,U_17613)),tc_fun(U_17613,U_17614),U_17616),hAPP(c_COMBB(tc_prod(U_17612,U_17613),U_17614,U_17613),U_17615)),hAPP(hAPP(c_COMBB(U_17612,tc_fun(U_17613,tc_prod(U_17612,U_17613)),U_17616),c_Product__Type_OPair(U_17612,U_17613)),U_17617)))),hAPP(hAPP(c_List_Ozip(U_17616,U_17613),U_17618),U_17619)),
    inference(clausify,[status(thm)],[f_4313_3]) ).

fof(f_4314_1,plain,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__zip__map2]) ).

fof(f_4314_2,plain,
    ! [U_17627,U_17626,U_17625,U_17624,U_17623,U_17622,U_17621,U_17620] : hAPP(hAPP(c_List_Omap(tc_prod(U_17620,U_17621),U_17622),U_17623),hAPP(hAPP(c_List_Ozip(U_17620,U_17621),U_17624),hAPP(hAPP(c_List_Omap(U_17625,U_17621),U_17626),U_17627))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17620,U_17625),U_17622),hAPP(c_Product__Type_Oprod_Oprod__case(U_17620,U_17625,U_17622),hAPP(hAPP(c_COMBB(tc_fun(U_17625,tc_prod(U_17620,U_17621)),tc_fun(U_17625,U_17622),U_17620),hAPP(c_COMBB(tc_prod(U_17620,U_17621),U_17622,U_17625),U_17623)),hAPP(hAPP(c_COMBC(U_17620,tc_fun(U_17625,U_17621),tc_fun(U_17625,tc_prod(U_17620,U_17621))),hAPP(hAPP(c_COMBB(tc_fun(U_17621,tc_prod(U_17620,U_17621)),tc_fun(tc_fun(U_17625,U_17621),tc_fun(U_17625,tc_prod(U_17620,U_17621))),U_17620),c_COMBB(U_17621,tc_prod(U_17620,U_17621),U_17625)),c_Product__Type_OPair(U_17620,U_17621))),U_17626)))),hAPP(hAPP(c_List_Ozip(U_17620,U_17625),U_17624),U_17627)),
    inference(variable_rename,[status(thm)],[f_4314_1]) ).

fof(f_4314_3,plain,
    ! [U_17620,U_17621,U_17622,U_17623,U_17624,U_17625,U_17626,U_17627] : hAPP(hAPP(c_List_Omap(tc_prod(U_17620,U_17621),U_17622),U_17623),hAPP(hAPP(c_List_Ozip(U_17620,U_17621),U_17624),hAPP(hAPP(c_List_Omap(U_17625,U_17621),U_17626),U_17627))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17620,U_17625),U_17622),hAPP(c_Product__Type_Oprod_Oprod__case(U_17620,U_17625,U_17622),hAPP(hAPP(c_COMBB(tc_fun(U_17625,tc_prod(U_17620,U_17621)),tc_fun(U_17625,U_17622),U_17620),hAPP(c_COMBB(tc_prod(U_17620,U_17621),U_17622,U_17625),U_17623)),hAPP(hAPP(c_COMBC(U_17620,tc_fun(U_17625,U_17621),tc_fun(U_17625,tc_prod(U_17620,U_17621))),hAPP(hAPP(c_COMBB(tc_fun(U_17621,tc_prod(U_17620,U_17621)),tc_fun(tc_fun(U_17625,U_17621),tc_fun(U_17625,tc_prod(U_17620,U_17621))),U_17620),c_COMBB(U_17621,tc_prod(U_17620,U_17621),U_17625)),c_Product__Type_OPair(U_17620,U_17621))),U_17626)))),hAPP(hAPP(c_List_Ozip(U_17620,U_17625),U_17624),U_17627)),
    inference(definitional_conversion,[status(esa)],[f_4314_2]) ).

cnf(f_4314_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17620,U_17621),U_17622),U_17623),hAPP(hAPP(c_List_Ozip(U_17620,U_17621),U_17624),hAPP(hAPP(c_List_Omap(U_17625,U_17621),U_17626),U_17627))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17620,U_17625),U_17622),hAPP(c_Product__Type_Oprod_Oprod__case(U_17620,U_17625,U_17622),hAPP(hAPP(c_COMBB(tc_fun(U_17625,tc_prod(U_17620,U_17621)),tc_fun(U_17625,U_17622),U_17620),hAPP(c_COMBB(tc_prod(U_17620,U_17621),U_17622,U_17625),U_17623)),hAPP(hAPP(c_COMBC(U_17620,tc_fun(U_17625,U_17621),tc_fun(U_17625,tc_prod(U_17620,U_17621))),hAPP(hAPP(c_COMBB(tc_fun(U_17621,tc_prod(U_17620,U_17621)),tc_fun(tc_fun(U_17625,U_17621),tc_fun(U_17625,tc_prod(U_17620,U_17621))),U_17620),c_COMBB(U_17621,tc_prod(U_17620,U_17621),U_17625)),c_Product__Type_OPair(U_17620,U_17621))),U_17626)))),hAPP(hAPP(c_List_Ozip(U_17620,U_17625),U_17624),U_17627)),
    inference(clausify,[status(thm)],[f_4314_3]) ).

fof(f_4315_1,plain,
    ! [V_xs_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
        | V_a_2 != V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( ( V_a_2 = V_b_2
          & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zip__same]) ).

fof(f_4315_2,plain,
    ! [U_17631,U_17630,U_17629,U_17628] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17628,U_17628)),hAPP(hAPP(c_Product__Type_OPair(U_17628,U_17628),U_17629),U_17630)),hAPP(c_List_Oset(tc_prod(U_17628,U_17628)),hAPP(hAPP(c_List_Ozip(U_17628,U_17628),U_17631),U_17631))))
        | U_17629 != U_17630
        | ~ hBOOL(hAPP(hAPP(c_member(U_17628),U_17629),hAPP(c_List_Oset(U_17628),U_17631))) )
      & ( ( U_17629 = U_17630
          & hBOOL(hAPP(hAPP(c_member(U_17628),U_17629),hAPP(c_List_Oset(U_17628),U_17631))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17628,U_17628)),hAPP(hAPP(c_Product__Type_OPair(U_17628,U_17628),U_17629),U_17630)),hAPP(c_List_Oset(tc_prod(U_17628,U_17628)),hAPP(hAPP(c_List_Ozip(U_17628,U_17628),U_17631),U_17631)))) ) ),
    inference(variable_rename,[status(thm)],[f_4315_1]) ).

fof(f_4315_3,plain,
    ( ! [U_17639,U_17637,U_17635,U_17633] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17633,U_17633)),hAPP(hAPP(c_Product__Type_OPair(U_17633,U_17633),U_17635),U_17637)),hAPP(c_List_Oset(tc_prod(U_17633,U_17633)),hAPP(hAPP(c_List_Ozip(U_17633,U_17633),U_17639),U_17639))))
        | U_17635 != U_17637
        | ~ hBOOL(hAPP(hAPP(c_member(U_17633),U_17635),hAPP(c_List_Oset(U_17633),U_17639))) )
    & ! [U_17638,U_17636,U_17634,U_17632] :
        ( ( U_17634 = U_17636
          & hBOOL(hAPP(hAPP(c_member(U_17632),U_17634),hAPP(c_List_Oset(U_17632),U_17638))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17632,U_17632)),hAPP(hAPP(c_Product__Type_OPair(U_17632,U_17632),U_17634),U_17636)),hAPP(c_List_Oset(tc_prod(U_17632,U_17632)),hAPP(hAPP(c_List_Ozip(U_17632,U_17632),U_17638),U_17638)))) ) ),
    inference(miniscope,[status(thm)],[f_4315_2]) ).

fof(f_4315_4,plain,
    ( ! [U_17634,U_17638,U_17632,U_17636] :
        ( U_17634 = U_17636
        | ~ sP1124(U_17634,U_17638,U_17632,U_17636) )
    & ! [U_17634,U_17638,U_17632,U_17636] :
        ( hBOOL(hAPP(hAPP(c_member(U_17632),U_17634),hAPP(c_List_Oset(U_17632),U_17638)))
        | ~ sP1124(U_17634,U_17638,U_17632,U_17636) )
    & ! [U_17637,U_17635,U_17633,U_17639] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17633,U_17633)),hAPP(hAPP(c_Product__Type_OPair(U_17633,U_17633),U_17635),U_17637)),hAPP(c_List_Oset(tc_prod(U_17633,U_17633)),hAPP(hAPP(c_List_Ozip(U_17633,U_17633),U_17639),U_17639))))
        | U_17635 != U_17637
        | ~ hBOOL(hAPP(hAPP(c_member(U_17633),U_17635),hAPP(c_List_Oset(U_17633),U_17639))) )
    & ! [U_17634,U_17638,U_17632,U_17636] :
        ( sP1124(U_17634,U_17638,U_17632,U_17636)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17632,U_17632)),hAPP(hAPP(c_Product__Type_OPair(U_17632,U_17632),U_17634),U_17636)),hAPP(c_List_Oset(tc_prod(U_17632,U_17632)),hAPP(hAPP(c_List_Ozip(U_17632,U_17632),U_17638),U_17638)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1124])],[f_4315_3]) ).

cnf(f_4315_5,plain,
    ( sP1124(U_17634,U_17638,U_17632,U_17636)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17632,U_17632)),hAPP(hAPP(c_Product__Type_OPair(U_17632,U_17632),U_17634),U_17636)),hAPP(c_List_Oset(tc_prod(U_17632,U_17632)),hAPP(hAPP(c_List_Ozip(U_17632,U_17632),U_17638),U_17638)))) ),
    inference(clausify,[status(thm)],[f_4315_4]) ).

cnf(f_4315_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17633,U_17633)),hAPP(hAPP(c_Product__Type_OPair(U_17633,U_17633),U_17635),U_17637)),hAPP(c_List_Oset(tc_prod(U_17633,U_17633)),hAPP(hAPP(c_List_Ozip(U_17633,U_17633),U_17639),U_17639))))
    | U_17635 != U_17637
    | ~ hBOOL(hAPP(hAPP(c_member(U_17633),U_17635),hAPP(c_List_Oset(U_17633),U_17639))) ),
    inference(clausify,[status(thm)],[f_4315_4]) ).

cnf(f_4315_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17632),U_17634),hAPP(c_List_Oset(U_17632),U_17638)))
    | ~ sP1124(U_17634,U_17638,U_17632,U_17636) ),
    inference(clausify,[status(thm)],[f_4315_4]) ).

cnf(f_4315_8,plain,
    ( U_17634 = U_17636
    | ~ sP1124(U_17634,U_17638,U_17632,U_17636) ),
    inference(clausify,[status(thm)],[f_4315_4]) ).

fof(f_4316_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__zip__leftD]) ).

fof(f_4316_2,plain,
    ! [U_17645,U_17644,U_17643,U_17642,U_17641,U_17640] :
      ( hBOOL(hAPP(hAPP(c_member(U_17640),U_17642),hAPP(c_List_Oset(U_17640),U_17644)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17640,U_17641)),hAPP(hAPP(c_Product__Type_OPair(U_17640,U_17641),U_17642),U_17643)),hAPP(c_List_Oset(tc_prod(U_17640,U_17641)),hAPP(hAPP(c_List_Ozip(U_17640,U_17641),U_17644),U_17645)))) ),
    inference(variable_rename,[status(thm)],[f_4316_1]) ).

fof(f_4316_3,plain,
    ! [U_17640,U_17641,U_17642,U_17643,U_17644,U_17645] :
      ( hBOOL(hAPP(hAPP(c_member(U_17640),U_17642),hAPP(c_List_Oset(U_17640),U_17644)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17640,U_17641)),hAPP(hAPP(c_Product__Type_OPair(U_17640,U_17641),U_17642),U_17643)),hAPP(c_List_Oset(tc_prod(U_17640,U_17641)),hAPP(hAPP(c_List_Ozip(U_17640,U_17641),U_17644),U_17645)))) ),
    inference(definitional_conversion,[status(esa)],[f_4316_2]) ).

cnf(f_4316_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17640),U_17642),hAPP(c_List_Oset(U_17640),U_17644)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17640,U_17641)),hAPP(hAPP(c_Product__Type_OPair(U_17640,U_17641),U_17642),U_17643)),hAPP(c_List_Oset(tc_prod(U_17640,U_17641)),hAPP(hAPP(c_List_Ozip(U_17640,U_17641),U_17644),U_17645)))) ),
    inference(clausify,[status(thm)],[f_4316_3]) ).

fof(f_4317_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__zip__rightD]) ).

fof(f_4317_2,plain,
    ! [U_17651,U_17650,U_17649,U_17648,U_17647,U_17646] :
      ( hBOOL(hAPP(hAPP(c_member(U_17647),U_17649),hAPP(c_List_Oset(U_17647),U_17651)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_Product__Type_OPair(U_17646,U_17647),U_17648),U_17649)),hAPP(c_List_Oset(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_List_Ozip(U_17646,U_17647),U_17650),U_17651)))) ),
    inference(variable_rename,[status(thm)],[f_4317_1]) ).

fof(f_4317_3,plain,
    ! [U_17651,U_17650,U_17649,U_17648,U_17647] :
      ( ! [U_17646] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_Product__Type_OPair(U_17646,U_17647),U_17648),U_17649)),hAPP(c_List_Oset(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_List_Ozip(U_17646,U_17647),U_17650),U_17651))))
      | hBOOL(hAPP(hAPP(c_member(U_17647),U_17649),hAPP(c_List_Oset(U_17647),U_17651))) ),
    inference(miniscope,[status(thm)],[f_4317_2]) ).

fof(f_4317_4,plain,
    ! [U_17646,U_17647,U_17648,U_17649,U_17650,U_17651] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_Product__Type_OPair(U_17646,U_17647),U_17648),U_17649)),hAPP(c_List_Oset(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_List_Ozip(U_17646,U_17647),U_17650),U_17651))))
      | hBOOL(hAPP(hAPP(c_member(U_17647),U_17649),hAPP(c_List_Oset(U_17647),U_17651))) ),
    inference(definitional_conversion,[status(esa)],[f_4317_3]) ).

cnf(f_4317_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_Product__Type_OPair(U_17646,U_17647),U_17648),U_17649)),hAPP(c_List_Oset(tc_prod(U_17646,U_17647)),hAPP(hAPP(c_List_Ozip(U_17646,U_17647),U_17650),U_17651))))
    | hBOOL(hAPP(hAPP(c_member(U_17647),U_17649),hAPP(c_List_Oset(U_17647),U_17651))) ),
    inference(clausify,[status(thm)],[f_4317_4]) ).

fof(f_4318_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__zipE]) ).

fof(f_4318_2,plain,
    ! [U_17657,U_17656,U_17655,U_17654,U_17653,U_17652] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_17653),U_17655),hAPP(c_List_Oset(U_17653),U_17657)))
        & hBOOL(hAPP(hAPP(c_member(U_17652),U_17654),hAPP(c_List_Oset(U_17652),U_17656))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17652,U_17653)),hAPP(hAPP(c_Product__Type_OPair(U_17652,U_17653),U_17654),U_17655)),hAPP(c_List_Oset(tc_prod(U_17652,U_17653)),hAPP(hAPP(c_List_Ozip(U_17652,U_17653),U_17656),U_17657)))) ),
    inference(variable_rename,[status(thm)],[f_4318_1]) ).

fof(f_4318_3,plain,
    ( ! [U_17652,U_17653,U_17654,U_17655,U_17656,U_17657] :
        ( hBOOL(hAPP(hAPP(c_member(U_17653),U_17655),hAPP(c_List_Oset(U_17653),U_17657)))
        | ~ sP1125(U_17652,U_17653,U_17654,U_17655,U_17656,U_17657) )
    & ! [U_17652,U_17653,U_17654,U_17655,U_17656,U_17657] :
        ( hBOOL(hAPP(hAPP(c_member(U_17652),U_17654),hAPP(c_List_Oset(U_17652),U_17656)))
        | ~ sP1125(U_17652,U_17653,U_17654,U_17655,U_17656,U_17657) )
    & ! [U_17652,U_17653,U_17654,U_17655,U_17656,U_17657] :
        ( sP1125(U_17652,U_17653,U_17654,U_17655,U_17656,U_17657)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17652,U_17653)),hAPP(hAPP(c_Product__Type_OPair(U_17652,U_17653),U_17654),U_17655)),hAPP(c_List_Oset(tc_prod(U_17652,U_17653)),hAPP(hAPP(c_List_Ozip(U_17652,U_17653),U_17656),U_17657)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1125])],[f_4318_2]) ).

cnf(f_4318_4,plain,
    ( sP1125(U_17652,U_17653,U_17654,U_17655,U_17656,U_17657)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17652,U_17653)),hAPP(hAPP(c_Product__Type_OPair(U_17652,U_17653),U_17654),U_17655)),hAPP(c_List_Oset(tc_prod(U_17652,U_17653)),hAPP(hAPP(c_List_Ozip(U_17652,U_17653),U_17656),U_17657)))) ),
    inference(clausify,[status(thm)],[f_4318_3]) ).

cnf(f_4318_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17652),U_17654),hAPP(c_List_Oset(U_17652),U_17656)))
    | ~ sP1125(U_17652,U_17653,U_17654,U_17655,U_17656,U_17657) ),
    inference(clausify,[status(thm)],[f_4318_3]) ).

cnf(f_4318_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17653),U_17655),hAPP(c_List_Oset(U_17653),U_17657)))
    | ~ sP1125(U_17652,U_17653,U_17654,U_17655,U_17656,U_17657) ),
    inference(clausify,[status(thm)],[f_4318_3]) ).

fof(f_4319_1,plain,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map__map]) ).

fof(f_4319_2,plain,
    ! [U_17665,U_17664,U_17663,U_17662,U_17661,U_17660,U_17659,U_17658] : hAPP(hAPP(c_List_Ozip(U_17658,U_17659),hAPP(hAPP(c_List_Omap(U_17660,U_17658),U_17661),U_17662)),hAPP(hAPP(c_List_Omap(U_17663,U_17659),U_17664),U_17665)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17660,U_17663),tc_prod(U_17658,U_17659)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17660,U_17663,tc_prod(U_17658,U_17659)),hAPP(hAPP(c_COMBC(U_17660,tc_fun(U_17663,U_17659),tc_fun(U_17663,tc_prod(U_17658,U_17659))),hAPP(hAPP(c_COMBB(tc_fun(U_17659,tc_prod(U_17658,U_17659)),tc_fun(tc_fun(U_17663,U_17659),tc_fun(U_17663,tc_prod(U_17658,U_17659))),U_17660),c_COMBB(U_17659,tc_prod(U_17658,U_17659),U_17663)),hAPP(hAPP(c_COMBB(U_17658,tc_fun(U_17659,tc_prod(U_17658,U_17659)),U_17660),c_Product__Type_OPair(U_17658,U_17659)),U_17661))),U_17664))),hAPP(hAPP(c_List_Ozip(U_17660,U_17663),U_17662),U_17665)),
    inference(variable_rename,[status(thm)],[f_4319_1]) ).

fof(f_4319_3,plain,
    ! [U_17658,U_17659,U_17660,U_17661,U_17662,U_17663,U_17664,U_17665] : hAPP(hAPP(c_List_Ozip(U_17658,U_17659),hAPP(hAPP(c_List_Omap(U_17660,U_17658),U_17661),U_17662)),hAPP(hAPP(c_List_Omap(U_17663,U_17659),U_17664),U_17665)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17660,U_17663),tc_prod(U_17658,U_17659)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17660,U_17663,tc_prod(U_17658,U_17659)),hAPP(hAPP(c_COMBC(U_17660,tc_fun(U_17663,U_17659),tc_fun(U_17663,tc_prod(U_17658,U_17659))),hAPP(hAPP(c_COMBB(tc_fun(U_17659,tc_prod(U_17658,U_17659)),tc_fun(tc_fun(U_17663,U_17659),tc_fun(U_17663,tc_prod(U_17658,U_17659))),U_17660),c_COMBB(U_17659,tc_prod(U_17658,U_17659),U_17663)),hAPP(hAPP(c_COMBB(U_17658,tc_fun(U_17659,tc_prod(U_17658,U_17659)),U_17660),c_Product__Type_OPair(U_17658,U_17659)),U_17661))),U_17664))),hAPP(hAPP(c_List_Ozip(U_17660,U_17663),U_17662),U_17665)),
    inference(definitional_conversion,[status(esa)],[f_4319_2]) ).

cnf(f_4319_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17658,U_17659),hAPP(hAPP(c_List_Omap(U_17660,U_17658),U_17661),U_17662)),hAPP(hAPP(c_List_Omap(U_17663,U_17659),U_17664),U_17665)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17660,U_17663),tc_prod(U_17658,U_17659)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17660,U_17663,tc_prod(U_17658,U_17659)),hAPP(hAPP(c_COMBC(U_17660,tc_fun(U_17663,U_17659),tc_fun(U_17663,tc_prod(U_17658,U_17659))),hAPP(hAPP(c_COMBB(tc_fun(U_17659,tc_prod(U_17658,U_17659)),tc_fun(tc_fun(U_17663,U_17659),tc_fun(U_17663,tc_prod(U_17658,U_17659))),U_17660),c_COMBB(U_17659,tc_prod(U_17658,U_17659),U_17663)),hAPP(hAPP(c_COMBB(U_17658,tc_fun(U_17659,tc_prod(U_17658,U_17659)),U_17660),c_Product__Type_OPair(U_17658,U_17659)),U_17661))),U_17664))),hAPP(hAPP(c_List_Ozip(U_17660,U_17663),U_17662),U_17665)),
    inference(clausify,[status(thm)],[f_4319_3]) ).

fof(f_4320_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map1]) ).

fof(f_4320_2,plain,
    ! [U_17671,U_17670,U_17669,U_17668,U_17667,U_17666] : hAPP(hAPP(c_List_Ozip(U_17666,U_17667),hAPP(hAPP(c_List_Omap(U_17668,U_17666),U_17669),U_17670)),U_17671) = hAPP(hAPP(c_List_Omap(tc_prod(U_17668,U_17667),tc_prod(U_17666,U_17667)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17668,U_17667,tc_prod(U_17666,U_17667)),hAPP(hAPP(c_COMBB(U_17666,tc_fun(U_17667,tc_prod(U_17666,U_17667)),U_17668),c_Product__Type_OPair(U_17666,U_17667)),U_17669))),hAPP(hAPP(c_List_Ozip(U_17668,U_17667),U_17670),U_17671)),
    inference(variable_rename,[status(thm)],[f_4320_1]) ).

fof(f_4320_3,plain,
    ! [U_17666,U_17667,U_17668,U_17669,U_17670,U_17671] : hAPP(hAPP(c_List_Ozip(U_17666,U_17667),hAPP(hAPP(c_List_Omap(U_17668,U_17666),U_17669),U_17670)),U_17671) = hAPP(hAPP(c_List_Omap(tc_prod(U_17668,U_17667),tc_prod(U_17666,U_17667)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17668,U_17667,tc_prod(U_17666,U_17667)),hAPP(hAPP(c_COMBB(U_17666,tc_fun(U_17667,tc_prod(U_17666,U_17667)),U_17668),c_Product__Type_OPair(U_17666,U_17667)),U_17669))),hAPP(hAPP(c_List_Ozip(U_17668,U_17667),U_17670),U_17671)),
    inference(definitional_conversion,[status(esa)],[f_4320_2]) ).

cnf(f_4320_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17666,U_17667),hAPP(hAPP(c_List_Omap(U_17668,U_17666),U_17669),U_17670)),U_17671) = hAPP(hAPP(c_List_Omap(tc_prod(U_17668,U_17667),tc_prod(U_17666,U_17667)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17668,U_17667,tc_prod(U_17666,U_17667)),hAPP(hAPP(c_COMBB(U_17666,tc_fun(U_17667,tc_prod(U_17666,U_17667)),U_17668),c_Product__Type_OPair(U_17666,U_17667)),U_17669))),hAPP(hAPP(c_List_Ozip(U_17668,U_17667),U_17670),U_17671)),
    inference(clausify,[status(thm)],[f_4320_3]) ).

fof(f_4321_1,plain,
    ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map2]) ).

fof(f_4321_2,plain,
    ! [U_17677,U_17676,U_17675,U_17674,U_17673,U_17672] : hAPP(hAPP(c_List_Ozip(U_17672,U_17673),U_17674),hAPP(hAPP(c_List_Omap(U_17675,U_17673),U_17676),U_17677)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17672,U_17675),tc_prod(U_17672,U_17673)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17672,U_17675,tc_prod(U_17672,U_17673)),hAPP(hAPP(c_COMBC(U_17672,tc_fun(U_17675,U_17673),tc_fun(U_17675,tc_prod(U_17672,U_17673))),hAPP(hAPP(c_COMBB(tc_fun(U_17673,tc_prod(U_17672,U_17673)),tc_fun(tc_fun(U_17675,U_17673),tc_fun(U_17675,tc_prod(U_17672,U_17673))),U_17672),c_COMBB(U_17673,tc_prod(U_17672,U_17673),U_17675)),c_Product__Type_OPair(U_17672,U_17673))),U_17676))),hAPP(hAPP(c_List_Ozip(U_17672,U_17675),U_17674),U_17677)),
    inference(variable_rename,[status(thm)],[f_4321_1]) ).

fof(f_4321_3,plain,
    ! [U_17672,U_17673,U_17674,U_17675,U_17676,U_17677] : hAPP(hAPP(c_List_Ozip(U_17672,U_17673),U_17674),hAPP(hAPP(c_List_Omap(U_17675,U_17673),U_17676),U_17677)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17672,U_17675),tc_prod(U_17672,U_17673)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17672,U_17675,tc_prod(U_17672,U_17673)),hAPP(hAPP(c_COMBC(U_17672,tc_fun(U_17675,U_17673),tc_fun(U_17675,tc_prod(U_17672,U_17673))),hAPP(hAPP(c_COMBB(tc_fun(U_17673,tc_prod(U_17672,U_17673)),tc_fun(tc_fun(U_17675,U_17673),tc_fun(U_17675,tc_prod(U_17672,U_17673))),U_17672),c_COMBB(U_17673,tc_prod(U_17672,U_17673),U_17675)),c_Product__Type_OPair(U_17672,U_17673))),U_17676))),hAPP(hAPP(c_List_Ozip(U_17672,U_17675),U_17674),U_17677)),
    inference(definitional_conversion,[status(esa)],[f_4321_2]) ).

cnf(f_4321_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17672,U_17673),U_17674),hAPP(hAPP(c_List_Omap(U_17675,U_17673),U_17676),U_17677)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17672,U_17675),tc_prod(U_17672,U_17673)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17672,U_17675,tc_prod(U_17672,U_17673)),hAPP(hAPP(c_COMBC(U_17672,tc_fun(U_17675,U_17673),tc_fun(U_17675,tc_prod(U_17672,U_17673))),hAPP(hAPP(c_COMBB(tc_fun(U_17673,tc_prod(U_17672,U_17673)),tc_fun(tc_fun(U_17675,U_17673),tc_fun(U_17675,tc_prod(U_17672,U_17673))),U_17672),c_COMBB(U_17673,tc_prod(U_17672,U_17673),U_17675)),c_Product__Type_OPair(U_17672,U_17673))),U_17676))),hAPP(hAPP(c_List_Ozip(U_17672,U_17675),U_17674),U_17677)),
    inference(clausify,[status(thm)],[f_4321_3]) ).

fof(f_4322_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert]) ).

fof(f_4322_2,plain,
    ! [U_17680,U_17679,U_17678] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17678,hAPP(hAPP(c_Set_Oinsert(U_17678),U_17680),U_17679)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17678,U_17678,c_COMBI(U_17678)),U_17680),c_List_Olinorder__class_Osorted__list__of__set(U_17678,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17678,tc_HOL_Obool)),U_17679),hAPP(hAPP(c_Set_Oinsert(U_17678),U_17680),c_Orderings_Obot__class_Obot(tc_fun(U_17678,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17678),U_17679))
      | ~ class_Orderings_Olinorder(U_17678) ),
    inference(variable_rename,[status(thm)],[f_4322_1]) ).

fof(f_4322_3,plain,
    ! [U_17678,U_17679,U_17680] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17678,hAPP(hAPP(c_Set_Oinsert(U_17678),U_17680),U_17679)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17678,U_17678,c_COMBI(U_17678)),U_17680),c_List_Olinorder__class_Osorted__list__of__set(U_17678,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17678,tc_HOL_Obool)),U_17679),hAPP(hAPP(c_Set_Oinsert(U_17678),U_17680),c_Orderings_Obot__class_Obot(tc_fun(U_17678,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17678),U_17679))
      | ~ class_Orderings_Olinorder(U_17678) ),
    inference(definitional_conversion,[status(esa)],[f_4322_2]) ).

cnf(f_4322_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17678,hAPP(hAPP(c_Set_Oinsert(U_17678),U_17680),U_17679)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17678,U_17678,c_COMBI(U_17678)),U_17680),c_List_Olinorder__class_Osorted__list__of__set(U_17678,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17678,tc_HOL_Obool)),U_17679),hAPP(hAPP(c_Set_Oinsert(U_17678),U_17680),c_Orderings_Obot__class_Obot(tc_fun(U_17678,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17678),U_17679))
    | ~ class_Orderings_Olinorder(U_17678) ),
    inference(clausify,[status(thm)],[f_4322_3]) ).

fof(f_4323_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
      ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2))
      | hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__upd]) ).

fof(f_4323_2,plain,
    ! [U_17688,U_17687,U_17686,U_17685,U_17684,U_17683,U_17682,U_17681] :
      ( c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17682)) = c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17685))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17683,tc_Option_Ooption(U_17681)),c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17682))),U_17686),hAPP(c_Option_Ooption_OSome(U_17681),U_17687)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17683,tc_Option_Ooption(U_17681)),c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17685))),U_17686),hAPP(c_Option_Ooption_OSome(U_17681),U_17688))
      | hBOOL(hAPP(hAPP(c_member(U_17683),U_17686),hAPP(c_List_Oset(U_17683),U_17684)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17685) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17682) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684) ),
    inference(variable_rename,[status(thm)],[f_4323_1]) ).

fof(f_4323_3,plain,
    ! [U_17681,U_17682,U_17683,U_17684,U_17685,U_17686,U_17687,U_17688] :
      ( c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17682)) = c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17685))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17683,tc_Option_Ooption(U_17681)),c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17682))),U_17686),hAPP(c_Option_Ooption_OSome(U_17681),U_17687)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17683,tc_Option_Ooption(U_17681)),c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17685))),U_17686),hAPP(c_Option_Ooption_OSome(U_17681),U_17688))
      | hBOOL(hAPP(hAPP(c_member(U_17683),U_17686),hAPP(c_List_Oset(U_17683),U_17684)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17685) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17682) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684) ),
    inference(definitional_conversion,[status(esa)],[f_4323_2]) ).

cnf(f_4323_4,plain,
    ( c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17682)) = c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17685))
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17683,tc_Option_Ooption(U_17681)),c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17682))),U_17686),hAPP(c_Option_Ooption_OSome(U_17681),U_17687)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17683,tc_Option_Ooption(U_17681)),c_Map_Omap__of(U_17683,U_17681,hAPP(hAPP(c_List_Ozip(U_17683,U_17681),U_17684),U_17685))),U_17686),hAPP(c_Option_Ooption_OSome(U_17681),U_17688))
    | hBOOL(hAPP(hAPP(c_member(U_17683),U_17686),hAPP(c_List_Oset(U_17683),U_17684)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17685) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17682) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684) ),
    inference(clausify,[status(thm)],[f_4323_3]) ).

fof(f_4324_1,plain,
    ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_length__zip]) ).

fof(f_4324_2,plain,
    ! [U_17692,U_17691,U_17690,U_17689] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_17689,U_17690))),hAPP(hAPP(c_List_Ozip(U_17689,U_17690),U_17691),U_17692)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17689)),U_17691)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17690)),U_17692)),
    inference(variable_rename,[status(thm)],[f_4324_1]) ).

fof(f_4324_3,plain,
    ! [U_17689,U_17690,U_17691,U_17692] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_17689,U_17690))),hAPP(hAPP(c_List_Ozip(U_17689,U_17690),U_17691),U_17692)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17689)),U_17691)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17690)),U_17692)),
    inference(definitional_conversion,[status(esa)],[f_4324_2]) ).

cnf(f_4324_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_17689,U_17690))),hAPP(hAPP(c_List_Ozip(U_17689,U_17690),U_17691),U_17692)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17689)),U_17691)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17690)),U_17692)),
    inference(clausify,[status(thm)],[f_4324_3]) ).

fof(f_4325_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_set__insort]) ).

fof(f_4325_2,plain,
    ! [U_17697,U_17696,U_17695,U_17694,U_17693] :
      ( hAPP(c_List_Oset(U_17694),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17694,U_17693,U_17695),U_17696),U_17697)) = hAPP(hAPP(c_Set_Oinsert(U_17694),U_17696),hAPP(c_List_Oset(U_17694),U_17697))
      | ~ class_Orderings_Olinorder(U_17693) ),
    inference(variable_rename,[status(thm)],[f_4325_1]) ).

fof(f_4325_3,plain,
    ! [U_17693,U_17694,U_17695,U_17696,U_17697] :
      ( hAPP(c_List_Oset(U_17694),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17694,U_17693,U_17695),U_17696),U_17697)) = hAPP(hAPP(c_Set_Oinsert(U_17694),U_17696),hAPP(c_List_Oset(U_17694),U_17697))
      | ~ class_Orderings_Olinorder(U_17693) ),
    inference(definitional_conversion,[status(esa)],[f_4325_2]) ).

cnf(f_4325_4,plain,
    ( hAPP(c_List_Oset(U_17694),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17694,U_17693,U_17695),U_17696),U_17697)) = hAPP(hAPP(c_Set_Oinsert(U_17694),U_17696),hAPP(c_List_Oset(U_17694),U_17697))
    | ~ class_Orderings_Olinorder(U_17693) ),
    inference(clausify,[status(thm)],[f_4325_3]) ).

fof(f_4326_1,plain,
    ! [V_ys,V_xs,T_a] :
      ( V_xs != V_ys
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) ),
    inference(fof_nnf,[status(thm)],[fact_neq__if__length__neq]) ).

fof(f_4326_2,plain,
    ! [U_17700,U_17699,U_17698] :
      ( U_17699 != U_17700
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17699) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17700) ),
    inference(variable_rename,[status(thm)],[f_4326_1]) ).

fof(f_4326_3,plain,
    ! [U_17700,U_17699] :
      ( ! [U_17698] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17699) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17700)
      | U_17699 != U_17700 ),
    inference(miniscope,[status(thm)],[f_4326_2]) ).

fof(f_4326_4,plain,
    ! [U_17698,U_17699,U_17700] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17699) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17700)
      | U_17699 != U_17700 ),
    inference(definitional_conversion,[status(esa)],[f_4326_3]) ).

cnf(f_4326_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17699) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17698)),U_17700)
    | U_17699 != U_17700 ),
    inference(clausify,[status(thm)],[f_4326_4]) ).

fof(f_4327_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_length__insort]) ).

fof(f_4327_2,plain,
    ! [U_17705,U_17704,U_17703,U_17702,U_17701] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17702,U_17701,U_17703),U_17704),U_17705)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17705))
      | ~ class_Orderings_Olinorder(U_17701) ),
    inference(variable_rename,[status(thm)],[f_4327_1]) ).

fof(f_4327_3,plain,
    ! [U_17701,U_17702,U_17703,U_17704,U_17705] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17702,U_17701,U_17703),U_17704),U_17705)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17705))
      | ~ class_Orderings_Olinorder(U_17701) ),
    inference(definitional_conversion,[status(esa)],[f_4327_2]) ).

cnf(f_4327_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17702,U_17701,U_17703),U_17704),U_17705)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17705))
    | ~ class_Orderings_Olinorder(U_17701) ),
    inference(clausify,[status(thm)],[f_4327_3]) ).

fof(f_4328_1,plain,
    ! [V_xs_2,V_y_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__left__comm]) ).

fof(f_4328_2,plain,
    ! [U_17709,U_17708,U_17707,U_17706] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17707),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17708),U_17709)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17708),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17707),U_17709))
      | ~ class_Orderings_Olinorder(U_17706) ),
    inference(variable_rename,[status(thm)],[f_4328_1]) ).

fof(f_4328_3,plain,
    ! [U_17706,U_17707,U_17708,U_17709] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17707),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17708),U_17709)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17708),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17707),U_17709))
      | ~ class_Orderings_Olinorder(U_17706) ),
    inference(definitional_conversion,[status(esa)],[f_4328_2]) ).

cnf(f_4328_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17707),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17708),U_17709)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17708),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17706,U_17706,c_COMBI(U_17706)),U_17707),U_17709))
    | ~ class_Orderings_Olinorder(U_17706) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

fof(f_4329_1,plain,
    ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2))
      | hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm]) ).

fof(f_4329_2,plain,
    ! [U_17715,U_17714,U_17713,U_17712,U_17711,U_17710] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17713),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17712),U_17715)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17712),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17713),U_17715))
      | hAPP(U_17711,U_17712) = hAPP(U_17711,U_17713)
      | ~ class_Orderings_Olinorder(U_17710) ),
    inference(variable_rename,[status(thm)],[f_4329_1]) ).

fof(f_4329_3,plain,
    ! [U_17710,U_17711,U_17712,U_17713,U_17714,U_17715] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17713),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17712),U_17715)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17712),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17713),U_17715))
      | hAPP(U_17711,U_17712) = hAPP(U_17711,U_17713)
      | ~ class_Orderings_Olinorder(U_17710) ),
    inference(definitional_conversion,[status(esa)],[f_4329_2]) ).

cnf(f_4329_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17713),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17712),U_17715)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17712),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17714,U_17710,U_17711),U_17713),U_17715))
    | hAPP(U_17711,U_17712) = hAPP(U_17711,U_17713)
    | ~ class_Orderings_Olinorder(U_17710) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

fof(f_4330_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort]) ).

fof(f_4330_2,plain,
    ! [U_17716] :
      ( c_Finite__Set_Ofun__left__comm(U_17716,tc_List_Olist(U_17716),c_List_Olinorder__class_Oinsort__key(U_17716,U_17716,c_COMBI(U_17716)))
      | ~ class_Orderings_Olinorder(U_17716) ),
    inference(variable_rename,[status(thm)],[f_4330_1]) ).

fof(f_4330_3,plain,
    ! [U_17716] :
      ( c_Finite__Set_Ofun__left__comm(U_17716,tc_List_Olist(U_17716),c_List_Olinorder__class_Oinsort__key(U_17716,U_17716,c_COMBI(U_17716)))
      | ~ class_Orderings_Olinorder(U_17716) ),
    inference(definitional_conversion,[status(esa)],[f_4330_2]) ).

cnf(f_4330_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_17716,tc_List_Olist(U_17716),c_List_Olinorder__class_Oinsort__key(U_17716,U_17716,c_COMBI(U_17716)))
    | ~ class_Orderings_Olinorder(U_17716) ),
    inference(clausify,[status(thm)],[f_4330_3]) ).

fof(f_4331_1,plain,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexn__length]) ).

fof(f_4331_2,plain,
    ! [U_17721,U_17720,U_17719,U_17718,U_17717] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17717)),U_17719) = U_17721
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17717)),U_17718) = U_17721 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17717),tc_List_Olist(U_17717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17717),tc_List_Olist(U_17717)),U_17718),U_17719)),hAPP(c_List_Olexn(U_17717,U_17720),U_17721))) ),
    inference(variable_rename,[status(thm)],[f_4331_1]) ).

fof(f_4331_3,plain,
    ( ! [U_17717,U_17718,U_17719,U_17721] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17717)),U_17719) = U_17721
        | ~ sP1126(U_17717,U_17718,U_17719,U_17721) )
    & ! [U_17717,U_17718,U_17719,U_17721] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17717)),U_17718) = U_17721
        | ~ sP1126(U_17717,U_17718,U_17719,U_17721) )
    & ! [U_17717,U_17718,U_17719,U_17720,U_17721] :
        ( sP1126(U_17717,U_17718,U_17719,U_17721)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17717),tc_List_Olist(U_17717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17717),tc_List_Olist(U_17717)),U_17718),U_17719)),hAPP(c_List_Olexn(U_17717,U_17720),U_17721))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1126])],[f_4331_2]) ).

cnf(f_4331_4,plain,
    ( sP1126(U_17717,U_17718,U_17719,U_17721)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17717),tc_List_Olist(U_17717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17717),tc_List_Olist(U_17717)),U_17718),U_17719)),hAPP(c_List_Olexn(U_17717,U_17720),U_17721))) ),
    inference(clausify,[status(thm)],[f_4331_3]) ).

cnf(f_4331_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17717)),U_17718) = U_17721
    | ~ sP1126(U_17717,U_17718,U_17719,U_17721) ),
    inference(clausify,[status(thm)],[f_4331_3]) ).

cnf(f_4331_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17717)),U_17719) = U_17721
    | ~ sP1126(U_17717,U_17718,U_17719,U_17721) ),
    inference(clausify,[status(thm)],[f_4331_3]) ).

fof(f_4332_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_length__map]) ).

fof(f_4332_2,plain,
    ! [U_17725,U_17724,U_17723,U_17722] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),hAPP(hAPP(c_List_Omap(U_17723,U_17722),U_17724),U_17725)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17723)),U_17725),
    inference(variable_rename,[status(thm)],[f_4332_1]) ).

fof(f_4332_3,plain,
    ! [U_17723,U_17722,U_17724,U_17725] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),hAPP(hAPP(c_List_Omap(U_17723,U_17722),U_17724),U_17725)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17723)),U_17725),
    inference(definitional_conversion,[status(esa)],[f_4332_2]) ).

cnf(f_4332_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),hAPP(hAPP(c_List_Omap(U_17723,U_17722),U_17724),U_17725)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17723)),U_17725),
    inference(clausify,[status(thm)],[f_4332_3]) ).

fof(f_4333_1,plain,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2)
      | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq]) ).

fof(f_4333_2,plain,
    ! [U_17732,U_17731,U_17730,U_17729,U_17728,U_17727,U_17726] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17726)),U_17729) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17730)),U_17732)
      | hAPP(hAPP(c_List_Omap(U_17726,U_17727),U_17728),U_17729) != hAPP(hAPP(c_List_Omap(U_17730,U_17727),U_17731),U_17732) ),
    inference(variable_rename,[status(thm)],[f_4333_1]) ).

fof(f_4333_3,plain,
    ! [U_17726,U_17727,U_17728,U_17729,U_17730,U_17731,U_17732] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17726)),U_17729) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17730)),U_17732)
      | hAPP(hAPP(c_List_Omap(U_17726,U_17727),U_17728),U_17729) != hAPP(hAPP(c_List_Omap(U_17730,U_17727),U_17731),U_17732) ),
    inference(definitional_conversion,[status(esa)],[f_4333_2]) ).

cnf(f_4333_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17726)),U_17729) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17730)),U_17732)
    | hAPP(hAPP(c_List_Omap(U_17726,U_17727),U_17728),U_17729) != hAPP(hAPP(c_List_Omap(U_17730,U_17727),U_17731),U_17732) ),
    inference(clausify,[status(thm)],[f_4333_3]) ).

fof(f_4334_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__insort]) ).

fof(f_4334_2,plain,
    ! [U_17735,U_17734,U_17733] :
      ( c_List_Oremove1(U_17733,U_17734,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17733,U_17733,c_COMBI(U_17733)),U_17734),U_17735)) = U_17735
      | ~ class_Orderings_Olinorder(U_17733) ),
    inference(variable_rename,[status(thm)],[f_4334_1]) ).

fof(f_4334_3,plain,
    ! [U_17734,U_17733,U_17735] :
      ( c_List_Oremove1(U_17733,U_17734,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17733,U_17733,c_COMBI(U_17733)),U_17734),U_17735)) = U_17735
      | ~ class_Orderings_Olinorder(U_17733) ),
    inference(definitional_conversion,[status(esa)],[f_4334_2]) ).

cnf(f_4334_4,plain,
    ( c_List_Oremove1(U_17733,U_17734,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17733,U_17733,c_COMBI(U_17733)),U_17734),U_17735)) = U_17735
    | ~ class_Orderings_Olinorder(U_17733) ),
    inference(clausify,[status(thm)],[f_4334_3]) ).

fof(f_4335_1,plain,
    ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_card__length]) ).

fof(f_4335_2,plain,
    ! [U_17737,U_17736] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_17736),hAPP(c_List_Oset(U_17736),U_17737))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17736)),U_17737))),
    inference(variable_rename,[status(thm)],[f_4335_1]) ).

fof(f_4335_3,plain,
    ! [U_17736,U_17737] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_17736),hAPP(c_List_Oset(U_17736),U_17737))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17736)),U_17737))),
    inference(definitional_conversion,[status(esa)],[f_4335_2]) ).

cnf(f_4335_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_17736),hAPP(c_List_Oset(U_17736),U_17737))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17736)),U_17737))),
    inference(clausify,[status(thm)],[f_4335_3]) ).

fof(f_4336_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__distinct]) ).

fof(f_4336_2,plain,
    ! [U_17739,U_17738] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17738),U_17739))
      | hAPP(c_Finite__Set_Ocard(U_17738),hAPP(c_List_Oset(U_17738),U_17739)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17738)),U_17739) ),
    inference(variable_rename,[status(thm)],[f_4336_1]) ).

fof(f_4336_3,plain,
    ! [U_17738,U_17739] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17738),U_17739))
      | hAPP(c_Finite__Set_Ocard(U_17738),hAPP(c_List_Oset(U_17738),U_17739)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17738)),U_17739) ),
    inference(definitional_conversion,[status(esa)],[f_4336_2]) ).

cnf(f_4336_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17738),U_17739))
    | hAPP(c_Finite__Set_Ocard(U_17738),hAPP(c_List_Oset(U_17738),U_17739)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17738)),U_17739) ),
    inference(clausify,[status(thm)],[f_4336_3]) ).

fof(f_4337_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__card]) ).

fof(f_4337_2,plain,
    ! [U_17741,U_17740] :
      ( hAPP(c_Finite__Set_Ocard(U_17740),hAPP(c_List_Oset(U_17740),U_17741)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17741)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17740),U_17741)) ),
    inference(variable_rename,[status(thm)],[f_4337_1]) ).

fof(f_4337_3,plain,
    ! [U_17740,U_17741] :
      ( hAPP(c_Finite__Set_Ocard(U_17740),hAPP(c_List_Oset(U_17740),U_17741)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17741)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17740),U_17741)) ),
    inference(definitional_conversion,[status(esa)],[f_4337_2]) ).

cnf(f_4337_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_17740),hAPP(c_List_Oset(U_17740),U_17741)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17741)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17740),U_17741)) ),
    inference(clausify,[status(thm)],[f_4337_3]) ).

fof(f_4338_1,plain,
    ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
      ( V_ys_2 = V_zs_2
      | c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) != c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__inject]) ).

fof(f_4338_2,plain,
    ! [U_17746,U_17745,U_17744,U_17743,U_17742] :
      ( U_17743 = U_17746
      | c_Map_Omap__of(U_17744,U_17742,hAPP(hAPP(c_List_Ozip(U_17744,U_17742),U_17745),U_17743)) != c_Map_Omap__of(U_17744,U_17742,hAPP(hAPP(c_List_Ozip(U_17744,U_17742),U_17745),U_17746))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17744),U_17745))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17742)),U_17746) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17745)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17742)),U_17743) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17745) ),
    inference(variable_rename,[status(thm)],[f_4338_1]) ).

fof(f_4338_3,plain,
    ! [U_17742,U_17743,U_17744,U_17745,U_17746] :
      ( U_17743 = U_17746
      | c_Map_Omap__of(U_17744,U_17742,hAPP(hAPP(c_List_Ozip(U_17744,U_17742),U_17745),U_17743)) != c_Map_Omap__of(U_17744,U_17742,hAPP(hAPP(c_List_Ozip(U_17744,U_17742),U_17745),U_17746))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17744),U_17745))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17742)),U_17746) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17745)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17742)),U_17743) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17745) ),
    inference(definitional_conversion,[status(esa)],[f_4338_2]) ).

cnf(f_4338_4,plain,
    ( U_17743 = U_17746
    | c_Map_Omap__of(U_17744,U_17742,hAPP(hAPP(c_List_Ozip(U_17744,U_17742),U_17745),U_17743)) != c_Map_Omap__of(U_17744,U_17742,hAPP(hAPP(c_List_Ozip(U_17744,U_17742),U_17745),U_17746))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17744),U_17745))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17742)),U_17746) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17745)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17742)),U_17743) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17745) ),
    inference(clausify,[status(thm)],[f_4338_3]) ).

fof(f_4339_1,plain,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__fst__zip]) ).

fof(f_4339_2,plain,
    ! [U_17750,U_17749,U_17748,U_17747] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17747,U_17749),U_17747),c_Product__Type_Ofst(U_17747,U_17749)),hAPP(hAPP(c_List_Ozip(U_17747,U_17749),U_17748),U_17750)) = U_17748
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17747)),U_17748) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),U_17750) ),
    inference(variable_rename,[status(thm)],[f_4339_1]) ).

fof(f_4339_3,plain,
    ! [U_17747,U_17748,U_17749,U_17750] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17747,U_17749),U_17747),c_Product__Type_Ofst(U_17747,U_17749)),hAPP(hAPP(c_List_Ozip(U_17747,U_17749),U_17748),U_17750)) = U_17748
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17747)),U_17748) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),U_17750) ),
    inference(definitional_conversion,[status(esa)],[f_4339_2]) ).

cnf(f_4339_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17747,U_17749),U_17747),c_Product__Type_Ofst(U_17747,U_17749)),hAPP(hAPP(c_List_Ozip(U_17747,U_17749),U_17748),U_17750)) = U_17748
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17747)),U_17748) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),U_17750) ),
    inference(clausify,[status(thm)],[f_4339_3]) ).

fof(f_4340_1,plain,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__snd__zip]) ).

fof(f_4340_2,plain,
    ! [U_17754,U_17753,U_17752,U_17751] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17751,U_17753),U_17753),c_Product__Type_Osnd(U_17751,U_17753)),hAPP(hAPP(c_List_Ozip(U_17751,U_17753),U_17752),U_17754)) = U_17754
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17751)),U_17752) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17753)),U_17754) ),
    inference(variable_rename,[status(thm)],[f_4340_1]) ).

fof(f_4340_3,plain,
    ! [U_17751,U_17752,U_17753,U_17754] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17751,U_17753),U_17753),c_Product__Type_Osnd(U_17751,U_17753)),hAPP(hAPP(c_List_Ozip(U_17751,U_17753),U_17752),U_17754)) = U_17754
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17751)),U_17752) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17753)),U_17754) ),
    inference(definitional_conversion,[status(esa)],[f_4340_2]) ).

cnf(f_4340_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17751,U_17753),U_17753),c_Product__Type_Osnd(U_17751,U_17753)),hAPP(hAPP(c_List_Ozip(U_17751,U_17753),U_17752),U_17754)) = U_17754
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17751)),U_17752) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17753)),U_17754) ),
    inference(clausify,[status(thm)],[f_4340_3]) ).

fof(f_4341_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
            & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insort]) ).

fof(f_4341_2,plain,
    ! [U_17759,U_17758,U_17757,U_17756,U_17755] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_17756),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17756,U_17755,U_17757),U_17758),U_17759)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17756),U_17759))
          | hBOOL(hAPP(hAPP(c_member(U_17756),U_17758),hAPP(c_List_Oset(U_17756),U_17759))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(U_17756),U_17759))
            & ~ hBOOL(hAPP(hAPP(c_member(U_17756),U_17758),hAPP(c_List_Oset(U_17756),U_17759))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17756),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17756,U_17755,U_17757),U_17758),U_17759))) ) )
      | ~ class_Orderings_Olinorder(U_17755) ),
    inference(variable_rename,[status(thm)],[f_4341_1]) ).

fof(f_4341_3,plain,
    ( ! [U_17756,U_17758,U_17759] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17756),U_17759))
        | ~ sP1127(U_17756,U_17758,U_17759) )
    & ! [U_17756,U_17758,U_17759] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17756),U_17758),hAPP(c_List_Oset(U_17756),U_17759)))
        | ~ sP1127(U_17756,U_17758,U_17759) )
    & ! [U_17756,U_17755,U_17757,U_17758,U_17759] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17756),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17756,U_17755,U_17757),U_17758),U_17759)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17756),U_17759))
        | hBOOL(hAPP(hAPP(c_member(U_17756),U_17758),hAPP(c_List_Oset(U_17756),U_17759)))
        | ~ sP1128(U_17756,U_17755,U_17757,U_17758,U_17759) )
    & ! [U_17756,U_17755,U_17757,U_17758,U_17759] :
        ( sP1127(U_17756,U_17758,U_17759)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17756),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17756,U_17755,U_17757),U_17758),U_17759)))
        | ~ sP1128(U_17756,U_17755,U_17757,U_17758,U_17759) )
    & ! [U_17756,U_17755,U_17757,U_17758,U_17759] :
        ( sP1128(U_17756,U_17755,U_17757,U_17758,U_17759)
        | ~ class_Orderings_Olinorder(U_17755) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1127,sP1128])],[f_4341_2]) ).

cnf(f_4341_4,plain,
    ( sP1128(U_17756,U_17755,U_17757,U_17758,U_17759)
    | ~ class_Orderings_Olinorder(U_17755) ),
    inference(clausify,[status(thm)],[f_4341_3]) ).

cnf(f_4341_5,plain,
    ( sP1127(U_17756,U_17758,U_17759)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17756),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17756,U_17755,U_17757),U_17758),U_17759)))
    | ~ sP1128(U_17756,U_17755,U_17757,U_17758,U_17759) ),
    inference(clausify,[status(thm)],[f_4341_3]) ).

cnf(f_4341_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17756),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17756,U_17755,U_17757),U_17758),U_17759)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17756),U_17759))
    | hBOOL(hAPP(hAPP(c_member(U_17756),U_17758),hAPP(c_List_Oset(U_17756),U_17759)))
    | ~ sP1128(U_17756,U_17755,U_17757,U_17758,U_17759) ),
    inference(clausify,[status(thm)],[f_4341_3]) ).

cnf(f_4341_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17756),U_17758),hAPP(c_List_Oset(U_17756),U_17759)))
    | ~ sP1127(U_17756,U_17758,U_17759) ),
    inference(clausify,[status(thm)],[f_4341_3]) ).

cnf(f_4341_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17756),U_17759))
    | ~ sP1127(U_17756,U_17758,U_17759) ),
    inference(clausify,[status(thm)],[f_4341_3]) ).

fof(f_4342_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set]) ).

fof(f_4342_2,plain,
    ! [U_17762,U_17761,U_17760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17760)),U_17762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17760),U_17761),hAPP(c_List_Oset(U_17760),U_17762))) ),
    inference(variable_rename,[status(thm)],[f_4342_1]) ).

fof(f_4342_3,plain,
    ! [U_17762,U_17761,U_17760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17760)),U_17762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17760),U_17761),hAPP(c_List_Oset(U_17760),U_17762))) ),
    inference(definitional_conversion,[status(esa)],[f_4342_2]) ).

cnf(f_4342_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17760)),U_17762)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17760),U_17761),hAPP(c_List_Oset(U_17760),U_17762))) ),
    inference(clausify,[status(thm)],[f_4342_3]) ).

fof(f_4343_1,plain,
    ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
          | hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) != V_ys_2
          | hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) != V_xs_2 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
            & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 )
          | hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) != V_zs_2 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_zip__eq__conv]) ).

fof(f_4343_2,plain,
    ! [U_17767,U_17766,U_17765,U_17764,U_17763] :
      ( ( ( hAPP(hAPP(c_List_Ozip(U_17763,U_17765),U_17764),U_17766) = U_17767
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17765),c_Product__Type_Osnd(U_17763,U_17765)),U_17767) != U_17766
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17763),c_Product__Type_Ofst(U_17763,U_17765)),U_17767) != U_17764 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17765),c_Product__Type_Osnd(U_17763,U_17765)),U_17767) = U_17766
            & hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17763),c_Product__Type_Ofst(U_17763,U_17765)),U_17767) = U_17764 )
          | hAPP(hAPP(c_List_Ozip(U_17763,U_17765),U_17764),U_17766) != U_17767 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17763)),U_17764) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) ),
    inference(variable_rename,[status(thm)],[f_4343_1]) ).

fof(f_4343_3,plain,
    ( ! [U_17763,U_17764,U_17765,U_17766,U_17767] :
        ( hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17765),c_Product__Type_Osnd(U_17763,U_17765)),U_17767) = U_17766
        | ~ sP1129(U_17763,U_17764,U_17765,U_17766,U_17767) )
    & ! [U_17763,U_17764,U_17765,U_17766,U_17767] :
        ( hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17763),c_Product__Type_Ofst(U_17763,U_17765)),U_17767) = U_17764
        | ~ sP1129(U_17763,U_17764,U_17765,U_17766,U_17767) )
    & ! [U_17763,U_17764,U_17765,U_17766,U_17767] :
        ( hAPP(hAPP(c_List_Ozip(U_17763,U_17765),U_17764),U_17766) = U_17767
        | hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17765),c_Product__Type_Osnd(U_17763,U_17765)),U_17767) != U_17766
        | hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17763),c_Product__Type_Ofst(U_17763,U_17765)),U_17767) != U_17764
        | ~ sP1130(U_17763,U_17764,U_17765,U_17766,U_17767) )
    & ! [U_17763,U_17764,U_17765,U_17766,U_17767] :
        ( sP1129(U_17763,U_17764,U_17765,U_17766,U_17767)
        | hAPP(hAPP(c_List_Ozip(U_17763,U_17765),U_17764),U_17766) != U_17767
        | ~ sP1130(U_17763,U_17764,U_17765,U_17766,U_17767) )
    & ! [U_17763,U_17764,U_17765,U_17766,U_17767] :
        ( sP1130(U_17763,U_17764,U_17765,U_17766,U_17767)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17763)),U_17764) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1129,sP1130])],[f_4343_2]) ).

cnf(f_4343_4,plain,
    ( sP1130(U_17763,U_17764,U_17765,U_17766,U_17767)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17763)),U_17764) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

cnf(f_4343_5,plain,
    ( sP1129(U_17763,U_17764,U_17765,U_17766,U_17767)
    | hAPP(hAPP(c_List_Ozip(U_17763,U_17765),U_17764),U_17766) != U_17767
    | ~ sP1130(U_17763,U_17764,U_17765,U_17766,U_17767) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

cnf(f_4343_6,plain,
    ( hAPP(hAPP(c_List_Ozip(U_17763,U_17765),U_17764),U_17766) = U_17767
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17765),c_Product__Type_Osnd(U_17763,U_17765)),U_17767) != U_17766
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17763),c_Product__Type_Ofst(U_17763,U_17765)),U_17767) != U_17764
    | ~ sP1130(U_17763,U_17764,U_17765,U_17766,U_17767) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

cnf(f_4343_7,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17763),c_Product__Type_Ofst(U_17763,U_17765)),U_17767) = U_17764
    | ~ sP1129(U_17763,U_17764,U_17765,U_17766,U_17767) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

cnf(f_4343_8,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17763,U_17765),U_17765),c_Product__Type_Osnd(U_17763,U_17765)),U_17767) = U_17766
    | ~ sP1129(U_17763,U_17764,U_17765,U_17766,U_17767) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

fof(f_4344_1,plain,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
    inference(fof_nnf,[status(thm)],[fact_lenlex__conv]) ).

fof(f_4344_2,plain,
    ! [U_17769,U_17768] : c_List_Olenlex(U_17768,U_17769) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17768),tc_List_Olist(U_17768),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBS(tc_List_Olist(U_17768),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17768))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17768)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBS(tc_List_Olist(U_17768),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17768))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17768)),c_member(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))))),c_Product__Type_OPair(tc_List_Olist(U_17768),tc_List_Olist(U_17768))))),c_List_Olex(U_17768,U_17769)))))),
    inference(variable_rename,[status(thm)],[f_4344_1]) ).

fof(f_4344_3,plain,
    ! [U_17768,U_17769] : c_List_Olenlex(U_17768,U_17769) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17768),tc_List_Olist(U_17768),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBS(tc_List_Olist(U_17768),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17768))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17768)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBS(tc_List_Olist(U_17768),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17768))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17768)),c_member(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))))),c_Product__Type_OPair(tc_List_Olist(U_17768),tc_List_Olist(U_17768))))),c_List_Olex(U_17768,U_17769)))))),
    inference(definitional_conversion,[status(esa)],[f_4344_2]) ).

cnf(f_4344_4,plain,
    c_List_Olenlex(U_17768,U_17769) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17768),tc_List_Olist(U_17768),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBS(tc_List_Olist(U_17768),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17768))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17768)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBS(tc_List_Olist(U_17768),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17768),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17768))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17768)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17768)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17768),tc_HOL_Obool)),tc_List_Olist(U_17768)),c_COMBC(tc_List_Olist(U_17768),tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17768),tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))),tc_fun(tc_List_Olist(U_17768),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_17768)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17768)),c_member(tc_prod(tc_List_Olist(U_17768),tc_List_Olist(U_17768))))),c_Product__Type_OPair(tc_List_Olist(U_17768),tc_List_Olist(U_17768))))),c_List_Olex(U_17768,U_17769)))))),
    inference(clausify,[status(thm)],[f_4344_3]) ).

fof(f_4345_1,plain,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_lenlex__def]) ).

fof(f_4345_2,plain,
    ! [U_17771,U_17770] : c_List_Olenlex(U_17770,U_17771) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770)),tc_List_Olist(U_17770)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_17770),c_Wellfounded_Oless__than,c_List_Olex(U_17770,U_17771))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17770),tc_List_Olist(U_17770),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_17770),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770))),tc_List_Olist(U_17770)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_17770))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17770)))),c_COMBI(tc_List_Olist(U_17770)))),
    inference(variable_rename,[status(thm)],[f_4345_1]) ).

fof(f_4345_3,plain,
    ! [U_17770,U_17771] : c_List_Olenlex(U_17770,U_17771) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770)),tc_List_Olist(U_17770)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_17770),c_Wellfounded_Oless__than,c_List_Olex(U_17770,U_17771))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17770),tc_List_Olist(U_17770),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_17770),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770))),tc_List_Olist(U_17770)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_17770))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17770)))),c_COMBI(tc_List_Olist(U_17770)))),
    inference(definitional_conversion,[status(esa)],[f_4345_2]) ).

cnf(f_4345_4,plain,
    c_List_Olenlex(U_17770,U_17771) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770)),tc_List_Olist(U_17770)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_17770),c_Wellfounded_Oless__than,c_List_Olex(U_17770,U_17771))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17770),tc_List_Olist(U_17770),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_17770),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17770))),tc_List_Olist(U_17770)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_17770))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17770)))),c_COMBI(tc_List_Olist(U_17770)))),
    inference(clausify,[status(thm)],[f_4345_3]) ).

fof(f_4346_1,plain,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq]) ).

fof(f_4346_2,plain,
    ! [U_17774,U_17773,U_17772] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17772)),hAPP(c_Set_OCollect(tc_List_Olist(U_17772)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17772),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17772)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17772),tc_fun(U_17772,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_HOL_Obool),tc_fun(tc_fun(U_17772,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17772)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17772,tc_HOL_Obool))),c_List_Oset(U_17772))),U_17773))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17772),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17772)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17772)))),U_17774)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17772),U_17773)) ),
    inference(variable_rename,[status(thm)],[f_4346_1]) ).

fof(f_4346_3,plain,
    ! [U_17772,U_17774,U_17773] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17772)),hAPP(c_Set_OCollect(tc_List_Olist(U_17772)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17772),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17772)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17772),tc_fun(U_17772,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_HOL_Obool),tc_fun(tc_fun(U_17772,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17772)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17772,tc_HOL_Obool))),c_List_Oset(U_17772))),U_17773))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17772),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17772)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17772)))),U_17774)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17772),U_17773)) ),
    inference(definitional_conversion,[status(esa)],[f_4346_2]) ).

cnf(f_4346_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17772)),hAPP(c_Set_OCollect(tc_List_Olist(U_17772)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17772),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17772)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17772),tc_fun(U_17772,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_HOL_Obool),tc_fun(tc_fun(U_17772,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17772)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17772,tc_HOL_Obool))),c_List_Oset(U_17772))),U_17773))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17772),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17772)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17772)))),U_17774)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17772),U_17773)) ),
    inference(clausify,[status(thm)],[f_4346_3]) ).

fof(f_4347_1,plain,
    ! [T_b,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__eq__iff__zip__eq]) ).

fof(f_4347_2,plain,
    ! [U_17779,U_17778,U_17777] :
      ( ( U_17777 = U_17778
        | ? [U_17776] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,U_17779,tc_HOL_Obool),c_fequal),U_17776))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17779,U_17779)),U_17776),hAPP(c_List_Oset(tc_prod(U_17779,U_17779)),hAPP(hAPP(c_List_Ozip(U_17779,U_17779),U_17777),U_17778)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)),U_17777) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)),U_17778) )
      & ( ( ! [U_17775] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,U_17779,tc_HOL_Obool),c_fequal),U_17775))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17779,U_17779)),U_17775),hAPP(c_List_Oset(tc_prod(U_17779,U_17779)),hAPP(hAPP(c_List_Ozip(U_17779,U_17779),U_17777),U_17778)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)),U_17777) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)),U_17778) )
        | U_17777 != U_17778 ) ),
    inference(variable_rename,[status(thm)],[f_4347_1]) ).

fof(f_4347_3,plain,
    ( ! [U_17785,U_17783,U_17781] :
        ( U_17781 = U_17783
        | ? [U_17776] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17785,U_17785,tc_HOL_Obool),c_fequal),U_17776))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17785,U_17785)),U_17776),hAPP(c_List_Oset(tc_prod(U_17785,U_17785)),hAPP(hAPP(c_List_Ozip(U_17785,U_17785),U_17781),U_17783)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17783) )
    & ! [U_17784,U_17782,U_17780] :
        ( ( ! [U_17775] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17784,U_17784,tc_HOL_Obool),c_fequal),U_17775))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17784,U_17784)),U_17775),hAPP(c_List_Oset(tc_prod(U_17784,U_17784)),hAPP(hAPP(c_List_Ozip(U_17784,U_17784),U_17780),U_17782)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17780) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17782) )
        | U_17780 != U_17782 ) ),
    inference(miniscope,[status(thm)],[f_4347_2]) ).

fof(f_4347_4,plain,
    ( ! [U_17785,U_17783,U_17781] :
        ( U_17781 = U_17783
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17785,U_17785,tc_HOL_Obool),c_fequal),sK453(U_17785,U_17783,U_17781)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17785,U_17785)),sK453(U_17785,U_17783,U_17781)),hAPP(c_List_Oset(tc_prod(U_17785,U_17785)),hAPP(hAPP(c_List_Ozip(U_17785,U_17785),U_17781),U_17783)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17783) )
    & ! [U_17784,U_17782,U_17780] :
        ( ( ! [U_17775] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17784,U_17784,tc_HOL_Obool),c_fequal),U_17775))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17784,U_17784)),U_17775),hAPP(c_List_Oset(tc_prod(U_17784,U_17784)),hAPP(hAPP(c_List_Ozip(U_17784,U_17784),U_17780),U_17782)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17780) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17782) )
        | U_17780 != U_17782 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_17776,sK453(U_17785,U_17783,U_17781))],[f_4347_3]) ).

fof(f_4347_5,plain,
    ( ! [U_17783,U_17781,U_17785] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17785,U_17785,tc_HOL_Obool),c_fequal),sK453(U_17785,U_17783,U_17781)))
        | ~ sP1132(U_17783,U_17781,U_17785) )
    & ! [U_17783,U_17781,U_17785] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17785,U_17785)),sK453(U_17785,U_17783,U_17781)),hAPP(c_List_Oset(tc_prod(U_17785,U_17785)),hAPP(hAPP(c_List_Ozip(U_17785,U_17785),U_17781),U_17783))))
        | ~ sP1132(U_17783,U_17781,U_17785) )
    & ! [U_17775,U_17784,U_17780,U_17782] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17784,U_17784,tc_HOL_Obool),c_fequal),U_17775))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17784,U_17784)),U_17775),hAPP(c_List_Oset(tc_prod(U_17784,U_17784)),hAPP(hAPP(c_List_Ozip(U_17784,U_17784),U_17780),U_17782))))
        | ~ sP1131(U_17775,U_17784,U_17780,U_17782) )
    & ! [U_17775,U_17784,U_17780,U_17782] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17780) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17782)
        | ~ sP1131(U_17775,U_17784,U_17780,U_17782) )
    & ! [U_17783,U_17781,U_17785] :
        ( U_17781 = U_17783
        | sP1132(U_17783,U_17781,U_17785)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17783) )
    & ! [U_17775,U_17784,U_17780,U_17782] :
        ( sP1131(U_17775,U_17784,U_17780,U_17782)
        | U_17780 != U_17782 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1131,sP1132])],[f_4347_4]) ).

cnf(f_4347_6,plain,
    ( sP1131(U_17775,U_17784,U_17780,U_17782)
    | U_17780 != U_17782 ),
    inference(clausify,[status(thm)],[f_4347_5]) ).

cnf(f_4347_7,plain,
    ( U_17781 = U_17783
    | sP1132(U_17783,U_17781,U_17785)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17785)),U_17783) ),
    inference(clausify,[status(thm)],[f_4347_5]) ).

cnf(f_4347_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17780) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)),U_17782)
    | ~ sP1131(U_17775,U_17784,U_17780,U_17782) ),
    inference(clausify,[status(thm)],[f_4347_5]) ).

cnf(f_4347_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17784,U_17784,tc_HOL_Obool),c_fequal),U_17775))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17784,U_17784)),U_17775),hAPP(c_List_Oset(tc_prod(U_17784,U_17784)),hAPP(hAPP(c_List_Ozip(U_17784,U_17784),U_17780),U_17782))))
    | ~ sP1131(U_17775,U_17784,U_17780,U_17782) ),
    inference(clausify,[status(thm)],[f_4347_5]) ).

cnf(f_4347_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17785,U_17785)),sK453(U_17785,U_17783,U_17781)),hAPP(c_List_Oset(tc_prod(U_17785,U_17785)),hAPP(hAPP(c_List_Ozip(U_17785,U_17785),U_17781),U_17783))))
    | ~ sP1132(U_17783,U_17781,U_17785) ),
    inference(clausify,[status(thm)],[f_4347_5]) ).

cnf(f_4347_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17785,U_17785,tc_HOL_Obool),c_fequal),sK453(U_17785,U_17783,U_17781)))
    | ~ sP1132(U_17783,U_17781,U_17785) ),
    inference(clausify,[status(thm)],[f_4347_5]) ).

fof(f_4348_1,plain,
    ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
          | hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) != c_Option_Ooption_ONone(T_c) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__None]) ).

fof(f_4348_2,plain,
    ! [U_17790,U_17789,U_17788,U_17787,U_17786] :
      ( ( ( hAPP(c_Map_Omap__of(U_17786,U_17788,hAPP(hAPP(c_List_Ozip(U_17786,U_17788),U_17787),U_17789)),U_17790) = c_Option_Ooption_ONone(U_17788)
          | hBOOL(hAPP(hAPP(c_member(U_17786),U_17790),hAPP(c_List_Oset(U_17786),U_17787))) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(U_17786),U_17790),hAPP(c_List_Oset(U_17786),U_17787)))
          | hAPP(c_Map_Omap__of(U_17786,U_17788,hAPP(hAPP(c_List_Ozip(U_17786,U_17788),U_17787),U_17789)),U_17790) != c_Option_Ooption_ONone(U_17788) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17786)),U_17787) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17788)),U_17789) ),
    inference(variable_rename,[status(thm)],[f_4348_1]) ).

fof(f_4348_3,plain,
    ( ! [U_17786,U_17788,U_17787,U_17789,U_17790] :
        ( hAPP(c_Map_Omap__of(U_17786,U_17788,hAPP(hAPP(c_List_Ozip(U_17786,U_17788),U_17787),U_17789)),U_17790) = c_Option_Ooption_ONone(U_17788)
        | hBOOL(hAPP(hAPP(c_member(U_17786),U_17790),hAPP(c_List_Oset(U_17786),U_17787)))
        | ~ sP1133(U_17786,U_17788,U_17787,U_17789,U_17790) )
    & ! [U_17786,U_17788,U_17787,U_17789,U_17790] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17786),U_17790),hAPP(c_List_Oset(U_17786),U_17787)))
        | hAPP(c_Map_Omap__of(U_17786,U_17788,hAPP(hAPP(c_List_Ozip(U_17786,U_17788),U_17787),U_17789)),U_17790) != c_Option_Ooption_ONone(U_17788)
        | ~ sP1133(U_17786,U_17788,U_17787,U_17789,U_17790) )
    & ! [U_17786,U_17788,U_17787,U_17789,U_17790] :
        ( sP1133(U_17786,U_17788,U_17787,U_17789,U_17790)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17786)),U_17787) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17788)),U_17789) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1133])],[f_4348_2]) ).

cnf(f_4348_4,plain,
    ( sP1133(U_17786,U_17788,U_17787,U_17789,U_17790)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17786)),U_17787) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17788)),U_17789) ),
    inference(clausify,[status(thm)],[f_4348_3]) ).

cnf(f_4348_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17786),U_17790),hAPP(c_List_Oset(U_17786),U_17787)))
    | hAPP(c_Map_Omap__of(U_17786,U_17788,hAPP(hAPP(c_List_Ozip(U_17786,U_17788),U_17787),U_17789)),U_17790) != c_Option_Ooption_ONone(U_17788)
    | ~ sP1133(U_17786,U_17788,U_17787,U_17789,U_17790) ),
    inference(clausify,[status(thm)],[f_4348_3]) ).

cnf(f_4348_6,plain,
    ( hAPP(c_Map_Omap__of(U_17786,U_17788,hAPP(hAPP(c_List_Ozip(U_17786,U_17788),U_17787),U_17789)),U_17790) = c_Option_Ooption_ONone(U_17788)
    | hBOOL(hAPP(hAPP(c_member(U_17786),U_17790),hAPP(c_List_Oset(U_17786),U_17787)))
    | ~ sP1133(U_17786,U_17788,U_17787,U_17789,U_17790) ),
    inference(clausify,[status(thm)],[f_4348_3]) ).

fof(f_4349_1,plain,
    ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
          | ! [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) != hAPP(c_Option_Ooption_OSome(T_c),B_y) )
        & ( ? [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__Some]) ).

fof(f_4349_2,plain,
    ! [U_17797,U_17796,U_17795,U_17794,U_17793] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794)))
          | ! [U_17792] : hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) != hAPP(c_Option_Ooption_OSome(U_17795),U_17792) )
        & ( ? [U_17791] : hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) = hAPP(c_Option_Ooption_OSome(U_17795),U_17791)
          | ~ hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17793)),U_17794) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)),U_17796) ),
    inference(variable_rename,[status(thm)],[f_4349_1]) ).

fof(f_4349_3,plain,
    ! [U_17797,U_17796,U_17795,U_17794,U_17793] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794)))
          | ! [U_17792] : hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) != hAPP(c_Option_Ooption_OSome(U_17795),U_17792) )
        & ( hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) = hAPP(c_Option_Ooption_OSome(U_17795),sK454(U_17797,U_17796,U_17795,U_17794,U_17793))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17793)),U_17794) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)),U_17796) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_17791,sK454(U_17797,U_17796,U_17795,U_17794,U_17793))],[f_4349_2]) ).

fof(f_4349_4,plain,
    ( ! [U_17794,U_17792,U_17793,U_17795,U_17796,U_17797] :
        ( hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794)))
        | hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) != hAPP(c_Option_Ooption_OSome(U_17795),U_17792)
        | ~ sP1134(U_17794,U_17792,U_17793,U_17795,U_17796,U_17797) )
    & ! [U_17794,U_17792,U_17793,U_17795,U_17796,U_17797] :
        ( hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) = hAPP(c_Option_Ooption_OSome(U_17795),sK454(U_17797,U_17796,U_17795,U_17794,U_17793))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794)))
        | ~ sP1134(U_17794,U_17792,U_17793,U_17795,U_17796,U_17797) )
    & ! [U_17794,U_17792,U_17793,U_17795,U_17796,U_17797] :
        ( sP1134(U_17794,U_17792,U_17793,U_17795,U_17796,U_17797)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17793)),U_17794) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)),U_17796) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1134])],[f_4349_3]) ).

cnf(f_4349_5,plain,
    ( sP1134(U_17794,U_17792,U_17793,U_17795,U_17796,U_17797)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17793)),U_17794) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)),U_17796) ),
    inference(clausify,[status(thm)],[f_4349_4]) ).

cnf(f_4349_6,plain,
    ( hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) = hAPP(c_Option_Ooption_OSome(U_17795),sK454(U_17797,U_17796,U_17795,U_17794,U_17793))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794)))
    | ~ sP1134(U_17794,U_17792,U_17793,U_17795,U_17796,U_17797) ),
    inference(clausify,[status(thm)],[f_4349_4]) ).

cnf(f_4349_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17793),U_17797),hAPP(c_List_Oset(U_17793),U_17794)))
    | hAPP(c_Map_Omap__of(U_17793,U_17795,hAPP(hAPP(c_List_Ozip(U_17793,U_17795),U_17794),U_17796)),U_17797) != hAPP(c_Option_Ooption_OSome(U_17795),U_17792)
    | ~ sP1134(U_17794,U_17792,U_17793,U_17795,U_17796,U_17797) ),
    inference(clausify,[status(thm)],[f_4349_4]) ).

fof(f_4350_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remove1]) ).

fof(f_4350_2,plain,
    ! [U_17800,U_17799,U_17798] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17798)),c_List_Oremove1(U_17798,U_17799,U_17800)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17798)),U_17800)
        | hBOOL(hAPP(hAPP(c_member(U_17798),U_17799),hAPP(c_List_Oset(U_17798),U_17800))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17798)),c_List_Oremove1(U_17798,U_17799,U_17800)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17798)),U_17800)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17798),U_17799),hAPP(c_List_Oset(U_17798),U_17800))) ) ),
    inference(variable_rename,[status(thm)],[f_4350_1]) ).

fof(f_4350_3,plain,
    ( ! [U_17806,U_17804,U_17802] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17802)),c_List_Oremove1(U_17802,U_17804,U_17806)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17802)),U_17806)
        | hBOOL(hAPP(hAPP(c_member(U_17802),U_17804),hAPP(c_List_Oset(U_17802),U_17806))) )
    & ! [U_17805,U_17803,U_17801] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17801)),c_List_Oremove1(U_17801,U_17803,U_17805)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17801)),U_17805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17801),U_17803),hAPP(c_List_Oset(U_17801),U_17805))) ) ),
    inference(miniscope,[status(thm)],[f_4350_2]) ).

fof(f_4350_4,plain,
    ( ! [U_17802,U_17804,U_17806] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17802)),c_List_Oremove1(U_17802,U_17804,U_17806)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17802)),U_17806)
        | hBOOL(hAPP(hAPP(c_member(U_17802),U_17804),hAPP(c_List_Oset(U_17802),U_17806))) )
    & ! [U_17801,U_17805,U_17803] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17801)),c_List_Oremove1(U_17801,U_17803,U_17805)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17801)),U_17805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17801),U_17803),hAPP(c_List_Oset(U_17801),U_17805))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4350_3]) ).

cnf(f_4350_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17801)),c_List_Oremove1(U_17801,U_17803,U_17805)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17801)),U_17805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17801),U_17803),hAPP(c_List_Oset(U_17801),U_17805))) ),
    inference(clausify,[status(thm)],[f_4350_4]) ).

cnf(f_4350_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17802)),c_List_Oremove1(U_17802,U_17804,U_17806)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17802)),U_17806)
    | hBOOL(hAPP(hAPP(c_member(U_17802),U_17804),hAPP(c_List_Oset(U_17802),U_17806))) ),
    inference(clausify,[status(thm)],[f_4350_4]) ).

fof(f_4351_1,plain,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_dom__map__of__zip]) ).

fof(f_4351_2,plain,
    ! [U_17810,U_17809,U_17808,U_17807] :
      ( c_Map_Odom(U_17807,U_17809,c_Map_Omap__of(U_17807,U_17809,hAPP(hAPP(c_List_Ozip(U_17807,U_17809),U_17808),U_17810))) = hAPP(c_List_Oset(U_17807),U_17808)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17807),U_17808))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17807)),U_17808) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17809)),U_17810) ),
    inference(variable_rename,[status(thm)],[f_4351_1]) ).

fof(f_4351_3,plain,
    ! [U_17807,U_17808,U_17809,U_17810] :
      ( c_Map_Odom(U_17807,U_17809,c_Map_Omap__of(U_17807,U_17809,hAPP(hAPP(c_List_Ozip(U_17807,U_17809),U_17808),U_17810))) = hAPP(c_List_Oset(U_17807),U_17808)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17807),U_17808))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17807)),U_17808) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17809)),U_17810) ),
    inference(definitional_conversion,[status(esa)],[f_4351_2]) ).

cnf(f_4351_4,plain,
    ( c_Map_Odom(U_17807,U_17809,c_Map_Omap__of(U_17807,U_17809,hAPP(hAPP(c_List_Ozip(U_17807,U_17809),U_17808),U_17810))) = hAPP(c_List_Oset(U_17807),U_17808)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17807),U_17808))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17807)),U_17808) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17809)),U_17810) ),
    inference(clausify,[status(thm)],[f_4351_3]) ).

fof(f_4352_1,plain,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le]) ).

fof(f_4352_2,plain,
    ! [U_17813,U_17812,U_17811] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17811)),hAPP(c_Set_OCollect(tc_List_Olist(U_17811)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17811),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17811)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17811),tc_fun(U_17811,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17811,tc_HOL_Obool),tc_fun(tc_fun(U_17811,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17811)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17811,tc_HOL_Obool))),c_List_Oset(U_17811))),U_17812))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17811),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17811)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17811)))),U_17813)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17811),U_17812)) ),
    inference(variable_rename,[status(thm)],[f_4352_1]) ).

fof(f_4352_3,plain,
    ! [U_17811,U_17812,U_17813] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17811)),hAPP(c_Set_OCollect(tc_List_Olist(U_17811)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17811),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17811)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17811),tc_fun(U_17811,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17811,tc_HOL_Obool),tc_fun(tc_fun(U_17811,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17811)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17811,tc_HOL_Obool))),c_List_Oset(U_17811))),U_17812))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17811),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17811)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17811)))),U_17813)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17811),U_17812)) ),
    inference(definitional_conversion,[status(esa)],[f_4352_2]) ).

cnf(f_4352_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17811)),hAPP(c_Set_OCollect(tc_List_Olist(U_17811)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17811),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17811)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17811),tc_fun(U_17811,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17811,tc_HOL_Obool),tc_fun(tc_fun(U_17811,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17811)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17811,tc_HOL_Obool))),c_List_Oset(U_17811))),U_17812))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17811),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17811)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17811)))),U_17813)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17811),U_17812)) ),
    inference(clausify,[status(thm)],[f_4352_3]) ).

fof(f_4353_1,plain,
    ! [V_A_2,T_b] :
      ( ( c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(f_4353_2,plain,
    ! [U_17815,U_17814] :
      ( ( c_Nitpick_Ocard_H(U_17814,U_17815) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17814),U_17815)) )
      & ( c_Nitpick_Ocard_H(U_17814,U_17815) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17814)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17814),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17814),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17814)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17814),tc_fun(U_17814,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17814,tc_HOL_Obool),tc_fun(tc_fun(U_17814,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17814)),c_fequal),c_List_Oset(U_17814))),U_17815))),c_List_Odistinct(U_17814))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17814),U_17815)) ) ),
    inference(variable_rename,[status(thm)],[f_4353_1]) ).

fof(f_4353_3,plain,
    ( ! [U_17819,U_17817] :
        ( c_Nitpick_Ocard_H(U_17817,U_17819) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17817),U_17819)) )
    & ! [U_17818,U_17816] :
        ( c_Nitpick_Ocard_H(U_17816,U_17818) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17816)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17816),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17816),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17816)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17816),tc_fun(U_17816,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17816,tc_HOL_Obool),tc_fun(tc_fun(U_17816,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17816)),c_fequal),c_List_Oset(U_17816))),U_17818))),c_List_Odistinct(U_17816))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17816),U_17818)) ) ),
    inference(miniscope,[status(thm)],[f_4353_2]) ).

fof(f_4353_4,plain,
    ( ! [U_17817,U_17819] :
        ( c_Nitpick_Ocard_H(U_17817,U_17819) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17817),U_17819)) )
    & ! [U_17818,U_17816] :
        ( c_Nitpick_Ocard_H(U_17816,U_17818) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17816)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17816),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17816),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17816)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17816),tc_fun(U_17816,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17816,tc_HOL_Obool),tc_fun(tc_fun(U_17816,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17816)),c_fequal),c_List_Oset(U_17816))),U_17818))),c_List_Odistinct(U_17816))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17816),U_17818)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4353_3]) ).

cnf(f_4353_5,plain,
    ( c_Nitpick_Ocard_H(U_17816,U_17818) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17816)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17816),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17816),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17816)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17816),tc_fun(U_17816,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17816,tc_HOL_Obool),tc_fun(tc_fun(U_17816,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17816)),c_fequal),c_List_Oset(U_17816))),U_17818))),c_List_Odistinct(U_17816))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17816),U_17818)) ),
    inference(clausify,[status(thm)],[f_4353_4]) ).

cnf(f_4353_6,plain,
    ( c_Nitpick_Ocard_H(U_17817,U_17819) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17817),U_17819)) ),
    inference(clausify,[status(thm)],[f_4353_4]) ).

fof(f_4354_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__iff__zip]) ).

fof(f_4354_2,plain,
    ! [U_17825,U_17824,U_17823,U_17822] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17822),tc_List_Olist(U_17822))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17822),tc_List_Olist(U_17822)),U_17823),U_17824)),c_List_Olistrel(U_17822,U_17825)))
        | ? [U_17821] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17822,U_17822,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17822,tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_fun(U_17822,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17822,tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_fun(U_17822,tc_HOL_Obool)),U_17822),c_COMBC(U_17822,tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17822,tc_prod(U_17822,U_17822)),tc_fun(U_17822,tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool)),U_17822),hAPP(c_COMBB(tc_prod(U_17822,U_17822),tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool),U_17822),c_member(tc_prod(U_17822,U_17822)))),c_Product__Type_OPair(U_17822,U_17822)))),U_17825)),U_17821))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17822,U_17822)),U_17821),hAPP(c_List_Oset(tc_prod(U_17822,U_17822)),hAPP(hAPP(c_List_Ozip(U_17822,U_17822),U_17823),U_17824)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17822)),U_17823) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17822)),U_17824) )
      & ( ( ! [U_17820] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17822,U_17822,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17822,tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_fun(U_17822,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17822,tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_fun(U_17822,tc_HOL_Obool)),U_17822),c_COMBC(U_17822,tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17822,tc_prod(U_17822,U_17822)),tc_fun(U_17822,tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool)),U_17822),hAPP(c_COMBB(tc_prod(U_17822,U_17822),tc_fun(tc_fun(tc_prod(U_17822,U_17822),tc_HOL_Obool),tc_HOL_Obool),U_17822),c_member(tc_prod(U_17822,U_17822)))),c_Product__Type_OPair(U_17822,U_17822)))),U_17825)),U_17820))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17822,U_17822)),U_17820),hAPP(c_List_Oset(tc_prod(U_17822,U_17822)),hAPP(hAPP(c_List_Ozip(U_17822,U_17822),U_17823),U_17824)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17822)),U_17823) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17822)),U_17824) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17822),tc_List_Olist(U_17822))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17822),tc_List_Olist(U_17822)),U_17823),U_17824)),c_List_Olistrel(U_17822,U_17825))) ) ),
    inference(variable_rename,[status(thm)],[f_4354_1]) ).

fof(f_4354_3,plain,
    ( ! [U_17833,U_17831,U_17829,U_17827] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17827),tc_List_Olist(U_17827))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17827),tc_List_Olist(U_17827)),U_17829),U_17831)),c_List_Olistrel(U_17827,U_17833)))
        | ? [U_17821] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17827,U_17827,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),U_17827),c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_prod(U_17827,U_17827)),tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),U_17827),hAPP(c_COMBB(tc_prod(U_17827,U_17827),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool),U_17827),c_member(tc_prod(U_17827,U_17827)))),c_Product__Type_OPair(U_17827,U_17827)))),U_17833)),U_17821))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17827,U_17827)),U_17821),hAPP(c_List_Oset(tc_prod(U_17827,U_17827)),hAPP(hAPP(c_List_Ozip(U_17827,U_17827),U_17829),U_17831)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17829) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17831) )
    & ! [U_17832,U_17830,U_17828,U_17826] :
        ( ( ! [U_17820] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17826,U_17826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),U_17826),c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_prod(U_17826,U_17826)),tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),U_17826),hAPP(c_COMBB(tc_prod(U_17826,U_17826),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool),U_17826),c_member(tc_prod(U_17826,U_17826)))),c_Product__Type_OPair(U_17826,U_17826)))),U_17832)),U_17820))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17826,U_17826)),U_17820),hAPP(c_List_Oset(tc_prod(U_17826,U_17826)),hAPP(hAPP(c_List_Ozip(U_17826,U_17826),U_17828),U_17830)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17828) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17830) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17826),tc_List_Olist(U_17826))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17826),tc_List_Olist(U_17826)),U_17828),U_17830)),c_List_Olistrel(U_17826,U_17832))) ) ),
    inference(miniscope,[status(thm)],[f_4354_2]) ).

fof(f_4354_4,plain,
    ( ! [U_17833,U_17831,U_17829,U_17827] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17827),tc_List_Olist(U_17827))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17827),tc_List_Olist(U_17827)),U_17829),U_17831)),c_List_Olistrel(U_17827,U_17833)))
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17827,U_17827,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),U_17827),c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_prod(U_17827,U_17827)),tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),U_17827),hAPP(c_COMBB(tc_prod(U_17827,U_17827),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool),U_17827),c_member(tc_prod(U_17827,U_17827)))),c_Product__Type_OPair(U_17827,U_17827)))),U_17833)),sK455(U_17833,U_17831,U_17829,U_17827)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17827,U_17827)),sK455(U_17833,U_17831,U_17829,U_17827)),hAPP(c_List_Oset(tc_prod(U_17827,U_17827)),hAPP(hAPP(c_List_Ozip(U_17827,U_17827),U_17829),U_17831)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17829) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17831) )
    & ! [U_17832,U_17830,U_17828,U_17826] :
        ( ( ! [U_17820] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17826,U_17826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),U_17826),c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_prod(U_17826,U_17826)),tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),U_17826),hAPP(c_COMBB(tc_prod(U_17826,U_17826),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool),U_17826),c_member(tc_prod(U_17826,U_17826)))),c_Product__Type_OPair(U_17826,U_17826)))),U_17832)),U_17820))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17826,U_17826)),U_17820),hAPP(c_List_Oset(tc_prod(U_17826,U_17826)),hAPP(hAPP(c_List_Ozip(U_17826,U_17826),U_17828),U_17830)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17828) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17830) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17826),tc_List_Olist(U_17826))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17826),tc_List_Olist(U_17826)),U_17828),U_17830)),c_List_Olistrel(U_17826,U_17832))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_17821,sK455(U_17833,U_17831,U_17829,U_17827))],[f_4354_3]) ).

fof(f_4354_5,plain,
    ( ! [U_17831,U_17829,U_17827,U_17833] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17827,U_17827,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),U_17827),c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_prod(U_17827,U_17827)),tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),U_17827),hAPP(c_COMBB(tc_prod(U_17827,U_17827),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool),U_17827),c_member(tc_prod(U_17827,U_17827)))),c_Product__Type_OPair(U_17827,U_17827)))),U_17833)),sK455(U_17833,U_17831,U_17829,U_17827)))
        | ~ sP1136(U_17831,U_17829,U_17827,U_17833) )
    & ! [U_17831,U_17829,U_17827,U_17833] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17827,U_17827)),sK455(U_17833,U_17831,U_17829,U_17827)),hAPP(c_List_Oset(tc_prod(U_17827,U_17827)),hAPP(hAPP(c_List_Ozip(U_17827,U_17827),U_17829),U_17831))))
        | ~ sP1136(U_17831,U_17829,U_17827,U_17833) )
    & ! [U_17820,U_17828,U_17826,U_17830,U_17832] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17826,U_17826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),U_17826),c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_prod(U_17826,U_17826)),tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),U_17826),hAPP(c_COMBB(tc_prod(U_17826,U_17826),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool),U_17826),c_member(tc_prod(U_17826,U_17826)))),c_Product__Type_OPair(U_17826,U_17826)))),U_17832)),U_17820))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17826,U_17826)),U_17820),hAPP(c_List_Oset(tc_prod(U_17826,U_17826)),hAPP(hAPP(c_List_Ozip(U_17826,U_17826),U_17828),U_17830))))
        | ~ sP1135(U_17820,U_17828,U_17826,U_17830,U_17832) )
    & ! [U_17820,U_17828,U_17826,U_17830,U_17832] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17828) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17830)
        | ~ sP1135(U_17820,U_17828,U_17826,U_17830,U_17832) )
    & ! [U_17831,U_17829,U_17827,U_17833] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17827),tc_List_Olist(U_17827))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17827),tc_List_Olist(U_17827)),U_17829),U_17831)),c_List_Olistrel(U_17827,U_17833)))
        | sP1136(U_17831,U_17829,U_17827,U_17833)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17829) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17831) )
    & ! [U_17820,U_17828,U_17826,U_17830,U_17832] :
        ( sP1135(U_17820,U_17828,U_17826,U_17830,U_17832)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17826),tc_List_Olist(U_17826))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17826),tc_List_Olist(U_17826)),U_17828),U_17830)),c_List_Olistrel(U_17826,U_17832))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1135,sP1136])],[f_4354_4]) ).

cnf(f_4354_6,plain,
    ( sP1135(U_17820,U_17828,U_17826,U_17830,U_17832)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17826),tc_List_Olist(U_17826))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17826),tc_List_Olist(U_17826)),U_17828),U_17830)),c_List_Olistrel(U_17826,U_17832))) ),
    inference(clausify,[status(thm)],[f_4354_5]) ).

cnf(f_4354_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17827),tc_List_Olist(U_17827))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17827),tc_List_Olist(U_17827)),U_17829),U_17831)),c_List_Olistrel(U_17827,U_17833)))
    | sP1136(U_17831,U_17829,U_17827,U_17833)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17829) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17827)),U_17831) ),
    inference(clausify,[status(thm)],[f_4354_5]) ).

cnf(f_4354_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17828) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17830)
    | ~ sP1135(U_17820,U_17828,U_17826,U_17830,U_17832) ),
    inference(clausify,[status(thm)],[f_4354_5]) ).

cnf(f_4354_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17826,U_17826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_fun(U_17826,tc_HOL_Obool)),U_17826),c_COMBC(U_17826,tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17826,tc_prod(U_17826,U_17826)),tc_fun(U_17826,tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool)),U_17826),hAPP(c_COMBB(tc_prod(U_17826,U_17826),tc_fun(tc_fun(tc_prod(U_17826,U_17826),tc_HOL_Obool),tc_HOL_Obool),U_17826),c_member(tc_prod(U_17826,U_17826)))),c_Product__Type_OPair(U_17826,U_17826)))),U_17832)),U_17820))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17826,U_17826)),U_17820),hAPP(c_List_Oset(tc_prod(U_17826,U_17826)),hAPP(hAPP(c_List_Ozip(U_17826,U_17826),U_17828),U_17830))))
    | ~ sP1135(U_17820,U_17828,U_17826,U_17830,U_17832) ),
    inference(clausify,[status(thm)],[f_4354_5]) ).

cnf(f_4354_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17827,U_17827)),sK455(U_17833,U_17831,U_17829,U_17827)),hAPP(c_List_Oset(tc_prod(U_17827,U_17827)),hAPP(hAPP(c_List_Ozip(U_17827,U_17827),U_17829),U_17831))))
    | ~ sP1136(U_17831,U_17829,U_17827,U_17833) ),
    inference(clausify,[status(thm)],[f_4354_5]) ).

cnf(f_4354_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17827,U_17827,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_fun(U_17827,tc_HOL_Obool)),U_17827),c_COMBC(U_17827,tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17827,tc_prod(U_17827,U_17827)),tc_fun(U_17827,tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool)),U_17827),hAPP(c_COMBB(tc_prod(U_17827,U_17827),tc_fun(tc_fun(tc_prod(U_17827,U_17827),tc_HOL_Obool),tc_HOL_Obool),U_17827),c_member(tc_prod(U_17827,U_17827)))),c_Product__Type_OPair(U_17827,U_17827)))),U_17833)),sK455(U_17833,U_17831,U_17829,U_17827)))
    | ~ sP1136(U_17831,U_17829,U_17827,U_17833) ),
    inference(clausify,[status(thm)],[f_4354_5]) ).

fof(f_4355_1,plain,
    ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__refl]) ).

fof(f_4355_2,plain,
    ! [U_17836,U_17835,U_17834] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17834),tc_List_Olist(U_17834))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17834),tc_List_Olist(U_17834)),U_17835),U_17835)),c_List_Olistrel(U_17834,c_Transitive__Closure_Ortrancl(U_17834,U_17836)))),
    inference(variable_rename,[status(thm)],[f_4355_1]) ).

fof(f_4355_3,plain,
    ! [U_17834,U_17835,U_17836] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17834),tc_List_Olist(U_17834))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17834),tc_List_Olist(U_17834)),U_17835),U_17835)),c_List_Olistrel(U_17834,c_Transitive__Closure_Ortrancl(U_17834,U_17836)))),
    inference(definitional_conversion,[status(esa)],[f_4355_2]) ).

cnf(f_4355_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17834),tc_List_Olist(U_17834))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17834),tc_List_Olist(U_17834)),U_17835),U_17835)),c_List_Olistrel(U_17834,c_Transitive__Closure_Ortrancl(U_17834,U_17836)))),
    inference(clausify,[status(thm)],[f_4355_3]) ).

fof(f_4356_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__eq__len]) ).

fof(f_4356_2,plain,
    ! [U_17840,U_17839,U_17838,U_17837] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17837)),U_17838) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17837)),U_17839)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17837),tc_List_Olist(U_17837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17837),tc_List_Olist(U_17837)),U_17838),U_17839)),c_List_Olistrel(U_17837,U_17840))) ),
    inference(variable_rename,[status(thm)],[f_4356_1]) ).

fof(f_4356_3,plain,
    ! [U_17837,U_17838,U_17839,U_17840] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17837)),U_17838) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17837)),U_17839)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17837),tc_List_Olist(U_17837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17837),tc_List_Olist(U_17837)),U_17838),U_17839)),c_List_Olistrel(U_17837,U_17840))) ),
    inference(definitional_conversion,[status(esa)],[f_4356_2]) ).

cnf(f_4356_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17837)),U_17838) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17837)),U_17839)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17837),tc_List_Olist(U_17837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17837),tc_List_Olist(U_17837)),U_17838),U_17839)),c_List_Olistrel(U_17837,U_17840))) ),
    inference(clausify,[status(thm)],[f_4356_3]) ).

fof(f_4357_1,plain,
    ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans]) ).

fof(f_4357_2,plain,
    ! [U_17845,U_17844,U_17843,U_17842,U_17841] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17842),U_17845)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17843),U_17845)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17842),U_17843)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844)))) ),
    inference(variable_rename,[status(thm)],[f_4357_1]) ).

fof(f_4357_3,plain,
    ! [U_17841,U_17842,U_17843,U_17844,U_17845] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17842),U_17845)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17843),U_17845)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17842),U_17843)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844)))) ),
    inference(definitional_conversion,[status(esa)],[f_4357_2]) ).

cnf(f_4357_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17842),U_17845)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17843),U_17845)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17841),tc_List_Olist(U_17841))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17841),tc_List_Olist(U_17841)),U_17842),U_17843)),c_List_Olistrel(U_17841,c_Transitive__Closure_Ortrancl(U_17841,U_17844)))) ),
    inference(clausify,[status(thm)],[f_4357_3]) ).

fof(f_4358_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__mono]) ).

fof(f_4358_2,plain,
    ! [U_17848,U_17847,U_17846] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_17846),tc_List_Olist(U_17846)),tc_HOL_Obool)),c_List_Olistrel(U_17846,U_17847)),c_List_Olistrel(U_17846,U_17848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_17846,U_17846),tc_HOL_Obool)),U_17847),U_17848)) ),
    inference(variable_rename,[status(thm)],[f_4358_1]) ).

fof(f_4358_3,plain,
    ! [U_17846,U_17847,U_17848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_17846),tc_List_Olist(U_17846)),tc_HOL_Obool)),c_List_Olistrel(U_17846,U_17847)),c_List_Olistrel(U_17846,U_17848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_17846,U_17846),tc_HOL_Obool)),U_17847),U_17848)) ),
    inference(definitional_conversion,[status(esa)],[f_4358_2]) ).

cnf(f_4358_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_17846),tc_List_Olist(U_17846)),tc_HOL_Obool)),c_List_Olistrel(U_17846,U_17847)),c_List_Olistrel(U_17846,U_17848)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_17846,U_17846),tc_HOL_Obool)),U_17847),U_17848)) ),
    inference(clausify,[status(thm)],[f_4358_3]) ).

fof(f_4359_1,plain,
    ! [V_xa_2,V_x_2,V_r_2,T_b] :
      ( ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2)))
        | ~ c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq]) ).

fof(f_4359_2,plain,
    ! [U_17852,U_17851,U_17850,U_17849] :
      ( ( c_List_Olistrelp(U_17849,hAPP(hAPP(c_COMBC(U_17849,tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_fun(U_17849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17849,tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_fun(U_17849,tc_HOL_Obool)),U_17849),c_COMBC(U_17849,tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17849,tc_prod(U_17849,U_17849)),tc_fun(U_17849,tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool)),U_17849),hAPP(c_COMBB(tc_prod(U_17849,U_17849),tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool),U_17849),c_member(tc_prod(U_17849,U_17849)))),c_Product__Type_OPair(U_17849,U_17849)))),U_17850),U_17851,U_17852)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17849),tc_List_Olist(U_17849))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17849),tc_List_Olist(U_17849)),U_17851),U_17852)),c_List_Olistrel(U_17849,U_17850))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17849),tc_List_Olist(U_17849))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17849),tc_List_Olist(U_17849)),U_17851),U_17852)),c_List_Olistrel(U_17849,U_17850)))
        | ~ c_List_Olistrelp(U_17849,hAPP(hAPP(c_COMBC(U_17849,tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_fun(U_17849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17849,tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_fun(U_17849,tc_HOL_Obool)),U_17849),c_COMBC(U_17849,tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17849,tc_prod(U_17849,U_17849)),tc_fun(U_17849,tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool)),U_17849),hAPP(c_COMBB(tc_prod(U_17849,U_17849),tc_fun(tc_fun(tc_prod(U_17849,U_17849),tc_HOL_Obool),tc_HOL_Obool),U_17849),c_member(tc_prod(U_17849,U_17849)))),c_Product__Type_OPair(U_17849,U_17849)))),U_17850),U_17851,U_17852) ) ),
    inference(variable_rename,[status(thm)],[f_4359_1]) ).

fof(f_4359_3,plain,
    ( ! [U_17860,U_17858,U_17856,U_17854] :
        ( c_List_Olistrelp(U_17854,hAPP(hAPP(c_COMBC(U_17854,tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_fun(U_17854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17854,tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_fun(U_17854,tc_HOL_Obool)),U_17854),c_COMBC(U_17854,tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17854,tc_prod(U_17854,U_17854)),tc_fun(U_17854,tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),U_17854),hAPP(c_COMBB(tc_prod(U_17854,U_17854),tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool),U_17854),c_member(tc_prod(U_17854,U_17854)))),c_Product__Type_OPair(U_17854,U_17854)))),U_17856),U_17858,U_17860)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17854),tc_List_Olist(U_17854))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17854),tc_List_Olist(U_17854)),U_17858),U_17860)),c_List_Olistrel(U_17854,U_17856))) )
    & ! [U_17859,U_17857,U_17855,U_17853] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17853),tc_List_Olist(U_17853))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17853),tc_List_Olist(U_17853)),U_17857),U_17859)),c_List_Olistrel(U_17853,U_17855)))
        | ~ c_List_Olistrelp(U_17853,hAPP(hAPP(c_COMBC(U_17853,tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_fun(U_17853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17853,tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_fun(U_17853,tc_HOL_Obool)),U_17853),c_COMBC(U_17853,tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17853,tc_prod(U_17853,U_17853)),tc_fun(U_17853,tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),U_17853),hAPP(c_COMBB(tc_prod(U_17853,U_17853),tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool),U_17853),c_member(tc_prod(U_17853,U_17853)))),c_Product__Type_OPair(U_17853,U_17853)))),U_17855),U_17857,U_17859) ) ),
    inference(miniscope,[status(thm)],[f_4359_2]) ).

fof(f_4359_4,plain,
    ( ! [U_17856,U_17854,U_17858,U_17860] :
        ( c_List_Olistrelp(U_17854,hAPP(hAPP(c_COMBC(U_17854,tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_fun(U_17854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17854,tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_fun(U_17854,tc_HOL_Obool)),U_17854),c_COMBC(U_17854,tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17854,tc_prod(U_17854,U_17854)),tc_fun(U_17854,tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),U_17854),hAPP(c_COMBB(tc_prod(U_17854,U_17854),tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool),U_17854),c_member(tc_prod(U_17854,U_17854)))),c_Product__Type_OPair(U_17854,U_17854)))),U_17856),U_17858,U_17860)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17854),tc_List_Olist(U_17854))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17854),tc_List_Olist(U_17854)),U_17858),U_17860)),c_List_Olistrel(U_17854,U_17856))) )
    & ! [U_17855,U_17853,U_17857,U_17859] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17853),tc_List_Olist(U_17853))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17853),tc_List_Olist(U_17853)),U_17857),U_17859)),c_List_Olistrel(U_17853,U_17855)))
        | ~ c_List_Olistrelp(U_17853,hAPP(hAPP(c_COMBC(U_17853,tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_fun(U_17853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17853,tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_fun(U_17853,tc_HOL_Obool)),U_17853),c_COMBC(U_17853,tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17853,tc_prod(U_17853,U_17853)),tc_fun(U_17853,tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),U_17853),hAPP(c_COMBB(tc_prod(U_17853,U_17853),tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool),U_17853),c_member(tc_prod(U_17853,U_17853)))),c_Product__Type_OPair(U_17853,U_17853)))),U_17855),U_17857,U_17859) ) ),
    inference(definitional_conversion,[status(esa)],[f_4359_3]) ).

cnf(f_4359_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17853),tc_List_Olist(U_17853))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17853),tc_List_Olist(U_17853)),U_17857),U_17859)),c_List_Olistrel(U_17853,U_17855)))
    | ~ c_List_Olistrelp(U_17853,hAPP(hAPP(c_COMBC(U_17853,tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_fun(U_17853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17853,tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_fun(U_17853,tc_HOL_Obool)),U_17853),c_COMBC(U_17853,tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17853,tc_prod(U_17853,U_17853)),tc_fun(U_17853,tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool)),U_17853),hAPP(c_COMBB(tc_prod(U_17853,U_17853),tc_fun(tc_fun(tc_prod(U_17853,U_17853),tc_HOL_Obool),tc_HOL_Obool),U_17853),c_member(tc_prod(U_17853,U_17853)))),c_Product__Type_OPair(U_17853,U_17853)))),U_17855),U_17857,U_17859) ),
    inference(clausify,[status(thm)],[f_4359_4]) ).

cnf(f_4359_6,plain,
    ( c_List_Olistrelp(U_17854,hAPP(hAPP(c_COMBC(U_17854,tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_fun(U_17854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17854,tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_fun(U_17854,tc_HOL_Obool)),U_17854),c_COMBC(U_17854,tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17854,tc_prod(U_17854,U_17854)),tc_fun(U_17854,tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool)),U_17854),hAPP(c_COMBB(tc_prod(U_17854,U_17854),tc_fun(tc_fun(tc_prod(U_17854,U_17854),tc_HOL_Obool),tc_HOL_Obool),U_17854),c_member(tc_prod(U_17854,U_17854)))),c_Product__Type_OPair(U_17854,U_17854)))),U_17856),U_17858,U_17860)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17854),tc_List_Olist(U_17854))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17854),tc_List_Olist(U_17854)),U_17858),U_17860)),c_List_Olistrel(U_17854,U_17856))) ),
    inference(clausify,[status(thm)],[f_4359_4]) ).

fof(f_4360_1,plain,
    ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))),
    inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

fof(f_4360_2,plain,
    ! [U_17863,U_17862,U_17861] : hAPP(c_List_Olexn(U_17861,U_17862),hAPP(c_Nat_OSuc,U_17863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_17861,tc_List_Olist(U_17861)),tc_prod(U_17861,tc_List_Olist(U_17861))),tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_Product__Type_Omap__pair(tc_prod(U_17861,tc_List_Olist(U_17861)),tc_List_Olist(U_17861),tc_prod(U_17861,tc_List_Olist(U_17861)),tc_List_Olist(U_17861),hAPP(c_Product__Type_Oprod_Oprod__case(U_17861,tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_List_Olist_OCons(U_17861)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17861,tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_List_Olist_OCons(U_17861)))),c_Wellfounded_Olex__prod(U_17861,tc_List_Olist(U_17861),U_17862,hAPP(c_List_Olexn(U_17861,U_17862),U_17863)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17861),tc_List_Olist(U_17861),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool)),tc_List_Olist(U_17861)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17861))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17861)))),hAPP(c_Nat_OSuc,U_17863))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17861)))),hAPP(c_Nat_OSuc,U_17863)))))),
    inference(variable_rename,[status(thm)],[f_4360_1]) ).

fof(f_4360_3,plain,
    ! [U_17861,U_17862,U_17863] : hAPP(c_List_Olexn(U_17861,U_17862),hAPP(c_Nat_OSuc,U_17863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_17861,tc_List_Olist(U_17861)),tc_prod(U_17861,tc_List_Olist(U_17861))),tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_Product__Type_Omap__pair(tc_prod(U_17861,tc_List_Olist(U_17861)),tc_List_Olist(U_17861),tc_prod(U_17861,tc_List_Olist(U_17861)),tc_List_Olist(U_17861),hAPP(c_Product__Type_Oprod_Oprod__case(U_17861,tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_List_Olist_OCons(U_17861)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17861,tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_List_Olist_OCons(U_17861)))),c_Wellfounded_Olex__prod(U_17861,tc_List_Olist(U_17861),U_17862,hAPP(c_List_Olexn(U_17861,U_17862),U_17863)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17861),tc_List_Olist(U_17861),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool)),tc_List_Olist(U_17861)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17861))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17861)))),hAPP(c_Nat_OSuc,U_17863))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17861)))),hAPP(c_Nat_OSuc,U_17863)))))),
    inference(definitional_conversion,[status(esa)],[f_4360_2]) ).

cnf(f_4360_4,plain,
    hAPP(c_List_Olexn(U_17861,U_17862),hAPP(c_Nat_OSuc,U_17863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_17861,tc_List_Olist(U_17861)),tc_prod(U_17861,tc_List_Olist(U_17861))),tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_Product__Type_Omap__pair(tc_prod(U_17861,tc_List_Olist(U_17861)),tc_List_Olist(U_17861),tc_prod(U_17861,tc_List_Olist(U_17861)),tc_List_Olist(U_17861),hAPP(c_Product__Type_Oprod_Oprod__case(U_17861,tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_List_Olist_OCons(U_17861)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17861,tc_List_Olist(U_17861),tc_List_Olist(U_17861)),c_List_Olist_OCons(U_17861)))),c_Wellfounded_Olex__prod(U_17861,tc_List_Olist(U_17861),U_17862,hAPP(c_List_Olexn(U_17861,U_17862),U_17863)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17861),tc_List_Olist(U_17861))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17861),tc_List_Olist(U_17861),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17861),tc_HOL_Obool)),tc_List_Olist(U_17861)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17861))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17861)))),hAPP(c_Nat_OSuc,U_17863))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17861),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17861)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17861)))),hAPP(c_Nat_OSuc,U_17863)))))),
    inference(clausify,[status(thm)],[f_4360_3]) ).

fof(f_4361_1,plain,
    ! [V_x,V_ys,V_xs,T_a] :
      ( V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) ),
    inference(fof_nnf,[status(thm)],[fact_impossible__Cons]) ).

fof(f_4361_2,plain,
    ! [U_17867,U_17866,U_17865,U_17864] :
      ( U_17865 != hAPP(hAPP(c_List_Olist_OCons(U_17864),U_17867),U_17866)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17864)),U_17865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17864)),U_17866))) ),
    inference(variable_rename,[status(thm)],[f_4361_1]) ).

fof(f_4361_3,plain,
    ! [U_17864,U_17865,U_17866,U_17867] :
      ( U_17865 != hAPP(hAPP(c_List_Olist_OCons(U_17864),U_17867),U_17866)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17864)),U_17865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17864)),U_17866))) ),
    inference(definitional_conversion,[status(esa)],[f_4361_2]) ).

cnf(f_4361_4,plain,
    ( U_17865 != hAPP(hAPP(c_List_Olist_OCons(U_17864),U_17867),U_17866)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17864)),U_17865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17864)),U_17866))) ),
    inference(clausify,[status(thm)],[f_4361_3]) ).

fof(f_4362_1,plain,
    ! [V_xs_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | V_y_2 = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__ConsD]) ).

fof(f_4362_2,plain,
    ! [U_17871,U_17870,U_17869,U_17868] :
      ( hBOOL(hAPP(hAPP(c_member(U_17868),U_17869),hAPP(c_List_Oset(U_17868),U_17871)))
      | U_17869 = U_17870
      | ~ hBOOL(hAPP(hAPP(c_member(U_17868),U_17869),hAPP(c_List_Oset(U_17868),hAPP(hAPP(c_List_Olist_OCons(U_17868),U_17870),U_17871)))) ),
    inference(variable_rename,[status(thm)],[f_4362_1]) ).

fof(f_4362_3,plain,
    ! [U_17868,U_17869,U_17870,U_17871] :
      ( hBOOL(hAPP(hAPP(c_member(U_17868),U_17869),hAPP(c_List_Oset(U_17868),U_17871)))
      | U_17869 = U_17870
      | ~ hBOOL(hAPP(hAPP(c_member(U_17868),U_17869),hAPP(c_List_Oset(U_17868),hAPP(hAPP(c_List_Olist_OCons(U_17868),U_17870),U_17871)))) ),
    inference(definitional_conversion,[status(esa)],[f_4362_2]) ).

cnf(f_4362_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17868),U_17869),hAPP(c_List_Oset(U_17868),U_17871)))
    | U_17869 = U_17870
    | ~ hBOOL(hAPP(hAPP(c_member(U_17868),U_17869),hAPP(c_List_Oset(U_17868),hAPP(hAPP(c_List_Olist_OCons(U_17868),U_17870),U_17871)))) ),
    inference(clausify,[status(thm)],[f_4362_3]) ).

fof(f_4363_1,plain,
    ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons__Cons]) ).

fof(f_4363_2,plain,
    ! [U_17877,U_17876,U_17875,U_17874,U_17873,U_17872] : hAPP(hAPP(c_List_Ozip(U_17872,U_17873),hAPP(hAPP(c_List_Olist_OCons(U_17872),U_17874),U_17875)),hAPP(hAPP(c_List_Olist_OCons(U_17873),U_17876),U_17877)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17872,U_17873)),hAPP(hAPP(c_Product__Type_OPair(U_17872,U_17873),U_17874),U_17876)),hAPP(hAPP(c_List_Ozip(U_17872,U_17873),U_17875),U_17877)),
    inference(variable_rename,[status(thm)],[f_4363_1]) ).

fof(f_4363_3,plain,
    ! [U_17872,U_17873,U_17874,U_17875,U_17876,U_17877] : hAPP(hAPP(c_List_Ozip(U_17872,U_17873),hAPP(hAPP(c_List_Olist_OCons(U_17872),U_17874),U_17875)),hAPP(hAPP(c_List_Olist_OCons(U_17873),U_17876),U_17877)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17872,U_17873)),hAPP(hAPP(c_Product__Type_OPair(U_17872,U_17873),U_17874),U_17876)),hAPP(hAPP(c_List_Ozip(U_17872,U_17873),U_17875),U_17877)),
    inference(definitional_conversion,[status(esa)],[f_4363_2]) ).

cnf(f_4363_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17872,U_17873),hAPP(hAPP(c_List_Olist_OCons(U_17872),U_17874),U_17875)),hAPP(hAPP(c_List_Olist_OCons(U_17873),U_17876),U_17877)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17872,U_17873)),hAPP(hAPP(c_Product__Type_OPair(U_17872,U_17873),U_17874),U_17876)),hAPP(hAPP(c_List_Ozip(U_17872,U_17873),U_17875),U_17877)),
    inference(clausify,[status(thm)],[f_4363_3]) ).

fof(f_4364_1,plain,
    ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__subset__Cons]) ).

fof(f_4364_2,plain,
    ! [U_17880,U_17879,U_17878] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17878,tc_HOL_Obool)),hAPP(c_List_Oset(U_17878),U_17879)),hAPP(c_List_Oset(U_17878),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17880),U_17879)))),
    inference(variable_rename,[status(thm)],[f_4364_1]) ).

fof(f_4364_3,plain,
    ! [U_17878,U_17879,U_17880] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17878,tc_HOL_Obool)),hAPP(c_List_Oset(U_17878),U_17879)),hAPP(c_List_Oset(U_17878),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17880),U_17879)))),
    inference(definitional_conversion,[status(esa)],[f_4364_2]) ).

cnf(f_4364_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17878,tc_HOL_Obool)),hAPP(c_List_Oset(U_17878),U_17879)),hAPP(c_List_Oset(U_17878),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17880),U_17879)))),
    inference(clausify,[status(thm)],[f_4364_3]) ).

fof(f_4365_1,plain,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(f_4365_2,plain,
    ! [U_17883,U_17882,U_17881] : hAPP(c_List_Oset(U_17881),hAPP(hAPP(c_List_Olist_OCons(U_17881),U_17882),U_17883)) = hAPP(hAPP(c_Set_Oinsert(U_17881),U_17882),hAPP(c_List_Oset(U_17881),U_17883)),
    inference(variable_rename,[status(thm)],[f_4365_1]) ).

fof(f_4365_3,plain,
    ! [U_17881,U_17882,U_17883] : hAPP(c_List_Oset(U_17881),hAPP(hAPP(c_List_Olist_OCons(U_17881),U_17882),U_17883)) = hAPP(hAPP(c_Set_Oinsert(U_17881),U_17882),hAPP(c_List_Oset(U_17881),U_17883)),
    inference(definitional_conversion,[status(esa)],[f_4365_2]) ).

cnf(f_4365_4,plain,
    hAPP(c_List_Oset(U_17881),hAPP(hAPP(c_List_Olist_OCons(U_17881),U_17882),U_17883)) = hAPP(hAPP(c_Set_Oinsert(U_17881),U_17882),hAPP(c_List_Oset(U_17881),U_17883)),
    inference(clausify,[status(thm)],[f_4365_3]) ).

fof(f_4366_1,plain,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(f_4366_2,plain,
    ! [U_17889,U_17888,U_17887,U_17886,U_17885,U_17884] : c_List_Ofoldr(U_17884,U_17885,U_17886,hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17887),U_17888),U_17889) = hAPP(hAPP(U_17886,U_17887),c_List_Ofoldr(U_17884,U_17885,U_17886,U_17888,U_17889)),
    inference(variable_rename,[status(thm)],[f_4366_1]) ).

fof(f_4366_3,plain,
    ! [U_17884,U_17885,U_17886,U_17887,U_17888,U_17889] : c_List_Ofoldr(U_17884,U_17885,U_17886,hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17887),U_17888),U_17889) = hAPP(hAPP(U_17886,U_17887),c_List_Ofoldr(U_17884,U_17885,U_17886,U_17888,U_17889)),
    inference(definitional_conversion,[status(esa)],[f_4366_2]) ).

cnf(f_4366_4,plain,
    c_List_Ofoldr(U_17884,U_17885,U_17886,hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17887),U_17888),U_17889) = hAPP(hAPP(U_17886,U_17887),c_List_Ofoldr(U_17884,U_17885,U_17886,U_17888,U_17889)),
    inference(clausify,[status(thm)],[f_4366_3]) ).

fof(f_4367_1,plain,
    ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
    inference(fof_nnf,[status(thm)],[fact_not__Cons__self]) ).

fof(f_4367_2,plain,
    ! [U_17892,U_17891,U_17890] : U_17890 != hAPP(hAPP(c_List_Olist_OCons(U_17891),U_17892),U_17890),
    inference(variable_rename,[status(thm)],[f_4367_1]) ).

fof(f_4367_3,plain,
    ! [U_17890,U_17891,U_17892] : U_17890 != hAPP(hAPP(c_List_Olist_OCons(U_17891),U_17892),U_17890),
    inference(definitional_conversion,[status(esa)],[f_4367_2]) ).

cnf(f_4367_4,plain,
    U_17890 != hAPP(hAPP(c_List_Olist_OCons(U_17891),U_17892),U_17890),
    inference(clausify,[status(thm)],[f_4367_3]) ).

fof(f_4368_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
    inference(fof_nnf,[status(thm)],[fact_not__Cons__self2]) ).

fof(f_4368_2,plain,
    ! [U_17895,U_17894,U_17893] : hAPP(hAPP(c_List_Olist_OCons(U_17893),U_17894),U_17895) != U_17895,
    inference(variable_rename,[status(thm)],[f_4368_1]) ).

fof(f_4368_3,plain,
    ! [U_17893,U_17894,U_17895] : hAPP(hAPP(c_List_Olist_OCons(U_17893),U_17894),U_17895) != U_17895,
    inference(definitional_conversion,[status(esa)],[f_4368_2]) ).

cnf(f_4368_4,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_17893),U_17894),U_17895) != U_17895,
    inference(clausify,[status(thm)],[f_4368_3]) ).

fof(f_4369_1,plain,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
        | V_list_2 != V_list_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_list_2 = V_list_H_2
          & V_a_2 = V_a_H_2 )
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list_Oinject]) ).

fof(f_4369_2,plain,
    ! [U_17900,U_17899,U_17898,U_17897,U_17896] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_17896),U_17897),U_17898) = hAPP(hAPP(c_List_Olist_OCons(U_17896),U_17899),U_17900)
        | U_17898 != U_17900
        | U_17897 != U_17899 )
      & ( ( U_17898 = U_17900
          & U_17897 = U_17899 )
        | hAPP(hAPP(c_List_Olist_OCons(U_17896),U_17897),U_17898) != hAPP(hAPP(c_List_Olist_OCons(U_17896),U_17899),U_17900) ) ),
    inference(variable_rename,[status(thm)],[f_4369_1]) ).

fof(f_4369_3,plain,
    ( ! [U_17910,U_17908,U_17906,U_17904] :
        ( ! [U_17902] : hAPP(hAPP(c_List_Olist_OCons(U_17902),U_17904),U_17906) = hAPP(hAPP(c_List_Olist_OCons(U_17902),U_17908),U_17910)
        | U_17906 != U_17910
        | U_17904 != U_17908 )
    & ! [U_17909,U_17907,U_17905,U_17903] :
        ( ! [U_17901] : hAPP(hAPP(c_List_Olist_OCons(U_17901),U_17903),U_17905) != hAPP(hAPP(c_List_Olist_OCons(U_17901),U_17907),U_17909)
        | ( U_17905 = U_17909
          & U_17903 = U_17907 ) ) ),
    inference(miniscope,[status(thm)],[f_4369_2]) ).

fof(f_4369_4,plain,
    ( ! [U_17905,U_17907,U_17903,U_17909] :
        ( U_17905 = U_17909
        | ~ sP1137(U_17905,U_17907,U_17903,U_17909) )
    & ! [U_17905,U_17907,U_17903,U_17909] :
        ( U_17903 = U_17907
        | ~ sP1137(U_17905,U_17907,U_17903,U_17909) )
    & ! [U_17910,U_17904,U_17906,U_17902,U_17908] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_17902),U_17904),U_17906) = hAPP(hAPP(c_List_Olist_OCons(U_17902),U_17908),U_17910)
        | U_17906 != U_17910
        | U_17904 != U_17908 )
    & ! [U_17905,U_17907,U_17903,U_17901,U_17909] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_17901),U_17903),U_17905) != hAPP(hAPP(c_List_Olist_OCons(U_17901),U_17907),U_17909)
        | sP1137(U_17905,U_17907,U_17903,U_17909) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1137])],[f_4369_3]) ).

cnf(f_4369_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_17901),U_17903),U_17905) != hAPP(hAPP(c_List_Olist_OCons(U_17901),U_17907),U_17909)
    | sP1137(U_17905,U_17907,U_17903,U_17909) ),
    inference(clausify,[status(thm)],[f_4369_4]) ).

cnf(f_4369_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_17902),U_17904),U_17906) = hAPP(hAPP(c_List_Olist_OCons(U_17902),U_17908),U_17910)
    | U_17906 != U_17910
    | U_17904 != U_17908 ),
    inference(clausify,[status(thm)],[f_4369_4]) ).

cnf(f_4369_7,plain,
    ( U_17903 = U_17907
    | ~ sP1137(U_17905,U_17907,U_17903,U_17909) ),
    inference(clausify,[status(thm)],[f_4369_4]) ).

cnf(f_4369_8,plain,
    ( U_17905 = U_17909
    | ~ sP1137(U_17905,U_17907,U_17903,U_17909) ),
    inference(clausify,[status(thm)],[f_4369_4]) ).

fof(f_4370_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
      ( ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
        | ~ c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
        | ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) )
      & ( ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
          & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) )
        | ~ c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J]) ).

fof(f_4370_2,plain,
    ! [U_17916,U_17915,U_17914,U_17913,U_17912,U_17911] :
      ( ( c_List_Olistrelp(U_17911,U_17912,hAPP(hAPP(c_List_Olist_OCons(U_17911),U_17913),U_17914),hAPP(hAPP(c_List_Olist_OCons(U_17911),U_17915),U_17916))
        | ~ c_List_Olistrelp(U_17911,U_17912,U_17914,U_17916)
        | ~ hBOOL(hAPP(hAPP(U_17912,U_17913),U_17915)) )
      & ( ( c_List_Olistrelp(U_17911,U_17912,U_17914,U_17916)
          & hBOOL(hAPP(hAPP(U_17912,U_17913),U_17915)) )
        | ~ c_List_Olistrelp(U_17911,U_17912,hAPP(hAPP(c_List_Olist_OCons(U_17911),U_17913),U_17914),hAPP(hAPP(c_List_Olist_OCons(U_17911),U_17915),U_17916)) ) ),
    inference(variable_rename,[status(thm)],[f_4370_1]) ).

fof(f_4370_3,plain,
    ( ! [U_17928,U_17926,U_17924,U_17922,U_17920,U_17918] :
        ( c_List_Olistrelp(U_17918,U_17920,hAPP(hAPP(c_List_Olist_OCons(U_17918),U_17922),U_17924),hAPP(hAPP(c_List_Olist_OCons(U_17918),U_17926),U_17928))
        | ~ c_List_Olistrelp(U_17918,U_17920,U_17924,U_17928)
        | ~ hBOOL(hAPP(hAPP(U_17920,U_17922),U_17926)) )
    & ! [U_17927,U_17925,U_17923,U_17921,U_17919,U_17917] :
        ( ( c_List_Olistrelp(U_17917,U_17919,U_17923,U_17927)
          & hBOOL(hAPP(hAPP(U_17919,U_17921),U_17925)) )
        | ~ c_List_Olistrelp(U_17917,U_17919,hAPP(hAPP(c_List_Olist_OCons(U_17917),U_17921),U_17923),hAPP(hAPP(c_List_Olist_OCons(U_17917),U_17925),U_17927)) ) ),
    inference(miniscope,[status(thm)],[f_4370_2]) ).

fof(f_4370_4,plain,
    ( ! [U_17923,U_17917,U_17919,U_17921,U_17927,U_17925] :
        ( c_List_Olistrelp(U_17917,U_17919,U_17923,U_17927)
        | ~ sP1138(U_17923,U_17917,U_17919,U_17921,U_17927,U_17925) )
    & ! [U_17923,U_17917,U_17919,U_17921,U_17927,U_17925] :
        ( hBOOL(hAPP(hAPP(U_17919,U_17921),U_17925))
        | ~ sP1138(U_17923,U_17917,U_17919,U_17921,U_17927,U_17925) )
    & ! [U_17928,U_17918,U_17924,U_17922,U_17920,U_17926] :
        ( c_List_Olistrelp(U_17918,U_17920,hAPP(hAPP(c_List_Olist_OCons(U_17918),U_17922),U_17924),hAPP(hAPP(c_List_Olist_OCons(U_17918),U_17926),U_17928))
        | ~ c_List_Olistrelp(U_17918,U_17920,U_17924,U_17928)
        | ~ hBOOL(hAPP(hAPP(U_17920,U_17922),U_17926)) )
    & ! [U_17923,U_17917,U_17919,U_17921,U_17927,U_17925] :
        ( sP1138(U_17923,U_17917,U_17919,U_17921,U_17927,U_17925)
        | ~ c_List_Olistrelp(U_17917,U_17919,hAPP(hAPP(c_List_Olist_OCons(U_17917),U_17921),U_17923),hAPP(hAPP(c_List_Olist_OCons(U_17917),U_17925),U_17927)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1138])],[f_4370_3]) ).

cnf(f_4370_5,plain,
    ( sP1138(U_17923,U_17917,U_17919,U_17921,U_17927,U_17925)
    | ~ c_List_Olistrelp(U_17917,U_17919,hAPP(hAPP(c_List_Olist_OCons(U_17917),U_17921),U_17923),hAPP(hAPP(c_List_Olist_OCons(U_17917),U_17925),U_17927)) ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

cnf(f_4370_6,plain,
    ( c_List_Olistrelp(U_17918,U_17920,hAPP(hAPP(c_List_Olist_OCons(U_17918),U_17922),U_17924),hAPP(hAPP(c_List_Olist_OCons(U_17918),U_17926),U_17928))
    | ~ c_List_Olistrelp(U_17918,U_17920,U_17924,U_17928)
    | ~ hBOOL(hAPP(hAPP(U_17920,U_17922),U_17926)) ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

cnf(f_4370_7,plain,
    ( hBOOL(hAPP(hAPP(U_17919,U_17921),U_17925))
    | ~ sP1138(U_17923,U_17917,U_17919,U_17921,U_17927,U_17925) ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

cnf(f_4370_8,plain,
    ( c_List_Olistrelp(U_17917,U_17919,U_17923,U_17927)
    | ~ sP1138(U_17923,U_17917,U_17919,U_17921,U_17927,U_17925) ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

fof(f_4371_1,plain,
    ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
      ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
      | ~ c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp_OCons]) ).

fof(f_4371_2,plain,
    ! [U_17934,U_17933,U_17932,U_17931,U_17930,U_17929] :
      ( c_List_Olistrelp(U_17932,U_17929,hAPP(hAPP(c_List_Olist_OCons(U_17932),U_17930),U_17933),hAPP(hAPP(c_List_Olist_OCons(U_17932),U_17931),U_17934))
      | ~ c_List_Olistrelp(U_17932,U_17929,U_17933,U_17934)
      | ~ hBOOL(hAPP(hAPP(U_17929,U_17930),U_17931)) ),
    inference(variable_rename,[status(thm)],[f_4371_1]) ).

fof(f_4371_3,plain,
    ! [U_17929,U_17932,U_17931,U_17933,U_17934,U_17930] :
      ( c_List_Olistrelp(U_17932,U_17929,hAPP(hAPP(c_List_Olist_OCons(U_17932),U_17930),U_17933),hAPP(hAPP(c_List_Olist_OCons(U_17932),U_17931),U_17934))
      | ~ c_List_Olistrelp(U_17932,U_17929,U_17933,U_17934)
      | ~ hBOOL(hAPP(hAPP(U_17929,U_17930),U_17931)) ),
    inference(definitional_conversion,[status(esa)],[f_4371_2]) ).

cnf(f_4371_4,plain,
    ( c_List_Olistrelp(U_17932,U_17929,hAPP(hAPP(c_List_Olist_OCons(U_17932),U_17930),U_17933),hAPP(hAPP(c_List_Olist_OCons(U_17932),U_17931),U_17934))
    | ~ c_List_Olistrelp(U_17932,U_17929,U_17933,U_17934)
    | ~ hBOOL(hAPP(hAPP(U_17929,U_17930),U_17931)) ),
    inference(clausify,[status(thm)],[f_4371_3]) ).

fof(f_4372_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(f_4372_2,plain,
    ! [U_17939,U_17938,U_17937,U_17936,U_17935] : hAPP(hAPP(c_List_Omap(U_17935,U_17936),U_17937),hAPP(hAPP(c_List_Olist_OCons(U_17935),U_17938),U_17939)) = hAPP(hAPP(c_List_Olist_OCons(U_17936),hAPP(U_17937,U_17938)),hAPP(hAPP(c_List_Omap(U_17935,U_17936),U_17937),U_17939)),
    inference(variable_rename,[status(thm)],[f_4372_1]) ).

fof(f_4372_3,plain,
    ! [U_17935,U_17936,U_17937,U_17938,U_17939] : hAPP(hAPP(c_List_Omap(U_17935,U_17936),U_17937),hAPP(hAPP(c_List_Olist_OCons(U_17935),U_17938),U_17939)) = hAPP(hAPP(c_List_Olist_OCons(U_17936),hAPP(U_17937,U_17938)),hAPP(hAPP(c_List_Omap(U_17935,U_17936),U_17937),U_17939)),
    inference(definitional_conversion,[status(esa)],[f_4372_2]) ).

cnf(f_4372_4,plain,
    hAPP(hAPP(c_List_Omap(U_17935,U_17936),U_17937),hAPP(hAPP(c_List_Olist_OCons(U_17935),U_17938),U_17939)) = hAPP(hAPP(c_List_Olist_OCons(U_17936),hAPP(U_17937,U_17938)),hAPP(hAPP(c_List_Omap(U_17935,U_17936),U_17937),U_17939)),
    inference(clausify,[status(thm)],[f_4372_3]) ).

fof(f_4373_1,plain,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs))
        | V_x = V_y )
      & ( c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs
        | V_x != V_y ) ),
    inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J]) ).

fof(f_4373_2,plain,
    ! [U_17943,U_17942,U_17941,U_17940] :
      ( ( c_List_Oremove1(U_17942,U_17940,hAPP(hAPP(c_List_Olist_OCons(U_17942),U_17941),U_17943)) = hAPP(hAPP(c_List_Olist_OCons(U_17942),U_17941),c_List_Oremove1(U_17942,U_17940,U_17943))
        | U_17940 = U_17941 )
      & ( c_List_Oremove1(U_17942,U_17940,hAPP(hAPP(c_List_Olist_OCons(U_17942),U_17941),U_17943)) = U_17943
        | U_17940 != U_17941 ) ),
    inference(variable_rename,[status(thm)],[f_4373_1]) ).

fof(f_4373_3,plain,
    ( ! [U_17951,U_17949,U_17947,U_17945] :
        ( c_List_Oremove1(U_17949,U_17945,hAPP(hAPP(c_List_Olist_OCons(U_17949),U_17947),U_17951)) = hAPP(hAPP(c_List_Olist_OCons(U_17949),U_17947),c_List_Oremove1(U_17949,U_17945,U_17951))
        | U_17945 = U_17947 )
    & ! [U_17950,U_17948,U_17946,U_17944] :
        ( c_List_Oremove1(U_17948,U_17944,hAPP(hAPP(c_List_Olist_OCons(U_17948),U_17946),U_17950)) = U_17950
        | U_17944 != U_17946 ) ),
    inference(miniscope,[status(thm)],[f_4373_2]) ).

fof(f_4373_4,plain,
    ( ! [U_17951,U_17945,U_17947,U_17949] :
        ( c_List_Oremove1(U_17949,U_17945,hAPP(hAPP(c_List_Olist_OCons(U_17949),U_17947),U_17951)) = hAPP(hAPP(c_List_Olist_OCons(U_17949),U_17947),c_List_Oremove1(U_17949,U_17945,U_17951))
        | U_17945 = U_17947 )
    & ! [U_17946,U_17950,U_17944,U_17948] :
        ( c_List_Oremove1(U_17948,U_17944,hAPP(hAPP(c_List_Olist_OCons(U_17948),U_17946),U_17950)) = U_17950
        | U_17944 != U_17946 ) ),
    inference(definitional_conversion,[status(esa)],[f_4373_3]) ).

cnf(f_4373_5,plain,
    ( c_List_Oremove1(U_17948,U_17944,hAPP(hAPP(c_List_Olist_OCons(U_17948),U_17946),U_17950)) = U_17950
    | U_17944 != U_17946 ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

cnf(f_4373_6,plain,
    ( c_List_Oremove1(U_17949,U_17945,hAPP(hAPP(c_List_Olist_OCons(U_17949),U_17947),U_17951)) = hAPP(hAPP(c_List_Olist_OCons(U_17949),U_17947),c_List_Oremove1(U_17949,U_17945,U_17951))
    | U_17945 = U_17947 ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

fof(f_4374_1,plain,
    ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(f_4374_2,plain,
    ! [U_17957,U_17956,U_17955,U_17954,U_17953,U_17952] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957)) = hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),U_17957))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17952),hAPP(U_17953,U_17954)),hAPP(U_17953,U_17955))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957)) = hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17952),hAPP(U_17953,U_17954)),hAPP(U_17953,U_17955))) ) )
      | ~ class_Orderings_Olinorder(U_17952) ),
    inference(variable_rename,[status(thm)],[f_4374_1]) ).

fof(f_4374_3,plain,
    ( ! [U_17953,U_17952,U_17954,U_17955,U_17956,U_17957] :
        ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957)) = hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),U_17957))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17952),hAPP(U_17953,U_17954)),hAPP(U_17953,U_17955)))
        | ~ sP1139(U_17953,U_17952,U_17954,U_17955,U_17956,U_17957) )
    & ! [U_17953,U_17952,U_17954,U_17955,U_17956,U_17957] :
        ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957)) = hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17952),hAPP(U_17953,U_17954)),hAPP(U_17953,U_17955)))
        | ~ sP1139(U_17953,U_17952,U_17954,U_17955,U_17956,U_17957) )
    & ! [U_17953,U_17952,U_17954,U_17955,U_17956,U_17957] :
        ( sP1139(U_17953,U_17952,U_17954,U_17955,U_17956,U_17957)
        | ~ class_Orderings_Olinorder(U_17952) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1139])],[f_4374_2]) ).

cnf(f_4374_4,plain,
    ( sP1139(U_17953,U_17952,U_17954,U_17955,U_17956,U_17957)
    | ~ class_Orderings_Olinorder(U_17952) ),
    inference(clausify,[status(thm)],[f_4374_3]) ).

cnf(f_4374_5,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957)) = hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17952),hAPP(U_17953,U_17954)),hAPP(U_17953,U_17955)))
    | ~ sP1139(U_17953,U_17952,U_17954,U_17955,U_17956,U_17957) ),
    inference(clausify,[status(thm)],[f_4374_3]) ).

cnf(f_4374_6,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),U_17957)) = hAPP(hAPP(c_List_Olist_OCons(U_17956),U_17955),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17956,U_17952,U_17953),U_17954),U_17957))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17952),hAPP(U_17953,U_17954)),hAPP(U_17953,U_17955)))
    | ~ sP1139(U_17953,U_17952,U_17954,U_17955,U_17956,U_17957) ),
    inference(clausify,[status(thm)],[f_4374_3]) ).

fof(f_4375_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(f_4375_2,plain,
    ! [U_17960,U_17959,U_17958] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17958),hAPP(hAPP(c_List_Olist_OCons(U_17958),U_17959),U_17960)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17958),U_17960))
        | hBOOL(hAPP(hAPP(c_member(U_17958),U_17959),hAPP(c_List_Oset(U_17958),U_17960))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(U_17958),U_17960))
          & ~ hBOOL(hAPP(hAPP(c_member(U_17958),U_17959),hAPP(c_List_Oset(U_17958),U_17960))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17958),hAPP(hAPP(c_List_Olist_OCons(U_17958),U_17959),U_17960))) ) ),
    inference(variable_rename,[status(thm)],[f_4375_1]) ).

fof(f_4375_3,plain,
    ( ! [U_17966,U_17964,U_17962] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17962),hAPP(hAPP(c_List_Olist_OCons(U_17962),U_17964),U_17966)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17962),U_17966))
        | hBOOL(hAPP(hAPP(c_member(U_17962),U_17964),hAPP(c_List_Oset(U_17962),U_17966))) )
    & ! [U_17965,U_17963,U_17961] :
        ( ( hBOOL(hAPP(c_List_Odistinct(U_17961),U_17965))
          & ~ hBOOL(hAPP(hAPP(c_member(U_17961),U_17963),hAPP(c_List_Oset(U_17961),U_17965))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17961),hAPP(hAPP(c_List_Olist_OCons(U_17961),U_17963),U_17965))) ) ),
    inference(miniscope,[status(thm)],[f_4375_2]) ).

fof(f_4375_4,plain,
    ( ! [U_17963,U_17961,U_17965] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17961),U_17965))
        | ~ sP1140(U_17963,U_17961,U_17965) )
    & ! [U_17963,U_17961,U_17965] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17961),U_17963),hAPP(c_List_Oset(U_17961),U_17965)))
        | ~ sP1140(U_17963,U_17961,U_17965) )
    & ! [U_17966,U_17962,U_17964] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17962),hAPP(hAPP(c_List_Olist_OCons(U_17962),U_17964),U_17966)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17962),U_17966))
        | hBOOL(hAPP(hAPP(c_member(U_17962),U_17964),hAPP(c_List_Oset(U_17962),U_17966))) )
    & ! [U_17963,U_17961,U_17965] :
        ( sP1140(U_17963,U_17961,U_17965)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17961),hAPP(hAPP(c_List_Olist_OCons(U_17961),U_17963),U_17965))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1140])],[f_4375_3]) ).

cnf(f_4375_5,plain,
    ( sP1140(U_17963,U_17961,U_17965)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17961),hAPP(hAPP(c_List_Olist_OCons(U_17961),U_17963),U_17965))) ),
    inference(clausify,[status(thm)],[f_4375_4]) ).

cnf(f_4375_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17962),hAPP(hAPP(c_List_Olist_OCons(U_17962),U_17964),U_17966)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17962),U_17966))
    | hBOOL(hAPP(hAPP(c_member(U_17962),U_17964),hAPP(c_List_Oset(U_17962),U_17966))) ),
    inference(clausify,[status(thm)],[f_4375_4]) ).

cnf(f_4375_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17961),U_17963),hAPP(c_List_Oset(U_17961),U_17965)))
    | ~ sP1140(U_17963,U_17961,U_17965) ),
    inference(clausify,[status(thm)],[f_4375_4]) ).

cnf(f_4375_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17961),U_17965))
    | ~ sP1140(U_17963,U_17961,U_17965) ),
    inference(clausify,[status(thm)],[f_4375_4]) ).

fof(f_4376_1,plain,
    ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
      ( ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Map_Omap__of(T_b,T_c,V_ps),V_k)
        | V_l = V_k )
      & ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v)
        | V_l != V_k ) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__Cons__code_I2_J]) ).

fof(f_4376_2,plain,
    ! [U_17972,U_17971,U_17970,U_17969,U_17968,U_17967] :
      ( ( hAPP(c_Map_Omap__of(U_17969,U_17970,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17969,U_17970)),hAPP(hAPP(c_Product__Type_OPair(U_17969,U_17970),U_17967),U_17971)),U_17972)),U_17968) = hAPP(c_Map_Omap__of(U_17969,U_17970,U_17972),U_17968)
        | U_17967 = U_17968 )
      & ( hAPP(c_Map_Omap__of(U_17969,U_17970,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17969,U_17970)),hAPP(hAPP(c_Product__Type_OPair(U_17969,U_17970),U_17967),U_17971)),U_17972)),U_17968) = hAPP(c_Option_Ooption_OSome(U_17970),U_17971)
        | U_17967 != U_17968 ) ),
    inference(variable_rename,[status(thm)],[f_4376_1]) ).

fof(f_4376_3,plain,
    ( ! [U_17984,U_17982,U_17980,U_17978,U_17976,U_17974] :
        ( hAPP(c_Map_Omap__of(U_17978,U_17980,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17978,U_17980)),hAPP(hAPP(c_Product__Type_OPair(U_17978,U_17980),U_17974),U_17982)),U_17984)),U_17976) = hAPP(c_Map_Omap__of(U_17978,U_17980,U_17984),U_17976)
        | U_17974 = U_17976 )
    & ! [U_17983,U_17981,U_17979,U_17977,U_17975,U_17973] :
        ( hAPP(c_Map_Omap__of(U_17977,U_17979,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17977,U_17979)),hAPP(hAPP(c_Product__Type_OPair(U_17977,U_17979),U_17973),U_17981)),U_17983)),U_17975) = hAPP(c_Option_Ooption_OSome(U_17979),U_17981)
        | U_17973 != U_17975 ) ),
    inference(miniscope,[status(thm)],[f_4376_2]) ).

fof(f_4376_4,plain,
    ( ! [U_17974,U_17976,U_17978,U_17980,U_17982,U_17984] :
        ( hAPP(c_Map_Omap__of(U_17978,U_17980,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17978,U_17980)),hAPP(hAPP(c_Product__Type_OPair(U_17978,U_17980),U_17974),U_17982)),U_17984)),U_17976) = hAPP(c_Map_Omap__of(U_17978,U_17980,U_17984),U_17976)
        | U_17974 = U_17976 )
    & ! [U_17979,U_17977,U_17973,U_17975,U_17981,U_17983] :
        ( hAPP(c_Map_Omap__of(U_17977,U_17979,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17977,U_17979)),hAPP(hAPP(c_Product__Type_OPair(U_17977,U_17979),U_17973),U_17981)),U_17983)),U_17975) = hAPP(c_Option_Ooption_OSome(U_17979),U_17981)
        | U_17973 != U_17975 ) ),
    inference(definitional_conversion,[status(esa)],[f_4376_3]) ).

cnf(f_4376_5,plain,
    ( hAPP(c_Map_Omap__of(U_17977,U_17979,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17977,U_17979)),hAPP(hAPP(c_Product__Type_OPair(U_17977,U_17979),U_17973),U_17981)),U_17983)),U_17975) = hAPP(c_Option_Ooption_OSome(U_17979),U_17981)
    | U_17973 != U_17975 ),
    inference(clausify,[status(thm)],[f_4376_4]) ).

cnf(f_4376_6,plain,
    ( hAPP(c_Map_Omap__of(U_17978,U_17980,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17978,U_17980)),hAPP(hAPP(c_Product__Type_OPair(U_17978,U_17980),U_17974),U_17982)),U_17984)),U_17976) = hAPP(c_Map_Omap__of(U_17978,U_17980,U_17984),U_17976)
    | U_17974 = U_17976 ),
    inference(clausify,[status(thm)],[f_4376_4]) ).

fof(f_4377_1,plain,
    ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I4_J]) ).

fof(f_4377_2,plain,
    ! [U_17987,U_17986,U_17985] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17985)),hAPP(hAPP(c_List_Olist_OCons(U_17985),U_17986),U_17987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17985)),U_17987)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4377_1]) ).

fof(f_4377_3,plain,
    ! [U_17985,U_17986,U_17987] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17985)),hAPP(hAPP(c_List_Olist_OCons(U_17985),U_17986),U_17987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17985)),U_17987)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4377_2]) ).

cnf(f_4377_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17985)),hAPP(hAPP(c_List_Olist_OCons(U_17985),U_17986),U_17987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17985)),U_17987)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4377_3]) ).

fof(f_4378_1,plain,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel_OCons]) ).

fof(f_4378_2,plain,
    ! [U_17993,U_17992,U_17991,U_17990,U_17989,U_17988] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17988),tc_List_Olist(U_17988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17988),tc_List_Olist(U_17988)),hAPP(hAPP(c_List_Olist_OCons(U_17988),U_17989),U_17992)),hAPP(hAPP(c_List_Olist_OCons(U_17988),U_17990),U_17993))),c_List_Olistrel(U_17988,U_17991)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17988),tc_List_Olist(U_17988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17988),tc_List_Olist(U_17988)),U_17992),U_17993)),c_List_Olistrel(U_17988,U_17991)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17988,U_17988)),hAPP(hAPP(c_Product__Type_OPair(U_17988,U_17988),U_17989),U_17990)),U_17991)) ),
    inference(variable_rename,[status(thm)],[f_4378_1]) ).

fof(f_4378_3,plain,
    ! [U_17988,U_17989,U_17990,U_17991,U_17992,U_17993] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17988),tc_List_Olist(U_17988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17988),tc_List_Olist(U_17988)),hAPP(hAPP(c_List_Olist_OCons(U_17988),U_17989),U_17992)),hAPP(hAPP(c_List_Olist_OCons(U_17988),U_17990),U_17993))),c_List_Olistrel(U_17988,U_17991)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17988),tc_List_Olist(U_17988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17988),tc_List_Olist(U_17988)),U_17992),U_17993)),c_List_Olistrel(U_17988,U_17991)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17988,U_17988)),hAPP(hAPP(c_Product__Type_OPair(U_17988,U_17988),U_17989),U_17990)),U_17991)) ),
    inference(definitional_conversion,[status(esa)],[f_4378_2]) ).

cnf(f_4378_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17988),tc_List_Olist(U_17988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17988),tc_List_Olist(U_17988)),hAPP(hAPP(c_List_Olist_OCons(U_17988),U_17989),U_17992)),hAPP(hAPP(c_List_Olist_OCons(U_17988),U_17990),U_17993))),c_List_Olistrel(U_17988,U_17991)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17988),tc_List_Olist(U_17988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17988),tc_List_Olist(U_17988)),U_17992),U_17993)),c_List_Olistrel(U_17988,U_17991)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17988,U_17988)),hAPP(hAPP(c_Product__Type_OPair(U_17988,U_17988),U_17989),U_17990)),U_17991)) ),
    inference(clausify,[status(thm)],[f_4378_3]) ).

fof(f_4379_1,plain,
    ! [V_ps_2,V_p_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__of(T_b,T_c,V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))),
    inference(fof_nnf,[status(thm)],[fact_map__of_Osimps_I2_J]) ).

fof(f_4379_2,plain,
    ! [U_17997,U_17996,U_17995,U_17994] : c_Map_Omap__of(U_17994,U_17995,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17994,U_17995)),U_17996),U_17997)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17994,tc_Option_Ooption(U_17995)),c_Map_Omap__of(U_17994,U_17995,U_17997)),hAPP(c_Product__Type_Ofst(U_17994,U_17995),U_17996)),hAPP(c_Option_Ooption_OSome(U_17995),hAPP(c_Product__Type_Osnd(U_17994,U_17995),U_17996))),
    inference(variable_rename,[status(thm)],[f_4379_1]) ).

fof(f_4379_3,plain,
    ! [U_17994,U_17995,U_17996,U_17997] : c_Map_Omap__of(U_17994,U_17995,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17994,U_17995)),U_17996),U_17997)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17994,tc_Option_Ooption(U_17995)),c_Map_Omap__of(U_17994,U_17995,U_17997)),hAPP(c_Product__Type_Ofst(U_17994,U_17995),U_17996)),hAPP(c_Option_Ooption_OSome(U_17995),hAPP(c_Product__Type_Osnd(U_17994,U_17995),U_17996))),
    inference(definitional_conversion,[status(esa)],[f_4379_2]) ).

cnf(f_4379_4,plain,
    c_Map_Omap__of(U_17994,U_17995,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17994,U_17995)),U_17996),U_17997)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17994,tc_Option_Ooption(U_17995)),c_Map_Omap__of(U_17994,U_17995,U_17997)),hAPP(c_Product__Type_Ofst(U_17994,U_17995),U_17996)),hAPP(c_Option_Ooption_OSome(U_17995),hAPP(c_Product__Type_Osnd(U_17994,U_17995),U_17996))),
    inference(clausify,[status(thm)],[f_4379_3]) ).

fof(f_4380_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
            | V_x_2 != V_y_2 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__in__lex]) ).

fof(f_4380_2,plain,
    ! [U_18003,U_18002,U_18001,U_18000,U_17999,U_17998] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17998),tc_List_Olist(U_17998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17998),tc_List_Olist(U_17998)),hAPP(hAPP(c_List_Olist_OCons(U_17998),U_17999),U_18000)),hAPP(hAPP(c_List_Olist_OCons(U_17998),U_18001),U_18002))),c_List_Olex(U_17998,U_18003)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17998),tc_List_Olist(U_17998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17998),tc_List_Olist(U_17998)),U_18000),U_18002)),c_List_Olex(U_17998,U_18003)))
            | U_17999 != U_18001 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17998)),U_18000) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17998)),U_18002)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17998,U_17998)),hAPP(hAPP(c_Product__Type_OPair(U_17998,U_17998),U_17999),U_18001)),U_18003)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17998),tc_List_Olist(U_17998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17998),tc_List_Olist(U_17998)),U_18000),U_18002)),c_List_Olex(U_17998,U_18003)))
          & U_17999 = U_18001 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17998)),U_18000) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17998)),U_18002)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17998,U_17998)),hAPP(hAPP(c_Product__Type_OPair(U_17998,U_17998),U_17999),U_18001)),U_18003)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17998),tc_List_Olist(U_17998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17998),tc_List_Olist(U_17998)),hAPP(hAPP(c_List_Olist_OCons(U_17998),U_17999),U_18000)),hAPP(hAPP(c_List_Olist_OCons(U_17998),U_18001),U_18002))),c_List_Olex(U_17998,U_18003))) ) ),
    inference(variable_rename,[status(thm)],[f_4380_1]) ).

fof(f_4380_3,plain,
    ( ! [U_18015,U_18013,U_18011,U_18009,U_18007,U_18005] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18005),tc_List_Olist(U_18005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18005),tc_List_Olist(U_18005)),hAPP(hAPP(c_List_Olist_OCons(U_18005),U_18007),U_18009)),hAPP(hAPP(c_List_Olist_OCons(U_18005),U_18011),U_18013))),c_List_Olex(U_18005,U_18015)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18005),tc_List_Olist(U_18005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18005),tc_List_Olist(U_18005)),U_18009),U_18013)),c_List_Olex(U_18005,U_18015)))
            | U_18007 != U_18011 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18005)),U_18009) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18005)),U_18013)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18005,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18005,U_18005),U_18007),U_18011)),U_18015)) ) ) )
    & ! [U_18014,U_18012,U_18010,U_18008,U_18006,U_18004] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18004),tc_List_Olist(U_18004))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18004),tc_List_Olist(U_18004)),U_18008),U_18012)),c_List_Olex(U_18004,U_18014)))
          & U_18006 = U_18010 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18004)),U_18008) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18004)),U_18012)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18004)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18004),U_18006),U_18010)),U_18014)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18004),tc_List_Olist(U_18004))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18004),tc_List_Olist(U_18004)),hAPP(hAPP(c_List_Olist_OCons(U_18004),U_18006),U_18008)),hAPP(hAPP(c_List_Olist_OCons(U_18004),U_18010),U_18012))),c_List_Olex(U_18004,U_18014))) ) ),
    inference(miniscope,[status(thm)],[f_4380_2]) ).

fof(f_4380_4,plain,
    ( ! [U_18005,U_18007,U_18009,U_18013,U_18011,U_18015] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18005),tc_List_Olist(U_18005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18005),tc_List_Olist(U_18005)),U_18009),U_18013)),c_List_Olex(U_18005,U_18015)))
        | U_18007 != U_18011
        | ~ sP1143(U_18005,U_18007,U_18009,U_18013,U_18011,U_18015) )
    & ! [U_18005,U_18007,U_18009,U_18013,U_18011,U_18015] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18005)),U_18009) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18005)),U_18013)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18005,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18005,U_18005),U_18007),U_18011)),U_18015))
        | ~ sP1143(U_18005,U_18007,U_18009,U_18013,U_18011,U_18015) )
    & ! [U_18004,U_18006,U_18008,U_18012,U_18010,U_18014] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18004),tc_List_Olist(U_18004))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18004),tc_List_Olist(U_18004)),U_18008),U_18012)),c_List_Olex(U_18004,U_18014)))
        | ~ sP1142(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) )
    & ! [U_18004,U_18006,U_18008,U_18012,U_18010,U_18014] :
        ( U_18006 = U_18010
        | ~ sP1142(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) )
    & ! [U_18004,U_18006,U_18008,U_18012,U_18010,U_18014] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18004)),U_18008) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18004)),U_18012)
        | ~ sP1141(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) )
    & ! [U_18004,U_18006,U_18008,U_18012,U_18010,U_18014] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18004)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18004),U_18006),U_18010)),U_18014))
        | ~ sP1141(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) )
    & ! [U_18005,U_18007,U_18009,U_18013,U_18011,U_18015] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18005),tc_List_Olist(U_18005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18005),tc_List_Olist(U_18005)),hAPP(hAPP(c_List_Olist_OCons(U_18005),U_18007),U_18009)),hAPP(hAPP(c_List_Olist_OCons(U_18005),U_18011),U_18013))),c_List_Olex(U_18005,U_18015)))
        | sP1143(U_18005,U_18007,U_18009,U_18013,U_18011,U_18015) )
    & ! [U_18004,U_18006,U_18008,U_18012,U_18010,U_18014] :
        ( sP1142(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014)
        | sP1141(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18004),tc_List_Olist(U_18004))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18004),tc_List_Olist(U_18004)),hAPP(hAPP(c_List_Olist_OCons(U_18004),U_18006),U_18008)),hAPP(hAPP(c_List_Olist_OCons(U_18004),U_18010),U_18012))),c_List_Olex(U_18004,U_18014))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1141,sP1142,sP1143])],[f_4380_3]) ).

cnf(f_4380_5,plain,
    ( sP1142(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014)
    | sP1141(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18004),tc_List_Olist(U_18004))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18004),tc_List_Olist(U_18004)),hAPP(hAPP(c_List_Olist_OCons(U_18004),U_18006),U_18008)),hAPP(hAPP(c_List_Olist_OCons(U_18004),U_18010),U_18012))),c_List_Olex(U_18004,U_18014))) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18005),tc_List_Olist(U_18005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18005),tc_List_Olist(U_18005)),hAPP(hAPP(c_List_Olist_OCons(U_18005),U_18007),U_18009)),hAPP(hAPP(c_List_Olist_OCons(U_18005),U_18011),U_18013))),c_List_Olex(U_18005,U_18015)))
    | sP1143(U_18005,U_18007,U_18009,U_18013,U_18011,U_18015) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18004)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18004),U_18006),U_18010)),U_18014))
    | ~ sP1141(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18004)),U_18008) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18004)),U_18012)
    | ~ sP1141(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_9,plain,
    ( U_18006 = U_18010
    | ~ sP1142(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18004),tc_List_Olist(U_18004))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18004),tc_List_Olist(U_18004)),U_18008),U_18012)),c_List_Olex(U_18004,U_18014)))
    | ~ sP1142(U_18004,U_18006,U_18008,U_18012,U_18010,U_18014) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_11,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18005)),U_18009) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18005)),U_18013)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18005,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18005,U_18005),U_18007),U_18011)),U_18015))
    | ~ sP1143(U_18005,U_18007,U_18009,U_18013,U_18011,U_18015) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

cnf(f_4380_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18005),tc_List_Olist(U_18005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18005),tc_List_Olist(U_18005)),U_18009),U_18013)),c_List_Olex(U_18005,U_18015)))
    | U_18007 != U_18011
    | ~ sP1143(U_18005,U_18007,U_18009,U_18013,U_18011,U_18015) ),
    inference(clausify,[status(thm)],[f_4380_4]) ).

fof(f_4381_1,plain,
    ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons]) ).

fof(f_4381_2,plain,
    ! [U_18019,U_18018,U_18017,U_18016] : hAPP(c_Relation_OImage(tc_List_Olist(U_18016),tc_List_Olist(U_18016),c_List_Olistrel(U_18016,U_18017)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18016)),hAPP(hAPP(c_List_Olist_OCons(U_18016),U_18018),U_18019)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18016),tc_HOL_Obool)))) = c_List_Oset__Cons(U_18016,hAPP(c_Relation_OImage(U_18016,U_18016,U_18017),hAPP(hAPP(c_Set_Oinsert(U_18016),U_18018),c_Orderings_Obot__class_Obot(tc_fun(U_18016,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_18016),tc_List_Olist(U_18016),c_List_Olistrel(U_18016,U_18017)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18016)),U_18019),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18016),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4381_1]) ).

fof(f_4381_3,plain,
    ! [U_18016,U_18018,U_18017,U_18019] : hAPP(c_Relation_OImage(tc_List_Olist(U_18016),tc_List_Olist(U_18016),c_List_Olistrel(U_18016,U_18017)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18016)),hAPP(hAPP(c_List_Olist_OCons(U_18016),U_18018),U_18019)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18016),tc_HOL_Obool)))) = c_List_Oset__Cons(U_18016,hAPP(c_Relation_OImage(U_18016,U_18016,U_18017),hAPP(hAPP(c_Set_Oinsert(U_18016),U_18018),c_Orderings_Obot__class_Obot(tc_fun(U_18016,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_18016),tc_List_Olist(U_18016),c_List_Olistrel(U_18016,U_18017)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18016)),U_18019),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18016),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4381_2]) ).

cnf(f_4381_4,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_18016),tc_List_Olist(U_18016),c_List_Olistrel(U_18016,U_18017)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18016)),hAPP(hAPP(c_List_Olist_OCons(U_18016),U_18018),U_18019)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18016),tc_HOL_Obool)))) = c_List_Oset__Cons(U_18016,hAPP(c_Relation_OImage(U_18016,U_18016,U_18017),hAPP(hAPP(c_Set_Oinsert(U_18016),U_18018),c_Orderings_Obot__class_Obot(tc_fun(U_18016,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_18016),tc_List_Olist(U_18016),c_List_Olistrel(U_18016,U_18017)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18016)),U_18019),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18016),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4381_3]) ).

fof(f_4382_1,plain,
    ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
    inference(fof_nnf,[status(thm)],[fact_set__Cons__def]) ).

fof(f_4382_2,plain,
    ! [U_18022,U_18021,U_18020] : c_List_Oset__Cons(U_18020,U_18021,U_18022) = hAPP(c_Set_OCollect(tc_List_Olist(U_18020)),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_18020)),c_HOL_OEx(U_18020)),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_HOL_Obool),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_HOL_Obool,U_18020),c_HOL_OEx(tc_List_Olist(U_18020)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_fun(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),c_COMBS(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_18020,tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),U_18020),c_COMBS(tc_List_Olist(U_18020),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18020),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18020)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020))),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020))),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),U_18020)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_List_Olist(U_18020)),c_COMBB(tc_List_Olist(U_18020),tc_HOL_Obool,tc_List_Olist(U_18020))),c_fequal))),c_List_Olist_OCons(U_18020)))))),hAPP(hAPP(c_COMBC(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),U_18020),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18020))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18020),c_fconj),hAPP(hAPP(c_COMBC(U_18020,tc_fun(U_18020,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18020)),U_18021)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18020))),U_18022)))))),
    inference(variable_rename,[status(thm)],[f_4382_1]) ).

fof(f_4382_3,plain,
    ! [U_18020,U_18021,U_18022] : c_List_Oset__Cons(U_18020,U_18021,U_18022) = hAPP(c_Set_OCollect(tc_List_Olist(U_18020)),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_18020)),c_HOL_OEx(U_18020)),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_HOL_Obool),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_HOL_Obool,U_18020),c_HOL_OEx(tc_List_Olist(U_18020)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_fun(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),c_COMBS(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_18020,tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),U_18020),c_COMBS(tc_List_Olist(U_18020),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18020),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18020)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020))),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020))),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),U_18020)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_List_Olist(U_18020)),c_COMBB(tc_List_Olist(U_18020),tc_HOL_Obool,tc_List_Olist(U_18020))),c_fequal))),c_List_Olist_OCons(U_18020)))))),hAPP(hAPP(c_COMBC(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),U_18020),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18020))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18020),c_fconj),hAPP(hAPP(c_COMBC(U_18020,tc_fun(U_18020,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18020)),U_18021)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18020))),U_18022)))))),
    inference(definitional_conversion,[status(esa)],[f_4382_2]) ).

cnf(f_4382_4,plain,
    c_List_Oset__Cons(U_18020,U_18021,U_18022) = hAPP(c_Set_OCollect(tc_List_Olist(U_18020)),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_18020)),c_HOL_OEx(U_18020)),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_HOL_Obool),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_HOL_Obool,U_18020),c_HOL_OEx(tc_List_Olist(U_18020)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_fun(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),c_COMBS(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_18020,tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),U_18020),c_COMBS(tc_List_Olist(U_18020),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_18020)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18020),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18020)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020))),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_fun(tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020))),tc_fun(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool))),tc_List_Olist(U_18020)),c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),U_18020)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_List_Olist(U_18020)),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),tc_List_Olist(U_18020)),c_COMBB(tc_List_Olist(U_18020),tc_HOL_Obool,tc_List_Olist(U_18020))),c_fequal))),c_List_Olist_OCons(U_18020)))))),hAPP(hAPP(c_COMBC(U_18020,tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool)),U_18020),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18020))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18020),c_fconj),hAPP(hAPP(c_COMBC(U_18020,tc_fun(U_18020,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18020)),U_18021)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18020),tc_fun(tc_List_Olist(U_18020),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18020))),U_18022)))))),
    inference(clausify,[status(thm)],[f_4382_3]) ).

fof(f_4383_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
      ( ? [B_x,B_xs] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
          & V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons2]) ).

fof(f_4383_2,plain,
    ! [U_18029,U_18028,U_18027,U_18026,U_18025] :
      ( ? [U_18024,U_18023] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18023),U_18028)),c_List_Olistrel(U_18025,U_18029)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18025,U_18025)),hAPP(hAPP(c_Product__Type_OPair(U_18025,U_18025),U_18024),U_18027)),U_18029))
          & U_18026 = hAPP(hAPP(c_List_Olist_OCons(U_18025),U_18024),U_18023) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18026),hAPP(hAPP(c_List_Olist_OCons(U_18025),U_18027),U_18028))),c_List_Olistrel(U_18025,U_18029))) ),
    inference(variable_rename,[status(thm)],[f_4383_1]) ).

fof(f_4383_3,plain,
    ! [U_18029,U_18028,U_18027,U_18026,U_18025] :
      ( ? [U_18023] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18023),U_18028)),c_List_Olistrel(U_18025,U_18029)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18025,U_18025)),hAPP(hAPP(c_Product__Type_OPair(U_18025,U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18027)),U_18029))
          & U_18026 = hAPP(hAPP(c_List_Olist_OCons(U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18023) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18026),hAPP(hAPP(c_List_Olist_OCons(U_18025),U_18027),U_18028))),c_List_Olistrel(U_18025,U_18029))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_18024,sK456(U_18029,U_18028,U_18027,U_18026,U_18025))],[f_4383_2]) ).

fof(f_4383_4,plain,
    ! [U_18029,U_18028,U_18027,U_18026,U_18025] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),sK457(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18028)),c_List_Olistrel(U_18025,U_18029)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18025,U_18025)),hAPP(hAPP(c_Product__Type_OPair(U_18025,U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18027)),U_18029))
        & U_18026 = hAPP(hAPP(c_List_Olist_OCons(U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),sK457(U_18029,U_18028,U_18027,U_18026,U_18025)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18026),hAPP(hAPP(c_List_Olist_OCons(U_18025),U_18027),U_18028))),c_List_Olistrel(U_18025,U_18029))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_18023,sK457(U_18029,U_18028,U_18027,U_18026,U_18025))],[f_4383_3]) ).

fof(f_4383_5,plain,
    ( ! [U_18025,U_18026,U_18027,U_18028,U_18029] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),sK457(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18028)),c_List_Olistrel(U_18025,U_18029)))
        | ~ sP1144(U_18025,U_18026,U_18027,U_18028,U_18029) )
    & ! [U_18025,U_18026,U_18027,U_18028,U_18029] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18025,U_18025)),hAPP(hAPP(c_Product__Type_OPair(U_18025,U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18027)),U_18029))
        | ~ sP1144(U_18025,U_18026,U_18027,U_18028,U_18029) )
    & ! [U_18025,U_18026,U_18027,U_18028,U_18029] :
        ( U_18026 = hAPP(hAPP(c_List_Olist_OCons(U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),sK457(U_18029,U_18028,U_18027,U_18026,U_18025))
        | ~ sP1144(U_18025,U_18026,U_18027,U_18028,U_18029) )
    & ! [U_18025,U_18026,U_18027,U_18028,U_18029] :
        ( sP1144(U_18025,U_18026,U_18027,U_18028,U_18029)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18026),hAPP(hAPP(c_List_Olist_OCons(U_18025),U_18027),U_18028))),c_List_Olistrel(U_18025,U_18029))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1144])],[f_4383_4]) ).

cnf(f_4383_6,plain,
    ( sP1144(U_18025,U_18026,U_18027,U_18028,U_18029)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),U_18026),hAPP(hAPP(c_List_Olist_OCons(U_18025),U_18027),U_18028))),c_List_Olistrel(U_18025,U_18029))) ),
    inference(clausify,[status(thm)],[f_4383_5]) ).

cnf(f_4383_7,plain,
    ( U_18026 = hAPP(hAPP(c_List_Olist_OCons(U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),sK457(U_18029,U_18028,U_18027,U_18026,U_18025))
    | ~ sP1144(U_18025,U_18026,U_18027,U_18028,U_18029) ),
    inference(clausify,[status(thm)],[f_4383_5]) ).

cnf(f_4383_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18025,U_18025)),hAPP(hAPP(c_Product__Type_OPair(U_18025,U_18025),sK456(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18027)),U_18029))
    | ~ sP1144(U_18025,U_18026,U_18027,U_18028,U_18029) ),
    inference(clausify,[status(thm)],[f_4383_5]) ).

cnf(f_4383_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18025),tc_List_Olist(U_18025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18025),tc_List_Olist(U_18025)),sK457(U_18029,U_18028,U_18027,U_18026,U_18025)),U_18028)),c_List_Olistrel(U_18025,U_18029)))
    | ~ sP1144(U_18025,U_18026,U_18027,U_18028,U_18029) ),
    inference(clausify,[status(thm)],[f_4383_5]) ).

fof(f_4384_1,plain,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
      ( ? [B_y,B_ys] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
          & V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons1]) ).

fof(f_4384_2,plain,
    ! [U_18036,U_18035,U_18034,U_18033,U_18032] :
      ( ? [U_18031,U_18030] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),U_18034),U_18030)),c_List_Olistrel(U_18032,U_18036)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18032,U_18032)),hAPP(hAPP(c_Product__Type_OPair(U_18032,U_18032),U_18033),U_18031)),U_18036))
          & U_18035 = hAPP(hAPP(c_List_Olist_OCons(U_18032),U_18031),U_18030) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),hAPP(hAPP(c_List_Olist_OCons(U_18032),U_18033),U_18034)),U_18035)),c_List_Olistrel(U_18032,U_18036))) ),
    inference(variable_rename,[status(thm)],[f_4384_1]) ).

fof(f_4384_3,plain,
    ! [U_18036,U_18035,U_18034,U_18033,U_18032] :
      ( ? [U_18030] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),U_18034),U_18030)),c_List_Olistrel(U_18032,U_18036)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18032,U_18032)),hAPP(hAPP(c_Product__Type_OPair(U_18032,U_18032),U_18033),sK458(U_18036,U_18035,U_18034,U_18033,U_18032))),U_18036))
          & U_18035 = hAPP(hAPP(c_List_Olist_OCons(U_18032),sK458(U_18036,U_18035,U_18034,U_18033,U_18032)),U_18030) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),hAPP(hAPP(c_List_Olist_OCons(U_18032),U_18033),U_18034)),U_18035)),c_List_Olistrel(U_18032,U_18036))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_18031,sK458(U_18036,U_18035,U_18034,U_18033,U_18032))],[f_4384_2]) ).

fof(f_4384_4,plain,
    ! [U_18036,U_18035,U_18034,U_18033,U_18032] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),U_18034),sK459(U_18036,U_18035,U_18034,U_18033,U_18032))),c_List_Olistrel(U_18032,U_18036)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18032,U_18032)),hAPP(hAPP(c_Product__Type_OPair(U_18032,U_18032),U_18033),sK458(U_18036,U_18035,U_18034,U_18033,U_18032))),U_18036))
        & U_18035 = hAPP(hAPP(c_List_Olist_OCons(U_18032),sK458(U_18036,U_18035,U_18034,U_18033,U_18032)),sK459(U_18036,U_18035,U_18034,U_18033,U_18032)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),hAPP(hAPP(c_List_Olist_OCons(U_18032),U_18033),U_18034)),U_18035)),c_List_Olistrel(U_18032,U_18036))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_18030,sK459(U_18036,U_18035,U_18034,U_18033,U_18032))],[f_4384_3]) ).

fof(f_4384_5,plain,
    ( ! [U_18032,U_18033,U_18034,U_18035,U_18036] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),U_18034),sK459(U_18036,U_18035,U_18034,U_18033,U_18032))),c_List_Olistrel(U_18032,U_18036)))
        | ~ sP1145(U_18032,U_18033,U_18034,U_18035,U_18036) )
    & ! [U_18032,U_18033,U_18034,U_18035,U_18036] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18032,U_18032)),hAPP(hAPP(c_Product__Type_OPair(U_18032,U_18032),U_18033),sK458(U_18036,U_18035,U_18034,U_18033,U_18032))),U_18036))
        | ~ sP1145(U_18032,U_18033,U_18034,U_18035,U_18036) )
    & ! [U_18032,U_18033,U_18034,U_18035,U_18036] :
        ( U_18035 = hAPP(hAPP(c_List_Olist_OCons(U_18032),sK458(U_18036,U_18035,U_18034,U_18033,U_18032)),sK459(U_18036,U_18035,U_18034,U_18033,U_18032))
        | ~ sP1145(U_18032,U_18033,U_18034,U_18035,U_18036) )
    & ! [U_18032,U_18033,U_18034,U_18035,U_18036] :
        ( sP1145(U_18032,U_18033,U_18034,U_18035,U_18036)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),hAPP(hAPP(c_List_Olist_OCons(U_18032),U_18033),U_18034)),U_18035)),c_List_Olistrel(U_18032,U_18036))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1145])],[f_4384_4]) ).

cnf(f_4384_6,plain,
    ( sP1145(U_18032,U_18033,U_18034,U_18035,U_18036)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),hAPP(hAPP(c_List_Olist_OCons(U_18032),U_18033),U_18034)),U_18035)),c_List_Olistrel(U_18032,U_18036))) ),
    inference(clausify,[status(thm)],[f_4384_5]) ).

cnf(f_4384_7,plain,
    ( U_18035 = hAPP(hAPP(c_List_Olist_OCons(U_18032),sK458(U_18036,U_18035,U_18034,U_18033,U_18032)),sK459(U_18036,U_18035,U_18034,U_18033,U_18032))
    | ~ sP1145(U_18032,U_18033,U_18034,U_18035,U_18036) ),
    inference(clausify,[status(thm)],[f_4384_5]) ).

cnf(f_4384_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18032,U_18032)),hAPP(hAPP(c_Product__Type_OPair(U_18032,U_18032),U_18033),sK458(U_18036,U_18035,U_18034,U_18033,U_18032))),U_18036))
    | ~ sP1145(U_18032,U_18033,U_18034,U_18035,U_18036) ),
    inference(clausify,[status(thm)],[f_4384_5]) ).

cnf(f_4384_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18032),tc_List_Olist(U_18032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18032),tc_List_Olist(U_18032)),U_18034),sK459(U_18036,U_18035,U_18034,U_18033,U_18032))),c_List_Olistrel(U_18032,U_18036)))
    | ~ sP1145(U_18032,U_18033,U_18034,U_18035,U_18036) ),
    inference(clausify,[status(thm)],[f_4384_5]) ).

fof(f_4385_1,plain,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
    inference(fof_nnf,[status(thm)],[fact_length__sublist]) ).

fof(f_4385_2,plain,
    ! [U_18039,U_18038,U_18037] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18037)),c_List_Osublist(U_18037,U_18038,U_18039)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18037)),U_18038)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18039)))),
    inference(variable_rename,[status(thm)],[f_4385_1]) ).

fof(f_4385_3,plain,
    ! [U_18037,U_18038,U_18039] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18037)),c_List_Osublist(U_18037,U_18038,U_18039)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18037)),U_18038)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18039)))),
    inference(definitional_conversion,[status(esa)],[f_4385_2]) ).

cnf(f_4385_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18037)),c_List_Osublist(U_18037,U_18038,U_18039)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18037)),U_18038)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18039)))),
    inference(clausify,[status(thm)],[f_4385_3]) ).

fof(f_4386_1,plain,
    ! [V_xs,V_x,T_a,V_i] :
      ( ( hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
      & ( hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pick_Osimps]) ).

fof(f_4386_2,plain,
    ! [U_18043,U_18042,U_18041,U_18040] :
      ( ( hAPP(c_Random_Opick(U_18041,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18041)),U_18042),U_18043)),U_18040) = hAPP(c_Random_Opick(U_18041,U_18043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18040),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18041),U_18042)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18040),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18041),U_18042))) )
      & ( hAPP(c_Random_Opick(U_18041,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18041)),U_18042),U_18043)),U_18040) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18041),U_18042)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18040),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18041),U_18042))) ) ),
    inference(variable_rename,[status(thm)],[f_4386_1]) ).

fof(f_4386_3,plain,
    ( ! [U_18051,U_18049,U_18047,U_18045] :
        ( hAPP(c_Random_Opick(U_18047,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18049),U_18051)),U_18045) = hAPP(c_Random_Opick(U_18047,U_18051),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18045),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047),U_18049)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18045),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047),U_18049))) )
    & ! [U_18050,U_18048,U_18046,U_18044] :
        ( hAPP(c_Random_Opick(U_18046,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18046)),U_18048),U_18050)),U_18044) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18046),U_18048)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18044),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18046),U_18048))) ) ),
    inference(miniscope,[status(thm)],[f_4386_2]) ).

fof(f_4386_4,plain,
    ( ! [U_18045,U_18047,U_18049,U_18051] :
        ( hAPP(c_Random_Opick(U_18047,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18049),U_18051)),U_18045) = hAPP(c_Random_Opick(U_18047,U_18051),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18045),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047),U_18049)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18045),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047),U_18049))) )
    & ! [U_18046,U_18050,U_18044,U_18048] :
        ( hAPP(c_Random_Opick(U_18046,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18046)),U_18048),U_18050)),U_18044) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18046),U_18048)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18044),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18046),U_18048))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4386_3]) ).

cnf(f_4386_5,plain,
    ( hAPP(c_Random_Opick(U_18046,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18046)),U_18048),U_18050)),U_18044) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18046),U_18048)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18044),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18046),U_18048))) ),
    inference(clausify,[status(thm)],[f_4386_4]) ).

cnf(f_4386_6,plain,
    ( hAPP(c_Random_Opick(U_18047,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18049),U_18051)),U_18045) = hAPP(c_Random_Opick(U_18047,U_18051),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18045),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047),U_18049)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18045),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047),U_18049))) ),
    inference(clausify,[status(thm)],[f_4386_4]) ).

fof(f_4387_1,plain,
    ! [V_I_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__sublistI]) ).

fof(f_4387_2,plain,
    ! [U_18054,U_18053,U_18052] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18052),c_List_Osublist(U_18052,U_18053,U_18054)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18052),U_18053)) ),
    inference(variable_rename,[status(thm)],[f_4387_1]) ).

fof(f_4387_3,plain,
    ! [U_18052,U_18054,U_18053] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18052),c_List_Osublist(U_18052,U_18053,U_18054)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18052),U_18053)) ),
    inference(definitional_conversion,[status(esa)],[f_4387_2]) ).

cnf(f_4387_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18052),c_List_Osublist(U_18052,U_18053,U_18054)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18052),U_18053)) ),
    inference(clausify,[status(thm)],[f_4387_3]) ).

fof(f_4388_1,plain,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__sublistD]) ).

fof(f_4388_2,plain,
    ! [U_18058,U_18057,U_18056,U_18055] :
      ( hBOOL(hAPP(hAPP(c_member(U_18055),U_18056),hAPP(c_List_Oset(U_18055),U_18057)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18055),U_18056),hAPP(c_List_Oset(U_18055),c_List_Osublist(U_18055,U_18057,U_18058)))) ),
    inference(variable_rename,[status(thm)],[f_4388_1]) ).

fof(f_4388_3,plain,
    ! [U_18055,U_18056,U_18057,U_18058] :
      ( hBOOL(hAPP(hAPP(c_member(U_18055),U_18056),hAPP(c_List_Oset(U_18055),U_18057)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18055),U_18056),hAPP(c_List_Oset(U_18055),c_List_Osublist(U_18055,U_18057,U_18058)))) ),
    inference(definitional_conversion,[status(esa)],[f_4388_2]) ).

cnf(f_4388_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18055),U_18056),hAPP(c_List_Oset(U_18055),U_18057)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18055),U_18056),hAPP(c_List_Oset(U_18055),c_List_Osublist(U_18055,U_18057,U_18058)))) ),
    inference(clausify,[status(thm)],[f_4388_3]) ).

fof(f_4389_1,plain,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_notin__set__sublistI]) ).

fof(f_4389_2,plain,
    ! [U_18062,U_18061,U_18060,U_18059] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_18059),U_18060),hAPP(c_List_Oset(U_18059),c_List_Osublist(U_18059,U_18061,U_18062))))
      | hBOOL(hAPP(hAPP(c_member(U_18059),U_18060),hAPP(c_List_Oset(U_18059),U_18061))) ),
    inference(variable_rename,[status(thm)],[f_4389_1]) ).

fof(f_4389_3,plain,
    ! [U_18059,U_18060,U_18061,U_18062] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_18059),U_18060),hAPP(c_List_Oset(U_18059),c_List_Osublist(U_18059,U_18061,U_18062))))
      | hBOOL(hAPP(hAPP(c_member(U_18059),U_18060),hAPP(c_List_Oset(U_18059),U_18061))) ),
    inference(definitional_conversion,[status(esa)],[f_4389_2]) ).

cnf(f_4389_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18059),U_18060),hAPP(c_List_Oset(U_18059),c_List_Osublist(U_18059,U_18061,U_18062))))
    | hBOOL(hAPP(hAPP(c_member(U_18059),U_18060),hAPP(c_List_Oset(U_18059),U_18061))) ),
    inference(clausify,[status(thm)],[f_4389_3]) ).

fof(f_4390_1,plain,
    ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__sublist__subset]) ).

fof(f_4390_2,plain,
    ! [U_18065,U_18064,U_18063] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18063,tc_HOL_Obool)),hAPP(c_List_Oset(U_18063),c_List_Osublist(U_18063,U_18064,U_18065))),hAPP(c_List_Oset(U_18063),U_18064))),
    inference(variable_rename,[status(thm)],[f_4390_1]) ).

fof(f_4390_3,plain,
    ! [U_18063,U_18064,U_18065] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18063,tc_HOL_Obool)),hAPP(c_List_Oset(U_18063),c_List_Osublist(U_18063,U_18064,U_18065))),hAPP(c_List_Oset(U_18063),U_18064))),
    inference(definitional_conversion,[status(esa)],[f_4390_2]) ).

cnf(f_4390_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18063,tc_HOL_Obool)),hAPP(c_List_Oset(U_18063),c_List_Osublist(U_18063,U_18064,U_18065))),hAPP(c_List_Oset(U_18063),U_18064))),
    inference(clausify,[status(thm)],[f_4390_3]) ).

fof(f_4391_1,plain,
    ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(f_4391_2,plain,
    ! [U_18068,U_18067,U_18066] : c_Random_Oselect__weight(U_18066,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18066)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18066),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_18067)),U_18068)) = c_Random_Oselect__weight(U_18066,U_18068),
    inference(variable_rename,[status(thm)],[f_4391_1]) ).

fof(f_4391_3,plain,
    ! [U_18066,U_18067,U_18068] : c_Random_Oselect__weight(U_18066,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18066)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18066),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_18067)),U_18068)) = c_Random_Oselect__weight(U_18066,U_18068),
    inference(definitional_conversion,[status(esa)],[f_4391_2]) ).

cnf(f_4391_4,plain,
    c_Random_Oselect__weight(U_18066,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18066)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18066),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_18067)),U_18068)) = c_Random_Oselect__weight(U_18066,U_18068),
    inference(clausify,[status(thm)],[f_4391_3]) ).

fof(f_4392_1,plain,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_pick__member]) ).

fof(f_4392_2,plain,
    ! [U_18071,U_18070,U_18069] :
      ( hBOOL(hAPP(hAPP(c_member(U_18070),hAPP(c_Random_Opick(U_18070,U_18071),U_18069)),hAPP(c_List_Oset(U_18070),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18070),U_18070),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18070)),U_18071))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18069),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18070),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18070)),U_18071)))) ),
    inference(variable_rename,[status(thm)],[f_4392_1]) ).

fof(f_4392_3,plain,
    ! [U_18069,U_18070,U_18071] :
      ( hBOOL(hAPP(hAPP(c_member(U_18070),hAPP(c_Random_Opick(U_18070,U_18071),U_18069)),hAPP(c_List_Oset(U_18070),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18070),U_18070),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18070)),U_18071))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18069),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18070),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18070)),U_18071)))) ),
    inference(definitional_conversion,[status(esa)],[f_4392_2]) ).

cnf(f_4392_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18070),hAPP(c_Random_Opick(U_18070,U_18071),U_18069)),hAPP(c_List_Oset(U_18070),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18070),U_18070),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18070)),U_18071))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18069),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18070),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18070)),U_18071)))) ),
    inference(clausify,[status(thm)],[f_4392_3]) ).

fof(f_4393_1,plain,
    ! [V_xs,V_x,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J]) ).

fof(f_4393_2,plain,
    ! [U_18074,U_18073,U_18072] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18072),hAPP(hAPP(c_List_Olist_OCons(U_18072),U_18073),U_18074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18072),U_18073),hAPP(c_List_Omonoid__add__class_Olistsum(U_18072),U_18074))
      | ~ class_Groups_Omonoid__add(U_18072) ),
    inference(variable_rename,[status(thm)],[f_4393_1]) ).

fof(f_4393_3,plain,
    ! [U_18072,U_18073,U_18074] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18072),hAPP(hAPP(c_List_Olist_OCons(U_18072),U_18073),U_18074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18072),U_18073),hAPP(c_List_Omonoid__add__class_Olistsum(U_18072),U_18074))
      | ~ class_Groups_Omonoid__add(U_18072) ),
    inference(definitional_conversion,[status(esa)],[f_4393_2]) ).

cnf(f_4393_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18072),hAPP(hAPP(c_List_Olist_OCons(U_18072),U_18073),U_18074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18072),U_18073),hAPP(c_List_Omonoid__add__class_Olistsum(U_18072),U_18074))
    | ~ class_Groups_Omonoid__add(U_18072) ),
    inference(clausify,[status(thm)],[f_4393_3]) ).

fof(f_4394_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__subtractf]) ).

fof(f_4394_2,plain,
    ! [U_18079,U_18078,U_18077,U_18076,U_18075] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),hAPP(hAPP(c_COMBS(U_18076,U_18075,U_18075),hAPP(hAPP(c_COMBB(U_18075,tc_fun(U_18075,U_18075),U_18076),c_Groups_Ominus__class_Ominus(U_18075)),U_18077)),U_18078)),U_18079)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18075),hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),U_18077),U_18079))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),U_18078),U_18079)))
      | ~ class_Groups_Oab__group__add(U_18075) ),
    inference(variable_rename,[status(thm)],[f_4394_1]) ).

fof(f_4394_3,plain,
    ! [U_18075,U_18076,U_18077,U_18078,U_18079] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),hAPP(hAPP(c_COMBS(U_18076,U_18075,U_18075),hAPP(hAPP(c_COMBB(U_18075,tc_fun(U_18075,U_18075),U_18076),c_Groups_Ominus__class_Ominus(U_18075)),U_18077)),U_18078)),U_18079)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18075),hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),U_18077),U_18079))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),U_18078),U_18079)))
      | ~ class_Groups_Oab__group__add(U_18075) ),
    inference(definitional_conversion,[status(esa)],[f_4394_2]) ).

cnf(f_4394_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),hAPP(hAPP(c_COMBS(U_18076,U_18075,U_18075),hAPP(hAPP(c_COMBB(U_18075,tc_fun(U_18075,U_18075),U_18076),c_Groups_Ominus__class_Ominus(U_18075)),U_18077)),U_18078)),U_18079)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18075),hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),U_18077),U_18079))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18075),hAPP(hAPP(c_List_Omap(U_18076,U_18075),U_18078),U_18079)))
    | ~ class_Groups_Oab__group__add(U_18075) ),
    inference(clausify,[status(thm)],[f_4394_3]) ).

fof(f_4395_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__addf]) ).

fof(f_4395_2,plain,
    ! [U_18084,U_18083,U_18082,U_18081,U_18080] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),hAPP(hAPP(c_COMBS(U_18081,U_18080,U_18080),hAPP(hAPP(c_COMBB(U_18080,tc_fun(U_18080,U_18080),U_18081),c_Groups_Oplus__class_Oplus(U_18080)),U_18082)),U_18083)),U_18084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18080),hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),U_18082),U_18084))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),U_18083),U_18084)))
      | ~ class_Groups_Ocomm__monoid__add(U_18080) ),
    inference(variable_rename,[status(thm)],[f_4395_1]) ).

fof(f_4395_3,plain,
    ! [U_18080,U_18081,U_18082,U_18083,U_18084] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),hAPP(hAPP(c_COMBS(U_18081,U_18080,U_18080),hAPP(hAPP(c_COMBB(U_18080,tc_fun(U_18080,U_18080),U_18081),c_Groups_Oplus__class_Oplus(U_18080)),U_18082)),U_18083)),U_18084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18080),hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),U_18082),U_18084))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),U_18083),U_18084)))
      | ~ class_Groups_Ocomm__monoid__add(U_18080) ),
    inference(definitional_conversion,[status(esa)],[f_4395_2]) ).

cnf(f_4395_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),hAPP(hAPP(c_COMBS(U_18081,U_18080,U_18080),hAPP(hAPP(c_COMBB(U_18080,tc_fun(U_18080,U_18080),U_18081),c_Groups_Oplus__class_Oplus(U_18080)),U_18082)),U_18083)),U_18084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18080),hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),U_18082),U_18084))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18080),hAPP(hAPP(c_List_Omap(U_18081,U_18080),U_18083),U_18084)))
    | ~ class_Groups_Ocomm__monoid__add(U_18080) ),
    inference(clausify,[status(thm)],[f_4395_3]) ).

fof(f_4396_1,plain,
    ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__const__mult]) ).

fof(f_4396_2,plain,
    ! [U_18089,U_18088,U_18087,U_18086,U_18085] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18085),hAPP(hAPP(c_List_Omap(U_18086,U_18085),hAPP(hAPP(c_COMBB(U_18085,U_18085,U_18086),hAPP(c_Groups_Otimes__class_Otimes(U_18085),U_18087)),U_18088)),U_18089)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18085),U_18087),hAPP(c_List_Omonoid__add__class_Olistsum(U_18085),hAPP(hAPP(c_List_Omap(U_18086,U_18085),U_18088),U_18089)))
      | ~ class_Rings_Osemiring__0(U_18085) ),
    inference(variable_rename,[status(thm)],[f_4396_1]) ).

fof(f_4396_3,plain,
    ! [U_18085,U_18086,U_18087,U_18088,U_18089] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18085),hAPP(hAPP(c_List_Omap(U_18086,U_18085),hAPP(hAPP(c_COMBB(U_18085,U_18085,U_18086),hAPP(c_Groups_Otimes__class_Otimes(U_18085),U_18087)),U_18088)),U_18089)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18085),U_18087),hAPP(c_List_Omonoid__add__class_Olistsum(U_18085),hAPP(hAPP(c_List_Omap(U_18086,U_18085),U_18088),U_18089)))
      | ~ class_Rings_Osemiring__0(U_18085) ),
    inference(definitional_conversion,[status(esa)],[f_4396_2]) ).

cnf(f_4396_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18085),hAPP(hAPP(c_List_Omap(U_18086,U_18085),hAPP(hAPP(c_COMBB(U_18085,U_18085,U_18086),hAPP(c_Groups_Otimes__class_Otimes(U_18085),U_18087)),U_18088)),U_18089)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18085),U_18087),hAPP(c_List_Omonoid__add__class_Olistsum(U_18085),hAPP(hAPP(c_List_Omap(U_18086,U_18085),U_18088),U_18089)))
    | ~ class_Rings_Osemiring__0(U_18085) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

fof(f_4397_1,plain,
    ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mult__const]) ).

fof(f_4397_2,plain,
    ! [U_18094,U_18093,U_18092,U_18091,U_18090] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18090),hAPP(hAPP(c_List_Omap(U_18091,U_18090),hAPP(hAPP(c_COMBC(U_18091,U_18090,U_18090),hAPP(hAPP(c_COMBB(U_18090,tc_fun(U_18090,U_18090),U_18091),c_Groups_Otimes__class_Otimes(U_18090)),U_18092)),U_18093)),U_18094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18090),hAPP(c_List_Omonoid__add__class_Olistsum(U_18090),hAPP(hAPP(c_List_Omap(U_18091,U_18090),U_18092),U_18094))),U_18093)
      | ~ class_Rings_Osemiring__0(U_18090) ),
    inference(variable_rename,[status(thm)],[f_4397_1]) ).

fof(f_4397_3,plain,
    ! [U_18090,U_18091,U_18092,U_18093,U_18094] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18090),hAPP(hAPP(c_List_Omap(U_18091,U_18090),hAPP(hAPP(c_COMBC(U_18091,U_18090,U_18090),hAPP(hAPP(c_COMBB(U_18090,tc_fun(U_18090,U_18090),U_18091),c_Groups_Otimes__class_Otimes(U_18090)),U_18092)),U_18093)),U_18094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18090),hAPP(c_List_Omonoid__add__class_Olistsum(U_18090),hAPP(hAPP(c_List_Omap(U_18091,U_18090),U_18092),U_18094))),U_18093)
      | ~ class_Rings_Osemiring__0(U_18090) ),
    inference(definitional_conversion,[status(esa)],[f_4397_2]) ).

cnf(f_4397_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18090),hAPP(hAPP(c_List_Omap(U_18091,U_18090),hAPP(hAPP(c_COMBC(U_18091,U_18090,U_18090),hAPP(hAPP(c_COMBB(U_18090,tc_fun(U_18090,U_18090),U_18091),c_Groups_Otimes__class_Otimes(U_18090)),U_18092)),U_18093)),U_18094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18090),hAPP(c_List_Omonoid__add__class_Olistsum(U_18090),hAPP(hAPP(c_List_Omap(U_18091,U_18090),U_18092),U_18094))),U_18093)
    | ~ class_Rings_Osemiring__0(U_18090) ),
    inference(clausify,[status(thm)],[f_4397_3]) ).

fof(f_4398_1,plain,
    ! [V_xs_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__0]) ).

fof(f_4398_2,plain,
    ! [U_18097,U_18096,U_18095] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18095),hAPP(hAPP(c_List_Omap(U_18096,U_18095),hAPP(c_COMBK(U_18095,U_18096),c_Groups_Ozero__class_Ozero(U_18095))),U_18097)) = c_Groups_Ozero__class_Ozero(U_18095)
      | ~ class_Groups_Omonoid__add(U_18095) ),
    inference(variable_rename,[status(thm)],[f_4398_1]) ).

fof(f_4398_3,plain,
    ! [U_18095,U_18096,U_18097] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18095),hAPP(hAPP(c_List_Omap(U_18096,U_18095),hAPP(c_COMBK(U_18095,U_18096),c_Groups_Ozero__class_Ozero(U_18095))),U_18097)) = c_Groups_Ozero__class_Ozero(U_18095)
      | ~ class_Groups_Omonoid__add(U_18095) ),
    inference(definitional_conversion,[status(esa)],[f_4398_2]) ).

cnf(f_4398_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18095),hAPP(hAPP(c_List_Omap(U_18096,U_18095),hAPP(c_COMBK(U_18095,U_18096),c_Groups_Ozero__class_Ozero(U_18095))),U_18097)) = c_Groups_Ozero__class_Ozero(U_18095)
    | ~ class_Groups_Omonoid__add(U_18095) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

fof(f_4399_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__abs]) ).

fof(f_4399_2,plain,
    ! [U_18099,U_18098] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18098),hAPP(c_Groups_Oabs__class_Oabs(U_18098),hAPP(c_List_Omonoid__add__class_Olistsum(U_18098),U_18099))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18098),hAPP(hAPP(c_List_Omap(U_18098,U_18098),c_Groups_Oabs__class_Oabs(U_18098)),U_18099))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_18098) ),
    inference(variable_rename,[status(thm)],[f_4399_1]) ).

fof(f_4399_3,plain,
    ! [U_18098,U_18099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18098),hAPP(c_Groups_Oabs__class_Oabs(U_18098),hAPP(c_List_Omonoid__add__class_Olistsum(U_18098),U_18099))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18098),hAPP(hAPP(c_List_Omap(U_18098,U_18098),c_Groups_Oabs__class_Oabs(U_18098)),U_18099))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_18098) ),
    inference(definitional_conversion,[status(esa)],[f_4399_2]) ).

cnf(f_4399_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18098),hAPP(c_Groups_Oabs__class_Oabs(U_18098),hAPP(c_List_Omonoid__add__class_Olistsum(U_18098),U_18099))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18098),hAPP(hAPP(c_List_Omap(U_18098,U_18098),c_Groups_Oabs__class_Oabs(U_18098)),U_18099))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_18098) ),
    inference(clausify,[status(thm)],[f_4399_3]) ).

fof(f_4400_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map]) ).

fof(f_4400_2,plain,
    ! [U_18103,U_18102,U_18101,U_18100] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18100),hAPP(c_List_Omonoid__add__class_Olistsum(U_18100),hAPP(hAPP(c_List_Omap(U_18101,U_18100),U_18102),U_18103))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18100),hAPP(hAPP(c_List_Omap(U_18101,U_18100),hAPP(c_Fun_Ocomp(U_18100,U_18100,U_18101,c_Groups_Ouminus__class_Ouminus(U_18100)),U_18102)),U_18103))
      | ~ class_Groups_Oab__group__add(U_18100) ),
    inference(variable_rename,[status(thm)],[f_4400_1]) ).

fof(f_4400_3,plain,
    ! [U_18100,U_18101,U_18102,U_18103] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18100),hAPP(c_List_Omonoid__add__class_Olistsum(U_18100),hAPP(hAPP(c_List_Omap(U_18101,U_18100),U_18102),U_18103))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18100),hAPP(hAPP(c_List_Omap(U_18101,U_18100),hAPP(c_Fun_Ocomp(U_18100,U_18100,U_18101,c_Groups_Ouminus__class_Ouminus(U_18100)),U_18102)),U_18103))
      | ~ class_Groups_Oab__group__add(U_18100) ),
    inference(definitional_conversion,[status(esa)],[f_4400_2]) ).

cnf(f_4400_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18100),hAPP(c_List_Omonoid__add__class_Olistsum(U_18100),hAPP(hAPP(c_List_Omap(U_18101,U_18100),U_18102),U_18103))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18100),hAPP(hAPP(c_List_Omap(U_18101,U_18100),hAPP(c_Fun_Ocomp(U_18100,U_18100,U_18101,c_Groups_Ouminus__class_Ouminus(U_18100)),U_18102)),U_18103))
    | ~ class_Groups_Oab__group__add(U_18100) ),
    inference(clausify,[status(thm)],[f_4400_3]) ).

fof(f_4401_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum]) ).

fof(f_4401_2,plain,
    ! [U_18105,U_18104] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18104),U_18105) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18104,U_18104),c_COMBI(U_18104)),hAPP(c_List_Oset(U_18104),U_18105))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18104),U_18105))
      | ~ class_Groups_Ocomm__monoid__add(U_18104) ),
    inference(variable_rename,[status(thm)],[f_4401_1]) ).

fof(f_4401_3,plain,
    ! [U_18104,U_18105] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18104),U_18105) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18104,U_18104),c_COMBI(U_18104)),hAPP(c_List_Oset(U_18104),U_18105))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18104),U_18105))
      | ~ class_Groups_Ocomm__monoid__add(U_18104) ),
    inference(definitional_conversion,[status(esa)],[f_4401_2]) ).

cnf(f_4401_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18104),U_18105) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18104,U_18104),c_COMBI(U_18104)),hAPP(c_List_Oset(U_18104),U_18105))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18104),U_18105))
    | ~ class_Groups_Ocomm__monoid__add(U_18104) ),
    inference(clausify,[status(thm)],[f_4401_3]) ).

fof(f_4402_1,plain,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_select__weight__def]) ).

fof(f_4402_2,plain,
    ! [U_18107,U_18106] : c_Random_Oselect__weight(U_18106,U_18107) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18106),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18106)),U_18107)))),hAPP(hAPP(c_COMBB(U_18106,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18106,U_18107))),
    inference(variable_rename,[status(thm)],[f_4402_1]) ).

fof(f_4402_3,plain,
    ! [U_18106,U_18107] : c_Random_Oselect__weight(U_18106,U_18107) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18106),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18106)),U_18107)))),hAPP(hAPP(c_COMBB(U_18106,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18106,U_18107))),
    inference(definitional_conversion,[status(esa)],[f_4402_2]) ).

cnf(f_4402_4,plain,
    c_Random_Oselect__weight(U_18106,U_18107) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18106),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18106)),U_18107)))),hAPP(hAPP(c_COMBB(U_18106,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18106,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18106,U_18107))),
    inference(clausify,[status(thm)],[f_4402_3]) ).

fof(f_4403_1,plain,
    ! [V_f_2,V_xs_2,T_b,T_c] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set]) ).

fof(f_4403_2,plain,
    ! [U_18111,U_18110,U_18109,U_18108] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18108),hAPP(hAPP(c_List_Omap(U_18109,U_18108),U_18111),U_18110)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18109,U_18108),U_18111),hAPP(c_List_Oset(U_18109),U_18110))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18109),U_18110))
      | ~ class_Groups_Ocomm__monoid__add(U_18108) ),
    inference(variable_rename,[status(thm)],[f_4403_1]) ).

fof(f_4403_3,plain,
    ! [U_18108,U_18109,U_18110,U_18111] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18108),hAPP(hAPP(c_List_Omap(U_18109,U_18108),U_18111),U_18110)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18109,U_18108),U_18111),hAPP(c_List_Oset(U_18109),U_18110))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18109),U_18110))
      | ~ class_Groups_Ocomm__monoid__add(U_18108) ),
    inference(definitional_conversion,[status(esa)],[f_4403_2]) ).

cnf(f_4403_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18108),hAPP(hAPP(c_List_Omap(U_18109,U_18108),U_18111),U_18110)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18109,U_18108),U_18111),hAPP(c_List_Oset(U_18109),U_18110))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18109),U_18110))
    | ~ class_Groups_Ocomm__monoid__add(U_18108) ),
    inference(clausify,[status(thm)],[f_4403_3]) ).

fof(f_4404_1,plain,
    ! [V_j_2,V_i_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int]) ).

fof(f_4404_2,plain,
    ! [U_18115,U_18114,U_18113,U_18112] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18112),U_18113),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18114,U_18115))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18112),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18112),U_18113),c_List_Oupto(U_18114,U_18115)))
      | ~ class_Groups_Ocomm__monoid__add(U_18112) ),
    inference(variable_rename,[status(thm)],[f_4404_1]) ).

fof(f_4404_3,plain,
    ! [U_18112,U_18113,U_18114,U_18115] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18112),U_18113),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18114,U_18115))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18112),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18112),U_18113),c_List_Oupto(U_18114,U_18115)))
      | ~ class_Groups_Ocomm__monoid__add(U_18112) ),
    inference(definitional_conversion,[status(esa)],[f_4404_2]) ).

cnf(f_4404_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18112),U_18113),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18114,U_18115))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18112),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18112),U_18113),c_List_Oupto(U_18114,U_18115)))
    | ~ class_Groups_Ocomm__monoid__add(U_18112) ),
    inference(clausify,[status(thm)],[f_4404_3]) ).

fof(f_4405_1,plain,
    ! [V_l_2,V_k_2,V_f_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int]) ).

fof(f_4405_2,plain,
    ! [U_18119,U_18118,U_18117,U_18116] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18116),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18116),U_18117),c_List_Oupto(U_18118,U_18119))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18116),U_18117),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18118,U_18119)))
      | ~ class_Groups_Ocomm__monoid__add(U_18116) ),
    inference(variable_rename,[status(thm)],[f_4405_1]) ).

fof(f_4405_3,plain,
    ! [U_18116,U_18117,U_18118,U_18119] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18116),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18116),U_18117),c_List_Oupto(U_18118,U_18119))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18116),U_18117),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18118,U_18119)))
      | ~ class_Groups_Ocomm__monoid__add(U_18116) ),
    inference(definitional_conversion,[status(esa)],[f_4405_2]) ).

cnf(f_4405_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18116),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18116),U_18117),c_List_Oupto(U_18118,U_18119))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18116),U_18117),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18118,U_18119)))
    | ~ class_Groups_Ocomm__monoid__add(U_18116) ),
    inference(clausify,[status(thm)],[f_4405_3]) ).

fof(f_4406_1,plain,
    ! [V_xs_2,V_r_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2)
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__triv]) ).

fof(f_4406_2,plain,
    ! [U_18123,U_18122,U_18121,U_18120] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18120),hAPP(hAPP(c_List_Omap(U_18121,U_18120),hAPP(c_COMBK(U_18120,U_18121),U_18122)),U_18123)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18120),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18121)),U_18123))),U_18122)
      | ~ class_Rings_Osemiring__1(U_18120) ),
    inference(variable_rename,[status(thm)],[f_4406_1]) ).

fof(f_4406_3,plain,
    ! [U_18120,U_18121,U_18122,U_18123] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18120),hAPP(hAPP(c_List_Omap(U_18121,U_18120),hAPP(c_COMBK(U_18120,U_18121),U_18122)),U_18123)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18120),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18121)),U_18123))),U_18122)
      | ~ class_Rings_Osemiring__1(U_18120) ),
    inference(definitional_conversion,[status(esa)],[f_4406_2]) ).

cnf(f_4406_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18120),hAPP(hAPP(c_List_Omap(U_18121,U_18120),hAPP(c_COMBK(U_18120,U_18121),U_18122)),U_18123)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18120),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18121)),U_18123))),U_18122)
    | ~ class_Rings_Osemiring__1(U_18120) ),
    inference(clausify,[status(thm)],[f_4406_3]) ).

fof(f_4407_1,plain,
    ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1]) ).

fof(f_4407_2,plain,
    ! [U_18128,U_18127,U_18126,U_18125,U_18124] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18124),hAPP(hAPP(c_List_Omap(U_18125,U_18124),U_18128),U_18127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18124),hAPP(U_18128,U_18126)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18124),hAPP(hAPP(c_List_Omap(U_18125,U_18124),U_18128),c_List_Oremove1(U_18125,U_18126,U_18127))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18125),U_18126),hAPP(c_List_Oset(U_18125),U_18127)))
      | ~ class_Groups_Ocomm__monoid__add(U_18124) ),
    inference(variable_rename,[status(thm)],[f_4407_1]) ).

fof(f_4407_3,plain,
    ! [U_18124,U_18125,U_18126,U_18127,U_18128] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18124),hAPP(hAPP(c_List_Omap(U_18125,U_18124),U_18128),U_18127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18124),hAPP(U_18128,U_18126)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18124),hAPP(hAPP(c_List_Omap(U_18125,U_18124),U_18128),c_List_Oremove1(U_18125,U_18126,U_18127))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18125),U_18126),hAPP(c_List_Oset(U_18125),U_18127)))
      | ~ class_Groups_Ocomm__monoid__add(U_18124) ),
    inference(definitional_conversion,[status(esa)],[f_4407_2]) ).

cnf(f_4407_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18124),hAPP(hAPP(c_List_Omap(U_18125,U_18124),U_18128),U_18127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18124),hAPP(U_18128,U_18126)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18124),hAPP(hAPP(c_List_Omap(U_18125,U_18124),U_18128),c_List_Oremove1(U_18125,U_18126,U_18127))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18125),U_18126),hAPP(c_List_Oset(U_18125),U_18127)))
    | ~ class_Groups_Ocomm__monoid__add(U_18124) ),
    inference(clausify,[status(thm)],[f_4407_3]) ).

fof(f_4408_1,plain,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_select__weight__member]) ).

fof(f_4408_2,plain,
    ! [U_18131,U_18130,U_18129] :
      ( hBOOL(hAPP(hAPP(c_member(U_18129),hAPP(c_Product__Type_Ofst(U_18129,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18129,U_18130),U_18131))),hAPP(c_List_Oset(U_18129),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18129),U_18129),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18129)),U_18130))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18129),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18129)),U_18130)))) ),
    inference(variable_rename,[status(thm)],[f_4408_1]) ).

fof(f_4408_3,plain,
    ! [U_18129,U_18130,U_18131] :
      ( hBOOL(hAPP(hAPP(c_member(U_18129),hAPP(c_Product__Type_Ofst(U_18129,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18129,U_18130),U_18131))),hAPP(c_List_Oset(U_18129),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18129),U_18129),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18129)),U_18130))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18129),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18129)),U_18130)))) ),
    inference(definitional_conversion,[status(esa)],[f_4408_2]) ).

cnf(f_4408_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18129),hAPP(c_Product__Type_Ofst(U_18129,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18129,U_18130),U_18131))),hAPP(c_List_Oset(U_18129),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18129),U_18129),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18129)),U_18130))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18129),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18129)),U_18130)))) ),
    inference(clausify,[status(thm)],[f_4408_3]) ).

fof(f_4409_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( ( ( c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(f_4409_2,plain,
    ! [U_18135,U_18134,U_18133,U_18132] :
      ( ( ( c_Nitpick_Osetsum_H(U_18133,U_18132,U_18135,U_18134) = c_Groups_Ozero__class_Ozero(U_18132)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18133),U_18134)) )
        & ( c_Nitpick_Osetsum_H(U_18133,U_18132,U_18135,U_18134) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18132),hAPP(hAPP(c_List_Omap(U_18133,U_18132),U_18135),c_Hilbert__Choice_OEps(tc_List_Olist(U_18133),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18133),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18133)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18133),tc_fun(U_18133,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18133,tc_HOL_Obool),tc_fun(tc_fun(U_18133,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18133)),c_fequal),c_List_Oset(U_18133))),U_18134))),c_List_Odistinct(U_18133)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18133),U_18134)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_18132) ),
    inference(variable_rename,[status(thm)],[f_4409_1]) ).

fof(f_4409_3,plain,
    ( ! [U_18132,U_18133,U_18134,U_18135] :
        ( c_Nitpick_Osetsum_H(U_18133,U_18132,U_18135,U_18134) = c_Groups_Ozero__class_Ozero(U_18132)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18133),U_18134))
        | ~ sP1146(U_18132,U_18133,U_18134,U_18135) )
    & ! [U_18132,U_18133,U_18134,U_18135] :
        ( c_Nitpick_Osetsum_H(U_18133,U_18132,U_18135,U_18134) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18132),hAPP(hAPP(c_List_Omap(U_18133,U_18132),U_18135),c_Hilbert__Choice_OEps(tc_List_Olist(U_18133),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18133),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18133)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18133),tc_fun(U_18133,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18133,tc_HOL_Obool),tc_fun(tc_fun(U_18133,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18133)),c_fequal),c_List_Oset(U_18133))),U_18134))),c_List_Odistinct(U_18133)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18133),U_18134))
        | ~ sP1146(U_18132,U_18133,U_18134,U_18135) )
    & ! [U_18132,U_18133,U_18134,U_18135] :
        ( sP1146(U_18132,U_18133,U_18134,U_18135)
        | ~ class_Groups_Ocomm__monoid__add(U_18132) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1146])],[f_4409_2]) ).

cnf(f_4409_4,plain,
    ( sP1146(U_18132,U_18133,U_18134,U_18135)
    | ~ class_Groups_Ocomm__monoid__add(U_18132) ),
    inference(clausify,[status(thm)],[f_4409_3]) ).

cnf(f_4409_5,plain,
    ( c_Nitpick_Osetsum_H(U_18133,U_18132,U_18135,U_18134) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18132),hAPP(hAPP(c_List_Omap(U_18133,U_18132),U_18135),c_Hilbert__Choice_OEps(tc_List_Olist(U_18133),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18133),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18133)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18133),tc_fun(U_18133,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18133,tc_HOL_Obool),tc_fun(tc_fun(U_18133,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18133)),c_fequal),c_List_Oset(U_18133))),U_18134))),c_List_Odistinct(U_18133)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18133),U_18134))
    | ~ sP1146(U_18132,U_18133,U_18134,U_18135) ),
    inference(clausify,[status(thm)],[f_4409_3]) ).

cnf(f_4409_6,plain,
    ( c_Nitpick_Osetsum_H(U_18133,U_18132,U_18135,U_18134) = c_Groups_Ozero__class_Ozero(U_18132)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18133),U_18134))
    | ~ sP1146(U_18132,U_18133,U_18134,U_18135) ),
    inference(clausify,[status(thm)],[f_4409_3]) ).

fof(f_4410_1,plain,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(f_4410_2,plain,
    ! [U_18140,U_18139,U_18138,U_18137,U_18136] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18139,U_18136,U_18137,U_18138,U_18140) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18139,U_18136,U_18137),U_18138),U_18140)
      | hBOOL(hAPP(hAPP(c_member(U_18136),hAPP(U_18137,U_18138)),hAPP(c_Set_Oimage(U_18139,U_18136,U_18137),hAPP(c_List_Oset(U_18139),U_18140))))
      | ~ class_Orderings_Olinorder(U_18136) ),
    inference(variable_rename,[status(thm)],[f_4410_1]) ).

fof(f_4410_3,plain,
    ! [U_18139,U_18136,U_18140,U_18137,U_18138] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18139,U_18136,U_18137,U_18138,U_18140) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18139,U_18136,U_18137),U_18138),U_18140)
      | hBOOL(hAPP(hAPP(c_member(U_18136),hAPP(U_18137,U_18138)),hAPP(c_Set_Oimage(U_18139,U_18136,U_18137),hAPP(c_List_Oset(U_18139),U_18140))))
      | ~ class_Orderings_Olinorder(U_18136) ),
    inference(definitional_conversion,[status(esa)],[f_4410_2]) ).

cnf(f_4410_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18139,U_18136,U_18137,U_18138,U_18140) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18139,U_18136,U_18137),U_18138),U_18140)
    | hBOOL(hAPP(hAPP(c_member(U_18136),hAPP(U_18137,U_18138)),hAPP(c_Set_Oimage(U_18139,U_18136,U_18137),hAPP(c_List_Oset(U_18139),U_18140))))
    | ~ class_Orderings_Olinorder(U_18136) ),
    inference(clausify,[status(thm)],[f_4410_3]) ).

fof(f_4411_1,plain,
    ! [V_ns_2] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [B_x] :
            ( B_x != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__eq__0__nat__iff__nat]) ).

fof(f_4411_2,plain,
    ! [U_18143] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18143) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_18142] :
            ( U_18142 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18142),hAPP(c_List_Oset(tc_Nat_Onat),U_18143))) ) )
      & ( ! [U_18141] :
            ( U_18141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18141),hAPP(c_List_Oset(tc_Nat_Onat),U_18143))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18143) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4411_1]) ).

fof(f_4411_3,plain,
    ( ! [U_18145] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_18142] :
            ( U_18142 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18142),hAPP(c_List_Oset(tc_Nat_Onat),U_18145))) ) )
    & ! [U_18144] :
        ( ! [U_18141] :
            ( U_18141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18141),hAPP(c_List_Oset(tc_Nat_Onat),U_18144))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4411_2]) ).

fof(f_4411_4,plain,
    ( ! [U_18145] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK460(U_18145) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK460(U_18145)),hAPP(c_List_Oset(tc_Nat_Onat),U_18145))) ) )
    & ! [U_18144] :
        ( ! [U_18141] :
            ( U_18141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18141),hAPP(c_List_Oset(tc_Nat_Onat),U_18144))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_18142,sK460(U_18145))],[f_4411_3]) ).

fof(f_4411_5,plain,
    ( ! [U_18145] :
        ( sK460(U_18145) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1147(U_18145) )
    & ! [U_18145] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK460(U_18145)),hAPP(c_List_Oset(tc_Nat_Onat),U_18145)))
        | ~ sP1147(U_18145) )
    & ! [U_18145] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1147(U_18145) )
    & ! [U_18141,U_18144] :
        ( U_18141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18141),hAPP(c_List_Oset(tc_Nat_Onat),U_18144)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1147])],[f_4411_4]) ).

cnf(f_4411_6,plain,
    ( U_18141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18141),hAPP(c_List_Oset(tc_Nat_Onat),U_18144)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4411_5]) ).

cnf(f_4411_7,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1147(U_18145) ),
    inference(clausify,[status(thm)],[f_4411_5]) ).

cnf(f_4411_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK460(U_18145)),hAPP(c_List_Oset(tc_Nat_Onat),U_18145)))
    | ~ sP1147(U_18145) ),
    inference(clausify,[status(thm)],[f_4411_5]) ).

cnf(f_4411_9,plain,
    ( sK460(U_18145) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1147(U_18145) ),
    inference(clausify,[status(thm)],[f_4411_5]) ).

fof(f_4412_1,plain,
    ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert]) ).

fof(f_4412_2,plain,
    ! [U_18150,U_18149,U_18148,U_18147,U_18146] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18147),c_List_Olinorder__class_Oinsort__insert__key(U_18147,U_18146,U_18149,U_18150,U_18148)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18147),U_18148))
      | ~ class_Orderings_Olinorder(U_18146) ),
    inference(variable_rename,[status(thm)],[f_4412_1]) ).

fof(f_4412_3,plain,
    ! [U_18146,U_18147,U_18148,U_18149,U_18150] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18147),c_List_Olinorder__class_Oinsort__insert__key(U_18147,U_18146,U_18149,U_18150,U_18148)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18147),U_18148))
      | ~ class_Orderings_Olinorder(U_18146) ),
    inference(definitional_conversion,[status(esa)],[f_4412_2]) ).

cnf(f_4412_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18147),c_List_Olinorder__class_Oinsort__insert__key(U_18147,U_18146,U_18149,U_18150,U_18148)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18147),U_18148))
    | ~ class_Orderings_Olinorder(U_18146) ),
    inference(clausify,[status(thm)],[f_4412_3]) ).

fof(f_4413_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__triv]) ).

fof(f_4413_2,plain,
    ! [U_18153,U_18152,U_18151] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18151,U_18151,c_COMBI(U_18151),U_18152,U_18153) = U_18153
      | ~ hBOOL(hAPP(hAPP(c_member(U_18151),U_18152),hAPP(c_List_Oset(U_18151),U_18153)))
      | ~ class_Orderings_Olinorder(U_18151) ),
    inference(variable_rename,[status(thm)],[f_4413_1]) ).

fof(f_4413_3,plain,
    ! [U_18151,U_18152,U_18153] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18151,U_18151,c_COMBI(U_18151),U_18152,U_18153) = U_18153
      | ~ hBOOL(hAPP(hAPP(c_member(U_18151),U_18152),hAPP(c_List_Oset(U_18151),U_18153)))
      | ~ class_Orderings_Olinorder(U_18151) ),
    inference(definitional_conversion,[status(esa)],[f_4413_2]) ).

cnf(f_4413_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18151,U_18151,c_COMBI(U_18151),U_18152,U_18153) = U_18153
    | ~ hBOOL(hAPP(hAPP(c_member(U_18151),U_18152),hAPP(c_List_Oset(U_18151),U_18153)))
    | ~ class_Orderings_Olinorder(U_18151) ),
    inference(clausify,[status(thm)],[f_4413_3]) ).

fof(f_4414_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_set__insort__insert]) ).

fof(f_4414_2,plain,
    ! [U_18156,U_18155,U_18154] :
      ( hAPP(c_List_Oset(U_18154),c_List_Olinorder__class_Oinsort__insert__key(U_18154,U_18154,c_COMBI(U_18154),U_18155,U_18156)) = hAPP(hAPP(c_Set_Oinsert(U_18154),U_18155),hAPP(c_List_Oset(U_18154),U_18156))
      | ~ class_Orderings_Olinorder(U_18154) ),
    inference(variable_rename,[status(thm)],[f_4414_1]) ).

fof(f_4414_3,plain,
    ! [U_18154,U_18155,U_18156] :
      ( hAPP(c_List_Oset(U_18154),c_List_Olinorder__class_Oinsort__insert__key(U_18154,U_18154,c_COMBI(U_18154),U_18155,U_18156)) = hAPP(hAPP(c_Set_Oinsert(U_18154),U_18155),hAPP(c_List_Oset(U_18154),U_18156))
      | ~ class_Orderings_Olinorder(U_18154) ),
    inference(definitional_conversion,[status(esa)],[f_4414_2]) ).

cnf(f_4414_4,plain,
    ( hAPP(c_List_Oset(U_18154),c_List_Olinorder__class_Oinsort__insert__key(U_18154,U_18154,c_COMBI(U_18154),U_18155,U_18156)) = hAPP(hAPP(c_Set_Oinsert(U_18154),U_18155),hAPP(c_List_Oset(U_18154),U_18156))
    | ~ class_Orderings_Olinorder(U_18154) ),
    inference(clausify,[status(thm)],[f_4414_3]) ).

fof(f_4415_1,plain,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv]) ).

fof(f_4415_2,plain,
    ! [U_18161,U_18160,U_18159,U_18158,U_18157] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18160,U_18157,U_18158,U_18159,U_18161) = U_18161
      | ~ hBOOL(hAPP(hAPP(c_member(U_18157),hAPP(U_18158,U_18159)),hAPP(c_Set_Oimage(U_18160,U_18157,U_18158),hAPP(c_List_Oset(U_18160),U_18161))))
      | ~ class_Orderings_Olinorder(U_18157) ),
    inference(variable_rename,[status(thm)],[f_4415_1]) ).

fof(f_4415_3,plain,
    ! [U_18157,U_18158,U_18159,U_18160,U_18161] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18160,U_18157,U_18158,U_18159,U_18161) = U_18161
      | ~ hBOOL(hAPP(hAPP(c_member(U_18157),hAPP(U_18158,U_18159)),hAPP(c_Set_Oimage(U_18160,U_18157,U_18158),hAPP(c_List_Oset(U_18160),U_18161))))
      | ~ class_Orderings_Olinorder(U_18157) ),
    inference(definitional_conversion,[status(esa)],[f_4415_2]) ).

cnf(f_4415_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18160,U_18157,U_18158,U_18159,U_18161) = U_18161
    | ~ hBOOL(hAPP(hAPP(c_member(U_18157),hAPP(U_18158,U_18159)),hAPP(c_Set_Oimage(U_18160,U_18157,U_18158),hAPP(c_List_Oset(U_18160),U_18161))))
    | ~ class_Orderings_Olinorder(U_18157) ),
    inference(clausify,[status(thm)],[f_4415_3]) ).

fof(f_4416_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__insort]) ).

fof(f_4416_2,plain,
    ! [U_18164,U_18163,U_18162] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18162,U_18162,c_COMBI(U_18162),U_18163,U_18164) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18162,U_18162,c_COMBI(U_18162)),U_18163),U_18164)
      | hBOOL(hAPP(hAPP(c_member(U_18162),U_18163),hAPP(c_List_Oset(U_18162),U_18164)))
      | ~ class_Orderings_Olinorder(U_18162) ),
    inference(variable_rename,[status(thm)],[f_4416_1]) ).

fof(f_4416_3,plain,
    ! [U_18162,U_18163,U_18164] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18162,U_18162,c_COMBI(U_18162),U_18163,U_18164) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18162,U_18162,c_COMBI(U_18162)),U_18163),U_18164)
      | hBOOL(hAPP(hAPP(c_member(U_18162),U_18163),hAPP(c_List_Oset(U_18162),U_18164)))
      | ~ class_Orderings_Olinorder(U_18162) ),
    inference(definitional_conversion,[status(esa)],[f_4416_2]) ).

cnf(f_4416_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18162,U_18162,c_COMBI(U_18162),U_18163,U_18164) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18162,U_18162,c_COMBI(U_18162)),U_18163),U_18164)
    | hBOOL(hAPP(hAPP(c_member(U_18162),U_18163),hAPP(c_List_Oset(U_18162),U_18164)))
    | ~ class_Orderings_Olinorder(U_18162) ),
    inference(clausify,[status(thm)],[f_4416_3]) ).

fof(f_4417_1,plain,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
            | V_a_2 != V_b_2 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons]) ).

fof(f_4417_2,plain,
    ! [U_18170,U_18169,U_18168,U_18167,U_18166,U_18165] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18165),tc_List_Olist(U_18165))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18165),tc_List_Olist(U_18165)),hAPP(hAPP(c_List_Olist_OCons(U_18165),U_18166),U_18167)),hAPP(hAPP(c_List_Olist_OCons(U_18165),U_18168),U_18169))),c_List_Olexord(U_18165,U_18170)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18165),tc_List_Olist(U_18165))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18165),tc_List_Olist(U_18165)),U_18167),U_18169)),c_List_Olexord(U_18165,U_18170)))
            | U_18166 != U_18168 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18165,U_18165)),hAPP(hAPP(c_Product__Type_OPair(U_18165,U_18165),U_18166),U_18168)),U_18170)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18165),tc_List_Olist(U_18165))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18165),tc_List_Olist(U_18165)),U_18167),U_18169)),c_List_Olexord(U_18165,U_18170)))
          & U_18166 = U_18168 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18165,U_18165)),hAPP(hAPP(c_Product__Type_OPair(U_18165,U_18165),U_18166),U_18168)),U_18170))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18165),tc_List_Olist(U_18165))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18165),tc_List_Olist(U_18165)),hAPP(hAPP(c_List_Olist_OCons(U_18165),U_18166),U_18167)),hAPP(hAPP(c_List_Olist_OCons(U_18165),U_18168),U_18169))),c_List_Olexord(U_18165,U_18170))) ) ),
    inference(variable_rename,[status(thm)],[f_4417_1]) ).

fof(f_4417_3,plain,
    ( ! [U_18182,U_18180,U_18178,U_18176,U_18174,U_18172] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18172),tc_List_Olist(U_18172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18172),tc_List_Olist(U_18172)),hAPP(hAPP(c_List_Olist_OCons(U_18172),U_18174),U_18176)),hAPP(hAPP(c_List_Olist_OCons(U_18172),U_18178),U_18180))),c_List_Olexord(U_18172,U_18182)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18172),tc_List_Olist(U_18172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18172),tc_List_Olist(U_18172)),U_18176),U_18180)),c_List_Olexord(U_18172,U_18182)))
            | U_18174 != U_18178 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18172,U_18172)),hAPP(hAPP(c_Product__Type_OPair(U_18172,U_18172),U_18174),U_18178)),U_18182)) ) )
    & ! [U_18181,U_18179,U_18177,U_18175,U_18173,U_18171] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18171),tc_List_Olist(U_18171))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18171),tc_List_Olist(U_18171)),U_18175),U_18179)),c_List_Olexord(U_18171,U_18181)))
          & U_18173 = U_18177 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18171,U_18171)),hAPP(hAPP(c_Product__Type_OPair(U_18171,U_18171),U_18173),U_18177)),U_18181))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18171),tc_List_Olist(U_18171))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18171),tc_List_Olist(U_18171)),hAPP(hAPP(c_List_Olist_OCons(U_18171),U_18173),U_18175)),hAPP(hAPP(c_List_Olist_OCons(U_18171),U_18177),U_18179))),c_List_Olexord(U_18171,U_18181))) ) ),
    inference(miniscope,[status(thm)],[f_4417_2]) ).

fof(f_4417_4,plain,
    ( ! [U_18174,U_18172,U_18178,U_18180,U_18176,U_18182] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18172),tc_List_Olist(U_18172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18172),tc_List_Olist(U_18172)),U_18176),U_18180)),c_List_Olexord(U_18172,U_18182)))
        | U_18174 != U_18178
        | ~ sP1149(U_18174,U_18172,U_18178,U_18180,U_18176,U_18182) )
    & ! [U_18174,U_18172,U_18178,U_18180,U_18176,U_18182] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18172,U_18172)),hAPP(hAPP(c_Product__Type_OPair(U_18172,U_18172),U_18174),U_18178)),U_18182))
        | ~ sP1149(U_18174,U_18172,U_18178,U_18180,U_18176,U_18182) )
    & ! [U_18171,U_18175,U_18179,U_18173,U_18177,U_18181] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18171),tc_List_Olist(U_18171))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18171),tc_List_Olist(U_18171)),U_18175),U_18179)),c_List_Olexord(U_18171,U_18181)))
        | ~ sP1148(U_18171,U_18175,U_18179,U_18173,U_18177,U_18181) )
    & ! [U_18171,U_18175,U_18179,U_18173,U_18177,U_18181] :
        ( U_18173 = U_18177
        | ~ sP1148(U_18171,U_18175,U_18179,U_18173,U_18177,U_18181) )
    & ! [U_18174,U_18172,U_18178,U_18180,U_18176,U_18182] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18172),tc_List_Olist(U_18172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18172),tc_List_Olist(U_18172)),hAPP(hAPP(c_List_Olist_OCons(U_18172),U_18174),U_18176)),hAPP(hAPP(c_List_Olist_OCons(U_18172),U_18178),U_18180))),c_List_Olexord(U_18172,U_18182)))
        | sP1149(U_18174,U_18172,U_18178,U_18180,U_18176,U_18182) )
    & ! [U_18171,U_18175,U_18179,U_18173,U_18177,U_18181] :
        ( sP1148(U_18171,U_18175,U_18179,U_18173,U_18177,U_18181)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18171,U_18171)),hAPP(hAPP(c_Product__Type_OPair(U_18171,U_18171),U_18173),U_18177)),U_18181))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18171),tc_List_Olist(U_18171))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18171),tc_List_Olist(U_18171)),hAPP(hAPP(c_List_Olist_OCons(U_18171),U_18173),U_18175)),hAPP(hAPP(c_List_Olist_OCons(U_18171),U_18177),U_18179))),c_List_Olexord(U_18171,U_18181))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1148,sP1149])],[f_4417_3]) ).

cnf(f_4417_5,plain,
    ( sP1148(U_18171,U_18175,U_18179,U_18173,U_18177,U_18181)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18171,U_18171)),hAPP(hAPP(c_Product__Type_OPair(U_18171,U_18171),U_18173),U_18177)),U_18181))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18171),tc_List_Olist(U_18171))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18171),tc_List_Olist(U_18171)),hAPP(hAPP(c_List_Olist_OCons(U_18171),U_18173),U_18175)),hAPP(hAPP(c_List_Olist_OCons(U_18171),U_18177),U_18179))),c_List_Olexord(U_18171,U_18181))) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

cnf(f_4417_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18172),tc_List_Olist(U_18172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18172),tc_List_Olist(U_18172)),hAPP(hAPP(c_List_Olist_OCons(U_18172),U_18174),U_18176)),hAPP(hAPP(c_List_Olist_OCons(U_18172),U_18178),U_18180))),c_List_Olexord(U_18172,U_18182)))
    | sP1149(U_18174,U_18172,U_18178,U_18180,U_18176,U_18182) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

cnf(f_4417_7,plain,
    ( U_18173 = U_18177
    | ~ sP1148(U_18171,U_18175,U_18179,U_18173,U_18177,U_18181) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

cnf(f_4417_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18171),tc_List_Olist(U_18171))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18171),tc_List_Olist(U_18171)),U_18175),U_18179)),c_List_Olexord(U_18171,U_18181)))
    | ~ sP1148(U_18171,U_18175,U_18179,U_18173,U_18177,U_18181) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

cnf(f_4417_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18172,U_18172)),hAPP(hAPP(c_Product__Type_OPair(U_18172,U_18172),U_18174),U_18178)),U_18182))
    | ~ sP1149(U_18174,U_18172,U_18178,U_18180,U_18176,U_18182) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

cnf(f_4417_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18172),tc_List_Olist(U_18172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18172),tc_List_Olist(U_18172)),U_18176),U_18180)),c_List_Olexord(U_18172,U_18182)))
    | U_18174 != U_18178
    | ~ sP1149(U_18174,U_18172,U_18178,U_18180,U_18176,U_18182) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

fof(f_4418_1,plain,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
    inference(fof_nnf,[status(thm)],[fact_set__zip]) ).

fof(f_4418_2,plain,
    ! [U_18186,U_18185,U_18184,U_18183] : hAPP(c_List_Oset(tc_prod(U_18183,U_18184)),hAPP(hAPP(c_List_Ozip(U_18183,U_18184),U_18185),U_18186)) = hAPP(c_Set_OCollect(tc_prod(U_18183,U_18184)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18183,U_18184)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18183,U_18184),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(U_18183,U_18184),tc_fun(tc_Nat_Onat,tc_prod(U_18183,U_18184)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18183,U_18184),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18183,U_18184)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),c_COMBB(tc_prod(U_18183,U_18184),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18184,tc_prod(U_18183,U_18184)),hAPP(hAPP(c_COMBB(U_18183,tc_fun(U_18184,tc_prod(U_18183,U_18184)),tc_Nat_Onat),c_Product__Type_OPair(U_18183,U_18184)),hAPP(c_List_Onth(U_18183),U_18185))),hAPP(c_List_Onth(U_18184),U_18186)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18183)),U_18185)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18184)),U_18186)))))),
    inference(variable_rename,[status(thm)],[f_4418_1]) ).

fof(f_4418_3,plain,
    ! [U_18183,U_18184,U_18185,U_18186] : hAPP(c_List_Oset(tc_prod(U_18183,U_18184)),hAPP(hAPP(c_List_Ozip(U_18183,U_18184),U_18185),U_18186)) = hAPP(c_Set_OCollect(tc_prod(U_18183,U_18184)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18183,U_18184)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18183,U_18184),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(U_18183,U_18184),tc_fun(tc_Nat_Onat,tc_prod(U_18183,U_18184)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18183,U_18184),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18183,U_18184)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),c_COMBB(tc_prod(U_18183,U_18184),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18184,tc_prod(U_18183,U_18184)),hAPP(hAPP(c_COMBB(U_18183,tc_fun(U_18184,tc_prod(U_18183,U_18184)),tc_Nat_Onat),c_Product__Type_OPair(U_18183,U_18184)),hAPP(c_List_Onth(U_18183),U_18185))),hAPP(c_List_Onth(U_18184),U_18186)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18183)),U_18185)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18184)),U_18186)))))),
    inference(definitional_conversion,[status(esa)],[f_4418_2]) ).

cnf(f_4418_4,plain,
    hAPP(c_List_Oset(tc_prod(U_18183,U_18184)),hAPP(hAPP(c_List_Ozip(U_18183,U_18184),U_18185),U_18186)) = hAPP(c_Set_OCollect(tc_prod(U_18183,U_18184)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18183,U_18184)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18183,U_18184),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(U_18183,U_18184),tc_fun(tc_Nat_Onat,tc_prod(U_18183,U_18184)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18183,U_18184),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18183,U_18184)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18183,U_18184)),c_COMBB(tc_prod(U_18183,U_18184),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18184,tc_prod(U_18183,U_18184)),hAPP(hAPP(c_COMBB(U_18183,tc_fun(U_18184,tc_prod(U_18183,U_18184)),tc_Nat_Onat),c_Product__Type_OPair(U_18183,U_18184)),hAPP(c_List_Onth(U_18183),U_18185))),hAPP(c_List_Onth(U_18184),U_18186)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18183)),U_18185)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18184)),U_18186)))))),
    inference(clausify,[status(thm)],[f_4418_3]) ).

fof(f_4419_1,plain,
    ! [V_ys,T_b,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__zip]) ).

fof(f_4419_2,plain,
    ! [U_18191,U_18190,U_18189,U_18188,U_18187] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_18188,U_18190)),hAPP(hAPP(c_List_Ozip(U_18188,U_18190),U_18189),U_18191)),U_18187) = hAPP(hAPP(c_Product__Type_OPair(U_18188,U_18190),hAPP(hAPP(c_List_Onth(U_18188),U_18189),U_18187)),hAPP(hAPP(c_List_Onth(U_18190),U_18191),U_18187))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18190)),U_18191)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18188)),U_18189))) ),
    inference(variable_rename,[status(thm)],[f_4419_1]) ).

fof(f_4419_3,plain,
    ! [U_18187,U_18188,U_18189,U_18190,U_18191] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_18188,U_18190)),hAPP(hAPP(c_List_Ozip(U_18188,U_18190),U_18189),U_18191)),U_18187) = hAPP(hAPP(c_Product__Type_OPair(U_18188,U_18190),hAPP(hAPP(c_List_Onth(U_18188),U_18189),U_18187)),hAPP(hAPP(c_List_Onth(U_18190),U_18191),U_18187))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18190)),U_18191)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18188)),U_18189))) ),
    inference(definitional_conversion,[status(esa)],[f_4419_2]) ).

cnf(f_4419_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(U_18188,U_18190)),hAPP(hAPP(c_List_Ozip(U_18188,U_18190),U_18189),U_18191)),U_18187) = hAPP(hAPP(c_Product__Type_OPair(U_18188,U_18190),hAPP(hAPP(c_List_Onth(U_18188),U_18189),U_18187)),hAPP(hAPP(c_List_Onth(U_18190),U_18191),U_18187))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18190)),U_18191)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18188)),U_18189))) ),
    inference(clausify,[status(thm)],[f_4419_3]) ).

fof(f_4420_1,plain,
    ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
      ( hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__map]) ).

fof(f_4420_2,plain,
    ! [U_18196,U_18195,U_18194,U_18193,U_18192] :
      ( hAPP(hAPP(c_List_Onth(U_18195),hAPP(hAPP(c_List_Omap(U_18193,U_18195),U_18196),U_18194)),U_18192) = hAPP(U_18196,hAPP(hAPP(c_List_Onth(U_18193),U_18194),U_18192))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18193)),U_18194))) ),
    inference(variable_rename,[status(thm)],[f_4420_1]) ).

fof(f_4420_3,plain,
    ! [U_18193,U_18192,U_18194,U_18195,U_18196] :
      ( hAPP(hAPP(c_List_Onth(U_18195),hAPP(hAPP(c_List_Omap(U_18193,U_18195),U_18196),U_18194)),U_18192) = hAPP(U_18196,hAPP(hAPP(c_List_Onth(U_18193),U_18194),U_18192))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18193)),U_18194))) ),
    inference(definitional_conversion,[status(esa)],[f_4420_2]) ).

cnf(f_4420_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18195),hAPP(hAPP(c_List_Omap(U_18193,U_18195),U_18196),U_18194)),U_18192) = hAPP(U_18196,hAPP(hAPP(c_List_Onth(U_18193),U_18194),U_18192))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18193)),U_18194))) ),
    inference(clausify,[status(thm)],[f_4420_3]) ).

fof(f_4421_1,plain,
    ! [V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) ),
    inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat]) ).

fof(f_4421_2,plain,
    ! [U_18198,U_18197] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18198),U_18197)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18198)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18198))) ),
    inference(variable_rename,[status(thm)],[f_4421_1]) ).

fof(f_4421_3,plain,
    ! [U_18197,U_18198] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18198),U_18197)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18198)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18198))) ),
    inference(definitional_conversion,[status(esa)],[f_4421_2]) ).

cnf(f_4421_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18198),U_18197)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18198)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18198))) ),
    inference(clausify,[status(thm)],[f_4421_3]) ).

fof(f_4422_1,plain,
    ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_nth_Osimps]) ).

fof(f_4422_2,plain,
    ! [U_18202,U_18201,U_18200,U_18199] : hAPP(hAPP(c_List_Onth(U_18199),hAPP(hAPP(c_List_Olist_OCons(U_18199),U_18200),U_18201)),U_18202) = c_Nat_Onat_Onat__case(U_18199,U_18200,hAPP(c_List_Onth(U_18199),U_18201),U_18202),
    inference(variable_rename,[status(thm)],[f_4422_1]) ).

fof(f_4422_3,plain,
    ! [U_18200,U_18199,U_18201,U_18202] : hAPP(hAPP(c_List_Onth(U_18199),hAPP(hAPP(c_List_Olist_OCons(U_18199),U_18200),U_18201)),U_18202) = c_Nat_Onat_Onat__case(U_18199,U_18200,hAPP(c_List_Onth(U_18199),U_18201),U_18202),
    inference(definitional_conversion,[status(esa)],[f_4422_2]) ).

cnf(f_4422_4,plain,
    hAPP(hAPP(c_List_Onth(U_18199),hAPP(hAPP(c_List_Olist_OCons(U_18199),U_18200),U_18201)),U_18202) = c_Nat_Onat_Onat__case(U_18199,U_18200,hAPP(c_List_Onth(U_18199),U_18201),U_18202),
    inference(clausify,[status(thm)],[f_4422_3]) ).

fof(f_4423_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_nth__Cons__0]) ).

fof(f_4423_2,plain,
    ! [U_18205,U_18204,U_18203] : hAPP(hAPP(c_List_Onth(U_18203),hAPP(hAPP(c_List_Olist_OCons(U_18203),U_18204),U_18205)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18204,
    inference(variable_rename,[status(thm)],[f_4423_1]) ).

fof(f_4423_3,plain,
    ! [U_18203,U_18204,U_18205] : hAPP(hAPP(c_List_Onth(U_18203),hAPP(hAPP(c_List_Olist_OCons(U_18203),U_18204),U_18205)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18204,
    inference(definitional_conversion,[status(esa)],[f_4423_2]) ).

cnf(f_4423_4,plain,
    hAPP(hAPP(c_List_Onth(U_18203),hAPP(hAPP(c_List_Olist_OCons(U_18203),U_18204),U_18205)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18204,
    inference(clausify,[status(thm)],[f_4423_3]) ).

fof(f_4424_1,plain,
    ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n),
    inference(fof_nnf,[status(thm)],[fact_nth__Cons__Suc]) ).

fof(f_4424_2,plain,
    ! [U_18209,U_18208,U_18207,U_18206] : hAPP(hAPP(c_List_Onth(U_18206),hAPP(hAPP(c_List_Olist_OCons(U_18206),U_18207),U_18208)),hAPP(c_Nat_OSuc,U_18209)) = hAPP(hAPP(c_List_Onth(U_18206),U_18208),U_18209),
    inference(variable_rename,[status(thm)],[f_4424_1]) ).

fof(f_4424_3,plain,
    ! [U_18206,U_18207,U_18208,U_18209] : hAPP(hAPP(c_List_Onth(U_18206),hAPP(hAPP(c_List_Olist_OCons(U_18206),U_18207),U_18208)),hAPP(c_Nat_OSuc,U_18209)) = hAPP(hAPP(c_List_Onth(U_18206),U_18208),U_18209),
    inference(definitional_conversion,[status(esa)],[f_4424_2]) ).

cnf(f_4424_4,plain,
    hAPP(hAPP(c_List_Onth(U_18206),hAPP(hAPP(c_List_Olist_OCons(U_18206),U_18207),U_18208)),hAPP(c_Nat_OSuc,U_18209)) = hAPP(hAPP(c_List_Onth(U_18206),U_18208),U_18209),
    inference(clausify,[status(thm)],[f_4424_3]) ).

fof(f_4425_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ? [B_i] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_i] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__set__conv__all__nth]) ).

fof(f_4425_2,plain,
    ! [U_18216,U_18215,U_18214] :
      ( ( ! [U_18213] :
            ( hBOOL(hAPP(U_18216,U_18213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18214),U_18213),hAPP(c_List_Oset(U_18214),U_18215))) )
        | ? [U_18212] :
            ( ~ hBOOL(hAPP(U_18216,hAPP(hAPP(c_List_Onth(U_18214),U_18215),U_18212)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18214)),U_18215))) ) )
      & ( ! [U_18211] :
            ( hBOOL(hAPP(U_18216,hAPP(hAPP(c_List_Onth(U_18214),U_18215),U_18211)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18214)),U_18215))) )
        | ? [U_18210] :
            ( ~ hBOOL(hAPP(U_18216,U_18210))
            & hBOOL(hAPP(hAPP(c_member(U_18214),U_18210),hAPP(c_List_Oset(U_18214),U_18215))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4425_1]) ).

fof(f_4425_3,plain,
    ( ! [U_18222,U_18220,U_18218] :
        ( ! [U_18213] :
            ( hBOOL(hAPP(U_18222,U_18213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18218),U_18213),hAPP(c_List_Oset(U_18218),U_18220))) )
        | ? [U_18212] :
            ( ~ hBOOL(hAPP(U_18222,hAPP(hAPP(c_List_Onth(U_18218),U_18220),U_18212)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18220))) ) )
    & ! [U_18221,U_18219,U_18217] :
        ( ! [U_18211] :
            ( hBOOL(hAPP(U_18221,hAPP(hAPP(c_List_Onth(U_18217),U_18219),U_18211)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18217)),U_18219))) )
        | ? [U_18210] :
            ( ~ hBOOL(hAPP(U_18221,U_18210))
            & hBOOL(hAPP(hAPP(c_member(U_18217),U_18210),hAPP(c_List_Oset(U_18217),U_18219))) ) ) ),
    inference(miniscope,[status(thm)],[f_4425_2]) ).

fof(f_4425_4,plain,
    ( ! [U_18222,U_18220,U_18218] :
        ( ! [U_18213] :
            ( hBOOL(hAPP(U_18222,U_18213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18218),U_18213),hAPP(c_List_Oset(U_18218),U_18220))) )
        | ? [U_18212] :
            ( ~ hBOOL(hAPP(U_18222,hAPP(hAPP(c_List_Onth(U_18218),U_18220),U_18212)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18220))) ) )
    & ! [U_18221,U_18219,U_18217] :
        ( ! [U_18211] :
            ( hBOOL(hAPP(U_18221,hAPP(hAPP(c_List_Onth(U_18217),U_18219),U_18211)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18217)),U_18219))) )
        | ( ~ hBOOL(hAPP(U_18221,sK461(U_18221,U_18219,U_18217)))
          & hBOOL(hAPP(hAPP(c_member(U_18217),sK461(U_18221,U_18219,U_18217)),hAPP(c_List_Oset(U_18217),U_18219))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_18210,sK461(U_18221,U_18219,U_18217))],[f_4425_3]) ).

fof(f_4425_5,plain,
    ( ! [U_18222,U_18220,U_18218] :
        ( ! [U_18213] :
            ( hBOOL(hAPP(U_18222,U_18213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18218),U_18213),hAPP(c_List_Oset(U_18218),U_18220))) )
        | ( ~ hBOOL(hAPP(U_18222,hAPP(hAPP(c_List_Onth(U_18218),U_18220),sK462(U_18222,U_18220,U_18218))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18222,U_18220,U_18218)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18220))) ) )
    & ! [U_18221,U_18219,U_18217] :
        ( ! [U_18211] :
            ( hBOOL(hAPP(U_18221,hAPP(hAPP(c_List_Onth(U_18217),U_18219),U_18211)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18217)),U_18219))) )
        | ( ~ hBOOL(hAPP(U_18221,sK461(U_18221,U_18219,U_18217)))
          & hBOOL(hAPP(hAPP(c_member(U_18217),sK461(U_18221,U_18219,U_18217)),hAPP(c_List_Oset(U_18217),U_18219))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_18212,sK462(U_18222,U_18220,U_18218))],[f_4425_4]) ).

fof(f_4425_6,plain,
    ( ! [U_18220,U_18222,U_18218] :
        ( ~ hBOOL(hAPP(U_18222,hAPP(hAPP(c_List_Onth(U_18218),U_18220),sK462(U_18222,U_18220,U_18218))))
        | ~ sP1151(U_18220,U_18222,U_18218) )
    & ! [U_18220,U_18222,U_18218] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18222,U_18220,U_18218)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18220)))
        | ~ sP1151(U_18220,U_18222,U_18218) )
    & ! [U_18217,U_18221,U_18219] :
        ( ~ hBOOL(hAPP(U_18221,sK461(U_18221,U_18219,U_18217)))
        | ~ sP1150(U_18217,U_18221,U_18219) )
    & ! [U_18217,U_18221,U_18219] :
        ( hBOOL(hAPP(hAPP(c_member(U_18217),sK461(U_18221,U_18219,U_18217)),hAPP(c_List_Oset(U_18217),U_18219)))
        | ~ sP1150(U_18217,U_18221,U_18219) )
    & ! [U_18220,U_18222,U_18213,U_18218] :
        ( hBOOL(hAPP(U_18222,U_18213))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18218),U_18213),hAPP(c_List_Oset(U_18218),U_18220)))
        | sP1151(U_18220,U_18222,U_18218) )
    & ! [U_18211,U_18217,U_18221,U_18219] :
        ( hBOOL(hAPP(U_18221,hAPP(hAPP(c_List_Onth(U_18217),U_18219),U_18211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18217)),U_18219)))
        | sP1150(U_18217,U_18221,U_18219) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1150,sP1151])],[f_4425_5]) ).

cnf(f_4425_7,plain,
    ( hBOOL(hAPP(U_18221,hAPP(hAPP(c_List_Onth(U_18217),U_18219),U_18211)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18217)),U_18219)))
    | sP1150(U_18217,U_18221,U_18219) ),
    inference(clausify,[status(thm)],[f_4425_6]) ).

cnf(f_4425_8,plain,
    ( hBOOL(hAPP(U_18222,U_18213))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18218),U_18213),hAPP(c_List_Oset(U_18218),U_18220)))
    | sP1151(U_18220,U_18222,U_18218) ),
    inference(clausify,[status(thm)],[f_4425_6]) ).

cnf(f_4425_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18217),sK461(U_18221,U_18219,U_18217)),hAPP(c_List_Oset(U_18217),U_18219)))
    | ~ sP1150(U_18217,U_18221,U_18219) ),
    inference(clausify,[status(thm)],[f_4425_6]) ).

cnf(f_4425_10,plain,
    ( ~ hBOOL(hAPP(U_18221,sK461(U_18221,U_18219,U_18217)))
    | ~ sP1150(U_18217,U_18221,U_18219) ),
    inference(clausify,[status(thm)],[f_4425_6]) ).

cnf(f_4425_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18222,U_18220,U_18218)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18220)))
    | ~ sP1151(U_18220,U_18222,U_18218) ),
    inference(clausify,[status(thm)],[f_4425_6]) ).

cnf(f_4425_12,plain,
    ( ~ hBOOL(hAPP(U_18222,hAPP(hAPP(c_List_Onth(U_18218),U_18220),sK462(U_18222,U_18220,U_18218))))
    | ~ sP1151(U_18220,U_18222,U_18218) ),
    inference(clausify,[status(thm)],[f_4425_6]) ).

fof(f_4426_1,plain,
    ! [T_b,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ? [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_i] :
              ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__eq__iff__nth__eq]) ).

fof(f_4426_2,plain,
    ! [U_18227,U_18226,U_18225] :
      ( ( U_18225 = U_18226
        | ? [U_18224] :
            ( hAPP(hAPP(c_List_Onth(U_18227),U_18225),U_18224) != hAPP(hAPP(c_List_Onth(U_18227),U_18226),U_18224)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18225))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18225) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18226) )
      & ( ( ! [U_18223] :
              ( hAPP(hAPP(c_List_Onth(U_18227),U_18225),U_18223) = hAPP(hAPP(c_List_Onth(U_18227),U_18226),U_18223)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18225))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18225) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18226) )
        | U_18225 != U_18226 ) ),
    inference(variable_rename,[status(thm)],[f_4426_1]) ).

fof(f_4426_3,plain,
    ( ! [U_18233,U_18231,U_18229] :
        ( U_18229 = U_18231
        | ? [U_18224] :
            ( hAPP(hAPP(c_List_Onth(U_18233),U_18229),U_18224) != hAPP(hAPP(c_List_Onth(U_18233),U_18231),U_18224)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18231) )
    & ! [U_18232,U_18230,U_18228] :
        ( ( ! [U_18223] :
              ( hAPP(hAPP(c_List_Onth(U_18232),U_18228),U_18223) = hAPP(hAPP(c_List_Onth(U_18232),U_18230),U_18223)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18230) )
        | U_18228 != U_18230 ) ),
    inference(miniscope,[status(thm)],[f_4426_2]) ).

fof(f_4426_4,plain,
    ( ! [U_18233,U_18231,U_18229] :
        ( U_18229 = U_18231
        | ( hAPP(hAPP(c_List_Onth(U_18233),U_18229),sK463(U_18233,U_18231,U_18229)) != hAPP(hAPP(c_List_Onth(U_18233),U_18231),sK463(U_18233,U_18231,U_18229))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18233,U_18231,U_18229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18231) )
    & ! [U_18232,U_18230,U_18228] :
        ( ( ! [U_18223] :
              ( hAPP(hAPP(c_List_Onth(U_18232),U_18228),U_18223) = hAPP(hAPP(c_List_Onth(U_18232),U_18230),U_18223)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18230) )
        | U_18228 != U_18230 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_18224,sK463(U_18233,U_18231,U_18229))],[f_4426_3]) ).

fof(f_4426_5,plain,
    ( ! [U_18229,U_18231,U_18233] :
        ( hAPP(hAPP(c_List_Onth(U_18233),U_18229),sK463(U_18233,U_18231,U_18229)) != hAPP(hAPP(c_List_Onth(U_18233),U_18231),sK463(U_18233,U_18231,U_18229))
        | ~ sP1153(U_18229,U_18231,U_18233) )
    & ! [U_18229,U_18231,U_18233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18233,U_18231,U_18229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229)))
        | ~ sP1153(U_18229,U_18231,U_18233) )
    & ! [U_18223,U_18228,U_18230,U_18232] :
        ( hAPP(hAPP(c_List_Onth(U_18232),U_18228),U_18223) = hAPP(hAPP(c_List_Onth(U_18232),U_18230),U_18223)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228)))
        | ~ sP1152(U_18223,U_18228,U_18230,U_18232) )
    & ! [U_18223,U_18228,U_18230,U_18232] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18230)
        | ~ sP1152(U_18223,U_18228,U_18230,U_18232) )
    & ! [U_18229,U_18231,U_18233] :
        ( U_18229 = U_18231
        | sP1153(U_18229,U_18231,U_18233)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18231) )
    & ! [U_18223,U_18228,U_18230,U_18232] :
        ( sP1152(U_18223,U_18228,U_18230,U_18232)
        | U_18228 != U_18230 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1152,sP1153])],[f_4426_4]) ).

cnf(f_4426_6,plain,
    ( sP1152(U_18223,U_18228,U_18230,U_18232)
    | U_18228 != U_18230 ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_7,plain,
    ( U_18229 = U_18231
    | sP1153(U_18229,U_18231,U_18233)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18231) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18230)
    | ~ sP1152(U_18223,U_18228,U_18230,U_18232) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_9,plain,
    ( hAPP(hAPP(c_List_Onth(U_18232),U_18228),U_18223) = hAPP(hAPP(c_List_Onth(U_18232),U_18230),U_18223)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18232)),U_18228)))
    | ~ sP1152(U_18223,U_18228,U_18230,U_18232) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18233,U_18231,U_18229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18233)),U_18229)))
    | ~ sP1153(U_18229,U_18231,U_18233) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_11,plain,
    ( hAPP(hAPP(c_List_Onth(U_18233),U_18229),sK463(U_18233,U_18231,U_18229)) != hAPP(hAPP(c_List_Onth(U_18233),U_18231),sK463(U_18233,U_18231,U_18229))
    | ~ sP1153(U_18229,U_18231,U_18233) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

fof(f_4427_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ? [B_i] :
            ( ? [B_j] :
                ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)
                & B_i != B_j
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_i] :
            ( ! [B_j] :
                ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)
                | B_i = B_j
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__conv__nth]) ).

fof(f_4427_2,plain,
    ! [U_18239,U_18238] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18238),U_18239))
        | ? [U_18237] :
            ( ? [U_18236] :
                ( hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18237) = hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18236)
                & U_18237 != U_18236
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18236),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) ) )
      & ( ! [U_18235] :
            ( ! [U_18234] :
                ( hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18235) != hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18234)
                | U_18235 = U_18234
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18234),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18235),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18238),U_18239)) ) ),
    inference(variable_rename,[status(thm)],[f_4427_1]) ).

fof(f_4427_3,plain,
    ( ! [U_18243,U_18241] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18241),U_18243))
        | ? [U_18237] :
            ( ? [U_18236] :
                ( hAPP(hAPP(c_List_Onth(U_18241),U_18243),U_18237) = hAPP(hAPP(c_List_Onth(U_18241),U_18243),U_18236)
                & U_18237 != U_18236
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18236),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243))) ) )
    & ! [U_18242,U_18240] :
        ( ! [U_18235] :
            ( ! [U_18234] :
                ( hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18235) != hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18234)
                | U_18235 = U_18234
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18234),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18235),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18240),U_18242)) ) ),
    inference(miniscope,[status(thm)],[f_4427_2]) ).

fof(f_4427_4,plain,
    ( ! [U_18243,U_18241] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18241),U_18243))
        | ( ? [U_18236] :
              ( hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK464(U_18243,U_18241)) = hAPP(hAPP(c_List_Onth(U_18241),U_18243),U_18236)
              & sK464(U_18243,U_18241) != U_18236
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18236),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243))) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK464(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243))) ) )
    & ! [U_18242,U_18240] :
        ( ! [U_18235] :
            ( ! [U_18234] :
                ( hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18235) != hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18234)
                | U_18235 = U_18234
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18234),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18235),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18240),U_18242)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_18237,sK464(U_18243,U_18241))],[f_4427_3]) ).

fof(f_4427_5,plain,
    ( ! [U_18243,U_18241] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18241),U_18243))
        | ( hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK464(U_18243,U_18241)) = hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK465(U_18243,U_18241))
          & sK464(U_18243,U_18241) != sK465(U_18243,U_18241)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK465(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK464(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243))) ) )
    & ! [U_18242,U_18240] :
        ( ! [U_18235] :
            ( ! [U_18234] :
                ( hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18235) != hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18234)
                | U_18235 = U_18234
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18234),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18235),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18240),U_18242)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_18236,sK465(U_18243,U_18241))],[f_4427_4]) ).

fof(f_4427_6,plain,
    ( ! [U_18241,U_18243] :
        ( hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK464(U_18243,U_18241)) = hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK465(U_18243,U_18241))
        | ~ sP1154(U_18241,U_18243) )
    & ! [U_18241,U_18243] :
        ( sK464(U_18243,U_18241) != sK465(U_18243,U_18241)
        | ~ sP1154(U_18241,U_18243) )
    & ! [U_18241,U_18243] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK465(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243)))
        | ~ sP1154(U_18241,U_18243) )
    & ! [U_18241,U_18243] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK464(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243)))
        | ~ sP1154(U_18241,U_18243) )
    & ! [U_18241,U_18243] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18241),U_18243))
        | sP1154(U_18241,U_18243) )
    & ! [U_18235,U_18234,U_18240,U_18242] :
        ( hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18235) != hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18234)
        | U_18235 = U_18234
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18234),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18235),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18240),U_18242)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1154])],[f_4427_5]) ).

cnf(f_4427_7,plain,
    ( hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18235) != hAPP(hAPP(c_List_Onth(U_18240),U_18242),U_18234)
    | U_18235 = U_18234
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18234),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18235),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18240)),U_18242)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18240),U_18242)) ),
    inference(clausify,[status(thm)],[f_4427_6]) ).

cnf(f_4427_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18241),U_18243))
    | sP1154(U_18241,U_18243) ),
    inference(clausify,[status(thm)],[f_4427_6]) ).

cnf(f_4427_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK464(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243)))
    | ~ sP1154(U_18241,U_18243) ),
    inference(clausify,[status(thm)],[f_4427_6]) ).

cnf(f_4427_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK465(U_18243,U_18241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)),U_18243)))
    | ~ sP1154(U_18241,U_18243) ),
    inference(clausify,[status(thm)],[f_4427_6]) ).

cnf(f_4427_11,plain,
    ( sK464(U_18243,U_18241) != sK465(U_18243,U_18241)
    | ~ sP1154(U_18241,U_18243) ),
    inference(clausify,[status(thm)],[f_4427_6]) ).

cnf(f_4427_12,plain,
    ( hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK464(U_18243,U_18241)) = hAPP(hAPP(c_List_Onth(U_18241),U_18243),sK465(U_18243,U_18241))
    | ~ sP1154(U_18241,U_18243) ),
    inference(clausify,[status(thm)],[f_4427_6]) ).

fof(f_4428_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( ( ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
          | V_i_2 != V_j_2 )
        & ( V_i_2 = V_j_2
          | hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq]) ).

fof(f_4428_2,plain,
    ! [U_18247,U_18246,U_18245,U_18244] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18246) = hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18247)
          | U_18246 != U_18247 )
        & ( U_18246 = U_18247
          | hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18246) != hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18247) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18247),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18246),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18244),U_18245)) ),
    inference(variable_rename,[status(thm)],[f_4428_1]) ).

fof(f_4428_3,plain,
    ( ! [U_18244,U_18246,U_18247,U_18245] :
        ( hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18246) = hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18247)
        | U_18246 != U_18247
        | ~ sP1155(U_18244,U_18246,U_18247,U_18245) )
    & ! [U_18244,U_18246,U_18247,U_18245] :
        ( U_18246 = U_18247
        | hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18246) != hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18247)
        | ~ sP1155(U_18244,U_18246,U_18247,U_18245) )
    & ! [U_18244,U_18246,U_18247,U_18245] :
        ( sP1155(U_18244,U_18246,U_18247,U_18245)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18247),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18246),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18244),U_18245)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1155])],[f_4428_2]) ).

cnf(f_4428_4,plain,
    ( sP1155(U_18244,U_18246,U_18247,U_18245)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18247),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18246),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18244),U_18245)) ),
    inference(clausify,[status(thm)],[f_4428_3]) ).

cnf(f_4428_5,plain,
    ( U_18246 = U_18247
    | hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18246) != hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18247)
    | ~ sP1155(U_18244,U_18246,U_18247,U_18245) ),
    inference(clausify,[status(thm)],[f_4428_3]) ).

cnf(f_4428_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18246) = hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18247)
    | U_18246 != U_18247
    | ~ sP1155(U_18244,U_18246,U_18247,U_18245) ),
    inference(clausify,[status(thm)],[f_4428_3]) ).

fof(f_4429_1,plain,
    ! [V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__mem]) ).

fof(f_4429_2,plain,
    ! [U_18250,U_18249,U_18248] :
      ( hBOOL(hAPP(hAPP(c_member(U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18250),U_18248)),hAPP(c_List_Oset(U_18249),U_18250)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18250))) ),
    inference(variable_rename,[status(thm)],[f_4429_1]) ).

fof(f_4429_3,plain,
    ! [U_18250,U_18249,U_18248] :
      ( hBOOL(hAPP(hAPP(c_member(U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18250),U_18248)),hAPP(c_List_Oset(U_18249),U_18250)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18250))) ),
    inference(definitional_conversion,[status(esa)],[f_4429_2]) ).

cnf(f_4429_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18250),U_18248)),hAPP(c_List_Oset(U_18249),U_18250)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18250))) ),
    inference(clausify,[status(thm)],[f_4429_3]) ).

fof(f_4430_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ! [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != V_x_2
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ? [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__nth]) ).

fof(f_4430_2,plain,
    ! [U_18255,U_18254,U_18253] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18253),U_18254),hAPP(c_List_Oset(U_18253),U_18255)))
        | ! [U_18252] :
            ( hAPP(hAPP(c_List_Onth(U_18253),U_18255),U_18252) != U_18254
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18253)),U_18255))) ) )
      & ( ? [U_18251] :
            ( hAPP(hAPP(c_List_Onth(U_18253),U_18255),U_18251) = U_18254
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18251),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18253)),U_18255))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18253),U_18254),hAPP(c_List_Oset(U_18253),U_18255))) ) ),
    inference(variable_rename,[status(thm)],[f_4430_1]) ).

fof(f_4430_3,plain,
    ( ! [U_18261,U_18259,U_18257] :
        ( hBOOL(hAPP(hAPP(c_member(U_18257),U_18259),hAPP(c_List_Oset(U_18257),U_18261)))
        | ! [U_18252] :
            ( hAPP(hAPP(c_List_Onth(U_18257),U_18261),U_18252) != U_18259
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18257)),U_18261))) ) )
    & ! [U_18260,U_18258,U_18256] :
        ( ? [U_18251] :
            ( hAPP(hAPP(c_List_Onth(U_18256),U_18260),U_18251) = U_18258
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18251),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18256)),U_18260))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18258),hAPP(c_List_Oset(U_18256),U_18260))) ) ),
    inference(miniscope,[status(thm)],[f_4430_2]) ).

fof(f_4430_4,plain,
    ( ! [U_18261,U_18259,U_18257] :
        ( hBOOL(hAPP(hAPP(c_member(U_18257),U_18259),hAPP(c_List_Oset(U_18257),U_18261)))
        | ! [U_18252] :
            ( hAPP(hAPP(c_List_Onth(U_18257),U_18261),U_18252) != U_18259
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18257)),U_18261))) ) )
    & ! [U_18260,U_18258,U_18256] :
        ( ( hAPP(hAPP(c_List_Onth(U_18256),U_18260),sK466(U_18260,U_18258,U_18256)) = U_18258
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK466(U_18260,U_18258,U_18256)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18256)),U_18260))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18258),hAPP(c_List_Oset(U_18256),U_18260))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_18251,sK466(U_18260,U_18258,U_18256))],[f_4430_3]) ).

fof(f_4430_5,plain,
    ( ! [U_18258,U_18256,U_18260] :
        ( hAPP(hAPP(c_List_Onth(U_18256),U_18260),sK466(U_18260,U_18258,U_18256)) = U_18258
        | ~ sP1156(U_18258,U_18256,U_18260) )
    & ! [U_18258,U_18256,U_18260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK466(U_18260,U_18258,U_18256)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18256)),U_18260)))
        | ~ sP1156(U_18258,U_18256,U_18260) )
    & ! [U_18252,U_18259,U_18257,U_18261] :
        ( hBOOL(hAPP(hAPP(c_member(U_18257),U_18259),hAPP(c_List_Oset(U_18257),U_18261)))
        | hAPP(hAPP(c_List_Onth(U_18257),U_18261),U_18252) != U_18259
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18257)),U_18261))) )
    & ! [U_18258,U_18256,U_18260] :
        ( sP1156(U_18258,U_18256,U_18260)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18258),hAPP(c_List_Oset(U_18256),U_18260))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1156])],[f_4430_4]) ).

cnf(f_4430_6,plain,
    ( sP1156(U_18258,U_18256,U_18260)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18258),hAPP(c_List_Oset(U_18256),U_18260))) ),
    inference(clausify,[status(thm)],[f_4430_5]) ).

cnf(f_4430_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18257),U_18259),hAPP(c_List_Oset(U_18257),U_18261)))
    | hAPP(hAPP(c_List_Onth(U_18257),U_18261),U_18252) != U_18259
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18257)),U_18261))) ),
    inference(clausify,[status(thm)],[f_4430_5]) ).

cnf(f_4430_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK466(U_18260,U_18258,U_18256)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18256)),U_18260)))
    | ~ sP1156(U_18258,U_18256,U_18260) ),
    inference(clausify,[status(thm)],[f_4430_5]) ).

cnf(f_4430_9,plain,
    ( hAPP(hAPP(c_List_Onth(U_18256),U_18260),sK466(U_18260,U_18258,U_18256)) = U_18258
    | ~ sP1156(U_18258,U_18256,U_18260) ),
    inference(clausify,[status(thm)],[f_4430_5]) ).

fof(f_4431_1,plain,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nth__Cons_H]) ).

fof(f_4431_2,plain,
    ! [U_18265,U_18264,U_18263,U_18262] :
      ( ( hAPP(hAPP(c_List_Onth(U_18263),hAPP(hAPP(c_List_Olist_OCons(U_18263),U_18264),U_18265)),U_18262) = hAPP(hAPP(c_List_Onth(U_18263),U_18265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18262),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18262 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_18263),hAPP(hAPP(c_List_Olist_OCons(U_18263),U_18264),U_18265)),U_18262) = U_18264
        | U_18262 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4431_1]) ).

fof(f_4431_3,plain,
    ( ! [U_18273,U_18271,U_18269,U_18267] :
        ( hAPP(hAPP(c_List_Onth(U_18269),hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18271),U_18273)),U_18267) = hAPP(hAPP(c_List_Onth(U_18269),U_18273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18267),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18272,U_18270,U_18268,U_18266] :
        ( hAPP(hAPP(c_List_Onth(U_18268),hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),U_18272)),U_18266) = U_18270
        | U_18266 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4431_2]) ).

fof(f_4431_4,plain,
    ( ! [U_18267,U_18269,U_18271,U_18273] :
        ( hAPP(hAPP(c_List_Onth(U_18269),hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18271),U_18273)),U_18267) = hAPP(hAPP(c_List_Onth(U_18269),U_18273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18267),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18268,U_18272,U_18266,U_18270] :
        ( hAPP(hAPP(c_List_Onth(U_18268),hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),U_18272)),U_18266) = U_18270
        | U_18266 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4431_3]) ).

cnf(f_4431_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18268),hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),U_18272)),U_18266) = U_18270
    | U_18266 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4431_4]) ).

cnf(f_4431_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18269),hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18271),U_18273)),U_18267) = hAPP(hAPP(c_List_Onth(U_18269),U_18273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18267),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_18267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4431_4]) ).

fof(f_4432_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_set__conv__nth]) ).

fof(f_4432_2,plain,
    ! [U_18275,U_18274] : hAPP(c_List_Oset(U_18274),U_18275) = hAPP(c_Set_OCollect(U_18274),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18274),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18274,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18274),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18274),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18274,tc_fun(tc_Nat_Onat,U_18274),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18274,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18274),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18274),c_COMBB(U_18274,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18274),U_18275))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18274)),U_18275))))),
    inference(variable_rename,[status(thm)],[f_4432_1]) ).

fof(f_4432_3,plain,
    ! [U_18274,U_18275] : hAPP(c_List_Oset(U_18274),U_18275) = hAPP(c_Set_OCollect(U_18274),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18274),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18274,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18274),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18274),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18274,tc_fun(tc_Nat_Onat,U_18274),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18274,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18274),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18274),c_COMBB(U_18274,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18274),U_18275))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18274)),U_18275))))),
    inference(definitional_conversion,[status(esa)],[f_4432_2]) ).

cnf(f_4432_4,plain,
    hAPP(c_List_Oset(U_18274),U_18275) = hAPP(c_Set_OCollect(U_18274),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18274),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18274,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18274),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18274),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18274,tc_fun(tc_Nat_Onat,U_18274),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18274,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18274),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18274),c_COMBB(U_18274,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18274),U_18275))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18274)),U_18275))))),
    inference(clausify,[status(thm)],[f_4432_3]) ).

fof(f_4433_1,plain,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of]) ).

fof(f_4433_2,plain,
    ! [U_18279,U_18278,U_18277,U_18276] :
      ( ( hAPP(hAPP(c_List_Onth(U_18277),hAPP(hAPP(c_List_Olist_OCons(U_18277),U_18278),U_18279)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18276)) = hAPP(hAPP(c_List_Onth(U_18277),U_18279),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18276)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18276) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_18277),hAPP(hAPP(c_List_Olist_OCons(U_18277),U_18278),U_18279)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18276)) = U_18278
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18276) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4433_1]) ).

fof(f_4433_3,plain,
    ( ! [U_18287,U_18285,U_18283,U_18281] :
        ( hAPP(hAPP(c_List_Onth(U_18283),hAPP(hAPP(c_List_Olist_OCons(U_18283),U_18285),U_18287)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281)) = hAPP(hAPP(c_List_Onth(U_18283),U_18287),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18286,U_18284,U_18282,U_18280] :
        ( hAPP(hAPP(c_List_Onth(U_18282),hAPP(hAPP(c_List_Olist_OCons(U_18282),U_18284),U_18286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18280)) = U_18284
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18280) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4433_2]) ).

fof(f_4433_4,plain,
    ( ! [U_18281,U_18283,U_18285,U_18287] :
        ( hAPP(hAPP(c_List_Onth(U_18283),hAPP(hAPP(c_List_Olist_OCons(U_18283),U_18285),U_18287)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281)) = hAPP(hAPP(c_List_Onth(U_18283),U_18287),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18286,U_18282,U_18280,U_18284] :
        ( hAPP(hAPP(c_List_Onth(U_18282),hAPP(hAPP(c_List_Olist_OCons(U_18282),U_18284),U_18286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18280)) = U_18284
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18280) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4433_3]) ).

cnf(f_4433_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18282),hAPP(hAPP(c_List_Olist_OCons(U_18282),U_18284),U_18286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18280)) = U_18284
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18280) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4433_4]) ).

cnf(f_4433_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18283),hAPP(hAPP(c_List_Olist_OCons(U_18283),U_18285),U_18287)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281)) = hAPP(hAPP(c_List_Onth(U_18283),U_18287),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18281) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4433_4]) ).

fof(f_4434_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth]) ).

fof(f_4434_2,plain,
    ! [U_18289,U_18288] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18288),U_18289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18288),hAPP(c_List_Onth(U_18288),U_18289)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18288)),U_18289)))
      | ~ class_Groups_Ocomm__monoid__add(U_18288) ),
    inference(variable_rename,[status(thm)],[f_4434_1]) ).

fof(f_4434_3,plain,
    ! [U_18288,U_18289] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18288),U_18289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18288),hAPP(c_List_Onth(U_18288),U_18289)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18288)),U_18289)))
      | ~ class_Groups_Ocomm__monoid__add(U_18288) ),
    inference(definitional_conversion,[status(esa)],[f_4434_2]) ).

cnf(f_4434_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18288),U_18289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18288),hAPP(c_List_Onth(U_18288),U_18289)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18288)),U_18289)))
    | ~ class_Groups_Ocomm__monoid__add(U_18288) ),
    inference(clausify,[status(thm)],[f_4434_3]) ).

fof(f_4435_1,plain,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))),
    inference(fof_nnf,[status(thm)],[fact_set__sublist]) ).

fof(f_4435_2,plain,
    ! [U_18292,U_18291,U_18290] : hAPP(c_List_Oset(U_18290),c_List_Osublist(U_18290,U_18291,U_18292)) = hAPP(c_Set_OCollect(U_18290),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18290),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18290,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18290),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18290),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18290,tc_fun(tc_Nat_Onat,U_18290),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18290,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18290),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18290),c_COMBB(U_18290,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18290),U_18291))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18290)),U_18291)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18292))))),
    inference(variable_rename,[status(thm)],[f_4435_1]) ).

fof(f_4435_3,plain,
    ! [U_18290,U_18291,U_18292] : hAPP(c_List_Oset(U_18290),c_List_Osublist(U_18290,U_18291,U_18292)) = hAPP(c_Set_OCollect(U_18290),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18290),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18290,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18290),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18290),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18290,tc_fun(tc_Nat_Onat,U_18290),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18290,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18290),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18290),c_COMBB(U_18290,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18290),U_18291))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18290)),U_18291)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18292))))),
    inference(definitional_conversion,[status(esa)],[f_4435_2]) ).

cnf(f_4435_4,plain,
    hAPP(c_List_Oset(U_18290),c_List_Osublist(U_18290,U_18291,U_18292)) = hAPP(c_Set_OCollect(U_18290),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18290),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18290,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18290),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18290),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18290,tc_fun(tc_Nat_Onat,U_18290),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18290,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18290),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18290),c_COMBB(U_18290,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18290),U_18291))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18290)),U_18291)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18292))))),
    inference(clausify,[status(thm)],[f_4435_3]) ).

fof(f_4436_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__lex]) ).

fof(f_4436_2,plain,
    ! [U_18296,U_18295,U_18294,U_18293] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18293),tc_List_Olist(U_18293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18293),tc_List_Olist(U_18293)),U_18294),U_18295)),c_List_Olex(U_18293,U_18296)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18293)),U_18294) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18293)),U_18295)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18293),tc_List_Olist(U_18293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18293),tc_List_Olist(U_18293)),U_18294),U_18295)),c_List_Olexord(U_18293,U_18296))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18293)),U_18294) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18293)),U_18295)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18293),tc_List_Olist(U_18293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18293),tc_List_Olist(U_18293)),U_18294),U_18295)),c_List_Olexord(U_18293,U_18296))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18293),tc_List_Olist(U_18293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18293),tc_List_Olist(U_18293)),U_18294),U_18295)),c_List_Olex(U_18293,U_18296))) ) ),
    inference(variable_rename,[status(thm)],[f_4436_1]) ).

fof(f_4436_3,plain,
    ( ! [U_18304,U_18302,U_18300,U_18298] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18298),tc_List_Olist(U_18298))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18298),tc_List_Olist(U_18298)),U_18300),U_18302)),c_List_Olex(U_18298,U_18304)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18300) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18302)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18298),tc_List_Olist(U_18298))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18298),tc_List_Olist(U_18298)),U_18300),U_18302)),c_List_Olexord(U_18298,U_18304))) )
    & ! [U_18303,U_18301,U_18299,U_18297] :
        ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18297)),U_18299) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18297)),U_18301)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18297),tc_List_Olist(U_18297))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18297),tc_List_Olist(U_18297)),U_18299),U_18301)),c_List_Olexord(U_18297,U_18303))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18297),tc_List_Olist(U_18297))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18297),tc_List_Olist(U_18297)),U_18299),U_18301)),c_List_Olex(U_18297,U_18303))) ) ),
    inference(miniscope,[status(thm)],[f_4436_2]) ).

fof(f_4436_4,plain,
    ( ! [U_18303,U_18299,U_18297,U_18301] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18297)),U_18299) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18297)),U_18301)
        | ~ sP1157(U_18303,U_18299,U_18297,U_18301) )
    & ! [U_18303,U_18299,U_18297,U_18301] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18297),tc_List_Olist(U_18297))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18297),tc_List_Olist(U_18297)),U_18299),U_18301)),c_List_Olexord(U_18297,U_18303)))
        | ~ sP1157(U_18303,U_18299,U_18297,U_18301) )
    & ! [U_18300,U_18298,U_18302,U_18304] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18298),tc_List_Olist(U_18298))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18298),tc_List_Olist(U_18298)),U_18300),U_18302)),c_List_Olex(U_18298,U_18304)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18300) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18302)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18298),tc_List_Olist(U_18298))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18298),tc_List_Olist(U_18298)),U_18300),U_18302)),c_List_Olexord(U_18298,U_18304))) )
    & ! [U_18303,U_18299,U_18297,U_18301] :
        ( sP1157(U_18303,U_18299,U_18297,U_18301)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18297),tc_List_Olist(U_18297))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18297),tc_List_Olist(U_18297)),U_18299),U_18301)),c_List_Olex(U_18297,U_18303))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1157])],[f_4436_3]) ).

cnf(f_4436_5,plain,
    ( sP1157(U_18303,U_18299,U_18297,U_18301)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18297),tc_List_Olist(U_18297))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18297),tc_List_Olist(U_18297)),U_18299),U_18301)),c_List_Olex(U_18297,U_18303))) ),
    inference(clausify,[status(thm)],[f_4436_4]) ).

cnf(f_4436_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18298),tc_List_Olist(U_18298))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18298),tc_List_Olist(U_18298)),U_18300),U_18302)),c_List_Olex(U_18298,U_18304)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18300) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18302)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18298),tc_List_Olist(U_18298))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18298),tc_List_Olist(U_18298)),U_18300),U_18302)),c_List_Olexord(U_18298,U_18304))) ),
    inference(clausify,[status(thm)],[f_4436_4]) ).

cnf(f_4436_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18297),tc_List_Olist(U_18297))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18297),tc_List_Olist(U_18297)),U_18299),U_18301)),c_List_Olexord(U_18297,U_18303)))
    | ~ sP1157(U_18303,U_18299,U_18297,U_18301) ),
    inference(clausify,[status(thm)],[f_4436_4]) ).

cnf(f_4436_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18297)),U_18299) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18297)),U_18301)
    | ~ sP1157(U_18303,U_18299,U_18297,U_18301) ),
    inference(clausify,[status(thm)],[f_4436_4]) ).

fof(f_4437_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
        | ? [B_n] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_n] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__iff__nth]) ).

fof(f_4437_2,plain,
    ! [U_18310,U_18309,U_18308,U_18307] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18307),tc_List_Olist(U_18307))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18307),tc_List_Olist(U_18307)),U_18308),U_18309)),c_List_Olistrel(U_18307,U_18310)))
        | ? [U_18306] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18307,U_18307)),hAPP(hAPP(c_Product__Type_OPair(U_18307,U_18307),hAPP(hAPP(c_List_Onth(U_18307),U_18308),U_18306)),hAPP(hAPP(c_List_Onth(U_18307),U_18309),U_18306))),U_18310))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18307)),U_18308))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18307)),U_18308) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18307)),U_18309) )
      & ( ( ! [U_18305] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18307,U_18307)),hAPP(hAPP(c_Product__Type_OPair(U_18307,U_18307),hAPP(hAPP(c_List_Onth(U_18307),U_18308),U_18305)),hAPP(hAPP(c_List_Onth(U_18307),U_18309),U_18305))),U_18310))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18305),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18307)),U_18308))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18307)),U_18308) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18307)),U_18309) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18307),tc_List_Olist(U_18307))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18307),tc_List_Olist(U_18307)),U_18308),U_18309)),c_List_Olistrel(U_18307,U_18310))) ) ),
    inference(variable_rename,[status(thm)],[f_4437_1]) ).

fof(f_4437_3,plain,
    ( ! [U_18318,U_18316,U_18314,U_18312] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18312),tc_List_Olist(U_18312))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18312),tc_List_Olist(U_18312)),U_18314),U_18316)),c_List_Olistrel(U_18312,U_18318)))
        | ? [U_18306] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18312,U_18312)),hAPP(hAPP(c_Product__Type_OPair(U_18312,U_18312),hAPP(hAPP(c_List_Onth(U_18312),U_18314),U_18306)),hAPP(hAPP(c_List_Onth(U_18312),U_18316),U_18306))),U_18318))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18316) )
    & ! [U_18317,U_18315,U_18313,U_18311] :
        ( ( ! [U_18305] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18311,U_18311)),hAPP(hAPP(c_Product__Type_OPair(U_18311,U_18311),hAPP(hAPP(c_List_Onth(U_18311),U_18313),U_18305)),hAPP(hAPP(c_List_Onth(U_18311),U_18315),U_18305))),U_18317))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18305),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18315) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18311),tc_List_Olist(U_18311))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18311),tc_List_Olist(U_18311)),U_18313),U_18315)),c_List_Olistrel(U_18311,U_18317))) ) ),
    inference(miniscope,[status(thm)],[f_4437_2]) ).

fof(f_4437_4,plain,
    ( ! [U_18318,U_18316,U_18314,U_18312] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18312),tc_List_Olist(U_18312))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18312),tc_List_Olist(U_18312)),U_18314),U_18316)),c_List_Olistrel(U_18312,U_18318)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18312,U_18312)),hAPP(hAPP(c_Product__Type_OPair(U_18312,U_18312),hAPP(hAPP(c_List_Onth(U_18312),U_18314),sK467(U_18318,U_18316,U_18314,U_18312))),hAPP(hAPP(c_List_Onth(U_18312),U_18316),sK467(U_18318,U_18316,U_18314,U_18312)))),U_18318))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK467(U_18318,U_18316,U_18314,U_18312)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18316) )
    & ! [U_18317,U_18315,U_18313,U_18311] :
        ( ( ! [U_18305] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18311,U_18311)),hAPP(hAPP(c_Product__Type_OPair(U_18311,U_18311),hAPP(hAPP(c_List_Onth(U_18311),U_18313),U_18305)),hAPP(hAPP(c_List_Onth(U_18311),U_18315),U_18305))),U_18317))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18305),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18315) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18311),tc_List_Olist(U_18311))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18311),tc_List_Olist(U_18311)),U_18313),U_18315)),c_List_Olistrel(U_18311,U_18317))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_18306,sK467(U_18318,U_18316,U_18314,U_18312))],[f_4437_3]) ).

fof(f_4437_5,plain,
    ( ! [U_18312,U_18314,U_18318,U_18316] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18312,U_18312)),hAPP(hAPP(c_Product__Type_OPair(U_18312,U_18312),hAPP(hAPP(c_List_Onth(U_18312),U_18314),sK467(U_18318,U_18316,U_18314,U_18312))),hAPP(hAPP(c_List_Onth(U_18312),U_18316),sK467(U_18318,U_18316,U_18314,U_18312)))),U_18318))
        | ~ sP1159(U_18312,U_18314,U_18318,U_18316) )
    & ! [U_18312,U_18314,U_18318,U_18316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK467(U_18318,U_18316,U_18314,U_18312)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314)))
        | ~ sP1159(U_18312,U_18314,U_18318,U_18316) )
    & ! [U_18305,U_18315,U_18311,U_18313,U_18317] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18311,U_18311)),hAPP(hAPP(c_Product__Type_OPair(U_18311,U_18311),hAPP(hAPP(c_List_Onth(U_18311),U_18313),U_18305)),hAPP(hAPP(c_List_Onth(U_18311),U_18315),U_18305))),U_18317))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18305),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313)))
        | ~ sP1158(U_18305,U_18315,U_18311,U_18313,U_18317) )
    & ! [U_18305,U_18315,U_18311,U_18313,U_18317] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18315)
        | ~ sP1158(U_18305,U_18315,U_18311,U_18313,U_18317) )
    & ! [U_18312,U_18314,U_18318,U_18316] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18312),tc_List_Olist(U_18312))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18312),tc_List_Olist(U_18312)),U_18314),U_18316)),c_List_Olistrel(U_18312,U_18318)))
        | sP1159(U_18312,U_18314,U_18318,U_18316)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18316) )
    & ! [U_18305,U_18315,U_18311,U_18313,U_18317] :
        ( sP1158(U_18305,U_18315,U_18311,U_18313,U_18317)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18311),tc_List_Olist(U_18311))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18311),tc_List_Olist(U_18311)),U_18313),U_18315)),c_List_Olistrel(U_18311,U_18317))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1158,sP1159])],[f_4437_4]) ).

cnf(f_4437_6,plain,
    ( sP1158(U_18305,U_18315,U_18311,U_18313,U_18317)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18311),tc_List_Olist(U_18311))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18311),tc_List_Olist(U_18311)),U_18313),U_18315)),c_List_Olistrel(U_18311,U_18317))) ),
    inference(clausify,[status(thm)],[f_4437_5]) ).

cnf(f_4437_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18312),tc_List_Olist(U_18312))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18312),tc_List_Olist(U_18312)),U_18314),U_18316)),c_List_Olistrel(U_18312,U_18318)))
    | sP1159(U_18312,U_18314,U_18318,U_18316)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18316) ),
    inference(clausify,[status(thm)],[f_4437_5]) ).

cnf(f_4437_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18315)
    | ~ sP1158(U_18305,U_18315,U_18311,U_18313,U_18317) ),
    inference(clausify,[status(thm)],[f_4437_5]) ).

cnf(f_4437_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18311,U_18311)),hAPP(hAPP(c_Product__Type_OPair(U_18311,U_18311),hAPP(hAPP(c_List_Onth(U_18311),U_18313),U_18305)),hAPP(hAPP(c_List_Onth(U_18311),U_18315),U_18305))),U_18317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18305),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18311)),U_18313)))
    | ~ sP1158(U_18305,U_18315,U_18311,U_18313,U_18317) ),
    inference(clausify,[status(thm)],[f_4437_5]) ).

cnf(f_4437_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK467(U_18318,U_18316,U_18314,U_18312)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18312)),U_18314)))
    | ~ sP1159(U_18312,U_18314,U_18318,U_18316) ),
    inference(clausify,[status(thm)],[f_4437_5]) ).

cnf(f_4437_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18312,U_18312)),hAPP(hAPP(c_Product__Type_OPair(U_18312,U_18312),hAPP(hAPP(c_List_Onth(U_18312),U_18314),sK467(U_18318,U_18316,U_18314,U_18312))),hAPP(hAPP(c_List_Onth(U_18312),U_18316),sK467(U_18318,U_18316,U_18314,U_18312)))),U_18318))
    | ~ sP1159(U_18312,U_18314,U_18318,U_18316) ),
    inference(clausify,[status(thm)],[f_4437_5]) ).

fof(f_4438_1,plain,
    ! [V_xs_2,T_b,V_l_2] :
      ( hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_pick__same]) ).

fof(f_4438_2,plain,
    ! [U_18321,U_18320,U_18319] :
      ( hAPP(c_Random_Opick(U_18320,hAPP(hAPP(c_List_Omap(U_18320,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18320)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18320),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18321)),hAPP(c_Code__Numeral_Oof__nat,U_18319)) = hAPP(hAPP(c_List_Onth(U_18320),U_18321),U_18319)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18319),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18320)),U_18321))) ),
    inference(variable_rename,[status(thm)],[f_4438_1]) ).

fof(f_4438_3,plain,
    ! [U_18320,U_18321,U_18319] :
      ( hAPP(c_Random_Opick(U_18320,hAPP(hAPP(c_List_Omap(U_18320,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18320)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18320),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18321)),hAPP(c_Code__Numeral_Oof__nat,U_18319)) = hAPP(hAPP(c_List_Onth(U_18320),U_18321),U_18319)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18319),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18320)),U_18321))) ),
    inference(definitional_conversion,[status(esa)],[f_4438_2]) ).

cnf(f_4438_4,plain,
    ( hAPP(c_Random_Opick(U_18320,hAPP(hAPP(c_List_Omap(U_18320,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18320)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18320),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18321)),hAPP(c_Code__Numeral_Oof__nat,U_18319)) = hAPP(hAPP(c_List_Onth(U_18320),U_18321),U_18319)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18319),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18320)),U_18321))) ),
    inference(clausify,[status(thm)],[f_4438_3]) ).

fof(f_4439_1,plain,
    ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))),
    inference(fof_nnf,[status(thm)],[fact_select__def]) ).

fof(f_4439_2,plain,
    ! [U_18323,U_18322] : c_Random_Oselect(U_18322,U_18323) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18322)),U_18323)))),hAPP(hAPP(c_COMBB(U_18322,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18322,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18322),U_18323)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[f_4439_1]) ).

fof(f_4439_3,plain,
    ! [U_18322,U_18323] : c_Random_Oselect(U_18322,U_18323) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18322)),U_18323)))),hAPP(hAPP(c_COMBB(U_18322,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18322,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18322),U_18323)),c_Code__Numeral_Onat__of))),
    inference(definitional_conversion,[status(esa)],[f_4439_2]) ).

cnf(f_4439_4,plain,
    c_Random_Oselect(U_18322,U_18323) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18322)),U_18323)))),hAPP(hAPP(c_COMBB(U_18322,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18322,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18322,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18322),U_18323)),c_Code__Numeral_Onat__of))),
    inference(clausify,[status(thm)],[f_4439_3]) ).

fof(f_4440_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
        | ( ! [B_i] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
              | hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) != hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
          & ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) != V_x_2
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) ) ) )
      & ( ? [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
            & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
        | ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__take__index__conv]) ).

fof(f_4440_2,plain,
    ! [U_18329,U_18328,U_18327,U_18326] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18326),tc_List_Olist(U_18326))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18326),tc_List_Olist(U_18326)),U_18327),U_18328)),c_List_Olexord(U_18326,U_18329)))
        | ( ! [U_18325] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18326,U_18326)),hAPP(hAPP(c_Product__Type_OPair(U_18326,U_18326),hAPP(hAPP(c_List_Onth(U_18326),U_18327),U_18325)),hAPP(hAPP(c_List_Onth(U_18326),U_18328),U_18325))),U_18329))
              | hAPP(hAPP(c_List_Otake(U_18326),U_18325),U_18327) != hAPP(hAPP(c_List_Otake(U_18326),U_18325),U_18328)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18325),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18327)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18328)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18326),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18327)),U_18328) != U_18327
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18327)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18328))) ) ) )
      & ( ? [U_18324] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18326,U_18326)),hAPP(hAPP(c_Product__Type_OPair(U_18326,U_18326),hAPP(hAPP(c_List_Onth(U_18326),U_18327),U_18324)),hAPP(hAPP(c_List_Onth(U_18326),U_18328),U_18324))),U_18329))
            & hAPP(hAPP(c_List_Otake(U_18326),U_18324),U_18327) = hAPP(hAPP(c_List_Otake(U_18326),U_18324),U_18328)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18324),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18327)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18328)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18326),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18327)),U_18328) = U_18327
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18327)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18326)),U_18328))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18326),tc_List_Olist(U_18326))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18326),tc_List_Olist(U_18326)),U_18327),U_18328)),c_List_Olexord(U_18326,U_18329))) ) ),
    inference(variable_rename,[status(thm)],[f_4440_1]) ).

fof(f_4440_3,plain,
    ( ! [U_18337,U_18335,U_18333,U_18331] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18331),tc_List_Olist(U_18331))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18331),tc_List_Olist(U_18331)),U_18333),U_18335)),c_List_Olexord(U_18331,U_18337)))
        | ( ! [U_18325] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18331,U_18331)),hAPP(hAPP(c_Product__Type_OPair(U_18331,U_18331),hAPP(hAPP(c_List_Onth(U_18331),U_18333),U_18325)),hAPP(hAPP(c_List_Onth(U_18331),U_18335),U_18325))),U_18337))
              | hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18333) != hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18335)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18325),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18331),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),U_18335) != U_18333
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335))) ) ) )
    & ! [U_18336,U_18334,U_18332,U_18330] :
        ( ? [U_18324] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18330,U_18330)),hAPP(hAPP(c_Product__Type_OPair(U_18330,U_18330),hAPP(hAPP(c_List_Onth(U_18330),U_18332),U_18324)),hAPP(hAPP(c_List_Onth(U_18330),U_18334),U_18324))),U_18336))
            & hAPP(hAPP(c_List_Otake(U_18330),U_18324),U_18332) = hAPP(hAPP(c_List_Otake(U_18330),U_18324),U_18334)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18324),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18330),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),U_18334) = U_18332
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18330),tc_List_Olist(U_18330))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18330),tc_List_Olist(U_18330)),U_18332),U_18334)),c_List_Olexord(U_18330,U_18336))) ) ),
    inference(miniscope,[status(thm)],[f_4440_2]) ).

fof(f_4440_4,plain,
    ( ! [U_18337,U_18335,U_18333,U_18331] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18331),tc_List_Olist(U_18331))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18331),tc_List_Olist(U_18331)),U_18333),U_18335)),c_List_Olexord(U_18331,U_18337)))
        | ( ! [U_18325] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18331,U_18331)),hAPP(hAPP(c_Product__Type_OPair(U_18331,U_18331),hAPP(hAPP(c_List_Onth(U_18331),U_18333),U_18325)),hAPP(hAPP(c_List_Onth(U_18331),U_18335),U_18325))),U_18337))
              | hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18333) != hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18335)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18325),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18331),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),U_18335) != U_18333
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335))) ) ) )
    & ! [U_18336,U_18334,U_18332,U_18330] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18330,U_18330)),hAPP(hAPP(c_Product__Type_OPair(U_18330,U_18330),hAPP(hAPP(c_List_Onth(U_18330),U_18332),sK468(U_18336,U_18334,U_18332,U_18330))),hAPP(hAPP(c_List_Onth(U_18330),U_18334),sK468(U_18336,U_18334,U_18332,U_18330)))),U_18336))
          & hAPP(hAPP(c_List_Otake(U_18330),sK468(U_18336,U_18334,U_18332,U_18330)),U_18332) = hAPP(hAPP(c_List_Otake(U_18330),sK468(U_18336,U_18334,U_18332,U_18330)),U_18334)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK468(U_18336,U_18334,U_18332,U_18330)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18330),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),U_18334) = U_18332
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18330),tc_List_Olist(U_18330))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18330),tc_List_Olist(U_18330)),U_18332),U_18334)),c_List_Olexord(U_18330,U_18336))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_18324,sK468(U_18336,U_18334,U_18332,U_18330))],[f_4440_3]) ).

fof(f_4440_5,plain,
    ( ! [U_18325,U_18331,U_18337,U_18333,U_18335] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18331,U_18331)),hAPP(hAPP(c_Product__Type_OPair(U_18331,U_18331),hAPP(hAPP(c_List_Onth(U_18331),U_18333),U_18325)),hAPP(hAPP(c_List_Onth(U_18331),U_18335),U_18325))),U_18337))
        | hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18333) != hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18335)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18325),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335))))
        | ~ sP1162(U_18325,U_18331,U_18337,U_18333,U_18335) )
    & ! [U_18325,U_18331,U_18337,U_18333,U_18335] :
        ( hAPP(hAPP(c_List_Otake(U_18331),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),U_18335) != U_18333
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335)))
        | ~ sP1162(U_18325,U_18331,U_18337,U_18333,U_18335) )
    & ! [U_18334,U_18330,U_18332,U_18336] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18330,U_18330)),hAPP(hAPP(c_Product__Type_OPair(U_18330,U_18330),hAPP(hAPP(c_List_Onth(U_18330),U_18332),sK468(U_18336,U_18334,U_18332,U_18330))),hAPP(hAPP(c_List_Onth(U_18330),U_18334),sK468(U_18336,U_18334,U_18332,U_18330)))),U_18336))
        | ~ sP1161(U_18334,U_18330,U_18332,U_18336) )
    & ! [U_18334,U_18330,U_18332,U_18336] :
        ( hAPP(hAPP(c_List_Otake(U_18330),sK468(U_18336,U_18334,U_18332,U_18330)),U_18332) = hAPP(hAPP(c_List_Otake(U_18330),sK468(U_18336,U_18334,U_18332,U_18330)),U_18334)
        | ~ sP1161(U_18334,U_18330,U_18332,U_18336) )
    & ! [U_18334,U_18330,U_18332,U_18336] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK468(U_18336,U_18334,U_18332,U_18330)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334))))
        | ~ sP1161(U_18334,U_18330,U_18332,U_18336) )
    & ! [U_18334,U_18330,U_18332] :
        ( hAPP(hAPP(c_List_Otake(U_18330),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),U_18334) = U_18332
        | ~ sP1160(U_18334,U_18330,U_18332) )
    & ! [U_18334,U_18330,U_18332] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334)))
        | ~ sP1160(U_18334,U_18330,U_18332) )
    & ! [U_18325,U_18331,U_18337,U_18333,U_18335] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18331),tc_List_Olist(U_18331))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18331),tc_List_Olist(U_18331)),U_18333),U_18335)),c_List_Olexord(U_18331,U_18337)))
        | sP1162(U_18325,U_18331,U_18337,U_18333,U_18335) )
    & ! [U_18334,U_18330,U_18332,U_18336] :
        ( sP1161(U_18334,U_18330,U_18332,U_18336)
        | sP1160(U_18334,U_18330,U_18332)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18330),tc_List_Olist(U_18330))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18330),tc_List_Olist(U_18330)),U_18332),U_18334)),c_List_Olexord(U_18330,U_18336))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1160,sP1161,sP1162])],[f_4440_4]) ).

cnf(f_4440_6,plain,
    ( sP1161(U_18334,U_18330,U_18332,U_18336)
    | sP1160(U_18334,U_18330,U_18332)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18330),tc_List_Olist(U_18330))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18330),tc_List_Olist(U_18330)),U_18332),U_18334)),c_List_Olexord(U_18330,U_18336))) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18331),tc_List_Olist(U_18331))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18331),tc_List_Olist(U_18331)),U_18333),U_18335)),c_List_Olexord(U_18331,U_18337)))
    | sP1162(U_18325,U_18331,U_18337,U_18333,U_18335) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334)))
    | ~ sP1160(U_18334,U_18330,U_18332) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_9,plain,
    ( hAPP(hAPP(c_List_Otake(U_18330),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),U_18334) = U_18332
    | ~ sP1160(U_18334,U_18330,U_18332) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK468(U_18336,U_18334,U_18332,U_18330)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18330)),U_18334))))
    | ~ sP1161(U_18334,U_18330,U_18332,U_18336) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_18330),sK468(U_18336,U_18334,U_18332,U_18330)),U_18332) = hAPP(hAPP(c_List_Otake(U_18330),sK468(U_18336,U_18334,U_18332,U_18330)),U_18334)
    | ~ sP1161(U_18334,U_18330,U_18332,U_18336) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18330,U_18330)),hAPP(hAPP(c_Product__Type_OPair(U_18330,U_18330),hAPP(hAPP(c_List_Onth(U_18330),U_18332),sK468(U_18336,U_18334,U_18332,U_18330))),hAPP(hAPP(c_List_Onth(U_18330),U_18334),sK468(U_18336,U_18334,U_18332,U_18330)))),U_18336))
    | ~ sP1161(U_18334,U_18330,U_18332,U_18336) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_13,plain,
    ( hAPP(hAPP(c_List_Otake(U_18331),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),U_18335) != U_18333
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335)))
    | ~ sP1162(U_18325,U_18331,U_18337,U_18333,U_18335) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

cnf(f_4440_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18331,U_18331)),hAPP(hAPP(c_Product__Type_OPair(U_18331,U_18331),hAPP(hAPP(c_List_Onth(U_18331),U_18333),U_18325)),hAPP(hAPP(c_List_Onth(U_18331),U_18335),U_18325))),U_18337))
    | hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18333) != hAPP(hAPP(c_List_Otake(U_18331),U_18325),U_18335)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18325),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18333)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18331)),U_18335))))
    | ~ sP1162(U_18325,U_18331,U_18337,U_18333,U_18335) ),
    inference(clausify,[status(thm)],[f_4440_5]) ).

fof(f_4441_1,plain,
    ! [V_xs_2,T_b,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take]) ).

fof(f_4441_2,plain,
    ! [U_18341,U_18340,U_18339,U_18338] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18340,tc_HOL_Obool)),hAPP(c_List_Oset(U_18340),hAPP(hAPP(c_List_Otake(U_18340),U_18338),U_18341))),hAPP(c_List_Oset(U_18340),hAPP(hAPP(c_List_Otake(U_18340),U_18339),U_18341))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18338),U_18339)) ),
    inference(variable_rename,[status(thm)],[f_4441_1]) ).

fof(f_4441_3,plain,
    ! [U_18339,U_18340,U_18338,U_18341] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18340,tc_HOL_Obool)),hAPP(c_List_Oset(U_18340),hAPP(hAPP(c_List_Otake(U_18340),U_18338),U_18341))),hAPP(c_List_Oset(U_18340),hAPP(hAPP(c_List_Otake(U_18340),U_18339),U_18341))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18338),U_18339)) ),
    inference(definitional_conversion,[status(esa)],[f_4441_2]) ).

cnf(f_4441_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18340,tc_HOL_Obool)),hAPP(c_List_Oset(U_18340),hAPP(hAPP(c_List_Otake(U_18340),U_18338),U_18341))),hAPP(c_List_Oset(U_18340),hAPP(hAPP(c_List_Otake(U_18340),U_18339),U_18341))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18338),U_18339)) ),
    inference(clausify,[status(thm)],[f_4441_3]) ).

fof(f_4442_1,plain,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__takeD]) ).

fof(f_4442_2,plain,
    ! [U_18345,U_18344,U_18343,U_18342] :
      ( hBOOL(hAPP(hAPP(c_member(U_18342),U_18343),hAPP(c_List_Oset(U_18342),U_18345)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18342),U_18343),hAPP(c_List_Oset(U_18342),hAPP(hAPP(c_List_Otake(U_18342),U_18344),U_18345)))) ),
    inference(variable_rename,[status(thm)],[f_4442_1]) ).

fof(f_4442_3,plain,
    ! [U_18342,U_18343,U_18344,U_18345] :
      ( hBOOL(hAPP(hAPP(c_member(U_18342),U_18343),hAPP(c_List_Oset(U_18342),U_18345)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18342),U_18343),hAPP(c_List_Oset(U_18342),hAPP(hAPP(c_List_Otake(U_18342),U_18344),U_18345)))) ),
    inference(definitional_conversion,[status(esa)],[f_4442_2]) ).

cnf(f_4442_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18342),U_18343),hAPP(c_List_Oset(U_18342),U_18345)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18342),U_18343),hAPP(c_List_Oset(U_18342),hAPP(hAPP(c_List_Otake(U_18342),U_18344),U_18345)))) ),
    inference(clausify,[status(thm)],[f_4442_3]) ).

fof(f_4443_1,plain,
    ! [V_xs,T_a,V_n,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__take]) ).

fof(f_4443_2,plain,
    ! [U_18349,U_18348,U_18347,U_18346] :
      ( hAPP(hAPP(c_List_Onth(U_18348),hAPP(hAPP(c_List_Otake(U_18348),U_18347),U_18349)),U_18346) = hAPP(hAPP(c_List_Onth(U_18348),U_18349),U_18346)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18346),U_18347)) ),
    inference(variable_rename,[status(thm)],[f_4443_1]) ).

fof(f_4443_3,plain,
    ! [U_18346,U_18347,U_18348,U_18349] :
      ( hAPP(hAPP(c_List_Onth(U_18348),hAPP(hAPP(c_List_Otake(U_18348),U_18347),U_18349)),U_18346) = hAPP(hAPP(c_List_Onth(U_18348),U_18349),U_18346)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18346),U_18347)) ),
    inference(definitional_conversion,[status(esa)],[f_4443_2]) ).

cnf(f_4443_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18348),hAPP(hAPP(c_List_Otake(U_18348),U_18347),U_18349)),U_18346) = hAPP(hAPP(c_List_Onth(U_18348),U_18349),U_18346)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18346),U_18347)) ),
    inference(clausify,[status(thm)],[f_4443_3]) ).

fof(f_4444_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__take__subset]) ).

fof(f_4444_2,plain,
    ! [U_18352,U_18351,U_18350] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18350,tc_HOL_Obool)),hAPP(c_List_Oset(U_18350),hAPP(hAPP(c_List_Otake(U_18350),U_18351),U_18352))),hAPP(c_List_Oset(U_18350),U_18352))),
    inference(variable_rename,[status(thm)],[f_4444_1]) ).

fof(f_4444_3,plain,
    ! [U_18350,U_18351,U_18352] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18350,tc_HOL_Obool)),hAPP(c_List_Oset(U_18350),hAPP(hAPP(c_List_Otake(U_18350),U_18351),U_18352))),hAPP(c_List_Oset(U_18350),U_18352))),
    inference(definitional_conversion,[status(esa)],[f_4444_2]) ).

cnf(f_4444_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18350,tc_HOL_Obool)),hAPP(c_List_Oset(U_18350),hAPP(hAPP(c_List_Otake(U_18350),U_18351),U_18352))),hAPP(c_List_Oset(U_18350),U_18352))),
    inference(clausify,[status(thm)],[f_4444_3]) ).

fof(f_4445_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_take__all]) ).

fof(f_4445_2,plain,
    ! [U_18355,U_18354,U_18353] :
      ( hAPP(hAPP(c_List_Otake(U_18353),U_18355),U_18354) = U_18354
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18353)),U_18354)),U_18355)) ),
    inference(variable_rename,[status(thm)],[f_4445_1]) ).

fof(f_4445_3,plain,
    ! [U_18353,U_18354,U_18355] :
      ( hAPP(hAPP(c_List_Otake(U_18353),U_18355),U_18354) = U_18354
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18353)),U_18354)),U_18355)) ),
    inference(definitional_conversion,[status(esa)],[f_4445_2]) ).

cnf(f_4445_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_18353),U_18355),U_18354) = U_18354
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18353)),U_18354)),U_18355)) ),
    inference(clausify,[status(thm)],[f_4445_3]) ).

fof(f_4446_1,plain,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__take]) ).

fof(f_4446_2,plain,
    ! [U_18358,U_18357,U_18356] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18356),hAPP(hAPP(c_List_Otake(U_18356),U_18358),U_18357)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18356),U_18357)) ),
    inference(variable_rename,[status(thm)],[f_4446_1]) ).

fof(f_4446_3,plain,
    ! [U_18356,U_18357,U_18358] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18356),hAPP(hAPP(c_List_Otake(U_18356),U_18358),U_18357)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18356),U_18357)) ),
    inference(definitional_conversion,[status(esa)],[f_4446_2]) ).

cnf(f_4446_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18356),hAPP(hAPP(c_List_Otake(U_18356),U_18358),U_18357)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18356),U_18357)) ),
    inference(clausify,[status(thm)],[f_4446_3]) ).

fof(f_4447_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_take__take]) ).

fof(f_4447_2,plain,
    ! [U_18362,U_18361,U_18360,U_18359] : hAPP(hAPP(c_List_Otake(U_18359),U_18360),hAPP(hAPP(c_List_Otake(U_18359),U_18361),U_18362)) = hAPP(hAPP(c_List_Otake(U_18359),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18360),U_18361)),U_18362),
    inference(variable_rename,[status(thm)],[f_4447_1]) ).

fof(f_4447_3,plain,
    ! [U_18359,U_18360,U_18361,U_18362] : hAPP(hAPP(c_List_Otake(U_18359),U_18360),hAPP(hAPP(c_List_Otake(U_18359),U_18361),U_18362)) = hAPP(hAPP(c_List_Otake(U_18359),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18360),U_18361)),U_18362),
    inference(definitional_conversion,[status(esa)],[f_4447_2]) ).

cnf(f_4447_4,plain,
    hAPP(hAPP(c_List_Otake(U_18359),U_18360),hAPP(hAPP(c_List_Otake(U_18359),U_18361),U_18362)) = hAPP(hAPP(c_List_Otake(U_18359),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18360),U_18361)),U_18362),
    inference(clausify,[status(thm)],[f_4447_3]) ).

fof(f_4448_1,plain,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_take__zip]) ).

fof(f_4448_2,plain,
    ! [U_18367,U_18366,U_18365,U_18364,U_18363] : hAPP(hAPP(c_List_Otake(tc_prod(U_18363,U_18364)),U_18365),hAPP(hAPP(c_List_Ozip(U_18363,U_18364),U_18366),U_18367)) = hAPP(hAPP(c_List_Ozip(U_18363,U_18364),hAPP(hAPP(c_List_Otake(U_18363),U_18365),U_18366)),hAPP(hAPP(c_List_Otake(U_18364),U_18365),U_18367)),
    inference(variable_rename,[status(thm)],[f_4448_1]) ).

fof(f_4448_3,plain,
    ! [U_18363,U_18364,U_18365,U_18366,U_18367] : hAPP(hAPP(c_List_Otake(tc_prod(U_18363,U_18364)),U_18365),hAPP(hAPP(c_List_Ozip(U_18363,U_18364),U_18366),U_18367)) = hAPP(hAPP(c_List_Ozip(U_18363,U_18364),hAPP(hAPP(c_List_Otake(U_18363),U_18365),U_18366)),hAPP(hAPP(c_List_Otake(U_18364),U_18365),U_18367)),
    inference(definitional_conversion,[status(esa)],[f_4448_2]) ).

cnf(f_4448_4,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(U_18363,U_18364)),U_18365),hAPP(hAPP(c_List_Ozip(U_18363,U_18364),U_18366),U_18367)) = hAPP(hAPP(c_List_Ozip(U_18363,U_18364),hAPP(hAPP(c_List_Otake(U_18363),U_18365),U_18366)),hAPP(hAPP(c_List_Otake(U_18364),U_18365),U_18367)),
    inference(clausify,[status(thm)],[f_4448_3]) ).

fof(f_4449_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    inference(fof_nnf,[status(thm)],[fact_length__take]) ).

fof(f_4449_2,plain,
    ! [U_18370,U_18369,U_18368] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),hAPP(hAPP(c_List_Otake(U_18368),U_18369),U_18370)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18370)),U_18369),
    inference(variable_rename,[status(thm)],[f_4449_1]) ).

fof(f_4449_3,plain,
    ! [U_18368,U_18369,U_18370] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),hAPP(hAPP(c_List_Otake(U_18368),U_18369),U_18370)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18370)),U_18369),
    inference(definitional_conversion,[status(esa)],[f_4449_2]) ).

cnf(f_4449_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),hAPP(hAPP(c_List_Otake(U_18368),U_18369),U_18370)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18370)),U_18369),
    inference(clausify,[status(thm)],[f_4449_3]) ).

fof(f_4450_1,plain,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__Suc__Cons]) ).

fof(f_4450_2,plain,
    ! [U_18374,U_18373,U_18372,U_18371] : hAPP(hAPP(c_List_Otake(U_18371),hAPP(c_Nat_OSuc,U_18372)),hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18373),U_18374)) = hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18373),hAPP(hAPP(c_List_Otake(U_18371),U_18372),U_18374)),
    inference(variable_rename,[status(thm)],[f_4450_1]) ).

fof(f_4450_3,plain,
    ! [U_18371,U_18372,U_18373,U_18374] : hAPP(hAPP(c_List_Otake(U_18371),hAPP(c_Nat_OSuc,U_18372)),hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18373),U_18374)) = hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18373),hAPP(hAPP(c_List_Otake(U_18371),U_18372),U_18374)),
    inference(definitional_conversion,[status(esa)],[f_4450_2]) ).

cnf(f_4450_4,plain,
    hAPP(hAPP(c_List_Otake(U_18371),hAPP(c_Nat_OSuc,U_18372)),hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18373),U_18374)) = hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18373),hAPP(hAPP(c_List_Otake(U_18371),U_18372),U_18374)),
    inference(clausify,[status(thm)],[f_4450_3]) ).

fof(f_4451_1,plain,
    ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(f_4451_2,plain,
    ! [U_18377,U_18376,U_18375] : c_List_Osublist(U_18375,U_18376,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18377)) = hAPP(hAPP(c_List_Otake(U_18375),U_18377),U_18376),
    inference(variable_rename,[status(thm)],[f_4451_1]) ).

fof(f_4451_3,plain,
    ! [U_18375,U_18376,U_18377] : c_List_Osublist(U_18375,U_18376,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18377)) = hAPP(hAPP(c_List_Otake(U_18375),U_18377),U_18376),
    inference(definitional_conversion,[status(esa)],[f_4451_2]) ).

cnf(f_4451_4,plain,
    c_List_Osublist(U_18375,U_18376,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18377)) = hAPP(hAPP(c_List_Otake(U_18375),U_18377),U_18376),
    inference(clausify,[status(thm)],[f_4451_3]) ).

fof(f_4452_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_take__map]) ).

fof(f_4452_2,plain,
    ! [U_18382,U_18381,U_18380,U_18379,U_18378] : hAPP(hAPP(c_List_Otake(U_18378),U_18379),hAPP(hAPP(c_List_Omap(U_18380,U_18378),U_18381),U_18382)) = hAPP(hAPP(c_List_Omap(U_18380,U_18378),U_18381),hAPP(hAPP(c_List_Otake(U_18380),U_18379),U_18382)),
    inference(variable_rename,[status(thm)],[f_4452_1]) ).

fof(f_4452_3,plain,
    ! [U_18378,U_18379,U_18380,U_18381,U_18382] : hAPP(hAPP(c_List_Otake(U_18378),U_18379),hAPP(hAPP(c_List_Omap(U_18380,U_18378),U_18381),U_18382)) = hAPP(hAPP(c_List_Omap(U_18380,U_18378),U_18381),hAPP(hAPP(c_List_Otake(U_18380),U_18379),U_18382)),
    inference(definitional_conversion,[status(esa)],[f_4452_2]) ).

cnf(f_4452_4,plain,
    hAPP(hAPP(c_List_Otake(U_18378),U_18379),hAPP(hAPP(c_List_Omap(U_18380,U_18378),U_18381),U_18382)) = hAPP(hAPP(c_List_Omap(U_18380,U_18378),U_18381),hAPP(hAPP(c_List_Otake(U_18380),U_18379),U_18382)),
    inference(clausify,[status(thm)],[f_4452_3]) ).

fof(f_4453_1,plain,
    ! [V_n,V_ns,V_k] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__update__nat]) ).

fof(f_4453_2,plain,
    ! [U_18385,U_18384,U_18383] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18384),U_18383),U_18385)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18384)),U_18385)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18384),U_18383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18383),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18384))) ),
    inference(variable_rename,[status(thm)],[f_4453_1]) ).

fof(f_4453_3,plain,
    ! [U_18383,U_18384,U_18385] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18384),U_18383),U_18385)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18384)),U_18385)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18384),U_18383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18383),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18384))) ),
    inference(definitional_conversion,[status(esa)],[f_4453_2]) ).

cnf(f_4453_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18384),U_18383),U_18385)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18384)),U_18385)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18384),U_18383))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18383),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18384))) ),
    inference(clausify,[status(thm)],[f_4453_3]) ).

fof(f_4454_1,plain,
    ! [T_b,V_xs_2] :
      ( c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2)
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_select__weigth__select]) ).

fof(f_4454_2,plain,
    ! [U_18387,U_18386] :
      ( c_Random_Oselect__weight(U_18387,hAPP(hAPP(c_List_Omap(U_18387,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18387)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18387),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18386)) = c_Random_Oselect(U_18387,U_18386)
      | U_18386 = c_List_Olist_ONil(U_18387) ),
    inference(variable_rename,[status(thm)],[f_4454_1]) ).

fof(f_4454_3,plain,
    ! [U_18387,U_18386] :
      ( c_Random_Oselect__weight(U_18387,hAPP(hAPP(c_List_Omap(U_18387,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18387)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18387),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18386)) = c_Random_Oselect(U_18387,U_18386)
      | U_18386 = c_List_Olist_ONil(U_18387) ),
    inference(definitional_conversion,[status(esa)],[f_4454_2]) ).

cnf(f_4454_4,plain,
    ( c_Random_Oselect__weight(U_18387,hAPP(hAPP(c_List_Omap(U_18387,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18387)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18387),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18386)) = c_Random_Oselect(U_18387,U_18386)
    | U_18386 = c_List_Olist_ONil(U_18387) ),
    inference(clausify,[status(thm)],[f_4454_3]) ).

fof(f_4455_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil2]) ).

fof(f_4455_2,plain,
    ! [U_18390,U_18389,U_18388] :
      ( U_18389 = c_List_Olist_ONil(U_18388)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18388),tc_List_Olist(U_18388))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18388),tc_List_Olist(U_18388)),U_18389),c_List_Olist_ONil(U_18388))),c_List_Olistrel(U_18388,U_18390))) ),
    inference(variable_rename,[status(thm)],[f_4455_1]) ).

fof(f_4455_3,plain,
    ! [U_18388,U_18389,U_18390] :
      ( U_18389 = c_List_Olist_ONil(U_18388)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18388),tc_List_Olist(U_18388))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18388),tc_List_Olist(U_18388)),U_18389),c_List_Olist_ONil(U_18388))),c_List_Olistrel(U_18388,U_18390))) ),
    inference(definitional_conversion,[status(esa)],[f_4455_2]) ).

cnf(f_4455_4,plain,
    ( U_18389 = c_List_Olist_ONil(U_18388)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18388),tc_List_Olist(U_18388))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18388),tc_List_Olist(U_18388)),U_18389),c_List_Olist_ONil(U_18388))),c_List_Olistrel(U_18388,U_18390))) ),
    inference(clausify,[status(thm)],[f_4455_3]) ).

fof(f_4456_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil1]) ).

fof(f_4456_2,plain,
    ! [U_18393,U_18392,U_18391] :
      ( U_18392 = c_List_Olist_ONil(U_18391)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18391),tc_List_Olist(U_18391))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18391),tc_List_Olist(U_18391)),c_List_Olist_ONil(U_18391)),U_18392)),c_List_Olistrel(U_18391,U_18393))) ),
    inference(variable_rename,[status(thm)],[f_4456_1]) ).

fof(f_4456_3,plain,
    ! [U_18391,U_18392,U_18393] :
      ( U_18392 = c_List_Olist_ONil(U_18391)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18391),tc_List_Olist(U_18391))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18391),tc_List_Olist(U_18391)),c_List_Olist_ONil(U_18391)),U_18392)),c_List_Olistrel(U_18391,U_18393))) ),
    inference(definitional_conversion,[status(esa)],[f_4456_2]) ).

cnf(f_4456_4,plain,
    ( U_18392 = c_List_Olist_ONil(U_18391)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18391),tc_List_Olist(U_18391))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18391),tc_List_Olist(U_18391)),c_List_Olist_ONil(U_18391)),U_18392)),c_List_Olistrel(U_18391,U_18393))) ),
    inference(clausify,[status(thm)],[f_4456_3]) ).

fof(f_4457_1,plain,
    ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_list__update__id]) ).

fof(f_4457_2,plain,
    ! [U_18396,U_18395,U_18394] : hAPP(hAPP(c_List_Olist__update(U_18394,U_18395),U_18396),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18396)) = U_18395,
    inference(variable_rename,[status(thm)],[f_4457_1]) ).

fof(f_4457_3,plain,
    ! [U_18394,U_18395,U_18396] : hAPP(hAPP(c_List_Olist__update(U_18394,U_18395),U_18396),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18396)) = U_18395,
    inference(definitional_conversion,[status(esa)],[f_4457_2]) ).

cnf(f_4457_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18394,U_18395),U_18396),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18396)) = U_18395,
    inference(clausify,[status(thm)],[f_4457_3]) ).

fof(f_4458_1,plain,
    ! [V_x,V_xs,T_a,V_j,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)
      | V_i = V_j ),
    inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq]) ).

fof(f_4458_2,plain,
    ! [U_18401,U_18400,U_18399,U_18398,U_18397] :
      ( hAPP(hAPP(c_List_Onth(U_18399),hAPP(hAPP(c_List_Olist__update(U_18399,U_18400),U_18397),U_18401)),U_18398) = hAPP(hAPP(c_List_Onth(U_18399),U_18400),U_18398)
      | U_18397 = U_18398 ),
    inference(variable_rename,[status(thm)],[f_4458_1]) ).

fof(f_4458_3,plain,
    ! [U_18397,U_18398,U_18399,U_18400,U_18401] :
      ( hAPP(hAPP(c_List_Onth(U_18399),hAPP(hAPP(c_List_Olist__update(U_18399,U_18400),U_18397),U_18401)),U_18398) = hAPP(hAPP(c_List_Onth(U_18399),U_18400),U_18398)
      | U_18397 = U_18398 ),
    inference(definitional_conversion,[status(esa)],[f_4458_2]) ).

cnf(f_4458_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18399),hAPP(hAPP(c_List_Olist__update(U_18399,U_18400),U_18397),U_18401)),U_18398) = hAPP(hAPP(c_List_Onth(U_18399),U_18400),U_18398)
    | U_18397 = U_18398 ),
    inference(clausify,[status(thm)],[f_4458_3]) ).

fof(f_4459_1,plain,
    ! [V_x,V_i,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__beyond]) ).

fof(f_4459_2,plain,
    ! [U_18405,U_18404,U_18403,U_18402] :
      ( hAPP(hAPP(c_List_Olist__update(U_18402,U_18403),U_18404),U_18405) = U_18403
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18402)),U_18403)),U_18404)) ),
    inference(variable_rename,[status(thm)],[f_4459_1]) ).

fof(f_4459_3,plain,
    ! [U_18402,U_18403,U_18404,U_18405] :
      ( hAPP(hAPP(c_List_Olist__update(U_18402,U_18403),U_18404),U_18405) = U_18403
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18402)),U_18403)),U_18404)) ),
    inference(definitional_conversion,[status(esa)],[f_4459_2]) ).

cnf(f_4459_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18402,U_18403),U_18404),U_18405) = U_18403
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18402)),U_18403)),U_18404)) ),
    inference(clausify,[status(thm)],[f_4459_3]) ).

fof(f_4460_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ( V_xs_2 != c_List_Olist_ONil(T_b)
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__eq__Nil]) ).

fof(f_4460_2,plain,
    ! [U_18408,U_18407,U_18406] :
      ( ( hAPP(hAPP(c_List_Otake(U_18406),U_18407),U_18408) = c_List_Olist_ONil(U_18406)
        | ( U_18408 != c_List_Olist_ONil(U_18406)
          & U_18407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_18408 = c_List_Olist_ONil(U_18406)
        | U_18407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18406),U_18407),U_18408) != c_List_Olist_ONil(U_18406) ) ),
    inference(variable_rename,[status(thm)],[f_4460_1]) ).

fof(f_4460_3,plain,
    ( ! [U_18414,U_18412,U_18410] :
        ( hAPP(hAPP(c_List_Otake(U_18410),U_18412),U_18414) = c_List_Olist_ONil(U_18410)
        | ( U_18414 != c_List_Olist_ONil(U_18410)
          & U_18412 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_18413,U_18411,U_18409] :
        ( U_18413 = c_List_Olist_ONil(U_18409)
        | U_18411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18409),U_18411),U_18413) != c_List_Olist_ONil(U_18409) ) ),
    inference(miniscope,[status(thm)],[f_4460_2]) ).

fof(f_4460_4,plain,
    ( ! [U_18414,U_18412,U_18410] :
        ( U_18414 != c_List_Olist_ONil(U_18410)
        | ~ sP1163(U_18414,U_18412,U_18410) )
    & ! [U_18414,U_18412,U_18410] :
        ( U_18412 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1163(U_18414,U_18412,U_18410) )
    & ! [U_18414,U_18412,U_18410] :
        ( hAPP(hAPP(c_List_Otake(U_18410),U_18412),U_18414) = c_List_Olist_ONil(U_18410)
        | sP1163(U_18414,U_18412,U_18410) )
    & ! [U_18411,U_18409,U_18413] :
        ( U_18413 = c_List_Olist_ONil(U_18409)
        | U_18411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18409),U_18411),U_18413) != c_List_Olist_ONil(U_18409) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1163])],[f_4460_3]) ).

cnf(f_4460_5,plain,
    ( U_18413 = c_List_Olist_ONil(U_18409)
    | U_18411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_18409),U_18411),U_18413) != c_List_Olist_ONil(U_18409) ),
    inference(clausify,[status(thm)],[f_4460_4]) ).

cnf(f_4460_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18410),U_18412),U_18414) = c_List_Olist_ONil(U_18410)
    | sP1163(U_18414,U_18412,U_18410) ),
    inference(clausify,[status(thm)],[f_4460_4]) ).

cnf(f_4460_7,plain,
    ( U_18412 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1163(U_18414,U_18412,U_18410) ),
    inference(clausify,[status(thm)],[f_4460_4]) ).

cnf(f_4460_8,plain,
    ( U_18414 != c_List_Olist_ONil(U_18410)
    | ~ sP1163(U_18414,U_18412,U_18410) ),
    inference(clausify,[status(thm)],[f_4460_4]) ).

fof(f_4461_1,plain,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_take__0]) ).

fof(f_4461_2,plain,
    ! [U_18416,U_18415] : hAPP(hAPP(c_List_Otake(U_18415),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18416) = c_List_Olist_ONil(U_18415),
    inference(variable_rename,[status(thm)],[f_4461_1]) ).

fof(f_4461_3,plain,
    ! [U_18415,U_18416] : hAPP(hAPP(c_List_Otake(U_18415),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18416) = c_List_Olist_ONil(U_18415),
    inference(definitional_conversion,[status(esa)],[f_4461_2]) ).

cnf(f_4461_4,plain,
    hAPP(hAPP(c_List_Otake(U_18415),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18416) = c_List_Olist_ONil(U_18415),
    inference(clausify,[status(thm)],[f_4461_3]) ).

fof(f_4462_1,plain,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_take__Nil]) ).

fof(f_4462_2,plain,
    ! [U_18418,U_18417] : hAPP(hAPP(c_List_Otake(U_18417),U_18418),c_List_Olist_ONil(U_18417)) = c_List_Olist_ONil(U_18417),
    inference(variable_rename,[status(thm)],[f_4462_1]) ).

fof(f_4462_3,plain,
    ! [U_18417,U_18418] : hAPP(hAPP(c_List_Otake(U_18417),U_18418),c_List_Olist_ONil(U_18417)) = c_List_Olist_ONil(U_18417),
    inference(definitional_conversion,[status(esa)],[f_4462_2]) ).

cnf(f_4462_4,plain,
    hAPP(hAPP(c_List_Otake(U_18417),U_18418),c_List_Olist_ONil(U_18417)) = c_List_Olist_ONil(U_18417),
    inference(clausify,[status(thm)],[f_4462_3]) ).

fof(f_4463_1,plain,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I3_J]) ).

fof(f_4463_2,plain,
    ! [U_18419] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18419)),c_List_Olist_ONil(U_18419)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4463_1]) ).

fof(f_4463_3,plain,
    ! [U_18419] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18419)),c_List_Olist_ONil(U_18419)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4463_2]) ).

cnf(f_4463_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18419)),c_List_Olist_ONil(U_18419)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4463_3]) ).

fof(f_4464_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__0__conv]) ).

fof(f_4464_2,plain,
    ! [U_18421,U_18420] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18420)),U_18421) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18421 != c_List_Olist_ONil(U_18420) )
      & ( U_18421 = c_List_Olist_ONil(U_18420)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18420)),U_18421) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4464_1]) ).

fof(f_4464_3,plain,
    ( ! [U_18425,U_18423] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18423)),U_18425) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18425 != c_List_Olist_ONil(U_18423) )
    & ! [U_18424,U_18422] :
        ( U_18424 = c_List_Olist_ONil(U_18422)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),U_18424) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4464_2]) ).

fof(f_4464_4,plain,
    ( ! [U_18425,U_18423] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18423)),U_18425) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18425 != c_List_Olist_ONil(U_18423) )
    & ! [U_18424,U_18422] :
        ( U_18424 = c_List_Olist_ONil(U_18422)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),U_18424) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4464_3]) ).

cnf(f_4464_5,plain,
    ( U_18424 = c_List_Olist_ONil(U_18422)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),U_18424) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4464_4]) ).

cnf(f_4464_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18423)),U_18425) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_18425 != c_List_Olist_ONil(U_18423) ),
    inference(clausify,[status(thm)],[f_4464_4]) ).

fof(f_4465_1,plain,
    ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__list__update]) ).

fof(f_4465_2,plain,
    ! [U_18429,U_18428,U_18427,U_18426] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18426)),hAPP(hAPP(c_List_Olist__update(U_18426,U_18427),U_18428),U_18429)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18426)),U_18427),
    inference(variable_rename,[status(thm)],[f_4465_1]) ).

fof(f_4465_3,plain,
    ! [U_18426,U_18427,U_18428,U_18429] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18426)),hAPP(hAPP(c_List_Olist__update(U_18426,U_18427),U_18428),U_18429)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18426)),U_18427),
    inference(definitional_conversion,[status(esa)],[f_4465_2]) ).

cnf(f_4465_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18426)),hAPP(hAPP(c_List_Olist__update(U_18426,U_18427),U_18428),U_18429)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18426)),U_18427),
    inference(clausify,[status(thm)],[f_4465_3]) ).

fof(f_4466_1,plain,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_take__Cons]) ).

fof(f_4466_2,plain,
    ! [U_18433,U_18432,U_18431,U_18430] : hAPP(hAPP(c_List_Otake(U_18430),U_18431),hAPP(hAPP(c_List_Olist_OCons(U_18430),U_18432),U_18433)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18430),c_List_Olist_ONil(U_18430),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18430),tc_List_Olist(U_18430),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18430),U_18432)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18430),tc_List_Olist(U_18430)),c_List_Otake(U_18430)),U_18433)),U_18431),
    inference(variable_rename,[status(thm)],[f_4466_1]) ).

fof(f_4466_3,plain,
    ! [U_18430,U_18431,U_18432,U_18433] : hAPP(hAPP(c_List_Otake(U_18430),U_18431),hAPP(hAPP(c_List_Olist_OCons(U_18430),U_18432),U_18433)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18430),c_List_Olist_ONil(U_18430),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18430),tc_List_Olist(U_18430),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18430),U_18432)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18430),tc_List_Olist(U_18430)),c_List_Otake(U_18430)),U_18433)),U_18431),
    inference(definitional_conversion,[status(esa)],[f_4466_2]) ).

cnf(f_4466_4,plain,
    hAPP(hAPP(c_List_Otake(U_18430),U_18431),hAPP(hAPP(c_List_Olist_OCons(U_18430),U_18432),U_18433)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18430),c_List_Olist_ONil(U_18430),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18430),tc_List_Olist(U_18430),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18430),U_18432)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18430),tc_List_Olist(U_18430)),c_List_Otake(U_18430)),U_18433)),U_18431),
    inference(clausify,[status(thm)],[f_4466_3]) ).

fof(f_4467_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_c) )
      & ( V_xs_2 = c_List_Olist_ONil(T_c)
        | c_List_Olist_ONil(T_b) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv]) ).

fof(f_4467_2,plain,
    ! [U_18437,U_18436,U_18435,U_18434] :
      ( ( c_List_Olist_ONil(U_18434) = hAPP(hAPP(c_List_Omap(U_18435,U_18434),U_18436),U_18437)
        | U_18437 != c_List_Olist_ONil(U_18435) )
      & ( U_18437 = c_List_Olist_ONil(U_18435)
        | c_List_Olist_ONil(U_18434) != hAPP(hAPP(c_List_Omap(U_18435,U_18434),U_18436),U_18437) ) ),
    inference(variable_rename,[status(thm)],[f_4467_1]) ).

fof(f_4467_3,plain,
    ( ! [U_18445,U_18443,U_18441] :
        ( ! [U_18439] : c_List_Olist_ONil(U_18439) = hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18443),U_18445)
        | U_18445 != c_List_Olist_ONil(U_18441) )
    & ! [U_18444,U_18442,U_18440] :
        ( ! [U_18438] : c_List_Olist_ONil(U_18438) != hAPP(hAPP(c_List_Omap(U_18440,U_18438),U_18442),U_18444)
        | U_18444 = c_List_Olist_ONil(U_18440) ) ),
    inference(miniscope,[status(thm)],[f_4467_2]) ).

fof(f_4467_4,plain,
    ( ! [U_18443,U_18439,U_18441,U_18445] :
        ( c_List_Olist_ONil(U_18439) = hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18443),U_18445)
        | U_18445 != c_List_Olist_ONil(U_18441) )
    & ! [U_18442,U_18440,U_18438,U_18444] :
        ( c_List_Olist_ONil(U_18438) != hAPP(hAPP(c_List_Omap(U_18440,U_18438),U_18442),U_18444)
        | U_18444 = c_List_Olist_ONil(U_18440) ) ),
    inference(definitional_conversion,[status(esa)],[f_4467_3]) ).

cnf(f_4467_5,plain,
    ( c_List_Olist_ONil(U_18438) != hAPP(hAPP(c_List_Omap(U_18440,U_18438),U_18442),U_18444)
    | U_18444 = c_List_Olist_ONil(U_18440) ),
    inference(clausify,[status(thm)],[f_4467_4]) ).

cnf(f_4467_6,plain,
    ( c_List_Olist_ONil(U_18439) = hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18443),U_18445)
    | U_18445 != c_List_Olist_ONil(U_18441) ),
    inference(clausify,[status(thm)],[f_4467_4]) ).

fof(f_4468_1,plain,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(f_4468_2,plain,
    ! [U_18448,U_18447,U_18446] : hAPP(hAPP(c_List_Omap(U_18446,U_18447),U_18448),c_List_Olist_ONil(U_18446)) = c_List_Olist_ONil(U_18447),
    inference(variable_rename,[status(thm)],[f_4468_1]) ).

fof(f_4468_3,plain,
    ! [U_18446,U_18447,U_18448] : hAPP(hAPP(c_List_Omap(U_18446,U_18447),U_18448),c_List_Olist_ONil(U_18446)) = c_List_Olist_ONil(U_18447),
    inference(definitional_conversion,[status(esa)],[f_4468_2]) ).

cnf(f_4468_4,plain,
    hAPP(hAPP(c_List_Omap(U_18446,U_18447),U_18448),c_List_Olist_ONil(U_18446)) = c_List_Olist_ONil(U_18447),
    inference(clausify,[status(thm)],[f_4468_3]) ).

fof(f_4469_1,plain,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_map__update]) ).

fof(f_4469_2,plain,
    ! [U_18454,U_18453,U_18452,U_18451,U_18450,U_18449] : hAPP(hAPP(c_List_Omap(U_18449,U_18450),U_18451),hAPP(hAPP(c_List_Olist__update(U_18449,U_18452),U_18453),U_18454)) = hAPP(hAPP(c_List_Olist__update(U_18450,hAPP(hAPP(c_List_Omap(U_18449,U_18450),U_18451),U_18452)),U_18453),hAPP(U_18451,U_18454)),
    inference(variable_rename,[status(thm)],[f_4469_1]) ).

fof(f_4469_3,plain,
    ! [U_18449,U_18450,U_18451,U_18452,U_18453,U_18454] : hAPP(hAPP(c_List_Omap(U_18449,U_18450),U_18451),hAPP(hAPP(c_List_Olist__update(U_18449,U_18452),U_18453),U_18454)) = hAPP(hAPP(c_List_Olist__update(U_18450,hAPP(hAPP(c_List_Omap(U_18449,U_18450),U_18451),U_18452)),U_18453),hAPP(U_18451,U_18454)),
    inference(definitional_conversion,[status(esa)],[f_4469_2]) ).

cnf(f_4469_4,plain,
    hAPP(hAPP(c_List_Omap(U_18449,U_18450),U_18451),hAPP(hAPP(c_List_Olist__update(U_18449,U_18452),U_18453),U_18454)) = hAPP(hAPP(c_List_Olist__update(U_18450,hAPP(hAPP(c_List_Omap(U_18449,U_18450),U_18451),U_18452)),U_18453),hAPP(U_18451,U_18454)),
    inference(clausify,[status(thm)],[f_4469_3]) ).

fof(f_4470_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_c) )
      & ( V_xs_2 = c_List_Olist_ONil(T_c)
        | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv]) ).

fof(f_4470_2,plain,
    ! [U_18458,U_18457,U_18456,U_18455] :
      ( ( hAPP(hAPP(c_List_Omap(U_18455,U_18456),U_18457),U_18458) = c_List_Olist_ONil(U_18456)
        | U_18458 != c_List_Olist_ONil(U_18455) )
      & ( U_18458 = c_List_Olist_ONil(U_18455)
        | hAPP(hAPP(c_List_Omap(U_18455,U_18456),U_18457),U_18458) != c_List_Olist_ONil(U_18456) ) ),
    inference(variable_rename,[status(thm)],[f_4470_1]) ).

fof(f_4470_3,plain,
    ( ! [U_18466,U_18464,U_18462,U_18460] :
        ( hAPP(hAPP(c_List_Omap(U_18460,U_18462),U_18464),U_18466) = c_List_Olist_ONil(U_18462)
        | U_18466 != c_List_Olist_ONil(U_18460) )
    & ! [U_18465,U_18463,U_18461,U_18459] :
        ( U_18465 = c_List_Olist_ONil(U_18459)
        | hAPP(hAPP(c_List_Omap(U_18459,U_18461),U_18463),U_18465) != c_List_Olist_ONil(U_18461) ) ),
    inference(miniscope,[status(thm)],[f_4470_2]) ).

fof(f_4470_4,plain,
    ( ! [U_18460,U_18466,U_18462,U_18464] :
        ( hAPP(hAPP(c_List_Omap(U_18460,U_18462),U_18464),U_18466) = c_List_Olist_ONil(U_18462)
        | U_18466 != c_List_Olist_ONil(U_18460) )
    & ! [U_18461,U_18465,U_18463,U_18459] :
        ( U_18465 = c_List_Olist_ONil(U_18459)
        | hAPP(hAPP(c_List_Omap(U_18459,U_18461),U_18463),U_18465) != c_List_Olist_ONil(U_18461) ) ),
    inference(definitional_conversion,[status(esa)],[f_4470_3]) ).

cnf(f_4470_5,plain,
    ( U_18465 = c_List_Olist_ONil(U_18459)
    | hAPP(hAPP(c_List_Omap(U_18459,U_18461),U_18463),U_18465) != c_List_Olist_ONil(U_18461) ),
    inference(clausify,[status(thm)],[f_4470_4]) ).

cnf(f_4470_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_18460,U_18462),U_18464),U_18466) = c_List_Olist_ONil(U_18462)
    | U_18466 != c_List_Olist_ONil(U_18460) ),
    inference(clausify,[status(thm)],[f_4470_4]) ).

fof(f_4471_1,plain,
    ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_zip__update]) ).

fof(f_4471_2,plain,
    ! [U_18473,U_18472,U_18471,U_18470,U_18469,U_18468,U_18467] : hAPP(hAPP(c_List_Ozip(U_18467,U_18468),hAPP(hAPP(c_List_Olist__update(U_18467,U_18469),U_18470),U_18471)),hAPP(hAPP(c_List_Olist__update(U_18468,U_18472),U_18470),U_18473)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18467,U_18468),hAPP(hAPP(c_List_Ozip(U_18467,U_18468),U_18469),U_18472)),U_18470),hAPP(hAPP(c_Product__Type_OPair(U_18467,U_18468),U_18471),U_18473)),
    inference(variable_rename,[status(thm)],[f_4471_1]) ).

fof(f_4471_3,plain,
    ! [U_18467,U_18468,U_18469,U_18470,U_18471,U_18472,U_18473] : hAPP(hAPP(c_List_Ozip(U_18467,U_18468),hAPP(hAPP(c_List_Olist__update(U_18467,U_18469),U_18470),U_18471)),hAPP(hAPP(c_List_Olist__update(U_18468,U_18472),U_18470),U_18473)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18467,U_18468),hAPP(hAPP(c_List_Ozip(U_18467,U_18468),U_18469),U_18472)),U_18470),hAPP(hAPP(c_Product__Type_OPair(U_18467,U_18468),U_18471),U_18473)),
    inference(definitional_conversion,[status(esa)],[f_4471_2]) ).

cnf(f_4471_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18467,U_18468),hAPP(hAPP(c_List_Olist__update(U_18467,U_18469),U_18470),U_18471)),hAPP(hAPP(c_List_Olist__update(U_18468,U_18472),U_18470),U_18473)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18467,U_18468),hAPP(hAPP(c_List_Ozip(U_18467,U_18468),U_18469),U_18472)),U_18470),hAPP(hAPP(c_Product__Type_OPair(U_18467,U_18468),U_18471),U_18473)),
    inference(clausify,[status(thm)],[f_4471_3]) ).

fof(f_4472_1,plain,
    ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))),
    inference(fof_nnf,[status(thm)],[fact_update__zip]) ).

fof(f_4472_2,plain,
    ! [U_18479,U_18478,U_18477,U_18476,U_18475,U_18474] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_18474,U_18475),hAPP(hAPP(c_List_Ozip(U_18474,U_18475),U_18476),U_18477)),U_18478),U_18479) = hAPP(hAPP(c_List_Ozip(U_18474,U_18475),hAPP(hAPP(c_List_Olist__update(U_18474,U_18476),U_18478),hAPP(c_Product__Type_Ofst(U_18474,U_18475),U_18479))),hAPP(hAPP(c_List_Olist__update(U_18475,U_18477),U_18478),hAPP(c_Product__Type_Osnd(U_18474,U_18475),U_18479))),
    inference(variable_rename,[status(thm)],[f_4472_1]) ).

fof(f_4472_3,plain,
    ! [U_18474,U_18475,U_18476,U_18477,U_18478,U_18479] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_18474,U_18475),hAPP(hAPP(c_List_Ozip(U_18474,U_18475),U_18476),U_18477)),U_18478),U_18479) = hAPP(hAPP(c_List_Ozip(U_18474,U_18475),hAPP(hAPP(c_List_Olist__update(U_18474,U_18476),U_18478),hAPP(c_Product__Type_Ofst(U_18474,U_18475),U_18479))),hAPP(hAPP(c_List_Olist__update(U_18475,U_18477),U_18478),hAPP(c_Product__Type_Osnd(U_18474,U_18475),U_18479))),
    inference(definitional_conversion,[status(esa)],[f_4472_2]) ).

cnf(f_4472_4,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(U_18474,U_18475),hAPP(hAPP(c_List_Ozip(U_18474,U_18475),U_18476),U_18477)),U_18478),U_18479) = hAPP(hAPP(c_List_Ozip(U_18474,U_18475),hAPP(hAPP(c_List_Olist__update(U_18474,U_18476),U_18478),hAPP(c_Product__Type_Ofst(U_18474,U_18475),U_18479))),hAPP(hAPP(c_List_Olist__update(U_18475,U_18477),U_18478),hAPP(c_Product__Type_Osnd(U_18474,U_18475),U_18479))),
    inference(clausify,[status(thm)],[f_4472_3]) ).

fof(f_4473_1,plain,
    ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_sublist__nil]) ).

fof(f_4473_2,plain,
    ! [U_18481,U_18480] : c_List_Osublist(U_18480,c_List_Olist_ONil(U_18480),U_18481) = c_List_Olist_ONil(U_18480),
    inference(variable_rename,[status(thm)],[f_4473_1]) ).

fof(f_4473_3,plain,
    ! [U_18480,U_18481] : c_List_Osublist(U_18480,c_List_Olist_ONil(U_18480),U_18481) = c_List_Olist_ONil(U_18480),
    inference(definitional_conversion,[status(esa)],[f_4473_2]) ).

cnf(f_4473_4,plain,
    c_List_Osublist(U_18480,c_List_Olist_ONil(U_18480),U_18481) = c_List_Olist_ONil(U_18480),
    inference(clausify,[status(thm)],[f_4473_3]) ).

fof(f_4474_1,plain,
    ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_sublist__empty]) ).

fof(f_4474_2,plain,
    ! [U_18483,U_18482] : c_List_Osublist(U_18482,U_18483,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18482),
    inference(variable_rename,[status(thm)],[f_4474_1]) ).

fof(f_4474_3,plain,
    ! [U_18482,U_18483] : c_List_Osublist(U_18482,U_18483,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18482),
    inference(definitional_conversion,[status(esa)],[f_4474_2]) ).

cnf(f_4474_4,plain,
    c_List_Osublist(U_18482,U_18483,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18482),
    inference(clausify,[status(thm)],[f_4474_3]) ).

fof(f_4475_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J]) ).

fof(f_4475_2,plain,
    ! [U_18487,U_18486,U_18485,U_18484] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18485,U_18484,U_18486),U_18487),c_List_Olist_ONil(U_18485)) = hAPP(hAPP(c_List_Olist_OCons(U_18485),U_18487),c_List_Olist_ONil(U_18485))
      | ~ class_Orderings_Olinorder(U_18484) ),
    inference(variable_rename,[status(thm)],[f_4475_1]) ).

fof(f_4475_3,plain,
    ! [U_18484,U_18485,U_18486,U_18487] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18485,U_18484,U_18486),U_18487),c_List_Olist_ONil(U_18485)) = hAPP(hAPP(c_List_Olist_OCons(U_18485),U_18487),c_List_Olist_ONil(U_18485))
      | ~ class_Orderings_Olinorder(U_18484) ),
    inference(definitional_conversion,[status(esa)],[f_4475_2]) ).

cnf(f_4475_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18485,U_18484,U_18486),U_18487),c_List_Olist_ONil(U_18485)) = hAPP(hAPP(c_List_Olist_OCons(U_18485),U_18487),c_List_Olist_ONil(U_18485))
    | ~ class_Orderings_Olinorder(U_18484) ),
    inference(clausify,[status(thm)],[f_4475_3]) ).

fof(f_4476_1,plain,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
    inference(fof_nnf,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(f_4476_2,plain,
    ! [U_18492,U_18491,U_18490,U_18489,U_18488] : hAPP(hAPP(c_List_Olist__update(U_18488,hAPP(hAPP(c_List_Olist_OCons(U_18488),U_18489),U_18490)),U_18491),U_18492) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18488),hAPP(hAPP(c_List_Olist_OCons(U_18488),U_18492),U_18490),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18488),tc_List_Olist(U_18488),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18488),U_18489)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18488,tc_List_Olist(U_18488)),c_List_Olist__update(U_18488,U_18490)),U_18492)),U_18491),
    inference(variable_rename,[status(thm)],[f_4476_1]) ).

fof(f_4476_3,plain,
    ! [U_18488,U_18489,U_18490,U_18491,U_18492] : hAPP(hAPP(c_List_Olist__update(U_18488,hAPP(hAPP(c_List_Olist_OCons(U_18488),U_18489),U_18490)),U_18491),U_18492) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18488),hAPP(hAPP(c_List_Olist_OCons(U_18488),U_18492),U_18490),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18488),tc_List_Olist(U_18488),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18488),U_18489)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18488,tc_List_Olist(U_18488)),c_List_Olist__update(U_18488,U_18490)),U_18492)),U_18491),
    inference(definitional_conversion,[status(esa)],[f_4476_2]) ).

cnf(f_4476_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18488,hAPP(hAPP(c_List_Olist_OCons(U_18488),U_18489),U_18490)),U_18491),U_18492) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18488),hAPP(hAPP(c_List_Olist_OCons(U_18488),U_18492),U_18490),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18488),tc_List_Olist(U_18488),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18488),U_18489)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18488,tc_List_Olist(U_18488)),c_List_Olist__update(U_18488,U_18490)),U_18492)),U_18491),
    inference(clausify,[status(thm)],[f_4476_3]) ).

fof(f_4477_1,plain,
    ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs),
    inference(fof_nnf,[status(thm)],[fact_list__update__code_I2_J]) ).

fof(f_4477_2,plain,
    ! [U_18496,U_18495,U_18494,U_18493] : hAPP(hAPP(c_List_Olist__update(U_18493,hAPP(hAPP(c_List_Olist_OCons(U_18493),U_18494),U_18495)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18496) = hAPP(hAPP(c_List_Olist_OCons(U_18493),U_18496),U_18495),
    inference(variable_rename,[status(thm)],[f_4477_1]) ).

fof(f_4477_3,plain,
    ! [U_18494,U_18495,U_18493,U_18496] : hAPP(hAPP(c_List_Olist__update(U_18493,hAPP(hAPP(c_List_Olist_OCons(U_18493),U_18494),U_18495)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18496) = hAPP(hAPP(c_List_Olist_OCons(U_18493),U_18496),U_18495),
    inference(definitional_conversion,[status(esa)],[f_4477_2]) ).

cnf(f_4477_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18493,hAPP(hAPP(c_List_Olist_OCons(U_18493),U_18494),U_18495)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18496) = hAPP(hAPP(c_List_Olist_OCons(U_18493),U_18496),U_18495),
    inference(clausify,[status(thm)],[f_4477_3]) ).

fof(f_4478_1,plain,
    ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)),
    inference(fof_nnf,[status(thm)],[fact_list__update__code_I3_J]) ).

fof(f_4478_2,plain,
    ! [U_18501,U_18500,U_18499,U_18498,U_18497] : hAPP(hAPP(c_List_Olist__update(U_18497,hAPP(hAPP(c_List_Olist_OCons(U_18497),U_18498),U_18499)),hAPP(c_Nat_OSuc,U_18500)),U_18501) = hAPP(hAPP(c_List_Olist_OCons(U_18497),U_18498),hAPP(hAPP(c_List_Olist__update(U_18497,U_18499),U_18500),U_18501)),
    inference(variable_rename,[status(thm)],[f_4478_1]) ).

fof(f_4478_3,plain,
    ! [U_18497,U_18498,U_18499,U_18500,U_18501] : hAPP(hAPP(c_List_Olist__update(U_18497,hAPP(hAPP(c_List_Olist_OCons(U_18497),U_18498),U_18499)),hAPP(c_Nat_OSuc,U_18500)),U_18501) = hAPP(hAPP(c_List_Olist_OCons(U_18497),U_18498),hAPP(hAPP(c_List_Olist__update(U_18497,U_18499),U_18500),U_18501)),
    inference(definitional_conversion,[status(esa)],[f_4478_2]) ).

cnf(f_4478_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18497,hAPP(hAPP(c_List_Olist_OCons(U_18497),U_18498),U_18499)),hAPP(c_Nat_OSuc,U_18500)),U_18501) = hAPP(hAPP(c_List_Olist_OCons(U_18497),U_18498),hAPP(hAPP(c_List_Olist__update(U_18497,U_18499),U_18500),U_18501)),
    inference(clausify,[status(thm)],[f_4478_3]) ).

fof(f_4479_1,plain,
    ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I3_J]) ).

fof(f_4479_2,plain,
    ! [U_18504,U_18503,U_18502] : hAPP(hAPP(c_List_Olist_OCons(U_18502),U_18503),U_18504) != c_List_Olist_ONil(U_18502),
    inference(variable_rename,[status(thm)],[f_4479_1]) ).

fof(f_4479_3,plain,
    ! [U_18502,U_18504,U_18503] : hAPP(hAPP(c_List_Olist_OCons(U_18502),U_18503),U_18504) != c_List_Olist_ONil(U_18502),
    inference(definitional_conversion,[status(esa)],[f_4479_2]) ).

cnf(f_4479_4,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_18502),U_18503),U_18504) != c_List_Olist_ONil(U_18502),
    inference(clausify,[status(thm)],[f_4479_3]) ).

fof(f_4480_1,plain,
    ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H),
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I2_J]) ).

fof(f_4480_2,plain,
    ! [U_18507,U_18506,U_18505] : c_List_Olist_ONil(U_18505) != hAPP(hAPP(c_List_Olist_OCons(U_18505),U_18506),U_18507),
    inference(variable_rename,[status(thm)],[f_4480_1]) ).

fof(f_4480_3,plain,
    ! [U_18505,U_18506,U_18507] : c_List_Olist_ONil(U_18505) != hAPP(hAPP(c_List_Olist_OCons(U_18505),U_18506),U_18507),
    inference(definitional_conversion,[status(esa)],[f_4480_2]) ).

cnf(f_4480_4,plain,
    c_List_Olist_ONil(U_18505) != hAPP(hAPP(c_List_Olist_OCons(U_18505),U_18506),U_18507),
    inference(clausify,[status(thm)],[f_4480_3]) ).

fof(f_4481_1,plain,
    ! [T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty]) ).

fof(f_4481_2,plain,
    ! [U_18508] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18508,c_Orderings_Obot__class_Obot(tc_fun(U_18508,tc_HOL_Obool))) = c_List_Olist_ONil(U_18508)
      | ~ class_Orderings_Olinorder(U_18508) ),
    inference(variable_rename,[status(thm)],[f_4481_1]) ).

fof(f_4481_3,plain,
    ! [U_18508] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18508,c_Orderings_Obot__class_Obot(tc_fun(U_18508,tc_HOL_Obool))) = c_List_Olist_ONil(U_18508)
      | ~ class_Orderings_Olinorder(U_18508) ),
    inference(definitional_conversion,[status(esa)],[f_4481_2]) ).

cnf(f_4481_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_18508,c_Orderings_Obot__class_Obot(tc_fun(U_18508,tc_HOL_Obool))) = c_List_Olist_ONil(U_18508)
    | ~ class_Orderings_Olinorder(U_18508) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

fof(f_4482_1,plain,
    ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_zip_Osimps_I1_J]) ).

fof(f_4482_2,plain,
    ! [U_18511,U_18510,U_18509] : hAPP(hAPP(c_List_Ozip(U_18509,U_18510),U_18511),c_List_Olist_ONil(U_18510)) = c_List_Olist_ONil(tc_prod(U_18509,U_18510)),
    inference(variable_rename,[status(thm)],[f_4482_1]) ).

fof(f_4482_3,plain,
    ! [U_18509,U_18510,U_18511] : hAPP(hAPP(c_List_Ozip(U_18509,U_18510),U_18511),c_List_Olist_ONil(U_18510)) = c_List_Olist_ONil(tc_prod(U_18509,U_18510)),
    inference(definitional_conversion,[status(esa)],[f_4482_2]) ).

cnf(f_4482_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18509,U_18510),U_18511),c_List_Olist_ONil(U_18510)) = c_List_Olist_ONil(tc_prod(U_18509,U_18510)),
    inference(clausify,[status(thm)],[f_4482_3]) ).

fof(f_4483_1,plain,
    ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_zip__Nil]) ).

fof(f_4483_2,plain,
    ! [U_18514,U_18513,U_18512] : hAPP(hAPP(c_List_Ozip(U_18512,U_18513),c_List_Olist_ONil(U_18512)),U_18514) = c_List_Olist_ONil(tc_prod(U_18512,U_18513)),
    inference(variable_rename,[status(thm)],[f_4483_1]) ).

fof(f_4483_3,plain,
    ! [U_18512,U_18513,U_18514] : hAPP(hAPP(c_List_Ozip(U_18512,U_18513),c_List_Olist_ONil(U_18512)),U_18514) = c_List_Olist_ONil(tc_prod(U_18512,U_18513)),
    inference(definitional_conversion,[status(esa)],[f_4483_2]) ).

cnf(f_4483_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18512,U_18513),c_List_Olist_ONil(U_18512)),U_18514) = c_List_Olist_ONil(tc_prod(U_18512,U_18513)),
    inference(clausify,[status(thm)],[f_4483_3]) ).

fof(f_4484_1,plain,
    ! [V_i,V_j] :
      ( c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_upto__empty]) ).

fof(f_4484_2,plain,
    ! [U_18516,U_18515] :
      ( c_List_Oupto(U_18516,U_18515) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18515),U_18516)) ),
    inference(variable_rename,[status(thm)],[f_4484_1]) ).

fof(f_4484_3,plain,
    ! [U_18515,U_18516] :
      ( c_List_Oupto(U_18516,U_18515) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18515),U_18516)) ),
    inference(definitional_conversion,[status(esa)],[f_4484_2]) ).

cnf(f_4484_4,plain,
    ( c_List_Oupto(U_18516,U_18515) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18515),U_18516)) ),
    inference(clausify,[status(thm)],[f_4484_3]) ).

fof(f_4485_1,plain,
    ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(f_4485_2,plain,
    ! [U_18520,U_18519,U_18518,U_18517] : c_List_Ofoldr(U_18517,U_18518,U_18519,c_List_Olist_ONil(U_18517),U_18520) = U_18520,
    inference(variable_rename,[status(thm)],[f_4485_1]) ).

fof(f_4485_3,plain,
    ! [U_18518,U_18517,U_18519,U_18520] : c_List_Ofoldr(U_18517,U_18518,U_18519,c_List_Olist_ONil(U_18517),U_18520) = U_18520,
    inference(definitional_conversion,[status(esa)],[f_4485_2]) ).

cnf(f_4485_4,plain,
    c_List_Ofoldr(U_18517,U_18518,U_18519,c_List_Olist_ONil(U_18517),U_18520) = U_18520,
    inference(clausify,[status(thm)],[f_4485_3]) ).

fof(f_4486_1,plain,
    ! [V_k,T_a,T_b] : hAPP(c_Map_Omap__of(T_b,T_a,c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_map__of__Cons__code_I1_J]) ).

fof(f_4486_2,plain,
    ! [U_18523,U_18522,U_18521] : hAPP(c_Map_Omap__of(U_18521,U_18522,c_List_Olist_ONil(tc_prod(U_18521,U_18522))),U_18523) = c_Option_Ooption_ONone(U_18522),
    inference(variable_rename,[status(thm)],[f_4486_1]) ).

fof(f_4486_3,plain,
    ! [U_18521,U_18522,U_18523] : hAPP(c_Map_Omap__of(U_18521,U_18522,c_List_Olist_ONil(tc_prod(U_18521,U_18522))),U_18523) = c_Option_Ooption_ONone(U_18522),
    inference(definitional_conversion,[status(esa)],[f_4486_2]) ).

cnf(f_4486_4,plain,
    hAPP(c_Map_Omap__of(U_18521,U_18522,c_List_Olist_ONil(tc_prod(U_18521,U_18522))),U_18523) = c_Option_Ooption_ONone(U_18522),
    inference(clausify,[status(thm)],[f_4486_3]) ).

fof(f_4487_1,plain,
    ! [V_x_1,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b,c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b),
    inference(fof_nnf,[status(thm)],[fact_map__of_Osimps_I1_J]) ).

fof(f_4487_2,plain,
    ! [U_18526,U_18525,U_18524] : hAPP(c_Map_Omap__of(U_18524,U_18525,c_List_Olist_ONil(tc_prod(U_18524,U_18525))),U_18526) = c_Option_Ooption_ONone(U_18525),
    inference(variable_rename,[status(thm)],[f_4487_1]) ).

fof(f_4487_3,plain,
    ! [U_18524,U_18525,U_18526] : hAPP(c_Map_Omap__of(U_18524,U_18525,c_List_Olist_ONil(tc_prod(U_18524,U_18525))),U_18526) = c_Option_Ooption_ONone(U_18525),
    inference(definitional_conversion,[status(esa)],[f_4487_2]) ).

cnf(f_4487_4,plain,
    hAPP(c_Map_Omap__of(U_18524,U_18525,c_List_Olist_ONil(tc_prod(U_18524,U_18525))),U_18526) = c_Option_Ooption_ONone(U_18525),
    inference(clausify,[status(thm)],[f_4487_3]) ).

fof(f_4488_1,plain,
    ! [V_x_2,V_k_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__nonempty]) ).

fof(f_4488_2,plain,
    ! [U_18530,U_18529,U_18528,U_18527] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_18527,U_18528),U_18529),U_18530) = c_List_Olist_ONil(U_18527)
        | U_18528 != c_List_Olist_ONil(U_18527) )
      & ( U_18528 = c_List_Olist_ONil(U_18527)
        | hAPP(hAPP(c_List_Olist__update(U_18527,U_18528),U_18529),U_18530) != c_List_Olist_ONil(U_18527) ) ),
    inference(variable_rename,[status(thm)],[f_4488_1]) ).

fof(f_4488_3,plain,
    ( ! [U_18538,U_18536,U_18534,U_18532] :
        ( hAPP(hAPP(c_List_Olist__update(U_18532,U_18534),U_18536),U_18538) = c_List_Olist_ONil(U_18532)
        | U_18534 != c_List_Olist_ONil(U_18532) )
    & ! [U_18537,U_18535,U_18533,U_18531] :
        ( U_18533 = c_List_Olist_ONil(U_18531)
        | hAPP(hAPP(c_List_Olist__update(U_18531,U_18533),U_18535),U_18537) != c_List_Olist_ONil(U_18531) ) ),
    inference(miniscope,[status(thm)],[f_4488_2]) ).

fof(f_4488_4,plain,
    ( ! [U_18532,U_18538,U_18534,U_18536] :
        ( hAPP(hAPP(c_List_Olist__update(U_18532,U_18534),U_18536),U_18538) = c_List_Olist_ONil(U_18532)
        | U_18534 != c_List_Olist_ONil(U_18532) )
    & ! [U_18537,U_18533,U_18531,U_18535] :
        ( U_18533 = c_List_Olist_ONil(U_18531)
        | hAPP(hAPP(c_List_Olist__update(U_18531,U_18533),U_18535),U_18537) != c_List_Olist_ONil(U_18531) ) ),
    inference(definitional_conversion,[status(esa)],[f_4488_3]) ).

cnf(f_4488_5,plain,
    ( U_18533 = c_List_Olist_ONil(U_18531)
    | hAPP(hAPP(c_List_Olist__update(U_18531,U_18533),U_18535),U_18537) != c_List_Olist_ONil(U_18531) ),
    inference(clausify,[status(thm)],[f_4488_4]) ).

cnf(f_4488_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18532,U_18534),U_18536),U_18538) = c_List_Olist_ONil(U_18532)
    | U_18534 != c_List_Olist_ONil(U_18532) ),
    inference(clausify,[status(thm)],[f_4488_4]) ).

fof(f_4489_1,plain,
    ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_list__update_Osimps_I1_J]) ).

fof(f_4489_2,plain,
    ! [U_18541,U_18540,U_18539] : hAPP(hAPP(c_List_Olist__update(U_18539,c_List_Olist_ONil(U_18539)),U_18540),U_18541) = c_List_Olist_ONil(U_18539),
    inference(variable_rename,[status(thm)],[f_4489_1]) ).

fof(f_4489_3,plain,
    ! [U_18539,U_18540,U_18541] : hAPP(hAPP(c_List_Olist__update(U_18539,c_List_Olist_ONil(U_18539)),U_18540),U_18541) = c_List_Olist_ONil(U_18539),
    inference(definitional_conversion,[status(esa)],[f_4489_2]) ).

cnf(f_4489_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18539,c_List_Olist_ONil(U_18539)),U_18540),U_18541) = c_List_Olist_ONil(U_18539),
    inference(clausify,[status(thm)],[f_4489_3]) ).

fof(f_4490_1,plain,
    ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_list__update__code_I1_J]) ).

fof(f_4490_2,plain,
    ! [U_18544,U_18543,U_18542] : hAPP(hAPP(c_List_Olist__update(U_18542,c_List_Olist_ONil(U_18542)),U_18543),U_18544) = c_List_Olist_ONil(U_18542),
    inference(variable_rename,[status(thm)],[f_4490_1]) ).

fof(f_4490_3,plain,
    ! [U_18542,U_18543,U_18544] : hAPP(hAPP(c_List_Olist__update(U_18542,c_List_Olist_ONil(U_18542)),U_18543),U_18544) = c_List_Olist_ONil(U_18542),
    inference(definitional_conversion,[status(esa)],[f_4490_2]) ).

cnf(f_4490_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18542,c_List_Olist_ONil(U_18542)),U_18543),U_18544) = c_List_Olist_ONil(U_18542),
    inference(clausify,[status(thm)],[f_4490_3]) ).

fof(f_4491_1,plain,
    ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y),
    inference(fof_nnf,[status(thm)],[fact_list__update__overwrite]) ).

fof(f_4491_2,plain,
    ! [U_18549,U_18548,U_18547,U_18546,U_18545] : hAPP(hAPP(c_List_Olist__update(U_18545,hAPP(hAPP(c_List_Olist__update(U_18545,U_18546),U_18547),U_18548)),U_18547),U_18549) = hAPP(hAPP(c_List_Olist__update(U_18545,U_18546),U_18547),U_18549),
    inference(variable_rename,[status(thm)],[f_4491_1]) ).

fof(f_4491_3,plain,
    ! [U_18545,U_18546,U_18547,U_18548,U_18549] : hAPP(hAPP(c_List_Olist__update(U_18545,hAPP(hAPP(c_List_Olist__update(U_18545,U_18546),U_18547),U_18548)),U_18547),U_18549) = hAPP(hAPP(c_List_Olist__update(U_18545,U_18546),U_18547),U_18549),
    inference(definitional_conversion,[status(esa)],[f_4491_2]) ).

cnf(f_4491_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18545,hAPP(hAPP(c_List_Olist__update(U_18545,U_18546),U_18547),U_18548)),U_18547),U_18549) = hAPP(hAPP(c_List_Olist__update(U_18545,U_18546),U_18547),U_18549),
    inference(clausify,[status(thm)],[f_4491_3]) ).

fof(f_4492_1,plain,
    ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x)
      | V_i = V_i_H ),
    inference(fof_nnf,[status(thm)],[fact_list__update__swap]) ).

fof(f_4492_2,plain,
    ! [U_18555,U_18554,U_18553,U_18552,U_18551,U_18550] :
      ( hAPP(hAPP(c_List_Olist__update(U_18552,hAPP(hAPP(c_List_Olist__update(U_18552,U_18553),U_18550),U_18554)),U_18551),U_18555) = hAPP(hAPP(c_List_Olist__update(U_18552,hAPP(hAPP(c_List_Olist__update(U_18552,U_18553),U_18551),U_18555)),U_18550),U_18554)
      | U_18550 = U_18551 ),
    inference(variable_rename,[status(thm)],[f_4492_1]) ).

fof(f_4492_3,plain,
    ! [U_18550,U_18551,U_18552,U_18553,U_18554,U_18555] :
      ( hAPP(hAPP(c_List_Olist__update(U_18552,hAPP(hAPP(c_List_Olist__update(U_18552,U_18553),U_18550),U_18554)),U_18551),U_18555) = hAPP(hAPP(c_List_Olist__update(U_18552,hAPP(hAPP(c_List_Olist__update(U_18552,U_18553),U_18551),U_18555)),U_18550),U_18554)
      | U_18550 = U_18551 ),
    inference(definitional_conversion,[status(esa)],[f_4492_2]) ).

cnf(f_4492_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18552,hAPP(hAPP(c_List_Olist__update(U_18552,U_18553),U_18550),U_18554)),U_18551),U_18555) = hAPP(hAPP(c_List_Olist__update(U_18552,hAPP(hAPP(c_List_Olist__update(U_18552,U_18553),U_18551),U_18555)),U_18550),U_18554)
    | U_18550 = U_18551 ),
    inference(clausify,[status(thm)],[f_4492_3]) ).

fof(f_4493_1,plain,
    ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I1_J]) ).

fof(f_4493_2,plain,
    ! [U_18557,U_18556] : c_List_Oremove1(U_18556,U_18557,c_List_Olist_ONil(U_18556)) = c_List_Olist_ONil(U_18556),
    inference(variable_rename,[status(thm)],[f_4493_1]) ).

fof(f_4493_3,plain,
    ! [U_18557,U_18556] : c_List_Oremove1(U_18556,U_18557,c_List_Olist_ONil(U_18556)) = c_List_Olist_ONil(U_18556),
    inference(definitional_conversion,[status(esa)],[f_4493_2]) ).

cnf(f_4493_4,plain,
    c_List_Oremove1(U_18556,U_18557,c_List_Olist_ONil(U_18556)) = c_List_Olist_ONil(U_18556),
    inference(clausify,[status(thm)],[f_4493_3]) ).

fof(f_4494_1,plain,
    ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
    inference(fof_nnf,[status(thm)],[fact_distinct_Osimps_I1_J]) ).

fof(f_4494_2,plain,
    ! [U_18558] : hBOOL(hAPP(c_List_Odistinct(U_18558),c_List_Olist_ONil(U_18558))),
    inference(variable_rename,[status(thm)],[f_4494_1]) ).

fof(f_4494_3,plain,
    ! [U_18558] : hBOOL(hAPP(c_List_Odistinct(U_18558),c_List_Olist_ONil(U_18558))),
    inference(definitional_conversion,[status(esa)],[f_4494_2]) ).

cnf(f_4494_4,plain,
    hBOOL(hAPP(c_List_Odistinct(U_18558),c_List_Olist_ONil(U_18558))),
    inference(clausify,[status(thm)],[f_4494_3]) ).

fof(f_4495_1,plain,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__not__Nil]) ).

fof(f_4495_2,plain,
    ! [U_18563,U_18562,U_18561,U_18560,U_18559] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18560,U_18559,U_18561),U_18562),U_18563) != c_List_Olist_ONil(U_18560)
      | ~ class_Orderings_Olinorder(U_18559) ),
    inference(variable_rename,[status(thm)],[f_4495_1]) ).

fof(f_4495_3,plain,
    ! [U_18559,U_18560,U_18561,U_18562,U_18563] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18560,U_18559,U_18561),U_18562),U_18563) != c_List_Olist_ONil(U_18560)
      | ~ class_Orderings_Olinorder(U_18559) ),
    inference(definitional_conversion,[status(esa)],[f_4495_2]) ).

cnf(f_4495_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18560,U_18559,U_18561),U_18562),U_18563) != c_List_Olist_ONil(U_18560)
    | ~ class_Orderings_Olinorder(U_18559) ),
    inference(clausify,[status(thm)],[f_4495_3]) ).

fof(f_4496_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_listrelp_ONil]) ).

fof(f_4496_2,plain,
    ! [U_18565,U_18564] : c_List_Olistrelp(U_18564,U_18565,c_List_Olist_ONil(U_18564),c_List_Olist_ONil(U_18564)),
    inference(variable_rename,[status(thm)],[f_4496_1]) ).

fof(f_4496_3,plain,
    ! [U_18565,U_18564] : c_List_Olistrelp(U_18564,U_18565,c_List_Olist_ONil(U_18564),c_List_Olist_ONil(U_18564)),
    inference(definitional_conversion,[status(esa)],[f_4496_2]) ).

cnf(f_4496_4,plain,
    c_List_Olistrelp(U_18564,U_18565,c_List_Olist_ONil(U_18564),c_List_Olist_ONil(U_18564)),
    inference(clausify,[status(thm)],[f_4496_3]) ).

fof(f_4497_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(f_4497_2,plain,
    ! [U_18567,U_18566] : c_List_Olistrelp(U_18566,U_18567,c_List_Olist_ONil(U_18566),c_List_Olist_ONil(U_18566)),
    inference(variable_rename,[status(thm)],[f_4497_1]) ).

fof(f_4497_3,plain,
    ! [U_18566,U_18567] : c_List_Olistrelp(U_18566,U_18567,c_List_Olist_ONil(U_18566),c_List_Olist_ONil(U_18566)),
    inference(definitional_conversion,[status(esa)],[f_4497_2]) ).

cnf(f_4497_4,plain,
    c_List_Olistrelp(U_18566,U_18567,c_List_Olist_ONil(U_18566),c_List_Olist_ONil(U_18566)),
    inference(clausify,[status(thm)],[f_4497_3]) ).

fof(f_4498_1,plain,
    ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(f_4498_2,plain,
    ! [U_18568] : hAPP(c_List_Oset(U_18568),c_List_Olist_ONil(U_18568)) = c_Orderings_Obot__class_Obot(tc_fun(U_18568,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4498_1]) ).

fof(f_4498_3,plain,
    ! [U_18568] : hAPP(c_List_Oset(U_18568),c_List_Olist_ONil(U_18568)) = c_Orderings_Obot__class_Obot(tc_fun(U_18568,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4498_2]) ).

cnf(f_4498_4,plain,
    hAPP(c_List_Oset(U_18568),c_List_Olist_ONil(U_18568)) = c_Orderings_Obot__class_Obot(tc_fun(U_18568,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4498_3]) ).

fof(f_4499_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_List_Oset(T_b),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty2]) ).

fof(f_4499_2,plain,
    ! [U_18570,U_18569] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_18569,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18569),U_18570)
        | U_18570 != c_List_Olist_ONil(U_18569) )
      & ( U_18570 = c_List_Olist_ONil(U_18569)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18569,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18569),U_18570) ) ),
    inference(variable_rename,[status(thm)],[f_4499_1]) ).

fof(f_4499_3,plain,
    ( ! [U_18574,U_18572] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_18572,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18572),U_18574)
        | U_18574 != c_List_Olist_ONil(U_18572) )
    & ! [U_18573,U_18571] :
        ( U_18573 = c_List_Olist_ONil(U_18571)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18571,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18571),U_18573) ) ),
    inference(miniscope,[status(thm)],[f_4499_2]) ).

fof(f_4499_4,plain,
    ( ! [U_18572,U_18574] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_18572,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18572),U_18574)
        | U_18574 != c_List_Olist_ONil(U_18572) )
    & ! [U_18573,U_18571] :
        ( U_18573 = c_List_Olist_ONil(U_18571)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18571,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18571),U_18573) ) ),
    inference(definitional_conversion,[status(esa)],[f_4499_3]) ).

cnf(f_4499_5,plain,
    ( U_18573 = c_List_Olist_ONil(U_18571)
    | c_Orderings_Obot__class_Obot(tc_fun(U_18571,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18571),U_18573) ),
    inference(clausify,[status(thm)],[f_4499_4]) ).

cnf(f_4499_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_18572,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18572),U_18574)
    | U_18574 != c_List_Olist_ONil(U_18572) ),
    inference(clausify,[status(thm)],[f_4499_4]) ).

fof(f_4500_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Oset(T_b),V_xs_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty]) ).

fof(f_4500_2,plain,
    ! [U_18576,U_18575] :
      ( ( hAPP(c_List_Oset(U_18575),U_18576) = c_Orderings_Obot__class_Obot(tc_fun(U_18575,tc_HOL_Obool))
        | U_18576 != c_List_Olist_ONil(U_18575) )
      & ( U_18576 = c_List_Olist_ONil(U_18575)
        | hAPP(c_List_Oset(U_18575),U_18576) != c_Orderings_Obot__class_Obot(tc_fun(U_18575,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4500_1]) ).

fof(f_4500_3,plain,
    ( ! [U_18580,U_18578] :
        ( hAPP(c_List_Oset(U_18578),U_18580) = c_Orderings_Obot__class_Obot(tc_fun(U_18578,tc_HOL_Obool))
        | U_18580 != c_List_Olist_ONil(U_18578) )
    & ! [U_18579,U_18577] :
        ( U_18579 = c_List_Olist_ONil(U_18577)
        | hAPP(c_List_Oset(U_18577),U_18579) != c_Orderings_Obot__class_Obot(tc_fun(U_18577,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4500_2]) ).

fof(f_4500_4,plain,
    ( ! [U_18578,U_18580] :
        ( hAPP(c_List_Oset(U_18578),U_18580) = c_Orderings_Obot__class_Obot(tc_fun(U_18578,tc_HOL_Obool))
        | U_18580 != c_List_Olist_ONil(U_18578) )
    & ! [U_18579,U_18577] :
        ( U_18579 = c_List_Olist_ONil(U_18577)
        | hAPP(c_List_Oset(U_18577),U_18579) != c_Orderings_Obot__class_Obot(tc_fun(U_18577,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4500_3]) ).

cnf(f_4500_5,plain,
    ( U_18579 = c_List_Olist_ONil(U_18577)
    | hAPP(c_List_Oset(U_18577),U_18579) != c_Orderings_Obot__class_Obot(tc_fun(U_18577,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4500_4]) ).

cnf(f_4500_6,plain,
    ( hAPP(c_List_Oset(U_18578),U_18580) = c_Orderings_Obot__class_Obot(tc_fun(U_18578,tc_HOL_Obool))
    | U_18580 != c_List_Olist_ONil(U_18578) ),
    inference(clausify,[status(thm)],[f_4500_4]) ).

fof(f_4501_1,plain,
    ! [T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J]) ).

fof(f_4501_2,plain,
    ! [U_18581] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18581),c_List_Olist_ONil(U_18581)) = c_Groups_Ozero__class_Ozero(U_18581)
      | ~ class_Groups_Omonoid__add(U_18581) ),
    inference(variable_rename,[status(thm)],[f_4501_1]) ).

fof(f_4501_3,plain,
    ! [U_18581] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18581),c_List_Olist_ONil(U_18581)) = c_Groups_Ozero__class_Ozero(U_18581)
      | ~ class_Groups_Omonoid__add(U_18581) ),
    inference(definitional_conversion,[status(esa)],[f_4501_2]) ).

cnf(f_4501_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18581),c_List_Olist_ONil(U_18581)) = c_Groups_Ozero__class_Ozero(U_18581)
    | ~ class_Groups_Omonoid__add(U_18581) ),
    inference(clausify,[status(thm)],[f_4501_3]) ).

fof(f_4502_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
        | V_xs_2 = c_List_Olist_ONil(T_b) )
      & ( V_xs_2 != c_List_Olist_ONil(T_b)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv]) ).

fof(f_4502_2,plain,
    ! [U_18583,U_18582] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18582)),U_18583)))
        | U_18583 = c_List_Olist_ONil(U_18582) )
      & ( U_18583 != c_List_Olist_ONil(U_18582)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18582)),U_18583))) ) ),
    inference(variable_rename,[status(thm)],[f_4502_1]) ).

fof(f_4502_3,plain,
    ( ! [U_18587,U_18585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18585)),U_18587)))
        | U_18587 = c_List_Olist_ONil(U_18585) )
    & ! [U_18586,U_18584] :
        ( U_18586 != c_List_Olist_ONil(U_18584)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18584)),U_18586))) ) ),
    inference(miniscope,[status(thm)],[f_4502_2]) ).

fof(f_4502_4,plain,
    ( ! [U_18585,U_18587] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18585)),U_18587)))
        | U_18587 = c_List_Olist_ONil(U_18585) )
    & ! [U_18586,U_18584] :
        ( U_18586 != c_List_Olist_ONil(U_18584)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18584)),U_18586))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4502_3]) ).

cnf(f_4502_5,plain,
    ( U_18586 != c_List_Olist_ONil(U_18584)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18584)),U_18586))) ),
    inference(clausify,[status(thm)],[f_4502_4]) ).

cnf(f_4502_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18585)),U_18587)))
    | U_18587 = c_List_Olist_ONil(U_18585) ),
    inference(clausify,[status(thm)],[f_4502_4]) ).

fof(f_4503_1,plain,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__update__subsetI]) ).

fof(f_4503_2,plain,
    ! [U_18592,U_18591,U_18590,U_18589,U_18588] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18588,tc_HOL_Obool)),hAPP(c_List_Oset(U_18588),hAPP(hAPP(c_List_Olist__update(U_18588,U_18589),U_18592),U_18591))),U_18590))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18591),U_18590))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18588,tc_HOL_Obool)),hAPP(c_List_Oset(U_18588),U_18589)),U_18590)) ),
    inference(variable_rename,[status(thm)],[f_4503_1]) ).

fof(f_4503_3,plain,
    ! [U_18588,U_18589,U_18590,U_18591,U_18592] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18588,tc_HOL_Obool)),hAPP(c_List_Oset(U_18588),hAPP(hAPP(c_List_Olist__update(U_18588,U_18589),U_18592),U_18591))),U_18590))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18591),U_18590))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18588,tc_HOL_Obool)),hAPP(c_List_Oset(U_18588),U_18589)),U_18590)) ),
    inference(definitional_conversion,[status(esa)],[f_4503_2]) ).

cnf(f_4503_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18588,tc_HOL_Obool)),hAPP(c_List_Oset(U_18588),hAPP(hAPP(c_List_Olist__update(U_18588,U_18589),U_18592),U_18591))),U_18590))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18591),U_18590))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18588,tc_HOL_Obool)),hAPP(c_List_Oset(U_18588),U_18589)),U_18590)) ),
    inference(clausify,[status(thm)],[f_4503_3]) ).

fof(f_4504_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_take__1__Cons]) ).

fof(f_4504_2,plain,
    ! [U_18595,U_18594,U_18593] : hAPP(hAPP(c_List_Otake(U_18593),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18594),U_18595)) = hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18594),c_List_Olist_ONil(U_18593)),
    inference(variable_rename,[status(thm)],[f_4504_1]) ).

fof(f_4504_3,plain,
    ! [U_18593,U_18594,U_18595] : hAPP(hAPP(c_List_Otake(U_18593),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18594),U_18595)) = hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18594),c_List_Olist_ONil(U_18593)),
    inference(definitional_conversion,[status(esa)],[f_4504_2]) ).

cnf(f_4504_4,plain,
    hAPP(hAPP(c_List_Otake(U_18593),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18594),U_18595)) = hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18594),c_List_Olist_ONil(U_18593)),
    inference(clausify,[status(thm)],[f_4504_3]) ).

fof(f_4505_1,plain,
    ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__update__subset__insert]) ).

fof(f_4505_2,plain,
    ! [U_18599,U_18598,U_18597,U_18596] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18596,tc_HOL_Obool)),hAPP(c_List_Oset(U_18596),hAPP(hAPP(c_List_Olist__update(U_18596,U_18597),U_18598),U_18599))),hAPP(hAPP(c_Set_Oinsert(U_18596),U_18599),hAPP(c_List_Oset(U_18596),U_18597)))),
    inference(variable_rename,[status(thm)],[f_4505_1]) ).

fof(f_4505_3,plain,
    ! [U_18596,U_18597,U_18598,U_18599] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18596,tc_HOL_Obool)),hAPP(c_List_Oset(U_18596),hAPP(hAPP(c_List_Olist__update(U_18596,U_18597),U_18598),U_18599))),hAPP(hAPP(c_Set_Oinsert(U_18596),U_18599),hAPP(c_List_Oset(U_18596),U_18597)))),
    inference(definitional_conversion,[status(esa)],[f_4505_2]) ).

cnf(f_4505_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18596,tc_HOL_Obool)),hAPP(c_List_Oset(U_18596),hAPP(hAPP(c_List_Olist__update(U_18596,U_18597),U_18598),U_18599))),hAPP(hAPP(c_Set_Oinsert(U_18596),U_18599),hAPP(c_List_Oset(U_18596),U_18597)))),
    inference(clausify,[status(thm)],[f_4505_3]) ).

fof(f_4506_1,plain,
    ! [V_x,V_j,V_xs,T_a,V_i] :
      ( ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)
          | V_i = V_j )
        & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x
          | V_i != V_j ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__list__update]) ).

fof(f_4506_2,plain,
    ! [U_18604,U_18603,U_18602,U_18601,U_18600] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_18601),hAPP(hAPP(c_List_Olist__update(U_18601,U_18602),U_18600),U_18604)),U_18603) = hAPP(hAPP(c_List_Onth(U_18601),U_18602),U_18603)
          | U_18600 = U_18603 )
        & ( hAPP(hAPP(c_List_Onth(U_18601),hAPP(hAPP(c_List_Olist__update(U_18601,U_18602),U_18600),U_18604)),U_18603) = U_18604
          | U_18600 != U_18603 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18601)),U_18602))) ),
    inference(variable_rename,[status(thm)],[f_4506_1]) ).

fof(f_4506_3,plain,
    ( ! [U_18600,U_18601,U_18602,U_18603,U_18604] :
        ( hAPP(hAPP(c_List_Onth(U_18601),hAPP(hAPP(c_List_Olist__update(U_18601,U_18602),U_18600),U_18604)),U_18603) = hAPP(hAPP(c_List_Onth(U_18601),U_18602),U_18603)
        | U_18600 = U_18603
        | ~ sP1164(U_18600,U_18601,U_18602,U_18603,U_18604) )
    & ! [U_18600,U_18601,U_18602,U_18603,U_18604] :
        ( hAPP(hAPP(c_List_Onth(U_18601),hAPP(hAPP(c_List_Olist__update(U_18601,U_18602),U_18600),U_18604)),U_18603) = U_18604
        | U_18600 != U_18603
        | ~ sP1164(U_18600,U_18601,U_18602,U_18603,U_18604) )
    & ! [U_18600,U_18601,U_18602,U_18603,U_18604] :
        ( sP1164(U_18600,U_18601,U_18602,U_18603,U_18604)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18601)),U_18602))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1164])],[f_4506_2]) ).

cnf(f_4506_4,plain,
    ( sP1164(U_18600,U_18601,U_18602,U_18603,U_18604)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18601)),U_18602))) ),
    inference(clausify,[status(thm)],[f_4506_3]) ).

cnf(f_4506_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18601),hAPP(hAPP(c_List_Olist__update(U_18601,U_18602),U_18600),U_18604)),U_18603) = U_18604
    | U_18600 != U_18603
    | ~ sP1164(U_18600,U_18601,U_18602,U_18603,U_18604) ),
    inference(clausify,[status(thm)],[f_4506_3]) ).

cnf(f_4506_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18601),hAPP(hAPP(c_List_Olist__update(U_18601,U_18602),U_18600),U_18604)),U_18603) = hAPP(hAPP(c_List_Onth(U_18601),U_18602),U_18603)
    | U_18600 = U_18603
    | ~ sP1164(U_18600,U_18601,U_18602,U_18603,U_18604) ),
    inference(clausify,[status(thm)],[f_4506_3]) ).

fof(f_4507_1,plain,
    ! [V_x_2,V_xs_2,T_b,V_i_2] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
          | hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) != V_x_2 )
        & ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2
          | hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) != V_xs_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__same__conv]) ).

fof(f_4507_2,plain,
    ! [U_18608,U_18607,U_18606,U_18605] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(U_18606,U_18607),U_18605),U_18608) = U_18607
          | hAPP(hAPP(c_List_Onth(U_18606),U_18607),U_18605) != U_18608 )
        & ( hAPP(hAPP(c_List_Onth(U_18606),U_18607),U_18605) = U_18608
          | hAPP(hAPP(c_List_Olist__update(U_18606,U_18607),U_18605),U_18608) != U_18607 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18606)),U_18607))) ),
    inference(variable_rename,[status(thm)],[f_4507_1]) ).

fof(f_4507_3,plain,
    ( ! [U_18607,U_18606,U_18605,U_18608] :
        ( hAPP(hAPP(c_List_Olist__update(U_18606,U_18607),U_18605),U_18608) = U_18607
        | hAPP(hAPP(c_List_Onth(U_18606),U_18607),U_18605) != U_18608
        | ~ sP1165(U_18607,U_18606,U_18605,U_18608) )
    & ! [U_18607,U_18606,U_18605,U_18608] :
        ( hAPP(hAPP(c_List_Onth(U_18606),U_18607),U_18605) = U_18608
        | hAPP(hAPP(c_List_Olist__update(U_18606,U_18607),U_18605),U_18608) != U_18607
        | ~ sP1165(U_18607,U_18606,U_18605,U_18608) )
    & ! [U_18607,U_18606,U_18605,U_18608] :
        ( sP1165(U_18607,U_18606,U_18605,U_18608)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18606)),U_18607))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1165])],[f_4507_2]) ).

cnf(f_4507_4,plain,
    ( sP1165(U_18607,U_18606,U_18605,U_18608)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18606)),U_18607))) ),
    inference(clausify,[status(thm)],[f_4507_3]) ).

cnf(f_4507_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18606),U_18607),U_18605) = U_18608
    | hAPP(hAPP(c_List_Olist__update(U_18606,U_18607),U_18605),U_18608) != U_18607
    | ~ sP1165(U_18607,U_18606,U_18605,U_18608) ),
    inference(clausify,[status(thm)],[f_4507_3]) ).

cnf(f_4507_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18606,U_18607),U_18605),U_18608) = U_18607
    | hAPP(hAPP(c_List_Onth(U_18606),U_18607),U_18605) != U_18608
    | ~ sP1165(U_18607,U_18606,U_18605,U_18608) ),
    inference(clausify,[status(thm)],[f_4507_3]) ).

fof(f_4508_1,plain,
    ! [V_x,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq]) ).

fof(f_4508_2,plain,
    ! [U_18612,U_18611,U_18610,U_18609] :
      ( hAPP(hAPP(c_List_Onth(U_18610),hAPP(hAPP(c_List_Olist__update(U_18610,U_18611),U_18609),U_18612)),U_18609) = U_18612
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18611))) ),
    inference(variable_rename,[status(thm)],[f_4508_1]) ).

fof(f_4508_3,plain,
    ! [U_18609,U_18610,U_18611,U_18612] :
      ( hAPP(hAPP(c_List_Onth(U_18610),hAPP(hAPP(c_List_Olist__update(U_18610,U_18611),U_18609),U_18612)),U_18609) = U_18612
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18611))) ),
    inference(definitional_conversion,[status(esa)],[f_4508_2]) ).

cnf(f_4508_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18610),hAPP(hAPP(c_List_Olist__update(U_18610,U_18611),U_18609),U_18612)),U_18609) = U_18612
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18611))) ),
    inference(clausify,[status(thm)],[f_4508_3]) ).

fof(f_4509_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_listrel_ONil]) ).

fof(f_4509_2,plain,
    ! [U_18614,U_18613] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18613),tc_List_Olist(U_18613))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18613),tc_List_Olist(U_18613)),c_List_Olist_ONil(U_18613)),c_List_Olist_ONil(U_18613))),c_List_Olistrel(U_18613,U_18614))),
    inference(variable_rename,[status(thm)],[f_4509_1]) ).

fof(f_4509_3,plain,
    ! [U_18613,U_18614] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18613),tc_List_Olist(U_18613))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18613),tc_List_Olist(U_18613)),c_List_Olist_ONil(U_18613)),c_List_Olist_ONil(U_18613))),c_List_Olistrel(U_18613,U_18614))),
    inference(definitional_conversion,[status(esa)],[f_4509_2]) ).

cnf(f_4509_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18613),tc_List_Olist(U_18613))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18613),tc_List_Olist(U_18613)),c_List_Olist_ONil(U_18613)),c_List_Olist_ONil(U_18613))),c_List_Olistrel(U_18613,U_18614))),
    inference(clausify,[status(thm)],[f_4509_3]) ).

fof(f_4510_1,plain,
    ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_lexord__Nil__right]) ).

fof(f_4510_2,plain,
    ! [U_18617,U_18616,U_18615] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18615),tc_List_Olist(U_18615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18615),tc_List_Olist(U_18615)),U_18616),c_List_Olist_ONil(U_18615))),c_List_Olexord(U_18615,U_18617))),
    inference(variable_rename,[status(thm)],[f_4510_1]) ).

fof(f_4510_3,plain,
    ! [U_18615,U_18616,U_18617] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18615),tc_List_Olist(U_18615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18615),tc_List_Olist(U_18615)),U_18616),c_List_Olist_ONil(U_18615))),c_List_Olexord(U_18615,U_18617))),
    inference(definitional_conversion,[status(esa)],[f_4510_2]) ).

cnf(f_4510_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18615),tc_List_Olist(U_18615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18615),tc_List_Olist(U_18615)),U_18616),c_List_Olist_ONil(U_18615))),c_List_Olexord(U_18615,U_18617))),
    inference(clausify,[status(thm)],[f_4510_3]) ).

fof(f_4511_1,plain,
    ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_Nil__notin__lex]) ).

fof(f_4511_2,plain,
    ! [U_18620,U_18619,U_18618] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18618),tc_List_Olist(U_18618))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18618),tc_List_Olist(U_18618)),c_List_Olist_ONil(U_18618)),U_18619)),c_List_Olex(U_18618,U_18620))),
    inference(variable_rename,[status(thm)],[f_4511_1]) ).

fof(f_4511_3,plain,
    ! [U_18618,U_18619,U_18620] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18618),tc_List_Olist(U_18618))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18618),tc_List_Olist(U_18618)),c_List_Olist_ONil(U_18618)),U_18619)),c_List_Olex(U_18618,U_18620))),
    inference(definitional_conversion,[status(esa)],[f_4511_2]) ).

cnf(f_4511_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18618),tc_List_Olist(U_18618))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18618),tc_List_Olist(U_18618)),c_List_Olist_ONil(U_18618)),U_18619)),c_List_Olex(U_18618,U_18620))),
    inference(clausify,[status(thm)],[f_4511_3]) ).

fof(f_4512_1,plain,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(f_4512_2,plain,
    ! [U_18623,U_18622,U_18621] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18621),tc_List_Olist(U_18621))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18621),tc_List_Olist(U_18621)),U_18622),c_List_Olist_ONil(U_18621))),c_List_Olex(U_18621,U_18623))),
    inference(variable_rename,[status(thm)],[f_4512_1]) ).

fof(f_4512_3,plain,
    ! [U_18621,U_18622,U_18623] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18621),tc_List_Olist(U_18621))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18621),tc_List_Olist(U_18621)),U_18622),c_List_Olist_ONil(U_18621))),c_List_Olex(U_18621,U_18623))),
    inference(definitional_conversion,[status(esa)],[f_4512_2]) ).

cnf(f_4512_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18621),tc_List_Olist(U_18621))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18621),tc_List_Olist(U_18621)),U_18622),c_List_Olist_ONil(U_18621))),c_List_Olex(U_18621,U_18623))),
    inference(clausify,[status(thm)],[f_4512_3]) ).

fof(f_4513_1,plain,
    ! [V_x_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_set__update__memI]) ).

fof(f_4513_2,plain,
    ! [U_18627,U_18626,U_18625,U_18624] :
      ( hBOOL(hAPP(hAPP(c_member(U_18625),U_18627),hAPP(c_List_Oset(U_18625),hAPP(hAPP(c_List_Olist__update(U_18625,U_18626),U_18624),U_18627))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18625)),U_18626))) ),
    inference(variable_rename,[status(thm)],[f_4513_1]) ).

fof(f_4513_3,plain,
    ! [U_18624,U_18625,U_18626,U_18627] :
      ( hBOOL(hAPP(hAPP(c_member(U_18625),U_18627),hAPP(c_List_Oset(U_18625),hAPP(hAPP(c_List_Olist__update(U_18625,U_18626),U_18624),U_18627))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18625)),U_18626))) ),
    inference(definitional_conversion,[status(esa)],[f_4513_2]) ).

cnf(f_4513_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18625),U_18627),hAPP(c_List_Oset(U_18625),hAPP(hAPP(c_List_Olist__update(U_18625,U_18626),U_18624),U_18627))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18625)),U_18626))) ),
    inference(clausify,[status(thm)],[f_4513_3]) ).

fof(f_4514_1,plain,
    ! [V_j,V_i] :
      ( ( c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) )
      & ( c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Osimps]) ).

fof(f_4514_2,plain,
    ! [U_18629,U_18628] :
      ( ( c_List_Oupto(U_18628,U_18629) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18628),U_18629)) )
      & ( c_List_Oupto(U_18628,U_18629) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18628),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18628),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18629))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18628),U_18629)) ) ),
    inference(variable_rename,[status(thm)],[f_4514_1]) ).

fof(f_4514_3,plain,
    ( ! [U_18633,U_18631] :
        ( c_List_Oupto(U_18631,U_18633) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18631),U_18633)) )
    & ! [U_18632,U_18630] :
        ( c_List_Oupto(U_18630,U_18632) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18630),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18630),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18632))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18630),U_18632)) ) ),
    inference(miniscope,[status(thm)],[f_4514_2]) ).

fof(f_4514_4,plain,
    ( ! [U_18631,U_18633] :
        ( c_List_Oupto(U_18631,U_18633) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18631),U_18633)) )
    & ! [U_18632,U_18630] :
        ( c_List_Oupto(U_18630,U_18632) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18630),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18630),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18632))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18630),U_18632)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4514_3]) ).

cnf(f_4514_5,plain,
    ( c_List_Oupto(U_18630,U_18632) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18630),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18630),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18632))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18630),U_18632)) ),
    inference(clausify,[status(thm)],[f_4514_4]) ).

cnf(f_4514_6,plain,
    ( c_List_Oupto(U_18631,U_18633) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18631),U_18633)) ),
    inference(clausify,[status(thm)],[f_4514_4]) ).

fof(f_4515_1,plain,
    ! [V_x_2,T_b,V_A_2] :
      ( ( c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) )
      & ( c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sublist__singleton]) ).

fof(f_4515_2,plain,
    ! [U_18636,U_18635,U_18634] :
      ( ( c_List_Osublist(U_18635,hAPP(hAPP(c_List_Olist_OCons(U_18635),U_18636),c_List_Olist_ONil(U_18635)),U_18634) = c_List_Olist_ONil(U_18635)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18634)) )
      & ( c_List_Osublist(U_18635,hAPP(hAPP(c_List_Olist_OCons(U_18635),U_18636),c_List_Olist_ONil(U_18635)),U_18634) = hAPP(hAPP(c_List_Olist_OCons(U_18635),U_18636),c_List_Olist_ONil(U_18635))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18634)) ) ),
    inference(variable_rename,[status(thm)],[f_4515_1]) ).

fof(f_4515_3,plain,
    ( ! [U_18642,U_18640,U_18638] :
        ( c_List_Osublist(U_18640,hAPP(hAPP(c_List_Olist_OCons(U_18640),U_18642),c_List_Olist_ONil(U_18640)),U_18638) = c_List_Olist_ONil(U_18640)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18638)) )
    & ! [U_18641,U_18639,U_18637] :
        ( c_List_Osublist(U_18639,hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),c_List_Olist_ONil(U_18639)),U_18637) = hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),c_List_Olist_ONil(U_18639))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18637)) ) ),
    inference(miniscope,[status(thm)],[f_4515_2]) ).

fof(f_4515_4,plain,
    ( ! [U_18638,U_18640,U_18642] :
        ( c_List_Osublist(U_18640,hAPP(hAPP(c_List_Olist_OCons(U_18640),U_18642),c_List_Olist_ONil(U_18640)),U_18638) = c_List_Olist_ONil(U_18640)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18638)) )
    & ! [U_18637,U_18639,U_18641] :
        ( c_List_Osublist(U_18639,hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),c_List_Olist_ONil(U_18639)),U_18637) = hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),c_List_Olist_ONil(U_18639))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18637)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4515_3]) ).

cnf(f_4515_5,plain,
    ( c_List_Osublist(U_18639,hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),c_List_Olist_ONil(U_18639)),U_18637) = hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),c_List_Olist_ONil(U_18639))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18637)) ),
    inference(clausify,[status(thm)],[f_4515_4]) ).

cnf(f_4515_6,plain,
    ( c_List_Osublist(U_18640,hAPP(hAPP(c_List_Olist_OCons(U_18640),U_18642),c_List_Olist_ONil(U_18640)),U_18638) = c_List_Olist_ONil(U_18640)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18638)) ),
    inference(clausify,[status(thm)],[f_4515_4]) ).

fof(f_4516_1,plain,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__Cons_H]) ).

fof(f_4516_2,plain,
    ! [U_18646,U_18645,U_18644,U_18643] :
      ( ( hAPP(hAPP(c_List_Otake(U_18644),U_18643),hAPP(hAPP(c_List_Olist_OCons(U_18644),U_18645),U_18646)) = hAPP(hAPP(c_List_Olist_OCons(U_18644),U_18645),hAPP(hAPP(c_List_Otake(U_18644),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18643),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18646))
        | U_18643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_18644),U_18643),hAPP(hAPP(c_List_Olist_OCons(U_18644),U_18645),U_18646)) = c_List_Olist_ONil(U_18644)
        | U_18643 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4516_1]) ).

fof(f_4516_3,plain,
    ( ! [U_18654,U_18652,U_18650,U_18648] :
        ( hAPP(hAPP(c_List_Otake(U_18650),U_18648),hAPP(hAPP(c_List_Olist_OCons(U_18650),U_18652),U_18654)) = hAPP(hAPP(c_List_Olist_OCons(U_18650),U_18652),hAPP(hAPP(c_List_Otake(U_18650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18648),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18654))
        | U_18648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18653,U_18651,U_18649,U_18647] :
        ( hAPP(hAPP(c_List_Otake(U_18649),U_18647),hAPP(hAPP(c_List_Olist_OCons(U_18649),U_18651),U_18653)) = c_List_Olist_ONil(U_18649)
        | U_18647 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4516_2]) ).

fof(f_4516_4,plain,
    ( ! [U_18648,U_18650,U_18652,U_18654] :
        ( hAPP(hAPP(c_List_Otake(U_18650),U_18648),hAPP(hAPP(c_List_Olist_OCons(U_18650),U_18652),U_18654)) = hAPP(hAPP(c_List_Olist_OCons(U_18650),U_18652),hAPP(hAPP(c_List_Otake(U_18650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18648),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18654))
        | U_18648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18651,U_18653,U_18649,U_18647] :
        ( hAPP(hAPP(c_List_Otake(U_18649),U_18647),hAPP(hAPP(c_List_Olist_OCons(U_18649),U_18651),U_18653)) = c_List_Olist_ONil(U_18649)
        | U_18647 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4516_3]) ).

cnf(f_4516_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_18649),U_18647),hAPP(hAPP(c_List_Olist_OCons(U_18649),U_18651),U_18653)) = c_List_Olist_ONil(U_18649)
    | U_18647 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

cnf(f_4516_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18650),U_18648),hAPP(hAPP(c_List_Olist_OCons(U_18650),U_18652),U_18654)) = hAPP(hAPP(c_List_Olist_OCons(U_18650),U_18652),hAPP(hAPP(c_List_Otake(U_18650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18648),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18654))
    | U_18648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

fof(f_4517_1,plain,
    ! [V_n,V_m] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) ),
    inference(fof_nnf,[status(thm)],[fact_upto__rec__number__of]) ).

fof(f_4517_2,plain,
    ! [U_18656,U_18655] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18655),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18656)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18655)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18656))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18655),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18656)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18655)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18655)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18656)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18655)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18656))) ) ),
    inference(variable_rename,[status(thm)],[f_4517_1]) ).

fof(f_4517_3,plain,
    ( ! [U_18660,U_18658] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18658),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18660)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18658)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18660))) )
    & ! [U_18659,U_18657] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659))) ) ),
    inference(miniscope,[status(thm)],[f_4517_2]) ).

fof(f_4517_4,plain,
    ( ! [U_18658,U_18660] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18658),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18660)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18658)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18660))) )
    & ! [U_18657,U_18659] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4517_3]) ).

cnf(f_4517_5,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18657)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18659))) ),
    inference(clausify,[status(thm)],[f_4517_4]) ).

cnf(f_4517_6,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18658),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18660)) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18658)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18660))) ),
    inference(clausify,[status(thm)],[f_4517_4]) ).

fof(f_4518_1,plain,
    ! [V_s_2,T_b,V_xs_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2)))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_select]) ).

fof(f_4518_2,plain,
    ! [U_18663,U_18662,U_18661] :
      ( hBOOL(hAPP(hAPP(c_member(U_18662),hAPP(c_Product__Type_Ofst(U_18662,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_18662,U_18661),U_18663))),hAPP(c_List_Oset(U_18662),U_18661)))
      | U_18661 = c_List_Olist_ONil(U_18662) ),
    inference(variable_rename,[status(thm)],[f_4518_1]) ).

fof(f_4518_3,plain,
    ! [U_18662,U_18661,U_18663] :
      ( hBOOL(hAPP(hAPP(c_member(U_18662),hAPP(c_Product__Type_Ofst(U_18662,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_18662,U_18661),U_18663))),hAPP(c_List_Oset(U_18662),U_18661)))
      | U_18661 = c_List_Olist_ONil(U_18662) ),
    inference(definitional_conversion,[status(esa)],[f_4518_2]) ).

cnf(f_4518_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18662),hAPP(c_Product__Type_Ofst(U_18662,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_18662,U_18661),U_18663))),hAPP(c_List_Oset(U_18662),U_18661)))
    | U_18661 = c_List_Olist_ONil(U_18662) ),
    inference(clausify,[status(thm)],[f_4518_3]) ).

fof(f_4519_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil]) ).

fof(f_4519_2,plain,
    ! [U_18665,U_18664] : hAPP(c_Relation_OImage(tc_List_Olist(U_18664),tc_List_Olist(U_18664),c_List_Olistrel(U_18664,U_18665)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18664)),c_List_Olist_ONil(U_18664)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18664),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18664)),c_List_Olist_ONil(U_18664)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18664),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4519_1]) ).

fof(f_4519_3,plain,
    ! [U_18664,U_18665] : hAPP(c_Relation_OImage(tc_List_Olist(U_18664),tc_List_Olist(U_18664),c_List_Olistrel(U_18664,U_18665)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18664)),c_List_Olist_ONil(U_18664)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18664),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18664)),c_List_Olist_ONil(U_18664)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18664),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4519_2]) ).

cnf(f_4519_4,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_18664),tc_List_Olist(U_18664),c_List_Olistrel(U_18664,U_18665)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18664)),c_List_Olist_ONil(U_18664)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18664),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18664)),c_List_Olist_ONil(U_18664)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18664),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4519_3]) ).

fof(f_4520_1,plain,
    ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(f_4520_2,plain,
    ! [U_18667,U_18666] : c_List_Oset__Cons(U_18666,U_18667,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18666)),c_List_Olist_ONil(U_18666)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18666),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_18666,tc_List_Olist(U_18666),hAPP(hAPP(c_COMBC(U_18666,tc_List_Olist(U_18666),tc_List_Olist(U_18666)),c_List_Olist_OCons(U_18666)),c_List_Olist_ONil(U_18666))),U_18667),
    inference(variable_rename,[status(thm)],[f_4520_1]) ).

fof(f_4520_3,plain,
    ! [U_18666,U_18667] : c_List_Oset__Cons(U_18666,U_18667,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18666)),c_List_Olist_ONil(U_18666)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18666),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_18666,tc_List_Olist(U_18666),hAPP(hAPP(c_COMBC(U_18666,tc_List_Olist(U_18666),tc_List_Olist(U_18666)),c_List_Olist_OCons(U_18666)),c_List_Olist_ONil(U_18666))),U_18667),
    inference(definitional_conversion,[status(esa)],[f_4520_2]) ).

cnf(f_4520_4,plain,
    c_List_Oset__Cons(U_18666,U_18667,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18666)),c_List_Olist_ONil(U_18666)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18666),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_18666,tc_List_Olist(U_18666),hAPP(hAPP(c_COMBC(U_18666,tc_List_Olist(U_18666),tc_List_Olist(U_18666)),c_List_Olist_OCons(U_18666)),c_List_Olist_ONil(U_18666))),U_18667),
    inference(clausify,[status(thm)],[f_4520_3]) ).

fof(f_4521_1,plain,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of]) ).

fof(f_4521_2,plain,
    ! [U_18671,U_18670,U_18669,U_18668] :
      ( ( hAPP(hAPP(c_List_Otake(U_18669),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18668)),hAPP(hAPP(c_List_Olist_OCons(U_18669),U_18670),U_18671)) = hAPP(hAPP(c_List_Olist_OCons(U_18669),U_18670),hAPP(hAPP(c_List_Otake(U_18669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18668)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18671))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18668) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_18669),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18668)),hAPP(hAPP(c_List_Olist_OCons(U_18669),U_18670),U_18671)) = c_List_Olist_ONil(U_18669)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18668) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4521_1]) ).

fof(f_4521_3,plain,
    ( ! [U_18679,U_18677,U_18675,U_18673] :
        ( hAPP(hAPP(c_List_Otake(U_18675),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673)),hAPP(hAPP(c_List_Olist_OCons(U_18675),U_18677),U_18679)) = hAPP(hAPP(c_List_Olist_OCons(U_18675),U_18677),hAPP(hAPP(c_List_Otake(U_18675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18679))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18678,U_18676,U_18674,U_18672] :
        ( hAPP(hAPP(c_List_Otake(U_18674),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18672)),hAPP(hAPP(c_List_Olist_OCons(U_18674),U_18676),U_18678)) = c_List_Olist_ONil(U_18674)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18672) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4521_2]) ).

fof(f_4521_4,plain,
    ( ! [U_18673,U_18675,U_18677,U_18679] :
        ( hAPP(hAPP(c_List_Otake(U_18675),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673)),hAPP(hAPP(c_List_Olist_OCons(U_18675),U_18677),U_18679)) = hAPP(hAPP(c_List_Olist_OCons(U_18675),U_18677),hAPP(hAPP(c_List_Otake(U_18675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18679))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18678,U_18674,U_18672,U_18676] :
        ( hAPP(hAPP(c_List_Otake(U_18674),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18672)),hAPP(hAPP(c_List_Olist_OCons(U_18674),U_18676),U_18678)) = c_List_Olist_ONil(U_18674)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18672) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4521_3]) ).

cnf(f_4521_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_18674),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18672)),hAPP(hAPP(c_List_Olist_OCons(U_18674),U_18676),U_18678)) = c_List_Olist_ONil(U_18674)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18672) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4521_4]) ).

cnf(f_4521_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18675),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673)),hAPP(hAPP(c_List_Olist_OCons(U_18675),U_18677),U_18679)) = hAPP(hAPP(c_List_Olist_OCons(U_18675),U_18677),hAPP(hAPP(c_List_Otake(U_18675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18679))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18673) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4521_4]) ).

fof(f_4522_1,plain,
    ! [V_i_2,V_a_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__list__update]) ).

fof(f_4522_2,plain,
    ! [U_18683,U_18682,U_18681,U_18680] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18680),hAPP(hAPP(c_List_Olist__update(U_18680,U_18681),U_18683),U_18682)))
      | hBOOL(hAPP(hAPP(c_member(U_18680),U_18682),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18680,tc_HOL_Obool)),hAPP(c_List_Oset(U_18680),U_18681)),hAPP(hAPP(c_Set_Oinsert(U_18680),hAPP(hAPP(c_List_Onth(U_18680),U_18681),U_18683)),c_Orderings_Obot__class_Obot(tc_fun(U_18680,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18680),U_18681)) ),
    inference(variable_rename,[status(thm)],[f_4522_1]) ).

fof(f_4522_3,plain,
    ! [U_18680,U_18681,U_18682,U_18683] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18680),hAPP(hAPP(c_List_Olist__update(U_18680,U_18681),U_18683),U_18682)))
      | hBOOL(hAPP(hAPP(c_member(U_18680),U_18682),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18680,tc_HOL_Obool)),hAPP(c_List_Oset(U_18680),U_18681)),hAPP(hAPP(c_Set_Oinsert(U_18680),hAPP(hAPP(c_List_Onth(U_18680),U_18681),U_18683)),c_Orderings_Obot__class_Obot(tc_fun(U_18680,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18680),U_18681)) ),
    inference(definitional_conversion,[status(esa)],[f_4522_2]) ).

cnf(f_4522_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18680),hAPP(hAPP(c_List_Olist__update(U_18680,U_18681),U_18683),U_18682)))
    | hBOOL(hAPP(hAPP(c_member(U_18680),U_18682),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18680,tc_HOL_Obool)),hAPP(c_List_Oset(U_18680),U_18681)),hAPP(hAPP(c_Set_Oinsert(U_18680),hAPP(hAPP(c_List_Onth(U_18680),U_18681),U_18683)),c_Orderings_Obot__class_Obot(tc_fun(U_18680,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18680),U_18681)) ),
    inference(clausify,[status(thm)],[f_4522_3]) ).

fof(f_4523_1,plain,
    ! [V_j_2,V_i_2] :
      ( ( ( c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) )
        & ( c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2))) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Opsimps]) ).

fof(f_4523_2,plain,
    ! [U_18685,U_18684] :
      ( ( ( c_List_Oupto(U_18684,U_18685) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18684),U_18685)) )
        & ( c_List_Oupto(U_18684,U_18685) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18684),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18684),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18685))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18684),U_18685)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18684),U_18685))) ),
    inference(variable_rename,[status(thm)],[f_4523_1]) ).

fof(f_4523_3,plain,
    ( ! [U_18684,U_18685] :
        ( c_List_Oupto(U_18684,U_18685) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18684),U_18685))
        | ~ sP1166(U_18684,U_18685) )
    & ! [U_18684,U_18685] :
        ( c_List_Oupto(U_18684,U_18685) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18684),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18684),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18684),U_18685))
        | ~ sP1166(U_18684,U_18685) )
    & ! [U_18684,U_18685] :
        ( sP1166(U_18684,U_18685)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18684),U_18685))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1166])],[f_4523_2]) ).

cnf(f_4523_4,plain,
    ( sP1166(U_18684,U_18685)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18684),U_18685))) ),
    inference(clausify,[status(thm)],[f_4523_3]) ).

cnf(f_4523_5,plain,
    ( c_List_Oupto(U_18684,U_18685) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18684),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18684),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18684),U_18685))
    | ~ sP1166(U_18684,U_18685) ),
    inference(clausify,[status(thm)],[f_4523_3]) ).

cnf(f_4523_6,plain,
    ( c_List_Oupto(U_18684,U_18685) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18684),U_18685))
    | ~ sP1166(U_18684,U_18685) ),
    inference(clausify,[status(thm)],[f_4523_3]) ).

fof(f_4524_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2))
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2)
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps]) ).

fof(f_4524_2,plain,
    ! [U_18690,U_18689,U_18688,U_18687,U_18686] :
      ( ( hAPP(c_Lazy__Sequence_Oanamorph(U_18687,U_18688,U_18689,U_18686),U_18690) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18688),U_18687),tc_prod(U_18688,U_18687),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18688),U_18687),c_List_Olist_ONil(U_18688)),U_18690),hAPP(c_Product__Type_Oprod_Oprod__case(U_18688,U_18687,tc_prod(tc_List_Olist(U_18688),U_18687)),hAPP(hAPP(c_COMBC(U_18688,tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687)),tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18688),U_18687),tc_prod(tc_List_Olist(U_18688),U_18687)),tc_fun(tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687)),tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687))),U_18688),c_COMBB(tc_prod(tc_List_Olist(U_18688),U_18687),tc_prod(tc_List_Olist(U_18688),U_18687),U_18687)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18688),tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687))),tc_fun(tc_prod(tc_List_Olist(U_18688),U_18687),tc_prod(tc_List_Olist(U_18688),U_18687)),U_18688),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18688),U_18687,tc_prod(tc_List_Olist(U_18688),U_18687))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18688),tc_List_Olist(U_18688)),tc_fun(tc_List_Olist(U_18688),tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687))),U_18688),hAPP(c_COMBB(tc_List_Olist(U_18688),tc_fun(U_18687,tc_prod(tc_List_Olist(U_18688),U_18687)),tc_List_Olist(U_18688)),c_Product__Type_OPair(tc_List_Olist(U_18688),U_18687))),c_List_Olist_OCons(U_18688))))),c_Lazy__Sequence_Oanamorph(U_18687,U_18688,U_18689,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18686),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18689,U_18690))
        | U_18686 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Lazy__Sequence_Oanamorph(U_18687,U_18688,U_18689,U_18686),U_18690) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18688),U_18687),c_List_Olist_ONil(U_18688)),U_18690)
        | U_18686 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4524_1]) ).

fof(f_4524_3,plain,
    ( ! [U_18700,U_18698,U_18696,U_18694,U_18692] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18694,U_18696,U_18698,U_18692),U_18700) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(U_18696,U_18694),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18696),U_18694),c_List_Olist_ONil(U_18696)),U_18700),hAPP(c_Product__Type_Oprod_Oprod__case(U_18696,U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),hAPP(hAPP(c_COMBC(U_18696,tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),U_18696),c_COMBB(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694),U_18694)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),tc_fun(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694)),U_18696),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18696),U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18696),tc_List_Olist(U_18696)),tc_fun(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),U_18696),hAPP(c_COMBB(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_List_Olist(U_18696)),c_Product__Type_OPair(tc_List_Olist(U_18696),U_18694))),c_List_Olist_OCons(U_18696))))),c_Lazy__Sequence_Oanamorph(U_18694,U_18696,U_18698,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18692),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18698,U_18700))
        | U_18692 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_18699,U_18697,U_18695,U_18693,U_18691] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18693,U_18695,U_18697,U_18691),U_18699) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18695),U_18693),c_List_Olist_ONil(U_18695)),U_18699)
        | U_18691 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4524_2]) ).

fof(f_4524_4,plain,
    ( ! [U_18692,U_18698,U_18694,U_18696,U_18700] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18694,U_18696,U_18698,U_18692),U_18700) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(U_18696,U_18694),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18696),U_18694),c_List_Olist_ONil(U_18696)),U_18700),hAPP(c_Product__Type_Oprod_Oprod__case(U_18696,U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),hAPP(hAPP(c_COMBC(U_18696,tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),U_18696),c_COMBB(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694),U_18694)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),tc_fun(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694)),U_18696),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18696),U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18696),tc_List_Olist(U_18696)),tc_fun(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),U_18696),hAPP(c_COMBB(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_List_Olist(U_18696)),c_Product__Type_OPair(tc_List_Olist(U_18696),U_18694))),c_List_Olist_OCons(U_18696))))),c_Lazy__Sequence_Oanamorph(U_18694,U_18696,U_18698,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18692),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18698,U_18700))
        | U_18692 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_18691,U_18693,U_18699,U_18695,U_18697] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18693,U_18695,U_18697,U_18691),U_18699) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18695),U_18693),c_List_Olist_ONil(U_18695)),U_18699)
        | U_18691 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_4524_3]) ).

cnf(f_4524_5,plain,
    ( hAPP(c_Lazy__Sequence_Oanamorph(U_18693,U_18695,U_18697,U_18691),U_18699) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18695),U_18693),c_List_Olist_ONil(U_18695)),U_18699)
    | U_18691 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4524_4]) ).

cnf(f_4524_6,plain,
    ( hAPP(c_Lazy__Sequence_Oanamorph(U_18694,U_18696,U_18698,U_18692),U_18700) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(U_18696,U_18694),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18696),U_18694),c_List_Olist_ONil(U_18696)),U_18700),hAPP(c_Product__Type_Oprod_Oprod__case(U_18696,U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),hAPP(hAPP(c_COMBC(U_18696,tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),U_18696),c_COMBB(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694),U_18694)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),tc_fun(tc_prod(tc_List_Olist(U_18696),U_18694),tc_prod(tc_List_Olist(U_18696),U_18694)),U_18696),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18696),U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18696),tc_List_Olist(U_18696)),tc_fun(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694))),U_18696),hAPP(c_COMBB(tc_List_Olist(U_18696),tc_fun(U_18694,tc_prod(tc_List_Olist(U_18696),U_18694)),tc_List_Olist(U_18696)),c_Product__Type_OPair(tc_List_Olist(U_18696),U_18694))),c_List_Olist_OCons(U_18696))))),c_Lazy__Sequence_Oanamorph(U_18694,U_18696,U_18698,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18692),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18698,U_18700))
    | U_18692 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4524_4]) ).

fof(f_4525_1,plain,
    ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(f_4525_2,plain,
    ! [U_18701] : c_List_Olistset(U_18701,c_List_Olist_ONil(tc_fun(U_18701,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18701)),c_List_Olist_ONil(U_18701)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18701),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4525_1]) ).

fof(f_4525_3,plain,
    ! [U_18701] : c_List_Olistset(U_18701,c_List_Olist_ONil(tc_fun(U_18701,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18701)),c_List_Olist_ONil(U_18701)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18701),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4525_2]) ).

cnf(f_4525_4,plain,
    c_List_Olistset(U_18701,c_List_Olist_ONil(tc_fun(U_18701,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18701)),c_List_Olist_ONil(U_18701)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18701),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4525_3]) ).

fof(f_4526_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons]) ).

fof(f_4526_2,plain,
    ! [U_18706,U_18705,U_18704,U_18703,U_18702] : hAPP(hAPP(c_List_Ozip(U_18702,U_18703),U_18704),hAPP(hAPP(c_List_Olist_OCons(U_18703),U_18705),U_18706)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18702,U_18703)),U_18702,c_List_Olist_ONil(tc_prod(U_18702,U_18703)),hAPP(hAPP(c_COMBC(U_18702,tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703)))),U_18702),c_COMBB(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(U_18702))),hAPP(hAPP(c_COMBB(tc_prod(U_18702,U_18703),tc_fun(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703))),U_18702),c_List_Olist_OCons(tc_prod(U_18702,U_18703))),hAPP(hAPP(c_COMBC(U_18702,U_18703,tc_prod(U_18702,U_18703)),c_Product__Type_OPair(U_18702,U_18703)),U_18705)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18702),tc_List_Olist(U_18703),tc_List_Olist(tc_prod(U_18702,U_18703))),c_List_Ozip(U_18702,U_18703)),U_18706))),U_18704),
    inference(variable_rename,[status(thm)],[f_4526_1]) ).

fof(f_4526_3,plain,
    ! [U_18702,U_18703,U_18704,U_18705,U_18706] : hAPP(hAPP(c_List_Ozip(U_18702,U_18703),U_18704),hAPP(hAPP(c_List_Olist_OCons(U_18703),U_18705),U_18706)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18702,U_18703)),U_18702,c_List_Olist_ONil(tc_prod(U_18702,U_18703)),hAPP(hAPP(c_COMBC(U_18702,tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703)))),U_18702),c_COMBB(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(U_18702))),hAPP(hAPP(c_COMBB(tc_prod(U_18702,U_18703),tc_fun(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703))),U_18702),c_List_Olist_OCons(tc_prod(U_18702,U_18703))),hAPP(hAPP(c_COMBC(U_18702,U_18703,tc_prod(U_18702,U_18703)),c_Product__Type_OPair(U_18702,U_18703)),U_18705)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18702),tc_List_Olist(U_18703),tc_List_Olist(tc_prod(U_18702,U_18703))),c_List_Ozip(U_18702,U_18703)),U_18706))),U_18704),
    inference(definitional_conversion,[status(esa)],[f_4526_2]) ).

cnf(f_4526_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18702,U_18703),U_18704),hAPP(hAPP(c_List_Olist_OCons(U_18703),U_18705),U_18706)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18702,U_18703)),U_18702,c_List_Olist_ONil(tc_prod(U_18702,U_18703)),hAPP(hAPP(c_COMBC(U_18702,tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703))),tc_fun(tc_List_Olist(U_18702),tc_List_Olist(tc_prod(U_18702,U_18703)))),U_18702),c_COMBB(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(U_18702))),hAPP(hAPP(c_COMBB(tc_prod(U_18702,U_18703),tc_fun(tc_List_Olist(tc_prod(U_18702,U_18703)),tc_List_Olist(tc_prod(U_18702,U_18703))),U_18702),c_List_Olist_OCons(tc_prod(U_18702,U_18703))),hAPP(hAPP(c_COMBC(U_18702,U_18703,tc_prod(U_18702,U_18703)),c_Product__Type_OPair(U_18702,U_18703)),U_18705)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18702),tc_List_Olist(U_18703),tc_List_Olist(tc_prod(U_18702,U_18703))),c_List_Ozip(U_18702,U_18703)),U_18706))),U_18704),
    inference(clausify,[status(thm)],[f_4526_3]) ).

fof(f_4527_1,plain,
    ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2),
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I5_J]) ).

fof(f_4527_2,plain,
    ! [U_18712,U_18711,U_18710,U_18709,U_18708,U_18707] : hAPP(c_List_Olist_Olist__case(U_18707,U_18708,U_18709,U_18710),hAPP(hAPP(c_List_Olist_OCons(U_18708),U_18711),U_18712)) = hAPP(hAPP(U_18710,U_18711),U_18712),
    inference(variable_rename,[status(thm)],[f_4527_1]) ).

fof(f_4527_3,plain,
    ! [U_18707,U_18708,U_18709,U_18710,U_18711,U_18712] : hAPP(c_List_Olist_Olist__case(U_18707,U_18708,U_18709,U_18710),hAPP(hAPP(c_List_Olist_OCons(U_18708),U_18711),U_18712)) = hAPP(hAPP(U_18710,U_18711),U_18712),
    inference(definitional_conversion,[status(esa)],[f_4527_2]) ).

cnf(f_4527_4,plain,
    hAPP(c_List_Olist_Olist__case(U_18707,U_18708,U_18709,U_18710),hAPP(hAPP(c_List_Olist_OCons(U_18708),U_18711),U_18712)) = hAPP(hAPP(U_18710,U_18711),U_18712),
    inference(clausify,[status(thm)],[f_4527_3]) ).

fof(f_4528_1,plain,
    ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(f_4528_2,plain,
    ! [U_18716,U_18715,U_18714,U_18713] : hAPP(c_List_Olist_Olist__case(U_18713,U_18714,U_18715,U_18716),c_List_Olist_ONil(U_18714)) = U_18715,
    inference(variable_rename,[status(thm)],[f_4528_1]) ).

fof(f_4528_3,plain,
    ! [U_18713,U_18714,U_18715,U_18716] : hAPP(c_List_Olist_Olist__case(U_18713,U_18714,U_18715,U_18716),c_List_Olist_ONil(U_18714)) = U_18715,
    inference(definitional_conversion,[status(esa)],[f_4528_2]) ).

cnf(f_4528_4,plain,
    hAPP(c_List_Olist_Olist__case(U_18713,U_18714,U_18715,U_18716),c_List_Olist_ONil(U_18714)) = U_18715,
    inference(clausify,[status(thm)],[f_4528_3]) ).

fof(f_4529_1,plain,
    ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)),
    inference(fof_nnf,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(f_4529_2,plain,
    ! [U_18719,U_18718,U_18717] : c_List_Olistset(U_18717,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18717,tc_HOL_Obool)),U_18718),U_18719)) = c_List_Oset__Cons(U_18717,U_18718,c_List_Olistset(U_18717,U_18719)),
    inference(variable_rename,[status(thm)],[f_4529_1]) ).

fof(f_4529_3,plain,
    ! [U_18717,U_18718,U_18719] : c_List_Olistset(U_18717,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18717,tc_HOL_Obool)),U_18718),U_18719)) = c_List_Oset__Cons(U_18717,U_18718,c_List_Olistset(U_18717,U_18719)),
    inference(definitional_conversion,[status(esa)],[f_4529_2]) ).

cnf(f_4529_4,plain,
    c_List_Olistset(U_18717,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18717,tc_HOL_Obool)),U_18718),U_18719)) = c_List_Oset__Cons(U_18717,U_18718,c_List_Olistset(U_18717,U_18719)),
    inference(clausify,[status(thm)],[f_4529_3]) ).

fof(f_4530_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons1]) ).

fof(f_4530_2,plain,
    ! [U_18724,U_18723,U_18722,U_18721,U_18720] : hAPP(hAPP(c_List_Ozip(U_18720,U_18721),hAPP(hAPP(c_List_Olist_OCons(U_18720),U_18722),U_18723)),U_18724) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18720,U_18721)),U_18721,c_List_Olist_ONil(tc_prod(U_18720,U_18721)),hAPP(hAPP(c_COMBC(U_18721,tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721)))),U_18721),c_COMBB(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(U_18721))),hAPP(hAPP(c_COMBB(tc_prod(U_18720,U_18721),tc_fun(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721))),U_18721),c_List_Olist_OCons(tc_prod(U_18720,U_18721))),hAPP(c_Product__Type_OPair(U_18720,U_18721),U_18722)))),hAPP(c_List_Ozip(U_18720,U_18721),U_18723))),U_18724),
    inference(variable_rename,[status(thm)],[f_4530_1]) ).

fof(f_4530_3,plain,
    ! [U_18720,U_18721,U_18722,U_18723,U_18724] : hAPP(hAPP(c_List_Ozip(U_18720,U_18721),hAPP(hAPP(c_List_Olist_OCons(U_18720),U_18722),U_18723)),U_18724) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18720,U_18721)),U_18721,c_List_Olist_ONil(tc_prod(U_18720,U_18721)),hAPP(hAPP(c_COMBC(U_18721,tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721)))),U_18721),c_COMBB(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(U_18721))),hAPP(hAPP(c_COMBB(tc_prod(U_18720,U_18721),tc_fun(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721))),U_18721),c_List_Olist_OCons(tc_prod(U_18720,U_18721))),hAPP(c_Product__Type_OPair(U_18720,U_18721),U_18722)))),hAPP(c_List_Ozip(U_18720,U_18721),U_18723))),U_18724),
    inference(definitional_conversion,[status(esa)],[f_4530_2]) ).

cnf(f_4530_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18720,U_18721),hAPP(hAPP(c_List_Olist_OCons(U_18720),U_18722),U_18723)),U_18724) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18720,U_18721)),U_18721,c_List_Olist_ONil(tc_prod(U_18720,U_18721)),hAPP(hAPP(c_COMBC(U_18721,tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721))),tc_fun(tc_List_Olist(U_18721),tc_List_Olist(tc_prod(U_18720,U_18721)))),U_18721),c_COMBB(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(U_18721))),hAPP(hAPP(c_COMBB(tc_prod(U_18720,U_18721),tc_fun(tc_List_Olist(tc_prod(U_18720,U_18721)),tc_List_Olist(tc_prod(U_18720,U_18721))),U_18721),c_List_Olist_OCons(tc_prod(U_18720,U_18721))),hAPP(c_Product__Type_OPair(U_18720,U_18721),U_18722)))),hAPP(c_List_Ozip(U_18720,U_18721),U_18723))),U_18724),
    inference(clausify,[status(thm)],[f_4530_3]) ).

fof(f_4531_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
          & ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Opinduct]) ).

fof(f_4531_2,plain,
    ! [U_18729,U_18728,U_18727] :
      ( hBOOL(hAPP(hAPP(U_18729,U_18727),U_18728))
      | ? [U_18726,U_18725] :
          ( ~ hBOOL(hAPP(hAPP(U_18729,U_18726),U_18725))
          & ( hBOOL(hAPP(hAPP(U_18729,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18726),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_18725))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18726),U_18725)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18726),U_18725))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18727),U_18728))) ),
    inference(variable_rename,[status(thm)],[f_4531_1]) ).

fof(f_4531_3,plain,
    ! [U_18729,U_18728,U_18727] :
      ( hBOOL(hAPP(hAPP(U_18729,U_18727),U_18728))
      | ? [U_18725] :
          ( ~ hBOOL(hAPP(hAPP(U_18729,sK469(U_18729,U_18728,U_18727)),U_18725))
          & ( hBOOL(hAPP(hAPP(U_18729,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_18725))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),U_18725)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),U_18725))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18727),U_18728))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_18726,sK469(U_18729,U_18728,U_18727))],[f_4531_2]) ).

fof(f_4531_4,plain,
    ! [U_18729,U_18728,U_18727] :
      ( hBOOL(hAPP(hAPP(U_18729,U_18727),U_18728))
      | ( ~ hBOOL(hAPP(hAPP(U_18729,sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727)))
        & ( hBOOL(hAPP(hAPP(U_18729,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK470(U_18729,U_18728,U_18727)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18727),U_18728))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_18725,sK470(U_18729,U_18728,U_18727))],[f_4531_3]) ).

fof(f_4531_5,plain,
    ( ! [U_18727,U_18728,U_18729] :
        ( ~ hBOOL(hAPP(hAPP(U_18729,sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727)))
        | ~ sP1167(U_18727,U_18728,U_18729) )
    & ! [U_18727,U_18728,U_18729] :
        ( hBOOL(hAPP(hAPP(U_18729,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK470(U_18729,U_18728,U_18727)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727)))
        | ~ sP1167(U_18727,U_18728,U_18729) )
    & ! [U_18727,U_18728,U_18729] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727))))
        | ~ sP1167(U_18727,U_18728,U_18729) )
    & ! [U_18727,U_18728,U_18729] :
        ( hBOOL(hAPP(hAPP(U_18729,U_18727),U_18728))
        | sP1167(U_18727,U_18728,U_18729)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18727),U_18728))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1167])],[f_4531_4]) ).

cnf(f_4531_6,plain,
    ( hBOOL(hAPP(hAPP(U_18729,U_18727),U_18728))
    | sP1167(U_18727,U_18728,U_18729)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18727),U_18728))) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727))))
    | ~ sP1167(U_18727,U_18728,U_18729) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_8,plain,
    ( hBOOL(hAPP(hAPP(U_18729,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK470(U_18729,U_18728,U_18727)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727)))
    | ~ sP1167(U_18727,U_18728,U_18729) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_18729,sK469(U_18729,U_18728,U_18727)),sK470(U_18729,U_18728,U_18727)))
    | ~ sP1167(U_18727,U_18728,U_18729) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

fof(f_4532_1,plain,
    ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
      ( ( c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2)))) )
      & ( c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__upds__conv__if]) ).

fof(f_4532_2,plain,
    ! [U_18736,U_18735,U_18734,U_18733,U_18732,U_18731,U_18730] :
      ( ( c_Map_Omap__upds(U_18730,U_18732,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18730,tc_Option_Ooption(U_18732)),U_18735),U_18731),hAPP(c_Option_Ooption_OSome(U_18732),U_18736)),U_18734,U_18733) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18730,tc_Option_Ooption(U_18732)),c_Map_Omap__upds(U_18730,U_18732,U_18735,U_18734,U_18733)),U_18731),hAPP(c_Option_Ooption_OSome(U_18732),U_18736))
        | hBOOL(hAPP(hAPP(c_member(U_18730),U_18731),hAPP(c_List_Oset(U_18730),hAPP(hAPP(c_List_Otake(U_18730),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733)),U_18734)))) )
      & ( c_Map_Omap__upds(U_18730,U_18732,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18730,tc_Option_Ooption(U_18732)),U_18735),U_18731),hAPP(c_Option_Ooption_OSome(U_18732),U_18736)),U_18734,U_18733) = c_Map_Omap__upds(U_18730,U_18732,U_18735,U_18734,U_18733)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18730),U_18731),hAPP(c_List_Oset(U_18730),hAPP(hAPP(c_List_Otake(U_18730),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733)),U_18734)))) ) ),
    inference(variable_rename,[status(thm)],[f_4532_1]) ).

fof(f_4532_3,plain,
    ( ! [U_18750,U_18748,U_18746,U_18744,U_18742,U_18740,U_18738] :
        ( c_Map_Omap__upds(U_18738,U_18742,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18738,tc_Option_Ooption(U_18742)),U_18748),U_18740),hAPP(c_Option_Ooption_OSome(U_18742),U_18750)),U_18746,U_18744) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18738,tc_Option_Ooption(U_18742)),c_Map_Omap__upds(U_18738,U_18742,U_18748,U_18746,U_18744)),U_18740),hAPP(c_Option_Ooption_OSome(U_18742),U_18750))
        | hBOOL(hAPP(hAPP(c_member(U_18738),U_18740),hAPP(c_List_Oset(U_18738),hAPP(hAPP(c_List_Otake(U_18738),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18742)),U_18744)),U_18746)))) )
    & ! [U_18749,U_18747,U_18745,U_18743,U_18741,U_18739,U_18737] :
        ( c_Map_Omap__upds(U_18737,U_18741,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18737,tc_Option_Ooption(U_18741)),U_18747),U_18739),hAPP(c_Option_Ooption_OSome(U_18741),U_18749)),U_18745,U_18743) = c_Map_Omap__upds(U_18737,U_18741,U_18747,U_18745,U_18743)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18737),U_18739),hAPP(c_List_Oset(U_18737),hAPP(hAPP(c_List_Otake(U_18737),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18741)),U_18743)),U_18745)))) ) ),
    inference(miniscope,[status(thm)],[f_4532_2]) ).

fof(f_4532_4,plain,
    ( ! [U_18738,U_18740,U_18742,U_18744,U_18746,U_18748,U_18750] :
        ( c_Map_Omap__upds(U_18738,U_18742,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18738,tc_Option_Ooption(U_18742)),U_18748),U_18740),hAPP(c_Option_Ooption_OSome(U_18742),U_18750)),U_18746,U_18744) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18738,tc_Option_Ooption(U_18742)),c_Map_Omap__upds(U_18738,U_18742,U_18748,U_18746,U_18744)),U_18740),hAPP(c_Option_Ooption_OSome(U_18742),U_18750))
        | hBOOL(hAPP(hAPP(c_member(U_18738),U_18740),hAPP(c_List_Oset(U_18738),hAPP(hAPP(c_List_Otake(U_18738),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18742)),U_18744)),U_18746)))) )
    & ! [U_18741,U_18743,U_18739,U_18737,U_18745,U_18747,U_18749] :
        ( c_Map_Omap__upds(U_18737,U_18741,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18737,tc_Option_Ooption(U_18741)),U_18747),U_18739),hAPP(c_Option_Ooption_OSome(U_18741),U_18749)),U_18745,U_18743) = c_Map_Omap__upds(U_18737,U_18741,U_18747,U_18745,U_18743)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18737),U_18739),hAPP(c_List_Oset(U_18737),hAPP(hAPP(c_List_Otake(U_18737),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18741)),U_18743)),U_18745)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4532_3]) ).

cnf(f_4532_5,plain,
    ( c_Map_Omap__upds(U_18737,U_18741,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18737,tc_Option_Ooption(U_18741)),U_18747),U_18739),hAPP(c_Option_Ooption_OSome(U_18741),U_18749)),U_18745,U_18743) = c_Map_Omap__upds(U_18737,U_18741,U_18747,U_18745,U_18743)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18737),U_18739),hAPP(c_List_Oset(U_18737),hAPP(hAPP(c_List_Otake(U_18737),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18741)),U_18743)),U_18745)))) ),
    inference(clausify,[status(thm)],[f_4532_4]) ).

cnf(f_4532_6,plain,
    ( c_Map_Omap__upds(U_18738,U_18742,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18738,tc_Option_Ooption(U_18742)),U_18748),U_18740),hAPP(c_Option_Ooption_OSome(U_18742),U_18750)),U_18746,U_18744) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18738,tc_Option_Ooption(U_18742)),c_Map_Omap__upds(U_18738,U_18742,U_18748,U_18746,U_18744)),U_18740),hAPP(c_Option_Ooption_OSome(U_18742),U_18750))
    | hBOOL(hAPP(hAPP(c_member(U_18738),U_18740),hAPP(c_List_Oset(U_18738),hAPP(hAPP(c_List_Otake(U_18738),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18742)),U_18744)),U_18746)))) ),
    inference(clausify,[status(thm)],[f_4532_4]) ).

fof(f_4533_1,plain,
    ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_map__upds__Nil1]) ).

fof(f_4533_2,plain,
    ! [U_18754,U_18753,U_18752,U_18751] : c_Map_Omap__upds(U_18751,U_18752,U_18753,c_List_Olist_ONil(U_18751),U_18754) = U_18753,
    inference(variable_rename,[status(thm)],[f_4533_1]) ).

fof(f_4533_3,plain,
    ! [U_18753,U_18754,U_18751,U_18752] : c_Map_Omap__upds(U_18751,U_18752,U_18753,c_List_Olist_ONil(U_18751),U_18754) = U_18753,
    inference(definitional_conversion,[status(esa)],[f_4533_2]) ).

cnf(f_4533_4,plain,
    c_Map_Omap__upds(U_18751,U_18752,U_18753,c_List_Olist_ONil(U_18751),U_18754) = U_18753,
    inference(clausify,[status(thm)],[f_4533_3]) ).

fof(f_4534_1,plain,
    ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_map__upds__Nil2]) ).

fof(f_4534_2,plain,
    ! [U_18758,U_18757,U_18756,U_18755] : c_Map_Omap__upds(U_18755,U_18756,U_18757,U_18758,c_List_Olist_ONil(U_18756)) = U_18757,
    inference(variable_rename,[status(thm)],[f_4534_1]) ).

fof(f_4534_3,plain,
    ! [U_18755,U_18756,U_18757,U_18758] : c_Map_Omap__upds(U_18755,U_18756,U_18757,U_18758,c_List_Olist_ONil(U_18756)) = U_18757,
    inference(definitional_conversion,[status(esa)],[f_4534_2]) ).

cnf(f_4534_4,plain,
    c_Map_Omap__upds(U_18755,U_18756,U_18757,U_18758,c_List_Olist_ONil(U_18756)) = U_18757,
    inference(clausify,[status(thm)],[f_4534_3]) ).

fof(f_4535_1,plain,
    ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
      ( hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__apply__nontin]) ).

fof(f_4535_2,plain,
    ! [U_18764,U_18763,U_18762,U_18761,U_18760,U_18759] :
      ( hAPP(c_Map_Omap__upds(U_18759,U_18762,U_18763,U_18761,U_18764),U_18760) = hAPP(U_18763,U_18760)
      | hBOOL(hAPP(hAPP(c_member(U_18759),U_18760),hAPP(c_List_Oset(U_18759),U_18761))) ),
    inference(variable_rename,[status(thm)],[f_4535_1]) ).

fof(f_4535_3,plain,
    ! [U_18759,U_18760,U_18761,U_18762,U_18763,U_18764] :
      ( hAPP(c_Map_Omap__upds(U_18759,U_18762,U_18763,U_18761,U_18764),U_18760) = hAPP(U_18763,U_18760)
      | hBOOL(hAPP(hAPP(c_member(U_18759),U_18760),hAPP(c_List_Oset(U_18759),U_18761))) ),
    inference(definitional_conversion,[status(esa)],[f_4535_2]) ).

cnf(f_4535_4,plain,
    ( hAPP(c_Map_Omap__upds(U_18759,U_18762,U_18763,U_18761,U_18764),U_18760) = hAPP(U_18763,U_18760)
    | hBOOL(hAPP(hAPP(c_member(U_18759),U_18760),hAPP(c_List_Oset(U_18759),U_18761))) ),
    inference(clausify,[status(thm)],[f_4535_3]) ).

fof(f_4536_1,plain,
    ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_map__add__upds]) ).

fof(f_4536_2,plain,
    ! [U_18770,U_18769,U_18768,U_18767,U_18766,U_18765] : c_Map_Omap__add(U_18765,U_18766,U_18767,c_Map_Omap__upds(U_18765,U_18766,U_18768,U_18769,U_18770)) = c_Map_Omap__upds(U_18765,U_18766,c_Map_Omap__add(U_18765,U_18766,U_18767,U_18768),U_18769,U_18770),
    inference(variable_rename,[status(thm)],[f_4536_1]) ).

fof(f_4536_3,plain,
    ! [U_18766,U_18765,U_18767,U_18768,U_18769,U_18770] : c_Map_Omap__add(U_18765,U_18766,U_18767,c_Map_Omap__upds(U_18765,U_18766,U_18768,U_18769,U_18770)) = c_Map_Omap__upds(U_18765,U_18766,c_Map_Omap__add(U_18765,U_18766,U_18767,U_18768),U_18769,U_18770),
    inference(definitional_conversion,[status(esa)],[f_4536_2]) ).

cnf(f_4536_4,plain,
    c_Map_Omap__add(U_18765,U_18766,U_18767,c_Map_Omap__upds(U_18765,U_18766,U_18768,U_18769,U_18770)) = c_Map_Omap__upds(U_18765,U_18766,c_Map_Omap__add(U_18765,U_18766,U_18767,U_18768),U_18769,U_18770),
    inference(clausify,[status(thm)],[f_4536_3]) ).

fof(f_4537_1,plain,
    ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2),
    inference(fof_nnf,[status(thm)],[fact_map__upds__Cons]) ).

fof(f_4537_2,plain,
    ! [U_18777,U_18776,U_18775,U_18774,U_18773,U_18772,U_18771] : c_Map_Omap__upds(U_18771,U_18772,U_18773,hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18774),U_18775),hAPP(hAPP(c_List_Olist_OCons(U_18772),U_18776),U_18777)) = c_Map_Omap__upds(U_18771,U_18772,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18771,tc_Option_Ooption(U_18772)),U_18773),U_18774),hAPP(c_Option_Ooption_OSome(U_18772),U_18776)),U_18775,U_18777),
    inference(variable_rename,[status(thm)],[f_4537_1]) ).

fof(f_4537_3,plain,
    ! [U_18771,U_18772,U_18773,U_18774,U_18775,U_18776,U_18777] : c_Map_Omap__upds(U_18771,U_18772,U_18773,hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18774),U_18775),hAPP(hAPP(c_List_Olist_OCons(U_18772),U_18776),U_18777)) = c_Map_Omap__upds(U_18771,U_18772,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18771,tc_Option_Ooption(U_18772)),U_18773),U_18774),hAPP(c_Option_Ooption_OSome(U_18772),U_18776)),U_18775,U_18777),
    inference(definitional_conversion,[status(esa)],[f_4537_2]) ).

cnf(f_4537_4,plain,
    c_Map_Omap__upds(U_18771,U_18772,U_18773,hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18774),U_18775),hAPP(hAPP(c_List_Olist_OCons(U_18772),U_18776),U_18777)) = c_Map_Omap__upds(U_18771,U_18772,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18771,tc_Option_Ooption(U_18772)),U_18773),U_18774),hAPP(c_Option_Ooption_OSome(U_18772),U_18776)),U_18775,U_18777),
    inference(clausify,[status(thm)],[f_4537_3]) ).

fof(f_4538_1,plain,
    ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
      ( c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__list__update2__drop]) ).

fof(f_4538_2,plain,
    ! [U_18784,U_18783,U_18782,U_18781,U_18780,U_18779,U_18778] :
      ( c_Map_Omap__upds(U_18778,U_18781,U_18783,U_18779,hAPP(hAPP(c_List_Olist__update(U_18781,U_18782),U_18780),U_18784)) = c_Map_Omap__upds(U_18778,U_18781,U_18783,U_18779,U_18782)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18781)),U_18782)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18779)),U_18780)) ),
    inference(variable_rename,[status(thm)],[f_4538_1]) ).

fof(f_4538_3,plain,
    ! [U_18778,U_18779,U_18780,U_18781,U_18782,U_18783,U_18784] :
      ( c_Map_Omap__upds(U_18778,U_18781,U_18783,U_18779,hAPP(hAPP(c_List_Olist__update(U_18781,U_18782),U_18780),U_18784)) = c_Map_Omap__upds(U_18778,U_18781,U_18783,U_18779,U_18782)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18781)),U_18782)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18779)),U_18780)) ),
    inference(definitional_conversion,[status(esa)],[f_4538_2]) ).

cnf(f_4538_4,plain,
    ( c_Map_Omap__upds(U_18778,U_18781,U_18783,U_18779,hAPP(hAPP(c_List_Olist__update(U_18781,U_18782),U_18780),U_18784)) = c_Map_Omap__upds(U_18778,U_18781,U_18783,U_18779,U_18782)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18781)),U_18782)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18779)),U_18780)) ),
    inference(clausify,[status(thm)],[f_4538_3]) ).

fof(f_4539_1,plain,
    ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
      ( c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__twist]) ).

fof(f_4539_2,plain,
    ! [U_18791,U_18790,U_18789,U_18788,U_18787,U_18786,U_18785] :
      ( c_Map_Omap__upds(U_18785,U_18788,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18785,tc_Option_Ooption(U_18788)),U_18789),U_18786),hAPP(c_Option_Ooption_OSome(U_18788),U_18790)),U_18787,U_18791) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18785,tc_Option_Ooption(U_18788)),c_Map_Omap__upds(U_18785,U_18788,U_18789,U_18787,U_18791)),U_18786),hAPP(c_Option_Ooption_OSome(U_18788),U_18790))
      | hBOOL(hAPP(hAPP(c_member(U_18785),U_18786),hAPP(c_List_Oset(U_18785),U_18787))) ),
    inference(variable_rename,[status(thm)],[f_4539_1]) ).

fof(f_4539_3,plain,
    ! [U_18785,U_18786,U_18787,U_18788,U_18789,U_18790,U_18791] :
      ( c_Map_Omap__upds(U_18785,U_18788,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18785,tc_Option_Ooption(U_18788)),U_18789),U_18786),hAPP(c_Option_Ooption_OSome(U_18788),U_18790)),U_18787,U_18791) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18785,tc_Option_Ooption(U_18788)),c_Map_Omap__upds(U_18785,U_18788,U_18789,U_18787,U_18791)),U_18786),hAPP(c_Option_Ooption_OSome(U_18788),U_18790))
      | hBOOL(hAPP(hAPP(c_member(U_18785),U_18786),hAPP(c_List_Oset(U_18785),U_18787))) ),
    inference(definitional_conversion,[status(esa)],[f_4539_2]) ).

cnf(f_4539_4,plain,
    ( c_Map_Omap__upds(U_18785,U_18788,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18785,tc_Option_Ooption(U_18788)),U_18789),U_18786),hAPP(c_Option_Ooption_OSome(U_18788),U_18790)),U_18787,U_18791) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18785,tc_Option_Ooption(U_18788)),c_Map_Omap__upds(U_18785,U_18788,U_18789,U_18787,U_18791)),U_18786),hAPP(c_Option_Ooption_OSome(U_18788),U_18790))
    | hBOOL(hAPP(hAPP(c_member(U_18785),U_18786),hAPP(c_List_Oset(U_18785),U_18787))) ),
    inference(clausify,[status(thm)],[f_4539_3]) ).

fof(f_4540_1,plain,
    ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__upds]) ).

fof(f_4540_2,plain,
    ! [U_18797,U_18796,U_18795,U_18794,U_18793,U_18792] :
      ( c_Map_Orestrict__map(U_18792,U_18794,c_Map_Omap__upds(U_18792,U_18794,U_18797,U_18793,U_18795),U_18796) = c_Map_Omap__upds(U_18792,U_18794,c_Map_Orestrict__map(U_18792,U_18794,U_18797,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18792,tc_HOL_Obool)),U_18796),hAPP(c_List_Oset(U_18792),U_18793))),U_18793,U_18795)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18792,tc_HOL_Obool)),hAPP(c_List_Oset(U_18792),U_18793)),U_18796))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18793) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18794)),U_18795) ),
    inference(variable_rename,[status(thm)],[f_4540_1]) ).

fof(f_4540_3,plain,
    ! [U_18792,U_18793,U_18794,U_18795,U_18796,U_18797] :
      ( c_Map_Orestrict__map(U_18792,U_18794,c_Map_Omap__upds(U_18792,U_18794,U_18797,U_18793,U_18795),U_18796) = c_Map_Omap__upds(U_18792,U_18794,c_Map_Orestrict__map(U_18792,U_18794,U_18797,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18792,tc_HOL_Obool)),U_18796),hAPP(c_List_Oset(U_18792),U_18793))),U_18793,U_18795)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18792,tc_HOL_Obool)),hAPP(c_List_Oset(U_18792),U_18793)),U_18796))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18793) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18794)),U_18795) ),
    inference(definitional_conversion,[status(esa)],[f_4540_2]) ).

cnf(f_4540_4,plain,
    ( c_Map_Orestrict__map(U_18792,U_18794,c_Map_Omap__upds(U_18792,U_18794,U_18797,U_18793,U_18795),U_18796) = c_Map_Omap__upds(U_18792,U_18794,c_Map_Orestrict__map(U_18792,U_18794,U_18797,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18792,tc_HOL_Obool)),U_18796),hAPP(c_List_Oset(U_18792),U_18793))),U_18793,U_18795)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18792,tc_HOL_Obool)),hAPP(c_List_Oset(U_18792),U_18793)),U_18796))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18793) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18794)),U_18795) ),
    inference(clausify,[status(thm)],[f_4540_3]) ).

fof(f_4541_1,plain,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)),
    inference(fof_nnf,[status(thm)],[fact_dom__map__upds]) ).

fof(f_4541_2,plain,
    ! [U_18802,U_18801,U_18800,U_18799,U_18798] : c_Map_Odom(U_18798,U_18799,c_Map_Omap__upds(U_18798,U_18799,U_18800,U_18801,U_18802)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18798,tc_HOL_Obool)),hAPP(c_List_Oset(U_18798),hAPP(hAPP(c_List_Otake(U_18798),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18799)),U_18802)),U_18801))),c_Map_Odom(U_18798,U_18799,U_18800)),
    inference(variable_rename,[status(thm)],[f_4541_1]) ).

fof(f_4541_3,plain,
    ! [U_18798,U_18799,U_18800,U_18801,U_18802] : c_Map_Odom(U_18798,U_18799,c_Map_Omap__upds(U_18798,U_18799,U_18800,U_18801,U_18802)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18798,tc_HOL_Obool)),hAPP(c_List_Oset(U_18798),hAPP(hAPP(c_List_Otake(U_18798),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18799)),U_18802)),U_18801))),c_Map_Odom(U_18798,U_18799,U_18800)),
    inference(definitional_conversion,[status(esa)],[f_4541_2]) ).

cnf(f_4541_4,plain,
    c_Map_Odom(U_18798,U_18799,c_Map_Omap__upds(U_18798,U_18799,U_18800,U_18801,U_18802)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18798,tc_HOL_Obool)),hAPP(c_List_Oset(U_18798),hAPP(hAPP(c_List_Otake(U_18798),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18799)),U_18802)),U_18801))),c_Map_Odom(U_18798,U_18799,U_18800)),
    inference(clausify,[status(thm)],[f_4541_3]) ).

fof(f_4542_1,plain,
    ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__append1]) ).

fof(f_4542_2,plain,
    ! [U_18808,U_18807,U_18806,U_18805,U_18804,U_18803] :
      ( c_Map_Omap__upds(U_18803,U_18805,U_18807,hAPP(hAPP(c_List_Oappend(U_18803),U_18804),hAPP(hAPP(c_List_Olist_OCons(U_18803),U_18808),c_List_Olist_ONil(U_18803))),U_18806) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18803,tc_Option_Ooption(U_18805)),c_Map_Omap__upds(U_18803,U_18805,U_18807,U_18804,U_18806)),U_18808),hAPP(c_Option_Ooption_OSome(U_18805),hAPP(hAPP(c_List_Onth(U_18805),U_18806),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18803)),U_18804))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18803)),U_18804)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18805)),U_18806))) ),
    inference(variable_rename,[status(thm)],[f_4542_1]) ).

fof(f_4542_3,plain,
    ! [U_18803,U_18804,U_18805,U_18806,U_18807,U_18808] :
      ( c_Map_Omap__upds(U_18803,U_18805,U_18807,hAPP(hAPP(c_List_Oappend(U_18803),U_18804),hAPP(hAPP(c_List_Olist_OCons(U_18803),U_18808),c_List_Olist_ONil(U_18803))),U_18806) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18803,tc_Option_Ooption(U_18805)),c_Map_Omap__upds(U_18803,U_18805,U_18807,U_18804,U_18806)),U_18808),hAPP(c_Option_Ooption_OSome(U_18805),hAPP(hAPP(c_List_Onth(U_18805),U_18806),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18803)),U_18804))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18803)),U_18804)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18805)),U_18806))) ),
    inference(definitional_conversion,[status(esa)],[f_4542_2]) ).

cnf(f_4542_4,plain,
    ( c_Map_Omap__upds(U_18803,U_18805,U_18807,hAPP(hAPP(c_List_Oappend(U_18803),U_18804),hAPP(hAPP(c_List_Olist_OCons(U_18803),U_18808),c_List_Olist_ONil(U_18803))),U_18806) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18803,tc_Option_Ooption(U_18805)),c_Map_Omap__upds(U_18803,U_18805,U_18807,U_18804,U_18806)),U_18808),hAPP(c_Option_Ooption_OSome(U_18805),hAPP(hAPP(c_List_Onth(U_18805),U_18806),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18803)),U_18804))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18803)),U_18804)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18805)),U_18806))) ),
    inference(clausify,[status(thm)],[f_4542_3]) ).

fof(f_4543_1,plain,
    ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__Cons]) ).

fof(f_4543_2,plain,
    ! [U_18812,U_18811,U_18810,U_18809] : c_List_Osublist(U_18809,hAPP(hAPP(c_List_Olist_OCons(U_18809),U_18810),U_18811),U_18812) = hAPP(hAPP(c_List_Oappend(U_18809),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_18809)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18812)),hAPP(hAPP(c_List_Olist_OCons(U_18809),U_18810),c_List_Olist_ONil(U_18809))),c_List_Olist_ONil(U_18809))),c_List_Osublist(U_18809,U_18811,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_18812)))),
    inference(variable_rename,[status(thm)],[f_4543_1]) ).

fof(f_4543_3,plain,
    ! [U_18809,U_18810,U_18811,U_18812] : c_List_Osublist(U_18809,hAPP(hAPP(c_List_Olist_OCons(U_18809),U_18810),U_18811),U_18812) = hAPP(hAPP(c_List_Oappend(U_18809),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_18809)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18812)),hAPP(hAPP(c_List_Olist_OCons(U_18809),U_18810),c_List_Olist_ONil(U_18809))),c_List_Olist_ONil(U_18809))),c_List_Osublist(U_18809,U_18811,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_18812)))),
    inference(definitional_conversion,[status(esa)],[f_4543_2]) ).

cnf(f_4543_4,plain,
    c_List_Osublist(U_18809,hAPP(hAPP(c_List_Olist_OCons(U_18809),U_18810),U_18811),U_18812) = hAPP(hAPP(c_List_Oappend(U_18809),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_18809)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18812)),hAPP(hAPP(c_List_Olist_OCons(U_18809),U_18810),c_List_Olist_ONil(U_18809))),c_List_Olist_ONil(U_18809))),c_List_Osublist(U_18809,U_18811,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_18812)))),
    inference(clausify,[status(thm)],[f_4543_3]) ).

fof(f_4544_1,plain,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
        | V_x_2 != V_y_2
        | V_xs_2 != V_ys_2 )
      & ( ( V_x_2 = V_y_2
          & V_xs_2 = V_ys_2 )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) != hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append1__eq__conv]) ).

fof(f_4544_2,plain,
    ! [U_18817,U_18816,U_18815,U_18814,U_18813] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18813),U_18814),hAPP(hAPP(c_List_Olist_OCons(U_18813),U_18815),c_List_Olist_ONil(U_18813))) = hAPP(hAPP(c_List_Oappend(U_18813),U_18816),hAPP(hAPP(c_List_Olist_OCons(U_18813),U_18817),c_List_Olist_ONil(U_18813)))
        | U_18815 != U_18817
        | U_18814 != U_18816 )
      & ( ( U_18815 = U_18817
          & U_18814 = U_18816 )
        | hAPP(hAPP(c_List_Oappend(U_18813),U_18814),hAPP(hAPP(c_List_Olist_OCons(U_18813),U_18815),c_List_Olist_ONil(U_18813))) != hAPP(hAPP(c_List_Oappend(U_18813),U_18816),hAPP(hAPP(c_List_Olist_OCons(U_18813),U_18817),c_List_Olist_ONil(U_18813))) ) ),
    inference(variable_rename,[status(thm)],[f_4544_1]) ).

fof(f_4544_3,plain,
    ( ! [U_18827,U_18825,U_18823,U_18821] :
        ( ! [U_18819] : hAPP(hAPP(c_List_Oappend(U_18819),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18819),U_18823),c_List_Olist_ONil(U_18819))) = hAPP(hAPP(c_List_Oappend(U_18819),U_18825),hAPP(hAPP(c_List_Olist_OCons(U_18819),U_18827),c_List_Olist_ONil(U_18819)))
        | U_18823 != U_18827
        | U_18821 != U_18825 )
    & ! [U_18826,U_18824,U_18822,U_18820] :
        ( ! [U_18818] : hAPP(hAPP(c_List_Oappend(U_18818),U_18820),hAPP(hAPP(c_List_Olist_OCons(U_18818),U_18822),c_List_Olist_ONil(U_18818))) != hAPP(hAPP(c_List_Oappend(U_18818),U_18824),hAPP(hAPP(c_List_Olist_OCons(U_18818),U_18826),c_List_Olist_ONil(U_18818)))
        | ( U_18822 = U_18826
          & U_18820 = U_18824 ) ) ),
    inference(miniscope,[status(thm)],[f_4544_2]) ).

fof(f_4544_4,plain,
    ( ! [U_18822,U_18826,U_18820,U_18824] :
        ( U_18822 = U_18826
        | ~ sP1168(U_18822,U_18826,U_18820,U_18824) )
    & ! [U_18822,U_18826,U_18820,U_18824] :
        ( U_18820 = U_18824
        | ~ sP1168(U_18822,U_18826,U_18820,U_18824) )
    & ! [U_18825,U_18821,U_18823,U_18819,U_18827] :
        ( hAPP(hAPP(c_List_Oappend(U_18819),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18819),U_18823),c_List_Olist_ONil(U_18819))) = hAPP(hAPP(c_List_Oappend(U_18819),U_18825),hAPP(hAPP(c_List_Olist_OCons(U_18819),U_18827),c_List_Olist_ONil(U_18819)))
        | U_18823 != U_18827
        | U_18821 != U_18825 )
    & ! [U_18822,U_18826,U_18820,U_18818,U_18824] :
        ( hAPP(hAPP(c_List_Oappend(U_18818),U_18820),hAPP(hAPP(c_List_Olist_OCons(U_18818),U_18822),c_List_Olist_ONil(U_18818))) != hAPP(hAPP(c_List_Oappend(U_18818),U_18824),hAPP(hAPP(c_List_Olist_OCons(U_18818),U_18826),c_List_Olist_ONil(U_18818)))
        | sP1168(U_18822,U_18826,U_18820,U_18824) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1168])],[f_4544_3]) ).

cnf(f_4544_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18818),U_18820),hAPP(hAPP(c_List_Olist_OCons(U_18818),U_18822),c_List_Olist_ONil(U_18818))) != hAPP(hAPP(c_List_Oappend(U_18818),U_18824),hAPP(hAPP(c_List_Olist_OCons(U_18818),U_18826),c_List_Olist_ONil(U_18818)))
    | sP1168(U_18822,U_18826,U_18820,U_18824) ),
    inference(clausify,[status(thm)],[f_4544_4]) ).

cnf(f_4544_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18819),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18819),U_18823),c_List_Olist_ONil(U_18819))) = hAPP(hAPP(c_List_Oappend(U_18819),U_18825),hAPP(hAPP(c_List_Olist_OCons(U_18819),U_18827),c_List_Olist_ONil(U_18819)))
    | U_18823 != U_18827
    | U_18821 != U_18825 ),
    inference(clausify,[status(thm)],[f_4544_4]) ).

cnf(f_4544_7,plain,
    ( U_18820 = U_18824
    | ~ sP1168(U_18822,U_18826,U_18820,U_18824) ),
    inference(clausify,[status(thm)],[f_4544_4]) ).

cnf(f_4544_8,plain,
    ( U_18822 = U_18826
    | ~ sP1168(U_18822,U_18826,U_18820,U_18824) ),
    inference(clausify,[status(thm)],[f_4544_4]) ).

fof(f_4545_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
        | ( ! [B_ys_H] :
              ( V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
              | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) != V_ys_2 )
          & ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) != V_zs_2
            | V_ys_2 != c_List_Olist_ONil(T_b) ) ) )
      & ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) != hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv]) ).

fof(f_4545_2,plain,
    ! [U_18834,U_18833,U_18832,U_18831,U_18830] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18830),U_18831),U_18832) = hAPP(hAPP(c_List_Oappend(U_18830),U_18833),U_18834)
        | ( ! [U_18829] :
              ( U_18832 != hAPP(hAPP(c_List_Oappend(U_18830),U_18829),U_18834)
              | hAPP(hAPP(c_List_Olist_OCons(U_18830),U_18831),U_18829) != U_18833 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_18830),U_18831),U_18832) != U_18834
            | U_18833 != c_List_Olist_ONil(U_18830) ) ) )
      & ( ? [U_18828] :
            ( U_18832 = hAPP(hAPP(c_List_Oappend(U_18830),U_18828),U_18834)
            & hAPP(hAPP(c_List_Olist_OCons(U_18830),U_18831),U_18828) = U_18833 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_18830),U_18831),U_18832) = U_18834
          & U_18833 = c_List_Olist_ONil(U_18830) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18830),U_18831),U_18832) != hAPP(hAPP(c_List_Oappend(U_18830),U_18833),U_18834) ) ),
    inference(variable_rename,[status(thm)],[f_4545_1]) ).

fof(f_4545_3,plain,
    ( ! [U_18844,U_18842,U_18840,U_18838,U_18836] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) = hAPP(hAPP(c_List_Oappend(U_18836),U_18842),U_18844)
        | ( ! [U_18829] :
              ( U_18840 != hAPP(hAPP(c_List_Oappend(U_18836),U_18829),U_18844)
              | hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18829) != U_18842 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) != U_18844
            | U_18842 != c_List_Olist_ONil(U_18836) ) ) )
    & ! [U_18843,U_18841,U_18839,U_18837,U_18835] :
        ( ? [U_18828] :
            ( U_18839 = hAPP(hAPP(c_List_Oappend(U_18835),U_18828),U_18843)
            & hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18828) = U_18841 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) = U_18843
          & U_18841 = c_List_Olist_ONil(U_18835) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) != hAPP(hAPP(c_List_Oappend(U_18835),U_18841),U_18843) ) ),
    inference(miniscope,[status(thm)],[f_4545_2]) ).

fof(f_4545_4,plain,
    ( ! [U_18844,U_18842,U_18840,U_18838,U_18836] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) = hAPP(hAPP(c_List_Oappend(U_18836),U_18842),U_18844)
        | ( ! [U_18829] :
              ( U_18840 != hAPP(hAPP(c_List_Oappend(U_18836),U_18829),U_18844)
              | hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18829) != U_18842 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) != U_18844
            | U_18842 != c_List_Olist_ONil(U_18836) ) ) )
    & ! [U_18843,U_18841,U_18839,U_18837,U_18835] :
        ( ( U_18839 = hAPP(hAPP(c_List_Oappend(U_18835),sK471(U_18843,U_18841,U_18839,U_18837,U_18835)),U_18843)
          & hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),sK471(U_18843,U_18841,U_18839,U_18837,U_18835)) = U_18841 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) = U_18843
          & U_18841 = c_List_Olist_ONil(U_18835) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) != hAPP(hAPP(c_List_Oappend(U_18835),U_18841),U_18843) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_18828,sK471(U_18843,U_18841,U_18839,U_18837,U_18835))],[f_4545_3]) ).

fof(f_4545_5,plain,
    ( ! [U_18829,U_18836,U_18844,U_18842,U_18838,U_18840] :
        ( U_18840 != hAPP(hAPP(c_List_Oappend(U_18836),U_18829),U_18844)
        | hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18829) != U_18842
        | ~ sP1171(U_18829,U_18836,U_18844,U_18842,U_18838,U_18840) )
    & ! [U_18829,U_18836,U_18844,U_18842,U_18838,U_18840] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) != U_18844
        | U_18842 != c_List_Olist_ONil(U_18836)
        | ~ sP1171(U_18829,U_18836,U_18844,U_18842,U_18838,U_18840) )
    & ! [U_18835,U_18837,U_18841,U_18839,U_18843] :
        ( U_18839 = hAPP(hAPP(c_List_Oappend(U_18835),sK471(U_18843,U_18841,U_18839,U_18837,U_18835)),U_18843)
        | ~ sP1170(U_18835,U_18837,U_18841,U_18839,U_18843) )
    & ! [U_18835,U_18837,U_18841,U_18839,U_18843] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),sK471(U_18843,U_18841,U_18839,U_18837,U_18835)) = U_18841
        | ~ sP1170(U_18835,U_18837,U_18841,U_18839,U_18843) )
    & ! [U_18835,U_18837,U_18841,U_18839,U_18843] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) = U_18843
        | ~ sP1169(U_18835,U_18837,U_18841,U_18839,U_18843) )
    & ! [U_18835,U_18837,U_18841,U_18839,U_18843] :
        ( U_18841 = c_List_Olist_ONil(U_18835)
        | ~ sP1169(U_18835,U_18837,U_18841,U_18839,U_18843) )
    & ! [U_18829,U_18836,U_18844,U_18842,U_18838,U_18840] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) = hAPP(hAPP(c_List_Oappend(U_18836),U_18842),U_18844)
        | sP1171(U_18829,U_18836,U_18844,U_18842,U_18838,U_18840) )
    & ! [U_18835,U_18837,U_18841,U_18839,U_18843] :
        ( sP1170(U_18835,U_18837,U_18841,U_18839,U_18843)
        | sP1169(U_18835,U_18837,U_18841,U_18839,U_18843)
        | hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) != hAPP(hAPP(c_List_Oappend(U_18835),U_18841),U_18843) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1169,sP1170,sP1171])],[f_4545_4]) ).

cnf(f_4545_6,plain,
    ( sP1170(U_18835,U_18837,U_18841,U_18839,U_18843)
    | sP1169(U_18835,U_18837,U_18841,U_18839,U_18843)
    | hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) != hAPP(hAPP(c_List_Oappend(U_18835),U_18841),U_18843) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_7,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) = hAPP(hAPP(c_List_Oappend(U_18836),U_18842),U_18844)
    | sP1171(U_18829,U_18836,U_18844,U_18842,U_18838,U_18840) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_8,plain,
    ( U_18841 = c_List_Olist_ONil(U_18835)
    | ~ sP1169(U_18835,U_18837,U_18841,U_18839,U_18843) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_9,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),U_18839) = U_18843
    | ~ sP1169(U_18835,U_18837,U_18841,U_18839,U_18843) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_10,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18835),U_18837),sK471(U_18843,U_18841,U_18839,U_18837,U_18835)) = U_18841
    | ~ sP1170(U_18835,U_18837,U_18841,U_18839,U_18843) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_11,plain,
    ( U_18839 = hAPP(hAPP(c_List_Oappend(U_18835),sK471(U_18843,U_18841,U_18839,U_18837,U_18835)),U_18843)
    | ~ sP1170(U_18835,U_18837,U_18841,U_18839,U_18843) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_12,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18840) != U_18844
    | U_18842 != c_List_Olist_ONil(U_18836)
    | ~ sP1171(U_18829,U_18836,U_18844,U_18842,U_18838,U_18840) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

cnf(f_4545_13,plain,
    ( U_18840 != hAPP(hAPP(c_List_Oappend(U_18836),U_18829),U_18844)
    | hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18829) != U_18842
    | ~ sP1171(U_18829,U_18836,U_18844,U_18842,U_18838,U_18840) ),
    inference(clausify,[status(thm)],[f_4545_5]) ).

fof(f_4546_1,plain,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | ( ! [B_ys_H] :
              ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) != V_xs_2
              | V_ys_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
          & ( V_zs_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
            | V_ys_2 != c_List_Olist_ONil(T_b) ) ) )
      & ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv]) ).

fof(f_4546_2,plain,
    ! [U_18851,U_18850,U_18849,U_18848,U_18847] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18847),U_18848),U_18849) = hAPP(hAPP(c_List_Olist_OCons(U_18847),U_18850),U_18851)
        | ( ! [U_18846] :
              ( hAPP(hAPP(c_List_Oappend(U_18847),U_18846),U_18849) != U_18851
              | U_18848 != hAPP(hAPP(c_List_Olist_OCons(U_18847),U_18850),U_18846) )
          & ( U_18849 != hAPP(hAPP(c_List_Olist_OCons(U_18847),U_18850),U_18851)
            | U_18848 != c_List_Olist_ONil(U_18847) ) ) )
      & ( ? [U_18845] :
            ( hAPP(hAPP(c_List_Oappend(U_18847),U_18845),U_18849) = U_18851
            & U_18848 = hAPP(hAPP(c_List_Olist_OCons(U_18847),U_18850),U_18845) )
        | ( U_18849 = hAPP(hAPP(c_List_Olist_OCons(U_18847),U_18850),U_18851)
          & U_18848 = c_List_Olist_ONil(U_18847) )
        | hAPP(hAPP(c_List_Oappend(U_18847),U_18848),U_18849) != hAPP(hAPP(c_List_Olist_OCons(U_18847),U_18850),U_18851) ) ),
    inference(variable_rename,[status(thm)],[f_4546_1]) ).

fof(f_4546_3,plain,
    ( ! [U_18861,U_18859,U_18857,U_18855,U_18853] :
        ( hAPP(hAPP(c_List_Oappend(U_18853),U_18855),U_18857) = hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
        | ( ! [U_18846] :
              ( hAPP(hAPP(c_List_Oappend(U_18853),U_18846),U_18857) != U_18861
              | U_18855 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18846) )
          & ( U_18857 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
            | U_18855 != c_List_Olist_ONil(U_18853) ) ) )
    & ! [U_18860,U_18858,U_18856,U_18854,U_18852] :
        ( ? [U_18845] :
            ( hAPP(hAPP(c_List_Oappend(U_18852),U_18845),U_18856) = U_18860
            & U_18854 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18845) )
        | ( U_18856 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860)
          & U_18854 = c_List_Olist_ONil(U_18852) )
        | hAPP(hAPP(c_List_Oappend(U_18852),U_18854),U_18856) != hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860) ) ),
    inference(miniscope,[status(thm)],[f_4546_2]) ).

fof(f_4546_4,plain,
    ( ! [U_18861,U_18859,U_18857,U_18855,U_18853] :
        ( hAPP(hAPP(c_List_Oappend(U_18853),U_18855),U_18857) = hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
        | ( ! [U_18846] :
              ( hAPP(hAPP(c_List_Oappend(U_18853),U_18846),U_18857) != U_18861
              | U_18855 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18846) )
          & ( U_18857 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
            | U_18855 != c_List_Olist_ONil(U_18853) ) ) )
    & ! [U_18860,U_18858,U_18856,U_18854,U_18852] :
        ( ( hAPP(hAPP(c_List_Oappend(U_18852),sK472(U_18860,U_18858,U_18856,U_18854,U_18852)),U_18856) = U_18860
          & U_18854 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),sK472(U_18860,U_18858,U_18856,U_18854,U_18852)) )
        | ( U_18856 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860)
          & U_18854 = c_List_Olist_ONil(U_18852) )
        | hAPP(hAPP(c_List_Oappend(U_18852),U_18854),U_18856) != hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_18845,sK472(U_18860,U_18858,U_18856,U_18854,U_18852))],[f_4546_3]) ).

fof(f_4546_5,plain,
    ( ! [U_18855,U_18846,U_18861,U_18857,U_18859,U_18853] :
        ( hAPP(hAPP(c_List_Oappend(U_18853),U_18846),U_18857) != U_18861
        | U_18855 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18846)
        | ~ sP1174(U_18855,U_18846,U_18861,U_18857,U_18859,U_18853) )
    & ! [U_18855,U_18846,U_18861,U_18857,U_18859,U_18853] :
        ( U_18857 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
        | U_18855 != c_List_Olist_ONil(U_18853)
        | ~ sP1174(U_18855,U_18846,U_18861,U_18857,U_18859,U_18853) )
    & ! [U_18854,U_18858,U_18852,U_18856,U_18860] :
        ( hAPP(hAPP(c_List_Oappend(U_18852),sK472(U_18860,U_18858,U_18856,U_18854,U_18852)),U_18856) = U_18860
        | ~ sP1173(U_18854,U_18858,U_18852,U_18856,U_18860) )
    & ! [U_18854,U_18858,U_18852,U_18856,U_18860] :
        ( U_18854 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),sK472(U_18860,U_18858,U_18856,U_18854,U_18852))
        | ~ sP1173(U_18854,U_18858,U_18852,U_18856,U_18860) )
    & ! [U_18854,U_18858,U_18852,U_18856,U_18860] :
        ( U_18856 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860)
        | ~ sP1172(U_18854,U_18858,U_18852,U_18856,U_18860) )
    & ! [U_18854,U_18858,U_18852,U_18856,U_18860] :
        ( U_18854 = c_List_Olist_ONil(U_18852)
        | ~ sP1172(U_18854,U_18858,U_18852,U_18856,U_18860) )
    & ! [U_18855,U_18846,U_18861,U_18857,U_18859,U_18853] :
        ( hAPP(hAPP(c_List_Oappend(U_18853),U_18855),U_18857) = hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
        | sP1174(U_18855,U_18846,U_18861,U_18857,U_18859,U_18853) )
    & ! [U_18854,U_18858,U_18852,U_18856,U_18860] :
        ( sP1173(U_18854,U_18858,U_18852,U_18856,U_18860)
        | sP1172(U_18854,U_18858,U_18852,U_18856,U_18860)
        | hAPP(hAPP(c_List_Oappend(U_18852),U_18854),U_18856) != hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1172,sP1173,sP1174])],[f_4546_4]) ).

cnf(f_4546_6,plain,
    ( sP1173(U_18854,U_18858,U_18852,U_18856,U_18860)
    | sP1172(U_18854,U_18858,U_18852,U_18856,U_18860)
    | hAPP(hAPP(c_List_Oappend(U_18852),U_18854),U_18856) != hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18853),U_18855),U_18857) = hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
    | sP1174(U_18855,U_18846,U_18861,U_18857,U_18859,U_18853) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_8,plain,
    ( U_18854 = c_List_Olist_ONil(U_18852)
    | ~ sP1172(U_18854,U_18858,U_18852,U_18856,U_18860) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_9,plain,
    ( U_18856 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),U_18860)
    | ~ sP1172(U_18854,U_18858,U_18852,U_18856,U_18860) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_10,plain,
    ( U_18854 = hAPP(hAPP(c_List_Olist_OCons(U_18852),U_18858),sK472(U_18860,U_18858,U_18856,U_18854,U_18852))
    | ~ sP1173(U_18854,U_18858,U_18852,U_18856,U_18860) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18852),sK472(U_18860,U_18858,U_18856,U_18854,U_18852)),U_18856) = U_18860
    | ~ sP1173(U_18854,U_18858,U_18852,U_18856,U_18860) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_12,plain,
    ( U_18857 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18861)
    | U_18855 != c_List_Olist_ONil(U_18853)
    | ~ sP1174(U_18855,U_18846,U_18861,U_18857,U_18859,U_18853) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

cnf(f_4546_13,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18853),U_18846),U_18857) != U_18861
    | U_18855 != hAPP(hAPP(c_List_Olist_OCons(U_18853),U_18859),U_18846)
    | ~ sP1174(U_18855,U_18846,U_18861,U_18857,U_18859,U_18853) ),
    inference(clausify,[status(thm)],[f_4546_5]) ).

fof(f_4547_1,plain,
    ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop]) ).

fof(f_4547_2,plain,
    ! [U_18867,U_18866,U_18865,U_18864,U_18863,U_18862] :
      ( c_Map_Omap__upds(U_18862,U_18864,U_18866,hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18867),U_18865) = c_Map_Omap__upds(U_18862,U_18864,U_18866,U_18863,U_18865)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18862)),U_18863) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18864)),U_18865) ),
    inference(variable_rename,[status(thm)],[f_4547_1]) ).

fof(f_4547_3,plain,
    ! [U_18865,U_18866,U_18864,U_18867,U_18863,U_18862] :
      ( c_Map_Omap__upds(U_18862,U_18864,U_18866,hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18867),U_18865) = c_Map_Omap__upds(U_18862,U_18864,U_18866,U_18863,U_18865)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18862)),U_18863) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18864)),U_18865) ),
    inference(definitional_conversion,[status(esa)],[f_4547_2]) ).

cnf(f_4547_4,plain,
    ( c_Map_Omap__upds(U_18862,U_18864,U_18866,hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18867),U_18865) = c_Map_Omap__upds(U_18862,U_18864,U_18866,U_18863,U_18865)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18862)),U_18863) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18864)),U_18865) ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

fof(f_4548_1,plain,
    ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upds__append2__drop]) ).

fof(f_4548_2,plain,
    ! [U_18873,U_18872,U_18871,U_18870,U_18869,U_18868] :
      ( c_Map_Omap__upds(U_18868,U_18870,U_18872,U_18869,hAPP(hAPP(c_List_Oappend(U_18870),U_18871),U_18873)) = c_Map_Omap__upds(U_18868,U_18870,U_18872,U_18869,U_18871)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18868)),U_18869) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18870)),U_18871) ),
    inference(variable_rename,[status(thm)],[f_4548_1]) ).

fof(f_4548_3,plain,
    ! [U_18869,U_18868,U_18870,U_18871,U_18872,U_18873] :
      ( c_Map_Omap__upds(U_18868,U_18870,U_18872,U_18869,hAPP(hAPP(c_List_Oappend(U_18870),U_18871),U_18873)) = c_Map_Omap__upds(U_18868,U_18870,U_18872,U_18869,U_18871)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18868)),U_18869) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18870)),U_18871) ),
    inference(definitional_conversion,[status(esa)],[f_4548_2]) ).

cnf(f_4548_4,plain,
    ( c_Map_Omap__upds(U_18868,U_18870,U_18872,U_18869,hAPP(hAPP(c_List_Oappend(U_18870),U_18871),U_18873)) = c_Map_Omap__upds(U_18868,U_18870,U_18872,U_18869,U_18871)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18868)),U_18869) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18870)),U_18871) ),
    inference(clausify,[status(thm)],[f_4548_3]) ).

fof(f_4549_1,plain,
    ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_list__update__length]) ).

fof(f_4549_2,plain,
    ! [U_18878,U_18877,U_18876,U_18875,U_18874] : hAPP(hAPP(c_List_Olist__update(U_18874,hAPP(hAPP(c_List_Oappend(U_18874),U_18875),hAPP(hAPP(c_List_Olist_OCons(U_18874),U_18876),U_18877))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18874)),U_18875)),U_18878) = hAPP(hAPP(c_List_Oappend(U_18874),U_18875),hAPP(hAPP(c_List_Olist_OCons(U_18874),U_18878),U_18877)),
    inference(variable_rename,[status(thm)],[f_4549_1]) ).

fof(f_4549_3,plain,
    ! [U_18874,U_18875,U_18876,U_18877,U_18878] : hAPP(hAPP(c_List_Olist__update(U_18874,hAPP(hAPP(c_List_Oappend(U_18874),U_18875),hAPP(hAPP(c_List_Olist_OCons(U_18874),U_18876),U_18877))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18874)),U_18875)),U_18878) = hAPP(hAPP(c_List_Oappend(U_18874),U_18875),hAPP(hAPP(c_List_Olist_OCons(U_18874),U_18878),U_18877)),
    inference(definitional_conversion,[status(esa)],[f_4549_2]) ).

cnf(f_4549_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18874,hAPP(hAPP(c_List_Oappend(U_18874),U_18875),hAPP(hAPP(c_List_Olist_OCons(U_18874),U_18876),U_18877))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18874)),U_18875)),U_18878) = hAPP(hAPP(c_List_Oappend(U_18874),U_18875),hAPP(hAPP(c_List_Olist_OCons(U_18874),U_18878),U_18877)),
    inference(clausify,[status(thm)],[f_4549_3]) ).

fof(f_4550_1,plain,
    ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_nth__append__length]) ).

fof(f_4550_2,plain,
    ! [U_18882,U_18881,U_18880,U_18879] : hAPP(hAPP(c_List_Onth(U_18879),hAPP(hAPP(c_List_Oappend(U_18879),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18879),U_18881),U_18882))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18879)),U_18880)) = U_18881,
    inference(variable_rename,[status(thm)],[f_4550_1]) ).

fof(f_4550_3,plain,
    ! [U_18879,U_18880,U_18881,U_18882] : hAPP(hAPP(c_List_Onth(U_18879),hAPP(hAPP(c_List_Oappend(U_18879),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18879),U_18881),U_18882))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18879)),U_18880)) = U_18881,
    inference(definitional_conversion,[status(esa)],[f_4550_2]) ).

cnf(f_4550_4,plain,
    hAPP(hAPP(c_List_Onth(U_18879),hAPP(hAPP(c_List_Oappend(U_18879),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18879),U_18881),U_18882))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18879)),U_18880)) = U_18881,
    inference(clausify,[status(thm)],[f_4550_3]) ).

fof(f_4551_1,plain,
    ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)
      | V_xs != hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
      | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) != V_ys ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI]) ).

fof(f_4551_2,plain,
    ! [U_18888,U_18887,U_18886,U_18885,U_18884,U_18883] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_18883),U_18884),U_18887) = hAPP(hAPP(c_List_Oappend(U_18883),U_18886),U_18888)
      | U_18887 != hAPP(hAPP(c_List_Oappend(U_18883),U_18885),U_18888)
      | hAPP(hAPP(c_List_Olist_OCons(U_18883),U_18884),U_18885) != U_18886 ),
    inference(variable_rename,[status(thm)],[f_4551_1]) ).

fof(f_4551_3,plain,
    ! [U_18883,U_18884,U_18885,U_18886,U_18887,U_18888] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_18883),U_18884),U_18887) = hAPP(hAPP(c_List_Oappend(U_18883),U_18886),U_18888)
      | U_18887 != hAPP(hAPP(c_List_Oappend(U_18883),U_18885),U_18888)
      | hAPP(hAPP(c_List_Olist_OCons(U_18883),U_18884),U_18885) != U_18886 ),
    inference(definitional_conversion,[status(esa)],[f_4551_2]) ).

cnf(f_4551_4,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18883),U_18884),U_18887) = hAPP(hAPP(c_List_Oappend(U_18883),U_18886),U_18888)
    | U_18887 != hAPP(hAPP(c_List_Oappend(U_18883),U_18885),U_18888)
    | hAPP(hAPP(c_List_Olist_OCons(U_18883),U_18884),U_18885) != U_18886 ),
    inference(clausify,[status(thm)],[f_4551_3]) ).

fof(f_4552_1,plain,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_append__Cons]) ).

fof(f_4552_2,plain,
    ! [U_18892,U_18891,U_18890,U_18889] : hAPP(hAPP(c_List_Oappend(U_18889),hAPP(hAPP(c_List_Olist_OCons(U_18889),U_18890),U_18891)),U_18892) = hAPP(hAPP(c_List_Olist_OCons(U_18889),U_18890),hAPP(hAPP(c_List_Oappend(U_18889),U_18891),U_18892)),
    inference(variable_rename,[status(thm)],[f_4552_1]) ).

fof(f_4552_3,plain,
    ! [U_18889,U_18890,U_18891,U_18892] : hAPP(hAPP(c_List_Oappend(U_18889),hAPP(hAPP(c_List_Olist_OCons(U_18889),U_18890),U_18891)),U_18892) = hAPP(hAPP(c_List_Olist_OCons(U_18889),U_18890),hAPP(hAPP(c_List_Oappend(U_18889),U_18891),U_18892)),
    inference(definitional_conversion,[status(esa)],[f_4552_2]) ).

cnf(f_4552_4,plain,
    hAPP(hAPP(c_List_Oappend(U_18889),hAPP(hAPP(c_List_Olist_OCons(U_18889),U_18890),U_18891)),U_18892) = hAPP(hAPP(c_List_Olist_OCons(U_18889),U_18890),hAPP(hAPP(c_List_Oappend(U_18889),U_18891),U_18892)),
    inference(clausify,[status(thm)],[f_4552_3]) ).

fof(f_4553_1,plain,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_take__append]) ).

fof(f_4553_2,plain,
    ! [U_18896,U_18895,U_18894,U_18893] : hAPP(hAPP(c_List_Otake(U_18893),U_18894),hAPP(hAPP(c_List_Oappend(U_18893),U_18895),U_18896)) = hAPP(hAPP(c_List_Oappend(U_18893),hAPP(hAPP(c_List_Otake(U_18893),U_18894),U_18895)),hAPP(hAPP(c_List_Otake(U_18893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18894),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18893)),U_18895))),U_18896)),
    inference(variable_rename,[status(thm)],[f_4553_1]) ).

fof(f_4553_3,plain,
    ! [U_18893,U_18894,U_18895,U_18896] : hAPP(hAPP(c_List_Otake(U_18893),U_18894),hAPP(hAPP(c_List_Oappend(U_18893),U_18895),U_18896)) = hAPP(hAPP(c_List_Oappend(U_18893),hAPP(hAPP(c_List_Otake(U_18893),U_18894),U_18895)),hAPP(hAPP(c_List_Otake(U_18893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18894),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18893)),U_18895))),U_18896)),
    inference(definitional_conversion,[status(esa)],[f_4553_2]) ).

cnf(f_4553_4,plain,
    hAPP(hAPP(c_List_Otake(U_18893),U_18894),hAPP(hAPP(c_List_Oappend(U_18893),U_18895),U_18896)) = hAPP(hAPP(c_List_Oappend(U_18893),hAPP(hAPP(c_List_Otake(U_18893),U_18894),U_18895)),hAPP(hAPP(c_List_Otake(U_18893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18894),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18893)),U_18895))),U_18896)),
    inference(clausify,[status(thm)],[f_4553_3]) ).

fof(f_4554_1,plain,
    ! [V_x,V_ys,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__append1]) ).

fof(f_4554_2,plain,
    ! [U_18901,U_18900,U_18899,U_18898,U_18897] :
      ( hAPP(hAPP(c_List_Olist__update(U_18898,hAPP(hAPP(c_List_Oappend(U_18898),U_18899),U_18900)),U_18897),U_18901) = hAPP(hAPP(c_List_Oappend(U_18898),hAPP(hAPP(c_List_Olist__update(U_18898,U_18899),U_18897),U_18901)),U_18900)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18897),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18898)),U_18899))) ),
    inference(variable_rename,[status(thm)],[f_4554_1]) ).

fof(f_4554_3,plain,
    ! [U_18897,U_18898,U_18899,U_18900,U_18901] :
      ( hAPP(hAPP(c_List_Olist__update(U_18898,hAPP(hAPP(c_List_Oappend(U_18898),U_18899),U_18900)),U_18897),U_18901) = hAPP(hAPP(c_List_Oappend(U_18898),hAPP(hAPP(c_List_Olist__update(U_18898,U_18899),U_18897),U_18901)),U_18900)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18897),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18898)),U_18899))) ),
    inference(definitional_conversion,[status(esa)],[f_4554_2]) ).

cnf(f_4554_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18898,hAPP(hAPP(c_List_Oappend(U_18898),U_18899),U_18900)),U_18897),U_18901) = hAPP(hAPP(c_List_Oappend(U_18898),hAPP(hAPP(c_List_Olist__update(U_18898,U_18899),U_18897),U_18901)),U_18900)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18897),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18898)),U_18899))) ),
    inference(clausify,[status(thm)],[f_4554_3]) ).

fof(f_4555_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__append]) ).

fof(f_4555_2,plain,
    ! [U_18905,U_18904,U_18903,U_18902] :
      ( ( c_List_Oremove1(U_18902,U_18903,hAPP(hAPP(c_List_Oappend(U_18902),U_18904),U_18905)) = hAPP(hAPP(c_List_Oappend(U_18902),U_18904),c_List_Oremove1(U_18902,U_18903,U_18905))
        | hBOOL(hAPP(hAPP(c_member(U_18902),U_18903),hAPP(c_List_Oset(U_18902),U_18904))) )
      & ( c_List_Oremove1(U_18902,U_18903,hAPP(hAPP(c_List_Oappend(U_18902),U_18904),U_18905)) = hAPP(hAPP(c_List_Oappend(U_18902),c_List_Oremove1(U_18902,U_18903,U_18904)),U_18905)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18902),U_18903),hAPP(c_List_Oset(U_18902),U_18904))) ) ),
    inference(variable_rename,[status(thm)],[f_4555_1]) ).

fof(f_4555_3,plain,
    ( ! [U_18913,U_18911,U_18909,U_18907] :
        ( c_List_Oremove1(U_18907,U_18909,hAPP(hAPP(c_List_Oappend(U_18907),U_18911),U_18913)) = hAPP(hAPP(c_List_Oappend(U_18907),U_18911),c_List_Oremove1(U_18907,U_18909,U_18913))
        | hBOOL(hAPP(hAPP(c_member(U_18907),U_18909),hAPP(c_List_Oset(U_18907),U_18911))) )
    & ! [U_18912,U_18910,U_18908,U_18906] :
        ( c_List_Oremove1(U_18906,U_18908,hAPP(hAPP(c_List_Oappend(U_18906),U_18910),U_18912)) = hAPP(hAPP(c_List_Oappend(U_18906),c_List_Oremove1(U_18906,U_18908,U_18910)),U_18912)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18906),U_18908),hAPP(c_List_Oset(U_18906),U_18910))) ) ),
    inference(miniscope,[status(thm)],[f_4555_2]) ).

fof(f_4555_4,plain,
    ( ! [U_18913,U_18907,U_18909,U_18911] :
        ( c_List_Oremove1(U_18907,U_18909,hAPP(hAPP(c_List_Oappend(U_18907),U_18911),U_18913)) = hAPP(hAPP(c_List_Oappend(U_18907),U_18911),c_List_Oremove1(U_18907,U_18909,U_18913))
        | hBOOL(hAPP(hAPP(c_member(U_18907),U_18909),hAPP(c_List_Oset(U_18907),U_18911))) )
    & ! [U_18908,U_18912,U_18910,U_18906] :
        ( c_List_Oremove1(U_18906,U_18908,hAPP(hAPP(c_List_Oappend(U_18906),U_18910),U_18912)) = hAPP(hAPP(c_List_Oappend(U_18906),c_List_Oremove1(U_18906,U_18908,U_18910)),U_18912)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18906),U_18908),hAPP(c_List_Oset(U_18906),U_18910))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4555_3]) ).

cnf(f_4555_5,plain,
    ( c_List_Oremove1(U_18906,U_18908,hAPP(hAPP(c_List_Oappend(U_18906),U_18910),U_18912)) = hAPP(hAPP(c_List_Oappend(U_18906),c_List_Oremove1(U_18906,U_18908,U_18910)),U_18912)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18906),U_18908),hAPP(c_List_Oset(U_18906),U_18910))) ),
    inference(clausify,[status(thm)],[f_4555_4]) ).

cnf(f_4555_6,plain,
    ( c_List_Oremove1(U_18907,U_18909,hAPP(hAPP(c_List_Oappend(U_18907),U_18911),U_18913)) = hAPP(hAPP(c_List_Oappend(U_18907),U_18911),c_List_Oremove1(U_18907,U_18909,U_18913))
    | hBOOL(hAPP(hAPP(c_member(U_18907),U_18909),hAPP(c_List_Oset(U_18907),U_18911))) ),
    inference(clausify,[status(thm)],[f_4555_4]) ).

fof(f_4556_1,plain,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_length__append]) ).

fof(f_4556_2,plain,
    ! [U_18916,U_18915,U_18914] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),hAPP(hAPP(c_List_Oappend(U_18914),U_18915),U_18916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),U_18915)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),U_18916)),
    inference(variable_rename,[status(thm)],[f_4556_1]) ).

fof(f_4556_3,plain,
    ! [U_18914,U_18915,U_18916] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),hAPP(hAPP(c_List_Oappend(U_18914),U_18915),U_18916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),U_18915)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),U_18916)),
    inference(definitional_conversion,[status(esa)],[f_4556_2]) ).

cnf(f_4556_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),hAPP(hAPP(c_List_Oappend(U_18914),U_18915),U_18916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),U_18915)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18914)),U_18916)),
    inference(clausify,[status(thm)],[f_4556_3]) ).

fof(f_4557_1,plain,
    ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) ),
    inference(fof_nnf,[status(thm)],[fact_zip__append]) ).

fof(f_4557_2,plain,
    ! [U_18922,U_18921,U_18920,U_18919,U_18918,U_18917] :
      ( hAPP(hAPP(c_List_Ozip(U_18917,U_18919),hAPP(hAPP(c_List_Oappend(U_18917),U_18918),U_18921)),hAPP(hAPP(c_List_Oappend(U_18919),U_18920),U_18922)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18917,U_18919)),hAPP(hAPP(c_List_Ozip(U_18917,U_18919),U_18918),U_18920)),hAPP(hAPP(c_List_Ozip(U_18917,U_18919),U_18921),U_18922))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18921) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18922)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18918) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18920) ),
    inference(variable_rename,[status(thm)],[f_4557_1]) ).

fof(f_4557_3,plain,
    ! [U_18917,U_18918,U_18919,U_18920,U_18921,U_18922] :
      ( hAPP(hAPP(c_List_Ozip(U_18917,U_18919),hAPP(hAPP(c_List_Oappend(U_18917),U_18918),U_18921)),hAPP(hAPP(c_List_Oappend(U_18919),U_18920),U_18922)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18917,U_18919)),hAPP(hAPP(c_List_Ozip(U_18917,U_18919),U_18918),U_18920)),hAPP(hAPP(c_List_Ozip(U_18917,U_18919),U_18921),U_18922))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18921) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18922)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18918) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18920) ),
    inference(definitional_conversion,[status(esa)],[f_4557_2]) ).

cnf(f_4557_4,plain,
    ( hAPP(hAPP(c_List_Ozip(U_18917,U_18919),hAPP(hAPP(c_List_Oappend(U_18917),U_18918),U_18921)),hAPP(hAPP(c_List_Oappend(U_18919),U_18920),U_18922)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18917,U_18919)),hAPP(hAPP(c_List_Ozip(U_18917,U_18919),U_18918),U_18920)),hAPP(hAPP(c_List_Ozip(U_18917,U_18919),U_18921),U_18922))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18921) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18922)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18918) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18920) ),
    inference(clausify,[status(thm)],[f_4557_3]) ).

fof(f_4558_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__append]) ).

fof(f_4558_2,plain,
    ! [U_18927,U_18926,U_18925,U_18924,U_18923] : hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),hAPP(hAPP(c_List_Oappend(U_18923),U_18926),U_18927)) = hAPP(hAPP(c_List_Oappend(U_18924),hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),U_18926)),hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),U_18927)),
    inference(variable_rename,[status(thm)],[f_4558_1]) ).

fof(f_4558_3,plain,
    ! [U_18924,U_18923,U_18925,U_18926,U_18927] : hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),hAPP(hAPP(c_List_Oappend(U_18923),U_18926),U_18927)) = hAPP(hAPP(c_List_Oappend(U_18924),hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),U_18926)),hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),U_18927)),
    inference(definitional_conversion,[status(esa)],[f_4558_2]) ).

cnf(f_4558_4,plain,
    hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),hAPP(hAPP(c_List_Oappend(U_18923),U_18926),U_18927)) = hAPP(hAPP(c_List_Oappend(U_18924),hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),U_18926)),hAPP(hAPP(c_List_Omap(U_18923,U_18924),U_18925),U_18927)),
    inference(clausify,[status(thm)],[f_4558_3]) ).

fof(f_4559_1,plain,
    ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n),
    inference(fof_nnf,[status(thm)],[fact_nth__append__length__plus]) ).

fof(f_4559_2,plain,
    ! [U_18931,U_18930,U_18929,U_18928] : hAPP(hAPP(c_List_Onth(U_18928),hAPP(hAPP(c_List_Oappend(U_18928),U_18929),U_18930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18928)),U_18929)),U_18931)) = hAPP(hAPP(c_List_Onth(U_18928),U_18930),U_18931),
    inference(variable_rename,[status(thm)],[f_4559_1]) ).

fof(f_4559_3,plain,
    ! [U_18928,U_18929,U_18930,U_18931] : hAPP(hAPP(c_List_Onth(U_18928),hAPP(hAPP(c_List_Oappend(U_18928),U_18929),U_18930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18928)),U_18929)),U_18931)) = hAPP(hAPP(c_List_Onth(U_18928),U_18930),U_18931),
    inference(definitional_conversion,[status(esa)],[f_4559_2]) ).

cnf(f_4559_4,plain,
    hAPP(hAPP(c_List_Onth(U_18928),hAPP(hAPP(c_List_Oappend(U_18928),U_18929),U_18930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18928)),U_18929)),U_18931)) = hAPP(hAPP(c_List_Onth(U_18928),U_18930),U_18931),
    inference(clausify,[status(thm)],[f_4559_3]) ).

fof(f_4560_1,plain,
    ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr__append]) ).

fof(f_4560_2,plain,
    ! [U_18937,U_18936,U_18935,U_18934,U_18933,U_18932] : c_List_Ofoldr(U_18932,U_18933,U_18934,hAPP(hAPP(c_List_Oappend(U_18932),U_18935),U_18936),U_18937) = c_List_Ofoldr(U_18932,U_18933,U_18934,U_18935,c_List_Ofoldr(U_18932,U_18933,U_18934,U_18936,U_18937)),
    inference(variable_rename,[status(thm)],[f_4560_1]) ).

fof(f_4560_3,plain,
    ! [U_18932,U_18933,U_18934,U_18935,U_18936,U_18937] : c_List_Ofoldr(U_18932,U_18933,U_18934,hAPP(hAPP(c_List_Oappend(U_18932),U_18935),U_18936),U_18937) = c_List_Ofoldr(U_18932,U_18933,U_18934,U_18935,c_List_Ofoldr(U_18932,U_18933,U_18934,U_18936,U_18937)),
    inference(definitional_conversion,[status(esa)],[f_4560_2]) ).

cnf(f_4560_4,plain,
    c_List_Ofoldr(U_18932,U_18933,U_18934,hAPP(hAPP(c_List_Oappend(U_18932),U_18935),U_18936),U_18937) = c_List_Ofoldr(U_18932,U_18933,U_18934,U_18935,c_List_Ofoldr(U_18932,U_18933,U_18934,U_18936,U_18937)),
    inference(clausify,[status(thm)],[f_4560_3]) ).

fof(f_4561_1,plain,
    ! [V_ys_2,V_xs_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_ys_2),c_Map_Omap__of(T_b,T_c,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__of__append]) ).

fof(f_4561_2,plain,
    ! [U_18941,U_18940,U_18939,U_18938] : c_Map_Omap__of(U_18938,U_18939,hAPP(hAPP(c_List_Oappend(tc_prod(U_18938,U_18939)),U_18940),U_18941)) = c_Map_Omap__add(U_18938,U_18939,c_Map_Omap__of(U_18938,U_18939,U_18941),c_Map_Omap__of(U_18938,U_18939,U_18940)),
    inference(variable_rename,[status(thm)],[f_4561_1]) ).

fof(f_4561_3,plain,
    ! [U_18939,U_18938,U_18940,U_18941] : c_Map_Omap__of(U_18938,U_18939,hAPP(hAPP(c_List_Oappend(tc_prod(U_18938,U_18939)),U_18940),U_18941)) = c_Map_Omap__add(U_18938,U_18939,c_Map_Omap__of(U_18938,U_18939,U_18941),c_Map_Omap__of(U_18938,U_18939,U_18940)),
    inference(definitional_conversion,[status(esa)],[f_4561_2]) ).

cnf(f_4561_4,plain,
    c_Map_Omap__of(U_18938,U_18939,hAPP(hAPP(c_List_Oappend(tc_prod(U_18938,U_18939)),U_18940),U_18941)) = c_Map_Omap__add(U_18938,U_18939,c_Map_Omap__of(U_18938,U_18939,U_18941),c_Map_Omap__of(U_18938,U_18939,U_18940)),
    inference(clausify,[status(thm)],[f_4561_3]) ).

fof(f_4562_1,plain,
    ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)),
    inference(fof_nnf,[status(thm)],[fact_append__assoc]) ).

fof(f_4562_2,plain,
    ! [U_18945,U_18944,U_18943,U_18942] : hAPP(hAPP(c_List_Oappend(U_18942),hAPP(hAPP(c_List_Oappend(U_18942),U_18943),U_18944)),U_18945) = hAPP(hAPP(c_List_Oappend(U_18942),U_18943),hAPP(hAPP(c_List_Oappend(U_18942),U_18944),U_18945)),
    inference(variable_rename,[status(thm)],[f_4562_1]) ).

fof(f_4562_3,plain,
    ! [U_18942,U_18943,U_18944,U_18945] : hAPP(hAPP(c_List_Oappend(U_18942),hAPP(hAPP(c_List_Oappend(U_18942),U_18943),U_18944)),U_18945) = hAPP(hAPP(c_List_Oappend(U_18942),U_18943),hAPP(hAPP(c_List_Oappend(U_18942),U_18944),U_18945)),
    inference(definitional_conversion,[status(esa)],[f_4562_2]) ).

cnf(f_4562_4,plain,
    hAPP(hAPP(c_List_Oappend(U_18942),hAPP(hAPP(c_List_Oappend(U_18942),U_18943),U_18944)),U_18945) = hAPP(hAPP(c_List_Oappend(U_18942),U_18943),hAPP(hAPP(c_List_Oappend(U_18942),U_18944),U_18945)),
    inference(clausify,[status(thm)],[f_4562_3]) ).

fof(f_4563_1,plain,
    ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
        | ! [B_us] :
            ( ( V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
              | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) != V_zs_2 )
            & ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) != V_tsa_2
              | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) )
      & ( ? [B_us] :
            ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
              & hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
            | ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
              & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2]) ).

fof(f_4563_2,plain,
    ! [U_18952,U_18951,U_18950,U_18949,U_18948] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18948),U_18949),U_18950) = hAPP(hAPP(c_List_Oappend(U_18948),U_18951),U_18952)
        | ! [U_18947] :
            ( ( U_18950 != hAPP(hAPP(c_List_Oappend(U_18948),U_18947),U_18952)
              | hAPP(hAPP(c_List_Oappend(U_18948),U_18949),U_18947) != U_18951 )
            & ( hAPP(hAPP(c_List_Oappend(U_18948),U_18947),U_18950) != U_18952
              | U_18949 != hAPP(hAPP(c_List_Oappend(U_18948),U_18951),U_18947) ) ) )
      & ( ? [U_18946] :
            ( ( U_18950 = hAPP(hAPP(c_List_Oappend(U_18948),U_18946),U_18952)
              & hAPP(hAPP(c_List_Oappend(U_18948),U_18949),U_18946) = U_18951 )
            | ( hAPP(hAPP(c_List_Oappend(U_18948),U_18946),U_18950) = U_18952
              & U_18949 = hAPP(hAPP(c_List_Oappend(U_18948),U_18951),U_18946) ) )
        | hAPP(hAPP(c_List_Oappend(U_18948),U_18949),U_18950) != hAPP(hAPP(c_List_Oappend(U_18948),U_18951),U_18952) ) ),
    inference(variable_rename,[status(thm)],[f_4563_1]) ).

fof(f_4563_3,plain,
    ( ! [U_18966,U_18964,U_18962,U_18960,U_18958] :
        ( hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18962) = hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18966)
        | ( ! [U_18956] :
              ( U_18962 != hAPP(hAPP(c_List_Oappend(U_18958),U_18956),U_18966)
              | hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18956) != U_18964 )
          & ! [U_18955] :
              ( hAPP(hAPP(c_List_Oappend(U_18958),U_18955),U_18962) != U_18966
              | U_18960 != hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18955) ) ) )
    & ! [U_18965,U_18963,U_18961,U_18959,U_18957] :
        ( ? [U_18954] :
            ( U_18961 = hAPP(hAPP(c_List_Oappend(U_18957),U_18954),U_18965)
            & hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18954) = U_18963 )
        | ? [U_18953] :
            ( hAPP(hAPP(c_List_Oappend(U_18957),U_18953),U_18961) = U_18965
            & U_18959 = hAPP(hAPP(c_List_Oappend(U_18957),U_18963),U_18953) )
        | hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18961) != hAPP(hAPP(c_List_Oappend(U_18957),U_18963),U_18965) ) ),
    inference(miniscope,[status(thm)],[f_4563_2]) ).

fof(f_4563_4,plain,
    ( ! [U_18966,U_18964,U_18962,U_18960,U_18958] :
        ( hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18962) = hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18966)
        | ( ! [U_18956] :
              ( U_18962 != hAPP(hAPP(c_List_Oappend(U_18958),U_18956),U_18966)
              | hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18956) != U_18964 )
          & ! [U_18955] :
              ( hAPP(hAPP(c_List_Oappend(U_18958),U_18955),U_18962) != U_18966
              | U_18960 != hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18955) ) ) )
    & ! [U_18965,U_18963,U_18961,U_18959,U_18957] :
        ( ? [U_18954] :
            ( U_18961 = hAPP(hAPP(c_List_Oappend(U_18957),U_18954),U_18965)
            & hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18954) = U_18963 )
        | ( hAPP(hAPP(c_List_Oappend(U_18957),sK473(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18961) = U_18965
          & U_18959 = hAPP(hAPP(c_List_Oappend(U_18957),U_18963),sK473(U_18965,U_18963,U_18961,U_18959,U_18957)) )
        | hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18961) != hAPP(hAPP(c_List_Oappend(U_18957),U_18963),U_18965) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_18953,sK473(U_18965,U_18963,U_18961,U_18959,U_18957))],[f_4563_3]) ).

fof(f_4563_5,plain,
    ( ! [U_18966,U_18964,U_18962,U_18960,U_18958] :
        ( hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18962) = hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18966)
        | ( ! [U_18956] :
              ( U_18962 != hAPP(hAPP(c_List_Oappend(U_18958),U_18956),U_18966)
              | hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18956) != U_18964 )
          & ! [U_18955] :
              ( hAPP(hAPP(c_List_Oappend(U_18958),U_18955),U_18962) != U_18966
              | U_18960 != hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18955) ) ) )
    & ! [U_18965,U_18963,U_18961,U_18959,U_18957] :
        ( ( U_18961 = hAPP(hAPP(c_List_Oappend(U_18957),sK474(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18965)
          & hAPP(hAPP(c_List_Oappend(U_18957),U_18959),sK474(U_18965,U_18963,U_18961,U_18959,U_18957)) = U_18963 )
        | ( hAPP(hAPP(c_List_Oappend(U_18957),sK473(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18961) = U_18965
          & U_18959 = hAPP(hAPP(c_List_Oappend(U_18957),U_18963),sK473(U_18965,U_18963,U_18961,U_18959,U_18957)) )
        | hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18961) != hAPP(hAPP(c_List_Oappend(U_18957),U_18963),U_18965) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_18954,sK474(U_18965,U_18963,U_18961,U_18959,U_18957))],[f_4563_4]) ).

fof(f_4563_6,plain,
    ( ! [U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966] :
        ( U_18962 != hAPP(hAPP(c_List_Oappend(U_18958),U_18956),U_18966)
        | hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18956) != U_18964
        | ~ sP1177(U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966) )
    & ! [U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966] :
        ( hAPP(hAPP(c_List_Oappend(U_18958),U_18955),U_18962) != U_18966
        | U_18960 != hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18955)
        | ~ sP1177(U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966) )
    & ! [U_18965,U_18961,U_18959,U_18957,U_18963] :
        ( U_18961 = hAPP(hAPP(c_List_Oappend(U_18957),sK474(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18965)
        | ~ sP1176(U_18965,U_18961,U_18959,U_18957,U_18963) )
    & ! [U_18965,U_18961,U_18959,U_18957,U_18963] :
        ( hAPP(hAPP(c_List_Oappend(U_18957),U_18959),sK474(U_18965,U_18963,U_18961,U_18959,U_18957)) = U_18963
        | ~ sP1176(U_18965,U_18961,U_18959,U_18957,U_18963) )
    & ! [U_18965,U_18961,U_18959,U_18957,U_18963] :
        ( hAPP(hAPP(c_List_Oappend(U_18957),sK473(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18961) = U_18965
        | ~ sP1175(U_18965,U_18961,U_18959,U_18957,U_18963) )
    & ! [U_18965,U_18961,U_18959,U_18957,U_18963] :
        ( U_18959 = hAPP(hAPP(c_List_Oappend(U_18957),U_18963),sK473(U_18965,U_18963,U_18961,U_18959,U_18957))
        | ~ sP1175(U_18965,U_18961,U_18959,U_18957,U_18963) )
    & ! [U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966] :
        ( hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18962) = hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18966)
        | sP1177(U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966) )
    & ! [U_18965,U_18961,U_18959,U_18957,U_18963] :
        ( sP1176(U_18965,U_18961,U_18959,U_18957,U_18963)
        | sP1175(U_18965,U_18961,U_18959,U_18957,U_18963)
        | hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18961) != hAPP(hAPP(c_List_Oappend(U_18957),U_18963),U_18965) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1175,sP1176,sP1177])],[f_4563_5]) ).

cnf(f_4563_7,plain,
    ( sP1176(U_18965,U_18961,U_18959,U_18957,U_18963)
    | sP1175(U_18965,U_18961,U_18959,U_18957,U_18963)
    | hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18961) != hAPP(hAPP(c_List_Oappend(U_18957),U_18963),U_18965) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18962) = hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18966)
    | sP1177(U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_9,plain,
    ( U_18959 = hAPP(hAPP(c_List_Oappend(U_18957),U_18963),sK473(U_18965,U_18963,U_18961,U_18959,U_18957))
    | ~ sP1175(U_18965,U_18961,U_18959,U_18957,U_18963) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18957),sK473(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18961) = U_18965
    | ~ sP1175(U_18965,U_18961,U_18959,U_18957,U_18963) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18957),U_18959),sK474(U_18965,U_18963,U_18961,U_18959,U_18957)) = U_18963
    | ~ sP1176(U_18965,U_18961,U_18959,U_18957,U_18963) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_12,plain,
    ( U_18961 = hAPP(hAPP(c_List_Oappend(U_18957),sK474(U_18965,U_18963,U_18961,U_18959,U_18957)),U_18965)
    | ~ sP1176(U_18965,U_18961,U_18959,U_18957,U_18963) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_13,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18958),U_18955),U_18962) != U_18966
    | U_18960 != hAPP(hAPP(c_List_Oappend(U_18958),U_18964),U_18955)
    | ~ sP1177(U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

cnf(f_4563_14,plain,
    ( U_18962 != hAPP(hAPP(c_List_Oappend(U_18958),U_18956),U_18966)
    | hAPP(hAPP(c_List_Oappend(U_18958),U_18960),U_18956) != U_18964
    | ~ sP1177(U_18955,U_18958,U_18956,U_18960,U_18964,U_18962,U_18966) ),
    inference(clausify,[status(thm)],[f_4563_6]) ).

fof(f_4564_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
        | V_ys_2 != V_zs_2 )
      & ( V_ys_2 = V_zs_2
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_same__append__eq]) ).

fof(f_4564_2,plain,
    ! [U_18970,U_18969,U_18968,U_18967] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18967),U_18968),U_18969) = hAPP(hAPP(c_List_Oappend(U_18967),U_18968),U_18970)
        | U_18969 != U_18970 )
      & ( U_18969 = U_18970
        | hAPP(hAPP(c_List_Oappend(U_18967),U_18968),U_18969) != hAPP(hAPP(c_List_Oappend(U_18967),U_18968),U_18970) ) ),
    inference(variable_rename,[status(thm)],[f_4564_1]) ).

fof(f_4564_3,plain,
    ( ! [U_18978,U_18976] :
        ( ! [U_18974,U_18972] : hAPP(hAPP(c_List_Oappend(U_18972),U_18974),U_18976) = hAPP(hAPP(c_List_Oappend(U_18972),U_18974),U_18978)
        | U_18976 != U_18978 )
    & ! [U_18977,U_18975] :
        ( ! [U_18973,U_18971] : hAPP(hAPP(c_List_Oappend(U_18971),U_18973),U_18975) != hAPP(hAPP(c_List_Oappend(U_18971),U_18973),U_18977)
        | U_18975 = U_18977 ) ),
    inference(miniscope,[status(thm)],[f_4564_2]) ).

fof(f_4564_4,plain,
    ( ! [U_18978,U_18972,U_18976,U_18974] :
        ( hAPP(hAPP(c_List_Oappend(U_18972),U_18974),U_18976) = hAPP(hAPP(c_List_Oappend(U_18972),U_18974),U_18978)
        | U_18976 != U_18978 )
    & ! [U_18977,U_18973,U_18971,U_18975] :
        ( hAPP(hAPP(c_List_Oappend(U_18971),U_18973),U_18975) != hAPP(hAPP(c_List_Oappend(U_18971),U_18973),U_18977)
        | U_18975 = U_18977 ) ),
    inference(definitional_conversion,[status(esa)],[f_4564_3]) ).

cnf(f_4564_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18971),U_18973),U_18975) != hAPP(hAPP(c_List_Oappend(U_18971),U_18973),U_18977)
    | U_18975 = U_18977 ),
    inference(clausify,[status(thm)],[f_4564_4]) ).

cnf(f_4564_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18972),U_18974),U_18976) = hAPP(hAPP(c_List_Oappend(U_18972),U_18974),U_18978)
    | U_18976 != U_18978 ),
    inference(clausify,[status(thm)],[f_4564_4]) ).

fof(f_4565_1,plain,
    ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
        | V_ys_2 != V_zs_2 )
      & ( V_ys_2 = V_zs_2
        | hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__same__eq]) ).

fof(f_4565_2,plain,
    ! [U_18982,U_18981,U_18980,U_18979] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18979),U_18980),U_18981) = hAPP(hAPP(c_List_Oappend(U_18979),U_18982),U_18981)
        | U_18980 != U_18982 )
      & ( U_18980 = U_18982
        | hAPP(hAPP(c_List_Oappend(U_18979),U_18980),U_18981) != hAPP(hAPP(c_List_Oappend(U_18979),U_18982),U_18981) ) ),
    inference(variable_rename,[status(thm)],[f_4565_1]) ).

fof(f_4565_3,plain,
    ( ! [U_18990,U_18988,U_18986] :
        ( ! [U_18984] : hAPP(hAPP(c_List_Oappend(U_18984),U_18986),U_18988) = hAPP(hAPP(c_List_Oappend(U_18984),U_18990),U_18988)
        | U_18986 != U_18990 )
    & ! [U_18989,U_18987,U_18985] :
        ( ! [U_18983] : hAPP(hAPP(c_List_Oappend(U_18983),U_18985),U_18987) != hAPP(hAPP(c_List_Oappend(U_18983),U_18989),U_18987)
        | U_18985 = U_18989 ) ),
    inference(miniscope,[status(thm)],[f_4565_2]) ).

fof(f_4565_4,plain,
    ( ! [U_18988,U_18984,U_18986,U_18990] :
        ( hAPP(hAPP(c_List_Oappend(U_18984),U_18986),U_18988) = hAPP(hAPP(c_List_Oappend(U_18984),U_18990),U_18988)
        | U_18986 != U_18990 )
    & ! [U_18987,U_18983,U_18985,U_18989] :
        ( hAPP(hAPP(c_List_Oappend(U_18983),U_18985),U_18987) != hAPP(hAPP(c_List_Oappend(U_18983),U_18989),U_18987)
        | U_18985 = U_18989 ) ),
    inference(definitional_conversion,[status(esa)],[f_4565_3]) ).

cnf(f_4565_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18983),U_18985),U_18987) != hAPP(hAPP(c_List_Oappend(U_18983),U_18989),U_18987)
    | U_18985 = U_18989 ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

cnf(f_4565_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18984),U_18986),U_18988) = hAPP(hAPP(c_List_Oappend(U_18984),U_18990),U_18988)
    | U_18986 != U_18990 ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

fof(f_4566_1,plain,
    ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us)
      | V_ys != hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
      | hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) != V_zs ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__appendI]) ).

fof(f_4566_2,plain,
    ! [U_18996,U_18995,U_18994,U_18993,U_18992,U_18991] :
      ( hAPP(hAPP(c_List_Oappend(U_18991),U_18992),U_18995) = hAPP(hAPP(c_List_Oappend(U_18991),U_18994),U_18996)
      | U_18995 != hAPP(hAPP(c_List_Oappend(U_18991),U_18993),U_18996)
      | hAPP(hAPP(c_List_Oappend(U_18991),U_18992),U_18993) != U_18994 ),
    inference(variable_rename,[status(thm)],[f_4566_1]) ).

fof(f_4566_3,plain,
    ! [U_18991,U_18992,U_18993,U_18994,U_18995,U_18996] :
      ( hAPP(hAPP(c_List_Oappend(U_18991),U_18992),U_18995) = hAPP(hAPP(c_List_Oappend(U_18991),U_18994),U_18996)
      | U_18995 != hAPP(hAPP(c_List_Oappend(U_18991),U_18993),U_18996)
      | hAPP(hAPP(c_List_Oappend(U_18991),U_18992),U_18993) != U_18994 ),
    inference(definitional_conversion,[status(esa)],[f_4566_2]) ).

cnf(f_4566_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18991),U_18992),U_18995) = hAPP(hAPP(c_List_Oappend(U_18991),U_18994),U_18996)
    | U_18995 != hAPP(hAPP(c_List_Oappend(U_18991),U_18993),U_18996)
    | hAPP(hAPP(c_List_Oappend(U_18991),U_18992),U_18993) != U_18994 ),
    inference(clausify,[status(thm)],[f_4566_3]) ).

fof(f_4567_1,plain,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_set__append]) ).

fof(f_4567_2,plain,
    ! [U_18999,U_18998,U_18997] : hAPP(c_List_Oset(U_18997),hAPP(hAPP(c_List_Oappend(U_18997),U_18998),U_18999)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18997,tc_HOL_Obool)),hAPP(c_List_Oset(U_18997),U_18998)),hAPP(c_List_Oset(U_18997),U_18999)),
    inference(variable_rename,[status(thm)],[f_4567_1]) ).

fof(f_4567_3,plain,
    ! [U_18997,U_18998,U_18999] : hAPP(c_List_Oset(U_18997),hAPP(hAPP(c_List_Oappend(U_18997),U_18998),U_18999)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18997,tc_HOL_Obool)),hAPP(c_List_Oset(U_18997),U_18998)),hAPP(c_List_Oset(U_18997),U_18999)),
    inference(definitional_conversion,[status(esa)],[f_4567_2]) ).

cnf(f_4567_4,plain,
    hAPP(c_List_Oset(U_18997),hAPP(hAPP(c_List_Oappend(U_18997),U_18998),U_18999)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18997,tc_HOL_Obool)),hAPP(c_List_Oset(U_18997),U_18998)),hAPP(c_List_Oset(U_18997),U_18999)),
    inference(clausify,[status(thm)],[f_4567_3]) ).

fof(f_4568_1,plain,
    ! [V_ys,V_xs,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__append]) ).

fof(f_4568_2,plain,
    ! [U_19002,U_19001,U_19000] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),hAPP(hAPP(c_List_Oappend(U_19000),U_19001),U_19002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19000),hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),U_19001)),hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),U_19002))
      | ~ class_Groups_Omonoid__add(U_19000) ),
    inference(variable_rename,[status(thm)],[f_4568_1]) ).

fof(f_4568_3,plain,
    ! [U_19000,U_19001,U_19002] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),hAPP(hAPP(c_List_Oappend(U_19000),U_19001),U_19002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19000),hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),U_19001)),hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),U_19002))
      | ~ class_Groups_Omonoid__add(U_19000) ),
    inference(definitional_conversion,[status(esa)],[f_4568_2]) ).

cnf(f_4568_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),hAPP(hAPP(c_List_Oappend(U_19000),U_19001),U_19002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19000),hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),U_19001)),hAPP(c_List_Omonoid__add__class_Olistsum(U_19000),U_19002))
    | ~ class_Groups_Omonoid__add(U_19000) ),
    inference(clausify,[status(thm)],[f_4568_3]) ).

fof(f_4569_1,plain,
    ! [T_a,V_ys,V_xs] :
      ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys)
      | V_xs != V_ys ),
    inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI]) ).

fof(f_4569_2,plain,
    ! [U_19005,U_19004,U_19003] :
      ( U_19003 = hAPP(hAPP(c_List_Oappend(U_19005),c_List_Olist_ONil(U_19005)),U_19004)
      | U_19003 != U_19004 ),
    inference(variable_rename,[status(thm)],[f_4569_1]) ).

fof(f_4569_3,plain,
    ! [U_19003,U_19004,U_19005] :
      ( U_19003 = hAPP(hAPP(c_List_Oappend(U_19005),c_List_Olist_ONil(U_19005)),U_19004)
      | U_19003 != U_19004 ),
    inference(definitional_conversion,[status(esa)],[f_4569_2]) ).

cnf(f_4569_4,plain,
    ( U_19003 = hAPP(hAPP(c_List_Oappend(U_19005),c_List_Olist_ONil(U_19005)),U_19004)
    | U_19003 != U_19004 ),
    inference(clausify,[status(thm)],[f_4569_3]) ).

fof(f_4570_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__self__conv2]) ).

fof(f_4570_2,plain,
    ! [U_19008,U_19007,U_19006] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19006),U_19007),U_19008) = U_19008
        | U_19007 != c_List_Olist_ONil(U_19006) )
      & ( U_19007 = c_List_Olist_ONil(U_19006)
        | hAPP(hAPP(c_List_Oappend(U_19006),U_19007),U_19008) != U_19008 ) ),
    inference(variable_rename,[status(thm)],[f_4570_1]) ).

fof(f_4570_3,plain,
    ( ! [U_19014,U_19012,U_19010] :
        ( hAPP(hAPP(c_List_Oappend(U_19010),U_19012),U_19014) = U_19014
        | U_19012 != c_List_Olist_ONil(U_19010) )
    & ! [U_19013,U_19011,U_19009] :
        ( U_19011 = c_List_Olist_ONil(U_19009)
        | hAPP(hAPP(c_List_Oappend(U_19009),U_19011),U_19013) != U_19013 ) ),
    inference(miniscope,[status(thm)],[f_4570_2]) ).

fof(f_4570_4,plain,
    ( ! [U_19014,U_19010,U_19012] :
        ( hAPP(hAPP(c_List_Oappend(U_19010),U_19012),U_19014) = U_19014
        | U_19012 != c_List_Olist_ONil(U_19010) )
    & ! [U_19011,U_19009,U_19013] :
        ( U_19011 = c_List_Olist_ONil(U_19009)
        | hAPP(hAPP(c_List_Oappend(U_19009),U_19011),U_19013) != U_19013 ) ),
    inference(definitional_conversion,[status(esa)],[f_4570_3]) ).

cnf(f_4570_5,plain,
    ( U_19011 = c_List_Olist_ONil(U_19009)
    | hAPP(hAPP(c_List_Oappend(U_19009),U_19011),U_19013) != U_19013 ),
    inference(clausify,[status(thm)],[f_4570_4]) ).

cnf(f_4570_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19010),U_19012),U_19014) = U_19014
    | U_19012 != c_List_Olist_ONil(U_19010) ),
    inference(clausify,[status(thm)],[f_4570_4]) ).

fof(f_4571_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
        | V_ys_2 != c_List_Olist_ONil(T_b) )
      & ( V_ys_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__self__conv]) ).

fof(f_4571_2,plain,
    ! [U_19017,U_19016,U_19015] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19015),U_19016),U_19017) = U_19016
        | U_19017 != c_List_Olist_ONil(U_19015) )
      & ( U_19017 = c_List_Olist_ONil(U_19015)
        | hAPP(hAPP(c_List_Oappend(U_19015),U_19016),U_19017) != U_19016 ) ),
    inference(variable_rename,[status(thm)],[f_4571_1]) ).

fof(f_4571_3,plain,
    ( ! [U_19023,U_19021,U_19019] :
        ( hAPP(hAPP(c_List_Oappend(U_19019),U_19021),U_19023) = U_19021
        | U_19023 != c_List_Olist_ONil(U_19019) )
    & ! [U_19022,U_19020,U_19018] :
        ( U_19022 = c_List_Olist_ONil(U_19018)
        | hAPP(hAPP(c_List_Oappend(U_19018),U_19020),U_19022) != U_19020 ) ),
    inference(miniscope,[status(thm)],[f_4571_2]) ).

fof(f_4571_4,plain,
    ( ! [U_19019,U_19021,U_19023] :
        ( hAPP(hAPP(c_List_Oappend(U_19019),U_19021),U_19023) = U_19021
        | U_19023 != c_List_Olist_ONil(U_19019) )
    & ! [U_19020,U_19022,U_19018] :
        ( U_19022 = c_List_Olist_ONil(U_19018)
        | hAPP(hAPP(c_List_Oappend(U_19018),U_19020),U_19022) != U_19020 ) ),
    inference(definitional_conversion,[status(esa)],[f_4571_3]) ).

cnf(f_4571_5,plain,
    ( U_19022 = c_List_Olist_ONil(U_19018)
    | hAPP(hAPP(c_List_Oappend(U_19018),U_19020),U_19022) != U_19020 ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19019),U_19021),U_19023) = U_19021
    | U_19023 != c_List_Olist_ONil(U_19019) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

fof(f_4572_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
        | V_ys_2 != c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( ( V_ys_2 = c_List_Olist_ONil(T_b)
          & V_xs_2 = c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv]) ).

fof(f_4572_2,plain,
    ! [U_19026,U_19025,U_19024] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19024),U_19025),U_19026) = c_List_Olist_ONil(U_19024)
        | U_19026 != c_List_Olist_ONil(U_19024)
        | U_19025 != c_List_Olist_ONil(U_19024) )
      & ( ( U_19026 = c_List_Olist_ONil(U_19024)
          & U_19025 = c_List_Olist_ONil(U_19024) )
        | hAPP(hAPP(c_List_Oappend(U_19024),U_19025),U_19026) != c_List_Olist_ONil(U_19024) ) ),
    inference(variable_rename,[status(thm)],[f_4572_1]) ).

fof(f_4572_3,plain,
    ( ! [U_19032,U_19030,U_19028] :
        ( hAPP(hAPP(c_List_Oappend(U_19028),U_19030),U_19032) = c_List_Olist_ONil(U_19028)
        | U_19032 != c_List_Olist_ONil(U_19028)
        | U_19030 != c_List_Olist_ONil(U_19028) )
    & ! [U_19031,U_19029,U_19027] :
        ( ( U_19031 = c_List_Olist_ONil(U_19027)
          & U_19029 = c_List_Olist_ONil(U_19027) )
        | hAPP(hAPP(c_List_Oappend(U_19027),U_19029),U_19031) != c_List_Olist_ONil(U_19027) ) ),
    inference(miniscope,[status(thm)],[f_4572_2]) ).

fof(f_4572_4,plain,
    ( ! [U_19027,U_19031,U_19029] :
        ( U_19031 = c_List_Olist_ONil(U_19027)
        | ~ sP1178(U_19027,U_19031,U_19029) )
    & ! [U_19027,U_19031,U_19029] :
        ( U_19029 = c_List_Olist_ONil(U_19027)
        | ~ sP1178(U_19027,U_19031,U_19029) )
    & ! [U_19030,U_19028,U_19032] :
        ( hAPP(hAPP(c_List_Oappend(U_19028),U_19030),U_19032) = c_List_Olist_ONil(U_19028)
        | U_19032 != c_List_Olist_ONil(U_19028)
        | U_19030 != c_List_Olist_ONil(U_19028) )
    & ! [U_19027,U_19031,U_19029] :
        ( sP1178(U_19027,U_19031,U_19029)
        | hAPP(hAPP(c_List_Oappend(U_19027),U_19029),U_19031) != c_List_Olist_ONil(U_19027) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1178])],[f_4572_3]) ).

cnf(f_4572_5,plain,
    ( sP1178(U_19027,U_19031,U_19029)
    | hAPP(hAPP(c_List_Oappend(U_19027),U_19029),U_19031) != c_List_Olist_ONil(U_19027) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

cnf(f_4572_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19028),U_19030),U_19032) = c_List_Olist_ONil(U_19028)
    | U_19032 != c_List_Olist_ONil(U_19028)
    | U_19030 != c_List_Olist_ONil(U_19028) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

cnf(f_4572_7,plain,
    ( U_19029 = c_List_Olist_ONil(U_19027)
    | ~ sP1178(U_19027,U_19031,U_19029) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

cnf(f_4572_8,plain,
    ( U_19031 = c_List_Olist_ONil(U_19027)
    | ~ sP1178(U_19027,U_19031,U_19029) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

fof(f_4573_1,plain,
    ! [V_xs_2,T_b,V_ys_2] :
      ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_self__append__conv2]) ).

fof(f_4573_2,plain,
    ! [U_19035,U_19034,U_19033] :
      ( ( U_19033 = hAPP(hAPP(c_List_Oappend(U_19034),U_19035),U_19033)
        | U_19035 != c_List_Olist_ONil(U_19034) )
      & ( U_19035 = c_List_Olist_ONil(U_19034)
        | U_19033 != hAPP(hAPP(c_List_Oappend(U_19034),U_19035),U_19033) ) ),
    inference(variable_rename,[status(thm)],[f_4573_1]) ).

fof(f_4573_3,plain,
    ( ! [U_19041,U_19039] :
        ( ! [U_19037] : U_19037 = hAPP(hAPP(c_List_Oappend(U_19039),U_19041),U_19037)
        | U_19041 != c_List_Olist_ONil(U_19039) )
    & ! [U_19040,U_19038] :
        ( ! [U_19036] : U_19036 != hAPP(hAPP(c_List_Oappend(U_19038),U_19040),U_19036)
        | U_19040 = c_List_Olist_ONil(U_19038) ) ),
    inference(miniscope,[status(thm)],[f_4573_2]) ).

fof(f_4573_4,plain,
    ( ! [U_19041,U_19037,U_19039] :
        ( U_19037 = hAPP(hAPP(c_List_Oappend(U_19039),U_19041),U_19037)
        | U_19041 != c_List_Olist_ONil(U_19039) )
    & ! [U_19036,U_19040,U_19038] :
        ( U_19036 != hAPP(hAPP(c_List_Oappend(U_19038),U_19040),U_19036)
        | U_19040 = c_List_Olist_ONil(U_19038) ) ),
    inference(definitional_conversion,[status(esa)],[f_4573_3]) ).

cnf(f_4573_5,plain,
    ( U_19036 != hAPP(hAPP(c_List_Oappend(U_19038),U_19040),U_19036)
    | U_19040 = c_List_Olist_ONil(U_19038) ),
    inference(clausify,[status(thm)],[f_4573_4]) ).

cnf(f_4573_6,plain,
    ( U_19037 = hAPP(hAPP(c_List_Oappend(U_19039),U_19041),U_19037)
    | U_19041 != c_List_Olist_ONil(U_19039) ),
    inference(clausify,[status(thm)],[f_4573_4]) ).

fof(f_4574_1,plain,
    ! [V_ys_2,T_b,V_xs_2] :
      ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_b) )
      & ( V_ys_2 = c_List_Olist_ONil(T_b)
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_self__append__conv]) ).

fof(f_4574_2,plain,
    ! [U_19044,U_19043,U_19042] :
      ( ( U_19042 = hAPP(hAPP(c_List_Oappend(U_19043),U_19042),U_19044)
        | U_19044 != c_List_Olist_ONil(U_19043) )
      & ( U_19044 = c_List_Olist_ONil(U_19043)
        | U_19042 != hAPP(hAPP(c_List_Oappend(U_19043),U_19042),U_19044) ) ),
    inference(variable_rename,[status(thm)],[f_4574_1]) ).

fof(f_4574_3,plain,
    ( ! [U_19050,U_19048] :
        ( ! [U_19046] : U_19046 = hAPP(hAPP(c_List_Oappend(U_19048),U_19046),U_19050)
        | U_19050 != c_List_Olist_ONil(U_19048) )
    & ! [U_19049,U_19047] :
        ( ! [U_19045] : U_19045 != hAPP(hAPP(c_List_Oappend(U_19047),U_19045),U_19049)
        | U_19049 = c_List_Olist_ONil(U_19047) ) ),
    inference(miniscope,[status(thm)],[f_4574_2]) ).

fof(f_4574_4,plain,
    ( ! [U_19050,U_19046,U_19048] :
        ( U_19046 = hAPP(hAPP(c_List_Oappend(U_19048),U_19046),U_19050)
        | U_19050 != c_List_Olist_ONil(U_19048) )
    & ! [U_19049,U_19047,U_19045] :
        ( U_19045 != hAPP(hAPP(c_List_Oappend(U_19047),U_19045),U_19049)
        | U_19049 = c_List_Olist_ONil(U_19047) ) ),
    inference(definitional_conversion,[status(esa)],[f_4574_3]) ).

cnf(f_4574_5,plain,
    ( U_19045 != hAPP(hAPP(c_List_Oappend(U_19047),U_19045),U_19049)
    | U_19049 = c_List_Olist_ONil(U_19047) ),
    inference(clausify,[status(thm)],[f_4574_4]) ).

cnf(f_4574_6,plain,
    ( U_19046 = hAPP(hAPP(c_List_Oappend(U_19048),U_19046),U_19050)
    | U_19050 != c_List_Olist_ONil(U_19048) ),
    inference(clausify,[status(thm)],[f_4574_4]) ).

fof(f_4575_1,plain,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_append__Nil2]) ).

fof(f_4575_2,plain,
    ! [U_19052,U_19051] : hAPP(hAPP(c_List_Oappend(U_19051),U_19052),c_List_Olist_ONil(U_19051)) = U_19052,
    inference(variable_rename,[status(thm)],[f_4575_1]) ).

fof(f_4575_3,plain,
    ! [U_19051,U_19052] : hAPP(hAPP(c_List_Oappend(U_19051),U_19052),c_List_Olist_ONil(U_19051)) = U_19052,
    inference(definitional_conversion,[status(esa)],[f_4575_2]) ).

cnf(f_4575_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19051),U_19052),c_List_Olist_ONil(U_19051)) = U_19052,
    inference(clausify,[status(thm)],[f_4575_3]) ).

fof(f_4576_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( ( V_ys_2 = c_List_Olist_ONil(T_b)
          & V_xs_2 = c_List_Olist_ONil(T_b) )
        | c_List_Olist_ONil(T_b) != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv]) ).

fof(f_4576_2,plain,
    ! [U_19055,U_19054,U_19053] :
      ( ( c_List_Olist_ONil(U_19053) = hAPP(hAPP(c_List_Oappend(U_19053),U_19054),U_19055)
        | U_19055 != c_List_Olist_ONil(U_19053)
        | U_19054 != c_List_Olist_ONil(U_19053) )
      & ( ( U_19055 = c_List_Olist_ONil(U_19053)
          & U_19054 = c_List_Olist_ONil(U_19053) )
        | c_List_Olist_ONil(U_19053) != hAPP(hAPP(c_List_Oappend(U_19053),U_19054),U_19055) ) ),
    inference(variable_rename,[status(thm)],[f_4576_1]) ).

fof(f_4576_3,plain,
    ( ! [U_19061,U_19059,U_19057] :
        ( c_List_Olist_ONil(U_19057) = hAPP(hAPP(c_List_Oappend(U_19057),U_19059),U_19061)
        | U_19061 != c_List_Olist_ONil(U_19057)
        | U_19059 != c_List_Olist_ONil(U_19057) )
    & ! [U_19060,U_19058,U_19056] :
        ( ( U_19060 = c_List_Olist_ONil(U_19056)
          & U_19058 = c_List_Olist_ONil(U_19056) )
        | c_List_Olist_ONil(U_19056) != hAPP(hAPP(c_List_Oappend(U_19056),U_19058),U_19060) ) ),
    inference(miniscope,[status(thm)],[f_4576_2]) ).

fof(f_4576_4,plain,
    ( ! [U_19056,U_19060,U_19058] :
        ( U_19060 = c_List_Olist_ONil(U_19056)
        | ~ sP1179(U_19056,U_19060,U_19058) )
    & ! [U_19056,U_19060,U_19058] :
        ( U_19058 = c_List_Olist_ONil(U_19056)
        | ~ sP1179(U_19056,U_19060,U_19058) )
    & ! [U_19059,U_19057,U_19061] :
        ( c_List_Olist_ONil(U_19057) = hAPP(hAPP(c_List_Oappend(U_19057),U_19059),U_19061)
        | U_19061 != c_List_Olist_ONil(U_19057)
        | U_19059 != c_List_Olist_ONil(U_19057) )
    & ! [U_19056,U_19060,U_19058] :
        ( sP1179(U_19056,U_19060,U_19058)
        | c_List_Olist_ONil(U_19056) != hAPP(hAPP(c_List_Oappend(U_19056),U_19058),U_19060) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1179])],[f_4576_3]) ).

cnf(f_4576_5,plain,
    ( sP1179(U_19056,U_19060,U_19058)
    | c_List_Olist_ONil(U_19056) != hAPP(hAPP(c_List_Oappend(U_19056),U_19058),U_19060) ),
    inference(clausify,[status(thm)],[f_4576_4]) ).

cnf(f_4576_6,plain,
    ( c_List_Olist_ONil(U_19057) = hAPP(hAPP(c_List_Oappend(U_19057),U_19059),U_19061)
    | U_19061 != c_List_Olist_ONil(U_19057)
    | U_19059 != c_List_Olist_ONil(U_19057) ),
    inference(clausify,[status(thm)],[f_4576_4]) ).

cnf(f_4576_7,plain,
    ( U_19058 = c_List_Olist_ONil(U_19056)
    | ~ sP1179(U_19056,U_19060,U_19058) ),
    inference(clausify,[status(thm)],[f_4576_4]) ).

cnf(f_4576_8,plain,
    ( U_19060 = c_List_Olist_ONil(U_19056)
    | ~ sP1179(U_19056,U_19060,U_19058) ),
    inference(clausify,[status(thm)],[f_4576_4]) ).

fof(f_4577_1,plain,
    ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
    inference(fof_nnf,[status(thm)],[fact_append__Nil]) ).

fof(f_4577_2,plain,
    ! [U_19063,U_19062] : hAPP(hAPP(c_List_Oappend(U_19062),c_List_Olist_ONil(U_19062)),U_19063) = U_19063,
    inference(variable_rename,[status(thm)],[f_4577_1]) ).

fof(f_4577_3,plain,
    ! [U_19062,U_19063] : hAPP(hAPP(c_List_Oappend(U_19062),c_List_Olist_ONil(U_19062)),U_19063) = U_19063,
    inference(definitional_conversion,[status(esa)],[f_4577_2]) ).

cnf(f_4577_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19062),c_List_Olist_ONil(U_19062)),U_19063) = U_19063,
    inference(clausify,[status(thm)],[f_4577_3]) ).

fof(f_4578_1,plain,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI]) ).

fof(f_4578_2,plain,
    ! [U_19068,U_19067,U_19066,U_19065,U_19064] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19064),tc_List_Olist(U_19064))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19064),tc_List_Olist(U_19064)),hAPP(hAPP(c_List_Oappend(U_19064),U_19068),U_19065)),hAPP(hAPP(c_List_Oappend(U_19064),U_19068),U_19066))),c_List_Olexord(U_19064,U_19067)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19064),tc_List_Olist(U_19064))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19064),tc_List_Olist(U_19064)),U_19065),U_19066)),c_List_Olexord(U_19064,U_19067))) ),
    inference(variable_rename,[status(thm)],[f_4578_1]) ).

fof(f_4578_3,plain,
    ! [U_19064,U_19065,U_19066,U_19067,U_19068] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19064),tc_List_Olist(U_19064))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19064),tc_List_Olist(U_19064)),hAPP(hAPP(c_List_Oappend(U_19064),U_19068),U_19065)),hAPP(hAPP(c_List_Oappend(U_19064),U_19068),U_19066))),c_List_Olexord(U_19064,U_19067)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19064),tc_List_Olist(U_19064))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19064),tc_List_Olist(U_19064)),U_19065),U_19066)),c_List_Olexord(U_19064,U_19067))) ),
    inference(definitional_conversion,[status(esa)],[f_4578_2]) ).

cnf(f_4578_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19064),tc_List_Olist(U_19064))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19064),tc_List_Olist(U_19064)),hAPP(hAPP(c_List_Oappend(U_19064),U_19068),U_19065)),hAPP(hAPP(c_List_Oappend(U_19064),U_19068),U_19066))),c_List_Olexord(U_19064,U_19067)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19064),tc_List_Olist(U_19064))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19064),tc_List_Olist(U_19064)),U_19065),U_19066)),c_List_Olexord(U_19064,U_19067))) ),
    inference(clausify,[status(thm)],[f_4578_3]) ).

fof(f_4579_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
          & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__append]) ).

fof(f_4579_2,plain,
    ! [U_19071,U_19070,U_19069] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19069),hAPP(hAPP(c_List_Oappend(U_19069),U_19070),U_19071)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19069,tc_HOL_Obool)),hAPP(c_List_Oset(U_19069),U_19070)),hAPP(c_List_Oset(U_19069),U_19071)) != c_Orderings_Obot__class_Obot(tc_fun(U_19069,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19069),U_19071))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19069),U_19070)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19069,tc_HOL_Obool)),hAPP(c_List_Oset(U_19069),U_19070)),hAPP(c_List_Oset(U_19069),U_19071)) = c_Orderings_Obot__class_Obot(tc_fun(U_19069,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_19069),U_19071))
          & hBOOL(hAPP(c_List_Odistinct(U_19069),U_19070)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19069),hAPP(hAPP(c_List_Oappend(U_19069),U_19070),U_19071))) ) ),
    inference(variable_rename,[status(thm)],[f_4579_1]) ).

fof(f_4579_3,plain,
    ( ! [U_19077,U_19075,U_19073] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19073),hAPP(hAPP(c_List_Oappend(U_19073),U_19075),U_19077)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19073,tc_HOL_Obool)),hAPP(c_List_Oset(U_19073),U_19075)),hAPP(c_List_Oset(U_19073),U_19077)) != c_Orderings_Obot__class_Obot(tc_fun(U_19073,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19073),U_19077))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19073),U_19075)) )
    & ! [U_19076,U_19074,U_19072] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19072,tc_HOL_Obool)),hAPP(c_List_Oset(U_19072),U_19074)),hAPP(c_List_Oset(U_19072),U_19076)) = c_Orderings_Obot__class_Obot(tc_fun(U_19072,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_19072),U_19076))
          & hBOOL(hAPP(c_List_Odistinct(U_19072),U_19074)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19072),hAPP(hAPP(c_List_Oappend(U_19072),U_19074),U_19076))) ) ),
    inference(miniscope,[status(thm)],[f_4579_2]) ).

fof(f_4579_4,plain,
    ( ! [U_19074,U_19072,U_19076] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19072,tc_HOL_Obool)),hAPP(c_List_Oset(U_19072),U_19074)),hAPP(c_List_Oset(U_19072),U_19076)) = c_Orderings_Obot__class_Obot(tc_fun(U_19072,tc_HOL_Obool))
        | ~ sP1180(U_19074,U_19072,U_19076) )
    & ! [U_19074,U_19072,U_19076] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19072),U_19076))
        | ~ sP1180(U_19074,U_19072,U_19076) )
    & ! [U_19074,U_19072,U_19076] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19072),U_19074))
        | ~ sP1180(U_19074,U_19072,U_19076) )
    & ! [U_19073,U_19075,U_19077] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19073),hAPP(hAPP(c_List_Oappend(U_19073),U_19075),U_19077)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19073,tc_HOL_Obool)),hAPP(c_List_Oset(U_19073),U_19075)),hAPP(c_List_Oset(U_19073),U_19077)) != c_Orderings_Obot__class_Obot(tc_fun(U_19073,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19073),U_19077))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19073),U_19075)) )
    & ! [U_19074,U_19072,U_19076] :
        ( sP1180(U_19074,U_19072,U_19076)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19072),hAPP(hAPP(c_List_Oappend(U_19072),U_19074),U_19076))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1180])],[f_4579_3]) ).

cnf(f_4579_5,plain,
    ( sP1180(U_19074,U_19072,U_19076)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19072),hAPP(hAPP(c_List_Oappend(U_19072),U_19074),U_19076))) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

cnf(f_4579_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19073),hAPP(hAPP(c_List_Oappend(U_19073),U_19075),U_19077)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19073,tc_HOL_Obool)),hAPP(c_List_Oset(U_19073),U_19075)),hAPP(c_List_Oset(U_19073),U_19077)) != c_Orderings_Obot__class_Obot(tc_fun(U_19073,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19073),U_19077))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19073),U_19075)) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

cnf(f_4579_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19072),U_19074))
    | ~ sP1180(U_19074,U_19072,U_19076) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

cnf(f_4579_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19072),U_19076))
    | ~ sP1180(U_19074,U_19072,U_19076) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

cnf(f_4579_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19072,tc_HOL_Obool)),hAPP(c_List_Oset(U_19072),U_19074)),hAPP(c_List_Oset(U_19072),U_19076)) = c_Orderings_Obot__class_Obot(tc_fun(U_19072,tc_HOL_Obool))
    | ~ sP1180(U_19074,U_19072,U_19076) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

fof(f_4580_1,plain,
    ! [V_ys,V_xs,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nth__append]) ).

fof(f_4580_2,plain,
    ! [U_19081,U_19080,U_19079,U_19078] :
      ( ( hAPP(hAPP(c_List_Onth(U_19079),hAPP(hAPP(c_List_Oappend(U_19079),U_19080),U_19081)),U_19078) = hAPP(hAPP(c_List_Onth(U_19079),U_19081),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19078),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19079)),U_19080)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19078),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19079)),U_19080))) )
      & ( hAPP(hAPP(c_List_Onth(U_19079),hAPP(hAPP(c_List_Oappend(U_19079),U_19080),U_19081)),U_19078) = hAPP(hAPP(c_List_Onth(U_19079),U_19080),U_19078)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19078),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19079)),U_19080))) ) ),
    inference(variable_rename,[status(thm)],[f_4580_1]) ).

fof(f_4580_3,plain,
    ( ! [U_19089,U_19087,U_19085,U_19083] :
        ( hAPP(hAPP(c_List_Onth(U_19085),hAPP(hAPP(c_List_Oappend(U_19085),U_19087),U_19089)),U_19083) = hAPP(hAPP(c_List_Onth(U_19085),U_19089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19085)),U_19087)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19085)),U_19087))) )
    & ! [U_19088,U_19086,U_19084,U_19082] :
        ( hAPP(hAPP(c_List_Onth(U_19084),hAPP(hAPP(c_List_Oappend(U_19084),U_19086),U_19088)),U_19082) = hAPP(hAPP(c_List_Onth(U_19084),U_19086),U_19082)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19082),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19084)),U_19086))) ) ),
    inference(miniscope,[status(thm)],[f_4580_2]) ).

fof(f_4580_4,plain,
    ( ! [U_19083,U_19085,U_19087,U_19089] :
        ( hAPP(hAPP(c_List_Onth(U_19085),hAPP(hAPP(c_List_Oappend(U_19085),U_19087),U_19089)),U_19083) = hAPP(hAPP(c_List_Onth(U_19085),U_19089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19085)),U_19087)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19085)),U_19087))) )
    & ! [U_19088,U_19084,U_19082,U_19086] :
        ( hAPP(hAPP(c_List_Onth(U_19084),hAPP(hAPP(c_List_Oappend(U_19084),U_19086),U_19088)),U_19082) = hAPP(hAPP(c_List_Onth(U_19084),U_19086),U_19082)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19082),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19084)),U_19086))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4580_3]) ).

cnf(f_4580_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_19084),hAPP(hAPP(c_List_Oappend(U_19084),U_19086),U_19088)),U_19082) = hAPP(hAPP(c_List_Onth(U_19084),U_19086),U_19082)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19082),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19084)),U_19086))) ),
    inference(clausify,[status(thm)],[f_4580_4]) ).

cnf(f_4580_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_19085),hAPP(hAPP(c_List_Oappend(U_19085),U_19087),U_19089)),U_19083) = hAPP(hAPP(c_List_Onth(U_19085),U_19089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19085)),U_19087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19085)),U_19087))) ),
    inference(clausify,[status(thm)],[f_4580_4]) ).

fof(f_4581_1,plain,
    ! [V_x,V_ys,V_xs,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__append]) ).

fof(f_4581_2,plain,
    ! [U_19094,U_19093,U_19092,U_19091,U_19090] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_19091,hAPP(hAPP(c_List_Oappend(U_19091),U_19092),U_19093)),U_19090),U_19094) = hAPP(hAPP(c_List_Oappend(U_19091),U_19092),hAPP(hAPP(c_List_Olist__update(U_19091,U_19093),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19090),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19091)),U_19092))),U_19094))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19090),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19091)),U_19092))) )
      & ( hAPP(hAPP(c_List_Olist__update(U_19091,hAPP(hAPP(c_List_Oappend(U_19091),U_19092),U_19093)),U_19090),U_19094) = hAPP(hAPP(c_List_Oappend(U_19091),hAPP(hAPP(c_List_Olist__update(U_19091,U_19092),U_19090),U_19094)),U_19093)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19090),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19091)),U_19092))) ) ),
    inference(variable_rename,[status(thm)],[f_4581_1]) ).

fof(f_4581_3,plain,
    ( ! [U_19104,U_19102,U_19100,U_19098,U_19096] :
        ( hAPP(hAPP(c_List_Olist__update(U_19098,hAPP(hAPP(c_List_Oappend(U_19098),U_19100),U_19102)),U_19096),U_19104) = hAPP(hAPP(c_List_Oappend(U_19098),U_19100),hAPP(hAPP(c_List_Olist__update(U_19098,U_19102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19096),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19098)),U_19100))),U_19104))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19096),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19098)),U_19100))) )
    & ! [U_19103,U_19101,U_19099,U_19097,U_19095] :
        ( hAPP(hAPP(c_List_Olist__update(U_19097,hAPP(hAPP(c_List_Oappend(U_19097),U_19099),U_19101)),U_19095),U_19103) = hAPP(hAPP(c_List_Oappend(U_19097),hAPP(hAPP(c_List_Olist__update(U_19097,U_19099),U_19095),U_19103)),U_19101)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19095),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19097)),U_19099))) ) ),
    inference(miniscope,[status(thm)],[f_4581_2]) ).

fof(f_4581_4,plain,
    ( ! [U_19096,U_19098,U_19100,U_19102,U_19104] :
        ( hAPP(hAPP(c_List_Olist__update(U_19098,hAPP(hAPP(c_List_Oappend(U_19098),U_19100),U_19102)),U_19096),U_19104) = hAPP(hAPP(c_List_Oappend(U_19098),U_19100),hAPP(hAPP(c_List_Olist__update(U_19098,U_19102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19096),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19098)),U_19100))),U_19104))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19096),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19098)),U_19100))) )
    & ! [U_19097,U_19099,U_19101,U_19095,U_19103] :
        ( hAPP(hAPP(c_List_Olist__update(U_19097,hAPP(hAPP(c_List_Oappend(U_19097),U_19099),U_19101)),U_19095),U_19103) = hAPP(hAPP(c_List_Oappend(U_19097),hAPP(hAPP(c_List_Olist__update(U_19097,U_19099),U_19095),U_19103)),U_19101)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19095),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19097)),U_19099))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4581_3]) ).

cnf(f_4581_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19097,hAPP(hAPP(c_List_Oappend(U_19097),U_19099),U_19101)),U_19095),U_19103) = hAPP(hAPP(c_List_Oappend(U_19097),hAPP(hAPP(c_List_Olist__update(U_19097,U_19099),U_19095),U_19103)),U_19101)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19095),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19097)),U_19099))) ),
    inference(clausify,[status(thm)],[f_4581_4]) ).

cnf(f_4581_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19098,hAPP(hAPP(c_List_Oappend(U_19098),U_19100),U_19102)),U_19096),U_19104) = hAPP(hAPP(c_List_Oappend(U_19098),U_19100),hAPP(hAPP(c_List_Olist__update(U_19098,U_19102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19096),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19098)),U_19100))),U_19104))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19096),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19098)),U_19100))) ),
    inference(clausify,[status(thm)],[f_4581_4]) ).

fof(f_4582_1,plain,
    ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__append]) ).

fof(f_4582_2,plain,
    ! [U_19108,U_19107,U_19106,U_19105] : c_List_Osublist(U_19105,hAPP(hAPP(c_List_Oappend(U_19105),U_19106),U_19107),U_19108) = hAPP(hAPP(c_List_Oappend(U_19105),c_List_Osublist(U_19105,U_19106,U_19108)),c_List_Osublist(U_19105,U_19107,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19105)),U_19106)))),U_19108)))),
    inference(variable_rename,[status(thm)],[f_4582_1]) ).

fof(f_4582_3,plain,
    ! [U_19105,U_19106,U_19107,U_19108] : c_List_Osublist(U_19105,hAPP(hAPP(c_List_Oappend(U_19105),U_19106),U_19107),U_19108) = hAPP(hAPP(c_List_Oappend(U_19105),c_List_Osublist(U_19105,U_19106,U_19108)),c_List_Osublist(U_19105,U_19107,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19105)),U_19106)))),U_19108)))),
    inference(definitional_conversion,[status(esa)],[f_4582_2]) ).

cnf(f_4582_4,plain,
    c_List_Osublist(U_19105,hAPP(hAPP(c_List_Oappend(U_19105),U_19106),U_19107),U_19108) = hAPP(hAPP(c_List_Oappend(U_19105),c_List_Osublist(U_19105,U_19106,U_19108)),c_List_Osublist(U_19105,U_19107,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19105)),U_19106)))),U_19108)))),
    inference(clausify,[status(thm)],[f_4582_3]) ).

fof(f_4583_1,plain,
    ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI]) ).

fof(f_4583_2,plain,
    ! [U_19115,U_19114,U_19113,U_19112,U_19111,U_19110,U_19109] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19109),tc_List_Olist(U_19109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19109),tc_List_Olist(U_19109)),hAPP(hAPP(c_List_Oappend(U_19109),U_19113),hAPP(hAPP(c_List_Olist_OCons(U_19109),U_19110),U_19114))),hAPP(hAPP(c_List_Oappend(U_19109),U_19113),hAPP(hAPP(c_List_Olist_OCons(U_19109),U_19111),U_19115)))),c_List_Olexord(U_19109,U_19112)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19109,U_19109)),hAPP(hAPP(c_Product__Type_OPair(U_19109,U_19109),U_19110),U_19111)),U_19112)) ),
    inference(variable_rename,[status(thm)],[f_4583_1]) ).

fof(f_4583_3,plain,
    ! [U_19109,U_19110,U_19111,U_19112,U_19113,U_19114,U_19115] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19109),tc_List_Olist(U_19109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19109),tc_List_Olist(U_19109)),hAPP(hAPP(c_List_Oappend(U_19109),U_19113),hAPP(hAPP(c_List_Olist_OCons(U_19109),U_19110),U_19114))),hAPP(hAPP(c_List_Oappend(U_19109),U_19113),hAPP(hAPP(c_List_Olist_OCons(U_19109),U_19111),U_19115)))),c_List_Olexord(U_19109,U_19112)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19109,U_19109)),hAPP(hAPP(c_Product__Type_OPair(U_19109,U_19109),U_19110),U_19111)),U_19112)) ),
    inference(definitional_conversion,[status(esa)],[f_4583_2]) ).

cnf(f_4583_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19109),tc_List_Olist(U_19109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19109),tc_List_Olist(U_19109)),hAPP(hAPP(c_List_Oappend(U_19109),U_19113),hAPP(hAPP(c_List_Olist_OCons(U_19109),U_19110),U_19114))),hAPP(hAPP(c_List_Oappend(U_19109),U_19113),hAPP(hAPP(c_List_Olist_OCons(U_19109),U_19111),U_19115)))),c_List_Olexord(U_19109,U_19112)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19109,U_19109)),hAPP(hAPP(c_Product__Type_OPair(U_19109,U_19109),U_19110),U_19111)),U_19112)) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

fof(f_4584_1,plain,
    ! [V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth]) ).

fof(f_4584_2,plain,
    ! [U_19118,U_19117,U_19116] :
      ( hAPP(hAPP(c_List_Otake(U_19117),hAPP(c_Nat_OSuc,U_19116)),U_19118) = hAPP(hAPP(c_List_Oappend(U_19117),hAPP(hAPP(c_List_Otake(U_19117),U_19116),U_19118)),hAPP(hAPP(c_List_Olist_OCons(U_19117),hAPP(hAPP(c_List_Onth(U_19117),U_19118),U_19116)),c_List_Olist_ONil(U_19117)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19116),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19118))) ),
    inference(variable_rename,[status(thm)],[f_4584_1]) ).

fof(f_4584_3,plain,
    ! [U_19116,U_19117,U_19118] :
      ( hAPP(hAPP(c_List_Otake(U_19117),hAPP(c_Nat_OSuc,U_19116)),U_19118) = hAPP(hAPP(c_List_Oappend(U_19117),hAPP(hAPP(c_List_Otake(U_19117),U_19116),U_19118)),hAPP(hAPP(c_List_Olist_OCons(U_19117),hAPP(hAPP(c_List_Onth(U_19117),U_19118),U_19116)),c_List_Olist_ONil(U_19117)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19116),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19118))) ),
    inference(definitional_conversion,[status(esa)],[f_4584_2]) ).

cnf(f_4584_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19117),hAPP(c_Nat_OSuc,U_19116)),U_19118) = hAPP(hAPP(c_List_Oappend(U_19117),hAPP(hAPP(c_List_Otake(U_19117),U_19116),U_19118)),hAPP(hAPP(c_List_Olist_OCons(U_19117),hAPP(hAPP(c_List_Onth(U_19117),U_19118),U_19116)),c_List_Olist_ONil(U_19117)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19116),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19118))) ),
    inference(clausify,[status(thm)],[f_4584_3]) ).

fof(f_4585_1,plain,
    ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
            | V_xs_2 != V_ys_2 )
          & ( V_x_2 != V_y_2
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          & V_xs_2 = V_ys_2 )
        | ( V_x_2 = V_y_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff]) ).

fof(f_4585_2,plain,
    ! [U_19124,U_19123,U_19122,U_19121,U_19120,U_19119] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19119),tc_List_Olist(U_19119))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19119),tc_List_Olist(U_19119)),hAPP(hAPP(c_List_Oappend(U_19119),U_19120),hAPP(hAPP(c_List_Olist_OCons(U_19119),U_19121),c_List_Olist_ONil(U_19119)))),hAPP(hAPP(c_List_Oappend(U_19119),U_19122),hAPP(hAPP(c_List_Olist_OCons(U_19119),U_19123),c_List_Olist_ONil(U_19119))))),c_List_Olistrel1(U_19119,U_19124)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19119,U_19119)),hAPP(hAPP(c_Product__Type_OPair(U_19119,U_19119),U_19121),U_19123)),U_19124))
            | U_19120 != U_19122 )
          & ( U_19121 != U_19123
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19119),tc_List_Olist(U_19119))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19119),tc_List_Olist(U_19119)),U_19120),U_19122)),c_List_Olistrel1(U_19119,U_19124))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19119,U_19119)),hAPP(hAPP(c_Product__Type_OPair(U_19119,U_19119),U_19121),U_19123)),U_19124))
          & U_19120 = U_19122 )
        | ( U_19121 = U_19123
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19119),tc_List_Olist(U_19119))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19119),tc_List_Olist(U_19119)),U_19120),U_19122)),c_List_Olistrel1(U_19119,U_19124))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19119),tc_List_Olist(U_19119))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19119),tc_List_Olist(U_19119)),hAPP(hAPP(c_List_Oappend(U_19119),U_19120),hAPP(hAPP(c_List_Olist_OCons(U_19119),U_19121),c_List_Olist_ONil(U_19119)))),hAPP(hAPP(c_List_Oappend(U_19119),U_19122),hAPP(hAPP(c_List_Olist_OCons(U_19119),U_19123),c_List_Olist_ONil(U_19119))))),c_List_Olistrel1(U_19119,U_19124))) ) ),
    inference(variable_rename,[status(thm)],[f_4585_1]) ).

fof(f_4585_3,plain,
    ( ! [U_19136,U_19134,U_19132,U_19130,U_19128,U_19126] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),hAPP(hAPP(c_List_Oappend(U_19126),U_19128),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19130),c_List_Olist_ONil(U_19126)))),hAPP(hAPP(c_List_Oappend(U_19126),U_19132),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19134),c_List_Olist_ONil(U_19126))))),c_List_Olistrel1(U_19126,U_19136)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19126,U_19126)),hAPP(hAPP(c_Product__Type_OPair(U_19126,U_19126),U_19130),U_19134)),U_19136))
            | U_19128 != U_19132 )
          & ( U_19130 != U_19134
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),U_19128),U_19132)),c_List_Olistrel1(U_19126,U_19136))) ) ) )
    & ! [U_19135,U_19133,U_19131,U_19129,U_19127,U_19125] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19125,U_19125)),hAPP(hAPP(c_Product__Type_OPair(U_19125,U_19125),U_19129),U_19133)),U_19135))
          & U_19127 = U_19131 )
        | ( U_19129 = U_19133
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19125),tc_List_Olist(U_19125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19125),tc_List_Olist(U_19125)),U_19127),U_19131)),c_List_Olistrel1(U_19125,U_19135))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19125),tc_List_Olist(U_19125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19125),tc_List_Olist(U_19125)),hAPP(hAPP(c_List_Oappend(U_19125),U_19127),hAPP(hAPP(c_List_Olist_OCons(U_19125),U_19129),c_List_Olist_ONil(U_19125)))),hAPP(hAPP(c_List_Oappend(U_19125),U_19131),hAPP(hAPP(c_List_Olist_OCons(U_19125),U_19133),c_List_Olist_ONil(U_19125))))),c_List_Olistrel1(U_19125,U_19135))) ) ),
    inference(miniscope,[status(thm)],[f_4585_2]) ).

fof(f_4585_4,plain,
    ( ! [U_19126,U_19134,U_19128,U_19130,U_19132,U_19136] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19126,U_19126)),hAPP(hAPP(c_Product__Type_OPair(U_19126,U_19126),U_19130),U_19134)),U_19136))
        | U_19128 != U_19132
        | ~ sP1183(U_19126,U_19134,U_19128,U_19130,U_19132,U_19136) )
    & ! [U_19126,U_19134,U_19128,U_19130,U_19132,U_19136] :
        ( U_19130 != U_19134
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),U_19128),U_19132)),c_List_Olistrel1(U_19126,U_19136)))
        | ~ sP1183(U_19126,U_19134,U_19128,U_19130,U_19132,U_19136) )
    & ! [U_19125,U_19133,U_19135,U_19127,U_19129,U_19131] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19125,U_19125)),hAPP(hAPP(c_Product__Type_OPair(U_19125,U_19125),U_19129),U_19133)),U_19135))
        | ~ sP1182(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) )
    & ! [U_19125,U_19133,U_19135,U_19127,U_19129,U_19131] :
        ( U_19127 = U_19131
        | ~ sP1182(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) )
    & ! [U_19125,U_19133,U_19135,U_19127,U_19129,U_19131] :
        ( U_19129 = U_19133
        | ~ sP1181(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) )
    & ! [U_19125,U_19133,U_19135,U_19127,U_19129,U_19131] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19125),tc_List_Olist(U_19125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19125),tc_List_Olist(U_19125)),U_19127),U_19131)),c_List_Olistrel1(U_19125,U_19135)))
        | ~ sP1181(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) )
    & ! [U_19126,U_19134,U_19128,U_19130,U_19132,U_19136] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),hAPP(hAPP(c_List_Oappend(U_19126),U_19128),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19130),c_List_Olist_ONil(U_19126)))),hAPP(hAPP(c_List_Oappend(U_19126),U_19132),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19134),c_List_Olist_ONil(U_19126))))),c_List_Olistrel1(U_19126,U_19136)))
        | sP1183(U_19126,U_19134,U_19128,U_19130,U_19132,U_19136) )
    & ! [U_19125,U_19133,U_19135,U_19127,U_19129,U_19131] :
        ( sP1182(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131)
        | sP1181(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19125),tc_List_Olist(U_19125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19125),tc_List_Olist(U_19125)),hAPP(hAPP(c_List_Oappend(U_19125),U_19127),hAPP(hAPP(c_List_Olist_OCons(U_19125),U_19129),c_List_Olist_ONil(U_19125)))),hAPP(hAPP(c_List_Oappend(U_19125),U_19131),hAPP(hAPP(c_List_Olist_OCons(U_19125),U_19133),c_List_Olist_ONil(U_19125))))),c_List_Olistrel1(U_19125,U_19135))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1181,sP1182,sP1183])],[f_4585_3]) ).

cnf(f_4585_5,plain,
    ( sP1182(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131)
    | sP1181(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19125),tc_List_Olist(U_19125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19125),tc_List_Olist(U_19125)),hAPP(hAPP(c_List_Oappend(U_19125),U_19127),hAPP(hAPP(c_List_Olist_OCons(U_19125),U_19129),c_List_Olist_ONil(U_19125)))),hAPP(hAPP(c_List_Oappend(U_19125),U_19131),hAPP(hAPP(c_List_Olist_OCons(U_19125),U_19133),c_List_Olist_ONil(U_19125))))),c_List_Olistrel1(U_19125,U_19135))) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),hAPP(hAPP(c_List_Oappend(U_19126),U_19128),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19130),c_List_Olist_ONil(U_19126)))),hAPP(hAPP(c_List_Oappend(U_19126),U_19132),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19134),c_List_Olist_ONil(U_19126))))),c_List_Olistrel1(U_19126,U_19136)))
    | sP1183(U_19126,U_19134,U_19128,U_19130,U_19132,U_19136) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19125),tc_List_Olist(U_19125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19125),tc_List_Olist(U_19125)),U_19127),U_19131)),c_List_Olistrel1(U_19125,U_19135)))
    | ~ sP1181(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_8,plain,
    ( U_19129 = U_19133
    | ~ sP1181(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_9,plain,
    ( U_19127 = U_19131
    | ~ sP1182(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19125,U_19125)),hAPP(hAPP(c_Product__Type_OPair(U_19125,U_19125),U_19129),U_19133)),U_19135))
    | ~ sP1182(U_19125,U_19133,U_19135,U_19127,U_19129,U_19131) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_11,plain,
    ( U_19130 != U_19134
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),U_19128),U_19132)),c_List_Olistrel1(U_19126,U_19136)))
    | ~ sP1183(U_19126,U_19134,U_19128,U_19130,U_19132,U_19136) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19126,U_19126)),hAPP(hAPP(c_Product__Type_OPair(U_19126,U_19126),U_19130),U_19134)),U_19136))
    | U_19128 != U_19132
    | ~ sP1183(U_19126,U_19134,U_19128,U_19130,U_19132,U_19136) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

fof(f_4586_1,plain,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
      | ? [B_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__leftD]) ).

fof(f_4586_2,plain,
    ! [U_19142,U_19141,U_19140,U_19139,U_19138] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19140),U_19141)),c_List_Olexord(U_19138,U_19142)))
      | ? [U_19137] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),U_19137),U_19137)),U_19142))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19140)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19141))),c_List_Olexord(U_19138,U_19142))) ),
    inference(variable_rename,[status(thm)],[f_4586_1]) ).

fof(f_4586_3,plain,
    ! [U_19142,U_19141,U_19140,U_19139,U_19138] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19140),U_19141)),c_List_Olexord(U_19138,U_19142)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),sK475(U_19142,U_19141,U_19140,U_19139,U_19138)),sK475(U_19142,U_19141,U_19140,U_19139,U_19138))),U_19142))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19140)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19141))),c_List_Olexord(U_19138,U_19142))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_19137,sK475(U_19142,U_19141,U_19140,U_19139,U_19138))],[f_4586_2]) ).

fof(f_4586_4,plain,
    ! [U_19139,U_19138,U_19141,U_19142,U_19140] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19140),U_19141)),c_List_Olexord(U_19138,U_19142)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),sK475(U_19142,U_19141,U_19140,U_19139,U_19138)),sK475(U_19142,U_19141,U_19140,U_19139,U_19138))),U_19142))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19140)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19141))),c_List_Olexord(U_19138,U_19142))) ),
    inference(definitional_conversion,[status(esa)],[f_4586_3]) ).

cnf(f_4586_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19140),U_19141)),c_List_Olexord(U_19138,U_19142)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),sK475(U_19142,U_19141,U_19140,U_19139,U_19138)),sK475(U_19142,U_19141,U_19140,U_19139,U_19138))),U_19142))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19140)),hAPP(hAPP(c_List_Oappend(U_19138),U_19139),U_19141))),c_List_Olexord(U_19138,U_19142))) ),
    inference(clausify,[status(thm)],[f_4586_4]) ).

fof(f_4587_1,plain,
    ! [V_xs_2,V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I]) ).

fof(f_4587_2,plain,
    ! [U_19146,U_19145,U_19144,U_19143] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),U_19146)),c_Wellfounded_Oacc(tc_List_Olist(U_19143),c_List_Olistrel1(U_19143,U_19145))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19143)),U_19146),c_Wellfounded_Oacc(tc_List_Olist(U_19143),c_List_Olistrel1(U_19143,U_19145))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19143),U_19144),c_Wellfounded_Oacc(U_19143,U_19145))) ),
    inference(variable_rename,[status(thm)],[f_4587_1]) ).

fof(f_4587_3,plain,
    ! [U_19146,U_19143,U_19144,U_19145] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),U_19146)),c_Wellfounded_Oacc(tc_List_Olist(U_19143),c_List_Olistrel1(U_19143,U_19145))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19143)),U_19146),c_Wellfounded_Oacc(tc_List_Olist(U_19143),c_List_Olistrel1(U_19143,U_19145))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19143),U_19144),c_Wellfounded_Oacc(U_19143,U_19145))) ),
    inference(definitional_conversion,[status(esa)],[f_4587_2]) ).

cnf(f_4587_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),U_19146)),c_Wellfounded_Oacc(tc_List_Olist(U_19143),c_List_Olistrel1(U_19143,U_19145))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19143)),U_19146),c_Wellfounded_Oacc(tc_List_Olist(U_19143),c_List_Olistrel1(U_19143,U_19145))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19143),U_19144),c_Wellfounded_Oacc(U_19143,U_19145))) ),
    inference(clausify,[status(thm)],[f_4587_3]) ).

fof(f_4588_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_listrel1__converse]) ).

fof(f_4588_2,plain,
    ! [U_19148,U_19147] : c_List_Olistrel1(U_19147,hAPP(c_Relation_Oconverse(U_19147,U_19147),U_19148)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olistrel1(U_19147,U_19148)),
    inference(variable_rename,[status(thm)],[f_4588_1]) ).

fof(f_4588_3,plain,
    ! [U_19147,U_19148] : c_List_Olistrel1(U_19147,hAPP(c_Relation_Oconverse(U_19147,U_19147),U_19148)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olistrel1(U_19147,U_19148)),
    inference(definitional_conversion,[status(esa)],[f_4588_2]) ).

cnf(f_4588_4,plain,
    c_List_Olistrel1(U_19147,hAPP(c_Relation_Oconverse(U_19147,U_19147),U_19148)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olistrel1(U_19147,U_19148)),
    inference(clausify,[status(thm)],[f_4588_3]) ).

fof(f_4589_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(f_4589_2,plain,
    ! [U_19150,U_19149] : c_List_Olistrel(U_19149,c_Transitive__Closure_Ortrancl(U_19149,U_19150)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19149),c_List_Olistrel1(U_19149,U_19150)),
    inference(variable_rename,[status(thm)],[f_4589_1]) ).

fof(f_4589_3,plain,
    ! [U_19149,U_19150] : c_List_Olistrel(U_19149,c_Transitive__Closure_Ortrancl(U_19149,U_19150)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19149),c_List_Olistrel1(U_19149,U_19150)),
    inference(definitional_conversion,[status(esa)],[f_4589_2]) ).

cnf(f_4589_4,plain,
    c_List_Olistrel(U_19149,c_Transitive__Closure_Ortrancl(U_19149,U_19150)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19149),c_List_Olistrel1(U_19149,U_19150)),
    inference(clausify,[status(thm)],[f_4589_3]) ).

fof(f_4590_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__mono]) ).

fof(f_4590_2,plain,
    ! [U_19153,U_19152,U_19151] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19151),tc_List_Olist(U_19151)),tc_HOL_Obool)),c_List_Olistrel1(U_19151,U_19152)),c_List_Olistrel1(U_19151,U_19153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19151,U_19151),tc_HOL_Obool)),U_19152),U_19153)) ),
    inference(variable_rename,[status(thm)],[f_4590_1]) ).

fof(f_4590_3,plain,
    ! [U_19151,U_19152,U_19153] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19151),tc_List_Olist(U_19151)),tc_HOL_Obool)),c_List_Olistrel1(U_19151,U_19152)),c_List_Olistrel1(U_19151,U_19153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19151,U_19151),tc_HOL_Obool)),U_19152),U_19153)) ),
    inference(definitional_conversion,[status(esa)],[f_4590_2]) ).

cnf(f_4590_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19151),tc_List_Olist(U_19151)),tc_HOL_Obool)),c_List_Olistrel1(U_19151,U_19152)),c_List_Olistrel1(U_19151,U_19153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19151,U_19151),tc_HOL_Obool)),U_19152),U_19153)) ),
    inference(clausify,[status(thm)],[f_4590_3]) ).

fof(f_4591_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(f_4591_2,plain,
    ! [U_19155,U_19154] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19154),tc_List_Olist(U_19154)),tc_HOL_Obool)),c_List_Olistrel1(U_19154,c_Transitive__Closure_Ortrancl(U_19154,U_19155))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19154),c_List_Olistrel1(U_19154,U_19155)))),
    inference(variable_rename,[status(thm)],[f_4591_1]) ).

fof(f_4591_3,plain,
    ! [U_19154,U_19155] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19154),tc_List_Olist(U_19154)),tc_HOL_Obool)),c_List_Olistrel1(U_19154,c_Transitive__Closure_Ortrancl(U_19154,U_19155))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19154),c_List_Olistrel1(U_19154,U_19155)))),
    inference(definitional_conversion,[status(esa)],[f_4591_2]) ).

cnf(f_4591_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19154),tc_List_Olist(U_19154)),tc_HOL_Obool)),c_List_Olistrel1(U_19154,c_Transitive__Closure_Ortrancl(U_19154,U_19155))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19154),c_List_Olistrel1(U_19154,U_19155)))),
    inference(clausify,[status(thm)],[f_4591_3]) ).

fof(f_4592_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(f_4592_2,plain,
    ! [U_19157,U_19156] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19156),tc_List_Olist(U_19156)),tc_HOL_Obool)),c_List_Olistrel(U_19156,U_19157)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19156),c_List_Olistrel1(U_19156,U_19157)))),
    inference(variable_rename,[status(thm)],[f_4592_1]) ).

fof(f_4592_3,plain,
    ! [U_19156,U_19157] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19156),tc_List_Olist(U_19156)),tc_HOL_Obool)),c_List_Olistrel(U_19156,U_19157)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19156),c_List_Olistrel1(U_19156,U_19157)))),
    inference(definitional_conversion,[status(esa)],[f_4592_2]) ).

cnf(f_4592_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19156),tc_List_Olist(U_19156)),tc_HOL_Obool)),c_List_Olistrel(U_19156,U_19157)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19156),c_List_Olistrel1(U_19156,U_19157)))),
    inference(clausify,[status(thm)],[f_4592_3]) ).

fof(f_4593_1,plain,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1]) ).

fof(f_4593_2,plain,
    ! [U_19162,U_19161,U_19160,U_19159,U_19158] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19158),tc_List_Olist(U_19158))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19158),tc_List_Olist(U_19158)),hAPP(hAPP(c_List_Olist_OCons(U_19158),U_19162),U_19159)),hAPP(hAPP(c_List_Olist_OCons(U_19158),U_19162),U_19160))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19158),c_List_Olistrel1(U_19158,U_19161))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19158),tc_List_Olist(U_19158))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19158),tc_List_Olist(U_19158)),U_19159),U_19160)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19158),c_List_Olistrel1(U_19158,U_19161)))) ),
    inference(variable_rename,[status(thm)],[f_4593_1]) ).

fof(f_4593_3,plain,
    ! [U_19158,U_19159,U_19160,U_19161,U_19162] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19158),tc_List_Olist(U_19158))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19158),tc_List_Olist(U_19158)),hAPP(hAPP(c_List_Olist_OCons(U_19158),U_19162),U_19159)),hAPP(hAPP(c_List_Olist_OCons(U_19158),U_19162),U_19160))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19158),c_List_Olistrel1(U_19158,U_19161))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19158),tc_List_Olist(U_19158))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19158),tc_List_Olist(U_19158)),U_19159),U_19160)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19158),c_List_Olistrel1(U_19158,U_19161)))) ),
    inference(definitional_conversion,[status(esa)],[f_4593_2]) ).

cnf(f_4593_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19158),tc_List_Olist(U_19158))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19158),tc_List_Olist(U_19158)),hAPP(hAPP(c_List_Olist_OCons(U_19158),U_19162),U_19159)),hAPP(hAPP(c_List_Olist_OCons(U_19158),U_19162),U_19160))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19158),c_List_Olistrel1(U_19158,U_19161))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19158),tc_List_Olist(U_19158))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19158),tc_List_Olist(U_19158)),U_19159),U_19160)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19158),c_List_Olistrel1(U_19158,U_19161)))) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

fof(f_4594_1,plain,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I2]) ).

fof(f_4594_2,plain,
    ! [U_19167,U_19166,U_19165,U_19164,U_19163] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19163),tc_List_Olist(U_19163))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19163),tc_List_Olist(U_19163)),hAPP(hAPP(c_List_Olist_OCons(U_19163),U_19167),U_19164)),hAPP(hAPP(c_List_Olist_OCons(U_19163),U_19167),U_19165))),c_List_Olistrel1(U_19163,U_19166)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19163),tc_List_Olist(U_19163))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19163),tc_List_Olist(U_19163)),U_19164),U_19165)),c_List_Olistrel1(U_19163,U_19166))) ),
    inference(variable_rename,[status(thm)],[f_4594_1]) ).

fof(f_4594_3,plain,
    ! [U_19163,U_19164,U_19165,U_19166,U_19167] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19163),tc_List_Olist(U_19163))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19163),tc_List_Olist(U_19163)),hAPP(hAPP(c_List_Olist_OCons(U_19163),U_19167),U_19164)),hAPP(hAPP(c_List_Olist_OCons(U_19163),U_19167),U_19165))),c_List_Olistrel1(U_19163,U_19166)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19163),tc_List_Olist(U_19163))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19163),tc_List_Olist(U_19163)),U_19164),U_19165)),c_List_Olistrel1(U_19163,U_19166))) ),
    inference(definitional_conversion,[status(esa)],[f_4594_2]) ).

cnf(f_4594_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19163),tc_List_Olist(U_19163))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19163),tc_List_Olist(U_19163)),hAPP(hAPP(c_List_Olist_OCons(U_19163),U_19167),U_19164)),hAPP(hAPP(c_List_Olist_OCons(U_19163),U_19167),U_19165))),c_List_Olistrel1(U_19163,U_19166)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19163),tc_List_Olist(U_19163))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19163),tc_List_Olist(U_19163)),U_19164),U_19165)),c_List_Olistrel1(U_19163,U_19166))) ),
    inference(clausify,[status(thm)],[f_4594_3]) ).

fof(f_4595_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len]) ).

fof(f_4595_2,plain,
    ! [U_19171,U_19170,U_19169,U_19168] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19169) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19170)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19168),tc_List_Olist(U_19168))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19168),tc_List_Olist(U_19168)),U_19169),U_19170)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19168),c_List_Olistrel1(U_19168,U_19171)))) ),
    inference(variable_rename,[status(thm)],[f_4595_1]) ).

fof(f_4595_3,plain,
    ! [U_19168,U_19169,U_19170,U_19171] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19169) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19170)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19168),tc_List_Olist(U_19168))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19168),tc_List_Olist(U_19168)),U_19169),U_19170)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19168),c_List_Olistrel1(U_19168,U_19171)))) ),
    inference(definitional_conversion,[status(esa)],[f_4595_2]) ).

cnf(f_4595_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19169) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19170)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19168),tc_List_Olist(U_19168))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19168),tc_List_Olist(U_19168)),U_19169),U_19170)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19168),c_List_Olistrel1(U_19168,U_19171)))) ),
    inference(clausify,[status(thm)],[f_4595_3]) ).

fof(f_4596_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len]) ).

fof(f_4596_2,plain,
    ! [U_19175,U_19174,U_19173,U_19172] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19172)),U_19173) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19172)),U_19174)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19172),tc_List_Olist(U_19172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19172),tc_List_Olist(U_19172)),U_19173),U_19174)),c_List_Olistrel1(U_19172,U_19175))) ),
    inference(variable_rename,[status(thm)],[f_4596_1]) ).

fof(f_4596_3,plain,
    ! [U_19172,U_19173,U_19174,U_19175] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19172)),U_19173) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19172)),U_19174)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19172),tc_List_Olist(U_19172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19172),tc_List_Olist(U_19172)),U_19173),U_19174)),c_List_Olistrel1(U_19172,U_19175))) ),
    inference(definitional_conversion,[status(esa)],[f_4596_2]) ).

cnf(f_4596_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19172)),U_19173) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19172)),U_19174)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19172),tc_List_Olist(U_19172))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19172),tc_List_Olist(U_19172)),U_19173),U_19174)),c_List_Olistrel1(U_19172,U_19175))) ),
    inference(clausify,[status(thm)],[f_4596_3]) ).

fof(f_4597_1,plain,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(f_4597_2,plain,
    ! [U_19178,U_19177,U_19176] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19176),tc_List_Olist(U_19176))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19176),tc_List_Olist(U_19176)),c_List_Olist_ONil(U_19176)),U_19177)),c_List_Olistrel1(U_19176,U_19178))),
    inference(variable_rename,[status(thm)],[f_4597_1]) ).

fof(f_4597_3,plain,
    ! [U_19176,U_19177,U_19178] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19176),tc_List_Olist(U_19176))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19176),tc_List_Olist(U_19176)),c_List_Olist_ONil(U_19176)),U_19177)),c_List_Olistrel1(U_19176,U_19178))),
    inference(definitional_conversion,[status(esa)],[f_4597_2]) ).

cnf(f_4597_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19176),tc_List_Olist(U_19176))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19176),tc_List_Olist(U_19176)),c_List_Olist_ONil(U_19176)),U_19177)),c_List_Olistrel1(U_19176,U_19178))),
    inference(clausify,[status(thm)],[f_4597_3]) ).

fof(f_4598_1,plain,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(f_4598_2,plain,
    ! [U_19181,U_19180,U_19179] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19179),tc_List_Olist(U_19179))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19179),tc_List_Olist(U_19179)),U_19180),c_List_Olist_ONil(U_19179))),c_List_Olistrel1(U_19179,U_19181))),
    inference(variable_rename,[status(thm)],[f_4598_1]) ).

fof(f_4598_3,plain,
    ! [U_19179,U_19180,U_19181] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19179),tc_List_Olist(U_19179))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19179),tc_List_Olist(U_19179)),U_19180),c_List_Olist_ONil(U_19179))),c_List_Olistrel1(U_19179,U_19181))),
    inference(definitional_conversion,[status(esa)],[f_4598_2]) ).

cnf(f_4598_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19179),tc_List_Olist(U_19179))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19179),tc_List_Olist(U_19179)),U_19180),c_List_Olist_ONil(U_19179))),c_List_Olistrel1(U_19179,U_19181))),
    inference(clausify,[status(thm)],[f_4598_3]) ).

fof(f_4599_1,plain,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
          | V_xs_2 != V_ys_2 )
        & ( V_us_2 != V_vs_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__listrel1I]) ).

fof(f_4599_2,plain,
    ! [U_19187,U_19186,U_19185,U_19184,U_19183,U_19182] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),hAPP(hAPP(c_List_Oappend(U_19182),U_19183),U_19186)),hAPP(hAPP(c_List_Oappend(U_19182),U_19184),U_19187))),c_List_Olistrel1(U_19182,U_19185)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),U_19186),U_19187)),c_List_Olistrel1(U_19182,U_19185)))
          | U_19183 != U_19184 )
        & ( U_19186 != U_19187
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),U_19183),U_19184)),c_List_Olistrel1(U_19182,U_19185))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4599_1]) ).

fof(f_4599_3,plain,
    ( ! [U_19182,U_19183,U_19184,U_19185,U_19186,U_19187] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),U_19186),U_19187)),c_List_Olistrel1(U_19182,U_19185)))
        | U_19183 != U_19184
        | ~ sP1184(U_19182,U_19183,U_19184,U_19185,U_19186,U_19187) )
    & ! [U_19182,U_19183,U_19184,U_19185,U_19186,U_19187] :
        ( U_19186 != U_19187
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),U_19183),U_19184)),c_List_Olistrel1(U_19182,U_19185)))
        | ~ sP1184(U_19182,U_19183,U_19184,U_19185,U_19186,U_19187) )
    & ! [U_19182,U_19183,U_19184,U_19185,U_19186,U_19187] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),hAPP(hAPP(c_List_Oappend(U_19182),U_19183),U_19186)),hAPP(hAPP(c_List_Oappend(U_19182),U_19184),U_19187))),c_List_Olistrel1(U_19182,U_19185)))
        | sP1184(U_19182,U_19183,U_19184,U_19185,U_19186,U_19187) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1184])],[f_4599_2]) ).

cnf(f_4599_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),hAPP(hAPP(c_List_Oappend(U_19182),U_19183),U_19186)),hAPP(hAPP(c_List_Oappend(U_19182),U_19184),U_19187))),c_List_Olistrel1(U_19182,U_19185)))
    | sP1184(U_19182,U_19183,U_19184,U_19185,U_19186,U_19187) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_5,plain,
    ( U_19186 != U_19187
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),U_19183),U_19184)),c_List_Olistrel1(U_19182,U_19185)))
    | ~ sP1184(U_19182,U_19183,U_19184,U_19185,U_19186,U_19187) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19182),tc_List_Olist(U_19182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19182),tc_List_Olist(U_19182)),U_19186),U_19187)),c_List_Olistrel1(U_19182,U_19185)))
    | U_19183 != U_19184
    | ~ sP1184(U_19182,U_19183,U_19184,U_19185,U_19186,U_19187) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

fof(f_4600_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse]) ).

fof(f_4600_2,plain,
    ! [U_19191,U_19190,U_19189,U_19188] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19188),tc_List_Olist(U_19188))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19188),tc_List_Olist(U_19188)),U_19189),U_19190)),c_List_Olistrel1(U_19188,hAPP(c_Relation_Oconverse(U_19188,U_19188),U_19191))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19188),tc_List_Olist(U_19188))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19188),tc_List_Olist(U_19188)),U_19189),U_19190)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19188),tc_List_Olist(U_19188)),c_List_Olistrel1(U_19188,U_19191)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19188),tc_List_Olist(U_19188))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19188),tc_List_Olist(U_19188)),U_19189),U_19190)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19188),tc_List_Olist(U_19188)),c_List_Olistrel1(U_19188,U_19191))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19188),tc_List_Olist(U_19188))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19188),tc_List_Olist(U_19188)),U_19189),U_19190)),c_List_Olistrel1(U_19188,hAPP(c_Relation_Oconverse(U_19188,U_19188),U_19191)))) ) ),
    inference(variable_rename,[status(thm)],[f_4600_1]) ).

fof(f_4600_3,plain,
    ( ! [U_19199,U_19197,U_19195,U_19193] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19193),tc_List_Olist(U_19193))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),U_19195),U_19197)),c_List_Olistrel1(U_19193,hAPP(c_Relation_Oconverse(U_19193,U_19193),U_19199))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19193),tc_List_Olist(U_19193))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),U_19195),U_19197)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),c_List_Olistrel1(U_19193,U_19199)))) )
    & ! [U_19198,U_19196,U_19194,U_19192] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19192),tc_List_Olist(U_19192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),U_19194),U_19196)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),c_List_Olistrel1(U_19192,U_19198))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19192),tc_List_Olist(U_19192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),U_19194),U_19196)),c_List_Olistrel1(U_19192,hAPP(c_Relation_Oconverse(U_19192,U_19192),U_19198)))) ) ),
    inference(miniscope,[status(thm)],[f_4600_2]) ).

fof(f_4600_4,plain,
    ( ! [U_19193,U_19195,U_19197,U_19199] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19193),tc_List_Olist(U_19193))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),U_19195),U_19197)),c_List_Olistrel1(U_19193,hAPP(c_Relation_Oconverse(U_19193,U_19193),U_19199))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19193),tc_List_Olist(U_19193))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),U_19195),U_19197)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),c_List_Olistrel1(U_19193,U_19199)))) )
    & ! [U_19194,U_19198,U_19192,U_19196] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19192),tc_List_Olist(U_19192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),U_19194),U_19196)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),c_List_Olistrel1(U_19192,U_19198))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19192),tc_List_Olist(U_19192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),U_19194),U_19196)),c_List_Olistrel1(U_19192,hAPP(c_Relation_Oconverse(U_19192,U_19192),U_19198)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4600_3]) ).

cnf(f_4600_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19192),tc_List_Olist(U_19192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),U_19194),U_19196)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),c_List_Olistrel1(U_19192,U_19198))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19192),tc_List_Olist(U_19192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19192),tc_List_Olist(U_19192)),U_19194),U_19196)),c_List_Olistrel1(U_19192,hAPP(c_Relation_Oconverse(U_19192,U_19192),U_19198)))) ),
    inference(clausify,[status(thm)],[f_4600_4]) ).

cnf(f_4600_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19193),tc_List_Olist(U_19193))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),U_19195),U_19197)),c_List_Olistrel1(U_19193,hAPP(c_Relation_Oconverse(U_19193,U_19193),U_19199))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19193),tc_List_Olist(U_19193))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),U_19195),U_19197)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19193),tc_List_Olist(U_19193)),c_List_Olistrel1(U_19193,U_19199)))) ),
    inference(clausify,[status(thm)],[f_4600_4]) ).

fof(f_4601_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel]) ).

fof(f_4601_2,plain,
    ! [U_19203,U_19202,U_19201,U_19200] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19200),tc_List_Olist(U_19200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19200),tc_List_Olist(U_19200)),U_19201),U_19202)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19200),c_List_Olistrel1(U_19200,U_19203))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19200),tc_List_Olist(U_19200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19200),tc_List_Olist(U_19200)),U_19201),U_19202)),c_List_Olistrel(U_19200,U_19203))) ),
    inference(variable_rename,[status(thm)],[f_4601_1]) ).

fof(f_4601_3,plain,
    ! [U_19200,U_19201,U_19202,U_19203] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19200),tc_List_Olist(U_19200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19200),tc_List_Olist(U_19200)),U_19201),U_19202)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19200),c_List_Olistrel1(U_19200,U_19203))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19200),tc_List_Olist(U_19200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19200),tc_List_Olist(U_19200)),U_19201),U_19202)),c_List_Olistrel(U_19200,U_19203))) ),
    inference(definitional_conversion,[status(esa)],[f_4601_2]) ).

cnf(f_4601_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19200),tc_List_Olist(U_19200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19200),tc_List_Olist(U_19200)),U_19201),U_19202)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19200),c_List_Olistrel1(U_19200,U_19203))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19200),tc_List_Olist(U_19200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19200),tc_List_Olist(U_19200)),U_19201),U_19202)),c_List_Olistrel(U_19200,U_19203))) ),
    inference(clausify,[status(thm)],[f_4601_3]) ).

fof(f_4602_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1]) ).

fof(f_4602_2,plain,
    ! [U_19207,U_19206,U_19205,U_19204] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19204),tc_List_Olist(U_19204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19204),tc_List_Olist(U_19204)),U_19205),U_19206)),c_List_Olistrel(U_19204,c_Transitive__Closure_Ortrancl(U_19204,U_19207))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19204),tc_List_Olist(U_19204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19204),tc_List_Olist(U_19204)),U_19205),U_19206)),c_List_Olistrel1(U_19204,U_19207))) ),
    inference(variable_rename,[status(thm)],[f_4602_1]) ).

fof(f_4602_3,plain,
    ! [U_19204,U_19205,U_19206,U_19207] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19204),tc_List_Olist(U_19204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19204),tc_List_Olist(U_19204)),U_19205),U_19206)),c_List_Olistrel(U_19204,c_Transitive__Closure_Ortrancl(U_19204,U_19207))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19204),tc_List_Olist(U_19204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19204),tc_List_Olist(U_19204)),U_19205),U_19206)),c_List_Olistrel1(U_19204,U_19207))) ),
    inference(definitional_conversion,[status(esa)],[f_4602_2]) ).

cnf(f_4602_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19204),tc_List_Olist(U_19204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19204),tc_List_Olist(U_19204)),U_19205),U_19206)),c_List_Olistrel(U_19204,c_Transitive__Closure_Ortrancl(U_19204,U_19207))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19204),tc_List_Olist(U_19204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19204),tc_List_Olist(U_19204)),U_19205),U_19206)),c_List_Olistrel1(U_19204,U_19207))) ),
    inference(clausify,[status(thm)],[f_4602_3]) ).

fof(f_4603_1,plain,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I1]) ).

fof(f_4603_2,plain,
    ! [U_19212,U_19211,U_19210,U_19209,U_19208] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19208),tc_List_Olist(U_19208))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19208),tc_List_Olist(U_19208)),hAPP(hAPP(c_List_Olist_OCons(U_19208),U_19209),U_19212)),hAPP(hAPP(c_List_Olist_OCons(U_19208),U_19210),U_19212))),c_List_Olistrel1(U_19208,U_19211)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19208,U_19208)),hAPP(hAPP(c_Product__Type_OPair(U_19208,U_19208),U_19209),U_19210)),U_19211)) ),
    inference(variable_rename,[status(thm)],[f_4603_1]) ).

fof(f_4603_3,plain,
    ! [U_19208,U_19209,U_19210,U_19211,U_19212] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19208),tc_List_Olist(U_19208))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19208),tc_List_Olist(U_19208)),hAPP(hAPP(c_List_Olist_OCons(U_19208),U_19209),U_19212)),hAPP(hAPP(c_List_Olist_OCons(U_19208),U_19210),U_19212))),c_List_Olistrel1(U_19208,U_19211)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19208,U_19208)),hAPP(hAPP(c_Product__Type_OPair(U_19208,U_19208),U_19209),U_19210)),U_19211)) ),
    inference(definitional_conversion,[status(esa)],[f_4603_2]) ).

cnf(f_4603_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19208),tc_List_Olist(U_19208))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19208),tc_List_Olist(U_19208)),hAPP(hAPP(c_List_Olist_OCons(U_19208),U_19209),U_19212)),hAPP(hAPP(c_List_Olist_OCons(U_19208),U_19210),U_19212))),c_List_Olistrel1(U_19208,U_19211)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19208,U_19208)),hAPP(hAPP(c_Product__Type_OPair(U_19208,U_19208),U_19209),U_19210)),U_19211)) ),
    inference(clausify,[status(thm)],[f_4603_3]) ).

fof(f_4604_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
            | V_x_2 != V_y_2 )
          & ( V_xs_2 != V_ys_2
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons]) ).

fof(f_4604_2,plain,
    ! [U_19218,U_19217,U_19216,U_19215,U_19214,U_19213] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19213),tc_List_Olist(U_19213))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19213),tc_List_Olist(U_19213)),hAPP(hAPP(c_List_Olist_OCons(U_19213),U_19214),U_19215)),hAPP(hAPP(c_List_Olist_OCons(U_19213),U_19216),U_19217))),c_List_Olistrel1(U_19213,U_19218)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19213),tc_List_Olist(U_19213))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19213),tc_List_Olist(U_19213)),U_19215),U_19217)),c_List_Olistrel1(U_19213,U_19218)))
            | U_19214 != U_19216 )
          & ( U_19215 != U_19217
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19213,U_19213)),hAPP(hAPP(c_Product__Type_OPair(U_19213,U_19213),U_19214),U_19216)),U_19218)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19213),tc_List_Olist(U_19213))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19213),tc_List_Olist(U_19213)),U_19215),U_19217)),c_List_Olistrel1(U_19213,U_19218)))
          & U_19214 = U_19216 )
        | ( U_19215 = U_19217
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19213,U_19213)),hAPP(hAPP(c_Product__Type_OPair(U_19213,U_19213),U_19214),U_19216)),U_19218)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19213),tc_List_Olist(U_19213))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19213),tc_List_Olist(U_19213)),hAPP(hAPP(c_List_Olist_OCons(U_19213),U_19214),U_19215)),hAPP(hAPP(c_List_Olist_OCons(U_19213),U_19216),U_19217))),c_List_Olistrel1(U_19213,U_19218))) ) ),
    inference(variable_rename,[status(thm)],[f_4604_1]) ).

fof(f_4604_3,plain,
    ( ! [U_19230,U_19228,U_19226,U_19224,U_19222,U_19220] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19220),tc_List_Olist(U_19220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19220),tc_List_Olist(U_19220)),hAPP(hAPP(c_List_Olist_OCons(U_19220),U_19222),U_19224)),hAPP(hAPP(c_List_Olist_OCons(U_19220),U_19226),U_19228))),c_List_Olistrel1(U_19220,U_19230)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19220),tc_List_Olist(U_19220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19220),tc_List_Olist(U_19220)),U_19224),U_19228)),c_List_Olistrel1(U_19220,U_19230)))
            | U_19222 != U_19226 )
          & ( U_19224 != U_19228
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19220,U_19220)),hAPP(hAPP(c_Product__Type_OPair(U_19220,U_19220),U_19222),U_19226)),U_19230)) ) ) )
    & ! [U_19229,U_19227,U_19225,U_19223,U_19221,U_19219] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19219),tc_List_Olist(U_19219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19219),tc_List_Olist(U_19219)),U_19223),U_19227)),c_List_Olistrel1(U_19219,U_19229)))
          & U_19221 = U_19225 )
        | ( U_19223 = U_19227
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19219,U_19219)),hAPP(hAPP(c_Product__Type_OPair(U_19219,U_19219),U_19221),U_19225)),U_19229)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19219),tc_List_Olist(U_19219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19219),tc_List_Olist(U_19219)),hAPP(hAPP(c_List_Olist_OCons(U_19219),U_19221),U_19223)),hAPP(hAPP(c_List_Olist_OCons(U_19219),U_19225),U_19227))),c_List_Olistrel1(U_19219,U_19229))) ) ),
    inference(miniscope,[status(thm)],[f_4604_2]) ).

fof(f_4604_4,plain,
    ( ! [U_19220,U_19222,U_19224,U_19228,U_19226,U_19230] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19220),tc_List_Olist(U_19220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19220),tc_List_Olist(U_19220)),U_19224),U_19228)),c_List_Olistrel1(U_19220,U_19230)))
        | U_19222 != U_19226
        | ~ sP1187(U_19220,U_19222,U_19224,U_19228,U_19226,U_19230) )
    & ! [U_19220,U_19222,U_19224,U_19228,U_19226,U_19230] :
        ( U_19224 != U_19228
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19220,U_19220)),hAPP(hAPP(c_Product__Type_OPair(U_19220,U_19220),U_19222),U_19226)),U_19230))
        | ~ sP1187(U_19220,U_19222,U_19224,U_19228,U_19226,U_19230) )
    & ! [U_19219,U_19221,U_19223,U_19225,U_19227,U_19229] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19219),tc_List_Olist(U_19219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19219),tc_List_Olist(U_19219)),U_19223),U_19227)),c_List_Olistrel1(U_19219,U_19229)))
        | ~ sP1186(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) )
    & ! [U_19219,U_19221,U_19223,U_19225,U_19227,U_19229] :
        ( U_19221 = U_19225
        | ~ sP1186(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) )
    & ! [U_19219,U_19221,U_19223,U_19225,U_19227,U_19229] :
        ( U_19223 = U_19227
        | ~ sP1185(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) )
    & ! [U_19219,U_19221,U_19223,U_19225,U_19227,U_19229] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19219,U_19219)),hAPP(hAPP(c_Product__Type_OPair(U_19219,U_19219),U_19221),U_19225)),U_19229))
        | ~ sP1185(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) )
    & ! [U_19220,U_19222,U_19224,U_19228,U_19226,U_19230] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19220),tc_List_Olist(U_19220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19220),tc_List_Olist(U_19220)),hAPP(hAPP(c_List_Olist_OCons(U_19220),U_19222),U_19224)),hAPP(hAPP(c_List_Olist_OCons(U_19220),U_19226),U_19228))),c_List_Olistrel1(U_19220,U_19230)))
        | sP1187(U_19220,U_19222,U_19224,U_19228,U_19226,U_19230) )
    & ! [U_19219,U_19221,U_19223,U_19225,U_19227,U_19229] :
        ( sP1186(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229)
        | sP1185(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19219),tc_List_Olist(U_19219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19219),tc_List_Olist(U_19219)),hAPP(hAPP(c_List_Olist_OCons(U_19219),U_19221),U_19223)),hAPP(hAPP(c_List_Olist_OCons(U_19219),U_19225),U_19227))),c_List_Olistrel1(U_19219,U_19229))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1185,sP1186,sP1187])],[f_4604_3]) ).

cnf(f_4604_5,plain,
    ( sP1186(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229)
    | sP1185(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19219),tc_List_Olist(U_19219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19219),tc_List_Olist(U_19219)),hAPP(hAPP(c_List_Olist_OCons(U_19219),U_19221),U_19223)),hAPP(hAPP(c_List_Olist_OCons(U_19219),U_19225),U_19227))),c_List_Olistrel1(U_19219,U_19229))) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19220),tc_List_Olist(U_19220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19220),tc_List_Olist(U_19220)),hAPP(hAPP(c_List_Olist_OCons(U_19220),U_19222),U_19224)),hAPP(hAPP(c_List_Olist_OCons(U_19220),U_19226),U_19228))),c_List_Olistrel1(U_19220,U_19230)))
    | sP1187(U_19220,U_19222,U_19224,U_19228,U_19226,U_19230) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19219,U_19219)),hAPP(hAPP(c_Product__Type_OPair(U_19219,U_19219),U_19221),U_19225)),U_19229))
    | ~ sP1185(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_8,plain,
    ( U_19223 = U_19227
    | ~ sP1185(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_9,plain,
    ( U_19221 = U_19225
    | ~ sP1186(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19219),tc_List_Olist(U_19219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19219),tc_List_Olist(U_19219)),U_19223),U_19227)),c_List_Olistrel1(U_19219,U_19229)))
    | ~ sP1186(U_19219,U_19221,U_19223,U_19225,U_19227,U_19229) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_11,plain,
    ( U_19224 != U_19228
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19220,U_19220)),hAPP(hAPP(c_Product__Type_OPair(U_19220,U_19220),U_19222),U_19226)),U_19230))
    | ~ sP1187(U_19220,U_19222,U_19224,U_19228,U_19226,U_19230) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19220),tc_List_Olist(U_19220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19220),tc_List_Olist(U_19220)),U_19224),U_19228)),c_List_Olistrel1(U_19220,U_19230)))
    | U_19222 != U_19226
    | ~ sP1187(U_19220,U_19222,U_19224,U_19228,U_19226,U_19230) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

fof(f_4605_1,plain,
    ! [V_r_H_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2)))
      | ~ c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel]) ).

fof(f_4605_2,plain,
    ! [U_19233,U_19232,U_19231] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19231),tc_List_Olist(U_19231)),tc_HOL_Obool)),c_List_Olistrel1(U_19231,U_19232)),c_List_Olistrel(U_19231,U_19233)))
      | ~ c_Relation_Orefl__on(U_19231,c_Orderings_Otop__class_Otop(tc_fun(U_19231,tc_HOL_Obool)),U_19233)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19231,U_19231),tc_HOL_Obool)),U_19232),U_19233)) ),
    inference(variable_rename,[status(thm)],[f_4605_1]) ).

fof(f_4605_3,plain,
    ! [U_19231,U_19232,U_19233] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19231),tc_List_Olist(U_19231)),tc_HOL_Obool)),c_List_Olistrel1(U_19231,U_19232)),c_List_Olistrel(U_19231,U_19233)))
      | ~ c_Relation_Orefl__on(U_19231,c_Orderings_Otop__class_Otop(tc_fun(U_19231,tc_HOL_Obool)),U_19233)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19231,U_19231),tc_HOL_Obool)),U_19232),U_19233)) ),
    inference(definitional_conversion,[status(esa)],[f_4605_2]) ).

cnf(f_4605_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19231),tc_List_Olist(U_19231)),tc_HOL_Obool)),c_List_Olistrel1(U_19231,U_19232)),c_List_Olistrel(U_19231,U_19233)))
    | ~ c_Relation_Orefl__on(U_19231,c_Orderings_Otop__class_Otop(tc_fun(U_19231,tc_HOL_Obool)),U_19233)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19231,U_19231),tc_HOL_Obool)),U_19232),U_19233)) ),
    inference(clausify,[status(thm)],[f_4605_3]) ).

fof(f_4606_1,plain,
    ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
      | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
      | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I]) ).

fof(f_4606_2,plain,
    ! [U_19241,U_19240,U_19239,U_19238,U_19237,U_19236,U_19235,U_19234] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19234),tc_List_Olist(U_19234))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19234),tc_List_Olist(U_19234)),U_19238),U_19241)),c_List_Olistrel1(U_19234,U_19237)))
      | U_19241 != hAPP(hAPP(c_List_Oappend(U_19234),U_19239),hAPP(hAPP(c_List_Olist_OCons(U_19234),U_19236),U_19240))
      | U_19238 != hAPP(hAPP(c_List_Oappend(U_19234),U_19239),hAPP(hAPP(c_List_Olist_OCons(U_19234),U_19235),U_19240))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19234,U_19234)),hAPP(hAPP(c_Product__Type_OPair(U_19234,U_19234),U_19235),U_19236)),U_19237)) ),
    inference(variable_rename,[status(thm)],[f_4606_1]) ).

fof(f_4606_3,plain,
    ! [U_19234,U_19238,U_19236,U_19237,U_19240,U_19239,U_19235,U_19241] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19234),tc_List_Olist(U_19234))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19234),tc_List_Olist(U_19234)),U_19238),U_19241)),c_List_Olistrel1(U_19234,U_19237)))
      | U_19241 != hAPP(hAPP(c_List_Oappend(U_19234),U_19239),hAPP(hAPP(c_List_Olist_OCons(U_19234),U_19236),U_19240))
      | U_19238 != hAPP(hAPP(c_List_Oappend(U_19234),U_19239),hAPP(hAPP(c_List_Olist_OCons(U_19234),U_19235),U_19240))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19234,U_19234)),hAPP(hAPP(c_Product__Type_OPair(U_19234,U_19234),U_19235),U_19236)),U_19237)) ),
    inference(definitional_conversion,[status(esa)],[f_4606_2]) ).

cnf(f_4606_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19234),tc_List_Olist(U_19234))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19234),tc_List_Olist(U_19234)),U_19238),U_19241)),c_List_Olistrel1(U_19234,U_19237)))
    | U_19241 != hAPP(hAPP(c_List_Oappend(U_19234),U_19239),hAPP(hAPP(c_List_Olist_OCons(U_19234),U_19236),U_19240))
    | U_19238 != hAPP(hAPP(c_List_Oappend(U_19234),U_19239),hAPP(hAPP(c_List_Olist_OCons(U_19234),U_19235),U_19240))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19234,U_19234)),hAPP(hAPP(c_Product__Type_OPair(U_19234,U_19234),U_19235),U_19236)),U_19237)) ),
    inference(clausify,[status(thm)],[f_4606_3]) ).

fof(f_4607_1,plain,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2]) ).

fof(f_4607_2,plain,
    ! [U_19247,U_19246,U_19245,U_19244,U_19243,U_19242] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19242),tc_List_Olist(U_19242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19242),tc_List_Olist(U_19242)),hAPP(hAPP(c_List_Olist_OCons(U_19242),U_19243),U_19246)),hAPP(hAPP(c_List_Olist_OCons(U_19242),U_19244),U_19247))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19242),c_List_Olistrel1(U_19242,U_19245))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19242),tc_List_Olist(U_19242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19242),tc_List_Olist(U_19242)),U_19246),U_19247)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19242),c_List_Olistrel1(U_19242,U_19245))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19242,U_19242)),hAPP(hAPP(c_Product__Type_OPair(U_19242,U_19242),U_19243),U_19244)),c_Transitive__Closure_Ortrancl(U_19242,U_19245))) ),
    inference(variable_rename,[status(thm)],[f_4607_1]) ).

fof(f_4607_3,plain,
    ! [U_19242,U_19243,U_19244,U_19245,U_19246,U_19247] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19242),tc_List_Olist(U_19242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19242),tc_List_Olist(U_19242)),hAPP(hAPP(c_List_Olist_OCons(U_19242),U_19243),U_19246)),hAPP(hAPP(c_List_Olist_OCons(U_19242),U_19244),U_19247))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19242),c_List_Olistrel1(U_19242,U_19245))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19242),tc_List_Olist(U_19242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19242),tc_List_Olist(U_19242)),U_19246),U_19247)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19242),c_List_Olistrel1(U_19242,U_19245))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19242,U_19242)),hAPP(hAPP(c_Product__Type_OPair(U_19242,U_19242),U_19243),U_19244)),c_Transitive__Closure_Ortrancl(U_19242,U_19245))) ),
    inference(definitional_conversion,[status(esa)],[f_4607_2]) ).

cnf(f_4607_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19242),tc_List_Olist(U_19242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19242),tc_List_Olist(U_19242)),hAPP(hAPP(c_List_Olist_OCons(U_19242),U_19243),U_19246)),hAPP(hAPP(c_List_Olist_OCons(U_19242),U_19244),U_19247))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19242),c_List_Olistrel1(U_19242,U_19245))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19242),tc_List_Olist(U_19242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19242),tc_List_Olist(U_19242)),U_19246),U_19247)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19242),c_List_Olistrel1(U_19242,U_19245))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19242,U_19242)),hAPP(hAPP(c_Product__Type_OPair(U_19242,U_19242),U_19243),U_19244)),c_Transitive__Closure_Ortrancl(U_19242,U_19245))) ),
    inference(clausify,[status(thm)],[f_4607_3]) ).

fof(f_4608_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
        | ! [B_y,B_n] :
            ( V_ys_2 != hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) ) )
      & ( ? [B_y,B_n] :
            ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__iff__update]) ).

fof(f_4608_2,plain,
    ! [U_19255,U_19254,U_19253,U_19252] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19252),tc_List_Olist(U_19252))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19252),tc_List_Olist(U_19252)),U_19253),U_19254)),c_List_Olistrel1(U_19252,U_19255)))
        | ! [U_19251,U_19250] :
            ( U_19254 != hAPP(hAPP(c_List_Olist__update(U_19252,U_19253),U_19250),U_19251)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),U_19253)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19252,U_19252)),hAPP(hAPP(c_Product__Type_OPair(U_19252,U_19252),hAPP(hAPP(c_List_Onth(U_19252),U_19253),U_19250)),U_19251)),U_19255)) ) )
      & ( ? [U_19249,U_19248] :
            ( U_19254 = hAPP(hAPP(c_List_Olist__update(U_19252,U_19253),U_19248),U_19249)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),U_19253)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19252,U_19252)),hAPP(hAPP(c_Product__Type_OPair(U_19252,U_19252),hAPP(hAPP(c_List_Onth(U_19252),U_19253),U_19248)),U_19249)),U_19255)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19252),tc_List_Olist(U_19252))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19252),tc_List_Olist(U_19252)),U_19253),U_19254)),c_List_Olistrel1(U_19252,U_19255))) ) ),
    inference(variable_rename,[status(thm)],[f_4608_1]) ).

fof(f_4608_3,plain,
    ( ! [U_19263,U_19261,U_19259,U_19257] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19257),tc_List_Olist(U_19257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19257),tc_List_Olist(U_19257)),U_19259),U_19261)),c_List_Olistrel1(U_19257,U_19263)))
        | ! [U_19251,U_19250] :
            ( U_19261 != hAPP(hAPP(c_List_Olist__update(U_19257,U_19259),U_19250),U_19251)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19257)),U_19259)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19257,U_19257)),hAPP(hAPP(c_Product__Type_OPair(U_19257,U_19257),hAPP(hAPP(c_List_Onth(U_19257),U_19259),U_19250)),U_19251)),U_19263)) ) )
    & ! [U_19262,U_19260,U_19258,U_19256] :
        ( ? [U_19249,U_19248] :
            ( U_19260 = hAPP(hAPP(c_List_Olist__update(U_19256,U_19258),U_19248),U_19249)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19256)),U_19258)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19256,U_19256)),hAPP(hAPP(c_Product__Type_OPair(U_19256,U_19256),hAPP(hAPP(c_List_Onth(U_19256),U_19258),U_19248)),U_19249)),U_19262)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19256),tc_List_Olist(U_19256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19256),tc_List_Olist(U_19256)),U_19258),U_19260)),c_List_Olistrel1(U_19256,U_19262))) ) ),
    inference(miniscope,[status(thm)],[f_4608_2]) ).

fof(f_4608_4,plain,
    ( ! [U_19263,U_19261,U_19259,U_19257] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19257),tc_List_Olist(U_19257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19257),tc_List_Olist(U_19257)),U_19259),U_19261)),c_List_Olistrel1(U_19257,U_19263)))
        | ! [U_19251,U_19250] :
            ( U_19261 != hAPP(hAPP(c_List_Olist__update(U_19257,U_19259),U_19250),U_19251)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19257)),U_19259)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19257,U_19257)),hAPP(hAPP(c_Product__Type_OPair(U_19257,U_19257),hAPP(hAPP(c_List_Onth(U_19257),U_19259),U_19250)),U_19251)),U_19263)) ) )
    & ! [U_19262,U_19260,U_19258,U_19256] :
        ( ? [U_19248] :
            ( U_19260 = hAPP(hAPP(c_List_Olist__update(U_19256,U_19258),U_19248),sK476(U_19262,U_19260,U_19258,U_19256))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19256)),U_19258)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19256,U_19256)),hAPP(hAPP(c_Product__Type_OPair(U_19256,U_19256),hAPP(hAPP(c_List_Onth(U_19256),U_19258),U_19248)),sK476(U_19262,U_19260,U_19258,U_19256))),U_19262)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19256),tc_List_Olist(U_19256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19256),tc_List_Olist(U_19256)),U_19258),U_19260)),c_List_Olistrel1(U_19256,U_19262))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_19249,sK476(U_19262,U_19260,U_19258,U_19256))],[f_4608_3]) ).

fof(f_4608_5,plain,
    ( ! [U_19263,U_19261,U_19259,U_19257] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19257),tc_List_Olist(U_19257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19257),tc_List_Olist(U_19257)),U_19259),U_19261)),c_List_Olistrel1(U_19257,U_19263)))
        | ! [U_19251,U_19250] :
            ( U_19261 != hAPP(hAPP(c_List_Olist__update(U_19257,U_19259),U_19250),U_19251)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19257)),U_19259)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19257,U_19257)),hAPP(hAPP(c_Product__Type_OPair(U_19257,U_19257),hAPP(hAPP(c_List_Onth(U_19257),U_19259),U_19250)),U_19251)),U_19263)) ) )
    & ! [U_19262,U_19260,U_19258,U_19256] :
        ( ( U_19260 = hAPP(hAPP(c_List_Olist__update(U_19256,U_19258),sK477(U_19262,U_19260,U_19258,U_19256)),sK476(U_19262,U_19260,U_19258,U_19256))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK477(U_19262,U_19260,U_19258,U_19256)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19256)),U_19258)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19256,U_19256)),hAPP(hAPP(c_Product__Type_OPair(U_19256,U_19256),hAPP(hAPP(c_List_Onth(U_19256),U_19258),sK477(U_19262,U_19260,U_19258,U_19256))),sK476(U_19262,U_19260,U_19258,U_19256))),U_19262)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19256),tc_List_Olist(U_19256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19256),tc_List_Olist(U_19256)),U_19258),U_19260)),c_List_Olistrel1(U_19256,U_19262))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_19248,sK477(U_19262,U_19260,U_19258,U_19256))],[f_4608_4]) ).

fof(f_4608_6,plain,
    ( ! [U_19258,U_19262,U_19256,U_19260] :
        ( U_19260 = hAPP(hAPP(c_List_Olist__update(U_19256,U_19258),sK477(U_19262,U_19260,U_19258,U_19256)),sK476(U_19262,U_19260,U_19258,U_19256))
        | ~ sP1188(U_19258,U_19262,U_19256,U_19260) )
    & ! [U_19258,U_19262,U_19256,U_19260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK477(U_19262,U_19260,U_19258,U_19256)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19256)),U_19258)))
        | ~ sP1188(U_19258,U_19262,U_19256,U_19260) )
    & ! [U_19258,U_19262,U_19256,U_19260] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19256,U_19256)),hAPP(hAPP(c_Product__Type_OPair(U_19256,U_19256),hAPP(hAPP(c_List_Onth(U_19256),U_19258),sK477(U_19262,U_19260,U_19258,U_19256))),sK476(U_19262,U_19260,U_19258,U_19256))),U_19262))
        | ~ sP1188(U_19258,U_19262,U_19256,U_19260) )
    & ! [U_19250,U_19251,U_19257,U_19259,U_19261,U_19263] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19257),tc_List_Olist(U_19257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19257),tc_List_Olist(U_19257)),U_19259),U_19261)),c_List_Olistrel1(U_19257,U_19263)))
        | U_19261 != hAPP(hAPP(c_List_Olist__update(U_19257,U_19259),U_19250),U_19251)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19257)),U_19259)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19257,U_19257)),hAPP(hAPP(c_Product__Type_OPair(U_19257,U_19257),hAPP(hAPP(c_List_Onth(U_19257),U_19259),U_19250)),U_19251)),U_19263)) )
    & ! [U_19258,U_19262,U_19256,U_19260] :
        ( sP1188(U_19258,U_19262,U_19256,U_19260)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19256),tc_List_Olist(U_19256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19256),tc_List_Olist(U_19256)),U_19258),U_19260)),c_List_Olistrel1(U_19256,U_19262))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1188])],[f_4608_5]) ).

cnf(f_4608_7,plain,
    ( sP1188(U_19258,U_19262,U_19256,U_19260)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19256),tc_List_Olist(U_19256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19256),tc_List_Olist(U_19256)),U_19258),U_19260)),c_List_Olistrel1(U_19256,U_19262))) ),
    inference(clausify,[status(thm)],[f_4608_6]) ).

cnf(f_4608_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19257),tc_List_Olist(U_19257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19257),tc_List_Olist(U_19257)),U_19259),U_19261)),c_List_Olistrel1(U_19257,U_19263)))
    | U_19261 != hAPP(hAPP(c_List_Olist__update(U_19257,U_19259),U_19250),U_19251)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19257)),U_19259)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19257,U_19257)),hAPP(hAPP(c_Product__Type_OPair(U_19257,U_19257),hAPP(hAPP(c_List_Onth(U_19257),U_19259),U_19250)),U_19251)),U_19263)) ),
    inference(clausify,[status(thm)],[f_4608_6]) ).

cnf(f_4608_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19256,U_19256)),hAPP(hAPP(c_Product__Type_OPair(U_19256,U_19256),hAPP(hAPP(c_List_Onth(U_19256),U_19258),sK477(U_19262,U_19260,U_19258,U_19256))),sK476(U_19262,U_19260,U_19258,U_19256))),U_19262))
    | ~ sP1188(U_19258,U_19262,U_19256,U_19260) ),
    inference(clausify,[status(thm)],[f_4608_6]) ).

cnf(f_4608_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK477(U_19262,U_19260,U_19258,U_19256)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19256)),U_19258)))
    | ~ sP1188(U_19258,U_19262,U_19256,U_19260) ),
    inference(clausify,[status(thm)],[f_4608_6]) ).

cnf(f_4608_11,plain,
    ( U_19260 = hAPP(hAPP(c_List_Olist__update(U_19256,U_19258),sK477(U_19262,U_19260,U_19258,U_19256)),sK476(U_19262,U_19260,U_19258,U_19256))
    | ~ sP1188(U_19258,U_19262,U_19256,U_19260) ),
    inference(clausify,[status(thm)],[f_4608_6]) ).

fof(f_4609_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ? [B_x,B_y] :
          ( ? [B_us,B_vs] :
              ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs))
              & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1E]) ).

fof(f_4609_2,plain,
    ! [U_19271,U_19270,U_19269,U_19268] :
      ( ? [U_19267,U_19266] :
          ( ? [U_19265,U_19264] :
              ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),U_19265),hAPP(hAPP(c_List_Olist_OCons(U_19268),U_19266),U_19264))
              & U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),U_19265),hAPP(hAPP(c_List_Olist_OCons(U_19268),U_19267),U_19264)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),U_19267),U_19266)),U_19271)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ),
    inference(variable_rename,[status(thm)],[f_4609_1]) ).

fof(f_4609_3,plain,
    ! [U_19271,U_19270,U_19269,U_19268] :
      ( ? [U_19266] :
          ( ? [U_19265,U_19264] :
              ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),U_19265),hAPP(hAPP(c_List_Olist_OCons(U_19268),U_19266),U_19264))
              & U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),U_19265),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),U_19264)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),U_19266)),U_19271)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_19267,sK478(U_19271,U_19270,U_19269,U_19268))],[f_4609_2]) ).

fof(f_4609_4,plain,
    ! [U_19271,U_19270,U_19269,U_19268] :
      ( ( ? [U_19265,U_19264] :
            ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),U_19265),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK479(U_19271,U_19270,U_19269,U_19268)),U_19264))
            & U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),U_19265),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),U_19264)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK479(U_19271,U_19270,U_19269,U_19268))),U_19271)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_19266,sK479(U_19271,U_19270,U_19269,U_19268))],[f_4609_3]) ).

fof(f_4609_5,plain,
    ! [U_19271,U_19270,U_19269,U_19268] :
      ( ( ? [U_19264] :
            ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK479(U_19271,U_19270,U_19269,U_19268)),U_19264))
            & U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),U_19264)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK479(U_19271,U_19270,U_19269,U_19268))),U_19271)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_19265,sK480(U_19271,U_19270,U_19269,U_19268))],[f_4609_4]) ).

fof(f_4609_6,plain,
    ! [U_19271,U_19270,U_19269,U_19268] :
      ( ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK479(U_19271,U_19270,U_19269,U_19268)),sK481(U_19271,U_19270,U_19269,U_19268)))
        & U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK481(U_19271,U_19270,U_19269,U_19268)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK479(U_19271,U_19270,U_19269,U_19268))),U_19271)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_19264,sK481(U_19271,U_19270,U_19269,U_19268))],[f_4609_5]) ).

fof(f_4609_7,plain,
    ( ! [U_19268,U_19269,U_19270,U_19271] :
        ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK479(U_19271,U_19270,U_19269,U_19268)),sK481(U_19271,U_19270,U_19269,U_19268)))
        | ~ sP1189(U_19268,U_19269,U_19270,U_19271) )
    & ! [U_19268,U_19269,U_19270,U_19271] :
        ( U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK481(U_19271,U_19270,U_19269,U_19268)))
        | ~ sP1189(U_19268,U_19269,U_19270,U_19271) )
    & ! [U_19268,U_19269,U_19270,U_19271] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK479(U_19271,U_19270,U_19269,U_19268))),U_19271))
        | ~ sP1189(U_19268,U_19269,U_19270,U_19271) )
    & ! [U_19268,U_19269,U_19270,U_19271] :
        ( sP1189(U_19268,U_19269,U_19270,U_19271)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1189])],[f_4609_6]) ).

cnf(f_4609_8,plain,
    ( sP1189(U_19268,U_19269,U_19270,U_19271)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19268),tc_List_Olist(U_19268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19268),tc_List_Olist(U_19268)),U_19269),U_19270)),c_List_Olistrel1(U_19268,U_19271))) ),
    inference(clausify,[status(thm)],[f_4609_7]) ).

cnf(f_4609_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19268,U_19268)),hAPP(hAPP(c_Product__Type_OPair(U_19268,U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK479(U_19271,U_19270,U_19269,U_19268))),U_19271))
    | ~ sP1189(U_19268,U_19269,U_19270,U_19271) ),
    inference(clausify,[status(thm)],[f_4609_7]) ).

cnf(f_4609_10,plain,
    ( U_19269 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK478(U_19271,U_19270,U_19269,U_19268)),sK481(U_19271,U_19270,U_19269,U_19268)))
    | ~ sP1189(U_19268,U_19269,U_19270,U_19271) ),
    inference(clausify,[status(thm)],[f_4609_7]) ).

cnf(f_4609_11,plain,
    ( U_19270 = hAPP(hAPP(c_List_Oappend(U_19268),sK480(U_19271,U_19270,U_19269,U_19268)),hAPP(hAPP(c_List_Olist_OCons(U_19268),sK479(U_19271,U_19270,U_19269,U_19268)),sK481(U_19271,U_19270,U_19269,U_19268)))
    | ~ sP1189(U_19268,U_19269,U_19270,U_19271) ),
    inference(clausify,[status(thm)],[f_4609_7]) ).

fof(f_4610_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_rotate1__def]) ).

fof(f_4610_2,plain,
    ! [U_19273,U_19272] : hAPP(c_List_Orotate1(U_19272),U_19273) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19272),U_19272,c_List_Olist_ONil(U_19272),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19272),tc_fun(tc_List_Olist(U_19272),tc_List_Olist(U_19272)),U_19272),hAPP(c_COMBC(tc_List_Olist(U_19272),tc_List_Olist(U_19272),tc_List_Olist(U_19272)),c_List_Oappend(U_19272))),hAPP(hAPP(c_COMBC(U_19272,tc_List_Olist(U_19272),tc_List_Olist(U_19272)),c_List_Olist_OCons(U_19272)),c_List_Olist_ONil(U_19272)))),U_19273),
    inference(variable_rename,[status(thm)],[f_4610_1]) ).

fof(f_4610_3,plain,
    ! [U_19273,U_19272] : hAPP(c_List_Orotate1(U_19272),U_19273) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19272),U_19272,c_List_Olist_ONil(U_19272),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19272),tc_fun(tc_List_Olist(U_19272),tc_List_Olist(U_19272)),U_19272),hAPP(c_COMBC(tc_List_Olist(U_19272),tc_List_Olist(U_19272),tc_List_Olist(U_19272)),c_List_Oappend(U_19272))),hAPP(hAPP(c_COMBC(U_19272,tc_List_Olist(U_19272),tc_List_Olist(U_19272)),c_List_Olist_OCons(U_19272)),c_List_Olist_ONil(U_19272)))),U_19273),
    inference(definitional_conversion,[status(esa)],[f_4610_2]) ).

cnf(f_4610_4,plain,
    hAPP(c_List_Orotate1(U_19272),U_19273) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19272),U_19272,c_List_Olist_ONil(U_19272),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19272),tc_fun(tc_List_Olist(U_19272),tc_List_Olist(U_19272)),U_19272),hAPP(c_COMBC(tc_List_Olist(U_19272),tc_List_Olist(U_19272),tc_List_Olist(U_19272)),c_List_Oappend(U_19272))),hAPP(hAPP(c_COMBC(U_19272,tc_List_Olist(U_19272),tc_List_Olist(U_19272)),c_List_Olist_OCons(U_19272)),c_List_Olist_ONil(U_19272)))),U_19273),
    inference(clausify,[status(thm)],[f_4610_3]) ).

fof(f_4611_1,plain,
    ! [V_a,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop]) ).

fof(f_4611_2,plain,
    ! [U_19277,U_19276,U_19275,U_19274] :
      ( hAPP(hAPP(c_List_Olist__update(U_19275,U_19276),U_19274),U_19277) = hAPP(hAPP(c_List_Oappend(U_19275),hAPP(hAPP(c_List_Otake(U_19275),U_19274),U_19276)),hAPP(hAPP(c_List_Olist_OCons(U_19275),U_19277),hAPP(hAPP(c_List_Odrop(U_19275),hAPP(c_Nat_OSuc,U_19274)),U_19276)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19276))) ),
    inference(variable_rename,[status(thm)],[f_4611_1]) ).

fof(f_4611_3,plain,
    ! [U_19274,U_19275,U_19276,U_19277] :
      ( hAPP(hAPP(c_List_Olist__update(U_19275,U_19276),U_19274),U_19277) = hAPP(hAPP(c_List_Oappend(U_19275),hAPP(hAPP(c_List_Otake(U_19275),U_19274),U_19276)),hAPP(hAPP(c_List_Olist_OCons(U_19275),U_19277),hAPP(hAPP(c_List_Odrop(U_19275),hAPP(c_Nat_OSuc,U_19274)),U_19276)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19276))) ),
    inference(definitional_conversion,[status(esa)],[f_4611_2]) ).

cnf(f_4611_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19275,U_19276),U_19274),U_19277) = hAPP(hAPP(c_List_Oappend(U_19275),hAPP(hAPP(c_List_Otake(U_19275),U_19274),U_19276)),hAPP(hAPP(c_List_Olist_OCons(U_19275),U_19277),hAPP(hAPP(c_List_Odrop(U_19275),hAPP(c_Nat_OSuc,U_19274)),U_19276)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19276))) ),
    inference(clausify,[status(thm)],[f_4611_3]) ).

fof(f_4612_1,plain,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_drop__append]) ).

fof(f_4612_2,plain,
    ! [U_19281,U_19280,U_19279,U_19278] : hAPP(hAPP(c_List_Odrop(U_19278),U_19279),hAPP(hAPP(c_List_Oappend(U_19278),U_19280),U_19281)) = hAPP(hAPP(c_List_Oappend(U_19278),hAPP(hAPP(c_List_Odrop(U_19278),U_19279),U_19280)),hAPP(hAPP(c_List_Odrop(U_19278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19279),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19278)),U_19280))),U_19281)),
    inference(variable_rename,[status(thm)],[f_4612_1]) ).

fof(f_4612_3,plain,
    ! [U_19278,U_19279,U_19280,U_19281] : hAPP(hAPP(c_List_Odrop(U_19278),U_19279),hAPP(hAPP(c_List_Oappend(U_19278),U_19280),U_19281)) = hAPP(hAPP(c_List_Oappend(U_19278),hAPP(hAPP(c_List_Odrop(U_19278),U_19279),U_19280)),hAPP(hAPP(c_List_Odrop(U_19278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19279),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19278)),U_19280))),U_19281)),
    inference(definitional_conversion,[status(esa)],[f_4612_2]) ).

cnf(f_4612_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19278),U_19279),hAPP(hAPP(c_List_Oappend(U_19278),U_19280),U_19281)) = hAPP(hAPP(c_List_Oappend(U_19278),hAPP(hAPP(c_List_Odrop(U_19278),U_19279),U_19280)),hAPP(hAPP(c_List_Odrop(U_19278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19279),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19278)),U_19280))),U_19281)),
    inference(clausify,[status(thm)],[f_4612_3]) ).

fof(f_4613_1,plain,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_drop__Nil]) ).

fof(f_4613_2,plain,
    ! [U_19283,U_19282] : hAPP(hAPP(c_List_Odrop(U_19282),U_19283),c_List_Olist_ONil(U_19282)) = c_List_Olist_ONil(U_19282),
    inference(variable_rename,[status(thm)],[f_4613_1]) ).

fof(f_4613_3,plain,
    ! [U_19283,U_19282] : hAPP(hAPP(c_List_Odrop(U_19282),U_19283),c_List_Olist_ONil(U_19282)) = c_List_Olist_ONil(U_19282),
    inference(definitional_conversion,[status(esa)],[f_4613_2]) ).

cnf(f_4613_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19282),U_19283),c_List_Olist_ONil(U_19282)) = c_List_Olist_ONil(U_19282),
    inference(clausify,[status(thm)],[f_4613_3]) ).

fof(f_4614_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Orotate1(T_b),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv]) ).

fof(f_4614_2,plain,
    ! [U_19285,U_19284] :
      ( ( hAPP(c_List_Orotate1(U_19284),U_19285) = c_List_Olist_ONil(U_19284)
        | U_19285 != c_List_Olist_ONil(U_19284) )
      & ( U_19285 = c_List_Olist_ONil(U_19284)
        | hAPP(c_List_Orotate1(U_19284),U_19285) != c_List_Olist_ONil(U_19284) ) ),
    inference(variable_rename,[status(thm)],[f_4614_1]) ).

fof(f_4614_3,plain,
    ( ! [U_19289,U_19287] :
        ( hAPP(c_List_Orotate1(U_19287),U_19289) = c_List_Olist_ONil(U_19287)
        | U_19289 != c_List_Olist_ONil(U_19287) )
    & ! [U_19288,U_19286] :
        ( U_19288 = c_List_Olist_ONil(U_19286)
        | hAPP(c_List_Orotate1(U_19286),U_19288) != c_List_Olist_ONil(U_19286) ) ),
    inference(miniscope,[status(thm)],[f_4614_2]) ).

fof(f_4614_4,plain,
    ( ! [U_19289,U_19287] :
        ( hAPP(c_List_Orotate1(U_19287),U_19289) = c_List_Olist_ONil(U_19287)
        | U_19289 != c_List_Olist_ONil(U_19287) )
    & ! [U_19288,U_19286] :
        ( U_19288 = c_List_Olist_ONil(U_19286)
        | hAPP(c_List_Orotate1(U_19286),U_19288) != c_List_Olist_ONil(U_19286) ) ),
    inference(definitional_conversion,[status(esa)],[f_4614_3]) ).

cnf(f_4614_5,plain,
    ( U_19288 = c_List_Olist_ONil(U_19286)
    | hAPP(c_List_Orotate1(U_19286),U_19288) != c_List_Olist_ONil(U_19286) ),
    inference(clausify,[status(thm)],[f_4614_4]) ).

cnf(f_4614_6,plain,
    ( hAPP(c_List_Orotate1(U_19287),U_19289) = c_List_Olist_ONil(U_19287)
    | U_19289 != c_List_Olist_ONil(U_19287) ),
    inference(clausify,[status(thm)],[f_4614_4]) ).

fof(f_4615_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__take]) ).

fof(f_4615_2,plain,
    ! [U_19293,U_19292,U_19291,U_19290] : hAPP(hAPP(c_List_Odrop(U_19290),U_19291),hAPP(hAPP(c_List_Otake(U_19290),U_19292),U_19293)) = hAPP(hAPP(c_List_Otake(U_19290),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19292),U_19291)),hAPP(hAPP(c_List_Odrop(U_19290),U_19291),U_19293)),
    inference(variable_rename,[status(thm)],[f_4615_1]) ).

fof(f_4615_3,plain,
    ! [U_19290,U_19292,U_19291,U_19293] : hAPP(hAPP(c_List_Odrop(U_19290),U_19291),hAPP(hAPP(c_List_Otake(U_19290),U_19292),U_19293)) = hAPP(hAPP(c_List_Otake(U_19290),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19292),U_19291)),hAPP(hAPP(c_List_Odrop(U_19290),U_19291),U_19293)),
    inference(definitional_conversion,[status(esa)],[f_4615_2]) ).

cnf(f_4615_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19290),U_19291),hAPP(hAPP(c_List_Otake(U_19290),U_19292),U_19293)) = hAPP(hAPP(c_List_Otake(U_19290),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19292),U_19291)),hAPP(hAPP(c_List_Odrop(U_19290),U_19291),U_19293)),
    inference(clausify,[status(thm)],[f_4615_3]) ).

fof(f_4616_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__drop]) ).

fof(f_4616_2,plain,
    ! [U_19297,U_19296,U_19295,U_19294] : hAPP(hAPP(c_List_Otake(U_19294),U_19295),hAPP(hAPP(c_List_Odrop(U_19294),U_19296),U_19297)) = hAPP(hAPP(c_List_Odrop(U_19294),U_19296),hAPP(hAPP(c_List_Otake(U_19294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19295),U_19296)),U_19297)),
    inference(variable_rename,[status(thm)],[f_4616_1]) ).

fof(f_4616_3,plain,
    ! [U_19294,U_19295,U_19296,U_19297] : hAPP(hAPP(c_List_Otake(U_19294),U_19295),hAPP(hAPP(c_List_Odrop(U_19294),U_19296),U_19297)) = hAPP(hAPP(c_List_Odrop(U_19294),U_19296),hAPP(hAPP(c_List_Otake(U_19294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19295),U_19296)),U_19297)),
    inference(definitional_conversion,[status(esa)],[f_4616_2]) ).

cnf(f_4616_4,plain,
    hAPP(hAPP(c_List_Otake(U_19294),U_19295),hAPP(hAPP(c_List_Odrop(U_19294),U_19296),U_19297)) = hAPP(hAPP(c_List_Odrop(U_19294),U_19296),hAPP(hAPP(c_List_Otake(U_19294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19295),U_19296)),U_19297)),
    inference(clausify,[status(thm)],[f_4616_3]) ).

fof(f_4617_1,plain,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__dropD]) ).

fof(f_4617_2,plain,
    ! [U_19301,U_19300,U_19299,U_19298] :
      ( hBOOL(hAPP(hAPP(c_member(U_19298),U_19299),hAPP(c_List_Oset(U_19298),U_19301)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19298),U_19299),hAPP(c_List_Oset(U_19298),hAPP(hAPP(c_List_Odrop(U_19298),U_19300),U_19301)))) ),
    inference(variable_rename,[status(thm)],[f_4617_1]) ).

fof(f_4617_3,plain,
    ! [U_19298,U_19299,U_19300,U_19301] :
      ( hBOOL(hAPP(hAPP(c_member(U_19298),U_19299),hAPP(c_List_Oset(U_19298),U_19301)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19298),U_19299),hAPP(c_List_Oset(U_19298),hAPP(hAPP(c_List_Odrop(U_19298),U_19300),U_19301)))) ),
    inference(definitional_conversion,[status(esa)],[f_4617_2]) ).

cnf(f_4617_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19298),U_19299),hAPP(c_List_Oset(U_19298),U_19301)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19298),U_19299),hAPP(c_List_Oset(U_19298),hAPP(hAPP(c_List_Odrop(U_19298),U_19300),U_19301)))) ),
    inference(clausify,[status(thm)],[f_4617_3]) ).

fof(f_4618_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rotate1]) ).

fof(f_4618_2,plain,
    ! [U_19303,U_19302] : hAPP(c_List_Oset(U_19302),hAPP(c_List_Orotate1(U_19302),U_19303)) = hAPP(c_List_Oset(U_19302),U_19303),
    inference(variable_rename,[status(thm)],[f_4618_1]) ).

fof(f_4618_3,plain,
    ! [U_19302,U_19303] : hAPP(c_List_Oset(U_19302),hAPP(c_List_Orotate1(U_19302),U_19303)) = hAPP(c_List_Oset(U_19302),U_19303),
    inference(definitional_conversion,[status(esa)],[f_4618_2]) ).

cnf(f_4618_4,plain,
    hAPP(c_List_Oset(U_19302),hAPP(c_List_Orotate1(U_19302),U_19303)) = hAPP(c_List_Oset(U_19302),U_19303),
    inference(clausify,[status(thm)],[f_4618_3]) ).

fof(f_4619_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__drop__subset]) ).

fof(f_4619_2,plain,
    ! [U_19306,U_19305,U_19304] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19304,tc_HOL_Obool)),hAPP(c_List_Oset(U_19304),hAPP(hAPP(c_List_Odrop(U_19304),U_19305),U_19306))),hAPP(c_List_Oset(U_19304),U_19306))),
    inference(variable_rename,[status(thm)],[f_4619_1]) ).

fof(f_4619_3,plain,
    ! [U_19304,U_19305,U_19306] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19304,tc_HOL_Obool)),hAPP(c_List_Oset(U_19304),hAPP(hAPP(c_List_Odrop(U_19304),U_19305),U_19306))),hAPP(c_List_Oset(U_19304),U_19306))),
    inference(definitional_conversion,[status(esa)],[f_4619_2]) ).

cnf(f_4619_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19304,tc_HOL_Obool)),hAPP(c_List_Oset(U_19304),hAPP(hAPP(c_List_Odrop(U_19304),U_19305),U_19306))),hAPP(c_List_Oset(U_19304),U_19306))),
    inference(clausify,[status(thm)],[f_4619_3]) ).

fof(f_4620_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct1__rotate]) ).

fof(f_4620_2,plain,
    ! [U_19308,U_19307] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19307),hAPP(c_List_Orotate1(U_19307),U_19308)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19307),U_19308)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19307),U_19308))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19307),hAPP(c_List_Orotate1(U_19307),U_19308))) ) ),
    inference(variable_rename,[status(thm)],[f_4620_1]) ).

fof(f_4620_3,plain,
    ( ! [U_19312,U_19310] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19310),hAPP(c_List_Orotate1(U_19310),U_19312)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19310),U_19312)) )
    & ! [U_19311,U_19309] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19309),U_19311))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19309),hAPP(c_List_Orotate1(U_19309),U_19311))) ) ),
    inference(miniscope,[status(thm)],[f_4620_2]) ).

fof(f_4620_4,plain,
    ( ! [U_19310,U_19312] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19310),hAPP(c_List_Orotate1(U_19310),U_19312)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19310),U_19312)) )
    & ! [U_19311,U_19309] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19309),U_19311))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19309),hAPP(c_List_Orotate1(U_19309),U_19311))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4620_3]) ).

cnf(f_4620_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19309),U_19311))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19309),hAPP(c_List_Orotate1(U_19309),U_19311))) ),
    inference(clausify,[status(thm)],[f_4620_4]) ).

cnf(f_4620_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19310),hAPP(c_List_Orotate1(U_19310),U_19312)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19310),U_19312)) ),
    inference(clausify,[status(thm)],[f_4620_4]) ).

fof(f_4621_1,plain,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__drop]) ).

fof(f_4621_2,plain,
    ! [U_19315,U_19314,U_19313] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19313),hAPP(hAPP(c_List_Odrop(U_19313),U_19315),U_19314)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19313),U_19314)) ),
    inference(variable_rename,[status(thm)],[f_4621_1]) ).

fof(f_4621_3,plain,
    ! [U_19313,U_19314,U_19315] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19313),hAPP(hAPP(c_List_Odrop(U_19313),U_19315),U_19314)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19313),U_19314)) ),
    inference(definitional_conversion,[status(esa)],[f_4621_2]) ).

cnf(f_4621_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19313),hAPP(hAPP(c_List_Odrop(U_19313),U_19315),U_19314)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19313),U_19314)) ),
    inference(clausify,[status(thm)],[f_4621_3]) ).

fof(f_4622_1,plain,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_drop__0]) ).

fof(f_4622_2,plain,
    ! [U_19317,U_19316] : hAPP(hAPP(c_List_Odrop(U_19316),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19317) = U_19317,
    inference(variable_rename,[status(thm)],[f_4622_1]) ).

fof(f_4622_3,plain,
    ! [U_19316,U_19317] : hAPP(hAPP(c_List_Odrop(U_19316),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19317) = U_19317,
    inference(definitional_conversion,[status(esa)],[f_4622_2]) ).

cnf(f_4622_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19316),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19317) = U_19317,
    inference(clausify,[status(thm)],[f_4622_3]) ).

fof(f_4623_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_drop__drop]) ).

fof(f_4623_2,plain,
    ! [U_19321,U_19320,U_19319,U_19318] : hAPP(hAPP(c_List_Odrop(U_19318),U_19319),hAPP(hAPP(c_List_Odrop(U_19318),U_19320),U_19321)) = hAPP(hAPP(c_List_Odrop(U_19318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19319),U_19320)),U_19321),
    inference(variable_rename,[status(thm)],[f_4623_1]) ).

fof(f_4623_3,plain,
    ! [U_19318,U_19319,U_19320,U_19321] : hAPP(hAPP(c_List_Odrop(U_19318),U_19319),hAPP(hAPP(c_List_Odrop(U_19318),U_19320),U_19321)) = hAPP(hAPP(c_List_Odrop(U_19318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19319),U_19320)),U_19321),
    inference(definitional_conversion,[status(esa)],[f_4623_2]) ).

cnf(f_4623_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19318),U_19319),hAPP(hAPP(c_List_Odrop(U_19318),U_19320),U_19321)) = hAPP(hAPP(c_List_Odrop(U_19318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19319),U_19320)),U_19321),
    inference(clausify,[status(thm)],[f_4623_3]) ).

fof(f_4624_1,plain,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_drop__zip]) ).

fof(f_4624_2,plain,
    ! [U_19326,U_19325,U_19324,U_19323,U_19322] : hAPP(hAPP(c_List_Odrop(tc_prod(U_19322,U_19323)),U_19324),hAPP(hAPP(c_List_Ozip(U_19322,U_19323),U_19325),U_19326)) = hAPP(hAPP(c_List_Ozip(U_19322,U_19323),hAPP(hAPP(c_List_Odrop(U_19322),U_19324),U_19325)),hAPP(hAPP(c_List_Odrop(U_19323),U_19324),U_19326)),
    inference(variable_rename,[status(thm)],[f_4624_1]) ).

fof(f_4624_3,plain,
    ! [U_19322,U_19323,U_19324,U_19325,U_19326] : hAPP(hAPP(c_List_Odrop(tc_prod(U_19322,U_19323)),U_19324),hAPP(hAPP(c_List_Ozip(U_19322,U_19323),U_19325),U_19326)) = hAPP(hAPP(c_List_Ozip(U_19322,U_19323),hAPP(hAPP(c_List_Odrop(U_19322),U_19324),U_19325)),hAPP(hAPP(c_List_Odrop(U_19323),U_19324),U_19326)),
    inference(definitional_conversion,[status(esa)],[f_4624_2]) ).

cnf(f_4624_4,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(U_19322,U_19323)),U_19324),hAPP(hAPP(c_List_Ozip(U_19322,U_19323),U_19325),U_19326)) = hAPP(hAPP(c_List_Ozip(U_19322,U_19323),hAPP(hAPP(c_List_Odrop(U_19322),U_19324),U_19325)),hAPP(hAPP(c_List_Odrop(U_19323),U_19324),U_19326)),
    inference(clausify,[status(thm)],[f_4624_3]) ).

fof(f_4625_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_drop__map]) ).

fof(f_4625_2,plain,
    ! [U_19331,U_19330,U_19329,U_19328,U_19327] : hAPP(hAPP(c_List_Odrop(U_19327),U_19328),hAPP(hAPP(c_List_Omap(U_19329,U_19327),U_19330),U_19331)) = hAPP(hAPP(c_List_Omap(U_19329,U_19327),U_19330),hAPP(hAPP(c_List_Odrop(U_19329),U_19328),U_19331)),
    inference(variable_rename,[status(thm)],[f_4625_1]) ).

fof(f_4625_3,plain,
    ! [U_19327,U_19328,U_19329,U_19330,U_19331] : hAPP(hAPP(c_List_Odrop(U_19327),U_19328),hAPP(hAPP(c_List_Omap(U_19329,U_19327),U_19330),U_19331)) = hAPP(hAPP(c_List_Omap(U_19329,U_19327),U_19330),hAPP(hAPP(c_List_Odrop(U_19329),U_19328),U_19331)),
    inference(definitional_conversion,[status(esa)],[f_4625_2]) ).

cnf(f_4625_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19327),U_19328),hAPP(hAPP(c_List_Omap(U_19329,U_19327),U_19330),U_19331)) = hAPP(hAPP(c_List_Omap(U_19329,U_19327),U_19330),hAPP(hAPP(c_List_Odrop(U_19329),U_19328),U_19331)),
    inference(clausify,[status(thm)],[f_4625_3]) ).

fof(f_4626_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__rotate1]) ).

fof(f_4626_2,plain,
    ! [U_19333,U_19332] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19332)),hAPP(c_List_Orotate1(U_19332),U_19333)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19332)),U_19333),
    inference(variable_rename,[status(thm)],[f_4626_1]) ).

fof(f_4626_3,plain,
    ! [U_19332,U_19333] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19332)),hAPP(c_List_Orotate1(U_19332),U_19333)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19332)),U_19333),
    inference(definitional_conversion,[status(esa)],[f_4626_2]) ).

cnf(f_4626_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19332)),hAPP(c_List_Orotate1(U_19332),U_19333)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19332)),U_19333),
    inference(clausify,[status(thm)],[f_4626_3]) ).

fof(f_4627_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    inference(fof_nnf,[status(thm)],[fact_length__drop]) ).

fof(f_4627_2,plain,
    ! [U_19336,U_19335,U_19334] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),hAPP(hAPP(c_List_Odrop(U_19334),U_19335),U_19336)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),U_19336)),U_19335),
    inference(variable_rename,[status(thm)],[f_4627_1]) ).

fof(f_4627_3,plain,
    ! [U_19334,U_19335,U_19336] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),hAPP(hAPP(c_List_Odrop(U_19334),U_19335),U_19336)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),U_19336)),U_19335),
    inference(definitional_conversion,[status(esa)],[f_4627_2]) ).

cnf(f_4627_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),hAPP(hAPP(c_List_Odrop(U_19334),U_19335),U_19336)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),U_19336)),U_19335),
    inference(clausify,[status(thm)],[f_4627_3]) ).

fof(f_4628_1,plain,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs),
    inference(fof_nnf,[status(thm)],[fact_drop__Suc__Cons]) ).

fof(f_4628_2,plain,
    ! [U_19340,U_19339,U_19338,U_19337] : hAPP(hAPP(c_List_Odrop(U_19337),hAPP(c_Nat_OSuc,U_19338)),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19339),U_19340)) = hAPP(hAPP(c_List_Odrop(U_19337),U_19338),U_19340),
    inference(variable_rename,[status(thm)],[f_4628_1]) ).

fof(f_4628_3,plain,
    ! [U_19337,U_19338,U_19339,U_19340] : hAPP(hAPP(c_List_Odrop(U_19337),hAPP(c_Nat_OSuc,U_19338)),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19339),U_19340)) = hAPP(hAPP(c_List_Odrop(U_19337),U_19338),U_19340),
    inference(definitional_conversion,[status(esa)],[f_4628_2]) ).

cnf(f_4628_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19337),hAPP(c_Nat_OSuc,U_19338)),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19339),U_19340)) = hAPP(hAPP(c_List_Odrop(U_19337),U_19338),U_19340),
    inference(clausify,[status(thm)],[f_4628_3]) ).

fof(f_4629_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_drop__1__Cons]) ).

fof(f_4629_2,plain,
    ! [U_19343,U_19342,U_19341] : hAPP(hAPP(c_List_Odrop(U_19341),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19341),U_19342),U_19343)) = U_19343,
    inference(variable_rename,[status(thm)],[f_4629_1]) ).

fof(f_4629_3,plain,
    ! [U_19341,U_19342,U_19343] : hAPP(hAPP(c_List_Odrop(U_19341),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19341),U_19342),U_19343)) = U_19343,
    inference(definitional_conversion,[status(esa)],[f_4629_2]) ).

cnf(f_4629_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19341),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19341),U_19342),U_19343)) = U_19343,
    inference(clausify,[status(thm)],[f_4629_3]) ).

fof(f_4630_1,plain,
    ! [V_ys,V_y,V_xs,V_n,T_a] :
      ( hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y
      | hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) ),
    inference(fof_nnf,[status(thm)],[fact_nth__via__drop]) ).

fof(f_4630_2,plain,
    ! [U_19348,U_19347,U_19346,U_19345,U_19344] :
      ( hAPP(hAPP(c_List_Onth(U_19344),U_19346),U_19345) = U_19347
      | hAPP(hAPP(c_List_Odrop(U_19344),U_19345),U_19346) != hAPP(hAPP(c_List_Olist_OCons(U_19344),U_19347),U_19348) ),
    inference(variable_rename,[status(thm)],[f_4630_1]) ).

fof(f_4630_3,plain,
    ! [U_19344,U_19345,U_19346,U_19347,U_19348] :
      ( hAPP(hAPP(c_List_Onth(U_19344),U_19346),U_19345) = U_19347
      | hAPP(hAPP(c_List_Odrop(U_19344),U_19345),U_19346) != hAPP(hAPP(c_List_Olist_OCons(U_19344),U_19347),U_19348) ),
    inference(definitional_conversion,[status(esa)],[f_4630_2]) ).

cnf(f_4630_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_19344),U_19346),U_19345) = U_19347
    | hAPP(hAPP(c_List_Odrop(U_19344),U_19345),U_19346) != hAPP(hAPP(c_List_Olist_OCons(U_19344),U_19347),U_19348) ),
    inference(clausify,[status(thm)],[f_4630_3]) ).

fof(f_4631_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_drop__all]) ).

fof(f_4631_2,plain,
    ! [U_19351,U_19350,U_19349] :
      ( hAPP(hAPP(c_List_Odrop(U_19349),U_19351),U_19350) = c_List_Olist_ONil(U_19349)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19349)),U_19350)),U_19351)) ),
    inference(variable_rename,[status(thm)],[f_4631_1]) ).

fof(f_4631_3,plain,
    ! [U_19349,U_19350,U_19351] :
      ( hAPP(hAPP(c_List_Odrop(U_19349),U_19351),U_19350) = c_List_Olist_ONil(U_19349)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19349)),U_19350)),U_19351)) ),
    inference(definitional_conversion,[status(esa)],[f_4631_2]) ).

cnf(f_4631_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19349),U_19351),U_19350) = c_List_Olist_ONil(U_19349)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19349)),U_19350)),U_19351)) ),
    inference(clausify,[status(thm)],[f_4631_3]) ).

fof(f_4632_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2))
        | hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil]) ).

fof(f_4632_2,plain,
    ! [U_19354,U_19353,U_19352] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19352),U_19353),U_19354) = c_List_Olist_ONil(U_19352)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19352)),U_19354)),U_19353)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19352)),U_19354)),U_19353))
        | hAPP(hAPP(c_List_Odrop(U_19352),U_19353),U_19354) != c_List_Olist_ONil(U_19352) ) ),
    inference(variable_rename,[status(thm)],[f_4632_1]) ).

fof(f_4632_3,plain,
    ( ! [U_19360,U_19358,U_19356] :
        ( hAPP(hAPP(c_List_Odrop(U_19356),U_19358),U_19360) = c_List_Olist_ONil(U_19356)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19356)),U_19360)),U_19358)) )
    & ! [U_19359,U_19357,U_19355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19355)),U_19359)),U_19357))
        | hAPP(hAPP(c_List_Odrop(U_19355),U_19357),U_19359) != c_List_Olist_ONil(U_19355) ) ),
    inference(miniscope,[status(thm)],[f_4632_2]) ).

fof(f_4632_4,plain,
    ( ! [U_19356,U_19358,U_19360] :
        ( hAPP(hAPP(c_List_Odrop(U_19356),U_19358),U_19360) = c_List_Olist_ONil(U_19356)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19356)),U_19360)),U_19358)) )
    & ! [U_19359,U_19357,U_19355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19355)),U_19359)),U_19357))
        | hAPP(hAPP(c_List_Odrop(U_19355),U_19357),U_19359) != c_List_Olist_ONil(U_19355) ) ),
    inference(definitional_conversion,[status(esa)],[f_4632_3]) ).

cnf(f_4632_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19355)),U_19359)),U_19357))
    | hAPP(hAPP(c_List_Odrop(U_19355),U_19357),U_19359) != c_List_Olist_ONil(U_19355) ),
    inference(clausify,[status(thm)],[f_4632_4]) ).

cnf(f_4632_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19356),U_19358),U_19360) = c_List_Olist_ONil(U_19356)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19356)),U_19360)),U_19358)) ),
    inference(clausify,[status(thm)],[f_4632_4]) ).

fof(f_4633_1,plain,
    ! [V_xs_2,T_b,V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop]) ).

fof(f_4633_2,plain,
    ! [U_19364,U_19363,U_19362,U_19361] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19363,tc_HOL_Obool)),hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Odrop(U_19363),U_19362),U_19364))),hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Odrop(U_19363),U_19361),U_19364))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19361),U_19362)) ),
    inference(variable_rename,[status(thm)],[f_4633_1]) ).

fof(f_4633_3,plain,
    ! [U_19361,U_19362,U_19363,U_19364] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19363,tc_HOL_Obool)),hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Odrop(U_19363),U_19362),U_19364))),hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Odrop(U_19363),U_19361),U_19364))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19361),U_19362)) ),
    inference(definitional_conversion,[status(esa)],[f_4633_2]) ).

cnf(f_4633_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19363,tc_HOL_Obool)),hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Odrop(U_19363),U_19362),U_19364))),hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Odrop(U_19363),U_19361),U_19364))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19361),U_19362)) ),
    inference(clausify,[status(thm)],[f_4633_3]) ).

fof(f_4634_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_append__take__drop__id]) ).

fof(f_4634_2,plain,
    ! [U_19367,U_19366,U_19365] : hAPP(hAPP(c_List_Oappend(U_19365),hAPP(hAPP(c_List_Otake(U_19365),U_19366),U_19367)),hAPP(hAPP(c_List_Odrop(U_19365),U_19366),U_19367)) = U_19367,
    inference(variable_rename,[status(thm)],[f_4634_1]) ).

fof(f_4634_3,plain,
    ! [U_19365,U_19366,U_19367] : hAPP(hAPP(c_List_Oappend(U_19365),hAPP(hAPP(c_List_Otake(U_19365),U_19366),U_19367)),hAPP(hAPP(c_List_Odrop(U_19365),U_19366),U_19367)) = U_19367,
    inference(definitional_conversion,[status(esa)],[f_4634_2]) ).

cnf(f_4634_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19365),hAPP(hAPP(c_List_Otake(U_19365),U_19366),U_19367)),hAPP(hAPP(c_List_Odrop(U_19365),U_19366),U_19367)) = U_19367,
    inference(clausify,[status(thm)],[f_4634_3]) ).

fof(f_4635_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
        | V_ys_2 != hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
        | V_xs_2 != hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) )
      & ( ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
          & V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != V_zs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj]) ).

fof(f_4635_2,plain,
    ! [U_19371,U_19370,U_19369,U_19368] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19368),U_19369),U_19370) = U_19371
        | U_19370 != hAPP(hAPP(c_List_Odrop(U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19368)),U_19369)),U_19371)
        | U_19369 != hAPP(hAPP(c_List_Otake(U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19368)),U_19369)),U_19371) )
      & ( ( U_19370 = hAPP(hAPP(c_List_Odrop(U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19368)),U_19369)),U_19371)
          & U_19369 = hAPP(hAPP(c_List_Otake(U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19368)),U_19369)),U_19371) )
        | hAPP(hAPP(c_List_Oappend(U_19368),U_19369),U_19370) != U_19371 ) ),
    inference(variable_rename,[status(thm)],[f_4635_1]) ).

fof(f_4635_3,plain,
    ( ! [U_19379,U_19377,U_19375,U_19373] :
        ( hAPP(hAPP(c_List_Oappend(U_19373),U_19375),U_19377) = U_19379
        | U_19377 != hAPP(hAPP(c_List_Odrop(U_19373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19373)),U_19375)),U_19379)
        | U_19375 != hAPP(hAPP(c_List_Otake(U_19373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19373)),U_19375)),U_19379) )
    & ! [U_19378,U_19376,U_19374,U_19372] :
        ( ( U_19376 = hAPP(hAPP(c_List_Odrop(U_19372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19374)),U_19378)
          & U_19374 = hAPP(hAPP(c_List_Otake(U_19372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19374)),U_19378) )
        | hAPP(hAPP(c_List_Oappend(U_19372),U_19374),U_19376) != U_19378 ) ),
    inference(miniscope,[status(thm)],[f_4635_2]) ).

fof(f_4635_4,plain,
    ( ! [U_19374,U_19378,U_19372,U_19376] :
        ( U_19376 = hAPP(hAPP(c_List_Odrop(U_19372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19374)),U_19378)
        | ~ sP1190(U_19374,U_19378,U_19372,U_19376) )
    & ! [U_19374,U_19378,U_19372,U_19376] :
        ( U_19374 = hAPP(hAPP(c_List_Otake(U_19372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19374)),U_19378)
        | ~ sP1190(U_19374,U_19378,U_19372,U_19376) )
    & ! [U_19377,U_19373,U_19379,U_19375] :
        ( hAPP(hAPP(c_List_Oappend(U_19373),U_19375),U_19377) = U_19379
        | U_19377 != hAPP(hAPP(c_List_Odrop(U_19373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19373)),U_19375)),U_19379)
        | U_19375 != hAPP(hAPP(c_List_Otake(U_19373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19373)),U_19375)),U_19379) )
    & ! [U_19374,U_19378,U_19372,U_19376] :
        ( sP1190(U_19374,U_19378,U_19372,U_19376)
        | hAPP(hAPP(c_List_Oappend(U_19372),U_19374),U_19376) != U_19378 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1190])],[f_4635_3]) ).

cnf(f_4635_5,plain,
    ( sP1190(U_19374,U_19378,U_19372,U_19376)
    | hAPP(hAPP(c_List_Oappend(U_19372),U_19374),U_19376) != U_19378 ),
    inference(clausify,[status(thm)],[f_4635_4]) ).

cnf(f_4635_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19373),U_19375),U_19377) = U_19379
    | U_19377 != hAPP(hAPP(c_List_Odrop(U_19373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19373)),U_19375)),U_19379)
    | U_19375 != hAPP(hAPP(c_List_Otake(U_19373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19373)),U_19375)),U_19379) ),
    inference(clausify,[status(thm)],[f_4635_4]) ).

cnf(f_4635_7,plain,
    ( U_19374 = hAPP(hAPP(c_List_Otake(U_19372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19374)),U_19378)
    | ~ sP1190(U_19374,U_19378,U_19372,U_19376) ),
    inference(clausify,[status(thm)],[f_4635_4]) ).

cnf(f_4635_8,plain,
    ( U_19376 = hAPP(hAPP(c_List_Odrop(U_19372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19374)),U_19378)
    | ~ sP1190(U_19374,U_19378,U_19372,U_19376) ),
    inference(clausify,[status(thm)],[f_4635_4]) ).

fof(f_4636_1,plain,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons]) ).

fof(f_4636_2,plain,
    ! [U_19383,U_19382,U_19381,U_19380] : hAPP(hAPP(c_List_Odrop(U_19380),U_19381),hAPP(hAPP(c_List_Olist_OCons(U_19380),U_19382),U_19383)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19380),hAPP(hAPP(c_List_Olist_OCons(U_19380),U_19382),U_19383),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19380),tc_List_Olist(U_19380)),c_List_Odrop(U_19380)),U_19383),U_19381),
    inference(variable_rename,[status(thm)],[f_4636_1]) ).

fof(f_4636_3,plain,
    ! [U_19380,U_19381,U_19383,U_19382] : hAPP(hAPP(c_List_Odrop(U_19380),U_19381),hAPP(hAPP(c_List_Olist_OCons(U_19380),U_19382),U_19383)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19380),hAPP(hAPP(c_List_Olist_OCons(U_19380),U_19382),U_19383),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19380),tc_List_Olist(U_19380)),c_List_Odrop(U_19380)),U_19383),U_19381),
    inference(definitional_conversion,[status(esa)],[f_4636_2]) ).

cnf(f_4636_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19380),U_19381),hAPP(hAPP(c_List_Olist_OCons(U_19380),U_19382),U_19383)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19380),hAPP(hAPP(c_List_Olist_OCons(U_19380),U_19382),U_19383),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19380),tc_List_Olist(U_19380)),c_List_Odrop(U_19380)),U_19383),U_19381),
    inference(clausify,[status(thm)],[f_4636_3]) ).

fof(f_4637_1,plain,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons_H]) ).

fof(f_4637_2,plain,
    ! [U_19387,U_19386,U_19385,U_19384] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19385),U_19384),hAPP(hAPP(c_List_Olist_OCons(U_19385),U_19386),U_19387)) = hAPP(hAPP(c_List_Odrop(U_19385),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19384),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19387)
        | U_19384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_19385),U_19384),hAPP(hAPP(c_List_Olist_OCons(U_19385),U_19386),U_19387)) = hAPP(hAPP(c_List_Olist_OCons(U_19385),U_19386),U_19387)
        | U_19384 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4637_1]) ).

fof(f_4637_3,plain,
    ( ! [U_19395,U_19393,U_19391,U_19389] :
        ( hAPP(hAPP(c_List_Odrop(U_19391),U_19389),hAPP(hAPP(c_List_Olist_OCons(U_19391),U_19393),U_19395)) = hAPP(hAPP(c_List_Odrop(U_19391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19389),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19395)
        | U_19389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19394,U_19392,U_19390,U_19388] :
        ( hAPP(hAPP(c_List_Odrop(U_19390),U_19388),hAPP(hAPP(c_List_Olist_OCons(U_19390),U_19392),U_19394)) = hAPP(hAPP(c_List_Olist_OCons(U_19390),U_19392),U_19394)
        | U_19388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4637_2]) ).

fof(f_4637_4,plain,
    ( ! [U_19389,U_19391,U_19393,U_19395] :
        ( hAPP(hAPP(c_List_Odrop(U_19391),U_19389),hAPP(hAPP(c_List_Olist_OCons(U_19391),U_19393),U_19395)) = hAPP(hAPP(c_List_Odrop(U_19391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19389),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19395)
        | U_19389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19390,U_19392,U_19394,U_19388] :
        ( hAPP(hAPP(c_List_Odrop(U_19390),U_19388),hAPP(hAPP(c_List_Olist_OCons(U_19390),U_19392),U_19394)) = hAPP(hAPP(c_List_Olist_OCons(U_19390),U_19392),U_19394)
        | U_19388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4637_3]) ).

cnf(f_4637_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19390),U_19388),hAPP(hAPP(c_List_Olist_OCons(U_19390),U_19392),U_19394)) = hAPP(hAPP(c_List_Olist_OCons(U_19390),U_19392),U_19394)
    | U_19388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4637_4]) ).

cnf(f_4637_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19391),U_19389),hAPP(hAPP(c_List_Olist_OCons(U_19391),U_19393),U_19395)) = hAPP(hAPP(c_List_Odrop(U_19391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19389),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19395)
    | U_19389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4637_4]) ).

fof(f_4638_1,plain,
    ! [V_xs,T_a,V_i,V_n] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__drop]) ).

fof(f_4638_2,plain,
    ! [U_19399,U_19398,U_19397,U_19396] :
      ( hAPP(hAPP(c_List_Onth(U_19398),hAPP(hAPP(c_List_Odrop(U_19398),U_19396),U_19399)),U_19397) = hAPP(hAPP(c_List_Onth(U_19398),U_19399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19396),U_19397))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19396),U_19397)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19398)),U_19399))) ),
    inference(variable_rename,[status(thm)],[f_4638_1]) ).

fof(f_4638_3,plain,
    ! [U_19396,U_19397,U_19398,U_19399] :
      ( hAPP(hAPP(c_List_Onth(U_19398),hAPP(hAPP(c_List_Odrop(U_19398),U_19396),U_19399)),U_19397) = hAPP(hAPP(c_List_Onth(U_19398),U_19399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19396),U_19397))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19396),U_19397)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19398)),U_19399))) ),
    inference(definitional_conversion,[status(esa)],[f_4638_2]) ).

cnf(f_4638_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_19398),hAPP(hAPP(c_List_Odrop(U_19398),U_19396),U_19399)),U_19397) = hAPP(hAPP(c_List_Onth(U_19398),U_19399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19396),U_19397))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19396),U_19397)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19398)),U_19399))) ),
    inference(clausify,[status(thm)],[f_4638_3]) ).

fof(f_4639_1,plain,
    ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
        | ( ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) != V_ys_092_060_094isub_0622_2
            | hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) != V_ys_092_060_094isub_0621_2 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) )
        | ( ( V_xs_092_060_094isub_0622_2 != hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
            | V_xs_092_060_094isub_0621_2 != hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
              & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) )
          & ( ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
              & V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) ) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) != hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv__if]) ).

fof(f_4639_2,plain,
    ! [U_19404,U_19403,U_19402,U_19401,U_19400] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19400),U_19401),U_19402) = hAPP(hAPP(c_List_Oappend(U_19400),U_19403),U_19404)
        | ( ( hAPP(hAPP(c_List_Oappend(U_19400),hAPP(hAPP(c_List_Odrop(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403)),U_19401)),U_19402) != U_19404
            | hAPP(hAPP(c_List_Otake(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403)),U_19401) != U_19403 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403))) )
        | ( ( U_19402 != hAPP(hAPP(c_List_Oappend(U_19400),hAPP(hAPP(c_List_Odrop(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),U_19403)),U_19404)
            | U_19401 != hAPP(hAPP(c_List_Otake(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),U_19403) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(U_19400),hAPP(hAPP(c_List_Odrop(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403)),U_19401)),U_19402) = U_19404
              & hAPP(hAPP(c_List_Otake(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403)),U_19401) = U_19403 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403))) )
          & ( ( U_19402 = hAPP(hAPP(c_List_Oappend(U_19400),hAPP(hAPP(c_List_Odrop(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),U_19403)),U_19404)
              & U_19401 = hAPP(hAPP(c_List_Otake(U_19400),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),U_19403) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19401)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19400)),U_19403))) ) )
        | hAPP(hAPP(c_List_Oappend(U_19400),U_19401),U_19402) != hAPP(hAPP(c_List_Oappend(U_19400),U_19403),U_19404) ) ),
    inference(variable_rename,[status(thm)],[f_4639_1]) ).

fof(f_4639_3,plain,
    ( ! [U_19414,U_19412,U_19410,U_19408,U_19406] :
        ( hAPP(hAPP(c_List_Oappend(U_19406),U_19408),U_19410) = hAPP(hAPP(c_List_Oappend(U_19406),U_19412),U_19414)
        | ( ( hAPP(hAPP(c_List_Oappend(U_19406),hAPP(hAPP(c_List_Odrop(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)),U_19408)),U_19410) != U_19414
            | hAPP(hAPP(c_List_Otake(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)),U_19408) != U_19412 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412))) )
        | ( ( U_19410 != hAPP(hAPP(c_List_Oappend(U_19406),hAPP(hAPP(c_List_Odrop(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),U_19412)),U_19414)
            | U_19408 != hAPP(hAPP(c_List_Otake(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),U_19412) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412))) ) )
    & ! [U_19413,U_19411,U_19409,U_19407,U_19405] :
        ( ( ( ( hAPP(hAPP(c_List_Oappend(U_19405),hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)),U_19407)),U_19409) = U_19413
              & hAPP(hAPP(c_List_Otake(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)),U_19407) = U_19411 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411))) )
          & ( ( U_19409 = hAPP(hAPP(c_List_Oappend(U_19405),hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),U_19411)),U_19413)
              & U_19407 = hAPP(hAPP(c_List_Otake(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),U_19411) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411))) ) )
        | hAPP(hAPP(c_List_Oappend(U_19405),U_19407),U_19409) != hAPP(hAPP(c_List_Oappend(U_19405),U_19411),U_19413) ) ),
    inference(miniscope,[status(thm)],[f_4639_2]) ).

fof(f_4639_4,plain,
    ( ! [U_19406,U_19412,U_19410,U_19408,U_19414] :
        ( hAPP(hAPP(c_List_Oappend(U_19406),hAPP(hAPP(c_List_Odrop(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)),U_19408)),U_19410) != U_19414
        | hAPP(hAPP(c_List_Otake(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)),U_19408) != U_19412
        | ~ sP1195(U_19406,U_19412,U_19410,U_19408,U_19414) )
    & ! [U_19406,U_19412,U_19410,U_19408,U_19414] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)))
        | ~ sP1195(U_19406,U_19412,U_19410,U_19408,U_19414) )
    & ! [U_19406,U_19412,U_19410,U_19408,U_19414] :
        ( U_19410 != hAPP(hAPP(c_List_Oappend(U_19406),hAPP(hAPP(c_List_Odrop(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),U_19412)),U_19414)
        | U_19408 != hAPP(hAPP(c_List_Otake(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),U_19412)
        | ~ sP1194(U_19406,U_19412,U_19410,U_19408,U_19414) )
    & ! [U_19406,U_19412,U_19410,U_19408,U_19414] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)))
        | ~ sP1194(U_19406,U_19412,U_19410,U_19408,U_19414) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( hAPP(hAPP(c_List_Oappend(U_19405),hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)),U_19407)),U_19409) = U_19413
        | ~ sP1192(U_19407,U_19405,U_19411,U_19409,U_19413) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( hAPP(hAPP(c_List_Otake(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)),U_19407) = U_19411
        | ~ sP1192(U_19407,U_19405,U_19411,U_19409,U_19413) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( U_19409 = hAPP(hAPP(c_List_Oappend(U_19405),hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),U_19411)),U_19413)
        | ~ sP1191(U_19407,U_19405,U_19411,U_19409,U_19413) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( U_19407 = hAPP(hAPP(c_List_Otake(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),U_19411)
        | ~ sP1191(U_19407,U_19405,U_19411,U_19409,U_19413) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( sP1192(U_19407,U_19405,U_19411,U_19409,U_19413)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)))
        | ~ sP1193(U_19407,U_19405,U_19411,U_19409,U_19413) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( sP1191(U_19407,U_19405,U_19411,U_19409,U_19413)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)))
        | ~ sP1193(U_19407,U_19405,U_19411,U_19409,U_19413) )
    & ! [U_19406,U_19412,U_19410,U_19408,U_19414] :
        ( hAPP(hAPP(c_List_Oappend(U_19406),U_19408),U_19410) = hAPP(hAPP(c_List_Oappend(U_19406),U_19412),U_19414)
        | sP1195(U_19406,U_19412,U_19410,U_19408,U_19414)
        | sP1194(U_19406,U_19412,U_19410,U_19408,U_19414) )
    & ! [U_19407,U_19405,U_19411,U_19409,U_19413] :
        ( sP1193(U_19407,U_19405,U_19411,U_19409,U_19413)
        | hAPP(hAPP(c_List_Oappend(U_19405),U_19407),U_19409) != hAPP(hAPP(c_List_Oappend(U_19405),U_19411),U_19413) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1191,sP1192,sP1193,sP1194,sP1195])],[f_4639_3]) ).

cnf(f_4639_5,plain,
    ( sP1193(U_19407,U_19405,U_19411,U_19409,U_19413)
    | hAPP(hAPP(c_List_Oappend(U_19405),U_19407),U_19409) != hAPP(hAPP(c_List_Oappend(U_19405),U_19411),U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19406),U_19408),U_19410) = hAPP(hAPP(c_List_Oappend(U_19406),U_19412),U_19414)
    | sP1195(U_19406,U_19412,U_19410,U_19408,U_19414)
    | sP1194(U_19406,U_19412,U_19410,U_19408,U_19414) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_7,plain,
    ( sP1191(U_19407,U_19405,U_19411,U_19409,U_19413)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)))
    | ~ sP1193(U_19407,U_19405,U_19411,U_19409,U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_8,plain,
    ( sP1192(U_19407,U_19405,U_19411,U_19409,U_19413)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)))
    | ~ sP1193(U_19407,U_19405,U_19411,U_19409,U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_9,plain,
    ( U_19407 = hAPP(hAPP(c_List_Otake(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),U_19411)
    | ~ sP1191(U_19407,U_19405,U_19411,U_19409,U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_10,plain,
    ( U_19409 = hAPP(hAPP(c_List_Oappend(U_19405),hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19407)),U_19411)),U_19413)
    | ~ sP1191(U_19407,U_19405,U_19411,U_19409,U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)),U_19407) = U_19411
    | ~ sP1192(U_19407,U_19405,U_19411,U_19409,U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_12,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19405),hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19405)),U_19411)),U_19407)),U_19409) = U_19413
    | ~ sP1192(U_19407,U_19405,U_19411,U_19409,U_19413) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)))
    | ~ sP1194(U_19406,U_19412,U_19410,U_19408,U_19414) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_14,plain,
    ( U_19410 != hAPP(hAPP(c_List_Oappend(U_19406),hAPP(hAPP(c_List_Odrop(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),U_19412)),U_19414)
    | U_19408 != hAPP(hAPP(c_List_Otake(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),U_19412)
    | ~ sP1194(U_19406,U_19412,U_19410,U_19408,U_19414) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)))
    | ~ sP1195(U_19406,U_19412,U_19410,U_19408,U_19414) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

cnf(f_4639_16,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19406),hAPP(hAPP(c_List_Odrop(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)),U_19408)),U_19410) != U_19414
    | hAPP(hAPP(c_List_Otake(U_19406),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19406)),U_19412)),U_19408) != U_19412
    | ~ sP1195(U_19406,U_19412,U_19410,U_19408,U_19414) ),
    inference(clausify,[status(thm)],[f_4639_4]) ).

fof(f_4640_1,plain,
    ! [V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__drop_H]) ).

fof(f_4640_2,plain,
    ! [U_19417,U_19416,U_19415] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19416),hAPP(hAPP(c_List_Onth(U_19416),U_19417),U_19415)),hAPP(hAPP(c_List_Odrop(U_19416),hAPP(c_Nat_OSuc,U_19415)),U_19417)) = hAPP(hAPP(c_List_Odrop(U_19416),U_19415),U_19417)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19415),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19416)),U_19417))) ),
    inference(variable_rename,[status(thm)],[f_4640_1]) ).

fof(f_4640_3,plain,
    ! [U_19415,U_19416,U_19417] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19416),hAPP(hAPP(c_List_Onth(U_19416),U_19417),U_19415)),hAPP(hAPP(c_List_Odrop(U_19416),hAPP(c_Nat_OSuc,U_19415)),U_19417)) = hAPP(hAPP(c_List_Odrop(U_19416),U_19415),U_19417)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19415),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19416)),U_19417))) ),
    inference(definitional_conversion,[status(esa)],[f_4640_2]) ).

cnf(f_4640_4,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19416),hAPP(hAPP(c_List_Onth(U_19416),U_19417),U_19415)),hAPP(hAPP(c_List_Odrop(U_19416),hAPP(c_Nat_OSuc,U_19415)),U_19417)) = hAPP(hAPP(c_List_Odrop(U_19416),U_19415),U_19417)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19415),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19416)),U_19417))) ),
    inference(clausify,[status(thm)],[f_4640_3]) ).

fof(f_4641_1,plain,
    ! [V_xs,V_x,T_b,T_a] :
      ( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
      & hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__simps]) ).

fof(f_4641_2,plain,
    ! [U_19421,U_19420,U_19419,U_19418] :
      ( hAPP(c_List_Orotate1(U_19419),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),U_19421)) = hAPP(hAPP(c_List_Oappend(U_19419),U_19421),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),c_List_Olist_ONil(U_19419)))
      & hAPP(c_List_Orotate1(U_19418),c_List_Olist_ONil(U_19418)) = c_List_Olist_ONil(U_19418) ),
    inference(variable_rename,[status(thm)],[f_4641_1]) ).

fof(f_4641_3,plain,
    ( ! [U_19421,U_19420,U_19419] : hAPP(c_List_Orotate1(U_19419),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),U_19421)) = hAPP(hAPP(c_List_Oappend(U_19419),U_19421),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),c_List_Olist_ONil(U_19419)))
    & ! [U_19418] : hAPP(c_List_Orotate1(U_19418),c_List_Olist_ONil(U_19418)) = c_List_Olist_ONil(U_19418) ),
    inference(miniscope,[status(thm)],[f_4641_2]) ).

fof(f_4641_4,plain,
    ( ! [U_19419,U_19420,U_19421] : hAPP(c_List_Orotate1(U_19419),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),U_19421)) = hAPP(hAPP(c_List_Oappend(U_19419),U_19421),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),c_List_Olist_ONil(U_19419)))
    & ! [U_19418] : hAPP(c_List_Orotate1(U_19418),c_List_Olist_ONil(U_19418)) = c_List_Olist_ONil(U_19418) ),
    inference(definitional_conversion,[status(esa)],[f_4641_3]) ).

cnf(f_4641_5,plain,
    hAPP(c_List_Orotate1(U_19418),c_List_Olist_ONil(U_19418)) = c_List_Olist_ONil(U_19418),
    inference(clausify,[status(thm)],[f_4641_4]) ).

cnf(f_4641_6,plain,
    hAPP(c_List_Orotate1(U_19419),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),U_19421)) = hAPP(hAPP(c_List_Oappend(U_19419),U_19421),hAPP(hAPP(c_List_Olist_OCons(U_19419),U_19420),c_List_Olist_ONil(U_19419))),
    inference(clausify,[status(thm)],[f_4641_4]) ).

fof(f_4642_1,plain,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of]) ).

fof(f_4642_2,plain,
    ! [U_19425,U_19424,U_19423,U_19422] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19423),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422)),hAPP(hAPP(c_List_Olist_OCons(U_19423),U_19424),U_19425)) = hAPP(hAPP(c_List_Odrop(U_19423),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19425)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_19423),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422)),hAPP(hAPP(c_List_Olist_OCons(U_19423),U_19424),U_19425)) = hAPP(hAPP(c_List_Olist_OCons(U_19423),U_19424),U_19425)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4642_1]) ).

fof(f_4642_3,plain,
    ( ! [U_19433,U_19431,U_19429,U_19427] :
        ( hAPP(hAPP(c_List_Odrop(U_19429),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427)),hAPP(hAPP(c_List_Olist_OCons(U_19429),U_19431),U_19433)) = hAPP(hAPP(c_List_Odrop(U_19429),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19433)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19432,U_19430,U_19428,U_19426] :
        ( hAPP(hAPP(c_List_Odrop(U_19428),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426)),hAPP(hAPP(c_List_Olist_OCons(U_19428),U_19430),U_19432)) = hAPP(hAPP(c_List_Olist_OCons(U_19428),U_19430),U_19432)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4642_2]) ).

fof(f_4642_4,plain,
    ( ! [U_19429,U_19427,U_19431,U_19433] :
        ( hAPP(hAPP(c_List_Odrop(U_19429),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427)),hAPP(hAPP(c_List_Olist_OCons(U_19429),U_19431),U_19433)) = hAPP(hAPP(c_List_Odrop(U_19429),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19433)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19428,U_19432,U_19426,U_19430] :
        ( hAPP(hAPP(c_List_Odrop(U_19428),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426)),hAPP(hAPP(c_List_Olist_OCons(U_19428),U_19430),U_19432)) = hAPP(hAPP(c_List_Olist_OCons(U_19428),U_19430),U_19432)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4642_3]) ).

cnf(f_4642_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19428),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426)),hAPP(hAPP(c_List_Olist_OCons(U_19428),U_19430),U_19432)) = hAPP(hAPP(c_List_Olist_OCons(U_19428),U_19430),U_19432)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4642_4]) ).

cnf(f_4642_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19429),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427)),hAPP(hAPP(c_List_Olist_OCons(U_19429),U_19431),U_19433)) = hAPP(hAPP(c_List_Odrop(U_19429),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19433)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19427) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4642_4]) ).

fof(f_4643_1,plain,
    ! [V_xs,T_a,V_j,V_i] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__add]) ).

fof(f_4643_2,plain,
    ! [U_19437,U_19436,U_19435,U_19434] :
      ( hAPP(hAPP(c_List_Otake(U_19436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19434),U_19435)),U_19437) = hAPP(hAPP(c_List_Oappend(U_19436),hAPP(hAPP(c_List_Otake(U_19436),U_19434),U_19437)),hAPP(hAPP(c_List_Otake(U_19436),U_19435),hAPP(hAPP(c_List_Odrop(U_19436),U_19434),U_19437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19434),U_19435)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19436)),U_19437))) ),
    inference(variable_rename,[status(thm)],[f_4643_1]) ).

fof(f_4643_3,plain,
    ! [U_19434,U_19435,U_19436,U_19437] :
      ( hAPP(hAPP(c_List_Otake(U_19436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19434),U_19435)),U_19437) = hAPP(hAPP(c_List_Oappend(U_19436),hAPP(hAPP(c_List_Otake(U_19436),U_19434),U_19437)),hAPP(hAPP(c_List_Otake(U_19436),U_19435),hAPP(hAPP(c_List_Odrop(U_19436),U_19434),U_19437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19434),U_19435)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19436)),U_19437))) ),
    inference(definitional_conversion,[status(esa)],[f_4643_2]) ).

cnf(f_4643_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19434),U_19435)),U_19437) = hAPP(hAPP(c_List_Oappend(U_19436),hAPP(hAPP(c_List_Otake(U_19436),U_19434),U_19437)),hAPP(hAPP(c_List_Otake(U_19436),U_19435),hAPP(hAPP(c_List_Odrop(U_19436),U_19434),U_19437)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19434),U_19435)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19436)),U_19437))) ),
    inference(clausify,[status(thm)],[f_4643_3]) ).

fof(f_4644_1,plain,
    ! [V_xs,T_a] :
      ( hAPP(c_List_Orotate1(T_a),V_xs) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__length01]) ).

fof(f_4644_2,plain,
    ! [U_19439,U_19438] :
      ( hAPP(c_List_Orotate1(U_19438),U_19439) = U_19439
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19438)),U_19439)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4644_1]) ).

fof(f_4644_3,plain,
    ! [U_19438,U_19439] :
      ( hAPP(c_List_Orotate1(U_19438),U_19439) = U_19439
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19438)),U_19439)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definitional_conversion,[status(esa)],[f_4644_2]) ).

cnf(f_4644_4,plain,
    ( hAPP(c_List_Orotate1(U_19438),U_19439) = U_19439
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19438)),U_19439)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4644_3]) ).

fof(f_4645_1,plain,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
    inference(fof_nnf,[status(thm)],[fact_zip__append1]) ).

fof(f_4645_2,plain,
    ! [U_19444,U_19443,U_19442,U_19441,U_19440] : hAPP(hAPP(c_List_Ozip(U_19440,U_19441),hAPP(hAPP(c_List_Oappend(U_19440),U_19442),U_19443)),U_19444) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19440,U_19441)),hAPP(hAPP(c_List_Ozip(U_19440,U_19441),U_19442),hAPP(hAPP(c_List_Otake(U_19441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19440)),U_19442)),U_19444))),hAPP(hAPP(c_List_Ozip(U_19440,U_19441),U_19443),hAPP(hAPP(c_List_Odrop(U_19441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19440)),U_19442)),U_19444))),
    inference(variable_rename,[status(thm)],[f_4645_1]) ).

fof(f_4645_3,plain,
    ! [U_19440,U_19441,U_19442,U_19443,U_19444] : hAPP(hAPP(c_List_Ozip(U_19440,U_19441),hAPP(hAPP(c_List_Oappend(U_19440),U_19442),U_19443)),U_19444) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19440,U_19441)),hAPP(hAPP(c_List_Ozip(U_19440,U_19441),U_19442),hAPP(hAPP(c_List_Otake(U_19441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19440)),U_19442)),U_19444))),hAPP(hAPP(c_List_Ozip(U_19440,U_19441),U_19443),hAPP(hAPP(c_List_Odrop(U_19441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19440)),U_19442)),U_19444))),
    inference(definitional_conversion,[status(esa)],[f_4645_2]) ).

cnf(f_4645_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19440,U_19441),hAPP(hAPP(c_List_Oappend(U_19440),U_19442),U_19443)),U_19444) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19440,U_19441)),hAPP(hAPP(c_List_Ozip(U_19440,U_19441),U_19442),hAPP(hAPP(c_List_Otake(U_19441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19440)),U_19442)),U_19444))),hAPP(hAPP(c_List_Ozip(U_19440,U_19441),U_19443),hAPP(hAPP(c_List_Odrop(U_19441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19440)),U_19442)),U_19444))),
    inference(clausify,[status(thm)],[f_4645_3]) ).

fof(f_4646_1,plain,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
    inference(fof_nnf,[status(thm)],[fact_zip__append2]) ).

fof(f_4646_2,plain,
    ! [U_19449,U_19448,U_19447,U_19446,U_19445] : hAPP(hAPP(c_List_Ozip(U_19445,U_19446),U_19447),hAPP(hAPP(c_List_Oappend(U_19446),U_19448),U_19449)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19445,U_19446)),hAPP(hAPP(c_List_Ozip(U_19445,U_19446),hAPP(hAPP(c_List_Otake(U_19445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19446)),U_19448)),U_19447)),U_19448)),hAPP(hAPP(c_List_Ozip(U_19445,U_19446),hAPP(hAPP(c_List_Odrop(U_19445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19446)),U_19448)),U_19447)),U_19449)),
    inference(variable_rename,[status(thm)],[f_4646_1]) ).

fof(f_4646_3,plain,
    ! [U_19445,U_19446,U_19447,U_19448,U_19449] : hAPP(hAPP(c_List_Ozip(U_19445,U_19446),U_19447),hAPP(hAPP(c_List_Oappend(U_19446),U_19448),U_19449)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19445,U_19446)),hAPP(hAPP(c_List_Ozip(U_19445,U_19446),hAPP(hAPP(c_List_Otake(U_19445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19446)),U_19448)),U_19447)),U_19448)),hAPP(hAPP(c_List_Ozip(U_19445,U_19446),hAPP(hAPP(c_List_Odrop(U_19445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19446)),U_19448)),U_19447)),U_19449)),
    inference(definitional_conversion,[status(esa)],[f_4646_2]) ).

cnf(f_4646_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19445,U_19446),U_19447),hAPP(hAPP(c_List_Oappend(U_19446),U_19448),U_19449)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19445,U_19446)),hAPP(hAPP(c_List_Ozip(U_19445,U_19446),hAPP(hAPP(c_List_Otake(U_19445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19446)),U_19448)),U_19447)),U_19448)),hAPP(hAPP(c_List_Ozip(U_19445,U_19446),hAPP(hAPP(c_List_Odrop(U_19445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19446)),U_19448)),U_19447)),U_19449)),
    inference(clausify,[status(thm)],[f_4646_3]) ).

fof(f_4647_1,plain,
    ! [V_xs,T_a,V_i] :
      ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop]) ).

fof(f_4647_2,plain,
    ! [U_19452,U_19451,U_19450] :
      ( U_19452 = hAPP(hAPP(c_List_Oappend(U_19451),hAPP(hAPP(c_List_Otake(U_19451),U_19450),U_19452)),hAPP(hAPP(c_List_Olist_OCons(U_19451),hAPP(hAPP(c_List_Onth(U_19451),U_19452),U_19450)),hAPP(hAPP(c_List_Odrop(U_19451),hAPP(c_Nat_OSuc,U_19450)),U_19452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19450),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19451)),U_19452))) ),
    inference(variable_rename,[status(thm)],[f_4647_1]) ).

fof(f_4647_3,plain,
    ! [U_19450,U_19451,U_19452] :
      ( U_19452 = hAPP(hAPP(c_List_Oappend(U_19451),hAPP(hAPP(c_List_Otake(U_19451),U_19450),U_19452)),hAPP(hAPP(c_List_Olist_OCons(U_19451),hAPP(hAPP(c_List_Onth(U_19451),U_19452),U_19450)),hAPP(hAPP(c_List_Odrop(U_19451),hAPP(c_Nat_OSuc,U_19450)),U_19452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19450),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19451)),U_19452))) ),
    inference(definitional_conversion,[status(esa)],[f_4647_2]) ).

cnf(f_4647_4,plain,
    ( U_19452 = hAPP(hAPP(c_List_Oappend(U_19451),hAPP(hAPP(c_List_Otake(U_19451),U_19450),U_19452)),hAPP(hAPP(c_List_Olist_OCons(U_19451),hAPP(hAPP(c_List_Onth(U_19451),U_19452),U_19450)),hAPP(hAPP(c_List_Odrop(U_19451),hAPP(c_Nat_OSuc,U_19450)),U_19452)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19450),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19451)),U_19452))) ),
    inference(clausify,[status(thm)],[f_4647_3]) ).

fof(f_4648_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__hd__drop]) ).

fof(f_4648_2,plain,
    ! [U_19455,U_19454,U_19453] :
      ( hAPP(hAPP(c_List_Oappend(U_19454),hAPP(hAPP(c_List_Otake(U_19454),U_19453),U_19455)),hAPP(hAPP(c_List_Olist_OCons(U_19454),hAPP(c_List_Ohd(U_19454),hAPP(hAPP(c_List_Odrop(U_19454),U_19453),U_19455))),c_List_Olist_ONil(U_19454))) = hAPP(hAPP(c_List_Otake(U_19454),hAPP(c_Nat_OSuc,U_19453)),U_19455)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19455))) ),
    inference(variable_rename,[status(thm)],[f_4648_1]) ).

fof(f_4648_3,plain,
    ! [U_19453,U_19454,U_19455] :
      ( hAPP(hAPP(c_List_Oappend(U_19454),hAPP(hAPP(c_List_Otake(U_19454),U_19453),U_19455)),hAPP(hAPP(c_List_Olist_OCons(U_19454),hAPP(c_List_Ohd(U_19454),hAPP(hAPP(c_List_Odrop(U_19454),U_19453),U_19455))),c_List_Olist_ONil(U_19454))) = hAPP(hAPP(c_List_Otake(U_19454),hAPP(c_Nat_OSuc,U_19453)),U_19455)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19455))) ),
    inference(definitional_conversion,[status(esa)],[f_4648_2]) ).

cnf(f_4648_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19454),hAPP(hAPP(c_List_Otake(U_19454),U_19453),U_19455)),hAPP(hAPP(c_List_Olist_OCons(U_19454),hAPP(c_List_Ohd(U_19454),hAPP(hAPP(c_List_Odrop(U_19454),U_19453),U_19455))),c_List_Olist_ONil(U_19454))) = hAPP(hAPP(c_List_Otake(U_19454),hAPP(c_Nat_OSuc,U_19453)),U_19455)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19455))) ),
    inference(clausify,[status(thm)],[f_4648_3]) ).

fof(f_4649_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth]) ).

fof(f_4649_2,plain,
    ! [U_19458,U_19457,U_19456] :
      ( hAPP(c_List_Ohd(U_19457),hAPP(hAPP(c_List_Odrop(U_19457),U_19458),U_19456)) = hAPP(hAPP(c_List_Onth(U_19457),U_19456),U_19458)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19458),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19457)),U_19456)))
      | U_19456 = c_List_Olist_ONil(U_19457) ),
    inference(variable_rename,[status(thm)],[f_4649_1]) ).

fof(f_4649_3,plain,
    ! [U_19456,U_19457,U_19458] :
      ( hAPP(c_List_Ohd(U_19457),hAPP(hAPP(c_List_Odrop(U_19457),U_19458),U_19456)) = hAPP(hAPP(c_List_Onth(U_19457),U_19456),U_19458)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19458),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19457)),U_19456)))
      | U_19456 = c_List_Olist_ONil(U_19457) ),
    inference(definitional_conversion,[status(esa)],[f_4649_2]) ).

cnf(f_4649_4,plain,
    ( hAPP(c_List_Ohd(U_19457),hAPP(hAPP(c_List_Odrop(U_19457),U_19458),U_19456)) = hAPP(hAPP(c_List_Onth(U_19457),U_19456),U_19458)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19458),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19457)),U_19456)))
    | U_19456 = c_List_Olist_ONil(U_19457) ),
    inference(clausify,[status(thm)],[f_4649_3]) ).

fof(f_4650_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__append2]) ).

fof(f_4650_2,plain,
    ! [U_19461,U_19460,U_19459] :
      ( hAPP(c_List_Ohd(U_19460),hAPP(hAPP(c_List_Oappend(U_19460),U_19459),U_19461)) = hAPP(c_List_Ohd(U_19460),U_19459)
      | U_19459 = c_List_Olist_ONil(U_19460) ),
    inference(variable_rename,[status(thm)],[f_4650_1]) ).

fof(f_4650_3,plain,
    ! [U_19460,U_19459,U_19461] :
      ( hAPP(c_List_Ohd(U_19460),hAPP(hAPP(c_List_Oappend(U_19460),U_19459),U_19461)) = hAPP(c_List_Ohd(U_19460),U_19459)
      | U_19459 = c_List_Olist_ONil(U_19460) ),
    inference(definitional_conversion,[status(esa)],[f_4650_2]) ).

cnf(f_4650_4,plain,
    ( hAPP(c_List_Ohd(U_19460),hAPP(hAPP(c_List_Oappend(U_19460),U_19459),U_19461)) = hAPP(c_List_Ohd(U_19460),U_19459)
    | U_19459 = c_List_Olist_ONil(U_19460) ),
    inference(clausify,[status(thm)],[f_4650_3]) ).

fof(f_4651_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs)
        | V_xs = c_List_Olist_ONil(T_a) )
      & ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys)
        | V_xs != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_hd__append]) ).

fof(f_4651_2,plain,
    ! [U_19464,U_19463,U_19462] :
      ( ( hAPP(c_List_Ohd(U_19463),hAPP(hAPP(c_List_Oappend(U_19463),U_19462),U_19464)) = hAPP(c_List_Ohd(U_19463),U_19462)
        | U_19462 = c_List_Olist_ONil(U_19463) )
      & ( hAPP(c_List_Ohd(U_19463),hAPP(hAPP(c_List_Oappend(U_19463),U_19462),U_19464)) = hAPP(c_List_Ohd(U_19463),U_19464)
        | U_19462 != c_List_Olist_ONil(U_19463) ) ),
    inference(variable_rename,[status(thm)],[f_4651_1]) ).

fof(f_4651_3,plain,
    ( ! [U_19470,U_19468,U_19466] :
        ( hAPP(c_List_Ohd(U_19468),hAPP(hAPP(c_List_Oappend(U_19468),U_19466),U_19470)) = hAPP(c_List_Ohd(U_19468),U_19466)
        | U_19466 = c_List_Olist_ONil(U_19468) )
    & ! [U_19469,U_19467,U_19465] :
        ( hAPP(c_List_Ohd(U_19467),hAPP(hAPP(c_List_Oappend(U_19467),U_19465),U_19469)) = hAPP(c_List_Ohd(U_19467),U_19469)
        | U_19465 != c_List_Olist_ONil(U_19467) ) ),
    inference(miniscope,[status(thm)],[f_4651_2]) ).

fof(f_4651_4,plain,
    ( ! [U_19466,U_19468,U_19470] :
        ( hAPP(c_List_Ohd(U_19468),hAPP(hAPP(c_List_Oappend(U_19468),U_19466),U_19470)) = hAPP(c_List_Ohd(U_19468),U_19466)
        | U_19466 = c_List_Olist_ONil(U_19468) )
    & ! [U_19469,U_19467,U_19465] :
        ( hAPP(c_List_Ohd(U_19467),hAPP(hAPP(c_List_Oappend(U_19467),U_19465),U_19469)) = hAPP(c_List_Ohd(U_19467),U_19469)
        | U_19465 != c_List_Olist_ONil(U_19467) ) ),
    inference(definitional_conversion,[status(esa)],[f_4651_3]) ).

cnf(f_4651_5,plain,
    ( hAPP(c_List_Ohd(U_19467),hAPP(hAPP(c_List_Oappend(U_19467),U_19465),U_19469)) = hAPP(c_List_Ohd(U_19467),U_19469)
    | U_19465 != c_List_Olist_ONil(U_19467) ),
    inference(clausify,[status(thm)],[f_4651_4]) ).

cnf(f_4651_6,plain,
    ( hAPP(c_List_Ohd(U_19468),hAPP(hAPP(c_List_Oappend(U_19468),U_19466),U_19470)) = hAPP(c_List_Ohd(U_19468),U_19466)
    | U_19466 = c_List_Olist_ONil(U_19468) ),
    inference(clausify,[status(thm)],[f_4651_4]) ).

fof(f_4652_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_hd_Osimps]) ).

fof(f_4652_2,plain,
    ! [U_19473,U_19472,U_19471] : hAPP(c_List_Ohd(U_19471),hAPP(hAPP(c_List_Olist_OCons(U_19471),U_19472),U_19473)) = U_19472,
    inference(variable_rename,[status(thm)],[f_4652_1]) ).

fof(f_4652_3,plain,
    ! [U_19471,U_19472,U_19473] : hAPP(c_List_Ohd(U_19471),hAPP(hAPP(c_List_Olist_OCons(U_19471),U_19472),U_19473)) = U_19472,
    inference(definitional_conversion,[status(esa)],[f_4652_2]) ).

cnf(f_4652_4,plain,
    hAPP(c_List_Ohd(U_19471),hAPP(hAPP(c_List_Olist_OCons(U_19471),U_19472),U_19473)) = U_19472,
    inference(clausify,[status(thm)],[f_4652_3]) ).

fof(f_4653_1,plain,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__map]) ).

fof(f_4653_2,plain,
    ! [U_19477,U_19476,U_19475,U_19474] :
      ( hAPP(c_List_Ohd(U_19476),hAPP(hAPP(c_List_Omap(U_19475,U_19476),U_19477),U_19474)) = hAPP(U_19477,hAPP(c_List_Ohd(U_19475),U_19474))
      | U_19474 = c_List_Olist_ONil(U_19475) ),
    inference(variable_rename,[status(thm)],[f_4653_1]) ).

fof(f_4653_3,plain,
    ! [U_19474,U_19475,U_19476,U_19477] :
      ( hAPP(c_List_Ohd(U_19476),hAPP(hAPP(c_List_Omap(U_19475,U_19476),U_19477),U_19474)) = hAPP(U_19477,hAPP(c_List_Ohd(U_19475),U_19474))
      | U_19474 = c_List_Olist_ONil(U_19475) ),
    inference(definitional_conversion,[status(esa)],[f_4653_2]) ).

cnf(f_4653_4,plain,
    ( hAPP(c_List_Ohd(U_19476),hAPP(hAPP(c_List_Omap(U_19475,U_19476),U_19477),U_19474)) = hAPP(U_19477,hAPP(c_List_Ohd(U_19475),U_19474))
    | U_19474 = c_List_Olist_ONil(U_19475) ),
    inference(clausify,[status(thm)],[f_4653_3]) ).

fof(f_4654_1,plain,
    ! [T_b,V_xs_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2)))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__in__set]) ).

fof(f_4654_2,plain,
    ! [U_19479,U_19478] :
      ( hBOOL(hAPP(hAPP(c_member(U_19479),hAPP(c_List_Ohd(U_19479),U_19478)),hAPP(c_List_Oset(U_19479),U_19478)))
      | U_19478 = c_List_Olist_ONil(U_19479) ),
    inference(variable_rename,[status(thm)],[f_4654_1]) ).

fof(f_4654_3,plain,
    ! [U_19478,U_19479] :
      ( hBOOL(hAPP(hAPP(c_member(U_19479),hAPP(c_List_Ohd(U_19479),U_19478)),hAPP(c_List_Oset(U_19479),U_19478)))
      | U_19478 = c_List_Olist_ONil(U_19479) ),
    inference(definitional_conversion,[status(esa)],[f_4654_2]) ).

cnf(f_4654_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19479),hAPP(c_List_Ohd(U_19479),U_19478)),hAPP(c_List_Oset(U_19479),U_19478)))
    | U_19478 = c_List_Olist_ONil(U_19479) ),
    inference(clausify,[status(thm)],[f_4654_3]) ).

fof(f_4655_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__conv__nth]) ).

fof(f_4655_2,plain,
    ! [U_19481,U_19480] :
      ( hAPP(c_List_Ohd(U_19481),U_19480) = hAPP(hAPP(c_List_Onth(U_19481),U_19480),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_19480 = c_List_Olist_ONil(U_19481) ),
    inference(variable_rename,[status(thm)],[f_4655_1]) ).

fof(f_4655_3,plain,
    ! [U_19480,U_19481] :
      ( hAPP(c_List_Ohd(U_19481),U_19480) = hAPP(hAPP(c_List_Onth(U_19481),U_19480),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_19480 = c_List_Olist_ONil(U_19481) ),
    inference(definitional_conversion,[status(esa)],[f_4655_2]) ).

cnf(f_4655_4,plain,
    ( hAPP(c_List_Ohd(U_19481),U_19480) = hAPP(hAPP(c_List_Onth(U_19481),U_19480),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_19480 = c_List_Olist_ONil(U_19481) ),
    inference(clausify,[status(thm)],[f_4655_3]) ).

fof(f_4656_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl]) ).

fof(f_4656_2,plain,
    ! [U_19483,U_19482] :
      ( hAPP(c_List_Orotate1(U_19483),U_19482) = hAPP(hAPP(c_List_Oappend(U_19483),hAPP(c_List_Otl(U_19483),U_19482)),hAPP(hAPP(c_List_Olist_OCons(U_19483),hAPP(c_List_Ohd(U_19483),U_19482)),c_List_Olist_ONil(U_19483)))
      | U_19482 = c_List_Olist_ONil(U_19483) ),
    inference(variable_rename,[status(thm)],[f_4656_1]) ).

fof(f_4656_3,plain,
    ! [U_19482,U_19483] :
      ( hAPP(c_List_Orotate1(U_19483),U_19482) = hAPP(hAPP(c_List_Oappend(U_19483),hAPP(c_List_Otl(U_19483),U_19482)),hAPP(hAPP(c_List_Olist_OCons(U_19483),hAPP(c_List_Ohd(U_19483),U_19482)),c_List_Olist_ONil(U_19483)))
      | U_19482 = c_List_Olist_ONil(U_19483) ),
    inference(definitional_conversion,[status(esa)],[f_4656_2]) ).

cnf(f_4656_4,plain,
    ( hAPP(c_List_Orotate1(U_19483),U_19482) = hAPP(hAPP(c_List_Oappend(U_19483),hAPP(c_List_Otl(U_19483),U_19482)),hAPP(hAPP(c_List_Olist_OCons(U_19483),hAPP(c_List_Ohd(U_19483),U_19482)),c_List_Olist_ONil(U_19483)))
    | U_19482 = c_List_Olist_ONil(U_19483) ),
    inference(clausify,[status(thm)],[f_4656_3]) ).

fof(f_4657_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth]) ).

fof(f_4657_2,plain,
    ! [U_19486,U_19485,U_19484] :
      ( hAPP(c_List_Ohd(U_19485),hAPP(c_List_Orotate(U_19485,U_19486),U_19484)) = hAPP(hAPP(c_List_Onth(U_19485),U_19484),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19486,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19485)),U_19484)))
      | U_19484 = c_List_Olist_ONil(U_19485) ),
    inference(variable_rename,[status(thm)],[f_4657_1]) ).

fof(f_4657_3,plain,
    ! [U_19484,U_19485,U_19486] :
      ( hAPP(c_List_Ohd(U_19485),hAPP(c_List_Orotate(U_19485,U_19486),U_19484)) = hAPP(hAPP(c_List_Onth(U_19485),U_19484),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19486,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19485)),U_19484)))
      | U_19484 = c_List_Olist_ONil(U_19485) ),
    inference(definitional_conversion,[status(esa)],[f_4657_2]) ).

cnf(f_4657_4,plain,
    ( hAPP(c_List_Ohd(U_19485),hAPP(c_List_Orotate(U_19485,U_19486),U_19484)) = hAPP(hAPP(c_List_Onth(U_19485),U_19484),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19486,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19485)),U_19484)))
    | U_19484 = c_List_Olist_ONil(U_19485) ),
    inference(clausify,[status(thm)],[f_4657_3]) ).

fof(f_4658_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__Suc]) ).

fof(f_4658_2,plain,
    ! [U_19489,U_19488,U_19487] : hAPP(hAPP(c_List_Odrop(U_19487),hAPP(c_Nat_OSuc,U_19488)),U_19489) = hAPP(hAPP(c_List_Odrop(U_19487),U_19488),hAPP(c_List_Otl(U_19487),U_19489)),
    inference(variable_rename,[status(thm)],[f_4658_1]) ).

fof(f_4658_3,plain,
    ! [U_19487,U_19488,U_19489] : hAPP(hAPP(c_List_Odrop(U_19487),hAPP(c_Nat_OSuc,U_19488)),U_19489) = hAPP(hAPP(c_List_Odrop(U_19487),U_19488),hAPP(c_List_Otl(U_19487),U_19489)),
    inference(definitional_conversion,[status(esa)],[f_4658_2]) ).

cnf(f_4658_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19487),hAPP(c_Nat_OSuc,U_19488)),U_19489) = hAPP(hAPP(c_List_Odrop(U_19487),U_19488),hAPP(c_List_Otl(U_19487),U_19489)),
    inference(clausify,[status(thm)],[f_4658_3]) ).

fof(f_4659_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__tl]) ).

fof(f_4659_2,plain,
    ! [U_19492,U_19491,U_19490] : hAPP(hAPP(c_List_Odrop(U_19490),U_19491),hAPP(c_List_Otl(U_19490),U_19492)) = hAPP(c_List_Otl(U_19490),hAPP(hAPP(c_List_Odrop(U_19490),U_19491),U_19492)),
    inference(variable_rename,[status(thm)],[f_4659_1]) ).

fof(f_4659_3,plain,
    ! [U_19490,U_19491,U_19492] : hAPP(hAPP(c_List_Odrop(U_19490),U_19491),hAPP(c_List_Otl(U_19490),U_19492)) = hAPP(c_List_Otl(U_19490),hAPP(hAPP(c_List_Odrop(U_19490),U_19491),U_19492)),
    inference(definitional_conversion,[status(esa)],[f_4659_2]) ).

cnf(f_4659_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19490),U_19491),hAPP(c_List_Otl(U_19490),U_19492)) = hAPP(c_List_Otl(U_19490),hAPP(hAPP(c_List_Odrop(U_19490),U_19491),U_19492)),
    inference(clausify,[status(thm)],[f_4659_3]) ).

fof(f_4660_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__drop]) ).

fof(f_4660_2,plain,
    ! [U_19495,U_19494,U_19493] : hAPP(c_List_Otl(U_19493),hAPP(hAPP(c_List_Odrop(U_19493),U_19494),U_19495)) = hAPP(hAPP(c_List_Odrop(U_19493),U_19494),hAPP(c_List_Otl(U_19493),U_19495)),
    inference(variable_rename,[status(thm)],[f_4660_1]) ).

fof(f_4660_3,plain,
    ! [U_19493,U_19494,U_19495] : hAPP(c_List_Otl(U_19493),hAPP(hAPP(c_List_Odrop(U_19493),U_19494),U_19495)) = hAPP(hAPP(c_List_Odrop(U_19493),U_19494),hAPP(c_List_Otl(U_19493),U_19495)),
    inference(definitional_conversion,[status(esa)],[f_4660_2]) ).

cnf(f_4660_4,plain,
    hAPP(c_List_Otl(U_19493),hAPP(hAPP(c_List_Odrop(U_19493),U_19494),U_19495)) = hAPP(hAPP(c_List_Odrop(U_19493),U_19494),hAPP(c_List_Otl(U_19493),U_19495)),
    inference(clausify,[status(thm)],[f_4660_3]) ).

fof(f_4661_1,plain,
    ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(f_4661_2,plain,
    ! [U_19496] : hAPP(c_List_Otl(U_19496),c_List_Olist_ONil(U_19496)) = c_List_Olist_ONil(U_19496),
    inference(variable_rename,[status(thm)],[f_4661_1]) ).

fof(f_4661_3,plain,
    ! [U_19496] : hAPP(c_List_Otl(U_19496),c_List_Olist_ONil(U_19496)) = c_List_Olist_ONil(U_19496),
    inference(definitional_conversion,[status(esa)],[f_4661_2]) ).

cnf(f_4661_4,plain,
    hAPP(c_List_Otl(U_19496),c_List_Olist_ONil(U_19496)) = c_List_Olist_ONil(U_19496),
    inference(clausify,[status(thm)],[f_4661_3]) ).

fof(f_4662_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv]) ).

fof(f_4662_2,plain,
    ! [U_19499,U_19498,U_19497] :
      ( ( hAPP(c_List_Orotate(U_19497,U_19498),U_19499) = c_List_Olist_ONil(U_19497)
        | U_19499 != c_List_Olist_ONil(U_19497) )
      & ( U_19499 = c_List_Olist_ONil(U_19497)
        | hAPP(c_List_Orotate(U_19497,U_19498),U_19499) != c_List_Olist_ONil(U_19497) ) ),
    inference(variable_rename,[status(thm)],[f_4662_1]) ).

fof(f_4662_3,plain,
    ( ! [U_19505,U_19503,U_19501] :
        ( hAPP(c_List_Orotate(U_19501,U_19503),U_19505) = c_List_Olist_ONil(U_19501)
        | U_19505 != c_List_Olist_ONil(U_19501) )
    & ! [U_19504,U_19502,U_19500] :
        ( U_19504 = c_List_Olist_ONil(U_19500)
        | hAPP(c_List_Orotate(U_19500,U_19502),U_19504) != c_List_Olist_ONil(U_19500) ) ),
    inference(miniscope,[status(thm)],[f_4662_2]) ).

fof(f_4662_4,plain,
    ( ! [U_19505,U_19501,U_19503] :
        ( hAPP(c_List_Orotate(U_19501,U_19503),U_19505) = c_List_Olist_ONil(U_19501)
        | U_19505 != c_List_Olist_ONil(U_19501) )
    & ! [U_19502,U_19500,U_19504] :
        ( U_19504 = c_List_Olist_ONil(U_19500)
        | hAPP(c_List_Orotate(U_19500,U_19502),U_19504) != c_List_Olist_ONil(U_19500) ) ),
    inference(definitional_conversion,[status(esa)],[f_4662_3]) ).

cnf(f_4662_5,plain,
    ( U_19504 = c_List_Olist_ONil(U_19500)
    | hAPP(c_List_Orotate(U_19500,U_19502),U_19504) != c_List_Olist_ONil(U_19500) ),
    inference(clausify,[status(thm)],[f_4662_4]) ).

cnf(f_4662_6,plain,
    ( hAPP(c_List_Orotate(U_19501,U_19503),U_19505) = c_List_Olist_ONil(U_19501)
    | U_19505 != c_List_Olist_ONil(U_19501) ),
    inference(clausify,[status(thm)],[f_4662_4]) ).

fof(f_4663_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__tl]) ).

fof(f_4663_2,plain,
    ! [U_19508,U_19507,U_19506] : hAPP(hAPP(c_List_Otake(U_19506),U_19507),hAPP(c_List_Otl(U_19506),U_19508)) = hAPP(c_List_Otl(U_19506),hAPP(hAPP(c_List_Otake(U_19506),hAPP(c_Nat_OSuc,U_19507)),U_19508)),
    inference(variable_rename,[status(thm)],[f_4663_1]) ).

fof(f_4663_3,plain,
    ! [U_19506,U_19507,U_19508] : hAPP(hAPP(c_List_Otake(U_19506),U_19507),hAPP(c_List_Otl(U_19506),U_19508)) = hAPP(c_List_Otl(U_19506),hAPP(hAPP(c_List_Otake(U_19506),hAPP(c_Nat_OSuc,U_19507)),U_19508)),
    inference(definitional_conversion,[status(esa)],[f_4663_2]) ).

cnf(f_4663_4,plain,
    hAPP(hAPP(c_List_Otake(U_19506),U_19507),hAPP(c_List_Otl(U_19506),U_19508)) = hAPP(c_List_Otl(U_19506),hAPP(hAPP(c_List_Otake(U_19506),hAPP(c_Nat_OSuc,U_19507)),U_19508)),
    inference(clausify,[status(thm)],[f_4663_3]) ).

fof(f_4664_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rotate]) ).

fof(f_4664_2,plain,
    ! [U_19511,U_19510,U_19509] : hAPP(c_List_Oset(U_19509),hAPP(c_List_Orotate(U_19509,U_19510),U_19511)) = hAPP(c_List_Oset(U_19509),U_19511),
    inference(variable_rename,[status(thm)],[f_4664_1]) ).

fof(f_4664_3,plain,
    ! [U_19509,U_19510,U_19511] : hAPP(c_List_Oset(U_19509),hAPP(c_List_Orotate(U_19509,U_19510),U_19511)) = hAPP(c_List_Oset(U_19509),U_19511),
    inference(definitional_conversion,[status(esa)],[f_4664_2]) ).

cnf(f_4664_4,plain,
    hAPP(c_List_Oset(U_19509),hAPP(c_List_Orotate(U_19509,U_19510),U_19511)) = hAPP(c_List_Oset(U_19509),U_19511),
    inference(clausify,[status(thm)],[f_4664_3]) ).

fof(f_4665_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__rotate]) ).

fof(f_4665_2,plain,
    ! [U_19514,U_19513,U_19512] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19512),hAPP(c_List_Orotate(U_19512,U_19513),U_19514)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19512),U_19514)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19512),U_19514))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19512),hAPP(c_List_Orotate(U_19512,U_19513),U_19514))) ) ),
    inference(variable_rename,[status(thm)],[f_4665_1]) ).

fof(f_4665_3,plain,
    ( ! [U_19520,U_19518,U_19516] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19516),hAPP(c_List_Orotate(U_19516,U_19518),U_19520)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19516),U_19520)) )
    & ! [U_19519,U_19517,U_19515] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19515),U_19519))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19515),hAPP(c_List_Orotate(U_19515,U_19517),U_19519))) ) ),
    inference(miniscope,[status(thm)],[f_4665_2]) ).

fof(f_4665_4,plain,
    ( ! [U_19516,U_19518,U_19520] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19516),hAPP(c_List_Orotate(U_19516,U_19518),U_19520)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19516),U_19520)) )
    & ! [U_19517,U_19519,U_19515] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19515),U_19519))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19515),hAPP(c_List_Orotate(U_19515,U_19517),U_19519))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4665_3]) ).

cnf(f_4665_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19515),U_19519))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19515),hAPP(c_List_Orotate(U_19515,U_19517),U_19519))) ),
    inference(clausify,[status(thm)],[f_4665_4]) ).

cnf(f_4665_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19516),hAPP(c_List_Orotate(U_19516,U_19518),U_19520)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19516),U_19520)) ),
    inference(clausify,[status(thm)],[f_4665_4]) ).

fof(f_4666_1,plain,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__tl]) ).

fof(f_4666_2,plain,
    ! [U_19522,U_19521] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19521),hAPP(c_List_Otl(U_19521),U_19522)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19521),U_19522)) ),
    inference(variable_rename,[status(thm)],[f_4666_1]) ).

fof(f_4666_3,plain,
    ! [U_19521,U_19522] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19521),hAPP(c_List_Otl(U_19521),U_19522)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19521),U_19522)) ),
    inference(definitional_conversion,[status(esa)],[f_4666_2]) ).

cnf(f_4666_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19521),hAPP(c_List_Otl(U_19521),U_19522)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19521),U_19522)) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

fof(f_4667_1,plain,
    ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_rotate__rotate]) ).

fof(f_4667_2,plain,
    ! [U_19526,U_19525,U_19524,U_19523] : hAPP(c_List_Orotate(U_19523,U_19524),hAPP(c_List_Orotate(U_19523,U_19525),U_19526)) = hAPP(c_List_Orotate(U_19523,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19524),U_19525)),U_19526),
    inference(variable_rename,[status(thm)],[f_4667_1]) ).

fof(f_4667_3,plain,
    ! [U_19523,U_19524,U_19525,U_19526] : hAPP(c_List_Orotate(U_19523,U_19524),hAPP(c_List_Orotate(U_19523,U_19525),U_19526)) = hAPP(c_List_Orotate(U_19523,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19524),U_19525)),U_19526),
    inference(definitional_conversion,[status(esa)],[f_4667_2]) ).

cnf(f_4667_4,plain,
    hAPP(c_List_Orotate(U_19523,U_19524),hAPP(c_List_Orotate(U_19523,U_19525),U_19526)) = hAPP(c_List_Orotate(U_19523,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19524),U_19525)),U_19526),
    inference(clausify,[status(thm)],[f_4667_3]) ).

fof(f_4668_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rotate__map]) ).

fof(f_4668_2,plain,
    ! [U_19531,U_19530,U_19529,U_19528,U_19527] : hAPP(c_List_Orotate(U_19527,U_19528),hAPP(hAPP(c_List_Omap(U_19529,U_19527),U_19530),U_19531)) = hAPP(hAPP(c_List_Omap(U_19529,U_19527),U_19530),hAPP(c_List_Orotate(U_19529,U_19528),U_19531)),
    inference(variable_rename,[status(thm)],[f_4668_1]) ).

fof(f_4668_3,plain,
    ! [U_19527,U_19528,U_19529,U_19530,U_19531] : hAPP(c_List_Orotate(U_19527,U_19528),hAPP(hAPP(c_List_Omap(U_19529,U_19527),U_19530),U_19531)) = hAPP(hAPP(c_List_Omap(U_19529,U_19527),U_19530),hAPP(c_List_Orotate(U_19529,U_19528),U_19531)),
    inference(definitional_conversion,[status(esa)],[f_4668_2]) ).

cnf(f_4668_4,plain,
    hAPP(c_List_Orotate(U_19527,U_19528),hAPP(hAPP(c_List_Omap(U_19529,U_19527),U_19530),U_19531)) = hAPP(hAPP(c_List_Omap(U_19529,U_19527),U_19530),hAPP(c_List_Orotate(U_19529,U_19528),U_19531)),
    inference(clausify,[status(thm)],[f_4668_3]) ).

fof(f_4669_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__tl]) ).

fof(f_4669_2,plain,
    ! [U_19535,U_19534,U_19533,U_19532] : hAPP(hAPP(c_List_Omap(U_19532,U_19533),U_19534),hAPP(c_List_Otl(U_19532),U_19535)) = hAPP(c_List_Otl(U_19533),hAPP(hAPP(c_List_Omap(U_19532,U_19533),U_19534),U_19535)),
    inference(variable_rename,[status(thm)],[f_4669_1]) ).

fof(f_4669_3,plain,
    ! [U_19532,U_19533,U_19534,U_19535] : hAPP(hAPP(c_List_Omap(U_19532,U_19533),U_19534),hAPP(c_List_Otl(U_19532),U_19535)) = hAPP(c_List_Otl(U_19533),hAPP(hAPP(c_List_Omap(U_19532,U_19533),U_19534),U_19535)),
    inference(definitional_conversion,[status(esa)],[f_4669_2]) ).

cnf(f_4669_4,plain,
    hAPP(hAPP(c_List_Omap(U_19532,U_19533),U_19534),hAPP(c_List_Otl(U_19532),U_19535)) = hAPP(c_List_Otl(U_19533),hAPP(hAPP(c_List_Omap(U_19532,U_19533),U_19534),U_19535)),
    inference(clausify,[status(thm)],[f_4669_3]) ).

fof(f_4670_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__rotate]) ).

fof(f_4670_2,plain,
    ! [U_19538,U_19537,U_19536] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19536)),hAPP(c_List_Orotate(U_19536,U_19537),U_19538)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19536)),U_19538),
    inference(variable_rename,[status(thm)],[f_4670_1]) ).

fof(f_4670_3,plain,
    ! [U_19536,U_19537,U_19538] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19536)),hAPP(c_List_Orotate(U_19536,U_19537),U_19538)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19536)),U_19538),
    inference(definitional_conversion,[status(esa)],[f_4670_2]) ).

cnf(f_4670_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19536)),hAPP(c_List_Orotate(U_19536,U_19537),U_19538)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19536)),U_19538),
    inference(clausify,[status(thm)],[f_4670_3]) ).

fof(f_4671_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs),
    inference(fof_nnf,[status(thm)],[fact_rotate__conv__mod]) ).

fof(f_4671_2,plain,
    ! [U_19541,U_19540,U_19539] : hAPP(c_List_Orotate(U_19539,U_19540),U_19541) = hAPP(c_List_Orotate(U_19539,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19540,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19539)),U_19541))),U_19541),
    inference(variable_rename,[status(thm)],[f_4671_1]) ).

fof(f_4671_3,plain,
    ! [U_19539,U_19540,U_19541] : hAPP(c_List_Orotate(U_19539,U_19540),U_19541) = hAPP(c_List_Orotate(U_19539,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19540,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19539)),U_19541))),U_19541),
    inference(definitional_conversion,[status(esa)],[f_4671_2]) ).

cnf(f_4671_4,plain,
    hAPP(c_List_Orotate(U_19539,U_19540),U_19541) = hAPP(c_List_Orotate(U_19539,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19540,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19539)),U_19541))),U_19541),
    inference(clausify,[status(thm)],[f_4671_3]) ).

fof(f_4672_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(f_4672_2,plain,
    ! [U_19544,U_19543,U_19542] : hAPP(c_List_Otl(U_19542),hAPP(hAPP(c_List_Olist_OCons(U_19542),U_19543),U_19544)) = U_19544,
    inference(variable_rename,[status(thm)],[f_4672_1]) ).

fof(f_4672_3,plain,
    ! [U_19542,U_19543,U_19544] : hAPP(c_List_Otl(U_19542),hAPP(hAPP(c_List_Olist_OCons(U_19542),U_19543),U_19544)) = U_19544,
    inference(definitional_conversion,[status(esa)],[f_4672_2]) ).

cnf(f_4672_4,plain,
    hAPP(c_List_Otl(U_19542),hAPP(hAPP(c_List_Olist_OCons(U_19542),U_19543),U_19544)) = U_19544,
    inference(clausify,[status(thm)],[f_4672_3]) ).

fof(f_4673_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_tl__append2]) ).

fof(f_4673_2,plain,
    ! [U_19547,U_19546,U_19545] :
      ( hAPP(c_List_Otl(U_19546),hAPP(hAPP(c_List_Oappend(U_19546),U_19545),U_19547)) = hAPP(hAPP(c_List_Oappend(U_19546),hAPP(c_List_Otl(U_19546),U_19545)),U_19547)
      | U_19545 = c_List_Olist_ONil(U_19546) ),
    inference(variable_rename,[status(thm)],[f_4673_1]) ).

fof(f_4673_3,plain,
    ! [U_19545,U_19546,U_19547] :
      ( hAPP(c_List_Otl(U_19546),hAPP(hAPP(c_List_Oappend(U_19546),U_19545),U_19547)) = hAPP(hAPP(c_List_Oappend(U_19546),hAPP(c_List_Otl(U_19546),U_19545)),U_19547)
      | U_19545 = c_List_Olist_ONil(U_19546) ),
    inference(definitional_conversion,[status(esa)],[f_4673_2]) ).

cnf(f_4673_4,plain,
    ( hAPP(c_List_Otl(U_19546),hAPP(hAPP(c_List_Oappend(U_19546),U_19545),U_19547)) = hAPP(hAPP(c_List_Oappend(U_19546),hAPP(c_List_Otl(U_19546),U_19545)),U_19547)
    | U_19545 = c_List_Olist_ONil(U_19546) ),
    inference(clausify,[status(thm)],[f_4673_3]) ).

fof(f_4674_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate1__rotate__swap]) ).

fof(f_4674_2,plain,
    ! [U_19550,U_19549,U_19548] : hAPP(c_List_Orotate1(U_19548),hAPP(c_List_Orotate(U_19548,U_19549),U_19550)) = hAPP(c_List_Orotate(U_19548,U_19549),hAPP(c_List_Orotate1(U_19548),U_19550)),
    inference(variable_rename,[status(thm)],[f_4674_1]) ).

fof(f_4674_3,plain,
    ! [U_19548,U_19549,U_19550] : hAPP(c_List_Orotate1(U_19548),hAPP(c_List_Orotate(U_19548,U_19549),U_19550)) = hAPP(c_List_Orotate(U_19548,U_19549),hAPP(c_List_Orotate1(U_19548),U_19550)),
    inference(definitional_conversion,[status(esa)],[f_4674_2]) ).

cnf(f_4674_4,plain,
    hAPP(c_List_Orotate1(U_19548),hAPP(c_List_Orotate(U_19548,U_19549),U_19550)) = hAPP(c_List_Orotate(U_19548,U_19549),hAPP(c_List_Orotate1(U_19548),U_19550)),
    inference(clausify,[status(thm)],[f_4674_3]) ).

fof(f_4675_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate__Suc]) ).

fof(f_4675_2,plain,
    ! [U_19553,U_19552,U_19551] : hAPP(c_List_Orotate(U_19551,hAPP(c_Nat_OSuc,U_19552)),U_19553) = hAPP(c_List_Orotate1(U_19551),hAPP(c_List_Orotate(U_19551,U_19552),U_19553)),
    inference(variable_rename,[status(thm)],[f_4675_1]) ).

fof(f_4675_3,plain,
    ! [U_19551,U_19552,U_19553] : hAPP(c_List_Orotate(U_19551,hAPP(c_Nat_OSuc,U_19552)),U_19553) = hAPP(c_List_Orotate1(U_19551),hAPP(c_List_Orotate(U_19551,U_19552),U_19553)),
    inference(definitional_conversion,[status(esa)],[f_4675_2]) ).

cnf(f_4675_4,plain,
    hAPP(c_List_Orotate(U_19551,hAPP(c_Nat_OSuc,U_19552)),U_19553) = hAPP(c_List_Orotate1(U_19551),hAPP(c_List_Orotate(U_19551,U_19552),U_19553)),
    inference(clausify,[status(thm)],[f_4675_3]) ).

fof(f_4676_1,plain,
    ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)),
    inference(fof_nnf,[status(thm)],[fact_rotate__def]) ).

fof(f_4676_2,plain,
    ! [U_19555,U_19554] : c_List_Orotate(U_19554,U_19555) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19554),tc_List_Olist(U_19554)),U_19555),c_List_Orotate1(U_19554)),
    inference(variable_rename,[status(thm)],[f_4676_1]) ).

fof(f_4676_3,plain,
    ! [U_19554,U_19555] : c_List_Orotate(U_19554,U_19555) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19554),tc_List_Olist(U_19554)),U_19555),c_List_Orotate1(U_19554)),
    inference(definitional_conversion,[status(esa)],[f_4676_2]) ).

cnf(f_4676_4,plain,
    c_List_Orotate(U_19554,U_19555) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19554),tc_List_Olist(U_19554)),U_19555),c_List_Orotate1(U_19554)),
    inference(clausify,[status(thm)],[f_4676_3]) ).

fof(f_4677_1,plain,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_tl__append]) ).

fof(f_4677_2,plain,
    ! [U_19558,U_19557,U_19556] : hAPP(c_List_Otl(U_19556),hAPP(hAPP(c_List_Oappend(U_19556),U_19557),U_19558)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19556),U_19556,hAPP(c_List_Otl(U_19556),U_19558),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19556),tc_List_Olist(U_19556)),U_19556),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19556),tc_List_Olist(U_19556),tc_List_Olist(U_19556)),c_List_Oappend(U_19556)),U_19558))),U_19557),
    inference(variable_rename,[status(thm)],[f_4677_1]) ).

fof(f_4677_3,plain,
    ! [U_19556,U_19557,U_19558] : hAPP(c_List_Otl(U_19556),hAPP(hAPP(c_List_Oappend(U_19556),U_19557),U_19558)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19556),U_19556,hAPP(c_List_Otl(U_19556),U_19558),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19556),tc_List_Olist(U_19556)),U_19556),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19556),tc_List_Olist(U_19556),tc_List_Olist(U_19556)),c_List_Oappend(U_19556)),U_19558))),U_19557),
    inference(definitional_conversion,[status(esa)],[f_4677_2]) ).

cnf(f_4677_4,plain,
    hAPP(c_List_Otl(U_19556),hAPP(hAPP(c_List_Oappend(U_19556),U_19557),U_19558)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19556),U_19556,hAPP(c_List_Otl(U_19556),U_19558),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19556),tc_List_Olist(U_19556)),U_19556),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19556),tc_List_Olist(U_19556),tc_List_Olist(U_19556)),c_List_Oappend(U_19556)),U_19558))),U_19557),
    inference(clausify,[status(thm)],[f_4677_3]) ).

fof(f_4678_1,plain,
    ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
    inference(fof_nnf,[status(thm)],[fact_rotate0]) ).

fof(f_4678_2,plain,
    ! [U_19559] : c_List_Orotate(U_19559,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19559)),
    inference(variable_rename,[status(thm)],[f_4678_1]) ).

fof(f_4678_3,plain,
    ! [U_19559] : c_List_Orotate(U_19559,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19559)),
    inference(definitional_conversion,[status(esa)],[f_4678_2]) ).

cnf(f_4678_4,plain,
    c_List_Orotate(U_19559,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19559)),
    inference(clausify,[status(thm)],[f_4678_3]) ).

fof(f_4679_1,plain,
    ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_rotate__add]) ).

fof(f_4679_2,plain,
    ! [U_19562,U_19561,U_19560] : c_List_Orotate(U_19560,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19561),U_19562)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19560),tc_List_Olist(U_19560),tc_List_Olist(U_19560),c_List_Orotate(U_19560,U_19561)),c_List_Orotate(U_19560,U_19562)),
    inference(variable_rename,[status(thm)],[f_4679_1]) ).

fof(f_4679_3,plain,
    ! [U_19560,U_19561,U_19562] : c_List_Orotate(U_19560,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19561),U_19562)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19560),tc_List_Olist(U_19560),tc_List_Olist(U_19560),c_List_Orotate(U_19560,U_19561)),c_List_Orotate(U_19560,U_19562)),
    inference(definitional_conversion,[status(esa)],[f_4679_2]) ).

cnf(f_4679_4,plain,
    c_List_Orotate(U_19560,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19561),U_19562)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19560),tc_List_Olist(U_19560),tc_List_Olist(U_19560),c_List_Orotate(U_19560,U_19561)),c_List_Orotate(U_19560,U_19562)),
    inference(clausify,[status(thm)],[f_4679_3]) ).

fof(f_4680_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__id]) ).

fof(f_4680_2,plain,
    ! [U_19565,U_19564,U_19563] :
      ( hAPP(c_List_Orotate(U_19564,U_19563),U_19565) = U_19565
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19563,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19564)),U_19565)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4680_1]) ).

fof(f_4680_3,plain,
    ! [U_19563,U_19564,U_19565] :
      ( hAPP(c_List_Orotate(U_19564,U_19563),U_19565) = U_19565
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19563,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19564)),U_19565)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_4680_2]) ).

cnf(f_4680_4,plain,
    ( hAPP(c_List_Orotate(U_19564,U_19563),U_19565) = U_19565
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19563,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19564)),U_19565)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4680_3]) ).

fof(f_4681_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__length01]) ).

fof(f_4681_2,plain,
    ! [U_19568,U_19567,U_19566] :
      ( hAPP(c_List_Orotate(U_19566,U_19568),U_19567) = U_19567
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19566)),U_19567)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4681_1]) ).

fof(f_4681_3,plain,
    ! [U_19566,U_19567,U_19568] :
      ( hAPP(c_List_Orotate(U_19566,U_19568),U_19567) = U_19567
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19566)),U_19567)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definitional_conversion,[status(esa)],[f_4681_2]) ).

cnf(f_4681_4,plain,
    ( hAPP(c_List_Orotate(U_19566,U_19568),U_19567) = U_19567
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19566)),U_19567)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4681_3]) ).

fof(f_4682_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__tl]) ).

fof(f_4682_2,plain,
    ! [U_19570,U_19569] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19569)),hAPP(c_List_Otl(U_19569),U_19570)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19569)),U_19570)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4682_1]) ).

fof(f_4682_3,plain,
    ! [U_19569,U_19570] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19569)),hAPP(c_List_Otl(U_19569),U_19570)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19569)),U_19570)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4682_2]) ).

cnf(f_4682_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19569)),hAPP(c_List_Otl(U_19569),U_19570)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19569)),U_19570)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4682_3]) ).

fof(f_4683_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__take]) ).

fof(f_4683_2,plain,
    ! [U_19573,U_19572,U_19571] : hAPP(c_List_Otl(U_19571),hAPP(hAPP(c_List_Otake(U_19571),U_19572),U_19573)) = hAPP(hAPP(c_List_Otake(U_19571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19572),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_19571),U_19573)),
    inference(variable_rename,[status(thm)],[f_4683_1]) ).

fof(f_4683_3,plain,
    ! [U_19572,U_19571,U_19573] : hAPP(c_List_Otl(U_19571),hAPP(hAPP(c_List_Otake(U_19571),U_19572),U_19573)) = hAPP(hAPP(c_List_Otake(U_19571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19572),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_19571),U_19573)),
    inference(definitional_conversion,[status(esa)],[f_4683_2]) ).

cnf(f_4683_4,plain,
    hAPP(c_List_Otl(U_19571),hAPP(hAPP(c_List_Otake(U_19571),U_19572),U_19573)) = hAPP(hAPP(c_List_Otake(U_19571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19572),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_19571),U_19573)),
    inference(clausify,[status(thm)],[f_4683_3]) ).

fof(f_4684_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_take__Suc]) ).

fof(f_4684_2,plain,
    ! [U_19576,U_19575,U_19574] :
      ( hAPP(hAPP(c_List_Otake(U_19575),hAPP(c_Nat_OSuc,U_19576)),U_19574) = hAPP(hAPP(c_List_Olist_OCons(U_19575),hAPP(c_List_Ohd(U_19575),U_19574)),hAPP(hAPP(c_List_Otake(U_19575),U_19576),hAPP(c_List_Otl(U_19575),U_19574)))
      | U_19574 = c_List_Olist_ONil(U_19575) ),
    inference(variable_rename,[status(thm)],[f_4684_1]) ).

fof(f_4684_3,plain,
    ! [U_19574,U_19575,U_19576] :
      ( hAPP(hAPP(c_List_Otake(U_19575),hAPP(c_Nat_OSuc,U_19576)),U_19574) = hAPP(hAPP(c_List_Olist_OCons(U_19575),hAPP(c_List_Ohd(U_19575),U_19574)),hAPP(hAPP(c_List_Otake(U_19575),U_19576),hAPP(c_List_Otl(U_19575),U_19574)))
      | U_19574 = c_List_Olist_ONil(U_19575) ),
    inference(definitional_conversion,[status(esa)],[f_4684_2]) ).

cnf(f_4684_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19575),hAPP(c_Nat_OSuc,U_19576)),U_19574) = hAPP(hAPP(c_List_Olist_OCons(U_19575),hAPP(c_List_Ohd(U_19575),U_19574)),hAPP(hAPP(c_List_Otake(U_19575),U_19576),hAPP(c_List_Otl(U_19575),U_19574)))
    | U_19574 = c_List_Olist_ONil(U_19575) ),
    inference(clausify,[status(thm)],[f_4684_3]) ).

fof(f_4685_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate__drop__take]) ).

fof(f_4685_2,plain,
    ! [U_19579,U_19578,U_19577] : hAPP(c_List_Orotate(U_19577,U_19578),U_19579) = hAPP(hAPP(c_List_Oappend(U_19577),hAPP(hAPP(c_List_Odrop(U_19577),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19578,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19577)),U_19579))),U_19579)),hAPP(hAPP(c_List_Otake(U_19577),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19578,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19577)),U_19579))),U_19579)),
    inference(variable_rename,[status(thm)],[f_4685_1]) ).

fof(f_4685_3,plain,
    ! [U_19577,U_19578,U_19579] : hAPP(c_List_Orotate(U_19577,U_19578),U_19579) = hAPP(hAPP(c_List_Oappend(U_19577),hAPP(hAPP(c_List_Odrop(U_19577),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19578,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19577)),U_19579))),U_19579)),hAPP(hAPP(c_List_Otake(U_19577),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19578,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19577)),U_19579))),U_19579)),
    inference(definitional_conversion,[status(esa)],[f_4685_2]) ).

cnf(f_4685_4,plain,
    hAPP(c_List_Orotate(U_19577,U_19578),U_19579) = hAPP(hAPP(c_List_Oappend(U_19577),hAPP(hAPP(c_List_Odrop(U_19577),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19578,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19577)),U_19579))),U_19579)),hAPP(hAPP(c_List_Otake(U_19577),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19578,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19577)),U_19579))),U_19579)),
    inference(clausify,[status(thm)],[f_4685_3]) ).

fof(f_4686_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__set]) ).

fof(f_4686_2,plain,
    ! [U_19581,U_19580] :
      ( hAPP(c_Finite__Set_Ofold1(U_19580,c_Groups_Otimes__class_Otimes(U_19580)),hAPP(c_List_Oset(U_19580),U_19581)) = hAPP(c_List_Ofoldl(U_19580,U_19580,c_Groups_Otimes__class_Otimes(U_19580),hAPP(c_List_Ohd(U_19580),U_19581)),hAPP(c_List_Otl(U_19580),U_19581))
      | U_19581 = c_List_Olist_ONil(U_19580)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_19580) ),
    inference(variable_rename,[status(thm)],[f_4686_1]) ).

fof(f_4686_3,plain,
    ! [U_19580,U_19581] :
      ( hAPP(c_Finite__Set_Ofold1(U_19580,c_Groups_Otimes__class_Otimes(U_19580)),hAPP(c_List_Oset(U_19580),U_19581)) = hAPP(c_List_Ofoldl(U_19580,U_19580,c_Groups_Otimes__class_Otimes(U_19580),hAPP(c_List_Ohd(U_19580),U_19581)),hAPP(c_List_Otl(U_19580),U_19581))
      | U_19581 = c_List_Olist_ONil(U_19580)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_19580) ),
    inference(definitional_conversion,[status(esa)],[f_4686_2]) ).

cnf(f_4686_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_19580,c_Groups_Otimes__class_Otimes(U_19580)),hAPP(c_List_Oset(U_19580),U_19581)) = hAPP(c_List_Ofoldl(U_19580,U_19580,c_Groups_Otimes__class_Otimes(U_19580),hAPP(c_List_Ohd(U_19580),U_19581)),hAPP(c_List_Otl(U_19580),U_19581))
    | U_19581 = c_List_Olist_ONil(U_19580)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_19580) ),
    inference(clausify,[status(thm)],[f_4686_3]) ).

fof(f_4687_1,plain,
    ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I2_J]) ).

fof(f_4687_2,plain,
    ! [U_19585,U_19584,U_19583,U_19582] : c_List_Olist_Olist__size(U_19582,U_19583,hAPP(hAPP(c_List_Olist_OCons(U_19582),U_19584),U_19585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19583,U_19584)),c_List_Olist_Olist__size(U_19582,U_19583,U_19585))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4687_1]) ).

fof(f_4687_3,plain,
    ! [U_19582,U_19583,U_19584,U_19585] : c_List_Olist_Olist__size(U_19582,U_19583,hAPP(hAPP(c_List_Olist_OCons(U_19582),U_19584),U_19585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19583,U_19584)),c_List_Olist_Olist__size(U_19582,U_19583,U_19585))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4687_2]) ).

cnf(f_4687_4,plain,
    c_List_Olist_Olist__size(U_19582,U_19583,hAPP(hAPP(c_List_Olist_OCons(U_19582),U_19584),U_19585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19583,U_19584)),c_List_Olist_Olist__size(U_19582,U_19583,U_19585))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4687_3]) ).

fof(f_4688_1,plain,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__append]) ).

fof(f_4688_2,plain,
    ! [U_19591,U_19590,U_19589,U_19588,U_19587,U_19586] : hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,U_19589),hAPP(hAPP(c_List_Oappend(U_19587),U_19590),U_19591)) = hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,U_19589),U_19590)),U_19591),
    inference(variable_rename,[status(thm)],[f_4688_1]) ).

fof(f_4688_3,plain,
    ! [U_19586,U_19587,U_19588,U_19589,U_19590,U_19591] : hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,U_19589),hAPP(hAPP(c_List_Oappend(U_19587),U_19590),U_19591)) = hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,U_19589),U_19590)),U_19591),
    inference(definitional_conversion,[status(esa)],[f_4688_2]) ).

cnf(f_4688_4,plain,
    hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,U_19589),hAPP(hAPP(c_List_Oappend(U_19587),U_19590),U_19591)) = hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,hAPP(c_List_Ofoldl(U_19586,U_19587,U_19588,U_19589),U_19590)),U_19591),
    inference(clausify,[status(thm)],[f_4688_3]) ).

fof(f_4689_1,plain,
    ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__Cons]) ).

fof(f_4689_2,plain,
    ! [U_19597,U_19596,U_19595,U_19594,U_19593,U_19592] : hAPP(c_List_Ofoldl(U_19592,U_19593,U_19594,U_19595),hAPP(hAPP(c_List_Olist_OCons(U_19593),U_19596),U_19597)) = hAPP(c_List_Ofoldl(U_19592,U_19593,U_19594,hAPP(hAPP(U_19594,U_19595),U_19596)),U_19597),
    inference(variable_rename,[status(thm)],[f_4689_1]) ).

fof(f_4689_3,plain,
    ! [U_19592,U_19593,U_19594,U_19595,U_19596,U_19597] : hAPP(c_List_Ofoldl(U_19592,U_19593,U_19594,U_19595),hAPP(hAPP(c_List_Olist_OCons(U_19593),U_19596),U_19597)) = hAPP(c_List_Ofoldl(U_19592,U_19593,U_19594,hAPP(hAPP(U_19594,U_19595),U_19596)),U_19597),
    inference(definitional_conversion,[status(esa)],[f_4689_2]) ).

cnf(f_4689_4,plain,
    hAPP(c_List_Ofoldl(U_19592,U_19593,U_19594,U_19595),hAPP(hAPP(c_List_Olist_OCons(U_19593),U_19596),U_19597)) = hAPP(c_List_Ofoldl(U_19592,U_19593,U_19594,hAPP(hAPP(U_19594,U_19595),U_19596)),U_19597),
    inference(clausify,[status(thm)],[f_4689_3]) ).

fof(f_4690_1,plain,
    ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__map]) ).

fof(f_4690_2,plain,
    ! [U_19604,U_19603,U_19602,U_19601,U_19600,U_19599,U_19598] : hAPP(c_List_Ofoldl(U_19598,U_19599,U_19600,U_19601),hAPP(hAPP(c_List_Omap(U_19602,U_19599),U_19603),U_19604)) = hAPP(c_List_Ofoldl(U_19598,U_19602,hAPP(hAPP(c_COMBC(U_19598,tc_fun(U_19602,U_19599),tc_fun(U_19602,U_19598)),hAPP(hAPP(c_COMBB(tc_fun(U_19599,U_19598),tc_fun(tc_fun(U_19602,U_19599),tc_fun(U_19602,U_19598)),U_19598),c_COMBB(U_19599,U_19598,U_19602)),U_19600)),U_19603),U_19601),U_19604),
    inference(variable_rename,[status(thm)],[f_4690_1]) ).

fof(f_4690_3,plain,
    ! [U_19598,U_19599,U_19600,U_19601,U_19602,U_19603,U_19604] : hAPP(c_List_Ofoldl(U_19598,U_19599,U_19600,U_19601),hAPP(hAPP(c_List_Omap(U_19602,U_19599),U_19603),U_19604)) = hAPP(c_List_Ofoldl(U_19598,U_19602,hAPP(hAPP(c_COMBC(U_19598,tc_fun(U_19602,U_19599),tc_fun(U_19602,U_19598)),hAPP(hAPP(c_COMBB(tc_fun(U_19599,U_19598),tc_fun(tc_fun(U_19602,U_19599),tc_fun(U_19602,U_19598)),U_19598),c_COMBB(U_19599,U_19598,U_19602)),U_19600)),U_19603),U_19601),U_19604),
    inference(definitional_conversion,[status(esa)],[f_4690_2]) ).

cnf(f_4690_4,plain,
    hAPP(c_List_Ofoldl(U_19598,U_19599,U_19600,U_19601),hAPP(hAPP(c_List_Omap(U_19602,U_19599),U_19603),U_19604)) = hAPP(c_List_Ofoldl(U_19598,U_19602,hAPP(hAPP(c_COMBC(U_19598,tc_fun(U_19602,U_19599),tc_fun(U_19602,U_19598)),hAPP(hAPP(c_COMBB(tc_fun(U_19599,U_19598),tc_fun(tc_fun(U_19602,U_19599),tc_fun(U_19602,U_19598)),U_19598),c_COMBB(U_19599,U_19598,U_19602)),U_19600)),U_19603),U_19601),U_19604),
    inference(clausify,[status(thm)],[f_4690_3]) ).

fof(f_4691_1,plain,
    ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_list__size__map]) ).

fof(f_4691_2,plain,
    ! [U_19609,U_19608,U_19607,U_19606,U_19605] : c_List_Olist_Olist__size(U_19605,U_19606,hAPP(hAPP(c_List_Omap(U_19607,U_19605),U_19608),U_19609)) = c_List_Olist_Olist__size(U_19607,hAPP(c_Fun_Ocomp(U_19605,tc_Nat_Onat,U_19607,U_19606),U_19608),U_19609),
    inference(variable_rename,[status(thm)],[f_4691_1]) ).

fof(f_4691_3,plain,
    ! [U_19605,U_19607,U_19606,U_19608,U_19609] : c_List_Olist_Olist__size(U_19605,U_19606,hAPP(hAPP(c_List_Omap(U_19607,U_19605),U_19608),U_19609)) = c_List_Olist_Olist__size(U_19607,hAPP(c_Fun_Ocomp(U_19605,tc_Nat_Onat,U_19607,U_19606),U_19608),U_19609),
    inference(definitional_conversion,[status(esa)],[f_4691_2]) ).

cnf(f_4691_4,plain,
    c_List_Olist_Olist__size(U_19605,U_19606,hAPP(hAPP(c_List_Omap(U_19607,U_19605),U_19608),U_19609)) = c_List_Olist_Olist__size(U_19607,hAPP(c_Fun_Ocomp(U_19605,tc_Nat_Onat,U_19607,U_19606),U_19608),U_19609),
    inference(clausify,[status(thm)],[f_4691_3]) ).

fof(f_4692_1,plain,
    ! [V_a_2,V_xs_2,T_b] :
      ( c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2)
      | ~ class_Groups_Oab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl]) ).

fof(f_4692_2,plain,
    ! [U_19612,U_19611,U_19610] :
      ( c_List_Ofoldr(U_19610,U_19610,c_Groups_Oplus__class_Oplus(U_19610),U_19611,U_19612) = hAPP(c_List_Ofoldl(U_19610,U_19610,c_Groups_Oplus__class_Oplus(U_19610),U_19612),U_19611)
      | ~ class_Groups_Oab__semigroup__add(U_19610) ),
    inference(variable_rename,[status(thm)],[f_4692_1]) ).

fof(f_4692_3,plain,
    ! [U_19610,U_19611,U_19612] :
      ( c_List_Ofoldr(U_19610,U_19610,c_Groups_Oplus__class_Oplus(U_19610),U_19611,U_19612) = hAPP(c_List_Ofoldl(U_19610,U_19610,c_Groups_Oplus__class_Oplus(U_19610),U_19612),U_19611)
      | ~ class_Groups_Oab__semigroup__add(U_19610) ),
    inference(definitional_conversion,[status(esa)],[f_4692_2]) ).

cnf(f_4692_4,plain,
    ( c_List_Ofoldr(U_19610,U_19610,c_Groups_Oplus__class_Oplus(U_19610),U_19611,U_19612) = hAPP(c_List_Ofoldl(U_19610,U_19610,c_Groups_Oplus__class_Oplus(U_19610),U_19612),U_19611)
    | ~ class_Groups_Oab__semigroup__add(U_19610) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

fof(f_4693_1,plain,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2))
      | ~ class_Groups_Osemigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__assoc]) ).

fof(f_4693_2,plain,
    ! [U_19616,U_19615,U_19614,U_19613] :
      ( hAPP(c_List_Ofoldl(U_19613,U_19613,c_Groups_Oplus__class_Oplus(U_19613),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19613),U_19614),U_19615)),U_19616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19613),U_19614),hAPP(c_List_Ofoldl(U_19613,U_19613,c_Groups_Oplus__class_Oplus(U_19613),U_19615),U_19616))
      | ~ class_Groups_Osemigroup__add(U_19613) ),
    inference(variable_rename,[status(thm)],[f_4693_1]) ).

fof(f_4693_3,plain,
    ! [U_19613,U_19614,U_19615,U_19616] :
      ( hAPP(c_List_Ofoldl(U_19613,U_19613,c_Groups_Oplus__class_Oplus(U_19613),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19613),U_19614),U_19615)),U_19616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19613),U_19614),hAPP(c_List_Ofoldl(U_19613,U_19613,c_Groups_Oplus__class_Oplus(U_19613),U_19615),U_19616))
      | ~ class_Groups_Osemigroup__add(U_19613) ),
    inference(definitional_conversion,[status(esa)],[f_4693_2]) ).

cnf(f_4693_4,plain,
    ( hAPP(c_List_Ofoldl(U_19613,U_19613,c_Groups_Oplus__class_Oplus(U_19613),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19613),U_19614),U_19615)),U_19616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19613),U_19614),hAPP(c_List_Ofoldl(U_19613,U_19613,c_Groups_Oplus__class_Oplus(U_19613),U_19615),U_19616))
    | ~ class_Groups_Osemigroup__add(U_19613) ),
    inference(clausify,[status(thm)],[f_4693_3]) ).

fof(f_4694_1,plain,
    ! [V_zs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2)
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__absorb0]) ).

fof(f_4694_2,plain,
    ! [U_19619,U_19618,U_19617] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19617),U_19618),hAPP(c_List_Ofoldl(U_19617,U_19617,c_Groups_Oplus__class_Oplus(U_19617),c_Groups_Ozero__class_Ozero(U_19617)),U_19619)) = hAPP(c_List_Ofoldl(U_19617,U_19617,c_Groups_Oplus__class_Oplus(U_19617),U_19618),U_19619)
      | ~ class_Groups_Omonoid__add(U_19617) ),
    inference(variable_rename,[status(thm)],[f_4694_1]) ).

fof(f_4694_3,plain,
    ! [U_19617,U_19618,U_19619] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19617),U_19618),hAPP(c_List_Ofoldl(U_19617,U_19617,c_Groups_Oplus__class_Oplus(U_19617),c_Groups_Ozero__class_Ozero(U_19617)),U_19619)) = hAPP(c_List_Ofoldl(U_19617,U_19617,c_Groups_Oplus__class_Oplus(U_19617),U_19618),U_19619)
      | ~ class_Groups_Omonoid__add(U_19617) ),
    inference(definitional_conversion,[status(esa)],[f_4694_2]) ).

cnf(f_4694_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19617),U_19618),hAPP(c_List_Ofoldl(U_19617,U_19617,c_Groups_Oplus__class_Oplus(U_19617),c_Groups_Ozero__class_Ozero(U_19617)),U_19619)) = hAPP(c_List_Ofoldl(U_19617,U_19617,c_Groups_Oplus__class_Oplus(U_19617),U_19618),U_19619)
    | ~ class_Groups_Omonoid__add(U_19617) ),
    inference(clausify,[status(thm)],[f_4694_3]) ).

fof(f_4695_1,plain,
    ! [V_ns_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_start__le__sum]) ).

fof(f_4695_2,plain,
    ! [U_19622,U_19621,U_19620] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19620),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19621),U_19622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19620),U_19621)) ),
    inference(variable_rename,[status(thm)],[f_4695_1]) ).

fof(f_4695_3,plain,
    ! [U_19620,U_19621,U_19622] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19620),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19621),U_19622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19620),U_19621)) ),
    inference(definitional_conversion,[status(esa)],[f_4695_2]) ).

cnf(f_4695_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19620),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19621),U_19622)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19620),U_19621)) ),
    inference(clausify,[status(thm)],[f_4695_3]) ).

fof(f_4696_1,plain,
    ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_foldl__Nil]) ).

fof(f_4696_2,plain,
    ! [U_19626,U_19625,U_19624,U_19623] : hAPP(c_List_Ofoldl(U_19623,U_19624,U_19625,U_19626),c_List_Olist_ONil(U_19624)) = U_19626,
    inference(variable_rename,[status(thm)],[f_4696_1]) ).

fof(f_4696_3,plain,
    ! [U_19623,U_19624,U_19625,U_19626] : hAPP(c_List_Ofoldl(U_19623,U_19624,U_19625,U_19626),c_List_Olist_ONil(U_19624)) = U_19626,
    inference(definitional_conversion,[status(esa)],[f_4696_2]) ).

cnf(f_4696_4,plain,
    hAPP(c_List_Ofoldl(U_19623,U_19624,U_19625,U_19626),c_List_Olist_ONil(U_19624)) = U_19626,
    inference(clausify,[status(thm)],[f_4696_3]) ).

fof(f_4697_1,plain,
    ! [T_b] :
      ( c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b))
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__foldl]) ).

fof(f_4697_2,plain,
    ! [U_19627] :
      ( c_List_Omonoid__add__class_Olistsum(U_19627) = c_List_Ofoldl(U_19627,U_19627,c_Groups_Oplus__class_Oplus(U_19627),c_Groups_Ozero__class_Ozero(U_19627))
      | ~ class_Groups_Omonoid__add(U_19627) ),
    inference(variable_rename,[status(thm)],[f_4697_1]) ).

fof(f_4697_3,plain,
    ! [U_19627] :
      ( c_List_Omonoid__add__class_Olistsum(U_19627) = c_List_Ofoldl(U_19627,U_19627,c_Groups_Oplus__class_Oplus(U_19627),c_Groups_Ozero__class_Ozero(U_19627))
      | ~ class_Groups_Omonoid__add(U_19627) ),
    inference(definitional_conversion,[status(esa)],[f_4697_2]) ).

cnf(f_4697_4,plain,
    ( c_List_Omonoid__add__class_Olistsum(U_19627) = c_List_Ofoldl(U_19627,U_19627,c_Groups_Oplus__class_Oplus(U_19627),c_Groups_Ozero__class_Ozero(U_19627))
    | ~ class_Groups_Omonoid__add(U_19627) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

fof(f_4698_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr1]) ).

fof(f_4698_2,plain,
    ! [U_19629,U_19628] :
      ( hAPP(c_List_Ofoldl(U_19628,U_19628,c_Groups_Oplus__class_Oplus(U_19628),c_Groups_Ozero__class_Ozero(U_19628)),U_19629) = c_List_Ofoldr(U_19628,U_19628,c_Groups_Oplus__class_Oplus(U_19628),U_19629,c_Groups_Ozero__class_Ozero(U_19628))
      | ~ class_Groups_Omonoid__add(U_19628) ),
    inference(variable_rename,[status(thm)],[f_4698_1]) ).

fof(f_4698_3,plain,
    ! [U_19628,U_19629] :
      ( hAPP(c_List_Ofoldl(U_19628,U_19628,c_Groups_Oplus__class_Oplus(U_19628),c_Groups_Ozero__class_Ozero(U_19628)),U_19629) = c_List_Ofoldr(U_19628,U_19628,c_Groups_Oplus__class_Oplus(U_19628),U_19629,c_Groups_Ozero__class_Ozero(U_19628))
      | ~ class_Groups_Omonoid__add(U_19628) ),
    inference(definitional_conversion,[status(esa)],[f_4698_2]) ).

cnf(f_4698_4,plain,
    ( hAPP(c_List_Ofoldl(U_19628,U_19628,c_Groups_Oplus__class_Oplus(U_19628),c_Groups_Ozero__class_Ozero(U_19628)),U_19629) = c_List_Ofoldr(U_19628,U_19628,c_Groups_Oplus__class_Oplus(U_19628),U_19629,c_Groups_Ozero__class_Ozero(U_19628))
    | ~ class_Groups_Omonoid__add(U_19628) ),
    inference(clausify,[status(thm)],[f_4698_3]) ).

fof(f_4699_1,plain,
    ! [V_xs_2,V_a_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma]) ).

fof(f_4699_2,plain,
    ! [U_19632,U_19631,U_19630] :
      ( hAPP(c_List_Ofoldl(U_19630,U_19630,c_Groups_Oplus__class_Oplus(U_19630),U_19631),U_19632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19630),U_19631),c_List_Ofoldr(U_19630,U_19630,c_Groups_Oplus__class_Oplus(U_19630),U_19632,c_Groups_Ozero__class_Ozero(U_19630)))
      | ~ class_Groups_Omonoid__add(U_19630) ),
    inference(variable_rename,[status(thm)],[f_4699_1]) ).

fof(f_4699_3,plain,
    ! [U_19630,U_19631,U_19632] :
      ( hAPP(c_List_Ofoldl(U_19630,U_19630,c_Groups_Oplus__class_Oplus(U_19630),U_19631),U_19632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19630),U_19631),c_List_Ofoldr(U_19630,U_19630,c_Groups_Oplus__class_Oplus(U_19630),U_19632,c_Groups_Ozero__class_Ozero(U_19630)))
      | ~ class_Groups_Omonoid__add(U_19630) ),
    inference(definitional_conversion,[status(esa)],[f_4699_2]) ).

cnf(f_4699_4,plain,
    ( hAPP(c_List_Ofoldl(U_19630,U_19630,c_Groups_Oplus__class_Oplus(U_19630),U_19631),U_19632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19630),U_19631),c_List_Ofoldr(U_19630,U_19630,c_Groups_Oplus__class_Oplus(U_19630),U_19632,c_Groups_Ozero__class_Ozero(U_19630)))
    | ~ class_Groups_Omonoid__add(U_19630) ),
    inference(clausify,[status(thm)],[f_4699_3]) ).

fof(f_4700_1,plain,
    ! [V_ns_2,V_m_2] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [B_x] :
            ( B_x != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) )
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [B_x] :
              ( B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) )
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_sum__eq__0__conv]) ).

fof(f_4700_2,plain,
    ! [U_19636,U_19635] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19635),U_19636) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_19634] :
            ( U_19634 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19634),hAPP(c_List_Oset(tc_Nat_Onat),U_19636))) )
        | U_19635 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [U_19633] :
              ( U_19633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19633),hAPP(c_List_Oset(tc_Nat_Onat),U_19636))) )
          & U_19635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19635),U_19636) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4700_1]) ).

fof(f_4700_3,plain,
    ( ! [U_19640,U_19638] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19638),U_19640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_19634] :
            ( U_19634 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19634),hAPP(c_List_Oset(tc_Nat_Onat),U_19640))) )
        | U_19638 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19639,U_19637] :
        ( ( ! [U_19633] :
              ( U_19633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19633),hAPP(c_List_Oset(tc_Nat_Onat),U_19639))) )
          & U_19637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19637),U_19639) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4700_2]) ).

fof(f_4700_4,plain,
    ( ! [U_19640,U_19638] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19638),U_19640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK482(U_19640,U_19638) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK482(U_19640,U_19638)),hAPP(c_List_Oset(tc_Nat_Onat),U_19640))) )
        | U_19638 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19639,U_19637] :
        ( ( ! [U_19633] :
              ( U_19633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19633),hAPP(c_List_Oset(tc_Nat_Onat),U_19639))) )
          & U_19637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19637),U_19639) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_19634,sK482(U_19640,U_19638))],[f_4700_3]) ).

fof(f_4700_5,plain,
    ( ! [U_19640,U_19638] :
        ( sK482(U_19640,U_19638) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1197(U_19640,U_19638) )
    & ! [U_19640,U_19638] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK482(U_19640,U_19638)),hAPP(c_List_Oset(tc_Nat_Onat),U_19640)))
        | ~ sP1197(U_19640,U_19638) )
    & ! [U_19633,U_19637,U_19639] :
        ( U_19633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19633),hAPP(c_List_Oset(tc_Nat_Onat),U_19639)))
        | ~ sP1196(U_19633,U_19637,U_19639) )
    & ! [U_19633,U_19637,U_19639] :
        ( U_19637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1196(U_19633,U_19637,U_19639) )
    & ! [U_19640,U_19638] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19638),U_19640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1197(U_19640,U_19638)
        | U_19638 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19633,U_19637,U_19639] :
        ( sP1196(U_19633,U_19637,U_19639)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19637),U_19639) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1196,sP1197])],[f_4700_4]) ).

cnf(f_4700_6,plain,
    ( sP1196(U_19633,U_19637,U_19639)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19637),U_19639) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4700_5]) ).

cnf(f_4700_7,plain,
    ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19638),U_19640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1197(U_19640,U_19638)
    | U_19638 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4700_5]) ).

cnf(f_4700_8,plain,
    ( U_19637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1196(U_19633,U_19637,U_19639) ),
    inference(clausify,[status(thm)],[f_4700_5]) ).

cnf(f_4700_9,plain,
    ( U_19633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19633),hAPP(c_List_Oset(tc_Nat_Onat),U_19639)))
    | ~ sP1196(U_19633,U_19637,U_19639) ),
    inference(clausify,[status(thm)],[f_4700_5]) ).

cnf(f_4700_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK482(U_19640,U_19638)),hAPP(c_List_Oset(tc_Nat_Onat),U_19640)))
    | ~ sP1197(U_19640,U_19638) ),
    inference(clausify,[status(thm)],[f_4700_5]) ).

cnf(f_4700_11,plain,
    ( sK482(U_19640,U_19638) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1197(U_19640,U_19638) ),
    inference(clausify,[status(thm)],[f_4700_5]) ).

fof(f_4701_1,plain,
    ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(f_4701_2,plain,
    ! [U_19642,U_19641] : c_List_Olist_Olist__size(U_19641,U_19642,c_List_Olist_ONil(U_19641)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4701_1]) ).

fof(f_4701_3,plain,
    ! [U_19642,U_19641] : c_List_Olist_Olist__size(U_19641,U_19642,c_List_Olist_ONil(U_19641)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4701_2]) ).

cnf(f_4701_4,plain,
    c_List_Olist_Olist__size(U_19641,U_19642,c_List_Olist_ONil(U_19641)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4701_3]) ).

fof(f_4702_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set]) ).

fof(f_4702_2,plain,
    ! [U_19647,U_19646,U_19645,U_19644,U_19643] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_19643,U_19644,U_19645),U_19646),hAPP(c_List_Oset(U_19643),U_19647)) = hAPP(c_List_Ofoldl(U_19644,U_19643,hAPP(c_COMBC(U_19643,U_19644,U_19644),U_19645),U_19646),U_19647)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_19643,U_19644,U_19645) ),
    inference(variable_rename,[status(thm)],[f_4702_1]) ).

fof(f_4702_3,plain,
    ! [U_19645,U_19643,U_19644,U_19646,U_19647] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_19643,U_19644,U_19645),U_19646),hAPP(c_List_Oset(U_19643),U_19647)) = hAPP(c_List_Ofoldl(U_19644,U_19643,hAPP(c_COMBC(U_19643,U_19644,U_19644),U_19645),U_19646),U_19647)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_19643,U_19644,U_19645) ),
    inference(definitional_conversion,[status(esa)],[f_4702_2]) ).

cnf(f_4702_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_19643,U_19644,U_19645),U_19646),hAPP(c_List_Oset(U_19643),U_19647)) = hAPP(c_List_Ofoldl(U_19644,U_19643,hAPP(c_COMBC(U_19643,U_19644,U_19644),U_19645),U_19646),U_19647)
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_19643,U_19644,U_19645) ),
    inference(clausify,[status(thm)],[f_4702_3]) ).

fof(f_4703_1,plain,
    ! [V_xs_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__set__fold]) ).

fof(f_4703_2,plain,
    ! [U_19649,U_19648] :
      ( c_Complete__Lattice_OSup__class_OSup(U_19648,hAPP(c_List_Oset(U_19648),U_19649)) = hAPP(c_List_Ofoldl(U_19648,U_19648,c_Lattices_Osemilattice__sup__class_Osup(U_19648),c_Orderings_Obot__class_Obot(U_19648)),U_19649)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19648) ),
    inference(variable_rename,[status(thm)],[f_4703_1]) ).

fof(f_4703_3,plain,
    ! [U_19649,U_19648] :
      ( c_Complete__Lattice_OSup__class_OSup(U_19648,hAPP(c_List_Oset(U_19648),U_19649)) = hAPP(c_List_Ofoldl(U_19648,U_19648,c_Lattices_Osemilattice__sup__class_Osup(U_19648),c_Orderings_Obot__class_Obot(U_19648)),U_19649)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19648) ),
    inference(definitional_conversion,[status(esa)],[f_4703_2]) ).

cnf(f_4703_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_19648,hAPP(c_List_Oset(U_19648),U_19649)) = hAPP(c_List_Ofoldl(U_19648,U_19648,c_Lattices_Osemilattice__sup__class_Osup(U_19648),c_Orderings_Obot__class_Obot(U_19648)),U_19649)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19648) ),
    inference(clausify,[status(thm)],[f_4703_3]) ).

fof(f_4704_1,plain,
    ! [V_xs_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__set__fold]) ).

fof(f_4704_2,plain,
    ! [U_19651,U_19650] :
      ( c_Complete__Lattice_OInf__class_OInf(U_19650,hAPP(c_List_Oset(U_19650),U_19651)) = hAPP(c_List_Ofoldl(U_19650,U_19650,c_Lattices_Osemilattice__inf__class_Oinf(U_19650),c_Orderings_Otop__class_Otop(U_19650)),U_19651)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19650) ),
    inference(variable_rename,[status(thm)],[f_4704_1]) ).

fof(f_4704_3,plain,
    ! [U_19650,U_19651] :
      ( c_Complete__Lattice_OInf__class_OInf(U_19650,hAPP(c_List_Oset(U_19650),U_19651)) = hAPP(c_List_Ofoldl(U_19650,U_19650,c_Lattices_Osemilattice__inf__class_Oinf(U_19650),c_Orderings_Otop__class_Otop(U_19650)),U_19651)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19650) ),
    inference(definitional_conversion,[status(esa)],[f_4704_2]) ).

cnf(f_4704_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_19650,hAPP(c_List_Oset(U_19650),U_19651)) = hAPP(c_List_Ofoldl(U_19650,U_19650,c_Lattices_Osemilattice__inf__class_Oinf(U_19650),c_Orderings_Otop__class_Otop(U_19650)),U_19651)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19650) ),
    inference(clausify,[status(thm)],[f_4704_3]) ).

fof(f_4705_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2)
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold]) ).

fof(f_4705_2,plain,
    ! [U_19654,U_19653,U_19652] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_19652,hAPP(c_List_Oset(U_19652),hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19653),U_19654))) = hAPP(c_List_Ofoldl(U_19652,U_19652,c_Lattices_Osemilattice__sup__class_Osup(U_19652),U_19653),U_19654)
      | ~ class_Lattices_Olattice(U_19652) ),
    inference(variable_rename,[status(thm)],[f_4705_1]) ).

fof(f_4705_3,plain,
    ! [U_19652,U_19653,U_19654] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_19652,hAPP(c_List_Oset(U_19652),hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19653),U_19654))) = hAPP(c_List_Ofoldl(U_19652,U_19652,c_Lattices_Osemilattice__sup__class_Osup(U_19652),U_19653),U_19654)
      | ~ class_Lattices_Olattice(U_19652) ),
    inference(definitional_conversion,[status(esa)],[f_4705_2]) ).

cnf(f_4705_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_19652,hAPP(c_List_Oset(U_19652),hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19653),U_19654))) = hAPP(c_List_Ofoldl(U_19652,U_19652,c_Lattices_Osemilattice__sup__class_Osup(U_19652),U_19653),U_19654)
    | ~ class_Lattices_Olattice(U_19652) ),
    inference(clausify,[status(thm)],[f_4705_3]) ).

fof(f_4706_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2)
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold]) ).

fof(f_4706_2,plain,
    ! [U_19657,U_19656,U_19655] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_19655,hAPP(c_List_Oset(U_19655),hAPP(hAPP(c_List_Olist_OCons(U_19655),U_19656),U_19657))) = hAPP(c_List_Ofoldl(U_19655,U_19655,c_Lattices_Osemilattice__inf__class_Oinf(U_19655),U_19656),U_19657)
      | ~ class_Lattices_Olattice(U_19655) ),
    inference(variable_rename,[status(thm)],[f_4706_1]) ).

fof(f_4706_3,plain,
    ! [U_19655,U_19656,U_19657] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_19655,hAPP(c_List_Oset(U_19655),hAPP(hAPP(c_List_Olist_OCons(U_19655),U_19656),U_19657))) = hAPP(c_List_Ofoldl(U_19655,U_19655,c_Lattices_Osemilattice__inf__class_Oinf(U_19655),U_19656),U_19657)
      | ~ class_Lattices_Olattice(U_19655) ),
    inference(definitional_conversion,[status(esa)],[f_4706_2]) ).

cnf(f_4706_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_19655,hAPP(c_List_Oset(U_19655),hAPP(hAPP(c_List_Olist_OCons(U_19655),U_19656),U_19657))) = hAPP(c_List_Ofoldl(U_19655,U_19655,c_Lattices_Osemilattice__inf__class_Oinf(U_19655),U_19656),U_19657)
    | ~ class_Lattices_Olattice(U_19655) ),
    inference(clausify,[status(thm)],[f_4706_3]) ).

fof(f_4707_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold]) ).

fof(f_4707_2,plain,
    ! [U_19660,U_19659,U_19658] :
      ( c_Big__Operators_Olinorder__class_OMin(U_19658,hAPP(c_List_Oset(U_19658),hAPP(hAPP(c_List_Olist_OCons(U_19658),U_19659),U_19660))) = hAPP(c_List_Ofoldl(U_19658,U_19658,c_Orderings_Oord__class_Omin(U_19658),U_19659),U_19660)
      | ~ class_Orderings_Olinorder(U_19658) ),
    inference(variable_rename,[status(thm)],[f_4707_1]) ).

fof(f_4707_3,plain,
    ! [U_19658,U_19659,U_19660] :
      ( c_Big__Operators_Olinorder__class_OMin(U_19658,hAPP(c_List_Oset(U_19658),hAPP(hAPP(c_List_Olist_OCons(U_19658),U_19659),U_19660))) = hAPP(c_List_Ofoldl(U_19658,U_19658,c_Orderings_Oord__class_Omin(U_19658),U_19659),U_19660)
      | ~ class_Orderings_Olinorder(U_19658) ),
    inference(definitional_conversion,[status(esa)],[f_4707_2]) ).

cnf(f_4707_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_19658,hAPP(c_List_Oset(U_19658),hAPP(hAPP(c_List_Olist_OCons(U_19658),U_19659),U_19660))) = hAPP(c_List_Ofoldl(U_19658,U_19658,c_Orderings_Oord__class_Omin(U_19658),U_19659),U_19660)
    | ~ class_Orderings_Olinorder(U_19658) ),
    inference(clausify,[status(thm)],[f_4707_3]) ).

fof(f_4708_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold]) ).

fof(f_4708_2,plain,
    ! [U_19663,U_19662,U_19661] :
      ( c_Big__Operators_Olinorder__class_OMax(U_19661,hAPP(c_List_Oset(U_19661),hAPP(hAPP(c_List_Olist_OCons(U_19661),U_19662),U_19663))) = hAPP(c_List_Ofoldl(U_19661,U_19661,c_Orderings_Oord__class_Omax(U_19661),U_19662),U_19663)
      | ~ class_Orderings_Olinorder(U_19661) ),
    inference(variable_rename,[status(thm)],[f_4708_1]) ).

fof(f_4708_3,plain,
    ! [U_19661,U_19662,U_19663] :
      ( c_Big__Operators_Olinorder__class_OMax(U_19661,hAPP(c_List_Oset(U_19661),hAPP(hAPP(c_List_Olist_OCons(U_19661),U_19662),U_19663))) = hAPP(c_List_Ofoldl(U_19661,U_19661,c_Orderings_Oord__class_Omax(U_19661),U_19662),U_19663)
      | ~ class_Orderings_Olinorder(U_19661) ),
    inference(definitional_conversion,[status(esa)],[f_4708_2]) ).

cnf(f_4708_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_19661,hAPP(c_List_Oset(U_19661),hAPP(hAPP(c_List_Olist_OCons(U_19661),U_19662),U_19663))) = hAPP(c_List_Ofoldl(U_19661,U_19661,c_Orderings_Oord__class_Omax(U_19661),U_19662),U_19663)
    | ~ class_Orderings_Olinorder(U_19661) ),
    inference(clausify,[status(thm)],[f_4708_3]) ).

fof(f_4709_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold]) ).

fof(f_4709_2,plain,
    ! [U_19666,U_19665,U_19664] :
      ( c_Big__Operators_Olattice_OInf__fin(U_19664,c_Orderings_Oord__class_Omin(U_19664),hAPP(c_List_Oset(U_19664),hAPP(hAPP(c_List_Olist_OCons(U_19664),U_19665),U_19666))) = hAPP(c_List_Ofoldl(U_19664,U_19664,c_Orderings_Oord__class_Omin(U_19664),U_19665),U_19666)
      | ~ class_Orderings_Olinorder(U_19664) ),
    inference(variable_rename,[status(thm)],[f_4709_1]) ).

fof(f_4709_3,plain,
    ! [U_19664,U_19665,U_19666] :
      ( c_Big__Operators_Olattice_OInf__fin(U_19664,c_Orderings_Oord__class_Omin(U_19664),hAPP(c_List_Oset(U_19664),hAPP(hAPP(c_List_Olist_OCons(U_19664),U_19665),U_19666))) = hAPP(c_List_Ofoldl(U_19664,U_19664,c_Orderings_Oord__class_Omin(U_19664),U_19665),U_19666)
      | ~ class_Orderings_Olinorder(U_19664) ),
    inference(definitional_conversion,[status(esa)],[f_4709_2]) ).

cnf(f_4709_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_19664,c_Orderings_Oord__class_Omin(U_19664),hAPP(c_List_Oset(U_19664),hAPP(hAPP(c_List_Olist_OCons(U_19664),U_19665),U_19666))) = hAPP(c_List_Ofoldl(U_19664,U_19664,c_Orderings_Oord__class_Omin(U_19664),U_19665),U_19666)
    | ~ class_Orderings_Olinorder(U_19664) ),
    inference(clausify,[status(thm)],[f_4709_3]) ).

fof(f_4710_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold]) ).

fof(f_4710_2,plain,
    ! [U_19669,U_19668,U_19667] :
      ( c_Big__Operators_Olattice_OSup__fin(U_19667,c_Orderings_Oord__class_Omax(U_19667),hAPP(c_List_Oset(U_19667),hAPP(hAPP(c_List_Olist_OCons(U_19667),U_19668),U_19669))) = hAPP(c_List_Ofoldl(U_19667,U_19667,c_Orderings_Oord__class_Omax(U_19667),U_19668),U_19669)
      | ~ class_Orderings_Olinorder(U_19667) ),
    inference(variable_rename,[status(thm)],[f_4710_1]) ).

fof(f_4710_3,plain,
    ! [U_19667,U_19668,U_19669] :
      ( c_Big__Operators_Olattice_OSup__fin(U_19667,c_Orderings_Oord__class_Omax(U_19667),hAPP(c_List_Oset(U_19667),hAPP(hAPP(c_List_Olist_OCons(U_19667),U_19668),U_19669))) = hAPP(c_List_Ofoldl(U_19667,U_19667,c_Orderings_Oord__class_Omax(U_19667),U_19668),U_19669)
      | ~ class_Orderings_Olinorder(U_19667) ),
    inference(definitional_conversion,[status(esa)],[f_4710_2]) ).

cnf(f_4710_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_19667,c_Orderings_Oord__class_Omax(U_19667),hAPP(c_List_Oset(U_19667),hAPP(hAPP(c_List_Olist_OCons(U_19667),U_19668),U_19669))) = hAPP(c_List_Ofoldl(U_19667,U_19667,c_Orderings_Oord__class_Omax(U_19667),U_19668),U_19669)
    | ~ class_Orderings_Olinorder(U_19667) ),
    inference(clausify,[status(thm)],[f_4710_3]) ).

fof(f_4711_1,plain,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold]) ).

fof(f_4711_2,plain,
    ! [U_19673,U_19672,U_19671,U_19670] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19671,U_19670),hAPP(c_List_Oset(U_19671),U_19672)),U_19673) = hAPP(c_List_Ofoldl(U_19670,U_19671,hAPP(c_COMBC(U_19671,U_19670,U_19670),hAPP(hAPP(c_COMBB(U_19670,tc_fun(U_19670,U_19670),U_19671),c_Lattices_Osemilattice__sup__class_Osup(U_19670)),U_19673)),c_Orderings_Obot__class_Obot(U_19670)),U_19672)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19670) ),
    inference(variable_rename,[status(thm)],[f_4711_1]) ).

fof(f_4711_3,plain,
    ! [U_19670,U_19671,U_19672,U_19673] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19671,U_19670),hAPP(c_List_Oset(U_19671),U_19672)),U_19673) = hAPP(c_List_Ofoldl(U_19670,U_19671,hAPP(c_COMBC(U_19671,U_19670,U_19670),hAPP(hAPP(c_COMBB(U_19670,tc_fun(U_19670,U_19670),U_19671),c_Lattices_Osemilattice__sup__class_Osup(U_19670)),U_19673)),c_Orderings_Obot__class_Obot(U_19670)),U_19672)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19670) ),
    inference(definitional_conversion,[status(esa)],[f_4711_2]) ).

cnf(f_4711_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19671,U_19670),hAPP(c_List_Oset(U_19671),U_19672)),U_19673) = hAPP(c_List_Ofoldl(U_19670,U_19671,hAPP(c_COMBC(U_19671,U_19670,U_19670),hAPP(hAPP(c_COMBB(U_19670,tc_fun(U_19670,U_19670),U_19671),c_Lattices_Osemilattice__sup__class_Osup(U_19670)),U_19673)),c_Orderings_Obot__class_Obot(U_19670)),U_19672)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19670) ),
    inference(clausify,[status(thm)],[f_4711_3]) ).

fof(f_4712_1,plain,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__set__fold]) ).

fof(f_4712_2,plain,
    ! [U_19677,U_19676,U_19675,U_19674] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19675,U_19674),hAPP(c_List_Oset(U_19675),U_19676)),U_19677) = hAPP(c_List_Ofoldl(U_19674,U_19675,hAPP(c_COMBC(U_19675,U_19674,U_19674),hAPP(hAPP(c_COMBB(U_19674,tc_fun(U_19674,U_19674),U_19675),c_Lattices_Osemilattice__inf__class_Oinf(U_19674)),U_19677)),c_Orderings_Otop__class_Otop(U_19674)),U_19676)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19674) ),
    inference(variable_rename,[status(thm)],[f_4712_1]) ).

fof(f_4712_3,plain,
    ! [U_19674,U_19675,U_19676,U_19677] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19675,U_19674),hAPP(c_List_Oset(U_19675),U_19676)),U_19677) = hAPP(c_List_Ofoldl(U_19674,U_19675,hAPP(c_COMBC(U_19675,U_19674,U_19674),hAPP(hAPP(c_COMBB(U_19674,tc_fun(U_19674,U_19674),U_19675),c_Lattices_Osemilattice__inf__class_Oinf(U_19674)),U_19677)),c_Orderings_Otop__class_Otop(U_19674)),U_19676)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19674) ),
    inference(definitional_conversion,[status(esa)],[f_4712_2]) ).

cnf(f_4712_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19675,U_19674),hAPP(c_List_Oset(U_19675),U_19676)),U_19677) = hAPP(c_List_Ofoldl(U_19674,U_19675,hAPP(c_COMBC(U_19675,U_19674,U_19674),hAPP(hAPP(c_COMBB(U_19674,tc_fun(U_19674,U_19674),U_19675),c_Lattices_Osemilattice__inf__class_Oinf(U_19674)),U_19677)),c_Orderings_Otop__class_Otop(U_19674)),U_19676)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19674) ),
    inference(clausify,[status(thm)],[f_4712_3]) ).

fof(f_4713_1,plain,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__estimation]) ).

fof(f_4713_2,plain,
    ! [U_19682,U_19681,U_19680,U_19679,U_19678] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19681),c_List_Olist_Olist__size(U_19678,U_19682,U_19680)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19681),hAPP(U_19682,U_19679)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19678),U_19679),hAPP(c_List_Oset(U_19678),U_19680))) ),
    inference(variable_rename,[status(thm)],[f_4713_1]) ).

fof(f_4713_3,plain,
    ! [U_19678,U_19679,U_19680,U_19681,U_19682] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19681),c_List_Olist_Olist__size(U_19678,U_19682,U_19680)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19681),hAPP(U_19682,U_19679)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19678),U_19679),hAPP(c_List_Oset(U_19678),U_19680))) ),
    inference(definitional_conversion,[status(esa)],[f_4713_2]) ).

cnf(f_4713_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19681),c_List_Olist_Olist__size(U_19678,U_19682,U_19680)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19681),hAPP(U_19682,U_19679)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19678),U_19679),hAPP(c_List_Oset(U_19678),U_19680))) ),
    inference(clausify,[status(thm)],[f_4713_3]) ).

fof(f_4714_1,plain,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H]) ).

fof(f_4714_2,plain,
    ! [U_19687,U_19686,U_19685,U_19684,U_19683] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19686),c_List_Olist_Olist__size(U_19683,U_19687,U_19685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19686),hAPP(U_19687,U_19684)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19683),U_19684),hAPP(c_List_Oset(U_19683),U_19685))) ),
    inference(variable_rename,[status(thm)],[f_4714_1]) ).

fof(f_4714_3,plain,
    ! [U_19683,U_19684,U_19685,U_19686,U_19687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19686),c_List_Olist_Olist__size(U_19683,U_19687,U_19685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19686),hAPP(U_19687,U_19684)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19683),U_19684),hAPP(c_List_Oset(U_19683),U_19685))) ),
    inference(definitional_conversion,[status(esa)],[f_4714_2]) ).

cnf(f_4714_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19686),c_List_Olist_Olist__size(U_19683,U_19687,U_19685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19686),hAPP(U_19687,U_19684)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19683),U_19684),hAPP(c_List_Oset(U_19683),U_19685))) ),
    inference(clausify,[status(thm)],[f_4714_3]) ).

fof(f_4715_1,plain,
    ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__upds__fold__map__upd]) ).

fof(f_4715_2,plain,
    ! [U_19692,U_19691,U_19690,U_19689,U_19688] : c_Map_Omap__upds(U_19688,U_19689,U_19690,U_19691,U_19692) = hAPP(c_List_Ofoldl(tc_fun(U_19688,tc_Option_Ooption(U_19689)),tc_prod(U_19688,U_19689),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),tc_fun(tc_prod(U_19688,U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),c_Product__Type_Oprod_Oprod__case(U_19688,U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),hAPP(hAPP(c_COMBC(tc_fun(U_19688,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),c_COMBC(U_19688,tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689)))),tc_fun(U_19688,tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689))),tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),U_19688),c_COMBB(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689)),U_19689))),c_Fun_Ofun__upd(U_19688,tc_Option_Ooption(U_19689))))),c_Option_Ooption_OSome(U_19689))),U_19690),hAPP(hAPP(c_List_Ozip(U_19688,U_19689),U_19691),U_19692)),
    inference(variable_rename,[status(thm)],[f_4715_1]) ).

fof(f_4715_3,plain,
    ! [U_19688,U_19689,U_19690,U_19691,U_19692] : c_Map_Omap__upds(U_19688,U_19689,U_19690,U_19691,U_19692) = hAPP(c_List_Ofoldl(tc_fun(U_19688,tc_Option_Ooption(U_19689)),tc_prod(U_19688,U_19689),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),tc_fun(tc_prod(U_19688,U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),c_Product__Type_Oprod_Oprod__case(U_19688,U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),hAPP(hAPP(c_COMBC(tc_fun(U_19688,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),c_COMBC(U_19688,tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689)))),tc_fun(U_19688,tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689))),tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),U_19688),c_COMBB(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689)),U_19689))),c_Fun_Ofun__upd(U_19688,tc_Option_Ooption(U_19689))))),c_Option_Ooption_OSome(U_19689))),U_19690),hAPP(hAPP(c_List_Ozip(U_19688,U_19689),U_19691),U_19692)),
    inference(definitional_conversion,[status(esa)],[f_4715_2]) ).

cnf(f_4715_4,plain,
    c_Map_Omap__upds(U_19688,U_19689,U_19690,U_19691,U_19692) = hAPP(c_List_Ofoldl(tc_fun(U_19688,tc_Option_Ooption(U_19689)),tc_prod(U_19688,U_19689),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),tc_fun(tc_prod(U_19688,U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),c_Product__Type_Oprod_Oprod__case(U_19688,U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),hAPP(hAPP(c_COMBC(tc_fun(U_19688,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19688,tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),c_COMBC(U_19688,tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),hAPP(hAPP(c_COMBB(tc_fun(U_19688,tc_fun(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689)))),tc_fun(U_19688,tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689))))),tc_fun(U_19688,tc_Option_Ooption(U_19689))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689))),tc_fun(tc_fun(U_19689,tc_Option_Ooption(U_19689)),tc_fun(U_19689,tc_fun(U_19688,tc_Option_Ooption(U_19689)))),U_19688),c_COMBB(tc_Option_Ooption(U_19689),tc_fun(U_19688,tc_Option_Ooption(U_19689)),U_19689))),c_Fun_Ofun__upd(U_19688,tc_Option_Ooption(U_19689))))),c_Option_Ooption_OSome(U_19689))),U_19690),hAPP(hAPP(c_List_Ozip(U_19688,U_19689),U_19691),U_19692)),
    inference(clausify,[status(thm)],[f_4715_3]) ).

fof(f_4716_1,plain,
    ! [V_ns_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) ),
    inference(fof_nnf,[status(thm)],[fact_elem__le__sum]) ).

fof(f_4716_2,plain,
    ! [U_19694,U_19693] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19693),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19694)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19693),hAPP(c_List_Oset(tc_Nat_Onat),U_19694))) ),
    inference(variable_rename,[status(thm)],[f_4716_1]) ).

fof(f_4716_3,plain,
    ! [U_19693,U_19694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19693),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19694)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19693),hAPP(c_List_Oset(tc_Nat_Onat),U_19694))) ),
    inference(definitional_conversion,[status(esa)],[f_4716_2]) ).

cnf(f_4716_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19693),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19694)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19693),hAPP(c_List_Oset(tc_Nat_Onat),U_19694))) ),
    inference(clausify,[status(thm)],[f_4716_3]) ).

fof(f_4717_1,plain,
    ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(f_4717_2,plain,
    ! [U_19697,U_19696,U_19695] : c_List_Olist_Olist__size(U_19695,U_19696,U_19697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(U_19695,tc_Nat_Onat),U_19696),U_19697))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19697)),
    inference(variable_rename,[status(thm)],[f_4717_1]) ).

fof(f_4717_3,plain,
    ! [U_19695,U_19696,U_19697] : c_List_Olist_Olist__size(U_19695,U_19696,U_19697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(U_19695,tc_Nat_Onat),U_19696),U_19697))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19697)),
    inference(definitional_conversion,[status(esa)],[f_4717_2]) ).

cnf(f_4717_4,plain,
    c_List_Olist_Olist__size(U_19695,U_19696,U_19697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(U_19695,tc_Nat_Onat),U_19696),U_19697))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19697)),
    inference(clausify,[status(thm)],[f_4717_3]) ).

fof(f_4718_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__subset]) ).

fof(f_4718_2,plain,
    ! [U_19700,U_19699,U_19698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19698),tc_List_Olist(U_19698)),tc_HOL_Obool)),c_List_Olistrel(U_19698,U_19699)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_19698),tc_List_Olist(U_19698)),c_List_Olists(U_19698,U_19700)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19698),tc_HOL_Obool),tc_List_Olist(U_19698)),c_List_Olists(U_19698,U_19700)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19698,U_19698),tc_HOL_Obool)),U_19699),hAPP(hAPP(c_Product__Type_OSigma(U_19698,U_19698),U_19700),hAPP(c_COMBK(tc_fun(U_19698,tc_HOL_Obool),U_19698),U_19700)))) ),
    inference(variable_rename,[status(thm)],[f_4718_1]) ).

fof(f_4718_3,plain,
    ! [U_19698,U_19699,U_19700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19698),tc_List_Olist(U_19698)),tc_HOL_Obool)),c_List_Olistrel(U_19698,U_19699)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_19698),tc_List_Olist(U_19698)),c_List_Olists(U_19698,U_19700)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19698),tc_HOL_Obool),tc_List_Olist(U_19698)),c_List_Olists(U_19698,U_19700)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19698,U_19698),tc_HOL_Obool)),U_19699),hAPP(hAPP(c_Product__Type_OSigma(U_19698,U_19698),U_19700),hAPP(c_COMBK(tc_fun(U_19698,tc_HOL_Obool),U_19698),U_19700)))) ),
    inference(definitional_conversion,[status(esa)],[f_4718_2]) ).

cnf(f_4718_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19698),tc_List_Olist(U_19698)),tc_HOL_Obool)),c_List_Olistrel(U_19698,U_19699)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_19698),tc_List_Olist(U_19698)),c_List_Olists(U_19698,U_19700)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19698),tc_HOL_Obool),tc_List_Olist(U_19698)),c_List_Olists(U_19698,U_19700)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19698,U_19698),tc_HOL_Obool)),U_19699),hAPP(hAPP(c_Product__Type_OSigma(U_19698,U_19698),U_19700),hAPP(c_COMBK(tc_fun(U_19698,tc_HOL_Obool),U_19698),U_19700)))) ),
    inference(clausify,[status(thm)],[f_4718_3]) ).

fof(f_4719_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__accI]) ).

fof(f_4719_2,plain,
    ! [U_19703,U_19702,U_19701] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19701)),U_19702),c_List_Olists(U_19701,c_Wellfounded_Oacc(U_19701,U_19703))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19701)),U_19702),c_Wellfounded_Oacc(tc_List_Olist(U_19701),c_List_Olistrel1(U_19701,U_19703)))) ),
    inference(variable_rename,[status(thm)],[f_4719_1]) ).

fof(f_4719_3,plain,
    ! [U_19701,U_19702,U_19703] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19701)),U_19702),c_List_Olists(U_19701,c_Wellfounded_Oacc(U_19701,U_19703))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19701)),U_19702),c_Wellfounded_Oacc(tc_List_Olist(U_19701),c_List_Olistrel1(U_19701,U_19703)))) ),
    inference(definitional_conversion,[status(esa)],[f_4719_2]) ).

cnf(f_4719_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19701)),U_19702),c_List_Olists(U_19701,c_Wellfounded_Oacc(U_19701,U_19703))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19701)),U_19702),c_Wellfounded_Oacc(tc_List_Olist(U_19701),c_List_Olistrel1(U_19701,U_19703)))) ),
    inference(clausify,[status(thm)],[f_4719_3]) ).

fof(f_4720_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_lists_ONil]) ).

fof(f_4720_2,plain,
    ! [U_19705,U_19704] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19704)),c_List_Olist_ONil(U_19704)),c_List_Olists(U_19704,U_19705))),
    inference(variable_rename,[status(thm)],[f_4720_1]) ).

fof(f_4720_3,plain,
    ! [U_19704,U_19705] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19704)),c_List_Olist_ONil(U_19704)),c_List_Olists(U_19704,U_19705))),
    inference(definitional_conversion,[status(esa)],[f_4720_2]) ).

cnf(f_4720_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19704)),c_List_Olist_ONil(U_19704)),c_List_Olists(U_19704,U_19705))),
    inference(clausify,[status(thm)],[f_4720_3]) ).

fof(f_4721_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__refl__on]) ).

fof(f_4721_2,plain,
    ! [U_19708,U_19707,U_19706] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_19706),c_List_Olists(U_19706,U_19707),c_List_Olistrel(U_19706,U_19708))
      | ~ c_Relation_Orefl__on(U_19706,U_19707,U_19708) ),
    inference(variable_rename,[status(thm)],[f_4721_1]) ).

fof(f_4721_3,plain,
    ! [U_19706,U_19707,U_19708] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_19706),c_List_Olists(U_19706,U_19707),c_List_Olistrel(U_19706,U_19708))
      | ~ c_Relation_Orefl__on(U_19706,U_19707,U_19708) ),
    inference(definitional_conversion,[status(esa)],[f_4721_2]) ).

cnf(f_4721_4,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(U_19706),c_List_Olists(U_19706,U_19707),c_List_Olistrel(U_19706,U_19708))
    | ~ c_Relation_Orefl__on(U_19706,U_19707,U_19708) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

fof(f_4722_1,plain,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lists__UNIV]) ).

fof(f_4722_2,plain,
    ! [U_19709] : c_List_Olists(U_19709,c_Orderings_Otop__class_Otop(tc_fun(U_19709,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_19709),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4722_1]) ).

fof(f_4722_3,plain,
    ! [U_19709] : c_List_Olists(U_19709,c_Orderings_Otop__class_Otop(tc_fun(U_19709,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_19709),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4722_2]) ).

cnf(f_4722_4,plain,
    c_List_Olists(U_19709,c_Orderings_Otop__class_Otop(tc_fun(U_19709,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_19709),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4722_3]) ).

fof(f_4723_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__listrel]) ).

fof(f_4723_2,plain,
    ! [U_19712,U_19711,U_19710] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_19710),c_List_Olists(U_19710,U_19711),c_List_Olistrel(U_19710,U_19712))
      | ~ c_Equiv__Relations_Oequiv(U_19710,U_19711,U_19712) ),
    inference(variable_rename,[status(thm)],[f_4723_1]) ).

fof(f_4723_3,plain,
    ! [U_19710,U_19711,U_19712] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_19710),c_List_Olists(U_19710,U_19711),c_List_Olistrel(U_19710,U_19712))
      | ~ c_Equiv__Relations_Oequiv(U_19710,U_19711,U_19712) ),
    inference(definitional_conversion,[status(esa)],[f_4723_2]) ).

cnf(f_4723_4,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_19710),c_List_Olists(U_19710,U_19711),c_List_Olistrel(U_19710,U_19712))
    | ~ c_Equiv__Relations_Oequiv(U_19710,U_19711,U_19712) ),
    inference(clausify,[status(thm)],[f_4723_3]) ).

fof(f_4724_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lists__mono]) ).

fof(f_4724_2,plain,
    ! [U_19715,U_19714,U_19713] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_19713),tc_HOL_Obool)),c_List_Olists(U_19713,U_19714)),c_List_Olists(U_19713,U_19715)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19713,tc_HOL_Obool)),U_19714),U_19715)) ),
    inference(variable_rename,[status(thm)],[f_4724_1]) ).

fof(f_4724_3,plain,
    ! [U_19713,U_19714,U_19715] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_19713),tc_HOL_Obool)),c_List_Olists(U_19713,U_19714)),c_List_Olists(U_19713,U_19715)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19713,tc_HOL_Obool)),U_19714),U_19715)) ),
    inference(definitional_conversion,[status(esa)],[f_4724_2]) ).

cnf(f_4724_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_19713),tc_HOL_Obool)),c_List_Olists(U_19713,U_19714)),c_List_Olists(U_19713,U_19715)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19713,tc_HOL_Obool)),U_19714),U_19715)) ),
    inference(clausify,[status(thm)],[f_4724_3]) ).

fof(f_4725_1,plain,
    ! [V_A_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv]) ).

fof(f_4725_2,plain,
    ! [U_19719,U_19718,U_19717,U_19716] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19716)),hAPP(hAPP(c_List_Oappend(U_19716),U_19717),U_19718)),c_List_Olists(U_19716,U_19719)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19716)),U_19718),c_List_Olists(U_19716,U_19719)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19716)),U_19717),c_List_Olists(U_19716,U_19719))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19716)),U_19718),c_List_Olists(U_19716,U_19719)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19716)),U_19717),c_List_Olists(U_19716,U_19719))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19716)),hAPP(hAPP(c_List_Oappend(U_19716),U_19717),U_19718)),c_List_Olists(U_19716,U_19719))) ) ),
    inference(variable_rename,[status(thm)],[f_4725_1]) ).

fof(f_4725_3,plain,
    ( ! [U_19727,U_19725,U_19723,U_19721] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),hAPP(hAPP(c_List_Oappend(U_19721),U_19723),U_19725)),c_List_Olists(U_19721,U_19727)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),U_19725),c_List_Olists(U_19721,U_19727)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),U_19723),c_List_Olists(U_19721,U_19727))) )
    & ! [U_19726,U_19724,U_19722,U_19720] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),U_19724),c_List_Olists(U_19720,U_19726)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),U_19722),c_List_Olists(U_19720,U_19726))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),hAPP(hAPP(c_List_Oappend(U_19720),U_19722),U_19724)),c_List_Olists(U_19720,U_19726))) ) ),
    inference(miniscope,[status(thm)],[f_4725_2]) ).

fof(f_4725_4,plain,
    ( ! [U_19722,U_19720,U_19724,U_19726] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),U_19724),c_List_Olists(U_19720,U_19726)))
        | ~ sP1198(U_19722,U_19720,U_19724,U_19726) )
    & ! [U_19722,U_19720,U_19724,U_19726] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),U_19722),c_List_Olists(U_19720,U_19726)))
        | ~ sP1198(U_19722,U_19720,U_19724,U_19726) )
    & ! [U_19725,U_19721,U_19727,U_19723] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),hAPP(hAPP(c_List_Oappend(U_19721),U_19723),U_19725)),c_List_Olists(U_19721,U_19727)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),U_19725),c_List_Olists(U_19721,U_19727)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),U_19723),c_List_Olists(U_19721,U_19727))) )
    & ! [U_19722,U_19720,U_19724,U_19726] :
        ( sP1198(U_19722,U_19720,U_19724,U_19726)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),hAPP(hAPP(c_List_Oappend(U_19720),U_19722),U_19724)),c_List_Olists(U_19720,U_19726))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1198])],[f_4725_3]) ).

cnf(f_4725_5,plain,
    ( sP1198(U_19722,U_19720,U_19724,U_19726)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),hAPP(hAPP(c_List_Oappend(U_19720),U_19722),U_19724)),c_List_Olists(U_19720,U_19726))) ),
    inference(clausify,[status(thm)],[f_4725_4]) ).

cnf(f_4725_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),hAPP(hAPP(c_List_Oappend(U_19721),U_19723),U_19725)),c_List_Olists(U_19721,U_19727)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),U_19725),c_List_Olists(U_19721,U_19727)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19721)),U_19723),c_List_Olists(U_19721,U_19727))) ),
    inference(clausify,[status(thm)],[f_4725_4]) ).

cnf(f_4725_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),U_19722),c_List_Olists(U_19720,U_19726)))
    | ~ sP1198(U_19722,U_19720,U_19724,U_19726) ),
    inference(clausify,[status(thm)],[f_4725_4]) ).

cnf(f_4725_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19720)),U_19724),c_List_Olists(U_19720,U_19726)))
    | ~ sP1198(U_19722,U_19720,U_19724,U_19726) ),
    inference(clausify,[status(thm)],[f_4725_4]) ).

fof(f_4726_1,plain,
    ! [V_A_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff]) ).

fof(f_4726_2,plain,
    ! [U_19731,U_19730,U_19729,U_19728] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19728)),hAPP(hAPP(c_List_Olist_OCons(U_19728),U_19729),U_19730)),c_List_Olists(U_19728,U_19731)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19728)),U_19730),c_List_Olists(U_19728,U_19731)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19728),U_19729),U_19731)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19728)),U_19730),c_List_Olists(U_19728,U_19731)))
          & hBOOL(hAPP(hAPP(c_member(U_19728),U_19729),U_19731)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19728)),hAPP(hAPP(c_List_Olist_OCons(U_19728),U_19729),U_19730)),c_List_Olists(U_19728,U_19731))) ) ),
    inference(variable_rename,[status(thm)],[f_4726_1]) ).

fof(f_4726_3,plain,
    ( ! [U_19739,U_19737,U_19735,U_19733] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19733)),hAPP(hAPP(c_List_Olist_OCons(U_19733),U_19735),U_19737)),c_List_Olists(U_19733,U_19739)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19733)),U_19737),c_List_Olists(U_19733,U_19739)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19733),U_19735),U_19739)) )
    & ! [U_19738,U_19736,U_19734,U_19732] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19732)),U_19736),c_List_Olists(U_19732,U_19738)))
          & hBOOL(hAPP(hAPP(c_member(U_19732),U_19734),U_19738)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19732)),hAPP(hAPP(c_List_Olist_OCons(U_19732),U_19734),U_19736)),c_List_Olists(U_19732,U_19738))) ) ),
    inference(miniscope,[status(thm)],[f_4726_2]) ).

fof(f_4726_4,plain,
    ( ! [U_19734,U_19738,U_19732,U_19736] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19732)),U_19736),c_List_Olists(U_19732,U_19738)))
        | ~ sP1199(U_19734,U_19738,U_19732,U_19736) )
    & ! [U_19734,U_19738,U_19732,U_19736] :
        ( hBOOL(hAPP(hAPP(c_member(U_19732),U_19734),U_19738))
        | ~ sP1199(U_19734,U_19738,U_19732,U_19736) )
    & ! [U_19733,U_19739,U_19735,U_19737] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19733)),hAPP(hAPP(c_List_Olist_OCons(U_19733),U_19735),U_19737)),c_List_Olists(U_19733,U_19739)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19733)),U_19737),c_List_Olists(U_19733,U_19739)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19733),U_19735),U_19739)) )
    & ! [U_19734,U_19738,U_19732,U_19736] :
        ( sP1199(U_19734,U_19738,U_19732,U_19736)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19732)),hAPP(hAPP(c_List_Olist_OCons(U_19732),U_19734),U_19736)),c_List_Olists(U_19732,U_19738))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1199])],[f_4726_3]) ).

cnf(f_4726_5,plain,
    ( sP1199(U_19734,U_19738,U_19732,U_19736)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19732)),hAPP(hAPP(c_List_Olist_OCons(U_19732),U_19734),U_19736)),c_List_Olists(U_19732,U_19738))) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

cnf(f_4726_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19733)),hAPP(hAPP(c_List_Olist_OCons(U_19733),U_19735),U_19737)),c_List_Olists(U_19733,U_19739)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19733)),U_19737),c_List_Olists(U_19733,U_19739)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19733),U_19735),U_19739)) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

cnf(f_4726_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19732),U_19734),U_19738))
    | ~ sP1199(U_19734,U_19738,U_19732,U_19736) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

cnf(f_4726_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19732)),U_19736),c_List_Olists(U_19732,U_19738)))
    | ~ sP1199(U_19734,U_19738,U_19732,U_19736) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

fof(f_4727_1,plain,
    ! [V_A_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__lists__conv__set]) ).

fof(f_4727_2,plain,
    ! [U_19744,U_19743,U_19742] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19742)),U_19743),c_List_Olists(U_19742,U_19744)))
        | ? [U_19741] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_19742),U_19741),U_19744))
            & hBOOL(hAPP(hAPP(c_member(U_19742),U_19741),hAPP(c_List_Oset(U_19742),U_19743))) ) )
      & ( ! [U_19740] :
            ( hBOOL(hAPP(hAPP(c_member(U_19742),U_19740),U_19744))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19742),U_19740),hAPP(c_List_Oset(U_19742),U_19743))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19742)),U_19743),c_List_Olists(U_19742,U_19744))) ) ),
    inference(variable_rename,[status(thm)],[f_4727_1]) ).

fof(f_4727_3,plain,
    ( ! [U_19750,U_19748,U_19746] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19746)),U_19748),c_List_Olists(U_19746,U_19750)))
        | ? [U_19741] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_19746),U_19741),U_19750))
            & hBOOL(hAPP(hAPP(c_member(U_19746),U_19741),hAPP(c_List_Oset(U_19746),U_19748))) ) )
    & ! [U_19749,U_19747,U_19745] :
        ( ! [U_19740] :
            ( hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),U_19749))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),hAPP(c_List_Oset(U_19745),U_19747))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19745)),U_19747),c_List_Olists(U_19745,U_19749))) ) ),
    inference(miniscope,[status(thm)],[f_4727_2]) ).

fof(f_4727_4,plain,
    ( ! [U_19750,U_19748,U_19746] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19746)),U_19748),c_List_Olists(U_19746,U_19750)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_19746),sK483(U_19750,U_19748,U_19746)),U_19750))
          & hBOOL(hAPP(hAPP(c_member(U_19746),sK483(U_19750,U_19748,U_19746)),hAPP(c_List_Oset(U_19746),U_19748))) ) )
    & ! [U_19749,U_19747,U_19745] :
        ( ! [U_19740] :
            ( hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),U_19749))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),hAPP(c_List_Oset(U_19745),U_19747))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19745)),U_19747),c_List_Olists(U_19745,U_19749))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_19741,sK483(U_19750,U_19748,U_19746))],[f_4727_3]) ).

fof(f_4727_5,plain,
    ( ! [U_19750,U_19748,U_19746] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_19746),sK483(U_19750,U_19748,U_19746)),U_19750))
        | ~ sP1200(U_19750,U_19748,U_19746) )
    & ! [U_19750,U_19748,U_19746] :
        ( hBOOL(hAPP(hAPP(c_member(U_19746),sK483(U_19750,U_19748,U_19746)),hAPP(c_List_Oset(U_19746),U_19748)))
        | ~ sP1200(U_19750,U_19748,U_19746) )
    & ! [U_19750,U_19748,U_19746] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19746)),U_19748),c_List_Olists(U_19746,U_19750)))
        | sP1200(U_19750,U_19748,U_19746) )
    & ! [U_19740,U_19747,U_19745,U_19749] :
        ( hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),U_19749))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),hAPP(c_List_Oset(U_19745),U_19747)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19745)),U_19747),c_List_Olists(U_19745,U_19749))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1200])],[f_4727_4]) ).

cnf(f_4727_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),U_19749))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),hAPP(c_List_Oset(U_19745),U_19747)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19745)),U_19747),c_List_Olists(U_19745,U_19749))) ),
    inference(clausify,[status(thm)],[f_4727_5]) ).

cnf(f_4727_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19746)),U_19748),c_List_Olists(U_19746,U_19750)))
    | sP1200(U_19750,U_19748,U_19746) ),
    inference(clausify,[status(thm)],[f_4727_5]) ).

cnf(f_4727_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19746),sK483(U_19750,U_19748,U_19746)),hAPP(c_List_Oset(U_19746),U_19748)))
    | ~ sP1200(U_19750,U_19748,U_19746) ),
    inference(clausify,[status(thm)],[f_4727_5]) ).

cnf(f_4727_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_19746),sK483(U_19750,U_19748,U_19746)),U_19750))
    | ~ sP1200(U_19750,U_19748,U_19746) ),
    inference(clausify,[status(thm)],[f_4727_5]) ).

fof(f_4728_1,plain,
    ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_lists__eq__set]) ).

fof(f_4728_2,plain,
    ! [U_19752,U_19751] : c_List_Olists(U_19751,U_19752) = hAPP(c_Set_OCollect(tc_List_Olist(U_19751)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19751),tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_fun(tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_19751)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_19751,tc_HOL_Obool))),c_List_Oset(U_19751))),U_19752)),
    inference(variable_rename,[status(thm)],[f_4728_1]) ).

fof(f_4728_3,plain,
    ! [U_19751,U_19752] : c_List_Olists(U_19751,U_19752) = hAPP(c_Set_OCollect(tc_List_Olist(U_19751)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19751),tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_fun(tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_19751)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_19751,tc_HOL_Obool))),c_List_Oset(U_19751))),U_19752)),
    inference(definitional_conversion,[status(esa)],[f_4728_2]) ).

cnf(f_4728_4,plain,
    c_List_Olists(U_19751,U_19752) = hAPP(c_Set_OCollect(tc_List_Olist(U_19751)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19751),tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_fun(tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_19751)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_19751,tc_HOL_Obool))),c_List_Oset(U_19751))),U_19752)),
    inference(clausify,[status(thm)],[f_4728_3]) ).

fof(f_4729_1,plain,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_lists__empty]) ).

fof(f_4729_2,plain,
    ! [U_19753] : c_List_Olists(U_19753,c_Orderings_Obot__class_Obot(tc_fun(U_19753,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19753)),c_List_Olist_ONil(U_19753)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19753),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4729_1]) ).

fof(f_4729_3,plain,
    ! [U_19753] : c_List_Olists(U_19753,c_Orderings_Obot__class_Obot(tc_fun(U_19753,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19753)),c_List_Olist_ONil(U_19753)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19753),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4729_2]) ).

cnf(f_4729_4,plain,
    c_List_Olists(U_19753,c_Orderings_Obot__class_Obot(tc_fun(U_19753,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19753)),c_List_Olist_ONil(U_19753)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19753),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4729_3]) ).

fof(f_4730_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__accD]) ).

fof(f_4730_2,plain,
    ! [U_19756,U_19755,U_19754] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19754)),U_19755),c_Wellfounded_Oacc(tc_List_Olist(U_19754),c_List_Olistrel1(U_19754,U_19756))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19754)),U_19755),c_List_Olists(U_19754,c_Wellfounded_Oacc(U_19754,U_19756)))) ),
    inference(variable_rename,[status(thm)],[f_4730_1]) ).

fof(f_4730_3,plain,
    ! [U_19754,U_19755,U_19756] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19754)),U_19755),c_Wellfounded_Oacc(tc_List_Olist(U_19754),c_List_Olistrel1(U_19754,U_19756))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19754)),U_19755),c_List_Olists(U_19754,c_Wellfounded_Oacc(U_19754,U_19756)))) ),
    inference(definitional_conversion,[status(esa)],[f_4730_2]) ).

cnf(f_4730_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19754)),U_19755),c_Wellfounded_Oacc(tc_List_Olist(U_19754),c_List_Olistrel1(U_19754,U_19756))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19754)),U_19755),c_List_Olists(U_19754,c_Wellfounded_Oacc(U_19754,U_19756)))) ),
    inference(clausify,[status(thm)],[f_4730_3]) ).

fof(f_4731_1,plain,
    ! [V_r_2,V_x_2,T_b,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
      | ! [B_b,B_z] : V_y_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI]) ).

fof(f_4731_2,plain,
    ! [U_19762,U_19761,U_19760,U_19759] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19760),tc_List_Olist(U_19760))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19760),tc_List_Olist(U_19760)),U_19761),hAPP(hAPP(c_List_Oappend(U_19760),U_19761),U_19759))),c_List_Olexord(U_19760,U_19762)))
      | ! [U_19758,U_19757] : U_19759 != hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19758),U_19757) ),
    inference(variable_rename,[status(thm)],[f_4731_1]) ).

fof(f_4731_3,plain,
    ! [U_19758,U_19757,U_19759,U_19760,U_19761,U_19762] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19760),tc_List_Olist(U_19760))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19760),tc_List_Olist(U_19760)),U_19761),hAPP(hAPP(c_List_Oappend(U_19760),U_19761),U_19759))),c_List_Olexord(U_19760,U_19762)))
      | U_19759 != hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19758),U_19757) ),
    inference(definitional_conversion,[status(esa)],[f_4731_2]) ).

cnf(f_4731_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19760),tc_List_Olist(U_19760))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19760),tc_List_Olist(U_19760)),U_19761),hAPP(hAPP(c_List_Oappend(U_19760),U_19761),U_19759))),c_List_Olexord(U_19760,U_19762)))
    | U_19759 != hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19758),U_19757) ),
    inference(clausify,[status(thm)],[f_4731_3]) ).

fof(f_4732_1,plain,
    ! [V_r_2,V_y_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
        | ! [B_a,B_x] : V_y_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) )
      & ( ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left]) ).

fof(f_4732_2,plain,
    ! [U_19769,U_19768,U_19767] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19767),tc_List_Olist(U_19767))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19767),tc_List_Olist(U_19767)),c_List_Olist_ONil(U_19767)),U_19768)),c_List_Olexord(U_19767,U_19769)))
        | ! [U_19766,U_19765] : U_19768 != hAPP(hAPP(c_List_Olist_OCons(U_19767),U_19766),U_19765) )
      & ( ? [U_19764,U_19763] : U_19768 = hAPP(hAPP(c_List_Olist_OCons(U_19767),U_19764),U_19763)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19767),tc_List_Olist(U_19767))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19767),tc_List_Olist(U_19767)),c_List_Olist_ONil(U_19767)),U_19768)),c_List_Olexord(U_19767,U_19769))) ) ),
    inference(variable_rename,[status(thm)],[f_4732_1]) ).

fof(f_4732_3,plain,
    ( ! [U_19775,U_19773,U_19771] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19771),tc_List_Olist(U_19771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19771),tc_List_Olist(U_19771)),c_List_Olist_ONil(U_19771)),U_19773)),c_List_Olexord(U_19771,U_19775)))
        | ! [U_19766,U_19765] : U_19773 != hAPP(hAPP(c_List_Olist_OCons(U_19771),U_19766),U_19765) )
    & ! [U_19774,U_19772,U_19770] :
        ( ? [U_19764,U_19763] : U_19772 = hAPP(hAPP(c_List_Olist_OCons(U_19770),U_19764),U_19763)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19770),tc_List_Olist(U_19770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19770),tc_List_Olist(U_19770)),c_List_Olist_ONil(U_19770)),U_19772)),c_List_Olexord(U_19770,U_19774))) ) ),
    inference(miniscope,[status(thm)],[f_4732_2]) ).

fof(f_4732_4,plain,
    ( ! [U_19775,U_19773,U_19771] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19771),tc_List_Olist(U_19771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19771),tc_List_Olist(U_19771)),c_List_Olist_ONil(U_19771)),U_19773)),c_List_Olexord(U_19771,U_19775)))
        | ! [U_19766,U_19765] : U_19773 != hAPP(hAPP(c_List_Olist_OCons(U_19771),U_19766),U_19765) )
    & ! [U_19774,U_19772,U_19770] :
        ( ? [U_19763] : U_19772 = hAPP(hAPP(c_List_Olist_OCons(U_19770),sK484(U_19774,U_19772,U_19770)),U_19763)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19770),tc_List_Olist(U_19770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19770),tc_List_Olist(U_19770)),c_List_Olist_ONil(U_19770)),U_19772)),c_List_Olexord(U_19770,U_19774))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_19764,sK484(U_19774,U_19772,U_19770))],[f_4732_3]) ).

fof(f_4732_5,plain,
    ( ! [U_19775,U_19773,U_19771] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19771),tc_List_Olist(U_19771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19771),tc_List_Olist(U_19771)),c_List_Olist_ONil(U_19771)),U_19773)),c_List_Olexord(U_19771,U_19775)))
        | ! [U_19766,U_19765] : U_19773 != hAPP(hAPP(c_List_Olist_OCons(U_19771),U_19766),U_19765) )
    & ! [U_19774,U_19772,U_19770] :
        ( U_19772 = hAPP(hAPP(c_List_Olist_OCons(U_19770),sK484(U_19774,U_19772,U_19770)),sK485(U_19774,U_19772,U_19770))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19770),tc_List_Olist(U_19770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19770),tc_List_Olist(U_19770)),c_List_Olist_ONil(U_19770)),U_19772)),c_List_Olexord(U_19770,U_19774))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_19763,sK485(U_19774,U_19772,U_19770))],[f_4732_4]) ).

fof(f_4732_6,plain,
    ( ! [U_19765,U_19766,U_19771,U_19773,U_19775] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19771),tc_List_Olist(U_19771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19771),tc_List_Olist(U_19771)),c_List_Olist_ONil(U_19771)),U_19773)),c_List_Olexord(U_19771,U_19775)))
        | U_19773 != hAPP(hAPP(c_List_Olist_OCons(U_19771),U_19766),U_19765) )
    & ! [U_19772,U_19770,U_19774] :
        ( U_19772 = hAPP(hAPP(c_List_Olist_OCons(U_19770),sK484(U_19774,U_19772,U_19770)),sK485(U_19774,U_19772,U_19770))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19770),tc_List_Olist(U_19770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19770),tc_List_Olist(U_19770)),c_List_Olist_ONil(U_19770)),U_19772)),c_List_Olexord(U_19770,U_19774))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4732_5]) ).

cnf(f_4732_7,plain,
    ( U_19772 = hAPP(hAPP(c_List_Olist_OCons(U_19770),sK484(U_19774,U_19772,U_19770)),sK485(U_19774,U_19772,U_19770))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19770),tc_List_Olist(U_19770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19770),tc_List_Olist(U_19770)),c_List_Olist_ONil(U_19770)),U_19772)),c_List_Olexord(U_19770,U_19774))) ),
    inference(clausify,[status(thm)],[f_4732_6]) ).

cnf(f_4732_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19771),tc_List_Olist(U_19771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19771),tc_List_Olist(U_19771)),c_List_Olist_ONil(U_19771)),U_19773)),c_List_Olexord(U_19771,U_19775)))
    | U_19773 != hAPP(hAPP(c_List_Olist_OCons(U_19771),U_19766),U_19765) ),
    inference(clausify,[status(thm)],[f_4732_6]) ).

fof(f_4733_1,plain,
    ! [V_x,V_k,T_a,V_xs] :
      ( ( ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs)
          | V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x
          | V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__list__update]) ).

fof(f_4733_2,plain,
    ! [U_19779,U_19778,U_19777,U_19776] :
      ( ( ( c_List_Olast(U_19777,hAPP(hAPP(c_List_Olist__update(U_19777,U_19776),U_19778),U_19779)) = c_List_Olast(U_19777,U_19776)
          | U_19778 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(U_19777,hAPP(hAPP(c_List_Olist__update(U_19777,U_19776),U_19778),U_19779)) = U_19779
          | U_19778 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | U_19776 = c_List_Olist_ONil(U_19777) ),
    inference(variable_rename,[status(thm)],[f_4733_1]) ).

fof(f_4733_3,plain,
    ( ! [U_19777,U_19776,U_19778,U_19779] :
        ( c_List_Olast(U_19777,hAPP(hAPP(c_List_Olist__update(U_19777,U_19776),U_19778),U_19779)) = c_List_Olast(U_19777,U_19776)
        | U_19778 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ sP1201(U_19777,U_19776,U_19778,U_19779) )
    & ! [U_19777,U_19776,U_19778,U_19779] :
        ( c_List_Olast(U_19777,hAPP(hAPP(c_List_Olist__update(U_19777,U_19776),U_19778),U_19779)) = U_19779
        | U_19778 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ sP1201(U_19777,U_19776,U_19778,U_19779) )
    & ! [U_19777,U_19776,U_19778,U_19779] :
        ( sP1201(U_19777,U_19776,U_19778,U_19779)
        | U_19776 = c_List_Olist_ONil(U_19777) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1201])],[f_4733_2]) ).

cnf(f_4733_4,plain,
    ( sP1201(U_19777,U_19776,U_19778,U_19779)
    | U_19776 = c_List_Olist_ONil(U_19777) ),
    inference(clausify,[status(thm)],[f_4733_3]) ).

cnf(f_4733_5,plain,
    ( c_List_Olast(U_19777,hAPP(hAPP(c_List_Olist__update(U_19777,U_19776),U_19778),U_19779)) = U_19779
    | U_19778 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ sP1201(U_19777,U_19776,U_19778,U_19779) ),
    inference(clausify,[status(thm)],[f_4733_3]) ).

cnf(f_4733_6,plain,
    ( c_List_Olast(U_19777,hAPP(hAPP(c_List_Olist__update(U_19777,U_19776),U_19778),U_19779)) = c_List_Olast(U_19777,U_19776)
    | U_19778 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ sP1201(U_19777,U_19776,U_19778,U_19779) ),
    inference(clausify,[status(thm)],[f_4733_3]) ).

fof(f_4734_1,plain,
    ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(T_c)
      | ~ class_Groups_Omonoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mono]) ).

fof(f_4734_2,plain,
    ! [U_19785,U_19784,U_19783,U_19782,U_19781] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19784),U_19783))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19785),U_19783))))
      | ? [U_19780] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(U_19784,U_19780)),hAPP(U_19785,U_19780)))
          & hBOOL(hAPP(hAPP(c_member(U_19782),U_19780),hAPP(c_List_Oset(U_19782),U_19783))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_19781)
      | ~ class_Groups_Omonoid__add(U_19781) ),
    inference(variable_rename,[status(thm)],[f_4734_1]) ).

fof(f_4734_3,plain,
    ! [U_19785,U_19784,U_19783,U_19782,U_19781] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19784),U_19783))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19785),U_19783))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(U_19784,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))),hAPP(U_19785,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))))
        & hBOOL(hAPP(hAPP(c_member(U_19782),sK486(U_19785,U_19784,U_19783,U_19782,U_19781)),hAPP(c_List_Oset(U_19782),U_19783))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_19781)
      | ~ class_Groups_Omonoid__add(U_19781) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_19780,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))],[f_4734_2]) ).

fof(f_4734_4,plain,
    ( ! [U_19781,U_19782,U_19783,U_19784,U_19785] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(U_19784,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))),hAPP(U_19785,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))))
        | ~ sP1202(U_19781,U_19782,U_19783,U_19784,U_19785) )
    & ! [U_19781,U_19782,U_19783,U_19784,U_19785] :
        ( hBOOL(hAPP(hAPP(c_member(U_19782),sK486(U_19785,U_19784,U_19783,U_19782,U_19781)),hAPP(c_List_Oset(U_19782),U_19783)))
        | ~ sP1202(U_19781,U_19782,U_19783,U_19784,U_19785) )
    & ! [U_19781,U_19782,U_19783,U_19784,U_19785] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19784),U_19783))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19785),U_19783))))
        | sP1202(U_19781,U_19782,U_19783,U_19784,U_19785)
        | ~ class_Groups_Oordered__ab__semigroup__add(U_19781)
        | ~ class_Groups_Omonoid__add(U_19781) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1202])],[f_4734_3]) ).

cnf(f_4734_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19784),U_19783))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19781),hAPP(hAPP(c_List_Omap(U_19782,U_19781),U_19785),U_19783))))
    | sP1202(U_19781,U_19782,U_19783,U_19784,U_19785)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_19781)
    | ~ class_Groups_Omonoid__add(U_19781) ),
    inference(clausify,[status(thm)],[f_4734_4]) ).

cnf(f_4734_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19782),sK486(U_19785,U_19784,U_19783,U_19782,U_19781)),hAPP(c_List_Oset(U_19782),U_19783)))
    | ~ sP1202(U_19781,U_19782,U_19783,U_19784,U_19785) ),
    inference(clausify,[status(thm)],[f_4734_4]) ).

cnf(f_4734_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19781),hAPP(U_19784,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))),hAPP(U_19785,sK486(U_19785,U_19784,U_19783,U_19782,U_19781))))
    | ~ sP1202(U_19781,U_19782,U_19783,U_19784,U_19785) ),
    inference(clausify,[status(thm)],[f_4734_4]) ).

fof(f_4735_1,plain,
    ! [V_x,T_a,V_xs] :
      ( ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs)
        | V_xs = c_List_Olist_ONil(T_a) )
      & ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x
        | V_xs != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_last_Osimps]) ).

fof(f_4735_2,plain,
    ! [U_19788,U_19787,U_19786] :
      ( ( c_List_Olast(U_19787,hAPP(hAPP(c_List_Olist_OCons(U_19787),U_19788),U_19786)) = c_List_Olast(U_19787,U_19786)
        | U_19786 = c_List_Olist_ONil(U_19787) )
      & ( c_List_Olast(U_19787,hAPP(hAPP(c_List_Olist_OCons(U_19787),U_19788),U_19786)) = U_19788
        | U_19786 != c_List_Olist_ONil(U_19787) ) ),
    inference(variable_rename,[status(thm)],[f_4735_1]) ).

fof(f_4735_3,plain,
    ( ! [U_19794,U_19792,U_19790] :
        ( c_List_Olast(U_19792,hAPP(hAPP(c_List_Olist_OCons(U_19792),U_19794),U_19790)) = c_List_Olast(U_19792,U_19790)
        | U_19790 = c_List_Olist_ONil(U_19792) )
    & ! [U_19793,U_19791,U_19789] :
        ( c_List_Olast(U_19791,hAPP(hAPP(c_List_Olist_OCons(U_19791),U_19793),U_19789)) = U_19793
        | U_19789 != c_List_Olist_ONil(U_19791) ) ),
    inference(miniscope,[status(thm)],[f_4735_2]) ).

fof(f_4735_4,plain,
    ( ! [U_19790,U_19792,U_19794] :
        ( c_List_Olast(U_19792,hAPP(hAPP(c_List_Olist_OCons(U_19792),U_19794),U_19790)) = c_List_Olast(U_19792,U_19790)
        | U_19790 = c_List_Olist_ONil(U_19792) )
    & ! [U_19789,U_19791,U_19793] :
        ( c_List_Olast(U_19791,hAPP(hAPP(c_List_Olist_OCons(U_19791),U_19793),U_19789)) = U_19793
        | U_19789 != c_List_Olist_ONil(U_19791) ) ),
    inference(definitional_conversion,[status(esa)],[f_4735_3]) ).

cnf(f_4735_5,plain,
    ( c_List_Olast(U_19791,hAPP(hAPP(c_List_Olist_OCons(U_19791),U_19793),U_19789)) = U_19793
    | U_19789 != c_List_Olist_ONil(U_19791) ),
    inference(clausify,[status(thm)],[f_4735_4]) ).

cnf(f_4735_6,plain,
    ( c_List_Olast(U_19792,hAPP(hAPP(c_List_Olist_OCons(U_19792),U_19794),U_19790)) = c_List_Olast(U_19792,U_19790)
    | U_19790 = c_List_Olist_ONil(U_19792) ),
    inference(clausify,[status(thm)],[f_4735_4]) ).

fof(f_4736_1,plain,
    ! [V_x,T_a,V_xs] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__ConsR]) ).

fof(f_4736_2,plain,
    ! [U_19797,U_19796,U_19795] :
      ( c_List_Olast(U_19796,hAPP(hAPP(c_List_Olist_OCons(U_19796),U_19797),U_19795)) = c_List_Olast(U_19796,U_19795)
      | U_19795 = c_List_Olist_ONil(U_19796) ),
    inference(variable_rename,[status(thm)],[f_4736_1]) ).

fof(f_4736_3,plain,
    ! [U_19795,U_19796,U_19797] :
      ( c_List_Olast(U_19796,hAPP(hAPP(c_List_Olist_OCons(U_19796),U_19797),U_19795)) = c_List_Olast(U_19796,U_19795)
      | U_19795 = c_List_Olist_ONil(U_19796) ),
    inference(definitional_conversion,[status(esa)],[f_4736_2]) ).

cnf(f_4736_4,plain,
    ( c_List_Olast(U_19796,hAPP(hAPP(c_List_Olist_OCons(U_19796),U_19797),U_19795)) = c_List_Olast(U_19796,U_19795)
    | U_19795 = c_List_Olist_ONil(U_19796) ),
    inference(clausify,[status(thm)],[f_4736_3]) ).

fof(f_4737_1,plain,
    ! [V_x,T_a,V_xs] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x
      | V_xs != c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__ConsL]) ).

fof(f_4737_2,plain,
    ! [U_19800,U_19799,U_19798] :
      ( c_List_Olast(U_19799,hAPP(hAPP(c_List_Olist_OCons(U_19799),U_19800),U_19798)) = U_19800
      | U_19798 != c_List_Olist_ONil(U_19799) ),
    inference(variable_rename,[status(thm)],[f_4737_1]) ).

fof(f_4737_3,plain,
    ! [U_19798,U_19799,U_19800] :
      ( c_List_Olast(U_19799,hAPP(hAPP(c_List_Olist_OCons(U_19799),U_19800),U_19798)) = U_19800
      | U_19798 != c_List_Olist_ONil(U_19799) ),
    inference(definitional_conversion,[status(esa)],[f_4737_2]) ).

cnf(f_4737_4,plain,
    ( c_List_Olast(U_19799,hAPP(hAPP(c_List_Olist_OCons(U_19799),U_19800),U_19798)) = U_19800
    | U_19798 != c_List_Olist_ONil(U_19799) ),
    inference(clausify,[status(thm)],[f_4737_3]) ).

fof(f_4738_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys)
        | V_ys = c_List_Olist_ONil(T_a) )
      & ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs)
        | V_ys != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_last__append]) ).

fof(f_4738_2,plain,
    ! [U_19803,U_19802,U_19801] :
      ( ( c_List_Olast(U_19802,hAPP(hAPP(c_List_Oappend(U_19802),U_19803),U_19801)) = c_List_Olast(U_19802,U_19801)
        | U_19801 = c_List_Olist_ONil(U_19802) )
      & ( c_List_Olast(U_19802,hAPP(hAPP(c_List_Oappend(U_19802),U_19803),U_19801)) = c_List_Olast(U_19802,U_19803)
        | U_19801 != c_List_Olist_ONil(U_19802) ) ),
    inference(variable_rename,[status(thm)],[f_4738_1]) ).

fof(f_4738_3,plain,
    ( ! [U_19809,U_19807,U_19805] :
        ( c_List_Olast(U_19807,hAPP(hAPP(c_List_Oappend(U_19807),U_19809),U_19805)) = c_List_Olast(U_19807,U_19805)
        | U_19805 = c_List_Olist_ONil(U_19807) )
    & ! [U_19808,U_19806,U_19804] :
        ( c_List_Olast(U_19806,hAPP(hAPP(c_List_Oappend(U_19806),U_19808),U_19804)) = c_List_Olast(U_19806,U_19808)
        | U_19804 != c_List_Olist_ONil(U_19806) ) ),
    inference(miniscope,[status(thm)],[f_4738_2]) ).

fof(f_4738_4,plain,
    ( ! [U_19805,U_19807,U_19809] :
        ( c_List_Olast(U_19807,hAPP(hAPP(c_List_Oappend(U_19807),U_19809),U_19805)) = c_List_Olast(U_19807,U_19805)
        | U_19805 = c_List_Olist_ONil(U_19807) )
    & ! [U_19806,U_19808,U_19804] :
        ( c_List_Olast(U_19806,hAPP(hAPP(c_List_Oappend(U_19806),U_19808),U_19804)) = c_List_Olast(U_19806,U_19808)
        | U_19804 != c_List_Olist_ONil(U_19806) ) ),
    inference(definitional_conversion,[status(esa)],[f_4738_3]) ).

cnf(f_4738_5,plain,
    ( c_List_Olast(U_19806,hAPP(hAPP(c_List_Oappend(U_19806),U_19808),U_19804)) = c_List_Olast(U_19806,U_19808)
    | U_19804 != c_List_Olist_ONil(U_19806) ),
    inference(clausify,[status(thm)],[f_4738_4]) ).

cnf(f_4738_6,plain,
    ( c_List_Olast(U_19807,hAPP(hAPP(c_List_Oappend(U_19807),U_19809),U_19805)) = c_List_Olast(U_19807,U_19805)
    | U_19805 = c_List_Olist_ONil(U_19807) ),
    inference(clausify,[status(thm)],[f_4738_4]) ).

fof(f_4739_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys)
      | V_ys = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__appendR]) ).

fof(f_4739_2,plain,
    ! [U_19812,U_19811,U_19810] :
      ( c_List_Olast(U_19811,hAPP(hAPP(c_List_Oappend(U_19811),U_19812),U_19810)) = c_List_Olast(U_19811,U_19810)
      | U_19810 = c_List_Olist_ONil(U_19811) ),
    inference(variable_rename,[status(thm)],[f_4739_1]) ).

fof(f_4739_3,plain,
    ! [U_19810,U_19811,U_19812] :
      ( c_List_Olast(U_19811,hAPP(hAPP(c_List_Oappend(U_19811),U_19812),U_19810)) = c_List_Olast(U_19811,U_19810)
      | U_19810 = c_List_Olist_ONil(U_19811) ),
    inference(definitional_conversion,[status(esa)],[f_4739_2]) ).

cnf(f_4739_4,plain,
    ( c_List_Olast(U_19811,hAPP(hAPP(c_List_Oappend(U_19811),U_19812),U_19810)) = c_List_Olast(U_19811,U_19810)
    | U_19810 = c_List_Olist_ONil(U_19811) ),
    inference(clausify,[status(thm)],[f_4739_3]) ).

fof(f_4740_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs)
      | V_ys != c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__appendL]) ).

fof(f_4740_2,plain,
    ! [U_19815,U_19814,U_19813] :
      ( c_List_Olast(U_19814,hAPP(hAPP(c_List_Oappend(U_19814),U_19815),U_19813)) = c_List_Olast(U_19814,U_19815)
      | U_19813 != c_List_Olist_ONil(U_19814) ),
    inference(variable_rename,[status(thm)],[f_4740_1]) ).

fof(f_4740_3,plain,
    ! [U_19813,U_19814,U_19815] :
      ( c_List_Olast(U_19814,hAPP(hAPP(c_List_Oappend(U_19814),U_19815),U_19813)) = c_List_Olast(U_19814,U_19815)
      | U_19813 != c_List_Olist_ONil(U_19814) ),
    inference(definitional_conversion,[status(esa)],[f_4740_2]) ).

cnf(f_4740_4,plain,
    ( c_List_Olast(U_19814,hAPP(hAPP(c_List_Oappend(U_19814),U_19815),U_19813)) = c_List_Olast(U_19814,U_19815)
    | U_19813 != c_List_Olist_ONil(U_19814) ),
    inference(clausify,[status(thm)],[f_4740_3]) ).

fof(f_4741_1,plain,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_last__map]) ).

fof(f_4741_2,plain,
    ! [U_19819,U_19818,U_19817,U_19816] :
      ( c_List_Olast(U_19818,hAPP(hAPP(c_List_Omap(U_19817,U_19818),U_19819),U_19816)) = hAPP(U_19819,c_List_Olast(U_19817,U_19816))
      | U_19816 = c_List_Olist_ONil(U_19817) ),
    inference(variable_rename,[status(thm)],[f_4741_1]) ).

fof(f_4741_3,plain,
    ! [U_19816,U_19817,U_19818,U_19819] :
      ( c_List_Olast(U_19818,hAPP(hAPP(c_List_Omap(U_19817,U_19818),U_19819),U_19816)) = hAPP(U_19819,c_List_Olast(U_19817,U_19816))
      | U_19816 = c_List_Olist_ONil(U_19817) ),
    inference(definitional_conversion,[status(esa)],[f_4741_2]) ).

cnf(f_4741_4,plain,
    ( c_List_Olast(U_19818,hAPP(hAPP(c_List_Omap(U_19817,U_19818),U_19819),U_19816)) = hAPP(U_19819,c_List_Olast(U_19817,U_19816))
    | U_19816 = c_List_Olist_ONil(U_19817) ),
    inference(clausify,[status(thm)],[f_4741_3]) ).

fof(f_4742_1,plain,
    ! [T_b,V_as_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2)))
      | V_as_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_last__in__set]) ).

fof(f_4742_2,plain,
    ! [U_19821,U_19820] :
      ( hBOOL(hAPP(hAPP(c_member(U_19821),c_List_Olast(U_19821,U_19820)),hAPP(c_List_Oset(U_19821),U_19820)))
      | U_19820 = c_List_Olist_ONil(U_19821) ),
    inference(variable_rename,[status(thm)],[f_4742_1]) ).

fof(f_4742_3,plain,
    ! [U_19820,U_19821] :
      ( hBOOL(hAPP(hAPP(c_member(U_19821),c_List_Olast(U_19821,U_19820)),hAPP(c_List_Oset(U_19821),U_19820)))
      | U_19820 = c_List_Olist_ONil(U_19821) ),
    inference(definitional_conversion,[status(esa)],[f_4742_2]) ).

cnf(f_4742_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19821),c_List_Olast(U_19821,U_19820)),hAPP(c_List_Oset(U_19821),U_19820)))
    | U_19820 = c_List_Olist_ONil(U_19821) ),
    inference(clausify,[status(thm)],[f_4742_3]) ).

fof(f_4743_1,plain,
    ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
    inference(fof_nnf,[status(thm)],[fact_last__snoc]) ).

fof(f_4743_2,plain,
    ! [U_19824,U_19823,U_19822] : c_List_Olast(U_19822,hAPP(hAPP(c_List_Oappend(U_19822),U_19823),hAPP(hAPP(c_List_Olist_OCons(U_19822),U_19824),c_List_Olist_ONil(U_19822)))) = U_19824,
    inference(variable_rename,[status(thm)],[f_4743_1]) ).

fof(f_4743_3,plain,
    ! [U_19822,U_19823,U_19824] : c_List_Olast(U_19822,hAPP(hAPP(c_List_Oappend(U_19822),U_19823),hAPP(hAPP(c_List_Olist_OCons(U_19822),U_19824),c_List_Olist_ONil(U_19822)))) = U_19824,
    inference(definitional_conversion,[status(esa)],[f_4743_2]) ).

cnf(f_4743_4,plain,
    c_List_Olast(U_19822,hAPP(hAPP(c_List_Oappend(U_19822),U_19823),hAPP(hAPP(c_List_Olist_OCons(U_19822),U_19824),c_List_Olist_ONil(U_19822)))) = U_19824,
    inference(clausify,[status(thm)],[f_4743_3]) ).

fof(f_4744_1,plain,
    ! [V_xs,T_a,V_n] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_last__drop]) ).

fof(f_4744_2,plain,
    ! [U_19827,U_19826,U_19825] :
      ( c_List_Olast(U_19826,hAPP(hAPP(c_List_Odrop(U_19826),U_19825),U_19827)) = c_List_Olast(U_19826,U_19827)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19825),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19826)),U_19827))) ),
    inference(variable_rename,[status(thm)],[f_4744_1]) ).

fof(f_4744_3,plain,
    ! [U_19825,U_19826,U_19827] :
      ( c_List_Olast(U_19826,hAPP(hAPP(c_List_Odrop(U_19826),U_19825),U_19827)) = c_List_Olast(U_19826,U_19827)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19825),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19826)),U_19827))) ),
    inference(definitional_conversion,[status(esa)],[f_4744_2]) ).

cnf(f_4744_4,plain,
    ( c_List_Olast(U_19826,hAPP(hAPP(c_List_Odrop(U_19826),U_19825),U_19827)) = c_List_Olast(U_19826,U_19827)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19825),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19826)),U_19827))) ),
    inference(clausify,[status(thm)],[f_4744_3]) ).

fof(f_4745_1,plain,
    ! [T_a,V_xs] :
      ( c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__conv__nth]) ).

fof(f_4745_2,plain,
    ! [U_19829,U_19828] :
      ( c_List_Olast(U_19829,U_19828) = hAPP(hAPP(c_List_Onth(U_19829),U_19828),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19829)),U_19828)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_19828 = c_List_Olist_ONil(U_19829) ),
    inference(variable_rename,[status(thm)],[f_4745_1]) ).

fof(f_4745_3,plain,
    ! [U_19828,U_19829] :
      ( c_List_Olast(U_19829,U_19828) = hAPP(hAPP(c_List_Onth(U_19829),U_19828),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19829)),U_19828)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_19828 = c_List_Olist_ONil(U_19829) ),
    inference(definitional_conversion,[status(esa)],[f_4745_2]) ).

cnf(f_4745_4,plain,
    ( c_List_Olast(U_19829,U_19828) = hAPP(hAPP(c_List_Onth(U_19829),U_19828),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19829)),U_19828)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_19828 = c_List_Olist_ONil(U_19829) ),
    inference(clausify,[status(thm)],[f_4745_3]) ).

fof(f_4746_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
      | V_x_2 = V_y_2
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
          & B_a != B_b
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__linear]) ).

fof(f_4746_2,plain,
    ! [U_19835,U_19834,U_19833,U_19832] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19835),U_19834)),c_List_Olexord(U_19832,U_19833)))
      | U_19834 = U_19835
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19834),U_19835)),c_List_Olexord(U_19832,U_19833)))
      | ? [U_19831,U_19830] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),U_19830),U_19831)),U_19833))
          & U_19831 != U_19830
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),U_19831),U_19830)),U_19833)) ) ),
    inference(variable_rename,[status(thm)],[f_4746_1]) ).

fof(f_4746_3,plain,
    ! [U_19835,U_19834,U_19833,U_19832] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19835),U_19834)),c_List_Olexord(U_19832,U_19833)))
      | U_19834 = U_19835
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19834),U_19835)),c_List_Olexord(U_19832,U_19833)))
      | ? [U_19830] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),U_19830),sK487(U_19835,U_19834,U_19833,U_19832))),U_19833))
          & sK487(U_19835,U_19834,U_19833,U_19832) != U_19830
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK487(U_19835,U_19834,U_19833,U_19832)),U_19830)),U_19833)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_19831,sK487(U_19835,U_19834,U_19833,U_19832))],[f_4746_2]) ).

fof(f_4746_4,plain,
    ! [U_19835,U_19834,U_19833,U_19832] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19835),U_19834)),c_List_Olexord(U_19832,U_19833)))
      | U_19834 = U_19835
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19834),U_19835)),c_List_Olexord(U_19832,U_19833)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK488(U_19835,U_19834,U_19833,U_19832)),sK487(U_19835,U_19834,U_19833,U_19832))),U_19833))
        & sK487(U_19835,U_19834,U_19833,U_19832) != sK488(U_19835,U_19834,U_19833,U_19832)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK487(U_19835,U_19834,U_19833,U_19832)),sK488(U_19835,U_19834,U_19833,U_19832))),U_19833)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_19830,sK488(U_19835,U_19834,U_19833,U_19832))],[f_4746_3]) ).

fof(f_4746_5,plain,
    ( ! [U_19832,U_19833,U_19834,U_19835] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK488(U_19835,U_19834,U_19833,U_19832)),sK487(U_19835,U_19834,U_19833,U_19832))),U_19833))
        | ~ sP1203(U_19832,U_19833,U_19834,U_19835) )
    & ! [U_19832,U_19833,U_19834,U_19835] :
        ( sK487(U_19835,U_19834,U_19833,U_19832) != sK488(U_19835,U_19834,U_19833,U_19832)
        | ~ sP1203(U_19832,U_19833,U_19834,U_19835) )
    & ! [U_19832,U_19833,U_19834,U_19835] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK487(U_19835,U_19834,U_19833,U_19832)),sK488(U_19835,U_19834,U_19833,U_19832))),U_19833))
        | ~ sP1203(U_19832,U_19833,U_19834,U_19835) )
    & ! [U_19832,U_19833,U_19834,U_19835] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19835),U_19834)),c_List_Olexord(U_19832,U_19833)))
        | U_19834 = U_19835
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19834),U_19835)),c_List_Olexord(U_19832,U_19833)))
        | sP1203(U_19832,U_19833,U_19834,U_19835) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1203])],[f_4746_4]) ).

cnf(f_4746_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19835),U_19834)),c_List_Olexord(U_19832,U_19833)))
    | U_19834 = U_19835
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19832),tc_List_Olist(U_19832))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19832),tc_List_Olist(U_19832)),U_19834),U_19835)),c_List_Olexord(U_19832,U_19833)))
    | sP1203(U_19832,U_19833,U_19834,U_19835) ),
    inference(clausify,[status(thm)],[f_4746_5]) ).

cnf(f_4746_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK487(U_19835,U_19834,U_19833,U_19832)),sK488(U_19835,U_19834,U_19833,U_19832))),U_19833))
    | ~ sP1203(U_19832,U_19833,U_19834,U_19835) ),
    inference(clausify,[status(thm)],[f_4746_5]) ).

cnf(f_4746_8,plain,
    ( sK487(U_19835,U_19834,U_19833,U_19832) != sK488(U_19835,U_19834,U_19833,U_19832)
    | ~ sP1203(U_19832,U_19833,U_19834,U_19835) ),
    inference(clausify,[status(thm)],[f_4746_5]) ).

cnf(f_4746_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19832,U_19832)),hAPP(hAPP(c_Product__Type_OPair(U_19832,U_19832),sK488(U_19835,U_19834,U_19833,U_19832)),sK487(U_19835,U_19834,U_19833,U_19832))),U_19833))
    | ~ sP1203(U_19832,U_19833,U_19834,U_19835) ),
    inference(clausify,[status(thm)],[f_4746_5]) ).

fof(f_4747_1,plain,
    ! [V_y_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
      | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__irreflexive]) ).

fof(f_4747_2,plain,
    ! [U_19839,U_19838,U_19837] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19837),tc_List_Olist(U_19837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19837),tc_List_Olist(U_19837)),U_19839),U_19839)),c_List_Olexord(U_19837,U_19838)))
      | ? [U_19836] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),U_19836),U_19836)),U_19838)) ),
    inference(variable_rename,[status(thm)],[f_4747_1]) ).

fof(f_4747_3,plain,
    ! [U_19839,U_19838,U_19837] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19837),tc_List_Olist(U_19837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19837),tc_List_Olist(U_19837)),U_19839),U_19839)),c_List_Olexord(U_19837,U_19838)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),sK489(U_19839,U_19838,U_19837)),sK489(U_19839,U_19838,U_19837))),U_19838)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_19836,sK489(U_19839,U_19838,U_19837))],[f_4747_2]) ).

fof(f_4747_4,plain,
    ! [U_19837,U_19838,U_19839] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19837),tc_List_Olist(U_19837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19837),tc_List_Olist(U_19837)),U_19839),U_19839)),c_List_Olexord(U_19837,U_19838)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),sK489(U_19839,U_19838,U_19837)),sK489(U_19839,U_19838,U_19837))),U_19838)) ),
    inference(definitional_conversion,[status(esa)],[f_4747_3]) ).

cnf(f_4747_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19837),tc_List_Olist(U_19837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19837),tc_List_Olist(U_19837)),U_19839),U_19839)),c_List_Olexord(U_19837,U_19838)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),sK489(U_19839,U_19838,U_19837)),sK489(U_19839,U_19838,U_19837))),U_19838)) ),
    inference(clausify,[status(thm)],[f_4747_4]) ).

fof(f_4748_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
        | ( ! [B_a,B_l] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
              | V_a_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
          & V_a_2 != c_List_Olist_ONil(T_b) ) )
      & ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_b)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lists_Osimps]) ).

fof(f_4748_2,plain,
    ! [U_19846,U_19845,U_19844] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19844)),U_19845),c_List_Olists(U_19844,U_19846)))
        | ( ! [U_19843,U_19842] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19844)),U_19842),c_List_Olists(U_19844,U_19846)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19844),U_19843),U_19846))
              | U_19845 != hAPP(hAPP(c_List_Olist_OCons(U_19844),U_19843),U_19842) )
          & U_19845 != c_List_Olist_ONil(U_19844) ) )
      & ( ? [U_19841,U_19840] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19844)),U_19840),c_List_Olists(U_19844,U_19846)))
            & hBOOL(hAPP(hAPP(c_member(U_19844),U_19841),U_19846))
            & U_19845 = hAPP(hAPP(c_List_Olist_OCons(U_19844),U_19841),U_19840) )
        | U_19845 = c_List_Olist_ONil(U_19844)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19844)),U_19845),c_List_Olists(U_19844,U_19846))) ) ),
    inference(variable_rename,[status(thm)],[f_4748_1]) ).

fof(f_4748_3,plain,
    ( ! [U_19852,U_19850,U_19848] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19850),c_List_Olists(U_19848,U_19852)))
        | ( ! [U_19843] :
              ( ! [U_19842] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19842),c_List_Olists(U_19848,U_19852)))
                  | U_19850 != hAPP(hAPP(c_List_Olist_OCons(U_19848),U_19843),U_19842) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19848),U_19843),U_19852)) )
          & U_19850 != c_List_Olist_ONil(U_19848) ) )
    & ! [U_19851,U_19849,U_19847] :
        ( ? [U_19841] :
            ( ? [U_19840] :
                ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19840),c_List_Olists(U_19847,U_19851)))
                & U_19849 = hAPP(hAPP(c_List_Olist_OCons(U_19847),U_19841),U_19840) )
            & hBOOL(hAPP(hAPP(c_member(U_19847),U_19841),U_19851)) )
        | U_19849 = c_List_Olist_ONil(U_19847)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19849),c_List_Olists(U_19847,U_19851))) ) ),
    inference(miniscope,[status(thm)],[f_4748_2]) ).

fof(f_4748_4,plain,
    ( ! [U_19852,U_19850,U_19848] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19850),c_List_Olists(U_19848,U_19852)))
        | ( ! [U_19843] :
              ( ! [U_19842] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19842),c_List_Olists(U_19848,U_19852)))
                  | U_19850 != hAPP(hAPP(c_List_Olist_OCons(U_19848),U_19843),U_19842) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19848),U_19843),U_19852)) )
          & U_19850 != c_List_Olist_ONil(U_19848) ) )
    & ! [U_19851,U_19849,U_19847] :
        ( ( ? [U_19840] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19840),c_List_Olists(U_19847,U_19851)))
              & U_19849 = hAPP(hAPP(c_List_Olist_OCons(U_19847),sK490(U_19851,U_19849,U_19847)),U_19840) )
          & hBOOL(hAPP(hAPP(c_member(U_19847),sK490(U_19851,U_19849,U_19847)),U_19851)) )
        | U_19849 = c_List_Olist_ONil(U_19847)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19849),c_List_Olists(U_19847,U_19851))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_19841,sK490(U_19851,U_19849,U_19847))],[f_4748_3]) ).

fof(f_4748_5,plain,
    ( ! [U_19852,U_19850,U_19848] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19850),c_List_Olists(U_19848,U_19852)))
        | ( ! [U_19843] :
              ( ! [U_19842] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19842),c_List_Olists(U_19848,U_19852)))
                  | U_19850 != hAPP(hAPP(c_List_Olist_OCons(U_19848),U_19843),U_19842) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19848),U_19843),U_19852)) )
          & U_19850 != c_List_Olist_ONil(U_19848) ) )
    & ! [U_19851,U_19849,U_19847] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),sK491(U_19851,U_19849,U_19847)),c_List_Olists(U_19847,U_19851)))
          & U_19849 = hAPP(hAPP(c_List_Olist_OCons(U_19847),sK490(U_19851,U_19849,U_19847)),sK491(U_19851,U_19849,U_19847))
          & hBOOL(hAPP(hAPP(c_member(U_19847),sK490(U_19851,U_19849,U_19847)),U_19851)) )
        | U_19849 = c_List_Olist_ONil(U_19847)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19849),c_List_Olists(U_19847,U_19851))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_19840,sK491(U_19851,U_19849,U_19847))],[f_4748_4]) ).

fof(f_4748_6,plain,
    ( ! [U_19852,U_19842,U_19843,U_19848,U_19850] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19842),c_List_Olists(U_19848,U_19852)))
        | U_19850 != hAPP(hAPP(c_List_Olist_OCons(U_19848),U_19843),U_19842)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19848),U_19843),U_19852))
        | ~ sP1205(U_19852,U_19842,U_19843,U_19848,U_19850) )
    & ! [U_19852,U_19842,U_19843,U_19848,U_19850] :
        ( U_19850 != c_List_Olist_ONil(U_19848)
        | ~ sP1205(U_19852,U_19842,U_19843,U_19848,U_19850) )
    & ! [U_19847,U_19851,U_19849] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),sK491(U_19851,U_19849,U_19847)),c_List_Olists(U_19847,U_19851)))
        | ~ sP1204(U_19847,U_19851,U_19849) )
    & ! [U_19847,U_19851,U_19849] :
        ( U_19849 = hAPP(hAPP(c_List_Olist_OCons(U_19847),sK490(U_19851,U_19849,U_19847)),sK491(U_19851,U_19849,U_19847))
        | ~ sP1204(U_19847,U_19851,U_19849) )
    & ! [U_19847,U_19851,U_19849] :
        ( hBOOL(hAPP(hAPP(c_member(U_19847),sK490(U_19851,U_19849,U_19847)),U_19851))
        | ~ sP1204(U_19847,U_19851,U_19849) )
    & ! [U_19852,U_19842,U_19843,U_19848,U_19850] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19850),c_List_Olists(U_19848,U_19852)))
        | sP1205(U_19852,U_19842,U_19843,U_19848,U_19850) )
    & ! [U_19847,U_19851,U_19849] :
        ( sP1204(U_19847,U_19851,U_19849)
        | U_19849 = c_List_Olist_ONil(U_19847)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19849),c_List_Olists(U_19847,U_19851))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1204,sP1205])],[f_4748_5]) ).

cnf(f_4748_7,plain,
    ( sP1204(U_19847,U_19851,U_19849)
    | U_19849 = c_List_Olist_ONil(U_19847)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),U_19849),c_List_Olists(U_19847,U_19851))) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

cnf(f_4748_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19850),c_List_Olists(U_19848,U_19852)))
    | sP1205(U_19852,U_19842,U_19843,U_19848,U_19850) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

cnf(f_4748_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19847),sK490(U_19851,U_19849,U_19847)),U_19851))
    | ~ sP1204(U_19847,U_19851,U_19849) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

cnf(f_4748_10,plain,
    ( U_19849 = hAPP(hAPP(c_List_Olist_OCons(U_19847),sK490(U_19851,U_19849,U_19847)),sK491(U_19851,U_19849,U_19847))
    | ~ sP1204(U_19847,U_19851,U_19849) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

cnf(f_4748_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19847)),sK491(U_19851,U_19849,U_19847)),c_List_Olists(U_19847,U_19851)))
    | ~ sP1204(U_19847,U_19851,U_19849) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

cnf(f_4748_12,plain,
    ( U_19850 != c_List_Olist_ONil(U_19848)
    | ~ sP1205(U_19852,U_19842,U_19843,U_19848,U_19850) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

cnf(f_4748_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19848)),U_19842),c_List_Olists(U_19848,U_19852)))
    | U_19850 != hAPP(hAPP(c_List_Olist_OCons(U_19848),U_19843),U_19842)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19848),U_19843),U_19852))
    | ~ sP1205(U_19852,U_19842,U_19843,U_19848,U_19850) ),
    inference(clausify,[status(thm)],[f_4748_6]) ).

fof(f_4749_1,plain,
    ! [V_g_2,V_f_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__pointwise]) ).

fof(f_4749_2,plain,
    ! [U_19857,U_19856,U_19855,U_19854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19854,U_19856,U_19855)),c_List_Olist_Olist__size(U_19854,U_19857,U_19855)))
      | ? [U_19853] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19856,U_19853)),hAPP(U_19857,U_19853)))
          & hBOOL(hAPP(hAPP(c_member(U_19854),U_19853),hAPP(c_List_Oset(U_19854),U_19855))) ) ),
    inference(variable_rename,[status(thm)],[f_4749_1]) ).

fof(f_4749_3,plain,
    ! [U_19857,U_19856,U_19855,U_19854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19854,U_19856,U_19855)),c_List_Olist_Olist__size(U_19854,U_19857,U_19855)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19856,sK492(U_19857,U_19856,U_19855,U_19854))),hAPP(U_19857,sK492(U_19857,U_19856,U_19855,U_19854))))
        & hBOOL(hAPP(hAPP(c_member(U_19854),sK492(U_19857,U_19856,U_19855,U_19854)),hAPP(c_List_Oset(U_19854),U_19855))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_19853,sK492(U_19857,U_19856,U_19855,U_19854))],[f_4749_2]) ).

fof(f_4749_4,plain,
    ( ! [U_19856,U_19854,U_19857,U_19855] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19856,sK492(U_19857,U_19856,U_19855,U_19854))),hAPP(U_19857,sK492(U_19857,U_19856,U_19855,U_19854))))
        | ~ sP1206(U_19856,U_19854,U_19857,U_19855) )
    & ! [U_19856,U_19854,U_19857,U_19855] :
        ( hBOOL(hAPP(hAPP(c_member(U_19854),sK492(U_19857,U_19856,U_19855,U_19854)),hAPP(c_List_Oset(U_19854),U_19855)))
        | ~ sP1206(U_19856,U_19854,U_19857,U_19855) )
    & ! [U_19856,U_19854,U_19857,U_19855] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19854,U_19856,U_19855)),c_List_Olist_Olist__size(U_19854,U_19857,U_19855)))
        | sP1206(U_19856,U_19854,U_19857,U_19855) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1206])],[f_4749_3]) ).

cnf(f_4749_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19854,U_19856,U_19855)),c_List_Olist_Olist__size(U_19854,U_19857,U_19855)))
    | sP1206(U_19856,U_19854,U_19857,U_19855) ),
    inference(clausify,[status(thm)],[f_4749_4]) ).

cnf(f_4749_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19854),sK492(U_19857,U_19856,U_19855,U_19854)),hAPP(c_List_Oset(U_19854),U_19855)))
    | ~ sP1206(U_19856,U_19854,U_19857,U_19855) ),
    inference(clausify,[status(thm)],[f_4749_4]) ).

cnf(f_4749_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19856,sK492(U_19857,U_19856,U_19855,U_19854))),hAPP(U_19857,sK492(U_19857,U_19856,U_19855,U_19854))))
    | ~ sP1206(U_19856,U_19854,U_19857,U_19855) ),
    inference(clausify,[status(thm)],[f_4749_4]) ).

fof(f_4750_1,plain,
    ! [V_xs,T_a,V_n] :
      ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_butlast__take]) ).

fof(f_4750_2,plain,
    ! [U_19860,U_19859,U_19858] :
      ( c_List_Obutlast(U_19859,hAPP(hAPP(c_List_Otake(U_19859),U_19858),U_19860)) = hAPP(hAPP(c_List_Otake(U_19859),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19858),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19860)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19858),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19859)),U_19860))) ),
    inference(variable_rename,[status(thm)],[f_4750_1]) ).

fof(f_4750_3,plain,
    ! [U_19858,U_19859,U_19860] :
      ( c_List_Obutlast(U_19859,hAPP(hAPP(c_List_Otake(U_19859),U_19858),U_19860)) = hAPP(hAPP(c_List_Otake(U_19859),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19858),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19860)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19858),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19859)),U_19860))) ),
    inference(definitional_conversion,[status(esa)],[f_4750_2]) ).

cnf(f_4750_4,plain,
    ( c_List_Obutlast(U_19859,hAPP(hAPP(c_List_Otake(U_19859),U_19858),U_19860)) = hAPP(hAPP(c_List_Otake(U_19859),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19858),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19860)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19858),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19859)),U_19860))) ),
    inference(clausify,[status(thm)],[f_4750_3]) ).

fof(f_4751_1,plain,
    ! [V_ys,V_xs,T_a,V_k] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys)
      | ? [B_i] :
          ( hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__take__lemma]) ).

fof(f_4751_2,plain,
    ! [U_19865,U_19864,U_19863,U_19862] :
      ( hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19864) = hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19865)
      | ? [U_19861] :
          ( hAPP(hAPP(c_List_Onth(U_19863),U_19864),U_19861) != hAPP(hAPP(c_List_Onth(U_19863),U_19865),U_19861)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19861),U_19862)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19865)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19864))) ),
    inference(variable_rename,[status(thm)],[f_4751_1]) ).

fof(f_4751_3,plain,
    ! [U_19865,U_19864,U_19863,U_19862] :
      ( hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19864) = hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19865)
      | ( hAPP(hAPP(c_List_Onth(U_19863),U_19864),sK493(U_19865,U_19864,U_19863,U_19862)) != hAPP(hAPP(c_List_Onth(U_19863),U_19865),sK493(U_19865,U_19864,U_19863,U_19862))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK493(U_19865,U_19864,U_19863,U_19862)),U_19862)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19865)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19864))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_19861,sK493(U_19865,U_19864,U_19863,U_19862))],[f_4751_2]) ).

fof(f_4751_4,plain,
    ( ! [U_19862,U_19863,U_19864,U_19865] :
        ( hAPP(hAPP(c_List_Onth(U_19863),U_19864),sK493(U_19865,U_19864,U_19863,U_19862)) != hAPP(hAPP(c_List_Onth(U_19863),U_19865),sK493(U_19865,U_19864,U_19863,U_19862))
        | ~ sP1207(U_19862,U_19863,U_19864,U_19865) )
    & ! [U_19862,U_19863,U_19864,U_19865] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK493(U_19865,U_19864,U_19863,U_19862)),U_19862))
        | ~ sP1207(U_19862,U_19863,U_19864,U_19865) )
    & ! [U_19862,U_19863,U_19864,U_19865] :
        ( hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19864) = hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19865)
        | sP1207(U_19862,U_19863,U_19864,U_19865)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19865)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19864))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1207])],[f_4751_3]) ).

cnf(f_4751_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19864) = hAPP(hAPP(c_List_Otake(U_19863),U_19862),U_19865)
    | sP1207(U_19862,U_19863,U_19864,U_19865)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19865)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19863)),U_19864))) ),
    inference(clausify,[status(thm)],[f_4751_4]) ).

cnf(f_4751_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK493(U_19865,U_19864,U_19863,U_19862)),U_19862))
    | ~ sP1207(U_19862,U_19863,U_19864,U_19865) ),
    inference(clausify,[status(thm)],[f_4751_4]) ).

cnf(f_4751_7,plain,
    ( hAPP(hAPP(c_List_Onth(U_19863),U_19864),sK493(U_19865,U_19864,U_19863,U_19862)) != hAPP(hAPP(c_List_Onth(U_19863),U_19865),sK493(U_19865,U_19864,U_19863,U_19862))
    | ~ sP1207(U_19862,U_19863,U_19864,U_19865) ),
    inference(clausify,[status(thm)],[f_4751_4]) ).

fof(f_4752_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__butlast]) ).

fof(f_4752_2,plain,
    ! [U_19869,U_19868,U_19867,U_19866] : hAPP(hAPP(c_List_Omap(U_19866,U_19867),U_19868),c_List_Obutlast(U_19866,U_19869)) = c_List_Obutlast(U_19867,hAPP(hAPP(c_List_Omap(U_19866,U_19867),U_19868),U_19869)),
    inference(variable_rename,[status(thm)],[f_4752_1]) ).

fof(f_4752_3,plain,
    ! [U_19869,U_19868,U_19867,U_19866] : hAPP(hAPP(c_List_Omap(U_19866,U_19867),U_19868),c_List_Obutlast(U_19866,U_19869)) = c_List_Obutlast(U_19867,hAPP(hAPP(c_List_Omap(U_19866,U_19867),U_19868),U_19869)),
    inference(definitional_conversion,[status(esa)],[f_4752_2]) ).

cnf(f_4752_4,plain,
    hAPP(hAPP(c_List_Omap(U_19866,U_19867),U_19868),c_List_Obutlast(U_19866,U_19869)) = c_List_Obutlast(U_19867,hAPP(hAPP(c_List_Omap(U_19866,U_19867),U_19868),U_19869)),
    inference(clausify,[status(thm)],[f_4752_3]) ).

fof(f_4753_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys))
        | V_ys = c_List_Olist_ONil(T_a) )
      & ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs)
        | V_ys != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_butlast__append]) ).

fof(f_4753_2,plain,
    ! [U_19872,U_19871,U_19870] :
      ( ( c_List_Obutlast(U_19871,hAPP(hAPP(c_List_Oappend(U_19871),U_19872),U_19870)) = hAPP(hAPP(c_List_Oappend(U_19871),U_19872),c_List_Obutlast(U_19871,U_19870))
        | U_19870 = c_List_Olist_ONil(U_19871) )
      & ( c_List_Obutlast(U_19871,hAPP(hAPP(c_List_Oappend(U_19871),U_19872),U_19870)) = c_List_Obutlast(U_19871,U_19872)
        | U_19870 != c_List_Olist_ONil(U_19871) ) ),
    inference(variable_rename,[status(thm)],[f_4753_1]) ).

fof(f_4753_3,plain,
    ( ! [U_19878,U_19876,U_19874] :
        ( c_List_Obutlast(U_19876,hAPP(hAPP(c_List_Oappend(U_19876),U_19878),U_19874)) = hAPP(hAPP(c_List_Oappend(U_19876),U_19878),c_List_Obutlast(U_19876,U_19874))
        | U_19874 = c_List_Olist_ONil(U_19876) )
    & ! [U_19877,U_19875,U_19873] :
        ( c_List_Obutlast(U_19875,hAPP(hAPP(c_List_Oappend(U_19875),U_19877),U_19873)) = c_List_Obutlast(U_19875,U_19877)
        | U_19873 != c_List_Olist_ONil(U_19875) ) ),
    inference(miniscope,[status(thm)],[f_4753_2]) ).

fof(f_4753_4,plain,
    ( ! [U_19874,U_19876,U_19878] :
        ( c_List_Obutlast(U_19876,hAPP(hAPP(c_List_Oappend(U_19876),U_19878),U_19874)) = hAPP(hAPP(c_List_Oappend(U_19876),U_19878),c_List_Obutlast(U_19876,U_19874))
        | U_19874 = c_List_Olist_ONil(U_19876) )
    & ! [U_19875,U_19877,U_19873] :
        ( c_List_Obutlast(U_19875,hAPP(hAPP(c_List_Oappend(U_19875),U_19877),U_19873)) = c_List_Obutlast(U_19875,U_19877)
        | U_19873 != c_List_Olist_ONil(U_19875) ) ),
    inference(definitional_conversion,[status(esa)],[f_4753_3]) ).

cnf(f_4753_5,plain,
    ( c_List_Obutlast(U_19875,hAPP(hAPP(c_List_Oappend(U_19875),U_19877),U_19873)) = c_List_Obutlast(U_19875,U_19877)
    | U_19873 != c_List_Olist_ONil(U_19875) ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

cnf(f_4753_6,plain,
    ( c_List_Obutlast(U_19876,hAPP(hAPP(c_List_Oappend(U_19876),U_19878),U_19874)) = hAPP(hAPP(c_List_Oappend(U_19876),U_19878),c_List_Obutlast(U_19876,U_19874))
    | U_19874 = c_List_Olist_ONil(U_19876) ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

fof(f_4754_1,plain,
    ! [V_x,T_a,V_xs] :
      ( ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs))
        | V_xs = c_List_Olist_ONil(T_a) )
      & ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)
        | V_xs != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J]) ).

fof(f_4754_2,plain,
    ! [U_19881,U_19880,U_19879] :
      ( ( c_List_Obutlast(U_19880,hAPP(hAPP(c_List_Olist_OCons(U_19880),U_19881),U_19879)) = hAPP(hAPP(c_List_Olist_OCons(U_19880),U_19881),c_List_Obutlast(U_19880,U_19879))
        | U_19879 = c_List_Olist_ONil(U_19880) )
      & ( c_List_Obutlast(U_19880,hAPP(hAPP(c_List_Olist_OCons(U_19880),U_19881),U_19879)) = c_List_Olist_ONil(U_19880)
        | U_19879 != c_List_Olist_ONil(U_19880) ) ),
    inference(variable_rename,[status(thm)],[f_4754_1]) ).

fof(f_4754_3,plain,
    ( ! [U_19887,U_19885,U_19883] :
        ( c_List_Obutlast(U_19885,hAPP(hAPP(c_List_Olist_OCons(U_19885),U_19887),U_19883)) = hAPP(hAPP(c_List_Olist_OCons(U_19885),U_19887),c_List_Obutlast(U_19885,U_19883))
        | U_19883 = c_List_Olist_ONil(U_19885) )
    & ! [U_19886,U_19884,U_19882] :
        ( c_List_Obutlast(U_19884,hAPP(hAPP(c_List_Olist_OCons(U_19884),U_19886),U_19882)) = c_List_Olist_ONil(U_19884)
        | U_19882 != c_List_Olist_ONil(U_19884) ) ),
    inference(miniscope,[status(thm)],[f_4754_2]) ).

fof(f_4754_4,plain,
    ( ! [U_19883,U_19885,U_19887] :
        ( c_List_Obutlast(U_19885,hAPP(hAPP(c_List_Olist_OCons(U_19885),U_19887),U_19883)) = hAPP(hAPP(c_List_Olist_OCons(U_19885),U_19887),c_List_Obutlast(U_19885,U_19883))
        | U_19883 = c_List_Olist_ONil(U_19885) )
    & ! [U_19884,U_19886,U_19882] :
        ( c_List_Obutlast(U_19884,hAPP(hAPP(c_List_Olist_OCons(U_19884),U_19886),U_19882)) = c_List_Olist_ONil(U_19884)
        | U_19882 != c_List_Olist_ONil(U_19884) ) ),
    inference(definitional_conversion,[status(esa)],[f_4754_3]) ).

cnf(f_4754_5,plain,
    ( c_List_Obutlast(U_19884,hAPP(hAPP(c_List_Olist_OCons(U_19884),U_19886),U_19882)) = c_List_Olist_ONil(U_19884)
    | U_19882 != c_List_Olist_ONil(U_19884) ),
    inference(clausify,[status(thm)],[f_4754_4]) ).

cnf(f_4754_6,plain,
    ( c_List_Obutlast(U_19885,hAPP(hAPP(c_List_Olist_OCons(U_19885),U_19887),U_19883)) = hAPP(hAPP(c_List_Olist_OCons(U_19885),U_19887),c_List_Obutlast(U_19885,U_19883))
    | U_19883 = c_List_Olist_ONil(U_19885) ),
    inference(clausify,[status(thm)],[f_4754_4]) ).

fof(f_4755_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__butlastD]) ).

fof(f_4755_2,plain,
    ! [U_19890,U_19889,U_19888] :
      ( hBOOL(hAPP(hAPP(c_member(U_19888),U_19889),hAPP(c_List_Oset(U_19888),U_19890)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19888),U_19889),hAPP(c_List_Oset(U_19888),c_List_Obutlast(U_19888,U_19890)))) ),
    inference(variable_rename,[status(thm)],[f_4755_1]) ).

fof(f_4755_3,plain,
    ! [U_19888,U_19889,U_19890] :
      ( hBOOL(hAPP(hAPP(c_member(U_19888),U_19889),hAPP(c_List_Oset(U_19888),U_19890)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19888),U_19889),hAPP(c_List_Oset(U_19888),c_List_Obutlast(U_19888,U_19890)))) ),
    inference(definitional_conversion,[status(esa)],[f_4755_2]) ).

cnf(f_4755_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19888),U_19889),hAPP(c_List_Oset(U_19888),U_19890)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19888),U_19889),hAPP(c_List_Oset(U_19888),c_List_Obutlast(U_19888,U_19890)))) ),
    inference(clausify,[status(thm)],[f_4755_3]) ).

fof(f_4756_1,plain,
    ! [T_a,V_xs] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__butlast]) ).

fof(f_4756_2,plain,
    ! [U_19892,U_19891] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19892),c_List_Obutlast(U_19892,U_19891)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19892),U_19891))
      | U_19891 = c_List_Olist_ONil(U_19892) ),
    inference(variable_rename,[status(thm)],[f_4756_1]) ).

fof(f_4756_3,plain,
    ! [U_19891,U_19892] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19892),c_List_Obutlast(U_19892,U_19891)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19892),U_19891))
      | U_19891 = c_List_Olist_ONil(U_19892) ),
    inference(definitional_conversion,[status(esa)],[f_4756_2]) ).

cnf(f_4756_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19892),c_List_Obutlast(U_19892,U_19891)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19892),U_19891))
    | U_19891 = c_List_Olist_ONil(U_19892) ),
    inference(clausify,[status(thm)],[f_4756_3]) ).

fof(f_4757_1,plain,
    ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I1_J]) ).

fof(f_4757_2,plain,
    ! [U_19893] : c_List_Obutlast(U_19893,c_List_Olist_ONil(U_19893)) = c_List_Olist_ONil(U_19893),
    inference(variable_rename,[status(thm)],[f_4757_1]) ).

fof(f_4757_3,plain,
    ! [U_19893] : c_List_Obutlast(U_19893,c_List_Olist_ONil(U_19893)) = c_List_Olist_ONil(U_19893),
    inference(definitional_conversion,[status(esa)],[f_4757_2]) ).

cnf(f_4757_4,plain,
    c_List_Obutlast(U_19893,c_List_Olist_ONil(U_19893)) = c_List_Olist_ONil(U_19893),
    inference(clausify,[status(thm)],[f_4757_3]) ).

fof(f_4758_1,plain,
    ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_butlast__drop]) ).

fof(f_4758_2,plain,
    ! [U_19896,U_19895,U_19894] : c_List_Obutlast(U_19894,hAPP(hAPP(c_List_Odrop(U_19894),U_19895),U_19896)) = hAPP(hAPP(c_List_Odrop(U_19894),U_19895),c_List_Obutlast(U_19894,U_19896)),
    inference(variable_rename,[status(thm)],[f_4758_1]) ).

fof(f_4758_3,plain,
    ! [U_19896,U_19895,U_19894] : c_List_Obutlast(U_19894,hAPP(hAPP(c_List_Odrop(U_19894),U_19895),U_19896)) = hAPP(hAPP(c_List_Odrop(U_19894),U_19895),c_List_Obutlast(U_19894,U_19896)),
    inference(definitional_conversion,[status(esa)],[f_4758_2]) ).

cnf(f_4758_4,plain,
    c_List_Obutlast(U_19894,hAPP(hAPP(c_List_Odrop(U_19894),U_19895),U_19896)) = hAPP(hAPP(c_List_Odrop(U_19894),U_19895),c_List_Obutlast(U_19894,U_19896)),
    inference(clausify,[status(thm)],[f_4758_3]) ).

fof(f_4759_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__butlast]) ).

fof(f_4759_2,plain,
    ! [U_19899,U_19898,U_19897] : hAPP(hAPP(c_List_Odrop(U_19897),U_19898),c_List_Obutlast(U_19897,U_19899)) = c_List_Obutlast(U_19897,hAPP(hAPP(c_List_Odrop(U_19897),U_19898),U_19899)),
    inference(variable_rename,[status(thm)],[f_4759_1]) ).

fof(f_4759_3,plain,
    ! [U_19897,U_19898,U_19899] : hAPP(hAPP(c_List_Odrop(U_19897),U_19898),c_List_Obutlast(U_19897,U_19899)) = c_List_Obutlast(U_19897,hAPP(hAPP(c_List_Odrop(U_19897),U_19898),U_19899)),
    inference(definitional_conversion,[status(esa)],[f_4759_2]) ).

cnf(f_4759_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19897),U_19898),c_List_Obutlast(U_19897,U_19899)) = c_List_Obutlast(U_19897,hAPP(hAPP(c_List_Odrop(U_19897),U_19898),U_19899)),
    inference(clausify,[status(thm)],[f_4759_3]) ).

fof(f_4760_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI]) ).

fof(f_4760_2,plain,
    ! [U_19903,U_19902,U_19901,U_19900] :
      ( hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,hAPP(hAPP(c_List_Oappend(U_19900),U_19902),U_19903)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,U_19903))))
        & ~ hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,U_19902)))) ) ),
    inference(variable_rename,[status(thm)],[f_4760_1]) ).

fof(f_4760_3,plain,
    ( ! [U_19900,U_19901,U_19902,U_19903] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,U_19903))))
        | ~ sP1208(U_19900,U_19901,U_19902,U_19903) )
    & ! [U_19900,U_19901,U_19902,U_19903] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,U_19902))))
        | ~ sP1208(U_19900,U_19901,U_19902,U_19903) )
    & ! [U_19900,U_19901,U_19902,U_19903] :
        ( hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,hAPP(hAPP(c_List_Oappend(U_19900),U_19902),U_19903)))))
        | sP1208(U_19900,U_19901,U_19902,U_19903) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1208])],[f_4760_2]) ).

cnf(f_4760_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,hAPP(hAPP(c_List_Oappend(U_19900),U_19902),U_19903)))))
    | sP1208(U_19900,U_19901,U_19902,U_19903) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

cnf(f_4760_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,U_19902))))
    | ~ sP1208(U_19900,U_19901,U_19902,U_19903) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

cnf(f_4760_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_19900),U_19901),hAPP(c_List_Oset(U_19900),c_List_Obutlast(U_19900,U_19903))))
    | ~ sP1208(U_19900,U_19901,U_19902,U_19903) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

fof(f_4761_1,plain,
    ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_butlast__snoc]) ).

fof(f_4761_2,plain,
    ! [U_19906,U_19905,U_19904] : c_List_Obutlast(U_19904,hAPP(hAPP(c_List_Oappend(U_19904),U_19905),hAPP(hAPP(c_List_Olist_OCons(U_19904),U_19906),c_List_Olist_ONil(U_19904)))) = U_19905,
    inference(variable_rename,[status(thm)],[f_4761_1]) ).

fof(f_4761_3,plain,
    ! [U_19904,U_19905,U_19906] : c_List_Obutlast(U_19904,hAPP(hAPP(c_List_Oappend(U_19904),U_19905),hAPP(hAPP(c_List_Olist_OCons(U_19904),U_19906),c_List_Olist_ONil(U_19904)))) = U_19905,
    inference(definitional_conversion,[status(esa)],[f_4761_2]) ).

cnf(f_4761_4,plain,
    c_List_Obutlast(U_19904,hAPP(hAPP(c_List_Oappend(U_19904),U_19905),hAPP(hAPP(c_List_Olist_OCons(U_19904),U_19906),c_List_Olist_ONil(U_19904)))) = U_19905,
    inference(clausify,[status(thm)],[f_4761_3]) ).

fof(f_4762_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__butlast]) ).

fof(f_4762_2,plain,
    ! [U_19909,U_19908,U_19907] :
      ( hAPP(hAPP(c_List_Otake(U_19908),U_19907),c_List_Obutlast(U_19908,U_19909)) = hAPP(hAPP(c_List_Otake(U_19908),U_19907),U_19909)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19907),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19908)),U_19909))) ),
    inference(variable_rename,[status(thm)],[f_4762_1]) ).

fof(f_4762_3,plain,
    ! [U_19907,U_19908,U_19909] :
      ( hAPP(hAPP(c_List_Otake(U_19908),U_19907),c_List_Obutlast(U_19908,U_19909)) = hAPP(hAPP(c_List_Otake(U_19908),U_19907),U_19909)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19907),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19908)),U_19909))) ),
    inference(definitional_conversion,[status(esa)],[f_4762_2]) ).

cnf(f_4762_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19908),U_19907),c_List_Obutlast(U_19908,U_19909)) = hAPP(hAPP(c_List_Otake(U_19908),U_19907),U_19909)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19907),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19908)),U_19909))) ),
    inference(clausify,[status(thm)],[f_4762_3]) ).

fof(f_4763_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__butlast]) ).

fof(f_4763_2,plain,
    ! [U_19911,U_19910] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19910)),c_List_Obutlast(U_19910,U_19911)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19910)),U_19911)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4763_1]) ).

fof(f_4763_3,plain,
    ! [U_19910,U_19911] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19910)),c_List_Obutlast(U_19910,U_19911)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19910)),U_19911)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4763_2]) ).

cnf(f_4763_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19910)),c_List_Obutlast(U_19910,U_19911)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19910)),U_19911)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4763_3]) ).

fof(f_4764_1,plain,
    ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs),
    inference(fof_nnf,[status(thm)],[fact_butlast__conv__take]) ).

fof(f_4764_2,plain,
    ! [U_19913,U_19912] : c_List_Obutlast(U_19912,U_19913) = hAPP(hAPP(c_List_Otake(U_19912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19912)),U_19913)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19913),
    inference(variable_rename,[status(thm)],[f_4764_1]) ).

fof(f_4764_3,plain,
    ! [U_19912,U_19913] : c_List_Obutlast(U_19912,U_19913) = hAPP(hAPP(c_List_Otake(U_19912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19912)),U_19913)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19913),
    inference(definitional_conversion,[status(esa)],[f_4764_2]) ).

cnf(f_4764_4,plain,
    c_List_Obutlast(U_19912,U_19913) = hAPP(hAPP(c_List_Otake(U_19912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19912)),U_19913)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19913),
    inference(clausify,[status(thm)],[f_4764_3]) ).

fof(f_4765_1,plain,
    ! [V_x,V_xs,T_a,V_k] :
      ( ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x)
        | V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs)
        | V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_butlast__list__update]) ).

fof(f_4765_2,plain,
    ! [U_19917,U_19916,U_19915,U_19914] :
      ( ( c_List_Obutlast(U_19915,hAPP(hAPP(c_List_Olist__update(U_19915,U_19916),U_19914),U_19917)) = hAPP(hAPP(c_List_Olist__update(U_19915,c_List_Obutlast(U_19915,U_19916)),U_19914),U_19917)
        | U_19914 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19915)),U_19916)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(U_19915,hAPP(hAPP(c_List_Olist__update(U_19915,U_19916),U_19914),U_19917)) = c_List_Obutlast(U_19915,U_19916)
        | U_19914 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19915)),U_19916)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_4765_1]) ).

fof(f_4765_3,plain,
    ( ! [U_19925,U_19923,U_19921,U_19919] :
        ( c_List_Obutlast(U_19921,hAPP(hAPP(c_List_Olist__update(U_19921,U_19923),U_19919),U_19925)) = hAPP(hAPP(c_List_Olist__update(U_19921,c_List_Obutlast(U_19921,U_19923)),U_19919),U_19925)
        | U_19919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),U_19923)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_19924,U_19922,U_19920,U_19918] :
        ( c_List_Obutlast(U_19920,hAPP(hAPP(c_List_Olist__update(U_19920,U_19922),U_19918),U_19924)) = c_List_Obutlast(U_19920,U_19922)
        | U_19918 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19920)),U_19922)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_4765_2]) ).

fof(f_4765_4,plain,
    ( ! [U_19919,U_19921,U_19923,U_19925] :
        ( c_List_Obutlast(U_19921,hAPP(hAPP(c_List_Olist__update(U_19921,U_19923),U_19919),U_19925)) = hAPP(hAPP(c_List_Olist__update(U_19921,c_List_Obutlast(U_19921,U_19923)),U_19919),U_19925)
        | U_19919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),U_19923)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_19920,U_19924,U_19918,U_19922] :
        ( c_List_Obutlast(U_19920,hAPP(hAPP(c_List_Olist__update(U_19920,U_19922),U_19918),U_19924)) = c_List_Obutlast(U_19920,U_19922)
        | U_19918 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19920)),U_19922)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4765_3]) ).

cnf(f_4765_5,plain,
    ( c_List_Obutlast(U_19920,hAPP(hAPP(c_List_Olist__update(U_19920,U_19922),U_19918),U_19924)) = c_List_Obutlast(U_19920,U_19922)
    | U_19918 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19920)),U_19922)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4765_4]) ).

cnf(f_4765_6,plain,
    ( c_List_Obutlast(U_19921,hAPP(hAPP(c_List_Olist__update(U_19921,U_19923),U_19919),U_19925)) = hAPP(hAPP(c_List_Olist__update(U_19921,c_List_Obutlast(U_19921,U_19923)),U_19919),U_19925)
    | U_19919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),U_19923)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4765_4]) ).

fof(f_4766_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id]) ).

fof(f_4766_2,plain,
    ! [U_19927,U_19926] :
      ( hAPP(hAPP(c_List_Oappend(U_19927),c_List_Obutlast(U_19927,U_19926)),hAPP(hAPP(c_List_Olist_OCons(U_19927),c_List_Olast(U_19927,U_19926)),c_List_Olist_ONil(U_19927))) = U_19926
      | U_19926 = c_List_Olist_ONil(U_19927) ),
    inference(variable_rename,[status(thm)],[f_4766_1]) ).

fof(f_4766_3,plain,
    ! [U_19926,U_19927] :
      ( hAPP(hAPP(c_List_Oappend(U_19927),c_List_Obutlast(U_19927,U_19926)),hAPP(hAPP(c_List_Olist_OCons(U_19927),c_List_Olast(U_19927,U_19926)),c_List_Olist_ONil(U_19927))) = U_19926
      | U_19926 = c_List_Olist_ONil(U_19927) ),
    inference(definitional_conversion,[status(esa)],[f_4766_2]) ).

cnf(f_4766_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19927),c_List_Obutlast(U_19927,U_19926)),hAPP(hAPP(c_List_Olist_OCons(U_19927),c_List_Olast(U_19927,U_19926)),c_List_Olist_ONil(U_19927))) = U_19926
    | U_19926 = c_List_Olist_ONil(U_19927) ),
    inference(clausify,[status(thm)],[f_4766_3]) ).

fof(f_4767_1,plain,
    ! [V_ys_2,V_x_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
        | c_List_Olast(T_b,V_ys_2) != V_x_2
        | c_List_Obutlast(T_b,V_ys_2) != V_xs_2
        | V_ys_2 = c_List_Olist_ONil(T_b) )
      & ( ( c_List_Olast(T_b,V_ys_2) = V_x_2
          & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
          & V_ys_2 != c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast]) ).

fof(f_4767_2,plain,
    ! [U_19931,U_19930,U_19929,U_19928] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19928),U_19929),hAPP(hAPP(c_List_Olist_OCons(U_19928),U_19930),c_List_Olist_ONil(U_19928))) = U_19931
        | c_List_Olast(U_19928,U_19931) != U_19930
        | c_List_Obutlast(U_19928,U_19931) != U_19929
        | U_19931 = c_List_Olist_ONil(U_19928) )
      & ( ( c_List_Olast(U_19928,U_19931) = U_19930
          & c_List_Obutlast(U_19928,U_19931) = U_19929
          & U_19931 != c_List_Olist_ONil(U_19928) )
        | hAPP(hAPP(c_List_Oappend(U_19928),U_19929),hAPP(hAPP(c_List_Olist_OCons(U_19928),U_19930),c_List_Olist_ONil(U_19928))) != U_19931 ) ),
    inference(variable_rename,[status(thm)],[f_4767_1]) ).

fof(f_4767_3,plain,
    ( ! [U_19939,U_19937,U_19935,U_19933] :
        ( hAPP(hAPP(c_List_Oappend(U_19933),U_19935),hAPP(hAPP(c_List_Olist_OCons(U_19933),U_19937),c_List_Olist_ONil(U_19933))) = U_19939
        | c_List_Olast(U_19933,U_19939) != U_19937
        | c_List_Obutlast(U_19933,U_19939) != U_19935
        | U_19939 = c_List_Olist_ONil(U_19933) )
    & ! [U_19938,U_19936,U_19934,U_19932] :
        ( ( c_List_Olast(U_19932,U_19938) = U_19936
          & c_List_Obutlast(U_19932,U_19938) = U_19934
          & U_19938 != c_List_Olist_ONil(U_19932) )
        | hAPP(hAPP(c_List_Oappend(U_19932),U_19934),hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19936),c_List_Olist_ONil(U_19932))) != U_19938 ) ),
    inference(miniscope,[status(thm)],[f_4767_2]) ).

fof(f_4767_4,plain,
    ( ! [U_19938,U_19934,U_19932,U_19936] :
        ( c_List_Olast(U_19932,U_19938) = U_19936
        | ~ sP1209(U_19938,U_19934,U_19932,U_19936) )
    & ! [U_19938,U_19934,U_19932,U_19936] :
        ( c_List_Obutlast(U_19932,U_19938) = U_19934
        | ~ sP1209(U_19938,U_19934,U_19932,U_19936) )
    & ! [U_19938,U_19934,U_19932,U_19936] :
        ( U_19938 != c_List_Olist_ONil(U_19932)
        | ~ sP1209(U_19938,U_19934,U_19932,U_19936) )
    & ! [U_19935,U_19933,U_19937,U_19939] :
        ( hAPP(hAPP(c_List_Oappend(U_19933),U_19935),hAPP(hAPP(c_List_Olist_OCons(U_19933),U_19937),c_List_Olist_ONil(U_19933))) = U_19939
        | c_List_Olast(U_19933,U_19939) != U_19937
        | c_List_Obutlast(U_19933,U_19939) != U_19935
        | U_19939 = c_List_Olist_ONil(U_19933) )
    & ! [U_19938,U_19934,U_19932,U_19936] :
        ( sP1209(U_19938,U_19934,U_19932,U_19936)
        | hAPP(hAPP(c_List_Oappend(U_19932),U_19934),hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19936),c_List_Olist_ONil(U_19932))) != U_19938 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1209])],[f_4767_3]) ).

cnf(f_4767_5,plain,
    ( sP1209(U_19938,U_19934,U_19932,U_19936)
    | hAPP(hAPP(c_List_Oappend(U_19932),U_19934),hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19936),c_List_Olist_ONil(U_19932))) != U_19938 ),
    inference(clausify,[status(thm)],[f_4767_4]) ).

cnf(f_4767_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19933),U_19935),hAPP(hAPP(c_List_Olist_OCons(U_19933),U_19937),c_List_Olist_ONil(U_19933))) = U_19939
    | c_List_Olast(U_19933,U_19939) != U_19937
    | c_List_Obutlast(U_19933,U_19939) != U_19935
    | U_19939 = c_List_Olist_ONil(U_19933) ),
    inference(clausify,[status(thm)],[f_4767_4]) ).

cnf(f_4767_7,plain,
    ( U_19938 != c_List_Olist_ONil(U_19932)
    | ~ sP1209(U_19938,U_19934,U_19932,U_19936) ),
    inference(clausify,[status(thm)],[f_4767_4]) ).

cnf(f_4767_8,plain,
    ( c_List_Obutlast(U_19932,U_19938) = U_19934
    | ~ sP1209(U_19938,U_19934,U_19932,U_19936) ),
    inference(clausify,[status(thm)],[f_4767_4]) ).

cnf(f_4767_9,plain,
    ( c_List_Olast(U_19932,U_19938) = U_19936
    | ~ sP1209(U_19938,U_19934,U_19932,U_19936) ),
    inference(clausify,[status(thm)],[f_4767_4]) ).

fof(f_4768_1,plain,
    ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__max]) ).

fof(f_4768_2,plain,
    ! [U_19943,U_19942,U_19941,U_19940] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19940)),U_19941))),c_List_Ofoldr(tc_List_Olist(U_19942),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19942))),U_19943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19940)),U_19941)),c_List_Ofoldr(tc_List_Olist(U_19942),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19942),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19942)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19942),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19942)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19942),tc_List_Olist(U_19942),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19942)))),U_19943),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[f_4768_1]) ).

fof(f_4768_3,plain,
    ! [U_19940,U_19941,U_19942,U_19943] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19940)),U_19941))),c_List_Ofoldr(tc_List_Olist(U_19942),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19942))),U_19943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19940)),U_19941)),c_List_Ofoldr(tc_List_Olist(U_19942),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19942),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19942)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19942),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19942)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19942),tc_List_Olist(U_19942),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19942)))),U_19943),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_4768_2]) ).

cnf(f_4768_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19940)),U_19941))),c_List_Ofoldr(tc_List_Olist(U_19942),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19942))),U_19943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19940)),U_19941)),c_List_Ofoldr(tc_List_Olist(U_19942),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19942),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19942)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19942)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19942),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19942)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19942),tc_List_Olist(U_19942),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19942)))),U_19943),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_4768_3]) ).

fof(f_4769_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2)
      | c_List_Opartition(T_b,V_P_2,V_xs_2) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) ),
    inference(fof_nnf,[status(thm)],[fact_partition__set]) ).

fof(f_4769_2,plain,
    ! [U_19948,U_19947,U_19946,U_19945,U_19944] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19944,tc_HOL_Obool)),hAPP(c_List_Oset(U_19944),U_19947)),hAPP(c_List_Oset(U_19944),U_19948)) = hAPP(c_List_Oset(U_19944),U_19946)
      | c_List_Opartition(U_19944,U_19945,U_19946) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19944),tc_List_Olist(U_19944)),U_19947),U_19948) ),
    inference(variable_rename,[status(thm)],[f_4769_1]) ).

fof(f_4769_3,plain,
    ! [U_19944,U_19945,U_19946,U_19947,U_19948] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19944,tc_HOL_Obool)),hAPP(c_List_Oset(U_19944),U_19947)),hAPP(c_List_Oset(U_19944),U_19948)) = hAPP(c_List_Oset(U_19944),U_19946)
      | c_List_Opartition(U_19944,U_19945,U_19946) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19944),tc_List_Olist(U_19944)),U_19947),U_19948) ),
    inference(definitional_conversion,[status(esa)],[f_4769_2]) ).

cnf(f_4769_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19944,tc_HOL_Obool)),hAPP(c_List_Oset(U_19944),U_19947)),hAPP(c_List_Oset(U_19944),U_19948)) = hAPP(c_List_Oset(U_19944),U_19946)
    | c_List_Opartition(U_19944,U_19945,U_19946) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19944),tc_List_Olist(U_19944)),U_19947),U_19948) ),
    inference(clausify,[status(thm)],[f_4769_3]) ).

fof(f_4770_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__filter__le]) ).

fof(f_4770_2,plain,
    ! [U_19951,U_19950,U_19949] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19949)),hAPP(c_List_Ofilter(U_19949,U_19950),U_19951))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19949)),U_19951))),
    inference(variable_rename,[status(thm)],[f_4770_1]) ).

fof(f_4770_3,plain,
    ! [U_19949,U_19950,U_19951] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19949)),hAPP(c_List_Ofilter(U_19949,U_19950),U_19951))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19949)),U_19951))),
    inference(definitional_conversion,[status(esa)],[f_4770_2]) ).

cnf(f_4770_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19949)),hAPP(c_List_Ofilter(U_19949,U_19950),U_19951))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19949)),U_19951))),
    inference(clausify,[status(thm)],[f_4770_3]) ).

fof(f_4771_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_filter__is__subset]) ).

fof(f_4771_2,plain,
    ! [U_19954,U_19953,U_19952] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19952,tc_HOL_Obool)),hAPP(c_List_Oset(U_19952),hAPP(c_List_Ofilter(U_19952,U_19953),U_19954))),hAPP(c_List_Oset(U_19952),U_19954))),
    inference(variable_rename,[status(thm)],[f_4771_1]) ).

fof(f_4771_3,plain,
    ! [U_19952,U_19953,U_19954] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19952,tc_HOL_Obool)),hAPP(c_List_Oset(U_19952),hAPP(c_List_Ofilter(U_19952,U_19953),U_19954))),hAPP(c_List_Oset(U_19952),U_19954))),
    inference(definitional_conversion,[status(esa)],[f_4771_2]) ).

cnf(f_4771_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19952,tc_HOL_Obool)),hAPP(c_List_Oset(U_19952),hAPP(c_List_Ofilter(U_19952,U_19953),U_19954))),hAPP(c_List_Oset(U_19952),U_19954))),
    inference(clausify,[status(thm)],[f_4771_3]) ).

fof(f_4772_1,plain,
    ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(f_4772_2,plain,
    ! [U_19956,U_19955] : hAPP(c_List_Ofilter(U_19955,U_19956),c_List_Olist_ONil(U_19955)) = c_List_Olist_ONil(U_19955),
    inference(variable_rename,[status(thm)],[f_4772_1]) ).

fof(f_4772_3,plain,
    ! [U_19955,U_19956] : hAPP(c_List_Ofilter(U_19955,U_19956),c_List_Olist_ONil(U_19955)) = c_List_Olist_ONil(U_19955),
    inference(definitional_conversion,[status(esa)],[f_4772_2]) ).

cnf(f_4772_4,plain,
    hAPP(c_List_Ofilter(U_19955,U_19956),c_List_Olist_ONil(U_19955)) = c_List_Olist_ONil(U_19955),
    inference(clausify,[status(thm)],[f_4772_3]) ).

fof(f_4773_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__empty__conv]) ).

fof(f_4773_2,plain,
    ! [U_19961,U_19960,U_19959] :
      ( ( hAPP(c_List_Ofilter(U_19959,U_19960),U_19961) = c_List_Olist_ONil(U_19959)
        | ? [U_19958] :
            ( hBOOL(hAPP(U_19960,U_19958))
            & hBOOL(hAPP(hAPP(c_member(U_19959),U_19958),hAPP(c_List_Oset(U_19959),U_19961))) ) )
      & ( ! [U_19957] :
            ( ~ hBOOL(hAPP(U_19960,U_19957))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19959),U_19957),hAPP(c_List_Oset(U_19959),U_19961))) )
        | hAPP(c_List_Ofilter(U_19959,U_19960),U_19961) != c_List_Olist_ONil(U_19959) ) ),
    inference(variable_rename,[status(thm)],[f_4773_1]) ).

fof(f_4773_3,plain,
    ( ! [U_19967,U_19965,U_19963] :
        ( hAPP(c_List_Ofilter(U_19963,U_19965),U_19967) = c_List_Olist_ONil(U_19963)
        | ? [U_19958] :
            ( hBOOL(hAPP(U_19965,U_19958))
            & hBOOL(hAPP(hAPP(c_member(U_19963),U_19958),hAPP(c_List_Oset(U_19963),U_19967))) ) )
    & ! [U_19966,U_19964,U_19962] :
        ( ! [U_19957] :
            ( ~ hBOOL(hAPP(U_19964,U_19957))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19962),U_19957),hAPP(c_List_Oset(U_19962),U_19966))) )
        | hAPP(c_List_Ofilter(U_19962,U_19964),U_19966) != c_List_Olist_ONil(U_19962) ) ),
    inference(miniscope,[status(thm)],[f_4773_2]) ).

fof(f_4773_4,plain,
    ( ! [U_19967,U_19965,U_19963] :
        ( hAPP(c_List_Ofilter(U_19963,U_19965),U_19967) = c_List_Olist_ONil(U_19963)
        | ( hBOOL(hAPP(U_19965,sK494(U_19967,U_19965,U_19963)))
          & hBOOL(hAPP(hAPP(c_member(U_19963),sK494(U_19967,U_19965,U_19963)),hAPP(c_List_Oset(U_19963),U_19967))) ) )
    & ! [U_19966,U_19964,U_19962] :
        ( ! [U_19957] :
            ( ~ hBOOL(hAPP(U_19964,U_19957))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19962),U_19957),hAPP(c_List_Oset(U_19962),U_19966))) )
        | hAPP(c_List_Ofilter(U_19962,U_19964),U_19966) != c_List_Olist_ONil(U_19962) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_19958,sK494(U_19967,U_19965,U_19963))],[f_4773_3]) ).

fof(f_4773_5,plain,
    ( ! [U_19967,U_19965,U_19963] :
        ( hBOOL(hAPP(U_19965,sK494(U_19967,U_19965,U_19963)))
        | ~ sP1210(U_19967,U_19965,U_19963) )
    & ! [U_19967,U_19965,U_19963] :
        ( hBOOL(hAPP(hAPP(c_member(U_19963),sK494(U_19967,U_19965,U_19963)),hAPP(c_List_Oset(U_19963),U_19967)))
        | ~ sP1210(U_19967,U_19965,U_19963) )
    & ! [U_19967,U_19965,U_19963] :
        ( hAPP(c_List_Ofilter(U_19963,U_19965),U_19967) = c_List_Olist_ONil(U_19963)
        | sP1210(U_19967,U_19965,U_19963) )
    & ! [U_19964,U_19957,U_19962,U_19966] :
        ( ~ hBOOL(hAPP(U_19964,U_19957))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19962),U_19957),hAPP(c_List_Oset(U_19962),U_19966)))
        | hAPP(c_List_Ofilter(U_19962,U_19964),U_19966) != c_List_Olist_ONil(U_19962) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1210])],[f_4773_4]) ).

cnf(f_4773_6,plain,
    ( ~ hBOOL(hAPP(U_19964,U_19957))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19962),U_19957),hAPP(c_List_Oset(U_19962),U_19966)))
    | hAPP(c_List_Ofilter(U_19962,U_19964),U_19966) != c_List_Olist_ONil(U_19962) ),
    inference(clausify,[status(thm)],[f_4773_5]) ).

cnf(f_4773_7,plain,
    ( hAPP(c_List_Ofilter(U_19963,U_19965),U_19967) = c_List_Olist_ONil(U_19963)
    | sP1210(U_19967,U_19965,U_19963) ),
    inference(clausify,[status(thm)],[f_4773_5]) ).

cnf(f_4773_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19963),sK494(U_19967,U_19965,U_19963)),hAPP(c_List_Oset(U_19963),U_19967)))
    | ~ sP1210(U_19967,U_19965,U_19963) ),
    inference(clausify,[status(thm)],[f_4773_5]) ).

cnf(f_4773_9,plain,
    ( hBOOL(hAPP(U_19965,sK494(U_19967,U_19965,U_19963)))
    | ~ sP1210(U_19967,U_19965,U_19963) ),
    inference(clausify,[status(thm)],[f_4773_5]) ).

fof(f_4774_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__id__conv]) ).

fof(f_4774_2,plain,
    ! [U_19972,U_19971,U_19970] :
      ( ( hAPP(c_List_Ofilter(U_19970,U_19971),U_19972) = U_19972
        | ? [U_19969] :
            ( ~ hBOOL(hAPP(U_19971,U_19969))
            & hBOOL(hAPP(hAPP(c_member(U_19970),U_19969),hAPP(c_List_Oset(U_19970),U_19972))) ) )
      & ( ! [U_19968] :
            ( hBOOL(hAPP(U_19971,U_19968))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19970),U_19968),hAPP(c_List_Oset(U_19970),U_19972))) )
        | hAPP(c_List_Ofilter(U_19970,U_19971),U_19972) != U_19972 ) ),
    inference(variable_rename,[status(thm)],[f_4774_1]) ).

fof(f_4774_3,plain,
    ( ! [U_19978,U_19976,U_19974] :
        ( hAPP(c_List_Ofilter(U_19974,U_19976),U_19978) = U_19978
        | ? [U_19969] :
            ( ~ hBOOL(hAPP(U_19976,U_19969))
            & hBOOL(hAPP(hAPP(c_member(U_19974),U_19969),hAPP(c_List_Oset(U_19974),U_19978))) ) )
    & ! [U_19977,U_19975,U_19973] :
        ( ! [U_19968] :
            ( hBOOL(hAPP(U_19975,U_19968))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19973),U_19968),hAPP(c_List_Oset(U_19973),U_19977))) )
        | hAPP(c_List_Ofilter(U_19973,U_19975),U_19977) != U_19977 ) ),
    inference(miniscope,[status(thm)],[f_4774_2]) ).

fof(f_4774_4,plain,
    ( ! [U_19978,U_19976,U_19974] :
        ( hAPP(c_List_Ofilter(U_19974,U_19976),U_19978) = U_19978
        | ( ~ hBOOL(hAPP(U_19976,sK495(U_19978,U_19976,U_19974)))
          & hBOOL(hAPP(hAPP(c_member(U_19974),sK495(U_19978,U_19976,U_19974)),hAPP(c_List_Oset(U_19974),U_19978))) ) )
    & ! [U_19977,U_19975,U_19973] :
        ( ! [U_19968] :
            ( hBOOL(hAPP(U_19975,U_19968))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19973),U_19968),hAPP(c_List_Oset(U_19973),U_19977))) )
        | hAPP(c_List_Ofilter(U_19973,U_19975),U_19977) != U_19977 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_19969,sK495(U_19978,U_19976,U_19974))],[f_4774_3]) ).

fof(f_4774_5,plain,
    ( ! [U_19976,U_19978,U_19974] :
        ( ~ hBOOL(hAPP(U_19976,sK495(U_19978,U_19976,U_19974)))
        | ~ sP1211(U_19976,U_19978,U_19974) )
    & ! [U_19976,U_19978,U_19974] :
        ( hBOOL(hAPP(hAPP(c_member(U_19974),sK495(U_19978,U_19976,U_19974)),hAPP(c_List_Oset(U_19974),U_19978)))
        | ~ sP1211(U_19976,U_19978,U_19974) )
    & ! [U_19976,U_19978,U_19974] :
        ( hAPP(c_List_Ofilter(U_19974,U_19976),U_19978) = U_19978
        | sP1211(U_19976,U_19978,U_19974) )
    & ! [U_19968,U_19977,U_19973,U_19975] :
        ( hBOOL(hAPP(U_19975,U_19968))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19973),U_19968),hAPP(c_List_Oset(U_19973),U_19977)))
        | hAPP(c_List_Ofilter(U_19973,U_19975),U_19977) != U_19977 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1211])],[f_4774_4]) ).

cnf(f_4774_6,plain,
    ( hBOOL(hAPP(U_19975,U_19968))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19973),U_19968),hAPP(c_List_Oset(U_19973),U_19977)))
    | hAPP(c_List_Ofilter(U_19973,U_19975),U_19977) != U_19977 ),
    inference(clausify,[status(thm)],[f_4774_5]) ).

cnf(f_4774_7,plain,
    ( hAPP(c_List_Ofilter(U_19974,U_19976),U_19978) = U_19978
    | sP1211(U_19976,U_19978,U_19974) ),
    inference(clausify,[status(thm)],[f_4774_5]) ).

cnf(f_4774_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19974),sK495(U_19978,U_19976,U_19974)),hAPP(c_List_Oset(U_19974),U_19978)))
    | ~ sP1211(U_19976,U_19978,U_19974) ),
    inference(clausify,[status(thm)],[f_4774_5]) ).

cnf(f_4774_9,plain,
    ( ~ hBOOL(hAPP(U_19976,sK495(U_19978,U_19976,U_19974)))
    | ~ sP1211(U_19976,U_19978,U_19974) ),
    inference(clausify,[status(thm)],[f_4774_5]) ).

fof(f_4775_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort__triv]) ).

fof(f_4775_2,plain,
    ! [U_19984,U_19983,U_19982,U_19981,U_19980,U_19979] :
      ( hAPP(c_List_Ofilter(U_19982,U_19980),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19982,U_19979,U_19983),U_19981),U_19984)) = hAPP(c_List_Ofilter(U_19982,U_19980),U_19984)
      | hBOOL(hAPP(U_19980,U_19981))
      | ~ class_Orderings_Olinorder(U_19979) ),
    inference(variable_rename,[status(thm)],[f_4775_1]) ).

fof(f_4775_3,plain,
    ! [U_19981,U_19979,U_19980,U_19982,U_19983,U_19984] :
      ( hAPP(c_List_Ofilter(U_19982,U_19980),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19982,U_19979,U_19983),U_19981),U_19984)) = hAPP(c_List_Ofilter(U_19982,U_19980),U_19984)
      | hBOOL(hAPP(U_19980,U_19981))
      | ~ class_Orderings_Olinorder(U_19979) ),
    inference(definitional_conversion,[status(esa)],[f_4775_2]) ).

cnf(f_4775_4,plain,
    ( hAPP(c_List_Ofilter(U_19982,U_19980),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19982,U_19979,U_19983),U_19981),U_19984)) = hAPP(c_List_Ofilter(U_19982,U_19980),U_19984)
    | hBOOL(hAPP(U_19980,U_19981))
    | ~ class_Orderings_Olinorder(U_19979) ),
    inference(clausify,[status(thm)],[f_4775_3]) ).

fof(f_4776_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__filter]) ).

fof(f_4776_2,plain,
    ! [U_19987,U_19986,U_19985] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19985),hAPP(c_List_Ofilter(U_19985,U_19987),U_19986)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19985),U_19986)) ),
    inference(variable_rename,[status(thm)],[f_4776_1]) ).

fof(f_4776_3,plain,
    ! [U_19985,U_19986,U_19987] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19985),hAPP(c_List_Ofilter(U_19985,U_19987),U_19986)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19985),U_19986)) ),
    inference(definitional_conversion,[status(esa)],[f_4776_2]) ).

cnf(f_4776_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19985),hAPP(c_List_Ofilter(U_19985,U_19987),U_19986)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19985),U_19986)) ),
    inference(clausify,[status(thm)],[f_4776_3]) ).

fof(f_4777_1,plain,
    ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__remove1]) ).

fof(f_4777_2,plain,
    ! [U_19991,U_19990,U_19989,U_19988] : hAPP(c_List_Ofilter(U_19988,U_19989),c_List_Oremove1(U_19988,U_19990,U_19991)) = c_List_Oremove1(U_19988,U_19990,hAPP(c_List_Ofilter(U_19988,U_19989),U_19991)),
    inference(variable_rename,[status(thm)],[f_4777_1]) ).

fof(f_4777_3,plain,
    ! [U_19988,U_19989,U_19990,U_19991] : hAPP(c_List_Ofilter(U_19988,U_19989),c_List_Oremove1(U_19988,U_19990,U_19991)) = c_List_Oremove1(U_19988,U_19990,hAPP(c_List_Ofilter(U_19988,U_19989),U_19991)),
    inference(definitional_conversion,[status(esa)],[f_4777_2]) ).

cnf(f_4777_4,plain,
    hAPP(c_List_Ofilter(U_19988,U_19989),c_List_Oremove1(U_19988,U_19990,U_19991)) = c_List_Oremove1(U_19988,U_19990,hAPP(c_List_Ofilter(U_19988,U_19989),U_19991)),
    inference(clausify,[status(thm)],[f_4777_3]) ).

fof(f_4778_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__filter__not]) ).

fof(f_4778_2,plain,
    ! [U_19995,U_19994,U_19993,U_19992] :
      ( c_List_Oremove1(U_19994,U_19993,hAPP(c_List_Ofilter(U_19994,U_19992),U_19995)) = hAPP(c_List_Ofilter(U_19994,U_19992),U_19995)
      | hBOOL(hAPP(U_19992,U_19993)) ),
    inference(variable_rename,[status(thm)],[f_4778_1]) ).

fof(f_4778_3,plain,
    ! [U_19992,U_19993,U_19994,U_19995] :
      ( c_List_Oremove1(U_19994,U_19993,hAPP(c_List_Ofilter(U_19994,U_19992),U_19995)) = hAPP(c_List_Ofilter(U_19994,U_19992),U_19995)
      | hBOOL(hAPP(U_19992,U_19993)) ),
    inference(definitional_conversion,[status(esa)],[f_4778_2]) ).

cnf(f_4778_4,plain,
    ( c_List_Oremove1(U_19994,U_19993,hAPP(c_List_Ofilter(U_19994,U_19992),U_19995)) = hAPP(c_List_Ofilter(U_19994,U_19992),U_19995)
    | hBOOL(hAPP(U_19992,U_19993)) ),
    inference(clausify,[status(thm)],[f_4778_3]) ).

fof(f_4779_1,plain,
    ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_filter__filter]) ).

fof(f_4779_2,plain,
    ! [U_19999,U_19998,U_19997,U_19996] : hAPP(c_List_Ofilter(U_19996,U_19997),hAPP(c_List_Ofilter(U_19996,U_19998),U_19999)) = hAPP(c_List_Ofilter(U_19996,hAPP(hAPP(c_COMBS(U_19996,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19996),c_fconj),U_19998)),U_19997)),U_19999),
    inference(variable_rename,[status(thm)],[f_4779_1]) ).

fof(f_4779_3,plain,
    ! [U_19996,U_19997,U_19998,U_19999] : hAPP(c_List_Ofilter(U_19996,U_19997),hAPP(c_List_Ofilter(U_19996,U_19998),U_19999)) = hAPP(c_List_Ofilter(U_19996,hAPP(hAPP(c_COMBS(U_19996,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19996),c_fconj),U_19998)),U_19997)),U_19999),
    inference(definitional_conversion,[status(esa)],[f_4779_2]) ).

cnf(f_4779_4,plain,
    hAPP(c_List_Ofilter(U_19996,U_19997),hAPP(c_List_Ofilter(U_19996,U_19998),U_19999)) = hAPP(c_List_Ofilter(U_19996,hAPP(hAPP(c_COMBS(U_19996,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19996),c_fconj),U_19998)),U_19997)),U_19999),
    inference(clausify,[status(thm)],[f_4779_3]) ).

fof(f_4780_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter1]) ).

fof(f_4780_2,plain,
    ! [U_20002,U_20001,U_20000] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_20000),tc_List_Olist(U_20000)),c_List_Opartition(U_20000,U_20001,U_20002)) = hAPP(c_List_Ofilter(U_20000,U_20001),U_20002),
    inference(variable_rename,[status(thm)],[f_4780_1]) ).

fof(f_4780_3,plain,
    ! [U_20000,U_20001,U_20002] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_20000),tc_List_Olist(U_20000)),c_List_Opartition(U_20000,U_20001,U_20002)) = hAPP(c_List_Ofilter(U_20000,U_20001),U_20002),
    inference(definitional_conversion,[status(esa)],[f_4780_2]) ).

cnf(f_4780_4,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(U_20000),tc_List_Olist(U_20000)),c_List_Opartition(U_20000,U_20001,U_20002)) = hAPP(c_List_Ofilter(U_20000,U_20001),U_20002),
    inference(clausify,[status(thm)],[f_4780_3]) ).

fof(f_4781_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(f_4781_2,plain,
    ! [U_20005,U_20004,U_20003] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),hAPP(c_List_Ofilter(U_20003,U_20004),U_20005))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),hAPP(c_List_Ofilter(U_20003,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20003),c_fNot),U_20004)),U_20005))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),U_20005),
    inference(variable_rename,[status(thm)],[f_4781_1]) ).

fof(f_4781_3,plain,
    ! [U_20003,U_20004,U_20005] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),hAPP(c_List_Ofilter(U_20003,U_20004),U_20005))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),hAPP(c_List_Ofilter(U_20003,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20003),c_fNot),U_20004)),U_20005))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),U_20005),
    inference(definitional_conversion,[status(esa)],[f_4781_2]) ).

cnf(f_4781_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),hAPP(c_List_Ofilter(U_20003,U_20004),U_20005))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),hAPP(c_List_Ofilter(U_20003,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20003),c_fNot),U_20004)),U_20005))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20003)),U_20005),
    inference(clausify,[status(thm)],[f_4781_3]) ).

fof(f_4782_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(f_4782_2,plain,
    ! [U_20009,U_20008,U_20007,U_20006] :
      ( ( hAPP(c_List_Ofilter(U_20008,U_20006),hAPP(hAPP(c_List_Olist_OCons(U_20008),U_20007),U_20009)) = hAPP(c_List_Ofilter(U_20008,U_20006),U_20009)
        | hBOOL(hAPP(U_20006,U_20007)) )
      & ( hAPP(c_List_Ofilter(U_20008,U_20006),hAPP(hAPP(c_List_Olist_OCons(U_20008),U_20007),U_20009)) = hAPP(hAPP(c_List_Olist_OCons(U_20008),U_20007),hAPP(c_List_Ofilter(U_20008,U_20006),U_20009))
        | ~ hBOOL(hAPP(U_20006,U_20007)) ) ),
    inference(variable_rename,[status(thm)],[f_4782_1]) ).

fof(f_4782_3,plain,
    ( ! [U_20017,U_20015,U_20013,U_20011] :
        ( hAPP(c_List_Ofilter(U_20015,U_20011),hAPP(hAPP(c_List_Olist_OCons(U_20015),U_20013),U_20017)) = hAPP(c_List_Ofilter(U_20015,U_20011),U_20017)
        | hBOOL(hAPP(U_20011,U_20013)) )
    & ! [U_20016,U_20014,U_20012,U_20010] :
        ( hAPP(c_List_Ofilter(U_20014,U_20010),hAPP(hAPP(c_List_Olist_OCons(U_20014),U_20012),U_20016)) = hAPP(hAPP(c_List_Olist_OCons(U_20014),U_20012),hAPP(c_List_Ofilter(U_20014,U_20010),U_20016))
        | ~ hBOOL(hAPP(U_20010,U_20012)) ) ),
    inference(miniscope,[status(thm)],[f_4782_2]) ).

fof(f_4782_4,plain,
    ( ! [U_20011,U_20013,U_20015,U_20017] :
        ( hAPP(c_List_Ofilter(U_20015,U_20011),hAPP(hAPP(c_List_Olist_OCons(U_20015),U_20013),U_20017)) = hAPP(c_List_Ofilter(U_20015,U_20011),U_20017)
        | hBOOL(hAPP(U_20011,U_20013)) )
    & ! [U_20014,U_20012,U_20010,U_20016] :
        ( hAPP(c_List_Ofilter(U_20014,U_20010),hAPP(hAPP(c_List_Olist_OCons(U_20014),U_20012),U_20016)) = hAPP(hAPP(c_List_Olist_OCons(U_20014),U_20012),hAPP(c_List_Ofilter(U_20014,U_20010),U_20016))
        | ~ hBOOL(hAPP(U_20010,U_20012)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4782_3]) ).

cnf(f_4782_5,plain,
    ( hAPP(c_List_Ofilter(U_20014,U_20010),hAPP(hAPP(c_List_Olist_OCons(U_20014),U_20012),U_20016)) = hAPP(hAPP(c_List_Olist_OCons(U_20014),U_20012),hAPP(c_List_Ofilter(U_20014,U_20010),U_20016))
    | ~ hBOOL(hAPP(U_20010,U_20012)) ),
    inference(clausify,[status(thm)],[f_4782_4]) ).

cnf(f_4782_6,plain,
    ( hAPP(c_List_Ofilter(U_20015,U_20011),hAPP(hAPP(c_List_Olist_OCons(U_20015),U_20013),U_20017)) = hAPP(c_List_Ofilter(U_20015,U_20011),U_20017)
    | hBOOL(hAPP(U_20011,U_20013)) ),
    inference(clausify,[status(thm)],[f_4782_4]) ).

fof(f_4783_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__append]) ).

fof(f_4783_2,plain,
    ! [U_20021,U_20020,U_20019,U_20018] : hAPP(c_List_Ofilter(U_20018,U_20019),hAPP(hAPP(c_List_Oappend(U_20018),U_20020),U_20021)) = hAPP(hAPP(c_List_Oappend(U_20018),hAPP(c_List_Ofilter(U_20018,U_20019),U_20020)),hAPP(c_List_Ofilter(U_20018,U_20019),U_20021)),
    inference(variable_rename,[status(thm)],[f_4783_1]) ).

fof(f_4783_3,plain,
    ! [U_20018,U_20019,U_20020,U_20021] : hAPP(c_List_Ofilter(U_20018,U_20019),hAPP(hAPP(c_List_Oappend(U_20018),U_20020),U_20021)) = hAPP(hAPP(c_List_Oappend(U_20018),hAPP(c_List_Ofilter(U_20018,U_20019),U_20020)),hAPP(c_List_Ofilter(U_20018,U_20019),U_20021)),
    inference(definitional_conversion,[status(esa)],[f_4783_2]) ).

cnf(f_4783_4,plain,
    hAPP(c_List_Ofilter(U_20018,U_20019),hAPP(hAPP(c_List_Oappend(U_20018),U_20020),U_20021)) = hAPP(hAPP(c_List_Oappend(U_20018),hAPP(c_List_Ofilter(U_20018,U_20019),U_20020)),hAPP(c_List_Ofilter(U_20018,U_20019),U_20021)),
    inference(clausify,[status(thm)],[f_4783_3]) ).

fof(f_4784_1,plain,
    ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition__filter__conv]) ).

fof(f_4784_2,plain,
    ! [U_20024,U_20023,U_20022] : c_List_Opartition(U_20022,U_20023,U_20024) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20022),tc_List_Olist(U_20022)),hAPP(c_List_Ofilter(U_20022,U_20023),U_20024)),hAPP(c_List_Ofilter(U_20022,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20022,c_fNot),U_20023)),U_20024)),
    inference(variable_rename,[status(thm)],[f_4784_1]) ).

fof(f_4784_3,plain,
    ! [U_20022,U_20023,U_20024] : c_List_Opartition(U_20022,U_20023,U_20024) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20022),tc_List_Olist(U_20022)),hAPP(c_List_Ofilter(U_20022,U_20023),U_20024)),hAPP(c_List_Ofilter(U_20022,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20022,c_fNot),U_20023)),U_20024)),
    inference(definitional_conversion,[status(esa)],[f_4784_2]) ).

cnf(f_4784_4,plain,
    c_List_Opartition(U_20022,U_20023,U_20024) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20022),tc_List_Olist(U_20022)),hAPP(c_List_Ofilter(U_20022,U_20023),U_20024)),hAPP(c_List_Ofilter(U_20022,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20022,c_fNot),U_20023)),U_20024)),
    inference(clausify,[status(thm)],[f_4784_3]) ).

fof(f_4785_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__map]) ).

fof(f_4785_2,plain,
    ! [U_20029,U_20028,U_20027,U_20026,U_20025] : hAPP(c_List_Ofilter(U_20025,U_20026),hAPP(hAPP(c_List_Omap(U_20027,U_20025),U_20028),U_20029)) = hAPP(hAPP(c_List_Omap(U_20027,U_20025),U_20028),hAPP(c_List_Ofilter(U_20027,hAPP(c_Fun_Ocomp(U_20025,tc_HOL_Obool,U_20027,U_20026),U_20028)),U_20029)),
    inference(variable_rename,[status(thm)],[f_4785_1]) ).

fof(f_4785_3,plain,
    ! [U_20025,U_20026,U_20027,U_20028,U_20029] : hAPP(c_List_Ofilter(U_20025,U_20026),hAPP(hAPP(c_List_Omap(U_20027,U_20025),U_20028),U_20029)) = hAPP(hAPP(c_List_Omap(U_20027,U_20025),U_20028),hAPP(c_List_Ofilter(U_20027,hAPP(c_Fun_Ocomp(U_20025,tc_HOL_Obool,U_20027,U_20026),U_20028)),U_20029)),
    inference(definitional_conversion,[status(esa)],[f_4785_2]) ).

cnf(f_4785_4,plain,
    hAPP(c_List_Ofilter(U_20025,U_20026),hAPP(hAPP(c_List_Omap(U_20027,U_20025),U_20028),U_20029)) = hAPP(hAPP(c_List_Omap(U_20027,U_20025),U_20028),hAPP(c_List_Ofilter(U_20027,hAPP(c_Fun_Ocomp(U_20025,tc_HOL_Obool,U_20027,U_20026),U_20028)),U_20029)),
    inference(clausify,[status(thm)],[f_4785_3]) ).

fof(f_4786_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter2]) ).

fof(f_4786_2,plain,
    ! [U_20032,U_20031,U_20030] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_20030),tc_List_Olist(U_20030)),c_List_Opartition(U_20030,U_20031,U_20032)) = hAPP(c_List_Ofilter(U_20030,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20030,c_fNot),U_20031)),U_20032),
    inference(variable_rename,[status(thm)],[f_4786_1]) ).

fof(f_4786_3,plain,
    ! [U_20030,U_20031,U_20032] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_20030),tc_List_Olist(U_20030)),c_List_Opartition(U_20030,U_20031,U_20032)) = hAPP(c_List_Ofilter(U_20030,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20030,c_fNot),U_20031)),U_20032),
    inference(definitional_conversion,[status(esa)],[f_4786_2]) ).

cnf(f_4786_4,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(U_20030),tc_List_Olist(U_20030)),c_List_Opartition(U_20030,U_20031,U_20032)) = hAPP(c_List_Ofilter(U_20030,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20030,c_fNot),U_20031)),U_20032),
    inference(clausify,[status(thm)],[f_4786_3]) ).

fof(f_4787_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_set__filter]) ).

fof(f_4787_2,plain,
    ! [U_20035,U_20034,U_20033] : hAPP(c_List_Oset(U_20033),hAPP(c_List_Ofilter(U_20033,U_20034),U_20035)) = hAPP(c_Set_OCollect(U_20033),hAPP(hAPP(c_COMBS(U_20033,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20033),c_fconj),hAPP(hAPP(c_COMBC(U_20033,tc_fun(U_20033,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20033)),hAPP(c_List_Oset(U_20033),U_20035)))),U_20034)),
    inference(variable_rename,[status(thm)],[f_4787_1]) ).

fof(f_4787_3,plain,
    ! [U_20033,U_20034,U_20035] : hAPP(c_List_Oset(U_20033),hAPP(c_List_Ofilter(U_20033,U_20034),U_20035)) = hAPP(c_Set_OCollect(U_20033),hAPP(hAPP(c_COMBS(U_20033,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20033),c_fconj),hAPP(hAPP(c_COMBC(U_20033,tc_fun(U_20033,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20033)),hAPP(c_List_Oset(U_20033),U_20035)))),U_20034)),
    inference(definitional_conversion,[status(esa)],[f_4787_2]) ).

cnf(f_4787_4,plain,
    hAPP(c_List_Oset(U_20033),hAPP(c_List_Ofilter(U_20033,U_20034),U_20035)) = hAPP(c_Set_OCollect(U_20033),hAPP(hAPP(c_COMBS(U_20033,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20033),c_fconj),hAPP(hAPP(c_COMBC(U_20033,tc_fun(U_20033,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20033)),hAPP(c_List_Oset(U_20033),U_20035)))),U_20034)),
    inference(clausify,[status(thm)],[f_4787_3]) ).

fof(f_4788_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__filter__map]) ).

fof(f_4788_2,plain,
    ! [U_20040,U_20039,U_20038,U_20037,U_20036] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20036)),hAPP(c_List_Ofilter(U_20036,U_20037),hAPP(hAPP(c_List_Omap(U_20038,U_20036),U_20039),U_20040))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20038)),hAPP(c_List_Ofilter(U_20038,hAPP(c_Fun_Ocomp(U_20036,tc_HOL_Obool,U_20038,U_20037),U_20039)),U_20040)),
    inference(variable_rename,[status(thm)],[f_4788_1]) ).

fof(f_4788_3,plain,
    ! [U_20040,U_20036,U_20037,U_20038,U_20039] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20036)),hAPP(c_List_Ofilter(U_20036,U_20037),hAPP(hAPP(c_List_Omap(U_20038,U_20036),U_20039),U_20040))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20038)),hAPP(c_List_Ofilter(U_20038,hAPP(c_Fun_Ocomp(U_20036,tc_HOL_Obool,U_20038,U_20037),U_20039)),U_20040)),
    inference(definitional_conversion,[status(esa)],[f_4788_2]) ).

cnf(f_4788_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20036)),hAPP(c_List_Ofilter(U_20036,U_20037),hAPP(hAPP(c_List_Omap(U_20038,U_20036),U_20039),U_20040))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20038)),hAPP(c_List_Ofilter(U_20038,hAPP(c_Fun_Ocomp(U_20036,tc_HOL_Obool,U_20038,U_20037),U_20039)),U_20040)),
    inference(clausify,[status(thm)],[f_4788_3]) ).

fof(f_4789_1,plain,
    ! [V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__filter__less]) ).

fof(f_4789_2,plain,
    ! [U_20044,U_20043,U_20042,U_20041] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20041)),hAPP(c_List_Ofilter(U_20041,U_20044),U_20043))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20041)),U_20043)))
      | hBOOL(hAPP(U_20044,U_20042))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20041),U_20042),hAPP(c_List_Oset(U_20041),U_20043))) ),
    inference(variable_rename,[status(thm)],[f_4789_1]) ).

fof(f_4789_3,plain,
    ! [U_20041,U_20042,U_20043,U_20044] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20041)),hAPP(c_List_Ofilter(U_20041,U_20044),U_20043))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20041)),U_20043)))
      | hBOOL(hAPP(U_20044,U_20042))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20041),U_20042),hAPP(c_List_Oset(U_20041),U_20043))) ),
    inference(definitional_conversion,[status(esa)],[f_4789_2]) ).

cnf(f_4789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20041)),hAPP(c_List_Ofilter(U_20041,U_20044),U_20043))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20041)),U_20043)))
    | hBOOL(hAPP(U_20044,U_20042))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20041),U_20042),hAPP(c_List_Oset(U_20041),U_20043))) ),
    inference(clausify,[status(thm)],[f_4789_3]) ).

fof(f_4790_1,plain,
    ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_set__minus__filter__out]) ).

fof(f_4790_2,plain,
    ! [U_20047,U_20046,U_20045] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_20045,tc_HOL_Obool)),hAPP(c_List_Oset(U_20045),U_20046)),hAPP(hAPP(c_Set_Oinsert(U_20045),U_20047),c_Orderings_Obot__class_Obot(tc_fun(U_20045,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_20045),hAPP(c_List_Ofilter(U_20045,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20045),c_fNot),hAPP(hAPP(c_COMBC(U_20045,U_20045,tc_HOL_Obool),c_fequal),U_20047))),U_20046)),
    inference(variable_rename,[status(thm)],[f_4790_1]) ).

fof(f_4790_3,plain,
    ! [U_20045,U_20046,U_20047] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_20045,tc_HOL_Obool)),hAPP(c_List_Oset(U_20045),U_20046)),hAPP(hAPP(c_Set_Oinsert(U_20045),U_20047),c_Orderings_Obot__class_Obot(tc_fun(U_20045,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_20045),hAPP(c_List_Ofilter(U_20045,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20045),c_fNot),hAPP(hAPP(c_COMBC(U_20045,U_20045,tc_HOL_Obool),c_fequal),U_20047))),U_20046)),
    inference(definitional_conversion,[status(esa)],[f_4790_2]) ).

cnf(f_4790_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_20045,tc_HOL_Obool)),hAPP(c_List_Oset(U_20045),U_20046)),hAPP(hAPP(c_Set_Oinsert(U_20045),U_20047),c_Orderings_Obot__class_Obot(tc_fun(U_20045,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_20045),hAPP(c_List_Ofilter(U_20045,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20045),c_fNot),hAPP(hAPP(c_COMBC(U_20045,U_20045,tc_HOL_Obool),c_fequal),U_20047))),U_20046)),
    inference(clausify,[status(thm)],[f_4790_3]) ).

fof(f_4791_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) )
        & ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) ) )
      | c_List_Opartition(T_b,V_P_2,V_xs_2) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) ),
    inference(fof_nnf,[status(thm)],[fact_partition__P]) ).

fof(f_4791_2,plain,
    ! [U_20054,U_20053,U_20052,U_20051,U_20050] :
      ( ( ! [U_20049] :
            ( ~ hBOOL(hAPP(U_20051,U_20049))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20050),U_20049),hAPP(c_List_Oset(U_20050),U_20054))) )
        & ! [U_20048] :
            ( hBOOL(hAPP(U_20051,U_20048))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20050),U_20048),hAPP(c_List_Oset(U_20050),U_20053))) ) )
      | c_List_Opartition(U_20050,U_20051,U_20052) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20050),tc_List_Olist(U_20050)),U_20053),U_20054) ),
    inference(variable_rename,[status(thm)],[f_4791_1]) ).

fof(f_4791_3,plain,
    ( ! [U_20048,U_20049,U_20050,U_20051,U_20053,U_20054] :
        ( ~ hBOOL(hAPP(U_20051,U_20049))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20050),U_20049),hAPP(c_List_Oset(U_20050),U_20054)))
        | ~ sP1212(U_20048,U_20049,U_20050,U_20051,U_20053,U_20054) )
    & ! [U_20048,U_20049,U_20050,U_20051,U_20053,U_20054] :
        ( hBOOL(hAPP(U_20051,U_20048))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20050),U_20048),hAPP(c_List_Oset(U_20050),U_20053)))
        | ~ sP1212(U_20048,U_20049,U_20050,U_20051,U_20053,U_20054) )
    & ! [U_20048,U_20049,U_20050,U_20051,U_20052,U_20053,U_20054] :
        ( sP1212(U_20048,U_20049,U_20050,U_20051,U_20053,U_20054)
        | c_List_Opartition(U_20050,U_20051,U_20052) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20050),tc_List_Olist(U_20050)),U_20053),U_20054) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1212])],[f_4791_2]) ).

cnf(f_4791_4,plain,
    ( sP1212(U_20048,U_20049,U_20050,U_20051,U_20053,U_20054)
    | c_List_Opartition(U_20050,U_20051,U_20052) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20050),tc_List_Olist(U_20050)),U_20053),U_20054) ),
    inference(clausify,[status(thm)],[f_4791_3]) ).

cnf(f_4791_5,plain,
    ( hBOOL(hAPP(U_20051,U_20048))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20050),U_20048),hAPP(c_List_Oset(U_20050),U_20053)))
    | ~ sP1212(U_20048,U_20049,U_20050,U_20051,U_20053,U_20054) ),
    inference(clausify,[status(thm)],[f_4791_3]) ).

cnf(f_4791_6,plain,
    ( ~ hBOOL(hAPP(U_20051,U_20049))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20050),U_20049),hAPP(c_List_Oset(U_20050),U_20054)))
    | ~ sP1212(U_20048,U_20049,U_20050,U_20051,U_20053,U_20054) ),
    inference(clausify,[status(thm)],[f_4791_3]) ).

fof(f_4792_1,plain,
    ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I1_J]) ).

fof(f_4792_2,plain,
    ! [U_20056,U_20055] : c_List_Opartition(U_20055,U_20056,c_List_Olist_ONil(U_20055)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20055),tc_List_Olist(U_20055)),c_List_Olist_ONil(U_20055)),c_List_Olist_ONil(U_20055)),
    inference(variable_rename,[status(thm)],[f_4792_1]) ).

fof(f_4792_3,plain,
    ! [U_20056,U_20055] : c_List_Opartition(U_20055,U_20056,c_List_Olist_ONil(U_20055)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20055),tc_List_Olist(U_20055)),c_List_Olist_ONil(U_20055)),c_List_Olist_ONil(U_20055)),
    inference(definitional_conversion,[status(esa)],[f_4792_2]) ).

cnf(f_4792_4,plain,
    c_List_Opartition(U_20055,U_20056,c_List_Olist_ONil(U_20055)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20055),tc_List_Olist(U_20055)),c_List_Olist_ONil(U_20055)),c_List_Olist_ONil(U_20055)),
    inference(clausify,[status(thm)],[f_4792_3]) ).

fof(f_4793_1,plain,
    ! [V_s_2,V_xs_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_filter__in__sublist]) ).

fof(f_4793_2,plain,
    ! [U_20059,U_20058,U_20057] :
      ( hAPP(c_List_Ofilter(U_20057,hAPP(hAPP(c_COMBC(U_20057,tc_fun(U_20057,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20057)),hAPP(c_List_Oset(U_20057),c_List_Osublist(U_20057,U_20058,U_20059)))),U_20058) = c_List_Osublist(U_20057,U_20058,U_20059)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20057),U_20058)) ),
    inference(variable_rename,[status(thm)],[f_4793_1]) ).

fof(f_4793_3,plain,
    ! [U_20057,U_20058,U_20059] :
      ( hAPP(c_List_Ofilter(U_20057,hAPP(hAPP(c_COMBC(U_20057,tc_fun(U_20057,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20057)),hAPP(c_List_Oset(U_20057),c_List_Osublist(U_20057,U_20058,U_20059)))),U_20058) = c_List_Osublist(U_20057,U_20058,U_20059)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20057),U_20058)) ),
    inference(definitional_conversion,[status(esa)],[f_4793_2]) ).

cnf(f_4793_4,plain,
    ( hAPP(c_List_Ofilter(U_20057,hAPP(hAPP(c_COMBC(U_20057,tc_fun(U_20057,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20057)),hAPP(c_List_Oset(U_20057),c_List_Osublist(U_20057,U_20058,U_20059)))),U_20058) = c_List_Osublist(U_20057,U_20058,U_20059)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20057),U_20058)) ),
    inference(clausify,[status(thm)],[f_4793_3]) ).

fof(f_4794_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(f_4794_2,plain,
    ! [U_20063,U_20062,U_20061,U_20060] : c_List_Opartition(U_20060,U_20061,hAPP(hAPP(c_List_Olist_OCons(U_20060),U_20062),U_20063)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20060),tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_fun(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),c_COMBS(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_List_Olist(U_20060)),hAPP(c_If(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(U_20061,U_20062)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_List_Olist(U_20060)),c_Product__Type_OPair(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(c_List_Olist_OCons(U_20060),U_20062))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_fun(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),c_COMBB(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_List_Olist(U_20060))),c_Product__Type_OPair(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(c_List_Olist_OCons(U_20060),U_20062)))),c_List_Opartition(U_20060,U_20061,U_20063)),
    inference(variable_rename,[status(thm)],[f_4794_1]) ).

fof(f_4794_3,plain,
    ! [U_20060,U_20061,U_20062,U_20063] : c_List_Opartition(U_20060,U_20061,hAPP(hAPP(c_List_Olist_OCons(U_20060),U_20062),U_20063)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20060),tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_fun(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),c_COMBS(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_List_Olist(U_20060)),hAPP(c_If(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(U_20061,U_20062)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_List_Olist(U_20060)),c_Product__Type_OPair(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(c_List_Olist_OCons(U_20060),U_20062))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_fun(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),c_COMBB(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_List_Olist(U_20060))),c_Product__Type_OPair(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(c_List_Olist_OCons(U_20060),U_20062)))),c_List_Opartition(U_20060,U_20061,U_20063)),
    inference(definitional_conversion,[status(esa)],[f_4794_2]) ).

cnf(f_4794_4,plain,
    c_List_Opartition(U_20060,U_20061,hAPP(hAPP(c_List_Olist_OCons(U_20060),U_20062),U_20063)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20060),tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_fun(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),c_COMBS(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_List_Olist(U_20060),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_List_Olist(U_20060)),hAPP(c_If(tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(U_20061,U_20062)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_List_Olist(U_20060)),c_Product__Type_OPair(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),hAPP(c_List_Olist_OCons(U_20060),U_20062))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20060),tc_fun(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060))),tc_fun(tc_fun(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_fun(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),tc_List_Olist(U_20060)),c_COMBB(tc_List_Olist(U_20060),tc_prod(tc_List_Olist(U_20060),tc_List_Olist(U_20060)),tc_List_Olist(U_20060))),c_Product__Type_OPair(tc_List_Olist(U_20060),tc_List_Olist(U_20060)))),hAPP(c_List_Olist_OCons(U_20060),U_20062)))),c_List_Opartition(U_20060,U_20061,U_20063)),
    inference(clausify,[status(thm)],[f_4794_3]) ).

fof(f_4795_1,plain,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_length__filter__conv__card]) ).

fof(f_4795_2,plain,
    ! [U_20066,U_20065,U_20064] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20064)),hAPP(c_List_Ofilter(U_20064,U_20065),U_20066)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20064)),U_20066)))),hAPP(hAPP(c_COMBB(U_20064,tc_HOL_Obool,tc_Nat_Onat),U_20065),hAPP(c_List_Onth(U_20064),U_20066))))),
    inference(variable_rename,[status(thm)],[f_4795_1]) ).

fof(f_4795_3,plain,
    ! [U_20064,U_20065,U_20066] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20064)),hAPP(c_List_Ofilter(U_20064,U_20065),U_20066)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20064)),U_20066)))),hAPP(hAPP(c_COMBB(U_20064,tc_HOL_Obool,tc_Nat_Onat),U_20065),hAPP(c_List_Onth(U_20064),U_20066))))),
    inference(definitional_conversion,[status(esa)],[f_4795_2]) ).

cnf(f_4795_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20064)),hAPP(c_List_Ofilter(U_20064,U_20065),U_20066)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20064)),U_20066)))),hAPP(hAPP(c_COMBB(U_20064,tc_HOL_Obool,tc_Nat_Onat),U_20065),hAPP(c_List_Onth(U_20064),U_20066))))),
    inference(clausify,[status(thm)],[f_4795_3]) ).

fof(f_4796_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__filter__def]) ).

fof(f_4796_2,plain,
    ! [U_20070,U_20069,U_20068,U_20067] : c_List_Omap__filter(U_20067,U_20068,U_20069,U_20070) = hAPP(hAPP(c_List_Omap(U_20067,U_20068),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_20068),U_20068,U_20067,c_Option_Othe(U_20068)),U_20069)),hAPP(c_List_Ofilter(U_20067,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20067),c_fNot),hAPP(hAPP(c_COMBC(U_20067,tc_Option_Ooption(U_20068),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_20068),tc_fun(tc_Option_Ooption(U_20068),tc_HOL_Obool),U_20067),c_fequal),U_20069)),c_Option_Ooption_ONone(U_20068)))),U_20070)),
    inference(variable_rename,[status(thm)],[f_4796_1]) ).

fof(f_4796_3,plain,
    ! [U_20067,U_20068,U_20069,U_20070] : c_List_Omap__filter(U_20067,U_20068,U_20069,U_20070) = hAPP(hAPP(c_List_Omap(U_20067,U_20068),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_20068),U_20068,U_20067,c_Option_Othe(U_20068)),U_20069)),hAPP(c_List_Ofilter(U_20067,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20067),c_fNot),hAPP(hAPP(c_COMBC(U_20067,tc_Option_Ooption(U_20068),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_20068),tc_fun(tc_Option_Ooption(U_20068),tc_HOL_Obool),U_20067),c_fequal),U_20069)),c_Option_Ooption_ONone(U_20068)))),U_20070)),
    inference(definitional_conversion,[status(esa)],[f_4796_2]) ).

cnf(f_4796_4,plain,
    c_List_Omap__filter(U_20067,U_20068,U_20069,U_20070) = hAPP(hAPP(c_List_Omap(U_20067,U_20068),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_20068),U_20068,U_20067,c_Option_Othe(U_20068)),U_20069)),hAPP(c_List_Ofilter(U_20067,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20067),c_fNot),hAPP(hAPP(c_COMBC(U_20067,tc_Option_Ooption(U_20068),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_20068),tc_fun(tc_Option_Ooption(U_20068),tc_HOL_Obool),U_20067),c_fequal),U_20069)),c_Option_Ooption_ONone(U_20068)))),U_20070)),
    inference(clausify,[status(thm)],[f_4796_3]) ).

fof(f_4797_1,plain,
    ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__max__length]) ).

fof(f_4797_2,plain,
    ! [U_20072,U_20071] : c_List_Ofoldr(tc_List_Olist(U_20071),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20071)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20071))),c_List_Otranspose(U_20071,U_20072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20071))),hAPP(c_List_Ofilter(tc_List_Olist(U_20071),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20071)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20071),tc_List_Olist(U_20071),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20071)))),U_20072)),
    inference(variable_rename,[status(thm)],[f_4797_1]) ).

fof(f_4797_3,plain,
    ! [U_20071,U_20072] : c_List_Ofoldr(tc_List_Olist(U_20071),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20071)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20071))),c_List_Otranspose(U_20071,U_20072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20071))),hAPP(c_List_Ofilter(tc_List_Olist(U_20071),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20071)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20071),tc_List_Olist(U_20071),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20071)))),U_20072)),
    inference(definitional_conversion,[status(esa)],[f_4797_2]) ).

cnf(f_4797_4,plain,
    c_List_Ofoldr(tc_List_Olist(U_20071),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20071)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20071))),c_List_Otranspose(U_20071,U_20072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20071))),hAPP(c_List_Ofilter(tc_List_Olist(U_20071),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20071)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20071),tc_List_Olist(U_20071),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20071)))),U_20072)),
    inference(clausify,[status(thm)],[f_4797_3]) ).

fof(f_4798_1,plain,
    ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
      ( hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
      | hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__filter__in]) ).

fof(f_4798_2,plain,
    ! [U_20078,U_20077,U_20076,U_20075,U_20074,U_20073] :
      ( hAPP(c_Map_Omap__of(U_20073,U_20074,hAPP(c_List_Ofilter(tc_prod(U_20073,U_20074),hAPP(c_Product__Type_Oprod_Oprod__case(U_20073,U_20074,tc_HOL_Obool),U_20078)),U_20075)),U_20076) = hAPP(c_Option_Ooption_OSome(U_20074),U_20077)
      | ~ hBOOL(hAPP(hAPP(U_20078,U_20076),U_20077))
      | hAPP(c_Map_Omap__of(U_20073,U_20074,U_20075),U_20076) != hAPP(c_Option_Ooption_OSome(U_20074),U_20077) ),
    inference(variable_rename,[status(thm)],[f_4798_1]) ).

fof(f_4798_3,plain,
    ! [U_20073,U_20074,U_20075,U_20076,U_20077,U_20078] :
      ( hAPP(c_Map_Omap__of(U_20073,U_20074,hAPP(c_List_Ofilter(tc_prod(U_20073,U_20074),hAPP(c_Product__Type_Oprod_Oprod__case(U_20073,U_20074,tc_HOL_Obool),U_20078)),U_20075)),U_20076) = hAPP(c_Option_Ooption_OSome(U_20074),U_20077)
      | ~ hBOOL(hAPP(hAPP(U_20078,U_20076),U_20077))
      | hAPP(c_Map_Omap__of(U_20073,U_20074,U_20075),U_20076) != hAPP(c_Option_Ooption_OSome(U_20074),U_20077) ),
    inference(definitional_conversion,[status(esa)],[f_4798_2]) ).

cnf(f_4798_4,plain,
    ( hAPP(c_Map_Omap__of(U_20073,U_20074,hAPP(c_List_Ofilter(tc_prod(U_20073,U_20074),hAPP(c_Product__Type_Oprod_Oprod__case(U_20073,U_20074,tc_HOL_Obool),U_20078)),U_20075)),U_20076) = hAPP(c_Option_Ooption_OSome(U_20074),U_20077)
    | ~ hBOOL(hAPP(hAPP(U_20078,U_20076),U_20077))
    | hAPP(c_Map_Omap__of(U_20073,U_20074,U_20075),U_20076) != hAPP(c_Option_Ooption_OSome(U_20074),U_20077) ),
    inference(clausify,[status(thm)],[f_4798_3]) ).

fof(f_4799_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__map__map]) ).

fof(f_4799_2,plain,
    ! [U_20082,U_20081,U_20080,U_20079] : c_List_Otranspose(U_20079,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20080),tc_List_Olist(U_20079)),hAPP(c_List_Omap(U_20080,U_20079),U_20081)),U_20082)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20080),tc_List_Olist(U_20079)),hAPP(c_List_Omap(U_20080,U_20079),U_20081)),c_List_Otranspose(U_20080,U_20082)),
    inference(variable_rename,[status(thm)],[f_4799_1]) ).

fof(f_4799_3,plain,
    ! [U_20080,U_20079,U_20081,U_20082] : c_List_Otranspose(U_20079,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20080),tc_List_Olist(U_20079)),hAPP(c_List_Omap(U_20080,U_20079),U_20081)),U_20082)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20080),tc_List_Olist(U_20079)),hAPP(c_List_Omap(U_20080,U_20079),U_20081)),c_List_Otranspose(U_20080,U_20082)),
    inference(definitional_conversion,[status(esa)],[f_4799_2]) ).

cnf(f_4799_4,plain,
    c_List_Otranspose(U_20079,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20080),tc_List_Olist(U_20079)),hAPP(c_List_Omap(U_20080,U_20079),U_20081)),U_20082)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20080),tc_List_Olist(U_20079)),hAPP(c_List_Omap(U_20080,U_20079),U_20081)),c_List_Otranspose(U_20080,U_20082)),
    inference(clausify,[status(thm)],[f_4799_3]) ).

fof(f_4800_1,plain,
    ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I2_J]) ).

fof(f_4800_2,plain,
    ! [U_20084,U_20083] : c_List_Otranspose(U_20083,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20083)),c_List_Olist_ONil(U_20083)),U_20084)) = c_List_Otranspose(U_20083,U_20084),
    inference(variable_rename,[status(thm)],[f_4800_1]) ).

fof(f_4800_3,plain,
    ! [U_20083,U_20084] : c_List_Otranspose(U_20083,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20083)),c_List_Olist_ONil(U_20083)),U_20084)) = c_List_Otranspose(U_20083,U_20084),
    inference(definitional_conversion,[status(esa)],[f_4800_2]) ).

cnf(f_4800_4,plain,
    c_List_Otranspose(U_20083,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20083)),c_List_Olist_ONil(U_20083)),U_20084)) = c_List_Otranspose(U_20083,U_20084),
    inference(clausify,[status(thm)],[f_4800_3]) ).

fof(f_4801_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_b)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_b)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) )
        | c_List_Otranspose(T_b,V_xs_2) != c_List_Olist_ONil(tc_List_Olist(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__empty]) ).

fof(f_4801_2,plain,
    ! [U_20088,U_20087] :
      ( ( c_List_Otranspose(U_20087,U_20088) = c_List_Olist_ONil(tc_List_Olist(U_20087))
        | ? [U_20086] :
            ( U_20086 != c_List_Olist_ONil(U_20087)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20087)),U_20086),hAPP(c_List_Oset(tc_List_Olist(U_20087)),U_20088))) ) )
      & ( ! [U_20085] :
            ( U_20085 = c_List_Olist_ONil(U_20087)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20087)),U_20085),hAPP(c_List_Oset(tc_List_Olist(U_20087)),U_20088))) )
        | c_List_Otranspose(U_20087,U_20088) != c_List_Olist_ONil(tc_List_Olist(U_20087)) ) ),
    inference(variable_rename,[status(thm)],[f_4801_1]) ).

fof(f_4801_3,plain,
    ( ! [U_20092,U_20090] :
        ( c_List_Otranspose(U_20090,U_20092) = c_List_Olist_ONil(tc_List_Olist(U_20090))
        | ? [U_20086] :
            ( U_20086 != c_List_Olist_ONil(U_20090)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20086),hAPP(c_List_Oset(tc_List_Olist(U_20090)),U_20092))) ) )
    & ! [U_20091,U_20089] :
        ( ! [U_20085] :
            ( U_20085 = c_List_Olist_ONil(U_20089)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20089)),U_20085),hAPP(c_List_Oset(tc_List_Olist(U_20089)),U_20091))) )
        | c_List_Otranspose(U_20089,U_20091) != c_List_Olist_ONil(tc_List_Olist(U_20089)) ) ),
    inference(miniscope,[status(thm)],[f_4801_2]) ).

fof(f_4801_4,plain,
    ( ! [U_20092,U_20090] :
        ( c_List_Otranspose(U_20090,U_20092) = c_List_Olist_ONil(tc_List_Olist(U_20090))
        | ( sK496(U_20092,U_20090) != c_List_Olist_ONil(U_20090)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),sK496(U_20092,U_20090)),hAPP(c_List_Oset(tc_List_Olist(U_20090)),U_20092))) ) )
    & ! [U_20091,U_20089] :
        ( ! [U_20085] :
            ( U_20085 = c_List_Olist_ONil(U_20089)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20089)),U_20085),hAPP(c_List_Oset(tc_List_Olist(U_20089)),U_20091))) )
        | c_List_Otranspose(U_20089,U_20091) != c_List_Olist_ONil(tc_List_Olist(U_20089)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_20086,sK496(U_20092,U_20090))],[f_4801_3]) ).

fof(f_4801_5,plain,
    ( ! [U_20092,U_20090] :
        ( sK496(U_20092,U_20090) != c_List_Olist_ONil(U_20090)
        | ~ sP1213(U_20092,U_20090) )
    & ! [U_20092,U_20090] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),sK496(U_20092,U_20090)),hAPP(c_List_Oset(tc_List_Olist(U_20090)),U_20092)))
        | ~ sP1213(U_20092,U_20090) )
    & ! [U_20092,U_20090] :
        ( c_List_Otranspose(U_20090,U_20092) = c_List_Olist_ONil(tc_List_Olist(U_20090))
        | sP1213(U_20092,U_20090) )
    & ! [U_20091,U_20085,U_20089] :
        ( U_20085 = c_List_Olist_ONil(U_20089)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20089)),U_20085),hAPP(c_List_Oset(tc_List_Olist(U_20089)),U_20091)))
        | c_List_Otranspose(U_20089,U_20091) != c_List_Olist_ONil(tc_List_Olist(U_20089)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1213])],[f_4801_4]) ).

cnf(f_4801_6,plain,
    ( U_20085 = c_List_Olist_ONil(U_20089)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20089)),U_20085),hAPP(c_List_Oset(tc_List_Olist(U_20089)),U_20091)))
    | c_List_Otranspose(U_20089,U_20091) != c_List_Olist_ONil(tc_List_Olist(U_20089)) ),
    inference(clausify,[status(thm)],[f_4801_5]) ).

cnf(f_4801_7,plain,
    ( c_List_Otranspose(U_20090,U_20092) = c_List_Olist_ONil(tc_List_Olist(U_20090))
    | sP1213(U_20092,U_20090) ),
    inference(clausify,[status(thm)],[f_4801_5]) ).

cnf(f_4801_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),sK496(U_20092,U_20090)),hAPP(c_List_Oset(tc_List_Olist(U_20090)),U_20092)))
    | ~ sP1213(U_20092,U_20090) ),
    inference(clausify,[status(thm)],[f_4801_5]) ).

cnf(f_4801_9,plain,
    ( sK496(U_20092,U_20090) != c_List_Olist_ONil(U_20090)
    | ~ sP1213(U_20092,U_20090) ),
    inference(clausify,[status(thm)],[f_4801_5]) ).

fof(f_4802_1,plain,
    ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_map__filter__simps_I2_J]) ).

fof(f_4802_2,plain,
    ! [U_20095,U_20094,U_20093] : c_List_Omap__filter(U_20093,U_20094,U_20095,c_List_Olist_ONil(U_20093)) = c_List_Olist_ONil(U_20094),
    inference(variable_rename,[status(thm)],[f_4802_1]) ).

fof(f_4802_3,plain,
    ! [U_20095,U_20094,U_20093] : c_List_Omap__filter(U_20093,U_20094,U_20095,c_List_Olist_ONil(U_20093)) = c_List_Olist_ONil(U_20094),
    inference(definitional_conversion,[status(esa)],[f_4802_2]) ).

cnf(f_4802_4,plain,
    c_List_Omap__filter(U_20093,U_20094,U_20095,c_List_Olist_ONil(U_20093)) = c_List_Olist_ONil(U_20094),
    inference(clausify,[status(thm)],[f_4802_3]) ).

fof(f_4803_1,plain,
    ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I1_J]) ).

fof(f_4803_2,plain,
    ! [U_20096] : c_List_Otranspose(U_20096,c_List_Olist_ONil(tc_List_Olist(U_20096))) = c_List_Olist_ONil(tc_List_Olist(U_20096)),
    inference(variable_rename,[status(thm)],[f_4803_1]) ).

fof(f_4803_3,plain,
    ! [U_20096] : c_List_Otranspose(U_20096,c_List_Olist_ONil(tc_List_Olist(U_20096))) = c_List_Olist_ONil(tc_List_Olist(U_20096)),
    inference(definitional_conversion,[status(esa)],[f_4803_2]) ).

cnf(f_4803_4,plain,
    c_List_Otranspose(U_20096,c_List_Olist_ONil(tc_List_Olist(U_20096))) = c_List_Olist_ONil(tc_List_Olist(U_20096)),
    inference(clausify,[status(thm)],[f_4803_3]) ).

fof(f_4804_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_map__filter__simps_I1_J]) ).

fof(f_4804_2,plain,
    ! [U_20101,U_20100,U_20099,U_20098,U_20097] : c_List_Omap__filter(U_20097,U_20098,U_20099,hAPP(hAPP(c_List_Olist_OCons(U_20097),U_20100),U_20101)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_20098),U_20098,c_List_Omap__filter(U_20097,U_20098,U_20099,U_20101),hAPP(hAPP(c_COMBC(U_20098,tc_List_Olist(U_20098),tc_List_Olist(U_20098)),c_List_Olist_OCons(U_20098)),c_List_Omap__filter(U_20097,U_20098,U_20099,U_20101))),hAPP(U_20099,U_20100)),
    inference(variable_rename,[status(thm)],[f_4804_1]) ).

fof(f_4804_3,plain,
    ! [U_20097,U_20098,U_20099,U_20100,U_20101] : c_List_Omap__filter(U_20097,U_20098,U_20099,hAPP(hAPP(c_List_Olist_OCons(U_20097),U_20100),U_20101)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_20098),U_20098,c_List_Omap__filter(U_20097,U_20098,U_20099,U_20101),hAPP(hAPP(c_COMBC(U_20098,tc_List_Olist(U_20098),tc_List_Olist(U_20098)),c_List_Olist_OCons(U_20098)),c_List_Omap__filter(U_20097,U_20098,U_20099,U_20101))),hAPP(U_20099,U_20100)),
    inference(definitional_conversion,[status(esa)],[f_4804_2]) ).

cnf(f_4804_4,plain,
    c_List_Omap__filter(U_20097,U_20098,U_20099,hAPP(hAPP(c_List_Olist_OCons(U_20097),U_20100),U_20101)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_20098),U_20098,c_List_Omap__filter(U_20097,U_20098,U_20099,U_20101),hAPP(hAPP(c_COMBC(U_20098,tc_List_Olist(U_20098),tc_List_Olist(U_20098)),c_List_Olist_OCons(U_20098)),c_List_Omap__filter(U_20097,U_20098,U_20099,U_20101))),hAPP(U_20099,U_20100)),
    inference(clausify,[status(thm)],[f_4804_3]) ).

fof(f_4805_1,plain,
    ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).

fof(f_4805_2,plain,
    ! [U_20105,U_20104,U_20103,U_20102] : hAPP(hAPP(c_List_Omap(tc_prod(U_20102,tc_Nat_Onat),U_20102),c_Product__Type_Ofst(U_20102,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20102,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20102,tc_Nat_Onat)),U_20103),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20102,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20102,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20102,tc_Nat_Onat),U_20104),U_20105))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20102,tc_Nat_Onat),U_20102),c_Product__Type_Ofst(U_20102,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20102,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20102,tc_Nat_Onat)),U_20103),c_Product__Type_Osnd(U_20102,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20102,tc_Nat_Onat),U_20104),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20105)))),
    inference(variable_rename,[status(thm)],[f_4805_1]) ).

fof(f_4805_3,plain,
    ! [U_20102,U_20103,U_20104,U_20105] : hAPP(hAPP(c_List_Omap(tc_prod(U_20102,tc_Nat_Onat),U_20102),c_Product__Type_Ofst(U_20102,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20102,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20102,tc_Nat_Onat)),U_20103),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20102,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20102,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20102,tc_Nat_Onat),U_20104),U_20105))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20102,tc_Nat_Onat),U_20102),c_Product__Type_Ofst(U_20102,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20102,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20102,tc_Nat_Onat)),U_20103),c_Product__Type_Osnd(U_20102,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20102,tc_Nat_Onat),U_20104),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20105)))),
    inference(definitional_conversion,[status(esa)],[f_4805_2]) ).

cnf(f_4805_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_20102,tc_Nat_Onat),U_20102),c_Product__Type_Ofst(U_20102,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20102,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20102,tc_Nat_Onat)),U_20103),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20102,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20102,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20102,tc_Nat_Onat),U_20104),U_20105))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20102,tc_Nat_Onat),U_20102),c_Product__Type_Ofst(U_20102,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20102,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20102,tc_Nat_Onat)),U_20103),c_Product__Type_Osnd(U_20102,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20102,tc_Nat_Onat),U_20104),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20105)))),
    inference(clausify,[status(thm)],[f_4805_3]) ).

fof(f_4806_1,plain,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(f_4806_2,plain,
    ! [U_20107,U_20106] : c_Random_Oselect__weight(U_20106,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20106),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20106,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20106,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20106)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20107)) = c_Random_Oselect__weight(U_20106,U_20107),
    inference(variable_rename,[status(thm)],[f_4806_1]) ).

fof(f_4806_3,plain,
    ! [U_20106,U_20107] : c_Random_Oselect__weight(U_20106,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20106),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20106,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20106,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20106)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20107)) = c_Random_Oselect__weight(U_20106,U_20107),
    inference(definitional_conversion,[status(esa)],[f_4806_2]) ).

cnf(f_4806_4,plain,
    c_Random_Oselect__weight(U_20106,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20106),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20106,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20106,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20106)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20107)) = c_Random_Oselect__weight(U_20106,U_20107),
    inference(clausify,[status(thm)],[f_4806_3]) ).

fof(f_4807_1,plain,
    ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_pick__drop__zero]) ).

fof(f_4807_2,plain,
    ! [U_20109,U_20108] : c_Random_Opick(U_20108,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20108),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20108,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20108,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20108)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20109)) = c_Random_Opick(U_20108,U_20109),
    inference(variable_rename,[status(thm)],[f_4807_1]) ).

fof(f_4807_3,plain,
    ! [U_20108,U_20109] : c_Random_Opick(U_20108,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20108),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20108,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20108,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20108)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20109)) = c_Random_Opick(U_20108,U_20109),
    inference(definitional_conversion,[status(esa)],[f_4807_2]) ).

cnf(f_4807_4,plain,
    c_Random_Opick(U_20108,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20108),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20108,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20108,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20108)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20109)) = c_Random_Opick(U_20108,U_20109),
    inference(clausify,[status(thm)],[f_4807_3]) ).

fof(f_4808_1,plain,
    ! [V_xs_2,T_b,V_i_2] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__transpose]) ).

fof(f_4808_2,plain,
    ! [U_20112,U_20111,U_20110] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20111)),c_List_Otranspose(U_20111,U_20112)),U_20110) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20111),U_20111),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20111),tc_Nat_Onat,U_20111),c_List_Onth(U_20111)),U_20110)),hAPP(c_List_Ofilter(tc_List_Olist(U_20111),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20111)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20110)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20111)))),U_20112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20111))),c_List_Otranspose(U_20111,U_20112)))) ),
    inference(variable_rename,[status(thm)],[f_4808_1]) ).

fof(f_4808_3,plain,
    ! [U_20110,U_20111,U_20112] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20111)),c_List_Otranspose(U_20111,U_20112)),U_20110) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20111),U_20111),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20111),tc_Nat_Onat,U_20111),c_List_Onth(U_20111)),U_20110)),hAPP(c_List_Ofilter(tc_List_Olist(U_20111),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20111)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20110)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20111)))),U_20112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20111))),c_List_Otranspose(U_20111,U_20112)))) ),
    inference(definitional_conversion,[status(esa)],[f_4808_2]) ).

cnf(f_4808_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20111)),c_List_Otranspose(U_20111,U_20112)),U_20110) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20111),U_20111),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20111),tc_Nat_Onat,U_20111),c_List_Onth(U_20111)),U_20110)),hAPP(c_List_Ofilter(tc_List_Olist(U_20111),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20111)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20110)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20111)))),U_20112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20111))),c_List_Otranspose(U_20111,U_20112)))) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

fof(f_4809_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__transpose]) ).

fof(f_4809_2,plain,
    ! [U_20114,U_20113] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20113))),c_List_Otranspose(U_20113,U_20114)) = c_List_Ofoldr(tc_List_Olist(U_20113),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20113)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20113))),U_20114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4809_1]) ).

fof(f_4809_3,plain,
    ! [U_20113,U_20114] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20113))),c_List_Otranspose(U_20113,U_20114)) = c_List_Ofoldr(tc_List_Olist(U_20113),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20113)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20113))),U_20114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4809_2]) ).

cnf(f_4809_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20113))),c_List_Otranspose(U_20113,U_20114)) = c_List_Ofoldr(tc_List_Olist(U_20113),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20113)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20113))),U_20114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4809_3]) ).

fof(f_4810_1,plain,
    ! [V_xs_2,V_P_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_P_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_map__filter__map__filter]) ).

fof(f_4810_2,plain,
    ! [U_20119,U_20118,U_20117,U_20116,U_20115] : hAPP(hAPP(c_List_Omap(U_20115,U_20116),U_20117),hAPP(c_List_Ofilter(U_20115,U_20118),U_20119)) = c_List_Omap__filter(U_20115,U_20116,hAPP(hAPP(c_COMBC(U_20115,tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116)),hAPP(hAPP(c_COMBS(U_20115,tc_Option_Ooption(U_20116),tc_fun(tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20116),tc_fun(tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116))),U_20115),c_If(tc_Option_Ooption(U_20116))),U_20118)),hAPP(hAPP(c_COMBB(U_20116,tc_Option_Ooption(U_20116),U_20115),c_Option_Ooption_OSome(U_20116)),U_20117))),c_Option_Ooption_ONone(U_20116)),U_20119),
    inference(variable_rename,[status(thm)],[f_4810_1]) ).

fof(f_4810_3,plain,
    ! [U_20115,U_20116,U_20117,U_20118,U_20119] : hAPP(hAPP(c_List_Omap(U_20115,U_20116),U_20117),hAPP(c_List_Ofilter(U_20115,U_20118),U_20119)) = c_List_Omap__filter(U_20115,U_20116,hAPP(hAPP(c_COMBC(U_20115,tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116)),hAPP(hAPP(c_COMBS(U_20115,tc_Option_Ooption(U_20116),tc_fun(tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20116),tc_fun(tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116))),U_20115),c_If(tc_Option_Ooption(U_20116))),U_20118)),hAPP(hAPP(c_COMBB(U_20116,tc_Option_Ooption(U_20116),U_20115),c_Option_Ooption_OSome(U_20116)),U_20117))),c_Option_Ooption_ONone(U_20116)),U_20119),
    inference(definitional_conversion,[status(esa)],[f_4810_2]) ).

cnf(f_4810_4,plain,
    hAPP(hAPP(c_List_Omap(U_20115,U_20116),U_20117),hAPP(c_List_Ofilter(U_20115,U_20118),U_20119)) = c_List_Omap__filter(U_20115,U_20116,hAPP(hAPP(c_COMBC(U_20115,tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116)),hAPP(hAPP(c_COMBS(U_20115,tc_Option_Ooption(U_20116),tc_fun(tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20116),tc_fun(tc_Option_Ooption(U_20116),tc_Option_Ooption(U_20116))),U_20115),c_If(tc_Option_Ooption(U_20116))),U_20118)),hAPP(hAPP(c_COMBB(U_20116,tc_Option_Ooption(U_20116),U_20115),c_Option_Ooption_OSome(U_20116)),U_20117))),c_Option_Ooption_ONone(U_20116)),U_20119),
    inference(clausify,[status(thm)],[f_4810_3]) ).

fof(f_4811_1,plain,
    ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2
      | hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) != V_a_2
      | ~ c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key__remove1]) ).

fof(f_4811_2,plain,
    ! [U_20124,U_20123,U_20122,U_20121,U_20120] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20121,U_20120,U_20124),U_20122),c_List_Oremove1(U_20121,U_20122,U_20123)) = U_20123
      | hAPP(c_List_Ohd(U_20121),hAPP(c_List_Ofilter(U_20121,hAPP(hAPP(c_COMBB(U_20120,tc_HOL_Obool,U_20121),hAPP(c_fequal,hAPP(U_20124,U_20122))),U_20124)),U_20123)) != U_20122
      | ~ c_List_Olinorder__class_Osorted(U_20120,hAPP(hAPP(c_List_Omap(U_20121,U_20120),U_20124),U_20123))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20121),U_20122),hAPP(c_List_Oset(U_20121),U_20123)))
      | ~ class_Orderings_Olinorder(U_20120) ),
    inference(variable_rename,[status(thm)],[f_4811_1]) ).

fof(f_4811_3,plain,
    ! [U_20120,U_20121,U_20122,U_20123,U_20124] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20121,U_20120,U_20124),U_20122),c_List_Oremove1(U_20121,U_20122,U_20123)) = U_20123
      | hAPP(c_List_Ohd(U_20121),hAPP(c_List_Ofilter(U_20121,hAPP(hAPP(c_COMBB(U_20120,tc_HOL_Obool,U_20121),hAPP(c_fequal,hAPP(U_20124,U_20122))),U_20124)),U_20123)) != U_20122
      | ~ c_List_Olinorder__class_Osorted(U_20120,hAPP(hAPP(c_List_Omap(U_20121,U_20120),U_20124),U_20123))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20121),U_20122),hAPP(c_List_Oset(U_20121),U_20123)))
      | ~ class_Orderings_Olinorder(U_20120) ),
    inference(definitional_conversion,[status(esa)],[f_4811_2]) ).

cnf(f_4811_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20121,U_20120,U_20124),U_20122),c_List_Oremove1(U_20121,U_20122,U_20123)) = U_20123
    | hAPP(c_List_Ohd(U_20121),hAPP(c_List_Ofilter(U_20121,hAPP(hAPP(c_COMBB(U_20120,tc_HOL_Obool,U_20121),hAPP(c_fequal,hAPP(U_20124,U_20122))),U_20124)),U_20123)) != U_20122
    | ~ c_List_Olinorder__class_Osorted(U_20120,hAPP(hAPP(c_List_Omap(U_20121,U_20120),U_20124),U_20123))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20121),U_20122),hAPP(c_List_Oset(U_20121),U_20123)))
    | ~ class_Orderings_Olinorder(U_20120) ),
    inference(clausify,[status(thm)],[f_4811_3]) ).

fof(f_4812_1,plain,
    ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_sublist__def]) ).

fof(f_4812_2,plain,
    ! [U_20127,U_20126,U_20125] : c_List_Osublist(U_20125,U_20126,U_20127) = hAPP(hAPP(c_List_Omap(tc_prod(U_20125,tc_Nat_Onat),U_20125),c_Product__Type_Ofst(U_20125,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20125,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20125,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20125,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20125,tc_Nat_Onat))),U_20127)),hAPP(hAPP(c_List_Ozip(U_20125,tc_Nat_Onat),U_20126),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20125)),U_20126))))),
    inference(variable_rename,[status(thm)],[f_4812_1]) ).

fof(f_4812_3,plain,
    ! [U_20125,U_20126,U_20127] : c_List_Osublist(U_20125,U_20126,U_20127) = hAPP(hAPP(c_List_Omap(tc_prod(U_20125,tc_Nat_Onat),U_20125),c_Product__Type_Ofst(U_20125,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20125,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20125,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20125,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20125,tc_Nat_Onat))),U_20127)),hAPP(hAPP(c_List_Ozip(U_20125,tc_Nat_Onat),U_20126),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20125)),U_20126))))),
    inference(definitional_conversion,[status(esa)],[f_4812_2]) ).

cnf(f_4812_4,plain,
    c_List_Osublist(U_20125,U_20126,U_20127) = hAPP(hAPP(c_List_Omap(tc_prod(U_20125,tc_Nat_Onat),U_20125),c_Product__Type_Ofst(U_20125,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20125,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20125,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20125,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20125,tc_Nat_Onat))),U_20127)),hAPP(hAPP(c_List_Ozip(U_20125,tc_Nat_Onat),U_20126),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20125)),U_20126))))),
    inference(clausify,[status(thm)],[f_4812_3]) ).

fof(f_4813_1,plain,
    ! [T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_ONil]) ).

fof(f_4813_2,plain,
    ! [U_20128] :
      ( c_List_Olinorder__class_Osorted(U_20128,c_List_Olist_ONil(U_20128))
      | ~ class_Orderings_Olinorder(U_20128) ),
    inference(variable_rename,[status(thm)],[f_4813_1]) ).

fof(f_4813_3,plain,
    ! [U_20128] :
      ( c_List_Olinorder__class_Osorted(U_20128,c_List_Olist_ONil(U_20128))
      | ~ class_Orderings_Olinorder(U_20128) ),
    inference(definitional_conversion,[status(esa)],[f_4813_2]) ).

cnf(f_4813_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20128,c_List_Olist_ONil(U_20128))
    | ~ class_Orderings_Olinorder(U_20128) ),
    inference(clausify,[status(thm)],[f_4813_3]) ).

fof(f_4814_1,plain,
    ! [V_x,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__single]) ).

fof(f_4814_2,plain,
    ! [U_20130,U_20129] :
      ( c_List_Olinorder__class_Osorted(U_20129,hAPP(hAPP(c_List_Olist_OCons(U_20129),U_20130),c_List_Olist_ONil(U_20129)))
      | ~ class_Orderings_Olinorder(U_20129) ),
    inference(variable_rename,[status(thm)],[f_4814_1]) ).

fof(f_4814_3,plain,
    ! [U_20129,U_20130] :
      ( c_List_Olinorder__class_Osorted(U_20129,hAPP(hAPP(c_List_Olist_OCons(U_20129),U_20130),c_List_Olist_ONil(U_20129)))
      | ~ class_Orderings_Olinorder(U_20129) ),
    inference(definitional_conversion,[status(esa)],[f_4814_2]) ).

cnf(f_4814_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20129,hAPP(hAPP(c_List_Olist_OCons(U_20129),U_20130),c_List_Olist_ONil(U_20129)))
    | ~ class_Orderings_Olinorder(U_20129) ),
    inference(clausify,[status(thm)],[f_4814_3]) ).

fof(f_4815_1,plain,
    ! [V_xs_2,V_g_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__same]) ).

fof(f_4815_2,plain,
    ! [U_20133,U_20132,U_20131] :
      ( c_List_Olinorder__class_Osorted(U_20131,hAPP(c_List_Ofilter(U_20131,hAPP(hAPP(c_COMBC(U_20131,U_20131,tc_HOL_Obool),c_fequal),hAPP(U_20132,U_20133))),U_20133))
      | ~ class_Orderings_Olinorder(U_20131) ),
    inference(variable_rename,[status(thm)],[f_4815_1]) ).

fof(f_4815_3,plain,
    ! [U_20131,U_20132,U_20133] :
      ( c_List_Olinorder__class_Osorted(U_20131,hAPP(c_List_Ofilter(U_20131,hAPP(hAPP(c_COMBC(U_20131,U_20131,tc_HOL_Obool),c_fequal),hAPP(U_20132,U_20133))),U_20133))
      | ~ class_Orderings_Olinorder(U_20131) ),
    inference(definitional_conversion,[status(esa)],[f_4815_2]) ).

cnf(f_4815_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20131,hAPP(c_List_Ofilter(U_20131,hAPP(hAPP(c_COMBC(U_20131,U_20131,tc_HOL_Obool),c_fequal),hAPP(U_20132,U_20133))),U_20133))
    | ~ class_Orderings_Olinorder(U_20131) ),
    inference(clausify,[status(thm)],[f_4815_3]) ).

fof(f_4816_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__map__same]) ).

fof(f_4816_2,plain,
    ! [U_20138,U_20137,U_20136,U_20135,U_20134] :
      ( c_List_Olinorder__class_Osorted(U_20134,hAPP(hAPP(c_List_Omap(U_20135,U_20134),U_20136),hAPP(c_List_Ofilter(U_20135,hAPP(hAPP(c_COMBC(U_20135,U_20134,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20134,tc_fun(U_20134,tc_HOL_Obool),U_20135),c_fequal),U_20136)),hAPP(U_20137,U_20138))),U_20138)))
      | ~ class_Orderings_Olinorder(U_20134) ),
    inference(variable_rename,[status(thm)],[f_4816_1]) ).

fof(f_4816_3,plain,
    ! [U_20134,U_20135,U_20136,U_20137,U_20138] :
      ( c_List_Olinorder__class_Osorted(U_20134,hAPP(hAPP(c_List_Omap(U_20135,U_20134),U_20136),hAPP(c_List_Ofilter(U_20135,hAPP(hAPP(c_COMBC(U_20135,U_20134,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20134,tc_fun(U_20134,tc_HOL_Obool),U_20135),c_fequal),U_20136)),hAPP(U_20137,U_20138))),U_20138)))
      | ~ class_Orderings_Olinorder(U_20134) ),
    inference(definitional_conversion,[status(esa)],[f_4816_2]) ).

cnf(f_4816_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20134,hAPP(hAPP(c_List_Omap(U_20135,U_20134),U_20136),hAPP(c_List_Ofilter(U_20135,hAPP(hAPP(c_COMBC(U_20135,U_20134,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20134,tc_fun(U_20134,tc_HOL_Obool),U_20135),c_fequal),U_20136)),hAPP(U_20137,U_20138))),U_20138)))
    | ~ class_Orderings_Olinorder(U_20134) ),
    inference(clausify,[status(thm)],[f_4816_3]) ).

fof(f_4817_1,plain,
    ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__filter]) ).

fof(f_4817_2,plain,
    ! [U_20143,U_20142,U_20141,U_20140,U_20139] :
      ( c_List_Olinorder__class_Osorted(U_20139,hAPP(hAPP(c_List_Omap(U_20140,U_20139),U_20141),hAPP(c_List_Ofilter(U_20140,U_20143),U_20142)))
      | ~ c_List_Olinorder__class_Osorted(U_20139,hAPP(hAPP(c_List_Omap(U_20140,U_20139),U_20141),U_20142))
      | ~ class_Orderings_Olinorder(U_20139) ),
    inference(variable_rename,[status(thm)],[f_4817_1]) ).

fof(f_4817_3,plain,
    ! [U_20140,U_20139,U_20141,U_20142,U_20143] :
      ( c_List_Olinorder__class_Osorted(U_20139,hAPP(hAPP(c_List_Omap(U_20140,U_20139),U_20141),hAPP(c_List_Ofilter(U_20140,U_20143),U_20142)))
      | ~ c_List_Olinorder__class_Osorted(U_20139,hAPP(hAPP(c_List_Omap(U_20140,U_20139),U_20141),U_20142))
      | ~ class_Orderings_Olinorder(U_20139) ),
    inference(definitional_conversion,[status(esa)],[f_4817_2]) ).

cnf(f_4817_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20139,hAPP(hAPP(c_List_Omap(U_20140,U_20139),U_20141),hAPP(c_List_Ofilter(U_20140,U_20143),U_20142)))
    | ~ c_List_Olinorder__class_Osorted(U_20139,hAPP(hAPP(c_List_Omap(U_20140,U_20139),U_20141),U_20142))
    | ~ class_Orderings_Olinorder(U_20139) ),
    inference(clausify,[status(thm)],[f_4817_3]) ).

fof(f_4818_1,plain,
    ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i),
    inference(fof_nnf,[status(thm)],[fact_length__upt]) ).

fof(f_4818_2,plain,
    ! [U_20145,U_20144] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20144,U_20145)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20145),U_20144),
    inference(variable_rename,[status(thm)],[f_4818_1]) ).

fof(f_4818_3,plain,
    ! [U_20145,U_20144] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20144,U_20145)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20145),U_20144),
    inference(definitional_conversion,[status(esa)],[f_4818_2]) ).

cnf(f_4818_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20144,U_20145)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20145),U_20144),
    inference(clausify,[status(thm)],[f_4818_3]) ).

fof(f_4819_1,plain,
    ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
      ( ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) != V_xs_2
        | V_i_2 != V_x_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2
          & V_i_2 = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) )
        | c_List_Oupt(V_i_2,V_j_2) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv]) ).

fof(f_4819_2,plain,
    ! [U_20149,U_20148,U_20147,U_20146] :
      ( ( c_List_Oupt(U_20146,U_20147) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20148),U_20149)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20146),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20147) != U_20149
        | U_20146 != U_20148
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20146),U_20147)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20146),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20147) = U_20149
          & U_20146 = U_20148
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20146),U_20147)) )
        | c_List_Oupt(U_20146,U_20147) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20148),U_20149) ) ),
    inference(variable_rename,[status(thm)],[f_4819_1]) ).

fof(f_4819_3,plain,
    ( ! [U_20157,U_20155,U_20153,U_20151] :
        ( c_List_Oupt(U_20151,U_20153) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20155),U_20157)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20151),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20153) != U_20157
        | U_20151 != U_20155
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20151),U_20153)) )
    & ! [U_20156,U_20154,U_20152,U_20150] :
        ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20150),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20152) = U_20156
          & U_20150 = U_20154
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20150),U_20152)) )
        | c_List_Oupt(U_20150,U_20152) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20154),U_20156) ) ),
    inference(miniscope,[status(thm)],[f_4819_2]) ).

fof(f_4819_4,plain,
    ( ! [U_20152,U_20156,U_20150,U_20154] :
        ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20150),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20152) = U_20156
        | ~ sP1214(U_20152,U_20156,U_20150,U_20154) )
    & ! [U_20152,U_20156,U_20150,U_20154] :
        ( U_20150 = U_20154
        | ~ sP1214(U_20152,U_20156,U_20150,U_20154) )
    & ! [U_20152,U_20156,U_20150,U_20154] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20150),U_20152))
        | ~ sP1214(U_20152,U_20156,U_20150,U_20154) )
    & ! [U_20151,U_20157,U_20153,U_20155] :
        ( c_List_Oupt(U_20151,U_20153) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20155),U_20157)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20151),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20153) != U_20157
        | U_20151 != U_20155
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20151),U_20153)) )
    & ! [U_20152,U_20156,U_20150,U_20154] :
        ( sP1214(U_20152,U_20156,U_20150,U_20154)
        | c_List_Oupt(U_20150,U_20152) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20154),U_20156) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1214])],[f_4819_3]) ).

cnf(f_4819_5,plain,
    ( sP1214(U_20152,U_20156,U_20150,U_20154)
    | c_List_Oupt(U_20150,U_20152) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20154),U_20156) ),
    inference(clausify,[status(thm)],[f_4819_4]) ).

cnf(f_4819_6,plain,
    ( c_List_Oupt(U_20151,U_20153) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20155),U_20157)
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20151),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20153) != U_20157
    | U_20151 != U_20155
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20151),U_20153)) ),
    inference(clausify,[status(thm)],[f_4819_4]) ).

cnf(f_4819_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20150),U_20152))
    | ~ sP1214(U_20152,U_20156,U_20150,U_20154) ),
    inference(clausify,[status(thm)],[f_4819_4]) ).

cnf(f_4819_8,plain,
    ( U_20150 = U_20154
    | ~ sP1214(U_20152,U_20156,U_20150,U_20154) ),
    inference(clausify,[status(thm)],[f_4819_4]) ).

cnf(f_4819_9,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20150),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20152) = U_20156
    | ~ sP1214(U_20152,U_20156,U_20150,U_20154) ),
    inference(clausify,[status(thm)],[f_4819_4]) ).

fof(f_4820_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | V_xs = c_List_Olist_ONil(T_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__butlast]) ).

fof(f_4820_2,plain,
    ! [U_20159,U_20158] :
      ( c_List_Olinorder__class_Osorted(U_20158,c_List_Obutlast(U_20158,U_20159))
      | ~ c_List_Olinorder__class_Osorted(U_20158,U_20159)
      | U_20159 = c_List_Olist_ONil(U_20158)
      | ~ class_Orderings_Olinorder(U_20158) ),
    inference(variable_rename,[status(thm)],[f_4820_1]) ).

fof(f_4820_3,plain,
    ! [U_20159,U_20158] :
      ( c_List_Olinorder__class_Osorted(U_20158,c_List_Obutlast(U_20158,U_20159))
      | ~ c_List_Olinorder__class_Osorted(U_20158,U_20159)
      | U_20159 = c_List_Olist_ONil(U_20158)
      | ~ class_Orderings_Olinorder(U_20158) ),
    inference(definitional_conversion,[status(esa)],[f_4820_2]) ).

cnf(f_4820_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20158,c_List_Obutlast(U_20158,U_20159))
    | ~ c_List_Olinorder__class_Osorted(U_20158,U_20159)
    | U_20159 = c_List_Olist_ONil(U_20158)
    | ~ class_Orderings_Olinorder(U_20158) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

fof(f_4821_1,plain,
    ! [V_n,V_m] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__rec__number__of]) ).

fof(f_4821_2,plain,
    ! [U_20161,U_20160] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20161)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20161))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20161)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20160)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20161)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20161))) ) ),
    inference(variable_rename,[status(thm)],[f_4821_1]) ).

fof(f_4821_3,plain,
    ( ! [U_20165,U_20163] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20163),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20165)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20165))) )
    & ! [U_20164,U_20162] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164))) ) ),
    inference(miniscope,[status(thm)],[f_4821_2]) ).

fof(f_4821_4,plain,
    ( ! [U_20163,U_20165] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20163),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20165)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20165))) )
    & ! [U_20162,U_20164] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4821_3]) ).

cnf(f_4821_5,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20164))) ),
    inference(clausify,[status(thm)],[f_4821_4]) ).

cnf(f_4821_6,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20163),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20165)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20165))) ),
    inference(clausify,[status(thm)],[f_4821_4]) ).

fof(f_4822_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
          | ? [B_x] :
              ( ? [B_xa] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) )
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_b,V_ys_2)
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
        & ( ( ! [B_x] :
                ( ! [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
                    | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) )
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
            & c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__append]) ).

fof(f_4822_2,plain,
    ! [U_20172,U_20171,U_20170] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
          | ? [U_20169] :
              ( ? [U_20168] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),U_20169),U_20168))
                  & hBOOL(hAPP(hAPP(c_member(U_20170),U_20168),hAPP(c_List_Oset(U_20170),U_20172))) )
              & hBOOL(hAPP(hAPP(c_member(U_20170),U_20169),hAPP(c_List_Oset(U_20170),U_20171))) )
          | ~ c_List_Olinorder__class_Osorted(U_20170,U_20172)
          | ~ c_List_Olinorder__class_Osorted(U_20170,U_20171) )
        & ( ( ! [U_20167] :
                ( ! [U_20166] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),U_20167),U_20166))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20166),hAPP(c_List_Oset(U_20170),U_20172))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20167),hAPP(c_List_Oset(U_20170),U_20171))) )
            & c_List_Olinorder__class_Osorted(U_20170,U_20172)
            & c_List_Olinorder__class_Osorted(U_20170,U_20171) )
          | ~ c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172)) ) )
      | ~ class_Orderings_Olinorder(U_20170) ),
    inference(variable_rename,[status(thm)],[f_4822_1]) ).

fof(f_4822_3,plain,
    ! [U_20172,U_20171,U_20170] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
          | ( ? [U_20168] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),sK497(U_20172,U_20171,U_20170)),U_20168))
                & hBOOL(hAPP(hAPP(c_member(U_20170),U_20168),hAPP(c_List_Oset(U_20170),U_20172))) )
            & hBOOL(hAPP(hAPP(c_member(U_20170),sK497(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20171))) )
          | ~ c_List_Olinorder__class_Osorted(U_20170,U_20172)
          | ~ c_List_Olinorder__class_Osorted(U_20170,U_20171) )
        & ( ( ! [U_20167] :
                ( ! [U_20166] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),U_20167),U_20166))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20166),hAPP(c_List_Oset(U_20170),U_20172))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20167),hAPP(c_List_Oset(U_20170),U_20171))) )
            & c_List_Olinorder__class_Osorted(U_20170,U_20172)
            & c_List_Olinorder__class_Osorted(U_20170,U_20171) )
          | ~ c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172)) ) )
      | ~ class_Orderings_Olinorder(U_20170) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_20169,sK497(U_20172,U_20171,U_20170))],[f_4822_2]) ).

fof(f_4822_4,plain,
    ! [U_20172,U_20171,U_20170] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),sK497(U_20172,U_20171,U_20170)),sK498(U_20172,U_20171,U_20170)))
            & hBOOL(hAPP(hAPP(c_member(U_20170),sK498(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20172)))
            & hBOOL(hAPP(hAPP(c_member(U_20170),sK497(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20171))) )
          | ~ c_List_Olinorder__class_Osorted(U_20170,U_20172)
          | ~ c_List_Olinorder__class_Osorted(U_20170,U_20171) )
        & ( ( ! [U_20167] :
                ( ! [U_20166] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),U_20167),U_20166))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20166),hAPP(c_List_Oset(U_20170),U_20172))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20167),hAPP(c_List_Oset(U_20170),U_20171))) )
            & c_List_Olinorder__class_Osorted(U_20170,U_20172)
            & c_List_Olinorder__class_Osorted(U_20170,U_20171) )
          | ~ c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172)) ) )
      | ~ class_Orderings_Olinorder(U_20170) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_20168,sK498(U_20172,U_20171,U_20170))],[f_4822_3]) ).

fof(f_4822_5,plain,
    ( ! [U_20170,U_20171,U_20172] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),sK497(U_20172,U_20171,U_20170)),sK498(U_20172,U_20171,U_20170)))
        | ~ sP1216(U_20170,U_20171,U_20172) )
    & ! [U_20170,U_20171,U_20172] :
        ( hBOOL(hAPP(hAPP(c_member(U_20170),sK498(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20172)))
        | ~ sP1216(U_20170,U_20171,U_20172) )
    & ! [U_20170,U_20171,U_20172] :
        ( hBOOL(hAPP(hAPP(c_member(U_20170),sK497(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20171)))
        | ~ sP1216(U_20170,U_20171,U_20172) )
    & ! [U_20166,U_20167,U_20170,U_20171,U_20172] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),U_20167),U_20166))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20166),hAPP(c_List_Oset(U_20170),U_20172)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20167),hAPP(c_List_Oset(U_20170),U_20171)))
        | ~ sP1215(U_20166,U_20167,U_20170,U_20171,U_20172) )
    & ! [U_20166,U_20167,U_20170,U_20171,U_20172] :
        ( c_List_Olinorder__class_Osorted(U_20170,U_20172)
        | ~ sP1215(U_20166,U_20167,U_20170,U_20171,U_20172) )
    & ! [U_20166,U_20167,U_20170,U_20171,U_20172] :
        ( c_List_Olinorder__class_Osorted(U_20170,U_20171)
        | ~ sP1215(U_20166,U_20167,U_20170,U_20171,U_20172) )
    & ! [U_20166,U_20167,U_20170,U_20171,U_20172] :
        ( c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
        | sP1216(U_20170,U_20171,U_20172)
        | ~ c_List_Olinorder__class_Osorted(U_20170,U_20172)
        | ~ c_List_Olinorder__class_Osorted(U_20170,U_20171)
        | ~ sP1217(U_20166,U_20167,U_20170,U_20171,U_20172) )
    & ! [U_20166,U_20167,U_20170,U_20171,U_20172] :
        ( sP1215(U_20166,U_20167,U_20170,U_20171,U_20172)
        | ~ c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
        | ~ sP1217(U_20166,U_20167,U_20170,U_20171,U_20172) )
    & ! [U_20166,U_20167,U_20170,U_20171,U_20172] :
        ( sP1217(U_20166,U_20167,U_20170,U_20171,U_20172)
        | ~ class_Orderings_Olinorder(U_20170) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1215,sP1216,sP1217])],[f_4822_4]) ).

cnf(f_4822_6,plain,
    ( sP1217(U_20166,U_20167,U_20170,U_20171,U_20172)
    | ~ class_Orderings_Olinorder(U_20170) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_7,plain,
    ( sP1215(U_20166,U_20167,U_20170,U_20171,U_20172)
    | ~ c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
    | ~ sP1217(U_20166,U_20167,U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20170,hAPP(hAPP(c_List_Oappend(U_20170),U_20171),U_20172))
    | sP1216(U_20170,U_20171,U_20172)
    | ~ c_List_Olinorder__class_Osorted(U_20170,U_20172)
    | ~ c_List_Olinorder__class_Osorted(U_20170,U_20171)
    | ~ sP1217(U_20166,U_20167,U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_9,plain,
    ( c_List_Olinorder__class_Osorted(U_20170,U_20171)
    | ~ sP1215(U_20166,U_20167,U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_10,plain,
    ( c_List_Olinorder__class_Osorted(U_20170,U_20172)
    | ~ sP1215(U_20166,U_20167,U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),U_20167),U_20166))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20166),hAPP(c_List_Oset(U_20170),U_20172)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20170),U_20167),hAPP(c_List_Oset(U_20170),U_20171)))
    | ~ sP1215(U_20166,U_20167,U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20170),sK497(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20171)))
    | ~ sP1216(U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20170),sK498(U_20172,U_20171,U_20170)),hAPP(c_List_Oset(U_20170),U_20172)))
    | ~ sP1216(U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

cnf(f_4822_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20170),sK497(U_20172,U_20171,U_20170)),sK498(U_20172,U_20171,U_20170)))
    | ~ sP1216(U_20170,U_20171,U_20172) ),
    inference(clausify,[status(thm)],[f_4822_5]) ).

fof(f_4823_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
        & ( ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__Cons]) ).

fof(f_4823_2,plain,
    ! [U_20177,U_20176,U_20175] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177))
          | ? [U_20174] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),U_20174))
              & hBOOL(hAPP(hAPP(c_member(U_20175),U_20174),hAPP(c_List_Oset(U_20175),U_20177))) )
          | ~ c_List_Olinorder__class_Osorted(U_20175,U_20177) )
        & ( ( ! [U_20173] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),U_20173))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20175),U_20173),hAPP(c_List_Oset(U_20175),U_20177))) )
            & c_List_Olinorder__class_Osorted(U_20175,U_20177) )
          | ~ c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177)) ) )
      | ~ class_Orderings_Olinorder(U_20175) ),
    inference(variable_rename,[status(thm)],[f_4823_1]) ).

fof(f_4823_3,plain,
    ! [U_20177,U_20176,U_20175] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),sK499(U_20177,U_20176,U_20175)))
            & hBOOL(hAPP(hAPP(c_member(U_20175),sK499(U_20177,U_20176,U_20175)),hAPP(c_List_Oset(U_20175),U_20177))) )
          | ~ c_List_Olinorder__class_Osorted(U_20175,U_20177) )
        & ( ( ! [U_20173] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),U_20173))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20175),U_20173),hAPP(c_List_Oset(U_20175),U_20177))) )
            & c_List_Olinorder__class_Osorted(U_20175,U_20177) )
          | ~ c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177)) ) )
      | ~ class_Orderings_Olinorder(U_20175) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_20174,sK499(U_20177,U_20176,U_20175))],[f_4823_2]) ).

fof(f_4823_4,plain,
    ( ! [U_20176,U_20175,U_20177] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),sK499(U_20177,U_20176,U_20175)))
        | ~ sP1219(U_20176,U_20175,U_20177) )
    & ! [U_20176,U_20175,U_20177] :
        ( hBOOL(hAPP(hAPP(c_member(U_20175),sK499(U_20177,U_20176,U_20175)),hAPP(c_List_Oset(U_20175),U_20177)))
        | ~ sP1219(U_20176,U_20175,U_20177) )
    & ! [U_20176,U_20173,U_20175,U_20177] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),U_20173))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20175),U_20173),hAPP(c_List_Oset(U_20175),U_20177)))
        | ~ sP1218(U_20176,U_20173,U_20175,U_20177) )
    & ! [U_20176,U_20173,U_20175,U_20177] :
        ( c_List_Olinorder__class_Osorted(U_20175,U_20177)
        | ~ sP1218(U_20176,U_20173,U_20175,U_20177) )
    & ! [U_20176,U_20173,U_20175,U_20177] :
        ( c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177))
        | sP1219(U_20176,U_20175,U_20177)
        | ~ c_List_Olinorder__class_Osorted(U_20175,U_20177)
        | ~ sP1220(U_20176,U_20173,U_20175,U_20177) )
    & ! [U_20176,U_20173,U_20175,U_20177] :
        ( sP1218(U_20176,U_20173,U_20175,U_20177)
        | ~ c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177))
        | ~ sP1220(U_20176,U_20173,U_20175,U_20177) )
    & ! [U_20176,U_20173,U_20175,U_20177] :
        ( sP1220(U_20176,U_20173,U_20175,U_20177)
        | ~ class_Orderings_Olinorder(U_20175) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1218,sP1219,sP1220])],[f_4823_3]) ).

cnf(f_4823_5,plain,
    ( sP1220(U_20176,U_20173,U_20175,U_20177)
    | ~ class_Orderings_Olinorder(U_20175) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

cnf(f_4823_6,plain,
    ( sP1218(U_20176,U_20173,U_20175,U_20177)
    | ~ c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177))
    | ~ sP1220(U_20176,U_20173,U_20175,U_20177) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

cnf(f_4823_7,plain,
    ( c_List_Olinorder__class_Osorted(U_20175,hAPP(hAPP(c_List_Olist_OCons(U_20175),U_20176),U_20177))
    | sP1219(U_20176,U_20175,U_20177)
    | ~ c_List_Olinorder__class_Osorted(U_20175,U_20177)
    | ~ sP1220(U_20176,U_20173,U_20175,U_20177) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

cnf(f_4823_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20175,U_20177)
    | ~ sP1218(U_20176,U_20173,U_20175,U_20177) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

cnf(f_4823_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),U_20173))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20175),U_20173),hAPP(c_List_Oset(U_20175),U_20177)))
    | ~ sP1218(U_20176,U_20173,U_20175,U_20177) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

cnf(f_4823_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20175),sK499(U_20177,U_20176,U_20175)),hAPP(c_List_Oset(U_20175),U_20177)))
    | ~ sP1219(U_20176,U_20175,U_20177) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

cnf(f_4823_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20175),U_20176),sK499(U_20177,U_20176,U_20175)))
    | ~ sP1219(U_20176,U_20175,U_20177) ),
    inference(clausify,[status(thm)],[f_4823_4]) ).

fof(f_4824_1,plain,
    ! [V_j,V_i] :
      ( ( c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) )
      & ( c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__Suc]) ).

fof(f_4824_2,plain,
    ! [U_20179,U_20178] :
      ( ( c_List_Oupt(U_20178,hAPP(c_Nat_OSuc,U_20179)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20178),U_20179)) )
      & ( c_List_Oupt(U_20178,hAPP(c_Nat_OSuc,U_20179)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20178,U_20179)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20179),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20178),U_20179)) ) ),
    inference(variable_rename,[status(thm)],[f_4824_1]) ).

fof(f_4824_3,plain,
    ( ! [U_20183,U_20181] :
        ( c_List_Oupt(U_20181,hAPP(c_Nat_OSuc,U_20183)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20181),U_20183)) )
    & ! [U_20182,U_20180] :
        ( c_List_Oupt(U_20180,hAPP(c_Nat_OSuc,U_20182)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20180,U_20182)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20182),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20180),U_20182)) ) ),
    inference(miniscope,[status(thm)],[f_4824_2]) ).

fof(f_4824_4,plain,
    ( ! [U_20183,U_20181] :
        ( c_List_Oupt(U_20181,hAPP(c_Nat_OSuc,U_20183)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20181),U_20183)) )
    & ! [U_20180,U_20182] :
        ( c_List_Oupt(U_20180,hAPP(c_Nat_OSuc,U_20182)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20180,U_20182)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20182),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20180),U_20182)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4824_3]) ).

cnf(f_4824_5,plain,
    ( c_List_Oupt(U_20180,hAPP(c_Nat_OSuc,U_20182)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20180,U_20182)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20182),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20180),U_20182)) ),
    inference(clausify,[status(thm)],[f_4824_4]) ).

cnf(f_4824_6,plain,
    ( c_List_Oupt(U_20181,hAPP(c_Nat_OSuc,U_20183)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20181),U_20183)) ),
    inference(clausify,[status(thm)],[f_4824_4]) ).

fof(f_4825_1,plain,
    ! [V_j,V_i] :
      ( c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__Suc__append]) ).

fof(f_4825_2,plain,
    ! [U_20185,U_20184] :
      ( c_List_Oupt(U_20184,hAPP(c_Nat_OSuc,U_20185)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20184,U_20185)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20185),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20184),U_20185)) ),
    inference(variable_rename,[status(thm)],[f_4825_1]) ).

fof(f_4825_3,plain,
    ! [U_20185,U_20184] :
      ( c_List_Oupt(U_20184,hAPP(c_Nat_OSuc,U_20185)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20184,U_20185)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20185),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20184),U_20185)) ),
    inference(definitional_conversion,[status(esa)],[f_4825_2]) ).

cnf(f_4825_4,plain,
    ( c_List_Oupt(U_20184,hAPP(c_Nat_OSuc,U_20185)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20184,U_20185)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20185),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20184),U_20185)) ),
    inference(clausify,[status(thm)],[f_4825_3]) ).

fof(f_4826_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append]) ).

fof(f_4826_2,plain,
    ! [U_20188,U_20187,U_20186] :
      ( c_List_Oupt(U_20186,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20187),U_20188)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20186,U_20187)),c_List_Oupt(U_20187,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20187),U_20188)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20186),U_20187)) ),
    inference(variable_rename,[status(thm)],[f_4826_1]) ).

fof(f_4826_3,plain,
    ! [U_20186,U_20187,U_20188] :
      ( c_List_Oupt(U_20186,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20187),U_20188)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20186,U_20187)),c_List_Oupt(U_20187,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20187),U_20188)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20186),U_20187)) ),
    inference(definitional_conversion,[status(esa)],[f_4826_2]) ).

cnf(f_4826_4,plain,
    ( c_List_Oupt(U_20186,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20187),U_20188)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20186,U_20187)),c_List_Oupt(U_20187,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20187),U_20188)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20186),U_20187)) ),
    inference(clausify,[status(thm)],[f_4826_3]) ).

fof(f_4827_1,plain,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__many__eq]) ).

fof(f_4827_2,plain,
    ! [U_20192,U_20191,U_20190,U_20189] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20190),hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192)))
          | ~ c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20189),U_20190),U_20191)) )
        & ( ( c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20189),U_20190),U_20191)) )
          | ~ c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20190),hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))) ) )
      | ~ class_Orderings_Olinorder(U_20189) ),
    inference(variable_rename,[status(thm)],[f_4827_1]) ).

fof(f_4827_3,plain,
    ( ! [U_20189,U_20190,U_20191,U_20192] :
        ( c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))
        | ~ sP1221(U_20189,U_20190,U_20191,U_20192) )
    & ! [U_20189,U_20190,U_20191,U_20192] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20189),U_20190),U_20191))
        | ~ sP1221(U_20189,U_20190,U_20191,U_20192) )
    & ! [U_20189,U_20190,U_20191,U_20192] :
        ( c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20190),hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192)))
        | ~ c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20189),U_20190),U_20191))
        | ~ sP1222(U_20189,U_20190,U_20191,U_20192) )
    & ! [U_20189,U_20190,U_20191,U_20192] :
        ( sP1221(U_20189,U_20190,U_20191,U_20192)
        | ~ c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20190),hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192)))
        | ~ sP1222(U_20189,U_20190,U_20191,U_20192) )
    & ! [U_20189,U_20190,U_20191,U_20192] :
        ( sP1222(U_20189,U_20190,U_20191,U_20192)
        | ~ class_Orderings_Olinorder(U_20189) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1221,sP1222])],[f_4827_2]) ).

cnf(f_4827_4,plain,
    ( sP1222(U_20189,U_20190,U_20191,U_20192)
    | ~ class_Orderings_Olinorder(U_20189) ),
    inference(clausify,[status(thm)],[f_4827_3]) ).

cnf(f_4827_5,plain,
    ( sP1221(U_20189,U_20190,U_20191,U_20192)
    | ~ c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20190),hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192)))
    | ~ sP1222(U_20189,U_20190,U_20191,U_20192) ),
    inference(clausify,[status(thm)],[f_4827_3]) ).

cnf(f_4827_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20190),hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192)))
    | ~ c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20189),U_20190),U_20191))
    | ~ sP1222(U_20189,U_20190,U_20191,U_20192) ),
    inference(clausify,[status(thm)],[f_4827_3]) ).

cnf(f_4827_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20189),U_20190),U_20191))
    | ~ sP1221(U_20189,U_20190,U_20191,U_20192) ),
    inference(clausify,[status(thm)],[f_4827_3]) ).

cnf(f_4827_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20189,hAPP(hAPP(c_List_Olist_OCons(U_20189),U_20191),U_20192))
    | ~ sP1221(U_20189,U_20190,U_20191,U_20192) ),
    inference(clausify,[status(thm)],[f_4827_3]) ).

fof(f_4828_1,plain,
    ! [V_zs,V_y,V_x,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__many]) ).

fof(f_4828_2,plain,
    ! [U_20196,U_20195,U_20194,U_20193] :
      ( c_List_Olinorder__class_Osorted(U_20193,hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20194),hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20195),U_20196)))
      | ~ c_List_Olinorder__class_Osorted(U_20193,hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20195),U_20196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20193),U_20194),U_20195))
      | ~ class_Orderings_Olinorder(U_20193) ),
    inference(variable_rename,[status(thm)],[f_4828_1]) ).

fof(f_4828_3,plain,
    ! [U_20195,U_20196,U_20194,U_20193] :
      ( c_List_Olinorder__class_Osorted(U_20193,hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20194),hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20195),U_20196)))
      | ~ c_List_Olinorder__class_Osorted(U_20193,hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20195),U_20196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20193),U_20194),U_20195))
      | ~ class_Orderings_Olinorder(U_20193) ),
    inference(definitional_conversion,[status(esa)],[f_4828_2]) ).

cnf(f_4828_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20193,hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20194),hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20195),U_20196)))
    | ~ c_List_Olinorder__class_Osorted(U_20193,hAPP(hAPP(c_List_Olist_OCons(U_20193),U_20195),U_20196))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20193),U_20194),U_20195))
    | ~ class_Orderings_Olinorder(U_20193) ),
    inference(clausify,[status(thm)],[f_4828_3]) ).

fof(f_4829_1,plain,
    ! [V_n,V_m,V_i] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_take__upt]) ).

fof(f_4829_2,plain,
    ! [U_20199,U_20198,U_20197] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20198),c_List_Oupt(U_20197,U_20199)) = c_List_Oupt(U_20197,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20197),U_20198))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20197),U_20198)),U_20199)) ),
    inference(variable_rename,[status(thm)],[f_4829_1]) ).

fof(f_4829_3,plain,
    ! [U_20198,U_20197,U_20199] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20198),c_List_Oupt(U_20197,U_20199)) = c_List_Oupt(U_20197,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20197),U_20198))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20197),U_20198)),U_20199)) ),
    inference(definitional_conversion,[status(esa)],[f_4829_2]) ).

cnf(f_4829_4,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20198),c_List_Oupt(U_20197,U_20199)) = c_List_Oupt(U_20197,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20197),U_20198))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20197),U_20198)),U_20199)) ),
    inference(clausify,[status(thm)],[f_4829_3]) ).

fof(f_4830_1,plain,
    ! [V_j_2,V_i_2] :
      ( ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
          & V_j_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
        | V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(V_i_2,V_j_2) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv]) ).

fof(f_4830_2,plain,
    ! [U_20201,U_20200] :
      ( ( c_List_Oupt(U_20200,U_20201) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20201),U_20200))
          & U_20201 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20201),U_20200))
        | U_20201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20200,U_20201) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4830_1]) ).

fof(f_4830_3,plain,
    ( ! [U_20205,U_20203] :
        ( c_List_Oupt(U_20203,U_20205) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20205),U_20203))
          & U_20205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_20204,U_20202] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20204),U_20202))
        | U_20204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20202,U_20204) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4830_2]) ).

fof(f_4830_4,plain,
    ( ! [U_20203,U_20205] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20205),U_20203))
        | ~ sP1223(U_20203,U_20205) )
    & ! [U_20203,U_20205] :
        ( U_20205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1223(U_20203,U_20205) )
    & ! [U_20203,U_20205] :
        ( c_List_Oupt(U_20203,U_20205) = c_List_Olist_ONil(tc_Nat_Onat)
        | sP1223(U_20203,U_20205) )
    & ! [U_20204,U_20202] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20204),U_20202))
        | U_20204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20202,U_20204) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1223])],[f_4830_3]) ).

cnf(f_4830_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20204),U_20202))
    | U_20204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_20202,U_20204) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4830_4]) ).

cnf(f_4830_6,plain,
    ( c_List_Oupt(U_20203,U_20205) = c_List_Olist_ONil(tc_Nat_Onat)
    | sP1223(U_20203,U_20205) ),
    inference(clausify,[status(thm)],[f_4830_4]) ).

cnf(f_4830_7,plain,
    ( U_20205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1223(U_20203,U_20205) ),
    inference(clausify,[status(thm)],[f_4830_4]) ).

cnf(f_4830_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20205),U_20203))
    | ~ sP1223(U_20203,U_20205) ),
    inference(clausify,[status(thm)],[f_4830_4]) ).

fof(f_4831_1,plain,
    ! [V_i,V_j] :
      ( c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil]) ).

fof(f_4831_2,plain,
    ! [U_20207,U_20206] :
      ( c_List_Oupt(U_20207,U_20206) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20206),U_20207)) ),
    inference(variable_rename,[status(thm)],[f_4831_1]) ).

fof(f_4831_3,plain,
    ! [U_20206,U_20207] :
      ( c_List_Oupt(U_20207,U_20206) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20206),U_20207)) ),
    inference(definitional_conversion,[status(esa)],[f_4831_2]) ).

cnf(f_4831_4,plain,
    ( c_List_Oupt(U_20207,U_20206) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20206),U_20207)) ),
    inference(clausify,[status(thm)],[f_4831_3]) ).

fof(f_4832_1,plain,
    ! [V_n,V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__drop]) ).

fof(f_4832_2,plain,
    ! [U_20210,U_20209,U_20208] :
      ( c_List_Olinorder__class_Osorted(U_20208,hAPP(hAPP(c_List_Odrop(U_20208),U_20210),U_20209))
      | ~ c_List_Olinorder__class_Osorted(U_20208,U_20209)
      | ~ class_Orderings_Olinorder(U_20208) ),
    inference(variable_rename,[status(thm)],[f_4832_1]) ).

fof(f_4832_3,plain,
    ! [U_20209,U_20210,U_20208] :
      ( c_List_Olinorder__class_Osorted(U_20208,hAPP(hAPP(c_List_Odrop(U_20208),U_20210),U_20209))
      | ~ c_List_Olinorder__class_Osorted(U_20208,U_20209)
      | ~ class_Orderings_Olinorder(U_20208) ),
    inference(definitional_conversion,[status(esa)],[f_4832_2]) ).

cnf(f_4832_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20208,hAPP(hAPP(c_List_Odrop(U_20208),U_20210),U_20209))
    | ~ c_List_Olinorder__class_Osorted(U_20208,U_20209)
    | ~ class_Orderings_Olinorder(U_20208) ),
    inference(clausify,[status(thm)],[f_4832_3]) ).

fof(f_4833_1,plain,
    ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j),
    inference(fof_nnf,[status(thm)],[fact_drop__upt]) ).

fof(f_4833_2,plain,
    ! [U_20213,U_20212,U_20211] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20211),c_List_Oupt(U_20212,U_20213)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20212),U_20211),U_20213),
    inference(variable_rename,[status(thm)],[f_4833_1]) ).

fof(f_4833_3,plain,
    ! [U_20211,U_20212,U_20213] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20211),c_List_Oupt(U_20212,U_20213)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20212),U_20211),U_20213),
    inference(definitional_conversion,[status(esa)],[f_4833_2]) ).

cnf(f_4833_4,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20211),c_List_Oupt(U_20212,U_20213)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20212),U_20211),U_20213),
    inference(clausify,[status(thm)],[f_4833_3]) ).

fof(f_4834_1,plain,
    ! [V_j,V_i] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_hd__upt]) ).

fof(f_4834_2,plain,
    ! [U_20215,U_20214] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20214,U_20215)) = U_20214
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20214),U_20215)) ),
    inference(variable_rename,[status(thm)],[f_4834_1]) ).

fof(f_4834_3,plain,
    ! [U_20214,U_20215] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20214,U_20215)) = U_20214
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20214),U_20215)) ),
    inference(definitional_conversion,[status(esa)],[f_4834_2]) ).

cnf(f_4834_4,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20214,U_20215)) = U_20214
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20214),U_20215)) ),
    inference(clausify,[status(thm)],[f_4834_3]) ).

fof(f_4835_1,plain,
    ! [T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J]) ).

fof(f_4835_2,plain,
    ! [U_20216] :
      ( c_List_Olinorder__class_Osorted(U_20216,c_List_Olist_ONil(U_20216))
      | ~ class_Orderings_Olinorder(U_20216) ),
    inference(variable_rename,[status(thm)],[f_4835_1]) ).

fof(f_4835_3,plain,
    ! [U_20216] :
      ( c_List_Olinorder__class_Osorted(U_20216,c_List_Olist_ONil(U_20216))
      | ~ class_Orderings_Olinorder(U_20216) ),
    inference(definitional_conversion,[status(esa)],[f_4835_2]) ).

cnf(f_4835_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20216,c_List_Olist_ONil(U_20216))
    | ~ class_Orderings_Olinorder(U_20216) ),
    inference(clausify,[status(thm)],[f_4835_3]) ).

fof(f_4836_1,plain,
    ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_upt__0]) ).

fof(f_4836_2,plain,
    ! [U_20217] : c_List_Oupt(U_20217,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4836_1]) ).

fof(f_4836_3,plain,
    ! [U_20217] : c_List_Oupt(U_20217,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4836_2]) ).

cnf(f_4836_4,plain,
    c_List_Oupt(U_20217,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4836_3]) ).

fof(f_4837_1,plain,
    ! [V_n,V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__take]) ).

fof(f_4837_2,plain,
    ! [U_20220,U_20219,U_20218] :
      ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Otake(U_20218),U_20220),U_20219))
      | ~ c_List_Olinorder__class_Osorted(U_20218,U_20219)
      | ~ class_Orderings_Olinorder(U_20218) ),
    inference(variable_rename,[status(thm)],[f_4837_1]) ).

fof(f_4837_3,plain,
    ! [U_20218,U_20219,U_20220] :
      ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Otake(U_20218),U_20220),U_20219))
      | ~ c_List_Olinorder__class_Osorted(U_20218,U_20219)
      | ~ class_Orderings_Olinorder(U_20218) ),
    inference(definitional_conversion,[status(esa)],[f_4837_2]) ).

cnf(f_4837_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Otake(U_20218),U_20220),U_20219))
    | ~ c_List_Olinorder__class_Osorted(U_20218,U_20219)
    | ~ class_Orderings_Olinorder(U_20218) ),
    inference(clausify,[status(thm)],[f_4837_3]) ).

fof(f_4838_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2),
    inference(fof_nnf,[status(thm)],[fact_set__upt]) ).

fof(f_4838_2,plain,
    ! [U_20222,U_20221] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20221,U_20222)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20221),U_20222),
    inference(variable_rename,[status(thm)],[f_4838_1]) ).

fof(f_4838_3,plain,
    ! [U_20222,U_20221] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20221,U_20222)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20221),U_20222),
    inference(definitional_conversion,[status(esa)],[f_4838_2]) ).

cnf(f_4838_4,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20221,U_20222)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20221),U_20222),
    inference(clausify,[status(thm)],[f_4838_3]) ).

fof(f_4839_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__upt]) ).

fof(f_4839_2,plain,
    ! [U_20224,U_20223] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20223),U_20224) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20223,U_20224)),
    inference(variable_rename,[status(thm)],[f_4839_1]) ).

fof(f_4839_3,plain,
    ! [U_20223,U_20224] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20223),U_20224) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20223,U_20224)),
    inference(definitional_conversion,[status(esa)],[f_4839_2]) ).

cnf(f_4839_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20223),U_20224) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20223,U_20224)),
    inference(clausify,[status(thm)],[f_4839_3]) ).

fof(f_4840_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_List_Oset(T_b),V_xs_2) != hAPP(c_List_Oset(T_b),V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique]) ).

fof(f_4840_2,plain,
    ! [U_20227,U_20226,U_20225] :
      ( U_20226 = U_20227
      | hAPP(c_List_Oset(U_20225),U_20226) != hAPP(c_List_Oset(U_20225),U_20227)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20225),U_20227))
      | ~ c_List_Olinorder__class_Osorted(U_20225,U_20227)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20225),U_20226))
      | ~ c_List_Olinorder__class_Osorted(U_20225,U_20226)
      | ~ class_Orderings_Olinorder(U_20225) ),
    inference(variable_rename,[status(thm)],[f_4840_1]) ).

fof(f_4840_3,plain,
    ! [U_20225,U_20226,U_20227] :
      ( U_20226 = U_20227
      | hAPP(c_List_Oset(U_20225),U_20226) != hAPP(c_List_Oset(U_20225),U_20227)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20225),U_20227))
      | ~ c_List_Olinorder__class_Osorted(U_20225,U_20227)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20225),U_20226))
      | ~ c_List_Olinorder__class_Osorted(U_20225,U_20226)
      | ~ class_Orderings_Olinorder(U_20225) ),
    inference(definitional_conversion,[status(esa)],[f_4840_2]) ).

cnf(f_4840_4,plain,
    ( U_20226 = U_20227
    | hAPP(c_List_Oset(U_20225),U_20226) != hAPP(c_List_Oset(U_20225),U_20227)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20225),U_20227))
    | ~ c_List_Olinorder__class_Osorted(U_20225,U_20227)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20225),U_20226))
    | ~ c_List_Olinorder__class_Osorted(U_20225,U_20226)
    | ~ class_Orderings_Olinorder(U_20225) ),
    inference(clausify,[status(thm)],[f_4840_3]) ).

fof(f_4841_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
        & ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort]) ).

fof(f_4841_2,plain,
    ! [U_20230,U_20229,U_20228] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20228,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20228,U_20228,c_COMBI(U_20228)),U_20229),U_20230))
          | ~ c_List_Olinorder__class_Osorted(U_20228,U_20230) )
        & ( c_List_Olinorder__class_Osorted(U_20228,U_20230)
          | ~ c_List_Olinorder__class_Osorted(U_20228,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20228,U_20228,c_COMBI(U_20228)),U_20229),U_20230)) ) )
      | ~ class_Orderings_Olinorder(U_20228) ),
    inference(variable_rename,[status(thm)],[f_4841_1]) ).

fof(f_4841_3,plain,
    ( ! [U_20228,U_20230,U_20229] :
        ( c_List_Olinorder__class_Osorted(U_20228,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20228,U_20228,c_COMBI(U_20228)),U_20229),U_20230))
        | ~ c_List_Olinorder__class_Osorted(U_20228,U_20230)
        | ~ sP1224(U_20228,U_20230,U_20229) )
    & ! [U_20228,U_20230,U_20229] :
        ( c_List_Olinorder__class_Osorted(U_20228,U_20230)
        | ~ c_List_Olinorder__class_Osorted(U_20228,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20228,U_20228,c_COMBI(U_20228)),U_20229),U_20230))
        | ~ sP1224(U_20228,U_20230,U_20229) )
    & ! [U_20228,U_20230,U_20229] :
        ( sP1224(U_20228,U_20230,U_20229)
        | ~ class_Orderings_Olinorder(U_20228) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1224])],[f_4841_2]) ).

cnf(f_4841_4,plain,
    ( sP1224(U_20228,U_20230,U_20229)
    | ~ class_Orderings_Olinorder(U_20228) ),
    inference(clausify,[status(thm)],[f_4841_3]) ).

cnf(f_4841_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20228,U_20230)
    | ~ c_List_Olinorder__class_Osorted(U_20228,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20228,U_20228,c_COMBI(U_20228)),U_20229),U_20230))
    | ~ sP1224(U_20228,U_20230,U_20229) ),
    inference(clausify,[status(thm)],[f_4841_3]) ).

cnf(f_4841_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20228,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20228,U_20228,c_COMBI(U_20228)),U_20229),U_20230))
    | ~ c_List_Olinorder__class_Osorted(U_20228,U_20230)
    | ~ sP1224(U_20228,U_20230,U_20229) ),
    inference(clausify,[status(thm)],[f_4841_3]) ).

fof(f_4842_1,plain,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))),
    inference(fof_nnf,[status(thm)],[fact_distinct__upt]) ).

fof(f_4842_2,plain,
    ! [U_20232,U_20231] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20231,U_20232))),
    inference(variable_rename,[status(thm)],[f_4842_1]) ).

fof(f_4842_3,plain,
    ! [U_20232,U_20231] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20231,U_20232))),
    inference(definitional_conversion,[status(esa)],[f_4842_2]) ).

cnf(f_4842_4,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20231,U_20232))),
    inference(clausify,[status(thm)],[f_4842_3]) ).

fof(f_4843_1,plain,
    ! [V_a,V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__remove1]) ).

fof(f_4843_2,plain,
    ! [U_20235,U_20234,U_20233] :
      ( c_List_Olinorder__class_Osorted(U_20233,c_List_Oremove1(U_20233,U_20235,U_20234))
      | ~ c_List_Olinorder__class_Osorted(U_20233,U_20234)
      | ~ class_Orderings_Olinorder(U_20233) ),
    inference(variable_rename,[status(thm)],[f_4843_1]) ).

fof(f_4843_3,plain,
    ! [U_20233,U_20234,U_20235] :
      ( c_List_Olinorder__class_Osorted(U_20233,c_List_Oremove1(U_20233,U_20235,U_20234))
      | ~ c_List_Olinorder__class_Osorted(U_20233,U_20234)
      | ~ class_Orderings_Olinorder(U_20233) ),
    inference(definitional_conversion,[status(esa)],[f_4843_2]) ).

cnf(f_4843_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20233,c_List_Oremove1(U_20233,U_20235,U_20234))
    | ~ c_List_Olinorder__class_Osorted(U_20233,U_20234)
    | ~ class_Orderings_Olinorder(U_20233) ),
    inference(clausify,[status(thm)],[f_4843_3]) ).

fof(f_4844_1,plain,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)),
    inference(fof_nnf,[status(thm)],[fact_sorted__upt]) ).

fof(f_4844_2,plain,
    ! [U_20237,U_20236] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20236,U_20237)),
    inference(variable_rename,[status(thm)],[f_4844_1]) ).

fof(f_4844_3,plain,
    ! [U_20237,U_20236] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20236,U_20237)),
    inference(definitional_conversion,[status(esa)],[f_4844_2]) ).

cnf(f_4844_4,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20236,U_20237)),
    inference(clausify,[status(thm)],[f_4844_3]) ).

fof(f_4845_1,plain,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)),
    inference(fof_nnf,[status(thm)],[fact_sorted__upto]) ).

fof(f_4845_2,plain,
    ! [U_20239,U_20238] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20238,U_20239)),
    inference(variable_rename,[status(thm)],[f_4845_1]) ).

fof(f_4845_3,plain,
    ! [U_20238,U_20239] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20238,U_20239)),
    inference(definitional_conversion,[status(esa)],[f_4845_2]) ).

cnf(f_4845_4,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20238,U_20239)),
    inference(clausify,[status(thm)],[f_4845_3]) ).

fof(f_4846_1,plain,
    ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__range]) ).

fof(f_4846_2,plain,
    ! [U_20241,U_20240] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20240),U_20241)) = c_List_Oupt(U_20240,U_20241),
    inference(variable_rename,[status(thm)],[f_4846_1]) ).

fof(f_4846_3,plain,
    ! [U_20240,U_20241] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20240),U_20241)) = c_List_Oupt(U_20240,U_20241),
    inference(definitional_conversion,[status(esa)],[f_4846_2]) ).

cnf(f_4846_4,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20240),U_20241)) = c_List_Oupt(U_20240,U_20241),
    inference(clausify,[status(thm)],[f_4846_3]) ).

fof(f_4847_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert]) ).

fof(f_4847_2,plain,
    ! [U_20244,U_20243,U_20242] :
      ( c_List_Olinorder__class_Osorted(U_20242,c_List_Olinorder__class_Oinsort__insert__key(U_20242,U_20242,c_COMBI(U_20242),U_20244,U_20243))
      | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243)
      | ~ class_Orderings_Olinorder(U_20242) ),
    inference(variable_rename,[status(thm)],[f_4847_1]) ).

fof(f_4847_3,plain,
    ! [U_20243,U_20242,U_20244] :
      ( c_List_Olinorder__class_Osorted(U_20242,c_List_Olinorder__class_Oinsort__insert__key(U_20242,U_20242,c_COMBI(U_20242),U_20244,U_20243))
      | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243)
      | ~ class_Orderings_Olinorder(U_20242) ),
    inference(definitional_conversion,[status(esa)],[f_4847_2]) ).

cnf(f_4847_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20242,c_List_Olinorder__class_Oinsort__insert__key(U_20242,U_20242,c_COMBI(U_20242),U_20244,U_20243))
    | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243)
    | ~ class_Orderings_Olinorder(U_20242) ),
    inference(clausify,[status(thm)],[f_4847_3]) ).

fof(f_4848_1,plain,
    ! [V_j,V_i] :
      ( c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons]) ).

fof(f_4848_2,plain,
    ! [U_20246,U_20245] :
      ( c_List_Oupt(U_20245,U_20246) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20245),c_List_Oupt(hAPP(c_Nat_OSuc,U_20245),U_20246))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20245),U_20246)) ),
    inference(variable_rename,[status(thm)],[f_4848_1]) ).

fof(f_4848_3,plain,
    ! [U_20245,U_20246] :
      ( c_List_Oupt(U_20245,U_20246) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20245),c_List_Oupt(hAPP(c_Nat_OSuc,U_20245),U_20246))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20245),U_20246)) ),
    inference(definitional_conversion,[status(esa)],[f_4848_2]) ).

cnf(f_4848_4,plain,
    ( c_List_Oupt(U_20245,U_20246) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20245),c_List_Oupt(hAPP(c_Nat_OSuc,U_20245),U_20246))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20245),U_20246)) ),
    inference(clausify,[status(thm)],[f_4848_3]) ).

fof(f_4849_1,plain,
    ! [V_j,V_i] :
      ( ( c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) )
      & ( c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__rec]) ).

fof(f_4849_2,plain,
    ! [U_20248,U_20247] :
      ( ( c_List_Oupt(U_20247,U_20248) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20247),U_20248)) )
      & ( c_List_Oupt(U_20247,U_20248) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20247),c_List_Oupt(hAPP(c_Nat_OSuc,U_20247),U_20248))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20247),U_20248)) ) ),
    inference(variable_rename,[status(thm)],[f_4849_1]) ).

fof(f_4849_3,plain,
    ( ! [U_20252,U_20250] :
        ( c_List_Oupt(U_20250,U_20252) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20250),U_20252)) )
    & ! [U_20251,U_20249] :
        ( c_List_Oupt(U_20249,U_20251) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20249),c_List_Oupt(hAPP(c_Nat_OSuc,U_20249),U_20251))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20249),U_20251)) ) ),
    inference(miniscope,[status(thm)],[f_4849_2]) ).

fof(f_4849_4,plain,
    ( ! [U_20250,U_20252] :
        ( c_List_Oupt(U_20250,U_20252) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20250),U_20252)) )
    & ! [U_20251,U_20249] :
        ( c_List_Oupt(U_20249,U_20251) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20249),c_List_Oupt(hAPP(c_Nat_OSuc,U_20249),U_20251))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20249),U_20251)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4849_3]) ).

cnf(f_4849_5,plain,
    ( c_List_Oupt(U_20249,U_20251) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20249),c_List_Oupt(hAPP(c_Nat_OSuc,U_20249),U_20251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20249),U_20251)) ),
    inference(clausify,[status(thm)],[f_4849_4]) ).

cnf(f_4849_6,plain,
    ( c_List_Oupt(U_20250,U_20252) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20250),U_20252)) ),
    inference(clausify,[status(thm)],[f_4849_4]) ).

fof(f_4850_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__tl]) ).

fof(f_4850_2,plain,
    ! [U_20254,U_20253] :
      ( c_List_Olinorder__class_Osorted(U_20253,hAPP(c_List_Otl(U_20253),U_20254))
      | ~ c_List_Olinorder__class_Osorted(U_20253,U_20254)
      | ~ class_Orderings_Olinorder(U_20253) ),
    inference(variable_rename,[status(thm)],[f_4850_1]) ).

fof(f_4850_3,plain,
    ! [U_20254,U_20253] :
      ( c_List_Olinorder__class_Osorted(U_20253,hAPP(c_List_Otl(U_20253),U_20254))
      | ~ c_List_Olinorder__class_Osorted(U_20253,U_20254)
      | ~ class_Orderings_Olinorder(U_20253) ),
    inference(definitional_conversion,[status(esa)],[f_4850_2]) ).

cnf(f_4850_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20253,hAPP(c_List_Otl(U_20253),U_20254))
    | ~ c_List_Olinorder__class_Osorted(U_20253,U_20254)
    | ~ class_Orderings_Olinorder(U_20253) ),
    inference(clausify,[status(thm)],[f_4850_3]) ).

fof(f_4851_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) )
        & ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__key]) ).

fof(f_4851_2,plain,
    ! [U_20259,U_20258,U_20257,U_20256,U_20255] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20256,U_20255,U_20257),U_20258),U_20259)))
          | ~ c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),U_20259)) )
        & ( c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),U_20259))
          | ~ c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20256,U_20255,U_20257),U_20258),U_20259))) ) )
      | ~ class_Orderings_Olinorder(U_20255) ),
    inference(variable_rename,[status(thm)],[f_4851_1]) ).

fof(f_4851_3,plain,
    ( ! [U_20255,U_20256,U_20257,U_20258,U_20259] :
        ( c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20256,U_20255,U_20257),U_20258),U_20259)))
        | ~ c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),U_20259))
        | ~ sP1225(U_20255,U_20256,U_20257,U_20258,U_20259) )
    & ! [U_20255,U_20256,U_20257,U_20258,U_20259] :
        ( c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),U_20259))
        | ~ c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20256,U_20255,U_20257),U_20258),U_20259)))
        | ~ sP1225(U_20255,U_20256,U_20257,U_20258,U_20259) )
    & ! [U_20255,U_20256,U_20257,U_20258,U_20259] :
        ( sP1225(U_20255,U_20256,U_20257,U_20258,U_20259)
        | ~ class_Orderings_Olinorder(U_20255) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1225])],[f_4851_2]) ).

cnf(f_4851_4,plain,
    ( sP1225(U_20255,U_20256,U_20257,U_20258,U_20259)
    | ~ class_Orderings_Olinorder(U_20255) ),
    inference(clausify,[status(thm)],[f_4851_3]) ).

cnf(f_4851_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),U_20259))
    | ~ c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20256,U_20255,U_20257),U_20258),U_20259)))
    | ~ sP1225(U_20255,U_20256,U_20257,U_20258,U_20259) ),
    inference(clausify,[status(thm)],[f_4851_3]) ).

cnf(f_4851_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20256,U_20255,U_20257),U_20258),U_20259)))
    | ~ c_List_Olinorder__class_Osorted(U_20255,hAPP(hAPP(c_List_Omap(U_20256,U_20255),U_20257),U_20259))
    | ~ sP1225(U_20255,U_20256,U_20257,U_20258,U_20259) ),
    inference(clausify,[status(thm)],[f_4851_3]) ).

fof(f_4852_1,plain,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1]) ).

fof(f_4852_2,plain,
    ! [U_20264,U_20263,U_20262,U_20261,U_20260] :
      ( c_List_Olinorder__class_Osorted(U_20260,hAPP(hAPP(c_List_Omap(U_20261,U_20260),U_20262),c_List_Oremove1(U_20261,U_20264,U_20263)))
      | ~ c_List_Olinorder__class_Osorted(U_20260,hAPP(hAPP(c_List_Omap(U_20261,U_20260),U_20262),U_20263))
      | ~ class_Orderings_Olinorder(U_20260) ),
    inference(variable_rename,[status(thm)],[f_4852_1]) ).

fof(f_4852_3,plain,
    ! [U_20263,U_20264,U_20260,U_20261,U_20262] :
      ( c_List_Olinorder__class_Osorted(U_20260,hAPP(hAPP(c_List_Omap(U_20261,U_20260),U_20262),c_List_Oremove1(U_20261,U_20264,U_20263)))
      | ~ c_List_Olinorder__class_Osorted(U_20260,hAPP(hAPP(c_List_Omap(U_20261,U_20260),U_20262),U_20263))
      | ~ class_Orderings_Olinorder(U_20260) ),
    inference(definitional_conversion,[status(esa)],[f_4852_2]) ).

cnf(f_4852_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20260,hAPP(hAPP(c_List_Omap(U_20261,U_20260),U_20262),c_List_Oremove1(U_20261,U_20264,U_20263)))
    | ~ c_List_Olinorder__class_Osorted(U_20260,hAPP(hAPP(c_List_Omap(U_20261,U_20260),U_20262),U_20263))
    | ~ class_Orderings_Olinorder(U_20260) ),
    inference(clausify,[status(thm)],[f_4852_3]) ).

fof(f_4853_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_map__Suc__upt]) ).

fof(f_4853_2,plain,
    ! [U_20266,U_20265] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20265,U_20266)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20265),hAPP(c_Nat_OSuc,U_20266)),
    inference(variable_rename,[status(thm)],[f_4853_1]) ).

fof(f_4853_3,plain,
    ! [U_20266,U_20265] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20265,U_20266)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20265),hAPP(c_Nat_OSuc,U_20266)),
    inference(definitional_conversion,[status(esa)],[f_4853_2]) ).

cnf(f_4853_4,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20265,U_20266)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20265),hAPP(c_Nat_OSuc,U_20266)),
    inference(clausify,[status(thm)],[f_4853_3]) ).

fof(f_4854_1,plain,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key]) ).

fof(f_4854_2,plain,
    ! [U_20271,U_20270,U_20269,U_20268,U_20267] :
      ( c_List_Olinorder__class_Osorted(U_20267,hAPP(hAPP(c_List_Omap(U_20268,U_20267),U_20269),c_List_Olinorder__class_Oinsort__insert__key(U_20268,U_20267,U_20269,U_20271,U_20270)))
      | ~ c_List_Olinorder__class_Osorted(U_20267,hAPP(hAPP(c_List_Omap(U_20268,U_20267),U_20269),U_20270))
      | ~ class_Orderings_Olinorder(U_20267) ),
    inference(variable_rename,[status(thm)],[f_4854_1]) ).

fof(f_4854_3,plain,
    ! [U_20267,U_20268,U_20269,U_20270,U_20271] :
      ( c_List_Olinorder__class_Osorted(U_20267,hAPP(hAPP(c_List_Omap(U_20268,U_20267),U_20269),c_List_Olinorder__class_Oinsort__insert__key(U_20268,U_20267,U_20269,U_20271,U_20270)))
      | ~ c_List_Olinorder__class_Osorted(U_20267,hAPP(hAPP(c_List_Omap(U_20268,U_20267),U_20269),U_20270))
      | ~ class_Orderings_Olinorder(U_20267) ),
    inference(definitional_conversion,[status(esa)],[f_4854_2]) ).

cnf(f_4854_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20267,hAPP(hAPP(c_List_Omap(U_20268,U_20267),U_20269),c_List_Olinorder__class_Oinsort__insert__key(U_20268,U_20267,U_20269,U_20271,U_20270)))
    | ~ c_List_Olinorder__class_Osorted(U_20267,hAPP(hAPP(c_List_Omap(U_20268,U_20267),U_20269),U_20270))
    | ~ class_Orderings_Olinorder(U_20267) ),
    inference(clausify,[status(thm)],[f_4854_3]) ).

fof(f_4855_1,plain,
    ! [V_j,V_i] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_last__upt]) ).

fof(f_4855_2,plain,
    ! [U_20273,U_20272] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20272,U_20273)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20273),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20272),U_20273)) ),
    inference(variable_rename,[status(thm)],[f_4855_1]) ).

fof(f_4855_3,plain,
    ! [U_20273,U_20272] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20272,U_20273)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20273),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20272),U_20273)) ),
    inference(definitional_conversion,[status(esa)],[f_4855_2]) ).

cnf(f_4855_4,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20272,U_20273)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20273),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20272),U_20273)) ),
    inference(clausify,[status(thm)],[f_4855_3]) ).

fof(f_4856_1,plain,
    ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort]) ).

fof(f_4856_2,plain,
    ! [U_20279,U_20278,U_20277,U_20276,U_20275,U_20274] :
      ( hAPP(c_List_Ofilter(U_20275,U_20278),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20275,U_20274,U_20276),U_20279),U_20277)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20275,U_20274,U_20276),U_20279),hAPP(c_List_Ofilter(U_20275,U_20278),U_20277))
      | ~ hBOOL(hAPP(U_20278,U_20279))
      | ~ c_List_Olinorder__class_Osorted(U_20274,hAPP(hAPP(c_List_Omap(U_20275,U_20274),U_20276),U_20277))
      | ~ class_Orderings_Olinorder(U_20274) ),
    inference(variable_rename,[status(thm)],[f_4856_1]) ).

fof(f_4856_3,plain,
    ! [U_20274,U_20275,U_20276,U_20277,U_20278,U_20279] :
      ( hAPP(c_List_Ofilter(U_20275,U_20278),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20275,U_20274,U_20276),U_20279),U_20277)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20275,U_20274,U_20276),U_20279),hAPP(c_List_Ofilter(U_20275,U_20278),U_20277))
      | ~ hBOOL(hAPP(U_20278,U_20279))
      | ~ c_List_Olinorder__class_Osorted(U_20274,hAPP(hAPP(c_List_Omap(U_20275,U_20274),U_20276),U_20277))
      | ~ class_Orderings_Olinorder(U_20274) ),
    inference(definitional_conversion,[status(esa)],[f_4856_2]) ).

cnf(f_4856_4,plain,
    ( hAPP(c_List_Ofilter(U_20275,U_20278),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20275,U_20274,U_20276),U_20279),U_20277)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20275,U_20274,U_20276),U_20279),hAPP(c_List_Ofilter(U_20275,U_20278),U_20277))
    | ~ hBOOL(hAPP(U_20278,U_20279))
    | ~ c_List_Olinorder__class_Osorted(U_20274,hAPP(hAPP(c_List_Omap(U_20275,U_20274),U_20276),U_20277))
    | ~ class_Orderings_Olinorder(U_20274) ),
    inference(clausify,[status(thm)],[f_4856_3]) ).

fof(f_4857_1,plain,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_map__nth]) ).

fof(f_4857_2,plain,
    ! [U_20281,U_20280] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20280),hAPP(c_List_Onth(U_20280),U_20281)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),U_20281))) = U_20281,
    inference(variable_rename,[status(thm)],[f_4857_1]) ).

fof(f_4857_3,plain,
    ! [U_20281,U_20280] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20280),hAPP(c_List_Onth(U_20280),U_20281)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),U_20281))) = U_20281,
    inference(definitional_conversion,[status(esa)],[f_4857_2]) ).

cnf(f_4857_4,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20280),hAPP(c_List_Onth(U_20280),U_20281)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),U_20281))) = U_20281,
    inference(clausify,[status(thm)],[f_4857_3]) ).

fof(f_4858_1,plain,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__upt]) ).

fof(f_4858_2,plain,
    ! [U_20283,U_20282] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20282,U_20283) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20282,hAPP(c_Nat_OSuc,U_20283))),
    inference(variable_rename,[status(thm)],[f_4858_1]) ).

fof(f_4858_3,plain,
    ! [U_20282,U_20283] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20282,U_20283) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20282,hAPP(c_Nat_OSuc,U_20283))),
    inference(definitional_conversion,[status(esa)],[f_4858_2]) ).

cnf(f_4858_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20282,U_20283) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20282,hAPP(c_Nat_OSuc,U_20283))),
    inference(clausify,[status(thm)],[f_4858_3]) ).

fof(f_4859_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_atLeast__upt]) ).

fof(f_4859_2,plain,
    ! [U_20284] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20284) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20284)),
    inference(variable_rename,[status(thm)],[f_4859_1]) ).

fof(f_4859_3,plain,
    ! [U_20284] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20284) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20284)),
    inference(definitional_conversion,[status(esa)],[f_4859_2]) ).

cnf(f_4859_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20284) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20284)),
    inference(clausify,[status(thm)],[f_4859_3]) ).

fof(f_4860_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat]) ).

fof(f_4860_2,plain,
    ! [U_20288,U_20287,U_20286,U_20285] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20285),U_20286),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20287,U_20288))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20285),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20285),U_20286),c_List_Oupt(U_20287,U_20288)))
      | ~ class_Groups_Ocomm__monoid__add(U_20285) ),
    inference(variable_rename,[status(thm)],[f_4860_1]) ).

fof(f_4860_3,plain,
    ! [U_20285,U_20286,U_20287,U_20288] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20285),U_20286),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20287,U_20288))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20285),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20285),U_20286),c_List_Oupt(U_20287,U_20288)))
      | ~ class_Groups_Ocomm__monoid__add(U_20285) ),
    inference(definitional_conversion,[status(esa)],[f_4860_2]) ).

cnf(f_4860_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20285),U_20286),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20287,U_20288))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20285),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20285),U_20286),c_List_Oupt(U_20287,U_20288)))
    | ~ class_Groups_Ocomm__monoid__add(U_20285) ),
    inference(clausify,[status(thm)],[f_4860_3]) ).

fof(f_4861_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat]) ).

fof(f_4861_2,plain,
    ! [U_20292,U_20291,U_20290,U_20289] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20289),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20289),U_20290),c_List_Oupt(U_20291,U_20292))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20289),U_20290),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20291,U_20292)))
      | ~ class_Groups_Ocomm__monoid__add(U_20289) ),
    inference(variable_rename,[status(thm)],[f_4861_1]) ).

fof(f_4861_3,plain,
    ! [U_20289,U_20290,U_20291,U_20292] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20289),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20289),U_20290),c_List_Oupt(U_20291,U_20292))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20289),U_20290),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20291,U_20292)))
      | ~ class_Groups_Ocomm__monoid__add(U_20289) ),
    inference(definitional_conversion,[status(esa)],[f_4861_2]) ).

cnf(f_4861_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20289),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20289),U_20290),c_List_Oupt(U_20291,U_20292))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20289),U_20290),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20291,U_20292)))
    | ~ class_Groups_Ocomm__monoid__add(U_20289) ),
    inference(clausify,[status(thm)],[f_4861_3]) ).

fof(f_4862_1,plain,
    ! [V_j,V_k,V_i] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__upt]) ).

fof(f_4862_2,plain,
    ! [U_20295,U_20294,U_20293] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20293,U_20295)),U_20294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20293),U_20294)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20293),U_20294)),U_20295)) ),
    inference(variable_rename,[status(thm)],[f_4862_1]) ).

fof(f_4862_3,plain,
    ! [U_20293,U_20294,U_20295] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20293,U_20295)),U_20294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20293),U_20294)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20293),U_20294)),U_20295)) ),
    inference(definitional_conversion,[status(esa)],[f_4862_2]) ).

cnf(f_4862_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20293,U_20295)),U_20294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20293),U_20294)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20293),U_20294)),U_20295)) ),
    inference(clausify,[status(thm)],[f_4862_3]) ).

fof(f_4863_1,plain,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__upt]) ).

fof(f_4863_2,plain,
    ! [U_20297,U_20296] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20296,U_20297) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20296),hAPP(c_Nat_OSuc,U_20297))),
    inference(variable_rename,[status(thm)],[f_4863_1]) ).

fof(f_4863_3,plain,
    ! [U_20296,U_20297] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20296,U_20297) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20296),hAPP(c_Nat_OSuc,U_20297))),
    inference(definitional_conversion,[status(esa)],[f_4863_2]) ).

cnf(f_4863_4,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20296,U_20297) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20296),hAPP(c_Nat_OSuc,U_20297))),
    inference(clausify,[status(thm)],[f_4863_3]) ).

fof(f_4864_1,plain,
    ! [V_a1_2,V_a2_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
          | ~ c_List_Olinorder__class_Osorted(T_b,V_a1_2)
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) ) )
        & ( ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
            & ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) ) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I2_J]) ).

fof(f_4864_2,plain,
    ! [U_20302,U_20301,U_20300] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302))
          | ~ c_List_Olinorder__class_Osorted(U_20300,U_20302)
          | ? [U_20299] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),U_20299))
              & hBOOL(hAPP(hAPP(c_member(U_20300),U_20299),hAPP(c_List_Oset(U_20300),U_20302))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_20300,U_20302)
            & ! [U_20298] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),U_20298))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20300),U_20298),hAPP(c_List_Oset(U_20300),U_20302))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302)) ) )
      | ~ class_Orderings_Olinorder(U_20300) ),
    inference(variable_rename,[status(thm)],[f_4864_1]) ).

fof(f_4864_3,plain,
    ! [U_20302,U_20301,U_20300] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302))
          | ~ c_List_Olinorder__class_Osorted(U_20300,U_20302)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),sK500(U_20302,U_20301,U_20300)))
            & hBOOL(hAPP(hAPP(c_member(U_20300),sK500(U_20302,U_20301,U_20300)),hAPP(c_List_Oset(U_20300),U_20302))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_20300,U_20302)
            & ! [U_20298] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),U_20298))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20300),U_20298),hAPP(c_List_Oset(U_20300),U_20302))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302)) ) )
      | ~ class_Orderings_Olinorder(U_20300) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_20299,sK500(U_20302,U_20301,U_20300))],[f_4864_2]) ).

fof(f_4864_4,plain,
    ( ! [U_20300,U_20301,U_20302] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),sK500(U_20302,U_20301,U_20300)))
        | ~ sP1227(U_20300,U_20301,U_20302) )
    & ! [U_20300,U_20301,U_20302] :
        ( hBOOL(hAPP(hAPP(c_member(U_20300),sK500(U_20302,U_20301,U_20300)),hAPP(c_List_Oset(U_20300),U_20302)))
        | ~ sP1227(U_20300,U_20301,U_20302) )
    & ! [U_20298,U_20300,U_20301,U_20302] :
        ( c_List_Olinorder__class_Osorted(U_20300,U_20302)
        | ~ sP1226(U_20298,U_20300,U_20301,U_20302) )
    & ! [U_20298,U_20300,U_20301,U_20302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),U_20298))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20300),U_20298),hAPP(c_List_Oset(U_20300),U_20302)))
        | ~ sP1226(U_20298,U_20300,U_20301,U_20302) )
    & ! [U_20298,U_20300,U_20301,U_20302] :
        ( c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302))
        | ~ c_List_Olinorder__class_Osorted(U_20300,U_20302)
        | sP1227(U_20300,U_20301,U_20302)
        | ~ sP1228(U_20298,U_20300,U_20301,U_20302) )
    & ! [U_20298,U_20300,U_20301,U_20302] :
        ( sP1226(U_20298,U_20300,U_20301,U_20302)
        | ~ c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302))
        | ~ sP1228(U_20298,U_20300,U_20301,U_20302) )
    & ! [U_20298,U_20300,U_20301,U_20302] :
        ( sP1228(U_20298,U_20300,U_20301,U_20302)
        | ~ class_Orderings_Olinorder(U_20300) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1226,sP1227,sP1228])],[f_4864_3]) ).

cnf(f_4864_5,plain,
    ( sP1228(U_20298,U_20300,U_20301,U_20302)
    | ~ class_Orderings_Olinorder(U_20300) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

cnf(f_4864_6,plain,
    ( sP1226(U_20298,U_20300,U_20301,U_20302)
    | ~ c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302))
    | ~ sP1228(U_20298,U_20300,U_20301,U_20302) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

cnf(f_4864_7,plain,
    ( c_List_Olinorder__class_Osorted(U_20300,hAPP(hAPP(c_List_Olist_OCons(U_20300),U_20301),U_20302))
    | ~ c_List_Olinorder__class_Osorted(U_20300,U_20302)
    | sP1227(U_20300,U_20301,U_20302)
    | ~ sP1228(U_20298,U_20300,U_20301,U_20302) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

cnf(f_4864_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),U_20298))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20300),U_20298),hAPP(c_List_Oset(U_20300),U_20302)))
    | ~ sP1226(U_20298,U_20300,U_20301,U_20302) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

cnf(f_4864_9,plain,
    ( c_List_Olinorder__class_Osorted(U_20300,U_20302)
    | ~ sP1226(U_20298,U_20300,U_20301,U_20302) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

cnf(f_4864_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20300),sK500(U_20302,U_20301,U_20300)),hAPP(c_List_Oset(U_20300),U_20302)))
    | ~ sP1227(U_20300,U_20301,U_20302) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

cnf(f_4864_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20300),U_20301),sK500(U_20302,U_20301,U_20300)))
    | ~ sP1227(U_20300,U_20301,U_20302) ),
    inference(clausify,[status(thm)],[f_4864_4]) ).

fof(f_4865_1,plain,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__upt]) ).

fof(f_4865_2,plain,
    ! [U_20304,U_20303] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20303,U_20304) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20303),U_20304)),
    inference(variable_rename,[status(thm)],[f_4865_1]) ).

fof(f_4865_3,plain,
    ! [U_20304,U_20303] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20303,U_20304) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20303),U_20304)),
    inference(definitional_conversion,[status(esa)],[f_4865_2]) ).

cnf(f_4865_4,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20303,U_20304) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20303),U_20304)),
    inference(clausify,[status(thm)],[f_4865_3]) ).

fof(f_4866_1,plain,
    ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__map__upt]) ).

fof(f_4866_2,plain,
    ! [U_20309,U_20308,U_20307,U_20306,U_20305] :
      ( hAPP(hAPP(c_List_Onth(U_20308),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20308),U_20309),c_List_Oupt(U_20307,U_20306))),U_20305) = hAPP(U_20309,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20307),U_20305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20306),U_20307))) ),
    inference(variable_rename,[status(thm)],[f_4866_1]) ).

fof(f_4866_3,plain,
    ! [U_20305,U_20307,U_20309,U_20308,U_20306] :
      ( hAPP(hAPP(c_List_Onth(U_20308),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20308),U_20309),c_List_Oupt(U_20307,U_20306))),U_20305) = hAPP(U_20309,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20307),U_20305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20306),U_20307))) ),
    inference(definitional_conversion,[status(esa)],[f_4866_2]) ).

cnf(f_4866_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20308),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20308),U_20309),c_List_Oupt(U_20307,U_20306))),U_20305) = hAPP(U_20309,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20307),U_20305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20306),U_20307))) ),
    inference(clausify,[status(thm)],[f_4866_3]) ).

fof(f_4867_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
        & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
        & hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set]) ).

fof(f_4867_2,plain,
    ! [U_20311,U_20310] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_20310),c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311)))
        & c_List_Olinorder__class_Osorted(U_20310,c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311))
        & hAPP(c_List_Oset(U_20310),c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311)) = U_20311 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20310),U_20311))
      | ~ class_Orderings_Olinorder(U_20310) ),
    inference(variable_rename,[status(thm)],[f_4867_1]) ).

fof(f_4867_3,plain,
    ( ! [U_20310,U_20311] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20310),c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311)))
        | ~ sP1229(U_20310,U_20311) )
    & ! [U_20310,U_20311] :
        ( c_List_Olinorder__class_Osorted(U_20310,c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311))
        | ~ sP1229(U_20310,U_20311) )
    & ! [U_20310,U_20311] :
        ( hAPP(c_List_Oset(U_20310),c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311)) = U_20311
        | ~ sP1229(U_20310,U_20311) )
    & ! [U_20310,U_20311] :
        ( sP1229(U_20310,U_20311)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20310),U_20311))
        | ~ class_Orderings_Olinorder(U_20310) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1229])],[f_4867_2]) ).

cnf(f_4867_4,plain,
    ( sP1229(U_20310,U_20311)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20310),U_20311))
    | ~ class_Orderings_Olinorder(U_20310) ),
    inference(clausify,[status(thm)],[f_4867_3]) ).

cnf(f_4867_5,plain,
    ( hAPP(c_List_Oset(U_20310),c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311)) = U_20311
    | ~ sP1229(U_20310,U_20311) ),
    inference(clausify,[status(thm)],[f_4867_3]) ).

cnf(f_4867_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20310,c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311))
    | ~ sP1229(U_20310,U_20311) ),
    inference(clausify,[status(thm)],[f_4867_3]) ).

cnf(f_4867_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20310),c_List_Olinorder__class_Osorted__list__of__set(U_20310,U_20311)))
    | ~ sP1229(U_20310,U_20311) ),
    inference(clausify,[status(thm)],[f_4867_3]) ).

fof(f_4868_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_atMost__upto]) ).

fof(f_4868_2,plain,
    ! [U_20312] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20312) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20312))),
    inference(variable_rename,[status(thm)],[f_4868_1]) ).

fof(f_4868_3,plain,
    ! [U_20312] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20312) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20312))),
    inference(definitional_conversion,[status(esa)],[f_4868_2]) ).

cnf(f_4868_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20312) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20312))),
    inference(clausify,[status(thm)],[f_4868_3]) ).

fof(f_4869_1,plain,
    ! [V_xs_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__remove1]) ).

fof(f_4869_2,plain,
    ! [U_20315,U_20314,U_20313] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20313,U_20313,c_COMBI(U_20313)),U_20314),c_List_Oremove1(U_20313,U_20314,U_20315)) = U_20315
      | ~ c_List_Olinorder__class_Osorted(U_20313,U_20315)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20313),U_20314),hAPP(c_List_Oset(U_20313),U_20315)))
      | ~ class_Orderings_Olinorder(U_20313) ),
    inference(variable_rename,[status(thm)],[f_4869_1]) ).

fof(f_4869_3,plain,
    ! [U_20313,U_20314,U_20315] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20313,U_20313,c_COMBI(U_20313)),U_20314),c_List_Oremove1(U_20313,U_20314,U_20315)) = U_20315
      | ~ c_List_Olinorder__class_Osorted(U_20313,U_20315)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20313),U_20314),hAPP(c_List_Oset(U_20313),U_20315)))
      | ~ class_Orderings_Olinorder(U_20313) ),
    inference(definitional_conversion,[status(esa)],[f_4869_2]) ).

cnf(f_4869_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20313,U_20313,c_COMBI(U_20313)),U_20314),c_List_Oremove1(U_20313,U_20314,U_20315)) = U_20315
    | ~ c_List_Olinorder__class_Osorted(U_20313,U_20315)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20313),U_20314),hAPP(c_List_Oset(U_20313),U_20315)))
    | ~ class_Orderings_Olinorder(U_20313) ),
    inference(clausify,[status(thm)],[f_4869_3]) ).

fof(f_4870_1,plain,
    ! [V_j,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono]) ).

fof(f_4870_2,plain,
    ! [U_20319,U_20318,U_20317,U_20316] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20316),hAPP(hAPP(c_List_Onth(U_20316),U_20317),U_20318)),hAPP(hAPP(c_List_Onth(U_20316),U_20317),U_20319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20319),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20316)),U_20317)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20318),U_20319))
      | ~ c_List_Olinorder__class_Osorted(U_20316,U_20317)
      | ~ class_Orderings_Olinorder(U_20316) ),
    inference(variable_rename,[status(thm)],[f_4870_1]) ).

fof(f_4870_3,plain,
    ! [U_20316,U_20317,U_20318,U_20319] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20316),hAPP(hAPP(c_List_Onth(U_20316),U_20317),U_20318)),hAPP(hAPP(c_List_Onth(U_20316),U_20317),U_20319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20319),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20316)),U_20317)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20318),U_20319))
      | ~ c_List_Olinorder__class_Osorted(U_20316,U_20317)
      | ~ class_Orderings_Olinorder(U_20316) ),
    inference(definitional_conversion,[status(esa)],[f_4870_2]) ).

cnf(f_4870_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20316),hAPP(hAPP(c_List_Onth(U_20316),U_20317),U_20318)),hAPP(hAPP(c_List_Onth(U_20316),U_20317),U_20319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20319),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20316)),U_20317)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20318),U_20319))
    | ~ c_List_Olinorder__class_Osorted(U_20316,U_20317)
    | ~ class_Orderings_Olinorder(U_20316) ),
    inference(clausify,[status(thm)],[f_4870_3]) ).

fof(f_4871_1,plain,
    ! [V_xs_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
          | ? [B_j] :
              ( ? [B_i] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
        & ( ! [B_j] :
              ( ! [B_i] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__equals__nth__mono]) ).

fof(f_4871_2,plain,
    ! [U_20325,U_20324] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20324,U_20325)
          | ? [U_20323] :
              ( ? [U_20322] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20322)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20323)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20322),U_20323)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325))) ) )
        & ( ! [U_20321] :
              ( ! [U_20320] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20320)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20321)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20320),U_20321)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325))) )
          | ~ c_List_Olinorder__class_Osorted(U_20324,U_20325) ) )
      | ~ class_Orderings_Olinorder(U_20324) ),
    inference(variable_rename,[status(thm)],[f_4871_1]) ).

fof(f_4871_3,plain,
    ! [U_20325,U_20324] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20324,U_20325)
          | ( ? [U_20322] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20322)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK501(U_20325,U_20324))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20322),sK501(U_20325,U_20324))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK501(U_20325,U_20324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325))) ) )
        & ( ! [U_20321] :
              ( ! [U_20320] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20320)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20321)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20320),U_20321)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325))) )
          | ~ c_List_Olinorder__class_Osorted(U_20324,U_20325) ) )
      | ~ class_Orderings_Olinorder(U_20324) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_20323,sK501(U_20325,U_20324))],[f_4871_2]) ).

fof(f_4871_4,plain,
    ! [U_20325,U_20324] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20324,U_20325)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK502(U_20325,U_20324))),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK501(U_20325,U_20324))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK502(U_20325,U_20324)),sK501(U_20325,U_20324)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK501(U_20325,U_20324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325))) ) )
        & ( ! [U_20321] :
              ( ! [U_20320] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20320)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20321)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20320),U_20321)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325))) )
          | ~ c_List_Olinorder__class_Osorted(U_20324,U_20325) ) )
      | ~ class_Orderings_Olinorder(U_20324) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_20322,sK502(U_20325,U_20324))],[f_4871_3]) ).

fof(f_4871_5,plain,
    ( ! [U_20324,U_20325] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK502(U_20325,U_20324))),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK501(U_20325,U_20324))))
        | ~ sP1230(U_20324,U_20325) )
    & ! [U_20324,U_20325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK502(U_20325,U_20324)),sK501(U_20325,U_20324)))
        | ~ sP1230(U_20324,U_20325) )
    & ! [U_20324,U_20325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK501(U_20325,U_20324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325)))
        | ~ sP1230(U_20324,U_20325) )
    & ! [U_20320,U_20321,U_20324,U_20325] :
        ( c_List_Olinorder__class_Osorted(U_20324,U_20325)
        | sP1230(U_20324,U_20325)
        | ~ sP1231(U_20320,U_20321,U_20324,U_20325) )
    & ! [U_20320,U_20321,U_20324,U_20325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20320)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20321)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20320),U_20321))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325)))
        | ~ c_List_Olinorder__class_Osorted(U_20324,U_20325)
        | ~ sP1231(U_20320,U_20321,U_20324,U_20325) )
    & ! [U_20320,U_20321,U_20324,U_20325] :
        ( sP1231(U_20320,U_20321,U_20324,U_20325)
        | ~ class_Orderings_Olinorder(U_20324) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1230,sP1231])],[f_4871_4]) ).

cnf(f_4871_6,plain,
    ( sP1231(U_20320,U_20321,U_20324,U_20325)
    | ~ class_Orderings_Olinorder(U_20324) ),
    inference(clausify,[status(thm)],[f_4871_5]) ).

cnf(f_4871_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20320)),hAPP(hAPP(c_List_Onth(U_20324),U_20325),U_20321)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20320),U_20321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325)))
    | ~ c_List_Olinorder__class_Osorted(U_20324,U_20325)
    | ~ sP1231(U_20320,U_20321,U_20324,U_20325) ),
    inference(clausify,[status(thm)],[f_4871_5]) ).

cnf(f_4871_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20324,U_20325)
    | sP1230(U_20324,U_20325)
    | ~ sP1231(U_20320,U_20321,U_20324,U_20325) ),
    inference(clausify,[status(thm)],[f_4871_5]) ).

cnf(f_4871_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK501(U_20325,U_20324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20324)),U_20325)))
    | ~ sP1230(U_20324,U_20325) ),
    inference(clausify,[status(thm)],[f_4871_5]) ).

cnf(f_4871_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK502(U_20325,U_20324)),sK501(U_20325,U_20324)))
    | ~ sP1230(U_20324,U_20325) ),
    inference(clausify,[status(thm)],[f_4871_5]) ).

cnf(f_4871_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20324),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK502(U_20325,U_20324))),hAPP(hAPP(c_List_Onth(U_20324),U_20325),sK501(U_20325,U_20324))))
    | ~ sP1230(U_20324,U_20325) ),
    inference(clausify,[status(thm)],[f_4871_5]) ).

fof(f_4872_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_List_Oset(T_b),V_xs_2) != hAPP(c_List_Oset(T_b),V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
      | ~ c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique]) ).

fof(f_4872_2,plain,
    ! [U_20330,U_20329,U_20328,U_20327,U_20326] :
      ( U_20329 = U_20330
      | hAPP(c_List_Oset(U_20327),U_20329) != hAPP(c_List_Oset(U_20327),U_20330)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20326),hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20330)))
      | ~ c_List_Olinorder__class_Osorted(U_20326,hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20330))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20326),hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20329)))
      | ~ c_List_Olinorder__class_Osorted(U_20326,hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20329))
      | ~ c_Fun_Oinj__on(U_20327,U_20326,U_20328,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20327,tc_HOL_Obool)),hAPP(c_List_Oset(U_20327),U_20329)),hAPP(c_List_Oset(U_20327),U_20330)))
      | ~ class_Orderings_Olinorder(U_20326) ),
    inference(variable_rename,[status(thm)],[f_4872_1]) ).

fof(f_4872_3,plain,
    ! [U_20327,U_20328,U_20326,U_20329,U_20330] :
      ( U_20329 = U_20330
      | hAPP(c_List_Oset(U_20327),U_20329) != hAPP(c_List_Oset(U_20327),U_20330)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20326),hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20330)))
      | ~ c_List_Olinorder__class_Osorted(U_20326,hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20330))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20326),hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20329)))
      | ~ c_List_Olinorder__class_Osorted(U_20326,hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20329))
      | ~ c_Fun_Oinj__on(U_20327,U_20326,U_20328,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20327,tc_HOL_Obool)),hAPP(c_List_Oset(U_20327),U_20329)),hAPP(c_List_Oset(U_20327),U_20330)))
      | ~ class_Orderings_Olinorder(U_20326) ),
    inference(definitional_conversion,[status(esa)],[f_4872_2]) ).

cnf(f_4872_4,plain,
    ( U_20329 = U_20330
    | hAPP(c_List_Oset(U_20327),U_20329) != hAPP(c_List_Oset(U_20327),U_20330)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20326),hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20330)))
    | ~ c_List_Olinorder__class_Osorted(U_20326,hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20330))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20326),hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20329)))
    | ~ c_List_Olinorder__class_Osorted(U_20326,hAPP(hAPP(c_List_Omap(U_20327,U_20326),U_20328),U_20329))
    | ~ c_Fun_Oinj__on(U_20327,U_20326,U_20328,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20327,tc_HOL_Obool)),hAPP(c_List_Oset(U_20327),U_20329)),hAPP(c_List_Oset(U_20327),U_20330)))
    | ~ class_Orderings_Olinorder(U_20326) ),
    inference(clausify,[status(thm)],[f_4872_3]) ).

fof(f_4873_1,plain,
    ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(f_4873_2,plain,
    ! [U_20334,U_20333,U_20332,U_20331] : hAPP(hAPP(c_List_Omap(tc_prod(U_20331,tc_Nat_Onat),U_20331),c_Product__Type_Ofst(U_20331,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20331,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20331,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20331,tc_Nat_Onat))),U_20332)),hAPP(hAPP(c_List_Ozip(U_20331,tc_Nat_Onat),U_20333),c_List_Oupt(U_20334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20334),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20331)),U_20333)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20331,tc_Nat_Onat),U_20331),c_Product__Type_Ofst(U_20331,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20331,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20331,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(U_20331,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20331,tc_Nat_Onat))),U_20334))),U_20332)),hAPP(hAPP(c_List_Ozip(U_20331,tc_Nat_Onat),U_20333),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20331)),U_20333))))),
    inference(variable_rename,[status(thm)],[f_4873_1]) ).

fof(f_4873_3,plain,
    ! [U_20331,U_20334,U_20332,U_20333] : hAPP(hAPP(c_List_Omap(tc_prod(U_20331,tc_Nat_Onat),U_20331),c_Product__Type_Ofst(U_20331,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20331,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20331,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20331,tc_Nat_Onat))),U_20332)),hAPP(hAPP(c_List_Ozip(U_20331,tc_Nat_Onat),U_20333),c_List_Oupt(U_20334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20334),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20331)),U_20333)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20331,tc_Nat_Onat),U_20331),c_Product__Type_Ofst(U_20331,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20331,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20331,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(U_20331,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20331,tc_Nat_Onat))),U_20334))),U_20332)),hAPP(hAPP(c_List_Ozip(U_20331,tc_Nat_Onat),U_20333),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20331)),U_20333))))),
    inference(definitional_conversion,[status(esa)],[f_4873_2]) ).

cnf(f_4873_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_20331,tc_Nat_Onat),U_20331),c_Product__Type_Ofst(U_20331,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20331,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20331,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20331,tc_Nat_Onat))),U_20332)),hAPP(hAPP(c_List_Ozip(U_20331,tc_Nat_Onat),U_20333),c_List_Oupt(U_20334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20334),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20331)),U_20333)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20331,tc_Nat_Onat),U_20331),c_Product__Type_Ofst(U_20331,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20331,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_20331,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20331,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(U_20331,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20331,tc_Nat_Onat))),U_20334))),U_20332)),hAPP(hAPP(c_List_Ozip(U_20331,tc_Nat_Onat),U_20333),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20331)),U_20333))))),
    inference(clausify,[status(thm)],[f_4873_3]) ).

fof(f_4874_1,plain,
    ! [V_n_2,T_b,V_xs_2] :
      ( c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))
      | ? [B_i] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) != V_n_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) )
      | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__rectangle]) ).

fof(f_4874_2,plain,
    ! [U_20338,U_20337,U_20336] :
      ( c_List_Otranspose(U_20337,U_20336) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20337),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20337)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20337),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20337),tc_fun(tc_Nat_Onat,U_20337),tc_Nat_Onat),c_List_Onth(U_20337)),hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20338))
      | ? [U_20335] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20337)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336),U_20335)) != U_20338
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20335),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336))) )
      | ( U_20338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_20336 = c_List_Olist_ONil(tc_List_Olist(U_20337)) ) ),
    inference(variable_rename,[status(thm)],[f_4874_1]) ).

fof(f_4874_3,plain,
    ! [U_20338,U_20337,U_20336] :
      ( c_List_Otranspose(U_20337,U_20336) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20337),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20337)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20337),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20337),tc_fun(tc_Nat_Onat,U_20337),tc_Nat_Onat),c_List_Onth(U_20337)),hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20338))
      | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20337)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336),sK503(U_20338,U_20337,U_20336))) != U_20338
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK503(U_20338,U_20337,U_20336)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336))) )
      | ( U_20338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_20336 = c_List_Olist_ONil(tc_List_Olist(U_20337)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_20335,sK503(U_20338,U_20337,U_20336))],[f_4874_2]) ).

fof(f_4874_4,plain,
    ( ! [U_20336,U_20337,U_20338] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20337)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336),sK503(U_20338,U_20337,U_20336))) != U_20338
        | ~ sP1233(U_20336,U_20337,U_20338) )
    & ! [U_20336,U_20337,U_20338] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK503(U_20338,U_20337,U_20336)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336)))
        | ~ sP1233(U_20336,U_20337,U_20338) )
    & ! [U_20336,U_20337,U_20338] :
        ( U_20338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1232(U_20336,U_20337,U_20338) )
    & ! [U_20336,U_20337,U_20338] :
        ( U_20336 = c_List_Olist_ONil(tc_List_Olist(U_20337))
        | ~ sP1232(U_20336,U_20337,U_20338) )
    & ! [U_20336,U_20337,U_20338] :
        ( c_List_Otranspose(U_20337,U_20336) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20337),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20337)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20337),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20337),tc_fun(tc_Nat_Onat,U_20337),tc_Nat_Onat),c_List_Onth(U_20337)),hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20338))
        | sP1233(U_20336,U_20337,U_20338)
        | sP1232(U_20336,U_20337,U_20338) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1232,sP1233])],[f_4874_3]) ).

cnf(f_4874_5,plain,
    ( c_List_Otranspose(U_20337,U_20336) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20337),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20337)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20337)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20337),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20337),tc_fun(tc_Nat_Onat,U_20337),tc_Nat_Onat),c_List_Onth(U_20337)),hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20338))
    | sP1233(U_20336,U_20337,U_20338)
    | sP1232(U_20336,U_20337,U_20338) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

cnf(f_4874_6,plain,
    ( U_20336 = c_List_Olist_ONil(tc_List_Olist(U_20337))
    | ~ sP1232(U_20336,U_20337,U_20338) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

cnf(f_4874_7,plain,
    ( U_20338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1232(U_20336,U_20337,U_20338) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

cnf(f_4874_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK503(U_20338,U_20337,U_20336)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20337))),U_20336)))
    | ~ sP1233(U_20336,U_20337,U_20338) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

cnf(f_4874_9,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20337)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20337)),U_20336),sK503(U_20338,U_20337,U_20336))) != U_20338
    | ~ sP1233(U_20336,U_20337,U_20338) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

fof(f_4875_1,plain,
    ! [V_xss_2,T_b] :
      ( c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J]) ).

fof(f_4875_2,plain,
    ! [U_20340,U_20339] :
      ( c_List_Otranspose(U_20339,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20339)),c_List_Olist_ONil(U_20339)),U_20340)) = c_List_Otranspose(U_20339,U_20340)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20339)),c_List_Otranspose__rel(U_20339)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20339)),c_List_Olist_ONil(U_20339)),U_20340))) ),
    inference(variable_rename,[status(thm)],[f_4875_1]) ).

fof(f_4875_3,plain,
    ! [U_20339,U_20340] :
      ( c_List_Otranspose(U_20339,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20339)),c_List_Olist_ONil(U_20339)),U_20340)) = c_List_Otranspose(U_20339,U_20340)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20339)),c_List_Otranspose__rel(U_20339)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20339)),c_List_Olist_ONil(U_20339)),U_20340))) ),
    inference(definitional_conversion,[status(esa)],[f_4875_2]) ).

cnf(f_4875_4,plain,
    ( c_List_Otranspose(U_20339,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20339)),c_List_Olist_ONil(U_20339)),U_20340)) = c_List_Otranspose(U_20339,U_20340)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20339)),c_List_Otranspose__rel(U_20339)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20339)),c_List_Olist_ONil(U_20339)),U_20340))) ),
    inference(clausify,[status(thm)],[f_4875_3]) ).

fof(f_4876_1,plain,
    ! [T_b] :
      ( c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b)))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J]) ).

fof(f_4876_2,plain,
    ! [U_20341] :
      ( c_List_Otranspose(U_20341,c_List_Olist_ONil(tc_List_Olist(U_20341))) = c_List_Olist_ONil(tc_List_Olist(U_20341))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20341)),c_List_Otranspose__rel(U_20341)),c_List_Olist_ONil(tc_List_Olist(U_20341)))) ),
    inference(variable_rename,[status(thm)],[f_4876_1]) ).

fof(f_4876_3,plain,
    ! [U_20341] :
      ( c_List_Otranspose(U_20341,c_List_Olist_ONil(tc_List_Olist(U_20341))) = c_List_Olist_ONil(tc_List_Olist(U_20341))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20341)),c_List_Otranspose__rel(U_20341)),c_List_Olist_ONil(tc_List_Olist(U_20341)))) ),
    inference(definitional_conversion,[status(esa)],[f_4876_2]) ).

cnf(f_4876_4,plain,
    ( c_List_Otranspose(U_20341,c_List_Olist_ONil(tc_List_Olist(U_20341))) = c_List_Olist_ONil(tc_List_Olist(U_20341))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20341)),c_List_Otranspose__rel(U_20341)),c_List_Olist_ONil(tc_List_Olist(U_20341)))) ),
    inference(clausify,[status(thm)],[f_4876_3]) ).

fof(f_4877_1,plain,
    ! [V_i_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column]) ).

fof(f_4877_2,plain,
    ! [U_20344,U_20343,U_20342] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20342),U_20342),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20342),tc_Nat_Onat,U_20342),c_List_Onth(U_20342)),U_20344)),hAPP(c_List_Ofilter(tc_List_Olist(U_20342),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20342)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20344)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20342)))),c_List_Otranspose(U_20342,U_20343))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20342)),U_20343),U_20344)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20344),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20342))),U_20343)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20342),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20342))),U_20343))) ),
    inference(variable_rename,[status(thm)],[f_4877_1]) ).

fof(f_4877_3,plain,
    ! [U_20342,U_20343,U_20344] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20342),U_20342),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20342),tc_Nat_Onat,U_20342),c_List_Onth(U_20342)),U_20344)),hAPP(c_List_Ofilter(tc_List_Olist(U_20342),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20342)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20344)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20342)))),c_List_Otranspose(U_20342,U_20343))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20342)),U_20343),U_20344)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20344),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20342))),U_20343)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20342),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20342))),U_20343))) ),
    inference(definitional_conversion,[status(esa)],[f_4877_2]) ).

cnf(f_4877_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20342),U_20342),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20342),tc_Nat_Onat,U_20342),c_List_Onth(U_20342)),U_20344)),hAPP(c_List_Ofilter(tc_List_Olist(U_20342),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20342)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20344)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20342)))),c_List_Otranspose(U_20342,U_20343))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20342)),U_20343),U_20344)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20344),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20342))),U_20343)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20342),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20342))),U_20343))) ),
    inference(clausify,[status(thm)],[f_4877_3]) ).

fof(f_4878_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(f_4878_2,plain,
    ! [U_20346,U_20345] : c_List_Oconcat(U_20345,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20345),tc_List_Olist(U_20345)),c_List_Olist_Olist__case(tc_List_Olist(U_20345),U_20345,c_List_Olist_ONil(U_20345),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20345),tc_fun(tc_List_Olist(U_20345),tc_List_Olist(U_20345)),U_20345),c_COMBK(tc_List_Olist(U_20345),tc_List_Olist(U_20345))),hAPP(hAPP(c_COMBC(U_20345,tc_List_Olist(U_20345),tc_List_Olist(U_20345)),c_List_Olist_OCons(U_20345)),c_List_Olist_ONil(U_20345))))),U_20346)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20345),U_20345),c_List_Ohd(U_20345)),hAPP(c_List_Ofilter(tc_List_Olist(U_20345),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20345)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20345),tc_List_Olist(U_20345),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20345)))),U_20346)),
    inference(variable_rename,[status(thm)],[f_4878_1]) ).

fof(f_4878_3,plain,
    ! [U_20345,U_20346] : c_List_Oconcat(U_20345,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20345),tc_List_Olist(U_20345)),c_List_Olist_Olist__case(tc_List_Olist(U_20345),U_20345,c_List_Olist_ONil(U_20345),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20345),tc_fun(tc_List_Olist(U_20345),tc_List_Olist(U_20345)),U_20345),c_COMBK(tc_List_Olist(U_20345),tc_List_Olist(U_20345))),hAPP(hAPP(c_COMBC(U_20345,tc_List_Olist(U_20345),tc_List_Olist(U_20345)),c_List_Olist_OCons(U_20345)),c_List_Olist_ONil(U_20345))))),U_20346)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20345),U_20345),c_List_Ohd(U_20345)),hAPP(c_List_Ofilter(tc_List_Olist(U_20345),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20345)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20345),tc_List_Olist(U_20345),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20345)))),U_20346)),
    inference(definitional_conversion,[status(esa)],[f_4878_2]) ).

cnf(f_4878_4,plain,
    c_List_Oconcat(U_20345,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20345),tc_List_Olist(U_20345)),c_List_Olist_Olist__case(tc_List_Olist(U_20345),U_20345,c_List_Olist_ONil(U_20345),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20345),tc_fun(tc_List_Olist(U_20345),tc_List_Olist(U_20345)),U_20345),c_COMBK(tc_List_Olist(U_20345),tc_List_Olist(U_20345))),hAPP(hAPP(c_COMBC(U_20345,tc_List_Olist(U_20345),tc_List_Olist(U_20345)),c_List_Olist_OCons(U_20345)),c_List_Olist_ONil(U_20345))))),U_20346)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20345),U_20345),c_List_Ohd(U_20345)),hAPP(c_List_Ofilter(tc_List_Olist(U_20345),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20345)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20345),tc_List_Olist(U_20345),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20345)))),U_20346)),
    inference(clausify,[status(thm)],[f_4878_3]) ).

fof(f_4879_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__rev]) ).

fof(f_4879_2,plain,
    ! [U_20348,U_20347] : c_Fun_Oinj__on(tc_List_Olist(U_20347),tc_List_Olist(U_20347),c_List_Orev(U_20347),U_20348),
    inference(variable_rename,[status(thm)],[f_4879_1]) ).

fof(f_4879_3,plain,
    ! [U_20347,U_20348] : c_Fun_Oinj__on(tc_List_Olist(U_20347),tc_List_Olist(U_20347),c_List_Orev(U_20347),U_20348),
    inference(definitional_conversion,[status(esa)],[f_4879_2]) ).

cnf(f_4879_4,plain,
    c_Fun_Oinj__on(tc_List_Olist(U_20347),tc_List_Olist(U_20347),c_List_Orev(U_20347),U_20348),
    inference(clausify,[status(thm)],[f_4879_3]) ).

fof(f_4880_1,plain,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__concat]) ).

fof(f_4880_2,plain,
    ! [U_20351,U_20350,U_20349] : hAPP(c_List_Ofilter(U_20349,U_20350),c_List_Oconcat(U_20349,U_20351)) = c_List_Oconcat(U_20349,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20349),tc_List_Olist(U_20349)),c_List_Ofilter(U_20349,U_20350)),U_20351)),
    inference(variable_rename,[status(thm)],[f_4880_1]) ).

fof(f_4880_3,plain,
    ! [U_20349,U_20350,U_20351] : hAPP(c_List_Ofilter(U_20349,U_20350),c_List_Oconcat(U_20349,U_20351)) = c_List_Oconcat(U_20349,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20349),tc_List_Olist(U_20349)),c_List_Ofilter(U_20349,U_20350)),U_20351)),
    inference(definitional_conversion,[status(esa)],[f_4880_2]) ).

cnf(f_4880_4,plain,
    hAPP(c_List_Ofilter(U_20349,U_20350),c_List_Oconcat(U_20349,U_20351)) = c_List_Oconcat(U_20349,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20349),tc_List_Olist(U_20349)),c_List_Ofilter(U_20349,U_20350)),U_20351)),
    inference(clausify,[status(thm)],[f_4880_3]) ).

fof(f_4881_1,plain,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_length__concat]) ).

fof(f_4881_2,plain,
    ! [U_20353,U_20352] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20352)),c_List_Oconcat(U_20352,U_20353)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20352),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20352))),U_20353)),
    inference(variable_rename,[status(thm)],[f_4881_1]) ).

fof(f_4881_3,plain,
    ! [U_20352,U_20353] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20352)),c_List_Oconcat(U_20352,U_20353)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20352),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20352))),U_20353)),
    inference(definitional_conversion,[status(esa)],[f_4881_2]) ).

cnf(f_4881_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20352)),c_List_Oconcat(U_20352,U_20353)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20352),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20352))),U_20353)),
    inference(clausify,[status(thm)],[f_4881_3]) ).

fof(f_4882_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
        | hAPP(c_List_Orev(T_b),V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff]) ).

fof(f_4882_2,plain,
    ! [U_20357,U_20356,U_20355,U_20354] :
      ( ( hAPP(c_List_Orev(U_20354),U_20355) = hAPP(hAPP(c_List_Olist_OCons(U_20354),U_20356),U_20357)
        | U_20355 != hAPP(hAPP(c_List_Oappend(U_20354),hAPP(c_List_Orev(U_20354),U_20357)),hAPP(hAPP(c_List_Olist_OCons(U_20354),U_20356),c_List_Olist_ONil(U_20354))) )
      & ( U_20355 = hAPP(hAPP(c_List_Oappend(U_20354),hAPP(c_List_Orev(U_20354),U_20357)),hAPP(hAPP(c_List_Olist_OCons(U_20354),U_20356),c_List_Olist_ONil(U_20354)))
        | hAPP(c_List_Orev(U_20354),U_20355) != hAPP(hAPP(c_List_Olist_OCons(U_20354),U_20356),U_20357) ) ),
    inference(variable_rename,[status(thm)],[f_4882_1]) ).

fof(f_4882_3,plain,
    ( ! [U_20365,U_20363,U_20361,U_20359] :
        ( hAPP(c_List_Orev(U_20359),U_20361) = hAPP(hAPP(c_List_Olist_OCons(U_20359),U_20363),U_20365)
        | U_20361 != hAPP(hAPP(c_List_Oappend(U_20359),hAPP(c_List_Orev(U_20359),U_20365)),hAPP(hAPP(c_List_Olist_OCons(U_20359),U_20363),c_List_Olist_ONil(U_20359))) )
    & ! [U_20364,U_20362,U_20360,U_20358] :
        ( U_20360 = hAPP(hAPP(c_List_Oappend(U_20358),hAPP(c_List_Orev(U_20358),U_20364)),hAPP(hAPP(c_List_Olist_OCons(U_20358),U_20362),c_List_Olist_ONil(U_20358)))
        | hAPP(c_List_Orev(U_20358),U_20360) != hAPP(hAPP(c_List_Olist_OCons(U_20358),U_20362),U_20364) ) ),
    inference(miniscope,[status(thm)],[f_4882_2]) ).

fof(f_4882_4,plain,
    ( ! [U_20361,U_20359,U_20363,U_20365] :
        ( hAPP(c_List_Orev(U_20359),U_20361) = hAPP(hAPP(c_List_Olist_OCons(U_20359),U_20363),U_20365)
        | U_20361 != hAPP(hAPP(c_List_Oappend(U_20359),hAPP(c_List_Orev(U_20359),U_20365)),hAPP(hAPP(c_List_Olist_OCons(U_20359),U_20363),c_List_Olist_ONil(U_20359))) )
    & ! [U_20360,U_20364,U_20358,U_20362] :
        ( U_20360 = hAPP(hAPP(c_List_Oappend(U_20358),hAPP(c_List_Orev(U_20358),U_20364)),hAPP(hAPP(c_List_Olist_OCons(U_20358),U_20362),c_List_Olist_ONil(U_20358)))
        | hAPP(c_List_Orev(U_20358),U_20360) != hAPP(hAPP(c_List_Olist_OCons(U_20358),U_20362),U_20364) ) ),
    inference(definitional_conversion,[status(esa)],[f_4882_3]) ).

cnf(f_4882_5,plain,
    ( U_20360 = hAPP(hAPP(c_List_Oappend(U_20358),hAPP(c_List_Orev(U_20358),U_20364)),hAPP(hAPP(c_List_Olist_OCons(U_20358),U_20362),c_List_Olist_ONil(U_20358)))
    | hAPP(c_List_Orev(U_20358),U_20360) != hAPP(hAPP(c_List_Olist_OCons(U_20358),U_20362),U_20364) ),
    inference(clausify,[status(thm)],[f_4882_4]) ).

cnf(f_4882_6,plain,
    ( hAPP(c_List_Orev(U_20359),U_20361) = hAPP(hAPP(c_List_Olist_OCons(U_20359),U_20363),U_20365)
    | U_20361 != hAPP(hAPP(c_List_Oappend(U_20359),hAPP(c_List_Orev(U_20359),U_20365)),hAPP(hAPP(c_List_Olist_OCons(U_20359),U_20363),c_List_Olist_ONil(U_20359))) ),
    inference(clausify,[status(thm)],[f_4882_4]) ).

fof(f_4883_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))),
    inference(fof_nnf,[status(thm)],[fact_rev_Osimps_I2_J]) ).

fof(f_4883_2,plain,
    ! [U_20368,U_20367,U_20366] : hAPP(c_List_Orev(U_20366),hAPP(hAPP(c_List_Olist_OCons(U_20366),U_20367),U_20368)) = hAPP(hAPP(c_List_Oappend(U_20366),hAPP(c_List_Orev(U_20366),U_20368)),hAPP(hAPP(c_List_Olist_OCons(U_20366),U_20367),c_List_Olist_ONil(U_20366))),
    inference(variable_rename,[status(thm)],[f_4883_1]) ).

fof(f_4883_3,plain,
    ! [U_20366,U_20367,U_20368] : hAPP(c_List_Orev(U_20366),hAPP(hAPP(c_List_Olist_OCons(U_20366),U_20367),U_20368)) = hAPP(hAPP(c_List_Oappend(U_20366),hAPP(c_List_Orev(U_20366),U_20368)),hAPP(hAPP(c_List_Olist_OCons(U_20366),U_20367),c_List_Olist_ONil(U_20366))),
    inference(definitional_conversion,[status(esa)],[f_4883_2]) ).

cnf(f_4883_4,plain,
    hAPP(c_List_Orev(U_20366),hAPP(hAPP(c_List_Olist_OCons(U_20366),U_20367),U_20368)) = hAPP(hAPP(c_List_Oappend(U_20366),hAPP(c_List_Orev(U_20366),U_20368)),hAPP(hAPP(c_List_Olist_OCons(U_20366),U_20367),c_List_Olist_ONil(U_20366))),
    inference(clausify,[status(thm)],[f_4883_3]) ).

fof(f_4884_1,plain,
    ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_rev_Osimps_I1_J]) ).

fof(f_4884_2,plain,
    ! [U_20369] : hAPP(c_List_Orev(U_20369),c_List_Olist_ONil(U_20369)) = c_List_Olist_ONil(U_20369),
    inference(variable_rename,[status(thm)],[f_4884_1]) ).

fof(f_4884_3,plain,
    ! [U_20369] : hAPP(c_List_Orev(U_20369),c_List_Olist_ONil(U_20369)) = c_List_Olist_ONil(U_20369),
    inference(definitional_conversion,[status(esa)],[f_4884_2]) ).

cnf(f_4884_4,plain,
    hAPP(c_List_Orev(U_20369),c_List_Olist_ONil(U_20369)) = c_List_Olist_ONil(U_20369),
    inference(clausify,[status(thm)],[f_4884_3]) ).

fof(f_4885_1,plain,
    ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_concat_Osimps_I1_J]) ).

fof(f_4885_2,plain,
    ! [U_20370] : c_List_Oconcat(U_20370,c_List_Olist_ONil(tc_List_Olist(U_20370))) = c_List_Olist_ONil(U_20370),
    inference(variable_rename,[status(thm)],[f_4885_1]) ).

fof(f_4885_3,plain,
    ! [U_20370] : c_List_Oconcat(U_20370,c_List_Olist_ONil(tc_List_Olist(U_20370))) = c_List_Olist_ONil(U_20370),
    inference(definitional_conversion,[status(esa)],[f_4885_2]) ).

cnf(f_4885_4,plain,
    c_List_Oconcat(U_20370,c_List_Olist_ONil(tc_List_Olist(U_20370))) = c_List_Olist_ONil(U_20370),
    inference(clausify,[status(thm)],[f_4885_3]) ).

fof(f_4886_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | c_List_Olist_ONil(T_b) != hAPP(c_List_Orev(T_b),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv]) ).

fof(f_4886_2,plain,
    ! [U_20372,U_20371] :
      ( ( c_List_Olist_ONil(U_20371) = hAPP(c_List_Orev(U_20371),U_20372)
        | U_20372 != c_List_Olist_ONil(U_20371) )
      & ( U_20372 = c_List_Olist_ONil(U_20371)
        | c_List_Olist_ONil(U_20371) != hAPP(c_List_Orev(U_20371),U_20372) ) ),
    inference(variable_rename,[status(thm)],[f_4886_1]) ).

fof(f_4886_3,plain,
    ( ! [U_20376,U_20374] :
        ( c_List_Olist_ONil(U_20374) = hAPP(c_List_Orev(U_20374),U_20376)
        | U_20376 != c_List_Olist_ONil(U_20374) )
    & ! [U_20375,U_20373] :
        ( U_20375 = c_List_Olist_ONil(U_20373)
        | c_List_Olist_ONil(U_20373) != hAPP(c_List_Orev(U_20373),U_20375) ) ),
    inference(miniscope,[status(thm)],[f_4886_2]) ).

fof(f_4886_4,plain,
    ( ! [U_20376,U_20374] :
        ( c_List_Olist_ONil(U_20374) = hAPP(c_List_Orev(U_20374),U_20376)
        | U_20376 != c_List_Olist_ONil(U_20374) )
    & ! [U_20375,U_20373] :
        ( U_20375 = c_List_Olist_ONil(U_20373)
        | c_List_Olist_ONil(U_20373) != hAPP(c_List_Orev(U_20373),U_20375) ) ),
    inference(definitional_conversion,[status(esa)],[f_4886_3]) ).

cnf(f_4886_5,plain,
    ( U_20375 = c_List_Olist_ONil(U_20373)
    | c_List_Olist_ONil(U_20373) != hAPP(c_List_Orev(U_20373),U_20375) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

cnf(f_4886_6,plain,
    ( c_List_Olist_ONil(U_20374) = hAPP(c_List_Orev(U_20374),U_20376)
    | U_20376 != c_List_Olist_ONil(U_20374) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

fof(f_4887_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Orev(T_b),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv]) ).

fof(f_4887_2,plain,
    ! [U_20378,U_20377] :
      ( ( hAPP(c_List_Orev(U_20377),U_20378) = c_List_Olist_ONil(U_20377)
        | U_20378 != c_List_Olist_ONil(U_20377) )
      & ( U_20378 = c_List_Olist_ONil(U_20377)
        | hAPP(c_List_Orev(U_20377),U_20378) != c_List_Olist_ONil(U_20377) ) ),
    inference(variable_rename,[status(thm)],[f_4887_1]) ).

fof(f_4887_3,plain,
    ( ! [U_20382,U_20380] :
        ( hAPP(c_List_Orev(U_20380),U_20382) = c_List_Olist_ONil(U_20380)
        | U_20382 != c_List_Olist_ONil(U_20380) )
    & ! [U_20381,U_20379] :
        ( U_20381 = c_List_Olist_ONil(U_20379)
        | hAPP(c_List_Orev(U_20379),U_20381) != c_List_Olist_ONil(U_20379) ) ),
    inference(miniscope,[status(thm)],[f_4887_2]) ).

fof(f_4887_4,plain,
    ( ! [U_20380,U_20382] :
        ( hAPP(c_List_Orev(U_20380),U_20382) = c_List_Olist_ONil(U_20380)
        | U_20382 != c_List_Olist_ONil(U_20380) )
    & ! [U_20381,U_20379] :
        ( U_20381 = c_List_Olist_ONil(U_20379)
        | hAPP(c_List_Orev(U_20379),U_20381) != c_List_Olist_ONil(U_20379) ) ),
    inference(definitional_conversion,[status(esa)],[f_4887_3]) ).

cnf(f_4887_5,plain,
    ( U_20381 = c_List_Olist_ONil(U_20379)
    | hAPP(c_List_Orev(U_20379),U_20381) != c_List_Olist_ONil(U_20379) ),
    inference(clausify,[status(thm)],[f_4887_4]) ).

cnf(f_4887_6,plain,
    ( hAPP(c_List_Orev(U_20380),U_20382) = c_List_Olist_ONil(U_20380)
    | U_20382 != c_List_Olist_ONil(U_20380) ),
    inference(clausify,[status(thm)],[f_4887_4]) ).

fof(f_4888_1,plain,
    ! [V_xss_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_b)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_b)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) )
        | c_List_Olist_ONil(T_b) != c_List_Oconcat(T_b,V_xss_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__eq__concat__conv]) ).

fof(f_4888_2,plain,
    ! [U_20386,U_20385] :
      ( ( c_List_Olist_ONil(U_20385) = c_List_Oconcat(U_20385,U_20386)
        | ? [U_20384] :
            ( U_20384 != c_List_Olist_ONil(U_20385)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20385)),U_20384),hAPP(c_List_Oset(tc_List_Olist(U_20385)),U_20386))) ) )
      & ( ! [U_20383] :
            ( U_20383 = c_List_Olist_ONil(U_20385)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20385)),U_20383),hAPP(c_List_Oset(tc_List_Olist(U_20385)),U_20386))) )
        | c_List_Olist_ONil(U_20385) != c_List_Oconcat(U_20385,U_20386) ) ),
    inference(variable_rename,[status(thm)],[f_4888_1]) ).

fof(f_4888_3,plain,
    ( ! [U_20390,U_20388] :
        ( c_List_Olist_ONil(U_20388) = c_List_Oconcat(U_20388,U_20390)
        | ? [U_20384] :
            ( U_20384 != c_List_Olist_ONil(U_20388)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20388)),U_20384),hAPP(c_List_Oset(tc_List_Olist(U_20388)),U_20390))) ) )
    & ! [U_20389,U_20387] :
        ( ! [U_20383] :
            ( U_20383 = c_List_Olist_ONil(U_20387)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20387)),U_20383),hAPP(c_List_Oset(tc_List_Olist(U_20387)),U_20389))) )
        | c_List_Olist_ONil(U_20387) != c_List_Oconcat(U_20387,U_20389) ) ),
    inference(miniscope,[status(thm)],[f_4888_2]) ).

fof(f_4888_4,plain,
    ( ! [U_20390,U_20388] :
        ( c_List_Olist_ONil(U_20388) = c_List_Oconcat(U_20388,U_20390)
        | ( sK504(U_20390,U_20388) != c_List_Olist_ONil(U_20388)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20388)),sK504(U_20390,U_20388)),hAPP(c_List_Oset(tc_List_Olist(U_20388)),U_20390))) ) )
    & ! [U_20389,U_20387] :
        ( ! [U_20383] :
            ( U_20383 = c_List_Olist_ONil(U_20387)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20387)),U_20383),hAPP(c_List_Oset(tc_List_Olist(U_20387)),U_20389))) )
        | c_List_Olist_ONil(U_20387) != c_List_Oconcat(U_20387,U_20389) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_20384,sK504(U_20390,U_20388))],[f_4888_3]) ).

fof(f_4888_5,plain,
    ( ! [U_20390,U_20388] :
        ( sK504(U_20390,U_20388) != c_List_Olist_ONil(U_20388)
        | ~ sP1234(U_20390,U_20388) )
    & ! [U_20390,U_20388] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20388)),sK504(U_20390,U_20388)),hAPP(c_List_Oset(tc_List_Olist(U_20388)),U_20390)))
        | ~ sP1234(U_20390,U_20388) )
    & ! [U_20390,U_20388] :
        ( c_List_Olist_ONil(U_20388) = c_List_Oconcat(U_20388,U_20390)
        | sP1234(U_20390,U_20388) )
    & ! [U_20383,U_20387,U_20389] :
        ( U_20383 = c_List_Olist_ONil(U_20387)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20387)),U_20383),hAPP(c_List_Oset(tc_List_Olist(U_20387)),U_20389)))
        | c_List_Olist_ONil(U_20387) != c_List_Oconcat(U_20387,U_20389) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1234])],[f_4888_4]) ).

cnf(f_4888_6,plain,
    ( U_20383 = c_List_Olist_ONil(U_20387)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20387)),U_20383),hAPP(c_List_Oset(tc_List_Olist(U_20387)),U_20389)))
    | c_List_Olist_ONil(U_20387) != c_List_Oconcat(U_20387,U_20389) ),
    inference(clausify,[status(thm)],[f_4888_5]) ).

cnf(f_4888_7,plain,
    ( c_List_Olist_ONil(U_20388) = c_List_Oconcat(U_20388,U_20390)
    | sP1234(U_20390,U_20388) ),
    inference(clausify,[status(thm)],[f_4888_5]) ).

cnf(f_4888_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20388)),sK504(U_20390,U_20388)),hAPP(c_List_Oset(tc_List_Olist(U_20388)),U_20390)))
    | ~ sP1234(U_20390,U_20388) ),
    inference(clausify,[status(thm)],[f_4888_5]) ).

cnf(f_4888_9,plain,
    ( sK504(U_20390,U_20388) != c_List_Olist_ONil(U_20388)
    | ~ sP1234(U_20390,U_20388) ),
    inference(clausify,[status(thm)],[f_4888_5]) ).

fof(f_4889_1,plain,
    ! [V_xss_2,T_b] :
      ( ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_b)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_b)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) )
        | c_List_Oconcat(T_b,V_xss_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_concat__eq__Nil__conv]) ).

fof(f_4889_2,plain,
    ! [U_20394,U_20393] :
      ( ( c_List_Oconcat(U_20393,U_20394) = c_List_Olist_ONil(U_20393)
        | ? [U_20392] :
            ( U_20392 != c_List_Olist_ONil(U_20393)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20393)),U_20392),hAPP(c_List_Oset(tc_List_Olist(U_20393)),U_20394))) ) )
      & ( ! [U_20391] :
            ( U_20391 = c_List_Olist_ONil(U_20393)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20393)),U_20391),hAPP(c_List_Oset(tc_List_Olist(U_20393)),U_20394))) )
        | c_List_Oconcat(U_20393,U_20394) != c_List_Olist_ONil(U_20393) ) ),
    inference(variable_rename,[status(thm)],[f_4889_1]) ).

fof(f_4889_3,plain,
    ( ! [U_20398,U_20396] :
        ( c_List_Oconcat(U_20396,U_20398) = c_List_Olist_ONil(U_20396)
        | ? [U_20392] :
            ( U_20392 != c_List_Olist_ONil(U_20396)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20396)),U_20392),hAPP(c_List_Oset(tc_List_Olist(U_20396)),U_20398))) ) )
    & ! [U_20397,U_20395] :
        ( ! [U_20391] :
            ( U_20391 = c_List_Olist_ONil(U_20395)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20395)),U_20391),hAPP(c_List_Oset(tc_List_Olist(U_20395)),U_20397))) )
        | c_List_Oconcat(U_20395,U_20397) != c_List_Olist_ONil(U_20395) ) ),
    inference(miniscope,[status(thm)],[f_4889_2]) ).

fof(f_4889_4,plain,
    ( ! [U_20398,U_20396] :
        ( c_List_Oconcat(U_20396,U_20398) = c_List_Olist_ONil(U_20396)
        | ( sK505(U_20398,U_20396) != c_List_Olist_ONil(U_20396)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20396)),sK505(U_20398,U_20396)),hAPP(c_List_Oset(tc_List_Olist(U_20396)),U_20398))) ) )
    & ! [U_20397,U_20395] :
        ( ! [U_20391] :
            ( U_20391 = c_List_Olist_ONil(U_20395)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20395)),U_20391),hAPP(c_List_Oset(tc_List_Olist(U_20395)),U_20397))) )
        | c_List_Oconcat(U_20395,U_20397) != c_List_Olist_ONil(U_20395) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_20392,sK505(U_20398,U_20396))],[f_4889_3]) ).

fof(f_4889_5,plain,
    ( ! [U_20396,U_20398] :
        ( sK505(U_20398,U_20396) != c_List_Olist_ONil(U_20396)
        | ~ sP1235(U_20396,U_20398) )
    & ! [U_20396,U_20398] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20396)),sK505(U_20398,U_20396)),hAPP(c_List_Oset(tc_List_Olist(U_20396)),U_20398)))
        | ~ sP1235(U_20396,U_20398) )
    & ! [U_20396,U_20398] :
        ( c_List_Oconcat(U_20396,U_20398) = c_List_Olist_ONil(U_20396)
        | sP1235(U_20396,U_20398) )
    & ! [U_20397,U_20391,U_20395] :
        ( U_20391 = c_List_Olist_ONil(U_20395)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20395)),U_20391),hAPP(c_List_Oset(tc_List_Olist(U_20395)),U_20397)))
        | c_List_Oconcat(U_20395,U_20397) != c_List_Olist_ONil(U_20395) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1235])],[f_4889_4]) ).

cnf(f_4889_6,plain,
    ( U_20391 = c_List_Olist_ONil(U_20395)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20395)),U_20391),hAPP(c_List_Oset(tc_List_Olist(U_20395)),U_20397)))
    | c_List_Oconcat(U_20395,U_20397) != c_List_Olist_ONil(U_20395) ),
    inference(clausify,[status(thm)],[f_4889_5]) ).

cnf(f_4889_7,plain,
    ( c_List_Oconcat(U_20396,U_20398) = c_List_Olist_ONil(U_20396)
    | sP1235(U_20396,U_20398) ),
    inference(clausify,[status(thm)],[f_4889_5]) ).

cnf(f_4889_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20396)),sK505(U_20398,U_20396)),hAPP(c_List_Oset(tc_List_Olist(U_20396)),U_20398)))
    | ~ sP1235(U_20396,U_20398) ),
    inference(clausify,[status(thm)],[f_4889_5]) ).

cnf(f_4889_9,plain,
    ( sK505(U_20398,U_20396) != c_List_Olist_ONil(U_20396)
    | ~ sP1235(U_20396,U_20398) ),
    inference(clausify,[status(thm)],[f_4889_5]) ).

fof(f_4890_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | V_xs_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | hAPP(c_List_Orev(T_b),V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv]) ).

fof(f_4890_2,plain,
    ! [U_20401,U_20400,U_20399] :
      ( ( hAPP(c_List_Orev(U_20399),U_20400) = hAPP(hAPP(c_List_Olist_OCons(U_20399),U_20401),c_List_Olist_ONil(U_20399))
        | U_20400 != hAPP(hAPP(c_List_Olist_OCons(U_20399),U_20401),c_List_Olist_ONil(U_20399)) )
      & ( U_20400 = hAPP(hAPP(c_List_Olist_OCons(U_20399),U_20401),c_List_Olist_ONil(U_20399))
        | hAPP(c_List_Orev(U_20399),U_20400) != hAPP(hAPP(c_List_Olist_OCons(U_20399),U_20401),c_List_Olist_ONil(U_20399)) ) ),
    inference(variable_rename,[status(thm)],[f_4890_1]) ).

fof(f_4890_3,plain,
    ( ! [U_20407,U_20405,U_20403] :
        ( hAPP(c_List_Orev(U_20403),U_20405) = hAPP(hAPP(c_List_Olist_OCons(U_20403),U_20407),c_List_Olist_ONil(U_20403))
        | U_20405 != hAPP(hAPP(c_List_Olist_OCons(U_20403),U_20407),c_List_Olist_ONil(U_20403)) )
    & ! [U_20406,U_20404,U_20402] :
        ( U_20404 = hAPP(hAPP(c_List_Olist_OCons(U_20402),U_20406),c_List_Olist_ONil(U_20402))
        | hAPP(c_List_Orev(U_20402),U_20404) != hAPP(hAPP(c_List_Olist_OCons(U_20402),U_20406),c_List_Olist_ONil(U_20402)) ) ),
    inference(miniscope,[status(thm)],[f_4890_2]) ).

fof(f_4890_4,plain,
    ( ! [U_20405,U_20403,U_20407] :
        ( hAPP(c_List_Orev(U_20403),U_20405) = hAPP(hAPP(c_List_Olist_OCons(U_20403),U_20407),c_List_Olist_ONil(U_20403))
        | U_20405 != hAPP(hAPP(c_List_Olist_OCons(U_20403),U_20407),c_List_Olist_ONil(U_20403)) )
    & ! [U_20404,U_20406,U_20402] :
        ( U_20404 = hAPP(hAPP(c_List_Olist_OCons(U_20402),U_20406),c_List_Olist_ONil(U_20402))
        | hAPP(c_List_Orev(U_20402),U_20404) != hAPP(hAPP(c_List_Olist_OCons(U_20402),U_20406),c_List_Olist_ONil(U_20402)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4890_3]) ).

cnf(f_4890_5,plain,
    ( U_20404 = hAPP(hAPP(c_List_Olist_OCons(U_20402),U_20406),c_List_Olist_ONil(U_20402))
    | hAPP(c_List_Orev(U_20402),U_20404) != hAPP(hAPP(c_List_Olist_OCons(U_20402),U_20406),c_List_Olist_ONil(U_20402)) ),
    inference(clausify,[status(thm)],[f_4890_4]) ).

cnf(f_4890_6,plain,
    ( hAPP(c_List_Orev(U_20403),U_20405) = hAPP(hAPP(c_List_Olist_OCons(U_20403),U_20407),c_List_Olist_ONil(U_20403))
    | U_20405 != hAPP(hAPP(c_List_Olist_OCons(U_20403),U_20407),c_List_Olist_ONil(U_20403)) ),
    inference(clausify,[status(thm)],[f_4890_4]) ).

fof(f_4891_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
        | V_xs_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) != hAPP(c_List_Orev(T_b),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv]) ).

fof(f_4891_2,plain,
    ! [U_20410,U_20409,U_20408] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_20408),U_20409),c_List_Olist_ONil(U_20408)) = hAPP(c_List_Orev(U_20408),U_20410)
        | U_20410 != hAPP(hAPP(c_List_Olist_OCons(U_20408),U_20409),c_List_Olist_ONil(U_20408)) )
      & ( U_20410 = hAPP(hAPP(c_List_Olist_OCons(U_20408),U_20409),c_List_Olist_ONil(U_20408))
        | hAPP(hAPP(c_List_Olist_OCons(U_20408),U_20409),c_List_Olist_ONil(U_20408)) != hAPP(c_List_Orev(U_20408),U_20410) ) ),
    inference(variable_rename,[status(thm)],[f_4891_1]) ).

fof(f_4891_3,plain,
    ( ! [U_20416,U_20414,U_20412] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20412),U_20414),c_List_Olist_ONil(U_20412)) = hAPP(c_List_Orev(U_20412),U_20416)
        | U_20416 != hAPP(hAPP(c_List_Olist_OCons(U_20412),U_20414),c_List_Olist_ONil(U_20412)) )
    & ! [U_20415,U_20413,U_20411] :
        ( U_20415 = hAPP(hAPP(c_List_Olist_OCons(U_20411),U_20413),c_List_Olist_ONil(U_20411))
        | hAPP(hAPP(c_List_Olist_OCons(U_20411),U_20413),c_List_Olist_ONil(U_20411)) != hAPP(c_List_Orev(U_20411),U_20415) ) ),
    inference(miniscope,[status(thm)],[f_4891_2]) ).

fof(f_4891_4,plain,
    ( ! [U_20412,U_20414,U_20416] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20412),U_20414),c_List_Olist_ONil(U_20412)) = hAPP(c_List_Orev(U_20412),U_20416)
        | U_20416 != hAPP(hAPP(c_List_Olist_OCons(U_20412),U_20414),c_List_Olist_ONil(U_20412)) )
    & ! [U_20413,U_20415,U_20411] :
        ( U_20415 = hAPP(hAPP(c_List_Olist_OCons(U_20411),U_20413),c_List_Olist_ONil(U_20411))
        | hAPP(hAPP(c_List_Olist_OCons(U_20411),U_20413),c_List_Olist_ONil(U_20411)) != hAPP(c_List_Orev(U_20411),U_20415) ) ),
    inference(definitional_conversion,[status(esa)],[f_4891_3]) ).

cnf(f_4891_5,plain,
    ( U_20415 = hAPP(hAPP(c_List_Olist_OCons(U_20411),U_20413),c_List_Olist_ONil(U_20411))
    | hAPP(hAPP(c_List_Olist_OCons(U_20411),U_20413),c_List_Olist_ONil(U_20411)) != hAPP(c_List_Orev(U_20411),U_20415) ),
    inference(clausify,[status(thm)],[f_4891_4]) ).

cnf(f_4891_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_20412),U_20414),c_List_Olist_ONil(U_20412)) = hAPP(c_List_Orev(U_20412),U_20416)
    | U_20416 != hAPP(hAPP(c_List_Olist_OCons(U_20412),U_20414),c_List_Olist_ONil(U_20412)) ),
    inference(clausify,[status(thm)],[f_4891_4]) ).

fof(f_4892_1,plain,
    ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_concat_Osimps_I2_J]) ).

fof(f_4892_2,plain,
    ! [U_20419,U_20418,U_20417] : c_List_Oconcat(U_20417,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20417)),U_20418),U_20419)) = hAPP(hAPP(c_List_Oappend(U_20417),U_20418),c_List_Oconcat(U_20417,U_20419)),
    inference(variable_rename,[status(thm)],[f_4892_1]) ).

fof(f_4892_3,plain,
    ! [U_20417,U_20418,U_20419] : c_List_Oconcat(U_20417,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20417)),U_20418),U_20419)) = hAPP(hAPP(c_List_Oappend(U_20417),U_20418),c_List_Oconcat(U_20417,U_20419)),
    inference(definitional_conversion,[status(esa)],[f_4892_2]) ).

cnf(f_4892_4,plain,
    c_List_Oconcat(U_20417,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20417)),U_20418),U_20419)) = hAPP(hAPP(c_List_Oappend(U_20417),U_20418),c_List_Oconcat(U_20417,U_20419)),
    inference(clausify,[status(thm)],[f_4892_3]) ).

fof(f_4893_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_rev__concat]) ).

fof(f_4893_2,plain,
    ! [U_20421,U_20420] : hAPP(c_List_Orev(U_20420),c_List_Oconcat(U_20420,U_20421)) = c_List_Oconcat(U_20420,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20420),tc_List_Olist(U_20420)),c_List_Orev(U_20420)),hAPP(c_List_Orev(tc_List_Olist(U_20420)),U_20421))),
    inference(variable_rename,[status(thm)],[f_4893_1]) ).

fof(f_4893_3,plain,
    ! [U_20420,U_20421] : hAPP(c_List_Orev(U_20420),c_List_Oconcat(U_20420,U_20421)) = c_List_Oconcat(U_20420,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20420),tc_List_Olist(U_20420)),c_List_Orev(U_20420)),hAPP(c_List_Orev(tc_List_Olist(U_20420)),U_20421))),
    inference(definitional_conversion,[status(esa)],[f_4893_2]) ).

cnf(f_4893_4,plain,
    hAPP(c_List_Orev(U_20420),c_List_Oconcat(U_20420,U_20421)) = c_List_Oconcat(U_20420,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20420),tc_List_Olist(U_20420)),c_List_Orev(U_20420)),hAPP(c_List_Orev(tc_List_Olist(U_20420)),U_20421))),
    inference(clausify,[status(thm)],[f_4893_3]) ).

fof(f_4894_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__map]) ).

fof(f_4894_2,plain,
    ! [U_20425,U_20424,U_20423,U_20422] : hAPP(c_List_Orev(U_20422),hAPP(hAPP(c_List_Omap(U_20423,U_20422),U_20424),U_20425)) = hAPP(hAPP(c_List_Omap(U_20423,U_20422),U_20424),hAPP(c_List_Orev(U_20423),U_20425)),
    inference(variable_rename,[status(thm)],[f_4894_1]) ).

fof(f_4894_3,plain,
    ! [U_20422,U_20423,U_20424,U_20425] : hAPP(c_List_Orev(U_20422),hAPP(hAPP(c_List_Omap(U_20423,U_20422),U_20424),U_20425)) = hAPP(hAPP(c_List_Omap(U_20423,U_20422),U_20424),hAPP(c_List_Orev(U_20423),U_20425)),
    inference(definitional_conversion,[status(esa)],[f_4894_2]) ).

cnf(f_4894_4,plain,
    hAPP(c_List_Orev(U_20422),hAPP(hAPP(c_List_Omap(U_20423,U_20422),U_20424),U_20425)) = hAPP(hAPP(c_List_Omap(U_20423,U_20422),U_20424),hAPP(c_List_Orev(U_20423),U_20425)),
    inference(clausify,[status(thm)],[f_4894_3]) ).

fof(f_4895_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__concat]) ).

fof(f_4895_2,plain,
    ! [U_20429,U_20428,U_20427,U_20426] : hAPP(hAPP(c_List_Omap(U_20426,U_20427),U_20428),c_List_Oconcat(U_20426,U_20429)) = c_List_Oconcat(U_20427,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20426),tc_List_Olist(U_20427)),hAPP(c_List_Omap(U_20426,U_20427),U_20428)),U_20429)),
    inference(variable_rename,[status(thm)],[f_4895_1]) ).

fof(f_4895_3,plain,
    ! [U_20429,U_20428,U_20426,U_20427] : hAPP(hAPP(c_List_Omap(U_20426,U_20427),U_20428),c_List_Oconcat(U_20426,U_20429)) = c_List_Oconcat(U_20427,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20426),tc_List_Olist(U_20427)),hAPP(c_List_Omap(U_20426,U_20427),U_20428)),U_20429)),
    inference(definitional_conversion,[status(esa)],[f_4895_2]) ).

cnf(f_4895_4,plain,
    hAPP(hAPP(c_List_Omap(U_20426,U_20427),U_20428),c_List_Oconcat(U_20426,U_20429)) = c_List_Oconcat(U_20427,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20426),tc_List_Olist(U_20427)),hAPP(c_List_Omap(U_20426,U_20427),U_20428)),U_20429)),
    inference(clausify,[status(thm)],[f_4895_3]) ).

fof(f_4896_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_rev__foldl__cons]) ).

fof(f_4896_2,plain,
    ! [U_20431,U_20430] : hAPP(c_List_Orev(U_20430),U_20431) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20430),U_20430,hAPP(c_COMBC(U_20430,tc_List_Olist(U_20430),tc_List_Olist(U_20430)),c_List_Olist_OCons(U_20430)),c_List_Olist_ONil(U_20430)),U_20431),
    inference(variable_rename,[status(thm)],[f_4896_1]) ).

fof(f_4896_3,plain,
    ! [U_20430,U_20431] : hAPP(c_List_Orev(U_20430),U_20431) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20430),U_20430,hAPP(c_COMBC(U_20430,tc_List_Olist(U_20430),tc_List_Olist(U_20430)),c_List_Olist_OCons(U_20430)),c_List_Olist_ONil(U_20430)),U_20431),
    inference(definitional_conversion,[status(esa)],[f_4896_2]) ).

cnf(f_4896_4,plain,
    hAPP(c_List_Orev(U_20430),U_20431) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20430),U_20430,hAPP(c_COMBC(U_20430,tc_List_Olist(U_20430),tc_List_Olist(U_20430)),c_List_Olist_OCons(U_20430)),c_List_Olist_ONil(U_20430)),U_20431),
    inference(clausify,[status(thm)],[f_4896_3]) ).

fof(f_4897_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
    inference(fof_nnf,[status(thm)],[fact_concat__conv__foldl]) ).

fof(f_4897_2,plain,
    ! [U_20433,U_20432] : c_List_Oconcat(U_20432,U_20433) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20432),tc_List_Olist(U_20432),c_List_Oappend(U_20432),c_List_Olist_ONil(U_20432)),U_20433),
    inference(variable_rename,[status(thm)],[f_4897_1]) ).

fof(f_4897_3,plain,
    ! [U_20432,U_20433] : c_List_Oconcat(U_20432,U_20433) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20432),tc_List_Olist(U_20432),c_List_Oappend(U_20432),c_List_Olist_ONil(U_20432)),U_20433),
    inference(definitional_conversion,[status(esa)],[f_4897_2]) ).

cnf(f_4897_4,plain,
    c_List_Oconcat(U_20432,U_20433) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20432),tc_List_Olist(U_20432),c_List_Oappend(U_20432),c_List_Olist_ONil(U_20432)),U_20433),
    inference(clausify,[status(thm)],[f_4897_3]) ).

fof(f_4898_1,plain,
    ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_foldl__conv__concat]) ).

fof(f_4898_2,plain,
    ! [U_20436,U_20435,U_20434] : hAPP(c_List_Ofoldl(tc_List_Olist(U_20434),tc_List_Olist(U_20434),c_List_Oappend(U_20434),U_20435),U_20436) = hAPP(hAPP(c_List_Oappend(U_20434),U_20435),c_List_Oconcat(U_20434,U_20436)),
    inference(variable_rename,[status(thm)],[f_4898_1]) ).

fof(f_4898_3,plain,
    ! [U_20434,U_20435,U_20436] : hAPP(c_List_Ofoldl(tc_List_Olist(U_20434),tc_List_Olist(U_20434),c_List_Oappend(U_20434),U_20435),U_20436) = hAPP(hAPP(c_List_Oappend(U_20434),U_20435),c_List_Oconcat(U_20434,U_20436)),
    inference(definitional_conversion,[status(esa)],[f_4898_2]) ).

cnf(f_4898_4,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(U_20434),tc_List_Olist(U_20434),c_List_Oappend(U_20434),U_20435),U_20436) = hAPP(hAPP(c_List_Oappend(U_20434),U_20435),c_List_Oconcat(U_20434,U_20436)),
    inference(clausify,[status(thm)],[f_4898_3]) ).

fof(f_4899_1,plain,
    ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rev__append]) ).

fof(f_4899_2,plain,
    ! [U_20439,U_20438,U_20437] : hAPP(c_List_Orev(U_20437),hAPP(hAPP(c_List_Oappend(U_20437),U_20438),U_20439)) = hAPP(hAPP(c_List_Oappend(U_20437),hAPP(c_List_Orev(U_20437),U_20439)),hAPP(c_List_Orev(U_20437),U_20438)),
    inference(variable_rename,[status(thm)],[f_4899_1]) ).

fof(f_4899_3,plain,
    ! [U_20437,U_20438,U_20439] : hAPP(c_List_Orev(U_20437),hAPP(hAPP(c_List_Oappend(U_20437),U_20438),U_20439)) = hAPP(hAPP(c_List_Oappend(U_20437),hAPP(c_List_Orev(U_20437),U_20439)),hAPP(c_List_Orev(U_20437),U_20438)),
    inference(definitional_conversion,[status(esa)],[f_4899_2]) ).

cnf(f_4899_4,plain,
    hAPP(c_List_Orev(U_20437),hAPP(hAPP(c_List_Oappend(U_20437),U_20438),U_20439)) = hAPP(hAPP(c_List_Oappend(U_20437),hAPP(c_List_Orev(U_20437),U_20439)),hAPP(c_List_Orev(U_20437),U_20438)),
    inference(clausify,[status(thm)],[f_4899_3]) ).

fof(f_4900_1,plain,
    ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
    inference(fof_nnf,[status(thm)],[fact_concat__append]) ).

fof(f_4900_2,plain,
    ! [U_20442,U_20441,U_20440] : c_List_Oconcat(U_20440,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20440)),U_20441),U_20442)) = hAPP(hAPP(c_List_Oappend(U_20440),c_List_Oconcat(U_20440,U_20441)),c_List_Oconcat(U_20440,U_20442)),
    inference(variable_rename,[status(thm)],[f_4900_1]) ).

fof(f_4900_3,plain,
    ! [U_20440,U_20441,U_20442] : c_List_Oconcat(U_20440,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20440)),U_20441),U_20442)) = hAPP(hAPP(c_List_Oappend(U_20440),c_List_Oconcat(U_20440,U_20441)),c_List_Oconcat(U_20440,U_20442)),
    inference(definitional_conversion,[status(esa)],[f_4900_2]) ).

cnf(f_4900_4,plain,
    c_List_Oconcat(U_20440,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20440)),U_20441),U_20442)) = hAPP(hAPP(c_List_Oappend(U_20440),c_List_Oconcat(U_20440,U_20441)),c_List_Oconcat(U_20440,U_20442)),
    inference(clausify,[status(thm)],[f_4900_3]) ).

fof(f_4901_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__rev]) ).

fof(f_4901_2,plain,
    ! [U_20444,U_20443] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_20443),hAPP(c_List_Orev(U_20443),U_20444)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20443),U_20444)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_20443),U_20444))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20443),hAPP(c_List_Orev(U_20443),U_20444))) ) ),
    inference(variable_rename,[status(thm)],[f_4901_1]) ).

fof(f_4901_3,plain,
    ( ! [U_20448,U_20446] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20446),hAPP(c_List_Orev(U_20446),U_20448)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20446),U_20448)) )
    & ! [U_20447,U_20445] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20445),U_20447))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20445),hAPP(c_List_Orev(U_20445),U_20447))) ) ),
    inference(miniscope,[status(thm)],[f_4901_2]) ).

fof(f_4901_4,plain,
    ( ! [U_20446,U_20448] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20446),hAPP(c_List_Orev(U_20446),U_20448)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20446),U_20448)) )
    & ! [U_20445,U_20447] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20445),U_20447))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20445),hAPP(c_List_Orev(U_20445),U_20447))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4901_3]) ).

cnf(f_4901_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20445),U_20447))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20445),hAPP(c_List_Orev(U_20445),U_20447))) ),
    inference(clausify,[status(thm)],[f_4901_4]) ).

cnf(f_4901_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20446),hAPP(c_List_Orev(U_20446),U_20448)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20446),U_20448)) ),
    inference(clausify,[status(thm)],[f_4901_4]) ).

fof(f_4902_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
    inference(fof_nnf,[status(thm)],[fact_set__concat]) ).

fof(f_4902_2,plain,
    ! [U_20450,U_20449] : hAPP(c_List_Oset(U_20449),c_List_Oconcat(U_20449,U_20450)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20449),tc_fun(U_20449,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20449)),U_20450)),c_List_Oset(U_20449)),
    inference(variable_rename,[status(thm)],[f_4902_1]) ).

fof(f_4902_3,plain,
    ! [U_20449,U_20450] : hAPP(c_List_Oset(U_20449),c_List_Oconcat(U_20449,U_20450)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20449),tc_fun(U_20449,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20449)),U_20450)),c_List_Oset(U_20449)),
    inference(definitional_conversion,[status(esa)],[f_4902_2]) ).

cnf(f_4902_4,plain,
    hAPP(c_List_Oset(U_20449),c_List_Oconcat(U_20449,U_20450)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20449),tc_fun(U_20449,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20449)),U_20450)),c_List_Oset(U_20449)),
    inference(clausify,[status(thm)],[f_4902_3]) ).

fof(f_4903_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__rev]) ).

fof(f_4903_2,plain,
    ! [U_20452,U_20451] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20451)),hAPP(c_List_Orev(U_20451),U_20452)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20451)),U_20452),
    inference(variable_rename,[status(thm)],[f_4903_1]) ).

fof(f_4903_3,plain,
    ! [U_20451,U_20452] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20451)),hAPP(c_List_Orev(U_20451),U_20452)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20451)),U_20452),
    inference(definitional_conversion,[status(esa)],[f_4903_2]) ).

cnf(f_4903_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20451)),hAPP(c_List_Orev(U_20451),U_20452)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20451)),U_20452),
    inference(clausify,[status(thm)],[f_4903_3]) ).

fof(f_4904_1,plain,
    ! [V_xs,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__rev]) ).

fof(f_4904_2,plain,
    ! [U_20454,U_20453] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20453),hAPP(c_List_Orev(U_20453),U_20454)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20453),U_20454)
      | ~ class_Groups_Ocomm__monoid__add(U_20453) ),
    inference(variable_rename,[status(thm)],[f_4904_1]) ).

fof(f_4904_3,plain,
    ! [U_20453,U_20454] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20453),hAPP(c_List_Orev(U_20453),U_20454)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20453),U_20454)
      | ~ class_Groups_Ocomm__monoid__add(U_20453) ),
    inference(definitional_conversion,[status(esa)],[f_4904_2]) ).

cnf(f_4904_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20453),hAPP(c_List_Orev(U_20453),U_20454)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20453),U_20454)
    | ~ class_Groups_Ocomm__monoid__add(U_20453) ),
    inference(clausify,[status(thm)],[f_4904_3]) ).

fof(f_4905_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
        | V_xs_2 != V_ys_2 )
      & ( V_xs_2 = V_ys_2
        | hAPP(c_List_Orev(T_b),V_xs_2) != hAPP(c_List_Orev(T_b),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv]) ).

fof(f_4905_2,plain,
    ! [U_20457,U_20456,U_20455] :
      ( ( hAPP(c_List_Orev(U_20455),U_20456) = hAPP(c_List_Orev(U_20455),U_20457)
        | U_20456 != U_20457 )
      & ( U_20456 = U_20457
        | hAPP(c_List_Orev(U_20455),U_20456) != hAPP(c_List_Orev(U_20455),U_20457) ) ),
    inference(variable_rename,[status(thm)],[f_4905_1]) ).

fof(f_4905_3,plain,
    ( ! [U_20463,U_20461] :
        ( ! [U_20459] : hAPP(c_List_Orev(U_20459),U_20461) = hAPP(c_List_Orev(U_20459),U_20463)
        | U_20461 != U_20463 )
    & ! [U_20462,U_20460] :
        ( ! [U_20458] : hAPP(c_List_Orev(U_20458),U_20460) != hAPP(c_List_Orev(U_20458),U_20462)
        | U_20460 = U_20462 ) ),
    inference(miniscope,[status(thm)],[f_4905_2]) ).

fof(f_4905_4,plain,
    ( ! [U_20463,U_20459,U_20461] :
        ( hAPP(c_List_Orev(U_20459),U_20461) = hAPP(c_List_Orev(U_20459),U_20463)
        | U_20461 != U_20463 )
    & ! [U_20462,U_20458,U_20460] :
        ( hAPP(c_List_Orev(U_20458),U_20460) != hAPP(c_List_Orev(U_20458),U_20462)
        | U_20460 = U_20462 ) ),
    inference(definitional_conversion,[status(esa)],[f_4905_3]) ).

cnf(f_4905_5,plain,
    ( hAPP(c_List_Orev(U_20458),U_20460) != hAPP(c_List_Orev(U_20458),U_20462)
    | U_20460 = U_20462 ),
    inference(clausify,[status(thm)],[f_4905_4]) ).

cnf(f_4905_6,plain,
    ( hAPP(c_List_Orev(U_20459),U_20461) = hAPP(c_List_Orev(U_20459),U_20463)
    | U_20461 != U_20463 ),
    inference(clausify,[status(thm)],[f_4905_4]) ).

fof(f_4906_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
        | V_xs_2 != hAPP(c_List_Orev(T_b),V_ys_2) )
      & ( V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2)
        | hAPP(c_List_Orev(T_b),V_xs_2) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__swap]) ).

fof(f_4906_2,plain,
    ! [U_20466,U_20465,U_20464] :
      ( ( hAPP(c_List_Orev(U_20464),U_20465) = U_20466
        | U_20465 != hAPP(c_List_Orev(U_20464),U_20466) )
      & ( U_20465 = hAPP(c_List_Orev(U_20464),U_20466)
        | hAPP(c_List_Orev(U_20464),U_20465) != U_20466 ) ),
    inference(variable_rename,[status(thm)],[f_4906_1]) ).

fof(f_4906_3,plain,
    ( ! [U_20472,U_20470,U_20468] :
        ( hAPP(c_List_Orev(U_20468),U_20470) = U_20472
        | U_20470 != hAPP(c_List_Orev(U_20468),U_20472) )
    & ! [U_20471,U_20469,U_20467] :
        ( U_20469 = hAPP(c_List_Orev(U_20467),U_20471)
        | hAPP(c_List_Orev(U_20467),U_20469) != U_20471 ) ),
    inference(miniscope,[status(thm)],[f_4906_2]) ).

fof(f_4906_4,plain,
    ( ! [U_20468,U_20470,U_20472] :
        ( hAPP(c_List_Orev(U_20468),U_20470) = U_20472
        | U_20470 != hAPP(c_List_Orev(U_20468),U_20472) )
    & ! [U_20469,U_20471,U_20467] :
        ( U_20469 = hAPP(c_List_Orev(U_20467),U_20471)
        | hAPP(c_List_Orev(U_20467),U_20469) != U_20471 ) ),
    inference(definitional_conversion,[status(esa)],[f_4906_3]) ).

cnf(f_4906_5,plain,
    ( U_20469 = hAPP(c_List_Orev(U_20467),U_20471)
    | hAPP(c_List_Orev(U_20467),U_20469) != U_20471 ),
    inference(clausify,[status(thm)],[f_4906_4]) ).

cnf(f_4906_6,plain,
    ( hAPP(c_List_Orev(U_20468),U_20470) = U_20472
    | U_20470 != hAPP(c_List_Orev(U_20468),U_20472) ),
    inference(clausify,[status(thm)],[f_4906_4]) ).

fof(f_4907_1,plain,
    ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_rev__rev__ident]) ).

fof(f_4907_2,plain,
    ! [U_20474,U_20473] : hAPP(c_List_Orev(U_20473),hAPP(c_List_Orev(U_20473),U_20474)) = U_20474,
    inference(variable_rename,[status(thm)],[f_4907_1]) ).

fof(f_4907_3,plain,
    ! [U_20473,U_20474] : hAPP(c_List_Orev(U_20473),hAPP(c_List_Orev(U_20473),U_20474)) = U_20474,
    inference(definitional_conversion,[status(esa)],[f_4907_2]) ).

cnf(f_4907_4,plain,
    hAPP(c_List_Orev(U_20473),hAPP(c_List_Orev(U_20473),U_20474)) = U_20474,
    inference(clausify,[status(thm)],[f_4907_3]) ).

fof(f_4908_1,plain,
    ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr__foldl]) ).

fof(f_4908_2,plain,
    ! [U_20479,U_20478,U_20477,U_20476,U_20475] : c_List_Ofoldr(U_20475,U_20476,U_20477,U_20478,U_20479) = hAPP(c_List_Ofoldl(U_20476,U_20475,hAPP(c_COMBC(U_20475,U_20476,U_20476),U_20477),U_20479),hAPP(c_List_Orev(U_20475),U_20478)),
    inference(variable_rename,[status(thm)],[f_4908_1]) ).

fof(f_4908_3,plain,
    ! [U_20475,U_20476,U_20477,U_20478,U_20479] : c_List_Ofoldr(U_20475,U_20476,U_20477,U_20478,U_20479) = hAPP(c_List_Ofoldl(U_20476,U_20475,hAPP(c_COMBC(U_20475,U_20476,U_20476),U_20477),U_20479),hAPP(c_List_Orev(U_20475),U_20478)),
    inference(definitional_conversion,[status(esa)],[f_4908_2]) ).

cnf(f_4908_4,plain,
    c_List_Ofoldr(U_20475,U_20476,U_20477,U_20478,U_20479) = hAPP(c_List_Ofoldl(U_20476,U_20475,hAPP(c_COMBC(U_20475,U_20476,U_20476),U_20477),U_20479),hAPP(c_List_Orev(U_20475),U_20478)),
    inference(clausify,[status(thm)],[f_4908_3]) ).

fof(f_4909_1,plain,
    ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr]) ).

fof(f_4909_2,plain,
    ! [U_20484,U_20483,U_20482,U_20481,U_20480] : hAPP(c_List_Ofoldl(U_20480,U_20481,U_20482,U_20483),U_20484) = c_List_Ofoldr(U_20481,U_20480,hAPP(c_COMBC(U_20480,U_20481,U_20480),U_20482),hAPP(c_List_Orev(U_20481),U_20484),U_20483),
    inference(variable_rename,[status(thm)],[f_4909_1]) ).

fof(f_4909_3,plain,
    ! [U_20480,U_20481,U_20482,U_20483,U_20484] : hAPP(c_List_Ofoldl(U_20480,U_20481,U_20482,U_20483),U_20484) = c_List_Ofoldr(U_20481,U_20480,hAPP(c_COMBC(U_20480,U_20481,U_20480),U_20482),hAPP(c_List_Orev(U_20481),U_20484),U_20483),
    inference(definitional_conversion,[status(esa)],[f_4909_2]) ).

cnf(f_4909_4,plain,
    hAPP(c_List_Ofoldl(U_20480,U_20481,U_20482,U_20483),U_20484) = c_List_Ofoldr(U_20481,U_20480,hAPP(c_COMBC(U_20480,U_20481,U_20480),U_20482),hAPP(c_List_Orev(U_20481),U_20484),U_20483),
    inference(clausify,[status(thm)],[f_4909_3]) ).

fof(f_4910_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rev]) ).

fof(f_4910_2,plain,
    ! [U_20486,U_20485] : hAPP(c_List_Oset(U_20485),hAPP(c_List_Orev(U_20485),U_20486)) = hAPP(c_List_Oset(U_20485),U_20486),
    inference(variable_rename,[status(thm)],[f_4910_1]) ).

fof(f_4910_3,plain,
    ! [U_20485,U_20486] : hAPP(c_List_Oset(U_20485),hAPP(c_List_Orev(U_20485),U_20486)) = hAPP(c_List_Oset(U_20485),U_20486),
    inference(definitional_conversion,[status(esa)],[f_4910_2]) ).

cnf(f_4910_4,plain,
    hAPP(c_List_Oset(U_20485),hAPP(c_List_Orev(U_20485),U_20486)) = hAPP(c_List_Oset(U_20485),U_20486),
    inference(clausify,[status(thm)],[f_4910_3]) ).

fof(f_4911_1,plain,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) ),
    inference(fof_nnf,[status(thm)],[fact_zip__rev]) ).

fof(f_4911_2,plain,
    ! [U_20490,U_20489,U_20488,U_20487] :
      ( hAPP(hAPP(c_List_Ozip(U_20487,U_20489),hAPP(c_List_Orev(U_20487),U_20488)),hAPP(c_List_Orev(U_20489),U_20490)) = hAPP(c_List_Orev(tc_prod(U_20487,U_20489)),hAPP(hAPP(c_List_Ozip(U_20487,U_20489),U_20488),U_20490))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20487)),U_20488) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20489)),U_20490) ),
    inference(variable_rename,[status(thm)],[f_4911_1]) ).

fof(f_4911_3,plain,
    ! [U_20487,U_20488,U_20489,U_20490] :
      ( hAPP(hAPP(c_List_Ozip(U_20487,U_20489),hAPP(c_List_Orev(U_20487),U_20488)),hAPP(c_List_Orev(U_20489),U_20490)) = hAPP(c_List_Orev(tc_prod(U_20487,U_20489)),hAPP(hAPP(c_List_Ozip(U_20487,U_20489),U_20488),U_20490))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20487)),U_20488) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20489)),U_20490) ),
    inference(definitional_conversion,[status(esa)],[f_4911_2]) ).

cnf(f_4911_4,plain,
    ( hAPP(hAPP(c_List_Ozip(U_20487,U_20489),hAPP(c_List_Orev(U_20487),U_20488)),hAPP(c_List_Orev(U_20489),U_20490)) = hAPP(c_List_Orev(tc_prod(U_20487,U_20489)),hAPP(hAPP(c_List_Ozip(U_20487,U_20489),U_20488),U_20490))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20487)),U_20488) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20489)),U_20490) ),
    inference(clausify,[status(thm)],[f_4911_3]) ).

fof(f_4912_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__filter]) ).

fof(f_4912_2,plain,
    ! [U_20493,U_20492,U_20491] : hAPP(c_List_Orev(U_20491),hAPP(c_List_Ofilter(U_20491,U_20492),U_20493)) = hAPP(c_List_Ofilter(U_20491,U_20492),hAPP(c_List_Orev(U_20491),U_20493)),
    inference(variable_rename,[status(thm)],[f_4912_1]) ).

fof(f_4912_3,plain,
    ! [U_20491,U_20492,U_20493] : hAPP(c_List_Orev(U_20491),hAPP(c_List_Ofilter(U_20491,U_20492),U_20493)) = hAPP(c_List_Ofilter(U_20491,U_20492),hAPP(c_List_Orev(U_20491),U_20493)),
    inference(definitional_conversion,[status(esa)],[f_4912_2]) ).

cnf(f_4912_4,plain,
    hAPP(c_List_Orev(U_20491),hAPP(c_List_Ofilter(U_20491,U_20492),U_20493)) = hAPP(c_List_Ofilter(U_20491,U_20492),hAPP(c_List_Orev(U_20491),U_20493)),
    inference(clausify,[status(thm)],[f_4912_3]) ).

fof(f_4913_1,plain,
    ! [T_a,V_xs] :
      ( c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__rev]) ).

fof(f_4913_2,plain,
    ! [U_20495,U_20494] :
      ( c_List_Olast(U_20495,hAPP(c_List_Orev(U_20495),U_20494)) = hAPP(c_List_Ohd(U_20495),U_20494)
      | U_20494 = c_List_Olist_ONil(U_20495) ),
    inference(variable_rename,[status(thm)],[f_4913_1]) ).

fof(f_4913_3,plain,
    ! [U_20494,U_20495] :
      ( c_List_Olast(U_20495,hAPP(c_List_Orev(U_20495),U_20494)) = hAPP(c_List_Ohd(U_20495),U_20494)
      | U_20494 = c_List_Olist_ONil(U_20495) ),
    inference(definitional_conversion,[status(esa)],[f_4913_2]) ).

cnf(f_4913_4,plain,
    ( c_List_Olast(U_20495,hAPP(c_List_Orev(U_20495),U_20494)) = hAPP(c_List_Ohd(U_20495),U_20494)
    | U_20494 = c_List_Olist_ONil(U_20495) ),
    inference(clausify,[status(thm)],[f_4913_3]) ).

fof(f_4914_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__rev]) ).

fof(f_4914_2,plain,
    ! [U_20497,U_20496] :
      ( hAPP(c_List_Ohd(U_20497),hAPP(c_List_Orev(U_20497),U_20496)) = c_List_Olast(U_20497,U_20496)
      | U_20496 = c_List_Olist_ONil(U_20497) ),
    inference(variable_rename,[status(thm)],[f_4914_1]) ).

fof(f_4914_3,plain,
    ! [U_20496,U_20497] :
      ( hAPP(c_List_Ohd(U_20497),hAPP(c_List_Orev(U_20497),U_20496)) = c_List_Olast(U_20497,U_20496)
      | U_20496 = c_List_Olist_ONil(U_20497) ),
    inference(definitional_conversion,[status(esa)],[f_4914_2]) ).

cnf(f_4914_4,plain,
    ( hAPP(c_List_Ohd(U_20497),hAPP(c_List_Orev(U_20497),U_20496)) = c_List_Olast(U_20497,U_20496)
    | U_20496 = c_List_Olist_ONil(U_20497) ),
    inference(clausify,[status(thm)],[f_4914_3]) ).

fof(f_4915_1,plain,
    ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_sorted__transpose]) ).

fof(f_4915_2,plain,
    ! [U_20499,U_20498] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20498),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20498))),c_List_Otranspose(U_20498,U_20499)))),
    inference(variable_rename,[status(thm)],[f_4915_1]) ).

fof(f_4915_3,plain,
    ! [U_20498,U_20499] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20498),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20498))),c_List_Otranspose(U_20498,U_20499)))),
    inference(definitional_conversion,[status(esa)],[f_4915_2]) ).

cnf(f_4915_4,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20498),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20498))),c_List_Otranspose(U_20498,U_20499)))),
    inference(clausify,[status(thm)],[f_4915_3]) ).

fof(f_4916_1,plain,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rev__drop]) ).

fof(f_4916_2,plain,
    ! [U_20502,U_20501,U_20500] : hAPP(c_List_Orev(U_20500),hAPP(hAPP(c_List_Odrop(U_20500),U_20501),U_20502)) = hAPP(hAPP(c_List_Otake(U_20500),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20500)),U_20502)),U_20501)),hAPP(c_List_Orev(U_20500),U_20502)),
    inference(variable_rename,[status(thm)],[f_4916_1]) ).

fof(f_4916_3,plain,
    ! [U_20500,U_20501,U_20502] : hAPP(c_List_Orev(U_20500),hAPP(hAPP(c_List_Odrop(U_20500),U_20501),U_20502)) = hAPP(hAPP(c_List_Otake(U_20500),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20500)),U_20502)),U_20501)),hAPP(c_List_Orev(U_20500),U_20502)),
    inference(definitional_conversion,[status(esa)],[f_4916_2]) ).

cnf(f_4916_4,plain,
    hAPP(c_List_Orev(U_20500),hAPP(hAPP(c_List_Odrop(U_20500),U_20501),U_20502)) = hAPP(hAPP(c_List_Otake(U_20500),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20500)),U_20502)),U_20501)),hAPP(c_List_Orev(U_20500),U_20502)),
    inference(clausify,[status(thm)],[f_4916_3]) ).

fof(f_4917_1,plain,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rev__take]) ).

fof(f_4917_2,plain,
    ! [U_20505,U_20504,U_20503] : hAPP(c_List_Orev(U_20503),hAPP(hAPP(c_List_Otake(U_20503),U_20504),U_20505)) = hAPP(hAPP(c_List_Odrop(U_20503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20503)),U_20505)),U_20504)),hAPP(c_List_Orev(U_20503),U_20505)),
    inference(variable_rename,[status(thm)],[f_4917_1]) ).

fof(f_4917_3,plain,
    ! [U_20503,U_20504,U_20505] : hAPP(c_List_Orev(U_20503),hAPP(hAPP(c_List_Otake(U_20503),U_20504),U_20505)) = hAPP(hAPP(c_List_Odrop(U_20503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20503)),U_20505)),U_20504)),hAPP(c_List_Orev(U_20503),U_20505)),
    inference(definitional_conversion,[status(esa)],[f_4917_2]) ).

cnf(f_4917_4,plain,
    hAPP(c_List_Orev(U_20503),hAPP(hAPP(c_List_Otake(U_20503),U_20504),U_20505)) = hAPP(hAPP(c_List_Odrop(U_20503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20503)),U_20505)),U_20504)),hAPP(c_List_Orev(U_20503),U_20505)),
    inference(clausify,[status(thm)],[f_4917_3]) ).

fof(f_4918_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate__rev]) ).

fof(f_4918_2,plain,
    ! [U_20508,U_20507,U_20506] : hAPP(c_List_Orotate(U_20506,U_20507),hAPP(c_List_Orev(U_20506),U_20508)) = hAPP(c_List_Orev(U_20506),hAPP(c_List_Orotate(U_20506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20506)),U_20508)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20507,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20506)),U_20508)))),U_20508)),
    inference(variable_rename,[status(thm)],[f_4918_1]) ).

fof(f_4918_3,plain,
    ! [U_20506,U_20507,U_20508] : hAPP(c_List_Orotate(U_20506,U_20507),hAPP(c_List_Orev(U_20506),U_20508)) = hAPP(c_List_Orev(U_20506),hAPP(c_List_Orotate(U_20506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20506)),U_20508)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20507,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20506)),U_20508)))),U_20508)),
    inference(definitional_conversion,[status(esa)],[f_4918_2]) ).

cnf(f_4918_4,plain,
    hAPP(c_List_Orotate(U_20506,U_20507),hAPP(c_List_Orev(U_20506),U_20508)) = hAPP(c_List_Orev(U_20506),hAPP(c_List_Orotate(U_20506,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20506)),U_20508)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20507,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20506)),U_20508)))),U_20508)),
    inference(clausify,[status(thm)],[f_4918_3]) ).

fof(f_4919_1,plain,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(f_4919_2,plain,
    ! [U_20512,U_20511,U_20510,U_20509] : c_List_Otranspose(U_20509,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),hAPP(hAPP(c_List_Olist_OCons(U_20509),U_20510),U_20511)),U_20512)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),hAPP(hAPP(c_List_Olist_OCons(U_20509),U_20510),c_List_Oconcat(U_20509,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20509),tc_List_Olist(U_20509)),c_List_Olist_Olist__case(tc_List_Olist(U_20509),U_20509,c_List_Olist_ONil(U_20509),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20509),tc_fun(tc_List_Olist(U_20509),tc_List_Olist(U_20509)),U_20509),c_COMBK(tc_List_Olist(U_20509),tc_List_Olist(U_20509))),hAPP(hAPP(c_COMBC(U_20509,tc_List_Olist(U_20509),tc_List_Olist(U_20509)),c_List_Olist_OCons(U_20509)),c_List_Olist_ONil(U_20509))))),U_20512)))),c_List_Otranspose(U_20509,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),U_20511),c_List_Oconcat(tc_List_Olist(U_20509),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20509)),U_20509,c_List_Olist_ONil(tc_List_Olist(U_20509)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509))),U_20509),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509)),tc_List_Olist(tc_List_Olist(U_20509))),c_List_Olist_OCons(tc_List_Olist(U_20509))),c_List_Olist_ONil(tc_List_Olist(U_20509)))))),U_20512))))),
    inference(variable_rename,[status(thm)],[f_4919_1]) ).

fof(f_4919_3,plain,
    ! [U_20509,U_20510,U_20511,U_20512] : c_List_Otranspose(U_20509,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),hAPP(hAPP(c_List_Olist_OCons(U_20509),U_20510),U_20511)),U_20512)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),hAPP(hAPP(c_List_Olist_OCons(U_20509),U_20510),c_List_Oconcat(U_20509,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20509),tc_List_Olist(U_20509)),c_List_Olist_Olist__case(tc_List_Olist(U_20509),U_20509,c_List_Olist_ONil(U_20509),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20509),tc_fun(tc_List_Olist(U_20509),tc_List_Olist(U_20509)),U_20509),c_COMBK(tc_List_Olist(U_20509),tc_List_Olist(U_20509))),hAPP(hAPP(c_COMBC(U_20509,tc_List_Olist(U_20509),tc_List_Olist(U_20509)),c_List_Olist_OCons(U_20509)),c_List_Olist_ONil(U_20509))))),U_20512)))),c_List_Otranspose(U_20509,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),U_20511),c_List_Oconcat(tc_List_Olist(U_20509),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20509)),U_20509,c_List_Olist_ONil(tc_List_Olist(U_20509)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509))),U_20509),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509)),tc_List_Olist(tc_List_Olist(U_20509))),c_List_Olist_OCons(tc_List_Olist(U_20509))),c_List_Olist_ONil(tc_List_Olist(U_20509)))))),U_20512))))),
    inference(definitional_conversion,[status(esa)],[f_4919_2]) ).

cnf(f_4919_4,plain,
    c_List_Otranspose(U_20509,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),hAPP(hAPP(c_List_Olist_OCons(U_20509),U_20510),U_20511)),U_20512)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),hAPP(hAPP(c_List_Olist_OCons(U_20509),U_20510),c_List_Oconcat(U_20509,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20509),tc_List_Olist(U_20509)),c_List_Olist_Olist__case(tc_List_Olist(U_20509),U_20509,c_List_Olist_ONil(U_20509),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20509),tc_fun(tc_List_Olist(U_20509),tc_List_Olist(U_20509)),U_20509),c_COMBK(tc_List_Olist(U_20509),tc_List_Olist(U_20509))),hAPP(hAPP(c_COMBC(U_20509,tc_List_Olist(U_20509),tc_List_Olist(U_20509)),c_List_Olist_OCons(U_20509)),c_List_Olist_ONil(U_20509))))),U_20512)))),c_List_Otranspose(U_20509,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20509)),U_20511),c_List_Oconcat(tc_List_Olist(U_20509),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20509)),U_20509,c_List_Olist_ONil(tc_List_Olist(U_20509)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509))),U_20509),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20509),tc_List_Olist(tc_List_Olist(U_20509)),tc_List_Olist(tc_List_Olist(U_20509))),c_List_Olist_OCons(tc_List_Olist(U_20509))),c_List_Olist_ONil(tc_List_Olist(U_20509)))))),U_20512))))),
    inference(clausify,[status(thm)],[f_4919_3]) ).

fof(f_4920_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_rev__nth]) ).

fof(f_4920_2,plain,
    ! [U_20515,U_20514,U_20513] :
      ( hAPP(hAPP(c_List_Onth(U_20514),hAPP(c_List_Orev(U_20514),U_20515)),U_20513) = hAPP(hAPP(c_List_Onth(U_20514),U_20515),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20514)),U_20515)),hAPP(c_Nat_OSuc,U_20513)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20513),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20514)),U_20515))) ),
    inference(variable_rename,[status(thm)],[f_4920_1]) ).

fof(f_4920_3,plain,
    ! [U_20513,U_20514,U_20515] :
      ( hAPP(hAPP(c_List_Onth(U_20514),hAPP(c_List_Orev(U_20514),U_20515)),U_20513) = hAPP(hAPP(c_List_Onth(U_20514),U_20515),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20514)),U_20515)),hAPP(c_Nat_OSuc,U_20513)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20513),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20514)),U_20515))) ),
    inference(definitional_conversion,[status(esa)],[f_4920_2]) ).

cnf(f_4920_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20514),hAPP(c_List_Orev(U_20514),U_20515)),U_20513) = hAPP(hAPP(c_List_Onth(U_20514),U_20515),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20514)),U_20515)),hAPP(c_Nat_OSuc,U_20513)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20513),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20514)),U_20515))) ),
    inference(clausify,[status(thm)],[f_4920_3]) ).

fof(f_4921_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( V_xs_2 = V_ys_2
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
      | c_List_Oconcat(T_b,V_xs_2) != c_List_Oconcat(T_b,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_concat__injective]) ).

fof(f_4921_2,plain,
    ! [U_20519,U_20518,U_20517] :
      ( U_20518 = U_20519
      | ? [U_20516] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20517),tc_List_Olist(U_20517),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20517),tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),tc_List_Olist(U_20517)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20517))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20517)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517)))),U_20516))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),U_20516),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20517),tc_List_Olist(U_20517)),U_20518),U_20519)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20518) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20519)
      | c_List_Oconcat(U_20517,U_20518) != c_List_Oconcat(U_20517,U_20519) ),
    inference(variable_rename,[status(thm)],[f_4921_1]) ).

fof(f_4921_3,plain,
    ! [U_20519,U_20518,U_20517] :
      ( U_20518 = U_20519
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20517),tc_List_Olist(U_20517),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20517),tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),tc_List_Olist(U_20517)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20517))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20517)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517)))),sK506(U_20519,U_20518,U_20517)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),sK506(U_20519,U_20518,U_20517)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20517),tc_List_Olist(U_20517)),U_20518),U_20519)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20518) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20519)
      | c_List_Oconcat(U_20517,U_20518) != c_List_Oconcat(U_20517,U_20519) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_20516,sK506(U_20519,U_20518,U_20517))],[f_4921_2]) ).

fof(f_4921_4,plain,
    ( ! [U_20517,U_20518,U_20519] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20517),tc_List_Olist(U_20517),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20517),tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),tc_List_Olist(U_20517)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20517))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20517)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517)))),sK506(U_20519,U_20518,U_20517)))
        | ~ sP1236(U_20517,U_20518,U_20519) )
    & ! [U_20517,U_20518,U_20519] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),sK506(U_20519,U_20518,U_20517)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20517),tc_List_Olist(U_20517)),U_20518),U_20519))))
        | ~ sP1236(U_20517,U_20518,U_20519) )
    & ! [U_20517,U_20518,U_20519] :
        ( U_20518 = U_20519
        | sP1236(U_20517,U_20518,U_20519)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20518) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20519)
        | c_List_Oconcat(U_20517,U_20518) != c_List_Oconcat(U_20517,U_20519) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1236])],[f_4921_3]) ).

cnf(f_4921_5,plain,
    ( U_20518 = U_20519
    | sP1236(U_20517,U_20518,U_20519)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20518) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20517))),U_20519)
    | c_List_Oconcat(U_20517,U_20518) != c_List_Oconcat(U_20517,U_20519) ),
    inference(clausify,[status(thm)],[f_4921_4]) ).

cnf(f_4921_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),sK506(U_20519,U_20518,U_20517)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20517),tc_List_Olist(U_20517))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20517),tc_List_Olist(U_20517)),U_20518),U_20519))))
    | ~ sP1236(U_20517,U_20518,U_20519) ),
    inference(clausify,[status(thm)],[f_4921_4]) ).

cnf(f_4921_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20517),tc_List_Olist(U_20517),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20517),tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20517),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20517),tc_HOL_Obool)),tc_List_Olist(U_20517)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20517))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20517)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20517)))),sK506(U_20519,U_20518,U_20517)))
    | ~ sP1236(U_20517,U_20518,U_20519) ),
    inference(clausify,[status(thm)],[f_4921_4]) ).

fof(f_4922_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | c_List_Oconcat(T_b,V_xs_2) != c_List_Oconcat(T_b,V_ys_2) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_concat__eq__concat__iff]) ).

fof(f_4922_2,plain,
    ! [U_20523,U_20522,U_20521] :
      ( ( ( c_List_Oconcat(U_20521,U_20522) = c_List_Oconcat(U_20521,U_20523)
          | U_20522 != U_20523 )
        & ( U_20522 = U_20523
          | c_List_Oconcat(U_20521,U_20522) != c_List_Oconcat(U_20521,U_20523) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20522) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20523)
      | ? [U_20520] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20521),tc_List_Olist(U_20521),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20521),tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),tc_List_Olist(U_20521)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20521))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20521)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521)))),U_20520))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),U_20520),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20521),tc_List_Olist(U_20521)),U_20522),U_20523)))) ) ),
    inference(variable_rename,[status(thm)],[f_4922_1]) ).

fof(f_4922_3,plain,
    ! [U_20523,U_20522,U_20521] :
      ( ( ( c_List_Oconcat(U_20521,U_20522) = c_List_Oconcat(U_20521,U_20523)
          | U_20522 != U_20523 )
        & ( U_20522 = U_20523
          | c_List_Oconcat(U_20521,U_20522) != c_List_Oconcat(U_20521,U_20523) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20522) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20523)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20521),tc_List_Olist(U_20521),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20521),tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),tc_List_Olist(U_20521)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20521))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20521)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521)))),sK507(U_20523,U_20522,U_20521)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),sK507(U_20523,U_20522,U_20521)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20521),tc_List_Olist(U_20521)),U_20522),U_20523)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_20520,sK507(U_20523,U_20522,U_20521))],[f_4922_2]) ).

fof(f_4922_4,plain,
    ( ! [U_20521,U_20522,U_20523] :
        ( c_List_Oconcat(U_20521,U_20522) = c_List_Oconcat(U_20521,U_20523)
        | U_20522 != U_20523
        | ~ sP1238(U_20521,U_20522,U_20523) )
    & ! [U_20521,U_20522,U_20523] :
        ( U_20522 = U_20523
        | c_List_Oconcat(U_20521,U_20522) != c_List_Oconcat(U_20521,U_20523)
        | ~ sP1238(U_20521,U_20522,U_20523) )
    & ! [U_20521,U_20522,U_20523] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20521),tc_List_Olist(U_20521),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20521),tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),tc_List_Olist(U_20521)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20521))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20521)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521)))),sK507(U_20523,U_20522,U_20521)))
        | ~ sP1237(U_20521,U_20522,U_20523) )
    & ! [U_20521,U_20522,U_20523] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),sK507(U_20523,U_20522,U_20521)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20521),tc_List_Olist(U_20521)),U_20522),U_20523))))
        | ~ sP1237(U_20521,U_20522,U_20523) )
    & ! [U_20521,U_20522,U_20523] :
        ( sP1238(U_20521,U_20522,U_20523)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20522) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20523)
        | sP1237(U_20521,U_20522,U_20523) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1237,sP1238])],[f_4922_3]) ).

cnf(f_4922_5,plain,
    ( sP1238(U_20521,U_20522,U_20523)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20522) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20521))),U_20523)
    | sP1237(U_20521,U_20522,U_20523) ),
    inference(clausify,[status(thm)],[f_4922_4]) ).

cnf(f_4922_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),sK507(U_20523,U_20522,U_20521)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20521),tc_List_Olist(U_20521))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20521),tc_List_Olist(U_20521)),U_20522),U_20523))))
    | ~ sP1237(U_20521,U_20522,U_20523) ),
    inference(clausify,[status(thm)],[f_4922_4]) ).

cnf(f_4922_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20521),tc_List_Olist(U_20521),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20521),tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20521),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20521),tc_HOL_Obool)),tc_List_Olist(U_20521)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20521))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20521)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20521)))),sK507(U_20523,U_20522,U_20521)))
    | ~ sP1237(U_20521,U_20522,U_20523) ),
    inference(clausify,[status(thm)],[f_4922_4]) ).

cnf(f_4922_8,plain,
    ( U_20522 = U_20523
    | c_List_Oconcat(U_20521,U_20522) != c_List_Oconcat(U_20521,U_20523)
    | ~ sP1238(U_20521,U_20522,U_20523) ),
    inference(clausify,[status(thm)],[f_4922_4]) ).

cnf(f_4922_9,plain,
    ( c_List_Oconcat(U_20521,U_20522) = c_List_Oconcat(U_20521,U_20523)
    | U_20522 != U_20523
    | ~ sP1238(U_20521,U_20522,U_20523) ),
    inference(clausify,[status(thm)],[f_4922_4]) ).

fof(f_4923_1,plain,
    ! [V_y,V_xs,T_a,V_k] :
      ( hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_rev__update]) ).

fof(f_4923_2,plain,
    ! [U_20527,U_20526,U_20525,U_20524] :
      ( hAPP(c_List_Orev(U_20525),hAPP(hAPP(c_List_Olist__update(U_20525,U_20526),U_20524),U_20527)) = hAPP(hAPP(c_List_Olist__update(U_20525,hAPP(c_List_Orev(U_20525),U_20526)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20525)),U_20526)),U_20524)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20527)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20524),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20525)),U_20526))) ),
    inference(variable_rename,[status(thm)],[f_4923_1]) ).

fof(f_4923_3,plain,
    ! [U_20527,U_20526,U_20524,U_20525] :
      ( hAPP(c_List_Orev(U_20525),hAPP(hAPP(c_List_Olist__update(U_20525,U_20526),U_20524),U_20527)) = hAPP(hAPP(c_List_Olist__update(U_20525,hAPP(c_List_Orev(U_20525),U_20526)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20525)),U_20526)),U_20524)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20527)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20524),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20525)),U_20526))) ),
    inference(definitional_conversion,[status(esa)],[f_4923_2]) ).

cnf(f_4923_4,plain,
    ( hAPP(c_List_Orev(U_20525),hAPP(hAPP(c_List_Olist__update(U_20525,U_20526),U_20524),U_20527)) = hAPP(hAPP(c_List_Olist__update(U_20525,hAPP(c_List_Orev(U_20525),U_20526)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20525)),U_20526)),U_20524)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20527)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20524),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20525)),U_20526))) ),
    inference(clausify,[status(thm)],[f_4923_3]) ).

fof(f_4924_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_concat__map__singleton]) ).

fof(f_4924_2,plain,
    ! [U_20531,U_20530,U_20529,U_20528] : c_List_Oconcat(U_20528,hAPP(hAPP(c_List_Omap(U_20529,tc_List_Olist(U_20528)),hAPP(hAPP(c_COMBC(U_20529,tc_List_Olist(U_20528),tc_List_Olist(U_20528)),hAPP(hAPP(c_COMBB(U_20528,tc_fun(tc_List_Olist(U_20528),tc_List_Olist(U_20528)),U_20529),c_List_Olist_OCons(U_20528)),U_20530)),c_List_Olist_ONil(U_20528))),U_20531)) = hAPP(hAPP(c_List_Omap(U_20529,U_20528),U_20530),U_20531),
    inference(variable_rename,[status(thm)],[f_4924_1]) ).

fof(f_4924_3,plain,
    ! [U_20528,U_20529,U_20530,U_20531] : c_List_Oconcat(U_20528,hAPP(hAPP(c_List_Omap(U_20529,tc_List_Olist(U_20528)),hAPP(hAPP(c_COMBC(U_20529,tc_List_Olist(U_20528),tc_List_Olist(U_20528)),hAPP(hAPP(c_COMBB(U_20528,tc_fun(tc_List_Olist(U_20528),tc_List_Olist(U_20528)),U_20529),c_List_Olist_OCons(U_20528)),U_20530)),c_List_Olist_ONil(U_20528))),U_20531)) = hAPP(hAPP(c_List_Omap(U_20529,U_20528),U_20530),U_20531),
    inference(definitional_conversion,[status(esa)],[f_4924_2]) ).

cnf(f_4924_4,plain,
    c_List_Oconcat(U_20528,hAPP(hAPP(c_List_Omap(U_20529,tc_List_Olist(U_20528)),hAPP(hAPP(c_COMBC(U_20529,tc_List_Olist(U_20528),tc_List_Olist(U_20528)),hAPP(hAPP(c_COMBB(U_20528,tc_fun(tc_List_Olist(U_20528),tc_List_Olist(U_20528)),U_20529),c_List_Olist_OCons(U_20528)),U_20530)),c_List_Olist_ONil(U_20528))),U_20531)) = hAPP(hAPP(c_List_Omap(U_20529,U_20528),U_20530),U_20531),
    inference(clausify,[status(thm)],[f_4924_3]) ).

fof(f_4925_1,plain,
    ! [V_j,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono]) ).

fof(f_4925_2,plain,
    ! [U_20535,U_20534,U_20533,U_20532] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20532),hAPP(hAPP(c_List_Onth(U_20532),U_20533),U_20535)),hAPP(hAPP(c_List_Onth(U_20532),U_20533),U_20534)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20535),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20532)),U_20533)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20534),U_20535))
      | ~ c_List_Olinorder__class_Osorted(U_20532,hAPP(c_List_Orev(U_20532),U_20533))
      | ~ class_Orderings_Olinorder(U_20532) ),
    inference(variable_rename,[status(thm)],[f_4925_1]) ).

fof(f_4925_3,plain,
    ! [U_20532,U_20533,U_20534,U_20535] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20532),hAPP(hAPP(c_List_Onth(U_20532),U_20533),U_20535)),hAPP(hAPP(c_List_Onth(U_20532),U_20533),U_20534)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20535),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20532)),U_20533)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20534),U_20535))
      | ~ c_List_Olinorder__class_Osorted(U_20532,hAPP(c_List_Orev(U_20532),U_20533))
      | ~ class_Orderings_Olinorder(U_20532) ),
    inference(definitional_conversion,[status(esa)],[f_4925_2]) ).

cnf(f_4925_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20532),hAPP(hAPP(c_List_Onth(U_20532),U_20533),U_20535)),hAPP(hAPP(c_List_Onth(U_20532),U_20533),U_20534)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20535),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20532)),U_20533)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20534),U_20535))
    | ~ c_List_Olinorder__class_Osorted(U_20532,hAPP(c_List_Orev(U_20532),U_20533))
    | ~ class_Orderings_Olinorder(U_20532) ),
    inference(clausify,[status(thm)],[f_4925_3]) ).

fof(f_4926_1,plain,
    ! [V_y_2,V_xs_2,T_b] :
      ( ( ( c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2)
          | V_xs_2 = c_List_Olist_ONil(T_b) )
        & ( c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2
          | V_xs_2 != c_List_Olist_ONil(T_b) ) )
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted]) ).

fof(f_4926_2,plain,
    ! [U_20538,U_20537,U_20536] :
      ( ( ( c_List_Ofoldr(U_20536,U_20536,c_Orderings_Oord__class_Omax(U_20536),U_20537,U_20538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20536),hAPP(hAPP(c_List_Onth(U_20536),U_20537),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20538)
          | U_20537 = c_List_Olist_ONil(U_20536) )
        & ( c_List_Ofoldr(U_20536,U_20536,c_Orderings_Oord__class_Omax(U_20536),U_20537,U_20538) = U_20538
          | U_20537 != c_List_Olist_ONil(U_20536) ) )
      | ~ c_List_Olinorder__class_Osorted(U_20536,hAPP(c_List_Orev(U_20536),U_20537))
      | ~ class_Orderings_Olinorder(U_20536) ),
    inference(variable_rename,[status(thm)],[f_4926_1]) ).

fof(f_4926_3,plain,
    ( ! [U_20538,U_20537,U_20536] :
        ( c_List_Ofoldr(U_20536,U_20536,c_Orderings_Oord__class_Omax(U_20536),U_20537,U_20538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20536),hAPP(hAPP(c_List_Onth(U_20536),U_20537),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20538)
        | U_20537 = c_List_Olist_ONil(U_20536)
        | ~ sP1239(U_20538,U_20537,U_20536) )
    & ! [U_20538,U_20537,U_20536] :
        ( c_List_Ofoldr(U_20536,U_20536,c_Orderings_Oord__class_Omax(U_20536),U_20537,U_20538) = U_20538
        | U_20537 != c_List_Olist_ONil(U_20536)
        | ~ sP1239(U_20538,U_20537,U_20536) )
    & ! [U_20538,U_20537,U_20536] :
        ( sP1239(U_20538,U_20537,U_20536)
        | ~ c_List_Olinorder__class_Osorted(U_20536,hAPP(c_List_Orev(U_20536),U_20537))
        | ~ class_Orderings_Olinorder(U_20536) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1239])],[f_4926_2]) ).

cnf(f_4926_4,plain,
    ( sP1239(U_20538,U_20537,U_20536)
    | ~ c_List_Olinorder__class_Osorted(U_20536,hAPP(c_List_Orev(U_20536),U_20537))
    | ~ class_Orderings_Olinorder(U_20536) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

cnf(f_4926_5,plain,
    ( c_List_Ofoldr(U_20536,U_20536,c_Orderings_Oord__class_Omax(U_20536),U_20537,U_20538) = U_20538
    | U_20537 != c_List_Olist_ONil(U_20536)
    | ~ sP1239(U_20538,U_20537,U_20536) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

cnf(f_4926_6,plain,
    ( c_List_Ofoldr(U_20536,U_20536,c_Orderings_Oord__class_Omax(U_20536),U_20537,U_20538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20536),hAPP(hAPP(c_List_Onth(U_20536),U_20537),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20538)
    | U_20537 = c_List_Olist_ONil(U_20536)
    | ~ sP1239(U_20538,U_20537,U_20536) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

fof(f_4927_1,plain,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] :
      ( c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J]) ).

fof(f_4927_2,plain,
    ! [U_20542,U_20541,U_20540,U_20539] :
      ( c_List_Otranspose(U_20539,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),U_20541)),U_20542)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),c_List_Oconcat(U_20539,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20539),tc_List_Olist(U_20539)),c_List_Olist_Olist__case(tc_List_Olist(U_20539),U_20539,c_List_Olist_ONil(U_20539),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20539),tc_fun(tc_List_Olist(U_20539),tc_List_Olist(U_20539)),U_20539),c_COMBK(tc_List_Olist(U_20539),tc_List_Olist(U_20539))),hAPP(hAPP(c_COMBC(U_20539,tc_List_Olist(U_20539),tc_List_Olist(U_20539)),c_List_Olist_OCons(U_20539)),c_List_Olist_ONil(U_20539))))),U_20542)))),c_List_Otranspose(U_20539,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),U_20541),c_List_Oconcat(tc_List_Olist(U_20539),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20539)),U_20539,c_List_Olist_ONil(tc_List_Olist(U_20539)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539))),U_20539),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539)),tc_List_Olist(tc_List_Olist(U_20539))),c_List_Olist_OCons(tc_List_Olist(U_20539))),c_List_Olist_ONil(tc_List_Olist(U_20539)))))),U_20542)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20539)),c_List_Otranspose__rel(U_20539)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),U_20541)),U_20542))) ),
    inference(variable_rename,[status(thm)],[f_4927_1]) ).

fof(f_4927_3,plain,
    ! [U_20539,U_20540,U_20541,U_20542] :
      ( c_List_Otranspose(U_20539,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),U_20541)),U_20542)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),c_List_Oconcat(U_20539,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20539),tc_List_Olist(U_20539)),c_List_Olist_Olist__case(tc_List_Olist(U_20539),U_20539,c_List_Olist_ONil(U_20539),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20539),tc_fun(tc_List_Olist(U_20539),tc_List_Olist(U_20539)),U_20539),c_COMBK(tc_List_Olist(U_20539),tc_List_Olist(U_20539))),hAPP(hAPP(c_COMBC(U_20539,tc_List_Olist(U_20539),tc_List_Olist(U_20539)),c_List_Olist_OCons(U_20539)),c_List_Olist_ONil(U_20539))))),U_20542)))),c_List_Otranspose(U_20539,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),U_20541),c_List_Oconcat(tc_List_Olist(U_20539),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20539)),U_20539,c_List_Olist_ONil(tc_List_Olist(U_20539)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539))),U_20539),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539)),tc_List_Olist(tc_List_Olist(U_20539))),c_List_Olist_OCons(tc_List_Olist(U_20539))),c_List_Olist_ONil(tc_List_Olist(U_20539)))))),U_20542)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20539)),c_List_Otranspose__rel(U_20539)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),U_20541)),U_20542))) ),
    inference(definitional_conversion,[status(esa)],[f_4927_2]) ).

cnf(f_4927_4,plain,
    ( c_List_Otranspose(U_20539,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),U_20541)),U_20542)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),c_List_Oconcat(U_20539,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20539),tc_List_Olist(U_20539)),c_List_Olist_Olist__case(tc_List_Olist(U_20539),U_20539,c_List_Olist_ONil(U_20539),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20539),tc_fun(tc_List_Olist(U_20539),tc_List_Olist(U_20539)),U_20539),c_COMBK(tc_List_Olist(U_20539),tc_List_Olist(U_20539))),hAPP(hAPP(c_COMBC(U_20539,tc_List_Olist(U_20539),tc_List_Olist(U_20539)),c_List_Olist_OCons(U_20539)),c_List_Olist_ONil(U_20539))))),U_20542)))),c_List_Otranspose(U_20539,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),U_20541),c_List_Oconcat(tc_List_Olist(U_20539),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20539)),U_20539,c_List_Olist_ONil(tc_List_Olist(U_20539)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539))),U_20539),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20539),tc_List_Olist(tc_List_Olist(U_20539)),tc_List_Olist(tc_List_Olist(U_20539))),c_List_Olist_OCons(tc_List_Olist(U_20539))),c_List_Olist_ONil(tc_List_Olist(U_20539)))))),U_20542)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20539)),c_List_Otranspose__rel(U_20539)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20539)),hAPP(hAPP(c_List_Olist_OCons(U_20539),U_20540),U_20541)),U_20542))) ),
    inference(clausify,[status(thm)],[f_4927_3]) ).

fof(f_4928_1,plain,
    ! [V_xs_2,T_b] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted]) ).

fof(f_4928_2,plain,
    ! [U_20544,U_20543] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20543))),c_List_Otranspose(U_20543,U_20544)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20543)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20543)),U_20544),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | U_20544 = c_List_Olist_ONil(tc_List_Olist(U_20543)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20543))),c_List_Otranspose(U_20543,U_20544)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_20544 != c_List_Olist_ONil(tc_List_Olist(U_20543)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20543),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20543))),U_20544))) ),
    inference(variable_rename,[status(thm)],[f_4928_1]) ).

fof(f_4928_3,plain,
    ( ! [U_20543,U_20544] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20543))),c_List_Otranspose(U_20543,U_20544)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20543)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20543)),U_20544),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_20544 = c_List_Olist_ONil(tc_List_Olist(U_20543))
        | ~ sP1240(U_20543,U_20544) )
    & ! [U_20543,U_20544] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20543))),c_List_Otranspose(U_20543,U_20544)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_20544 != c_List_Olist_ONil(tc_List_Olist(U_20543))
        | ~ sP1240(U_20543,U_20544) )
    & ! [U_20543,U_20544] :
        ( sP1240(U_20543,U_20544)
        | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20543),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20543))),U_20544))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1240])],[f_4928_2]) ).

cnf(f_4928_4,plain,
    ( sP1240(U_20543,U_20544)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20543),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20543))),U_20544))) ),
    inference(clausify,[status(thm)],[f_4928_3]) ).

cnf(f_4928_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20543))),c_List_Otranspose(U_20543,U_20544)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_20544 != c_List_Olist_ONil(tc_List_Olist(U_20543))
    | ~ sP1240(U_20543,U_20544) ),
    inference(clausify,[status(thm)],[f_4928_3]) ).

cnf(f_4928_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20543))),c_List_Otranspose(U_20543,U_20544)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20543)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20543)),U_20544),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_20544 = c_List_Olist_ONil(tc_List_Olist(U_20543))
    | ~ sP1240(U_20543,U_20544) ),
    inference(clausify,[status(thm)],[f_4928_3]) ).

fof(f_4929_1,plain,
    ! [V_i_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column__length]) ).

fof(f_4929_2,plain,
    ! [U_20547,U_20546,U_20545] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20545))),hAPP(c_List_Ofilter(tc_List_Olist(U_20545),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20545)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20547)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)))),c_List_Otranspose(U_20545,U_20546))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20545)),U_20546),U_20547))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20547),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20545))),U_20546)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20545),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20545))),U_20546))) ),
    inference(variable_rename,[status(thm)],[f_4929_1]) ).

fof(f_4929_3,plain,
    ! [U_20546,U_20545,U_20547] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20545))),hAPP(c_List_Ofilter(tc_List_Olist(U_20545),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20545)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20547)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)))),c_List_Otranspose(U_20545,U_20546))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20545)),U_20546),U_20547))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20547),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20545))),U_20546)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20545),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20545))),U_20546))) ),
    inference(definitional_conversion,[status(esa)],[f_4929_2]) ).

cnf(f_4929_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20545))),hAPP(c_List_Ofilter(tc_List_Olist(U_20545),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20545)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20547)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)))),c_List_Otranspose(U_20545,U_20546))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20545)),U_20546),U_20547))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20547),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20545))),U_20546)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20545),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20545))),U_20546))) ),
    inference(clausify,[status(thm)],[f_4929_3]) ).

fof(f_4930_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(f_4930_2,plain,
    ! [U_20549,U_20548] : c_List_Oconcat(tc_List_Olist(U_20548),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20548)),U_20548,c_List_Olist_ONil(tc_List_Olist(U_20548)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548))),U_20548),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548)),tc_List_Olist(tc_List_Olist(U_20548))),c_List_Olist_OCons(tc_List_Olist(U_20548))),c_List_Olist_ONil(tc_List_Olist(U_20548)))))),U_20549)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20548),tc_List_Olist(U_20548)),c_List_Otl(U_20548)),hAPP(c_List_Ofilter(tc_List_Olist(U_20548),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20548)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20548),tc_List_Olist(U_20548),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20548)))),U_20549)),
    inference(variable_rename,[status(thm)],[f_4930_1]) ).

fof(f_4930_3,plain,
    ! [U_20548,U_20549] : c_List_Oconcat(tc_List_Olist(U_20548),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20548)),U_20548,c_List_Olist_ONil(tc_List_Olist(U_20548)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548))),U_20548),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548)),tc_List_Olist(tc_List_Olist(U_20548))),c_List_Olist_OCons(tc_List_Olist(U_20548))),c_List_Olist_ONil(tc_List_Olist(U_20548)))))),U_20549)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20548),tc_List_Olist(U_20548)),c_List_Otl(U_20548)),hAPP(c_List_Ofilter(tc_List_Olist(U_20548),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20548)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20548),tc_List_Olist(U_20548),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20548)))),U_20549)),
    inference(definitional_conversion,[status(esa)],[f_4930_2]) ).

cnf(f_4930_4,plain,
    c_List_Oconcat(tc_List_Olist(U_20548),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20548)),U_20548,c_List_Olist_ONil(tc_List_Olist(U_20548)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548))),U_20548),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20548),tc_List_Olist(tc_List_Olist(U_20548)),tc_List_Olist(tc_List_Olist(U_20548))),c_List_Olist_OCons(tc_List_Olist(U_20548))),c_List_Olist_ONil(tc_List_Olist(U_20548)))))),U_20549)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20548),tc_List_Olist(U_20548)),c_List_Otl(U_20548)),hAPP(c_List_Ofilter(tc_List_Olist(U_20548),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20548)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20548),tc_List_Olist(U_20548),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20548)))),U_20549)),
    inference(clausify,[status(thm)],[f_4930_3]) ).

fof(f_4931_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted]) ).

fof(f_4931_2,plain,
    ! [U_20553,U_20552,U_20551,U_20550] :
      ( hAPP(hAPP(c_List_Onth(U_20550),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20550)),c_List_Otranspose(U_20550,U_20551)),U_20552)),U_20553) = hAPP(hAPP(c_List_Onth(U_20550),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20550)),U_20551),U_20553)),U_20552)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20553),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20550))),hAPP(c_List_Ofilter(tc_List_Olist(U_20550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20550)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20552)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20550)))),U_20551))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20552),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20550))),c_List_Otranspose(U_20550,U_20551))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20550),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20550))),U_20551))) ),
    inference(variable_rename,[status(thm)],[f_4931_1]) ).

fof(f_4931_3,plain,
    ! [U_20550,U_20551,U_20552,U_20553] :
      ( hAPP(hAPP(c_List_Onth(U_20550),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20550)),c_List_Otranspose(U_20550,U_20551)),U_20552)),U_20553) = hAPP(hAPP(c_List_Onth(U_20550),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20550)),U_20551),U_20553)),U_20552)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20553),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20550))),hAPP(c_List_Ofilter(tc_List_Olist(U_20550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20550)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20552)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20550)))),U_20551))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20552),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20550))),c_List_Otranspose(U_20550,U_20551))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20550),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20550))),U_20551))) ),
    inference(definitional_conversion,[status(esa)],[f_4931_2]) ).

cnf(f_4931_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20550),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20550)),c_List_Otranspose(U_20550,U_20551)),U_20552)),U_20553) = hAPP(hAPP(c_List_Onth(U_20550),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20550)),U_20551),U_20553)),U_20552)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20553),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20550))),hAPP(c_List_Ofilter(tc_List_Olist(U_20550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20550)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20552)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20550)))),U_20551))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20552),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20550))),c_List_Otranspose(U_20550,U_20551))))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20550),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20550))),U_20551))) ),
    inference(clausify,[status(thm)],[f_4931_3]) ).

fof(f_4932_1,plain,
    ! [V_xs_2,T_b] :
      ( c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__transpose]) ).

fof(f_4932_2,plain,
    ! [U_20555,U_20554] :
      ( c_List_Otranspose(U_20554,c_List_Otranspose(U_20554,U_20555)) = c_List_OtakeWhile(tc_List_Olist(U_20554),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20554)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20554),tc_List_Olist(U_20554),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20554))),U_20555)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20554),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20554))),U_20555))) ),
    inference(variable_rename,[status(thm)],[f_4932_1]) ).

fof(f_4932_3,plain,
    ! [U_20554,U_20555] :
      ( c_List_Otranspose(U_20554,c_List_Otranspose(U_20554,U_20555)) = c_List_OtakeWhile(tc_List_Olist(U_20554),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20554)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20554),tc_List_Olist(U_20554),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20554))),U_20555)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20554),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20554))),U_20555))) ),
    inference(definitional_conversion,[status(esa)],[f_4932_2]) ).

cnf(f_4932_4,plain,
    ( c_List_Otranspose(U_20554,c_List_Otranspose(U_20554,U_20555)) = c_List_OtakeWhile(tc_List_Olist(U_20554),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20554)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20554),tc_List_Olist(U_20554),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20554))),U_20555)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20554),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20554))),U_20555))) ),
    inference(clausify,[status(thm)],[f_4932_3]) ).

fof(f_4933_1,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__functions_I2_J]) ).

fof(f_4933_2,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_4933_1]) ).

cnf(f_4933_3,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_4933_2]) ).

fof(f_4934_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__map]) ).

fof(f_4934_2,plain,
    ! [U_20560,U_20559,U_20558,U_20557,U_20556] : c_List_OtakeWhile(U_20556,U_20557,hAPP(hAPP(c_List_Omap(U_20558,U_20556),U_20559),U_20560)) = hAPP(hAPP(c_List_Omap(U_20558,U_20556),U_20559),c_List_OtakeWhile(U_20558,hAPP(c_Fun_Ocomp(U_20556,tc_HOL_Obool,U_20558,U_20557),U_20559),U_20560)),
    inference(variable_rename,[status(thm)],[f_4934_1]) ).

fof(f_4934_3,plain,
    ! [U_20556,U_20557,U_20558,U_20559,U_20560] : c_List_OtakeWhile(U_20556,U_20557,hAPP(hAPP(c_List_Omap(U_20558,U_20556),U_20559),U_20560)) = hAPP(hAPP(c_List_Omap(U_20558,U_20556),U_20559),c_List_OtakeWhile(U_20558,hAPP(c_Fun_Ocomp(U_20556,tc_HOL_Obool,U_20558,U_20557),U_20559),U_20560)),
    inference(definitional_conversion,[status(esa)],[f_4934_2]) ).

cnf(f_4934_4,plain,
    c_List_OtakeWhile(U_20556,U_20557,hAPP(hAPP(c_List_Omap(U_20558,U_20556),U_20559),U_20560)) = hAPP(hAPP(c_List_Omap(U_20558,U_20556),U_20559),c_List_OtakeWhile(U_20558,hAPP(c_Fun_Ocomp(U_20556,tc_HOL_Obool,U_20558,U_20557),U_20559),U_20560)),
    inference(clausify,[status(thm)],[f_4934_3]) ).

fof(f_4935_1,plain,
    ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_return__list__def]) ).

fof(f_4935_2,plain,
    ! [U_20561] : c_List_Oreturn__list(U_20561) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_20561),
    inference(variable_rename,[status(thm)],[f_4935_1]) ).

fof(f_4935_3,plain,
    ! [U_20561] : c_List_Oreturn__list(U_20561) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_20561),
    inference(definitional_conversion,[status(esa)],[f_4935_2]) ).

cnf(f_4935_4,plain,
    c_List_Oreturn__list(U_20561) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_20561),
    inference(clausify,[status(thm)],[f_4935_3]) ).

fof(f_4936_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__snd]) ).

fof(f_4936_2,plain,
    ! [U_20566,U_20565,U_20564,U_20563,U_20562] : hAPP(hAPP(c_List_Ozip(U_20562,U_20563),U_20564),c_List_OtakeWhile(U_20563,U_20565,U_20566)) = c_List_OtakeWhile(tc_prod(U_20562,U_20563),hAPP(c_Fun_Ocomp(U_20563,tc_HOL_Obool,tc_prod(U_20562,U_20563),U_20565),c_Product__Type_Osnd(U_20562,U_20563)),hAPP(hAPP(c_List_Ozip(U_20562,U_20563),U_20564),U_20566)),
    inference(variable_rename,[status(thm)],[f_4936_1]) ).

fof(f_4936_3,plain,
    ! [U_20562,U_20563,U_20564,U_20565,U_20566] : hAPP(hAPP(c_List_Ozip(U_20562,U_20563),U_20564),c_List_OtakeWhile(U_20563,U_20565,U_20566)) = c_List_OtakeWhile(tc_prod(U_20562,U_20563),hAPP(c_Fun_Ocomp(U_20563,tc_HOL_Obool,tc_prod(U_20562,U_20563),U_20565),c_Product__Type_Osnd(U_20562,U_20563)),hAPP(hAPP(c_List_Ozip(U_20562,U_20563),U_20564),U_20566)),
    inference(definitional_conversion,[status(esa)],[f_4936_2]) ).

cnf(f_4936_4,plain,
    hAPP(hAPP(c_List_Ozip(U_20562,U_20563),U_20564),c_List_OtakeWhile(U_20563,U_20565,U_20566)) = c_List_OtakeWhile(tc_prod(U_20562,U_20563),hAPP(c_Fun_Ocomp(U_20563,tc_HOL_Obool,tc_prod(U_20562,U_20563),U_20565),c_Product__Type_Osnd(U_20562,U_20563)),hAPP(hAPP(c_List_Ozip(U_20562,U_20563),U_20564),U_20566)),
    inference(clausify,[status(thm)],[f_4936_3]) ).

fof(f_4937_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__fst]) ).

fof(f_4937_2,plain,
    ! [U_20571,U_20570,U_20569,U_20568,U_20567] : hAPP(hAPP(c_List_Ozip(U_20567,U_20568),c_List_OtakeWhile(U_20567,U_20569,U_20570)),U_20571) = c_List_OtakeWhile(tc_prod(U_20567,U_20568),hAPP(c_Fun_Ocomp(U_20567,tc_HOL_Obool,tc_prod(U_20567,U_20568),U_20569),c_Product__Type_Ofst(U_20567,U_20568)),hAPP(hAPP(c_List_Ozip(U_20567,U_20568),U_20570),U_20571)),
    inference(variable_rename,[status(thm)],[f_4937_1]) ).

fof(f_4937_3,plain,
    ! [U_20567,U_20568,U_20569,U_20570,U_20571] : hAPP(hAPP(c_List_Ozip(U_20567,U_20568),c_List_OtakeWhile(U_20567,U_20569,U_20570)),U_20571) = c_List_OtakeWhile(tc_prod(U_20567,U_20568),hAPP(c_Fun_Ocomp(U_20567,tc_HOL_Obool,tc_prod(U_20567,U_20568),U_20569),c_Product__Type_Ofst(U_20567,U_20568)),hAPP(hAPP(c_List_Ozip(U_20567,U_20568),U_20570),U_20571)),
    inference(definitional_conversion,[status(esa)],[f_4937_2]) ).

cnf(f_4937_4,plain,
    hAPP(hAPP(c_List_Ozip(U_20567,U_20568),c_List_OtakeWhile(U_20567,U_20569,U_20570)),U_20571) = c_List_OtakeWhile(tc_prod(U_20567,U_20568),hAPP(c_Fun_Ocomp(U_20567,tc_HOL_Obool,tc_prod(U_20567,U_20568),U_20569),c_Product__Type_Ofst(U_20567,U_20568)),hAPP(hAPP(c_List_Ozip(U_20567,U_20568),U_20570),U_20571)),
    inference(clausify,[status(thm)],[f_4937_3]) ).

fof(f_4938_1,plain,
    ! [V_xs_2,V_P_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__takeWhileD]) ).

fof(f_4938_2,plain,
    ! [U_20575,U_20574,U_20573,U_20572] :
      ( ( hBOOL(hAPP(U_20574,U_20573))
        & hBOOL(hAPP(hAPP(c_member(U_20572),U_20573),hAPP(c_List_Oset(U_20572),U_20575))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_20572),U_20573),hAPP(c_List_Oset(U_20572),c_List_OtakeWhile(U_20572,U_20574,U_20575)))) ),
    inference(variable_rename,[status(thm)],[f_4938_1]) ).

fof(f_4938_3,plain,
    ( ! [U_20572,U_20573,U_20574,U_20575] :
        ( hBOOL(hAPP(U_20574,U_20573))
        | ~ sP1241(U_20572,U_20573,U_20574,U_20575) )
    & ! [U_20572,U_20573,U_20574,U_20575] :
        ( hBOOL(hAPP(hAPP(c_member(U_20572),U_20573),hAPP(c_List_Oset(U_20572),U_20575)))
        | ~ sP1241(U_20572,U_20573,U_20574,U_20575) )
    & ! [U_20572,U_20573,U_20574,U_20575] :
        ( sP1241(U_20572,U_20573,U_20574,U_20575)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20572),U_20573),hAPP(c_List_Oset(U_20572),c_List_OtakeWhile(U_20572,U_20574,U_20575)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1241])],[f_4938_2]) ).

cnf(f_4938_4,plain,
    ( sP1241(U_20572,U_20573,U_20574,U_20575)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20572),U_20573),hAPP(c_List_Oset(U_20572),c_List_OtakeWhile(U_20572,U_20574,U_20575)))) ),
    inference(clausify,[status(thm)],[f_4938_3]) ).

cnf(f_4938_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20572),U_20573),hAPP(c_List_Oset(U_20572),U_20575)))
    | ~ sP1241(U_20572,U_20573,U_20574,U_20575) ),
    inference(clausify,[status(thm)],[f_4938_3]) ).

cnf(f_4938_6,plain,
    ( hBOOL(hAPP(U_20574,U_20573))
    | ~ sP1241(U_20572,U_20573,U_20574,U_20575) ),
    inference(clausify,[status(thm)],[f_4938_3]) ).

fof(f_4939_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | c_List_OtakeWhile(T_b,V_P_2,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__all__conv]) ).

fof(f_4939_2,plain,
    ! [U_20580,U_20579,U_20578] :
      ( ( c_List_OtakeWhile(U_20578,U_20579,U_20580) = U_20580
        | ? [U_20577] :
            ( ~ hBOOL(hAPP(U_20579,U_20577))
            & hBOOL(hAPP(hAPP(c_member(U_20578),U_20577),hAPP(c_List_Oset(U_20578),U_20580))) ) )
      & ( ! [U_20576] :
            ( hBOOL(hAPP(U_20579,U_20576))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20578),U_20576),hAPP(c_List_Oset(U_20578),U_20580))) )
        | c_List_OtakeWhile(U_20578,U_20579,U_20580) != U_20580 ) ),
    inference(variable_rename,[status(thm)],[f_4939_1]) ).

fof(f_4939_3,plain,
    ( ! [U_20586,U_20584,U_20582] :
        ( c_List_OtakeWhile(U_20582,U_20584,U_20586) = U_20586
        | ? [U_20577] :
            ( ~ hBOOL(hAPP(U_20584,U_20577))
            & hBOOL(hAPP(hAPP(c_member(U_20582),U_20577),hAPP(c_List_Oset(U_20582),U_20586))) ) )
    & ! [U_20585,U_20583,U_20581] :
        ( ! [U_20576] :
            ( hBOOL(hAPP(U_20583,U_20576))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20581),U_20576),hAPP(c_List_Oset(U_20581),U_20585))) )
        | c_List_OtakeWhile(U_20581,U_20583,U_20585) != U_20585 ) ),
    inference(miniscope,[status(thm)],[f_4939_2]) ).

fof(f_4939_4,plain,
    ( ! [U_20586,U_20584,U_20582] :
        ( c_List_OtakeWhile(U_20582,U_20584,U_20586) = U_20586
        | ( ~ hBOOL(hAPP(U_20584,sK508(U_20586,U_20584,U_20582)))
          & hBOOL(hAPP(hAPP(c_member(U_20582),sK508(U_20586,U_20584,U_20582)),hAPP(c_List_Oset(U_20582),U_20586))) ) )
    & ! [U_20585,U_20583,U_20581] :
        ( ! [U_20576] :
            ( hBOOL(hAPP(U_20583,U_20576))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20581),U_20576),hAPP(c_List_Oset(U_20581),U_20585))) )
        | c_List_OtakeWhile(U_20581,U_20583,U_20585) != U_20585 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK508]),skolemize(U_20577,sK508(U_20586,U_20584,U_20582))],[f_4939_3]) ).

fof(f_4939_5,plain,
    ( ! [U_20584,U_20582,U_20586] :
        ( ~ hBOOL(hAPP(U_20584,sK508(U_20586,U_20584,U_20582)))
        | ~ sP1242(U_20584,U_20582,U_20586) )
    & ! [U_20584,U_20582,U_20586] :
        ( hBOOL(hAPP(hAPP(c_member(U_20582),sK508(U_20586,U_20584,U_20582)),hAPP(c_List_Oset(U_20582),U_20586)))
        | ~ sP1242(U_20584,U_20582,U_20586) )
    & ! [U_20584,U_20582,U_20586] :
        ( c_List_OtakeWhile(U_20582,U_20584,U_20586) = U_20586
        | sP1242(U_20584,U_20582,U_20586) )
    & ! [U_20576,U_20581,U_20585,U_20583] :
        ( hBOOL(hAPP(U_20583,U_20576))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20581),U_20576),hAPP(c_List_Oset(U_20581),U_20585)))
        | c_List_OtakeWhile(U_20581,U_20583,U_20585) != U_20585 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1242])],[f_4939_4]) ).

cnf(f_4939_6,plain,
    ( hBOOL(hAPP(U_20583,U_20576))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20581),U_20576),hAPP(c_List_Oset(U_20581),U_20585)))
    | c_List_OtakeWhile(U_20581,U_20583,U_20585) != U_20585 ),
    inference(clausify,[status(thm)],[f_4939_5]) ).

cnf(f_4939_7,plain,
    ( c_List_OtakeWhile(U_20582,U_20584,U_20586) = U_20586
    | sP1242(U_20584,U_20582,U_20586) ),
    inference(clausify,[status(thm)],[f_4939_5]) ).

cnf(f_4939_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20582),sK508(U_20586,U_20584,U_20582)),hAPP(c_List_Oset(U_20582),U_20586)))
    | ~ sP1242(U_20584,U_20582,U_20586) ),
    inference(clausify,[status(thm)],[f_4939_5]) ).

cnf(f_4939_9,plain,
    ( ~ hBOOL(hAPP(U_20584,sK508(U_20586,U_20584,U_20582)))
    | ~ sP1242(U_20584,U_20582,U_20586) ),
    inference(clausify,[status(thm)],[f_4939_5]) ).

fof(f_4940_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__takeWhile__le]) ).

fof(f_4940_2,plain,
    ! [U_20589,U_20588,U_20587] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20587)),c_List_OtakeWhile(U_20587,U_20588,U_20589))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20587)),U_20589))),
    inference(variable_rename,[status(thm)],[f_4940_1]) ).

fof(f_4940_3,plain,
    ! [U_20587,U_20588,U_20589] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20587)),c_List_OtakeWhile(U_20587,U_20588,U_20589))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20587)),U_20589))),
    inference(definitional_conversion,[status(esa)],[f_4940_2]) ).

cnf(f_4940_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20587)),c_List_OtakeWhile(U_20587,U_20588,U_20589))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20587)),U_20589))),
    inference(clausify,[status(thm)],[f_4940_3]) ).

fof(f_4941_1,plain,
    ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(f_4941_2,plain,
    ! [U_20592,U_20591,U_20590] : c_List_OtakeWhile(U_20590,U_20591,U_20592) = hAPP(hAPP(c_List_Otake(U_20590),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20590)),c_List_OtakeWhile(U_20590,U_20591,U_20592))),U_20592),
    inference(variable_rename,[status(thm)],[f_4941_1]) ).

fof(f_4941_3,plain,
    ! [U_20590,U_20591,U_20592] : c_List_OtakeWhile(U_20590,U_20591,U_20592) = hAPP(hAPP(c_List_Otake(U_20590),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20590)),c_List_OtakeWhile(U_20590,U_20591,U_20592))),U_20592),
    inference(definitional_conversion,[status(esa)],[f_4941_2]) ).

cnf(f_4941_4,plain,
    c_List_OtakeWhile(U_20590,U_20591,U_20592) = hAPP(hAPP(c_List_Otake(U_20590),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20590)),c_List_OtakeWhile(U_20590,U_20591,U_20592))),U_20592),
    inference(clausify,[status(thm)],[f_4941_3]) ).

fof(f_4942_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile]) ).

fof(f_4942_2,plain,
    ! [U_20595,U_20594,U_20593] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20593),c_List_OtakeWhile(U_20593,U_20595,U_20594)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20593),U_20594)) ),
    inference(variable_rename,[status(thm)],[f_4942_1]) ).

fof(f_4942_3,plain,
    ! [U_20593,U_20594,U_20595] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20593),c_List_OtakeWhile(U_20593,U_20595,U_20594)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20593),U_20594)) ),
    inference(definitional_conversion,[status(esa)],[f_4942_2]) ).

cnf(f_4942_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20593),c_List_OtakeWhile(U_20593,U_20595,U_20594)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20593),U_20594)) ),
    inference(clausify,[status(thm)],[f_4942_3]) ).

fof(f_4943_1,plain,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
      ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__tail]) ).

fof(f_4943_2,plain,
    ! [U_20600,U_20599,U_20598,U_20597,U_20596] :
      ( c_List_OtakeWhile(U_20598,U_20596,hAPP(hAPP(c_List_Oappend(U_20598),U_20599),hAPP(hAPP(c_List_Olist_OCons(U_20598),U_20597),U_20600))) = c_List_OtakeWhile(U_20598,U_20596,U_20599)
      | hBOOL(hAPP(U_20596,U_20597)) ),
    inference(variable_rename,[status(thm)],[f_4943_1]) ).

fof(f_4943_3,plain,
    ! [U_20597,U_20596,U_20598,U_20599,U_20600] :
      ( c_List_OtakeWhile(U_20598,U_20596,hAPP(hAPP(c_List_Oappend(U_20598),U_20599),hAPP(hAPP(c_List_Olist_OCons(U_20598),U_20597),U_20600))) = c_List_OtakeWhile(U_20598,U_20596,U_20599)
      | hBOOL(hAPP(U_20596,U_20597)) ),
    inference(definitional_conversion,[status(esa)],[f_4943_2]) ).

cnf(f_4943_4,plain,
    ( c_List_OtakeWhile(U_20598,U_20596,hAPP(hAPP(c_List_Oappend(U_20598),U_20599),hAPP(hAPP(c_List_Olist_OCons(U_20598),U_20597),U_20600))) = c_List_OtakeWhile(U_20598,U_20596,U_20599)
    | hBOOL(hAPP(U_20596,U_20597)) ),
    inference(clausify,[status(thm)],[f_4943_3]) ).

fof(f_4944_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(f_4944_2,plain,
    ! [U_20604,U_20603,U_20602,U_20601] :
      ( ( c_List_OtakeWhile(U_20603,U_20601,hAPP(hAPP(c_List_Olist_OCons(U_20603),U_20602),U_20604)) = c_List_Olist_ONil(U_20603)
        | hBOOL(hAPP(U_20601,U_20602)) )
      & ( c_List_OtakeWhile(U_20603,U_20601,hAPP(hAPP(c_List_Olist_OCons(U_20603),U_20602),U_20604)) = hAPP(hAPP(c_List_Olist_OCons(U_20603),U_20602),c_List_OtakeWhile(U_20603,U_20601,U_20604))
        | ~ hBOOL(hAPP(U_20601,U_20602)) ) ),
    inference(variable_rename,[status(thm)],[f_4944_1]) ).

fof(f_4944_3,plain,
    ( ! [U_20612,U_20610,U_20608,U_20606] :
        ( c_List_OtakeWhile(U_20610,U_20606,hAPP(hAPP(c_List_Olist_OCons(U_20610),U_20608),U_20612)) = c_List_Olist_ONil(U_20610)
        | hBOOL(hAPP(U_20606,U_20608)) )
    & ! [U_20611,U_20609,U_20607,U_20605] :
        ( c_List_OtakeWhile(U_20609,U_20605,hAPP(hAPP(c_List_Olist_OCons(U_20609),U_20607),U_20611)) = hAPP(hAPP(c_List_Olist_OCons(U_20609),U_20607),c_List_OtakeWhile(U_20609,U_20605,U_20611))
        | ~ hBOOL(hAPP(U_20605,U_20607)) ) ),
    inference(miniscope,[status(thm)],[f_4944_2]) ).

fof(f_4944_4,plain,
    ( ! [U_20606,U_20608,U_20610,U_20612] :
        ( c_List_OtakeWhile(U_20610,U_20606,hAPP(hAPP(c_List_Olist_OCons(U_20610),U_20608),U_20612)) = c_List_Olist_ONil(U_20610)
        | hBOOL(hAPP(U_20606,U_20608)) )
    & ! [U_20611,U_20605,U_20607,U_20609] :
        ( c_List_OtakeWhile(U_20609,U_20605,hAPP(hAPP(c_List_Olist_OCons(U_20609),U_20607),U_20611)) = hAPP(hAPP(c_List_Olist_OCons(U_20609),U_20607),c_List_OtakeWhile(U_20609,U_20605,U_20611))
        | ~ hBOOL(hAPP(U_20605,U_20607)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4944_3]) ).

cnf(f_4944_5,plain,
    ( c_List_OtakeWhile(U_20609,U_20605,hAPP(hAPP(c_List_Olist_OCons(U_20609),U_20607),U_20611)) = hAPP(hAPP(c_List_Olist_OCons(U_20609),U_20607),c_List_OtakeWhile(U_20609,U_20605,U_20611))
    | ~ hBOOL(hAPP(U_20605,U_20607)) ),
    inference(clausify,[status(thm)],[f_4944_4]) ).

cnf(f_4944_6,plain,
    ( c_List_OtakeWhile(U_20610,U_20606,hAPP(hAPP(c_List_Olist_OCons(U_20610),U_20608),U_20612)) = c_List_Olist_ONil(U_20610)
    | hBOOL(hAPP(U_20606,U_20608)) ),
    inference(clausify,[status(thm)],[f_4944_4]) ).

fof(f_4945_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile]) ).

fof(f_4945_2,plain,
    ! [U_20615,U_20614,U_20613] :
      ( c_List_Olinorder__class_Osorted(U_20613,c_List_OtakeWhile(U_20613,U_20615,U_20614))
      | ~ c_List_Olinorder__class_Osorted(U_20613,U_20614)
      | ~ class_Orderings_Olinorder(U_20613) ),
    inference(variable_rename,[status(thm)],[f_4945_1]) ).

fof(f_4945_3,plain,
    ! [U_20613,U_20615,U_20614] :
      ( c_List_Olinorder__class_Osorted(U_20613,c_List_OtakeWhile(U_20613,U_20615,U_20614))
      | ~ c_List_Olinorder__class_Osorted(U_20613,U_20614)
      | ~ class_Orderings_Olinorder(U_20613) ),
    inference(definitional_conversion,[status(esa)],[f_4945_2]) ).

cnf(f_4945_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20613,c_List_OtakeWhile(U_20613,U_20615,U_20614))
    | ~ c_List_Olinorder__class_Osorted(U_20613,U_20614)
    | ~ class_Orderings_Olinorder(U_20613) ),
    inference(clausify,[status(thm)],[f_4945_3]) ).

fof(f_4946_1,plain,
    ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(f_4946_2,plain,
    ! [U_20617,U_20616] : c_List_OtakeWhile(U_20616,U_20617,c_List_Olist_ONil(U_20616)) = c_List_Olist_ONil(U_20616),
    inference(variable_rename,[status(thm)],[f_4946_1]) ).

fof(f_4946_3,plain,
    ! [U_20616,U_20617] : c_List_OtakeWhile(U_20616,U_20617,c_List_Olist_ONil(U_20616)) = c_List_Olist_ONil(U_20616),
    inference(definitional_conversion,[status(esa)],[f_4946_2]) ).

cnf(f_4946_4,plain,
    c_List_OtakeWhile(U_20616,U_20617,c_List_Olist_ONil(U_20616)) = c_List_Olist_ONil(U_20616),
    inference(clausify,[status(thm)],[f_4946_3]) ).

fof(f_4947_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__append1]) ).

fof(f_4947_2,plain,
    ! [U_20622,U_20621,U_20620,U_20619,U_20618] :
      ( c_List_OtakeWhile(U_20618,U_20621,hAPP(hAPP(c_List_Oappend(U_20618),U_20620),U_20622)) = c_List_OtakeWhile(U_20618,U_20621,U_20620)
      | hBOOL(hAPP(U_20621,U_20619))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20618),U_20619),hAPP(c_List_Oset(U_20618),U_20620))) ),
    inference(variable_rename,[status(thm)],[f_4947_1]) ).

fof(f_4947_3,plain,
    ! [U_20618,U_20619,U_20620,U_20621,U_20622] :
      ( c_List_OtakeWhile(U_20618,U_20621,hAPP(hAPP(c_List_Oappend(U_20618),U_20620),U_20622)) = c_List_OtakeWhile(U_20618,U_20621,U_20620)
      | hBOOL(hAPP(U_20621,U_20619))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20618),U_20619),hAPP(c_List_Oset(U_20618),U_20620))) ),
    inference(definitional_conversion,[status(esa)],[f_4947_2]) ).

cnf(f_4947_4,plain,
    ( c_List_OtakeWhile(U_20618,U_20621,hAPP(hAPP(c_List_Oappend(U_20618),U_20620),U_20622)) = c_List_OtakeWhile(U_20618,U_20621,U_20620)
    | hBOOL(hAPP(U_20621,U_20619))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20618),U_20619),hAPP(c_List_Oset(U_20618),U_20620))) ),
    inference(clausify,[status(thm)],[f_4947_3]) ).

fof(f_4948_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(f_4948_2,plain,
    ! [U_20625,U_20624,U_20623] :
      ( ~ hBOOL(hAPP(U_20624,hAPP(hAPP(c_List_Onth(U_20623),U_20625),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),c_List_OtakeWhile(U_20623,U_20624,U_20625)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),c_List_OtakeWhile(U_20623,U_20624,U_20625))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),U_20625))) ),
    inference(variable_rename,[status(thm)],[f_4948_1]) ).

fof(f_4948_3,plain,
    ! [U_20624,U_20623,U_20625] :
      ( ~ hBOOL(hAPP(U_20624,hAPP(hAPP(c_List_Onth(U_20623),U_20625),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),c_List_OtakeWhile(U_20623,U_20624,U_20625)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),c_List_OtakeWhile(U_20623,U_20624,U_20625))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),U_20625))) ),
    inference(definitional_conversion,[status(esa)],[f_4948_2]) ).

cnf(f_4948_4,plain,
    ( ~ hBOOL(hAPP(U_20624,hAPP(hAPP(c_List_Onth(U_20623),U_20625),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),c_List_OtakeWhile(U_20623,U_20624,U_20625)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),c_List_OtakeWhile(U_20623,U_20624,U_20625))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20623)),U_20625))) ),
    inference(clausify,[status(thm)],[f_4948_3]) ).

fof(f_4949_1,plain,
    ! [V_xs_2,V_P_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__nth]) ).

fof(f_4949_2,plain,
    ! [U_20629,U_20628,U_20627,U_20626] :
      ( hAPP(hAPP(c_List_Onth(U_20627),c_List_OtakeWhile(U_20627,U_20628,U_20629)),U_20626) = hAPP(hAPP(c_List_Onth(U_20627),U_20629),U_20626)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20627)),c_List_OtakeWhile(U_20627,U_20628,U_20629)))) ),
    inference(variable_rename,[status(thm)],[f_4949_1]) ).

fof(f_4949_3,plain,
    ! [U_20627,U_20626,U_20628,U_20629] :
      ( hAPP(hAPP(c_List_Onth(U_20627),c_List_OtakeWhile(U_20627,U_20628,U_20629)),U_20626) = hAPP(hAPP(c_List_Onth(U_20627),U_20629),U_20626)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20627)),c_List_OtakeWhile(U_20627,U_20628,U_20629)))) ),
    inference(definitional_conversion,[status(esa)],[f_4949_2]) ).

cnf(f_4949_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20627),c_List_OtakeWhile(U_20627,U_20628,U_20629)),U_20626) = hAPP(hAPP(c_List_Onth(U_20627),U_20629),U_20626)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20627)),c_List_OtakeWhile(U_20627,U_20628,U_20629)))) ),
    inference(clausify,[status(thm)],[f_4949_3]) ).

fof(f_4950_1,plain,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))),
    inference(fof_nnf,[status(thm)],[fact_map__upds__def]) ).

fof(f_4950_2,plain,
    ! [U_20634,U_20633,U_20632,U_20631,U_20630] : c_Map_Omap__upds(U_20630,U_20631,U_20632,U_20633,U_20634) = c_Map_Omap__add(U_20630,U_20631,U_20632,c_Map_Omap__of(U_20630,U_20631,hAPP(c_List_Orev(tc_prod(U_20630,U_20631)),hAPP(hAPP(c_List_Ozip(U_20630,U_20631),U_20633),U_20634)))),
    inference(variable_rename,[status(thm)],[f_4950_1]) ).

fof(f_4950_3,plain,
    ! [U_20631,U_20630,U_20632,U_20633,U_20634] : c_Map_Omap__upds(U_20630,U_20631,U_20632,U_20633,U_20634) = c_Map_Omap__add(U_20630,U_20631,U_20632,c_Map_Omap__of(U_20630,U_20631,hAPP(c_List_Orev(tc_prod(U_20630,U_20631)),hAPP(hAPP(c_List_Ozip(U_20630,U_20631),U_20633),U_20634)))),
    inference(definitional_conversion,[status(esa)],[f_4950_2]) ).

cnf(f_4950_4,plain,
    c_Map_Omap__upds(U_20630,U_20631,U_20632,U_20633,U_20634) = c_Map_Omap__add(U_20630,U_20631,U_20632,c_Map_Omap__of(U_20630,U_20631,hAPP(c_List_Orev(tc_prod(U_20630,U_20631)),hAPP(hAPP(c_List_Ozip(U_20630,U_20631),U_20633),U_20634)))),
    inference(clausify,[status(thm)],[f_4950_3]) ).

fof(f_4951_1,plain,
    ! [T_b,V_xs_2] :
      ( c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last]) ).

fof(f_4951_2,plain,
    ! [U_20636,U_20635] :
      ( c_List_OtakeWhile(U_20636,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20636),c_fNot),hAPP(hAPP(c_COMBC(U_20636,U_20636,tc_HOL_Obool),c_fequal),c_List_Olast(U_20636,U_20635))),U_20635) = c_List_Obutlast(U_20636,U_20635)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20636),U_20635))
      | U_20635 = c_List_Olist_ONil(U_20636) ),
    inference(variable_rename,[status(thm)],[f_4951_1]) ).

fof(f_4951_3,plain,
    ! [U_20636,U_20635] :
      ( c_List_OtakeWhile(U_20636,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20636),c_fNot),hAPP(hAPP(c_COMBC(U_20636,U_20636,tc_HOL_Obool),c_fequal),c_List_Olast(U_20636,U_20635))),U_20635) = c_List_Obutlast(U_20636,U_20635)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20636),U_20635))
      | U_20635 = c_List_Olist_ONil(U_20636) ),
    inference(definitional_conversion,[status(esa)],[f_4951_2]) ).

cnf(f_4951_4,plain,
    ( c_List_OtakeWhile(U_20636,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20636),c_fNot),hAPP(hAPP(c_COMBC(U_20636,U_20636,tc_HOL_Obool),c_fequal),c_List_Olast(U_20636,U_20635))),U_20635) = c_List_Obutlast(U_20636,U_20635)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20636),U_20635))
    | U_20635 = c_List_Olist_ONil(U_20636) ),
    inference(clausify,[status(thm)],[f_4951_3]) ).

fof(f_4952_1,plain,
    ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev]) ).

fof(f_4952_2,plain,
    ! [U_20641,U_20640,U_20639,U_20638,U_20637] :
      ( hAPP(c_List_Ofilter(U_20638,hAPP(hAPP(c_COMBB(U_20637,tc_HOL_Obool,U_20638),hAPP(c_Orderings_Oord__class_Oless(U_20637),U_20641)),U_20639)),U_20640) = c_List_OtakeWhile(U_20638,hAPP(hAPP(c_COMBB(U_20637,tc_HOL_Obool,U_20638),hAPP(c_Orderings_Oord__class_Oless(U_20637),U_20641)),U_20639),U_20640)
      | ~ c_List_Olinorder__class_Osorted(U_20637,hAPP(c_List_Orev(U_20637),hAPP(hAPP(c_List_Omap(U_20638,U_20637),U_20639),U_20640)))
      | ~ class_Orderings_Olinorder(U_20637) ),
    inference(variable_rename,[status(thm)],[f_4952_1]) ).

fof(f_4952_3,plain,
    ! [U_20637,U_20638,U_20639,U_20640,U_20641] :
      ( hAPP(c_List_Ofilter(U_20638,hAPP(hAPP(c_COMBB(U_20637,tc_HOL_Obool,U_20638),hAPP(c_Orderings_Oord__class_Oless(U_20637),U_20641)),U_20639)),U_20640) = c_List_OtakeWhile(U_20638,hAPP(hAPP(c_COMBB(U_20637,tc_HOL_Obool,U_20638),hAPP(c_Orderings_Oord__class_Oless(U_20637),U_20641)),U_20639),U_20640)
      | ~ c_List_Olinorder__class_Osorted(U_20637,hAPP(c_List_Orev(U_20637),hAPP(hAPP(c_List_Omap(U_20638,U_20637),U_20639),U_20640)))
      | ~ class_Orderings_Olinorder(U_20637) ),
    inference(definitional_conversion,[status(esa)],[f_4952_2]) ).

cnf(f_4952_4,plain,
    ( hAPP(c_List_Ofilter(U_20638,hAPP(hAPP(c_COMBB(U_20637,tc_HOL_Obool,U_20638),hAPP(c_Orderings_Oord__class_Oless(U_20637),U_20641)),U_20639)),U_20640) = c_List_OtakeWhile(U_20638,hAPP(hAPP(c_COMBB(U_20637,tc_HOL_Obool,U_20638),hAPP(c_Orderings_Oord__class_Oless(U_20637),U_20641)),U_20639),U_20640)
    | ~ c_List_Olinorder__class_Osorted(U_20637,hAPP(c_List_Orev(U_20637),hAPP(hAPP(c_List_Omap(U_20638,U_20637),U_20639),U_20640)))
    | ~ class_Orderings_Olinorder(U_20637) ),
    inference(clausify,[status(thm)],[f_4952_3]) ).

fof(f_4953_1,plain,
    ! [V_l] :
      ( c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l
      | ~ c_List_Onat__list(V_l) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed]) ).

fof(f_4953_2,plain,
    ! [U_20642] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_20642)) = U_20642
      | ~ c_List_Onat__list(U_20642) ),
    inference(variable_rename,[status(thm)],[f_4953_1]) ).

fof(f_4953_3,plain,
    ! [U_20642] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_20642)) = U_20642
      | ~ c_List_Onat__list(U_20642) ),
    inference(definitional_conversion,[status(esa)],[f_4953_2]) ).

cnf(f_4953_4,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(U_20642)) = U_20642
    | ~ c_List_Onat__list(U_20642) ),
    inference(clausify,[status(thm)],[f_4953_3]) ).

fof(f_4954_1,plain,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__concat]) ).

fof(f_4954_2,plain,
    ! [U_20644,U_20643] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),c_List_Oremdups(U_20643,c_List_Oconcat(U_20643,U_20644))) = hAPP(c_Finite__Set_Ocard(U_20643),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20643),tc_fun(U_20643,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20643)),U_20644)),c_List_Oset(U_20643))),
    inference(variable_rename,[status(thm)],[f_4954_1]) ).

fof(f_4954_3,plain,
    ! [U_20643,U_20644] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),c_List_Oremdups(U_20643,c_List_Oconcat(U_20643,U_20644))) = hAPP(c_Finite__Set_Ocard(U_20643),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20643),tc_fun(U_20643,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20643)),U_20644)),c_List_Oset(U_20643))),
    inference(definitional_conversion,[status(esa)],[f_4954_2]) ).

cnf(f_4954_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),c_List_Oremdups(U_20643,c_List_Oconcat(U_20643,U_20644))) = hAPP(c_Finite__Set_Ocard(U_20643),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20643),tc_fun(U_20643,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20643)),U_20644)),c_List_Oset(U_20643))),
    inference(clausify,[status(thm)],[f_4954_3]) ).

fof(f_4955_1,plain,
    ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
    inference(fof_nnf,[status(thm)],[fact_distinct__remdups]) ).

fof(f_4955_2,plain,
    ! [U_20646,U_20645] : hBOOL(hAPP(c_List_Odistinct(U_20645),c_List_Oremdups(U_20645,U_20646))),
    inference(variable_rename,[status(thm)],[f_4955_1]) ).

fof(f_4955_3,plain,
    ! [U_20645,U_20646] : hBOOL(hAPP(c_List_Odistinct(U_20645),c_List_Oremdups(U_20645,U_20646))),
    inference(definitional_conversion,[status(esa)],[f_4955_2]) ).

cnf(f_4955_4,plain,
    hBOOL(hAPP(c_List_Odistinct(U_20645),c_List_Oremdups(U_20645,U_20646))),
    inference(clausify,[status(thm)],[f_4955_3]) ).

fof(f_4956_1,plain,
    ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__leq]) ).

fof(f_4956_2,plain,
    ! [U_20648,U_20647] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20647)),c_List_Oremdups(U_20647,U_20648))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20647)),U_20648))),
    inference(variable_rename,[status(thm)],[f_4956_1]) ).

fof(f_4956_3,plain,
    ! [U_20647,U_20648] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20647)),c_List_Oremdups(U_20647,U_20648))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20647)),U_20648))),
    inference(definitional_conversion,[status(esa)],[f_4956_2]) ).

cnf(f_4956_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20647)),c_List_Oremdups(U_20647,U_20648))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20647)),U_20648))),
    inference(clausify,[status(thm)],[f_4956_3]) ).

fof(f_4957_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__map__remdups]) ).

fof(f_4957_2,plain,
    ! [U_20652,U_20651,U_20650,U_20649] : c_List_Oremdups(U_20649,hAPP(hAPP(c_List_Omap(U_20650,U_20649),U_20651),c_List_Oremdups(U_20650,U_20652))) = c_List_Oremdups(U_20649,hAPP(hAPP(c_List_Omap(U_20650,U_20649),U_20651),U_20652)),
    inference(variable_rename,[status(thm)],[f_4957_1]) ).

fof(f_4957_3,plain,
    ! [U_20649,U_20650,U_20651,U_20652] : c_List_Oremdups(U_20649,hAPP(hAPP(c_List_Omap(U_20650,U_20649),U_20651),c_List_Oremdups(U_20650,U_20652))) = c_List_Oremdups(U_20649,hAPP(hAPP(c_List_Omap(U_20650,U_20649),U_20651),U_20652)),
    inference(definitional_conversion,[status(esa)],[f_4957_2]) ).

cnf(f_4957_4,plain,
    c_List_Oremdups(U_20649,hAPP(hAPP(c_List_Omap(U_20650,U_20649),U_20651),c_List_Oremdups(U_20650,U_20652))) = c_List_Oremdups(U_20649,hAPP(hAPP(c_List_Omap(U_20650,U_20649),U_20651),U_20652)),
    inference(clausify,[status(thm)],[f_4957_3]) ).

fof(f_4958_1,plain,
    ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_embed__list__def]) ).

fof(f_4958_2,plain,
    ! [U_20653] : c_List_Oembed__list(U_20653) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_20653),
    inference(variable_rename,[status(thm)],[f_4958_1]) ).

fof(f_4958_3,plain,
    ! [U_20653] : c_List_Oembed__list(U_20653) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_20653),
    inference(definitional_conversion,[status(esa)],[f_4958_2]) ).

cnf(f_4958_4,plain,
    c_List_Oembed__list(U_20653) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_20653),
    inference(clausify,[status(thm)],[f_4958_3]) ).

fof(f_4959_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__remdups]) ).

fof(f_4959_2,plain,
    ! [U_20655,U_20654] : hAPP(c_List_Oset(U_20654),c_List_Oremdups(U_20654,U_20655)) = hAPP(c_List_Oset(U_20654),U_20655),
    inference(variable_rename,[status(thm)],[f_4959_1]) ).

fof(f_4959_3,plain,
    ! [U_20654,U_20655] : hAPP(c_List_Oset(U_20654),c_List_Oremdups(U_20654,U_20655)) = hAPP(c_List_Oset(U_20654),U_20655),
    inference(definitional_conversion,[status(esa)],[f_4959_2]) ).

cnf(f_4959_4,plain,
    hAPP(c_List_Oset(U_20654),c_List_Oremdups(U_20654,U_20655)) = hAPP(c_List_Oset(U_20654),U_20655),
    inference(clausify,[status(thm)],[f_4959_3]) ).

fof(f_4960_1,plain,
    ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(f_4960_2,plain,
    ! [U_20656] : c_List_Oremdups(U_20656,c_List_Olist_ONil(U_20656)) = c_List_Olist_ONil(U_20656),
    inference(variable_rename,[status(thm)],[f_4960_1]) ).

fof(f_4960_3,plain,
    ! [U_20656] : c_List_Oremdups(U_20656,c_List_Olist_ONil(U_20656)) = c_List_Olist_ONil(U_20656),
    inference(definitional_conversion,[status(esa)],[f_4960_2]) ).

cnf(f_4960_4,plain,
    c_List_Oremdups(U_20656,c_List_Olist_ONil(U_20656)) = c_List_Olist_ONil(U_20656),
    inference(clausify,[status(thm)],[f_4960_3]) ).

fof(f_4961_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
        | V_x_2 != c_List_Olist_ONil(T_b) )
      & ( V_x_2 = c_List_Olist_ONil(T_b)
        | c_List_Olist_ONil(T_b) != c_List_Oremdups(T_b,V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff]) ).

fof(f_4961_2,plain,
    ! [U_20658,U_20657] :
      ( ( c_List_Olist_ONil(U_20657) = c_List_Oremdups(U_20657,U_20658)
        | U_20658 != c_List_Olist_ONil(U_20657) )
      & ( U_20658 = c_List_Olist_ONil(U_20657)
        | c_List_Olist_ONil(U_20657) != c_List_Oremdups(U_20657,U_20658) ) ),
    inference(variable_rename,[status(thm)],[f_4961_1]) ).

fof(f_4961_3,plain,
    ( ! [U_20662,U_20660] :
        ( c_List_Olist_ONil(U_20660) = c_List_Oremdups(U_20660,U_20662)
        | U_20662 != c_List_Olist_ONil(U_20660) )
    & ! [U_20661,U_20659] :
        ( U_20661 = c_List_Olist_ONil(U_20659)
        | c_List_Olist_ONil(U_20659) != c_List_Oremdups(U_20659,U_20661) ) ),
    inference(miniscope,[status(thm)],[f_4961_2]) ).

fof(f_4961_4,plain,
    ( ! [U_20662,U_20660] :
        ( c_List_Olist_ONil(U_20660) = c_List_Oremdups(U_20660,U_20662)
        | U_20662 != c_List_Olist_ONil(U_20660) )
    & ! [U_20661,U_20659] :
        ( U_20661 = c_List_Olist_ONil(U_20659)
        | c_List_Olist_ONil(U_20659) != c_List_Oremdups(U_20659,U_20661) ) ),
    inference(definitional_conversion,[status(esa)],[f_4961_3]) ).

cnf(f_4961_5,plain,
    ( U_20661 = c_List_Olist_ONil(U_20659)
    | c_List_Olist_ONil(U_20659) != c_List_Oremdups(U_20659,U_20661) ),
    inference(clausify,[status(thm)],[f_4961_4]) ).

cnf(f_4961_6,plain,
    ( c_List_Olist_ONil(U_20660) = c_List_Oremdups(U_20660,U_20662)
    | U_20662 != c_List_Olist_ONil(U_20660) ),
    inference(clausify,[status(thm)],[f_4961_4]) ).

fof(f_4962_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
        | V_x_2 != c_List_Olist_ONil(T_b) )
      & ( V_x_2 = c_List_Olist_ONil(T_b)
        | c_List_Oremdups(T_b,V_x_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff]) ).

fof(f_4962_2,plain,
    ! [U_20664,U_20663] :
      ( ( c_List_Oremdups(U_20663,U_20664) = c_List_Olist_ONil(U_20663)
        | U_20664 != c_List_Olist_ONil(U_20663) )
      & ( U_20664 = c_List_Olist_ONil(U_20663)
        | c_List_Oremdups(U_20663,U_20664) != c_List_Olist_ONil(U_20663) ) ),
    inference(variable_rename,[status(thm)],[f_4962_1]) ).

fof(f_4962_3,plain,
    ( ! [U_20668,U_20666] :
        ( c_List_Oremdups(U_20666,U_20668) = c_List_Olist_ONil(U_20666)
        | U_20668 != c_List_Olist_ONil(U_20666) )
    & ! [U_20667,U_20665] :
        ( U_20667 = c_List_Olist_ONil(U_20665)
        | c_List_Oremdups(U_20665,U_20667) != c_List_Olist_ONil(U_20665) ) ),
    inference(miniscope,[status(thm)],[f_4962_2]) ).

fof(f_4962_4,plain,
    ( ! [U_20666,U_20668] :
        ( c_List_Oremdups(U_20666,U_20668) = c_List_Olist_ONil(U_20666)
        | U_20668 != c_List_Olist_ONil(U_20666) )
    & ! [U_20667,U_20665] :
        ( U_20667 = c_List_Olist_ONil(U_20665)
        | c_List_Oremdups(U_20665,U_20667) != c_List_Olist_ONil(U_20665) ) ),
    inference(definitional_conversion,[status(esa)],[f_4962_3]) ).

cnf(f_4962_5,plain,
    ( U_20667 = c_List_Olist_ONil(U_20665)
    | c_List_Oremdups(U_20665,U_20667) != c_List_Olist_ONil(U_20665) ),
    inference(clausify,[status(thm)],[f_4962_4]) ).

cnf(f_4962_6,plain,
    ( c_List_Oremdups(U_20666,U_20668) = c_List_Olist_ONil(U_20666)
    | U_20668 != c_List_Olist_ONil(U_20666) ),
    inference(clausify,[status(thm)],[f_4962_4]) ).

fof(f_4963_1,plain,
    ! [V_l,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_l)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__remdups]) ).

fof(f_4963_2,plain,
    ! [U_20670,U_20669] :
      ( c_List_Olinorder__class_Osorted(U_20669,c_List_Oremdups(U_20669,U_20670))
      | ~ c_List_Olinorder__class_Osorted(U_20669,U_20670)
      | ~ class_Orderings_Olinorder(U_20669) ),
    inference(variable_rename,[status(thm)],[f_4963_1]) ).

fof(f_4963_3,plain,
    ! [U_20670,U_20669] :
      ( c_List_Olinorder__class_Osorted(U_20669,c_List_Oremdups(U_20669,U_20670))
      | ~ c_List_Olinorder__class_Osorted(U_20669,U_20670)
      | ~ class_Orderings_Olinorder(U_20669) ),
    inference(definitional_conversion,[status(esa)],[f_4963_2]) ).

cnf(f_4963_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20669,c_List_Oremdups(U_20669,U_20670))
    | ~ c_List_Olinorder__class_Osorted(U_20669,U_20670)
    | ~ class_Orderings_Olinorder(U_20669) ),
    inference(clausify,[status(thm)],[f_4963_3]) ).

fof(f_4964_1,plain,
    ! [V_x,V_xs,T_a] :
      ( c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__remdups]) ).

fof(f_4964_2,plain,
    ! [U_20673,U_20672,U_20671] :
      ( c_List_Oremove1(U_20671,U_20673,c_List_Oremdups(U_20671,U_20672)) = c_List_Oremdups(U_20671,c_List_Oremove1(U_20671,U_20673,U_20672))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20671),U_20672)) ),
    inference(variable_rename,[status(thm)],[f_4964_1]) ).

fof(f_4964_3,plain,
    ! [U_20671,U_20672,U_20673] :
      ( c_List_Oremove1(U_20671,U_20673,c_List_Oremdups(U_20671,U_20672)) = c_List_Oremdups(U_20671,c_List_Oremove1(U_20671,U_20673,U_20672))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20671),U_20672)) ),
    inference(definitional_conversion,[status(esa)],[f_4964_2]) ).

cnf(f_4964_4,plain,
    ( c_List_Oremove1(U_20671,U_20673,c_List_Oremdups(U_20671,U_20672)) = c_List_Oremdups(U_20671,c_List_Oremove1(U_20671,U_20673,U_20672))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20671),U_20672)) ),
    inference(clausify,[status(thm)],[f_4964_3]) ).

fof(f_4965_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Oremdups(T_a,V_xs) = V_xs
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id]) ).

fof(f_4965_2,plain,
    ! [U_20675,U_20674] :
      ( c_List_Oremdups(U_20674,U_20675) = U_20675
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20674),U_20675)) ),
    inference(variable_rename,[status(thm)],[f_4965_1]) ).

fof(f_4965_3,plain,
    ! [U_20674,U_20675] :
      ( c_List_Oremdups(U_20674,U_20675) = U_20675
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20674),U_20675)) ),
    inference(definitional_conversion,[status(esa)],[f_4965_2]) ).

cnf(f_4965_4,plain,
    ( c_List_Oremdups(U_20674,U_20675) = U_20675
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20674),U_20675)) ),
    inference(clausify,[status(thm)],[f_4965_3]) ).

fof(f_4966_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | c_List_Oremdups(T_b,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct]) ).

fof(f_4966_2,plain,
    ! [U_20677,U_20676] :
      ( ( c_List_Oremdups(U_20676,U_20677) = U_20677
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20676),U_20677)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_20676),U_20677))
        | c_List_Oremdups(U_20676,U_20677) != U_20677 ) ),
    inference(variable_rename,[status(thm)],[f_4966_1]) ).

fof(f_4966_3,plain,
    ( ! [U_20681,U_20679] :
        ( c_List_Oremdups(U_20679,U_20681) = U_20681
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20679),U_20681)) )
    & ! [U_20680,U_20678] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20678),U_20680))
        | c_List_Oremdups(U_20678,U_20680) != U_20680 ) ),
    inference(miniscope,[status(thm)],[f_4966_2]) ).

fof(f_4966_4,plain,
    ( ! [U_20679,U_20681] :
        ( c_List_Oremdups(U_20679,U_20681) = U_20681
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20679),U_20681)) )
    & ! [U_20680,U_20678] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20678),U_20680))
        | c_List_Oremdups(U_20678,U_20680) != U_20680 ) ),
    inference(definitional_conversion,[status(esa)],[f_4966_3]) ).

cnf(f_4966_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20678),U_20680))
    | c_List_Oremdups(U_20678,U_20680) != U_20680 ),
    inference(clausify,[status(thm)],[f_4966_4]) ).

cnf(f_4966_6,plain,
    ( c_List_Oremdups(U_20679,U_20681) = U_20681
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20679),U_20681)) ),
    inference(clausify,[status(thm)],[f_4966_4]) ).

fof(f_4967_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
        | c_List_Oremdups(T_b,V_xs_2) != V_xs_2 )
      & ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__eq]) ).

fof(f_4967_2,plain,
    ! [U_20683,U_20682] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20682)),c_List_Oremdups(U_20682,U_20683)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20682)),U_20683)
        | c_List_Oremdups(U_20682,U_20683) != U_20683 )
      & ( c_List_Oremdups(U_20682,U_20683) = U_20683
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20682)),c_List_Oremdups(U_20682,U_20683)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20682)),U_20683) ) ),
    inference(variable_rename,[status(thm)],[f_4967_1]) ).

fof(f_4967_3,plain,
    ( ! [U_20687,U_20685] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20685)),c_List_Oremdups(U_20685,U_20687)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20685)),U_20687)
        | c_List_Oremdups(U_20685,U_20687) != U_20687 )
    & ! [U_20686,U_20684] :
        ( c_List_Oremdups(U_20684,U_20686) = U_20686
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20684)),c_List_Oremdups(U_20684,U_20686)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20684)),U_20686) ) ),
    inference(miniscope,[status(thm)],[f_4967_2]) ).

fof(f_4967_4,plain,
    ( ! [U_20685,U_20687] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20685)),c_List_Oremdups(U_20685,U_20687)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20685)),U_20687)
        | c_List_Oremdups(U_20685,U_20687) != U_20687 )
    & ! [U_20686,U_20684] :
        ( c_List_Oremdups(U_20684,U_20686) = U_20686
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20684)),c_List_Oremdups(U_20684,U_20686)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20684)),U_20686) ) ),
    inference(definitional_conversion,[status(esa)],[f_4967_3]) ).

cnf(f_4967_5,plain,
    ( c_List_Oremdups(U_20684,U_20686) = U_20686
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20684)),c_List_Oremdups(U_20684,U_20686)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20684)),U_20686) ),
    inference(clausify,[status(thm)],[f_4967_4]) ).

cnf(f_4967_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20685)),c_List_Oremdups(U_20685,U_20687)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20685)),U_20687)
    | c_List_Oremdups(U_20685,U_20687) != U_20687 ),
    inference(clausify,[status(thm)],[f_4967_4]) ).

fof(f_4968_1,plain,
    ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
    inference(fof_nnf,[status(thm)],[fact_remdups__remdups]) ).

fof(f_4968_2,plain,
    ! [U_20689,U_20688] : c_List_Oremdups(U_20688,c_List_Oremdups(U_20688,U_20689)) = c_List_Oremdups(U_20688,U_20689),
    inference(variable_rename,[status(thm)],[f_4968_1]) ).

fof(f_4968_3,plain,
    ! [U_20689,U_20688] : c_List_Oremdups(U_20688,c_List_Oremdups(U_20688,U_20689)) = c_List_Oremdups(U_20688,U_20689),
    inference(definitional_conversion,[status(esa)],[f_4968_2]) ).

cnf(f_4968_4,plain,
    c_List_Oremdups(U_20688,c_List_Oremdups(U_20688,U_20689)) = c_List_Oremdups(U_20688,U_20689),
    inference(clausify,[status(thm)],[f_4968_3]) ).

fof(f_4969_1,plain,
    ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__filter]) ).

fof(f_4969_2,plain,
    ! [U_20692,U_20691,U_20690] : c_List_Oremdups(U_20690,hAPP(c_List_Ofilter(U_20690,U_20691),U_20692)) = hAPP(c_List_Ofilter(U_20690,U_20691),c_List_Oremdups(U_20690,U_20692)),
    inference(variable_rename,[status(thm)],[f_4969_1]) ).

fof(f_4969_3,plain,
    ! [U_20690,U_20691,U_20692] : c_List_Oremdups(U_20690,hAPP(c_List_Ofilter(U_20690,U_20691),U_20692)) = hAPP(c_List_Ofilter(U_20690,U_20691),c_List_Oremdups(U_20690,U_20692)),
    inference(definitional_conversion,[status(esa)],[f_4969_2]) ).

cnf(f_4969_4,plain,
    c_List_Oremdups(U_20690,hAPP(c_List_Ofilter(U_20690,U_20691),U_20692)) = hAPP(c_List_Ofilter(U_20690,U_20691),c_List_Oremdups(U_20690,U_20692)),
    inference(clausify,[status(thm)],[f_4969_3]) ).

fof(f_4970_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(f_4970_2,plain,
    ! [U_20695,U_20694,U_20693] :
      ( ( c_List_Oremdups(U_20693,hAPP(hAPP(c_List_Olist_OCons(U_20693),U_20694),U_20695)) = hAPP(hAPP(c_List_Olist_OCons(U_20693),U_20694),c_List_Oremdups(U_20693,U_20695))
        | hBOOL(hAPP(hAPP(c_member(U_20693),U_20694),hAPP(c_List_Oset(U_20693),U_20695))) )
      & ( c_List_Oremdups(U_20693,hAPP(hAPP(c_List_Olist_OCons(U_20693),U_20694),U_20695)) = c_List_Oremdups(U_20693,U_20695)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20693),U_20694),hAPP(c_List_Oset(U_20693),U_20695))) ) ),
    inference(variable_rename,[status(thm)],[f_4970_1]) ).

fof(f_4970_3,plain,
    ( ! [U_20701,U_20699,U_20697] :
        ( c_List_Oremdups(U_20697,hAPP(hAPP(c_List_Olist_OCons(U_20697),U_20699),U_20701)) = hAPP(hAPP(c_List_Olist_OCons(U_20697),U_20699),c_List_Oremdups(U_20697,U_20701))
        | hBOOL(hAPP(hAPP(c_member(U_20697),U_20699),hAPP(c_List_Oset(U_20697),U_20701))) )
    & ! [U_20700,U_20698,U_20696] :
        ( c_List_Oremdups(U_20696,hAPP(hAPP(c_List_Olist_OCons(U_20696),U_20698),U_20700)) = c_List_Oremdups(U_20696,U_20700)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20696),U_20698),hAPP(c_List_Oset(U_20696),U_20700))) ) ),
    inference(miniscope,[status(thm)],[f_4970_2]) ).

fof(f_4970_4,plain,
    ( ! [U_20697,U_20699,U_20701] :
        ( c_List_Oremdups(U_20697,hAPP(hAPP(c_List_Olist_OCons(U_20697),U_20699),U_20701)) = hAPP(hAPP(c_List_Olist_OCons(U_20697),U_20699),c_List_Oremdups(U_20697,U_20701))
        | hBOOL(hAPP(hAPP(c_member(U_20697),U_20699),hAPP(c_List_Oset(U_20697),U_20701))) )
    & ! [U_20698,U_20700,U_20696] :
        ( c_List_Oremdups(U_20696,hAPP(hAPP(c_List_Olist_OCons(U_20696),U_20698),U_20700)) = c_List_Oremdups(U_20696,U_20700)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20696),U_20698),hAPP(c_List_Oset(U_20696),U_20700))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4970_3]) ).

cnf(f_4970_5,plain,
    ( c_List_Oremdups(U_20696,hAPP(hAPP(c_List_Olist_OCons(U_20696),U_20698),U_20700)) = c_List_Oremdups(U_20696,U_20700)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20696),U_20698),hAPP(c_List_Oset(U_20696),U_20700))) ),
    inference(clausify,[status(thm)],[f_4970_4]) ).

cnf(f_4970_6,plain,
    ( c_List_Oremdups(U_20697,hAPP(hAPP(c_List_Olist_OCons(U_20697),U_20699),U_20701)) = hAPP(hAPP(c_List_Olist_OCons(U_20697),U_20699),c_List_Oremdups(U_20697,U_20701))
    | hBOOL(hAPP(hAPP(c_member(U_20697),U_20699),hAPP(c_List_Oset(U_20697),U_20701))) ),
    inference(clausify,[status(thm)],[f_4970_4]) ).

fof(f_4971_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(f_4971_2,plain,
    ! [U_20703,U_20702] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20702)),c_List_Oremdups(U_20702,U_20703)) = hAPP(c_Finite__Set_Ocard(U_20702),hAPP(c_List_Oset(U_20702),U_20703)),
    inference(variable_rename,[status(thm)],[f_4971_1]) ).

fof(f_4971_3,plain,
    ! [U_20703,U_20702] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20702)),c_List_Oremdups(U_20702,U_20703)) = hAPP(c_Finite__Set_Ocard(U_20702),hAPP(c_List_Oset(U_20702),U_20703)),
    inference(definitional_conversion,[status(esa)],[f_4971_2]) ).

cnf(f_4971_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20702)),c_List_Oremdups(U_20702,U_20703)) = hAPP(c_Finite__Set_Ocard(U_20702),hAPP(c_List_Oset(U_20702),U_20703)),
    inference(clausify,[status(thm)],[f_4971_3]) ).

fof(f_4972_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups]) ).

fof(f_4972_2,plain,
    ! [U_20708,U_20707,U_20706,U_20705,U_20704] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_20704,U_20705,U_20706),U_20707),hAPP(c_List_Oset(U_20704),U_20708)) = hAPP(c_List_Ofoldl(U_20705,U_20704,hAPP(c_COMBC(U_20704,U_20705,U_20705),U_20706),U_20707),c_List_Oremdups(U_20704,U_20708))
      | ~ c_Finite__Set_Ofun__left__comm(U_20704,U_20705,U_20706) ),
    inference(variable_rename,[status(thm)],[f_4972_1]) ).

fof(f_4972_3,plain,
    ! [U_20704,U_20705,U_20706,U_20707,U_20708] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_20704,U_20705,U_20706),U_20707),hAPP(c_List_Oset(U_20704),U_20708)) = hAPP(c_List_Ofoldl(U_20705,U_20704,hAPP(c_COMBC(U_20704,U_20705,U_20705),U_20706),U_20707),c_List_Oremdups(U_20704,U_20708))
      | ~ c_Finite__Set_Ofun__left__comm(U_20704,U_20705,U_20706) ),
    inference(definitional_conversion,[status(esa)],[f_4972_2]) ).

cnf(f_4972_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_20704,U_20705,U_20706),U_20707),hAPP(c_List_Oset(U_20704),U_20708)) = hAPP(c_List_Ofoldl(U_20705,U_20704,hAPP(c_COMBC(U_20704,U_20705,U_20705),U_20706),U_20707),c_List_Oremdups(U_20704,U_20708))
    | ~ c_Finite__Set_Ofun__left__comm(U_20704,U_20705,U_20706) ),
    inference(clausify,[status(thm)],[f_4972_3]) ).

fof(f_4973_1,plain,
    ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(f_4973_2,plain,
    ! [U_20710,U_20709] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_20709),U_20710) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_20709)),c_List_Oembed__list(U_20710))),
    inference(variable_rename,[status(thm)],[f_4973_1]) ).

fof(f_4973_3,plain,
    ! [U_20710,U_20709] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_20709),U_20710) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_20709)),c_List_Oembed__list(U_20710))),
    inference(definitional_conversion,[status(esa)],[f_4973_2]) ).

cnf(f_4973_4,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_20709),U_20710) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_20709)),c_List_Oembed__list(U_20710))),
    inference(clausify,[status(thm)],[f_4973_3]) ).

fof(f_4974_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev]) ).

fof(f_4974_2,plain,
    ! [U_20713,U_20712,U_20711] :
      ( c_List_OtakeWhile(U_20711,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20711),c_fNot),hAPP(hAPP(c_COMBC(U_20711,U_20711,tc_HOL_Obool),c_fequal),U_20713)),hAPP(c_List_Orev(U_20711),U_20712)) = hAPP(c_List_Orev(U_20711),hAPP(c_List_Otl(U_20711),c_List_OdropWhile(U_20711,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20711),c_fNot),hAPP(hAPP(c_COMBC(U_20711,U_20711,tc_HOL_Obool),c_fequal),U_20713)),U_20712)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20711),U_20713),hAPP(c_List_Oset(U_20711),U_20712)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20711),U_20712)) ),
    inference(variable_rename,[status(thm)],[f_4974_1]) ).

fof(f_4974_3,plain,
    ! [U_20711,U_20712,U_20713] :
      ( c_List_OtakeWhile(U_20711,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20711),c_fNot),hAPP(hAPP(c_COMBC(U_20711,U_20711,tc_HOL_Obool),c_fequal),U_20713)),hAPP(c_List_Orev(U_20711),U_20712)) = hAPP(c_List_Orev(U_20711),hAPP(c_List_Otl(U_20711),c_List_OdropWhile(U_20711,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20711),c_fNot),hAPP(hAPP(c_COMBC(U_20711,U_20711,tc_HOL_Obool),c_fequal),U_20713)),U_20712)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20711),U_20713),hAPP(c_List_Oset(U_20711),U_20712)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20711),U_20712)) ),
    inference(definitional_conversion,[status(esa)],[f_4974_2]) ).

cnf(f_4974_4,plain,
    ( c_List_OtakeWhile(U_20711,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20711),c_fNot),hAPP(hAPP(c_COMBC(U_20711,U_20711,tc_HOL_Obool),c_fequal),U_20713)),hAPP(c_List_Orev(U_20711),U_20712)) = hAPP(c_List_Orev(U_20711),hAPP(c_List_Otl(U_20711),c_List_OdropWhile(U_20711,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20711),c_fNot),hAPP(hAPP(c_COMBC(U_20711,U_20711,tc_HOL_Obool),c_fequal),U_20713)),U_20712)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20711),U_20713),hAPP(c_List_Oset(U_20711),U_20712)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20711),U_20712)) ),
    inference(clausify,[status(thm)],[f_4974_3]) ).

fof(f_4975_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev]) ).

fof(f_4975_2,plain,
    ! [U_20716,U_20715,U_20714] :
      ( c_List_OdropWhile(U_20714,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20714),c_fNot),hAPP(hAPP(c_COMBC(U_20714,U_20714,tc_HOL_Obool),c_fequal),U_20716)),hAPP(c_List_Orev(U_20714),U_20715)) = hAPP(hAPP(c_List_Olist_OCons(U_20714),U_20716),hAPP(c_List_Orev(U_20714),c_List_OtakeWhile(U_20714,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20714),c_fNot),hAPP(hAPP(c_COMBC(U_20714,U_20714,tc_HOL_Obool),c_fequal),U_20716)),U_20715)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20714),U_20716),hAPP(c_List_Oset(U_20714),U_20715)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20714),U_20715)) ),
    inference(variable_rename,[status(thm)],[f_4975_1]) ).

fof(f_4975_3,plain,
    ! [U_20714,U_20715,U_20716] :
      ( c_List_OdropWhile(U_20714,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20714),c_fNot),hAPP(hAPP(c_COMBC(U_20714,U_20714,tc_HOL_Obool),c_fequal),U_20716)),hAPP(c_List_Orev(U_20714),U_20715)) = hAPP(hAPP(c_List_Olist_OCons(U_20714),U_20716),hAPP(c_List_Orev(U_20714),c_List_OtakeWhile(U_20714,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20714),c_fNot),hAPP(hAPP(c_COMBC(U_20714,U_20714,tc_HOL_Obool),c_fequal),U_20716)),U_20715)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20714),U_20716),hAPP(c_List_Oset(U_20714),U_20715)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20714),U_20715)) ),
    inference(definitional_conversion,[status(esa)],[f_4975_2]) ).

cnf(f_4975_4,plain,
    ( c_List_OdropWhile(U_20714,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20714),c_fNot),hAPP(hAPP(c_COMBC(U_20714,U_20714,tc_HOL_Obool),c_fequal),U_20716)),hAPP(c_List_Orev(U_20714),U_20715)) = hAPP(hAPP(c_List_Olist_OCons(U_20714),U_20716),hAPP(c_List_Orev(U_20714),c_List_OtakeWhile(U_20714,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20714),c_fNot),hAPP(hAPP(c_COMBC(U_20714,U_20714,tc_HOL_Obool),c_fequal),U_20716)),U_20715)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20714),U_20716),hAPP(c_List_Oset(U_20714),U_20715)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20714),U_20715)) ),
    inference(clausify,[status(thm)],[f_4975_3]) ).

fof(f_4976_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__map]) ).

fof(f_4976_2,plain,
    ! [U_20721,U_20720,U_20719,U_20718,U_20717] : c_List_OdropWhile(U_20717,U_20718,hAPP(hAPP(c_List_Omap(U_20719,U_20717),U_20720),U_20721)) = hAPP(hAPP(c_List_Omap(U_20719,U_20717),U_20720),c_List_OdropWhile(U_20719,hAPP(c_Fun_Ocomp(U_20717,tc_HOL_Obool,U_20719,U_20718),U_20720),U_20721)),
    inference(variable_rename,[status(thm)],[f_4976_1]) ).

fof(f_4976_3,plain,
    ! [U_20717,U_20718,U_20719,U_20720,U_20721] : c_List_OdropWhile(U_20717,U_20718,hAPP(hAPP(c_List_Omap(U_20719,U_20717),U_20720),U_20721)) = hAPP(hAPP(c_List_Omap(U_20719,U_20717),U_20720),c_List_OdropWhile(U_20719,hAPP(c_Fun_Ocomp(U_20717,tc_HOL_Obool,U_20719,U_20718),U_20720),U_20721)),
    inference(definitional_conversion,[status(esa)],[f_4976_2]) ).

cnf(f_4976_4,plain,
    c_List_OdropWhile(U_20717,U_20718,hAPP(hAPP(c_List_Omap(U_20719,U_20717),U_20720),U_20721)) = hAPP(hAPP(c_List_Omap(U_20719,U_20717),U_20720),c_List_OdropWhile(U_20719,hAPP(c_Fun_Ocomp(U_20717,tc_HOL_Obool,U_20719,U_20718),U_20720),U_20721)),
    inference(clausify,[status(thm)],[f_4976_3]) ).

fof(f_4977_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(f_4977_2,plain,
    ! [U_20724,U_20723,U_20722] : hAPP(hAPP(c_List_Oappend(U_20722),c_List_OtakeWhile(U_20722,U_20723,U_20724)),c_List_OdropWhile(U_20722,U_20723,U_20724)) = U_20724,
    inference(variable_rename,[status(thm)],[f_4977_1]) ).

fof(f_4977_3,plain,
    ! [U_20722,U_20723,U_20724] : hAPP(hAPP(c_List_Oappend(U_20722),c_List_OtakeWhile(U_20722,U_20723,U_20724)),c_List_OdropWhile(U_20722,U_20723,U_20724)) = U_20724,
    inference(definitional_conversion,[status(esa)],[f_4977_2]) ).

cnf(f_4977_4,plain,
    hAPP(hAPP(c_List_Oappend(U_20722),c_List_OtakeWhile(U_20722,U_20723,U_20724)),c_List_OdropWhile(U_20722,U_20723,U_20724)) = U_20724,
    inference(clausify,[status(thm)],[f_4977_3]) ).

fof(f_4978_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__dropWhile__le]) ).

fof(f_4978_2,plain,
    ! [U_20727,U_20726,U_20725] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20725)),c_List_OdropWhile(U_20725,U_20726,U_20727))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20725)),U_20727))),
    inference(variable_rename,[status(thm)],[f_4978_1]) ).

fof(f_4978_3,plain,
    ! [U_20725,U_20726,U_20727] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20725)),c_List_OdropWhile(U_20725,U_20726,U_20727))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20725)),U_20727))),
    inference(definitional_conversion,[status(esa)],[f_4978_2]) ).

cnf(f_4978_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20725)),c_List_OdropWhile(U_20725,U_20726,U_20727))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20725)),U_20727))),
    inference(clausify,[status(thm)],[f_4978_3]) ).

fof(f_4979_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile]) ).

fof(f_4979_2,plain,
    ! [U_20730,U_20729,U_20728] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20728),c_List_OdropWhile(U_20728,U_20730,U_20729)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20728),U_20729)) ),
    inference(variable_rename,[status(thm)],[f_4979_1]) ).

fof(f_4979_3,plain,
    ! [U_20728,U_20729,U_20730] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20728),c_List_OdropWhile(U_20728,U_20730,U_20729)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20728),U_20729)) ),
    inference(definitional_conversion,[status(esa)],[f_4979_2]) ).

cnf(f_4979_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20728),c_List_OdropWhile(U_20728,U_20730,U_20729)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20728),U_20729)) ),
    inference(clausify,[status(thm)],[f_4979_3]) ).

fof(f_4980_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2)
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(f_4980_2,plain,
    ! [U_20734,U_20733,U_20732,U_20731] :
      ( ( c_List_OdropWhile(U_20733,U_20731,hAPP(hAPP(c_List_Olist_OCons(U_20733),U_20732),U_20734)) = hAPP(hAPP(c_List_Olist_OCons(U_20733),U_20732),U_20734)
        | hBOOL(hAPP(U_20731,U_20732)) )
      & ( c_List_OdropWhile(U_20733,U_20731,hAPP(hAPP(c_List_Olist_OCons(U_20733),U_20732),U_20734)) = c_List_OdropWhile(U_20733,U_20731,U_20734)
        | ~ hBOOL(hAPP(U_20731,U_20732)) ) ),
    inference(variable_rename,[status(thm)],[f_4980_1]) ).

fof(f_4980_3,plain,
    ( ! [U_20742,U_20740,U_20738,U_20736] :
        ( c_List_OdropWhile(U_20740,U_20736,hAPP(hAPP(c_List_Olist_OCons(U_20740),U_20738),U_20742)) = hAPP(hAPP(c_List_Olist_OCons(U_20740),U_20738),U_20742)
        | hBOOL(hAPP(U_20736,U_20738)) )
    & ! [U_20741,U_20739,U_20737,U_20735] :
        ( c_List_OdropWhile(U_20739,U_20735,hAPP(hAPP(c_List_Olist_OCons(U_20739),U_20737),U_20741)) = c_List_OdropWhile(U_20739,U_20735,U_20741)
        | ~ hBOOL(hAPP(U_20735,U_20737)) ) ),
    inference(miniscope,[status(thm)],[f_4980_2]) ).

fof(f_4980_4,plain,
    ( ! [U_20742,U_20736,U_20738,U_20740] :
        ( c_List_OdropWhile(U_20740,U_20736,hAPP(hAPP(c_List_Olist_OCons(U_20740),U_20738),U_20742)) = hAPP(hAPP(c_List_Olist_OCons(U_20740),U_20738),U_20742)
        | hBOOL(hAPP(U_20736,U_20738)) )
    & ! [U_20735,U_20737,U_20739,U_20741] :
        ( c_List_OdropWhile(U_20739,U_20735,hAPP(hAPP(c_List_Olist_OCons(U_20739),U_20737),U_20741)) = c_List_OdropWhile(U_20739,U_20735,U_20741)
        | ~ hBOOL(hAPP(U_20735,U_20737)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4980_3]) ).

cnf(f_4980_5,plain,
    ( c_List_OdropWhile(U_20739,U_20735,hAPP(hAPP(c_List_Olist_OCons(U_20739),U_20737),U_20741)) = c_List_OdropWhile(U_20739,U_20735,U_20741)
    | ~ hBOOL(hAPP(U_20735,U_20737)) ),
    inference(clausify,[status(thm)],[f_4980_4]) ).

cnf(f_4980_6,plain,
    ( c_List_OdropWhile(U_20740,U_20736,hAPP(hAPP(c_List_Olist_OCons(U_20740),U_20738),U_20742)) = hAPP(hAPP(c_List_Olist_OCons(U_20740),U_20738),U_20742)
    | hBOOL(hAPP(U_20736,U_20738)) ),
    inference(clausify,[status(thm)],[f_4980_4]) ).

fof(f_4981_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile]) ).

fof(f_4981_2,plain,
    ! [U_20745,U_20744,U_20743] :
      ( c_List_Olinorder__class_Osorted(U_20743,c_List_OdropWhile(U_20743,U_20745,U_20744))
      | ~ c_List_Olinorder__class_Osorted(U_20743,U_20744)
      | ~ class_Orderings_Olinorder(U_20743) ),
    inference(variable_rename,[status(thm)],[f_4981_1]) ).

fof(f_4981_3,plain,
    ! [U_20745,U_20743,U_20744] :
      ( c_List_Olinorder__class_Osorted(U_20743,c_List_OdropWhile(U_20743,U_20745,U_20744))
      | ~ c_List_Olinorder__class_Osorted(U_20743,U_20744)
      | ~ class_Orderings_Olinorder(U_20743) ),
    inference(definitional_conversion,[status(esa)],[f_4981_2]) ).

cnf(f_4981_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20743,c_List_OdropWhile(U_20743,U_20745,U_20744))
    | ~ c_List_Olinorder__class_Osorted(U_20743,U_20744)
    | ~ class_Orderings_Olinorder(U_20743) ),
    inference(clausify,[status(thm)],[f_4981_3]) ).

fof(f_4982_1,plain,
    ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(f_4982_2,plain,
    ! [U_20747,U_20746] : c_List_OdropWhile(U_20746,U_20747,c_List_Olist_ONil(U_20746)) = c_List_Olist_ONil(U_20746),
    inference(variable_rename,[status(thm)],[f_4982_1]) ).

fof(f_4982_3,plain,
    ! [U_20746,U_20747] : c_List_OdropWhile(U_20746,U_20747,c_List_Olist_ONil(U_20746)) = c_List_Olist_ONil(U_20746),
    inference(definitional_conversion,[status(esa)],[f_4982_2]) ).

cnf(f_4982_4,plain,
    c_List_OdropWhile(U_20746,U_20747,c_List_Olist_ONil(U_20746)) = c_List_Olist_ONil(U_20746),
    inference(clausify,[status(thm)],[f_4982_3]) ).

fof(f_4983_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
      | c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__dropWhile]) ).

fof(f_4983_2,plain,
    ! [U_20750,U_20749,U_20748] :
      ( ~ hBOOL(hAPP(U_20749,hAPP(c_List_Ohd(U_20748),c_List_OdropWhile(U_20748,U_20749,U_20750))))
      | c_List_OdropWhile(U_20748,U_20749,U_20750) = c_List_Olist_ONil(U_20748) ),
    inference(variable_rename,[status(thm)],[f_4983_1]) ).

fof(f_4983_3,plain,
    ! [U_20748,U_20749,U_20750] :
      ( ~ hBOOL(hAPP(U_20749,hAPP(c_List_Ohd(U_20748),c_List_OdropWhile(U_20748,U_20749,U_20750))))
      | c_List_OdropWhile(U_20748,U_20749,U_20750) = c_List_Olist_ONil(U_20748) ),
    inference(definitional_conversion,[status(esa)],[f_4983_2]) ).

cnf(f_4983_4,plain,
    ( ~ hBOOL(hAPP(U_20749,hAPP(c_List_Ohd(U_20748),c_List_OdropWhile(U_20748,U_20749,U_20750))))
    | c_List_OdropWhile(U_20748,U_20749,U_20750) = c_List_Olist_ONil(U_20748) ),
    inference(clausify,[status(thm)],[f_4983_3]) ).

fof(f_4984_1,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]) ).

fof(f_4984_2,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_4984_1]) ).

cnf(f_4984_3,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_4984_2]) ).

fof(f_4985_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))
      | ~ class_Lattices_Obounded__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice]) ).

fof(f_4985_2,plain,
    ! [U_20752,U_20751] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20752,U_20751))
      | ~ class_Lattices_Obounded__lattice(U_20751) ),
    inference(variable_rename,[status(thm)],[f_4985_1]) ).

fof(f_4985_3,plain,
    ! [U_20751,U_20752] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20752,U_20751))
      | ~ class_Lattices_Obounded__lattice(U_20751) ),
    inference(definitional_conversion,[status(esa)],[f_4985_2]) ).

cnf(f_4985_4,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(U_20752,U_20751))
    | ~ class_Lattices_Obounded__lattice(U_20751) ),
    inference(clausify,[status(thm)],[f_4985_3]) ).

fof(f_4986_1,plain,
    ! [T_2,T_1] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice]) ).

fof(f_4986_2,plain,
    ! [U_20754,U_20753] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20754,U_20753))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20753) ),
    inference(variable_rename,[status(thm)],[f_4986_1]) ).

fof(f_4986_3,plain,
    ! [U_20753,U_20754] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20754,U_20753))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20753) ),
    inference(definitional_conversion,[status(esa)],[f_4986_2]) ).

cnf(f_4986_4,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20754,U_20753))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20753) ),
    inference(clausify,[status(thm)],[f_4986_3]) ).

fof(f_4987_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1))
      | ~ class_Lattices_Obounded__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top]) ).

fof(f_4987_2,plain,
    ! [U_20756,U_20755] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20756,U_20755))
      | ~ class_Lattices_Obounded__lattice(U_20755) ),
    inference(variable_rename,[status(thm)],[f_4987_1]) ).

fof(f_4987_3,plain,
    ! [U_20755,U_20756] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20756,U_20755))
      | ~ class_Lattices_Obounded__lattice(U_20755) ),
    inference(definitional_conversion,[status(esa)],[f_4987_2]) ).

cnf(f_4987_4,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(U_20756,U_20755))
    | ~ class_Lattices_Obounded__lattice(U_20755) ),
    inference(clausify,[status(thm)],[f_4987_3]) ).

fof(f_4988_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1))
      | ~ class_Lattices_Obounded__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot]) ).

fof(f_4988_2,plain,
    ! [U_20758,U_20757] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20758,U_20757))
      | ~ class_Lattices_Obounded__lattice(U_20757) ),
    inference(variable_rename,[status(thm)],[f_4988_1]) ).

fof(f_4988_3,plain,
    ! [U_20757,U_20758] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20758,U_20757))
      | ~ class_Lattices_Obounded__lattice(U_20757) ),
    inference(definitional_conversion,[status(esa)],[f_4988_2]) ).

cnf(f_4988_4,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20758,U_20757))
    | ~ class_Lattices_Obounded__lattice(U_20757) ),
    inference(clausify,[status(thm)],[f_4988_3]) ).

fof(f_4989_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1))
      | ~ class_Lattices_Olattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup]) ).

fof(f_4989_2,plain,
    ! [U_20760,U_20759] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20760,U_20759))
      | ~ class_Lattices_Olattice(U_20759) ),
    inference(variable_rename,[status(thm)],[f_4989_1]) ).

fof(f_4989_3,plain,
    ! [U_20759,U_20760] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20760,U_20759))
      | ~ class_Lattices_Olattice(U_20759) ),
    inference(definitional_conversion,[status(esa)],[f_4989_2]) ).

cnf(f_4989_4,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(U_20760,U_20759))
    | ~ class_Lattices_Olattice(U_20759) ),
    inference(clausify,[status(thm)],[f_4989_3]) ).

fof(f_4990_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1))
      | ~ class_Lattices_Olattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf]) ).

fof(f_4990_2,plain,
    ! [U_20762,U_20761] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20762,U_20761))
      | ~ class_Lattices_Olattice(U_20761) ),
    inference(variable_rename,[status(thm)],[f_4990_1]) ).

fof(f_4990_3,plain,
    ! [U_20761,U_20762] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20762,U_20761))
      | ~ class_Lattices_Olattice(U_20761) ),
    inference(definitional_conversion,[status(esa)],[f_4990_2]) ).

cnf(f_4990_4,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(U_20762,U_20761))
    | ~ class_Lattices_Olattice(U_20761) ),
    inference(clausify,[status(thm)],[f_4990_3]) ).

fof(f_4991_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))
      | ~ class_Lattices_Odistrib__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice]) ).

fof(f_4991_2,plain,
    ! [U_20764,U_20763] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20764,U_20763))
      | ~ class_Lattices_Odistrib__lattice(U_20763) ),
    inference(variable_rename,[status(thm)],[f_4991_1]) ).

fof(f_4991_3,plain,
    ! [U_20764,U_20763] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20764,U_20763))
      | ~ class_Lattices_Odistrib__lattice(U_20763) ),
    inference(definitional_conversion,[status(esa)],[f_4991_2]) ).

cnf(f_4991_4,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(U_20764,U_20763))
    | ~ class_Lattices_Odistrib__lattice(U_20763) ),
    inference(clausify,[status(thm)],[f_4991_3]) ).

fof(f_4992_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
      | ~ class_Lattices_Oboolean__algebra(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra]) ).

fof(f_4992_2,plain,
    ! [U_20766,U_20765] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20766,U_20765))
      | ~ class_Lattices_Oboolean__algebra(U_20765) ),
    inference(variable_rename,[status(thm)],[f_4992_1]) ).

fof(f_4992_3,plain,
    ! [U_20766,U_20765] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20766,U_20765))
      | ~ class_Lattices_Oboolean__algebra(U_20765) ),
    inference(definitional_conversion,[status(esa)],[f_4992_2]) ).

cnf(f_4992_4,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(U_20766,U_20765))
    | ~ class_Lattices_Oboolean__algebra(U_20765) ),
    inference(clausify,[status(thm)],[f_4992_3]) ).

fof(f_4993_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Opreorder(tc_fun(T_2,T_1))
      | ~ class_Orderings_Opreorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).

fof(f_4993_2,plain,
    ! [U_20768,U_20767] :
      ( class_Orderings_Opreorder(tc_fun(U_20768,U_20767))
      | ~ class_Orderings_Opreorder(U_20767) ),
    inference(variable_rename,[status(thm)],[f_4993_1]) ).

fof(f_4993_3,plain,
    ! [U_20768,U_20767] :
      ( class_Orderings_Opreorder(tc_fun(U_20768,U_20767))
      | ~ class_Orderings_Opreorder(U_20767) ),
    inference(definitional_conversion,[status(esa)],[f_4993_2]) ).

cnf(f_4993_4,plain,
    ( class_Orderings_Opreorder(tc_fun(U_20768,U_20767))
    | ~ class_Orderings_Opreorder(U_20767) ),
    inference(clausify,[status(thm)],[f_4993_3]) ).

fof(f_4994_1,plain,
    ! [T_1,T_2] :
      ( class_Finite__Set_Ofinite(tc_fun(T_2,T_1))
      | ~ class_Finite__Set_Ofinite(T_1)
      | ~ class_Finite__Set_Ofinite(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite]) ).

fof(f_4994_2,plain,
    ! [U_20770,U_20769] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20769,U_20770))
      | ~ class_Finite__Set_Ofinite(U_20770)
      | ~ class_Finite__Set_Ofinite(U_20769) ),
    inference(variable_rename,[status(thm)],[f_4994_1]) ).

fof(f_4994_3,plain,
    ! [U_20770,U_20769] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20769,U_20770))
      | ~ class_Finite__Set_Ofinite(U_20770)
      | ~ class_Finite__Set_Ofinite(U_20769) ),
    inference(definitional_conversion,[status(esa)],[f_4994_2]) ).

cnf(f_4994_4,plain,
    ( class_Finite__Set_Ofinite(tc_fun(U_20769,U_20770))
    | ~ class_Finite__Set_Ofinite(U_20770)
    | ~ class_Finite__Set_Ofinite(U_20769) ),
    inference(clausify,[status(thm)],[f_4994_3]) ).

fof(f_4995_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(tc_fun(T_2,T_1))
      | ~ class_Lattices_Olattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice]) ).

fof(f_4995_2,plain,
    ! [U_20772,U_20771] :
      ( class_Lattices_Olattice(tc_fun(U_20772,U_20771))
      | ~ class_Lattices_Olattice(U_20771) ),
    inference(variable_rename,[status(thm)],[f_4995_1]) ).

fof(f_4995_3,plain,
    ! [U_20771,U_20772] :
      ( class_Lattices_Olattice(tc_fun(U_20772,U_20771))
      | ~ class_Lattices_Olattice(U_20771) ),
    inference(definitional_conversion,[status(esa)],[f_4995_2]) ).

cnf(f_4995_4,plain,
    ( class_Lattices_Olattice(tc_fun(U_20772,U_20771))
    | ~ class_Lattices_Olattice(U_20771) ),
    inference(clausify,[status(thm)],[f_4995_3]) ).

fof(f_4996_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Oorder(tc_fun(T_2,T_1))
      | ~ class_Orderings_Oorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).

fof(f_4996_2,plain,
    ! [U_20774,U_20773] :
      ( class_Orderings_Oorder(tc_fun(U_20774,U_20773))
      | ~ class_Orderings_Oorder(U_20773) ),
    inference(variable_rename,[status(thm)],[f_4996_1]) ).

fof(f_4996_3,plain,
    ! [U_20774,U_20773] :
      ( class_Orderings_Oorder(tc_fun(U_20774,U_20773))
      | ~ class_Orderings_Oorder(U_20773) ),
    inference(definitional_conversion,[status(esa)],[f_4996_2]) ).

cnf(f_4996_4,plain,
    ( class_Orderings_Oorder(tc_fun(U_20774,U_20773))
    | ~ class_Orderings_Oorder(U_20773) ),
    inference(clausify,[status(thm)],[f_4996_3]) ).

fof(f_4997_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Otop(tc_fun(T_2,T_1))
      | ~ class_Orderings_Otop(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop]) ).

fof(f_4997_2,plain,
    ! [U_20776,U_20775] :
      ( class_Orderings_Otop(tc_fun(U_20776,U_20775))
      | ~ class_Orderings_Otop(U_20775) ),
    inference(variable_rename,[status(thm)],[f_4997_1]) ).

fof(f_4997_3,plain,
    ! [U_20775,U_20776] :
      ( class_Orderings_Otop(tc_fun(U_20776,U_20775))
      | ~ class_Orderings_Otop(U_20775) ),
    inference(definitional_conversion,[status(esa)],[f_4997_2]) ).

cnf(f_4997_4,plain,
    ( class_Orderings_Otop(tc_fun(U_20776,U_20775))
    | ~ class_Orderings_Otop(U_20775) ),
    inference(clausify,[status(thm)],[f_4997_3]) ).

fof(f_4998_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Oord(tc_fun(T_2,T_1))
      | ~ class_Orderings_Oord(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).

fof(f_4998_2,plain,
    ! [U_20778,U_20777] :
      ( class_Orderings_Oord(tc_fun(U_20778,U_20777))
      | ~ class_Orderings_Oord(U_20777) ),
    inference(variable_rename,[status(thm)],[f_4998_1]) ).

fof(f_4998_3,plain,
    ! [U_20777,U_20778] :
      ( class_Orderings_Oord(tc_fun(U_20778,U_20777))
      | ~ class_Orderings_Oord(U_20777) ),
    inference(definitional_conversion,[status(esa)],[f_4998_2]) ).

cnf(f_4998_4,plain,
    ( class_Orderings_Oord(tc_fun(U_20778,U_20777))
    | ~ class_Orderings_Oord(U_20777) ),
    inference(clausify,[status(thm)],[f_4998_3]) ).

fof(f_4999_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Obot(tc_fun(T_2,T_1))
      | ~ class_Orderings_Obot(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot]) ).

fof(f_4999_2,plain,
    ! [U_20780,U_20779] :
      ( class_Orderings_Obot(tc_fun(U_20780,U_20779))
      | ~ class_Orderings_Obot(U_20779) ),
    inference(variable_rename,[status(thm)],[f_4999_1]) ).

fof(f_4999_3,plain,
    ! [U_20779,U_20780] :
      ( class_Orderings_Obot(tc_fun(U_20780,U_20779))
      | ~ class_Orderings_Obot(U_20779) ),
    inference(definitional_conversion,[status(esa)],[f_4999_2]) ).

cnf(f_4999_4,plain,
    ( class_Orderings_Obot(tc_fun(U_20780,U_20779))
    | ~ class_Orderings_Obot(U_20779) ),
    inference(clausify,[status(thm)],[f_4999_3]) ).

fof(f_5000_1,plain,
    ! [T_2,T_1] :
      ( class_Groups_Ouminus(tc_fun(T_2,T_1))
      | ~ class_Groups_Ouminus(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus]) ).

fof(f_5000_2,plain,
    ! [U_20782,U_20781] :
      ( class_Groups_Ouminus(tc_fun(U_20782,U_20781))
      | ~ class_Groups_Ouminus(U_20781) ),
    inference(variable_rename,[status(thm)],[f_5000_1]) ).

fof(f_5000_3,plain,
    ! [U_20781,U_20782] :
      ( class_Groups_Ouminus(tc_fun(U_20782,U_20781))
      | ~ class_Groups_Ouminus(U_20781) ),
    inference(definitional_conversion,[status(esa)],[f_5000_2]) ).

cnf(f_5000_4,plain,
    ( class_Groups_Ouminus(tc_fun(U_20782,U_20781))
    | ~ class_Groups_Ouminus(U_20781) ),
    inference(clausify,[status(thm)],[f_5000_3]) ).

fof(f_5001_1,plain,
    ! [T_2,T_1] :
      ( class_Groups_Ominus(tc_fun(T_2,T_1))
      | ~ class_Groups_Ominus(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus]) ).

fof(f_5001_2,plain,
    ! [U_20784,U_20783] :
      ( class_Groups_Ominus(tc_fun(U_20784,U_20783))
      | ~ class_Groups_Ominus(U_20783) ),
    inference(variable_rename,[status(thm)],[f_5001_1]) ).

fof(f_5001_3,plain,
    ! [U_20783,U_20784] :
      ( class_Groups_Ominus(tc_fun(U_20784,U_20783))
      | ~ class_Groups_Ominus(U_20783) ),
    inference(definitional_conversion,[status(esa)],[f_5001_2]) ).

cnf(f_5001_4,plain,
    ( class_Groups_Ominus(tc_fun(U_20784,U_20783))
    | ~ class_Groups_Ominus(U_20783) ),
    inference(clausify,[status(thm)],[f_5001_3]) ).

fof(f_5002_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_5002_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5002_1]) ).

cnf(f_5002_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5002_2]) ).

fof(f_5003_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_5003_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5003_1]) ).

cnf(f_5003_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5003_2]) ).

fof(f_5004_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_5004_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5004_1]) ).

cnf(f_5004_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5004_2]) ).

fof(f_5005_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_5005_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5005_1]) ).

cnf(f_5005_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5005_2]) ).

fof(f_5006_1,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).

fof(f_5006_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5006_1]) ).

cnf(f_5006_3,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5006_2]) ).

fof(f_5007_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]) ).

fof(f_5007_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5007_1]) ).

cnf(f_5007_3,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5007_2]) ).

fof(f_5008_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).

fof(f_5008_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5008_1]) ).

cnf(f_5008_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5008_2]) ).

fof(f_5009_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).

fof(f_5009_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5009_1]) ).

cnf(f_5009_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5009_2]) ).

fof(f_5010_1,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]) ).

fof(f_5010_2,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5010_1]) ).

cnf(f_5010_3,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5010_2]) ).

fof(f_5011_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).

fof(f_5011_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5011_1]) ).

cnf(f_5011_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5011_2]) ).

fof(f_5012_1,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).

fof(f_5012_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5012_1]) ).

cnf(f_5012_3,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5012_2]) ).

fof(f_5013_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_5013_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5013_1]) ).

cnf(f_5013_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5013_2]) ).

fof(f_5014_1,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]) ).

fof(f_5014_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5014_1]) ).

cnf(f_5014_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5014_2]) ).

fof(f_5015_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).

fof(f_5015_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5015_1]) ).

cnf(f_5015_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5015_2]) ).

fof(f_5016_1,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).

fof(f_5016_2,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5016_1]) ).

cnf(f_5016_3,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5016_2]) ).

fof(f_5017_1,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).

fof(f_5017_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5017_1]) ).

cnf(f_5017_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5017_2]) ).

fof(f_5018_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).

fof(f_5018_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5018_1]) ).

cnf(f_5018_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5018_2]) ).

fof(f_5019_1,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).

fof(f_5019_2,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5019_1]) ).

cnf(f_5019_3,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5019_2]) ).

fof(f_5020_1,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).

fof(f_5020_2,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5020_1]) ).

cnf(f_5020_3,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5020_2]) ).

fof(f_5021_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).

fof(f_5021_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5021_1]) ).

cnf(f_5021_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5021_2]) ).

fof(f_5022_1,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).

fof(f_5022_2,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5022_1]) ).

cnf(f_5022_3,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5022_2]) ).

fof(f_5023_1,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).

fof(f_5023_2,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5023_1]) ).

cnf(f_5023_3,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5023_2]) ).

fof(f_5024_1,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]) ).

fof(f_5024_2,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5024_1]) ).

cnf(f_5024_3,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5024_2]) ).

fof(f_5025_1,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]) ).

fof(f_5025_2,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5025_1]) ).

cnf(f_5025_3,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5025_2]) ).

fof(f_5026_1,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]) ).

fof(f_5026_2,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5026_1]) ).

cnf(f_5026_3,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5026_2]) ).

fof(f_5027_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).

fof(f_5027_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5027_1]) ).

cnf(f_5027_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5027_2]) ).

fof(f_5028_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).

fof(f_5028_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5028_1]) ).

cnf(f_5028_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5028_2]) ).

fof(f_5029_1,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).

fof(f_5029_2,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5029_1]) ).

cnf(f_5029_3,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5029_2]) ).

fof(f_5030_1,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).

fof(f_5030_2,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5030_1]) ).

cnf(f_5030_3,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5030_2]) ).

fof(f_5031_1,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).

fof(f_5031_2,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5031_1]) ).

cnf(f_5031_3,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5031_2]) ).

fof(f_5032_1,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).

fof(f_5032_2,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5032_1]) ).

cnf(f_5032_3,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5032_2]) ).

fof(f_5033_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).

fof(f_5033_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5033_1]) ).

cnf(f_5033_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5033_2]) ).

fof(f_5034_1,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).

fof(f_5034_2,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5034_1]) ).

cnf(f_5034_3,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5034_2]) ).

fof(f_5035_1,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).

fof(f_5035_2,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5035_1]) ).

cnf(f_5035_3,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5035_2]) ).

fof(f_5036_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).

fof(f_5036_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5036_1]) ).

cnf(f_5036_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5036_2]) ).

fof(f_5037_1,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]) ).

fof(f_5037_2,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5037_1]) ).

cnf(f_5037_3,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5037_2]) ).

fof(f_5038_1,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).

fof(f_5038_2,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5038_1]) ).

cnf(f_5038_3,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5038_2]) ).

fof(f_5039_1,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).

fof(f_5039_2,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5039_1]) ).

cnf(f_5039_3,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5039_2]) ).

fof(f_5040_1,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]) ).

fof(f_5040_2,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5040_1]) ).

cnf(f_5040_3,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5040_2]) ).

fof(f_5041_1,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).

fof(f_5041_2,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5041_1]) ).

cnf(f_5041_3,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5041_2]) ).

fof(f_5042_1,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).

fof(f_5042_2,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5042_1]) ).

cnf(f_5042_3,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5042_2]) ).

fof(f_5043_1,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).

fof(f_5043_2,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5043_1]) ).

cnf(f_5043_3,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5043_2]) ).

fof(f_5044_1,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).

fof(f_5044_2,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5044_1]) ).

cnf(f_5044_3,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5044_2]) ).

fof(f_5045_1,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).

fof(f_5045_2,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5045_1]) ).

cnf(f_5045_3,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5045_2]) ).

fof(f_5046_1,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).

fof(f_5046_2,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5046_1]) ).

cnf(f_5046_3,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5046_2]) ).

fof(f_5047_1,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).

fof(f_5047_2,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5047_1]) ).

cnf(f_5047_3,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5047_2]) ).

fof(f_5048_1,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).

fof(f_5048_2,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5048_1]) ).

cnf(f_5048_3,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5048_2]) ).

fof(f_5049_1,plain,
    class_Smallcheck_Osmall(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]) ).

fof(f_5049_2,plain,
    class_Smallcheck_Osmall(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5049_1]) ).

cnf(f_5049_3,plain,
    class_Smallcheck_Osmall(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5049_2]) ).

fof(f_5050_1,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).

fof(f_5050_2,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5050_1]) ).

cnf(f_5050_3,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5050_2]) ).

fof(f_5051_1,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).

fof(f_5051_2,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5051_1]) ).

cnf(f_5051_3,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5051_2]) ).

fof(f_5052_1,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Olattice]) ).

fof(f_5052_2,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5052_1]) ).

cnf(f_5052_3,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5052_2]) ).

fof(f_5053_1,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).

fof(f_5053_2,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5053_1]) ).

cnf(f_5053_3,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5053_2]) ).

fof(f_5054_1,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Oring__div]) ).

fof(f_5054_2,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5054_1]) ).

cnf(f_5054_3,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5054_2]) ).

fof(f_5055_1,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).

fof(f_5055_2,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5055_1]) ).

cnf(f_5055_3,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5055_2]) ).

fof(f_5056_1,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).

fof(f_5056_2,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5056_1]) ).

cnf(f_5056_3,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5056_2]) ).

fof(f_5057_1,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).

fof(f_5057_2,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5057_1]) ).

cnf(f_5057_3,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5057_2]) ).

fof(f_5058_1,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).

fof(f_5058_2,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5058_1]) ).

cnf(f_5058_3,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5058_2]) ).

fof(f_5059_1,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).

fof(f_5059_2,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5059_1]) ).

cnf(f_5059_3,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5059_2]) ).

fof(f_5060_1,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).

fof(f_5060_2,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5060_1]) ).

cnf(f_5060_3,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5060_2]) ).

fof(f_5061_1,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).

fof(f_5061_2,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5061_1]) ).

cnf(f_5061_3,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5061_2]) ).

fof(f_5062_1,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).

fof(f_5062_2,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5062_1]) ).

cnf(f_5062_3,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5062_2]) ).

fof(f_5063_1,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).

fof(f_5063_2,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5063_1]) ).

cnf(f_5063_3,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5063_2]) ).

fof(f_5064_1,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).

fof(f_5064_2,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5064_1]) ).

cnf(f_5064_3,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5064_2]) ).

fof(f_5065_1,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).

fof(f_5065_2,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5065_1]) ).

cnf(f_5065_3,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5065_2]) ).

fof(f_5066_1,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).

fof(f_5066_2,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5066_1]) ).

cnf(f_5066_3,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5066_2]) ).

fof(f_5067_1,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).

fof(f_5067_2,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5067_1]) ).

cnf(f_5067_3,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5067_2]) ).

fof(f_5068_1,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).

fof(f_5068_2,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5068_1]) ).

cnf(f_5068_3,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5068_2]) ).

fof(f_5069_1,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).

fof(f_5069_2,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5069_1]) ).

cnf(f_5069_3,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5069_2]) ).

fof(f_5070_1,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).

fof(f_5070_2,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5070_1]) ).

cnf(f_5070_3,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5070_2]) ).

fof(f_5071_1,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).

fof(f_5071_2,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5071_1]) ).

cnf(f_5071_3,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5071_2]) ).

fof(f_5072_1,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).

fof(f_5072_2,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5072_1]) ).

cnf(f_5072_3,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5072_2]) ).

fof(f_5073_1,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Odvd]) ).

fof(f_5073_2,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_5073_1]) ).

cnf(f_5073_3,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5073_2]) ).

fof(f_5074_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_5074_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5074_1]) ).

cnf(f_5074_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5074_2]) ).

fof(f_5075_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_5075_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5075_1]) ).

cnf(f_5075_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5075_2]) ).

fof(f_5076_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_5076_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5076_1]) ).

cnf(f_5076_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5076_2]) ).

fof(f_5077_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_5077_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5077_1]) ).

cnf(f_5077_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5077_2]) ).

fof(f_5078_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]) ).

fof(f_5078_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5078_1]) ).

cnf(f_5078_3,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5078_2]) ).

fof(f_5079_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).

fof(f_5079_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5079_1]) ).

cnf(f_5079_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5079_2]) ).

fof(f_5080_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).

fof(f_5080_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5080_1]) ).

cnf(f_5080_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5080_2]) ).

fof(f_5081_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).

fof(f_5081_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5081_1]) ).

cnf(f_5081_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5081_2]) ).

fof(f_5082_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_5082_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5082_1]) ).

cnf(f_5082_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5082_2]) ).

fof(f_5083_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).

fof(f_5083_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5083_1]) ).

cnf(f_5083_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5083_2]) ).

fof(f_5084_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).

fof(f_5084_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5084_1]) ).

cnf(f_5084_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5084_2]) ).

fof(f_5085_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).

fof(f_5085_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5085_1]) ).

cnf(f_5085_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5085_2]) ).

fof(f_5086_1,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).

fof(f_5086_2,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5086_1]) ).

cnf(f_5086_3,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5086_2]) ).

fof(f_5087_1,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).

fof(f_5087_2,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5087_1]) ).

cnf(f_5087_3,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5087_2]) ).

fof(f_5088_1,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]) ).

fof(f_5088_2,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5088_1]) ).

cnf(f_5088_3,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5088_2]) ).

fof(f_5089_1,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]) ).

fof(f_5089_2,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5089_1]) ).

cnf(f_5089_3,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5089_2]) ).

fof(f_5090_1,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]) ).

fof(f_5090_2,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5090_1]) ).

cnf(f_5090_3,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5090_2]) ).

fof(f_5091_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).

fof(f_5091_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5091_1]) ).

cnf(f_5091_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5091_2]) ).

fof(f_5092_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).

fof(f_5092_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5092_1]) ).

cnf(f_5092_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5092_2]) ).

fof(f_5093_1,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).

fof(f_5093_2,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5093_1]) ).

cnf(f_5093_3,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5093_2]) ).

fof(f_5094_1,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).

fof(f_5094_2,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5094_1]) ).

cnf(f_5094_3,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5094_2]) ).

fof(f_5095_1,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).

fof(f_5095_2,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5095_1]) ).

cnf(f_5095_3,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5095_2]) ).

fof(f_5096_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).

fof(f_5096_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5096_1]) ).

cnf(f_5096_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5096_2]) ).

fof(f_5097_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).

fof(f_5097_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5097_1]) ).

cnf(f_5097_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5097_2]) ).

fof(f_5098_1,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]) ).

fof(f_5098_2,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5098_1]) ).

cnf(f_5098_3,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5098_2]) ).

fof(f_5099_1,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).

fof(f_5099_2,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5099_1]) ).

cnf(f_5099_3,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5099_2]) ).

fof(f_5100_1,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).

fof(f_5100_2,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5100_1]) ).

cnf(f_5100_3,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5100_2]) ).

fof(f_5101_1,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]) ).

fof(f_5101_2,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5101_1]) ).

cnf(f_5101_3,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5101_2]) ).

fof(f_5102_1,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]) ).

fof(f_5102_2,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5102_1]) ).

cnf(f_5102_3,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5102_2]) ).

fof(f_5103_1,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).

fof(f_5103_2,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5103_1]) ).

cnf(f_5103_3,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5103_2]) ).

fof(f_5104_1,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).

fof(f_5104_2,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5104_1]) ).

cnf(f_5104_3,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5104_2]) ).

fof(f_5105_1,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).

fof(f_5105_2,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5105_1]) ).

cnf(f_5105_3,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5105_2]) ).

fof(f_5106_1,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).

fof(f_5106_2,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5106_1]) ).

cnf(f_5106_3,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5106_2]) ).

fof(f_5107_1,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).

fof(f_5107_2,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5107_1]) ).

cnf(f_5107_3,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5107_2]) ).

fof(f_5108_1,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).

fof(f_5108_2,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5108_1]) ).

cnf(f_5108_3,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5108_2]) ).

fof(f_5109_1,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).

fof(f_5109_2,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5109_1]) ).

cnf(f_5109_3,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5109_2]) ).

fof(f_5110_1,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]) ).

fof(f_5110_2,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5110_1]) ).

cnf(f_5110_3,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5110_2]) ).

fof(f_5111_1,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).

fof(f_5111_2,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5111_1]) ).

cnf(f_5111_3,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5111_2]) ).

fof(f_5112_1,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).

fof(f_5112_2,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5112_1]) ).

cnf(f_5112_3,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5112_2]) ).

fof(f_5113_1,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).

fof(f_5113_2,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5113_1]) ).

cnf(f_5113_3,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5113_2]) ).

fof(f_5114_1,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).

fof(f_5114_2,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5114_1]) ).

cnf(f_5114_3,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5114_2]) ).

fof(f_5115_1,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Obot]) ).

fof(f_5115_2,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5115_1]) ).

cnf(f_5115_3,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5115_2]) ).

fof(f_5116_1,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).

fof(f_5116_2,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5116_1]) ).

cnf(f_5116_3,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5116_2]) ).

fof(f_5117_1,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).

fof(f_5117_2,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5117_1]) ).

cnf(f_5117_3,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5117_2]) ).

fof(f_5118_1,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).

fof(f_5118_2,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5118_1]) ).

cnf(f_5118_3,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5118_2]) ).

fof(f_5119_1,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).

fof(f_5119_2,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5119_1]) ).

cnf(f_5119_3,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5119_2]) ).

fof(f_5120_1,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).

fof(f_5120_2,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5120_1]) ).

cnf(f_5120_3,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5120_2]) ).

fof(f_5121_1,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Odvd]) ).

fof(f_5121_2,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_5121_1]) ).

cnf(f_5121_3,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5121_2]) ).

fof(f_5122_1,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]) ).

fof(f_5122_2,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5122_1]) ).

cnf(f_5122_3,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5122_2]) ).

fof(f_5123_1,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).

fof(f_5123_2,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5123_1]) ).

cnf(f_5123_3,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5123_2]) ).

fof(f_5124_1,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]) ).

fof(f_5124_2,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5124_1]) ).

cnf(f_5124_3,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5124_2]) ).

fof(f_5125_1,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]) ).

fof(f_5125_2,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5125_1]) ).

cnf(f_5125_3,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5125_2]) ).

fof(f_5126_1,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]) ).

fof(f_5126_2,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5126_1]) ).

cnf(f_5126_3,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5126_2]) ).

fof(f_5127_1,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]) ).

fof(f_5127_2,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5127_1]) ).

cnf(f_5127_3,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5127_2]) ).

fof(f_5128_1,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).

fof(f_5128_2,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5128_1]) ).

cnf(f_5128_3,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5128_2]) ).

fof(f_5129_1,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).

fof(f_5129_2,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5129_1]) ).

cnf(f_5129_3,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5129_2]) ).

fof(f_5130_1,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]) ).

fof(f_5130_2,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5130_1]) ).

cnf(f_5130_3,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5130_2]) ).

fof(f_5131_1,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]) ).

fof(f_5131_2,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5131_1]) ).

cnf(f_5131_3,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5131_2]) ).

fof(f_5132_1,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).

fof(f_5132_2,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5132_1]) ).

cnf(f_5132_3,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5132_2]) ).

fof(f_5133_1,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).

fof(f_5133_2,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5133_1]) ).

cnf(f_5133_3,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5133_2]) ).

fof(f_5134_1,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).

fof(f_5134_2,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5134_1]) ).

cnf(f_5134_3,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5134_2]) ).

fof(f_5135_1,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).

fof(f_5135_2,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5135_1]) ).

cnf(f_5135_3,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5135_2]) ).

fof(f_5136_1,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).

fof(f_5136_2,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5136_1]) ).

cnf(f_5136_3,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5136_2]) ).

fof(f_5137_1,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).

fof(f_5137_2,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_5137_1]) ).

cnf(f_5137_3,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5137_2]) ).

fof(f_5138_1,plain,
    ! [T_1,T_2] :
      ( class_Finite__Set_Ofinite(tc_sum(T_2,T_1))
      | ~ class_Finite__Set_Ofinite(T_1)
      | ~ class_Finite__Set_Ofinite(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite]) ).

fof(f_5138_2,plain,
    ! [U_20786,U_20785] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20785,U_20786))
      | ~ class_Finite__Set_Ofinite(U_20786)
      | ~ class_Finite__Set_Ofinite(U_20785) ),
    inference(variable_rename,[status(thm)],[f_5138_1]) ).

fof(f_5138_3,plain,
    ! [U_20786,U_20785] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20785,U_20786))
      | ~ class_Finite__Set_Ofinite(U_20786)
      | ~ class_Finite__Set_Ofinite(U_20785) ),
    inference(definitional_conversion,[status(esa)],[f_5138_2]) ).

cnf(f_5138_4,plain,
    ( class_Finite__Set_Ofinite(tc_sum(U_20785,U_20786))
    | ~ class_Finite__Set_Ofinite(U_20786)
    | ~ class_Finite__Set_Ofinite(U_20785) ),
    inference(clausify,[status(thm)],[f_5138_3]) ).

fof(f_5139_1,plain,
    ! [T_1] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(T_1))
      | ~ class_Finite__Set_Ofinite(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite]) ).

fof(f_5139_2,plain,
    ! [U_20787] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20787))
      | ~ class_Finite__Set_Ofinite(U_20787) ),
    inference(variable_rename,[status(thm)],[f_5139_1]) ).

fof(f_5139_3,plain,
    ! [U_20787] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20787))
      | ~ class_Finite__Set_Ofinite(U_20787) ),
    inference(definitional_conversion,[status(esa)],[f_5139_2]) ).

cnf(f_5139_4,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20787))
    | ~ class_Finite__Set_Ofinite(U_20787) ),
    inference(clausify,[status(thm)],[f_5139_3]) ).

fof(f_5140_1,plain,
    ! [T_1,T_2] :
      ( class_Finite__Set_Ofinite(tc_prod(T_2,T_1))
      | ~ class_Finite__Set_Ofinite(T_1)
      | ~ class_Finite__Set_Ofinite(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite]) ).

fof(f_5140_2,plain,
    ! [U_20789,U_20788] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20788,U_20789))
      | ~ class_Finite__Set_Ofinite(U_20789)
      | ~ class_Finite__Set_Ofinite(U_20788) ),
    inference(variable_rename,[status(thm)],[f_5140_1]) ).

fof(f_5140_3,plain,
    ! [U_20789,U_20788] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20788,U_20789))
      | ~ class_Finite__Set_Ofinite(U_20789)
      | ~ class_Finite__Set_Ofinite(U_20788) ),
    inference(definitional_conversion,[status(esa)],[f_5140_2]) ).

cnf(f_5140_4,plain,
    ( class_Finite__Set_Ofinite(tc_prod(U_20788,U_20789))
    | ~ class_Finite__Set_Ofinite(U_20789)
    | ~ class_Finite__Set_Ofinite(U_20788) ),
    inference(clausify,[status(thm)],[f_5140_3]) ).

fof(f_5141_1,plain,
    ! [T_1,T_2] :
      ( class_Smallcheck_Osmall(tc_prod(T_2,T_1))
      | ~ class_Smallcheck_Osmall(T_1)
      | ~ class_Smallcheck_Osmall(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_prod__Smallcheck_Osmall]) ).

fof(f_5141_2,plain,
    ! [U_20791,U_20790] :
      ( class_Smallcheck_Osmall(tc_prod(U_20790,U_20791))
      | ~ class_Smallcheck_Osmall(U_20791)
      | ~ class_Smallcheck_Osmall(U_20790) ),
    inference(variable_rename,[status(thm)],[f_5141_1]) ).

fof(f_5141_3,plain,
    ! [U_20791,U_20790] :
      ( class_Smallcheck_Osmall(tc_prod(U_20790,U_20791))
      | ~ class_Smallcheck_Osmall(U_20791)
      | ~ class_Smallcheck_Osmall(U_20790) ),
    inference(definitional_conversion,[status(esa)],[f_5141_2]) ).

cnf(f_5141_4,plain,
    ( class_Smallcheck_Osmall(tc_prod(U_20790,U_20791))
    | ~ class_Smallcheck_Osmall(U_20791)
    | ~ class_Smallcheck_Osmall(U_20790) ),
    inference(clausify,[status(thm)],[f_5141_3]) ).

fof(f_5142_1,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).

fof(f_5142_2,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(definitional_conversion,[status(esa)],[f_5142_1]) ).

cnf(f_5142_3,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5142_2]) ).

fof(f_5143_1,plain,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]) ).

fof(f_5143_2,plain,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    inference(definitional_conversion,[status(esa)],[f_5143_1]) ).

cnf(f_5143_3,plain,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5143_2]) ).

fof(f_5144_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_5144_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5144_1]) ).

cnf(f_5144_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5144_2]) ).

fof(f_5145_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_5145_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5145_1]) ).

cnf(f_5145_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5145_2]) ).

fof(f_5146_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_5146_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5146_1]) ).

cnf(f_5146_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5146_2]) ).

fof(f_5147_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add]) ).

fof(f_5147_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5147_1]) ).

cnf(f_5147_3,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5147_2]) ).

fof(f_5148_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]) ).

fof(f_5148_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5148_1]) ).

cnf(f_5148_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5148_2]) ).

fof(f_5149_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]) ).

fof(f_5149_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5149_1]) ).

cnf(f_5149_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5149_2]) ).

fof(f_5150_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]) ).

fof(f_5150_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5150_1]) ).

cnf(f_5150_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5150_2]) ).

fof(f_5151_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_5151_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5151_1]) ).

cnf(f_5151_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5151_2]) ).

fof(f_5152_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]) ).

fof(f_5152_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5152_1]) ).

cnf(f_5152_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5152_2]) ).

fof(f_5153_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]) ).

fof(f_5153_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5153_1]) ).

cnf(f_5153_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5153_2]) ).

fof(f_5154_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]) ).

fof(f_5154_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5154_1]) ).

cnf(f_5154_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5154_2]) ).

fof(f_5155_1,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]) ).

fof(f_5155_2,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5155_1]) ).

cnf(f_5155_3,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5155_2]) ).

fof(f_5156_1,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]) ).

fof(f_5156_2,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5156_1]) ).

cnf(f_5156_3,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5156_2]) ).

fof(f_5157_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]) ).

fof(f_5157_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5157_1]) ).

cnf(f_5157_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5157_2]) ).

fof(f_5158_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]) ).

fof(f_5158_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5158_1]) ).

cnf(f_5158_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5158_2]) ).

fof(f_5159_1,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]) ).

fof(f_5159_2,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5159_1]) ).

cnf(f_5159_3,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5159_2]) ).

fof(f_5160_1,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]) ).

fof(f_5160_2,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5160_1]) ).

cnf(f_5160_3,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5160_2]) ).

fof(f_5161_1,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]) ).

fof(f_5161_2,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5161_1]) ).

cnf(f_5161_3,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5161_2]) ).

fof(f_5162_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]) ).

fof(f_5162_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5162_1]) ).

cnf(f_5162_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5162_2]) ).

fof(f_5163_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]) ).

fof(f_5163_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5163_1]) ).

cnf(f_5163_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5163_2]) ).

fof(f_5164_1,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]) ).

fof(f_5164_2,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5164_1]) ).

cnf(f_5164_3,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5164_2]) ).

fof(f_5165_1,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]) ).

fof(f_5165_2,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5165_1]) ).

cnf(f_5165_3,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5165_2]) ).

fof(f_5166_1,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]) ).

fof(f_5166_2,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5166_1]) ).

cnf(f_5166_3,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5166_2]) ).

fof(f_5167_1,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0]) ).

fof(f_5167_2,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5167_1]) ).

cnf(f_5167_3,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5167_2]) ).

fof(f_5168_1,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]) ).

fof(f_5168_2,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5168_1]) ).

cnf(f_5168_3,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5168_2]) ).

fof(f_5169_1,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]) ).

fof(f_5169_2,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5169_1]) ).

cnf(f_5169_3,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5169_2]) ).

fof(f_5170_1,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]) ).

fof(f_5170_2,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5170_1]) ).

cnf(f_5170_3,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5170_2]) ).

fof(f_5171_1,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]) ).

fof(f_5171_2,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5171_1]) ).

cnf(f_5171_3,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5171_2]) ).

fof(f_5172_1,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]) ).

fof(f_5172_2,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5172_1]) ).

cnf(f_5172_3,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5172_2]) ).

fof(f_5173_1,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]) ).

fof(f_5173_2,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5173_1]) ).

cnf(f_5173_3,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5173_2]) ).

fof(f_5174_1,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]) ).

fof(f_5174_2,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5174_1]) ).

cnf(f_5174_3,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5174_2]) ).

fof(f_5175_1,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]) ).

fof(f_5175_2,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5175_1]) ).

cnf(f_5175_3,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5175_2]) ).

fof(f_5176_1,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]) ).

fof(f_5176_2,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5176_1]) ).

cnf(f_5176_3,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5176_2]) ).

fof(f_5177_1,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]) ).

fof(f_5177_2,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5177_1]) ).

cnf(f_5177_3,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5177_2]) ).

fof(f_5178_1,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]) ).

fof(f_5178_2,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5178_1]) ).

cnf(f_5178_3,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5178_2]) ).

fof(f_5179_1,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]) ).

fof(f_5179_2,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5179_1]) ).

cnf(f_5179_3,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5179_2]) ).

fof(f_5180_1,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]) ).

fof(f_5180_2,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5180_1]) ).

cnf(f_5180_3,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5180_2]) ).

fof(f_5181_1,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]) ).

fof(f_5181_2,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5181_1]) ).

cnf(f_5181_3,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5181_2]) ).

fof(f_5182_1,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]) ).

fof(f_5182_2,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5182_1]) ).

cnf(f_5182_3,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5182_2]) ).

fof(f_5183_1,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]) ).

fof(f_5183_2,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5183_1]) ).

cnf(f_5183_3,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5183_2]) ).

fof(f_5184_1,plain,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Odvd]) ).

fof(f_5184_2,plain,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_5184_1]) ).

cnf(f_5184_3,plain,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5184_2]) ).

fof(f_5185_1,plain,
    ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
    inference(fof_nnf,[status(thm)],[help_c__COMBI__1]) ).

fof(f_5185_2,plain,
    ! [U_20793,U_20792] : hAPP(c_COMBI(U_20792),U_20793) = U_20793,
    inference(variable_rename,[status(thm)],[f_5185_1]) ).

fof(f_5185_3,plain,
    ! [U_20792,U_20793] : hAPP(c_COMBI(U_20792),U_20793) = U_20793,
    inference(definitional_conversion,[status(esa)],[f_5185_2]) ).

cnf(f_5185_4,plain,
    hAPP(c_COMBI(U_20792),U_20793) = U_20793,
    inference(clausify,[status(thm)],[f_5185_3]) ).

fof(f_5186_1,plain,
    ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
    inference(fof_nnf,[status(thm)],[help_c__COMBK__1]) ).

fof(f_5186_2,plain,
    ! [U_20797,U_20796,U_20795,U_20794] : hAPP(hAPP(c_COMBK(U_20794,U_20795),U_20796),U_20797) = U_20796,
    inference(variable_rename,[status(thm)],[f_5186_1]) ).

fof(f_5186_3,plain,
    ! [U_20794,U_20795,U_20796,U_20797] : hAPP(hAPP(c_COMBK(U_20794,U_20795),U_20796),U_20797) = U_20796,
    inference(definitional_conversion,[status(esa)],[f_5186_2]) ).

cnf(f_5186_4,plain,
    hAPP(hAPP(c_COMBK(U_20794,U_20795),U_20796),U_20797) = U_20796,
    inference(clausify,[status(thm)],[f_5186_3]) ).

fof(f_5187_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).

fof(f_5187_2,plain,
    ! [U_20803,U_20802,U_20801,U_20800,U_20799,U_20798] : hAPP(hAPP(hAPP(c_COMBB(U_20798,U_20799,U_20800),U_20801),U_20802),U_20803) = hAPP(U_20801,hAPP(U_20802,U_20803)),
    inference(variable_rename,[status(thm)],[f_5187_1]) ).

fof(f_5187_3,plain,
    ! [U_20798,U_20799,U_20800,U_20801,U_20802,U_20803] : hAPP(hAPP(hAPP(c_COMBB(U_20798,U_20799,U_20800),U_20801),U_20802),U_20803) = hAPP(U_20801,hAPP(U_20802,U_20803)),
    inference(definitional_conversion,[status(esa)],[f_5187_2]) ).

cnf(f_5187_4,plain,
    hAPP(hAPP(hAPP(c_COMBB(U_20798,U_20799,U_20800),U_20801),U_20802),U_20803) = hAPP(U_20801,hAPP(U_20802,U_20803)),
    inference(clausify,[status(thm)],[f_5187_3]) ).

fof(f_5188_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
    inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).

fof(f_5188_2,plain,
    ! [U_20809,U_20808,U_20807,U_20806,U_20805,U_20804] : hAPP(hAPP(hAPP(c_COMBC(U_20804,U_20805,U_20806),U_20807),U_20808),U_20809) = hAPP(hAPP(U_20807,U_20809),U_20808),
    inference(variable_rename,[status(thm)],[f_5188_1]) ).

fof(f_5188_3,plain,
    ! [U_20804,U_20805,U_20806,U_20807,U_20808,U_20809] : hAPP(hAPP(hAPP(c_COMBC(U_20804,U_20805,U_20806),U_20807),U_20808),U_20809) = hAPP(hAPP(U_20807,U_20809),U_20808),
    inference(definitional_conversion,[status(esa)],[f_5188_2]) ).

cnf(f_5188_4,plain,
    hAPP(hAPP(hAPP(c_COMBC(U_20804,U_20805,U_20806),U_20807),U_20808),U_20809) = hAPP(hAPP(U_20807,U_20809),U_20808),
    inference(clausify,[status(thm)],[f_5188_3]) ).

fof(f_5189_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).

fof(f_5189_2,plain,
    ! [U_20815,U_20814,U_20813,U_20812,U_20811,U_20810] : hAPP(hAPP(hAPP(c_COMBS(U_20810,U_20811,U_20812),U_20813),U_20814),U_20815) = hAPP(hAPP(U_20813,U_20815),hAPP(U_20814,U_20815)),
    inference(variable_rename,[status(thm)],[f_5189_1]) ).

fof(f_5189_3,plain,
    ! [U_20810,U_20811,U_20812,U_20813,U_20814,U_20815] : hAPP(hAPP(hAPP(c_COMBS(U_20810,U_20811,U_20812),U_20813),U_20814),U_20815) = hAPP(hAPP(U_20813,U_20815),hAPP(U_20814,U_20815)),
    inference(definitional_conversion,[status(esa)],[f_5189_2]) ).

cnf(f_5189_4,plain,
    hAPP(hAPP(hAPP(c_COMBS(U_20810,U_20811,U_20812),U_20813),U_20814),U_20815) = hAPP(hAPP(U_20813,U_20815),hAPP(U_20814,U_20815)),
    inference(clausify,[status(thm)],[f_5189_3]) ).

fof(f_5190_1,plain,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fequal__1]) ).

fof(f_5190_2,plain,
    ! [U_20817,U_20816] :
      ( U_20816 = U_20817
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20816),U_20817)) ),
    inference(variable_rename,[status(thm)],[f_5190_1]) ).

fof(f_5190_3,plain,
    ! [U_20816,U_20817] :
      ( U_20816 = U_20817
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20816),U_20817)) ),
    inference(definitional_conversion,[status(esa)],[f_5190_2]) ).

cnf(f_5190_4,plain,
    ( U_20816 = U_20817
    | ~ hBOOL(hAPP(hAPP(c_fequal,U_20816),U_20817)) ),
    inference(clausify,[status(thm)],[f_5190_3]) ).

fof(f_5191_1,plain,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
      | V_x_2 != V_y_2 ),
    inference(fof_nnf,[status(thm)],[help_c__fequal__2]) ).

fof(f_5191_2,plain,
    ! [U_20819,U_20818] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20818),U_20819))
      | U_20818 != U_20819 ),
    inference(variable_rename,[status(thm)],[f_5191_1]) ).

fof(f_5191_3,plain,
    ! [U_20818,U_20819] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20818),U_20819))
      | U_20818 != U_20819 ),
    inference(definitional_conversion,[status(esa)],[f_5191_2]) ).

cnf(f_5191_4,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,U_20818),U_20819))
    | U_20818 != U_20819 ),
    inference(clausify,[status(thm)],[f_5191_3]) ).

fof(f_5192_1,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_nnf,[status(thm)],[help_c__fFalse__1]) ).

fof(f_5192_2,plain,
    ~ hBOOL(c_fFalse),
    inference(definitional_conversion,[status(esa)],[f_5192_1]) ).

cnf(f_5192_3,plain,
    ~ hBOOL(c_fFalse),
    inference(clausify,[status(thm)],[f_5192_2]) ).

fof(f_5193_1,plain,
    hBOOL(c_fTrue),
    inference(fof_nnf,[status(thm)],[help_c__fTrue__1]) ).

fof(f_5193_2,plain,
    hBOOL(c_fTrue),
    inference(definitional_conversion,[status(esa)],[f_5193_1]) ).

cnf(f_5193_3,plain,
    hBOOL(c_fTrue),
    inference(clausify,[status(thm)],[f_5193_2]) ).

fof(f_5194_1,plain,
    ! [V_P_2] :
      ( ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__1]) ).

fof(f_5194_2,plain,
    ! [U_20820] :
      ( ~ hBOOL(U_20820)
      | ~ hBOOL(hAPP(c_fNot,U_20820)) ),
    inference(variable_rename,[status(thm)],[f_5194_1]) ).

fof(f_5194_3,plain,
    ! [U_20820] :
      ( ~ hBOOL(U_20820)
      | ~ hBOOL(hAPP(c_fNot,U_20820)) ),
    inference(definitional_conversion,[status(esa)],[f_5194_2]) ).

cnf(f_5194_4,plain,
    ( ~ hBOOL(U_20820)
    | ~ hBOOL(hAPP(c_fNot,U_20820)) ),
    inference(clausify,[status(thm)],[f_5194_3]) ).

fof(f_5195_1,plain,
    ! [V_P_2] :
      ( hBOOL(hAPP(c_fNot,V_P_2))
      | hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__2]) ).

fof(f_5195_2,plain,
    ! [U_20821] :
      ( hBOOL(hAPP(c_fNot,U_20821))
      | hBOOL(U_20821) ),
    inference(variable_rename,[status(thm)],[f_5195_1]) ).

fof(f_5195_3,plain,
    ! [U_20821] :
      ( hBOOL(hAPP(c_fNot,U_20821))
      | hBOOL(U_20821) ),
    inference(definitional_conversion,[status(esa)],[f_5195_2]) ).

cnf(f_5195_4,plain,
    ( hBOOL(hAPP(c_fNot,U_20821))
    | hBOOL(U_20821) ),
    inference(clausify,[status(thm)],[f_5195_3]) ).

fof(f_5196_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__1]) ).

fof(f_5196_2,plain,
    ! [U_20823,U_20822] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20822),U_20823))
      | ~ hBOOL(U_20823)
      | ~ hBOOL(U_20822) ),
    inference(variable_rename,[status(thm)],[f_5196_1]) ).

fof(f_5196_3,plain,
    ! [U_20823] :
      ( ! [U_20822] :
          ( hBOOL(hAPP(hAPP(c_fconj,U_20822),U_20823))
          | ~ hBOOL(U_20822) )
      | ~ hBOOL(U_20823) ),
    inference(miniscope,[status(thm)],[f_5196_2]) ).

fof(f_5196_4,plain,
    ! [U_20822,U_20823] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20822),U_20823))
      | ~ hBOOL(U_20822)
      | ~ hBOOL(U_20823) ),
    inference(definitional_conversion,[status(esa)],[f_5196_3]) ).

cnf(f_5196_5,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,U_20822),U_20823))
    | ~ hBOOL(U_20822)
    | ~ hBOOL(U_20823) ),
    inference(clausify,[status(thm)],[f_5196_4]) ).

fof(f_5197_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__2]) ).

fof(f_5197_2,plain,
    ! [U_20825,U_20824] :
      ( hBOOL(U_20824)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20824),U_20825)) ),
    inference(variable_rename,[status(thm)],[f_5197_1]) ).

fof(f_5197_3,plain,
    ! [U_20825,U_20824] :
      ( hBOOL(U_20824)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20824),U_20825)) ),
    inference(definitional_conversion,[status(esa)],[f_5197_2]) ).

cnf(f_5197_4,plain,
    ( hBOOL(U_20824)
    | ~ hBOOL(hAPP(hAPP(c_fconj,U_20824),U_20825)) ),
    inference(clausify,[status(thm)],[f_5197_3]) ).

fof(f_5198_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__3]) ).

fof(f_5198_2,plain,
    ! [U_20827,U_20826] :
      ( hBOOL(U_20827)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20826),U_20827)) ),
    inference(variable_rename,[status(thm)],[f_5198_1]) ).

fof(f_5198_3,plain,
    ! [U_20827] :
      ( ! [U_20826] : ~ hBOOL(hAPP(hAPP(c_fconj,U_20826),U_20827))
      | hBOOL(U_20827) ),
    inference(miniscope,[status(thm)],[f_5198_2]) ).

fof(f_5198_4,plain,
    ! [U_20826,U_20827] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20826),U_20827))
      | hBOOL(U_20827) ),
    inference(definitional_conversion,[status(esa)],[f_5198_3]) ).

cnf(f_5198_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20826),U_20827))
    | hBOOL(U_20827) ),
    inference(clausify,[status(thm)],[f_5198_4]) ).

fof(f_5199_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__1]) ).

fof(f_5199_2,plain,
    ! [U_20829,U_20828] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20828),U_20829))
      | ~ hBOOL(U_20828) ),
    inference(variable_rename,[status(thm)],[f_5199_1]) ).

fof(f_5199_3,plain,
    ! [U_20828,U_20829] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20828),U_20829))
      | ~ hBOOL(U_20828) ),
    inference(definitional_conversion,[status(esa)],[f_5199_2]) ).

cnf(f_5199_4,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20828),U_20829))
    | ~ hBOOL(U_20828) ),
    inference(clausify,[status(thm)],[f_5199_3]) ).

fof(f_5200_1,plain,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__2]) ).

fof(f_5200_2,plain,
    ! [U_20831,U_20830] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20831),U_20830))
      | ~ hBOOL(U_20830) ),
    inference(variable_rename,[status(thm)],[f_5200_1]) ).

fof(f_5200_3,plain,
    ! [U_20830,U_20831] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20831),U_20830))
      | ~ hBOOL(U_20830) ),
    inference(definitional_conversion,[status(esa)],[f_5200_2]) ).

cnf(f_5200_4,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20831),U_20830))
    | ~ hBOOL(U_20830) ),
    inference(clausify,[status(thm)],[f_5200_3]) ).

fof(f_5201_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__3]) ).

fof(f_5201_2,plain,
    ! [U_20833,U_20832] :
      ( hBOOL(U_20833)
      | hBOOL(U_20832)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20832),U_20833)) ),
    inference(variable_rename,[status(thm)],[f_5201_1]) ).

fof(f_5201_3,plain,
    ! [U_20833] :
      ( ! [U_20832] :
          ( hBOOL(U_20832)
          | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20832),U_20833)) )
      | hBOOL(U_20833) ),
    inference(miniscope,[status(thm)],[f_5201_2]) ).

fof(f_5201_4,plain,
    ! [U_20832,U_20833] :
      ( hBOOL(U_20832)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20832),U_20833))
      | hBOOL(U_20833) ),
    inference(definitional_conversion,[status(esa)],[f_5201_3]) ).

cnf(f_5201_5,plain,
    ( hBOOL(U_20832)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20832),U_20833))
    | hBOOL(U_20833) ),
    inference(clausify,[status(thm)],[f_5201_4]) ).

fof(f_5202_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__1]) ).

fof(f_5202_2,plain,
    ! [U_20835,U_20834] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20834),U_20835))
      | hBOOL(U_20834) ),
    inference(variable_rename,[status(thm)],[f_5202_1]) ).

fof(f_5202_3,plain,
    ! [U_20835,U_20834] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20834),U_20835))
      | hBOOL(U_20834) ),
    inference(definitional_conversion,[status(esa)],[f_5202_2]) ).

cnf(f_5202_4,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20834),U_20835))
    | hBOOL(U_20834) ),
    inference(clausify,[status(thm)],[f_5202_3]) ).

fof(f_5203_1,plain,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__2]) ).

fof(f_5203_2,plain,
    ! [U_20837,U_20836] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20837),U_20836))
      | ~ hBOOL(U_20836) ),
    inference(variable_rename,[status(thm)],[f_5203_1]) ).

fof(f_5203_3,plain,
    ! [U_20836,U_20837] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20837),U_20836))
      | ~ hBOOL(U_20836) ),
    inference(definitional_conversion,[status(esa)],[f_5203_2]) ).

cnf(f_5203_4,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20837),U_20836))
    | ~ hBOOL(U_20836) ),
    inference(clausify,[status(thm)],[f_5203_3]) ).

fof(f_5204_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__3]) ).

fof(f_5204_2,plain,
    ! [U_20839,U_20838] :
      ( hBOOL(U_20839)
      | ~ hBOOL(U_20838)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20838),U_20839)) ),
    inference(variable_rename,[status(thm)],[f_5204_1]) ).

fof(f_5204_3,plain,
    ! [U_20839] :
      ( ! [U_20838] :
          ( ~ hBOOL(U_20838)
          | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20838),U_20839)) )
      | hBOOL(U_20839) ),
    inference(miniscope,[status(thm)],[f_5204_2]) ).

fof(f_5204_4,plain,
    ! [U_20838,U_20839] :
      ( ~ hBOOL(U_20838)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20838),U_20839))
      | hBOOL(U_20839) ),
    inference(definitional_conversion,[status(esa)],[f_5204_3]) ).

cnf(f_5204_5,plain,
    ( ~ hBOOL(U_20838)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20838),U_20839))
    | hBOOL(U_20839) ),
    inference(clausify,[status(thm)],[f_5204_4]) ).

fof(f_5205_1,plain,
    ! [B_x] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_5205_2,plain,
    ! [U_20840] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),U_20840)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_20840),v_G)) ),
    inference(variable_rename,[status(thm)],[f_5205_1]) ).

fof(f_5205_3,plain,
    ! [U_20840] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),U_20840)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_20840),v_G)) ),
    inference(definitional_conversion,[status(esa)],[f_5205_2]) ).

cnf(f_5205_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),U_20840)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_20840),v_G)) ),
    inference(clausify,[status(thm)],[f_5205_3]) ).

fof(f_5206_1,plain,
    ! [B_Z,B_s] :
      ( ! [B_s_H] :
          ( v_Q(B_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s_H),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,B_s_H),c_Com_ORes)))
          | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,hAPP(c_Nat_OSuc,v_na),B_s_H) )
      | ~ v_P(B_Z,B_s) ),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

fof(f_5206_2,plain,
    ! [U_20843,U_20842] :
      ( ! [U_20841] :
          ( v_Q(U_20843,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_20841),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,U_20841),c_Com_ORes)))
          | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),U_20842,hAPP(c_Nat_OSuc,v_na),U_20841) )
      | ~ v_P(U_20843,U_20842) ),
    inference(variable_rename,[status(thm)],[f_5206_1]) ).

fof(f_5206_3,plain,
    ! [U_20841,U_20842,U_20843] :
      ( v_Q(U_20843,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_20841),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,U_20841),c_Com_ORes)))
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),U_20842,hAPP(c_Nat_OSuc,v_na),U_20841)
      | ~ v_P(U_20843,U_20842) ),
    inference(definitional_conversion,[status(esa)],[f_5206_2]) ).

cnf(f_5206_4,plain,
    ( v_Q(U_20843,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_20841),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,U_20841),c_Com_ORes)))
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),U_20842,hAPP(c_Nat_OSuc,v_na),U_20841)
    | ~ v_P(U_20843,U_20842) ),
    inference(clausify,[status(thm)],[f_5206_3]) ).

fof(f_5207_1,plain,
    v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
    inference(fof_nnf,[status(thm)],[conj_2]) ).

fof(f_5207_2,plain,
    v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
    inference(definitional_conversion,[status(esa)],[f_5207_1]) ).

cnf(f_5207_3,plain,
    v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
    inference(clausify,[status(thm)],[f_5207_2]) ).

fof(f_5208_1,plain,
    c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

fof(f_5208_2,plain,
    c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1),
    inference(definitional_conversion,[status(esa)],[f_5208_1]) ).

cnf(f_5208_3,plain,
    c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1),
    inference(clausify,[status(thm)],[f_5208_2]) ).

fof(f_5209_1,negated_conjecture,
    ~ v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
    inference(negate,[status(cth)],[conj_4]) ).

fof(f_5209_2,negated_conjecture,
    ~ v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
    inference(definitional_conversion,[status(esa)],[f_5209_1]) ).

cnf(f_5209_3,negated_conjecture,
    ~ v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
    inference(clausify,[status(thm)],[f_5209_2]) ).

cnf(f_2038_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2038_4]) ).

cnf(f_2040_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2040_4]) ).

cnf(f_2045_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2045_4]) ).

cnf(f_2046_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2046_4]) ).

cnf(f_2047_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2047_4]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( c_Option_Othe(Eq_x_0) = c_Option_Othe(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( c_Com_Ovname_OLoc(Eq_x_0) = c_Com_Ovname_OLoc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( c_Com_Ocom_OCall(Eq_x_0,Eq_x_1,Eq_x_2) = c_Com_Ocom_OCall(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple(Eq_x_0) = c_Hoare__Mirabelle_Otriple_Otriple(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( c_Natural_Oevalc(Eq_x_0) = c_Natural_Oevalc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( c_Com_Ocom_OLocal(Eq_x_0,Eq_x_1,Eq_x_2) = c_Com_Ocom_OLocal(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hoare__Mirabelle_Otriple_Otriple__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hoare__Mirabelle_Otriple_Otriple__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( c_Com_Ovname_Ovname__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Com_Ovname_Ovname__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( c_Com_Ovname_Ovname__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Com_Ovname_Ovname__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( c_Groups_Ozero__class_Ozero(Eq_x_0) = c_Groups_Ozero__class_Ozero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( c_Com_Ocom_OAss(Eq_x_0,Eq_x_1) = c_Com_Ocom_OAss(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple__size(Eq_x_0,Eq_x_1,Eq_x_2) = c_Hoare__Mirabelle_Otriple_Otriple__size(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( c_Com_Ovname_Ovname__size(Eq_x_0) = c_Com_Ovname_Ovname__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( tc_Hoare__Mirabelle_Otriple(Eq_x_0) = tc_Hoare__Mirabelle_Otriple(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( c_Nat_Osize__class_Osize(Eq_x_0) = c_Nat_Osize__class_Osize(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_Com_Ovname_OGlb(Eq_x_0) = c_Com_Ovname_OGlb(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( c_Com_Ocom_Ocom__size(Eq_x_0) = c_Com_Ocom_Ocom__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( c_Groups_Oplus__class_Oplus(Eq_x_0) = c_Groups_Oplus__class_Oplus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( c_Option_Ooption_ONone(Eq_x_0) = c_Option_Ooption_ONone(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( c_Option_Ooption_OSome(Eq_x_0) = c_Option_Ooption_OSome(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nat_Osemiring__1__class_Oof__nat__aux(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( c_Orderings_Oord__class_Oless(Eq_x_0) = c_Orderings_Oord__class_Oless(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( c_Option_Ooption_Ooption__size(Eq_x_0,Eq_x_1,Eq_x_2) = c_Option_Ooption_Ooption__size(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( c_Nat_Onat_Onat__size(Eq_x_0) = c_Nat_Onat_Onat__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( tc_Option_Ooption(Eq_x_0) = tc_Option_Ooption(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( c_Com_Ocom_OSemi(Eq_x_0,Eq_x_1) = c_Com_Ocom_OSemi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( c_Com_Ocom_OCond(Eq_x_0,Eq_x_1,Eq_x_2) = c_Com_Ocom_OCond(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( c_Option_Ooption_Ooption__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Option_Ooption_Ooption__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( c_Option_Ooption_Ooption__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Option_Ooption_Ooption__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( c_HOL_Obool_Obool__size(Eq_x_0) = c_HOL_Obool_Obool__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( c_Com_Ocom_OWhile(Eq_x_0,Eq_x_1) = c_Com_Ocom_OWhile(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(Eq_x_0) = c_Nat_Osemiring__1__class_Oof__nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( c_Int_Oring__1__class_Oof__int(Eq_x_0) = c_Int_Oring__1__class_Oof__int(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( c_Groups_Otimes__class_Otimes(Eq_x_0) = c_Groups_Otimes__class_Otimes(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( c_Groups_Ouminus__class_Ouminus(Eq_x_0) = c_Groups_Ouminus__class_Ouminus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( c_Groups_Oone__class_Oone(Eq_x_0) = c_Groups_Oone__class_Oone(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( c_Int_Onat__aux(Eq_x_0,Eq_x_1) = c_Int_Onat__aux(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,axiom,
    ( c_Groups_Osgn__class_Osgn(Eq_x_0,Eq_x_1) = c_Groups_Osgn__class_Osgn(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_44,axiom,
    ( c_Orderings_Oord__class_Oless__eq(Eq_x_0) = c_Orderings_Oord__class_Oless__eq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( c_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( c_SMT_Oz3mod(Eq_x_0,Eq_x_1) = c_SMT_Oz3mod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( c_Divides_Odiv__class_Odiv(Eq_x_0) = c_Divides_Odiv__class_Odiv(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( c_Nat__Transfer_Otsub(Eq_x_0,Eq_x_1) = c_Nat__Transfer_Otsub(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( c_SMT_Oz3div(Eq_x_0,Eq_x_1) = c_SMT_Oz3div(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( c_Groups_Ominus__class_Ominus(Eq_x_0) = c_Groups_Ominus__class_Ominus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_52,axiom,
    ( c_Power_Opower__class_Opower(Eq_x_0) = c_Power_Opower__class_Opower(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( c_Groups_Oabs__class_Oabs(Eq_x_0) = c_Groups_Oabs__class_Oabs(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_54,axiom,
    ( c_Int_Onumber__class_Onumber__of(Eq_x_0) = c_Int_Onumber__class_Onumber__of(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_55,axiom,
    ( c_Power_Opower_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( c_Int_Osucc(Eq_x_0) = c_Int_Osucc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_57,axiom,
    ( c_Int_Opred(Eq_x_0) = c_Int_Opred(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( c_Int_OBit1(Eq_x_0) = c_Int_OBit1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( c_Int_OBit0(Eq_x_0) = c_Int_OBit0(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( c_Rings_Oinverse__class_Odivide(Eq_x_0) = c_Rings_Oinverse__class_Odivide(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,axiom,
    ( c_Code__Numeral_Onat__of__aux(Eq_x_0,Eq_x_1) = c_Code__Numeral_Onat__of__aux(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(Eq_x_0) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( c_Random_Olog(Eq_x_0,Eq_x_1) = c_Random_Olog(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_65,axiom,
    ( c_Divides_OnegDivAlg(Eq_x_0,Eq_x_1) = c_Divides_OnegDivAlg(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( c_Product__Type_OPair(Eq_x_0,Eq_x_1) = c_Product__Type_OPair(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( c_Divides_Oadjust(Eq_x_0) = c_Divides_Oadjust(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,axiom,
    ( c_Random_Ominus__shift(Eq_x_0,Eq_x_1,Eq_x_2) = c_Random_Ominus__shift(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_69,axiom,
    ( c_Random_Oinc__shift(Eq_x_0,Eq_x_1) = c_Random_Oinc__shift(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_70,axiom,
    ( c_Divides_OposDivAlg(Eq_x_0,Eq_x_1) = c_Divides_OposDivAlg(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_71,axiom,
    ( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( c_Wellfounded_Oaccp(Eq_x_0,Eq_x_1) = c_Wellfounded_Oaccp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( c_Divides_Opdivmod(Eq_x_0,Eq_x_1) = c_Divides_Opdivmod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_74,axiom,
    ( c_Divides_Odivmod__int__rel(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__int__rel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_75,axiom,
    ( c_If(Eq_x_0) = c_If(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_76,axiom,
    ( c_Code__Numeral_OSuc__code__numeral(Eq_x_0) = c_Code__Numeral_OSuc__code__numeral(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( c_Divides_Odivmod__int(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( c_Product__Type_Osnd(Eq_x_0,Eq_x_1) = c_Product__Type_Osnd(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( c_Product__Type_Ofst(Eq_x_0,Eq_x_1) = c_Product__Type_Ofst(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( c_Product__Type_Oprod_Oprod__size(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Product__Type_Oprod_Oprod__size(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_81,axiom,
    ( c_Code__Numeral_Odiv__mod__code__numeral(Eq_x_0,Eq_x_1) = c_Code__Numeral_Odiv__mod__code__numeral(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( c_Divides_Odivmod__nat(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( c_Divides_Odivmod__nat__rel(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__nat__rel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( c_Random_Orange(Eq_x_0) = c_Random_Orange(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_85,axiom,
    ( c_Product__Type_Oprod_Oprod__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Product__Type_Oprod_Oprod__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( c_HOL_OLet(Eq_x_0,Eq_x_1) = c_HOL_OLet(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( c_COMBC(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBC(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( c_COMBS(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBS(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( c_COMBB(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBB(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,axiom,
    ( c_Random_Oiterate(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random_Oiterate(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_91,axiom,
    ( c_Product__Type_Oscomp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oscomp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,axiom,
    ( c_Product__Type_Oprod_Oprod__case(Eq_x_0,Eq_x_1,Eq_x_2) = c_Product__Type_Oprod_Oprod__case(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( c_Nat_Onat_Onat__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nat_Onat_Onat__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( c_Nat_Onat_Onat__rec(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nat_Onat_Onat__rec(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( c_COMBK(Eq_x_0,Eq_x_1) = c_COMBK(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_97,axiom,
    ( c_Product__Type_Oapsnd(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oapsnd(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( c_Hoare__Mirabelle_OMGT(Eq_x_0) = c_Hoare__Mirabelle_OMGT(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( c_Orderings_Oord__class_Omin(Eq_x_0) = c_Orderings_Oord__class_Omin(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( c_Orderings_Oord_Omin(Eq_x_0,Eq_x_1) = c_Orderings_Oord_Omin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( c_Orderings_Oord__class_Omax(Eq_x_0) = c_Orderings_Oord__class_Omax(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( c_Product__Type_Oapfst(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oapfst(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( c_Orderings_Oord_Omax(Eq_x_0,Eq_x_1) = c_Orderings_Oord_Omax(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( c_Nitpick_Onorm__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Onorm__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,axiom,
    ( c_Nitpick_Onat__gcd(Eq_x_0,Eq_x_1) = c_Nitpick_Onat__gcd(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_106,axiom,
    ( c_Nitpick_Oint__lcm(Eq_x_0,Eq_x_1) = c_Nitpick_Oint__lcm(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( c_Nitpick_Onat__lcm(Eq_x_0,Eq_x_1) = c_Nitpick_Onat__lcm(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( c_Nitpick_Ozero__frac(Eq_x_0) = c_Nitpick_Ozero__frac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_109,axiom,
    ( c_Nitpick_OAbs__Frac(Eq_x_0,Eq_x_1) = c_Nitpick_OAbs__Frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_110,axiom,
    ( c_Nitpick_Oone__frac(Eq_x_0) = c_Nitpick_Oone__frac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_111,axiom,
    ( c_Nitpick_Onumber__of__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Onumber__of__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_112,axiom,
    ( c_Nitpick_Ofrac(Eq_x_0) = c_Nitpick_Ofrac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_113,axiom,
    ( c_Product__Type_Ointernal__split(Eq_x_0,Eq_x_1,Eq_x_2) = c_Product__Type_Ointernal__split(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_114,axiom,
    ( c_Nitpick_Oplus__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Oplus__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( c_Nitpick_Odenom(Eq_x_0) = c_Nitpick_Odenom(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_116,axiom,
    ( c_Nitpick_Onum(Eq_x_0) = c_Nitpick_Onum(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( c_Nitpick_Opair__box_OPairBox(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Opair__box_OPairBox(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_118,axiom,
    ( c_Nitpick_Opair__box_Opair__box__size(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Opair__box_Opair__box__size(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_119,axiom,
    ( c_Nitpick_Otimes__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Otimes__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_120,axiom,
    ( c_Nitpick_Oof__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Oof__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_121,axiom,
    ( c_Nitpick_Oinverse__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Oinverse__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_122,axiom,
    ( c_Nitpick_Ouminus__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Ouminus__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,axiom,
    ( tc_Nitpick_Opair__box(Eq_x_0,Eq_x_1) = tc_Nitpick_Opair__box(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_124,axiom,
    ( c_Nitpick_Opair__box_Opair__box__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Opair__box_Opair__box__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_125,axiom,
    ( c_Nitpick_Opair__box_Opair__box__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Opair__box_Opair__box__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_126,axiom,
    ( c_HOL_OThe(Eq_x_0,Eq_x_1) = c_HOL_OThe(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_127,axiom,
    ( c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_128,axiom,
    ( c_Random__Sequence_ORandom(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random__Sequence_ORandom(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_129,axiom,
    ( tc_Lazy__Sequence_Olazy__sequence(Eq_x_0) = tc_Lazy__Sequence_Olazy__sequence(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_130,axiom,
    ( c_DSequence_Oempty(Eq_x_0) = c_DSequence_Oempty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( c_DSequence_Ounion(Eq_x_0) = c_DSequence_Ounion(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_132,axiom,
    ( c_DSequence_Osingle(Eq_x_0) = c_DSequence_Osingle(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_133,axiom,
    ( c_Random__Sequence_Oempty(Eq_x_0,Eq_x_1,Eq_x_2) = c_Random__Sequence_Oempty(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_134,axiom,
    ( c_Random__Sequence_Osingle(Eq_x_0) = c_Random__Sequence_Osingle(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_135,axiom,
    ( c_New__DSequence_Opos__not__seq(Eq_x_0) = c_New__DSequence_Opos__not__seq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_136,axiom,
    ( c_Lazy__Sequence_Ohb__not__seq(Eq_x_0) = c_Lazy__Sequence_Ohb__not__seq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_137,axiom,
    ( c_Quickcheck_Obeyond(Eq_x_0,Eq_x_1) = c_Quickcheck_Obeyond(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,axiom,
    ( c_New__Random__Sequence_Opos__not__random__dseq(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__not__random__dseq(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( c_New__DSequence_Opos__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Opos__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,axiom,
    ( c_Lazy__Sequence_Oempty(Eq_x_0) = c_Lazy__Sequence_Oempty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,axiom,
    ( c_Lazy__Sequence_Obind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Obind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_142,axiom,
    ( c_New__Random__Sequence_Opos__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = c_New__Random__Sequence_Opos__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_143,axiom,
    ( c_New__DSequence_Opos__empty(Eq_x_0) = c_New__DSequence_Opos__empty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_144,axiom,
    ( c_New__DSequence_Opos__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Opos__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( c_New__DSequence_Oneg__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Oneg__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_146,axiom,
    ( c_Lazy__Sequence_Ohit__bound(Eq_x_0) = c_Lazy__Sequence_Ohit__bound(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_147,axiom,
    ( c_Lazy__Sequence_Ohb__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Ohb__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( c_Product__Type_Ocurry(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Ocurry(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( c_New__Random__Sequence_Opos__empty(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__empty(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_150,axiom,
    ( c_New__Random__Sequence_Oneg__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = c_New__Random__Sequence_Oneg__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( c_New__Random__Sequence_Opos__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_152,axiom,
    ( c_New__DSequence_Oneg__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Oneg__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,axiom,
    ( c_Rings_Odvd__class_Odvd(Eq_x_0) = c_Rings_Odvd__class_Odvd(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_154,axiom,
    ( c_New__Random__Sequence_Oneg__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Oneg__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_155,axiom,
    ( c_Set_Oinsert(Eq_x_0) = c_Set_Oinsert(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_156,axiom,
    ( c_Orderings_Obot__class_Obot(Eq_x_0) = c_Orderings_Obot__class_Obot(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,axiom,
    ( c_Set_Othe__elem(Eq_x_0,Eq_x_1) = c_Set_Othe__elem(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_158,axiom,
    ( c_Option_Oset(Eq_x_0,Eq_x_1) = c_Option_Oset(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_159,axiom,
    ( c_member(Eq_x_0) = c_member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( c_FunDef_Oin__rel(Eq_x_0,Eq_x_1,Eq_x_2) = c_FunDef_Oin__rel(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( c_Partial__Function_Oflat__lub(Eq_x_0,Eq_x_1,Eq_x_2) = c_Partial__Function_Oflat__lub(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( c_Wellfounded_Omeasure(Eq_x_0) = c_Wellfounded_Omeasure(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_163,axiom,
    ( c_Wellfounded_Omlex__prod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Wellfounded_Omlex__prod(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_164,axiom,
    ( c_Nat_Osemiring__1__class_ONats(Eq_x_0) = c_Nat_Osemiring__1__class_ONats(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_165,axiom,
    ( c_Int_Oring__1__class_OInts(Eq_x_0) = c_Int_Oring__1__class_OInts(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_166,axiom,
    ( c_Wellfounded_Olex__prod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Wellfounded_Olex__prod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_167,axiom,
    ( c_Recdef_Osame__fst(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Recdef_Osame__fst(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_168,axiom,
    ( c_Wellfounded_Omin__ext(Eq_x_0,Eq_x_1) = c_Wellfounded_Omin__ext(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_169,axiom,
    ( c_Lattices_Osemilattice__sup__class_Osup(Eq_x_0) = c_Lattices_Osemilattice__sup__class_Osup(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_170,axiom,
    ( c_Wellfounded_Omax__ext(Eq_x_0,Eq_x_1) = c_Wellfounded_Omax__ext(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_171,axiom,
    ( c_Relation_Oinv__image(Eq_x_0,Eq_x_1) = c_Relation_Oinv__image(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_172,axiom,
    ( c_FunDef_Orp__inv__image(Eq_x_0,Eq_x_1) = c_FunDef_Orp__inv__image(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_173,axiom,
    ( c_Set_Oimage(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Oimage(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_174,axiom,
    ( c_Relation_OImage(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_OImage(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_175,axiom,
    ( c_Relation_OField(Eq_x_0) = c_Relation_OField(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_176,axiom,
    ( c_Wellfounded_Oacc(Eq_x_0,Eq_x_1) = c_Wellfounded_Oacc(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_177,axiom,
    ( c_Finite__Set_Ofinite(Eq_x_0) = c_Finite__Set_Ofinite(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,axiom,
    ( c_Wellfounded_Ofinite__psubset(Eq_x_0) = c_Wellfounded_Ofinite__psubset(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_179,axiom,
    ( c_Equiv__Relations_Oquotient(Eq_x_0) = c_Equiv__Relations_Oquotient(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( c_Lattices_Osemilattice__inf__class_Oinf(Eq_x_0) = c_Lattices_Osemilattice__inf__class_Oinf(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_181,axiom,
    ( c_SetInterval_Oord_OgreaterThanLessThan(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_SetInterval_Oord_OgreaterThanLessThan(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_182,axiom,
    ( c_SetInterval_Oord_OlessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OlessThan(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_183,axiom,
    ( c_SetInterval_Oord_OgreaterThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OgreaterThan(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_184,axiom,
    ( c_SetInterval_Oord_OatMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OatMost(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_185,axiom,
    ( c_SetInterval_Oord_OatLeast(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OatLeast(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_186,axiom,
    ( c_SetInterval_Oord_OgreaterThanAtMost(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_SetInterval_Oord_OgreaterThanAtMost(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_187,axiom,
    ( c_SetInterval_Oord_OatLeastLessThan(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_SetInterval_Oord_OatLeastLessThan(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_188,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_SetInterval_Oord_OatLeastAtMost(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_189,axiom,
    ( c_Big__Operators_Olattice__class_OInf__fin(Eq_x_0,Eq_x_1) = c_Big__Operators_Olattice__class_OInf__fin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_190,axiom,
    ( c_Big__Operators_Olattice__class_OSup__fin(Eq_x_0,Eq_x_1) = c_Big__Operators_Olattice__class_OSup__fin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_191,axiom,
    ( c_Big__Operators_Olinorder__class_OMax(Eq_x_0,Eq_x_1) = c_Big__Operators_Olinorder__class_OMax(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_192,axiom,
    ( c_Big__Operators_Olinorder__class_OMin(Eq_x_0,Eq_x_1) = c_Big__Operators_Olinorder__class_OMin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_193,axiom,
    ( c_Big__Operators_Olattice_OSup__fin(Eq_x_0,Eq_x_1,Eq_x_2) = c_Big__Operators_Olattice_OSup__fin(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_194,axiom,
    ( c_Big__Operators_Olattice_OInf__fin(Eq_x_0,Eq_x_1,Eq_x_2) = c_Big__Operators_Olattice_OInf__fin(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_195,axiom,
    ( c_Finite__Set_Ocard(Eq_x_0) = c_Finite__Set_Ocard(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_196,axiom,
    ( tc_sum(Eq_x_0,Eq_x_1) = tc_sum(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_197,axiom,
    ( c_Sum__Type_OPlus(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Sum__Type_OPlus(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_198,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_199,axiom,
    ( c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(Eq_x_0,Eq_x_1) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_200,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_201,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(Eq_x_0,Eq_x_1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_202,axiom,
    ( c_Relation_OId__on(Eq_x_0,Eq_x_1) = c_Relation_OId__on(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_203,axiom,
    ( c_Finite__Set_Ofold__image(Eq_x_0,Eq_x_1,Eq_x_2) = c_Finite__Set_Ofold__image(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_204,axiom,
    ( c_Set_OPow(Eq_x_0) = c_Set_OPow(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_205,axiom,
    ( c_Predicate_OPowp(Eq_x_0,Eq_x_1) = c_Predicate_OPowp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_206,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord__class_OatLeastAtMost(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_207,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(Eq_x_0,Eq_x_1) = c_SetInterval_Oord__class_OatLeastLessThan(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_208,axiom,
    ( c_SetInterval_Oord__class_OatMost(Eq_x_0) = c_SetInterval_Oord__class_OatMost(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_209,axiom,
    ( c_Fun_Ofun__upd(Eq_x_0,Eq_x_1) = c_Fun_Ofun__upd(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_210,axiom,
    ( c_Fun_Othe__inv__into(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Fun_Othe__inv__into(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_211,axiom,
    ( c_SetInterval_Oord__class_OlessThan(Eq_x_0) = c_SetInterval_Oord__class_OlessThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_212,axiom,
    ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(Eq_x_0,Eq_x_1) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_213,axiom,
    ( c_Map_Oran(Eq_x_0,Eq_x_1,Eq_x_2) = c_Map_Oran(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_214,axiom,
    ( c_Map_Orestrict__map(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Map_Orestrict__map(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_215,axiom,
    ( c_SetInterval_Oord__class_OatLeast(Eq_x_0) = c_SetInterval_Oord__class_OatLeast(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_216,axiom,
    ( c_SetInterval_Oord__class_OgreaterThan(Eq_x_0) = c_SetInterval_Oord__class_OgreaterThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_217,axiom,
    ( c_Map_Odom(Eq_x_0,Eq_x_1,Eq_x_2) = c_Map_Odom(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_218,axiom,
    ( c_Finite__Set_Ofold__graph(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Finite__Set_Ofold__graph(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_219,axiom,
    ( c_Finite__Set_Ofold1Set(Eq_x_0,Eq_x_1,Eq_x_2) = c_Finite__Set_Ofold1Set(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_220,axiom,
    ( c_Orderings_Otop__class_Otop(Eq_x_0) = c_Orderings_Otop__class_Otop(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_221,axiom,
    ( c_Set_Ovimage(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Ovimage(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_222,axiom,
    ( c_Product__Type_OSigma(Eq_x_0,Eq_x_1) = c_Product__Type_OSigma(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_223,axiom,
    ( c_Finite__Set_Ofold1(Eq_x_0,Eq_x_1) = c_Finite__Set_Ofold1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_224,axiom,
    ( c_Product__Type_Omap__pair(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Product__Type_Omap__pair(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_225,axiom,
    ( c_Set_OCollect(Eq_x_0) = c_Set_OCollect(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_226,axiom,
    ( c_Fun_Ooverride__on(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Fun_Ooverride__on(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_227,axiom,
    ( c_HOL_OEx(Eq_x_0) = c_HOL_OEx(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_228,axiom,
    ( c_Nitpick_Oprod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Oprod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_229,axiom,
    ( c_Int_Oint__ge__less__than2(Eq_x_0) = c_Int_Oint__ge__less__than2(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_230,axiom,
    ( c_Int_Oint__ge__less__than(Eq_x_0) = c_Int_Oint__ge__less__than(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_231,axiom,
    ( c_Fun_Oid(Eq_x_0) = c_Fun_Oid(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_232,axiom,
    ( c_Relation_Orel__comp(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_Orel__comp(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_233,axiom,
    ( tc_List_Olist(Eq_x_0) = tc_List_Olist(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_234,axiom,
    ( c_List_Olenlex(Eq_x_0,Eq_x_1) = c_List_Olenlex(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_235,axiom,
    ( c_List_Olex(Eq_x_0,Eq_x_1) = c_List_Olex(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_236,axiom,
    ( c_List_Olexn(Eq_x_0,Eq_x_1) = c_List_Olexn(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_237,axiom,
    ( c_Relation_ORange(Eq_x_0,Eq_x_1) = c_Relation_ORange(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_238,axiom,
    ( c_Predicate_ORangeP(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_ORangeP(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_239,axiom,
    ( c_Relation_ODomain(Eq_x_0,Eq_x_1) = c_Relation_ODomain(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_240,axiom,
    ( c_Predicate_ODomainP(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_ODomainP(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_241,axiom,
    ( c_Fun_Ocomp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Fun_Ocomp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_242,axiom,
    ( c_Nitpick_ORep__Frac(Eq_x_0) = c_Nitpick_ORep__Frac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_243,axiom,
    ( c_Hoare__Mirabelle_Opeek__and(Eq_x_0,Eq_x_1,Eq_x_2) = c_Hoare__Mirabelle_Opeek__and(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_244,axiom,
    ( c_Random__Sequence_Omap(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random__Sequence_Omap(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_245,axiom,
    ( c_Random__Sequence_Obind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random__Sequence_Obind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_246,axiom,
    ( c_New__Random__Sequence_Oneg__map(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Oneg__map(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_247,axiom,
    ( c_New__Random__Sequence_Oneg__single(Eq_x_0) = c_New__Random__Sequence_Oneg__single(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_248,axiom,
    ( c_New__DSequence_Oneg__single(Eq_x_0,Eq_x_1) = c_New__DSequence_Oneg__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_249,axiom,
    ( c_New__Random__Sequence_Opos__map(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__map(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_250,axiom,
    ( c_New__Random__Sequence_Opos__single(Eq_x_0) = c_New__Random__Sequence_Opos__single(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_251,axiom,
    ( c_Lazy__Sequence_Ohb__single(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Ohb__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_252,axiom,
    ( c_New__DSequence_Opos__single(Eq_x_0,Eq_x_1) = c_New__DSequence_Opos__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_253,axiom,
    ( c_Lazy__Sequence_Osingle(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Osingle(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_254,axiom,
    ( c_Hilbert__Choice_OEps(Eq_x_0,Eq_x_1) = c_Hilbert__Choice_OEps(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_255,axiom,
    ( c_Transitive__Closure_Otrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otrancl(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_256,axiom,
    ( c_Finite__Set_Ofold(Eq_x_0,Eq_x_1,Eq_x_2) = c_Finite__Set_Ofold(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_257,axiom,
    ( c_Transitive__Closure_Ortrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortrancl(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_258,axiom,
    ( c_Relation_Oconverse(Eq_x_0,Eq_x_1) = c_Relation_Oconverse(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_259,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(Eq_x_0,Eq_x_1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_260,axiom,
    ( c_HOL_OAll(Eq_x_0) = c_HOL_OAll(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_261,axiom,
    ( c_Set_OBall(Eq_x_0) = c_Set_OBall(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_262,axiom,
    ( c_Relation_OId(Eq_x_0) = c_Relation_OId(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_263,axiom,
    ( c_Nat_Ocompow(Eq_x_0,Eq_x_1) = c_Nat_Ocompow(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_264,axiom,
    ( c_Nat_Ofunpow(Eq_x_0) = c_Nat_Ofunpow(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_265,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(Eq_x_0,Eq_x_1) = c_Complete__Lattice_OInf__class_OInf(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_266,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(Eq_x_0,Eq_x_1) = c_Complete__Lattice_OSup__class_OSup(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_267,axiom,
    ( c_Map_Omap__add(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Map_Omap__add(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_268,axiom,
    ( c_Map_Omap__of(Eq_x_0,Eq_x_1,Eq_x_2) = c_Map_Omap__of(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_269,axiom,
    ( c_List_Ofoldr(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Ofoldr(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_270,axiom,
    ( c_Smallcheck_Oorelse(Eq_x_0,Eq_x_1,Eq_x_2) = c_Smallcheck_Oorelse(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_271,axiom,
    ( c_Smallcheck_Ofull__small__class_Ofull__small(Eq_x_0,Eq_x_1,Eq_x_2) = c_Smallcheck_Ofull__small__class_Ofull__small(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_272,axiom,
    ( c_Smallcheck_Ofull__small_H(Eq_x_0,Eq_x_1,Eq_x_2) = c_Smallcheck_Ofull__small_H(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_273,axiom,
    ( c_Smallcheck_Osmall_H(Eq_x_0,Eq_x_1,Eq_x_2) = c_Smallcheck_Osmall_H(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_274,axiom,
    ( c_Smallcheck_Osmall__class_Osmall(Eq_x_0) = c_Smallcheck_Osmall__class_Osmall(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_275,axiom,
    ( c_List_Omap(Eq_x_0,Eq_x_1) = c_List_Omap(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_276,axiom,
    ( c_Map_Omap__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Map_Omap__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_277,axiom,
    ( c_Option_Omap(Eq_x_0,Eq_x_1) = c_Option_Omap(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_278,axiom,
    ( c_List_Oset(Eq_x_0) = c_List_Oset(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_279,axiom,
    ( c_List_Odistinct(Eq_x_0) = c_List_Odistinct(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_280,axiom,
    ( c_List_Oupto(Eq_x_0,Eq_x_1) = c_List_Oupto(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_281,axiom,
    ( c_List_Oremove1(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oremove1(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_282,axiom,
    ( c_List_Olinorder__class_Osorted__list__of__set(Eq_x_0,Eq_x_1) = c_List_Olinorder__class_Osorted__list__of__set(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_283,axiom,
    ( c_List_Ozip(Eq_x_0,Eq_x_1) = c_List_Ozip(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_284,axiom,
    ( c_List_Olinorder__class_Oinsort__key(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olinorder__class_Oinsort__key(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_285,axiom,
    ( c_Nitpick_Ocard_H(Eq_x_0,Eq_x_1) = c_Nitpick_Ocard_H(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_286,axiom,
    ( c_List_Olistrel(Eq_x_0,Eq_x_1) = c_List_Olistrel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_287,axiom,
    ( c_List_Olist_OCons(Eq_x_0) = c_List_Olist_OCons(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_288,axiom,
    ( c_List_Oset__Cons(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oset__Cons(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_289,axiom,
    ( c_List_Osublist(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Osublist(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_290,axiom,
    ( c_Random_Opick(Eq_x_0,Eq_x_1) = c_Random_Opick(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_291,axiom,
    ( c_Random_Oselect__weight(Eq_x_0,Eq_x_1) = c_Random_Oselect__weight(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_292,axiom,
    ( c_List_Omonoid__add__class_Olistsum(Eq_x_0) = c_List_Omonoid__add__class_Olistsum(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_293,axiom,
    ( c_Nitpick_Osetsum_H(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Osetsum_H(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_294,axiom,
    ( c_List_Olinorder__class_Oinsort__insert__key(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Olinorder__class_Oinsort__insert__key(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_295,axiom,
    ( c_List_Olexord(Eq_x_0,Eq_x_1) = c_List_Olexord(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_296,axiom,
    ( c_List_Onth(Eq_x_0) = c_List_Onth(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_297,axiom,
    ( c_Random_Oselect(Eq_x_0,Eq_x_1) = c_Random_Oselect(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_298,axiom,
    ( c_List_Otake(Eq_x_0) = c_List_Otake(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_299,axiom,
    ( c_List_Olist__update(Eq_x_0,Eq_x_1) = c_List_Olist__update(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_300,axiom,
    ( c_List_Olist_ONil(Eq_x_0) = c_List_Olist_ONil(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_301,axiom,
    ( c_Lazy__Sequence_Oanamorph(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Oanamorph(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_302,axiom,
    ( c_List_Olistset(Eq_x_0,Eq_x_1) = c_List_Olistset(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_303,axiom,
    ( c_List_Olist_Olist__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Olist_Olist__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_304,axiom,
    ( c_Map_Omap__upds(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Map_Omap__upds(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_305,axiom,
    ( c_List_Oappend(Eq_x_0) = c_List_Oappend(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_306,axiom,
    ( c_List_Olistrel1(Eq_x_0,Eq_x_1) = c_List_Olistrel1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_307,axiom,
    ( c_List_Orotate1(Eq_x_0) = c_List_Orotate1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_308,axiom,
    ( c_List_Odrop(Eq_x_0) = c_List_Odrop(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_309,axiom,
    ( c_List_Ohd(Eq_x_0) = c_List_Ohd(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_310,axiom,
    ( c_List_Otl(Eq_x_0) = c_List_Otl(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_311,axiom,
    ( c_List_Orotate(Eq_x_0,Eq_x_1) = c_List_Orotate(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_312,axiom,
    ( c_List_Ofoldl(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Ofoldl(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_313,axiom,
    ( c_List_Olist_Olist__size(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olist_Olist__size(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_314,axiom,
    ( c_List_Olists(Eq_x_0,Eq_x_1) = c_List_Olists(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_315,axiom,
    ( c_List_Olast(Eq_x_0,Eq_x_1) = c_List_Olast(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_316,axiom,
    ( c_List_Obutlast(Eq_x_0,Eq_x_1) = c_List_Obutlast(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_317,axiom,
    ( c_List_Ofilter(Eq_x_0,Eq_x_1) = c_List_Ofilter(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_318,axiom,
    ( c_List_Opartition(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Opartition(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_319,axiom,
    ( c_List_Omap__filter(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Omap__filter(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_320,axiom,
    ( c_List_Otranspose(Eq_x_0,Eq_x_1) = c_List_Otranspose(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_321,axiom,
    ( c_List_Oupt(Eq_x_0,Eq_x_1) = c_List_Oupt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_322,axiom,
    ( c_List_Otranspose__rel(Eq_x_0) = c_List_Otranspose__rel(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_323,axiom,
    ( c_List_Orev(Eq_x_0) = c_List_Orev(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_324,axiom,
    ( c_List_Oconcat(Eq_x_0,Eq_x_1) = c_List_Oconcat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_325,axiom,
    ( c_List_OtakeWhile(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_OtakeWhile(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_326,axiom,
    ( c_List_Oreturn__list(Eq_x_0) = c_List_Oreturn__list(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_327,axiom,
    ( c_List_Oembed__list(Eq_x_0) = c_List_Oembed__list(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_328,axiom,
    ( c_List_Oremdups(Eq_x_0,Eq_x_1) = c_List_Oremdups(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_329,axiom,
    ( c_List_OdropWhile(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_OdropWhile(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_330,axiom,
    ( v_a(Eq_x_0) = v_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_331,axiom,
    ( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_332,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_333,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_334,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_335,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_336,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_337,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_338,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_339,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_340,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_341,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_342,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_343,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_344,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK15(Eq_x_0) = sK15(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_346,axiom,
    ( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,axiom,
    ( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_348,axiom,
    ( sK18(Eq_x_0) = sK18(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK20(Eq_x_0) = sK20(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,axiom,
    ( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_353,axiom,
    ( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_354,axiom,
    ( sK24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_355,axiom,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,axiom,
    ( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_358,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_359,axiom,
    ( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK31(Eq_x_0) = sK31(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_362,axiom,
    ( sK32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,axiom,
    ( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_364,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_365,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_366,axiom,
    ( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK37(Eq_x_0) = sK37(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_368,axiom,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_369,axiom,
    ( sK39(Eq_x_0) = sK39(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_370,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_371,axiom,
    ( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_372,axiom,
    ( sK42(Eq_x_0) = sK42(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_373,axiom,
    ( sK43(Eq_x_0) = sK43(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_374,axiom,
    ( sK44(Eq_x_0) = sK44(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_375,axiom,
    ( sK45(Eq_x_0) = sK45(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_376,axiom,
    ( sK46(Eq_x_0) = sK46(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_377,axiom,
    ( sK47(Eq_x_0) = sK47(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_378,axiom,
    ( sK48(Eq_x_0) = sK48(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_379,axiom,
    ( sK49(Eq_x_0) = sK49(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_380,axiom,
    ( sK50(Eq_x_0,Eq_x_1) = sK50(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_381,axiom,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_382,axiom,
    ( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_383,axiom,
    ( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_384,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_385,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_386,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_388,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_389,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_391,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_392,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_393,axiom,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_394,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_395,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_396,axiom,
    ( sK66(Eq_x_0,Eq_x_1) = sK66(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_397,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_398,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_399,axiom,
    ( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_400,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_401,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_402,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_403,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_404,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_405,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_406,axiom,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_407,axiom,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_408,axiom,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_409,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_410,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_411,axiom,
    ( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_412,axiom,
    ( sK82(Eq_x_0,Eq_x_1,Eq_x_2) = sK82(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_413,axiom,
    ( sK83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_414,axiom,
    ( sK84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_415,axiom,
    ( sK85(Eq_x_0,Eq_x_1,Eq_x_2) = sK85(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_416,axiom,
    ( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_417,axiom,
    ( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_418,axiom,
    ( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_419,axiom,
    ( sK89(Eq_x_0,Eq_x_1,Eq_x_2) = sK89(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_420,axiom,
    ( sK90(Eq_x_0,Eq_x_1,Eq_x_2) = sK90(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_421,axiom,
    ( sK91(Eq_x_0,Eq_x_1,Eq_x_2) = sK91(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_422,axiom,
    ( sK92(Eq_x_0,Eq_x_1,Eq_x_2) = sK92(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_423,axiom,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2) = sK93(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_424,axiom,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_425,axiom,
    ( sK95(Eq_x_0,Eq_x_1,Eq_x_2) = sK95(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_426,axiom,
    ( sK96(Eq_x_0,Eq_x_1,Eq_x_2) = sK96(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_427,axiom,
    ( sK97(Eq_x_0,Eq_x_1,Eq_x_2) = sK97(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_428,axiom,
    ( sK98(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_429,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK99(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_430,axiom,
    ( sK100(Eq_x_0,Eq_x_1,Eq_x_2) = sK100(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_431,axiom,
    ( sK101(Eq_x_0,Eq_x_1,Eq_x_2) = sK101(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_432,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_433,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_434,axiom,
    ( sK104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_435,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_436,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_437,axiom,
    ( sK107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_438,axiom,
    ( sK108(Eq_x_0,Eq_x_1) = sK108(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_439,axiom,
    ( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_440,axiom,
    ( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_441,axiom,
    ( sK111(Eq_x_0,Eq_x_1) = sK111(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_442,axiom,
    ( sK112(Eq_x_0,Eq_x_1) = sK112(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_443,axiom,
    ( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_444,axiom,
    ( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_445,axiom,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_446,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_447,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_448,axiom,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_449,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_450,axiom,
    ( sK120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_451,axiom,
    ( sK121(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_452,axiom,
    ( sK122(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK122(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_453,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_454,axiom,
    ( sK124(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK124(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_455,axiom,
    ( sK125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_456,axiom,
    ( sK126(Eq_x_0,Eq_x_1) = sK126(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_457,axiom,
    ( sK127(Eq_x_0) = sK127(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_458,axiom,
    ( sK128(Eq_x_0) = sK128(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_459,axiom,
    ( sK129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_460,axiom,
    ( sK130(Eq_x_0) = sK130(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_461,axiom,
    ( sK131(Eq_x_0,Eq_x_1,Eq_x_2) = sK131(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_462,axiom,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_463,axiom,
    ( sK133(Eq_x_0) = sK133(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_464,axiom,
    ( sK134(Eq_x_0,Eq_x_1) = sK134(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_465,axiom,
    ( sK135(Eq_x_0) = sK135(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_466,axiom,
    ( sK136(Eq_x_0,Eq_x_1) = sK136(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_467,axiom,
    ( sK137(Eq_x_0,Eq_x_1,Eq_x_2) = sK137(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_468,axiom,
    ( sK138(Eq_x_0,Eq_x_1,Eq_x_2) = sK138(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_469,axiom,
    ( sK139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK139(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_470,axiom,
    ( sK140(Eq_x_0,Eq_x_1) = sK140(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_471,axiom,
    ( sK141(Eq_x_0,Eq_x_1) = sK141(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_472,axiom,
    ( sK142(Eq_x_0,Eq_x_1) = sK142(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_473,axiom,
    ( sK143(Eq_x_0,Eq_x_1) = sK143(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_474,axiom,
    ( sK144(Eq_x_0,Eq_x_1) = sK144(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_475,axiom,
    ( sK145(Eq_x_0,Eq_x_1) = sK145(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_476,axiom,
    ( sK146(Eq_x_0,Eq_x_1) = sK146(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_477,axiom,
    ( sK147(Eq_x_0,Eq_x_1) = sK147(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_478,axiom,
    ( sK148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_479,axiom,
    ( sK149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_480,axiom,
    ( sK150(Eq_x_0,Eq_x_1) = sK150(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_481,axiom,
    ( sK151(Eq_x_0,Eq_x_1) = sK151(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_482,axiom,
    ( sK152(Eq_x_0,Eq_x_1) = sK152(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_483,axiom,
    ( sK153(Eq_x_0,Eq_x_1) = sK153(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_484,axiom,
    ( sK154(Eq_x_0,Eq_x_1,Eq_x_2) = sK154(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_485,axiom,
    ( sK155(Eq_x_0,Eq_x_1,Eq_x_2) = sK155(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_486,axiom,
    ( sK156(Eq_x_0,Eq_x_1,Eq_x_2) = sK156(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_487,axiom,
    ( sK157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_488,axiom,
    ( sK158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_489,axiom,
    ( sK159(Eq_x_0,Eq_x_1,Eq_x_2) = sK159(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_490,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2) = sK160(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_491,axiom,
    ( sK161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK161(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_492,axiom,
    ( sK162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_493,axiom,
    ( sK163(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_494,axiom,
    ( sK164(Eq_x_0,Eq_x_1,Eq_x_2) = sK164(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_495,axiom,
    ( sK165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_496,axiom,
    ( sK166(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK166(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_497,axiom,
    ( sK167(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_498,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_499,axiom,
    ( sK169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_500,axiom,
    ( sK170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK170(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_501,axiom,
    ( sK171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_502,axiom,
    ( sK172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_503,axiom,
    ( sK173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_504,axiom,
    ( sK174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_505,axiom,
    ( sK175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_506,axiom,
    ( sK176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_507,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_508,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10) = sK178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_509,axiom,
    ( sK179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10) = sK179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_510,axiom,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_511,axiom,
    ( sK181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_512,axiom,
    ( sK182(Eq_x_0,Eq_x_1,Eq_x_2) = sK182(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_513,axiom,
    ( sK183(Eq_x_0,Eq_x_1,Eq_x_2) = sK183(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_514,axiom,
    ( sK184(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK184(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_515,axiom,
    ( sK185(Eq_x_0,Eq_x_1,Eq_x_2) = sK185(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_516,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2) = sK186(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_517,axiom,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2) = sK187(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_518,axiom,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2) = sK188(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_519,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2) = sK189(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_520,axiom,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2) = sK190(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_521,axiom,
    ( sK191(Eq_x_0,Eq_x_1,Eq_x_2) = sK191(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_522,axiom,
    ( sK192(Eq_x_0,Eq_x_1,Eq_x_2) = sK192(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_523,axiom,
    ( sK193(Eq_x_0,Eq_x_1,Eq_x_2) = sK193(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_524,axiom,
    ( sK194(Eq_x_0,Eq_x_1,Eq_x_2) = sK194(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_525,axiom,
    ( sK195(Eq_x_0,Eq_x_1,Eq_x_2) = sK195(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_526,axiom,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_527,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK197(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_528,axiom,
    ( sK198(Eq_x_0,Eq_x_1,Eq_x_2) = sK198(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_529,axiom,
    ( sK199(Eq_x_0,Eq_x_1,Eq_x_2) = sK199(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_530,axiom,
    ( sK200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_531,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK201(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_532,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK202(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_533,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK203(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_534,axiom,
    ( sK204(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK204(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_535,axiom,
    ( sK205(Eq_x_0,Eq_x_1) = sK205(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_536,axiom,
    ( sK206(Eq_x_0,Eq_x_1) = sK206(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_537,axiom,
    ( sK207(Eq_x_0,Eq_x_1) = sK207(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_538,axiom,
    ( sK208(Eq_x_0,Eq_x_1) = sK208(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_539,axiom,
    ( sK209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_540,axiom,
    ( sK210(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK210(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_541,axiom,
    ( sK211(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK211(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_542,axiom,
    ( sK212(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK212(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_543,axiom,
    ( sK213(Eq_x_0,Eq_x_1,Eq_x_2) = sK213(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_544,axiom,
    ( sK214(Eq_x_0,Eq_x_1,Eq_x_2) = sK214(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_545,axiom,
    ( sK215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_546,axiom,
    ( sK216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_547,axiom,
    ( sK217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_548,axiom,
    ( sK218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_549,axiom,
    ( sK219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_550,axiom,
    ( sK220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_551,axiom,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2) = sK221(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_552,axiom,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2) = sK222(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_553,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_554,axiom,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_555,axiom,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_556,axiom,
    ( sK226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_557,axiom,
    ( sK227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_558,axiom,
    ( sK228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_559,axiom,
    ( sK229(Eq_x_0,Eq_x_1) = sK229(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_560,axiom,
    ( sK230(Eq_x_0,Eq_x_1) = sK230(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_561,axiom,
    ( sK231(Eq_x_0,Eq_x_1) = sK231(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_562,axiom,
    ( sK232(Eq_x_0,Eq_x_1) = sK232(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_563,axiom,
    ( sK233(Eq_x_0,Eq_x_1) = sK233(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_564,axiom,
    ( sK234(Eq_x_0,Eq_x_1) = sK234(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_565,axiom,
    ( sK235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_566,axiom,
    ( sK236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_567,axiom,
    ( sK237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_568,axiom,
    ( sK238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_569,axiom,
    ( sK239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK239(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_570,axiom,
    ( sK240(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK240(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_571,axiom,
    ( sK241(Eq_x_0,Eq_x_1) = sK241(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_572,axiom,
    ( sK242(Eq_x_0,Eq_x_1) = sK242(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_573,axiom,
    ( sK243(Eq_x_0,Eq_x_1) = sK243(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_574,axiom,
    ( sK244(Eq_x_0,Eq_x_1) = sK244(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_575,axiom,
    ( sK245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK245(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_576,axiom,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK246(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_577,axiom,
    ( sK247(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK247(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_578,axiom,
    ( sK248(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK248(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_579,axiom,
    ( sK249(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK249(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_580,axiom,
    ( sK250(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK250(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_581,axiom,
    ( sK251(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK251(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_582,axiom,
    ( sK252(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK252(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_583,axiom,
    ( sK253(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK253(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_584,axiom,
    ( sK254(Eq_x_0,Eq_x_1,Eq_x_2) = sK254(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_585,axiom,
    ( sK255(Eq_x_0,Eq_x_1,Eq_x_2) = sK255(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_586,axiom,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK256(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_587,axiom,
    ( sK257(Eq_x_0,Eq_x_1,Eq_x_2) = sK257(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_588,axiom,
    ( sK258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK258(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_589,axiom,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2) = sK259(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_590,axiom,
    ( sK260(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK260(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_591,axiom,
    ( sK261(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK261(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_592,axiom,
    ( sK262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK262(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_593,axiom,
    ( sK263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK263(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_594,axiom,
    ( sK264(Eq_x_0,Eq_x_1,Eq_x_2) = sK264(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_595,axiom,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK265(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_596,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_597,axiom,
    ( sK267(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK267(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_598,axiom,
    ( sK268(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK268(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_599,axiom,
    ( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK269(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_600,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK270(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_601,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_602,axiom,
    ( sK272(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_603,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_604,axiom,
    ( sK274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_605,axiom,
    ( sK275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_606,axiom,
    ( sK276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_607,axiom,
    ( sK277(Eq_x_0,Eq_x_1,Eq_x_2) = sK277(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_608,axiom,
    ( sK278(Eq_x_0) = sK278(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_609,axiom,
    ( sK279(Eq_x_0) = sK279(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_610,axiom,
    ( sK280(Eq_x_0) = sK280(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_611,axiom,
    ( sK281(Eq_x_0) = sK281(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_612,axiom,
    ( sK282(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK282(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_613,axiom,
    ( sK283(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK283(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_614,axiom,
    ( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK284(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_615,axiom,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_616,axiom,
    ( sK286(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK286(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_617,axiom,
    ( sK287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK287(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_618,axiom,
    ( sK288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK288(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_619,axiom,
    ( sK289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK289(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_620,axiom,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2) = sK290(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_621,axiom,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2) = sK291(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_622,axiom,
    ( sK292(Eq_x_0,Eq_x_1,Eq_x_2) = sK292(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_623,axiom,
    ( sK293(Eq_x_0,Eq_x_1,Eq_x_2) = sK293(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_624,axiom,
    ( sK294(Eq_x_0,Eq_x_1,Eq_x_2) = sK294(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_625,axiom,
    ( sK295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK295(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_626,axiom,
    ( sK296(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK296(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_627,axiom,
    ( sK297(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK297(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_628,axiom,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK298(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_629,axiom,
    ( sK299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK299(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_630,axiom,
    ( sK300(Eq_x_0,Eq_x_1) = sK300(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_631,axiom,
    ( sK301(Eq_x_0,Eq_x_1) = sK301(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_632,axiom,
    ( sK302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK302(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_633,axiom,
    ( sK303(Eq_x_0,Eq_x_1,Eq_x_2) = sK303(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_634,axiom,
    ( sK304(Eq_x_0,Eq_x_1,Eq_x_2) = sK304(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_635,axiom,
    ( sK305(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK305(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_636,axiom,
    ( sK306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_637,axiom,
    ( sK307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK307(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_638,axiom,
    ( sK308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK308(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_639,axiom,
    ( sK309(Eq_x_0,Eq_x_1,Eq_x_2) = sK309(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_640,axiom,
    ( sK310(Eq_x_0,Eq_x_1,Eq_x_2) = sK310(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_641,axiom,
    ( sK311(Eq_x_0,Eq_x_1,Eq_x_2) = sK311(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_642,axiom,
    ( sK312(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK312(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_643,axiom,
    ( sK313(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK313(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_644,axiom,
    ( sK314(Eq_x_0,Eq_x_1) = sK314(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_645,axiom,
    ( sK315(Eq_x_0) = sK315(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_646,axiom,
    ( sK316(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK316(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_647,axiom,
    ( sK317(Eq_x_0) = sK317(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_648,axiom,
    ( sK318(Eq_x_0) = sK318(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_649,axiom,
    ( sK319(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK319(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_650,axiom,
    ( sK320(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK320(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_651,axiom,
    ( sK321(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK321(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_652,axiom,
    ( sK322(Eq_x_0,Eq_x_1) = sK322(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_653,axiom,
    ( sK323(Eq_x_0,Eq_x_1) = sK323(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_654,axiom,
    ( sK324(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK324(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_655,axiom,
    ( sK325(Eq_x_0,Eq_x_1) = sK325(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_656,axiom,
    ( sK326(Eq_x_0,Eq_x_1,Eq_x_2) = sK326(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_657,axiom,
    ( sK327(Eq_x_0,Eq_x_1) = sK327(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_658,axiom,
    ( sK328(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK328(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_659,axiom,
    ( sK329(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK329(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_660,axiom,
    ( sK330(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK330(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_661,axiom,
    ( sK331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK331(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_662,axiom,
    ( sK332(Eq_x_0,Eq_x_1) = sK332(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_663,axiom,
    ( sK333(Eq_x_0,Eq_x_1) = sK333(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_664,axiom,
    ( sK334(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK334(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_665,axiom,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK335(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_666,axiom,
    ( sK336(Eq_x_0,Eq_x_1) = sK336(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_667,axiom,
    ( sK337(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK337(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_668,axiom,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2) = sK338(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_669,axiom,
    ( sK339(Eq_x_0,Eq_x_1,Eq_x_2) = sK339(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_670,axiom,
    ( sK340(Eq_x_0,Eq_x_1,Eq_x_2) = sK340(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_671,axiom,
    ( sK341(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK341(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_672,axiom,
    ( sK342(Eq_x_0) = sK342(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_673,axiom,
    ( sK343(Eq_x_0,Eq_x_1) = sK343(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_674,axiom,
    ( sK344(Eq_x_0,Eq_x_1,Eq_x_2) = sK344(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_675,axiom,
    ( sK345(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK345(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_676,axiom,
    ( sK346(Eq_x_0,Eq_x_1,Eq_x_2) = sK346(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_677,axiom,
    ( sK347(Eq_x_0,Eq_x_1,Eq_x_2) = sK347(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_678,axiom,
    ( sK348(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK348(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_679,axiom,
    ( sK349(Eq_x_0,Eq_x_1) = sK349(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_680,axiom,
    ( sK350(Eq_x_0,Eq_x_1,Eq_x_2) = sK350(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_681,axiom,
    ( sK351(Eq_x_0,Eq_x_1,Eq_x_2) = sK351(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_682,axiom,
    ( sK352(Eq_x_0,Eq_x_1,Eq_x_2) = sK352(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_683,axiom,
    ( sK353(Eq_x_0,Eq_x_1,Eq_x_2) = sK353(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_684,axiom,
    ( sK354(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK354(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_685,axiom,
    ( sK355(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK355(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_686,axiom,
    ( sK356(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK356(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_687,axiom,
    ( sK357(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK357(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_688,axiom,
    ( sK358(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK358(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_689,axiom,
    ( sK359(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK359(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_690,axiom,
    ( sK360(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK360(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_691,axiom,
    ( sK361(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK361(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_692,axiom,
    ( sK362(Eq_x_0,Eq_x_1) = sK362(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_693,axiom,
    ( sK363(Eq_x_0,Eq_x_1) = sK363(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_694,axiom,
    ( sK364(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK364(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_695,axiom,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2) = sK365(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_696,axiom,
    ( sK366(Eq_x_0,Eq_x_1,Eq_x_2) = sK366(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_697,axiom,
    ( sK367(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK367(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_698,axiom,
    ( sK368(Eq_x_0,Eq_x_1) = sK368(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_699,axiom,
    ( sK369(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK369(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_700,axiom,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK370(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_701,axiom,
    ( sK371(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK371(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_702,axiom,
    ( sK372(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK372(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_703,axiom,
    ( sK373(Eq_x_0,Eq_x_1,Eq_x_2) = sK373(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_704,axiom,
    ( sK374(Eq_x_0,Eq_x_1,Eq_x_2) = sK374(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_705,axiom,
    ( sK375(Eq_x_0,Eq_x_1,Eq_x_2) = sK375(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_706,axiom,
    ( sK376(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK376(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_707,axiom,
    ( sK377(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK377(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_708,axiom,
    ( sK378(Eq_x_0,Eq_x_1) = sK378(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_709,axiom,
    ( sK379(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK379(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_710,axiom,
    ( sK380(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK380(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_711,axiom,
    ( sK381(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK381(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_712,axiom,
    ( sK382(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK382(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_713,axiom,
    ( sK383(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK383(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_714,axiom,
    ( sK384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK384(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_715,axiom,
    ( sK385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK385(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_716,axiom,
    ( sK386(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK386(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_717,axiom,
    ( sK387(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK387(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_718,axiom,
    ( sK388(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK388(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_719,axiom,
    ( sK389(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK389(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_720,axiom,
    ( sK390(Eq_x_0,Eq_x_1,Eq_x_2) = sK390(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_721,axiom,
    ( sK391(Eq_x_0,Eq_x_1,Eq_x_2) = sK391(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_722,axiom,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2) = sK392(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_723,axiom,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2) = sK393(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_724,axiom,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2) = sK394(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_725,axiom,
    ( sK395(Eq_x_0,Eq_x_1,Eq_x_2) = sK395(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_726,axiom,
    ( sK396(Eq_x_0,Eq_x_1,Eq_x_2) = sK396(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_727,axiom,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK397(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_728,axiom,
    ( sK398(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK398(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_729,axiom,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK399(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_730,axiom,
    ( sK400(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK400(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_731,axiom,
    ( sK401(Eq_x_0,Eq_x_1,Eq_x_2) = sK401(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_732,axiom,
    ( sK402(Eq_x_0,Eq_x_1,Eq_x_2) = sK402(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_733,axiom,
    ( sK403(Eq_x_0,Eq_x_1,Eq_x_2) = sK403(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_734,axiom,
    ( sK404(Eq_x_0,Eq_x_1,Eq_x_2) = sK404(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_735,axiom,
    ( sK405(Eq_x_0,Eq_x_1,Eq_x_2) = sK405(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_736,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK406(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_737,axiom,
    ( sK407(Eq_x_0,Eq_x_1,Eq_x_2) = sK407(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_738,axiom,
    ( sK408(Eq_x_0,Eq_x_1) = sK408(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_739,axiom,
    ( sK409(Eq_x_0,Eq_x_1,Eq_x_2) = sK409(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_740,axiom,
    ( sK410(Eq_x_0,Eq_x_1,Eq_x_2) = sK410(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_741,axiom,
    ( sK411(Eq_x_0,Eq_x_1,Eq_x_2) = sK411(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_742,axiom,
    ( sK412(Eq_x_0,Eq_x_1,Eq_x_2) = sK412(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_743,axiom,
    ( sK413(Eq_x_0,Eq_x_1,Eq_x_2) = sK413(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_744,axiom,
    ( sK414(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK414(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_745,axiom,
    ( sK415(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK415(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_746,axiom,
    ( sK416(Eq_x_0,Eq_x_1) = sK416(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_747,axiom,
    ( sK417(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK417(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_748,axiom,
    ( sK418(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK418(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_749,axiom,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK419(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_750,axiom,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK420(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_751,axiom,
    ( sK421(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK421(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_752,axiom,
    ( sK422(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK422(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_753,axiom,
    ( sK423(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK423(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_754,axiom,
    ( sK424(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK424(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_755,axiom,
    ( sK425(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK425(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_756,axiom,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK426(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_757,axiom,
    ( sK427(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK427(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_758,axiom,
    ( sK428(Eq_x_0,Eq_x_1,Eq_x_2) = sK428(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_759,axiom,
    ( sK429(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK429(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_760,axiom,
    ( sK430(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK430(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_761,axiom,
    ( sK431(Eq_x_0,Eq_x_1) = sK431(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_762,axiom,
    ( sK432(Eq_x_0,Eq_x_1,Eq_x_2) = sK432(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_763,axiom,
    ( sK433(Eq_x_0,Eq_x_1) = sK433(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_764,axiom,
    ( sK434(Eq_x_0,Eq_x_1) = sK434(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_765,axiom,
    ( sK435(Eq_x_0,Eq_x_1,Eq_x_2) = sK435(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_766,axiom,
    ( sK436(Eq_x_0,Eq_x_1) = sK436(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_767,axiom,
    ( sK437(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK437(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_768,axiom,
    ( sK438(Eq_x_0,Eq_x_1,Eq_x_2) = sK438(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_769,axiom,
    ( sK439(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK439(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_770,axiom,
    ( sK440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK440(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_771,axiom,
    ( sK441(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK441(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_772,axiom,
    ( sK442(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK442(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_773,axiom,
    ( sK443(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK443(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_774,axiom,
    ( sK444(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK444(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_775,axiom,
    ( sK445(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK445(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_776,axiom,
    ( sK446(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK446(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_777,axiom,
    ( sK447(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK447(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_778,axiom,
    ( sK448(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK448(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_779,axiom,
    ( sK449(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK449(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_780,axiom,
    ( sK450(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK450(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_781,axiom,
    ( sK452(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK452(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_782,axiom,
    ( sK453(Eq_x_0,Eq_x_1,Eq_x_2) = sK453(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_783,axiom,
    ( sK454(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK454(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_784,axiom,
    ( sK455(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK455(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_785,axiom,
    ( sK456(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK456(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_786,axiom,
    ( sK457(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK457(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_787,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK458(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_788,axiom,
    ( sK459(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK459(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_789,axiom,
    ( sK460(Eq_x_0) = sK460(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_790,axiom,
    ( sK461(Eq_x_0,Eq_x_1,Eq_x_2) = sK461(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_791,axiom,
    ( sK462(Eq_x_0,Eq_x_1,Eq_x_2) = sK462(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_792,axiom,
    ( sK463(Eq_x_0,Eq_x_1,Eq_x_2) = sK463(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_793,axiom,
    ( sK464(Eq_x_0,Eq_x_1) = sK464(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_794,axiom,
    ( sK465(Eq_x_0,Eq_x_1) = sK465(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_795,axiom,
    ( sK466(Eq_x_0,Eq_x_1,Eq_x_2) = sK466(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_796,axiom,
    ( sK467(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK467(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_797,axiom,
    ( sK468(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK468(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_798,axiom,
    ( sK469(Eq_x_0,Eq_x_1,Eq_x_2) = sK469(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_799,axiom,
    ( sK470(Eq_x_0,Eq_x_1,Eq_x_2) = sK470(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_800,axiom,
    ( sK471(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK471(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_801,axiom,
    ( sK472(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK472(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_802,axiom,
    ( sK473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK473(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_803,axiom,
    ( sK474(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK474(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_804,axiom,
    ( sK475(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK475(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_805,axiom,
    ( sK476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK476(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_806,axiom,
    ( sK477(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK477(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_807,axiom,
    ( sK478(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK478(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_808,axiom,
    ( sK479(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK479(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_809,axiom,
    ( sK480(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK480(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_810,axiom,
    ( sK481(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK481(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_811,axiom,
    ( sK482(Eq_x_0,Eq_x_1) = sK482(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_812,axiom,
    ( sK483(Eq_x_0,Eq_x_1,Eq_x_2) = sK483(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_813,axiom,
    ( sK484(Eq_x_0,Eq_x_1,Eq_x_2) = sK484(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_814,axiom,
    ( sK485(Eq_x_0,Eq_x_1,Eq_x_2) = sK485(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_815,axiom,
    ( sK486(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK486(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_816,axiom,
    ( sK487(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK487(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_817,axiom,
    ( sK488(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK488(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_818,axiom,
    ( sK489(Eq_x_0,Eq_x_1,Eq_x_2) = sK489(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_819,axiom,
    ( sK490(Eq_x_0,Eq_x_1,Eq_x_2) = sK490(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_820,axiom,
    ( sK491(Eq_x_0,Eq_x_1,Eq_x_2) = sK491(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_821,axiom,
    ( sK492(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK492(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_822,axiom,
    ( sK493(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK493(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_823,axiom,
    ( sK494(Eq_x_0,Eq_x_1,Eq_x_2) = sK494(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_824,axiom,
    ( sK495(Eq_x_0,Eq_x_1,Eq_x_2) = sK495(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_825,axiom,
    ( sK496(Eq_x_0,Eq_x_1) = sK496(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_826,axiom,
    ( sK497(Eq_x_0,Eq_x_1,Eq_x_2) = sK497(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_827,axiom,
    ( sK498(Eq_x_0,Eq_x_1,Eq_x_2) = sK498(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_828,axiom,
    ( sK499(Eq_x_0,Eq_x_1,Eq_x_2) = sK499(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_829,axiom,
    ( sK500(Eq_x_0,Eq_x_1,Eq_x_2) = sK500(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_830,axiom,
    ( sK501(Eq_x_0,Eq_x_1) = sK501(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_831,axiom,
    ( sK502(Eq_x_0,Eq_x_1) = sK502(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_832,axiom,
    ( sK503(Eq_x_0,Eq_x_1,Eq_x_2) = sK503(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_833,axiom,
    ( sK504(Eq_x_0,Eq_x_1) = sK504(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_834,axiom,
    ( sK505(Eq_x_0,Eq_x_1) = sK505(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_835,axiom,
    ( sK506(Eq_x_0,Eq_x_1,Eq_x_2) = sK506(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_836,axiom,
    ( sK507(Eq_x_0,Eq_x_1,Eq_x_2) = sK507(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_837,axiom,
    ( sK508(Eq_x_0,Eq_x_1,Eq_x_2) = sK508(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_838,axiom,
    ( c_Hoare__Mirabelle_Otriple__valid(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Hoare__Mirabelle_Otriple__valid(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_839,axiom,
    ( c_Natural_Oevaln(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Natural_Oevaln(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_840,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_841,axiom,
    ( class_Groups_Ozero(Eq_y_0)
    | ~ class_Groups_Ozero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_842,axiom,
    ( class_Rings_Osemiring__1(Eq_y_0)
    | ~ class_Rings_Osemiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_843,axiom,
    ( class_Groups_Oab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_844,axiom,
    ( class_Groups_Ocancel__semigroup__add(Eq_y_0)
    | ~ class_Groups_Ocancel__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_845,axiom,
    ( class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_y_0)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_846,axiom,
    ( class_Groups_Oordered__cancel__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_847,axiom,
    ( class_Groups_Ocancel__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Ocancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_848,axiom,
    ( class_Groups_Oordered__comm__monoid__add(Eq_y_0)
    | ~ class_Groups_Oordered__comm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_849,axiom,
    ( class_Groups_Olinordered__ab__group__add(Eq_y_0)
    | ~ class_Groups_Olinordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_850,axiom,
    ( class_Groups_Omonoid__add(Eq_y_0)
    | ~ class_Groups_Omonoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_851,axiom,
    ( class_Groups_Ocomm__monoid__add(Eq_y_0)
    | ~ class_Groups_Ocomm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_852,axiom,
    ( class_Rings_Olinordered__semidom(Eq_y_0)
    | ~ class_Rings_Olinordered__semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_853,axiom,
    ( class_Rings_Olinordered__idom(Eq_y_0)
    | ~ class_Rings_Olinordered__idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_854,axiom,
    ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_y_0)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_855,axiom,
    ( class_Rings_Ocomm__semiring__1(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_856,axiom,
    ( c_Option_Ois__none(Eq_y_0,Eq_y_1)
    | ~ c_Option_Ois__none(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_857,axiom,
    ( class_Orderings_Oorder(Eq_y_0)
    | ~ class_Orderings_Oorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_858,axiom,
    ( class_Nat_Osemiring__char__0(Eq_y_0)
    | ~ class_Nat_Osemiring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_859,axiom,
    ( class_Orderings_Opreorder(Eq_y_0)
    | ~ class_Orderings_Opreorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_860,axiom,
    ( class_Orderings_Olinorder(Eq_y_0)
    | ~ class_Orderings_Olinorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_861,axiom,
    ( class_Orderings_Oord(Eq_y_0)
    | ~ class_Orderings_Oord(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_862,axiom,
    ( class_Rings_Oidom(Eq_y_0)
    | ~ class_Rings_Oidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_863,axiom,
    ( class_Rings_Oring__1__no__zero__divisors(Eq_y_0)
    | ~ class_Rings_Oring__1__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_864,axiom,
    ( class_Rings_Oring(Eq_y_0)
    | ~ class_Rings_Oring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_865,axiom,
    ( class_Int_Oring__char__0(Eq_y_0)
    | ~ class_Int_Oring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_866,axiom,
    ( class_Rings_Oring__1(Eq_y_0)
    | ~ class_Rings_Oring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_867,axiom,
    ( class_Groups_Oab__semigroup__mult(Eq_y_0)
    | ~ class_Groups_Oab__semigroup__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_868,axiom,
    ( class_Groups_Ogroup__add(Eq_y_0)
    | ~ class_Groups_Ogroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_869,axiom,
    ( class_Groups_Ocomm__monoid__mult(Eq_y_0)
    | ~ class_Groups_Ocomm__monoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_870,axiom,
    ( class_Groups_Omonoid__mult(Eq_y_0)
    | ~ class_Groups_Omonoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_871,axiom,
    ( class_Groups_Oone(Eq_y_0)
    | ~ class_Groups_Oone(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_872,axiom,
    ( class_Rings_Ocomm__ring__1(Eq_y_0)
    | ~ class_Rings_Ocomm__ring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_873,axiom,
    ( class_Groups_Oordered__ab__group__add(Eq_y_0)
    | ~ class_Groups_Oordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_874,axiom,
    ( class_Groups_Oab__group__add(Eq_y_0)
    | ~ class_Groups_Oab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_875,axiom,
    ( class_Rings_Omult__zero(Eq_y_0)
    | ~ class_Rings_Omult__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_876,axiom,
    ( class_Rings_Oring__no__zero__divisors(Eq_y_0)
    | ~ class_Rings_Oring__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_877,axiom,
    ( class_Rings_Ono__zero__divisors(Eq_y_0)
    | ~ class_Rings_Ono__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_878,axiom,
    ( class_Rings_Ozero__neq__one(Eq_y_0)
    | ~ class_Rings_Ozero__neq__one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_879,axiom,
    ( class_Rings_Ocomm__semiring(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_880,axiom,
    ( class_Rings_Osemiring(Eq_y_0)
    | ~ class_Rings_Osemiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_881,axiom,
    ( class_Rings_Olinordered__ring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__ring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_882,axiom,
    ( class_Rings_Olinordered__comm__semiring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__comm__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_883,axiom,
    ( class_Rings_Olinordered__semiring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_884,axiom,
    ( class_Rings_Olinordered__ring(Eq_y_0)
    | ~ class_Rings_Olinordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_885,axiom,
    ( class_Groups_Osgn__if(Eq_y_0)
    | ~ class_Groups_Osgn__if(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_886,axiom,
    ( class_Rings_Olinordered__semiring__1__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__1__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_887,axiom,
    ( class_Groups_Oordered__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oordered__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_888,axiom,
    ( class_Rings_Oordered__cancel__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__cancel__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_889,axiom,
    ( class_Rings_Oordered__ring(Eq_y_0)
    | ~ class_Rings_Oordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_890,axiom,
    ( class_Rings_Oordered__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_891,axiom,
    ( class_Rings_Oordered__comm__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__comm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_892,axiom,
    ( class_Rings_Olinordered__semiring(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_893,axiom,
    ( class_Rings_Olinordered__semiring__1(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_894,axiom,
    ( c_Nat__Transfer_Otransfer__morphism(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Nat__Transfer_Otransfer__morphism(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_895,axiom,
    ( class_Lattices_Oboolean__algebra(Eq_y_0)
    | ~ class_Lattices_Oboolean__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_896,axiom,
    ( class_Divides_Osemiring__div(Eq_y_0)
    | ~ class_Divides_Osemiring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_897,axiom,
    ( class_Divides_Oring__div(Eq_y_0)
    | ~ class_Divides_Oring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_898,axiom,
    ( class_Lattices_Oab__semigroup__idem__mult(Eq_y_0)
    | ~ class_Lattices_Oab__semigroup__idem__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_899,axiom,
    ( class_Groups_Ouminus(Eq_y_0)
    | ~ class_Groups_Ouminus(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_900,axiom,
    ( class_Fields_Olinordered__field__inverse__zero(Eq_y_0)
    | ~ class_Fields_Olinordered__field__inverse__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_901,axiom,
    ( class_Groups_Ominus(Eq_y_0)
    | ~ class_Groups_Ominus(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_902,axiom,
    ( class_Fields_Olinordered__field(Eq_y_0)
    | ~ class_Fields_Olinordered__field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_903,axiom,
    ( class_Int_Onumber__ring(Eq_y_0)
    | ~ class_Int_Onumber__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_904,axiom,
    ( class_Int_Onumber(Eq_y_0)
    | ~ class_Int_Onumber(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_905,axiom,
    ( class_Groups_Oordered__ab__group__add__abs(Eq_y_0)
    | ~ class_Groups_Oordered__ab__group__add__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_906,axiom,
    ( class_Rings_Oordered__ring__abs(Eq_y_0)
    | ~ class_Rings_Oordered__ring__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_907,axiom,
    ( class_Groups_Oabs__if(Eq_y_0)
    | ~ class_Groups_Oabs__if(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_908,axiom,
    ( class_Power_Opower(Eq_y_0)
    | ~ class_Power_Opower(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_909,axiom,
    ( class_Rings_Osemiring__0(Eq_y_0)
    | ~ class_Rings_Osemiring__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_910,axiom,
    ( c_Int_Oiszero(Eq_y_0,Eq_y_1)
    | ~ c_Int_Oiszero(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_911,axiom,
    ( c_Nat__Transfer_Ois__nat(Eq_y_0)
    | ~ c_Nat__Transfer_Ois__nat(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_912,axiom,
    ( class_Rings_Odivision__ring(Eq_y_0)
    | ~ class_Rings_Odivision__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_913,axiom,
    ( class_Rings_Odivision__ring__inverse__zero(Eq_y_0)
    | ~ class_Rings_Odivision__ring__inverse__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_914,axiom,
    ( class_Fields_Ofield__inverse__zero(Eq_y_0)
    | ~ class_Fields_Ofield__inverse__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_915,axiom,
    ( class_Fields_Ofield(Eq_y_0)
    | ~ class_Fields_Ofield(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_916,axiom,
    ( class_Rings_Oinverse(Eq_y_0)
    | ~ class_Rings_Oinverse(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_917,axiom,
    ( c_Nitpick_Oless__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Nitpick_Oless__frac(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_918,axiom,
    ( c_Nitpick_Oless__eq__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Nitpick_Oless__eq__frac(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_919,axiom,
    ( class_Rings_Odvd(Eq_y_0)
    | ~ class_Rings_Odvd(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_920,axiom,
    ( class_Rings_Ocomm__ring(Eq_y_0)
    | ~ class_Rings_Ocomm__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_921,axiom,
    ( c_Orderings_Oorder_Ostrict__mono(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Orderings_Oorder_Ostrict__mono(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_922,axiom,
    ( c_Orderings_Oorder_Omono(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Orderings_Oorder_Omono(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_923,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_924,axiom,
    ( class_Orderings_Obot(Eq_y_0)
    | ~ class_Orderings_Obot(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_925,axiom,
    ( c_Nitpick_Ofold__graph_H(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Nitpick_Ofold__graph_H(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_926,axiom,
    ( c_Nitpick_Orefl_H(Eq_y_0,Eq_y_1)
    | ~ c_Nitpick_Orefl_H(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_927,axiom,
    ( c_FunDef_Oreduction__pair(Eq_y_0,Eq_y_1)
    | ~ c_FunDef_Oreduction__pair(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_928,axiom,
    ( class_Lattices_Obounded__lattice__bot(Eq_y_0)
    | ~ class_Lattices_Obounded__lattice__bot(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_929,axiom,
    ( class_Lattices_Olattice(Eq_y_0)
    | ~ class_Lattices_Olattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_930,axiom,
    ( class_Lattices_Osemilattice__sup(Eq_y_0)
    | ~ class_Lattices_Osemilattice__sup(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_931,axiom,
    ( c_Wellfounded_Omax__extp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Wellfounded_Omax__extp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_932,axiom,
    ( c_Hoare__Mirabelle_Ohoare__valids(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Hoare__Mirabelle_Ohoare__valids(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_933,axiom,
    ( c_Relation_Oirrefl(Eq_y_0,Eq_y_1)
    | ~ c_Relation_Oirrefl(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_934,axiom,
    ( c_Nat__Transfer_Onat__set(Eq_y_0)
    | ~ c_Nat__Transfer_Onat__set(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_935,axiom,
    ( c_Equiv__Relations_Oequiv(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Equiv__Relations_Oequiv(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_936,axiom,
    ( class_Finite__Set_Ofinite(Eq_y_0)
    | ~ class_Finite__Set_Ofinite(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_937,axiom,
    ( c_Finite__Set_Ofolding__one(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofolding__one(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_938,axiom,
    ( c_Finite__Set_Ofolding__image__simple(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Finite__Set_Ofolding__image__simple(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_939,axiom,
    ( class_Lattices_Osemilattice__inf(Eq_y_0)
    | ~ class_Lattices_Osemilattice__inf(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_940,axiom,
    ( class_Lattices_Odistrib__lattice(Eq_y_0)
    | ~ class_Lattices_Odistrib__lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_941,axiom,
    ( c_Equiv__Relations_Ocongruent2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Equiv__Relations_Ocongruent2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_942,axiom,
    ( class_Complete__Lattice_Ocomplete__lattice(Eq_y_0)
    | ~ class_Complete__Lattice_Ocomplete__lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_943,axiom,
    ( c_Equiv__Relations_Ocongruent(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Equiv__Relations_Ocongruent(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_944,axiom,
    ( c_Big__Operators_Ocomm__monoid__big(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Big__Operators_Ocomm__monoid__big(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_945,axiom,
    ( c_Fun_Oinj__on(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Fun_Oinj__on(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_946,axiom,
    ( c_Finite__Set_Ofolding__one__idem(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofolding__one__idem(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_947,axiom,
    ( class_Lattices_Obounded__lattice__top(Eq_y_0)
    | ~ class_Lattices_Obounded__lattice__top(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_948,axiom,
    ( class_Orderings_Otop(Eq_y_0)
    | ~ class_Orderings_Otop(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_949,axiom,
    ( c_Equiv__Relations_Oequivp(Eq_y_0,Eq_y_1)
    | ~ c_Equiv__Relations_Oequivp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_950,axiom,
    ( c_Typedef_Otype__definition(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Typedef_Otype__definition(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_951,axiom,
    ( c_Big__Operators_Osemilattice__big(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Big__Operators_Osemilattice__big(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_952,axiom,
    ( c_Relation_Orefl__on(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Relation_Orefl__on(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_953,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofun__left__comm__idem(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_954,axiom,
    ( class_Groups_Olinordered__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Olinordered__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_955,axiom,
    ( c_Predicate_Oreflp(Eq_y_0,Eq_y_1)
    | ~ c_Predicate_Oreflp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_956,axiom,
    ( c_Predicate_Opred__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ c_Predicate_Opred__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_957,axiom,
    ( c_Wellfounded_Owf(Eq_y_0,Eq_y_1)
    | ~ c_Wellfounded_Owf(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_958,axiom,
    ( class_Orderings_Owellorder(Eq_y_0)
    | ~ class_Orderings_Owellorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_959,axiom,
    ( c_Wellfounded_OwfP(Eq_y_0,Eq_y_1)
    | ~ c_Wellfounded_OwfP(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_960,axiom,
    ( c_Wellfounded_Oacyclic(Eq_y_0,Eq_y_1)
    | ~ c_Wellfounded_Oacyclic(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_961,axiom,
    ( c_Nitpick_Owf_H(Eq_y_0,Eq_y_1)
    | ~ c_Nitpick_Owf_H(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_962,axiom,
    ( c_Nitpick_Ounknown(Eq_y_0)
    | ~ c_Nitpick_Ounknown(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_963,axiom,
    ( c_Finite__Set_Ofolding(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Finite__Set_Ofolding(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_964,axiom,
    ( c_Finite__Set_Ofolding__image(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Finite__Set_Ofolding__image(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_965,axiom,
    ( c_Finite__Set_Ofolding__idem(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Finite__Set_Ofolding__idem(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_966,axiom,
    ( c_Finite__Set_Ofun__left__comm(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofun__left__comm(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_967,axiom,
    ( c_Relation_Osingle__valued(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Relation_Osingle__valued(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_968,axiom,
    ( c_Relation_Ototal__on(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Relation_Ototal__on(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_969,axiom,
    ( c_Finite__Set_Ofolding__image__simple__idem(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_970,axiom,
    ( class_Smallcheck_Osmall(Eq_y_0)
    | ~ class_Smallcheck_Osmall(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_971,axiom,
    ( c_List_Onat__list(Eq_y_0)
    | ~ c_List_Onat__list(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_972,axiom,
    ( c_List_Olistrelp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_List_Olistrelp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_973,axiom,
    ( class_Groups_Osemigroup__add(Eq_y_0)
    | ~ class_Groups_Osemigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_974,axiom,
    ( c_List_Olinorder__class_Osorted(Eq_y_0,Eq_y_1)
    | ~ c_List_Olinorder__class_Osorted(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_975,axiom,
    ( class_Lattices_Obounded__lattice(Eq_y_0)
    | ~ class_Lattices_Obounded__lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_976,axiom,
    ( v_P(Eq_y_0,Eq_y_1)
    | ~ v_P(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_977,axiom,
    ( v_Q(Eq_y_0,Eq_y_1)
    | ~ v_Q(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_978,axiom,
    ( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_979,axiom,
    ( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_980,axiom,
    ( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_981,axiom,
    ( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_982,axiom,
    ( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_983,axiom,
    ( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_984,axiom,
    ( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_985,axiom,
    ( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_986,axiom,
    ( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_987,axiom,
    ( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_988,axiom,
    ( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_989,axiom,
    ( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_990,axiom,
    ( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_991,axiom,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_992,axiom,
    ( sP14(Eq_y_0,Eq_y_1)
    | ~ sP14(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_993,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_994,axiom,
    ( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_995,axiom,
    ( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_996,axiom,
    ( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_997,axiom,
    ( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_998,axiom,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_999,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1000,axiom,
    ( sP22(Eq_y_0,Eq_y_1)
    | ~ sP22(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1001,axiom,
    ( sP23(Eq_y_0,Eq_y_1)
    | ~ sP23(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1002,axiom,
    ( sP24(Eq_y_0,Eq_y_1)
    | ~ sP24(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1003,axiom,
    ( sP25(Eq_y_0,Eq_y_1)
    | ~ sP25(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1004,axiom,
    ( sP26(Eq_y_0,Eq_y_1)
    | ~ sP26(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1005,axiom,
    ( sP27(Eq_y_0,Eq_y_1)
    | ~ sP27(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1006,axiom,
    ( sP28(Eq_y_0,Eq_y_1)
    | ~ sP28(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1007,axiom,
    ( sP29(Eq_y_0,Eq_y_1)
    | ~ sP29(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1008,axiom,
    ( sP30(Eq_y_0,Eq_y_1)
    | ~ sP30(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1009,axiom,
    ( sP31(Eq_y_0,Eq_y_1)
    | ~ sP31(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1010,axiom,
    ( sP32(Eq_y_0,Eq_y_1)
    | ~ sP32(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1011,axiom,
    ( sP33(Eq_y_0,Eq_y_1)
    | ~ sP33(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1012,axiom,
    ( sP34(Eq_y_0,Eq_y_1)
    | ~ sP34(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1013,axiom,
    ( sP35(Eq_y_0,Eq_y_1)
    | ~ sP35(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1014,axiom,
    ( sP36(Eq_y_0,Eq_y_1)
    | ~ sP36(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1015,axiom,
    ( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1016,axiom,
    ( sP38(Eq_y_0,Eq_y_1)
    | ~ sP38(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1017,axiom,
    ( sP39(Eq_y_0,Eq_y_1)
    | ~ sP39(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1018,axiom,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1019,axiom,
    ( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1020,axiom,
    ( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1021,axiom,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1022,axiom,
    ( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1023,axiom,
    ( sP45(Eq_y_0,Eq_y_1)
    | ~ sP45(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1024,axiom,
    ( sP46(Eq_y_0,Eq_y_1)
    | ~ sP46(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1025,axiom,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1026,axiom,
    ( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1027,axiom,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1028,axiom,
    ( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1029,axiom,
    ( sP51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1030,axiom,
    ( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1031,axiom,
    ( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1032,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1033,axiom,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1034,axiom,
    ( sP56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1035,axiom,
    ( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1036,axiom,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1037,axiom,
    ( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1038,axiom,
    ( sP60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1039,axiom,
    ( sP61(Eq_y_0,Eq_y_1)
    | ~ sP61(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1040,axiom,
    ( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1041,axiom,
    ( sP63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1042,axiom,
    ( sP64(Eq_y_0,Eq_y_1)
    | ~ sP64(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1043,axiom,
    ( sP65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1044,axiom,
    ( sP66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1045,axiom,
    ( sP67(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1046,axiom,
    ( sP68(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1047,axiom,
    ( sP69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1048,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1049,axiom,
    ( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1050,axiom,
    ( sP72(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1051,axiom,
    ( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1052,axiom,
    ( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1053,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1054,axiom,
    ( sP76(Eq_y_0,Eq_y_1)
    | ~ sP76(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1055,axiom,
    ( sP77(Eq_y_0,Eq_y_1)
    | ~ sP77(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1056,axiom,
    ( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1057,axiom,
    ( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1058,axiom,
    ( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1059,axiom,
    ( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1060,axiom,
    ( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1061,axiom,
    ( sP83(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1062,axiom,
    ( sP84(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1063,axiom,
    ( sP85(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1064,axiom,
    ( sP86(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1065,axiom,
    ( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1066,axiom,
    ( sP88(Eq_y_0)
    | ~ sP88(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1067,axiom,
    ( sP89(Eq_y_0,Eq_y_1)
    | ~ sP89(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1068,axiom,
    ( sP90(Eq_y_0,Eq_y_1)
    | ~ sP90(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1069,axiom,
    ( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1070,axiom,
    ( sP92(Eq_y_0,Eq_y_1)
    | ~ sP92(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1071,axiom,
    ( sP93(Eq_y_0,Eq_y_1)
    | ~ sP93(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1072,axiom,
    ( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1073,axiom,
    ( sP95(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1074,axiom,
    ( sP96(Eq_y_0,Eq_y_1)
    | ~ sP96(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1075,axiom,
    ( sP97(Eq_y_0,Eq_y_1)
    | ~ sP97(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1076,axiom,
    ( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1077,axiom,
    ( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1078,axiom,
    ( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1079,axiom,
    ( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1080,axiom,
    ( sP102(Eq_y_0,Eq_y_1)
    | ~ sP102(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1081,axiom,
    ( sP103(Eq_y_0,Eq_y_1)
    | ~ sP103(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1082,axiom,
    ( sP104(Eq_y_0,Eq_y_1)
    | ~ sP104(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1083,axiom,
    ( sP105(Eq_y_0,Eq_y_1)
    | ~ sP105(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1084,axiom,
    ( sP106(Eq_y_0,Eq_y_1)
    | ~ sP106(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1085,axiom,
    ( sP107(Eq_y_0,Eq_y_1)
    | ~ sP107(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1086,axiom,
    ( sP108(Eq_y_0,Eq_y_1)
    | ~ sP108(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1087,axiom,
    ( sP109(Eq_y_0,Eq_y_1)
    | ~ sP109(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1088,axiom,
    ( sP110(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1089,axiom,
    ( sP111(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1090,axiom,
    ( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1091,axiom,
    ( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1092,axiom,
    ( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1093,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1094,axiom,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1095,axiom,
    ( sP117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1096,axiom,
    ( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1097,axiom,
    ( sP119(Eq_y_0,Eq_y_1)
    | ~ sP119(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1098,axiom,
    ( sP120(Eq_y_0,Eq_y_1)
    | ~ sP120(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1099,axiom,
    ( sP121(Eq_y_0,Eq_y_1)
    | ~ sP121(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1100,axiom,
    ( sP122(Eq_y_0,Eq_y_1)
    | ~ sP122(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1101,axiom,
    ( sP123(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1102,axiom,
    ( sP124(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1103,axiom,
    ( sP125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1104,axiom,
    ( sP126(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1105,axiom,
    ( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1106,axiom,
    ( sP128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1107,axiom,
    ( sP129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1108,axiom,
    ( sP130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1109,axiom,
    ( sP131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1110,axiom,
    ( sP132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1111,axiom,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1112,axiom,
    ( sP134(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1113,axiom,
    ( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1114,axiom,
    ( sP136(Eq_y_0,Eq_y_1)
    | ~ sP136(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1115,axiom,
    ( sP137(Eq_y_0,Eq_y_1)
    | ~ sP137(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1116,axiom,
    ( sP138(Eq_y_0,Eq_y_1)
    | ~ sP138(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1117,axiom,
    ( sP139(Eq_y_0,Eq_y_1)
    | ~ sP139(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1118,axiom,
    ( sP140(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP140(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1119,axiom,
    ( sP141(Eq_y_0,Eq_y_1)
    | ~ sP141(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1120,axiom,
    ( sP142(Eq_y_0,Eq_y_1)
    | ~ sP142(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1121,axiom,
    ( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1122,axiom,
    ( sP144(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1123,axiom,
    ( sP145(Eq_y_0,Eq_y_1)
    | ~ sP145(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1124,axiom,
    ( sP146(Eq_y_0,Eq_y_1)
    | ~ sP146(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1125,axiom,
    ( sP147(Eq_y_0,Eq_y_1)
    | ~ sP147(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1126,axiom,
    ( sP148(Eq_y_0)
    | ~ sP148(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1127,axiom,
    ( sP149(Eq_y_0,Eq_y_1)
    | ~ sP149(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1128,axiom,
    ( sP150(Eq_y_0,Eq_y_1)
    | ~ sP150(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1129,axiom,
    ( sP151(Eq_y_0,Eq_y_1)
    | ~ sP151(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1130,axiom,
    ( sP152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1131,axiom,
    ( sP153(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1132,axiom,
    ( sP154(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1133,axiom,
    ( sP155(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1134,axiom,
    ( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP156(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1135,axiom,
    ( sP157(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1136,axiom,
    ( sP158(Eq_y_0,Eq_y_1)
    | ~ sP158(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1137,axiom,
    ( sP159(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP159(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1138,axiom,
    ( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1139,axiom,
    ( sP161(Eq_y_0,Eq_y_1)
    | ~ sP161(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1140,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1141,axiom,
    ( sP163(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP163(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1142,axiom,
    ( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP164(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1143,axiom,
    ( sP165(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP165(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1144,axiom,
    ( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP166(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1145,axiom,
    ( sP167(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP167(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1146,axiom,
    ( sP168(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP168(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1147,axiom,
    ( sP169(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP169(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1148,axiom,
    ( sP170(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP170(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1149,axiom,
    ( sP171(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP171(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1150,axiom,
    ( sP172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1151,axiom,
    ( sP173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1152,axiom,
    ( sP174(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP174(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1153,axiom,
    ( sP175(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP175(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1154,axiom,
    ( sP176(Eq_y_0,Eq_y_1)
    | ~ sP176(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1155,axiom,
    ( sP177(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP177(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1156,axiom,
    ( sP178(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP178(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1157,axiom,
    ( sP179(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP179(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1158,axiom,
    ( sP180(Eq_y_0,Eq_y_1)
    | ~ sP180(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1159,axiom,
    ( sP181(Eq_y_0,Eq_y_1)
    | ~ sP181(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1160,axiom,
    ( sP182(Eq_y_0,Eq_y_1)
    | ~ sP182(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1161,axiom,
    ( sP183(Eq_y_0,Eq_y_1)
    | ~ sP183(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1162,axiom,
    ( sP184(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP184(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1163,axiom,
    ( sP185(Eq_y_0,Eq_y_1)
    | ~ sP185(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1164,axiom,
    ( sP186(Eq_y_0,Eq_y_1)
    | ~ sP186(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1165,axiom,
    ( sP187(Eq_y_0,Eq_y_1)
    | ~ sP187(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1166,axiom,
    ( sP188(Eq_y_0,Eq_y_1)
    | ~ sP188(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1167,axiom,
    ( sP189(Eq_y_0,Eq_y_1)
    | ~ sP189(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1168,axiom,
    ( sP190(Eq_y_0,Eq_y_1)
    | ~ sP190(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1169,axiom,
    ( sP191(Eq_y_0,Eq_y_1)
    | ~ sP191(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1170,axiom,
    ( sP192(Eq_y_0,Eq_y_1)
    | ~ sP192(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1171,axiom,
    ( sP193(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP193(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1172,axiom,
    ( sP194(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP194(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1173,axiom,
    ( sP195(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP195(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1174,axiom,
    ( sP196(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP196(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1175,axiom,
    ( sP197(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP197(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1176,axiom,
    ( sP198(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP198(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1177,axiom,
    ( sP199(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP199(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1178,axiom,
    ( sP200(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1179,axiom,
    ( sP201(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP201(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1180,axiom,
    ( sP202(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP202(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1181,axiom,
    ( sP203(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP203(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1182,axiom,
    ( sP204(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP204(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1183,axiom,
    ( sP205(Eq_y_0,Eq_y_1)
    | ~ sP205(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1184,axiom,
    ( sP206(Eq_y_0,Eq_y_1)
    | ~ sP206(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1185,axiom,
    ( sP207(Eq_y_0,Eq_y_1)
    | ~ sP207(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1186,axiom,
    ( sP208(Eq_y_0,Eq_y_1)
    | ~ sP208(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1187,axiom,
    ( sP209(Eq_y_0,Eq_y_1)
    | ~ sP209(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1188,axiom,
    ( sP210(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP210(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1189,axiom,
    ( sP211(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1190,axiom,
    ( sP212(Eq_y_0,Eq_y_1)
    | ~ sP212(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1191,axiom,
    ( sP213(Eq_y_0,Eq_y_1)
    | ~ sP213(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1192,axiom,
    ( sP214(Eq_y_0)
    | ~ sP214(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1193,axiom,
    ( sP215(Eq_y_0)
    | ~ sP215(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1194,axiom,
    ( sP216(Eq_y_0,Eq_y_1)
    | ~ sP216(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1195,axiom,
    ( sP217(Eq_y_0)
    | ~ sP217(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1196,axiom,
    ( sP218(Eq_y_0)
    | ~ sP218(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1197,axiom,
    ( sP219(Eq_y_0,Eq_y_1)
    | ~ sP219(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1198,axiom,
    ( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1199,axiom,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1200,axiom,
    ( sP222(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1201,axiom,
    ( sP223(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1202,axiom,
    ( sP224(Eq_y_0,Eq_y_1)
    | ~ sP224(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1203,axiom,
    ( sP225(Eq_y_0,Eq_y_1)
    | ~ sP225(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1204,axiom,
    ( sP226(Eq_y_0,Eq_y_1)
    | ~ sP226(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1205,axiom,
    ( sP227(Eq_y_0,Eq_y_1)
    | ~ sP227(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1206,axiom,
    ( sP228(Eq_y_0,Eq_y_1)
    | ~ sP228(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1207,axiom,
    ( sP229(Eq_y_0,Eq_y_1)
    | ~ sP229(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1208,axiom,
    ( sP230(Eq_y_0,Eq_y_1)
    | ~ sP230(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1209,axiom,
    ( sP231(Eq_y_0,Eq_y_1)
    | ~ sP231(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1210,axiom,
    ( sP232(Eq_y_0,Eq_y_1)
    | ~ sP232(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1211,axiom,
    ( sP233(Eq_y_0,Eq_y_1)
    | ~ sP233(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1212,axiom,
    ( sP234(Eq_y_0,Eq_y_1)
    | ~ sP234(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1213,axiom,
    ( sP235(Eq_y_0,Eq_y_1)
    | ~ sP235(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1214,axiom,
    ( sP236(Eq_y_0,Eq_y_1)
    | ~ sP236(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1215,axiom,
    ( sP237(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1216,axiom,
    ( sP238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1217,axiom,
    ( sP239(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1218,axiom,
    ( sP240(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP240(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1219,axiom,
    ( sP241(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP241(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1220,axiom,
    ( sP242(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP242(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1221,axiom,
    ( sP243(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP243(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1222,axiom,
    ( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1223,axiom,
    ( sP245(Eq_y_0,Eq_y_1)
    | ~ sP245(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1224,axiom,
    ( sP246(Eq_y_0,Eq_y_1)
    | ~ sP246(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1225,axiom,
    ( sP247(Eq_y_0,Eq_y_1)
    | ~ sP247(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1226,axiom,
    ( sP248(Eq_y_0,Eq_y_1)
    | ~ sP248(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1227,axiom,
    ( sP249(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP249(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1228,axiom,
    ( sP250(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP250(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1229,axiom,
    ( sP251(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP251(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1230,axiom,
    ( sP252(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP252(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1231,axiom,
    ( sP253(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP253(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1232,axiom,
    ( sP254(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP254(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1233,axiom,
    ( sP255(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1234,axiom,
    ( sP256(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP256(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1235,axiom,
    ( sP257(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP257(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1236,axiom,
    ( sP258(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1237,axiom,
    ( sP259(Eq_y_0,Eq_y_1)
    | ~ sP259(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1238,axiom,
    ( sP260(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP260(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1239,axiom,
    ( sP261(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP261(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1240,axiom,
    ( sP262(Eq_y_0,Eq_y_1)
    | ~ sP262(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1241,axiom,
    ( sP263(Eq_y_0,Eq_y_1)
    | ~ sP263(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1242,axiom,
    ( sP264(Eq_y_0,Eq_y_1)
    | ~ sP264(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1243,axiom,
    ( sP265(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP265(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1244,axiom,
    ( sP266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1245,axiom,
    ( sP267(Eq_y_0,Eq_y_1)
    | ~ sP267(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1246,axiom,
    ( sP268(Eq_y_0,Eq_y_1)
    | ~ sP268(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1247,axiom,
    ( sP269(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1248,axiom,
    ( sP270(Eq_y_0,Eq_y_1)
    | ~ sP270(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1249,axiom,
    ( sP271(Eq_y_0,Eq_y_1)
    | ~ sP271(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1250,axiom,
    ( sP272(Eq_y_0,Eq_y_1)
    | ~ sP272(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1251,axiom,
    ( sP273(Eq_y_0,Eq_y_1)
    | ~ sP273(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1252,axiom,
    ( sP274(Eq_y_0,Eq_y_1)
    | ~ sP274(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1253,axiom,
    ( sP275(Eq_y_0,Eq_y_1)
    | ~ sP275(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1254,axiom,
    ( sP276(Eq_y_0,Eq_y_1)
    | ~ sP276(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1255,axiom,
    ( sP277(Eq_y_0,Eq_y_1)
    | ~ sP277(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1256,axiom,
    ( sP278(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1257,axiom,
    ( sP279(Eq_y_0,Eq_y_1)
    | ~ sP279(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1258,axiom,
    ( sP280(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP280(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1259,axiom,
    ( sP281(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP281(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1260,axiom,
    ( sP282(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP282(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1261,axiom,
    ( sP283(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP283(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1262,axiom,
    ( sP284(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP284(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1263,axiom,
    ( sP285(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP285(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1264,axiom,
    ( sP286(Eq_y_0,Eq_y_1)
    | ~ sP286(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1265,axiom,
    ( sP287(Eq_y_0,Eq_y_1)
    | ~ sP287(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1266,axiom,
    ( sP288(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP288(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1267,axiom,
    ( sP289(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP289(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1268,axiom,
    ( sP290(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP290(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1269,axiom,
    ( sP291(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1270,axiom,
    ( sP292(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP292(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1271,axiom,
    ( sP293(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP293(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1272,axiom,
    ( sP294(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP294(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1273,axiom,
    ( sP295(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP295(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1274,axiom,
    ( sP296(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP296(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1275,axiom,
    ( sP297(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP297(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1276,axiom,
    ( sP298(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1277,axiom,
    ( sP299(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP299(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1278,axiom,
    ( sP300(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP300(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1279,axiom,
    ( sP301(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP301(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1280,axiom,
    ( sP302(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1281,axiom,
    ( sP303(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1282,axiom,
    ( sP304(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP304(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1283,axiom,
    ( sP305(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP305(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1284,axiom,
    ( sP306(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1285,axiom,
    ( sP307(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1286,axiom,
    ( sP308(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1287,axiom,
    ( sP309(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1288,axiom,
    ( sP310(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP310(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1289,axiom,
    ( sP311(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP311(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1290,axiom,
    ( sP312(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP312(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1291,axiom,
    ( sP313(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP313(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1292,axiom,
    ( sP314(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP314(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1293,axiom,
    ( sP315(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP315(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1294,axiom,
    ( sP316(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP316(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1295,axiom,
    ( sP317(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP317(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1296,axiom,
    ( sP318(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP318(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1297,axiom,
    ( sP319(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP319(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1298,axiom,
    ( sP320(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP320(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1299,axiom,
    ( sP321(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP321(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1300,axiom,
    ( sP322(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP322(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1301,axiom,
    ( sP323(Eq_y_0,Eq_y_1)
    | ~ sP323(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1302,axiom,
    ( sP324(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP324(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1303,axiom,
    ( sP325(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP325(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1304,axiom,
    ( sP326(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP326(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1305,axiom,
    ( sP327(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP327(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1306,axiom,
    ( sP328(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP328(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1307,axiom,
    ( sP329(Eq_y_0,Eq_y_1)
    | ~ sP329(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1308,axiom,
    ( sP330(Eq_y_0,Eq_y_1)
    | ~ sP330(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1309,axiom,
    ( sP331(Eq_y_0,Eq_y_1)
    | ~ sP331(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1310,axiom,
    ( sP332(Eq_y_0,Eq_y_1)
    | ~ sP332(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1311,axiom,
    ( sP333(Eq_y_0,Eq_y_1)
    | ~ sP333(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1312,axiom,
    ( sP334(Eq_y_0,Eq_y_1)
    | ~ sP334(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1313,axiom,
    ( sP335(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP335(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1314,axiom,
    ( sP336(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP336(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1315,axiom,
    ( sP337(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP337(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1316,axiom,
    ( sP338(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP338(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1317,axiom,
    ( sP339(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP339(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1318,axiom,
    ( sP340(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP340(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1319,axiom,
    ( sP341(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP341(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1320,axiom,
    ( sP342(Eq_y_0,Eq_y_1)
    | ~ sP342(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1321,axiom,
    ( sP343(Eq_y_0,Eq_y_1)
    | ~ sP343(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1322,axiom,
    ( sP344(Eq_y_0,Eq_y_1)
    | ~ sP344(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1323,axiom,
    ( sP345(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP345(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1324,axiom,
    ( sP346(Eq_y_0,Eq_y_1)
    | ~ sP346(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1325,axiom,
    ( sP347(Eq_y_0,Eq_y_1)
    | ~ sP347(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1326,axiom,
    ( sP348(Eq_y_0,Eq_y_1)
    | ~ sP348(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1327,axiom,
    ( sP349(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP349(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1328,axiom,
    ( sP350(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP350(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1329,axiom,
    ( sP351(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP351(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1330,axiom,
    ( sP352(Eq_y_0,Eq_y_1)
    | ~ sP352(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1331,axiom,
    ( sP353(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP353(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1332,axiom,
    ( sP354(Eq_y_0,Eq_y_1)
    | ~ sP354(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1333,axiom,
    ( sP355(Eq_y_0,Eq_y_1)
    | ~ sP355(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1334,axiom,
    ( sP356(Eq_y_0,Eq_y_1)
    | ~ sP356(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1335,axiom,
    ( sP357(Eq_y_0,Eq_y_1)
    | ~ sP357(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1336,axiom,
    ( sP358(Eq_y_0,Eq_y_1)
    | ~ sP358(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1337,axiom,
    ( sP359(Eq_y_0,Eq_y_1)
    | ~ sP359(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1338,axiom,
    ( sP360(Eq_y_0,Eq_y_1)
    | ~ sP360(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1339,axiom,
    ( sP361(Eq_y_0,Eq_y_1)
    | ~ sP361(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1340,axiom,
    ( sP362(Eq_y_0,Eq_y_1)
    | ~ sP362(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1341,axiom,
    ( sP363(Eq_y_0,Eq_y_1)
    | ~ sP363(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1342,axiom,
    ( sP364(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP364(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1343,axiom,
    ( sP365(Eq_y_0,Eq_y_1)
    | ~ sP365(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1344,axiom,
    ( sP366(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP366(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1345,axiom,
    ( sP367(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP367(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1346,axiom,
    ( sP368(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP368(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1347,axiom,
    ( sP369(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP369(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1348,axiom,
    ( sP370(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP370(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1349,axiom,
    ( sP371(Eq_y_0,Eq_y_1)
    | ~ sP371(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1350,axiom,
    ( sP372(Eq_y_0,Eq_y_1)
    | ~ sP372(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1351,axiom,
    ( sP373(Eq_y_0,Eq_y_1)
    | ~ sP373(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1352,axiom,
    ( sP374(Eq_y_0,Eq_y_1)
    | ~ sP374(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1353,axiom,
    ( sP375(Eq_y_0,Eq_y_1)
    | ~ sP375(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1354,axiom,
    ( sP376(Eq_y_0,Eq_y_1)
    | ~ sP376(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1355,axiom,
    ( sP377(Eq_y_0,Eq_y_1)
    | ~ sP377(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1356,axiom,
    ( sP378(Eq_y_0,Eq_y_1)
    | ~ sP378(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1357,axiom,
    ( sP379(Eq_y_0,Eq_y_1)
    | ~ sP379(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1358,axiom,
    ( sP380(Eq_y_0,Eq_y_1)
    | ~ sP380(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1359,axiom,
    ( sP381(Eq_y_0,Eq_y_1)
    | ~ sP381(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1360,axiom,
    ( sP382(Eq_y_0,Eq_y_1)
    | ~ sP382(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1361,axiom,
    ( sP383(Eq_y_0,Eq_y_1)
    | ~ sP383(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1362,axiom,
    ( sP384(Eq_y_0,Eq_y_1)
    | ~ sP384(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1363,axiom,
    ( sP385(Eq_y_0,Eq_y_1)
    | ~ sP385(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1364,axiom,
    ( sP386(Eq_y_0,Eq_y_1)
    | ~ sP386(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1365,axiom,
    ( sP387(Eq_y_0,Eq_y_1)
    | ~ sP387(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1366,axiom,
    ( sP388(Eq_y_0,Eq_y_1)
    | ~ sP388(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1367,axiom,
    ( sP389(Eq_y_0)
    | ~ sP389(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1368,axiom,
    ( sP390(Eq_y_0,Eq_y_1)
    | ~ sP390(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1369,axiom,
    ( sP391(Eq_y_0,Eq_y_1)
    | ~ sP391(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1370,axiom,
    ( sP392(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP392(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1371,axiom,
    ( sP393(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP393(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1372,axiom,
    ( sP394(Eq_y_0,Eq_y_1)
    | ~ sP394(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1373,axiom,
    ( sP395(Eq_y_0,Eq_y_1)
    | ~ sP395(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1374,axiom,
    ( sP396(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP396(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1375,axiom,
    ( sP397(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP397(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1376,axiom,
    ( sP398(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP398(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1377,axiom,
    ( sP399(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP399(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1378,axiom,
    ( sP400(Eq_y_0)
    | ~ sP400(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1379,axiom,
    ( sP401(Eq_y_0,Eq_y_1)
    | ~ sP401(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1380,axiom,
    ( sP402(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP402(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1381,axiom,
    ( sP403(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP403(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1382,axiom,
    ( sP404(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP404(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1383,axiom,
    ( sP405(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP405(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1384,axiom,
    ( sP406(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP406(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1385,axiom,
    ( sP407(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP407(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1386,axiom,
    ( sP408(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP408(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1387,axiom,
    ( sP409(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP409(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1388,axiom,
    ( sP410(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP410(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1389,axiom,
    ( sP411(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP411(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1390,axiom,
    ( sP412(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP412(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1391,axiom,
    ( sP413(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP413(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1392,axiom,
    ( sP414(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP414(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1393,axiom,
    ( sP415(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP415(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1394,axiom,
    ( sP416(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP416(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1395,axiom,
    ( sP417(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP417(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1396,axiom,
    ( sP418(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP418(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1397,axiom,
    ( sP419(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP419(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1398,axiom,
    ( sP420(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP420(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1399,axiom,
    ( sP421(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP421(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1400,axiom,
    ( sP422(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP422(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1401,axiom,
    ( sP423(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP423(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1402,axiom,
    ( sP424(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP424(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1403,axiom,
    ( sP425(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP425(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1404,axiom,
    ( sP426(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP426(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1405,axiom,
    ( sP427(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP427(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1406,axiom,
    ( sP428(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP428(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1407,axiom,
    ( sP429(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP429(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1408,axiom,
    ( sP430(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP430(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1409,axiom,
    ( sP431(Eq_y_0,Eq_y_1)
    | ~ sP431(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1410,axiom,
    ( sP432(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP432(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1411,axiom,
    ( sP433(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP433(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1412,axiom,
    ( sP434(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP434(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1413,axiom,
    ( sP435(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP435(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1414,axiom,
    ( sP436(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP436(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1415,axiom,
    ( sP437(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP437(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1416,axiom,
    ( sP438(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP438(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1417,axiom,
    ( sP439(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP439(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1418,axiom,
    ( sP440(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1419,axiom,
    ( sP441(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP441(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1420,axiom,
    ( sP442(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP442(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1421,axiom,
    ( sP443(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP443(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1422,axiom,
    ( sP444(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP444(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1423,axiom,
    ( sP445(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP445(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1424,axiom,
    ( sP446(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP446(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1425,axiom,
    ( sP447(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP447(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1426,axiom,
    ( sP448(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP448(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1427,axiom,
    ( sP449(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP449(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1428,axiom,
    ( sP450(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP450(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1429,axiom,
    ( sP451(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP451(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1430,axiom,
    ( sP452(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP452(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1431,axiom,
    ( sP453(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP453(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1432,axiom,
    ( sP454(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP454(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1433,axiom,
    ( sP455(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP455(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1434,axiom,
    ( sP456(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP456(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1435,axiom,
    ( sP457(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP457(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1436,axiom,
    ( sP458(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP458(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1437,axiom,
    ( sP459(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP459(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1438,axiom,
    ( sP460(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP460(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1439,axiom,
    ( sP461(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP461(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1440,axiom,
    ( sP462(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP462(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1441,axiom,
    ( sP463(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP463(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1442,axiom,
    ( sP464(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP464(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1443,axiom,
    ( sP465(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP465(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1444,axiom,
    ( sP466(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP466(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1445,axiom,
    ( sP467(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP467(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1446,axiom,
    ( sP468(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP468(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1447,axiom,
    ( sP469(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP469(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1448,axiom,
    ( sP470(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP470(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1449,axiom,
    ( sP471(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP471(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1450,axiom,
    ( sP472(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP472(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1451,axiom,
    ( sP473(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1452,axiom,
    ( sP474(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP474(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1453,axiom,
    ( sP475(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP475(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1454,axiom,
    ( sP476(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1455,axiom,
    ( sP477(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP477(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1456,axiom,
    ( sP478(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP478(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1457,axiom,
    ( sP479(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP479(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1458,axiom,
    ( sP480(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP480(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1459,axiom,
    ( sP481(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP481(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1460,axiom,
    ( sP482(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP482(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1461,axiom,
    ( sP483(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP483(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1462,axiom,
    ( sP484(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP484(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1463,axiom,
    ( sP485(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP485(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1464,axiom,
    ( sP486(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP486(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1465,axiom,
    ( sP487(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP487(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1466,axiom,
    ( sP488(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP488(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1467,axiom,
    ( sP489(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP489(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1468,axiom,
    ( sP490(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP490(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1469,axiom,
    ( sP491(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP491(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1470,axiom,
    ( sP492(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP492(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1471,axiom,
    ( sP493(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP493(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1472,axiom,
    ( sP494(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP494(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1473,axiom,
    ( sP495(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP495(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1474,axiom,
    ( sP496(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP496(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1475,axiom,
    ( sP497(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP497(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1476,axiom,
    ( sP498(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP498(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1477,axiom,
    ( sP499(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP499(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1478,axiom,
    ( sP500(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP500(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1479,axiom,
    ( sP501(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP501(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1480,axiom,
    ( sP502(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP502(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1481,axiom,
    ( sP503(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP503(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1482,axiom,
    ( sP504(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP504(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1483,axiom,
    ( sP505(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP505(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1484,axiom,
    ( sP506(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP506(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1485,axiom,
    ( sP507(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP507(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1486,axiom,
    ( sP508(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP508(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1487,axiom,
    ( sP509(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP509(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1488,axiom,
    ( sP510(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP510(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1489,axiom,
    ( sP511(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP511(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1490,axiom,
    ( sP512(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP512(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1491,axiom,
    ( sP513(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP513(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1492,axiom,
    ( sP514(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP514(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1493,axiom,
    ( sP515(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP515(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1494,axiom,
    ( sP516(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP516(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1495,axiom,
    ( sP517(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP517(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1496,axiom,
    ( sP518(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP518(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1497,axiom,
    ( sP519(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP519(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1498,axiom,
    ( sP520(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP520(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1499,axiom,
    ( sP521(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP521(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1500,axiom,
    ( sP522(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP522(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1501,axiom,
    ( sP523(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP523(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1502,axiom,
    ( sP524(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP524(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1503,axiom,
    ( sP525(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP525(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1504,axiom,
    ( sP526(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP526(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1505,axiom,
    ( sP527(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP527(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1506,axiom,
    ( sP528(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP528(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1507,axiom,
    ( sP529(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP529(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1508,axiom,
    ( sP530(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP530(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1509,axiom,
    ( sP531(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP531(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1510,axiom,
    ( sP532(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP532(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1511,axiom,
    ( sP533(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP533(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1512,axiom,
    ( sP534(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP534(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1513,axiom,
    ( sP535(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP535(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1514,axiom,
    ( sP536(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP536(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1515,axiom,
    ( sP537(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP537(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1516,axiom,
    ( sP538(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP538(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1517,axiom,
    ( sP539(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP539(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1518,axiom,
    ( sP540(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP540(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1519,axiom,
    ( sP541(Eq_y_0,Eq_y_1)
    | ~ sP541(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1520,axiom,
    ( sP542(Eq_y_0)
    | ~ sP542(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1521,axiom,
    ( sP543(Eq_y_0,Eq_y_1)
    | ~ sP543(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1522,axiom,
    ( sP544(Eq_y_0,Eq_y_1)
    | ~ sP544(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1523,axiom,
    ( sP545(Eq_y_0,Eq_y_1)
    | ~ sP545(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1524,axiom,
    ( sP546(Eq_y_0)
    | ~ sP546(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1525,axiom,
    ( sP547(Eq_y_0,Eq_y_1)
    | ~ sP547(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1526,axiom,
    ( sP548(Eq_y_0,Eq_y_1)
    | ~ sP548(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1527,axiom,
    ( sP549(Eq_y_0,Eq_y_1)
    | ~ sP549(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1528,axiom,
    ( sP550(Eq_y_0,Eq_y_1)
    | ~ sP550(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1529,axiom,
    ( sP551(Eq_y_0,Eq_y_1)
    | ~ sP551(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1530,axiom,
    ( sP552(Eq_y_0,Eq_y_1)
    | ~ sP552(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1531,axiom,
    ( sP553(Eq_y_0,Eq_y_1)
    | ~ sP553(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1532,axiom,
    ( sP554(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP554(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1533,axiom,
    ( sP555(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP555(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1534,axiom,
    ( sP556(Eq_y_0,Eq_y_1)
    | ~ sP556(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1535,axiom,
    ( sP557(Eq_y_0,Eq_y_1)
    | ~ sP557(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1536,axiom,
    ( sP558(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP558(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1537,axiom,
    ( sP559(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP559(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1538,axiom,
    ( sP560(Eq_y_0,Eq_y_1)
    | ~ sP560(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1539,axiom,
    ( sP561(Eq_y_0,Eq_y_1)
    | ~ sP561(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1540,axiom,
    ( sP562(Eq_y_0,Eq_y_1)
    | ~ sP562(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1541,axiom,
    ( sP563(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP563(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1542,axiom,
    ( sP564(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP564(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1543,axiom,
    ( sP565(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP565(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1544,axiom,
    ( sP566(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP566(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1545,axiom,
    ( sP567(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP567(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1546,axiom,
    ( sP568(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP568(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1547,axiom,
    ( sP569(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP569(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1548,axiom,
    ( sP570(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP570(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1549,axiom,
    ( sP571(Eq_y_0,Eq_y_1)
    | ~ sP571(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1550,axiom,
    ( sP572(Eq_y_0,Eq_y_1)
    | ~ sP572(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1551,axiom,
    ( sP573(Eq_y_0,Eq_y_1)
    | ~ sP573(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1552,axiom,
    ( sP574(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP574(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1553,axiom,
    ( sP575(Eq_y_0,Eq_y_1)
    | ~ sP575(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1554,axiom,
    ( sP576(Eq_y_0,Eq_y_1)
    | ~ sP576(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1555,axiom,
    ( sP577(Eq_y_0,Eq_y_1)
    | ~ sP577(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1556,axiom,
    ( sP578(Eq_y_0,Eq_y_1)
    | ~ sP578(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1557,axiom,
    ( sP579(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP579(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1558,axiom,
    ( sP580(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP580(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1559,axiom,
    ( sP581(Eq_y_0,Eq_y_1)
    | ~ sP581(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1560,axiom,
    ( sP582(Eq_y_0,Eq_y_1)
    | ~ sP582(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1561,axiom,
    ( sP583(Eq_y_0,Eq_y_1)
    | ~ sP583(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1562,axiom,
    ( sP584(Eq_y_0,Eq_y_1)
    | ~ sP584(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1563,axiom,
    ( sP585(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP585(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1564,axiom,
    ( sP586(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP586(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1565,axiom,
    ( sP587(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP587(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1566,axiom,
    ( sP588(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP588(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1567,axiom,
    ( sP589(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP589(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1568,axiom,
    ( sP590(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP590(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1569,axiom,
    ( sP591(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP591(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1570,axiom,
    ( sP592(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP592(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1571,axiom,
    ( sP593(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP593(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1572,axiom,
    ( sP594(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP594(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1573,axiom,
    ( sP595(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP595(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1574,axiom,
    ( sP596(Eq_y_0,Eq_y_1)
    | ~ sP596(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1575,axiom,
    ( sP597(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP597(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1576,axiom,
    ( sP598(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP598(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1577,axiom,
    ( sP599(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP599(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1578,axiom,
    ( sP600(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP600(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1579,axiom,
    ( sP601(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP601(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1580,axiom,
    ( sP602(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP602(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1581,axiom,
    ( sP603(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP603(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1582,axiom,
    ( sP604(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP604(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1583,axiom,
    ( sP605(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP605(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1584,axiom,
    ( sP606(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP606(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1585,axiom,
    ( sP607(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP607(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1586,axiom,
    ( sP608(Eq_y_0,Eq_y_1)
    | ~ sP608(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1587,axiom,
    ( sP609(Eq_y_0,Eq_y_1)
    | ~ sP609(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1588,axiom,
    ( sP610(Eq_y_0,Eq_y_1)
    | ~ sP610(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1589,axiom,
    ( sP611(Eq_y_0,Eq_y_1)
    | ~ sP611(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1590,axiom,
    ( sP612(Eq_y_0,Eq_y_1)
    | ~ sP612(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1591,axiom,
    ( sP613(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP613(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1592,axiom,
    ( sP614(Eq_y_0,Eq_y_1)
    | ~ sP614(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1593,axiom,
    ( sP615(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP615(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1594,axiom,
    ( sP616(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP616(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1595,axiom,
    ( sP617(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP617(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1596,axiom,
    ( sP618(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP618(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1597,axiom,
    ( sP619(Eq_y_0,Eq_y_1)
    | ~ sP619(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1598,axiom,
    ( sP620(Eq_y_0,Eq_y_1)
    | ~ sP620(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1599,axiom,
    ( sP621(Eq_y_0,Eq_y_1)
    | ~ sP621(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1600,axiom,
    ( sP622(Eq_y_0,Eq_y_1)
    | ~ sP622(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1601,axiom,
    ( sP623(Eq_y_0,Eq_y_1)
    | ~ sP623(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1602,axiom,
    ( sP624(Eq_y_0,Eq_y_1)
    | ~ sP624(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1603,axiom,
    ( sP625(Eq_y_0,Eq_y_1)
    | ~ sP625(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1604,axiom,
    ( sP626(Eq_y_0,Eq_y_1)
    | ~ sP626(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1605,axiom,
    ( sP627(Eq_y_0,Eq_y_1)
    | ~ sP627(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1606,axiom,
    ( sP628(Eq_y_0,Eq_y_1)
    | ~ sP628(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1607,axiom,
    ( sP629(Eq_y_0,Eq_y_1)
    | ~ sP629(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1608,axiom,
    ( sP630(Eq_y_0,Eq_y_1)
    | ~ sP630(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1609,axiom,
    ( sP631(Eq_y_0,Eq_y_1)
    | ~ sP631(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1610,axiom,
    ( sP632(Eq_y_0,Eq_y_1)
    | ~ sP632(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1611,axiom,
    ( sP633(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP633(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1612,axiom,
    ( sP634(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP634(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1613,axiom,
    ( sP635(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP635(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1614,axiom,
    ( sP636(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP636(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1615,axiom,
    ( sP637(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP637(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1616,axiom,
    ( sP638(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP638(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1617,axiom,
    ( sP639(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP639(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1618,axiom,
    ( sP640(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP640(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1619,axiom,
    ( sP641(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP641(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1620,axiom,
    ( sP642(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP642(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1621,axiom,
    ( sP643(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP643(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1622,axiom,
    ( sP644(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP644(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1623,axiom,
    ( sP645(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP645(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1624,axiom,
    ( sP646(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP646(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1625,axiom,
    ( sP647(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP647(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1626,axiom,
    ( sP648(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP648(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1627,axiom,
    ( sP649(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP649(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1628,axiom,
    ( sP650(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP650(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1629,axiom,
    ( sP651(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP651(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1630,axiom,
    ( sP652(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP652(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1631,axiom,
    ( sP653(Eq_y_0,Eq_y_1)
    | ~ sP653(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1632,axiom,
    ( sP654(Eq_y_0,Eq_y_1)
    | ~ sP654(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1633,axiom,
    ( sP655(Eq_y_0,Eq_y_1)
    | ~ sP655(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1634,axiom,
    ( sP656(Eq_y_0,Eq_y_1)
    | ~ sP656(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1635,axiom,
    ( sP657(Eq_y_0,Eq_y_1)
    | ~ sP657(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1636,axiom,
    ( sP658(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP658(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1637,axiom,
    ( sP659(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP659(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1638,axiom,
    ( sP660(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP660(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1639,axiom,
    ( sP661(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP661(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1640,axiom,
    ( sP662(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP662(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1641,axiom,
    ( sP663(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP663(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1642,axiom,
    ( sP664(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP664(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1643,axiom,
    ( sP665(Eq_y_0,Eq_y_1)
    | ~ sP665(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1644,axiom,
    ( sP666(Eq_y_0,Eq_y_1)
    | ~ sP666(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1645,axiom,
    ( sP667(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP667(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1646,axiom,
    ( sP668(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP668(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1647,axiom,
    ( sP669(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP669(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1648,axiom,
    ( sP670(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP670(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1649,axiom,
    ( sP671(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP671(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1650,axiom,
    ( sP672(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP672(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1651,axiom,
    ( sP673(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP673(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1652,axiom,
    ( sP674(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP674(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1653,axiom,
    ( sP675(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP675(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1654,axiom,
    ( sP676(Eq_y_0,Eq_y_1)
    | ~ sP676(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1655,axiom,
    ( sP677(Eq_y_0,Eq_y_1)
    | ~ sP677(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1656,axiom,
    ( sP678(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP678(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1657,axiom,
    ( sP679(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP679(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1658,axiom,
    ( sP680(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP680(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1659,axiom,
    ( sP681(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP681(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1660,axiom,
    ( sP682(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP682(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1661,axiom,
    ( sP683(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP683(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1662,axiom,
    ( sP684(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP684(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1663,axiom,
    ( sP685(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP685(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1664,axiom,
    ( sP686(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP686(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1665,axiom,
    ( sP687(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP687(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1666,axiom,
    ( sP688(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP688(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1667,axiom,
    ( sP689(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP689(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1668,axiom,
    ( sP690(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP690(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1669,axiom,
    ( sP691(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP691(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1670,axiom,
    ( sP692(Eq_y_0,Eq_y_1)
    | ~ sP692(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1671,axiom,
    ( sP693(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP693(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1672,axiom,
    ( sP694(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP694(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1673,axiom,
    ( sP695(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | ~ sP695(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1674,axiom,
    ( sP696(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP696(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1675,axiom,
    ( sP697(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP697(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1676,axiom,
    ( sP698(Eq_y_0,Eq_y_1)
    | ~ sP698(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1677,axiom,
    ( sP699(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP699(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1678,axiom,
    ( sP700(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP700(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1679,axiom,
    ( sP701(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP701(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1680,axiom,
    ( sP702(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP702(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1681,axiom,
    ( sP703(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP703(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1682,axiom,
    ( sP704(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP704(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1683,axiom,
    ( sP705(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP705(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1684,axiom,
    ( sP706(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP706(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1685,axiom,
    ( sP707(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP707(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1686,axiom,
    ( sP708(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP708(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1687,axiom,
    ( sP709(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP709(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1688,axiom,
    ( sP710(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP710(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1689,axiom,
    ( sP711(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP711(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1690,axiom,
    ( sP712(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP712(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1691,axiom,
    ( sP713(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP713(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1692,axiom,
    ( sP714(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP714(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1693,axiom,
    ( sP715(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP715(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1694,axiom,
    ( sP716(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP716(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1695,axiom,
    ( sP717(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP717(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1696,axiom,
    ( sP718(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP718(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1697,axiom,
    ( sP719(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP719(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1698,axiom,
    ( sP720(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP720(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1699,axiom,
    ( sP721(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP721(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1700,axiom,
    ( sP722(Eq_y_0,Eq_y_1)
    | ~ sP722(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1701,axiom,
    ( sP723(Eq_y_0,Eq_y_1)
    | ~ sP723(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1702,axiom,
    ( sP724(Eq_y_0,Eq_y_1)
    | ~ sP724(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1703,axiom,
    ( sP725(Eq_y_0)
    | ~ sP725(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1704,axiom,
    ( sP726(Eq_y_0,Eq_y_1)
    | ~ sP726(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1705,axiom,
    ( sP727(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP727(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1706,axiom,
    ( sP728(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP728(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1707,axiom,
    ( sP729(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP729(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1708,axiom,
    ( sP730(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP730(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1709,axiom,
    ( sP731(Eq_y_0)
    | ~ sP731(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1710,axiom,
    ( sP732(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP732(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1711,axiom,
    ( sP733(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP733(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1712,axiom,
    ( sP734(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP734(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1713,axiom,
    ( sP735(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | ~ sP735(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1714,axiom,
    ( sP736(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP736(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1715,axiom,
    ( sP737(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP737(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1716,axiom,
    ( sP738(Eq_y_0,Eq_y_1)
    | ~ sP738(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1717,axiom,
    ( sP739(Eq_y_0,Eq_y_1)
    | ~ sP739(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1718,axiom,
    ( sP740(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP740(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1719,axiom,
    ( sP741(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP741(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1720,axiom,
    ( sP742(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP742(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1721,axiom,
    ( sP743(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP743(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1722,axiom,
    ( sP744(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP744(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1723,axiom,
    ( sP745(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP745(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1724,axiom,
    ( sP746(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP746(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1725,axiom,
    ( sP747(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP747(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1726,axiom,
    ( sP748(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP748(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1727,axiom,
    ( sP749(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP749(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1728,axiom,
    ( sP750(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP750(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1729,axiom,
    ( sP751(Eq_y_0,Eq_y_1)
    | ~ sP751(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1730,axiom,
    ( sP752(Eq_y_0,Eq_y_1)
    | ~ sP752(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1731,axiom,
    ( sP753(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP753(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1732,axiom,
    ( sP754(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP754(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1733,axiom,
    ( sP755(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP755(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1734,axiom,
    ( sP756(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP756(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1735,axiom,
    ( sP757(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP757(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1736,axiom,
    ( sP758(Eq_y_0,Eq_y_1)
    | ~ sP758(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1737,axiom,
    ( sP759(Eq_y_0,Eq_y_1)
    | ~ sP759(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1738,axiom,
    ( sP760(Eq_y_0,Eq_y_1)
    | ~ sP760(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1739,axiom,
    ( sP761(Eq_y_0,Eq_y_1)
    | ~ sP761(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1740,axiom,
    ( sP762(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP762(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1741,axiom,
    ( sP763(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP763(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1742,axiom,
    ( sP764(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP764(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1743,axiom,
    ( sP765(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP765(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1744,axiom,
    ( sP766(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP766(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1745,axiom,
    ( sP767(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP767(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1746,axiom,
    ( sP768(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP768(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1747,axiom,
    ( sP769(Eq_y_0,Eq_y_1)
    | ~ sP769(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1748,axiom,
    ( sP770(Eq_y_0,Eq_y_1)
    | ~ sP770(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1749,axiom,
    ( sP771(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP771(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1750,axiom,
    ( sP772(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP772(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1751,axiom,
    ( sP773(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP773(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1752,axiom,
    ( sP774(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP774(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1753,axiom,
    ( sP775(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP775(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1754,axiom,
    ( sP776(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP776(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1755,axiom,
    ( sP777(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP777(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1756,axiom,
    ( sP778(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP778(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1757,axiom,
    ( sP779(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP779(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1758,axiom,
    ( sP780(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP780(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1759,axiom,
    ( sP781(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP781(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1760,axiom,
    ( sP782(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP782(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1761,axiom,
    ( sP783(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP783(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1762,axiom,
    ( sP784(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP784(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1763,axiom,
    ( sP785(Eq_y_0,Eq_y_1)
    | ~ sP785(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1764,axiom,
    ( sP786(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP786(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1765,axiom,
    ( sP787(Eq_y_0,Eq_y_1)
    | ~ sP787(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1766,axiom,
    ( sP788(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP788(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1767,axiom,
    ( sP789(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP789(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1768,axiom,
    ( sP790(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP790(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1769,axiom,
    ( sP791(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP791(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1770,axiom,
    ( sP792(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP792(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1771,axiom,
    ( sP793(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP793(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1772,axiom,
    ( sP794(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP794(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1773,axiom,
    ( sP795(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP795(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1774,axiom,
    ( sP796(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP796(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1775,axiom,
    ( sP797(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP797(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1776,axiom,
    ( sP798(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP798(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1777,axiom,
    ( sP799(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP799(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1778,axiom,
    ( sP800(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP800(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1779,axiom,
    ( sP801(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP801(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1780,axiom,
    ( sP802(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP802(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1781,axiom,
    ( sP803(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP803(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1782,axiom,
    ( sP804(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP804(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1783,axiom,
    ( sP805(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP805(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1784,axiom,
    ( sP806(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP806(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1785,axiom,
    ( sP807(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP807(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1786,axiom,
    ( sP808(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP808(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1787,axiom,
    ( sP809(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP809(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1788,axiom,
    ( sP810(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP810(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1789,axiom,
    ( sP811(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP811(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1790,axiom,
    ( sP812(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP812(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1791,axiom,
    ( sP813(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP813(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1792,axiom,
    ( sP814(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP814(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1793,axiom,
    ( sP815(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP815(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1794,axiom,
    ( sP816(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP816(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1795,axiom,
    ( sP817(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP817(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1796,axiom,
    ( sP818(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP818(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1797,axiom,
    ( sP819(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP819(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1798,axiom,
    ( sP820(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP820(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1799,axiom,
    ( sP821(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP821(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1800,axiom,
    ( sP822(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP822(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1801,axiom,
    ( sP823(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP823(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1802,axiom,
    ( sP824(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP824(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1803,axiom,
    ( sP825(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | ~ sP825(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1804,axiom,
    ( sP826(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP826(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1805,axiom,
    ( sP827(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP827(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1806,axiom,
    ( sP828(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP828(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1807,axiom,
    ( sP829(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP829(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1808,axiom,
    ( sP830(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP830(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1809,axiom,
    ( sP831(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP831(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1810,axiom,
    ( sP832(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP832(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1811,axiom,
    ( sP833(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP833(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1812,axiom,
    ( sP834(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP834(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1813,axiom,
    ( sP835(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP835(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1814,axiom,
    ( sP836(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP836(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1815,axiom,
    ( sP837(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP837(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1816,axiom,
    ( sP838(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP838(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1817,axiom,
    ( sP839(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP839(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1818,axiom,
    ( sP840(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP840(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1819,axiom,
    ( sP841(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP841(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1820,axiom,
    ( sP842(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP842(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1821,axiom,
    ( sP843(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP843(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1822,axiom,
    ( sP844(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP844(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1823,axiom,
    ( sP845(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP845(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1824,axiom,
    ( sP846(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP846(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1825,axiom,
    ( sP847(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP847(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1826,axiom,
    ( sP848(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP848(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1827,axiom,
    ( sP849(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP849(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1828,axiom,
    ( sP850(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP850(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1829,axiom,
    ( sP851(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP851(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1830,axiom,
    ( sP852(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP852(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1831,axiom,
    ( sP853(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP853(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1832,axiom,
    ( sP854(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP854(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1833,axiom,
    ( sP855(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP855(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1834,axiom,
    ( sP856(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP856(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1835,axiom,
    ( sP857(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP857(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1836,axiom,
    ( sP858(Eq_y_0,Eq_y_1)
    | ~ sP858(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1837,axiom,
    ( sP859(Eq_y_0,Eq_y_1)
    | ~ sP859(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1838,axiom,
    ( sP860(Eq_y_0,Eq_y_1)
    | ~ sP860(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1839,axiom,
    ( sP861(Eq_y_0,Eq_y_1)
    | ~ sP861(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1840,axiom,
    ( sP862(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP862(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1841,axiom,
    ( sP863(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP863(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1842,axiom,
    ( sP864(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP864(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1843,axiom,
    ( sP865(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP865(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1844,axiom,
    ( sP866(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP866(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1845,axiom,
    ( sP867(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP867(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1846,axiom,
    ( sP868(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP868(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1847,axiom,
    ( sP869(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP869(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1848,axiom,
    ( sP870(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP870(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1849,axiom,
    ( sP871(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP871(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1850,axiom,
    ( sP872(Eq_y_0,Eq_y_1)
    | ~ sP872(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1851,axiom,
    ( sP873(Eq_y_0,Eq_y_1)
    | ~ sP873(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1852,axiom,
    ( sP874(Eq_y_0,Eq_y_1)
    | ~ sP874(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1853,axiom,
    ( sP875(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP875(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1854,axiom,
    ( sP876(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP876(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1855,axiom,
    ( sP877(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP877(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1856,axiom,
    ( sP878(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP878(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1857,axiom,
    ( sP879(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP879(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1858,axiom,
    ( sP880(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP880(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1859,axiom,
    ( sP881(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP881(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1860,axiom,
    ( sP882(Eq_y_0,Eq_y_1)
    | ~ sP882(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1861,axiom,
    ( sP883(Eq_y_0,Eq_y_1)
    | ~ sP883(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1862,axiom,
    ( sP884(Eq_y_0,Eq_y_1)
    | ~ sP884(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1863,axiom,
    ( sP885(Eq_y_0,Eq_y_1)
    | ~ sP885(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1864,axiom,
    ( sP886(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP886(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1865,axiom,
    ( sP887(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP887(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1866,axiom,
    ( sP888(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP888(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1867,axiom,
    ( sP889(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP889(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1868,axiom,
    ( sP890(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP890(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1869,axiom,
    ( sP891(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP891(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1870,axiom,
    ( sP892(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP892(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1871,axiom,
    ( sP893(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP893(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1872,axiom,
    ( sP894(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP894(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1873,axiom,
    ( sP895(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP895(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1874,axiom,
    ( sP896(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP896(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1875,axiom,
    ( sP897(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP897(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1876,axiom,
    ( sP898(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP898(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1877,axiom,
    ( sP899(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP899(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1878,axiom,
    ( sP900(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP900(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1879,axiom,
    ( sP901(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP901(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1880,axiom,
    ( sP902(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP902(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1881,axiom,
    ( sP903(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP903(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1882,axiom,
    ( sP904(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP904(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1883,axiom,
    ( sP905(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP905(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1884,axiom,
    ( sP906(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP906(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1885,axiom,
    ( sP907(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP907(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1886,axiom,
    ( sP908(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP908(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1887,axiom,
    ( sP909(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP909(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1888,axiom,
    ( sP910(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP910(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1889,axiom,
    ( sP911(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP911(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1890,axiom,
    ( sP912(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP912(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1891,axiom,
    ( sP913(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP913(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1892,axiom,
    ( sP914(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP914(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1893,axiom,
    ( sP915(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP915(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1894,axiom,
    ( sP916(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP916(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1895,axiom,
    ( sP917(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP917(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1896,axiom,
    ( sP918(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP918(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1897,axiom,
    ( sP919(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP919(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1898,axiom,
    ( sP920(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP920(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1899,axiom,
    ( sP921(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP921(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1900,axiom,
    ( sP922(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP922(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1901,axiom,
    ( sP923(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP923(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1902,axiom,
    ( sP924(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP924(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1903,axiom,
    ( sP925(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP925(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1904,axiom,
    ( sP926(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP926(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1905,axiom,
    ( sP927(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP927(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1906,axiom,
    ( sP928(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP928(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1907,axiom,
    ( sP929(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP929(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1908,axiom,
    ( sP930(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP930(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1909,axiom,
    ( sP931(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP931(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1910,axiom,
    ( sP932(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP932(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1911,axiom,
    ( sP933(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP933(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1912,axiom,
    ( sP934(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP934(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1913,axiom,
    ( sP935(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP935(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1914,axiom,
    ( sP936(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP936(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1915,axiom,
    ( sP937(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP937(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1916,axiom,
    ( sP938(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP938(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1917,axiom,
    ( sP939(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP939(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1918,axiom,
    ( sP940(Eq_y_0,Eq_y_1)
    | ~ sP940(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1919,axiom,
    ( sP941(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP941(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1920,axiom,
    ( sP942(Eq_y_0,Eq_y_1)
    | ~ sP942(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1921,axiom,
    ( sP943(Eq_y_0,Eq_y_1)
    | ~ sP943(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1922,axiom,
    ( sP944(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP944(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1923,axiom,
    ( sP945(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP945(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1924,axiom,
    ( sP946(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP946(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1925,axiom,
    ( sP947(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP947(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1926,axiom,
    ( sP948(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP948(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1927,axiom,
    ( sP949(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP949(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1928,axiom,
    ( sP950(Eq_y_0)
    | ~ sP950(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1929,axiom,
    ( sP951(Eq_y_0)
    | ~ sP951(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1930,axiom,
    ( sP952(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP952(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1931,axiom,
    ( sP953(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP953(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1932,axiom,
    ( sP954(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP954(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1933,axiom,
    ( sP955(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP955(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1934,axiom,
    ( sP956(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP956(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1935,axiom,
    ( sP957(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP957(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1936,axiom,
    ( sP958(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP958(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1937,axiom,
    ( sP959(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP959(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1938,axiom,
    ( sP960(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP960(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1939,axiom,
    ( sP961(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP961(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1940,axiom,
    ( sP962(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP962(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1941,axiom,
    ( sP963(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP963(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1942,axiom,
    ( sP964(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP964(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1943,axiom,
    ( sP965(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP965(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1944,axiom,
    ( sP966(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP966(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1945,axiom,
    ( sP967(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP967(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1946,axiom,
    ( sP968(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP968(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1947,axiom,
    ( sP969(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP969(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1948,axiom,
    ( sP970(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP970(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1949,axiom,
    ( sP971(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP971(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1950,axiom,
    ( sP972(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP972(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1951,axiom,
    ( sP973(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP973(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1952,axiom,
    ( sP974(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP974(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1953,axiom,
    ( sP975(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP975(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1954,axiom,
    ( sP976(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP976(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1955,axiom,
    ( sP977(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP977(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1956,axiom,
    ( sP978(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP978(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1957,axiom,
    ( sP979(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP979(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1958,axiom,
    ( sP980(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP980(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1959,axiom,
    ( sP981(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP981(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1960,axiom,
    ( sP982(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP982(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1961,axiom,
    ( sP983(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP983(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1962,axiom,
    ( sP984(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP984(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1963,axiom,
    ( sP985(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP985(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1964,axiom,
    ( sP986(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP986(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1965,axiom,
    ( sP987(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP987(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1966,axiom,
    ( sP988(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP988(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1967,axiom,
    ( sP989(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP989(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1968,axiom,
    ( sP990(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP990(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1969,axiom,
    ( sP991(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP991(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1970,axiom,
    ( sP992(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP992(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1971,axiom,
    ( sP993(Eq_y_0,Eq_y_1)
    | ~ sP993(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1972,axiom,
    ( sP994(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP994(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1973,axiom,
    ( sP995(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP995(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1974,axiom,
    ( sP996(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP996(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1975,axiom,
    ( sP997(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP997(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1976,axiom,
    ( sP998(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP998(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1977,axiom,
    ( sP999(Eq_y_0,Eq_y_1)
    | ~ sP999(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1978,axiom,
    ( sP1000(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1000(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1979,axiom,
    ( sP1001(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1001(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1980,axiom,
    ( sP1002(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1002(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1981,axiom,
    ( sP1003(Eq_y_0,Eq_y_1)
    | ~ sP1003(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1982,axiom,
    ( sP1004(Eq_y_0,Eq_y_1)
    | ~ sP1004(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1983,axiom,
    ( sP1005(Eq_y_0,Eq_y_1)
    | ~ sP1005(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1984,axiom,
    ( sP1006(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1006(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1985,axiom,
    ( sP1007(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1007(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1986,axiom,
    ( sP1008(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1008(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1987,axiom,
    ( sP1009(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1009(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1988,axiom,
    ( sP1010(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1010(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1989,axiom,
    ( sP1011(Eq_y_0,Eq_y_1)
    | ~ sP1011(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1990,axiom,
    ( sP1012(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1012(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1991,axiom,
    ( sP1013(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1013(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1992,axiom,
    ( sP1014(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1014(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1993,axiom,
    ( sP1015(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1015(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1994,axiom,
    ( sP1016(Eq_y_0,Eq_y_1)
    | ~ sP1016(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1995,axiom,
    ( sP1017(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1017(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1996,axiom,
    ( sP1018(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1018(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1997,axiom,
    ( sP1019(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1019(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1998,axiom,
    ( sP1020(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1020(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1999,axiom,
    ( sP1021(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1021(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2000,axiom,
    ( sP1022(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1022(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2001,axiom,
    ( sP1023(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1023(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2002,axiom,
    ( sP1024(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1024(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2003,axiom,
    ( sP1025(Eq_y_0,Eq_y_1)
    | ~ sP1025(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2004,axiom,
    ( sP1026(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1026(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2005,axiom,
    ( sP1027(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1027(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2006,axiom,
    ( sP1028(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1028(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2007,axiom,
    ( sP1029(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1029(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2008,axiom,
    ( sP1030(Eq_y_0,Eq_y_1)
    | ~ sP1030(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2009,axiom,
    ( sP1031(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1031(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2010,axiom,
    ( sP1032(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1032(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2011,axiom,
    ( sP1033(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1033(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2012,axiom,
    ( sP1034(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1034(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2013,axiom,
    ( sP1035(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1035(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2014,axiom,
    ( sP1036(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1036(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2015,axiom,
    ( sP1037(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1037(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2016,axiom,
    ( sP1038(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1038(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2017,axiom,
    ( sP1039(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1039(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2018,axiom,
    ( sP1040(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1040(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2019,axiom,
    ( sP1041(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1041(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2020,axiom,
    ( sP1042(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1042(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2021,axiom,
    ( sP1043(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1043(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2022,axiom,
    ( sP1044(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1044(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2023,axiom,
    ( sP1045(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1045(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2024,axiom,
    ( sP1046(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1046(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2025,axiom,
    ( sP1047(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1047(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2026,axiom,
    ( sP1048(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1048(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2027,axiom,
    ( sP1049(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1049(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2028,axiom,
    ( sP1050(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1050(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2029,axiom,
    ( sP1051(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1051(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2030,axiom,
    ( sP1052(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1052(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2031,axiom,
    ( sP1053(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1053(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2032,axiom,
    ( sP1054(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1054(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2033,axiom,
    ( sP1055(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1055(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2034,axiom,
    ( sP1056(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1056(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2035,axiom,
    ( sP1057(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1057(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2036,axiom,
    ( sP1058(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1058(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2037,axiom,
    ( sP1059(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1059(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2038,axiom,
    ( sP1060(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1060(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2039,axiom,
    ( sP1061(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1061(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2040,axiom,
    ( sP1062(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1062(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2041,axiom,
    ( sP1063(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1063(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2042,axiom,
    ( sP1064(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1064(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2043,axiom,
    ( sP1065(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1065(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2044,axiom,
    ( sP1066(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1066(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2045,axiom,
    ( sP1067(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1067(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2046,axiom,
    ( sP1068(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1068(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2047,axiom,
    ( sP1069(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1069(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2048,axiom,
    ( sP1070(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1070(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2049,axiom,
    ( sP1071(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1071(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2050,axiom,
    ( sP1072(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1072(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2051,axiom,
    ( sP1073(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1073(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2052,axiom,
    ( sP1074(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1074(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2053,axiom,
    ( sP1075(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1075(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2054,axiom,
    ( sP1076(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1076(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2055,axiom,
    ( sP1077(Eq_y_0,Eq_y_1)
    | ~ sP1077(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2056,axiom,
    ( sP1078(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1078(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2057,axiom,
    ( sP1079(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1079(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2058,axiom,
    ( sP1080(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1080(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2059,axiom,
    ( sP1081(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1081(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2060,axiom,
    ( sP1082(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1082(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2061,axiom,
    ( sP1083(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1083(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2062,axiom,
    ( sP1084(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1084(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2063,axiom,
    ( sP1085(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1085(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2064,axiom,
    ( sP1086(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1086(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2065,axiom,
    ( sP1087(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1087(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2066,axiom,
    ( sP1088(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1088(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2067,axiom,
    ( sP1089(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1089(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2068,axiom,
    ( sP1090(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1090(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2069,axiom,
    ( sP1091(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1091(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2070,axiom,
    ( sP1092(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1092(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2071,axiom,
    ( sP1093(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1093(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2072,axiom,
    ( sP1094(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1094(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2073,axiom,
    ( sP1095(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1095(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2074,axiom,
    ( sP1096(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1096(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2075,axiom,
    ( sP1097(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1097(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2076,axiom,
    ( sP1098(Eq_y_0,Eq_y_1)
    | ~ sP1098(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2077,axiom,
    ( sP1099(Eq_y_0,Eq_y_1)
    | ~ sP1099(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2078,axiom,
    ( sP1100(Eq_y_0,Eq_y_1)
    | ~ sP1100(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2079,axiom,
    ( sP1101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2080,axiom,
    ( sP1102(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1102(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2081,axiom,
    ( sP1103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2082,axiom,
    ( sP1104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2083,axiom,
    ( sP1105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2084,axiom,
    ( sP1106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2085,axiom,
    ( sP1107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2086,axiom,
    ( sP1108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2087,axiom,
    ( sP1109(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1109(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2088,axiom,
    ( sP1110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2089,axiom,
    ( sP1111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2090,axiom,
    ( sP1112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2091,axiom,
    ( sP1113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2092,axiom,
    ( sP1114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2093,axiom,
    ( sP1115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2094,axiom,
    ( sP1116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2095,axiom,
    ( sP1117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2096,axiom,
    ( sP1119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2097,axiom,
    ( sP1120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2098,axiom,
    ( sP1121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1121(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2099,axiom,
    ( sP1122(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1122(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2100,axiom,
    ( sP1123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2101,axiom,
    ( sP1124(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1124(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2102,axiom,
    ( sP1125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2103,axiom,
    ( sP1126(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2104,axiom,
    ( sP1127(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1127(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2105,axiom,
    ( sP1128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2106,axiom,
    ( sP1129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2107,axiom,
    ( sP1130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2108,axiom,
    ( sP1131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2109,axiom,
    ( sP1132(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1132(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2110,axiom,
    ( sP1133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2111,axiom,
    ( sP1134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2112,axiom,
    ( sP1135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2113,axiom,
    ( sP1136(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2114,axiom,
    ( sP1137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2115,axiom,
    ( sP1138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1138(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2116,axiom,
    ( sP1139(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2117,axiom,
    ( sP1140(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1140(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2118,axiom,
    ( sP1141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2119,axiom,
    ( sP1142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2120,axiom,
    ( sP1143(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1143(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2121,axiom,
    ( sP1144(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2122,axiom,
    ( sP1145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2123,axiom,
    ( sP1146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2124,axiom,
    ( sP1147(Eq_y_0)
    | ~ sP1147(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2125,axiom,
    ( sP1148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2126,axiom,
    ( sP1149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2127,axiom,
    ( sP1150(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1150(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2128,axiom,
    ( sP1151(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1151(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2129,axiom,
    ( sP1152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2130,axiom,
    ( sP1153(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1153(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2131,axiom,
    ( sP1154(Eq_y_0,Eq_y_1)
    | ~ sP1154(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2132,axiom,
    ( sP1155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2133,axiom,
    ( sP1156(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1156(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2134,axiom,
    ( sP1157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2135,axiom,
    ( sP1158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2136,axiom,
    ( sP1159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1159(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2137,axiom,
    ( sP1160(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1160(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2138,axiom,
    ( sP1161(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2139,axiom,
    ( sP1162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2140,axiom,
    ( sP1163(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1163(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2141,axiom,
    ( sP1164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1164(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2142,axiom,
    ( sP1165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2143,axiom,
    ( sP1166(Eq_y_0,Eq_y_1)
    | ~ sP1166(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2144,axiom,
    ( sP1167(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1167(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2145,axiom,
    ( sP1168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2146,axiom,
    ( sP1169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2147,axiom,
    ( sP1170(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2148,axiom,
    ( sP1171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2149,axiom,
    ( sP1172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2150,axiom,
    ( sP1173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2151,axiom,
    ( sP1174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2152,axiom,
    ( sP1175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2153,axiom,
    ( sP1176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2154,axiom,
    ( sP1177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2155,axiom,
    ( sP1178(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1178(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2156,axiom,
    ( sP1179(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1179(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2157,axiom,
    ( sP1180(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1180(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2158,axiom,
    ( sP1181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2159,axiom,
    ( sP1182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1182(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2160,axiom,
    ( sP1183(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1183(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2161,axiom,
    ( sP1184(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1184(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2162,axiom,
    ( sP1185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1185(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2163,axiom,
    ( sP1186(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2164,axiom,
    ( sP1187(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1187(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2165,axiom,
    ( sP1188(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2166,axiom,
    ( sP1189(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2167,axiom,
    ( sP1190(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1190(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2168,axiom,
    ( sP1191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2169,axiom,
    ( sP1192(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1192(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2170,axiom,
    ( sP1193(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2171,axiom,
    ( sP1194(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1194(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2172,axiom,
    ( sP1195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1195(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2173,axiom,
    ( sP1196(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1196(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2174,axiom,
    ( sP1197(Eq_y_0,Eq_y_1)
    | ~ sP1197(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2175,axiom,
    ( sP1198(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1198(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2176,axiom,
    ( sP1199(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1199(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2177,axiom,
    ( sP1200(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1200(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2178,axiom,
    ( sP1201(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2179,axiom,
    ( sP1202(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2180,axiom,
    ( sP1203(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2181,axiom,
    ( sP1204(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1204(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2182,axiom,
    ( sP1205(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1205(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2183,axiom,
    ( sP1206(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1206(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2184,axiom,
    ( sP1207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1207(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2185,axiom,
    ( sP1208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2186,axiom,
    ( sP1209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2187,axiom,
    ( sP1210(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1210(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2188,axiom,
    ( sP1211(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1211(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2189,axiom,
    ( sP1212(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1212(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2190,axiom,
    ( sP1213(Eq_y_0,Eq_y_1)
    | ~ sP1213(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2191,axiom,
    ( sP1214(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2192,axiom,
    ( sP1215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2193,axiom,
    ( sP1216(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1216(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2194,axiom,
    ( sP1217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2195,axiom,
    ( sP1218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2196,axiom,
    ( sP1219(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1219(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2197,axiom,
    ( sP1220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2198,axiom,
    ( sP1221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2199,axiom,
    ( sP1222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2200,axiom,
    ( sP1223(Eq_y_0,Eq_y_1)
    | ~ sP1223(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2201,axiom,
    ( sP1224(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1224(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2202,axiom,
    ( sP1225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2203,axiom,
    ( sP1226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2204,axiom,
    ( sP1227(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1227(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2205,axiom,
    ( sP1228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2206,axiom,
    ( sP1229(Eq_y_0,Eq_y_1)
    | ~ sP1229(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2207,axiom,
    ( sP1230(Eq_y_0,Eq_y_1)
    | ~ sP1230(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2208,axiom,
    ( sP1231(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2209,axiom,
    ( sP1232(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1232(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2210,axiom,
    ( sP1233(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1233(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2211,axiom,
    ( sP1234(Eq_y_0,Eq_y_1)
    | ~ sP1234(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2212,axiom,
    ( sP1235(Eq_y_0,Eq_y_1)
    | ~ sP1235(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2213,axiom,
    ( sP1236(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1236(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2214,axiom,
    ( sP1237(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1237(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2215,axiom,
    ( sP1238(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1238(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2216,axiom,
    ( sP1239(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1239(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2217,axiom,
    ( sP1240(Eq_y_0,Eq_y_1)
    | ~ sP1240(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2218,axiom,
    ( sP1241(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1241(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2219,axiom,
    ( sP1242(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1242(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04  This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.05  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.58  % Computer : n018.cluster.edu
% 0.10/0.58  % Model    : x86_64 x86_64
% 0.10/0.58  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58  % Memory   : 8046.5625MB
% 0.10/0.58  % OS       : Linux 6.8.0-71-generic
% 0.10/0.58  % CPULimit : 300
% 0.10/0.58  % WCLimit  : 300
% 0.10/0.58  % DateTime : Sun Sep 20 05:24:12 UTC 2026
% 0.10/0.59  % CPUTime  : 
% 32.68/33.14  % SZS status Theorem for theBenchmark
% 32.68/33.14  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------